AND THE EQUILIBRIUM AND MOTION OF ELASTIC SOLIDS. 319 



It has been shown to be highly probable that the ratio of ^ to fi increases rapidly according as 

 the medium considered is softer and more plastic. For fluids therefore, and among them for 

 the luminiferous ether, we should expect the ratio of ^ to fi to be extremely great. Now if A^ be 

 the velocity of propagation of normal vibrations in the medium considered in Sect, iii., and T that 

 of transversal vibrations, it may be shown from equations (32) that 



3p ' p- 



This is very easily shown in the simplest case of plane waves : for if /3 = 7 = 0, a =f (x), the equations 

 (32) give ^ -4 = i ("»^ + *^) J^ ' whence a = (p (Nt - .r) + >// (Nt + x) ; and if a = 7 = 0, 



ft =/(.!■), the same equations give p 7^ = -B j^ , whence fi = ^(Tt - x) + ^ (Tt + x). Conse- 



quently we should expect to find the ratio of N to T extremely great. This agrees with a conclusion 



of the late Mr. Green's*. Since the equilibrium of any medium would be unstable if either 



J or B were negative, the least possible value of the ratio of N'" to T- is |, a result at which 



Mr. Green also arrived. As however it has been shown to be highly probable that A> 5 B even for 



A ^ 



the hardest solids, while for the softer ones — is much greater than 5, it is probable that — is 



B ^ 



greater than ^.3 for the hardest solids, and much greater for the softer ones. 



If we suppose that in the luminiferous ether — may be considered infinite, the equations 



of motion admit of a simplification. For if we put mA (— +—+ — ) = -/''" equations (3'i), 



\dx dy dx I 



and suppose mA to become infinite while p remains finite, the equations become 



d'a dp id} a d'a d 



" df dx [dx' dy- d-x'T { /ggx 



da dB dy [ 



and _ + J^ + -J: = 0. \ 



dx dy dx J 



When a vibratory motion is propagated in a medium of which (33) are the equations of 

 motion, it niay be shown that p = ^ (f) if the medium be indefinitely extended, or else if there be 

 no motion at its boundaries. In considering therefore the transmission of light in an uninterrupted 

 vacuum the terms involving p will disappear from equations {fiZ') ; but these terms are, I believe, 

 important in explaining Difl^raction, which is the principal phenomenon the laws of which depend 

 only on the equations of motion of the lumniferous ether in vacuum. It will be observed that putting 

 A - 'X, comes to the same thing as regarding the ether as incompressible with respect to those 

 motions which constitute Light. 



G. G. STOKES. 



" Cambridge Phi/otophiral Transactions, Vol. vii. Port I. p. 



