for Reflected and Refracted Light, 5 



within the denser medium ; Cauchy, less dense ; and Maccullagh, 

 equally dense in all media. The last-named writer has argued 

 that refraction cannot be dependent on the density of the aether 

 as such. He especially observes, that "in doubly-refracting 

 crystals, the density, being independent of the direction, could 

 not be conceived to vary with the refractive index'' (p. 39). And 

 Prof. Stokes has observed, that in the vibrations of sether, '^ di- 

 minution of velocity seems capable of being accounted for on 

 several distinct hypotheses/^ 



16. The expressions for the masses of sether vibrating in the 

 same time without and within the denser medium, are obtained 

 on these different suppositions as to the density of the sether, as 

 follows : — 



If V be the velocity of the incident ray, v^ that of the refracted, 



and the index /x= — , then at di perpendicular incidence, the simul- 

 taneously vibrating masses will be simply 



(m) _ ^ _ _ sin i 



(m^) "~i?y ""f^"" sinr* 



If the densities be S, 8^ then, according to the view of Fresnel, 

 h^ > hf and 



8^ sin^2 jjj^ 

 and we must multiply in this ratio, which gives 



K) /** : 



If S=8p according to the view of MaccuUagh, ) 



(m) 



17. In either case, for oblique incidences we must multiply by 

 the rectangular breadth of the rays on the same base or section 

 of the surface, which will be as cos i : cos r, or 



m _ (m) cos 2 ' . ' 



m^ ~~ (w^)cosr' 

 Thus, according to Fresnel, 



7w __ 1 cos i __ sin r cos i 

 ntj" fjL cos r sin i cos r 

 According to MaccuUagh, 



m __ cos i _ sin 2i 



■ -^ my ~"^cosr"~sin3/ •> :*; i ,r„i 



