ELASMOBRANCHH. 730 ELASTICITY. mains having been found in the Upper Silurian. It is among the ehisraobranchs that we find the most primitive type of iislies. One of these more generalized primitive groups, the Cestraeionts, nj.v. ) abundant in Paleozoic times, is repre- sented today by two or three species of Port Jackson shaVks" (q.v.). Xone of the elasmo- branchs are very small, and among them are .some of the largest of aquatic vertebrates. There are about 300 living si)eoies, all marine. ELAS'MOSAU'RTTS (Xoo-Lat., from Gk. iaffti6s, rhisiiios. metal plate + (raOpos. saiiros, lizard). A gigantic aquatic reptile of the order Sauropterygia, one of the few American repre- sentatives of the European plesiosaurs. Re- mains of this sea-ser|)ent have been found in the Cretaceous deposits of Xew Jersey. It resembled the plesiosaurs in shape, but had a flattened tail. See Plesiosaurus. ELAS'MOTHE'RIUM (Xeo-Lat., from Gk. ia<rn6s, rlasmos, metal plate -|- driplop, thcrion, wild beast). An extinct fossil rhinoceros of gi- gantic size, found in the Pleistocene deposits of Siberia and Russia. See Kmxoc-EROS. ELASTICITY (from Gk. iXainti/, elaunein, to drive, set in motion). A general property of matter (see Mattek) in virtue of which, if it is strained in any Avay by means of a force, it returns to its former condition more or less per- fectly when the force is removed. Solids. A solid body is distinguished by having under ordinary conditions a definite volume and shape, both of which may. however, be altered by the application of suitable forces. In general, when a solid is deformed in any way — e.g. l)ent, stretched, etc. — any small portion of it has both its size and shape changed. To secure a strain of the solid such that each minute portion preserves its shape and suffers a change in vol- ume only, it is necessary to apply a uniform pressure, i.e. a uniform force per square centi- meter, over the whole surface of the solid, thus compressing it equally in all directions. This can be done by immersing the solid body in some liquid — e. g. water — which can be i)ut under a great ])ressure. Let the original value of the vol- ume be V and of the pressure be p; then if, as the result of increasing the pressure by a small amount Ap, the volume is decreased a small amount At', the 'coefficient of elasticity for a change in volume' — or the 'bulk-modulus' — is defined to be ^■ = ? A» The ratio Al- ls called the 'strain' : and A», the change in the force per square centimeter, equals what is called the 'stress.' "Stress' is the alteration in the pressure of the portions of the solid on each other, i.e. it is an internal prop- erty. It is measured, however, by the external force producing the deformation; because, when this forc-e is applied, the body is compressed and there are forces of restitution produced which oppose the applied force and exactly balance it when there is no further compression. For any one substance, e.g. a definite kind of glass or iron, 7,- is a constant qtiantity. To produce a change in the shape of minute portions of a solid without sensibly altering their volumes, it is necessary to apply what is called a "shearing" stress, i.e. a combination of forces like that due to a pair of shears when used iu cutting a piece of paper or cloth. Thus, if a cubical block of wood is held between two "T" T boards lirmly screwed to it, and if the boards are pushed slightly sidewise, but in opposite direc- tions, the upper one to the right and the lower to the left, the block will have its shape changed to an oblique solid, as indicated in exaggerated form in the diagram, while the change in the volume will be infinitesimal. The angle through which tlie edge of the block is turned is taken as the measure of the strain: and the stress equals the force used to push one of the boards sidewise divided by the area of the cross-section of the block. This stress is an internal force, being due to the reaction of the solid against the shearing forces which tend to make one layer of the solid move over the other. When there is no further alteration under the action of these external forces, they must be exactly equal and opposite to the internal forces of restitution. Calling this ratio of the force to the area T. and the angle of the strain I, the coellicient of elasticity for a change in shape — or the coeffi- cient of rigidity — is defined as T "=T The simplest case in practice of a pure change in shape is when a wire or rod is twisted slightly round its axis of figure: this is called "tor- sion.' It can be shown from theoretical consid- erations that if a wire or rod with a circular cross-section is clamped at one end and the other end twisted around the axis through an angle if/, a moment will l)e required equal to rr r* n tp •21 where »■ is the radius of cross-section and I is the length of the wire. It is found that for any definite kind of matter, regardless of its size or shape, H is a constant quantity. By far the commonest deformation of a solid is that experienced when a rod or beam is stretched, compressed, or bent. In all these cases it is evident that it is simply a matter of chang- ing the length of the rod or beam, or of certain portions of it. Thus, if a wire of cross-section A and of length L is clamped at one end and under the stretching force F is elongated by an amount I. the strain is defined to be 7/I> and the stress equals F/A. This stress, although measured by the applied force, is the internal reaction. The ratio of these two, viz. : ^-T- Ai is called '^"oung's modulus' beeauRP its impor- tance was first emphasized by Thomas Young. In this deformation both the size and shape of
