186 The Aether as an Elastic Solid. 



where the constant A depends on the nature of the ponderable 

 body our equation becomes 



3 2 e 



(p + P1 A) ^ = - (k + Jw) grad div e + ^V 2 e, 

 ot 



which is essentially the same equation as is obtained in those 

 older theories which suppose the inertia of the luminiferous 

 medium to vary from one medium to another. So far there 

 would seem to be nothing very new in Boussinesq's work. But 

 when we proceed to consider crystal-optics, dispersion, and 

 rotatory polarization, the advantage of his method becomes 

 evident: he retains equation (1) as a formula universally true 

 at any rate for bodies at rest while equation (2) is varied 

 to suit the circumstances of the case. Thus dispersion can be 

 explained if, instead of equation (2), we take the relation 



e' = Ae - Z>V 2 e, 



where D is a constant which measures the dispersive power of 

 the substance : the rotation of the plane of polarization of sugar 

 solutions can be explained if we suppose that in these bodies 

 equation (2) is replaced by 



e' = AQ + B curl e, 



where B is a constant which measures the rotatory power ; and 

 the optical properties of crystals can be explained if we suppose 

 that for them equation (2) is to be replaced by the equations 



e x ' = Atfx, ey = A z e yt e z ' = A 3 e, 



When these values for the components of e' are substituted 

 in equation (1), we evidently obtain the same formulae as were 

 derived from the Stokes-Eankine-Eayleigh hypothesis of inertia 

 different in different directions in a crystal; to which Boussinesq's 

 theory of crystal-optics is practically equivalent. 



The optical properties of bodies in motion may be accounted 

 for by modifying equation (1), so that it takes the form 



a a a ay , 



- + W x + W y - + W~ C ,, 



ct cv oy ozj 



