Theory of a Contractile ^Ether to Optical Problems. 537 



the supposition that \ is less than the wave-length of any 

 part of the visible spectrum. Now \ is the wave-length 

 corresponding to the free periods of the matter vibrations. 

 Thus the free periods for the matter vibrations are less than 

 those for any visible light. The application of the theory to thin 

 metallic films, and to the small prisms investigated by Kundt, 

 requires further consideration, and must be left for the present. 



If this explanation be true, then a substance which is opaque 

 to light might be transparent to waves of greater length, all 

 that is required is that the length of such waves should be 

 greater than the critical length \. Professor J. J. Thomson 

 has recently found this to be the case for ebonite, which trans- 

 mits easily the long waves of electric disturbance in experi- 

 ments such as those of Hertz. Thus somewhere between 

 these electric vibrations and those of light, ebonite has a band 

 of strong absorption, and, moreover, there are no free periods 

 possible for the free-matter vibrations in ebonite, which are 

 less than the periods of the other vibrations. 



Thus, to explain the effect of a metallic medium there is no 

 need to invoke the aid of the terms in y 2 in the equations of 

 motion. Part of the effect may, it is true, be due to the exist- 

 ence of such terms ; it is sufficient, however, that X x should be 

 somewhat greater than X, then p? will, for some values of \ be 

 less than unity, and for others a real negative quantity. The 

 appendix to Sir W. Thomson's Baltimore Lectures contains a 

 discussion of this point, and the formulae there given become 

 those of the theory now considered if we write for Cx &c. in 

 Thomson's equation — 47t 2 C 1 /t 2 . (See ' Report on Double 

 Refraction/ p. 245 et seq.) 



The theory will, without serious modification, give us the 

 formula originally due to Fresnel and now fully verified by the 

 experiments of Fizeau and Michelson, connecting the velocity 

 of light in a moving medium with the velocity of the medium. 



For suppose that the aether is at rest, and that a transparent 

 body is moving through it with velocities L, M, N, parallel to 

 the axes. Then in estimating the relative accelerations of the 

 aether and the matter at a point fixed in the body, we must 



remember that the value of -=- will be 



at 



at ax ay dz 

 So that taking the case of motion in the direction of propa- 

 gation, the term p' j^- becomes p f (-j + N-^\ u ; and this, if 



we neglect X 2 as small compared with the other quantities, 

 gives us as the equation of motion, 



