Part 28

EPIDEM'IC, or EPIDEMIC DISEASE (Gr. _epi_, upon, and _d[=e]mos_, people), signifies a disease which attacks a people, suddenly spreading from one to the other in all directions, prevailing a certain time and then dying away. It usually travels from place to place in the direction of the most-frequented lines of communication. The reason is that such diseases are commonly due to some infective material capable of being conveyed from one individual to another, and of being transported from place to place. In Britain smallpox and cholera are occasionally epidemic, whilst scarlet fever, measles, chickenpox, diphtheria, typhoid fever, &c., are almost invariably so. Certain diseases which appear to be more mental than physical sometimes occur so numerously as to assume an epidemic form, such as St. Vitus's dance, convulsionary diseases, or suicidal mania.

EPIDEN'DRUM (Gr. _epi_, upon, and _dendron_, a tree), a large genus of tropical American orchids, most of the species of which are epiphytic, growing on trees. The flowers are very handsome, and a large number of the species are in cultivation.

EPIDER'MIS, in anatomy, the cuticle or scarf-skin of the body; a thin membrane covering the true skin of animals, consisting of two layers, an inner or mucous layer, called the _rete mucosum_, composed of active cells containing granules of colouring matter, and an outer or horny layer, consisting of flattened scale-like cells, dry, inactive, and effete, which are constantly being shed in the form of dust. Both layers are destitute of blood-vessels or nerves.

EPIDERMIS, in botany, the superficial layer of cells covering leaves and young stems. Its principal function is to restrict transpiration, for which purpose its outer wall is more or less cutinized, i.e. chemically modified so as to be very impervious to water and gases, especially the outermost part thereof, the so-called _cuticle_. Naturally both cuticle and epidermis as a whole are most strongly developed in drought-adapted plants or xerophytes (q.v.); and conversely the epidermis of submerged plants is not cutinized, nor is the superficial layer of ordinary roots. The epidermis frequently bears hairs of various kinds. Stems which undergo secondary growth in thickness soon cast off their epidermis, its r[^o]le being assumed by cork or bark. The water- and gas-proof covering provided by the epidermis is not continuous, but is interrupted by numerous minute pores or _stomata_, capable of opening and closing, through which accordingly a regulated interchange of gases takes place.

EP'IDOTE, a mineral of a green or grey colour, vitreous lustre, and partial transparency, a member of the garnet family. The primary form of the crystals is a right rhomboidal prism. The crystals occur in Norway, Siberia, Tyrol, and the United States.

EPIGAEA (-j[=e]'a), a genus of Ericaceous shrubs. _E. repens_, the trailing arbutus, is the May-flower of North America.

EPIGLOTTIS is a cartilaginous plate behind the tongue, which covers the glottis like a lid during the act of swallowing, and thus prevents foreign bodies from entering the larynx. In its ordinary position during respiration it is pointed upwards, but in the act of swallowing it is pressed downwards and backwards by the drawing up of the windpipe beneath the base of the tongue, and thus closes the entrance to the air-passages. See _Larynx_.

EP'IGRAM (Gr. _epi_, upon, _graphein_, to write), in a restricted sense, a short poem or piece in verse, which has only one subject, and finishes by a witty or ingenious turn of thought; in a general sense, a pointed or witty and antithetical saying. The term was originally given by the Greeks to a poetical inscription placed upon a tomb or public monument, and was afterwards extended to every little piece of verse expressing with precision a delicate or ingenious thought, as the pieces in the _Greek Anthology_. In Roman classical poetry the term was somewhat indiscriminately used, but the epigrams of Martial contain a great number with the modern epigrammatic character. Epigrams flourished in modern times after the Revival of Learning period, and all the Elizabethan versifiers tried their hand at them. Pope was a great master of the epigram, and the art was practised by Cl['e]ment Marot, Boileau, Voltaire, Schiller, Goethe, Byron, and Moore, and more recently by Sir William Watson.--Cf. Dodd, _Epigrammatists of Mediaeval and Modern Times_.

