150 On FresneVs Convection Coefficient. 



We have, also, 



c 2 fX 2 



If 6 ] be the angle of incidence and 6 2 the angle o£ 

 refraction, 



cos l = 7i 1 , and cos 2 = n 2 , 



h 4- 



Vl 



cos 



<p 





k + 



r- 2 



COS 



<t> 



sin #i = V 1 1 2 + ?n 1 2 , sin <9 2 = Vtf + ™2 2 ; 

 v 2 cos $ Vx cos (j> 



also m l = fjLm 2 , and li — fd 2 + /a 



.-. Z 1 2 + m i 2 = At 2 [Z 2 2 4- V] + V z s(a* 



snce 

 that is, if 



6' 2 Ci 



1' 2 COS (/> Vi COS <£ s 



Hence sin @i — a sin 0<>, if = — 



r c 2 c x 



or if 



fjb 2 C\ _^1_ /C 1 V __ K\ 



fXl C 2 V 2 fC 2 V K 2 ' 



2* 



K 2 pi 



Thus, if c x be the velocity of light in an}' medium at rest 

 in the sether, and if /^ be the absolute index of refraction of 

 the medium, the sine law of refraction will always be satisfied 

 if we assume that the velocity of light relative to the medium 

 when moving with velocity v in the sether, is 



Av 



Pi 



where A is a constant which must be the same for all media. 

 Further, the condition that the incident ray, the refracted 

 ray, and the normal shall lie in the same plane is 



li m x 



2 

 Therefore 



L m< 



, l'! COS (f) l'! cos (f) 



^ -| — 



6*1 _ l x c l i\ c 2 c x 



k+' 



V 2 COS (f) l 2 V 2 COS <f) V 2 ' Ci c 2 



c 2 c 2 



or K X _ <vj _ a^ 2 



*2 ~~ <*2 2 ~~ H<i ' 

 the same condition as before. 



