ELASTICITY

(Gr. iXoctrrvi, a spring; from iXoivvtu, I draw.) In Physics, that property which certain bodies po e of recovering their primitive form and dimensions after tbe external force by which they have been dilated or compre ed or bent is withdrawn. The theory of elasticity must be deduced from some hypothesis respecting the constitution of matter. The simplest and most general view which can be taken of the subject is, that all matter is composed of indefinitely small parts or molecules acted upon by attractive and repulsive forces. The attractive torces result from the action of the molecules on each other; the repulsive forces from the caloric with which the molecules are combined. From the combined action of these two forces, the attraction of matter and the repulsion of caloric, the different forms of matter and its varied physical properties may be explained. This view of the constitution of bodies supposes that the molecules are not in contact, but at a certain distance from each other, v/hich, though it is to be regarded as infinitely small in comparison of any distance apprehible by our senses, admits neverthele of increase and diminution. When a body is in a state of rest, the opposite forces which any two of its contiguous molecules exercise on each other are in equilibrium. The energy of the forces also depends on the distance between the two molecules, or, in mathematical language, is a function of that distance. If the distance be increased within the limits of the action of the forces, both forces are diminished; and if the distance is diminished, both are in385 ELASTIC CURVE. creased, but not in the same proportion. If the Interval at which the two forces balance each other be diminished, the repulsive force becomes stronger than the attractive force, and the two molecules are repelled from each other: on the contrary, if the distance be increased, the attractive force acquires the superiority, and the molecules are drawn towards each other. Let us now suppose a solid body, of which all the molecules are in a state of equilibrium, to receive the impre ion of an external force. The operation of the force is to produce a change in the distances of the molecules at the surface, in consequence of which the equilibrium is disturbed, and the molecules thrown into a state of vibration. This vibration is communicated to the interior molecules; and the body, under the action of the external force, undergoes a certain change of form. The molecules at the surface, which receive the impulse, transmit it to those in the interior of the body, and are reacted on by them with an equal force. In this manner the action is propagated through the whole ma , until it is destroyed by another exterior force, or by the resistance of an obstacle to the motion of the body itself. From this hypothesis respecting the constitution of matter, analytical expre ions may be deduced to represent the motions or the equilibrium of the molecules of a body acted upon by an external force which is not so great as to exceed the limits of its elasticity, or to produce a change in the distance of the molecules greater than the radius of the sphere of molecular action. These equations contain a numerical coefficient, which is constant for the same body, but variable for different bodies: and which has no influence on the law of elasticity, though it serves to measure its effects. It is therefore called the modulus of elasticity, or coefficient of elasticity; and is of the same nature and order of magnitude as the cohesive resistance which bodies oppose to rupture on being crushed, and may therefore be expre ed as so many pounds acting on a square inch of surface. The modulus of elasticity for each particular body must be determined by experiment, and has only been ascertained in a few instances. Elasticity is perfect when the body exactly recovers its primitive form, after the force by which it is bent or compre ed or dilated has been removed, in the same time as was required for the force to produce the alteration. This perfect elasticity is, however, not found in any of the bodies of nature; the aeriform fluids or gases are those whose elasticity approaches the nearest to it. Hard bodies, even tempered steel and ivory, po e it in a le degree; in fluid substances the elastic force is greatly diminished; and in soft bodies, as butter, moist clay, it entirely disappears. In solid bodies the elastic force is, in general, diminished by use, or by a long-continued application of a straining force. A bow which has been long bent, or a spring which has been long compre ed, will not entirely recover its original form. In many cases the elasticity of a body can be augmented by producing a closer aggregation of the molecules. The metals, for example, are rendered more elastic by hammering them cold, or by alloys. Iron and steel acquire a greater elasticity by tempering; that is, by producing a sudden contraction of their volumes wlien they have been expanded by heat. The principal phenomena of elastic bodies are the following:—1. That an elastic body (the elasticity being supjjosed perfect) exerts the same force In endeavouring to restore itself as that with which it was compre ed or bent. 2. The force of elastic bodies is exerted equally in all directions, but the effect chiefly takes place on the side on which the resistance is the least. 3. When an elastic solid body is made to vibrate by a sudden stroke, the vibrations are performed in equal times, to wliatever part of the body the stroke may be communicated. Thus, sonorous bodies always emit sounds of the same pitch; and the difference of the pitch dejjends on the greater or le frequency of the vibrations of the sonorous body. 4. A body perfectly incompre ible cannot be elastic, therefore bodies perfectly solid can have no elasticity; and hence, also, the small degree of elasticity belonging to the liquids which are eminently incompre ible. See Collision, Percu ion, Strength of Materials; also Atmosphere, Hydrouynamics, Pneumatics, and Vapour. [s. 398]