334 Mr KELLAND, ON THE TRANSMISSION OF LIGHT 



then cos {xx') = cos 6, 

 cos {x'y) = cos (j), 

 cos (x's) = cos x|/ ; 

 and cos (y'x) cos 6 + sin (y'x) cos <|) = ; 



cos e 



■■■ t^"(2'^^=-c5r^' 



also cos e cos (s'x) + cos <p cos (s:'y) + cos ^|/ cos (s'x) = 0, 



cos (y'x) cos (a'^) + sin (y'x) cos (ss'y) = 0, 



cos= (ji'x) + cos* (ss'y) + cos' (ss'ss) = 1 ; 



which three equations give 



cos (s'x) = - cot v|/ cos e, 



cos (z'y) = - cot x// cos (/>, 



cos («'») = sin \|/; 



and V = ^^' = ^•^' ^°^ e + lycos<l> + ^s cos >//, 

 5y' sin v(/ = - ^.r cos ^ + ^y cos 9, 

 ^s'= -Sx cot v|/ cos 0-^y cot x// cos cp + Sx sin x|/, 



aa; = S:r' cos ^ " %' ^ " ^«' ^o* ^ ^°' ^' 

 Sy = hx' cos <|) + 3y' ^ - ^»' cot x|. cos <^, 

 B& = Sx' cos^lr + S^' sin x|.. 



6. Making the substitutions, and caUing vi + n+p = /i, we obtain 



sin^ . 

 a = ;i-62(5x'cos0-^y'^-^«'cosx|.cos0r.— -p 



sul^^ 



sin. -2^ 



= /^ - 6^{Sx- cos= + ^y'^ ^ + ^«'^ cot^ >|, cos^ 9) . —p 



