112 Mr. R. T. Glazebrook on the Reflexion and 



S cos* +S 1 cos« 1 + D = S'cosa' + S"cosa" + D' . . (4) 

 S cos j3 + Si cos ft = S' cos j8' + S" cos /3" . . (5) 



S cos 7 + 8, cos y x = S' cos y' + S" cos y" . . (6) 



m cos a -f Z cos jS a mi cos a, + l Y cos A a 2mX) 



x S + x^ Sl + ^^ 



m' cos a' + ? cos j6' a; , m" cos a" + l n cos j3" a „ , 2m' , ,_ x 

 8+ ^ S +-aT D ( 7 ) 



A' 

 SZcos 7 



8^008 7! _ CTcosV gg cos / 

 + X x "" V + \" ? 



(8) 



with the conditions 



m __ mi _ m! __ m" _ 

 A< A.^ A A. 



and on eliminating D — D ; from (4) and (7) we find 

 I cos ft— m cos a a Z 1 cos ft — m x cos a x Q 



x b+ \ bl 



Z'cos/3' — m'cosa' . V cos B"—m n cosa. 1 '., 



— tit — b • (9) 



X' 



X" 



This equation, together with (5) (6) and (8), wil] determine 

 all our unknown quantities. It remains to express them in 

 terms of the angles of incidence and refraction and of the 

 directions of vibration. -p. -^ 



Let <j>, ()>', (/>" be the angles of incidence and refraction. 

 Let 0, l9 0', 0" be the angles between Qz and the directions 

 of vibration, and let 6', 6" be the angles between Oz and the 

 projections on the wave fronts of the directions of vibration 



(fig- i). 



