E´laps, a genus of poisonous American snakes, the type of the family Elapidæ, 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 Kléber 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 Chimæra (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 chimæroids), 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 chimæroids. 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 | , | dv | , | dw | , | dw | + | dv | , | du | + | dw | , | dv | + | du | , |
| dx | dy | dz | dy | dz | dz | dx | dx | dy |