EPIGRAPHY, a term used both for the study of inscriptions as a whole, and for the science which deals with their classification and decipherment. The attention of the epigraphist is given to inscriptions upon stone, brick, metal, and other comparatively permanent material, as compared with writings upon parchment, papyrus, or paper; but he excludes inscriptions upon coins, which are in the department of the numismatist. The science of epigraphy is of immense importance for a knowledge of the past, the subject including inscriptions so far apart in point of time as Egyptian records of the days of Mena (4700 B.C.), and the Greek hexameters that commemorate the death in Westmorland of a young Syrian soldier in the army of Septimius Severus. Of still more recent date are the Runic inscriptions discovered in Greenland, which seem to place beyond a doubt the fact of Icelandic explorers having reached that country in the eleventh or twelfth century. The most important inscriptions are Egyptian, Cuneiform (Babylonian and Assyrian), Semitic, Greek, Latin, Indian, and Runic. The inscribed writings include epitaphs on the dead, records of important events, dedications of public buildings, with such comparatively private matters as receipts, contracts, and other business transactions. While inscriptions form a valuable source of knowledge, they cannot be accepted as invariably reliable. Reasons might in some cases exist for making a false or misleading record, as in the case of a eulogistic tombstone, while mistakes in spelling and other details may be due to a careless workman. The literature which deals with the science of epigraphy is very large.

EPIGYNOUS (e-pij'i-nus) FLOWERS, those in which the gynaecium is _inferior_, i.e. embedded in, and adherent to, the hollowed-out receptacle, so that the other parts of the flower appear to be inserted on the top of the ovary.

EP'ILEPSY (Gr. _epil[=e]psia_, literally, a seizure), a nervous disease, the falling-sickness, so called because the patient falls suddenly to the ground. It depends on various causes, often exceedingly complicated and incapable of being removed; hence it is often an incurable periodical disease, appearing in single paroxysms. In its fully developed form, convulsions, attended by complete unconsciousness, are the prominent feature. Among the different causes may be mentioned intense emotional disturbance in early childhood, injury to the brain or its coverings at birth or subsequently, or some irritation within the skull itself, such as tumours, &c., developing later in life. Epileptiform fits due to the last-mentioned cause differ from those of true epilepsy, and are known as _Jacksonian epilepsy_ (cf. Sir W. K. Gowers, _The Borderland of Epilepsy_). It is, for the most part, preceded by a tingling sensation, creeping up from the foot or hand to the breast and head, or some other premonitory symptom such as spectral illusions, headache, giddiness, confusion of thought, sense of fear, &c.; but sometimes there are no precursive symptoms. During the paroxysm all that is to be attended to is to prevent the patient from injuring himself; and this is to be accomplished by raising the head gently and loosening all tight parts of the dress. It is advisable to protect the tongue from being bitten by introducing a piece of india-rubber, cork, or soft wood between the teeth.

EPILO'BIUM, the willow-herbs, a genus of plants, nat. ord. Onagraceae. The species are herbs or under-shrubs with pink or purple, rarely yellow, flowers, solitary in the axils of the leaves or in terminal leafy spikes. The seeds are tipped with a pencil of silky hairs, and are contained in a long four-celled capsule. There are more than fifty species scattered over the arctic and temperate regions of the world, ten of them being natives of Britain.

EPIMEN'IDES (-d[=e]z), an ancient Greek philosopher and poet, born in Crete in the seventh century before Christ, he was held for an infallible prophet, and by some is reckoned among the seven wise men, instead of Periander. He is supposed to be the prophet referred to by St. Paul in _Titus_, i, 12: "One of themselves, even a prophet of their own, said, The Cretians are alway liars, evil beasts, slow bellies".

EPIMETHEUS (ep-i-m[=e]'th[=u]s), in Greek mythology, the son of Iapetus, brother of Prometheus, and husband of Pandora. Epimetheus may be translated 'afterthought', as Prometheus 'forethought'.

['E]PINAL, a town of Eastern France, capital of the department of the Vosges, on the Moselle. It is well built and has handsome quays, an ancient Gothic church, a communal college, a public library of 30,000 volumes, a museum, and extensive fortifications. The town was occupied by the Germans in the Franco-Prussian War of 1870, and since that time a modern fortress has been constructed. The manufactures consist of articles in metal, cottons, linens, woollens, earthenware, and leather. The famous paper-mills of Archettes are in the vicinity. Pop. 30,000.

