ME. HOPKINS ON THE THEOEY OE THE MOTION OF OLACIEES. 
679 
leads to cubical extension or compression ; in the latter, merely to extension or compres- 
sion of the surface and not the volume of the element, which may be called swperjicial 
extension or compression. These changes of volume and form in any element must be 
produced by the forces acting on it. Thus we may conceive linear extension alone pro- 
duced at any interior point of the mass by two equal and opposite tensions acting on 
two elementary component particles there in the direction of the line joining their 
centres of gravity, while compression alone would result if those tensions were changed 
into pressures. In such cases extension or compression would be the result of forces 
which may be called direct or normal forces. In the case above mentioned, in which the 
volume and density of every element of the mass remain unaltered, there can be ho such 
direct normal action as that just mentioned. The action must be perpendicular to the 
normal, and must therefore be a transversal or tangential action. There would be no 
tendency to make the contiguous particles approach to or recede from each other, but 
to cause the one to slide tangentially past the other. 
If the body have a structure like that of any hard vitreous or crystalline mass, pres- 
sure at any point will tend to break or crush the body, and thus to destroy the conti- 
nuity of its structure. This tendency will be opposed by the resisting power of the sub- 
stance. The tendency of the direct or normal tension is to separate the contiguous 
particles, and thus produce a finite fissure, or a discontinuity in the mass. It is resisted 
by the normal cohesive power ; and in like manner the transverse or tangential action is 
resisted by the tangential cohesion, or that which prevents the component particles from 
sliding past each other. xYgain, when the component particles at any point of a body 
are relatively displaced, they have always a certain tendency to regain their originally 
undisturbed position ; and the force thus excited, considered with reference to the force 
of displacement at that point, affords a measure of what is called the elasticity of the 
body. Since the force of restitution may vary from zero to the corresponding force of 
displacement, the elasticity, when measured by their ratio, may vary from zero to unity. 
2. We may now define such terms as solid, plastic, viscous, and the like, with all the 
accuracy which their definitions admit of. We may call a body emphatically a solid body 
when it possesses the following properties: — (1) small extensibility and compressibility, 
(2) great power of resistance and great cohesive power, both normal and tangential, and 
(3) great elasticity. It will thus require a comparatively great force to produce any 
sensible relative displacement among the constituent molecules of the body : if we con- 
ceive the force required to become infinitely great, we arrive at absolute rigidity as the 
limit of solidity. Again, we shall best, perhaps, define plasticity or viscosity, if we 
suppose the forces of displacement to be such as to produce only a small transverse or 
tangential displacement of the constituent particles, i. e. a superficial, not a cubical, 
extension or compression. Then, if the force of restitution bear only an inappreciable 
ratio to the corresponding force of displacement, i. e. if the tangential elasticity be not 
of sensible magnitude, the mass may be emphatically said to be plastic. This is the 
essential condition of what may with strict propriety be termed plasticity ; it might also 
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