Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/179

 Thomson (Lord Kelvin), who discussed it long afterwards. It may be defined as an elastic medium of (negative) compressibility such as to make the velocity of the longitudinal wave zero: this implies that no work is required to be done in order to give the medium any small irrotational disturbance. An example is furnished by homogeneous foam free from air and held from collapse by adhesion to a containing vessel.

Cauchy, as we have seen, did not attempt to refute Green's objection that such a medium would be unstable; but, as Thomson remarked, every possible infinitesimal motion of the medium is, in the elementary dynamics of the subject, proved to be resolvable into coexistent wave-motions. If, then, the velocity of propagation for each of the two kinds of wave-motion is real, the equilibrium must be stable, provided the medium either extends through boundless space or has a fixed containing vessel as its boundary.

When the rigidity of the luminiferous medium is supposed to have the same value in all bodies, the conditions to be satisfied at an interface reduce to the continuity of the displacement e, of the tangential components of curl e, and of the scalar quantity (k + $4⁄3$n) div e across the interface.

Now we have seen that when a transverse wave is incident on an interface, it gives rise in general to reflected and refracted waves of both the transverse and the longitudinal species. In the case of the contractile aether, for which the velocity of propagation of the longitudinal waves is very small, the ordinary construction for refracted waves shows that the directions of propagation of the reflected and refracted longitudinal waves will be almost normal to the interface. The longitudinal waves will therefore contribute only to the component of displacement normal to the interface, not to the tangential components: in other words, the only tangential components of displacement at the interface are those due to the three transverse waves-the incident, reflected, and refracted. Moreover, the longitudinal waves do not contribute at all to curl e; and,