The Aether as an Elastic Solid. 171 



A way of escape from this conclusion suggested itself to 

 Stokes,* and later to Eankinet and Lord Kayleigh.J; What if the 

 aether in a crystal, instead of having its elasticity different in 

 different directions, were to have its rigidity invariable and its 

 inertia different in different directions ? This would bring the 

 theory of crystal- op tics into complete agreement with Fresnel's 

 and Green's theory of reflexion, in which the optical differences 

 between media are attributed to differences of inertia of the 

 aether contained within them. The only difficulty lies in 

 conceiving how aelotropy of inertia can exist; and all three 

 writers overcame this obstacle by pointing out that a solid 

 which is immersed in a fluid may have its effective inertia 

 different in different directions. For instance, a coin immersed 

 in water moves much more readily in its own plane than in the 

 direction at right angles to this. 



Suppose then that twice the kinetic energy per unit volume 

 of the aether within a crystal is represented by the expression 



and that the potential energy per unit volume has the same 

 value as in space void of ordinary matter. The aether is 

 assumed to be incompressible, so that div e is zero : the potential 

 energy per unit volume is therefore 



_ __ 



dz dx d 



where n denotes as usual the rigidity. 



* Stokes, in a letter to Lord Rayleigh, inserted in his Memoir and Scientific 

 Correspondence, ii, p. 99, explains that the idea presented itself to him while he 

 was writing the paper on Fluid Motion which appeared in Trans. Camh. Phil. 

 Soc., via (1843), p. 105. He suggested the wave-surface to which this theory 

 leads in Brit. Assoc. Rep., 1862, p. 269. 



t Phil. Mag. (4), i (1851), p. 441. J Phil. Mag. (4), xli (1871), p. 519. 



