164 The Aether as an Elastic Solid. 



Thus the potential energy per unit volume may be written 



. n^* ^ rr de y^. T de * 



d> = 6r + L + -I ^~ 



ox oy oz 



i T ] Wx \ ^ y\ -L. oe * 

 I 1 Ur + Ur- + Ur 



At this point Green's two theories of crystal-optics diverge 

 from each other. According to the first theory, the initial 

 stresses G-, H, I are zero, so that 





", *> >/>#>*>/' /, *' in order that the wave-surface may be Fresnel's, are the 

 following : 



(34 _/) ( 3c -/)=(/ + /')* 



((3a- 



(Za - h) (3 - h) = (h + A') 



These reduce to Green's relations when the additional equation b = c is assumed. 



Saint-Venant disputed the validity of Green's relations, asserting that they?are 

 compatible only with isotropy. On this controversy cf. E. T. Glazebrook, Brit. 

 Assoc. Report, 1885, p. 171, and Karl Pearson in Todhunter and Pearson's History 

 of Elasticity, ii, 147. 



