﻿The Hon. J. W. Strutt on Double Refraction. 523 



When 0=0, let t=Tj ; when 0=90°, let t=t 2 ; then 



T 2 = T2 C OS 2 + T|sin 2 0. 



There is, of course, one case which does not bring out the pe- 

 culiarity for whose sake the illustration is brought forward, I 

 mean when the ellipsoid becomes a sphere. The only effect of 

 the fluid is then to retard the motion, just as if the mass of the 

 sphere itself had been increased. 



From the problem generally we may infer that there is nothing 

 absurd in the idea of an inertia varying with the direction of 

 motion, and that the want of symmetry causing double refrac- 

 tion may be attributed with as great probability to the dynamical 

 as to the statical conditions of the question. We know nothing 

 about the real nature of the sether, and, if possible, still less about 

 its relations to ponderable matter ; and it is therefore the merest 

 assumption to say that the energy of motion within a crystal is 

 necessarily a symmetrical function of the velocities of displace- 

 ment. But this has virtually been done in all the theories 

 hitherto given. I would even go further, and ask whether, when 

 we consider the enormous velocity of light and the magnitude of 

 the forces which resist distortion, it is not on the whole more 

 probable that the relatively considerable effect of ponderable 

 matter is due to its action rather on the small quantity (the 

 inertia) than on the great quantity (the rigidity) ? 



Instead, then, of assuming for the energy of the medium 



let us take the most general quadratic function of f, tj, £ contain- 

 ing six constants. Even this form is somewhat restricted ; for it 

 may be that the energy cannot be expressed at all as the sum of 

 parts corresponding to the various elements of the sether. Ordi- 

 nary chromatic dispersion and rotatory polarization, which is a 

 phenomenon of the same nature, show that the mutual influence 

 of the parts is not restricted to a distance which may be regarded 

 as vanishingly small in comparison with the wave-length ; and 

 although in Cauchy's theory of dispersion the mutual action is 

 supposed to be of a statical character, yet the fact that there is 

 no dispersion in vacuum, when regarded from the point of view 

 of the present paper, leads rather to the conclusion that the mu- 

 tual influence is dynamical, by which I mean that it would show 

 itself in the expression of the kinetic rather than of the potential 

 energy. But it will only be following precedents to drop the 

 consideration of dispersion in explaining a theory of double re- 

 fraction, which may be done consistently by supposing the wave 

 very long. 



By a suitable choice of axes the terms involving the products 



