114 Mr. R. T. Grlazebrook on the Reflexion and 



amplitude of the electric displacement, then the two sets of 

 equations are identical, provided S cos % is proportional to 

 V 2 2, V being the velocity of light and ^ the angle between 

 the ray and the wave-normal; that is to say, provided that 

 the electric displacement is proportional to the component in 

 the wave -front of the actual displacement, and inversely pro- 

 portional to the square of the velocity of light. It must be 

 remembered that & does not determine the direction of vibra- 

 tion in the refracted wave, but the projection of that direction 



on the wave-front. 



Again, let i|r' be the angle between the plane through Oz 

 and the direction of vibration and the plane of the refracted 

 wave; then we have, if OP' (fig. 2) be the direction of vibra- 

 tion, OP' its projection on the wave-front, 



z¥' = &, zY=6\ P'P' = %', 



F«F=^, y«P=# yF=£, 



and we readily find that 



cosyS' = sin^'cos (fi — yjr'), 

 cos #' = cos 0'cos x'j 

 sin 0' cos ^'=:sin & cos ^. 

 So that the last two equations (16) and (17) become 

 (S sin 6 + Si sin X ) cosec <j) = 



S' sin 6' cos ^ cosec <fi + terms in S", 

 (Ssin 6— