The Aether as an Elastic Solid. 165 



This expression contains the correct number of constants, 

 namely, four: three of them represent the optical constants 

 of a biaxal crystal, and one (namely, ju) represents the square of 

 the velocity of propagation of longitudinal waves. It is found 

 that the two sheets of the wave-surface which correspond to the 

 two distortional waves form a Fresnel's wave-surface, the third 

 sheet, which corresponds to the longitudinal wave, being an 

 ellipsoid. The directions of polarization and the wave- velocities 

 of the distortional waves are identical with those assigned by 

 Fresnel, provided it is assumed that the direction of vibration 

 of the aether- particles is parallel to the plane of polarization ; 

 but this last assumption is of course inconsistent with Green's 

 theory of reflexion and refraction. 



In his Second Theory, Green, like Cauchy, used the condition 

 that for the waves whose fronts are parallel to the coordinate 

 planes, the wave- velocity depends only on the plane of polariza- 

 tion, and not on the direction of propagation. He thus obtained 

 the equations already found by Cauchy 



O-f-H-g-I-h. 



The wave-surface in this case also is Fresnel's, provided it 

 is assumed that the vibrations of the aether are executed at 

 right angles to the plane of polarization. 



The principle which underlies the Second Theories of Green 

 and Cauchy is that the aether in a crystal resembles an elastic 

 solid which is unequally pressed or pulled in different directions 

 by the unmoved ponderable matter. This idea appealed strongly 

 to W. Thomson (Kelvin), who long afterwards developed it 

 further,* arriving at the following interesting result : Let an 

 incompressible solid, isotropic when unstrained, be such that its 

 potential energy per unit volume is 



P 7 

 where q denotes its modulus of rigidity when unstrained, and 



* Proc. R. S. Edin. xv (1887), p. 21 : Phil. Mag. xxv (1888) p. 116 : Baltimore 

 Lectures (ed. 1904), pp. 228-259. 



