338 Mr KELLAND, ON THE TRANSMISSION OF LIGHT 



11 We proceed now to the determination of these directions, and to 

 commence with the last value of A, substituting in the equations of 1 ; 



■_ „ - A = m + n +p-S (m cos-' 9 +p sin- 0) + 2 (/« - p) 

 = 3msm-6 - 3^3 sin' 

 = 3 (m — p) sin^ ; 

 b - A = 3 {m - p) sin= (p, 

 c - A = 3{m - p) sin' \|r ; 

 .-. f 9 (m - py sin' 6 sin' ^ - 9 (»« - p)' cos- cos- ^ \ Q 

 = {9 (»» - J9)' cos' 9 cos cos >// + 9 ('« - pY sin" ^ cos cos x//} fi ; 

 or ( 1 - cos' 9 - cos' 0) Q = cos ^ cos x|/ ^, 

 cos' >!/ ■ Q = cos cos \f/^ R, 

 cos v// Q = cos ^ E, 

 Q R 



cos COS ^ 



Similarly, from the other equations we deduce 



Psin' 9 = Q COS cos 1^ + i? cos 9 cos v|^ 



„ „ /• , COS'\|/\ 



= Qcos0(cos<^ + ^^— j 



Qcose 



cos^ , 



sin'0 



or 



cos^ 



P Q 



cos cos (}) ' 



which shews that P, Q, P have the ratio 



cos 9, cos (p, cos \|/^ ; 



