The Aether as an Elastic Solid. 183 



the point-centres within the sphere of influence of m, we obtain 

 an equation of the form 



fft d'K o^E d'Z 



w = a &+Pw + y & + ---' 



where a, )3, 7 . . . denote constants. 



Each successive term on the right-hand side of this equation 

 involves an additional factor (A^) 2 /X 8 as compared with the pre- 

 ceding term, where X denotes the wave-length of the light : so 

 if the radii of influence of the point-centres were indefinitely 

 small in comparison with the wave-length of the light, the 

 equation would reduce to 



8^_ cP 



ar- = "&*' 



which is the ordinary equation of wave-propagation in one 

 dimension in non-dispersive media. But if the medium is so 

 coarse-grained that A is not large compared with the radii of 

 influence, we must retain the higher derivates of . Substi- 

 tuting 



in the differential equation with these higher derivates retained, 

 we have 



'2-irV 



which shows that c b the velocity of the light in the medium, 

 depends on the wave-length A ; as it should do in order to 

 explain dispersion. 



Dispersion is, then, according to the view of Fresnel and 

 Cauchy, a consequence of the coarse-grainedness of the medium. 

 Since the luminiferous medium was found to be dispersive only 

 within material bodies, it seemed natural to suppose that in 

 these bodies the aether is loaded by the molecules of matter, 

 and that dispersion depends essentially on the ratio of the 

 wave-length to the distance between adjacent material molecules. 