['E]PINAY, Louise Florence P['e]tronille, Madame d', French authoress, born in 1726, died 1783. She became the wife of M. Delalive d'['E]pinay, who was collector-general of taxes. In 1748 she became acquainted with Rousseau, and gave him a cottage in which he passed many of his days. She was the author of _Les Conversations d'['E]milie_, a companion-volume to Rousseau's _['E]mile; Lettres [`a] mon Fils_; and _Mes Moments heureux_. She left interesting memoirs and correspondence.

EPIPHA'NIUS, ST., was born in Palestine about 310, died 403. About 367 he was consecrated Bishop of Salamis or Constantia, in Cyprus. A zealous denouncer of heresy, he combated the opinions of Arius and Origen. His work _Panarion_ gives the history, together with the refutation, of a great number of heresies. His festival is on the 12th of May.

EPIPH'ANY (Gr. _epiphaneia_, a manifestation or showing forth), a festival, otherwise called the _manifestation of Christ to the Gentiles_, observed on the 6th of January in honour of the adoration of our Saviour by the three Magi, or wise men, who came to adore him and bring him presents, led by the star. As a separate festival it dates from 813.

EP'IPHYTE (Gr. _epi_, on, _phyton_, a plant), a plant which grows and flourishes on the trunks and branches of trees, adhering to the bark, as a moss, lichen, fern, &c., but which does not, like a parasite, derive any nourishment from the plant on which it grows. Most orchids are epiphytes, and so are many Bromeliaceae and Cactaceae. Epiphytic Angiosperms are characteristic of humid tropical regions. Depending as they do entirely on atmospheric moisture, they show many curious adaptations, and are nearly always more or less xerophytic in structure.

EPI'RUS (Gr. _Epeiros_), a country of ancient Greece corresponding to Southern Albania and the north-western division of modern Greece. The most interesting locality in it was Dodona. The inhabitants were only in part Greeks. The Molossians at last acquired the ascendancy, and the kings of this tribe took the name of kings of Epirus. The most celebrated King of Epirus was Pyrrhus, who made war upon the Romans. Epirus became a Roman province in 168 B.C., and shared the fortunes of Rome till it was conquered by the Turks. The population is about 250,000. In Nov., 1914, Greece, with the consent of the Great Powers, occupied North Epirus, and formally took possession of it in March, 1916. By the end of 1920, however, the occupation had not yet been recognized.--Epirus is also the name of an administrative province of Greece, formed after the Balkan campaigns (1912-3) out of the territory acquired by the country.

EPISTEMOL'OGY (Gr. _epist[=e]m[=e]_, knowledge), that department of metaphysics which investigates and explains the doctrine or theory of knowing. It deals with the validity of knowledge rather than with the analysis of the knowing mind, and is thus distinguished from _psychology_. It is also distinguished from _ontology_, which investigates real existence or the theory of being.

EPIS'TOLAE OBSCURO'RUM VIRO'RUM (_Letters of Obscure Men_), the title of a collection of satirical letters which appeared in Germany in 1515, and professed to be the composition of certain ecclesiastics and professors in Cologne and other places. It is considered as one of the most masterly pieces of sarcasm in the history of literature, and its importance is enhanced by the effect it had in promoting the cause of the Reformation. The authorship of this satire has been a fertile subject of controversy, and is yet apparently far from being settled. It was ascribed to Reuchlin, and afterwards to Reuchlin, Erasmus, and Hutten. By a Papal bull the work was placed on the Index of forbidden books.

EP'ITAPH (Gr. _epi_, upon, and _taphos_, tomb), an inscription upon a tomb or monument in honour or memory of the dead. Epitaphs were in use both among the Greeks and Romans. The Greeks distinguished by epitaphs only their illustrious men. Among the Romans they became a family institution, and private names were regularly recorded upon tombstones. The same practice has generally prevailed in Christian countries. On Christian tombstones epitaphs usually give brief facts of the deceased's life, sometimes also the pious hopes of survivors in reference to the resurrection or other doctrines of the Christian faith, &c. Many so-called epitaphs are mere witty _jeux d'esprit_, which might be described as epigrams, and which were never intended seriously for monumental inscriptions. Dr. Johnson and William Wordsworth wrote essays on epitaphs.--Cf. Andrews, _Curious Epitaphs_.

EPITHALAMIUM (Gr. _epi_, on, and _thalamos_, a chamber), a nuptial song or poem in praise of a bride and bridegroom. Among the Greeks and Romans it was sung by young men and maids at the door of the bridal chamber of a newly-married couple. Epithalamia have been written by Spenser, Ben Jonson, and Donne.

