230 ELASTIC AND ELECTRICAL THEORIES OF LIGHT. 



of the common perpendicular to both will be linear functions of the 

 direction-cosines of each, and a quadratic function of the direction- 

 cosines of the common perpendicular will be a quadratic function of 

 the direction-cosines of each. We may thus reconcile the theory 

 with the law of double refraction, in a certain sense, by supposing 

 that A D and 6 D are independent of the direction of displacement, 

 and that B ND and therefore V 2 is a quadratic function of the direction- 

 cosines of the common perpendicular to the wave-normal and the 

 displacement. But this supposition, besides its intrinsic improbability 

 so far as A D and & D are concerned, involves a direction of the dis- 

 placement 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 hydraulic stress. 

 In this case, by attributing certain definite physical properties to 

 the medium, we may make the function B ND 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 6 D independent of the direction of displacement. 

 But this supposition, 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 ponderable 

 molecules, and by a sort of action which hinders the passage 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 6 D , which it is difficult to 

 suppose 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 6 D 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 



* See note on page 224. 



