Part 9

EINSTEIN, Albert (1879- ), physicist, was born at Ulm, W[:u]rtemberg, Germany, of German-Jewish parents. He was educated at the Gymnasium in Munich, and, on leaving school in his sixteenth year, accompanied his parents to Milan. Six months later, he enrolled at the Technical High School in Zurich, where he studied from 1896 to 1900. He held a post in the Swiss Patent Office from 1902 to 1909, then various professorships in Zurich till 1914, when he received a call to the Prussian Academy of Science, Berlin, as successor to van't Hoff. Einstein has been twice married. He has become famous as the author of the Theory of Relativity (q.v.). The 'special theory', which deals chiefly with electrodynamics and optics, was published in 1905, and the 'general theory' or theory of gravitation, about ten years later. His name became popularly known in 1919, after observations made during the solar eclipse of that year had verified his prediction of the bending of rays of light coming from a star and passing close to the sun. He has made other valuable contributions to Theoretical Physics, among these being a theory of the Brownian movements and various important applications of the modern quantum theory of energy. In 1921 he visited the United States and Britain, and delivered many lectures on Relativity.

EISENACH ([=i]'z[.e]n-[=a]_h_), a town of Germany, in the former grand-duchy of Saxe-Weimar, near the mountains of Thuringia, at the junction of the Nesse and H[:o]rsel. It is an attractive town, and contains a palace erected in 1742. It has manufactures of pottery, leather, woollen yarn, &c. Sebastian Bach was born there in 1685. Near it lies the Wartburg, where Luther was kept for safety during 1521 and 1522. Pop. 38,362.

EISENBERG ([=i]'z[.e]n-ber_h_), a town of Germany, former duchy of Saxe-Altenburg, with a palace and various manufactures. Pop. 10,750.

EISLEBEN ([=i]s'l[=a]-b[.e]n), a town, Prussian Saxony, 25 miles north-west of Merseburg, celebrated as the place where Luther was born and where he died. There are many memorials of Luther, and also a bronze statue of the reformer erected in 1883. Copper is extensively worked in the neighbourhood. Pop. 24,630.

EISNER, Kurt, Bavarian revolutionary leader, born in 1867 at Berlin, of a Jewish family. He studied at the University of Marburg, and early acquired a vast erudition. Entering journalism, he contributed to the _Frankfurter Zeitung_, where he published an article attacking the Kaiser. For this he was condemned to nine months' imprisonment. He then wrote for the Socialist press and eventually became editor-in-chief of the _Vorw[:a]rts_. In 1907 he published a work entitled _The Fall of the Empire_ which attracted much attention, and in 1910 he attacked Prussian ascendancy in the _Munich Post_. Eisner took an active part in the Revolution of 1918, and was appointed Prime Minister of Bavaria. A revolutionary and a Socialist, he was, however, opposed to Bolshevism, which he did not hesitate to criticize violently. But his policy of separation, his aim of liberating the South German States, and his constant attacks upon the Kaiser and the whole military caste of Germany, brought him many enemies. Whilst on his way from his house to the Foreign Office he was shot at and killed by Count Arco Valley on 21st Feb., 1919.

EISTEDDFOD ([=i]-steth'v[=o]d; W. _eistedd_, to sit, and _bod_, to be; pl. _eisteddfodau_), an ancient assembly of Welsh bards for the purpose of musical and poetical contests, the judges being originally appointed by commissions from the native princes, and after the conquest from the English kings. There are two kinds of eisteddfodau, the national or general, and the provincial gatherings which take place in many parts of Wales. The last commission was issued by Queen Elizabeth in 1568, but the eisteddfod fell into abeyance during the seventeenth century. In 1798 the ancient custom was revived by the Gwynnedigion Society, and on a more elaborate scale by the Cambrian Society, which grew out of the Gwynnedigion. Eisteddfodau are now held annually in North and South Wales alternately, and are attended by many thousands of people. The festivals of 1919 and 1920 were held at Corwen and at Barry, Glamorgan, respectively.--Cf. Rhys and Brynmor Jones, _The Welsh People_.

