ELASTICITY (from Gk. elm/nein. to drive, set in motion). A general property of matter (see I\IArrEal in virtue of which, if it is strained in any way by beaus of a force, it returns to its former condition more or less per fectly when the force is removed.
Soups. 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. bent. stretched. etc.—any small portion of it has both its size and shape ehanged. 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 lie done by immersing the solid body in some liquid—e. g. water—which can be put under a great pressure. Let the original value of the vol ume be r and of the pressure be p; then if, as the result of increasing the pressure by a small amount ..1p. the volume is decreased a small amount Jr, the 'coefficient of elasticity for a change in volume'—or the 'bulk•modulus'—is defined to be A — Ar The ratio called the 'strain': and An, the change in the force per square centimeter, equals NN hat 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 force is applied, the body is coinpressed and there are forces of restitution produeed which oppose the applied force and exactly balance it when there is no further compression. For any one substanee, e.g. a definite kind of glass or iron, k is a constant quantity.
To prodnee a ehange 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 in cutting a piece of paper or cloth. Thus, if a cubical block of wood is held between two boards firmly strewed to it. and if the boards are pushed slightly sidewise. but in opposite diree 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 volute will he infinitesimal. The angle through which the 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 la3er of the solid move over the other. When there is no further alteration under the action of these external forces, they must he exactly equal and opposite to the internal forces of restitution. Calling this ratio of the force to the area 'I', and the angle of the strain i, the coefficient of elasticity for a change in shape—or the coeffi cient of rigidity—is defined as T = The simplest ease 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 eircular cross-section is clamped at one end and the other end twisted around the axis through an angle a moment will be required equal to r' a IP 2 I where r 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. a 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 eases 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 \ and of length i, is clamped at one end and under the stretching force is elongated by an amount F. the strain is defined to be //I, and the stress equals 1.7.k. This stress, although measured by the applied force, is the interim! reaction. The ratio of these two, viz.: is called 'Young's modulus' because its tance was first emphasized by Thomas Young. In this deformation both the size and shape of the parts of the wire are altered; and therefore Young's 11111,t depend upon both the bulk modulus and the coefficient of rigidity. Calling Young'• modulus E, it may be shown theoretically that 1 :la Solids differ greatly in their compressibility and in their rigidity; and they differ widely in the extent to which they may be deformed and yet, recover their former shape and size when released from the deforming forces. If the strain is too great. the body does not regain its former condition: the 'limits of elasticity' are said to have been passed. A body is called 'elastic' if these limits permit a large strain e.g. steel; while if these limits permit only small or minute strains, the body is said to he 'inelastic.' 11. however, the strain is small enough solids do return quite exactly to their former states; and for such small strains it is observed that the amount of the deformation produced varies directly as the deforming force. Phis is called `Hooke's law,' from the name of the one Who first proposed it, Hobert Hooke. :Many solids after being strained return to their previous condition slowly after the deforming force is removed: and nearly all take consider able time to reach their pernwnent strain when a force is applied. There i3 therefore a slight molecular 'slipping' in general in every deforma tion of a solid; this necessarily involves internal friction and the production of heat effects—in particular. rise in temperature. A 'perfect' solid might he defined as one ill which there is no internal friction: while the more inelastic a body is. the greater are the slipping awl the in ternal friction when there is a deformation.