266 ON THE REFLEXION AND REFRACTION OF LIGHT. 



I A sin ^ + IB cos -^ + Z>a cos (^r + e) + Ij3 cos (i/r + e) 



= 5-4 y sin ^ ZJ5 y cos T|T O + 5a cos ^ , 

 bA cos ^ 1>B sin ^Q act cos (I|T O + e) + /3 cos (\lr + 6 ) 



(J[ sin ^ + B cos ^J = 2 (^.^ sin ^jr + J? cos ^r ), 

 #/ 



- 2 



- 2 a sin (f 



V 



sn 



,) J = -5 a y sin 



V/ 



Expanding the two last equations, comparing separately the 

 coefficients of cosi/r and sin-^ OJ and observing that 



9 1 



suppose, 



we get 



B 



a cos e + p cos ^ = yu, a t 

 a sine + ft sin e y = 



In like manner the two first equations of (22) will give 

 = A + A t a sin e ft sin e^ 



.(23). 



= B + ^ + a cos e + /3 cos e, a /? 

 = ^ - B t + 1 (/3 sin e t - a sin e} ; 

 combining these with the system (23), there results 



= 5 - 5, + | (/9 sin , - a sin e) 



.-.(24). 