EJECT'MENT, in law, an action wherein the title to lands and tenements may be tried and the possession recovered. It is commenced by a writ addressed to the tenant in possession and all entitled to defend the possession, bearing that the plaintiff lays claim to the property in question, and calling upon all interested to appear within a certain time to defend their rights. In its older form the action was remarkable for the curious fictions on which procedure was based. The names of John Doe, an imaginary plaintiff, and of Richard Roe, an imaginary defendant, were familiar in cases of this kind in the English courts until 1852, when the Common Law Procedure Act abolished these fictitious suitors.

EJECTOR, in mechanical engineering, an appliance for ejecting gases, vapours, or liquids from closed spaces by the use of another gas, vapour, or liquid at a higher pressure. For instance, the air may be extracted from a condenser by an ejector. A jet of steam is directed along a short specially-shaped pipe leading from the condenser to the outside atmosphere. The velocity of the steam when it leaves the jet in the pipe is very high, and it blows out into the atmosphere in spite of the atmospheric pressure against it. In blowing out into the atmosphere it sucks the air in the condenser along with it, and after it has been in operation some time practically the whole of the air is sucked out of the condenser. The appliance works on the principle of momentum. The active jet mixes with the material to be ejected and imparts a common momentum to the mixture, which is sufficient to enable it to pass outside the vessel from which the ejection is taking place. The same principle is used in the mercury air-pump (see _Air-pump_).--BIBLIOGRAPHY: W. E. Dalby, _Steam Power_; _Modern Mechanical Engineering_ (The Gresham Publishing Company).

EKAT'ERINBURG, a town, Russia, in the government and 170 miles S.E. of Perm, founded in 1723 by Peter the Great. It is the mining and metallurgy centre of the Ural regions; and gem-cutting, the making of machinery, cloth, and candles are industries. Pop. 70,000.

EKAT'ERINODAR, a town of Russia in the Caucasus, chief town of the Kuban territory, on the River Kuban, a poorly-built place with a considerable trade. Pop. 107,360.

EKAT'ERINOSLAV, a town of the Ukraine, capital of a government of the same name, on the right bank of the Dnieper, 250 miles N.E. of Odessa. Founded in 1787, it is a manufacturing centre, producing iron, machinery, tobacco, and beer. Pop. 220,100.--The government, which is intersected by the Dnieper and reaches the Sea of Azov, has great mineral wealth, especially in coal (Donetz basin), iron, manganese, and rock-salt; and its fertile black-earth soil produces abundant crops of wheat and other grains. Area, 24,478 sq. miles; pop. 3,537,300.

ELAEAGNA'CEAE, the oleaster family of plants, a small nat. ord. of apetalous dicotyledons scattered over the northern regions. The only British member is the sea-buckthorn (_Hippophae rhamnoides_).

ELA'IN, the oily principle of fat obtained by submitting fat to the action of boiling alcohol, allowing the stearin to crystallize, and then evaporating the alcoholic solution. It is not unlike vegetable oil in its appearance and its properties, and forms soaps with alkalies.

E'LAM, the ancient name of a country on the eastern border of Babylonia. Its civilization dates back beyond 3000 B.C. Before 2000 B.C. it was strong enough to subdue part of Babylonia. Its power was finally broken by the last Assyrian monarchs. The capital was Susa, which became prominent again after the rise of Cyrus. Its splendour during the Persian period is reflected in the _Book of Esther_, in which it is referred to as 'Shushan'.

E'LAND, _Oreas_ (_Orias_) _canna_, a species of antelope inhabiting Africa, the largest of all its kind, being about the size of an ox. Its flesh, especially that of the thighs, which are dried and used in this state, is highly prized. It is now almost extinct south of the Limpopo, but it is plentiful in the Kalahari. The colour is a light or greyish brown, and it possesses a short mane. The horns, which are about 18 inches long and nearly straight, are spirally keeled.

EL'ANUS, the name of certain species of raptorial birds of the genus El[=a]nus, belonging to the kites. The type species is the black-winged kite (_E. caeruleus_) of Africa and South Asia, which strays to South-West Europe. A very similar form (_E. leucurus_) is native to tropical and subtropical America, and other species (_E. scriptus_ and _E. axillaris_) are Australian.

ELAPHOMYCES, a genus of Ascomycetous fungi, section Plectascineae, with closed, subterranean ascus-fruits resembling those of the genuine truffles (Tuberineae), but not closely allied to that family. _E. cervinus_ (Hart's truffle) is not infrequent in Britain; it forms 'mycorhiza' with roots of oak, beech, and various conifers.

