The Aether as an Elastic Solid. 159 



Thomson (Lord Kelvin), who discussed it long afterwards.* It 

 may be defined as an elastic medium of (negative) com- 

 pressibility 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 + ^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 ajid 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 trans- 

 verse waves the incident, reflected, and refracted. Moreover, 

 the longitudinal waves do not contribute at all to curl e ; and, 



* Phil. Mag. xxvi (1888), p. 414. 



