ELASTIC AND ELECTRICAL THEOEIES OF LIGHT. 231 



produce special distortions due to these particles. The nature of 

 these distortions is wholly determined by the direction of displace- 

 ment, and it 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.* 



But the difficulties of the elastic theory do not end with the 

 law of double refraction, although they are there more conspicuous 

 on account of the definite and simple law by which they can be 

 judged. It does not easily appear how the equation of energies 

 can be made to give anything like the proper law of the dispersion 

 of colors. Since for given directions of the wave-normal and dis- 

 placement, or in an isotropic body, B ND is constant, and also A D and 6 D , 

 except so far as the type of the vibration varies, the formula requires 

 that the square of the index of refraction (which is inversely as V 2 ) 

 should be equal to a constant diminished by a term proportional to 

 the square of the period, except so far as this law is modified by a 

 variation of the type of vibration. But experiment shows nothing 

 like this law. Now the variation in the type of vibration is some- 

 times very important, it plays the leading role in the phenomena 

 of selective absorption and abnormal dispersion, but this is certainly 

 not always the case. It seems hardly possible to suppose that the 

 type of vibration is always so variable as entirely to mask the law 

 which is indicated by the formula when A D and 6 D (with B ND ) are 

 regarded as constant. This is especially evident when we consider 

 that the effect on the wave-velocity of a small variation in the type of 

 vibration will be a small quantity of the second order.! 



The phenomena of dispersion, therefore, corroborate the conclusion 

 which seemed to follow inevitably from the law of double refraction 

 alone. 



* The reader may perhaps ask how the above reasoning is to be reconciled with the 

 fact that the law of double refraction has been so often deduced from the elastic theory. 

 The troublesome terms are 6 D and the variable part of A D , which express the direct 

 action of the ponderable molecules on the ether. So far as the (quite limited) reading 

 and recollection of the present writer extend, those who have sought to derive the law 

 of double refraction from the theory of elastic solids have generally either neglected this 

 direct action a neglect to which Professor Stokes calls attention more than once in his 

 celebrated "Report on Double Refraction" (Brit. Assoc., 1862, pp. 264, 268) or taking 

 account of this action they have made shipwreck upon a law different from Fresnel's and 

 contradicted by experiment. 



tSee pages 190, 191 of this volume, or Lord Rayleigh's Theory of Sound, vol. i, 

 p. 84. 