E'LAPS, a genus of poisonous American snakes, the type of the family Elapidae, to which belongs the cobra de capello.

EL-ARISH, Egyptian city on the Mediterranean, on the Wadi el-Arish, and chief city of the territory bearing the same name. It was taken by the French under Kl['e]ber in 1799, but abandoned the same year. Pop. about 5000.

ELASMOBRANCHII (-brang'ki-i), a sub-class of fishes, including sharks, dog-fishes, rays (skates); and also Chimaera (q.v.) and its allies. They are predaceous forms, in which the mouth is a transverse slit on the under side of the head, the numerous simple teeth are in several rows (except in chimaeroids), the short intestine possesses a spiral valve and opens into a cloaca. The tail is asymmetrical (heterocercal), and numerous placoid scales (dermal denticles) are embedded in the skin. The skeleton is cartilaginous; the heart possesses a muscular conus arteriosus with numerous rows of pocket-valves; and there are five (sometimes six or seven) pairs of gill-pouches opening by slits to the exterior, these not being covered by an external flap (operculum) except in chimaeroids. Fertilization is internal, and the male is provided with a pair of copulatory organs (claspers) projecting backwards from the pelvic fins. The eggs sometimes develop within the body of the mother, but are usually laid in horny pouches (mermaids' purses). The group is of great antiquity, and many extinct fossil types are known.

ELASMOTHE'RIUM, an extinct genus of Mammalia, found in the post-Pliocene strata of Europe, comprising animals of great size allied to the rhinoceros, and having probably one large horn and a smaller nasal horn.

ELASTIC BITUMEN, ELATERITE, or MINERAL CAOUTCHOUC, an elastic mineral bitumen of a blackish-brown colour, and subtranslucent. It has been found at Castleton, in Derbyshire.

ELASTICITY, the property in virtue of which bodies resist change of volume or of shape, and tend to regain their original bulk or shape when the deforming forces are removed. Solids possess elasticity of volume and of shape. Liquids and gases have elasticity of volume; they resist compression, but offer only a transient resistance to change of shape (see _Viscosity_). The elasticity of a gas is measured by the pressure to which the gas is subjected, if there is no change of temperature. When a gas is compressed suddenly, it has a greater elasticity on account of the rise of temperature which takes place. Liquids are less compressible than gases; water is compressed by about 1 part in 20,000 when the pressure on it is increased by one atmosphere. A knowledge of the elastic properties of solids is of importance in all branches of applied mechanics. Homogeneous solids offer definite resistance to compression, twisting, stretching, and bending, and this resistance is expressed by a number called a modulus. Let the deforming force be reckoned per unit of area, e.g. a pressure in tons per square inch; this is called the stress. The unital deformation produced by the stress is called the strain, for example, compression per unit of volume. The modulus is obtained by dividing the stress by the strain; if this is done with the above example, the ratio will give the bulk modulus. When the applied forces cause change of shape without change of volume, the ratio of stress to strain is called the shape modulus or the rigidity of the material. This property is brought into play when mechanical power is transmitted by means of shafting. Young's modulus is employed in the cases of stretching and bending. It is given by the ratio stretching force per unit area to stretch per unit length. In 1678 Hooke stated the law that stress is proportional to the strain which it causes. This law is found in practice to be true for metals within a certain range of stress which lies below the elastic limit. If the stress is increased beyond this limit, the material begins to give way, and permanent change of shape or volume takes place. In the processes of riveting and wire-drawing, the material is purposely strained beyond the elastic limit, whilst the correct working of a spring balance requires that the spring should never be overstrained. When metals are subjected to frequently repeated stresses, they undergo a weakening and are said to become fatigued, and are liable to give way under a smaller stress than would otherwise cause fracture. The speed with which sound waves are transmitted through a material depends on the elasticity of the material; such compressional waves in water have been employed by the Roumanian engineer, Constantinescu, to transmit power by means of water-pipes.

_Mathematical Theory._--Consider an elastic body at rest and free from strain. Let the body be subjected to forces, fulfilling the ordinary statical conditions of equilibrium, and therefore not tending to give the body any motion of translation or rotation as a whole. The particles of the body will move very slightly relative to each other; in other words, a system of strain will be set up in the body. To maintain this strain a definite system of stress is necessary. The problem for the mathematical theory is to determine the state of strain and stress at every point of the body when the applied forces are given. These applied forces may either be body forces (of which practically the only example is weight), or surface forces; the latter are pressures or tractions, and are defined by their directions and amounts per unit area. It is first of all necessary to show how strain and stress can be specified mathematically.

