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# Earley parser
## Example
Consider the following simple grammar for arithmetic expressions:
``` text
<P> ::= <S> # the start rule
<S> ::= <S> "+" <M> | <M>
<M> ::= <M> "*" <T> | <T>
<T> ::= "1" | "2" | "3" | "4"
```
With the input:
`2 + 3 * 4`
This is the sequence of state sets:
(state no.) Production (Origin) Comment
-------------------- -------------- ---------- -------------------------------
S(0): • 2 + 3 \* 4
1 P → • S 0 start rule
2 S → • S + M 0 predict from (1)
3 S → • M 0 predict from (1)
4 M → • M \* T 0 predict from (3)
5 M → • T 0 predict from (3)
6 T → • number 0 predict from (5)
S(1): 2 • + 3 \* 4
1 T → number • 0 scan from S(0)(6)
2 M → T • 0 complete from (1) and S(0)(5)
3 M → M • \* T 0 complete from (2) and S(0)(4)
4 S → M • 0 complete from (2) and S(0)(3)
5 S → S • + M 0 complete from (4) and S(0)(2)
6 P → S • 0 complete from (4) and S(0)(1)
S(2): 2 + • 3 \* 4
1 S → S + • M 0 scan from S(1)(5)
2 M → • M \* T 2 predict from (1)
3 M → • T 2 predict from (1)
4 T → • number 2 predict from (3)
S(3): 2 + 3 • \* 4
1 T → number • 2 scan from S(2)(4)
2 M → T • 2 complete from (1) and S(2)(3)
3 M → M • \* T 2 complete from (2) and S(2)(2)
4 S → S + M • 0 complete from (2) and S(2)(1)
5 S → S • + M 0 complete from (4) and S(0)(2)
6 P → S • 0 complete from (4) and S(0)(1)
S(4): 2 + 3 \* • 4
1 M → M \* • T 2 scan from S(3)(3)
2 T → • number 4 predict from (1)
S(5): 2 + 3 \* 4 •
1 T → number • 4 scan from S(4)(2)
2 M → M \* T • 2 complete from (1) and S(4)(1)
3 M → M • \* T 2 complete from (2) and S(2)(2)
4 S → S + M • 0 complete from (2) and S(2)(1)
5 S → S • + M 0 complete from (4) and S(0)(2)
6 P → S • 0 complete from (4) and S(0)(1)
The state (P → S •, 0) represents a completed parse. This state also appears in S(3) and S(1), which are complete sentences.
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# Earley parser
## Constructing the parse forest {#constructing_the_parse_forest}
Earley\'s dissertation briefly describes an algorithm for constructing parse trees by adding a set of pointers from each non-terminal in an Earley item back to the items that caused it to be recognized. But Tomita noticed that this does not take into account the relations between symbols, so if we consider the grammar S → SS \| b and the string bbb, it only notes that each S can match one or two b\'s, and thus produces spurious derivations for bb and bbbb as well as the two correct derivations for bbb.
Another method is to build the parse forest as you go, augmenting each Earley item with a pointer to a shared packed parse forest (SPPF) node labelled with a triple (s, i, j) where s is a symbol or an LR(0) item (production rule with dot), and i and j give the section of the input string derived by this node. A node\'s contents are either a pair of child pointers giving a single derivation, or a list of \"packed\" nodes each containing a pair of pointers and representing one derivation. SPPF nodes are unique (there is only one with a given label), but may contain more than one derivation for ambiguous parses. So even if an operation does not add an Earley item (because it already exists), it may still add a derivation to the item\'s parse forest.
- Predicted items have a null SPPF pointer.
- The scanner creates an SPPF node representing the non-terminal it is scanning.
- Then when the scanner or completer advance an item, they add a derivation whose children are the node from the item whose dot was advanced, and the one for the new symbol that was advanced over (the non-terminal or completed item).
SPPF nodes are never labeled with a completed LR(0) item: instead they are labelled with the symbol that is produced so that all derivations are combined under one node regardless of which alternative production they come from.
## Optimizations
Philippe McLean and R. Nigel Horspool in their paper [\"A Faster Earley Parser\"](https://link.springer.com/content/pdf/10.1007%2F3-540-61053-7_68.pdf) combine Earley parsing with LR parsing and achieve an improvement in an order of magnitude
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# Eusebius Amort
**Eusebius Amort** (November 15, 1692`{{snd}}`{=mediawiki}February 5, 1775) was a German Roman Catholic theologian.
## Life
Amort was born at Bibermuhle, near Tolz, in Upper Bavaria. He studied at Munich, and at an early age joined the Canons Regular at Polling, where, shortly after his ordination in 1717, he taught theology and philosophy. The Parnassus Boicus learned society was based on a plan started in 1720 by three Augustinian fathers: Eusebius Amort, Gelasius Hieber (1671--1731), a famous preacher in the German language and Agnellus Kandler (1692--1745), a genealogist and librarian. The initial plans fell through, but in 1722 they issued the first volume of the *Parnassus Boicus* journal, covering topics in the arts and sciences.
An academy formed by him at Polling became in time the model on which was based the Academy of Sciences of Munich.
In 1733 Amort went to Rome as theologian to Cardinal Niccolo Maria Lercari (died 1757). He returned to Polling in 1735 and devoted the rest of his life to the revival of learning in Bavaria. He died at Polling in 1775.
## Works
Amort, who had the reputation of being the most learned man of his age, was a voluminous writer on every conceivable subject, from poetry to astronomy, from dogmatic theology to mysticism. His best known works are:
- A manual of theology in 4 vols, *Theologia eclectica, moralis et scholastica* (Augsburg, 1752; revised by Pope Benedict XIV for the 1753 edition published at Bologna)
- A defence of Catholic doctrine, entitled *Demonstratio critica religionis Catholicae* (Augsburg, 1751)
- A work on indulgences, which has often been criticized by Protestant writers, *De Origine, Progressu, Valore, et Fructu Indulgentiorum* (Augsburg, 1735)
- The astronomical work *Nova philosophiae planetarum et artis criticae systemata* (Nuremberg, 1723).
A treatise on mysticism, *De Revelationibus et Visionibus, etc.* (2 vols, Augsburg 1744) was directed against the \"Mystic City of God,\" by the Spanish Franciscan nun, Maria de Agreda, and brought him into conflict with several of her Franciscan defenders.
The list of his other works, including his three erudite contributions to the question of authorship of the *Imitatio Christi*, will be found in C. Toussaint\'s scholarly article in Alfred Vacant\'s *Dictionnaire de theologie* (1900, cols 1115--1117)
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# Elizabeth Garrett Anderson
**Elizabeth Garrett Anderson** (9 June 1836 -- 17 December 1917) was an English physician and suffragist. She is known for being the first woman to qualify in Britain as a physician and surgeon and as a co-founder and dean of the London School of Medicine for Women, which was the first medical school in Britain to train women as doctors. She was the first female dean of a British medical school, the first woman in Britain to be elected to a school board and, as mayor of Aldeburgh, the first female mayor in Britain.
## Early life {#early_life}
Elizabeth was born in Whitechapel, London, and was the second of eleven children of Newson Garrett (1812--1893), from Leiston, Suffolk, and his wife, Louisa (born Dunnell; c. 1813--1903), from London.
Her paternal ancestors had been ironworkers in East Suffolk since the early seventeenth century. Newson was the youngest of three sons and not academically inclined, although he possessed the family\'s entrepreneurial spirit. When he finished school, Newson found few opportunities in Leiston, so he moved to London to make his fortune. There, he fell in love with his brother\'s sister-in-law, Louisa Dunnell, the daughter of an innkeeper of Suffolk origin. After their wedding, the couple went to live in a pawnbroker\'s shop at 1 Commercial Road, Whitechapel. The Garretts had their first three children in quick succession: Louisa, Elizabeth, and a son, Dunnell, who died at the age of six months. When Garrett was three years old, the family moved to 142 Long Acre, where they lived for two years, while one more child was born and her father advanced in his career, becoming not only the manager of a larger pawnbroker\'s shop, but also a silversmith. Garrett\'s grandfather, owner of the family engineering works, Richard Garrett & Sons, had died in 1837, leaving the business to his eldest son, Garrett\'s uncle. Despite his lack of capital, Newson was determined to be successful and in 1841, at the age of 29, he moved his family to Suffolk, where he bought a barley and coal merchants business in Snape, constructing Snape Maltings from 1846.
The Garretts lived in a square Georgian house opposite the church in Aldeburgh until 1852. Newson\'s malting business expanded and more children were born, Edmund (1840), Alice (1842), Agnes (1845), Millicent (1847), who was to become a leader in the constitutional campaign for women\'s suffrage, Sam (1850), Josephine (1853) and George (1854). By 1850, Newson was a prosperous businessman and was able to build Alde House, a mansion on a hill behind Aldeburgh. A \"by-product of the industrial revolution\", Garrett grew up in an atmosphere of \"triumphant economic pioneering\" and the Garrett children were to grow up to become achievers in the professional classes of late-Victorian England. Elizabeth was encouraged to take an interest in local politics and, contrary to practices at the time, was allowed the freedom to explore the town with its nearby salt-marshes, beach and the small port of Slaughden with its boatbuilders\' yards and sailmakers\' lofts.
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# Elizabeth Garrett Anderson
## Early education {#early_education}
There was no school in Aldeburgh, so Garrett learned reading, writing, and arithmetic from her mother. When she was 10 years old, a governess, Miss Edgeworth, a poor gentlewoman, was employed to educate Garrett and her sister. Mornings were spent in the schoolroom; there were regimented afternoon walks; educating the young ladies continued at mealtimes when Edgeworth ate with the family; at night, the governess slept in a curtained off area in the girls\' bedroom. Garrett reportedly despised her governess and sought to outwit the teacher in the classroom. When Garrett was 13 and her sister 15, they were sent to a private school, the Boarding School for Ladies in Blackheath, London, which was run by the step aunts of the poet Robert Browning. There, English literature, French, Italian and German as well as deportment, were taught.
Later in life, Garrett recalled the stupidity of her teachers there, though her schooling there did help establish a love of reading. Her main complaint about the school was the lack of science and mathematics instruction. Her reading there included works of Tennyson, Wordsworth, Milton, Coleridge, Trollope, Thackeray and George Eliot. Elizabeth and Louie were known as \"the bathing Garretts\", as their father had insisted they be allowed a hot bath once a week. However, they made what were to be lifelong friends there. When they finished in 1851, they were sent on a short tour abroad, ending with a memorable visit to the Great Exhibition in Hyde Park, London.
After this formal education, Garrett spent the next nine years tending to domestic duties, but she continued to study Latin and arithmetic in the mornings and also read widely. Her sister Millicent recalled Garrett\'s weekly lectures, \"Talks on Things in General\", when her younger siblings would gather while she discussed politics and current affairs from Garibaldi to Macaulay\'s *History of England*. In 1854, when she was eighteen, Garrett and her sister went on a long visit to their school friends, Jane and Anne Crow, in Gateshead where she met Emily Davies, the early feminist and future co-founder of Girton College, Cambridge. Davies was to be a lifelong friend and confidante, always ready to give sound advice during the important decisions of Garrett\'s career. It may have been in the *English Woman\'s Journal*, first issued in 1858, that Garrett first read of Elizabeth Blackwell, who had become the first female doctor in the United States in 1849. When Blackwell visited London in 1859, Garrett travelled to the capital. By then, her sister Louie was married and living in London. Garrett joined the Society for Promoting the Employment of Women, which organised Blackwell\'s lectures on \"Medicine as a Profession for Ladies\" and set up a private meeting between Garrett and the doctor. It is said that during a visit to Alde House around 1860, one evening while sitting by the fireside, Garrett and Davies selected careers for advancing the frontiers of women\'s rights; Garrett was to open the medical profession to women, Davies the doors to a university education for women, while 13-year-old Millicent was allocated politics and votes for women. At first Newson was opposed to the radical idea of his daughter becoming a physician but came round and agreed to do all in his power, both financially and otherwise, to support Garrett.
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# Elizabeth Garrett Anderson
## Medical education {#medical_education}
After an initial unsuccessful visit to leading doctors in Harley Street, Garrett decided to first spend six months as a surgery nurse at Middlesex Hospital, London in August 1860. On proving to be a good nurse, she was allowed to attend an outpatients\' clinic, then her first operation. She unsuccessfully attempted to enroll in the hospital\'s Medical School but was allowed to attend private tuition in Latin, Greek and pharmacology with the hospital\'s apothecary, while continuing her work as a nurse. She also employed a tutor to study anatomy and physiology three evenings a week. Eventually she was allowed into the dissecting room and the chemistry lectures. Gradually, Garrett became an unwelcome presence among the male students, who in 1861 presented a memorial to the school against her admittance as a fellow student, despite the support she enjoyed from the administration. She was obliged to leave the Middlesex Hospital but she did so with an honours certificate in chemistry and *materia medica*. Garrett then applied to several medical schools, including Oxford, Cambridge, Glasgow, Edinburgh, St Andrews and the Royal College of Surgeons, all of which refused her admittance.
A companion to Garrett in this effort was the lesser known Sophia Jex-Blake. While both are considered \"outstanding\" medical figures of the late 19th century, Garrett was able to obtain her credentials by way of a \"side door\" through a loophole in admissions at the Worshipful Society of Apothecaries. Having privately obtained a certificate in anatomy and physiology, she was admitted in 1862 by the Society of Apothecaries who, as a condition of their charter, could not legally exclude her on account of her sex. She was the only woman in the Apothecaries Hall who sat the exam that year. Among the 51 male candidates was William Heath Strange, who went on to found the Hampstead General Hospital, which was on the site now occupied by the Royal Free Hospital. She continued her battle to qualify by studying privately with various professors, including some at the University of St Andrews, the Edinburgh Royal Maternity and the London Hospital Medical School.
In 1865, Garrett finally took her exam and obtained a licence (LSA) from the Society of Apothecaries to practise medicine, the first woman qualified in Britain to do so openly (previously there was Dr James Barry who was born and raised female but presented as male from the age of 20). On the day, three out of seven candidates passed the exam, Garrett with the highest marks. The Society of Apothecaries immediately amended its regulations to prevent other women obtaining a licence meaning that Jex-Blake could not follow this same path; the new rule disallowed privately educated women to be eligible for examination. It was not until 1876 that the new Medical Act (39 and 40 Vict, Ch. 41) passed, which allowed British medical authorities to license all qualified applicants whatever their gender.
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# Elizabeth Garrett Anderson
## Career
Though she was now a licentiate of the Society of Apothecaries, as a woman, Garrett could not hold a medical post in any hospital. So in late 1865, Garrett opened her own practice at 20 Upper Berkeley Street, London. At first patients were scarce, but the practice gradually grew. After six months in practice, she wished to open an outpatients dispensary, to enable poor women to obtain medical help from a qualified practitioner of their own gender. In 1865, there was an outbreak of cholera in Britain, affecting both rich and poor, and in their panic, some people forgot any prejudices they had in relation to a female physician. The first death due to cholera occurred in 1866, but by then Garrett had already opened St Mary\'s Dispensary for Women and Children, at 69 Seymour Place. In the first year, she tended to 3,000 new patients, who made 9,300 outpatient visits to the dispensary. On hearing that the Dean of the faculty of medicine at the University of Sorbonne, Paris was in favour of admitting women as medical students, Garrett studied French so that she could apply for a medical degree, which she obtained in 1870 after some difficulty.
The same year she was elected to the first London School Board, an office newly opened to women; Garrett\'s was the highest vote among all the candidates. Also in that year, she was made a visiting physician of the East London Hospital for Children (later the Queen Elizabeth Hospital for Children), becoming the first woman in Britain to be appointed to a medical post, but she found the duties of these two positions to be incompatible with her principal work in her private practice and the dispensary, as well as her role as a new mother, so she resigned from these posts by 1873. In 1872, the dispensary became the New Hospital for Women and Children, treating women from all over London for gynaecological conditions; the hospital moved to new premises in Marylebone Street in 1874. Around this time, Garrett also entered into discussion with male medical views regarding women. In 1874, Henry Maudsley\'s article on Sex and Mind in Education appeared, which argued that education for women caused over-exertion and thus reduced their reproductive capacity, sometimes causing \"nervous and even mental disorders\". Garrett\'s counter-argument was that the real danger for women was not education but boredom and that fresh air and exercise were preferable to sitting by the fire with a novel. In the same year, she co-founded the London School of Medicine for Women with Sophia Jex-Blake and became a lecturer in what was then the only teaching hospital in Britain to offer courses for women. She continued to work there for the rest of her career and was dean of the school from 1883 to 1902. This school was later called the Royal Free Hospital School of Medicine, and became part of the medical school of University College London.
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# Elizabeth Garrett Anderson
## Career
### BMA membership {#bma_membership}
In 1873, Garrett gained membership of the British Medical Association (BMA). In 1878, a motion was proposed to exclude women following the election of Garrett Anderson and Frances Hoggan. The motion was opposed by Dr Norman Kerr who maintained the equal rights of members. This was \"one of several instances where Garrett, uniquely, was able to enter a hitherto all male medical institution which subsequently moved formally to exclude any women who might seek to follow her.\" In 1892, women were again admitted to the British Medical Association following a long campaign by Anderson and others. She, along with Dr Sarah Gray and Dr Eliza Walker Dunbar attended the BMA meeting at Nottingham that year, lobbying successfully for the readmission of women to the association. In 1897, Garrett Anderson was elected president of the East Anglian branch of the BMA.
Garrett Anderson worked steadily at the development of the New Hospital for Women and Children and in 1874 co-founded and served as dean of the London School of Medicine for Women (LSMW). Both institutions were handsomely and suitably housed and equipped. The New Hospital for Women commissioned a building in the Euston Road; the architect was J. M. Brydon, who took into his employment Anderson\'s sister Agnes Garrett and her cousin Rhoda Garrett, who contributed to its design. For many years, the hospital was staffed entirely by medical women. The schools (in Hunter Street, WC1) had over 200 students, most of them preparing for the medical degree of London University, which was opened to women in 1877.
## Women's suffrage movement {#womens_suffrage_movement}
Garrett Anderson was also active in the women\'s suffrage movement. In 1866, Garrett Anderson and Davies presented petitions with more than 1,500 signatures asking that female heads of household be given the right to vote. That year, Garrett Anderson joined the first British Women\'s Suffrage Committee. She was not as active as her sister, Millicent Garrett Fawcett, though Garrett Anderson became a member of the Central Committee of the National Society for Women\'s Suffrage in 1889. After her husband\'s death in 1907, she became more active. As mayor of Aldeburgh, she gave speeches for suffrage, before the increasing militant activity in the movement led to her withdrawal in 1911. Her daughter Louisa, also a physician, was more active and more militant, spending time in prison in 1912 for her suffrage activities.
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# Elizabeth Garrett Anderson
## Personal life {#personal_life}
Elizabeth Garrett Anderson once remarked that \"a doctor leads two lives, the professional and the private, and the boundaries between the two are never traversed\". In 1871, she married James George Skelton Anderson (died 1907) of the Orient Steam Navigation Company, but she did not give up her medical practice. She had three children, Louisa (1873--1943), Margaret (1874--1875), who died of meningitis, and Alan (1877--1952). Louisa also became a pioneering doctor of medicine and feminist activist.
They retired to Aldeburgh in 1902, moving to Alde House in 1903, after the death of Elizabeth\'s mother. Skelton died of a stroke in 1907. She enjoyed a happy marriage and in later life, devoted time to Alde House, gardening, and travelling with younger members of the extended family.
On 9 November 1908, she was elected mayor of Aldeburgh, the first female mayor in England. Her father had been mayor in 1889.
She died in 1917 and is buried in the churchyard of St Peter and St Paul\'s Church, Aldeburgh.
## Legacy
The New Hospital for Women was renamed the Elizabeth Garrett Anderson Hospital in 1918 and amalgamated with the Obstetric Hospital in 2001 to form the Elizabeth Garrett Anderson and Obstetric Hospital before relocating to become the University College Hospital Elizabeth Garrett Anderson Wing at UCH.
The former Elizabeth Garrett Anderson Hospital buildings are incorporated into the new National Headquarters for the public service trade union UNISON. The Elizabeth Garrett Anderson Gallery, a permanent installation set within the restored hospital building, uses a variety of media to set the story of Garrett Anderson, her hospital, and women\'s struggle to achieve equality in the field of medicine within the wider framework of 19th and 20th century social history.
The critical care centre at Ipswich Hospital was named the Garrett Anderson Centre in her honour and in recognition of her connection to the county of Suffolk.
The new medical school at the University of Worcester, due to accept its first students in 2023, is to be called the Elizabeth Garrett Anderson Building.
Elizabeth Garrett Anderson School, a secondary school for girls in Islington, London, is named after her.
The archives of Elizabeth Garrett Anderson are held at the Women\'s Library at the London School of Economics. The archives of the Elizabeth Garrett Anderson Hospital (formerly the New Hospital for Women) are held at the London Metropolitan Archives.
On 9 June 2016, Google Doodle commemorated her 180th birthday.
The Elizabeth Garrett Anderson Programme of the NHS Leadership Academy is a master\'s degree in leadership and management
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# Electronegativity
*Electronegative* (EP)}} thumb\|alt=A water molecule is put into a see-through egg shape, which is color-coded by electrostatic potential. A concentration of red is near the top of the shape, where the oxygen atom is, and gradually shifts through yellow, green, and then to blue near the lower-right and lower-left corners of the shape where the hydrogen atoms are.\|upright=1.5\|right\|Electrostatic potential map of a water molecule, where the oxygen atom has a more negative charge (red) than the positive (blue) hydrogen atoms **Electronegativity**, symbolized as *χ*, is the tendency for an atom of a given chemical element to attract shared electrons (or electron density) when forming a chemical bond. An atom\'s electronegativity is affected by both its atomic number and the distance at which its valence electrons reside from the charged nucleus. The higher the associated electronegativity, the more an atom or a substituent group attracts electrons. Electronegativity serves as a simple way to quantitatively estimate the bond energy, and the sign and magnitude of a bond\'s chemical polarity, which characterizes a bond along the continuous scale from covalent to ionic bonding. The loosely defined term **electropositivity** is the opposite of electronegativity: it characterizes an element\'s tendency to donate valence electrons.
On the most basic level, electronegativity is determined by factors like the nuclear charge (the more protons an atom has, the more \"pull\" it will have on electrons) and the number and location of other electrons in the atomic shells (the more electrons an atom has, the farther from the nucleus the valence electrons will be, and as a result, the less positive charge they will experience---both because of their increased distance from the nucleus and because the other electrons in the lower energy core orbitals will act to shield the valence electrons from the positively charged nucleus).
The term \"electronegativity\" was introduced by Jöns Jacob Berzelius in 1811, though the concept was known before that and was studied by many chemists including Avogadro. Despite its long history, an accurate scale of electronegativity was not developed until 1932, when Linus Pauling proposed an electronegativity scale that depends on bond energies, as a development of valence bond theory. It has been shown to correlate with several other chemical properties. Electronegativity cannot be directly measured and must be calculated from other atomic or molecular properties. Several methods of calculation have been proposed, and although there may be small differences in the numerical values of electronegativity, all methods show the same periodic trends between elements.
The most commonly used method of calculation is that originally proposed by Linus Pauling. This gives a dimensionless quantity, commonly referred to as the **Pauling scale** (*χ*~r~), on a relative scale running from 0.79 to 3.98 (hydrogen = 2.20). When other methods of calculation are used, it is conventional (although not obligatory) to quote the results on a scale that covers the same range of numerical values: this is known as electronegativity in *Pauling units*.
As it is usually calculated, electronegativity is not a property of an atom alone, but rather a property of an atom in a molecule. Even so, the electronegativity of an atom is strongly correlated with the first ionization energy. The electronegativity is slightly negatively correlated (for smaller electronegativity values) and rather strongly positively correlated (for most and larger electronegativity values) with the electron affinity. It is to be expected that the electronegativity of an element will vary with its chemical environment, but it is usually considered to be a transferable property, that is to say, that similar values will be valid in a variety of situations.
Cesium is the least electronegative element (0.79); fluorine is the most (3.98).
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# Electronegativity
## Methods of calculation {#methods_of_calculation}
### Pauling electronegativity {#pauling_electronegativity}
Pauling first proposed the concept of electronegativity in 1932 to explain why the covalent bond between two different atoms (A--B) is stronger than the average of the A--A and the B--B bonds. According to valence bond theory, of which Pauling was a notable proponent, this \"additional stabilization\" of the heteronuclear bond is due to the contribution of ionic canonical forms to the bonding.
The difference in electronegativity between atoms A and B is given by: $|\chi_{\rm A} - \chi_{\rm B}| = ({\rm eV})^{-1/2} \sqrt{E_{\rm d}({\rm AB}) - \frac{E_{\rm d}({\rm AA}) + E_{\rm d}({\rm BB})} 2}$ where the dissociation energies, *E*~d~, of the A--B, A--A and B--B bonds are expressed in electronvolts, the factor (eV)^−`{{frac|1|2}}`{=mediawiki}^ being included to ensure a dimensionless result. Hence, the difference in Pauling electronegativity between hydrogen and bromine is 0.73 (dissociation energies: H--Br, 3.79 eV; H--H, 4.52 eV; Br--Br 2.00 eV)
As only differences in electronegativity are defined, it is necessary to choose an arbitrary reference point to construct a scale. Hydrogen was chosen as the reference, as it forms covalent bonds with a large variety of elements: its electronegativity was fixed first at 2.1, later revised to 2.20. It is also necessary to decide which of the two elements is the more electronegative (equivalent to choosing one of the two possible signs for the square root). This is usually done using \"chemical intuition\": in the above example, hydrogen bromide dissolves in water to form H^+^ and Br^−^ ions, so it may be assumed that bromine is more electronegative than hydrogen. However, in principle, since the same electronegativities should be obtained for any two bonding compounds, the data are overdetermined, and the signs are unique once a reference point has been fixed (usually, for H or F).
To calculate Pauling electronegativity for an element, it is necessary to have data on the dissociation energies of at least two types of covalent bonds formed by that element. A. L. Allred updated Pauling\'s original values in 1961 to take account of the greater availability of thermodynamic data, and it is these \"revised Pauling\" values of the electronegativity that are most often used.
The essential point of Pauling electronegativity is that there is an underlying, quite accurate, semi-empirical formula for dissociation energies, namely: $E_{\rm d}({\rm AB}) = \frac{E_{\rm d}({\rm AA}) + E_{\rm d}({\rm BB})} 2 + (\chi_{\rm A} - \chi_{\rm B})^2 {\rm eV}$ or sometimes, a more accurate fit $E_{\rm d}({\rm AB}) =\sqrt{E_{\rm d}({\rm AA}) E_{\rm d}({\rm BB})}+1.3(\chi_{\rm A} - \chi_{\rm B})^2 {\rm eV}$
These are approximate equations but they hold with good accuracy. Pauling obtained the first equation by noting that a bond can be approximately represented as a quantum mechanical superposition of a covalent bond and two ionic bond states. The covalent energy of a bond is approximate, by quantum mechanical calculations, the geometric mean of the two energies of covalent bonds of the same molecules, and there is additional energy that comes from ionic factors, i.e. polar character of the bond.
The geometric mean is approximately equal to the arithmetic mean---which is applied in the first formula above---when the energies are of a similar value, e.g., except for the highly electropositive elements, where there is a larger difference of two dissociation energies; the geometric mean is more accurate and almost always gives positive excess energy, due to ionic bonding. The square root of this excess energy, Pauling notes, is approximately additive, and hence one can introduce the electronegativity. Thus, it is these semi-empirical formulas for bond energy that underlie the concept of Pauling electronegativity.
The formulas are approximate, but this rough approximation is good and gives the right intuition, with the notion of the polarity of the bond and some theoretical grounding in quantum mechanics. The electronegativities are then determined to best fit the data.
In more complex compounds, there is an additional error since electronegativity depends on the molecular environment of an atom. Also, the energy estimate can be only used for single, not for multiple bonds. The enthalpy of formation of a molecule containing only single bonds can subsequently be estimated based on an electronegativity table, and it depends on the constituents and the sum of squares of differences of electronegativities of all pairs of bonded atoms. Such a formula for estimating energy typically has a relative error on the order of 10% but can be used to get a rough qualitative idea and understanding of a molecule.
### Mulliken electronegativity {#mulliken_electronegativity}
thumb\|upright=1.35\|The correlation between Mulliken electronegativities (*x*-axis, in kJ/mol) and Pauling electronegativities (*y*-axis). Robert S. Mulliken proposed that the arithmetic mean of the first ionization energy (E~i~) and the electron affinity (E~ea~) should be a measure of the tendency of an atom to attract electrons: $\chi = \frac{E_{\rm i} + E_{\rm ea}} 2$
As this definition is not dependent on an arbitrary relative scale, it has also been termed **absolute electronegativity**, with the units of kilojoules per mole or electronvolts. However, it is more usual to use a linear transformation to transform these absolute values into values that resemble the more familiar Pauling values. For ionization energies and electron affinities in electronvolts, $\chi = 0.187(E_{\rm i} + E_{\rm ea}) + 0.17 \,$ and for energies in kilojoules per mole, $\chi = (1.97\times 10^{-3})(E_{\rm i} + E_{\rm ea}) + 0.19.$
The Mulliken electronegativity can only be calculated for an element whose electron affinity is known. Measured values are available for 72 elements, while approximate values have been estimated or calculated for the remaining elements.
The Mulliken electronegativity of an atom is sometimes said to be the negative of the chemical potential. By inserting the energetic definitions of the ionization potential and electron affinity into the Mulliken electronegativity, it is possible to show that the Mulliken chemical potential is a finite difference approximation of the electronic energy with respect to the number of electrons., i.e., $\mu(\rm Mulliken) = -\chi(\rm Mulliken) = {}-\frac{E_{\rm i} + E_{\rm ea}} 2$
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| 1 |
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# Electronegativity
## Methods of calculation {#methods_of_calculation}
### Allred--Rochow electronegativity {#allredrochow_electronegativity}
thumb\|upright=1.35\|The correlation between Allred--Rochow electronegativities (*x*-axis, in Å^−2^) and Pauling electronegativities (*y*-axis). A. Louis Allred and Eugene G. Rochow considered that electronegativity should be related to the charge experienced by an electron on the \"surface\" of an atom: The higher the charge per unit area of atomic surface the greater the tendency of that atom to attract electrons. The effective nuclear charge, *Z*~eff~, experienced by valence electrons can be estimated using Slater\'s rules, while the surface area of an atom in a molecule can be taken to be proportional to the square of the covalent radius, *r*~cov~. When *r*~cov~ is expressed in picometres, $\chi = 3590{{Z_{\rm eff}}\over{r^2_{\rm cov}}} + 0.744$
### Sanderson electronegativity equalization {#sanderson_electronegativity_equalization}
thumb\|upright=1.35\|The correlation between Sanderson electronegativities (*x*-axis, arbitrary units) and Pauling electronegativities (*y*-axis). R.T. Sanderson has also noted the relationship between Mulliken electronegativity and atomic size and has proposed a method of calculation based on the reciprocal of the atomic volume. With a knowledge of bond lengths, Sanderson\'s model allows the estimation of bond energies in a wide range of compounds. Sanderson\'s model has also been used to calculate molecular geometry, *s*-electron energy, NMR spin-spin coupling constants and other parameters for organic compounds. This work underlies the concept of **electronegativity equalization**, which suggests that electrons distribute themselves around a molecule to minimize or equalize the Mulliken electronegativity. This behavior is analogous to the equalization of chemical potential in macroscopic thermodynamics.
### Allen electronegativity {#allen_electronegativity}
thumb\|upright=1.35\|The correlation between Allen electronegativities (*x*-axis, in kJ/mol) and Pauling electronegativities (*y*-axis). Perhaps the simplest definition of electronegativity is that of Leland C. Allen, who has proposed that it is related to the average energy of the valence electrons in a free atom,
$\chi = {n_{\rm s}\varepsilon_{\rm s} + n_{\rm p}\varepsilon_{\rm p} \over n_{\rm s} + n_{\rm p}}$
where *ε*~s,p~ are the one-electron energies of s- and p-electrons in the free atom and *n*~s,p~ are the number of s- and p-electrons in the valence shell.
The one-electron energies can be determined directly from spectroscopic data, and so electronegativities calculated by this method are sometimes referred to as **spectroscopic electronegativities**. The necessary data are available for almost all elements, and this method allows the estimation of electronegativities for elements that cannot be treated by the other methods, e.g. francium, which has an Allen electronegativity of 0.67. However, it is not clear what should be considered to be valence electrons for the d- and f-block elements, which leads to an ambiguity regarding their electronegativities calculated by the Allen method.
On this scale, neon has the highest electronegativity of all elements, followed by fluorine, helium, and oxygen.
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# Electronegativity
## Correlation of electronegativity with other properties {#correlation_of_electronegativity_with_other_properties}
\[\[Image:Sn-119 isomer shifts in hexahalostannates.png\|thumb\|upright=1.35\|The variation of the isomer shift (*y*-axis, in mm/s) of \[SnX~6~\]^2−^ anions, as measured by ^119^Sn Mössbauer spectroscopy, against the sum of the Pauling electronegativities of the halide substituents (*x*-axis).\]\] The wide variety of methods of calculation of electronegativities, which all give results that correlate well with one another, is one indication of the number of chemical properties that might be affected by electronegativity. The most obvious application of electronegativities is in the discussion of bond polarity, for which the concept was introduced by Pauling. In general, the greater the difference in electronegativity between two atoms the more polar the bond that will be formed between them, with the atom having the higher electronegativity being at the negative end of the dipole. Pauling proposed an equation to relate the \"ionic character\" of a bond to the difference in electronegativity of the two atoms, although this has fallen somewhat into disuse.
Several correlations have been shown between infrared stretching frequencies of certain bonds and the electronegativities of the atoms involved: However, this is not surprising as such stretching frequencies depend in part on bond strength, which enters into the calculation of Pauling electronegativities. More convincing are the correlations between electronegativity and chemical shifts in NMR spectroscopy or isomer shifts in Mössbauer spectroscopy (see figure). Both these measurements depend on the s-electron density at the nucleus, and so is a good indication that the different measures of electronegativity describe \"the ability of an atom in a molecule to attract electrons to itself\".
## Trends in electronegativity {#trends_in_electronegativity}
### Periodic trends {#periodic_trends}
thumb\|upright=1.5\|The variation of Pauling electronegativity (*y*-axis) as one descends the main groups of the periodic table from the second period to the sixth period In general, electronegativity increases on passing from left to right along a period and decreases on descending a group. Hence, Fluorine is the most electronegative of the elements (not counting Noble gases), whereas Cesium is the least electronegative, at least of those elements for which substantial data is available.
There are some exceptions to this general rule. Gallium and Germanium have higher electronegativities than Aluminium and Silicon, respectively, because of the d-block contraction. Elements of the fourth period immediately after the first row of the transition metals have unusually small atomic radii because the 3d-electrons are not effective at shielding the increased nuclear charge, and smaller atomic size correlates with higher electronegativity (see Allred-Rochow electronegativity and Sanderson electronegativity above). The anomalously high electronegativity of lead, in particular, when compared to thallium and bismuth, is an artifact of electronegativity varying with oxidation state: its electronegativity conforms better to trends if it is quoted for the +2 state with a Pauling value of 1.87 instead of the +4 state.
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| 3 |
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# Electronegativity
## Trends in electronegativity {#trends_in_electronegativity}
### Variation of electronegativity with oxidation number {#variation_of_electronegativity_with_oxidation_number}
In inorganic chemistry, it is common to consider a single value of electronegativity to be valid for most \"normal\" situations. While this approach has the advantage of simplicity, it is clear that the electronegativity of an element is *not* an invariable atomic property and, in particular, increases with the oxidation state of the element.
Allred used the Pauling method to calculate separate electronegativities for different oxidation states of the handful of elements (including tin and lead) for which sufficient data were available. However, for most elements, there are not enough different covalent compounds for which bond dissociation energies are known to make this approach feasible.
+-------------------+---------+------------+---------+
| Acid | Formula | Chlorine\ | p*K*~a~ |
| | | oxidation\ | |
| | | state | |
+===================+=========+============+=========+
| Hypochlorous acid | HClO | +1 | +7.5 |
+-------------------+---------+------------+---------+
| Chlorous acid | HClO~2~ | +3 | +2.0 |
+-------------------+---------+------------+---------+
| Chloric acid | HClO~3~ | +5 | −1.0 |
+-------------------+---------+------------+---------+
| Perchloric acid | HClO~4~ | +7 | −10 |
+-------------------+---------+------------+---------+
| | | | |
+-------------------+---------+------------+---------+
The chemical effects of this increase in electronegativity can be seen both in the structures of oxides and halides and in the acidity of oxides and oxoacids. Hence CrO~3~ and Mn~2~O~7~ are acidic oxides with low melting points, while Cr~2~O~3~ is amphoteric and Mn~2~O~3~ is a completely basic oxide.
The effect can also be seen in the dissociation constants p*K*~a~ of the oxoacids of chlorine. The effect is much larger than could be explained by the negative charge being shared among a larger number of oxygen atoms, which would lead to a difference in p*K*~a~ of log~10~(`{{frac|1|4}}`{=mediawiki}) = −0.6 between hypochlorous acid and perchloric acid. As the oxidation state of the central chlorine atom increases, more electron density is drawn from the oxygen atoms onto the chlorine, diminishing the partial negative charge of individual oxygen atoms. At the same time, the positive partial charge on the hydrogen increases with a higher oxidation state. This explains the observed increased acidity with an increasing oxidation state in the oxoacids of chlorine.
### Electronegativity and hybridization scheme {#electronegativity_and_hybridization_scheme}
The electronegativity of an atom changes depending on the hybridization of the orbital employed in bonding. Electrons in s orbitals are held more tightly than electrons in p orbitals. Hence, a bond to an atom that employs an sp*^x^* hybrid orbital for bonding will be more heavily polarized to that atom when the hybrid orbital has more s character. That is, when electronegativities are compared for different hybridization schemes of a given element, the order `{{math|χ(sp<sup>3</sup>) < χ(sp<sup>2</sup>) < χ(sp)}}`{=mediawiki} holds (the trend should apply to non-integer hybridization indices as well).
Hybridization (Pauling)
--------------- -----------
C(sp^3^) 2.3
C(sp^2^) 2.6
C(sp) 3.1
\'generic\' C 2.5
## Group electronegativity {#group_electronegativity}
In organic chemistry, electronegativity is associated more with different functional groups than with individual atoms. The terms **group electronegativity** and **substituent electronegativity** are used synonymously. However, it is common to distinguish between the inductive effect and the resonance effect, which might be described as σ- and π-electronegativities, respectively. There are several linear free-energy relationships that have been used to quantify these effects, of which the Hammett equation is the best known. Kabachnik Parameters are group electronegativities for use in organophosphorus chemistry.
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| 4 |
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# Electronegativity
## Electropositivity
**Electropositivity** is a measure of an element\'s ability to donate electrons, and therefore form positive ions; thus, it is antipode to electronegativity.
Mainly, this is an attribute of metals, meaning that, in general, the greater the metallic character of an element the greater the electropositivity. Therefore, the alkali metals are the most electropositive of all. This is because they have a single electron in their outer shell and, as this is relatively far from the nucleus of the atom, it is easily lost; in other words, these metals have low ionization energies.
While electronegativity increases along periods in the periodic table and decreases down groups, electropositivity *decreases* along periods (from left to right) and *increases* down groups. This means that elements in the upper right of the periodic table of elements (oxygen, sulfur, chlorine, etc.) will have the greatest electronegativity, and those in the lower left (rubidium, cesium, and francium) the greatest electropositivity
| 157 |
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# European Charter for Regional or Minority Languages
The **European Charter for Regional or Minority Languages** (**ECRML**) is a European treaty (CETS 148) adopted in 1992 under the auspices of the Council of Europe to protect and promote historical regional and minority languages in Europe. However, the charter does not provide any criterion or definition for an idiom to be a minority or a regional language, and the classification stays in the hands of the national state.
The preparation for the charter was undertaken by the predecessor to the current Congress of Local and Regional Authorities, the Standing Conference of Local and Regional Authorities of Europe because involvement of local and regional government was essential. The actual charter was written in the Parliamentary Assembly based on the Congress\' Recommendations. It only applies to languages traditionally used by the nationals of the State Parties (thus excluding languages used by recent immigrants from other states, see immigrant languages), which significantly differ from the majority or official language (thus excluding what the state party wishes to consider as mere local dialects of the official or majority language) and that either have a territorial basis (and are therefore traditionally spoken by populations of regions or areas within the State) or are used by linguistic minorities within the State as a whole (thereby including such languages as Yiddish, Romani and Lemko, which are used over a wide geographic area).
Some states, such as Ukraine and Sweden, have tied the status of minority language to the recognized national minorities, which are defined by ethnic, cultural and/or religious criteria, thereby circumventing the Charter\'s notion of linguistic minority.
Languages that are official within regions, provinces or federal units within a State (for example Catalan in Spain) are not classified as official languages of the State and may therefore benefit from the Charter. On the other hand, Ireland has been unable to sign the Charter on behalf of the Irish language (although a minority language) as it is defined as the first official language of the state. The United Kingdom has ratified the Charter in respect to (among other languages) Welsh in Wales, Scots and Gaelic in Scotland, and Irish in Northern Ireland. France, although a signatory, has been constitutionally blocked from ratifying the Charter in respect to the languages of France.
The charter provides many actions state parties can take to protect and promote historical regional and minority languages. There are two levels of protection---all signatories must apply the lower level of protection to qualifying languages. Signatories may further declare that a qualifying language or languages will benefit from the higher level of protection, which lists a range of actions from which states must agree to undertake at least 35.
The Charter does not provide procedures for reactive judicial processing in case of lack of compliance but rather an elaborate proactive regular monitoring process in which the Committee of Experts drafts formal feedback and recommendations in regard to the situation in countries parties to the charter.
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| 0 |
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# European Charter for Regional or Minority Languages
## Protections
Countries can ratify the charter in respect of its minority languages based on Part II or Part III of the charter, which contain varying principles. Countries can treat languages differently under the charter, for example, in the United Kingdom, the Welsh language is ratified under the general Part II principles as well as the more specific Part III commitments, while the Cornish language is ratified only under Part II.
### Part II {#part_ii}
Part II of the Charter details eight main principles and objectives upon which States must base their policies and legislation. They are seen as a framework for the preservation of the languages concerned.
- Recognition of regional or minority languages as an expression of cultural wealth.
- Respect for the geographical area of each regional or minority language.
- The need for resolute action to promote such languages.
- The facilitation and/or encouragement of the use of such languages, in speech and writing, in public and private life.
- The provision of appropriate forms and means for the teaching and study of such languages at all appropriate stages.
- The promotion of relevant transnational exchanges.
- The prohibition of all forms of unjustified distinction, exclusion, restriction or preference relating to the use of a regional or minority language and intended to discourage or endanger its maintenance or development.
- The promotion by states of mutual understanding between all the country\'s linguistic groups.
### Part III {#part_iii}
Part III details comprehensive rules, across a number of sectors, by which states agree to abide. Each language to which Part III of the Charter is applied must be named specifically by the government. States must select at least thirty-five of the undertakings in respect to each language. Many provisions contain several options, of varying degrees of stringency, one of which has to be chosen \"according to the situation of each language\". The areas from which these specific undertakings must be chosen are as follows:
- Education
- Judicial authorities
- Administrative authorities and public services
- Media
- Cultural activities and facilities
- Economic and social life
- Transfrontier exchanges
| 360 |
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| 1 |
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# European Charter for Regional or Minority Languages
## Languages protected under the Charter {#languages_protected_under_the_charter}
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Country | Ratification | Language | Notes |
+=========+===================+===================================+=====================================================================================================================================================================================================================================================================================================================================+
| | 25 January 2002 | Assyrian | Part II and III |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | German | Part II |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Greek | Part II and III |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Kurdish | Part II and III |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Russian | Part II and III |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Ukrainian | Part II |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Yezidi | Part II and III |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | 28 June 2001 | Burgenland Croatian | (in Burgenland) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Czech | (in Vienna) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Hungarian | (in Burgenland and Vienna) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Romani | (in Burgenland) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Slovak | (in Vienna) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Slovene | (in Carinthia and Styria) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | 21 September 2010 | Albanian | Part II and III |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Czech | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | German | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Hungarian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Italian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Ladino | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Polish | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Romani | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Romanian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Rusyn (as Ruthenian) | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Slovak | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Slovenian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Turkish | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Ukrainian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Yiddish | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | 5 November 1997 | Czech | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | German | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Hungarian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Boyash Romanian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Istro-Romanian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Italian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Romani | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Rusyn (as Ruthenian) | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Serbian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Slovakian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Slovenian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Ukrainian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | 26 August 2002 | Armenian | Part II (Article 7.5) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Cypriot Maronite Arabic | Part II (Article 7) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | 15 November 2006 | Moravian Croatian | (part II only) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | German | (part II and part III in districts Cheb, Karlovy Vary, Sokolov, Liberec, Ústí nad Labem, Český Krumlov, Opava and Svitavy) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Polish | (part II; and part III in Moravia-Silesia, in districts Frydek-Místek and Karviná) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Romani | (part II only) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Slovak | (parts II and III, across the whole territory) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | 8 September 2000 | German | (in Southern Jutland) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | 9 November 1994 | Inari Sami | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Karelian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | North Sami | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Romani | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Russian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Skolt Sami | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Swedish | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Tatar | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Yiddish | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | 16 September 1998 | Danish | (in Schleswig-Holstein) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Low German | (part III in Bremen, Hamburg, Mecklenburg-Vorpommern, Lower Saxony and Schleswig-Holstein); (part II in Brandenburg, Northrhine-Westphalia and Saxony-Anhalt) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Lower Sorbian | (in Brandenburg) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | North Frisian | (in Schleswig-Holstein) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Romani | (across Germany) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Saterland Frisian | (in Lower Saxony) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Upper Sorbian | (in the Free State of Saxony) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | 26 April 1995 | Armenian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Boyash Romanian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Bulgarian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Croatian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | German | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Greek | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Polish | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Romani | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Romanian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Rusyn (as Ruthenian) | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Serbian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Slovak | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Slovene | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Ukrainian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | 18 November 1997 | No regional or minority languages | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | 22 June 2005 | No regional or minority languages | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | 15 February 2006 | Albanian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Bosnian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Croatian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Romani | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | 2 May 1996 | Frisian | (in Friesland, under part III) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Limburgish | (in Limburg, under part II) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Low Saxon | (across the Netherlands, under part II) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Papiamento | (on Bonaire under part III) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Romani | (across the Netherlands, under part II) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Yiddish | (across the Netherlands, under part II) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | 10 November 1993 | Kven/Finnish | (part II only) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Lule Sami | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | North Sami | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Romanes | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Romani | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | South Sami | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | 12 February 2009 | Armenian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Belarusian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Czech | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | German | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Karaim | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Kashub | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Lemko | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Lithuanian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Romani | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Russian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Slovakian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Tatar | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Ukrainian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Yiddish | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | 29 January 2008 | Albanian | (Part II only) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Armenian | (Part II only) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Bulgarian | (Part III only) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Croatian | (Part III only) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Czech | (Part III only) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | German | (Part III only) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Greek | (Part II only) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Hungarian | (Part III only) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Italian | (Part II only) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Macedonian | (Part II only) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Polish | (Part II only) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Romani | (Part II only) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Russian | Part II and III |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Rusyn (as Ruthenian) | (Part II only) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Serbian | (Part III only) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Slovak | (Part III only) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Tatar | (Part II only) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Turkish | (Part III only) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Ukrainian | (Part III only) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Yiddish | (Part II only) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | 15 February 2006 | Albanian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Bosnian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Bulgarian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Bunjevac | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Croatian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Czech | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | German | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Hungarian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Macedonian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Romani | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Romanian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Rusyn (as Ruthenian) | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Slovakian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Ukrainian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Vlach | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | 5 September 2001 | Bulgarian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Croatian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Czech | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | German | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Hungarian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Polish | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Romani | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Russian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Rusyn (as Ruthenian) | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Serbian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Ukrainian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Yiddish | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | 4 October 2000 | Croatian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | German | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Hungarian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Italian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Romani | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Serbian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | 9 April 2001 | Amazigh | in Melilla |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Aragonese | *luenga propia* in Aragon |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Aranese (Occitan) | in Catalonia |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Asturian language | present in Asturias; and in part of Leon, Zamora, Salamanca, Cantabria and Extremadura (recognized in Asturias, Castile and León) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Basque | (official in the Basque Country and part of Navarre) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Catalan | official in the Balearic Islands and Catalonia; *llengua pròpia* in Aragon. |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Darija | in Ceuta |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Extremaduran | in Extremadura |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Fala | in Extremadura |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Galician | present in Galicia; and in part of Asturias, Leon and Zamora provinces (official in Galicia) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Leonese | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Portuguese | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Valencian (A dialect of Catalan) | official in Valencia |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | 9 February 2000 | Finnish | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Lule Sami | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Meänkieli | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | North Sami | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Romani | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | South Sami | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Yiddish | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | 23 December 1997 | Franco-Provençal | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | French | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | German | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Italian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Romansh | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Yenish | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | 19 September 2005 | Armenian | Ukraine does not specify languages by name, but rather ratifies on behalf of \"the languages of the following ethnic minorities of Ukraine |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Belarusian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Bulgarian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Crimean Tatar | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Gagauz | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | German | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Greek | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Hungarian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Karaim | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Krimchak | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Moldovan | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Polish | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Romani | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Romanian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Russian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Rusyn (as Ruthenian) | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Slovakian | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Yiddish | |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | 27 March 2001 | Cornish | (Article 2, Part II only (Article 7)) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Irish | \ |
| | | | (Articles 2 and 3, Part II (Article 7) and Part III (Articles 8--14, with reservations)) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Scots | (Articles 2 and 3, Part II only (Article 7)) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Ulster-Scots | (Articles 2 and 3, Part II only (Article 7)) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Scottish Gaelic | \ |
| | | | (Articles 2 and 3, Part II (Article 7) and Part III (Articles 8--14, with reservations))\ |
| | | | (British Nationality Act 1981, Schedule 1, Article 1(1)(c)[1](https://www.legislation.gov.uk/ukpga/1981/61/schedule/1), and the Gaelic Language (Scotland) Act 2005 [2](https://www.legislation.gov.uk/asp/2005/7)) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | Welsh | \ |
| | | | (Articles 2 and 3, Part II (Article 7) and Part III (Articles 8--14, with reservations))\ |
| | | | (Welsh Language Act 1967 (repealed 21.12.1993) [3](https://www.legislation.gov.uk/ukpga/1967/66) and the Welsh Language Act 1993 [4](https://www.legislation.gov.uk/ukpga/1993/38)) |
+---------+-------------------+-----------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | 27 March 2001 | Manx Gaelic | (Article 2, Part II only (Article 7)) (extension : 23 April 2003 (declaration dated 22 April 2003) The Government of the United Kingdom declares \[on 23 April 2003\] that the Charter should extend to the *Isle of Man*, being a territory for whose international relations the Government of the United Kingdom is responsible
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| 2 |
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# Eight-bar blues
In music, an **eight-bar blues** is a common blues chord progression. Music writers have described it as \"the second most common blues form\" being \"common to folk, rock, and jazz forms of the blues\". It is often notated in `{{music|time|4|4}}`{=mediawiki} or `{{music|time|12|8}}`{=mediawiki} time with eight bars to the verse.
## Overview
Early examples of eight-bar blues standards include:
- \"Ain\'t Nobody\'s Business If I Do\" (Sara Martin, 1922)
- \"Trouble in Mind\" (Bertha Hill, 1926)
- \"How Long Blues\" (Leroy Carr, 1928)
- \"Nobody Knows You When You\'re Down and Out\" (Bessie Smith, 1929)
- \"It Hurts Me Too\" (Tampa Red, 1940)
- \"Key to the Highway\" (Big Bill Broonzy, 1941)
- \"Worried Life Blues\" (Big Maceo, 1941)
One variant using this progression is to couple one eight-bar blues melody with a different eight-bar blues bridge to create a blues variant of the standard 32-bar song: \"I Want a Little Girl\" (T-Bone Walker) and \"Great Balls of Fire\" (Jerry Lee Lewis)(
Eight-bar blues progressions have more variations than the more rigidly defined twelve bar format. The move to the IV chord usually happens at bar 3 (as opposed to 5 in twelve bar); however, \"the I chord moving to the V chord right away, in the second measure, is a characteristic of the eight-bar blues.\"
In the following examples each box represents a \'bar\' of music (the specific time signature is not relevant). The chord in the box is played for the full bar. If two chords are in the box they are each played for half a bar, etc. The chords are represented as scale degrees in Roman numeral analysis. Roman numerals are used so the musician may understand the progression of the chords regardless of the key it is played in.
\"Eight-bar blues chord progression\":
: {\|class=\"wikitable\" style=\"text-align:left; width:250px;\"
\|width=25%\|I \|width=25%\|V^7^ \|width=25%\|IV^7^ \|width=25%\|IV^7^ \|- \| I \|\| V^7^ IV^7^ \|\|I \|\|V^7^ \|- \|} `{{Listen|filename=Eight_bar_blues.mid|title=Eight-bar blues chord progression in C|plain=yes|style=margin-left:1em}}`{=mediawiki}
\"Worried Life Blues\" (probably the most common eight-bar blues progression):
: {\|class=\"wikitable\" style=\"text-align:left; width:250px;\"
\|width=25%\|I \|width=25%\|I \|width=25%\|IV \|width=25%\|IV \|- \| I \|\|V \|\|I IV\|\|I V \|- \|} `{{Listen|filename=Eight_bar_blues_progression_in_C.mid|title=Eight-bar blues progression in C|plain=yes|style=margin-left:1em}}`{=mediawiki}
\"Heartbreak Hotel\" (variation with the I on the first half):
: {\|class=\"wikitable\" style=\"text-align:left; width:250px;\"
\|width=25%\|I \|width=25%\|**I** \|width=25%\|I \|width=25%\|I \|- \| IV \|\|IV \|\|V \|\|I \|- \|}
J. B. Lenoir\'s \"Slow Down\" and \"Key to the Highway\" (variation with the V at bar 2):
: {\|class=\"wikitable\" style=\"text-align:left; width:250px;\"
\|width=25%\|I^7^ \|width=25%\|**V**^7^ \|width=25%\|IV^7^ \|width=25%\|IV^7^ \|- \|I^7^ \|\|V^7^ \|\|I^7^ \|\|V^7^ \|- \|}
\"Get a Haircut\" by George Thorogood (simple progression):
: {\|class=\"wikitable\" style=\"text-align:left; width:250px;\"
\|width=25%\|I \|width=25%\|I \|width=25%\|I \|width=25%\|I \|- \| IV \|\| IV \|\|V \|\|V \|- \|}
Jimmy Rogers\' \"Walkin\' By Myself\" (somewhat unorthodox example of the form):
: {\|class=\"wikitable\" style=\"text-align:left; width:250px;\"
\|width=25%\|I^7^ \|width=25%\|I^7^ \|width=25%\|I^7^ \|width=25%\|I^7^ \|- \|IV^7^ \|\|V^7^ \|\|I^7^ \|\|V^7^ \|- \|}
Howlin Wolf\'s version of \"Sitting on Top of the World\" is actually a 9 bar blues that adds an extra \"V\" chord at the end of the progression. The song uses movement between major and dominant 7th and major and minor fourth:
: {\|class=\"wikitable\" style=\"text-align:left; width:250px;\"
\|width=25%\|I \|width=25%\|I^7^ \|width=25%\|IV \|width=25%\|iv \|- \|I^7^ \|\|V \|\|I^7^ IV \|\|I^7^ V \|- \|}
The first four bar progression used by Wolf is also used in Nina Simone\'s 1965 version of \"Trouble in Mind\", but with a more uptempo beat than \"Sitting on Top of the World\":
: {\|class=\"wikitable\" style=\"text-align:left; width:250px;\"
\|width=25%\|I \|width=25%\|I^7^ \|width=25%\|IV \|width=25%\|iv \|- \|I VI^7^\|\|ii V\|\|I IV\|\|I V \|- \|}
The progression may be created by dropping the first four bars from the twelve-bar blues, as in the solo section of Bonnie Raitt\'s \"Love Me Like a Man\" and Buddy Guy\'s \"Mary Had a Little Lamb\":
: {\|class=\"wikitable\" style=\"text-align:left; width:250px;\"
\|width=25%\|IV^7^ \|width=25%\|IV^7^ \|width=25%\|I^7^ \|width=25%\|I^7^ \|- \|V^7^ \|\|IV^7^ \|\|I^7^ \|\|V^7^ \|- \|}
There are at least a few very successful songs using somewhat unusual chord progressions as well. For example, the song \"Ain\'t Nobody\'s Business\" as performed by Freddie King at least, uses a I--III--IV--iv progression in each of the first four bars. The same four bar progression is used by the band Radiohead to make up the bulk of the song \"Creep\".
: {\|class=\"wikitable\" style=\"text-align:left; width:250px;\"
\|width=25%\|I \|width=25%\|III \|width=25%\|IV \|width=25%\|iv \|- \|I \|\|vi \|\|ii \|\|V^7^ \|- \|}
The same chord progression can also be called a sixteen-bar blues, if each symbol above is taken to be a half note in `{{music|time|2|2}}`{=mediawiki} or `{{music|time|4|4}}`{=mediawiki} time. Examples are \"Nine Pound Hammer\" and Ray Charles\'s original instrumental \"Sweet Sixteen Bars\"
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# Edward Waring
**Edward Waring** `{{post-nominals|country=GBR|FRS}}`{=mediawiki} (c. 1736`{{spaced ndash}}`{=mediawiki}15 August 1798) was a British mathematician. He entered Magdalene College, Cambridge as a sizar and became Senior wrangler in 1757. He was elected a Fellow of Magdalene and in 1760 Lucasian Professor of Mathematics, holding the chair until his death. He made the assertion known as Waring\'s problem without proof in his writings *Meditationes Algebraicae*. Waring was elected a Fellow of the Royal Society in 1763 and awarded the Copley Medal in 1784.
## Early years {#early_years}
Waring was the eldest son of John and Elizabeth Waring, a prosperous farming couple. He received his early education in Shrewsbury School under a Mr Hotchkin and was admitted as a sizar at Magdalene College, Cambridge, on 24 March 1753, being also Millington exhibitioner.
His extraordinary talent for mathematics was recognised from his early years in Cambridge. In 1757 he graduated BA as senior wrangler and on 24 April 1758 was elected to a fellowship at Magdalene. He belonged to the Hyson Club, whose members included William Paley.
## Career
At the end of 1759 Waring published the first chapter of *Miscellanea Analytica*. On 28 January the next year he was appointed Lucasian professor of mathematics, one of the highest positions in Cambridge. William Samuel Powell, then tutor in St John\'s College, Cambridge opposed Waring\'s election and instead supported the candidacy of William Ludlam. In the polemic with Powell, Waring was backed by John Wilson. In fact Waring was very young and did not hold the MA, necessary for qualifying for the Lucasian chair, but this was granted him in 1760 by royal mandate. In 1762 he published the full *Miscellanea Analytica*, mainly devoted to the theory of numbers and algebraic equations. In 1763 he was elected to the Royal Society. He was awarded its Copley Medal in 1784 but withdrew from the society in 1795, after he had reached sixty, \'on account of \[his\] age\'. Waring was also a member of the academies of sciences of Göttingen and Bologna. In 1767 he took an MD degree, but his activity in medicine was quite limited. He carried out dissections with Richard Watson, professor of chemistry and later bishop of Llandaff. From about 1770 he was physician at Addenbrooke\'s Hospital at Cambridge, and he also practised at St Ives, Huntingdonshire, where he lived for some years after 1767. His career as a physician was not very successful since he was seriously short-sighted and a very shy man.
## Personal life {#personal_life}
Waring had a younger brother, Humphrey, who obtained a fellowship at Magdalene in 1775. In 1776 Waring married Mary Oswell, sister of a draper in Shrewsbury; they moved to Shrewsbury and then retired to Plealey, 8 miles out of the town, where Waring owned an estate of 215 acres in 1797
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# Edward Waring
## Work
Waring wrote a number of papers in the *Philosophical Transactions of the Royal Society*, dealing with the resolution of algebraic equations, number theory, series, approximation of roots, interpolation, the geometry of conic sections, and dynamics. The *Meditationes Algebraicae* (1770), where many of the results published in *Miscellanea Analytica* were reworked and expanded, was described by Joseph-Louis Lagrange as \'a work full of excellent researches\'. In this work Waring published many theorems concerning the solution of algebraic equations which attracted the attention of continental mathematicians, but his best results are in number theory. Included in this work was the so-called Goldbach conjecture (every even integer is the sum of two primes), and also the following conjecture: every odd integer is a prime or the sum of three primes. Lagrange had proved that every positive integer is the sum of not more than four squares; Waring suggested that every positive integer is either a cube or the sum of not more than nine cubes. He also advanced the hypothesis that every positive integer is either a biquadrate (fourth power) or the sum of not more than nineteen biquadrates. These hypotheses form what is known as Waring\'s problem. He also published a theorem, due to his friend John Wilson, concerning prime numbers; it was later proven rigorously by Lagrange.
In *Proprietates Algebraicarum Curvarum* (1772) Waring reissued in a much revised form the first four chapters of the second part of *Miscellanea Analytica*. He devoted himself to the classification of higher plane curves, improving results obtained by Isaac Newton, James Stirling, Leonhard Euler, and Gabriel Cramer. In 1794 he published a few copies of a philosophical work entitled *An Essay on the Principles of Human Knowledge*, which were circulated among his friends.
Waring\'s mathematical style is highly analytical. In fact he criticised those British mathematicians who adhered too strictly to geometry. It is indicative that he was one of the subscribers of John Landen\'s *Residual Analysis* (1764), one of the works in which the tradition of the Newtonian fluxional calculus was more severely criticised. In the preface of *Meditationes Analyticae* Waring showed a good knowledge of continental mathematicians such as Alexis Clairaut, Jean le Rond d\'Alembert, and Euler. He lamented the fact that in Great Britain mathematics was cultivated with less interest than on the continent, and clearly desired to be considered as highly as the great names in continental mathematics---there is no doubt that he was reading their work at a level never reached by any other eighteenth-century British mathematician. Most notably, at the end of chapter three of *Meditationes Analyticae* Waring presents some partial fluxional equations (partial differential equations in Leibnizian terminology); such equations are a mathematical instrument of great importance in the study of continuous bodies which was almost completely neglected in Britain before Waring\'s researches. One of the most interesting results in *Meditationes Analyticae* is a test for the convergence of series generally attributed to d\'Alembert (the \'ratio test\'). The theory of convergence of series (the object of which is to establish when the summation of an infinite number of terms can be said to have a finite \'sum\') was not much advanced in the eighteenth century.
Waring\'s work was known both in Britain and on the continent, but it is difficult to evaluate his impact on the development of mathematics. His work on algebraic equations contained in *Miscellanea Analytica* was translated into Italian by Vincenzo Riccati in 1770. Waring\'s style is not systematic and his exposition is often obscure. It seems that he never lectured and did not habitually correspond with other mathematicians. After Jérôme Lalande in 1796 observed, in *Notice sur la vie de Condorcet*, that in 1764 there was not a single first-rate analyst in England, Waring\'s reply, published after his death as \'Original letter of Dr Waring\' in the *Monthly Magazine*, stated that he had given \'somewhere between three and four hundred new propositions of one kind or another\'.
## Death
During his last years he sank into a deep religious melancholy, and a violent cold caused his death, in Plealey, on 15 August 1798. He was buried in the churchyard at Fitz, Shropshire
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# Eden Phillpotts
**Eden Phillpotts** (4 November 1862 -- 29 December 1960) was an English author, poet and dramatist. He was born in Mount Abu, India, was educated in Plymouth, Devon, and worked as an insurance officer for ten years before studying for the stage and eventually becoming a writer.
## Life
Eden Phillpotts was a great-nephew of Henry Phillpotts, Bishop of Exeter. His father Henry Phillpotts was a son of the bishop\'s younger brother Thomas Phillpotts. James Surtees Phillpotts the reforming headmaster of Bedford School was his second cousin.
Eden Phillpotts was born on 4 November 1862 at Mount Abu in Rajasthan. His father Henry was an officer in the Indian Army, while his mother Adelaide was the daughter of an Indian Civil Service officer posted in Madras, George Jenkins Waters.
Henry Phillpotts died in 1865, leaving Adelaide a widow at the age of 21. With her three small sons, of whom Eden was the eldest, she returned to England and settled in Plymouth.
Phillpotts was educated at Mannamead School in Plymouth. At school he showed no signs of a literary bent. In 1879, aged 17, he left home and went to London to earn his living. He found a job as a clerk with the Sun Fire Office.
Phillpotts\' ambition was to be an actor and he attended evening classes at a drama school for two years. He came to the conclusion that he would never make a name as an actor but might have success as a writer. In his spare time out of office hours he proceeded to create a stream of small works which he was able to sell. In due course he left the insurance company to concentrate on his writing, while also working part-time as assistant editor for the weekly *Black and White* magazine.
Eden Phillpotts maintained a steady output of three or four books a year for the next half century. He produced poetry, short stories, novels, plays and mystery tales. Many of his novels were about rural Devon life and some of his plays were distinguished by their effective use of regional dialect.
Eden Phillpotts died at his home in Broadclyst near Exeter, Devon, on 29 December 1960.
## Personal life {#personal_life}
Phillpotts was for many years the President of the Dartmoor Preservation Association and cared passionately about the conservation of Dartmoor. He was an agnostic and a supporter of the Rationalist Press Association.
Phillpotts was a friend of Agatha Christie, who was an admirer of his work and a regular visitor to his home. She dedicated her 1932 novel *Peril at End House* to Phillpotts, and in her autobiography, she expressed gratitude for his early advice on fiction writing and quoted some of it. Jorge Luis Borges was another Phillpotts admirer. Borges mentioned him numerous times, wrote at least two reviews of his novels, and included him in his \"Personal Library\", a collection of works selected to reflect his personal literary preferences.
Philpotts allegedly sexually abused his daughter Adelaide. In a 1976 interview for a book about her father, Adelaide described an incestuous \"relationship\" with him that she says lasted from the age of five or six until her early thirties, when he remarried. When she herself finally married at the age of 55 her father never forgave her, and never communicated with her again.
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# Eden Phillpotts
## Writings
Phillpotts wrote a great many books with a Dartmoor setting. One of his novels, *Widecombe Fair* (1913), inspired by an annual fair at the village of Widecombe-in-the-Moor, provided the scenario for his comic play *The Farmer\'s Wife* (1916). It went on to become a 1928 silent film of the same name, directed by Alfred Hitchcock. It was followed by a 1941 remake, directed by Norman Lee and Leslie Arliss. It became a BBC TV drama in 1955, directed by Owen Reed. Jan Stewer played Churdles Ash. The BBC had broadcast the play in 1934.
He co-wrote several plays with his daughter Adelaide Phillpotts, *The Farmer\'s Wife* and *Yellow Sands* (1926); she later claimed their relationship was incestuous. Eden is best known as the author of many novels, plays and poems about Dartmoor. His Dartmoor cycle of 18 novels and two volumes of short stories still has many avid readers despite the fact that many titles are out of print.
Philpotts also wrote a series of novels, each set against the background of a different trade or industry. Titles include: *Brunel\'s Tower* (a pottery) and *Storm in a Teacup* (hand-papermaking). Among his other works is *The Grey Room*, the plot of which is centred on a haunted room in an English manor house. He also wrote a number of other mystery novels, both under his own name and the pseudonym **Harrington Hext**. These include: *The Thing at Their Heels*, *The Red Redmaynes*, *The Monster*, *The Clue from the Stars*, and *The Captain\'s Curio*. *The Human Boy* was a collection of schoolboy stories in the same genre as Rudyard Kipling\'s *Stalky & Co.*, though different in mood and style. Late in his long writing career he wrote a few books of interest to science fiction and fantasy readers, the most noteworthy being *Saurus*, which involves an alien reptilian observing human life.
Eric Partridge praised the immediacy and impact of his dialect writing.
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# Eden Phillpotts
## Photographs
Postbridge Clapper Bridge 2005-07-21.jpg\|The clapper bridge at Postbridge, which is the central location of Phillpotts\' novel *The Thief of Virtue*.
## Works
**Novels**
- *The End of a Life* (1891)
- *Folly and Fresh Air* (1891)
- *A Tiger\'s Club* (1892)
- [*A Deal with the Devil*](https://www.fadedpage.com/showbook.php?pid=20180837) (1895)
- [*Some Every-day Folks*](https://archive.org/details/someeverydayfol00philgoog) (1895)
- [*My Laughing Philosopher*](https://archive.org/details/mylaughingphilo00philgoog) (1896)
- [*Down Dartmoor Way*](https://archive.org/details/downdartmoorway00philgoog) (1896)
- [*Lying Prophets: A Novel*](https://books.google.com/books?id=9tE_AQAAIAAJ) (1897)
- *Children of the Mist* (1898)
- *Sons of the Morning* (1900)
- [*The Good Red Earth*](https://archive.org/details/goodredearth00philgoog) (1901)
- *The River* (1902)
- [*Old Delabole*](https://books.google.com/books?id=-f8nAAAAMAAJ) (1903)
- [*The Golden Fetich*](https://archive.org/details/goldenfetich00philgoog) (1903)
- *The American Prisoner* (1904)
- [*The Farm of the Dagger*](https://archive.org/details/farmdagger00philgoog) (1904)
- *The Secret Woman* (1905)
- *The Poacher\'s Wife* (1906) AKA *Daniel Sweetland* (1906)
- *The Sinews of War: A Romance of London and the Sea* (1906) with Arnold Bennett
- *Doubloons* (1906) with Arnold Bennett
- *The Portreeve* (1906)
- *The Whirlwind* (1907)
- [*The Human Boy Again*](https://www.fadedpage.com/showbook.php?pid=20180837) (1908)
- [*The Mother*](https://archive.org/details/mother00philgoog) (1908)
- [*The Virgin in Judgment*](https://www.fadedpage.com/showbook.php?pid=20180842) (1908) AKA *A Fight to Finish* (1911)
- [*The Statue: A Story of International Intrigue and Mystery*](https://archive.org/details/statueastoryint00benngoog) (1908) with Arnold Bennett
- [*The Three Brothers*](https://archive.org/stream/threebrothers01philgoog#page/n12/mode/2up) (1909)
- [*The Fun of the Fair*](https://books.google.com/books?id=Gsw5AQAAMAAJ) (1909)
- *The Haven* (1909)
- [*The Flint Heart: A Fairy Story*](https://archive.org/details/flintheartfairys00philiala) (1910)
- *The Thief of Virtue* (1910)
- *The Beacon* (1911)
- [*Demeter\'s Daughter*](https://archive.org/details/demetersdaughte01philgoog) (1911)
- *The Three Knaves* (1912)
- *The Forest on the Hill* (1912)
- [*The Lovers: A Romance*](https://archive.org/stream/loversromance00philuoft#page/n9/mode/2up) (1912)
- *Widecombe Fair* (1913)
- [*The Joy of Youth*](https://archive.org/details/joyyouth01philgoog) (1913)
- [*The Old Time Before Them*](http://babel.hathitrust.org/cgi/pt?id=mdp.39015063947231;view=1up;seq=9) (1913)
- [*Faith Tresilion*](https://archive.org/details/faithtresilion02philgoog) (1914)
- *The Master of Merripit* (1914)
- *Brunel\'s Tower* (1915)
- [*The Green Alleys: A Comedy*](https://archive.org/details/greenalleysacom00philgoog) (1916)
- [*The Human Boy and the War*](https://www.fadedpage.com/showbook.php?pid=20180839) (1916)
- *The Banks of Colne: (the Nursery)* (1917)
- *The Girl and the Faun* (1917)
- [*The Spinners*](https://archive.org/details/spinners00philgoog) (1918)
- [*From the Angle of Seventeen*](https://archive.org/details/fromanglesevent00philgoog) (1912)
- *Evander* (1919)
- [*Storm in a Teacup*](https://archive.org/details/storminateacup01philgoog) (1919)
- *Miser\'s Money* (1920)
- [*Eudocia*](https://archive.org/details/eudociaacomedyr00philgoog) (1921)
- [*The Grey Room*](http://www.gutenberg.org/files/1577/1577-h/1577-h.htm) (1921)
- *The Bronze Venus* (1921)
- *Orphan Dinah* (1920)
- [*The Red Redmaynes*](https://archive.org/details/redredmaynes00philuoft) (1922)
- *Pan and the Twins* (1922)
- [*Number 87*](https://archive.org/details/number00philgoog) (1922)
- [*The Thing at Their Heels*](http://babel.hathitrust.org/cgi/pt?id=uc1.$b307410;view=1up;seq=9) (1923)
- *Children of Men* (1923)
- *Cheat-the-boys; a Story of the Devonshire Orchards* (1924)
- *Redcliff* (1924)
- *The Treasures of Typhon* (1924)
- *The Lavender Dragon* (1924)
- *Who Killed Diana?* (1924)
- *Circé\'s Island* (1924)
- *A Voice from the Dark* (1925)
- *The Monster* (1925)
- *George Westover* (1926)
- *The Marylebone Miser* (1926) AKA *Jig-Saw* (1926)
- [*Cornish Droll: A Novel*](https://archive.org/stream/cornishdrollnove00phil#page/n9/mode/2up) (1926)
- *The Miniature* (1926)
- *The Jury* (1927)
- *Arachne* (1928)
- *The Ring Fence* (1928)
- *Tryphena* (1929)
- *The Apes* (1929)
- *The Three Maidens* (1930)
- *Alcyone (a Fairy Story)* (1930)
- *\"Found Drowned\"* (1931)
- *A Clue from the Stars* (1932)
- *The Broom Squires* (1932)
- *Stormbury, A Story of Devon* (1932)
- *The Captain\'s Curio* (1933)
- *Bred in the Bone* (1933)
- *Witch\'s Cauldron* (1933)
- *Nancy Owlett* (1933)
- *Minions of the Moon* (1934)
- *Ned of the Caribbees* (1934)
- *Portrait of a Gentleman* (1934)
- *Mr. Digweed and Mr. Lumb: A Mystery Novel* (1934)
- *The Oldest Inhabitant: A Comedy* (1934)
- *A Close Call* (1936)
- *The Owl of Athene* (1936)
- *The White Camel: A Story of Arabia* (1936)
- *The Anniversary Murder* (1936)
- *The Wife of Elias: A Mystery Novel* (1937)
- *Wood-nymph* (1937)
- *Farce in Three Acts* (1937)
- *Portrait of a Scoundrel* (1938)
- [*Saurus*](https://www.fadedpage.com/showbook.php?pid=20120517) (1938)
- [*Lycanthrope, the Mystery of Sir William Wolf*](https://www.fadedpage.com/showbook.php?pid=20120828) (1938)
- *Dark Horses* (1938)
- *Golden Island* (1938)
- *Thorn in Her Flesh* (1939)
- *Tabletop* (1939) with Arnold Bennett
- *Monkshood* (1939)
- *Chorus of Clowns* (1940)
- *Goldcross* (1940)
- *Awake Deborah!* (1941)
- *Ghostwater* (1941)
- *The Deed Without a Name* (1942)
- *Pilgrims of the Night* (1942)
- *A Museum Piece* (1943)
- *Flower of the Gods* (1943)
- *The Changeling* (1944)
- *The Drums of Dombali* (1945)
- *They Were Seven: (A Mystery)* (1945)
- *Quartet* (1946)
- *The Fall of the House of Heron* (1948)
- *Address Unknown* (1949)
- *The Waters of Walla* (1950)
- *Through a Glass Darkly* (1951)
- *George and Georgina: A Mystery Story* (1952)
- *His Brother\'s Keeper* (1953)
- *The Widow Garland* (1955)
- *Connie Woodland* (1956)
- *Giglet Market* (1957)
- *There Was an Old Man* (1959)
**Short Fiction Books**
- [*My Adventure in the Flying Scotsman; a Romance of London and North-Western Railway Shares*](https://archive.org/stream/myadventureinfly00phil#page/n3/mode/2up) (1888)
- [*The Human Boy*](https://archive.org/details/humanboybyedenp00wardgoog) (1899)
- *Loup-garou!* (1899)
- *Summer Clouds and Other Stories* (1893)
- [*Fancy Free*](https://archive.org/details/fancyfree00phil) (1901)
- [*The Striking Hours*](https://archive.org/details/strikinghours00philgoog) (1901)
- [*The Transit of the Red Dragon: And Other Tales*](https://archive.org/details/transitreddrago00philgoog) (1903)
- [*Knock at a Venture*](https://archive.org/details/knockataventure01philgoog) (1905)
- *The Unlucky Number* (1906)
- [*The Folk Afield*](https://archive.org/details/folfafield00philgoog) (1907)
- [*Tales of the Tenements*](https://books.google.com/books?id=ZgY8AQAAMAAJ) (1910)
- *The Judge\'s Chair* (1914)
- [*The Human Boy and the War*](https://archive.org/details/humanboyandwar02philgoog) (1916)
- *Chronicles of St. Tid* (1918)
- [*Black, White, and Brindled*](http://babel.hathitrust.org/cgi/pt?id=uc1.$b243884;view=1up;seq=7) (1923)
- *Up Hill, Down Dale: A Volume of Short Stories* (1925)
- *Peacock House and Other Mysteries* (1926)
- *It happened Like That, a New Volume of Short Stories* (1928)
- *Brother Man* (1928)
- [*The Torch and Other Tales*](http://www.gutenberg.org/files/15737/15737-h/15737-h.htm) (1929)
- *Cherry Gambol and Other Stories* (1930)
- *They Could Do No Other: A Volume of Stories* (1932)
- *Once upon a Time* (1936)
- *The Hidden Hand* (1952)
**Poetry**
- [*Up-Along and Down-Along*](https://archive.org/details/upalonganddowna00shepgoog) (1905)
- [*Wild Fruit*](https://archive.org/details/wildfruit00philuoft) (1911)
- [*The Iscariot*](https://archive.org/stream/iscariot01phil#page/n7/mode/2up) (1912)
- [*Delight and Other Poems*](https://archive.org/stream/delight00phil#page/n9/mode/2up) (1916)
- [*Plain Song*](https://archive.org/stream/cu31924013536051#page/n7/mode/2up) (1917)
- [*A Shadow Passes*](https://archive.org/stream/shadowpasses00phil#page/n5/mode/2up) \[Observations and Poems\] (1918)
- [*As the Wind Blows*](https://archive.org/details/aswindblows00philgoog) (1920)
- [*A Dish of Apples*](https://archive.org/stream/dishofapples00philrich#page/n11/mode/2up) (1921)
- [*Pixies\' Plot*](https://www.fadedpage.com/showbook.php?pid=20180840) (1922)
- *Thoughts in Prose and Verse* (1924)
- *Cherry-Stones* (1924)
- *A Harvesting* (1924)
- *Brother Beast* (1928)
- *Goodwill* (1928)
- *For Remembrance* (1929)
- *A Hundred Sonnets* (1929)
- *A Hundred Lyrics* (1930)
- *Becoming* (1932)
- [*Song of a Sailor Man: A Narrative Poem*](http://babel.hathitrust.org/cgi/pt?id=mdp.39015059405921;view=1up;seq=7) (1933)
- *Sonnets from Nature* (1935)
- *A Dartmoor Village* (1937)
- *Miniatures* (1942)
- *The Enchanted Wood* (1948)
- *One Thing and Another* \[Essays and poems.\] (1954)
**Plays**
- [*The Prude\'s Progress: A Comedy*](https://archive.org/details/prudesprogressa00philgoog) with Jerome K. Jerome (1895)
- [*A Golden Wedding: An Original Comedy in One Act*](https://books.google.com/books?id=3lDTM-bEdH8C) (1899)
- *A Breezy Morning* (1904)
- [*A Pair of Knickerbockers*](https://books.google.com/books?id=R0YWAAAAYAAJ) (1900)
- [*Curtain Raisers*](https://archive.org/stream/curtainraisers00phil#page/n9/mode/2up) (1912)
- [*The Shadow; A Play in Three Acts*](http://babel.hathitrust.org/cgi/pt?id=uc2.ark:/13960/t52f7qs4v;view=1up;seq=7) (1913)
- [*The Mother: A Play in Four Acts*](https://archive.org/stream/motherplayinfour00phil#page/n5/mode/2up) (1914)
- [*The Secret Woman; A Play in Five Acts*](https://archive.org/stream/secretwomanplayi01phil#page/n5/mode/2up) (1914)
- [*The Angel in the House: A Comedy in Three Acts*](https://books.google.com/books?id=eUQWAAAAYAAJ) (1915)
- *[The Farmer\'s Wife](https://www.fadedpage.com/showbook.php?pid=20150250)* (1916)
- *Arachne; A Play* (1920) By Adelaide Eden Phillpotts
- [*St. George and the Dragons: A Comedy in Three Acts*](http://babel.hathitrust.org/cgi/pt?id=mdp.39015063753217;view=1up;seq=7) (1919) AKA \**The bishop\'s night out* (1929)
- *The Market-Money. A Play in One Act* (1923)
- *Bed Rock: A Comedy in Three Acts* (1924)
- *Devonshire Cream: A Comedy in Three Acts* (1925)
- *A Comedy Royal* (1925) Dramatization of *Eudocia (1921)*
- *Yellow Sands* (1926)
- *Blue Comet* (1927)
- *The Runaways: A Comedy in Three Acts* (1928)
- *Three Short Plays: The Market-money; Something to Talk about; The Purple Bedroom* (1928)
- *Buy a Broom: A Comedy in Three Acts* (1929)
- *Jane\'s Legacy: A Folk Play in Three Acts* (1931)
- *The Good Old Days: A Comedy in Three Acts* (1932) with his daughter
- *Bert: A Play in One Act* (1932)
- *A Cup of Happiness: A Comedy* (1933)
- *At the \'bus-stop: A Duologue for Two Women* (1943)
- *The Orange Orchard* (1951) Based on *The Waters of Walla*
**Nonfiction**
- *In Sugar-Cane Land* (1890)
- [*My Garden*](https://archive.org/stream/mygarden00philgoog#page/n10/mode/2up) (1906)
- *Dance of the Months.* \[Sketches of Dartmoor and poems.\] (1911)
- [*My Shrubs*](https://archive.org/stream/myshrubs00philuoft#page/n7/mode/2up) (1915)
- [*My Devon Year*](https://archive.org/details/mydevonyear01philgoog) (1916)
- *One Hundred Pictures from Eden Phillpotts / Selected by L.H. Brewitt* (1919)
- *A West Country Pilgrimage* (1920) \[Essays and verse.\]
- *A West Country Sketch Book* (1928) Essays from *Dance of the Months* and *A West Country Pilgrimage* with one new essay.
- *Essays in Little* (1931)
- *Handmade Paper: Its Method of Manufacture as Described in the Novel \"Storm in a Teacup\"* (1932)
- *A Year with Bisshe-Bantam* (1934)
- *A Mixed Grill* (1940) Essays.
- *From the Angle of 88* (1951)
- *Selected Letters* (1984)
### Omnibus
- *Dartmoor Omnibus* \[*Orphan Dinah*, *Three Brothers*, *Children of Men*, *The Whirlwind*\]
- [*Three plays: The shadows; The mother; The secret woman*](https://archive.org/stream/threeplaysshadow00phil#page/n5/mode/2up) (1913)
- *Circe\'s Island and The Girl & The Faun* (1925)
- *The Complete Human Boy. Comprising \"The Human Boy,\" \"The Human Boy Again,\" \"The Human Boy and the War,\" \"The Human Boy\'s Diary,\" \"From the Angle of Seventeen,\" Etc.* (1930)
- *West Country Plays* (1933) \[*Buy a Broom* and *A Cup of Happiness*
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# The American Prisoner
***The American Prisoner*** is a British novel written by Eden Phillpotts and published in 1904 and adapted into a film by the same name in 1929. The story concerns an English woman who lives at Fox Tor farm, and an American captured during the American War of Independence and held at the prison at Princetown on Dartmoor.
In the novel *Malherb* is a miscreant who destroys Childe\'s tomb and beats his servant. He is depicted as a victim of his own bad temper rather than a sadist.
Malherb is introduced as the younger son of a noble family and he builds the Fox Tor house to be the impressive gentleman\'s residence suggested by William Crossing rather than the humble cottage which it actually is
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# Electromagnetic field
An **electromagnetic field** (also **EM field**) is a physical field, varying in space and time, that represents the electric and magnetic influences generated by and acting upon electric charges. The field at any point in space and time can be regarded as a combination of an electric field and a magnetic field. Because of the interrelationship between the fields, a disturbance in the electric field can create a disturbance in the magnetic field which in turn affects the electric field, leading to an oscillation that propagates through space, known as an *electromagnetic wave*.
The way in which charges and currents (i.e. streams of charges) interact with the electromagnetic field is described by Maxwell\'s equations and the Lorentz force law. Maxwell\'s equations detail how the electric field converges towards or diverges away from electric charges, how the magnetic field curls around electrical currents, and how changes in the electric and magnetic fields influence each other. The Lorentz force law states that a charge subject to an electric field feels a force along the direction of the field, and a charge moving through a magnetic field feels a force that is perpendicular both to the magnetic field and to its direction of motion.
The electromagnetic field is described by classical electrodynamics, an example of a classical field theory. This theory describes many macroscopic physical phenomena accurately. However, it was unable to explain the photoelectric effect and atomic absorption spectroscopy, experiments at the atomic scale. That required the use of quantum mechanics, specifically the quantization of the electromagnetic field and the development of quantum electrodynamics.
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# Electromagnetic field
## History
The empirical investigation of electromagnetism is at least as old as the ancient Greek philosopher, mathematician and scientist Thales of Miletus, who around 600 BCE described his experiments rubbing fur of animals on various materials such as amber creating static electricity. By the 18th century, it was understood that objects can carry positive or negative electric charge, that two objects carrying charge of the same sign repel each other, that two objects carrying charges of opposite sign attract one another, and that the strength of this force falls off as the square of the distance between them. Michael Faraday visualized this in terms of the charges interacting via the electric field. An electric field is produced when the charge is stationary with respect to an observer measuring the properties of the charge, and a magnetic field as well as an electric field are produced when the charge moves, creating an electric current with respect to this observer. Over time, it was realized that the electric and magnetic fields are better thought of as two parts of a greater whole---the electromagnetic field. In 1820, Hans Christian Ørsted showed that an electric current can deflect a nearby compass needle, establishing that electricity and magnetism are closely related phenomena. Faraday then made the seminal observation that time-varying magnetic fields could induce electric currents in 1831.
In 1861, James Clerk Maxwell synthesized all the work to date on electrical and magnetic phenomena into a single mathematical theory, from which he then deduced that light is an electromagnetic wave. Maxwell\'s continuous field theory was very successful until evidence supporting the atomic model of matter emerged. Beginning in 1877, Hendrik Lorentz developed an atomic model of electromagnetism and in 1897 J. J. Thomson completed experiments that defined the electron. The Lorentz theory works for free charges in electromagnetic fields, but fails to predict the energy spectrum for bound charges in atoms and molecules. For that problem, quantum mechanics is needed, ultimately leading to the theory of quantum electrodynamics.
Practical applications of the new understanding of electromagnetic fields emerged in the late 1800s. The electrical generator and motor were invented using only the empirical findings like Faraday\'s and Ampere\'s laws combined with practical experience.
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# Electromagnetic field
## Mathematical description {#mathematical_description}
There are different mathematical ways of representing the electromagnetic field. The first one views the electric and magnetic fields as three-dimensional vector fields. These vector fields each have a value defined at every point of space and time and are thus often regarded as functions of the space and time coordinates. As such, they are often written as `{{math|'''E'''(''x'', ''y'', ''z'', ''t'')}}`{=mediawiki} (electric field) and `{{math|'''B'''(''x'', ''y'', ''z'', ''t'')}}`{=mediawiki} (magnetic field).
If only the electric field (`{{math|'''E'''}}`{=mediawiki}) is non-zero, and is constant in time, the field is said to be an electrostatic field. Similarly, if only the magnetic field (`{{math|'''B'''}}`{=mediawiki}) is non-zero and is constant in time, the field is said to be a magnetostatic field. However, if either the electric or magnetic field has a time-dependence, then both fields must be considered together as a coupled electromagnetic field using Maxwell\'s equations.
With the advent of special relativity, physical laws became amenable to the formalism of tensors. Maxwell\'s equations can be written in tensor form, generally viewed by physicists as a more elegant means of expressing physical laws.
The behavior of electric and magnetic fields, whether in cases of electrostatics, magnetostatics, or electrodynamics (electromagnetic fields), is governed by Maxwell\'s equations. In the vector field formalism, these are:
Gauss\'s law : $\nabla \cdot \mathbf{E} = \frac{\rho}{\varepsilon_0}$\
Gauss\'s law for magnetism : $\nabla \cdot \mathbf{B} = 0$\
Faraday\'s law : $\nabla \times \mathbf{E} = -\frac {\partial \mathbf{B}}{\partial t}$\
Ampère--Maxwell law : $\nabla \times \mathbf{B} = \mu_0 \mathbf{J} + \mu_0\varepsilon_0 \frac{\partial \mathbf{E}}{\partial t}$
where $\rho$ is the charge density, which is a function of time and position, $\varepsilon_0$ is the vacuum permittivity, $\mu_0$ is the vacuum permeability, and `{{math|'''J'''}}`{=mediawiki} is the current density vector, also a function of time and position. Inside a linear material, Maxwell\'s equations change by switching the permeability and permittivity of free space with the permeability and permittivity of the linear material in question. Inside other materials which possess more complex responses to electromagnetic fields, these terms are often represented by complex numbers, or tensors.
The Lorentz force law governs the interaction of the electromagnetic field with charged matter.
When a field travels across to different media, the behavior of the field changes according to the properties of the media.
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# Electromagnetic field
## Properties of the field {#properties_of_the_field}
### Electrostatics and magnetostatics {#electrostatics_and_magnetostatics}
The Maxwell equations simplify when the charge density at each point in space does not change over time and all electric currents likewise remain constant. All of the time derivatives vanish from the equations, leaving two expressions that involve the electric field, $\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0}$ and $\nabla\times\mathbf{E} = 0,$ along with two formulae that involve the magnetic field: $\nabla \cdot \mathbf{B} = 0$ and $\nabla \times \mathbf{B} = \mu_0 \mathbf{J}.$ These expressions are the basic equations of electrostatics, which focuses on situations where electrical charges do not move, and magnetostatics, the corresponding area of magnetic phenomena.
### Transformations of electromagnetic fields {#transformations_of_electromagnetic_fields}
Whether a physical effect is attributable to an electric field or to a magnetic field is dependent upon the observer, in a way that special relativity makes mathematically precise. For example, suppose that a laboratory contains a long straight wire that carries an electrical current. In the frame of reference where the laboratory is at rest, the wire is motionless and electrically neutral: the current, composed of negatively charged electrons, moves against a background of positively charged ions, and the densities of positive and negative charges cancel each other out. A test charge near the wire would feel no electrical force from the wire. However, if the test charge is in motion parallel to the current, the situation changes. In the rest frame of the test charge, the positive and negative charges in the wire are moving at different speeds, and so the positive and negative charge distributions are Lorentz-contracted by different amounts. Consequently, the wire has a nonzero net charge density, and the test charge must experience a nonzero electric field and thus a nonzero force. In the rest frame of the laboratory, there is no electric field to explain the test charge being pulled towards or pushed away from the wire. So, an observer in the laboratory rest frame concludes that a `{{em|magnetic}}`{=mediawiki} field must be present.
In general, a situation that one observer describes using only an electric field will be described by an observer in a different inertial frame using a combination of electric and magnetic fields. Analogously, a phenomenon that one observer describes using only a magnetic field will be, in a relatively moving reference frame, described by a combination of fields. The rules for relating the fields required in different reference frames are the Lorentz transformations of the fields.
Thus, electrostatics and magnetostatics are now seen as studies of the static EM field when a particular frame has been selected to suppress the other type of field, and since an EM field with both electric and magnetic will appear in any other frame, these \"simpler\" effects are merely a consequence of different frames of measurement. The fact that the two field variations can be reproduced just by changing the motion of the observer is further evidence that there is only a single actual field involved which is simply being observed differently.
### Reciprocal behavior of electric and magnetic fields {#reciprocal_behavior_of_electric_and_magnetic_fields}
The two Maxwell equations, Faraday\'s Law and the Ampère--Maxwell Law, illustrate a very practical feature of the electromagnetic field. Faraday\'s Law may be stated roughly as \"a changing magnetic field inside a loop creates an electric voltage around the loop\". This is the principle behind the electric generator.
Ampere\'s Law roughly states that \"an electrical current around a loop creates a magnetic field through the loop\". Thus, this law can be applied to generate a magnetic field and run an electric motor.
### Behavior of the fields in the absence of charges or currents {#behavior_of_the_fields_in_the_absence_of_charges_or_currents}
thumb\|upright=1.8\|A linearly polarized electromagnetic plane wave propagating parallel to the z-axis is a possible solution for the electromagnetic wave equations in free space. The electric field, `{{math|'''E'''}}`{=mediawiki}, and the magnetic field, `{{math|'''B'''}}`{=mediawiki}, are perpendicular to each other and the direction of propagation.\|400x200px Maxwell\'s equations can be combined to derive wave equations. The solutions of these equations take the form of an electromagnetic wave. In a volume of space not containing charges or currents (free space) -- that is, where $\rho$ and `{{math|'''J'''}}`{=mediawiki} are zero, the electric and magnetic fields satisfy these electromagnetic wave equations:
: $\left( \nabla^2 - { 1 \over {c}^2 } {\partial^2 \over \partial t^2} \right) \mathbf{E} \ \ = \ \ 0$
: $\left( \nabla^2 - { 1 \over {c}^2 } {\partial^2 \over \partial t^2} \right) \mathbf{B} \ \ = \ \ 0$
James Clerk Maxwell was the first to obtain this relationship by his completion of Maxwell\'s equations with the addition of a displacement current term to Ampere\'s circuital law. This unified the physical understanding of electricity, magnetism, and light: visible light is but one portion of the full range of electromagnetic waves, the electromagnetic spectrum.
### Time-varying EM fields in Maxwell\'s equations {#time_varying_em_fields_in_maxwells_equations}
An electromagnetic field very far from currents and charges (sources) is called electromagnetic radiation (EMR) since it radiates from the charges and currents in the source. Such radiation can occur across a wide range of frequencies called the electromagnetic spectrum, including radio waves, microwave, infrared, visible light, ultraviolet light, X-rays, and gamma rays. The many commercial applications of these radiations are discussed in the named and linked articles.
A notable application of visible light is that this type of energy from the Sun powers all life on Earth that either makes or uses oxygen.
A changing electromagnetic field which is physically close to currents and charges (see near and far field for a definition of \"close\") will have a dipole characteristic that is dominated by either a changing electric dipole, or a changing magnetic dipole. This type of dipole field near sources is called an electromagnetic *near-field*.
Changing `{{em|electric}}`{=mediawiki} dipole fields, as such, are used commercially as near-fields mainly as a source of dielectric heating. Otherwise, they appear parasitically around conductors which absorb EMR, and around antennas which have the purpose of generating EMR at greater distances.
Changing `{{em|magnetic}}`{=mediawiki} dipole fields (i.e., magnetic near-fields) are used commercially for many types of magnetic induction devices. These include motors and electrical transformers at low frequencies, and devices such as RFID tags, metal detectors, and MRI scanner coils at higher frequencies.
## Health and safety {#health_and_safety}
The potential effects of electromagnetic fields on human health vary widely depending on the frequency, intensity of the fields, and the length of the exposure. Low frequency, low intensity, and short duration exposure to electromagnetic radiation is generally considered safe. On the other hand, radiation from other parts of the electromagnetic spectrum, such as ultraviolet light and gamma rays, are known to cause significant harm in some circumstances
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# Evangelist (Latter Day Saints)
In the Latter Day Saint movement, an **evangelist** is an ordained office of the ministry. In some denominations of the movement, an evangelist is referred to as a **patriarch**. However, the latter term was deprecated by the Community of Christ after the church began ordaining women to the priesthood. Other denominations, such as The Church of Jesus Christ (Bickertonite), have an evangelist position independent of the original \"patriarch\" office instituted movement founder Joseph Smith.
## Early Latter Day Saint movement {#early_latter_day_saint_movement}
The first use of the term \"evangelist\" in Latter Day Saint theology were mainly consistent with how the term is used by Protestants and Catholics.
In 1833, Joseph Smith introduced the new office of patriarch, to which he ordained his father. The elder Smith was given the \"keys of the patriarchal Priesthood over the kingdom of God on earth\", the same power said to be held by the Biblical patriarchs, which included the power to give blessings upon one\'s posterity. The elder Smith, however, was also called to give patriarchal blessings to the fatherless within the church, and the church as a whole, a calling he passed onto his eldest surviving son Hyrum Smith prior to his death. Hyrum himself was killed in 1844 along with Joseph, resulting in a succession crisis that broke the Latter Day Saint movement into multiple denominations.
It is not known who first identified the term \"evangelist\" with the office of patriarch. However, in an 1835 church publication, W. W. Phelps stated,
: \"\[W\]ho is not desirous of receiving a father\'s or an evangelist\'s blessing? Who can read the ancient patriarchal blessings, recorded in the bible, for the benefit of the church, without a heart filled with joy \... ?\"
In 1839, Joseph Smith equated an evangelist with the office of patriarch, stating that \"an Evangelist is a Patriarch\".
The necessity of an evangelist in the church organization has been reinforced repeatedly, based on the passage in Ephesians 4:11, which states, \"And he gave some, apostles; and some, prophets; and some, evangelists; and some, pastors and teachers\". In 1834, while writing what he called the \"principles of salvation\", prominent early Latter Day Saint Oliver Cowdery stated that:
: \"We do not believe that he ever had a church on earth without revealing himself to that church: consequently, there were apostles, prophets, evangelists, pastors, and teachers, in the same.\"
Joseph Smith echoed Cowdery\'s statement in 1842, in a letter to a Chicago newspaper editor outlining the church\'s basic beliefs. Smith said that his religion \"believe\[s\] in the same organization that existed in the primitive church, viz: apostles, prophets, pastors, teachers, evangelists\".
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# Evangelist (Latter Day Saints)
## Community of Christ {#community_of_christ}
In the Community of Christ, which was formerly known as the Reorganized Church of Jesus Christ of Latter Day Saints (RLDS Church), an evangelist is an office in the Melchizedec Order of the priesthood.
An evangelist-patriarch\'s primary responsibility was to provide special blessings to members of the church; these blessings were considered one of the eight sacraments in the RLDS Church. The local evangelist-patriarchs of the church were governed by an individual with church-wide authority known as the Presiding Patriarch.
In 1984, when the first women began to be ordained to the office of evangelist-patriarch, the RLDS Church changed the title of the evangelist-patriarchs to simply \"evangelist\". Similarly, it changed the title of the Presiding Patriarch to the \"Presiding Evangelist\". To be an evangelist, a person must also be a high priest of the Melchizedec Order of the priesthood.
The primary duty of an evangelist in the Community of Christ remains the giving of sacramental \"evangelist\'s blessings\"; it is for this reason that evangelists are often referred to as \"ministers of blessing\". Ideally, an evangelist is free from administrative responsibilities in the church in order to allow them to be fully responsive to the Holy Spirit. The blessings---which are given by the laying on of hands---provide counsel and advice and confer spiritual blessings upon the recipient(s). Not only individuals, but also couples, families, households, groups and congregations may receive an evangelist\'s blessing. Any person, including nonmembers, eight years of age or older can receive a blessing, although the blessing is rarely offered for someone who has not reached adolescence. A recipient may receive multiple evangelist\'s blessings in their life. Evangelist\'s blessings may or may not be recorded. If it is recorded in written form, a copy is stored in the church archives at Independence, Missouri.
All evangelists belong to the Order of Evangelists, which is led by the Presiding Evangelist (currently Jane M. Gardner, since 2016).
## The Church of Jesus Christ (Bickertonite) {#the_church_of_jesus_christ_bickertonite}
In The Church of Jesus Christ (Bickertonite), the prescribed duties of an evangelist are to preach the gospel of Jesus Christ to every nation, kindred, language, and people. An evangelist is part of the Quorum of Seventy Evangelists.
### Quorum of Seventy Evangelists {#quorum_of_seventy_evangelists}
The Quorum of Seventy Evangelists is responsible for management of the International Missionary Programs of the church and assists Regions of the church with their individual Domestic Missionary Programs. The Quorum of Seventy oversees the activities of its Missionary Operating Committees to ensure the fulfilling of Christ\'s commandment to take the gospel to the entire world.
In 2007, the officers of the Quorum of Seventy Evangelists were:
- Evangelist Eugene Perri, President
- Evangelist Alex Gentile, Vice-President
- Evangelist Jeffrey Giannetti, Secretary
## The Church of Jesus Christ of Latter-day Saints {#the_church_of_jesus_christ_of_latter_day_saints}
In the Church of Jesus Christ of Latter-day Saints (LDS Church), an evangelist is considered to be an office of the Melchizedek priesthood. However, the term \"evangelist\" is rarely used for this position; instead, the church has retained the term \"patriarch\", the term most commonly used by Joseph Smith.
The most prominent reference to the term \"evangelist\" in the LDS Church\'s literature is found in its \"Articles of Faith\", derived from the Wentworth letter---a statement by Smith in 1842 to a Chicago newspaper editor---that the church believes in \"the same organization that existed in the primitive church\", including \"evangelists\". Smith taught that \"an Evangelist is an Patriarch\"
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# Elegiac couplet
The **elegiac couplet** or **elegiac distich** is a poetic form used by Greek lyric poets for a variety of themes usually of smaller scale than the epic. Roman poets, particularly Catullus, Propertius, Tibullus, and Ovid, adopted the same form in Latin many years later. As with the English heroic couplet, each pair of lines usually makes sense on its own, while forming part of a larger work.
Each couplet consists of a dactylic hexameter verse followed by a dactylic pentameter verse. The following is a graphic representation of its scansion:
`– ``uu`` | – ``uu`` | – ``uu`` | – ``uu`` | – uu | – x`\
`– ``uu`` | – ``uu`` | – || – uu | – uu | –`\
\
**`–`**` is one long syllable, `**`u`**` one short syllable, `**`uu`**` is one long or two short syllables, and `**`x`**` is one long or one short syllable (``anceps``).`
The form was felt by the ancients to contrast the rising action of the first verse with a falling quality in the second. The sentiment is summarized in a line from Ovid\'s *Amores* I.1.27 --- *Sex mihi surgat opus numeris, in quinque residat* --- \"Let my work rise in six steps, fall back in five.\" The effect is illustrated by Friedrich Schiller\'s couplet
:
:
translated into English by Samuel Taylor Coleridge as:
: In the hexameter rises the fountain\'s silvery column,
: In the pentameter aye falling in melody back.
and by Alfred, Lord Tennyson, as:
: Up goes the Hexameter with might as a fountain rising.
: Lightly the fountain falls, lightly the Pentameter.
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# Elegiac couplet
## Greek origins {#greek_origins}
The elegiac couplet is presumed to be the oldest Greek form of epodic poetry (a form where a later verse is sung in response or comment to a previous one). Scholars, who even in the past did not know who created it, theorize the form was originally used in Ionian dirges, with the name \"elegy\" derived from the Greek *ε, λεγε ε, λεγε*---\"Woe, cry woe, cry!\" Hence, the form was used initially for funeral songs, typically accompanied by an aulos, a double-reed wind instrument. Archilochus expanded use of the form to treat other themes, such as war, travel, and homespun philosophy. Between Archilochus and other imitators, the verse form became a common poetic vehicle for conveying any strong emotion.
At the end of the 7th century BCE, Mimnermus of Colophon struck on the innovation of using the verse for erotic poetry. He composed several elegies celebrating his love for the flute girl Nanno, and though fragmentary today, his poetry was clearly influential in the later Roman development of the form. Propertius, to cite one example, notes *Plus in amore valet Mimnermi versus Homero*---\"The verse of Mimnermus is stronger in love than Homer\".
The form continued to be popular throughout the Greek period and treated a number of different themes. Tyrtaeus composed elegies on a war theme, apparently for a Spartan audience. Theognis of Megara vented himself in couplets as an embittered aristocrat in a time of social change. Popular leaders were writers of elegies---Solon the lawgiver of Athens composed on political and ethical subjects---and even Plato and Aristotle dabbled with the meter.
A famous example of an elegiac couplet is the epitaph composed by Simonides of Ceos which Herodotus says was inscribed on a stone to commemorate those who died at the battle of Thermopylae in 490 BC:
:
: (Book VII, 228)
```{=html}
<!-- -->
```
:
:
```{=html}
<!-- -->
```
: \"O stranger, tell the Spartans that in this place
: we lie, obeying their commands.\"
Cicero translates it as follows (*Tusc. Disp.* 1.42.101), also using an elegiac couplet:
:
:
```{=html}
<!-- -->
```
: \"Say, stranger, in Sparta that you saw us lying here
: while we obey the sacred laws of our fatherland.\"
By the Hellenistic period, the Library of Alexandria made elegy its favorite and most highly developed form. They preferred the briefer style associated with elegy in contrast to the lengthier epic forms, and made it the singular medium for short epigrams. The founder of this school was Philitas of Cos. He was eclipsed only by the school\'s most admired exponent, Callimachus; their learned character and intricate art would have a heavy influence on the Romans.
## Roman elegy {#roman_elegy}
Like many Greek forms, elegy was adapted by the Romans for their own literature. The fragments of Ennius contain a few couplets, but it is the elegists of the mid-to-late first century BCE who are most commonly associated with the distinctive Roman form of the elegiac couplet. Catullus, the first of these, is an invaluable link between the Alexandrine school and the subsequent elegies of Tibullus, Propertius and Ovid. He shows a familiarity with the usual Alexandrine style of terse epigram and a wealth of mythological learning, as in his 66th poem, *label=none*, a direct translation of Callimachus\' *Lock of Berenice*. His 85th poem is famous:`{{Verse translation|lang=la|
:{{lang|la|Odi et amo. Quare id faciam, fortasse requiris?}}
:::{{lang|la|Nescio, sed fieri sentio et excrucior.}}
|
I hate and I love. Why do I do this, perhaps you ask?
I know not, but I feel it happen and am tormented.}}`{=mediawiki}
To read it correctly it is necessary to take account of the three elisions:
`– u u| – –| – u u|– – | – u u| – x`\
`Od'et a|mo. Qua|r'id faci|am, for|tasse re|quiris?`\
\
` – uu | – uu| – || – u u | – u u|–`\
`Nescio, | sed fie|ri || senti'et | excruci|or.`
Cornelius Gallus, an important statesman of this period, was also regarded by the ancients as a great elegist, but, except for a few lines, his work has been lost.
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# Elegiac couplet
## Elegy in the Augustan Age {#elegy_in_the_augustan_age}
The form reached its zenith with the collections of Tibullus and Propertius and several collections of Ovid (the *Amores*, *Ars Amatoria*, *Heroides*, *Tristia*, and *Epistulae ex Ponto*). The vogue of elegy during this time is seen in the so-called 3rd and 4th books of Tibullus. Many poems in these books were clearly not written by Tibullus but by others, perhaps part of a circle under Tibullus\' patron Messalla. Notable in this collection are the poems of Sulpicia, thought to be the only surviving work by a Classical Latin female poet. The six elegiac poems of Lygdamus in the collection are thought by some to be an anonymous early work by Ovid, though other scholars attribute them to an imitator of Ovid who may have lived in a much later period.
Through these poets---and in comparison with the earlier Catullus---it is possible to trace specific characteristics and evolutionary patterns in the Roman form of the verse:
- The Roman authors often write about their own love affairs. In contrast to their Greek originals, these poets are characters in his own stories, and write about love in a highly subjective way.
- The form began to be applied to new themes beyond the traditional love, loss, and other \"strong emotion\" verse. Propertius uses it to relate aetiological or \"origin\" myths such as the origins of Rome (IV.1) and the Temple of Apollo on the Palatine Hill (IV.6). Ovid\'s *Heroides*---though at first glance fictitious love letters---are described by Ovid himself as a new literary form, and can be read as character studies of famous heroines from mythology. Ovid\'s *Fasti* is a lengthy elegiac poem on the first six months of the Roman calendar.
- The Romans adopted the Alexandrine habit of concealing the name of their beloved in the poem with a pseudonym. Catullus\' Lesbia is notorious as the pseudonym of Clodia. But as the form developed, this habit becomes more artificial; Tibullus\' Delia and Propertius\' Cynthia, while likely real people, lack something of the specificity seen in Lesbia, while Ovid\'s Corinna is often considered a mere literary device.
- The poets become extremely strict with pentameters. For example:
:\*There is a trend toward the clear separation of the pentameter halves. Catullus, for example, allows an elision across the caesura in 18 cases, a rare occurrence in the later poets (Ovid, for example, never does this).
:\*The pentameter begins to show a semi-regular \"leonine\" rhyme between the two halves of the verse, e.g. Tib. I.1--2, where the *culti* ending the first half of the pentameter rhymes with the *soli* closing the verse:
:
:
:
: \"Let another man pile up riches for himself with yellow gold
: and hold many acres of cultivated land\"
:
: While Catullus shows this rhyme in about 1 in 5 couplets, the later elegists use it more frequently. Propertius II.34, for example, has the rhyme in nearly half its pentameters. Rhyming between adjacent lines and even in the two halves of the hexameter is also observed, more than would be expected by chance alone.
- The hexameter follows the usual rhetorical trends of the dactylic hexameter in this age. If anything, the elegists are even more interested in verbal effects like alliteration and assonance.
- Overall there is a tendency to make the elegiac couplet increasingly dactylic. In Catullus the proportion of dactylic feet (not counting the verse endings, which do not vary) is about 37%; this rises to 45% in Propertius books 2 and 3; and in Ovid\'s *Ars Amatoria* it rises as high as 57%.
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# Elegiac couplet
## Post-Augustan writers {#post_augustan_writers}
Although no classical poet wrote collections of love elegies after Ovid, the verse retained its popularity as a vehicle for popular occasional poetry. Elegiac verses appear, for example, in Petronius\' *Satyricon*, and Martial\'s Epigrams uses it for many witty stand-alone couplets and for longer pieces. The trend continues through the remainder of the empire; short elegies appear in Apuleius\'s story of Cupid and Psyche and in the minor writings of Ausonius.
## Medieval elegy {#medieval_elegy}
After the fall of the empire, one writer who produced elegiac verse was Maximianus. Various Christian writers also adopted the form; Venantius Fortunatus wrote some of his hymns in the meter, while later Alcuin and the Venerable Bede dabbled in the verse. The form also remained popular among the educated classes for gravestone epitaphs; many such epitaphs can be found in European cathedrals.
*De tribus puellis* is an example of a Latin *fabliau*, a genre of comedy which employed elegiac couplets in imitation of Ovid. The medieval theorist John of Garland wrote that \"all comedy is elegy, but the reverse is not true.\" Medieval Latin had a developed comedic genre known as elegiac comedy. Sometimes narrative, sometimes dramatic, it deviated from ancient practice because, as Ian Thompson writes, \"no ancient drama would ever have been written in elegiacs.\"
## Renaissance and modern period {#renaissance_and_modern_period}
With the Renaissance, more skilled writers interested in the revival of Roman culture attempted to recapture the spirit of the Augustan writers. The Dutch Latinist Johannes Secundus, for example, included Catullus-inspired love elegies in his *Liber Basiorum*, while the English poet John Milton wrote several lengthy elegies throughout his career. This trend continued down through the Recent Latin writers, whose close study of their Augustan counterparts reflects their general attempts to apply the cultural and literary forms of the ancient world to contemporary themes
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# Era
An **era** is a span of time defined for the purposes of chronology or historiography, as in the regnal eras in the history of a given monarchy, a calendar era used for a given calendar, or the geological eras defined for the history of Earth.
Comparable terms are Epoch, age, period, saeculum, aeon (Greek *aion*) and Sanskrit yuga.
## Etymology
The word has been in use in English since 1615, and is derived from Late Latin *aera* \"an era or epoch from which time is reckoned,\" probably identical to Latin *æra* \"counters used for calculation,\" plural of *æs* \"brass, money\".
The Latin word use in chronology seems to have begun in 5th century Visigothic Spain, where it appears in the *History* of Isidore of Seville, and in later texts. The Spanish era is calculated from 38 BC, Before Christ, perhaps because of a tax (cfr. indiction) levied in that year, or due to a miscalculation of the Battle of Actium, which occurred in 31 BC.
Like epoch, \"era\" in English originally meant \"the starting point of an age\"; the meaning \"system of chronological notation\" is c. 1646; that of \"historical period\" is 1741.
## Use in chronology {#use_in_chronology}
In chronology, an \"era\" is the highest level for the organization of the measurement of time. A \"calendar era\" indicates a span of many years which are numbered beginning at a specific reference date (epoch), which often marks the origin of a political state or cosmology, dynasty, ruler, the birth of a leader, or another significant historical or mythological event; it is generally called after its focus accordingly as in \"Victorian era\".
### Geological era {#geological_era}
In large-scale natural science, there is need for another time perspective, independent from human activity, and indeed spanning a far longer period (mainly prehistoric), where \"geologic era\" refers to well-defined time spans. The next-larger division of geologic time is the eon. The Phanerozoic Eon, for example, is subdivided into eras. There are currently three eras defined in the Phanerozoic; the following table lists them from youngest to oldest (BP is an abbreviation for \"before present\").
Era Beginning (millions of years BP) End (millions of years BP)
----------- ---------------------------------- ----------------------------
Cenozoic 66.038 N/A
Mesozoic 252.17 66.038
Paleozoic 542 252.17
The older Proterozoic and Archean eons are also divided into eras.
### Cosmological era {#cosmological_era}
For periods in the history of the universe, the term \"epoch\" is typically preferred, but \"era\" is used e.g. of the \"Stelliferous Era\".
### Calendar eras {#calendar_eras}
Calendar eras count the years since a particular date (epoch), often one with religious significance. *Anno mundi* (year of the world) refers to a group of calendar eras based on a calculation of the age of the world, assuming it was created as described in the Book of Genesis. In Jewish religious contexts one of the versions is still used, and many Eastern Orthodox religious calendars used another version until 1728. Hebrew year 5772 AM began at sunset on 28 September 2011 and ended on 16 September 2012. In the Western church, *Anno Domini* (*AD* also written *CE*), counting the years since the birth of Jesus on traditional calculations, was always dominant.
The Islamic calendar, which also has variants, counts years from the Hijra or emigration of the Islamic prophet Muhammad from Mecca to Medina, which occurred in 622 AD. The Islamic year is some days shorter than 365; January 2012 fell in 1433 AH (\"After Hijra\").
For a time ranging from 1872 to the Second World War, the Japanese used the imperial year system (*kōki*), counting from the year when the legendary Emperor Jimmu founded Japan, which occurred in 660 BC.
Many Buddhist calendars count from the death of the Buddha, which according to the most commonly used calculations was in 545--543 BCE or 483 BCE. Dates are given as \"BE\" for \"Buddhist Era\"; 2000 AD was 2543 BE in the Thai solar calendar.
Other calendar eras of the past counted from political events, such as the Seleucid era and the Ancient Roman *ab urbe condita* (\"AUC\"), counting from the foundation of the city.
### Regnal eras {#regnal_eras}
The word era also denotes the units used under a different, more arbitrary system where time is not represented as an endless continuum with a single reference year, but each unit starts counting from one again as if time starts again. The use of regnal years is a rather impractical system, and a challenge for historians if a single piece of the historical chronology is missing, and often reflects the preponderance in public life of an absolute ruler in many ancient cultures. Such traditions sometimes outlive the political power of the throne, and may even be based on mythological events or rulers who may not have existed (for example Rome numbering from the rule of Romulus and Remus). In a manner of speaking the use of the supposed date of the birth of Christ as a base year is a form of an era.
In East Asia, each emperor\'s reign may be subdivided into several reign periods, each being treated as a new era. The name of each was a motto or slogan chosen by the emperor. Different East Asian countries utilized slightly different systems, notably:
- Chinese eras
- Japanese era
- Korean eras
- Vietnamese eras
A similar practice survived in the United Kingdom until quite recently, but only for formal official writings: in daily life the ordinary year A.D. has been used for a long time, but Acts of Parliament were dated according to the years of the reign of the current monarch, so that \"61 & 62 Vict c. 37\" refers to the Local Government (Ireland) Act 1898 passed in the session of Parliament in the 61st/62nd year of the reign of Queen Victoria.
### Historiography
\"Era\" can be used to refer to well-defined periods in historiography, such as the Roman era, Elizabethan era, Victorian era, etc. Use of the term for more recent periods or topical history might include Soviet era, and \"musical eras\" in the history of modern popular music, such as the \"big band era\", \"disco era\", etc
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# Ed (software)
**`{{tt|ed}}`{=mediawiki}** (pronounced as distinct letters, `{{IPAc-en|ˌ|iː|ˈ|d|iː}}`{=mediawiki}) is a line editor for Unix and Unix-like operating systems. It was one of the first parts of the Unix operating system that was developed, in August 1969. It remains part of the POSIX and Open Group standards for Unix-based operating systems, alongside the more sophisticated full-screen editor vi.
## History and influence {#history_and_influence}
The ed text editor was one of the first three key elements of the Unix operating system---assembler, editor, and shell---developed by Ken Thompson in August 1969 on a PDP-7 at AT&T Bell Labs. Many features of ed came from the qed text editor developed at Thompson\'s alma mater University of California, Berkeley. Thompson was very familiar with qed, and had reimplemented it on the CTSS and Multics systems. Thompson\'s versions of qed were notable as the first to implement regular expressions. Regular expressions are also implemented in ed, though their implementation is considerably less general than that in qed.
Dennis M. Ritchie produced what Doug McIlroy later described as the \"definitive\" ed, and aspects of ed went on to influence ex, which in turn spawned vi. The non-interactive Unix command grep was inspired by a common special use of qed and later ed, where the command `g/re/p` performs a **g**lobal **r**egular **e**xpression search and **p**rints the lines containing matches. The Unix stream editor, sed implemented many of the scripting features of qed that were not supported by ed on Unix.`{{failed verification|date=June 2023}}`{=mediawiki}
## Features
Features of ed include:
- available on essentially all Unix systems (and mandatory on systems conforming to the Single Unix Specification).
- support for regular expressions
- powerful automation can be achieved by feeding commands from standard input
Known for its terseness, ed, compatible with teletype terminals like Teletype Model 33, gives almost no visual feedback, and has been called (by Peter H. Salus) \"the most user-hostile editor ever created\", even when compared to the contemporary (and notoriously complex) TECO.`{{r|penguin}}`{=mediawiki} For example, the message that ed will produce in case of error, *and* when it wants to make sure the user wishes to quit without saving, is \"?\". It does not report the current filename or line number, or even display the results of a change to the text, unless requested. Older versions (c. 1981) did not even ask for confirmation when a quit command was issued without the user saving changes. This terseness was appropriate in the early versions of Unix, when consoles were teletypes, modems were slow, and memory was precious. As computer technology improved and these constraints were loosened, editors with more visual feedback became the norm. In current practice, ed is rarely used interactively, but does find use in some shell scripts. For interactive use, ed was subsumed by the sam, vi and Emacs editors in the 1980s. ed can be found on virtually every version of Unix and Linux available, and as such is useful for people who have to work with multiple versions of Unix. On Unix-based operating systems, some utilities like SQL\*Plus run ed as the editor if the EDITOR and VISUAL environment variables are not defined. If something goes wrong, ed is sometimes the only editor available. This is often the only time when it is used interactively.
The version of ed provided by GNU has a few switches to enhance the feedback. Using `{{PreCode|ed -v -p:}}`{=mediawiki} provides a simple prompt and enables more useful feedback messages. The `{{PreCode|-p}}`{=mediawiki} switch is defined in POSIX since XPG2 (1987).
The ed commands are often imitated in other line-based editors. For example, CP/M\'s ED, EDLIN in early MS-DOS versions and 32-bit versions of Windows NT has a somewhat similar syntax, and text editors in many MUDs (LPMud and descendants, for example) use ed-like syntax. These editors, however, are typically more limited in function.
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# Ed (software)
## Example
Here is an example transcript of an ed session. For clarity, commands and text typed by the user are in normal face, and output from ed is **emphasized**.
`a`\
`{{as written|ed is the standard Unix text editor.}}`{=mediawiki}\
`This is line number two.`\
`.`\
`2i`\
` .`\
`,l`\
**`ed is the standard Unix text editor.$`**\
**`$`**\
**`This is line number two.$`**\
`w text.txt`\
**`63`**\
`{{codett|2=sed|3s/two/three/}}`{=mediawiki}\
`,l`\
**`ed is the standard Unix text editor.$`**\
**`$`**\
**`This is line number three.$`**\
`w text.txt`\
**`65`**\
`q`
The end result is a simple text file `text.txt` containing the following text:
`ed is the standard Unix text editor.`\
` This is line number three.`
Started with an empty file, the `a` command appends text (all ed commands are single letters). The command puts ed in *insert mode*, inserting the characters that follow and is terminated by a single dot on a line. The two lines that are entered before the dot end up in the file buffer. The `2i` command also goes into insert mode, and will insert the entered text (a single empty line in our case) before line two. All commands may be prefixed by a line number to operate on that line.
In the line `,l`, the lowercase L stands for the list command. The command is prefixed by a range, in this case `,` which is a shortcut for `1,$`. A range is two line numbers separated by a comma (`$` means the last line). In return, ed lists all lines, from first to last. These lines are ended with dollar signs, so that white space at the end of lines is clearly visible.
Once the empty line is inserted in line 2, the line which reads \"This is line number two.\" is now actually the third line. This error is corrected with `{{code|2=sed|3s/two/three/}}`{=mediawiki}, a substitution command. The `3` will apply it to the correct line; following the command is the text to be replaced, and then the replacement. Listing all lines with `,l` the line is shown now to be correct.
`w text.txt` writes the buffer to the file `text.txt` making ed respond with *65*, the number of characters written to the file. `q` will end an ed session
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# Edlin
**Edlin** is a line editor, and the only text editor provided with early versions of IBM PC DOS, MS-DOS and OS/2. Although superseded in MS-DOS 5.0 and later by the full-screen MS-DOS Editor, and by Notepad in Microsoft Windows, it continued to be included in the 32-bit versions of Microsoft operating systems up to Windows Server 2008 and Windows 10.
## History
Edlin was created by Tim Paterson in two weeks in 1980, for Seattle Computer Products\'s 86-DOS (QDOS) based on the CP/M context editor *ED*, itself distantly inspired by the DEC PDP-10 TOPS-10 EDIT text editor.
Microsoft acquired 86-DOS and, after some further development, sold it as MS-DOS, so Edlin was included in v1.0--v5.0 of MS-DOS. From MS-DOS 6 onwards, the only editor included was the new full-screen MS-DOS Editor.
Windows 95, 98 and ME ran on top of an embedded version of DOS, which reports itself as MS-DOS 7. As a successor to MS-DOS 6, this did not include Edlin.
However, Edlin is included in the 32-bit versions of Windows NT and its derivatives---up to and including Windows 10---because the NTVDM\'s DOS support in those operating systems is based on MS-DOS version 5.0. However, unlike most other external DOS commands, it has not been transformed into a native Win32 program. It also does not support long filenames, which were not added to MS-DOS and Windows until long after Edlin was written.
The FreeDOS version was developed by Gregory Pietsch.
## Usage
There are only a few commands. The short list can be found by entering a ? at the edlin prompt.
When a file is open, typing L lists the contents (e.g., `1,6L` lists lines 1 through 6). Each line is displayed with a line number in front of it.
`*1,6L`\
` 1: Edlin: The only text editor in early versions of DOS.`\
` 2:`\
` 3: Back in the day, I remember seeing web pages`\
` 4: branded with a logo at the bottom:`\
` 5: "This page created in edlin."`\
` 6: The things that some people put themselves through. ;-)`\
`*`
The currently selected line has an \*. To replace the contents of any line, the line number is entered and any text entered replaces the original. While editing a line pressing Ctrl-C cancels any changes. The \* marker remains on that line.
Entering I (optionally preceded with a line number) inserts one or more lines before the \* line or the line given. When finished entering lines, Ctrl-C returns to the edlin command prompt.
`*6I`\
` 6:*(...or similar)`\
` 7:*^C `\
` `\
`*7D`\
`*L`\
` 1: Edlin: The only text editor in early versions of DOS.`\
` 2:`\
` 3: Back in the day, I remember seeing web pages`\
` 4: branded with a logo at the bottom:`\
` 5: "This page created in edlin."`\
` 6: (...or similar)`\
`*`
: **i** - Inserts lines of text.
: **D** - deletes the specified line, again optionally starting with the number of a line, or a range of lines. E.g.: `2,4d` deletes lines 2 through 4. In the above example, line 7 was deleted.
```{=html}
<!-- -->
```
: **R** - is used to replace all occurrences of a piece of text in a given range of lines, for example, to replace a spelling error. Including the ? prompts for each change. E.g.: To replace \'prit\' with \'print\' and to prompt for each change: `?rprit^Zprint` (the \^Z represents pressing CTRL-Z). It is case-sensitive.
```{=html}
<!-- -->
```
: **S** - searches for given text. It is used in the same way as replace, but without the replacement text. A search for \'apple\' in the first 20 lines of a file is typed `1,20?sapple` (no space, unless that is part of the search) followed by a press of enter. For each match, it asks if it is the correct one, and accepts n or y (or Enter).
```{=html}
<!-- -->
```
: **P** - displays a listing of a range of lines. If no range is specified, P displays the complete file from the \* to the end. This is different from L in that P changes the current line to be the last line in the range.
```{=html}
<!-- -->
```
: **T** - transfers another file into the one being edited, with this syntax: \[line to insert at\]t\[full path to file\].
```{=html}
<!-- -->
```
: **W** - (write) saves the file.
```{=html}
<!-- -->
```
: **E** - saves the file and quits edlin.
```{=html}
<!-- -->
```
: **Q** - quits edlin without saving.
### Scripts
Edlin may be used as a non-interactive file editor in scripts by redirecting a series of edlin commands.
`edlin < script`
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# Edlin
## Usage
### FreeDOS Edlin {#freedos_edlin}
A GPL-licensed clone of Edlin that includes long filename support is available for download as part of the FreeDOS project. This runs on operating systems such as Linux or Unix as well as MS-DOS
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# Endoplasmic reticulum
`{{Organelle diagram}}`{=mediawiki}
The **endoplasmic reticulum** (**ER**) is a part of a transportation system of the eukaryotic cell, and has many other important functions such as protein folding. The word endoplasmic means \"within the cytoplasm\", and reticulum is Latin for \"little net\". It is a type of organelle made up of two subunits -- **rough endoplasmic reticulum** (**RER**), and **smooth endoplasmic reticulum** (**SER**). The endoplasmic reticulum is found in most eukaryotic cells and forms an interconnected network of flattened, membrane-enclosed sacs known as cisternae (in the RER), and tubular structures in the SER. The membranes of the ER are continuous with the outer nuclear membrane. The endoplasmic reticulum is not found in red blood cells, or spermatozoa.
There are two types of ER that share many of the same proteins and engage in certain common activities such as the synthesis of certain lipids and cholesterol. Different types of cells contain different ratios of the two types of ER depending on the activities of the cell. RER is found mainly toward the nucleus of the cell and SER towards the cell membrane or plasma membrane of cell.
The outer (cytosolic) face of the RER is studded with ribosomes that are the sites of protein synthesis. The RER is especially prominent in cells such as hepatocytes. The SER lacks ribosomes and functions in lipid synthesis but not metabolism, the production of steroid hormones, and detoxification. The SER is especially abundant in mammalian liver and gonad cells.
The ER was observed by light microscopy by Charles Garnier in 1897, who coined the term *ergastoplasm*. The lacy membranes of the endoplasmic reticulum were first seen by electron microscopy in 1945 by Keith R. Porter, Albert Claude, and Ernest F. Fullam.
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# Endoplasmic reticulum
## Structure
The general structure of the endoplasmic reticulum is a network of membranes called cisternae. These sac-like structures are held together by the cytoskeleton. The phospholipid membrane encloses the cisternal space (or lumen), which is continuous with the perinuclear space but separate from the cytosol. The functions of the endoplasmic reticulum can be summarized as the synthesis and export of proteins and membrane lipids, but varies between ER and cell type and cell function. The quantity of both rough and smooth endoplasmic reticulum in a cell can slowly interchange from one type to the other, depending on the changing metabolic activities of the cell. Transformation can include embedding of new proteins in membrane as well as structural changes. Changes in protein content may occur without noticeable structural changes.
### Rough endoplasmic reticulum {#rough_endoplasmic_reticulum}
The surface of the rough endoplasmic reticulum (often abbreviated *RER* or *rough ER*; also called *granular endoplasmic reticulum*) is studded with protein-manufacturing ribosomes giving it a \"rough\" appearance (hence its name). The binding site of the ribosome on the rough endoplasmic reticulum is the translocon. However, the ribosomes are not a stable part of this organelle\'s structure as they are constantly being bound and released from the membrane. A ribosome only binds to the RER once a specific protein-nucleic acid complex forms in the cytosol. This special complex forms when a free ribosome begins translating the mRNA of a protein destined for the secretory pathway. The first 5--30 amino acids polymerized encode a signal peptide, a molecular message that is recognized and bound by a signal recognition particle (SRP). Translation pauses and the ribosome complex binds to the RER translocon where translation continues with the nascent (new) protein forming into the RER lumen and/or membrane. The protein is processed in the ER lumen by an enzyme (a signal peptidase), which removes the signal peptide. Ribosomes at this point may be released back into the cytosol; however, non-translating ribosomes are also known to stay associated with translocons.
The membrane of the rough endoplasmic reticulum is in the form of large double-membrane sheets that are located near, and continuous with, the outer layer of the nuclear envelope. The double membrane sheets are stacked and connected through several right- or left-handed helical ramps, the \"Terasaki ramps\", giving rise to a structure resembling a parking garage. Although there is no continuous membrane between the endoplasmic reticulum and the Golgi apparatus, membrane-bound transport vesicles shuttle proteins between these two compartments. Vesicles are surrounded by coating proteins called COPI and COPII. COPII targets vesicles to the Golgi apparatus and COPI marks them to be brought back to the rough endoplasmic reticulum. The rough endoplasmic reticulum works in concert with the Golgi complex to target new proteins to their proper destinations. The second method of transport out of the endoplasmic reticulum involves areas called membrane contact sites, where the membranes of the endoplasmic reticulum and other organelles are held closely together, allowing the transfer of lipids and other small molecules.
The rough endoplasmic reticulum is key in multiple functions:
- Manufacture of lysosomal enzymes with a mannose-6-phosphate marker added in the *cis*-Golgi network.
- Manufacture of secreted proteins, either secreted constitutively with no tag or secreted in a regulatory manner involving clathrin and paired basic amino acids in the signal peptide.
- Integral membrane proteins that stay embedded in the membrane as vesicles exit and bind to new membranes. Rab proteins are key in targeting the membrane; SNAP and SNARE proteins are key in the fusion event.
- Initial glycosylation as assembly continues. This is N-linked (O-linking occurs in the Golgi).
- N-linked glycosylation: If the protein is properly folded, oligosaccharyltransferase recognizes the AA sequence NXS or NXT (with the S/T residue phosphorylated) and adds a 14-sugar backbone (2-*N*-acetylglucosamine, 9-branching mannose, and 3-glucose at the end) to the side-chain nitrogen of Asn.
The RER has ribosomes while the SER does not.
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# Endoplasmic reticulum
## Structure
### Smooth endoplasmic reticulum {#smooth_endoplasmic_reticulum}
In most cells the smooth endoplasmic reticulum (abbreviated **SER**) is scarce. Instead there are areas where the ER is partly smooth and partly rough, this area is called the transitional ER. The transitional ER gets its name because it contains ER exit sites. These are areas where the transport vesicles which contain lipids and proteins made in the ER, detach from the ER and start moving to the Golgi apparatus. Specialized cells can have a lot of smooth endoplasmic reticulum and in these cells the smooth ER has many functions. It synthesizes lipids, phospholipids, and steroids. Cells which secrete these products, such as those in the testes, ovaries, and sebaceous glands have an abundance of smooth endoplasmic reticulum. It also carries out the metabolism of carbohydrates, detoxification of natural metabolism products and of alcohol and drugs, attachment of receptors on cell membrane proteins, and steroid metabolism. In muscle cells, it regulates calcium ion concentration. Smooth endoplasmic reticulum is found in a variety of cell types (both animal and plant), and it serves different functions in each. The smooth endoplasmic reticulum also contains the enzyme glucose-6-phosphatase, which converts glucose-6-phosphate to glucose, a step in gluconeogenesis. It is connected to the nuclear envelope and consists of tubules that are located near the cell periphery. These tubes sometimes branch forming a network that is reticular in appearance. In some cells, there are dilated areas like the sacs of rough endoplasmic reticulum. The network of smooth endoplasmic reticulum allows for an increased surface area to be devoted to the action or storage of key enzymes and the products of these enzymes.
#### Sarcoplasmic reticulum {#sarcoplasmic_reticulum}
*Main article: Sarcoplasmic reticulum* `{{See also |Calcium-induced calcium release}}`{=mediawiki}
The sarcoplasmic reticulum (SR), from the Greek σάρξ *sarx* (\"flesh\"), is smooth ER found in muscle cells. The only structural difference between this organelle and the smooth endoplasmic reticulum is the composition of proteins they have, both bound to their membranes and drifting within the confines of their lumens. This fundamental difference is indicative of their functions: The endoplasmic reticulum synthesizes molecules, while the sarcoplasmic reticulum stores calcium ions and pumps them out into the sarcoplasm when the muscle fiber is stimulated. After their release from the sarcoplasmic reticulum, calcium ions interact with contractile proteins that utilize ATP to shorten the muscle fiber. The sarcoplasmic reticulum plays a major role in excitation-contraction coupling.
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# Endoplasmic reticulum
## Functions
The endoplasmic reticulum serves many general functions, including the folding of protein molecules in sacs called cisternae and the transport of synthesized proteins in vesicles to the Golgi apparatus. Rough endoplasmic reticulum is also involved in protein synthesis. Correct folding of newly made proteins is made possible by several endoplasmic reticulum chaperone proteins, including protein disulfide isomerase (PDI), ERp29, the Hsp70 family member BiP/Grp78, calnexin, calreticulin, and the peptidylprolyl isomerase family. Only properly folded proteins are transported from the rough ER to the Golgi apparatus -- unfolded proteins cause an unfolded protein response as a stress response in the ER. Disturbances in redox regulation, calcium regulation, glucose deprivation, and viral infection or the over-expression of proteins can lead to endoplasmic reticulum stress response (ER stress), a state in which the folding of proteins slows, leading to an increase in unfolded proteins. This stress is emerging as a potential cause of damage in hypoxia/ischemia, insulin resistance, and other disorders.
### Protein transport {#protein_transport}
Secretory proteins, mostly glycoproteins, are moved across the endoplasmic reticulum membrane. Proteins that are transported by the endoplasmic reticulum throughout the cell are marked with an address tag called a signal sequence. The N-terminus (one end) of a polypeptide chain (i.e., a protein) contains a few amino acids that work as an address tag, which are removed when the polypeptide reaches its destination. Nascent peptides reach the ER via the translocon, a membrane-embedded multiprotein complex. Proteins that are destined for places outside the endoplasmic reticulum are packed into transport vesicles and moved along the cytoskeleton toward their destination. In human fibroblasts, the ER is always co-distributed with microtubules and the depolymerisation of the latter cause its co-aggregation with mitochondria, which are also associated with the ER.
The endoplasmic reticulum is also part of a protein sorting pathway. It is, in essence, the transportation system of the eukaryotic cell. The majority of its resident proteins are retained within it through a retention motif. This motif is composed of four amino acids at the end of the protein sequence. The most common retention sequences are KDEL for lumen-located proteins and KKXX for transmembrane proteins. However, variations of KDEL and KKXX do occur, and other sequences can also give rise to endoplasmic reticulum retention. It is not known whether such variation can lead to sub-ER localizations. There are three KDEL (1, 2 and 3) receptors in mammalian cells, and they have a very high degree of sequence identity. The functional differences between these receptors remain to be established.
### Bioenergetics regulation of ER ATP supply by a CaATiER mechanism {#bioenergetics_regulation_of_er_atp_supply_by_a_caatier_mechanism}
The endoplasmic reticulum does not harbor an ATP-regeneration machinery, and therefore requires ATP import from mitochondria. The imported ATP is vital for the ER to carry out its house keeping cellular functions, such as for protein folding and trafficking.
The ER ATP transporter, SLC35B1/AXER, was recently cloned and characterized, and the mitochondria supply ATP to the ER through a *Ca^2+^-antagonized transport into the ER* (*CaATiER*) mechanism. The *CaATiER* mechanism shows sensitivity to cytosolic Ca^2+^ ranging from high nM to low μM range, with the Ca^2+^-sensing element yet to be identified and validated.
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# Endoplasmic reticulum
## Clinical significance {#clinical_significance}
Increased and supraphysiological ER stress in pancreatic β cells disrupts normal insulin secretion, leading to hyperinsulinemia and consequently peripheral insulin resistance associated with obesity in humans. Human clinical trials also suggested a causal link between obesity-induced increase in insulin secretion and peripheral insulin resistance.
Abnormalities in XBP1 lead to a heightened endoplasmic reticulum stress response and subsequently causes a higher susceptibility for inflammatory processes that may even contribute to Alzheimer\'s disease. In the colon, XBP1 anomalies have been linked to the inflammatory bowel diseases including Crohn\'s disease.
The unfolded protein response (UPR) is a cellular stress response related to the endoplasmic reticulum. The UPR is activated in response to an accumulation of unfolded or misfolded proteins in the lumen of the endoplasmic reticulum. The UPR functions to restore normal function of the cell by halting protein translation, degrading misfolded proteins, and activating the signaling pathways that lead to increasing the production of molecular chaperones involved in protein folding. Sustained overactivation of the UPR has been implicated in prion diseases as well as several other neurodegenerative diseases and the inhibition of the UPR could become a treatment for those diseases
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# Electric charge
**Electric charge** (symbol *q*, sometimes *Q*) is a physical property of matter that causes it to experience a force when placed in an electromagnetic field. Electric charge can be *positive* or *negative*. Like charges repel each other and unlike charges attract each other. An object with no net charge is referred to as electrically neutral. Early knowledge of how charged substances interact is now called classical electrodynamics, and is still accurate for problems that do not require consideration of quantum effects.
In an isolated system, the total charge stays the same - the amount of positive charge minus the amount of negative charge does not change over time. Electric charge is carried by subatomic particles. In ordinary matter, negative charge is carried by electrons, and positive charge is carried by the protons in the nuclei of atoms. If there are more electrons than protons in a piece of matter, it will have a negative charge, if there are fewer it will have a positive charge, and if there are equal numbers it will be neutral. Charge is *quantized*: it comes in integer multiples of individual small units called the elementary charge, *e*, about `{{physconst|e|round=3|after=,}}`{=mediawiki} which is the smallest charge that can exist freely. Particles called quarks have smaller charges, multiples of `{{sfrac|1|3}}`{=mediawiki}*e*, but they are found only combined in particles that have a charge that is an integer multiple of *e*. In the Standard Model, charge is an absolutely conserved quantum number. The proton has a charge of +*e*, and the electron has a charge of −*e*.
Today, a negative charge is defined as the charge carried by an electron and a positive charge is that carried by a proton. Before these particles were discovered, a positive charge was defined by Benjamin Franklin as the charge acquired by a glass rod when it is rubbed with a silk cloth.
Electric charges produce electric fields. A moving charge also produces a magnetic field. The interaction of electric charges with an electromagnetic field (a combination of an electric and a magnetic field) is the source of the electromagnetic (or Lorentz) force, which is one of the four fundamental interactions in physics. The study of photon-mediated interactions among charged particles is called quantum electrodynamics.
The SI derived unit of electric charge is the coulomb (C) named after French physicist Charles-Augustin de Coulomb. In electrical engineering it is also common to use the ampere-hour (A⋅h). In physics and chemistry it is common to use the elementary charge (*e*) as a unit. Chemistry also uses the Faraday constant, which is the charge of one mole of elementary charges.
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# Electric charge
## Overview
Charge is the fundamental property of matter that exhibits electrostatic attraction or repulsion in the presence of other matter with charge. Electric charge is a characteristic property of many subatomic particles. The charges of free-standing particles are integer multiples of the elementary charge *e*; we say that electric charge is *quantized*. Michael Faraday, in his electrolysis experiments, was the first to note the discrete nature of electric charge. Robert Millikan\'s oil drop experiment demonstrated this fact directly, and measured the elementary charge. It has been discovered that one type of particle, quarks, have fractional charges of either −`{{sfrac|1|3}}`{=mediawiki} or +`{{sfrac|2|3}}`{=mediawiki}, but it is believed they always occur in multiples of integral charge; free-standing quarks have never been observed.
By convention, the charge of an electron is negative, *−e*, while that of a proton is positive, *+e*. Charged particles whose charges have the same sign repel one another, and particles whose charges have different signs attract. Coulomb\'s law quantifies the electrostatic force between two particles by asserting that the force is proportional to the product of their charges, and inversely proportional to the square of the distance between them. The charge of an antiparticle equals that of the corresponding particle, but with opposite sign.
The electric charge of a macroscopic object is the sum of the electric charges of the particles that it is made up of. This charge is often small, because matter is made of atoms, and atoms typically have equal numbers of protons and electrons, in which case their charges cancel out, yielding a net charge of zero, thus making the atom neutral.
An *ion* is an atom (or group of atoms) that has lost one or more electrons, giving it a net positive charge (cation), or that has gained one or more electrons, giving it a net negative charge (anion). *Monatomic ions* are formed from single atoms, while *polyatomic ions* are formed from two or more atoms that have been bonded together, in each case yielding an ion with a positive or negative net charge. `{{multiple image
| align = right
| image1 = VFPt plus thumb.svg
| alt1 = [[Electric field]] induced by a positive electric charge
| width1 = 200
| image2 = VFPt minus thumb.svg
| alt2 = Electric field induced by a negative electric charge
| width2 = 200
| footer = Electric field induced by a positive electric charge (left) and a field induced by a negative electric charge (right).
}}`{=mediawiki}
During the formation of macroscopic objects, constituent atoms and ions usually combine to form structures composed of neutral *ionic compounds* electrically bound to neutral atoms. Thus macroscopic objects tend toward being neutral overall, but macroscopic objects are rarely perfectly net neutral.
Sometimes macroscopic objects contain ions distributed throughout the material, rigidly bound in place, giving an overall net positive or negative charge to the object. Also, macroscopic objects made of conductive elements can more or less easily (depending on the element) take on or give off electrons, and then maintain a net negative or positive charge indefinitely. When the net electric charge of an object is non-zero and motionless, the phenomenon is known as static electricity. This can easily be produced by rubbing two dissimilar materials together, such as rubbing amber with fur or glass with silk. In this way, non-conductive materials can be charged to a significant degree, either positively or negatively. Charge taken from one material is moved to the other material, leaving an opposite charge of the same magnitude behind. The law of *conservation of charge* always applies, giving the object from which a negative charge is taken a positive charge of the same magnitude, and vice versa.
Even when an object\'s net charge is zero, the charge can be distributed non-uniformly in the object (e.g., due to an external electromagnetic field, or bound polar molecules). In such cases, the object is said to be polarized. The charge due to polarization is known as bound charge, while the charge on an object produced by electrons gained or lost from outside the object is called *free charge*. The motion of electrons in conductive metals in a specific direction is known as electric current.
## Unit
The SI unit of quantity of electric charge is the coulomb (symbol: C). The coulomb is defined as the quantity of charge that passes through the cross section of an electrical conductor carrying one ampere for one second. This unit was proposed in 1946 and ratified in 1948. The lowercase symbol *q* is often used to denote a quantity of electric charge. The quantity of electric charge can be directly measured with an electrometer, or indirectly measured with a ballistic galvanometer.
The elementary charge is defined as a fundamental constant in the SI. The value for elementary charge, when expressed in SI units, is exactly `{{physconst|e|after=.}}`{=mediawiki}
After discovering the quantized character of charge, in 1891, George Stoney proposed the unit \'electron\' for this fundamental unit of electrical charge. J. J. Thomson subsequently discovered the particle that we now call the electron in 1897. The unit is today referred to as `{{em|elementary charge}}`{=mediawiki}, `{{em|fundamental unit of charge}}`{=mediawiki}, or simply denoted *e*, with the charge of an electron being −*e*. The charge of an isolated system should be a multiple of the elementary charge *e*, even if at large scales charge seems to behave as a continuous quantity. In some contexts it is meaningful to speak of fractions of an elementary charge; for example, in the fractional quantum Hall effect.
The unit faraday is sometimes used in electrochemistry. One faraday is the magnitude of the charge of one mole of elementary charges, i.e. `{{physconst|F|unit=C|after=.|ref=no}}`{=mediawiki}
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# Electric charge
## History
From ancient times, people were familiar with four types of phenomena that today would all be explained using the concept of electric charge: (a) lightning, (b) the torpedo fish (or electric ray), (c) St Elmo\'s Fire, and (d) that amber rubbed with fur would attract small, light objects. The first account of the `{{em|amber effect}}`{=mediawiki} is often attributed to the ancient Greek mathematician Thales of Miletus, who lived from c. 624 to c. 546 BC, but there are doubts about whether Thales left any writings; his account about amber is known from an account from early 200s. This account can be taken as evidence that the phenomenon was known since at least c. 600 BC, but Thales explained this phenomenon as evidence for inanimate objects having a soul. In other words, there was no indication of any conception of electric charge. More generally, the ancient Greeks did not understand the connections among these four kinds of phenomena. The Greeks observed that the charged amber buttons could attract light objects such as hair. They also found that if they rubbed the amber for long enough, they could even get an electric spark to jump, but there is also a claim that no mention of electric sparks appeared until late 17th century. This property derives from the triboelectric effect. In late 1100s, the substance jet, a compacted form of coal, was noted to have an amber effect, and in the middle of the 1500s, Girolamo Fracastoro, discovered that diamond also showed this effect. Some efforts were made by Fracastoro and others, especially Gerolamo Cardano to develop explanations for this phenomenon.
In contrast to astronomy, mechanics, and optics, which had been studied quantitatively since antiquity, the start of ongoing qualitative and quantitative research into electrical phenomena can be marked with the publication of *De Magnete* by the English scientist William Gilbert in 1600. In this book, there was a small section where Gilbert returned to the amber effect (as he called it) in addressing many of the earlier theories, and coined the Neo-Latin word *electrica* (from *ἤλεκτρον* (ēlektron), the Greek word for *amber*). The Latin word was translated into English as `{{em|electrics}}`{=mediawiki}. Gilbert is also credited with the term *electrical*, while the term *electricity* came later, first attributed to Sir Thomas Browne in his Pseudodoxia Epidemica from 1646. (For more linguistic details see Etymology of electricity.) Gilbert hypothesized that this amber effect could be explained by an effluvium (a small stream of particles that flows from the electric object, without diminishing its bulk or weight) that acts on other objects. This idea of a material electrical effluvium was influential in the 17th and 18th centuries. It was a precursor to ideas developed in the 18th century about \"electric fluid\" (Dufay, Nollet, Franklin) and \"electric charge\".
Around 1663 Otto von Guericke invented what was probably the first electrostatic generator, but he did not recognize it primarily as an electrical device and only conducted minimal electrical experiments with it. Other European pioneers were Robert Boyle, who in 1675 published the first book in English that was devoted solely to electrical phenomena. His work was largely a repetition of Gilbert\'s studies, but he also identified several more \"electrics\", and noted mutual attraction between two bodies.
In 1729 Stephen Gray was experimenting with static electricity, which he generated using a glass tube. He noticed that a cork, used to protect the tube from dust and moisture, also became electrified (charged). Further experiments (e.g., extending the cork by putting thin sticks into it) showed---for the first time---that electrical effluvia (as Gray called it) could be transmitted (conducted) over a distance. Gray managed to transmit charge with twine (765 feet) and wire (865 feet). Through these experiments, Gray discovered the importance of different materials, which facilitated or hindered the conduction of electrical effluvia. John Theophilus Desaguliers, who repeated many of Gray\'s experiments, is credited with coining the terms conductors and insulators to refer to the effects of different materials in these experiments. Gray also discovered electrical induction (i.e., where charge could be transmitted from one object to another without any direct physical contact). For example, he showed that by bringing a charged glass tube close to, but not touching, a lump of lead that was sustained by a thread, it was possible to make the lead become electrified (e.g., to attract and repel brass filings). He attempted to explain this phenomenon with the idea of electrical effluvia.
Gray\'s discoveries introduced an important shift in the historical development of knowledge about electric charge. The fact that electrical effluvia could be transferred from one object to another, opened the theoretical possibility that this property was not inseparably connected to the bodies that were electrified by rubbing. In 1733 Charles François de Cisternay du Fay, inspired by Gray\'s work, made a series of experiments (reported in *Mémoires de l\'Académie Royale des Sciences*), showing that more or less all substances could be \'electrified\' by rubbing, except for metals and fluids and proposed that electricity comes in two varieties that cancel each other, which he expressed in terms of a two-fluid theory. When glass was rubbed with silk, du Fay said that the glass was charged with *vitreous electricity*, and, when amber was rubbed with fur, the amber was charged with *resinous electricity*. In contemporary understanding, positive charge is now defined as the charge of a glass rod after being rubbed with a silk cloth, but it is arbitrary which type of charge is called positive and which is called negative. Another important two-fluid theory from this time was proposed by Jean-Antoine Nollet (1745).
Up until about 1745, the main explanation for electrical attraction and repulsion was the idea that electrified bodies gave off an effluvium. Benjamin Franklin started electrical experiments in late 1746, and by 1750 had developed a one-fluid theory of electricity, based on an experiment that showed that a rubbed glass received the same, but opposite, charge strength as the cloth used to rub the glass. Franklin imagined electricity as being a type of invisible fluid present in all matter and coined the term `{{em|charge}}`{=mediawiki} itself (as well as battery and some others); for example, he believed that it was the glass in a Leyden jar that held the accumulated charge. He posited that rubbing insulating surfaces together caused this fluid to change location, and that a flow of this fluid constitutes an electric current. He also posited that when matter contained an excess of the fluid it was `{{em|positively}}`{=mediawiki} charged and when it had a deficit it was `{{em|negatively}}`{=mediawiki} charged. He identified the term `{{em|positive}}`{=mediawiki} with vitreous electricity and `{{em|negative}}`{=mediawiki} with resinous electricity after performing an experiment with a glass tube he had received from his overseas colleague Peter Collinson. The experiment had participant A charge the glass tube and participant B receive a shock to the knuckle from the charged tube. Franklin identified participant B to be positively charged after having been shocked by the tube. There is some ambiguity about whether William Watson independently arrived at the same one-fluid explanation around the same time (1747). Watson, after seeing Franklin\'s letter to Collinson, claims that he had presented the same explanation as Franklin in spring 1747. Franklin had studied some of Watson\'s works prior to making his own experiments and analysis, which was probably significant for Franklin\'s own theorizing. One physicist suggests that Watson first proposed a one-fluid theory, which Franklin then elaborated further and more influentially. A historian of science argues that Watson missed a subtle difference between his ideas and Franklin\'s, so that Watson misinterpreted his ideas as being similar to Franklin\'s. In any case, there was no animosity between Watson and Franklin, and the Franklin model of electrical action, formulated in early 1747, eventually became widely accepted at that time. After Franklin\'s work, effluvia-based explanations were rarely put forward.
It is now known that the Franklin model was fundamentally correct. There is only one kind of electrical charge, and only one variable is required to keep track of the amount of charge.
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# Electric charge
## History
Until 1800 it was only possible to study conduction of electric charge by using an electrostatic discharge. In 1800 Alessandro Volta was the first to show that charge could be maintained in continuous motion through a closed path.
In 1833, Michael Faraday sought to remove any doubt that electricity is identical, regardless of the source by which it is produced. He discussed a variety of known forms, which he characterized as common electricity (e.g., static electricity, piezoelectricity, magnetic induction), voltaic electricity (e.g., electric current from a voltaic pile), and animal electricity (e.g., bioelectricity).
In 1838, Faraday raised a question about whether electricity was a fluid or fluids or a property of matter, like gravity. He investigated whether matter could be charged with one kind of charge independently of the other. He came to the conclusion that electric charge was a relation between two or more bodies, because he could not charge one body without having an opposite charge in another body.
In 1838, Faraday also put forth a theoretical explanation of electric force, while expressing neutrality about whether it originates from one, two, or no fluids. He focused on the idea that the normal state of particles is to be nonpolarized, and that when polarized, they seek to return to their natural, nonpolarized state.
In developing a field theory approach to electrodynamics (starting in the mid-1850s), James Clerk Maxwell stops considering electric charge as a special substance that accumulates in objects, and starts to understand electric charge as a consequence of the transformation of energy in the field. This pre-quantum understanding considered magnitude of electric charge to be a continuous quantity, even at the microscopic level.
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# Electric charge
## Role of charge in static electricity {#role_of_charge_in_static_electricity}
Static electricity refers to the electric charge of an object and the related electrostatic discharge when two objects are brought together that are not at equilibrium. An electrostatic discharge creates a change in the charge of each of the two objects.
### Electrification by sliding {#electrification_by_sliding}
When a piece of glass and a piece of resin---neither of which exhibit any electrical properties---are rubbed together and left with the rubbed surfaces in contact, they still exhibit no electrical properties. When separated, they attract each other.
A second piece of glass rubbed with a second piece of resin, then separated and suspended near the former pieces of glass and resin causes these phenomena:
- The two pieces of glass repel each other.
- Each piece of glass attracts each piece of resin.
- The two pieces of resin repel each other.
This attraction and repulsion is an *electrical phenomenon*, and the bodies that exhibit them are said to be *electrified*, or *electrically charged*. Bodies may be electrified in many other ways, as well as by sliding. The electrical properties of the two pieces of glass are similar to each other but opposite to those of the two pieces of resin: The glass attracts what the resin repels and repels what the resin attracts.
If a body electrified in any manner whatsoever behaves as the glass does, that is, if it repels the glass and attracts the resin, the body is said to be *vitreously* electrified, and if it attracts the glass and repels the resin it is said to be *resinously* electrified. All electrified bodies are either vitreously or resinously electrified.
An established convention in the scientific community defines vitreous electrification as positive, and resinous electrification as negative. The exactly opposite properties of the two kinds of electrification justify our indicating them by opposite signs, but the application of the positive sign to one rather than to the other kind must be considered as a matter of arbitrary convention---just as it is a matter of convention in mathematical diagram to reckon positive distances towards the right hand.
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# Electric charge
## Role of charge in electric current {#role_of_charge_in_electric_current}
Electric current is the flow of electric charge through an object. The most common charge carriers are the positively charged proton and the negatively charged electron. The movement of any of these charged particles constitutes an electric current. In many situations, it suffices to speak of the *conventional current* without regard to whether it is carried by positive charges moving in the direction of the conventional current or by negative charges moving in the opposite direction. This macroscopic viewpoint is an approximation that simplifies electromagnetic concepts and calculations.
At the opposite extreme, if one looks at the microscopic situation, one sees there are many ways of carrying an electric current, including: a flow of electrons; a flow of electron holes that act like positive particles; and both negative and positive particles (ions or other charged particles) flowing in opposite directions in an electrolytic solution or a plasma.
The direction of the conventional current in most metallic wires is opposite to the drift velocity of the actual charge carriers; i.e., the electrons.
## Conservation of electric charge {#conservation_of_electric_charge}
The total electric charge of an isolated system remains constant regardless of changes within the system itself. This law is inherent to all processes known to physics and can be derived in a local form from gauge invariance of the wave function. The conservation of charge results in the charge-current continuity equation. More generally, the rate of change in charge density *ρ* within a volume of integration *V* is equal to the area integral over the current density **J** through the closed surface *S* = ∂*V*, which is in turn equal to the net current *I*:
:
Thus, the conservation of electric charge, as expressed by the continuity equation, gives the result:
: $I = -\frac{\mathrm{d}q}{\mathrm{d}t}.$
The charge transferred between times $t_\mathrm{i}$ and $t_\mathrm{f}$ is obtained by integrating both sides:
: $q = \int_{t_{\mathrm{i}}}^{t_{\mathrm{f}}} I\, \mathrm{d}t$
where *I* is the net outward current through a closed surface and *q* is the electric charge contained within the volume defined by the surface.
## Relativistic invariance {#relativistic_invariance}
Aside from the properties described in articles about electromagnetism, electric charge is a relativistic invariant. This means that any particle that has electric charge *q* has the same electric charge regardless of how fast it is travelling. This property has been experimentally verified by showing that the electric charge of one helium nucleus (two protons and two neutrons bound together in a nucleus and moving around at high speeds) is the same as that of two deuterium nuclei (one proton and one neutron bound together, but moving much more slowly than they would if they were in a helium nucleus)
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# Ennius
**Quintus Ennius** (`{{IPA|la|ˈkᶣiːnt̪ʊs̺ ˈɛnːiʊs̺}}`{=mediawiki} ; c. 239) was a writer and poet who lived during the Roman Republic. He is often considered the father of Roman poetry. He was born in the small town of Rudiae, located near modern Lecce (ancient *Calabria*, today Salento), a town founded by the Messapians, and could speak Greek as well as Latin and Oscan (his native language). Although only fragments of his works survive, his influence in Latin literature was significant, particularly in his use of Greek literary models.
## Biography
Very little is reliably known about the life of Ennius. His contemporaries hardly mentioned him and much that is related about him could have been embroidered from references to himself in his now fragmentary writings. Some lines of the *Annales*, as well as ancient testimonies, for example, suggest that Ennius opened his epic with a recollection of a dream in which the ancient epic-writer Homer informed him that his spirit had been reborn into Ennius. It is true that the doctrine of the transmigration of souls once flourished in the areas of Italy settled by Greeks, but the statement might have been no more than a literary flourish. Ennius seems to have been given to making large claims, as in the report by Maurus Servius Honoratus that he claimed descent from Messapus, the legendary king of his native district. The partially Hellenised city of Rudiae (in modern Apulia), his place of birth, was certainly in the area settled by the Messapians. And this, he used to say, according to Aulus Gellius, had endowed him with a triple linguistic and cultural heritage, fancifully described as \"three hearts... Greek, Oscan and Latin\".
The public career of Ennius first really emerges in middle life, when he was serving in the army with the rank of centurion during the Second Punic War. While in Sardinia in the year 204 BCE, he is said to have attracted the attention of Cato the Elder and was taken by him to Rome. There he taught Greek and adapted Greek plays for a livelihood, and by his poetical compositions gained the friendship of some of the greatest men in Rome whose achievements he praised. Amongst these were Scipio Africanus and Fulvius Nobilior, whom he accompanied on his Aetolian campaign (189). Afterwards he made the capture of Ambracia, at which he was present, the subject of a play and of an episode in the *Annales*. It was through the influence of Nobilior\'s son Quintus that Ennius subsequently obtained Roman citizenship. But he himself lived plainly and simply in the literary quarter on the Aventine Hill with the poet Caecilius Statius, a fellow adapter of Greek plays.
At about the age of 70 Ennius died, immediately after producing his tragedy *Thyestes*. In the last book of his epic poem, in which he seems to have given various details of his personal history, he mentioned that he was in his 67th year at the date of its composition. He compared himself, in contemplation of the close of the great work of his life, to a gallant horse which, after having often won the prize at the Olympic Games, obtained his rest when weary with age. A similar feeling of pride at the completion of a great career is expressed in the memorial lines which he composed to be placed under his bust after death: \"Let no one weep for me, or celebrate my funeral with mourning; for I still live, as I pass to and fro through the mouths of men.\"
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# Ennius
## Literature
Ennius continued the nascent literary tradition by writing plays in Greek and Roman style (praetextae and palliatae), as well as his most famous work, a historical epic in hexameters called the *Annales*. Other minor works include the *Epicharmus*, *Epigrammata*, the *Euhemerus*, the *Hedyphagetica*, *Praecepta*/*Protrepticus*, *Saturae* (or *Satires*), *Scipio*, and *Sota*.
### The *Annales* {#the_annales}
The *Annales* was an epic poem in fifteen books, later expanded to eighteen, covering Roman history from the fall of Troy in 1184 BCE down to the censorship of Cato the Elder in 184 BCE. It was the first Latin poem to adopt the dactylic hexameter metre used in Greek epic and didactic poetry, leading it to become the standard metre for these genres in Latin poetry. The *Annals* became a school text for Roman schoolchildren, eventually supplanted by Virgil\'s *Aeneid*. About 600 lines survive.
### Minor works {#minor_works}
The *Epicharmus* was inspired by the philosophical hypotheses developed by the Sicilian poet and philosopher Epicharmus of Kos, after which Ennius\'s work took its name. In the *Epicharmus*, the poet describes a dream he had in which he died and was transported to some place of heavenly enlightenment. Here, he met Epicharmus, who explained the nature of the gods and taught Ennius the physics of the universe.
The *Euhemerus* presented a theological doctrine based on the ideas of Euhemerus of Messene, who argued that the gods of Olympus were not supernatural powers that interfere in the lives of humans, but rather heroes of old who after death were eventually regarded as deities due to their valor, bravery, or cultural impact (this belief is now known as euhemerism). Both Cicero and Lactantius write that the *Euhemerus* was a \"translat\[ion\] and a recount\[ing\]\" of Euhemerus\'s original work the *Sacred History*, but it is unclear if this means Ennius simply translated the original from Greek into Latin, or added in his own elements. Most of what is preserved of this work comes to us from Lactantius, and these snippets suggest that the *Euhemerus* was a prose text.
The *Hedyphagetica* took much of its substance from the gastronomical epic of Archestratus of Gela. The extant portions of Ennius\'s poem discuss where a reader might find the best type of fish. Most of the fragments, replete with unique terms for fish and numerous place names, are corrupt or damaged. The *Hedyphagetica* is written in hexameters, but differs from the *Annales* in regards to \"metrical practices\"; this difference is largely due to each works\' distinct subject matter.
The titles *Praecepta* and *Protrepticus* were likely used to refer to the same (possibly exhortatory) work. However, given this work\'s almost non-existent nature (only the word *pannibus*`{{em dash}}`{=mediawiki}an \"unusual\" form of the word *pannis*, meaning \"rags\"`{{em dash}}`{=mediawiki}is preserved in the work of the Latin grammarian Charisius), this position is extremely difficult to verify.
The *Saturae* is a collection of about thirty lines from satirical poems`{{em dash}}`{=mediawiki}making it the first extant instance of Roman satire. These lines are written in a variety of poetic metres. The poems in this collection \"were mostly concerned with practical wisdom, often driving home a lesson with the help of a fable.\"
Ennius\'s *Scipio* was a work (possibly a panegyric poem) that apparently celebrated the life and deeds of Scipio Africanus. Hardly anything remains of this work, and what is preserved is embedded in the works of others. Unfortunately, \"no quotation of \[*Scipio*\] supplies a context\". Some have proposed that the work was written before the *Annales*, and others have said that the work was written after Scipio\'s 201 BCE triumph that followed the Battle of Zama (202 BCE).
The *Sota* was a poem, potentially of some length, named after the Greek poet Sotades. The work, which followed a metre established by Sotades known as the \"Sotadeus\", concerned itself with a number of disparate topics and ideas.
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# Ennius
## Editions
- Quinto Ennio. *Le opere minori, Vol. I. Praecepta, Protrepticus, Saturae, Scipio, Sota*. Ed., tr., comm. Alessandro Russo. Pisa: Edizioni ETS, 2007 (Testi e studi di cultura classica, 40).
- Warmington, E. H. (1935). Ennius (Q. Ennius). *Remains of Old Latin.* Edited by Eric Herbert Warmington. Vol. 2: Ennius and Caecilius. Cambridge: Harvard University Press
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# Execution unit
In computer engineering, an **execution unit** (**E-unit** or **EU**) is a part of a processing unit that performs the operations and calculations forwarded from the instruction unit. It may have its own internal control sequence unit (not to be confused with a CPU\'s main control unit), some registers, and other internal units such as an arithmetic logic unit, address generation unit, floating-point unit, load--store unit, branch execution unit or other smaller and more specific components, and can be tailored to support a certain datatype, such as integers or floating-points.
It is common for modern processing units to have multiple parallel functional units within its execution units, which is referred to as superscalar design. The simplest arrangement is to use a single bus manager unit to manage the memory interface and the others to perform calculations. Additionally, modern execution units are usually pipelined
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# Eskilstuna Municipality
**Eskilstuna Municipality** (*Eskilstuna kommun*) is a municipality in Södermanland County in southeast Sweden, between Lake Mälaren and Lake Hjälmaren. The seat of the municipality is in the city of Eskilstuna.
The present municipality was formed in 1971 by the merger of the City of Eskilstuna, the City of Torshälla and five rural municipalities. It is the largest municipality in the Sörmland region in terms of population, having more than 1/3 of the overall county population.
## Geography
Eskilstuna Municipality is an inland municipality, although the low-lying Mälaren renders the lengthy lakeshore to be at 1 m above sea level. The highest point is at *Tyckenhed* in the southwest of the municipality at 114 m above sea level.
## Localities
- Alberga
- Ärla
- Borsökna
- Bälgviken
- Eskilstuna (seat)
- Hållsta
- Hällberga
- Hällbybrunn
- Kjulaås
- Kvicksund (partly in Västerås Municipality)
- Mesta
- Skiftinge
- Skogstorp
- Torshälla
- Tumbo
- Västra Borsökna
## Demographics
This is a demographic table based on Eskilstuna Municipality\'s electoral districts in the 2022 Swedish general election sourced from SVT\'s election platform, in turn taken from SCB official statistics.
In total there were 78,420 Swedish citizens of voting age resident in the municipality. 47.5% voted for the left coalition and 51.0% for the right coalition. Indicators are in percentage points except population totals and income.
Location
------------------------------ ------------------------------ -------------------------------- -------------------------------- ------------------------------ ------------------------------ ------------------------------ ------------------------------ ------------------------------ ----
data-sort-type=\"number\" \| data-sort-type=\"number\" \| data-sort-type=\"number\" \| % data-sort-type=\"number\" \| % data-sort-type=\"number\" \| data-sort-type=\"number\" \| data-sort-type=\"number\" \| data-sort-type=\"number\" \| data-sort-type=\"number\" \|
Balsta-Eskilshem Ö 1,529 1,191 51.0 47.6 74 66 34 20,021 35
Barva-Jäder 1,483 1,153 32.9 66.0 88 91 9 27,985 37
Borsökna V 1,348 936 42.0 56.9 87 80 20 30,866 49
Borsökna Ö 1,179 874 41.4 58.3 86 81 19 30,534 47
Edvardslund-Haga 1,770 1,355 48.6 50.2 82 75 25 25,389 39
Ekbacken 1,800 1,688 44.6 54.3 78 59 41 24,215 41
Ekeby-Brottsta 1,957 1,444 47.2 51.8 83 78 22 27,332 42
Eskilsparken 1,560 1,323 47.1 52.0 85 82 18 27,525 48
Eskilstuna Centrum N 1,592 1,593 45.0 52.6 73 61 39 24,920 45
Eskilstuna Centrum S 1,728 1,403 54.1 44.3 72 62 38 24,174 43
Forsbomsvreten 1,551 915 53.4 43.5 57 34 66 16,053 33
Fröslunda-Björkhultsvägen 1,998 1,060 72.4 23.2 42 19 81 12,134 16
Fröslunda-Tallåsparken 2,195 1,244 65.6 29.8 52 24 76 13,779 23
Gillberga-Lista 1,642 1,293 34.1 64.6 85 90 10 26,909 31
Gökstensparken 1,792 1,373 50.8 48.3 75 67 33 22,102 28
Hammarby-Vallby 1,355 1,120 35.5 63.8 86 86 14 30,153 42
Hisingsbacke 1,643 1,273 43.5 55.1 78 70 30 25,566 45
Holmberget-Rådhustorget 1,896 1,316 46.0 53.3 69 68 32 20,958 31
Hållsta 1,523 1,153 44.8 54.4 84 83 17 26,229 36
Hällbybrunns N 1,643 1,235 46.0 53.5 82 79 21 26,809 38
Hällbybrunns S-Råby Rekarne 2,047 1,531 40.8 58.5 86 80 20 28,024 40
Kjula 1,667 1,225 41.0 58.1 88 86 14 27,700 36
Krusgårdsberget 1,534 1,082 47.2 50.9 59 57 43 16,751 22
Köpmangatsområdet 1,556 1,350 52.2 47.0 83 81 19 25,805 46
Lindhaga 1,922 1,348 45.9 53.4 88 71 29 29,754 46
Lundby-Gredby 2,081 1,538 50.2 48.6 85 71 29 28,009 46
Lustigbacke 1,459 1,165 53.7 44.7 75 73 27 21,506 40
Mesta 1,849 1,437 50.0 49.1 86 72 28 26,898 41
Munktellstaden-Valhalla 1,890 1,522 49.1 49.5 78 64 36 25,731 42
Myrtorp 1,574 1,103 51.0 47.3 74 60 40 20,664 35
Mälarbaden-Mälby-Ängsholmen 1,606 1,237 35.1 64.5 85 85 15 31,296 50
Nyfors C 2,041 1,201 59.6 37.4 58 32 68 15,610 30
Nyfors Ö 1,629 1,287 51.2 47.4 72 60 40 22,735 39
Nyforstorget 1,544 1,031 56.4 41.1 55 24 76 14,496 33
Näshulta 1,002 825 46.5 53.4 83 91 9 26,350 33
Odlaren-Hagnesta 2,022 1,566 42.2 56.7 89 80 20 31,804 55
Råbergstorp-Lagersberg 3,056 1,506 63.5 31.3 38 14 86 9,689 20
Röksta-Eskilshem V 1,564 1,141 54.6 43.0 75 53 47 24,161 40
Skiftinge N 1,695 1,075 54.2 43.2 64 34 66 19,281 36
Skiftinge S 1,647 1,062 48.8 49.2 56 40 60 16,897 20
Skogstorp N 1,631 1,206 47.9 51.8 87 84 16 30,049 49
Skogstorp S 1,318 986 46.7 52.4 91 86 14 31,758 51
Slagsta S-Helgestahill 1,627 1,235 50.6 48.7 85 78 22 26,922 41
Slagsta-Måsta 1,146 884 43.6 55.4 82 57 43 25,223 35
Slottsbacken 1,452 1,223 44.6 54.0 80 71 29 23,172 35
Snopptorp-Skogsängen 1,678 1,314 51.0 47.4 79 73 27 24,201 48
Solvik-Kogne-Roxnäs 1,468 1,076 40.9 58.1 84 75 25 28,841 42
Stadsparken 1,683 1,420 51.6 46.7 76 66 34 21,685 38
Stenby 1,690 1,230 46.6 51.1 80 51 49 25,760 41
Stenkvista 1,317 970 37.1 61.8 86 84 16 27,526 38
Sundbyholm-Ostra 1,263 921 42.9 56.9 88 87 13 30,407 43
Sveaplan-Sjukhusområdet 1,363 1,101 43.6 55.0 77 69 31 24,345 37
Söderängsparken 1,818 1,380 46.8 50.9 76 72 28 23,208 42
Tumbo 1,815 1,372 32.4 66.3 88 87 13 32,233 48
Tunavallen 1,448 1,174 52.3 47.1 85 67 33 28,129 51
Viptorp 2,079 1,305 58.8 39.4 56 45 55 16,808 24
Västermalm 2,116 1,303 58.6 37.8 52 33 67 14,291 26
Västermarksparken 1,562 1,189 56.0 42.6 73 59 41 21,443 34
Årby-Navigatören 1,527 911 59.5 38.0 53 28 72 15,679 24
Årby-Notarien 1,505 724 73.2 22.1 41 12 88 9,958 21
Ärla 2,268 1,733 37.9 61.2 84 90 10 26,463 31
Ärsta 1,877 1,166 49.6 48.3 60 36 64 17,694 34
Öja-Västermo 1,604 1,279 41.8 57.1 83 92 8 23,672 28
Östermalm 1,550 1,144 46.5 52.7 77 69 31 24,292 35
Source: SVT
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# Eskilstuna Municipality
## Elections
### Riksdag
These are the results of the Riksdag elections of Eskilstuna Municipality since the 1972 municipality reform. The results of the Sweden Democrats were not published by SCB between 1988 and 1998 at a municipal level to the party\'s small nationwide size at the time. \"Votes\" denotes valid votes, whereas \"Turnout\" denotes also blank and invalid votes.
Year Turnout Votes V S MP C L KD M SD ND
------ --------- -------- ------ ------ ----- ------ ------ ------ ------ ------ -----
1973 91.5 55,242 4.5 52.3 0.0 19.9 11.0 1.6 10.3 0.0 0.0
1976 92.2 57,466 3.4 51.8 0.0 18.5 12.6 1.3 12.1 0.0 0.0
1979 91.1 56,858 4.0 53.6 0.0 13.1 12.0 1.1 15.6 0.0 0.0
1982 91.9 57,768 4.1 56.0 1.6 10.9 6.8 1.5 18.9 0.0 0.0
1985 89.9 57,305 4.4 54.9 1.3 8.1 14.1 0.0 16.9 0.0 0.0
1988 85.0 54,494 4.9 52.3 4.5 7.4 13.3 2.3 14.1 0.0 0.0
1991 85.3 54,763 4.0 46.4 2.7 5.7 9.8 5.9 17.5 0.0 7.2
1994 85.9 55,238 5.6 54.2 4.5 4.8 7.1 3.2 17.8 0.0 1.3
1998 79.7 50,641 11.5 44.9 4.8 3.5 4.3 10.0 18.9 0.0 0.0
2002 77.4 50,404 7.7 47.7 4.9 4.4 12.6 7.5 12.2 1.3 0.0
2006 79.6 53,595 5.4 44.1 5.4 6.0 6.9 5.8 21.6 2.8 0.0
2010 83.3 58,588 5.4 35.9 7.9 4.6 6.7 4.4 26.2 7.9 0.0
2014 84.0 61,217 5.4 35.5 6.1 4.3 4.4 3.6 21.3 16.6 0.0
2018 84.7 63,335 6.8 32.2 3.3 5.9 4.7 4.8 19.9 21.0 0.0
2022 80.4 62,313 5.9 33.0 3.5 5.1 3,6 4.7 18.5 24.2 0.0
**Blocs**
This lists the relative strength of the socialist and centre-right blocs since 1973, but parties not elected to the Riksdag are inserted as \"other\", including the Sweden Democrats results from 1988 to 2006, but also the Christian Democrats pre-1991 and the Greens in 1982, 1985, and 1991. The sources are identical to the table above. The coalition or government mandate marked in bold formed the government after the election. New Democracy got elected in 1991 but is still listed as \"other\" due to the short lifespan of the party. \"Elected\" is the total number of percentage points from the municipality that went to parties who were elected to the Riksdag.
Year Turnout Votes Left Right SD Other Elected
------ --------- -------- ---------- ---------- ------ ------- ---------
1973 91.5 55,242 **56.8** 41.2 0.0 2.0 98.0
1976 92.2 57,466 55.2 **43.2** 0.0 1.6 98.4
1979 91.1 56,858 57.6 **40.7** 0.0 1.7 98.3
1982 91.9 57,768 **60.1** 36.6 0.0 3.3 96.7
1985 89.9 57,305 **59.3** 39.1 0.0 1.6 98.4
1988 85.0 54,494 **61.7** 34.8 0.0 3.5 96.5
1991 85.3 54,763 50.4 **38.9** 0.0 11.7 96.5
1994 85.9 55,238 **64.3** 32.9 0.0 2.8 97.2
1998 79.7 50,641 **61.2** 36.7 0.0 2.1 97.9
2002 77.4 50,404 **60.3** 36.7 0.0 3.0 97.0
2006 79.6 53,595 54.9 **40.3** 0.0 4.8 95.2
2010 83.3 58,588 49.2 **41.9** 7.9 1.0 99.0
2014 84.0 61,217 **47.0** 33.6 16.6 2.8 97.2
2018 84.7 63,335 **42.3** 35.4 21.0 1.4 98
| 506 |
Eskilstuna Municipality
| 1 |
9,862 |
# Europe of Democracies and Diversities
**Europe of Democracies and Diversities** (EDD) was an Eurosceptic political group with seats in the European Parliament between 1999 and 2004. Following the 2004 European elections, the group reformed as Independence/Democracy (IND/DEM)
| 38 |
Europe of Democracies and Diversities
| 0 |
9,877 |
# Erg
The **erg** is a unit of energy equal to 10^−7^ joules (100 nJ). It is not an SI unit, instead originating from the centimetre--gram--second system of units (CGS). Its name is derived from `{{Transliteration|grc|ergon}}`{=mediawiki} (*ἔργον*), a Greek word meaning \'work\' or \'task\'.
An erg is the amount of work done by a force of one dyne exerted for a distance of one centimetre. In the CGS base units, it is equal to one gram centimetre-squared per second-squared (g⋅cm^2^/s^2^). It is thus equal to 10^−7^ joules or 100 nanojoules (nJ) in SI units.
- 1 erg = `{{val|e=-7|ul=J}}`{=mediawiki} = `{{val|100|ul=nJ}}`{=mediawiki}
- 1 erg = `{{val|e=-10|u=sn⋅m}}`{=mediawiki} = `{{val|100|u=psn⋅m}}`{=mediawiki} = `{{val|100|u=pico[[sthène]]-metres}}`{=mediawiki}
- 1 erg = `{{val|624.15|u=GeV}}`{=mediawiki} = `{{val|6.2415|e=11|ul=eV}}`{=mediawiki}
- 1 erg = `{{val|1|u=[[dyne|dyn]]⋅cm}}`{=mediawiki} = `{{val|1|u=g⋅cm<sup>2</sup>/s<sup>2</sup>}}`{=mediawiki}
- 1 erg = 1.000000 erg
## History
In 1864, Rudolf Clausius proposed the Greek word *ἐργον* (`{{Transliteration|grc|ergon}}`{=mediawiki}) for the unit of energy, work and heat. In 1873, a committee of the British Association for the Advancement of Science, including British physicists James Clerk Maxwell and William Thomson recommended the general adoption of the centimetre, the gramme, and the second as fundamental units (C.G.S. System of Units). To distinguish derived units, they recommended using the prefix \"C.G.S. unit of \...\" and requested that the word *erg* or *ergon* be strictly limited to refer to the *C.G.S. unit of energy*.
In 1922, chemist William Draper Harkins proposed the name micri-erg as a convenient unit to measure the surface energy of molecules in surface chemistry. It would equate to 10^−14^ erg, the equivalent to 10^−21^ joule.
The erg is not a part of the International System of Units (SI), which has been recommended since 1 January 1978 when the European Economic Community ratified a directive of 1971 that implemented SI as agreed by the General Conference of Weights and Measures. It is the unit of energy in Gaussian units, which are widely used in astrophysics`{{better source needed|reason=User-generated content|date=July 2021}}`{=mediawiki}, applications involving microscopic problems and relativistic electrodynamics, and sometimes in mechanics
| 332 |
Erg
| 0 |
9,883 |
# Eurocard (printed circuit board)
**Eurocard** is an IEEE standard format for printed circuit board (PCB) cards that can be plugged together into a standard chassis which, in turn, can be mounted in a 19-inch rack. The chassis consists of a series of slotted card guides on the top and bottom, into which the cards are slid so they stand on end, like books on a shelf. At the spine of each card is one or more connectors which plug into mating connectors on a backplane that closes the rear of the chassis.
## Dimensions
As the cards are assumed to be installed in a vertical orientation, the usual meanings of height and width are transposed: A card might be 233.35 mm \"high\", but only 20 mm \"wide\". Height is measured in rack units, \"U\", with 1 U being 1.75 in. This dimension refers to the subrack in which the card is to be mounted, rather than the card itself.
A single card is 100 mm high. Taller cards add a 133.35 mm, so that a double height card is 233.35 mm high and a triple 366.7 mm high.
Enclosure heights are multiples of 3U, with the cards always 33.35 mm shorter than the enclosure. Two common heights are 3U (a 100 mm card in a 5.25 in subrack) and 6U (a 233.35 mm card in a 10.5 in high subrack). As two 3U cards are shorter than a 6U card (by 33.35 mm), it is possible to install two 3U cards in one slot of a 6U subrack, with a mid-height structure for proper support.
Card widths are specified in horizontal pitch units \"HP\", with 1 HP being 0.20 in.
Card depths start at 100 mm and increase in 60 mm increments. The most common today is 160 mm, but standard hardware is available for depths of 100 mm, 160 mm, 220 mm, 280 mm, 340 mm, and 400 mm.
+-----------------------+-----+-----+-----+-----+-----+----------------+---------+
| | | | | | | ↑\ | ↑\ |
| | | | | | | 366.7\ | board\ |
| | | | | | | Triple-height\ | height\ |
| | | | | | | (9U) subrack | +0/−0.3 |
+-----------------------+-----+-----+-----+-----+-----+----------------+---------+
| | | | | | | ↑\ | |
| | | | | | | 233.35\ | |
| | | | | | | Double-height\ | |
| | | | | | | (6U) subrack | |
+-----------------------+-----+-----+-----+-----+-----+----------------+---------+
| | | | | | | ↑\ | |
| | | | | | | 100\ | |
| | | | | | | Single-height\ | |
| | | | | | | (3U) subrack | |
+-----------------------+-----+-----+-----+-----+-----+----------------+---------+
| ←\ | ←\ | ←\ | ←\ | ←\ | ←\ | | |
| 400 | 340 | 280 | 220 | 160 | 100 | | |
+-----------------------+-----+-----+-----+-----+-----+----------------+---------+
| ← board depth +0/−0.3 | | | | | | | |
+-----------------------+-----+-----+-----+-----+-----+----------------+---------+
: Valid Eurocard sizes. Dimensions in mm. Connectors on the right.
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# Eurocard (printed circuit board)
## Standards and architecture {#standards_and_architecture}
The Eurocard mechanical architecture was defined originally under IEC-60297-3. Today, the most widely recognized standards for this mechanical structure are IEEE 1101.1, IEEE 1101.10 (also known commonly as \"dot ten\") and IEEE 1101.11. IEEE 1101.10 covers the additional mechanical and electromagnetic interference features required for VITA 1.1-1997(R2002), which is the VME64 Extensions standard, as well as PICMG 2.0 (R3.0), which is the CompactPCI specification.
The IEEE 1101.11 standard covers rear plug-in units that are also called rear transition modules or RTMs.
The Eurocard is a mechanical system and does not define the specific connector to be used or the signals that are assigned to connector contacts.
The connector systems that are commonly used with Eurocard architectures include the original DIN 41612 connector that is also standardized as IEC 60603.2. This is the connector that is used for the VMEbus standard, which was IEEE 1014. The connector known as the 5-row DIN, which is used for the VME64 Extensions standard is IEC 61076-4-113. The VME64 Extension architecture defined by VITA 1.1-1997 (R2002).
Another popular computer architecture that utilizes the 6U-160 Eurocard is CompactPCI and CompactPCI Express. These are defined by PICMG 2.0R3 and PICMG Exp0 R1 respectively. Other computer architectures that utilize the Eurocard system are VME eXtensions for Instrumentation (VXI), PCI eXtensions for Instrumentation (PXI), and PXI Express.
A computer architecture that used the 6U-220 Eurocard format was Multibus-II, which was IEEE 1296.
Because the Eurocard system provided for so many modular card sizes and because connector manufacturers have continued to create new connectors that are compatible with this system, it is a popular mechanical standard that is also used for innumerable \"one-off\" applications.
Conduction-cooled Eurocards are used in military and aerospace applications. They are defined by the IEEE 1101.2-1992 (2001) standard.
The Eurocard standard is also the basis of the \"Eurorack\" format for modular electronic music synthesizers, popularized by Doepfer and other manufacturers
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# Eureka, Missouri
**Eureka** is a city mainly in St. Louis County, with a small portion in Jefferson County, Missouri, adjacent to Wildwood and Pacific. It is in the extreme southwest of the Greater St. Louis metro area. As of the 2020 census, the city had a population of 11,646. Since 1971, Eureka has been known as the home of the amusement park Six Flags St. Louis.
## History
The area\'s first known inhabitants were Shawnee Native Americans on the banks of the Meramec River; archaeological artifacts can still be found today as evidence of their past occupation of the area.
The village of Eureka was platted in 1858 along the route of the Pacific Railroad. By 1890, the village consisted of about 100 homes. As railroad workers cleared the way for the track, they saw level land with little to clear and declared \"Eureka!\" which is Greek for \"I\'ve found it.\" Thus, Eureka was founded. In 1898, Eureka became home to the St. Louis Children\'s Industrial Farm, established to give children from St. Louis tenement neighborhoods a chance to experience life in a rural setting. It later became Camp Wyman (now part of Wyman Center) and is one of the oldest camps in the United States. The first high school class in Eureka was held in 1909. Eureka was incorporated as a fourth-class city on April 7, 1954.
Historically, Eureka was wholly within St. Louis County. In September 2019, the city\'s Board of Aldermen voted to annex two commercial lots---one of them a 72.5-acre tract that houses Kirkwood Materials West, a sand and gravel quarry, and the other a 75-acre field, both at highways 109 and FF---located just across the Meramec River in Jefferson County into the city. On October 1, 2019, the city voted to annex the under construction 549-home Windswept Farms subdivision just to the south into the city. Both annexations were voluntary by the owners.
### City of Allenton {#city_of_allenton}
The railroad town of Allenton is a former community on U.S. Route 66 located (now) at the junction of Interstate 44 and Business Loop 44 in western St. Louis County. In 1985, it was annexed by the city of Eureka. The town is currently rural, with adjacent farmland and forested Ozark ridges. This community was declared blighted by St. Louis County in 1973.
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# Eureka, Missouri
## Geography
According to the United States Census Bureau, the city has a total area of 10.45 sqmi, of which 10.35 sqmi is land, and 0.10 sqmi is water.
### Floods
The city of Eureka has suffered multiple floods, the two most catastrophic being in 2015 and 2017. This caused the city and U.S. Army Corps of Engineers to evaluate a dozen strategic options, from the use of levees and walls, buyouts of high-risk properties, and the restoration of flood plain as water storage. Scientific researchers determined the flooding was a man-made calamity caused in part by \"inaccurate Federal Emergency Management Agency flood frequencies based on the assumption that today\'s river will behave as it has in the past greatly underestimating our real flood risk and leading to inappropriate development in floodways and floodplains.\"
#### 2015
The December 2015 North American storm complex deeply impacted the state of Missouri, with heavy rain and snow causing severe floods. The storm system was responsible for heavy rain that caused severe flooding. Parts of the state were hit with over 10 in of heavy rainfall. In Eureka, more than 100 boat rescues were conducted by the Eureka Fire Department of people and several pets from the second stories of homes near the Meramec River.
#### 2017 {#section_1}
A flooding event caused by a strong spring storm system brought multiple rounds of thunderstorms and heavy rain to portions of the Midwest the weekend of April 29--30, 2017. The middle portion of the Mississippi approached historical record flooding. The National Weather Service anticipated a 48.5 ft. crest at Cape Girardeau, Missouri, on May 5, 2017, which was within 6 inches of the January 2, 2016 crest of 48.86 ft. The first floor of a church flooded with about 48 inches of water, the same amount as in December 2015. Floodwater from the Meramec River covered athletic fields at Eureka High School, encroached on the school\'s buildings, and ruined the gymnasium floor.
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# Eureka, Missouri
## Demographics
### 2020 census
The 2020 United States census counted 11,646 people, 3,486 households, and 2,575 families in Eureka. The population density was 1,053.9 per square mile (406.9/km`{{sup|2}}`{=mediawiki}). There were 3,740 housing units at an average density of 338.5 per square mile (130.7/km`{{sup|2}}`{=mediawiki}). The racial makeup was 90.73% (10,566) White, 0.82% (96) Black or African-American, 0.12% (14) Native American, 1.57% (183) Asian, 0.05% (6) Pacific Islander, 0.76% (89) from other races, and 5.94% (692) from two or more races. Hispanic or Latino of any race was 2.1% (211) of the population.
Of the 3,486 households, 40.5% had children under the age of 18; 64.5% were married couples living together; 16.1% had a female householder with no husband present. Of all households, 20.1% consisted of individuals, and 11.4% had someone living alone who was 65 years of age or older. The average household size was 2.8, and the average family size was 3.4.
26.4% of the population was under the age of 18, 3.9% from 18 to 24, 20.4% from 25 to 44, 24.1% from 45 to 64, and 12.9% who were 65 years of age or older. The median age was 39.8 years. For every 100 females, the population had 109.5 males. For every 100 females ages 18 and older, there were 98.5 males.
The 2016-2020 5-year American Community Survey estimates show that the median household income was \$112,750 (with a margin of error of +/- \$13,390) and the median family income was \$121,977 (+/- \$8,559). Males had a median income of \$74,452 (+/- \$8,634) versus \$47,137 (+/- \$8,637) for females. The median income for those above 16 years old was \$59,316 (+/- \$9,813). Approximately, 0.0% of families and 0.6% of the population were below the poverty line, including 0.0% of those under the age of 18 and 0.8% of those ages 65 or over.
### 2010 census {#census_1}
As of the 2010 census, there were 10,189 people, 3,474 households, and 2,758 families residing in the city. The population density was 984.4 PD/sqmi. There were 3,683 housing units at an average density of 355.8 /sqmi. The racial makeup of the city was 94.9% White, 0.8% African American, 0.2% Native American, 1.9% Asian, 0.1% Pacific Islander, 0.3% from other races, and 1.7% from two or more races. Hispanic or Latino of any race were 2.0% of the population.
There were 3,474 households, of which 46.9% had children under the age of 18 living with them, 66.2% were married couples living together, 9.3% had a female householder with no husband present, 3.9% had a male householder with no wife present, and 20.6% were non-families. 17.2% of all households were made up of individuals, and 5.9% had someone living alone who was 65 years of age or older. The average household size was 2.87, and the average family size was 3.27.
The median age in the city was 37.1 years. 30.9% of residents were under the age of 18; 6% were between the ages of 18 and 24; 26.6% were from 25 to 44; 26.7% were from 45 to 64, and 9.6% were 65 years of age or older. The gender makeup of the city was 49.6% male and 50.4% female.
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# Eureka, Missouri
## Demographics
### 2000 census {#census_2}
As of the 2000 census, there were 7,676 people in the city, organized into 2,487 households and two families. Its population density was 763.7 PD/sqmi. There were 2,622 housing units at an average density of 260.9 /sqmi. The racial makeup of the city was 97.38% White, 0.82% Asian, 0.57% Black or African American, 0.20% Native American, no Pacific Islanders, 0.26% from other races, and 0.77% from two or more races. 1.22% of the population were Hispanic or Latino of any race.
There were 2,487 households, out of which half had children under the age of 18 living with them, 71.6% were married couples living together, 8.2% had a female householder with no husband present, and 17.0% were non-families. 13.8% of all households were made up of individuals, and 4.3% had someone living alone who was 65 years of age or older. The average household size was 2.98, and the average family size was 3.30.
In the city, the population was spread out, with 31.9% under the age of 18, 5.7% from 18 to 24, 34.4% from 25 to 44, 19.5% from 45 to 64, and 8.5% 65 years of age or older. The median age was 34 years. For every 100 females, there were 94.9 males. For every 100 females age 18 and over, there were 89.6 males.
The median income for a household in the city was \$74,301, and the median income for a family was \$80,625. Males had a median income of \$51,799 compared to \$33,269 for females. The per capita income for the city was \$27,553. 2.2% of the population and 1.3% of families were below the poverty line. Out of the total population, 3.1% of those under the age of 18 and 5.9% of those 65 and older were living below the poverty line.
## Education
Rockwood R-Vi School District operates three elementary schools, Lasalle Springs Middle School, and Eureka High School.
The city also contains two private schools: St. Mark\'s Lutheran Church and School and Most Sacred Heart Church and School.
The city has the Eureka Hills Branch lending library, a branch of the St. Louis County Library. It was moved to a newly built location that opened on June 2, 2021.
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# Eureka, Missouri
## News media {#news_media}
Local news coverage for the town and some of its neighbors is provided by the *Tri-County Journal*, the *Eureka and Pacific Current NewsMagazine*, and the *Washington Missourian*.
## Notable people {#notable_people}
- Clayton Echard, undrafted rookie for the Seattle Seahawks and star of season 26 of *The Bachelor*
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# Equation of state
In physics and chemistry, an **equation of state** is a thermodynamic equation relating state variables, which describe the state of matter under a given set of physical conditions, such as pressure, volume, temperature, or internal energy. Most modern equations of state are formulated in the Helmholtz free energy. Equations of state are useful in describing the properties of pure substances and mixtures in liquids, gases, and solid states as well as the state of matter in the interior of stars. Though there are many equations of state, none accurately predicts properties of substances under all conditions. The quest for a universal equation of state has spanned three centuries. `{{Thermodynamics|cTopic=[[Thermodynamic system|Systems]]}}`{=mediawiki} `{{toclimit|limit=3}}`{=mediawiki}
## Overview
At present, there is no single equation of state that accurately predicts the properties of all substances under all conditions. An example of an equation of state correlates densities of gases and liquids to temperatures and pressures, known as the ideal gas law, which is roughly accurate for weakly polar gases at low pressures and moderate temperatures. This equation becomes increasingly inaccurate at higher pressures and lower temperatures, and fails to predict condensation from a gas to a liquid.
The general form of an equation of state may be written as $f(p, V, T) = 0$
where $p$ is the pressure, $V$ the volume, and $T$ the temperature of the system. Yet also other variables may be used in that form. It is directly related to Gibbs phase rule, that is, the number of independent variables depends on the number of substances and phases in the system.
An equation used to model this relationship is called an equation of state. In most cases this model will comprise some empirical parameters that are usually adjusted to measurement data. Equations of state can also describe solids, including the transition of solids from one crystalline state to another. Equations of state are also used for the modeling of the state of matter in the interior of stars, including neutron stars, dense matter (quark--gluon plasmas) and radiation fields. A related concept is the perfect fluid equation of state used in cosmology.
Equations of state are applied in many fields such as process engineering and petroleum industry as well as pharmaceutical industry.
Any consistent set of units may be used, although SI units are preferred. Absolute temperature refers to the use of the Kelvin (K), with zero being absolute zero.
- $n$, number of moles of a substance
- $V_m$, $\frac{V}{n}$, molar volume, the volume of 1 mole of gas or liquid
- $R$, ideal gas constant ≈ 8.3144621 J/mol·K
- $p_c$, pressure at the critical point
- $V_c$, molar volume at the critical point
- $T_c$, absolute temperature at the critical point
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# Equation of state
## Historical background {#historical_background}
Equations of state essentially begin three centuries ago with the history of the ideal gas law:
$pV = nRT$
Boyle\'s law was one of the earliest formulation of an equation of state. In 1662, the Irish physicist and chemist Robert Boyle performed a series of experiments employing a J-shaped glass tube, which was sealed on one end. Mercury was added to the tube, trapping a fixed quantity of air in the short, sealed end of the tube. Then the volume of gas was measured as additional mercury was added to the tube. The pressure of the gas could be determined by the difference between the mercury level in the short end of the tube and that in the long, open end. Through these experiments, Boyle noted that the gas volume varied inversely with the pressure. In mathematical form, this can be stated as$$pV = \mathrm{constant}.$$The above relationship has also been attributed to Edme Mariotte and is sometimes referred to as Mariotte\'s law. However, Mariotte\'s work was not published until 1676.
In 1787 the French physicist Jacques Charles found that oxygen, nitrogen, hydrogen, carbon dioxide, and air expand to roughly the same extent over the same 80-kelvin interval. This is known today as Charles\'s law. Later, in 1802, Joseph Louis Gay-Lussac published results of similar experiments, indicating a linear relationship between volume and temperature$$\frac{V_1}{T_1} = \frac{V_2}{T_2}.$$Dalton\'s law (1801) of partial pressure states that the pressure of a mixture of gases is equal to the sum of the pressures of all of the constituent gases alone.
Mathematically, this can be represented for $n$ species as$$p_\text{total} = p_1 + p_2 + \cdots + p_n = \sum_{i=1}^n p_i.$$In 1834, Émile Clapeyron combined Boyle\'s law and Charles\' law into the first statement of the *ideal gas law*. Initially, the law was formulated as *pV~m~* = *R*(*T~C~* + 267) (with temperature expressed in degrees Celsius), where *R* is the gas constant. However, later work revealed that the number should actually be closer to 273.2, and then the Celsius scale was defined with $0~^{\circ}\mathrm{C} = 273.15~\mathrm{K}$, giving$$pV_m = R \left(T_C + 273.15\ {}^\circ\text{C}\right).$$In 1873, J. D. van der Waals introduced the first equation of state derived by the assumption of a finite volume occupied by the constituent molecules. His new formula revolutionized the study of equations of state, and was the starting point of cubic equations of state, which most famously continued via the Redlich--Kwong equation of state and the Soave modification of Redlich-Kwong.
The van der Waals equation of state can be written as
$\left(P+a\frac1{V_m^2}\right)(V_m-b)=R T$ where $a$ is a parameter describing the attractive energy between particles and $b$ is a parameter describing the volume of the particles.
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# Equation of state
## Ideal gas law {#ideal_gas_law}
### Classical ideal gas law {#classical_ideal_gas_law}
The classical ideal gas law may be written $pV = nRT.$
In the form shown above, the equation of state is thus $f(p, V, T) = pV - nRT = 0.$
If the calorically perfect gas approximation is used, then the ideal gas law may also be expressed as follows $p = \rho(\gamma - 1)e$ where $\rho$ is the number density of the gas (number of atoms/molecules per unit volume), $\gamma = C_p/C_v$ is the (constant) adiabatic index (ratio of specific heats), $e = C_v T$ is the internal energy per unit mass (the \"specific internal energy\"), $C_v$ is the specific heat capacity at constant volume, and $C_p$ is the specific heat capacity at constant pressure.
### Quantum ideal gas law {#quantum_ideal_gas_law}
Since for atomic and molecular gases, the classical ideal gas law is well suited in most cases, let us describe the equation of state for elementary particles with mass $m$ and spin $s$ that takes into account quantum effects. In the following, the upper sign will always correspond to Fermi--Dirac statistics and the lower sign to Bose--Einstein statistics. The equation of state of such gases with $N$ particles occupying a volume $V$ with temperature $T$ and pressure $p$ is given by
$p= \frac{(2s+1)\sqrt{2m^3k_\text{B}^5T^5}}{3\pi^2\hbar^3}\int_0^\infty\frac{z^{3/2}\,\mathrm{d}z}{e^{z-\mu/(k_\text{B} T)}\pm 1}$ where $k_\text{B}$ is the Boltzmann constant and $\mu(T,N/V)$ the chemical potential is given by the following implicit function $\frac{N}{V}=\frac{(2s+1)(m k_\text{B}T)^{3/2}}{\sqrt 2\pi^2\hbar^3}\int_0^\infty\frac{z^{1/2}\,\mathrm{d}z}{e^{z-\mu / (k_\text{B} T)}\pm 1}.$
In the limiting case where $e^{\mu / (k_\text{B} T)}\ll 1$, this equation of state will reduce to that of the classical ideal gas. It can be shown that the above equation of state in the limit $e^{\mu/(k_\text{B} T)}\ll 1$ reduces to
$pV = N k_\text{B} T\left[1\pm\frac{\pi^{3/2}}{2(2s+1)} \frac{N\hbar^3}{V(m k_\text{B} T)^{3/2}}+\cdots\right]$
With a fixed number density $N/V$, decreasing the temperature causes in Fermi gas, an increase in the value for pressure from its classical value implying an effective repulsion between particles (this is an apparent repulsion due to quantum exchange effects not because of actual interactions between particles since in ideal gas, interactional forces are neglected) and in Bose gas, a decrease in pressure from its classical value implying an effective attraction. The quantum nature of this equation is in it dependence on s and **ħ**.
## Cubic equations of state {#cubic_equations_of_state}
Cubic equations of state are called such because they can be rewritten as a cubic function of $V_m$. Cubic equations of state originated from the van der Waals equation of state. Hence, all cubic equations of state can be considered \'modified van der Waals equation of state\'. There is a very large number of such cubic equations of state. For process engineering, cubic equations of state are today still highly relevant, e.g. the Peng Robinson equation of state or the Soave Redlich Kwong equation of state.
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# Equation of state
## Virial equations of state {#virial_equations_of_state}
### Virial equation of state {#virial_equation_of_state}
$\frac{pV_m}{RT} = A + \frac{B}{V_m} + \frac{C}{V_m^2} + \frac{D}{V_m^3} + \cdots$
Although usually not the most convenient equation of state, the virial equation is important because it can be derived directly from statistical mechanics. This equation is also called the Kamerlingh Onnes equation. If appropriate assumptions are made about the mathematical form of intermolecular forces, theoretical expressions can be developed for each of the coefficients. *A* is the first virial coefficient, which has a constant value of 1 and makes the statement that when volume is large, all fluids behave like ideal gases. The second virial coefficient *B* corresponds to interactions between pairs of molecules, *C* to triplets, and so on. Accuracy can be increased indefinitely by considering higher order terms. The coefficients *B*, *C*, *D*, etc. are functions of temperature only.
### The BWR equation of state {#the_bwr_equation_of_state}
$\begin{align}
p = \rho RT &+
\left(B_0 RT - A_0 - \frac{C_0}{T^2} + \frac{D_0}{T^3} - \frac{E_0}{T^4}\right) \rho^2 +
\left(bRT - a - \frac{d}{T}\right) \rho^3 \\[2pt] &+
\alpha\left(a + \frac{d}{T}\right) \rho^6 +
\frac{c\rho^3}{T^2}\left(1 + \gamma\rho^2\right)\exp\left(-\gamma\rho^2\right)
\end{align}$
where
- $p$ is pressure
- $\rho$ is molar density
Values of the various parameters can be found in reference materials. The BWR equation of state has also frequently been used for the modelling of the Lennard-Jones fluid. There are several extensions and modifications of the classical BWR equation of state available.
The Benedict--Webb--Rubin--Starling equation of state is a modified BWR equation of state and can be written as $\begin{align}
p = \rho RT &+ \left(B_0 RT-A_0 - \frac{C_0}{T^2} + \frac{D_0}{T^3} - \frac{E_0}{T^4}\right) \rho^2 \\[2pt]
&+ \left(bRT-a-\frac{d}{T} + \frac{c}{T^2}\right) \rho^3 + \alpha\left(a+\frac{d}{T}\right) \rho^6
\end{align}$
Note that in this virial equation, the fourth and fifth virial terms are zero. The second virial coefficient is monotonically decreasing as temperature is lowered. The third virial coefficient is monotonically increasing as temperature is lowered.
The Lee--Kesler equation of state is based on the corresponding states principle, and is a modification of the BWR equation of state.
$p = \frac{RT}{V} \left( 1 + \frac{B}{V_r} + \frac{C}{V_r^2} + \frac{D}{V_r^5} + \frac{c_4}{T_r^3 V_r^2} \left( \beta + \frac{\gamma}{V_r^2} \right) \exp \left( -\frac{\gamma}{V_r^2} \right) \right)$
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# Equation of state
## Physically based equations of state {#physically_based_equations_of_state}
There is a large number of physically based equations of state available today. Most of those are formulated in the Helmholtz free energy as a function of temperature, density (and for mixtures additionally the composition). The Helmholtz energy is formulated as a sum of multiple terms modelling different types of molecular interaction or molecular structures, e.g. the formation of chains or dipolar interactions. Hence, physically based equations of state model the effect of molecular size, attraction and shape as well as hydrogen bonding and polar interactions of fluids. In general, physically based equations of state give more accurate results than traditional cubic equations of state, especially for systems containing liquids or solids. Most physically based equations of state are built on monomer term describing the Lennard-Jones fluid or the Mie fluid.
### Perturbation theory-based models {#perturbation_theory_based_models}
Perturbation theory is frequently used for modelling dispersive interactions in an equation of state. There is a large number of perturbation theory based equations of state available today, e.g. for the classical Lennard-Jones fluid. The two most important theories used for these types of equations of state are the Barker-Henderson perturbation theory and the Weeks--Chandler--Andersen perturbation theory.
### Statistical associating fluid theory (SAFT) {#statistical_associating_fluid_theory_saft}
An important contribution for physically based equations of state is the statistical associating fluid theory (SAFT) that contributes the Helmholtz energy that describes the association (a.k.a. hydrogen bonding) in fluids, which can also be applied for modelling chain formation (in the limit of infinite association strength). The SAFT equation of state was developed using statistical mechanical methods (in particular the perturbation theory of Wertheim) to describe the interactions between molecules in a system. The idea of a SAFT equation of state was first proposed by Chapman et al. in 1988 and 1989. Many different versions of the SAFT models have been proposed, but all use the same chain and association terms derived by Chapman et al.
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# Equation of state
## Multiparameter equations of state {#multiparameter_equations_of_state}
Multiparameter equations of state are empirical equations of state that can be used to represent pure fluids with high accuracy. Multiparameter equations of state are empirical correlations of experimental data and are usually formulated in the Helmholtz free energy. The functional form of these models is in most parts not physically motivated. They can be usually applied in both liquid and gaseous states. Empirical multiparameter equations of state represent the Helmholtz energy of the fluid as the sum of ideal gas and residual terms. Both terms are explicit in temperature and density: $\frac{a(T, \rho)}{RT} =
\frac{a^\mathrm{ideal\,gas}(\tau, \delta) + a^\textrm{residual}(\tau, \delta)}{RT}$ with $\tau = \frac{T_r}{T}, \delta = \frac{\rho}{\rho_r}$
The reduced density $\rho_r$ and reduced temperature $T_r$ are in most cases the critical values for the pure fluid. Because integration of the multiparameter equations of state is not required and thermodynamic properties can be determined using classical thermodynamic relations, there are few restrictions as to the functional form of the ideal or residual terms. Typical multiparameter equations of state use upwards of 50 fluid specific parameters, but are able to represent the fluid\'s properties with high accuracy. Multiparameter equations of state are available currently for about 50 of the most common industrial fluids including refrigerants. The IAPWS95 reference equation of state for water is also a multiparameter equations of state. Mixture models for multiparameter equations of state exist, as well. Yet, multiparameter equations of state applied to mixtures are known to exhibit artifacts at times.
One example of such an equation of state is the form proposed by Span and Wagner.
$\begin{align}
a^\mathrm{residual} ={}& \sum_{i=1}^8 \sum_{j=-8}^{12} n_{i,j} \delta^i \tau^{j/8}
+ \sum_{i=1}^5 \sum_{j=-8}^{24} n_{i,j} \delta^i \tau^{j/8} \exp\left(-\delta\right) \\
&+ \sum_{i=1}^5 \sum_{j=16}^{56} n_{i,j} \delta^i \tau^{j/8} \exp\left(-\delta^2\right)
+ \sum_{i=2}^4 \sum_{j=24}^{38} n_{i,j} \delta^i \tau^{j/2} \exp\left(-\delta^3\right)
\end{align}$
This is a somewhat simpler form that is intended to be used more in technical applications. Equations of state that require a higher accuracy use a more complicated form with more terms.
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# Equation of state
## List of further equations of state {#list_of_further_equations_of_state}
### Stiffened equation of state {#stiffened_equation_of_state}
When considering water under very high pressures, in situations such as underwater nuclear explosions, sonic shock lithotripsy, and sonoluminescence, the stiffened equation of state is often used:
$p = \rho(\gamma - 1)e - \gamma p^0 \,$
where $e$ is the internal energy per unit mass, $\gamma$ is an empirically determined constant typically taken to be about 6.1, and $p^0$ is another constant, representing the molecular attraction between water molecules. The magnitude of the correction is about 2 gigapascals (20,000 atmospheres).
The equation is stated in this form because the speed of sound in water is given by $c^2 = \gamma\left(p + p^0\right)/\rho$.
Thus water behaves as though it is an ideal gas that is *already* under about 20,000 atmospheres (2 GPa) pressure, and explains why water is commonly assumed to be incompressible: when the external pressure changes from 1 atmosphere to 2 atmospheres (100 kPa to 200 kPa), the water behaves as an ideal gas would when changing from 20,001 to 20,002 atmospheres (2000.1 MPa to 2000.2 MPa).
This equation mispredicts the specific heat capacity of water but few simple alternatives are available for severely nonisentropic processes such as strong shocks.
### Morse oscillator equation of state {#morse_oscillator_equation_of_state}
An equation of state of Morse oscillator has been derived, and it has the following form:
$p = \Gamma_1 \nu + \Gamma_2 \nu^2$
Where $\Gamma_1$ is the first order virial parameter and it depends on the temperature, $\Gamma_2$ is the second order virial parameter of Morse oscillator and it depends on the parameters of Morse oscillator in addition to the absolute temperature. $\nu$ is the fractional volume of the system.
### Ultrarelativistic equation of state {#ultrarelativistic_equation_of_state}
An ultrarelativistic fluid has equation of state $p = \rho_m c_s^2$ where $p$ is the pressure, $\rho_m$ is the mass density, and $c_s$ is the speed of sound.
### Ideal Bose equation of state {#ideal_bose_equation_of_state}
The equation of state for an ideal Bose gas is
$p V_m =
RT~\frac{\operatorname{Li}_{\alpha+1}(z)}{\zeta(\alpha)}
\left(\frac{T}{T_c}\right)^\alpha$
where *α* is an exponent specific to the system (e.g. in the absence of a potential field, α = 3/2), *z* is exp(*μ*/*k*~B~*T*) where *μ* is the chemical potential, Li is the polylogarithm, ζ is the Riemann zeta function, and *T*~*c*~ is the critical temperature at which a Bose--Einstein condensate begins to form.
### Jones--Wilkins--Lee equation of state for explosives (JWL equation) {#joneswilkinslee_equation_of_state_for_explosives_jwl_equation}
The equation of state from Jones--Wilkins--Lee is used to describe the detonation products of explosives. $p = A \left( 1 - \frac{\omega}{R_1 V} \right) \exp(-R_1 V) + B \left( 1 - \frac{\omega}{R_2 V} \right) \exp\left(-R_2 V\right) + \frac{\omega e_0}{V}$
The ratio $V = \rho_e / \rho$ is defined by using $\rho_e$, which is the density of the explosive (solid part) and $\rho$, which is the density of the detonation products. The parameters $A$, $B$, $R_1$, $R_2$ and $\omega$ are given by several references. In addition, the initial density (solid part) $\rho_0$, speed of detonation $V_D$, Chapman--Jouguet pressure $P_{CJ}$ and the chemical energy per unit volume of the explosive $e_0$ are given in such references. These parameters are obtained by fitting the JWL-EOS to experimental results. Typical parameters for some explosives are listed in the table below.
Material $\rho_e\,$ (g/cm^3^) $v_D\,$ (m/s) $p_{CJ}\,$ (GPa) $A\,$ (GPa) $B\,$ (GPa) $R_1$ $R_2$ $\omega$ $e_0\,$ (GPa)
--------------- ---------------------- --------------- ------------------ ------------- ------------- ------- ------- ---------- ---------------
TNT 1.630 6930 21.0 373.8 3.747 4.15 0.90 0.35 6.00
Composition B 1.717 7980 29.5 524.2 7.678 4.20 1.10 0.35 8.50
PBX 9501 1.844 36.3 852.4 18.02 4.55 1.3 0.38 10.2
### Others
- Tait equation for water and other liquids. Several equations are referred to as the **Tait equation**
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# Societas Europaea
A ***societas Europaea*** (`{{IPA|la-x-classic|sɔˈkɪ.ɛtaːs eu̯roːˈpae̯.a|lang|link=yes}}`{=mediawiki}, `{{IPA|la-x-church|soˈtʃi.etas eu̯roˈpe.a|lang|link=yes}}`{=mediawiki}; \"European society\" or \"company\"; plural: *\'\'\'societates Europaeae\'\'\'*; abbr. **SE**) is a public company registered in accordance with the corporate law of the European Union (EU), introduced in 2004 with the Council Regulation on the Statute for a European Company. Such a company may more easily transfer to or merge with companies in other member states.
As of April 2018, more than 3,000 registrations had been reported. Several of the Euro Stoxx 50 stock market index of leading eurozone companies have been registered as SE: Airbus, Allianz, BASF, E.ON, Fresenius, LVMH Moët Hennessy Louis Vuitton (and its subsidiary Dior), SAP, Schneider Electric, TotalEnergies, Unibail-Rodamco-Westfield and Vonovia.
National law continues to supplement the basic rules in the Regulation on formation and mergers. The European Company Regulation is complemented by an Employee Involvement Directive which manages the rules for participation by employees on the company\'s board of directors. There is also a statute allowing European Cooperative Societies.
## Formation
[The statute](https://eur-lex.europa.eu/EN/legal-content/summary/statute-for-a-european-company.html) provides five ways of forming a European limited company:
1. By merger of national companies from different member states
2. By creation of a European limited company as a parent company in a holding structure of joint stock companies and limited liability companies from different member states
3. By the creation of a joint venture between companies (or other entities) in different member states
4. By the creation of an SE subsidiary of a national company
5. By the conversion of a national company into an SE
Formation by merger is available only to public limited companies from different member states. Formation of an SE holding company is available to public and private limited companies with their registered offices in different member states or having subsidiaries or branches in member states other than that of their registered office. Formation of a joint subsidiary is available under the same circumstances to any legal entities governed by public or private law.
## Minimum capital {#minimum_capital}
The SE must have a minimum subscribed capital of €120,000 as per article 4(2) of the directive, subject to the provision that where a member state requires a larger capital for companies exercising certain types of activities, the same requirement will also apply to an SE with its registered office in that member state (article 4(3)).