EPITHE'LIUM, in anatomy, the cellular layer which lines the internal cavities and canals of the body, both closed and open, as the mouth, nose, respiratory organs, blood-vessels, &c., and which is analogous to the cuticle of the outer surface. There are several varieties of epithelium. The epithelium lining the blood-vessels is called sometimes _endothelium_.

EPIZO'A, a term applied to those parasitic animals which live upon the bodies of other animals, as lice, the itch-mite, &c.

EPIZO[:O]T'IC, or EPIZO[:O]TIC DISEASE, a disease that at some particular time and place attacks great numbers of the lower animals just as an epidemic attacks man. Pleuro-pneumonia is often an epizo[:o]tic, as is also the rinderpest.

EPOCH, or ERA, is a fixed point of time, commonly selected on account of some remarkable event by which it has been distinguished, and which is made the beginning or determining point of a particular year from which all other years, whether preceding or ensuing, are computed. The creation and the birth of Christ are the most important of the historical epochs. The creation has formed the foundation of various chronologies, the chief of which are: (1) The epoch adopted by Bossuet, Ussher, and other Catholic and Protestant divines, which places the creation in 4004 B.C. (2) The _Era of Constantinople_ (adopted by Russia), which places it in 5508 B.C. (3) The _Era of Antioch_, used till A.D. 284, placed the creation 5502 B.C. (4) The _Era of Alexandria_, which made the creation 5492 B.C. This is also the _Abyssinian Era_. (5) The _Jewish Era_, which places the creation in 3760 B.C. The Greeks computed their time by periods of four years, called _Olympiads_, from the occurrence every fourth year of the Olympic games. The first Olympiad, being the year in which Coroebus was victor in the Olympic games, was in the year 776 B.C. The Romans dated from the supposed era of the foundation of their city (Ab Urbe Condita, A.U.C.), the 21st of April, in the third year of the sixth Olympiad, or 753 B.C. (according to some authorities, 752 B.C.). The _Christian Era_, or mode of computing from the birth of Christ as a starting-point, was first introduced in the sixth century, and was generally adopted by the year 1000. This event is believed to have taken place earlier, perhaps by four years, than the received date. The Julian epoch, based on the coincidence of the solar, lunar, and indictional periods, is fixed at 4713 B.C., and is the only epoch established on an astronomical basis. The _Mohammedan Era_, or _Hej[)i]ra_, commences on 16th July, 622, and the years are computed by lunar months. The Chinese reckon their time by cycles of 60 years. Instead of numbering them as we do, they give a different name to every year in the cycle.

EPPING, a village of England, in Essex (giving name to a parliamentary division), 17 miles from London, in the midst of an ancient royal forest which one time covered nearly the whole of Essex. The unenclosed portion (5600 acres) was bought by the Corporation of London in 1882, and secured to the public as a free place of recreation. Pop. 4253.

EPSOM, a town in the county of Surrey, England, 15 miles S.W. of London, formerly celebrated for a mineral spring, from the water of which the well-known Epsom salts were manufactured. The principal attraction Epsom can now boast of is the grand race-meeting held on the Downs, the chief races being the Derby and Oaks. Epsom gives name to one of the seven parliamentary divisions of the county. Pop. 19,156.

EPSOM SALTS, sulphate of magnesium (MgSO_47H_2O), a cathartic salt which appears in capillary fibres or acicular crystals. It is found covering crevices of rocks, in mineral springs, &c.; but is commonly prepared by artificial processes from magnesian limestone by treating it with sulphuric acid, or by dissolving the mineral _kieserite_ (MgSO_4H_2O) in boiling water, allowing the insoluble matter to settle, and crystallizing out the Epsom salts from the clear solution. It is employed in medicine as a purgative, and in the arts. The name is derived from its having been first procured from the mineral waters at Epsom.

EPWORTH, a small town of N. Lincolnshire, 9 miles N. of Gainsborough, the birth-place of John Wesley, the founder of Methodism. Pop. 1836.

