The Aether as an Elastic Solid. 173 



The hypothesis that in crystals the inertia depends on 

 direction seemed therefore to be discredited when the theory 

 based on it was compared with the results of observation. But 

 when, in 1888, W. Thomson (Lord Kelvin) revived Cauchy's 

 theory of the labile aether, the question naturally arose as to 

 whether that theory could be extended so as to account for the 

 optical properties of crystals : and it was shown by E. T. 

 Glazebrook* that the correct formulae of crystal-optics ar& 

 obtained when the Cauchy-Thomson hypothesis of zero velocity 

 for the longitudinal wave is combined with the Stokes-Kankine- 

 Rayleigh hypothesis of aelotropic inertia. 



For on reference to the formulae which have been already 

 given, it is obvious that the equation of motion of an aether 

 having these properties must be 



(pie*, p z e y , p 3 O = -n curl curl e, 



where e denotes the displacement, n the rigidity, and (p lt p 2 , /o 3 ) 

 the inertia : and this equation leads by the usual analysis ta 

 Fresnel's wave-surface. The displacement e of the aethereal 

 particles is not, however, accurately in the wave-front, as in 

 Fresnel's theory, but is at right angles to the direction of the 

 ray, in the plane passing through the ray and the wave- 

 normal, f 



Having now traced the progress of the elastic-solid theory 

 so far as it is concerned with the propagation of light in 

 ordinary isotropic media and in crystals, we must consider the 

 attempts which were made about this time to account for the 

 optical properties of a more peculiar class of substances. 



It was found by Arago in 181 IJ that the state of 

 polarization of a beam of light is altered when the beam is 

 passed through a plate of quartz along the optic axis. The 



* Phil. Mag. xxvi (1888), p. 521 ; xxviii (1889), p. 110. 



t This theory of crystal-optics may be assimilated to the electro-magnetic theory 

 by interpreting the elastic displacement e as electric force, and the vector 

 (pifx, p^y, ptfz) as electric displacement. 



+ Mem. de 1'Institut, 1811, Part I, p. 115, sqq. 