## Registered office {#registered_office}
The registered office of the SE designated in the statutes must be the place where it has its central administration, that is to say its true centre of operations. The SE may transfer its registered office within the European Economic Area without dissolving the company in one member state in order to form a new one in another member state; however, such a transfer is subject to the provisions of 8 which require, inter alia, the drawing up of a transfer proposal, a report justifying the legal and economic aspects of the transfer and the issuing, by the competent authority in the member state in which the SE is registered, of a certificate attesting to the completion of the required acts and formalities.
## Laws applicable {#laws_applicable}
The order of precedence of the laws applicable to the SE is clarified.
## Registration and liquidation {#registration_and_liquidation}
The registration and completion of the liquidation of an SE must be disclosed for information purposes in the Official Journal of the European Communities. Every SE must be registered in the state where it has its registered office, in a register designated by the law of that state.
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# Societas Europaea
## Statutes
The statutes of the SE must provide as governing bodies the annual general meeting of shareholders and either a management board and a supervisory board (two-tier system) or an administrative board (single-tier system). Under the two-tier system the SE is managed by a management board. The member or members of the management board have the power to represent the company in dealings with third parties and in legal proceedings. They are appointed and removed by the supervisory board. No person may be a member of both the management board and the supervisory board of the same company at the same time. But the supervisory board may appoint one of its members to exercise the functions of a member of the management board in the event of absence through holidays. During such a period the function of the person concerned as a member of the supervisory board shall be suspended. Under the single-tier system, the SE is managed by an administrative board. The member or members of the administrative board have the power to represent the company in dealings with third parties and in legal proceedings. Under the single-tier system the administrative board may delegate the power of management to one or more of its members.
The following operations require the authorization of the supervisory board or the deliberation of the administrative board:
- any investment project requiring an amount more than the percentage of subscribed capital
- the conclusion of supply and performance contracts where the total turnover provided for therein is more than the percentage of turnover for the previous financial year
- the raising or granting of loans, the issue of debt securities and the assumption of liabilities of a third party or suretyship for a third party where the total money value in each case is more than the percentage of subscribed capital
- the setting-up, acquisition, disposal or closing down of undertakings, businesses or parts of businesses where the purchase price or disposal proceeds account for more than the percentage of subscribed capital
- the percentage referred to above is to be determined by the statutes of the SE. It may not be less than 5% nor more than 25%.
## Annual accounts {#annual_accounts}
The SE must draw up annual accounts comprising the balance sheet, the profit and loss account, and the notes to the accounts, and an annual report giving a fair view of the company\'s business and of its position; consolidated accounts may also be required.
## Taxation
In tax matters, the SE is treated the same as any other multinational, i.e., it is subject to the tax regime of the national legislation applicable to the company and its subsidiaries. SEs are subject to taxes and charges in all member states where their administrative centres are situated.
## Winding-up {#winding_up}
Winding-up, liquidation, insolvency, and suspension of payments are in large measure to be governed by national law. When an SE transfers its registered office outside the Community, or in any other manner no longer complies with requirements of article 7, the member state must take appropriate measures to ensure compliance or take necessary measures to ensure that the SE is liquidated.
## Status of the legislation and implementation {#status_of_the_legislation_and_implementation}
- Council Regulation (EC) No 2157/2001 of 8 October 2001 on the Statute for a European company (SE).
- Council Directive 2001/86/EC of 8 October 2001 supplementing the Statute for a European company with regard to the involvement of employees.
See also: Europa\'s collection of press releases, regulations, directives and FAQs on the European Company Statute.
### United Kingdom {#united_kingdom}
Following the withdrawal of the UK from the European Union, any SE registered in the United Kingdom converted to a United Kingdom *Societas* and **UK Societas** replaced SE in its name. UK Societas retain many of the elements from the SE framework but importantly without the ability to transfer their registered office outside of the UK.
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# Societas Europaea
## Employee participation {#employee_participation}
The regulation is complemented by the **Council Directive supplementing the Statute for a European Company with regard to the involvement of employees** (informally \"Council Directive on Employee Participation\"), adopted 8 October 2001. The directive establishes rules on worker involvement in the management of the SE.
EU member states differ in the degree of worker involvement in corporate management. In Germany, most large corporations are required to allow employees to elect a certain percentage of seats on the supervisory board. Other member states have no such requirement, and furthermore in these states such practices are largely unknown and considered a threat to the rights of management.
These differing traditions of worker involvement have held back the adoption of the statute for over a decade. States without worker involvement provisions were afraid that the SE might lead to having such provisions being imposed on their companies; and states with those provisions were afraid they might lead to those provisions being circumvented.
A compromise, contained in the directive, was worked out as follows: worker involvement provisions in the SE will be decided upon by negotiations between employees and management before the creation of the SE. If agreement cannot be reached, provisions contained in the directive will apply. The directive provides for worker involvement in the SE if a minimum percentage of employees from the entities coming together to form the SE enjoyed worker involvement provisions. The directive permits member states to not implement these default worker involvement provisions in their national law, but then an SE cannot be created in that member state if the provisions in the directive would apply and negotiations between workers and management are unsuccessful.
### Definition
Definition of employee participation: it does not mean participation in day-to-day decisions, which are a matter for the management, but participation in the supervision and strategic development of the company.
### Participation
- If the two parties do not reach a satisfactory arrangement, a set of standard principles set out in the annex to the directive becomes applicable.
- Several models of participation are possible: firstly, a model in which the employees form part of the supervisory board or of the administrative board, as the case may be; secondly, a model in which the employees are represented by a separate body; and finally, other models to be agreed between the management or administrative boards of the founder companies and the employees or their representatives in those companies, the level of information and consultation being the same as in the case of the second model. The general meeting may not approve the formation of an SE unless one of the models of participation defined in the directive has been chosen.
- The employees\' representatives must be provided with such financial and material resources and other facilities as enable them to perform their duties properly.
- With regard to a European company formed through a merger, the standard principles relating to worker participation will apply where at least 25% of the employees had the right to participate in decisions before the merger. Here a political agreement proved impossible until the Nice summit in December 2000. The compromise adopted by the heads of state or governments allowed a member state not to apply the directive to SEs formed from a merger, in which case the SE could not be registered in the member state in question unless an agreement had been concluded between the management and employees, or that no SE employee had the right of participation before the formation of the SE.
### Employment contracts and pensions {#employment_contracts_and_pensions}
Employment contracts and pensions are not covered by the directive. With regard to occupational pension schemes, the SE is covered by the provisions laid down in the proposal for a directive on institutions for occupational schemes, presented by the Commission in October 2000, in particular in connection with the possibility of introducing a single pension scheme for all their employees in the European Union.
## Development
Two approaches have been attempted to solve the problems cited above. One approach is to harmonise the company law of the member states. This approach has had some successes, but after thirty years only limited progress has been made. It is difficult to harmonise widely different regulatory systems, especially when they reflect different national attitudes to issues such as worker involvement in the management of the company.
The other approach is to construct a whole new system of EU company law, that co-exists with the individual company laws of the member states. Companies would have the choice of operating either under national regulations or under the EU-wide system. However, this approach has been only somewhat more effective than the harmonization approach: while states are not as concerned about having foreign traditions of corporate governance imposed on their companies, which the harmonization approach could well entail; they also wish to ensure that the EU-wide system would be palatable to the traditions of their national companies, so that they will not be put at a disadvantage compared to the other member states.
The European Company Statute represents a step in this direction, albeit a limited one. While it establishes some common EU rules on the SE, these rules are incomplete, and the holes in the rules are to be filled in using the law of the member state in which the SE is registered. This has been due to the difficulties of agreeing on common European rules on these issues.
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# Societas Europaea
## Registrations
As of 11 April 2018, 3,015 registrations have been made. In terms of registrations, the Czech Republic is vastly overrepresented, accounting for 79% of all *Societates Europaeae* as of December 2015. 9 of the 50 constituents of the Euro Stoxx 50 stock market index of leading eurozone companies were Societates Europaeae in 2015. On 8 October 2004, Dutch company MPIT Structured Financial Services was registered as Europe\'s first SE company.
Annual registrations by member state are presented in the following chart: {{ <Graph:Chart> \| type=stackedrect \| height = 200 \| width = 500 \| legend = \| yAxisTitle = Registrations \| y1 = 0 , 4 , 15 , 24 , 34 , 25 , 39 , 35 , 53 , 41 , 48 , 45 \| y2 = 0 , 0 , 0 , 19 , 91 , 93 , 136 , 275 , 426 , 378 , 191 , 125 \| y3 = 0 , 1 , 0 , 1 , 3 , 13 , 15 , 15 , 20 , 28 , 10 , 13 \| y4 = 7 , 8 , 13 , 32 , 30 , 26 , 11 , 31 , 30 , 14 , 15 , 30 \| colors = red , yellow , blue , gray \|yGrid= \| y1Title = Germany \|y2Title= Czech Republic \|y3Title= Slovakia \|y4Title= Other member states \| xAxisTitle = Year \| x = 2004 , 2005 , 2006 , 2007 , 2008 , 2009 , 2010 , 2011 , 2012 , 2013 , 2014 , 2015 }} `{{Pie chart
|caption=Sectors in which ''societates'' with more than five employees have been registered (2014)<ref>{{cite web|url=http://www.worker-participation.eu/European-Company-SE/Facts-Figures|title=Facts & Figures / European Company (SE) / Home - WORKER PARTICIPATION.eu|last=Cleverway|website=www.worker-participation.eu}}</ref>
|label1=Financial services
|value1=21
|color1=#0084ff
|label2=Services commerce
|value2=18
|color2=white
|label3=Metal
|value3=15
|color3=#1abb45
|label4=Chemical
|value4=11
|color4=#d00000
|label5=Other services
|value5=9
|color5=yellow
|label6=Information technology
|value6=7
|color6=pink
|label7=Other
|value7=5
|color7=silver
|label8=Construction industry
|value8=5
|color8=black
|label9=Food, hotel and catering
|value9=4
|color9=orange
|label10=Unknown
|value10=3
|color10=gray
|label11=Transport
|value11=2
|color11=red}}`{=mediawiki} Registrations of new *societates* are to be published in the *Official Journal of the European Union*. There is no official union-wide register of *societates*, as they are registered in the nation in which their corporate seats are located. *[worker-participation.eu](http://ecdb.worker-participation.eu)* does however maintain a database of current and planned registrations. Examples of companies include: `{{Legend|#ADD8E6|Components of the [[Euro Stoxx 50]] [[stock market index]] of leading [[eurozone]] companies}}`{=mediawiki}
+-------------------------------------+---------------------+
| Name | State in which the\ |
| | company is seated |
+=====================================+=====================+
| Airbus SE | |
+-------------------------------------+---------------------+
| Atos SE | |
+-------------------------------------+---------------------+
| AmRest SE | |
+-------------------------------------+---------------------+
| Aixtron SE | |
+-------------------------------------+---------------------+
| Axel Springer SE | |
+-------------------------------------+---------------------+
| Autopistas de Puerto Rico | |
+-------------------------------------+---------------------+
| Allianz SE | |
+-------------------------------------+---------------------+
| BASF SE | |
+-------------------------------------+---------------------+
| Bilfinger SE | |
+-------------------------------------+---------------------+
| Christian Dior SE | |
+-------------------------------------+---------------------+
| Colt CZ Group | |
+-------------------------------------+---------------------+
| Conrad Electronic | |
+-------------------------------------+---------------------+
| Dassault Systèmes | |
+-------------------------------------+---------------------+
| Deutsche Börse | |
+-------------------------------------+---------------------+
| E.ON SE | |
+-------------------------------------+---------------------+
| EPEX SPOT | |
+-------------------------------------+---------------------+
| Ferrovial SE | |
+-------------------------------------+---------------------+
| Fresenius SE | |
+-------------------------------------+---------------------+
| Getlink | |
+-------------------------------------+---------------------+
| Gfk SE | |
+-------------------------------------+---------------------+
| Graphisoft SE | |
+-------------------------------------+---------------------+
| KWS Saat SE | |
+-------------------------------------+---------------------+
| OHB SE | |
+-------------------------------------+---------------------+
| Puma SE | |
+-------------------------------------+---------------------+
| LVMH Moët Hennessy Louis Vuitton SE | |
+-------------------------------------+---------------------+
| MAN SE | |
+-------------------------------------+---------------------+
| New Work SE | |
+-------------------------------------+---------------------+
| Nordex SE | |
+-------------------------------------+---------------------+
| Porsche Automobil Holding SE | |
+-------------------------------------+---------------------+
| Rocket Internet | |
+-------------------------------------+---------------------+
| Hannover Rück SE | |
+-------------------------------------+---------------------+
| Vapiano SE | |
+-------------------------------------+---------------------+
| Senvion SE | |
+-------------------------------------+---------------------+
| HAWE Hydraulik SE | |
+-------------------------------------+---------------------+
| ADVA Optical Networking SE | |
+-------------------------------------+---------------------+
| Equens SE | |
+-------------------------------------+---------------------+
| Dekra SE | |
+-------------------------------------+---------------------+
| SGL Carbon SE | |
+-------------------------------------+---------------------+
| Prosafe SE | |
+-------------------------------------+---------------------+
| ProSiebenSat
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# Eubulides
**Eubulides** (*Εὐβουλίδης*; fl. 4th century BCE) of Miletus was a philosopher of the Megarian school who is famous for his paradoxes.
## Life
According to Diogenes Laërtius, Eubulides was a pupil of Euclid of Megara, the founder of the Megarian school. He was a contemporary of Aristotle, against whom he wrote with great bitterness. He taught logic to Demosthenes, and he is also said to have taught Apollonius Cronus, the teacher of Diodorus Cronus, and the historian Euphantus.
## Paradoxes of Eubulides {#paradoxes_of_eubulides}
Eubulides is most famous for inventing the forms of seven famous paradoxes, some of which, however, are also ascribed to Diodorus Cronus:
1. The Liar (*pseudomenos*) paradox:\
A man says: \"What I am saying now is a lie.\" If the statement is true, then he is lying, even though the statement is true. If the statement is a lie, then he is not actually lying, even though the statement is a lie. Thus, if the speaker is lying, he tells the truth, and vice versa.
2. The Masked Man (*enkekalymmenos*) paradox:\
\"Do you know this masked man?\" \"No.\" \"But he is your father. So -- do you not know your own father?\"
3. The Electra (*Elektra*) paradox:\
Electra doesn\'t know that the man approaching her is her brother, Orestes. Electra knows her brother. Does Electra know the man who is approaching?
4. The Overlooked Man (*dialanthanôn*) paradox:\
Alpha ignored the man approaching him and treated him as a stranger. The man was his father. Did Alpha ignore his own father and treat him as a stranger?
5. The Heap (*sôritês*) paradox:\
A single grain of sand is certainly not a heap. Nor is the addition of a single grain of sand enough to transform a non-heap into a heap: when we have a collection of grains of sand that is not a heap, then adding but one single grain will not create a heap. And yet we know that at some point we will have a heap.
6. The Bald Man (*phalakros*) paradox:\
A man with a full head of hair is obviously not bald. Now the removal of a single hair will not turn a non-bald man into a bald one. And yet it is obvious that a continuation of that process must eventually result in baldness.
7. The Horns (*keratinês*) paradox:\
What you have not lost, you have. But you have not lost horns. Therefore, you have horns.
The first paradox (the Liar) is probably the most famous, and is similar to the famous paradox of Epimenides the Cretan. The second, third and fourth paradoxes are variants of a single paradox and relate to the problem of what it means to \"know\" something and the identity of objects involved in an affirmation (compare the masked-man fallacy). The fifth and sixth paradoxes are also a single paradox and is usually thought to relate to the vagueness of language. The final paradox, the horns, is a paradox related to presupposition.
## Legacy
These paradoxes were very well known in ancient times, some are alluded to by Eubulides\' contemporary Aristotle and even partially by Plato. Chrysippus, the Stoic philosopher wrote about the paradoxes developed by Eubulides and characterized the Horns paradox as an intractable problem (aporoi logoi). Aulus Gellius mentions how the discussion of such paradoxes was considered (for him) after-dinner entertainment at the Saturnalia, but Seneca, on the other hand, considered them a waste of time: \"Not to know them does no harm, and mastering them does no good
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# Amplifier
An **amplifier**, **electronic amplifier** or (informally) **amp** is an electronic device that can increase the magnitude of a signal (a time-varying voltage or current). It is a two-port electronic circuit that uses electric power from a power supply to increase the amplitude (magnitude of the voltage or current) of a signal applied to its input terminals, producing a proportionally greater amplitude signal at its output. The amount of amplification provided by an amplifier is measured by its gain: the ratio of output voltage, current, or power to input. An amplifier is defined as a circuit that has a power gain greater than one.
An amplifier can be either a separate piece of equipment or an electrical circuit contained within another device. Amplification is fundamental to modern electronics, and amplifiers are widely used in almost all electronic equipment. Amplifiers can be categorized in different ways. One is by the frequency of the electronic signal being amplified. For example, audio amplifiers amplify signals of less than 20 kHz, radio frequency (RF) amplifiers amplify frequencies in the range between 20 kHz and 300 GHz, and servo amplifiers and instrumentation amplifiers may work with very low frequencies down to direct current. Amplifiers can also be categorized by their physical placement in the signal chain; a preamplifier may precede other signal processing stages, for example, while a power amplifier is usually used after other amplifier stages to provide enough output power for the final use of the signal. The first practical electrical device which could amplify was the triode vacuum tube, invented in 1906 by Lee De Forest, which led to the first amplifiers around 1912. Today most amplifiers use transistors.
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# Amplifier
## History
### Vacuum tubes {#vacuum_tubes}
The first practical prominent device that could amplify was the triode vacuum tube, invented in 1906 by Lee De Forest, which led to the first amplifiers around 1912. Vacuum tubes were used in almost all amplifiers until the 1960s--1970s when transistors replaced them. Today, most amplifiers use transistors, but vacuum tubes continue to be used in some applications. thumb\|upright=0.7\|De Forest\'s prototype audio amplifier of 1914. The Audion (triode) vacuum tube had a voltage gain of about 5, providing a total gain of approximately 125 for this three-stage amplifier.
The development of audio communication technology in form of the telephone, first patented in 1876, created the need to increase the amplitude of electrical signals to extend the transmission of signals over increasingly long distances. In telegraphy, this problem had been solved with intermediate devices at stations that replenished the dissipated energy by operating a signal recorder and transmitter back-to-back, forming a relay, so that a local energy source at each intermediate station powered the next leg of transmission. For duplex transmission, i.e. sending and receiving in both directions, bi-directional relay repeaters were developed starting with the work of C. F. Varley for telegraphic transmission. Duplex transmission was essential for telephony and the problem was not satisfactorily solved until 1904, when H. E. Shreeve of the American Telephone and Telegraph Company improved existing attempts at constructing a telephone repeater consisting of back-to-back carbon-granule transmitter and electrodynamic receiver pairs. The Shreeve repeater was first tested on a line between Boston and Amesbury, MA, and more refined devices remained in service for some time. After the turn of the century it was found that negative resistance mercury lamps could amplify, and were also tried in repeaters, with little success.
The development of thermionic valves which began around 1902, provided an entirely electronic method of amplifying signals. The first practical version of such devices was the Audion triode, invented in 1906 by Lee De Forest, which led to the first amplifiers around 1912. Since the only previous device which was widely used to strengthen a signal was the relay used in telegraph systems, the amplifying vacuum tube was first called an *electron relay*. The terms *amplifier* and *amplification*, derived from the Latin *amplificare*, (*to enlarge or expand*), were first used for this new capability around 1915 when triodes became widespread.
The amplifying vacuum tube revolutionized electrical technology. It made possible long-distance telephone lines, public address systems, radio broadcasting, talking motion pictures, practical audio recording, radar, television, and the first computers. For 50 years virtually all consumer electronic devices used vacuum tubes. Early tube amplifiers often had positive feedback (regeneration), which could increase gain but also make the amplifier unstable and prone to oscillation. Much of the mathematical theory of amplifiers was developed at Bell Telephone Laboratories during the 1920s to 1940s. Distortion levels in early amplifiers were high, usually around 5%, until 1934, when Harold Black developed negative feedback; this allowed the distortion levels to be greatly reduced, at the cost of lower gain. Other advances in the theory of amplification were made by Harry Nyquist and Hendrik Wade Bode.
The vacuum tube was virtually the only amplifying device, other than specialized power devices such as the magnetic amplifier and amplidyne, for 40 years. Power control circuitry used magnetic amplifiers until the latter half of the twentieth century when power semiconductor devices became more economical, with higher operating speeds. The old Shreeve electroacoustic carbon repeaters were used in adjustable amplifiers in telephone subscriber sets for the hearing impaired until the transistor provided smaller and higher quality amplifiers in the 1950s.
### Transistors
The first working transistor was a point-contact transistor invented by John Bardeen and Walter Brattain in 1947 at Bell Labs, where William Shockley later invented the bipolar junction transistor (BJT) in 1948. They were followed by the invention of the metal--oxide--semiconductor field-effect transistor (MOSFET) by Mohamed M. Atalla and Dawon Kahng at Bell Labs in 1959. Due to MOSFET scaling, the ability to scale down to increasingly small sizes, the MOSFET has since become the most widely used amplifier.
The replacement of bulky electron tubes with transistors during the 1960s and 1970s created a revolution in electronics, making possible a large class of portable electronic devices, such as the transistor radio developed in 1954. Today, use of vacuum tubes is limited to some high power applications, such as radio transmitters, as well as some musical instrument and high-end audiophile amplifiers.
Beginning in the 1970s, more and more transistors were connected on a single chip thereby creating higher scales of integration (such as small-scale, medium-scale and large-scale integration) in integrated circuits. Many amplifiers commercially available today are based on integrated circuits.
For special purposes, other active elements have been used. For example, in the early days of the satellite communication, parametric amplifiers were used. The core circuit was a diode whose capacitance was changed by an RF signal created locally. Under certain conditions, this RF signal provided energy that was modulated by the extremely weak satellite signal received at the earth station.
Advances in digital electronics since the late 20th century provided new alternatives to the conventional linear-gain amplifiers by using digital switching to vary the pulse-shape of fixed amplitude signals, resulting in devices such as the Class-D amplifier.
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# Amplifier
## Theory of Operation {#theory_of_operation}
In principle, an amplifier is an electrical two-port network that produces a signal at the output port that is a replica of the signal applied to the input port, but increased in magnitude.
The input port can be idealized as either being a voltage input, which takes no current, with the output proportional to the voltage across the port; or a current input, with no voltage across it, in which the output is proportional to the current through the port. The output port can be idealized as being either a dependent voltage source, with zero source resistance and its output voltage dependent on the input; or a dependent current source, with infinite source resistance and the output current dependent on the input. Combinations of these choices lead to four types of ideal amplifiers. In idealized form they are represented by each of the four types of dependent source used in linear analysis, as shown in the figure, namely:
Input Output Dependent source Amplifier type Gain units
------- -------- ----------------------------------------- ---------------------------- ------------
I I Current controlled current source, CCCS Current amplifier Unitless
I V Current controlled voltage source, CCVS Transresistance amplifier Ohm
V I Voltage controlled current source, VCCS Transconductance amplifier Siemens
V V Voltage controlled voltage source, VCVS Voltage amplifier Unitless
Each type of amplifier in its ideal form has an ideal input and output resistance that is the same as that of the corresponding dependent source:
Amplifier type Dependent source Input impedance Output impedance
------------------ ------------------ ----------------- ------------------
Current CCCS 0 ∞
Transresistance CCVS 0 0
Transconductance VCCS ∞ ∞
Voltage VCVS ∞ 0
In real amplifiers the ideal impedances are not possible to achieve, but these ideal elements can be used to construct equivalent circuits of real amplifiers by adding impedances (resistance, capacitance and inductance) to the input and output. For any particular circuit, a small-signal analysis is often used to find the actual impedance. A small-signal AC test current *I~x~* is applied to the input or output node, all external sources are set to AC zero, and the corresponding alternating voltage *V~x~* across the test current source determines the impedance seen at that node as *R = V~x~ / I~x~*.
Amplifiers designed to attach to a transmission line at input and output, especially RF amplifiers, do not fit into this classification approach. Rather than dealing with voltage or current individually, they ideally couple with an input or output impedance matched to the transmission line impedance, that is, match *ratios* of voltage to current. Many real RF amplifiers come close to this ideal. Although, for a given appropriate source and load impedance, RF amplifiers can be characterized as amplifying voltage or current, they fundamentally are amplifying power.
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# Amplifier
## Properties
Amplifier properties are given by parameters that include:
- Gain, the ratio between the magnitude of output and input signals
- Bandwidth, the width of the useful frequency range
- Efficiency, the ratio between the power of the output and total power consumption
- Linearity, the extent to which the proportion between input and output amplitude is the same for high amplitude and low amplitude input
- Noise, a measure of undesired noise mixed into the output
- Output dynamic range, the ratio of the largest and the smallest useful output levels
- Slew rate, the maximum rate of change of the output
- Rise time, settling time, ringing and overshoot that characterize the step response
- Stability, the ability to avoid self-oscillation
Amplifiers are described according to the properties of their inputs, their outputs, and how they relate. All amplifiers have gain, a multiplication factor that relates the magnitude of some property of the output signal to a property of the input signal. The gain may be specified as the ratio of output voltage to input voltage (voltage gain), output power to input power (power gain), or some combination of current, voltage, and power. In many cases the property of the output that varies is dependent on the same property of the input, making the gain unitless (though often expressed in decibels (dB)).
Most amplifiers are designed to be linear. That is, they provide constant gain for any normal input level and output signal. If an amplifier\'s gain is not linear, the output signal can become distorted. There are, however, cases where variable gain is useful. Certain signal processing applications use exponential gain amplifiers.
Amplifiers are usually designed to function well in a specific application, for example: radio and television transmitters and receivers, high-fidelity (\"hi-fi\") stereo equipment, microcomputers and other digital equipment, and guitar and other instrument amplifiers. Every amplifier includes at least one active device, such as a vacuum tube or transistor.
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# Amplifier
## Negative feedback {#negative_feedback}
Negative feedback is a technique used in most modern amplifiers to increase bandwidth, reduce distortion, and control gain. In a negative feedback amplifier part of the output is fed back and added to the input in the opposite phase, subtracting from the input. The main effect is to reduce the overall gain of the system. However, any unwanted signals introduced by the amplifier, such as distortion are also fed back. Since they are not part of the original input, they are added to the input in opposite phase, subtracting them from the input. In this way, negative feedback also reduces nonlinearity, distortion and other errors introduced by the amplifier. Large amounts of negative feedback can reduce errors to the point that the response of the amplifier itself becomes almost irrelevant as long as it has a large gain, and the output performance of the system (the \"closed loop performance\") is defined entirely by the components in the feedback loop. This technique is used particularly with operational amplifiers (op-amps).
Non-feedback amplifiers can achieve only about 1% distortion for audio-frequency signals. With negative feedback, distortion can typically be reduced to 0.001%. Noise, even crossover distortion, can be practically eliminated. Negative feedback also compensates for changing temperatures, and degrading or nonlinear components in the gain stage, but any change or nonlinearity in the components in the feedback loop will affect the output. Indeed, the ability of the feedback loop to define the output is used to make active filter circuits.
Another advantage of negative feedback is that it extends the bandwidth of the amplifier. The concept of feedback is used in operational amplifiers to precisely define gain, bandwidth, and other parameters entirely based on the components in the feedback loop.
Negative feedback can be applied at each stage of an amplifier to stabilize the operating point of active devices against minor changes in power-supply voltage or device characteristics.
Some feedback, positive or negative, is unavoidable and often undesirable---introduced, for example, by parasitic elements, such as inherent capacitance between input and output of devices such as transistors, and capacitive coupling of external wiring. Excessive frequency-dependent positive feedback can produce parasitic oscillation and turn an amplifier into an oscillator.
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# Amplifier
## Categories
### Active devices {#active_devices}
All amplifiers include some form of active device: this is the device that does the actual amplification. The active device can be a vacuum tube, discrete solid state component, such as a single transistor, or part of an integrated circuit, as in an op-amp.
Transistor amplifiers (or solid state amplifiers) are the most common type of amplifier in use today. A transistor is used as the active element. The gain of the amplifier is determined by the properties of the transistor itself as well as the circuit it is contained within.
Common active devices in transistor amplifiers include bipolar junction transistors (BJTs) and metal oxide semiconductor field-effect transistors (MOSFETs).
Applications are numerous. Some common examples are audio amplifiers in a home stereo or public address system, RF high power generation for semiconductor equipment, to RF and microwave applications such as radio transmitters.
Transistor-based amplification can be realized using various configurations: for example a bipolar junction transistor can realize common base, common collector or common emitter amplification; a MOSFET can realize common gate, common source or common drain amplification. Each configuration has different characteristics.
Vacuum-tube amplifiers (also known as tube amplifiers or valve amplifiers) use a vacuum tube as the active device. While semiconductor amplifiers have largely displaced valve amplifiers for low-power applications, valve amplifiers can be much more cost effective in high power applications such as radar, countermeasures equipment, and communications equipment. Many microwave amplifiers are specially designed valve amplifiers, such as the klystron, gyrotron, traveling wave tube, and crossed-field amplifier, and these microwave valves provide much greater single-device power output at microwave frequencies than solid-state devices. Vacuum tubes remain in use in some high end audio equipment, as well as in musical instrument amplifiers, due to a preference for \"tube sound\".
Magnetic amplifiers are devices somewhat similar to a transformer where one winding is used to control the saturation of a magnetic core and hence alter the impedance of the other winding. They have largely fallen out of use due to development in semiconductor amplifiers but are still useful in HVDC control, and in nuclear power control circuitry due to not being affected by radioactivity.
Negative resistances can be used as amplifiers, such as the tunnel diode amplifier.
### Power amplifiers {#power_amplifiers}
A power amplifier is an amplifier designed primarily to increase the power available to a load. In practice, amplifier power gain depends on the source and load impedances, as well as the inherent voltage and current gain. A radio frequency (RF) amplifier design typically optimizes impedances for power transfer, while audio and instrumentation amplifier designs normally optimize input and output impedance for least loading and highest signal integrity. An amplifier that is said to have a gain of 20 dB might have a voltage gain of 20 dB and an available power gain of much more than 20 dB (power ratio of 100)---yet actually deliver a much lower power gain if, for example, the input is from a 600 Ω microphone and the output connects to a 47 kΩ input socket for a power amplifier. In general, the power amplifier is the last \'amplifier\' or actual circuit in a signal chain (the output stage) and is the amplifier stage that requires attention to power efficiency.
Audio power amplifiers are typically used to drive loudspeakers. They will often have two output channels and deliver equal power to each. An RF power amplifier is found in radio transmitter final stages. A servo motor controller amplifies a control voltage to adjust the speed of a motor, or the position of a motorized system.
Power amplifier circuits (output stages) are classified as A, B, AB and C for analog designs---and class D and E for switching designs. The power amplifier classes are based on the proportion of each input cycle (conduction angle) during which an amplifying device passes current. The image of the conduction angle derives from amplifying a sinusoidal signal. If the device is always on, the conducting angle is 360°. If it is on for only half of each cycle, the angle is 180°. The angle of flow is closely related to the amplifier power efficiency.
### Operational amplifiers (op-amps) {#operational_amplifiers_op_amps}
*Main article: Operational amplifier, Instrumentation amplifier*`{{Unreferenced section|date=December 2024}}`{=mediawiki} An operational amplifier is an amplifier circuit which typically has very high open loop gain and differential inputs. Op amps have become very widely used as standardized \"gain blocks\" in circuits due to their versatility; their gain, bandwidth and other characteristics can be controlled by feedback through an external circuit. Though the term today commonly applies to integrated circuits, the original operational amplifier design used valves, and later designs used discrete transistor circuits.
A fully differential amplifier is similar to the operational amplifier, but also has differential outputs. These are usually constructed using BJTs or FETs.
### Distributed amplifiers {#distributed_amplifiers}
These use balanced transmission lines to separate individual single stage amplifiers, the outputs of which are summed by the same transmission line. The transmission line is a balanced type with the input at one end and on one side only of the balanced transmission line and the output at the opposite end is also the opposite side of the balanced transmission line. The gain of each stage adds linearly to the output rather than multiplies one on the other as in a cascade configuration. This allows a higher bandwidth to be achieved than could otherwise be realised even with the same gain stage elements.
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# Amplifier
## Categories
### Switched mode amplifiers {#switched_mode_amplifiers}
These nonlinear amplifiers have much higher efficiencies than linear amps, and are used where the power saving justifies the extra complexity. Class-D amplifiers are the main example of this type of amplification.
### Negative resistance amplifier {#negative_resistance_amplifier}
A negative resistance amplifier is a type of regenerative amplifier that can use the feedback between the transistor\'s source and gate to transform a capacitive impedance on the transistor\'s source to a negative resistance on its gate. Compared to other types of amplifiers, a negative resistance amplifier will require only a tiny amount of power to achieve very high gain, maintaining a good noise figure at the same time.
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# Amplifier
## Applications
### Video amplifiers {#video_amplifiers}
Video amplifiers are designed to process video signals and have varying bandwidths depending on whether the video signal is for SDTV, EDTV, HDTV 720p or 1080i/p etc. The specification of the bandwidth itself depends on what kind of filter is used---and at which point (`{{nowrap|−1 dB}}`{=mediawiki} or `{{nowrap|−3 dB}}`{=mediawiki} for example) the bandwidth is measured. Certain requirements for step response and overshoot are necessary for an acceptable TV image.
### Microwave amplifiers {#microwave_amplifiers}
Traveling wave tube amplifiers (TWTAs) are used for high power amplification at low microwave frequencies. They typically can amplify across a broad spectrum of frequencies; however, they are usually not as tunable as klystrons.
Klystrons are specialized linear-beam vacuum-devices, designed to provide high power, widely tunable amplification of millimetre and sub-millimetre waves. Klystrons are designed for large scale operations and despite having a narrower bandwidth than TWTAs, they have the advantage of coherently amplifying a reference signal so its output may be precisely controlled in amplitude, frequency and phase.
Solid-state devices such as silicon short channel MOSFETs like double-diffused metal--oxide--semiconductor (DMOS) FETs, GaAs FETs, SiGe and GaAs heterojunction bipolar transistors/HBTs, HEMTs, IMPATT diodes, and others, are used especially at lower microwave frequencies and power levels on the order of watts specifically in applications like portable RF terminals/cell phones and access points where size and efficiency are the drivers. New materials like gallium nitride (GaN) or GaN on silicon or on silicon carbide/SiC are emerging in HEMT transistors and applications where improved efficiency, wide bandwidth, operation roughly from few to few tens of GHz with output power of few watts to few hundred of watts are needed.
Depending on the amplifier specifications and size requirements microwave amplifiers can be realised as monolithically integrated, integrated as modules or based on discrete parts or any combination of those.
The maser is a non-electronic microwave amplifier.
### Musical instrument amplifiers {#musical_instrument_amplifiers}
Instrument amplifiers are a range of audio power amplifiers used to increase the sound level of musical instruments, for example guitars, during performances. An amplifier\'s tone mainly comes from the order and amount in which it applies EQ and distortion.
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# Amplifier
## Classification of amplifier stages and systems {#classification_of_amplifier_stages_and_systems}
### Common terminal {#common_terminal}
One set of classifications for amplifiers is based on which device terminal is common to both the input and the output circuit. In the case of bipolar junction transistors, the three classes are common emitter, common base, and common collector. For field-effect transistors, the corresponding configurations are common source, common gate, and common drain; for vacuum tubes, common cathode, common grid, and common plate.
The common emitter (or common source, common cathode, etc.) is most often configured to provide amplification of a voltage applied between base and emitter, and the output signal taken between collector and emitter is inverted, relative to the input. The common collector arrangement applies the input voltage between base and collector, and to take the output voltage between emitter and collector. This causes negative feedback, and the output voltage tends to follow the input voltage. This arrangement is also used as the input presents a high impedance and does not load the signal source, though the voltage amplification is less than one. The common-collector circuit is, therefore, better known as an emitter follower, source follower, or cathode follower.
