474 J. W. Gibbs — Elastic and Electrical Theories of Light. 



placement. But this supposition, besides its intrinsic improb- 

 ability so far as A D and J D are concerned, involves a direction 

 of the displacement which is certainly or almost certainly 

 wrong. 



We are thus driven to suppose that the undisturbed medium 

 is in a state of stress, which, moreover, is not a simple hy- 

 draulic stress. In this case, by attributing certain definite phy- 

 sical properties to the medium, we may make the function B^ 

 become independent of the direction of the wave-normal, and 

 reduce to a quadratic function of the direction-cosines of the 

 displacement.* This entirely satisfies Fresnel's Law, including 

 the direction of displacement, if we can suppose A D and 5 D in- 

 dependent of the direction of displacement. But this supposi- 

 tion, in any case difficult for aeolotropic bodies, seems quite 

 irreconcilable with that of a permanent (not hydrostatic) stress. 



For this stress can only be kept up by the action of the pon- 

 derable molecules, and by a sort of action which hinders the pas- 

 sage of the ether past the molecules. Now the phenomena of 

 reflection and refraction would be very different from what 

 they are, if the optical homogeneity of a crystal did not extend 

 up very close to the surface. This implies that the stress is 

 produced by the ponderable particles in a very thin lamina at 

 the surface of the crystal, much less in thickness, it would seem 

 probable, than a wave-length of yellow light. And this again 

 implies that the power of the ponderable particles to pin down 

 the ether, as it were, to a particular position is very great, and 

 that the term in the energy relating to the motion of the ether 

 relative to the ponderable particles is very important. This is 

 the term containing the factor 5 D , which it is difficult to sup- 

 pose independent of the direction of displacement because the 

 dimensions and arrangement of the particles are different in 

 different directions. But our present hypothesis has brought 

 in a new reason for supposing b v to depend on the direction of 

 displacement, viz : on account of the stress of the medium. A 

 general displacement of the medium midway between two 

 nodal planes, when it is restrained at innumerable points by 

 the ponderable particles, will produce special distortions due 

 to these particles. The nature of these distortions is wholly 

 determined by the direction of displacement, and is hard to 

 conceive of any reason why the energy of these distortions 

 should not vary with the direction of displacement, like the 

 energy of the general distortion of the wave-motion, which is 

 partly determined by the displacement and partly by the wave- 

 normal.f 



* See note on page 467. 



\ The reader may perhaps ask, how the above reasoning is to he reconciled 

 with the fact that the law of double refraction has been so often deduced from 

 the elastic theory. The troublesome terms are b D and the variable part of A D , 