_Strains._--If x, y, z are the co-ordinates of a point in the unstrained body, and if this point is displaced to (x + u, y + v, z + w) when the straining forces are applied, then u, v, w, which are supposed to be very small, are called the component displacements at (x, y, z). It is clear that if u, v, w were constant, the body would simply be displaced without strain. The state of strain can in fact be shown to depend on the first derivatives of u, v, w with respect to x, y, z. The strain round any given point consists simply of three stretches parallel to a certain set of three mutually perpendicular directions. These directions vary from point to point, so that this specification of the strain is inconvenient for calculations. A suitable method depends on the fact that the strain is known round a point when we know the values of the six quantities

du/dx, dv/dy, dw/dz, dw/dy + dv/dz, du/dz + dw/dx, dv/dx + du/dy,

at the point. These are called the components of strain at (x, y, z). The first three are _stretches_ parallel to the axes, the other three are _shearing_ strains. We may get an idea of the nature of these strains from two simple typical cases. 1. Let u = ex, v = 0, w = 0. This makes du/dx = e, and the other five strains zero. But we see that the displacement of every particle is perpendicular to the yz plane, and proportional to its distance from that plane. Every line parallel to the axis of x is therefore elongated by a definite fraction of its original length, the value of this fraction being e, which is du/dx. The strains du/dx, dv/dy, dw/dz are therefore _stretches_ parallel to the axes. 2. Let u = 0, v = cz, w = 0. This gives dv/dz + du/dy = c, and the other five strains zero. The displacement of every particle is parallel to the axis of y, and proportional to its distance from the plane xy. The strain is therefore a slide, or _shear_ of planes parallel to xy in the direction of the axis of y.

_Stresses._--To specify the stress round a point (x, y, z), consider a small plane area through the point. The material on one side of this acts on the material on the other side with a certain force whose components parallel to the axes are F, G, H, say, per unit area. If we know F, G, H for every orientation of the small plane area, the state of stress round (x, y, z) is defined. But it is easy to show, as below, that we can find F, G, H for every area if we know them for areas parallel to the co-ordinate planes. We are thus led to the specification of the stress round (x, y, z) by the six _components of stress_, [=xx], [=yy], [=zz], [=xy], [=xz], [=yz]; where [=xy], for example, means the force per unit area _parallel_ to Ox exerted on a plane _perpendicular_ to Oy by the material on the positive side of that plane on the material on its negative side. Thus e.g. the components of the force per unit area exerted across the yz plane through (x, y, z) by the material on the positive side of that plane are [=xx], [=xy], [=xz]. It is important to note that [=xy] = [=yx]. This is easily proved by considering the equilibrium of a small rectangular volume of the material round (x, y, z) as centre, with its edges parallel to the axes; if [=xy] were not equal to [=yx], there would be a residual couple in the plane xy.

_Relations between the Strains and the Stresses._--When the strains are known, the stresses can be found from a generalized Hooke's law, which can be deduced from the principle of energy, combined with consideration of symmetry. If the solid is isotropic, i.e. is symmetrical in its elastic properties in all directions round a point, the relations between stress and strain are of the form

[=xx] = [lambda](du/dx + dv/dy + dw/dz) + 2[mu]du/dx,

[=yz] = [mu](dw/dy + dv/dz);

the values of the other four components of strain can be written down from symmetry. Here [lambda] and [mu] are constants, each being a _modulus_ of elasticity. In particular [mu] is the _shape modulus_ or the _rigidity_, already referred to. The Young's modulus and the bulk modulus can easily be found in terms of [lambda] and [mu].

_Equations of Equilibrium in Terms of the Stresses._--A rectangular element dx, dy, dz, of the body is held in equilibrium by the body force, and the tractions on its faces arising from the stress. The tractions per unit area, parallel to the axis of x, on the six faces, are: on the plane x, -[=xx]; on the plane x + dx, [=xx] + (d/dx [=xx])dx; on the plane y, -[=xy]; on the plane y + dy, [=xy] + (d/dy [=xy])dy; and similarly for the plane z. Let the force acting on the mass of the body, such as its weight, be (X, Y, Z) per unit mass, and let [rho] be the density. By equating the sum of the x components of all the forces to zero, we get

d[=xx]/dx + d[=xy]/dy + d[=xz]/dz + [rho]X = 0;

Similarly d[=xy]/dx + d[=yy]/dy + d[=yz]/dz + [rho]Y = 0,

and d[=xz]/dx + d[=yz]/dy + d[=zz]/dz + [rho]Z = 0.