### Unilateral or bilateral {#unilateral_or_bilateral}
An amplifier whose output exhibits no feedback to its input side is described as \'unilateral\'. The input impedance of a unilateral amplifier is independent of load, and output impedance is independent of signal source impedance.
An amplifier that uses feedback to connect part of the output back to the input is a *bilateral* amplifier. Bilateral amplifier input impedance depends on the load, and output impedance on the signal source impedance. All amplifiers are bilateral to some degree; however they may often be modeled as unilateral under operating conditions where feedback is small enough to neglect for most purposes, simplifying analysis (see the common base article for an example).
### Inverting or non-inverting {#inverting_or_non_inverting}
Another way to classify amplifiers is by the phase relationship of the input signal to the output signal. An \'inverting\' amplifier produces an output 180 degrees out of phase with the input signal (that is, a polarity inversion or mirror image of the input as seen on an oscilloscope). A \'non-inverting\' amplifier maintains the phase of the input signal waveforms. An emitter follower is a type of non-inverting amplifier, indicating that the signal at the emitter of a transistor is following (that is, matching with unity gain but perhaps an offset) the input signal. Voltage follower is also non-inverting type of amplifier having unity gain.
This description can apply to a single stage of an amplifier, or to a complete amplifier system.
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# Amplifier
## Classification of amplifier stages and systems {#classification_of_amplifier_stages_and_systems}
### Function
Other amplifiers may be classified by their function or output characteristics. These functional descriptions usually apply to complete amplifier systems or sub-systems and rarely to individual stages.
- A **servo amplifier** indicates an integrated feedback loop to actively control the output at some desired level. A DC servo indicates use at frequencies down to DC levels, where the rapid fluctuations of an audio or RF signal do not occur. These are often used in mechanical actuators, or devices such as DC motors that must maintain a constant speed or torque. An **AC servo** amp. can do this for some AC motors.
- A **linear** amplifier responds to different frequency components independently, and does not generate harmonic distortion or intermodulation distortion. No amplifier can provide *perfect* linearity (even the most linear amplifier has some nonlinearities, since the amplifying devices---transistors or vacuum tubes---follow nonlinear power laws such as square-laws and rely on circuitry techniques to reduce those effects).
- A **nonlinear** amplifier generates significant distortion and so changes the harmonic content; there are situations where this is useful. Amplifier circuits intentionally providing a non-linear transfer function include:
- a device like a silicon controlled rectifier or a transistor used as a switch may be employed to turn either fully *on* or *off* a load such as a lamp based on a threshold in a continuously variable input.
- a non-linear amplifier in an analog computer or true RMS converter for example can provide a special transfer function, such as logarithmic or square-law.
- a Class C RF amplifier may be chosen because it can be very efficient---but is non-linear. Following such an amplifier with a so-called *tank* tuned circuit can reduce unwanted harmonics (distortion) sufficiently to make it useful in transmitters, or some desired harmonic may be selected by setting the resonant frequency of the tuned circuit to a higher frequency rather than fundamental frequency in frequency multiplier circuits.
- Automatic gain control circuits require an amplifier\'s gain be controlled by the time-averaged amplitude so that the output amplitude varies little when weak stations are being received. The non-linearities are assumed arranged so the relatively small signal amplitude suffers from little distortion (cross-channel interference or intermodulation) yet is still modulated by the relatively large gain-control DC voltage.
- AM detector circuits that use amplification such as anode-bend detectors, precision rectifiers and infinite impedance detectors (so excluding *unamplified* detectors such as cat\'s-whisker detectors), as well as peak detector circuits, rely on changes in amplification based on the signal\'s instantaneous amplitude to derive a direct current from an alternating current input.
- Operational amplifier comparator and detector circuits.
- A **wideband** amplifier has a precise amplification factor over a wide frequency range, and is often used to boost signals for relay in communications systems. A **narrowband** amp amplifies a specific narrow range of frequencies, to the exclusion of other frequencies.
- An **RF** amplifier amplifies signals in the radio frequency range of the electromagnetic spectrum, and is often used to increase the sensitivity of a receiver or the output power of a transmitter.
- An **audio amplifier** amplifies audio frequencies. This category subdivides into small signal amplification, and power amps that are optimised to driving speakers, sometimes with multiple amps grouped together as separate or bridgeable channels to accommodate different audio reproduction requirements. Frequently used terms within audio amplifiers include:
- Preamplifier (preamp.), which may include a phono stage with RIAA equalization, or tape head preamps with CCIR equalisation filters. They may include filters or tone control circuitry.
- Power amplifier (normally drives loudspeakers), headphone amplifiers, and public address amplifiers.
- Stereo amplifiers imply two channels of output (left and right), though the term simply means \"solid\" sound (referring to three-dimensional)---so quadraphonic stereo was used for amplifiers with four channels. 5.1 and 7.1 systems refer to Home theatre systems with 5 or 7 normal spatial channels, plus a subwoofer channel.
- Buffer amplifiers, which may include emitter followers, provide a high impedance input for a device (perhaps another amplifier, or perhaps an energy-hungry load such as lights) that would otherwise draw too much current from the source. Line drivers are a type of buffer that feeds long or interference-prone interconnect cables, possibly with differential outputs through twisted pair cables.
### Interstage coupling method {#interstage_coupling_method}
Amplifiers are sometimes classified by the coupling method of the signal at the input, output, or between stages. Different types of these include:
Resistive-capacitive (RC) coupled amplifier, using a network of resistors and capacitors: By design these amplifiers cannot amplify DC signals as the capacitors block the DC component of the input signal. RC-coupled amplifiers were used very often in circuits with vacuum tubes or discrete transistors. In the days of the integrated circuit a few more transistors on a chip are much cheaper and smaller than a capacitor.\
Inductive-capacitive (LC) coupled amplifier, using a network of inductors and capacitors: This kind of amplifier is most often used in selective radio-frequency circuits.\
Transformer coupled amplifier, using a transformer to match impedances or to decouple parts of the circuits :Quite often LC-coupled and transformer-coupled amplifiers cannot be distinguished as a transformer is some kind of inductor.\
Direct coupled amplifier, using no impedance and bias matching components: This class of amplifier was very uncommon in the vacuum tube days when the anode (output) voltage was at greater than several hundred volts and the grid (input) voltage at a few volts minus. So they were used only if the gain was specified down to DC (e.g., in an oscilloscope). In the context of modern electronics developers are encouraged to use directly coupled amplifiers whenever possible. In FET and CMOS technologies direct coupling is dominant since gates of MOSFETs theoretically pass no current through themselves. Therefore, DC component of the input signals is automatically filtered.
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# Amplifier
## Classification of amplifier stages and systems {#classification_of_amplifier_stages_and_systems}
### Frequency range {#frequency_range}
Depending on the frequency range and other properties amplifiers are designed according to different principles.
Frequency ranges down to DC are used only when this property is needed. Amplifiers for direct current signals are vulnerable to minor variations in the properties of components with time. Special methods, such as chopper stabilized amplifiers are used to prevent objectionable drift in the amplifier\'s properties for DC. \"DC-blocking\" capacitors can be added to remove DC and sub-sonic frequencies from audio amplifiers.
Depending on the frequency range specified different design principles must be used. Up to the MHz range only \"discrete\" properties need be considered; e.g., a terminal has an input impedance.
As soon as any connection within the circuit gets longer than perhaps 1% of the wavelength of the highest specified frequency (e.g., at 100 MHz the wavelength is 3 m, so the critical connection length is approx. 3 cm) design properties radically change. For example, a specified length and width of a PCB trace can be used as a selective or impedance-matching entity. Above a few hundred MHz, it gets difficult to use discrete elements, especially inductors. In most cases, PCB traces of very closely defined shapes are used instead (stripline techniques).
The frequency range handled by an amplifier might be specified in terms of bandwidth (normally implying a response that is 3 dB down when the frequency reaches the specified bandwidth), or by specifying a **frequency response** that is within a certain number of decibels between a lower and an upper frequency (e.g. \"20 Hz to 20 kHz plus or minus 1 dB\").
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# Amplifier
## Example amplifier circuit {#example_amplifier_circuit}
The practical amplifier circuit shown above could be the basis for a moderate-power audio amplifier. It features a typical (though substantially simplified) design as found in modern amplifiers, with a class-AB push--pull output stage, and uses some overall negative feedback. Bipolar transistors are shown, but this design would also be realizable with FETs or valves.
The input signal is coupled through capacitor C1 to the base of transistor Q1. The capacitor allows the AC signal to pass, but blocks the DC bias voltage established by resistors R1 and R2 so that any preceding circuit is not affected by it. Q1 and Q2 form a differential amplifier (an amplifier that multiplies the difference between two inputs by some constant), in an arrangement known as a long-tailed pair. This arrangement is used to conveniently allow the use of negative feedback, which is fed from the output to Q2 via R7 and R8.
The negative feedback into the difference amplifier allows the amplifier to compare the input to the actual output. The amplified signal from Q1 is directly fed to the second stage, Q3, which is a common emitter stage that provides further amplification of the signal and the DC bias for the output stages, Q4 and Q5. R6 provides the load for Q3 (a better design would probably use some form of active load here, such as a constant-current sink). So far, all of the amplifier is operating in class A. The output pair are arranged in class-AB push--pull, also called a complementary pair. They provide the majority of the current amplification (while consuming low quiescent current) and directly drive the load, connected via DC-blocking capacitor C2. The diodes D1 and D2 provide a small amount of constant voltage bias for the output pair, just biasing them into the conducting state so that crossover distortion is minimized. That is, the diodes push the output stage firmly into class-AB mode (assuming that the base-emitter drop of the output transistors is reduced by heat dissipation).
This design is simple, but a good basis for a practical design because it automatically stabilises its operating point, since feedback internally operates from DC up through the audio range and beyond. Further circuit elements would probably be found in a real design that would roll-off the frequency response above the needed range to prevent the possibility of unwanted oscillation. Also, the use of fixed diode bias as shown here can cause problems if the diodes are not both electrically and thermally matched to the output transistors`{{spaced ndash}}`{=mediawiki} if the output transistors turn on too much, they can easily overheat and destroy themselves, as the full current from the power supply is not limited at this stage.
A common solution to help stabilise the output devices is to include some emitter resistors, typically one ohm or so. Calculating the values of the circuit\'s resistors and capacitors is done based on the components employed and the intended use of the amp
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# Eadgyth
**Edith of England**, also spelt **Eadgyth** or **Ædgyth** (*Ēadgȳð*, *Edgitha*; 910--946), a member of the House of Wessex, was the East Frankish (German) queen from 936, by her marriage to King Otto the Great.
## Life
Edith was born to the reigning English king Edward the Elder by his second wife, Ælfflæd, and hence was a granddaughter of King Alfred the Great. She had an older sister, Eadgifu. She apparently spent her early years near Winchester in Wessex, moving about frequently with the court, and may have spent her later youth, with her mother, living for a time at a monastery.
At the request of the East Frankish king Henry the Fowler, who wished to stake a claim to equality and to seal the alliance between the two Saxon kingdoms, her half-brother King Æthelstan sent his sisters Edith and Edgiva to Germany. Henry\'s eldest son and heir to the throne Otto was instructed to choose whichever one pleased him best. Otto chose Edith, according to Hrotsvitha a woman \"of pure noble countenance, graceful character and truly royal appearance\", and married her in 930. In 929 King Otto I had granted the city of Magdeburg to his Edith as dower. She had a particular love for the town and often lived there.
thumb\|upright=1.4\|left\|Otto I and his wife Edith arrive near Magdeburg (Hugo Vogel 1898, Ständehaus Merseburg) In 936 Henry the Fowler died and his eldest son Otto, Edith\'s husband, was crowned king at Aachen Cathedral. A surviving report of the ceremony by the medieval chronicler Widukind of Corvey makes no mention of his wife having been crowned at this point, but according to Bishop Thietmar of Merseburg\'s chronicle, Eadgyth was nevertheless anointed as queen, albeit in a separate ceremony.
As queen consort, Edith undertook the usual state duties of a \"First Lady\": when she turns up in the records it is generally in connection with gifts to the state\'s favoured monasteries or memorials to holy women and saints. In this respect she seems to have been more diligent than her now widowed and subsequently sainted mother-in-law, Queen Matilda, whose own charitable activities only achieve a single recorded mention from the period of Eadgyth\'s time as queen. There was probably rivalry between the Benedictine Monastery of St Maurice founded at Magdeburg by Otto and Eadgyth in 937, a year after coming to the throne, and Matilda\'s foundation Quedlinburg Abbey, intended by her as a memorial to her husband, the late King Henry. Edith accompanied her husband on his travels, though not during battles. While Otto fought against the rebellious dukes Eberhard of Franconia and Gilbert of Lorraine in 939, she spent the hostilities at Lorsch Abbey. In 941 she effected a reconciliation between her husband and his mother.
Like her brother, Æthelstan, Edith was devoted to the cult of their ancestor Saint Oswald of Northumbria and was instrumental in introducing this cult into Germany after her marriage to the emperor. Her lasting influence may have caused certain monasteries and churches in the Duchy of Saxony to be dedicated to this saint.
Eadgyth\'s death in 946 at around the age of thirty-six, was unexpected. Otto apparently mourned the loss of a beloved spouse. He married Adelaide of Italy in 951.
## Children
Edith and Otto\'s children were:
- Liudolf, Duke of Swabia (930 -- 6 September 957)
- Liutgarde (931 -- 18 November 953), married the Lotharingian duke Conrad the Red in 947
both buried in St. Alban\'s Abbey, Mainz (since destroyed).
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# Eadgyth
## Tomb
Initially buried in the St Maurice monastery, Edith\'s tomb since the 16th century has been located in Magdeburg Cathedral. Long regarded as a cenotaph, a lead coffin inside a stone sarcophagus with her name on it was found and opened in 2008 by archaeologists during work on the building. An inscription recorded that it was the body of Eadgyth, reburied in 1510. The fragmented and incomplete bones were examined in 2009, then brought to Bristol, England, for tests in 2010.
The investigations at Bristol, applying isotope tests on tooth enamel, checked whether she was born and brought up in Wessex and Mercia, as written history indicated. Testing on the bones revealed that they are the remains of Eadgyth, from study made of the enamel of the teeth in her upper jaw. Testing of the enamel revealed that the individual entombed at Magdeburg had spent time as a youth in the chalky uplands of Wessex. The bones are the oldest found of a member of English royalty.
Following the tests the bones were re-interred in a new titanium coffin in her tomb at Magdeburg Cathedral on 22 October 2010
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# Æthelberht of Kent
**Æthelberht** (`{{IPAc-en|ˈ|æ|θ|əl|b|ɚ|t}}`{=mediawiki}; also **Æthelbert**, **Aethelberht**, **Aethelbert** or **Ethelbert**; *Æðelberht* `{{IPA|ang|ˈæðelberˠxt|}}`{=mediawiki}; c. 550 -- 24 February 616) was King of Kent from about 589 until his death. The eighth-century monk Bede, in his *Ecclesiastical History of the English People*, lists him as the third king to hold *imperium* over other Anglo-Saxon kingdoms. In the late ninth century *Anglo-Saxon Chronicle*, he is referred to as a *bretwalda*, or \"Britain-ruler\". He was the first Anglo-Saxon king to convert to Christianity.
Æthelberht was the son of Eormenric, succeeding him as king, according to the *Chronicle*. He married Bertha, the Christian daughter of Charibert I, king of the Franks, thus building an alliance with the most powerful state in contemporary Western Europe; the marriage probably took place before he came to the throne. Bertha\'s influence may have led to Pope Gregory I\'s decision to send Augustine as a missionary from Rome. Augustine landed on the Isle of Thanet in east Kent in 597. Shortly thereafter, Æthelberht converted to Christianity, churches were established, and wider-scale conversion to Christianity began in the kingdom. He provided the new church with land in Canterbury, thus helping to establish one of the foundation stones of English Christianity.
Æthelberht\'s law for Kent, the earliest written code in any Germanic language, instituted a complex system of fines; the law code is preserved in the *Textus Roffensis*. Kent was rich, with strong trade ties to the Continent, and Æthelberht may have instituted royal control over trade. Coinage probably began circulating in Kent during his reign for the first time since the Anglo-Saxon settlement. He later came to be regarded as a saint for his role in establishing Christianity among the Anglo-Saxons. His feast day was originally 24 February but was changed to 25 February.
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# Æthelberht of Kent
## Historical context {#historical_context}
In the fifth century, raids on Britain by continental peoples had developed into full-scale migrations. The newcomers are known to have included Angles, Saxons, Jutes and Frisians, and there is evidence of other groups as well. These groups captured territory in the east and south of England, but at about the end of the fifth century, a British victory at the battle of Mount Badon (Mons Badonicus) halted the Anglo-Saxon advance for fifty years. From about 550, however, the British began to lose ground once more, and within twenty-five years it appears that control of almost all of southern England was in the hands of the invaders.
Anglo-Saxons probably conquered Kent before Mons Badonicus. There is both documentary and archaeological evidence that Kent was primarily colonised by Jutes, from the southern part of the Jutland peninsula. According to legend, the brothers Hengist and Horsa landed in 449 as mercenaries for a British king, Vortigern. After a rebellion over pay and Horsa\'s death in battle, Hengist established the Kingdom of Kent. Some historians now think the underlying story of a rebelling mercenary force may be accurate; most now date the founding of the kingdom of Kent to the middle of the fifth-century, which is consistent with the legend.{{#tag:ref\|There is disagreement about the extent to which the legend can be treated as fact. For example, Barbara Yorke says \"Recent detailed studies \[. . .\] have confirmed that these accounts are largely mythic and that any reliable oral tradition which they may have embodied has been lost in the conventions of the origin-legend format\", but Richard Fletcher says of Hengist that \"there is no good reason for doubting his existence\", and James Campbell adds that \"although the origins of such annals are deeply mysterious, and suspect, they cannot be simply discarded\".\|group=\"note\"}} This early date, only a few decades after the departure of the Romans, also suggests that more of Roman civilization may have survived into Anglo-Saxon rule in Kent than in other areas.
Overlordship was a central feature of Anglo-Saxon politics which began before Æthelberht\'s time; kings were described as overlords as late as the ninth century. The Anglo-Saxon invasion may have involved military coordination of different groups within the invaders, with a leader who had authority over many different groups; Ælle of Sussex may have been such a leader. Once the new states began to form, conflicts among them began. Tribute from dependents could lead to wealth. A weaker state also might ask or pay for the protection of a stronger neighbour against a warlike third state.
Sources for this period in Kentish history include the *Ecclesiastical History of the English People*, written in 731 by Bede, a Northumbrian monk. Bede was interested primarily in England\'s Christianization. Since Æthelberht was the first Anglo-Saxon king to convert to Christianity, Bede provides more substantial information about him than about any earlier king. One of Bede\'s correspondents was Albinus, abbot of the monastery of St. Peter and St. Paul (subsequently renamed St. Augustine\'s) in Canterbury. The *Anglo-Saxon Chronicle*, a collection of annals assembled c. 890 in the kingdom of Wessex, mentions several events in Kent during Æthelberht\'s reign. Further mention of events in Kent occurs in the late sixth century history of the Franks by Gregory of Tours. This is the earliest surviving source to mention any Anglo-Saxon kingdom. Some of Pope Gregory the Great\'s letters concern the mission of St. Augustine to Kent in 597; these letters also mention the state of Kent and its relationships with neighbours. Other sources include regnal lists of the kings of Kent and early charters (land grants by kings to their followers or to the church). Although no originals survive from Æthelberht\'s reign, later copies exist. A law code from Æthelberht\'s reign also survives.
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# Æthelberht of Kent
## Ancestry, accession and chronology {#ancestry_accession_and_chronology}
According to Bede, Æthelberht was descended directly from Hengist. Bede gives the line of descent as follows: \"Ethelbert was son of Irminric, son of Octa, and after his grandfather Oeric, surnamed Oisc, the kings of the Kentish folk are commonly known as Oiscings. The father of Oeric was Hengist.\" An alternative form of this genealogy, found in the *Historia Brittonum* among other places, reverses the position of Octa and Oisc in the lineage. The first of these names that can be placed historically with reasonable confidence is Æthelberht\'s father, whose name now usually is spelled Eormenric. The only direct written reference to Eormenric is in Kentish genealogies, but Gregory of Tours does mention that Æthelberht\'s father was the king of Kent, though Gregory gives no date. Eormenric\'s name provides a hint of connections to the kingdom of the Franks, across the English channel; the element \"Eormen\" was rare in names of the Anglo-Saxon aristocracy, but much more common among Frankish nobles. One other member of Æthelberht\'s family is known: his sister, Ricole, who is recorded by both Bede and the *Anglo-Saxon Chronicle* as the mother of Sæberht, king of the East Saxons (i.e., Essex).
The dates of Æthelberht\'s birth and accession to the throne of Kent are both matters of debate. Bede, the earliest source to give dates, is thought to have drawn his information from correspondence with Albinus. Bede states that when Æthelberht died in 616 he had reigned for fifty-six years, placing his accession in 560. Bede also says that Æthelberht died twenty-one years after his baptism. Augustine\'s mission from Rome is known to have arrived in 597, and according to Bede, it was this mission that converted Æthelberht. Hence Bede\'s dates are inconsistent. The *Anglo-Saxon Chronicle*, an important source for early dates, is inconsistent with Bede and also has inconsistencies among different manuscript versions. Putting together the different dates in the *Chronicle* for birth, death and length of reign, it appears that Æthelberht\'s reign was thought to have been either 560--616 or 565--618 but that the surviving sources have confused the two traditions.
It is possible that Æthelberht was converted to Christianity before Augustine\'s arrival. Æthelberht\'s wife was a Christian and brought a Frankish bishop with her, to attend her at court, so Æthelberht would have had knowledge of Christianity before the mission reached Kent. It also is possible that Bede had the date of Æthelberht\'s death wrong; if, in fact, Æthelberht died in 618, this would be consistent with his baptism in 597, which is in accord with the tradition that Augustine converted the king within a year of his arrival.
Gregory of Tours, in his *Historia Francorum*, writes that Bertha, daughter of Charibert I, king of the Franks, married the son of the king of Kent. Bede says that Æthelberht received Bertha \"from her parents\". If Bede is interpreted literally, the marriage would have had to take place before 567, when Charibert died. The traditions for Æthelberht\'s reign, then, would imply that Æthelberht married Bertha before either 560 or 565.
The extreme length of Æthelberht\'s reign also has been regarded with skepticism by historians; it has been suggested that he died in the fifty-sixth year of his life, rather than the fifty-sixth year of his reign. This would place the year of his birth approximately at 560, and he would not then have been able to marry until the mid 570s. According to Gregory of Tours, Charibert was king when he married Ingoberg, Bertha\'s mother, which places that marriage no earlier than 561. It therefore is unlikely that Bertha was married much before about 580. These later dates for Bertha and Æthelberht also solve another possible problem: Æthelberht\'s daughter, Æthelburh, seems likely to have been Bertha\'s child, but the earlier dates would have Bertha aged sixty or so at Æthelburh\'s likely birthdate using the early dates.
Gregory, however, also says that he thinks that Ingoberg was seventy years old in 589; and this would make her about forty when she married Charibert. This is possible, but seems unlikely, especially as Charibert seems to have had a preference for younger women, again according to Gregory\'s account. This would imply an earlier birth date for Bertha. On the other hand, Gregory refers to Æthelberht at the time of his marriage to Bertha simply as \"a man of Kent\", and in the 589 passage concerning Ingoberg\'s death, which was written in about 590 or 591, he refers to Æthelberht as \"the son of the king of Kent\". If this does not simply reflect Gregory\'s ignorance of Kentish affairs, which seems unlikely given the close ties between Kent and the Franks, then some assert that Æthelberht\'s reign cannot have begun before 589.
While all of the contradictions above cannot be reconciled, the most probable dates that may be drawn from available data place Æthelberht\'s birth at approximately 560 and, perhaps, his marriage to Bertha at 580. His reign is most likely to have begun in 589 or 590.
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# Æthelberht of Kent
## Kingship of Kent {#kingship_of_kent}
The later history of Kent shows clear evidence of a system of joint kingship, with the kingdom being divided into east Kent and west Kent, although it appears that there generally was a dominant king. This evidence is less clear for the earlier period, but there are early charters, known to be forged, which nevertheless imply that Æthelberht ruled as joint king with his son, Eadbald. It may be that Æthelberht was king of east Kent and Eadbald became king of west Kent; the east Kent king seems generally to have been the dominant ruler later in Kentish history. Whether or not Eadbald became a joint king with Æthelberht, there is no question that Æthelberht had authority throughout the kingdom.
The division into two kingdoms is most likely to date back to the sixth century; east Kent may have conquered west Kent and preserved the institutions of kingship as a subkingdom. This was a common pattern in Anglo-Saxon England, as the more powerful kingdoms absorbed their weaker neighbours. An unusual feature of the Kentish system was that only sons of kings appeared to be legitimate claimants to the throne, although this did not eliminate all strife over the succession.
The main towns of the two kingdoms were Rochester, for west Kent, and Canterbury, for east Kent. Bede does not state that Æthelberht had a palace in Canterbury, but he does refer to Canterbury as Æthelberht\'s \"metropolis\", and it is clear that it is Æthelberht\'s seat.
## Relations with the Franks {#relations_with_the_franks}
There are many indications of close relations between Kent and the Franks. Æthelberht\'s marriage to Bertha certainly connected the two courts, although not as equals: the Franks would have thought of Æthelberht as an under-king. There is no record that Æthelberht ever accepted a continental king as his overlord and, as a result, historians are divided on the true nature of the relationship. Evidence for an explicit Frankish overlordship of Kent comes from a letter written by Pope Gregory the Great to Theuderic, king of Burgundy, and Theudebert, king of Austrasia. The letter concerned Augustine\'s mission to Kent in 597, and in it Gregory says that he believes \"that you wish your subjects in every respect to be converted to that faith in which you, their kings and lords, stand\". It may be that this is a papal compliment, rather than a description of the relationship between the kingdoms. It also has been suggested that Liudhard, Bertha\'s chaplain, was intended as a representative of the Frankish church in Kent, which also could be interpreted as evidence of overlordship.
A possible reason for the willingness of the Franks to connect themselves with the Kentish court is the fact that a Frankish king, Chilperic I, is recorded as having conquered a people known as the Euthiones during the mid-sixth century. If, as seems likely from the name, these people were the continental remnants of the Jutish invaders of Kent, then it may be that the marriage was intended as a unifying political move, reconnecting different branches of the same people. Another perspective on the marriage may be gained by considering that it is likely that Æthelberht was not yet king at the time he and Bertha were wed: it may be that Frankish support for him, acquired via the marriage, was instrumental in gaining the throne for him.
Regardless of the political relationship between Æthelberht and the Franks, there is abundant evidence of strong connections across the English Channel. There was a luxury trade between Kent and the Franks, and burial artefacts found include clothing, drink, and weapons that reflect Frankish cultural influence. The Kentish burials have a greater range of imported goods than those of the neighbouring Anglo-Saxon regions, which is not surprising given Kent\'s easier access to trade across the English Channel. In addition, the grave goods are both richer and more numerous in Kentish graves, implying that material wealth was derived from that trade. Frankish influences also may be detected in the social and agrarian organization of Kent. Other cultural influences may be seen in the burials as well, so it is not necessary to presume that there was direct settlement by the Franks in Kent.
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# Æthelberht of Kent
## Rise to dominance {#rise_to_dominance}
### Bretwalda
In his *Ecclesiastical History*, Bede includes his list of seven kings who held *imperium* over the other kingdoms south of the Humber. The usual translation for *imperium* is \"overlordship\". Bede names Æthelberht as the third on the list, after Ælle of Sussex and Ceawlin of Wessex. The anonymous annalist who composed one of the versions of the *Anglo-Saxon Chronicle* repeated Bede\'s list of seven kings in a famous entry under the year 827, with one additional king, Egbert of Wessex. The *Chronicle* also records that these kings held the title *bretwalda*, or \"Britain-ruler\". The exact meaning of *bretwalda* has been the subject of much debate; it has been described as a term \"of encomiastic poetry\", but there also is evidence that it implied a definite role of military leadership.
The prior *bretwalda*, Ceawlin, is recorded by the *Anglo-Saxon Chronicle* as having fought Æthelberht in 568 at a place called \"Wibbandun\" (\"Wibba\'s Mount\") whose location has not been identified. The entry states that Æthelberht lost the battle and was driven back to Kent. Comparison of the entries concerning the West Saxons in this section of the *Chronicle* with the West Saxon Genealogical Regnal List shows that their dating is unreliable: Ceawlin\'s reign is more likely to have been approximately 581--588, rather 560--592 as claimed in the *Chronicle*.
At some point Ceawlin lost his overlordship, perhaps after a battle at *Fethan leag*, thought to have been in Oxfordshire, which the *Chronicle* dates to 584, some eight years before he was deposed in 592 (again using the *Chronicle\'s* unreliable dating). Æthelberht certainly was a dominant ruler by 601, when Gregory the Great wrote to him: Gregory urges Æthelberht to spread Christianity among those kings and peoples subject to him, implying some level of overlordship. If the battle of Wibbandun was fought c. 590, as has been suggested, then Æthelberht must have gained his position as overlord at some time in the 590s. This dating for Wibbandun is slightly inconsistent with the proposed dates of 581--588 for Ceawlin\'s reign, but those dates are not thought to be precise, merely the most plausible given the available data.
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# Æthelberht of Kent
## Rise to dominance {#rise_to_dominance}
### Relationships with other kingdoms {#relationships_with_other_kingdoms}
In addition to the evidence of the *Chronicle* that Æthelberht was accorded the title of *bretwalda*, there is evidence of his domination in several of the southern kingdoms of the Heptarchy. In Essex, Æthelberht appears to have been in a position to exercise authority shortly after 604, when his intervention helped in the conversion of King Sæberht of Essex, his nephew, to Christianity. It was Æthelberht, and not Sæberht, who built and endowed St. Pauls in London, where St Paul\'s Cathedral now stands. Further evidence is provided by Bede, who explicitly describes Æthelberht as Sæberht\'s overlord.
Bede describes Æthelberht\'s relationship with Rædwald, king of East Anglia, in a passage that is not completely clear in meaning. It seems to imply that Rædwald retained *ducatus*, or military command of his people, even while Æthelberht held *imperium*. This implies that being a *bretwalda* usually included holding the military command of other kingdoms and also that it was more than that, since Æthelberht is *bretwalda* despite Rædwald\'s control of his own troops. Rædwald was converted to Christianity while in Kent but did not abandon his pagan beliefs; this, together with the fact that he retained military independence, implies that Æthelberht\'s overlordship of East Anglia was much weaker than his influence with the East Saxons. An alternative interpretation, however, is that the passage in Bede should be translated as \"Rædwald, king of the East Angles, who while Æthelberht lived, even conceded to him the military leadership of his people\"; if this is Bede\'s intent, then East Anglia firmly was under Æthelberht\'s overlordship.
There is no evidence that Æthelberht\'s influence in other kingdoms was enough for him to convert any other kings to Christianity, although this is partly due to the lack of sources---nothing is known of Sussex\'s history, for example, for almost all of the seventh and eighth centuries. Æthelberht was able to arrange a meeting in 602 in the Severn valley, on the northwestern borders of Wessex, however, and this may be an indication of the extent of his influence in the west. No evidence survives showing Kentish domination of Mercia, but it is known that Mercia was independent of Northumbria, so it is quite plausible that it was under Kentish overlordship.
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# Æthelberht of Kent
## Augustine\'s mission and early Christianisation {#augustines_mission_and_early_christianisation}
The native Britons had converted to Christianity under Roman rule. The Anglo-Saxon invasions separated the British church from European Christianity for centuries, so the church in Rome had no presence or authority in Britain, and in fact, Rome knew so little about the British church that it was unaware of any schism in customs. However, Æthelberht would have known something about the Roman church from his Frankish wife, Bertha, who had brought a bishop, Liudhard, with her across the Channel, and for whom Æthelberht built a chapel, St Martin\'s.
In 596, Pope Gregory the Great sent Augustine, prior of the monastery of St. Andrew in Rome, to England as a missionary, and in 597, a group of nearly forty monks, led by Augustine, landed on the Isle of Thanet in Kent. According to Bede, Æthelberht was sufficiently distrustful of the newcomers to insist on meeting them under the open sky, to prevent them from performing sorcery. The monks impressed Æthelberht, but he was not converted immediately. He agreed to allow the mission to settle in Canterbury and permitted them to preach.
It is not known when Æthelberht became a Christian. It is possible, despite Bede\'s account, that he already was a Christian before Augustine\'s mission arrived. It is likely that Liudhard and Bertha pressed Æthelberht to consider becoming a Christian before the arrival of the mission, and it is also likely that a condition of Æthelberht\'s marriage to Bertha was that Æthelberht would consider conversion. Conversion via the influence of the Frankish court would have been seen as an explicit recognition of Frankish overlordship, however, so it is possible that Æthelberht\'s delay of his conversion until it could be accomplished via Roman influence might have been an assertion of independence from Frankish control. It also has been argued that Augustine\'s hesitation---he turned back to Rome, asking to be released from the mission---is an indication that Æthelberht was a pagan at the time Augustine was sent.
At the latest, Æthelberht must have converted before 601, since that year Gregory wrote to him as a Christian king. An old tradition records that Æthelberht converted on 1 June, in the summer of the year that Augustine arrived. Through Æthelberht\'s influence Sæberht, king of Essex, also was converted, but there were limits to the effectiveness of the mission. The entire Kentish court did not convert: Eadbald, Æthelberht\'s son and heir, was a pagan at his accession. Rædwald, king of East Anglia, was only partly converted (apparently while at Æthelberht\'s court) and retained a pagan shrine next to the new Christian altar. Augustine also was unsuccessful in gaining the allegiance of the British clergy.
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# Æthelberht of Kent
## Law code {#law_code}
*Main article: Law of Æthelberht* Some time after the arrival of Augustine\'s mission, perhaps in 602 or 603, Æthelberht issued a set of laws, in ninety sections. These laws are by far the earliest surviving code composed in any of the Germanic countries, and they were almost certainly among the first documents written down in Anglo-Saxon, as literacy would have arrived in England with Augustine\'s mission. The only surviving early manuscript, the *Textus Roffensis*, dates from the twelfth century, and it now resides in the Medway Studies Centre in Strood, Kent. Æthelberht\'s code makes reference to the church in the very first item, which enumerates the compensation required for the property of a bishop, a deacon, a priest, and so on; but overall, the laws seem remarkably uninfluenced by Christian principles. Bede asserted that they were composed \"after the Roman manner\", but there is little discernible Roman influence either. In subject matter, the laws have been compared to the *Lex Salica* of the Franks, but it is not thought that Æthelberht based his new code on any specific previous model.
The laws are concerned with setting and enforcing the penalties for transgressions at all levels of society; the severity of the fine depended on the social rank of the victim. The king had a financial interest in enforcement, for part of the fines would come to him in many cases, but the king also was responsible for law and order, and avoiding blood feuds by enforcing the rules on compensation for injury was part of the way the king maintained control. Æthelberht\'s laws are mentioned by Alfred the Great, who compiled his own laws, making use of the prior codes created by Æthelberht, as well as those of Offa of Mercia and Ine of Wessex.
One of Æthelberht\'s laws seems to preserve a trace of a very old custom: the third item in the code states that \"If the king is drinking at a man\'s home, and anyone commits any evil deed there, he is to pay twofold compensation.\" This probably refers to the ancient custom of a king traveling the country, being hosted, and being provided for by his subjects wherever he went. The king\'s servants retained these rights for centuries after Æthelberht\'s time.
Items 77--81 in the code have been interpreted as a description of a woman\'s financial rights after a divorce or legal separation. These clauses define how much of the household goods a woman could keep in different circumstances, depending on whether she keeps custody of the children, for example. It has recently been suggested, however, that it would be more correct to interpret these clauses as referring to women who are widowed, rather than divorced.
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