AND REFRACTION OF LIGHT. 21 



bA cos v//o - bB sin \J/- - aa cos (>//■<, + e) + «/3 cos (\|/ + 0,) 



= bA t cos \^ — i B t sin v// — a,^ cos >^ , (22). 



— {A sin \|/- + B cos \|> ) = — (A, sin \js + -B, cos ^ ), 



1 1 



— \a sin (v|/ + e) + /3 sin (^ + e)\ = — i a l sin >/,„. 

 7 7/ 



Expanding the two last equations, comparing separately the coefficients 

 of cos >// and sin ^ , and observing that 



ff y 



— = — = m suppose, 



o/ 7/ 



we get 



# = m 2 ^, 



(23). 

 o cos e + /3 cos e, = /**<*,» 



a sin e + /3 sin e, = 0. 



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



= A + A / — a sin e — /3 sin e t , 



= A — A, + -j- 1 + t (p cos e t — a cos e), 



= 2? + -B, + a COS + /3 COS 0, — a /5 



= -B — -B, + t (/3 sin <?, — a sin e) ; 

 combining these with the system (23), there results 



= A + A t , 



= B + B, + (fx 2 - l),a,, 

 aa, a 



(24). 



= A - A, + -jr-' + t (/3 COS 9, - a COS e), 



= 2? — B t + v (/3 sin e t - a sin e). 