_The Surface Tractions in Terms of the Stresses._--Draw a small tetrahedron round (x, y, z) with its faces perpendicular to the axes and to the direction (l, m, n), and consider the equilibrium of this small body. Let F, G, H be the components per unit area of the force on the plane whose direction cosines, _drawn outwards_, are l, m, n. If A be the area of the face perpendicular to (l, m, n), we get, by resolving parallel to Ox,

F.A = [=xx].lA + [=xy].mA + [=xz].nA.

Hence F = l[=xx] + m[=xy] + n[=xz],

and similarly G = l[=xy] + m[=yy] + n[=yz],

H = l[=xz] + m[=yz] + n[=zz].

If (x, y, z) is a point at the surface of the body, and l, m, n are the direction cosines of the outward normal at that point, these values of F, G, H are the component of the force that must be applied from outside to the surface at (x, y, z) to maintain the state of stress.

_The Equations connecting the Displacements and the Applied Forces._--By using, in the equations of equilibrium, the values of the stresses in terms of the strains, we find the body equations of equilibrium in terms of displacements,

[mu](d^2u/dx^2 + d^2u/dy^2 + d^2u/dz^2) + ([lambda] + [mu])d/dx(du/dx + dv/dy + dw/dz) + X[rho] = 0,

with two similar equations.

The surface equations of equilibrium can also be written down at once by substituting the values of stresses in terms of strains in the expressions for F, G, H given above.

_The Problem of Equilibrium._--To find the strain under given forces we have to solve the body and surface equations of equilibrium, when X, Y, Z and F, G, H are given. This problem has not been completely solved except in a few cases. It was solved by Lam['e] and Lord Kelvin for a solid or hollow sphere; it has also been solved for an infinite solid bounded by two parallel planes, or by a circular cylinder. Many particular solutions, however, are known for bodies of other shapes. Some of these solutions are of great practical value, e.g. St. Venant's solutions for the torsion and flexure of prisms. For bodies in which one or two dimensions are small, i.e. for thin plates and shells, and for thin rods, approximate theories have been given, which are partly deduced from the above exact equations, and partly from plausible hypotheses, a complete treatment based on the exact equations being in most cases impracticable.

_The Problem of Vibrations._--When a body is vibrating, the mass acceleration parallel to Ox of the particle at (x, y, z) is [rho] dx dy dz d^2u/dt^2. The equations of vibration are therefore found by writing - d^2u/dt^2 instead of X, in the first body equation of equilibrium, and similarly with the others. The surface conditions will usually be that F, G, H are zero. The problem has been completely solved by H. Lamb for a solid or hollow sphere. For the elastic solid theory of the luminiferous ether, see _Ether_; for some practical solutions of the general equations of equilibrium, see _Strength of Materials_.--BIBLIOGRAPHY: A. E. H. Love, _Mathematical Theory of Elasticity_; Lord Kelvin and Tait, _Natural Philosophy_; Todhunter and Pearson, _History of Elasticity and Strength of Materials_.

EL'ATERIDAE, the name of a family of beetles, remarkable for their ability to throw themselves to a considerable height in the air, when placed on their back, by a vigorous muscular movement. Hence their names of springing-beetles, click-beetles, skip-jacks, &c. When alarmed, the elater counterfeits death. Flowers, grass, and decaying wood are the habitations of these animals, which are almost always found singly. The larvae are often very injurious to vegetation, especially those which devour the roots of herbaceous plants (as in the genus Agri[=o]tes), and are known from then slenderness and hardness as wire-worms. The fireflies of America belong to the family. In these a pair of luminous organs is found on the thorax, while there is a third on the under side of the base of the abdomen. The _Pyroph[)o]rus noctil[=u]cus_, called _cucujos_ in Brazil, is used as a personal ornament by ladies. The largest species of the genus Elater, the _Elater flabellicornis_, is 2-1/2 inches in length.