EQUATION, in algebra, a statement that two expressions have the same numerical value. An equation may be either identical or conditional. An example of an _identical equation_, or _identity_, is (x + y)(x - y) = x^2 - y^2. The left side here can be transformed into the right side, simply by applying the laws of algebra so as to carry out the operations indicated, without taking account in any way of the numerical values of x and y. An identical equation is, therefore, true for all values of the variables which appear in it. A _conditional_ equation is not true unless certain special values are assigned to the variables. Thus the equation 4x + 7 = 15 is not true for any value of x except 2. This value 2 is called a _root_, or _solution_, of the equation. An equation may have more than one root, e.g. x^2 + 6x = 7 has two roots, 1 and -7; and 2x^3 + 3x^2 = 2x + 3 has three roots, 1, -1, -3/2.

_Rational Integral Equations_ (_one Variable_).--The three equations just given are special cases of the class of rational integral algebraic equations. The general form of these is ax^n + bx^{n-1} + ... + kx + l = 0, where n is a positive integer, and a, b, ... k, l are given numbers. This equation is said to be of degree n. The branch of mathematics called the Theory of Equations is conventionally restricted to equations of this type. The fundamental result in this subject is that every rational integral equation has a root, a theorem which it is by no means easy to prove. It follows without difficulty that an equation of degree n has exactly n roots, real or imaginary. Two or more of the roots, however, may be equal to each other. To _solve_ an equation is to find its roots. The general equation of degree n can always be solved to any degree of approximation desired, when the numerical values of the coefficients a, b, ... are assigned. Graphical methods of solution are often the best (see _Graph_). When the coefficients a, b, ... are arbitrary, the general equation can be solved algebraically if n does not exceed 4, but not for greater values of n. It is not that the algebraical solution, or algebraic formula for the roots, when n is greater than 4, has not been discovered; it does not exist. This was proved more than a hundred years ago by Abel and Galois, two mathematicians of the highest distinction, who both died before they were thirty. For n = 2, the roots of the _quadratic_ equation ax^2 + bx + c = 0 are (-b +/- [sqrt]( b^2 - 4ac))/2a. For n = 3, the _cubic_ equation ax^3 + bx^2 + cx + d = 0 is reduced to the form z^3 + pz + q = 0 by putting x = z - b/3a ; the solution of z^3 + pz + q = 0 can be verified to be z = u - p/3u, where u is any one of the three cube roots of the quantity -1/2q + [sqrt](1/4q^2 + 1/27p^3). For n = 4, the _biquadratic_ equation is solved with the help of the solution of the cubic. The cubic was first solved by the Italian mathematician Tartaglia, who communicated the solution to Cardan, after binding him to keep it a secret. Cardan, however, gave the solution in his _Algebra_, published at N[:u]rnberg in 1545.

_Equations with more than one Variable._--A solution of an equation which contains more than one variable is a set of values of the variables making the equation true. Thus the equation x^2 - y^2 = 9 has solutions (x = 5, y = 4), (x = 3, y = 0), (x = 5, y = -4), and an unlimited number of others. When several variables occur, there are usually also several _simultaneous_ equations connecting them; a solution of these is a set of values of the variables making _all_ the equations true. When the number of equations is equal to the number of variables, there is in general a limited number of solutions of the system. Thus, e.g. the system of equations x^2 - y^2 = 9, 2x - y = 6 has two solutions (x = 3, y = 0) and (x = 5, y = 4), and no others. A useful rule is that the number of solutions of a system of this type is equal to the product of the degrees of the equations. Exceptions may arise when two solutions coalesce, or when infinite values of the variables occur.

Equations are of great importance in applied mathematics. The data of a problem generally lead to an equation, or a set of equations, among the quantities concerned. In practice a certain number of these quantities are known in any given case; the unknown quantities are then found by the solution of an equation or equations. Non-algebraic equations occur frequently--equations involving trigonometrical functions, for example. For a modern practical method of solving equations of many types, see _Nomography_.--BIBLIOGRAPHY: A. E. Layng, _Elementary Algebra_; C. Smith, _Algebra_. More advanced works are: G. Chrystal, _Algebra_; W. S. Burnside and A. W. Panton, _Theory of Equations_.

EQUATION, PERSONAL, the accustomed error, almost a constant quantity in the case of a practised observer, in timing a celestial phenomenon.

EQUATION OF PAYMENTS, an arithmetical rule for the purpose of ascertaining at what time it is equitable that a person should make payment of a whole debt which is due in different parts, payable at different times.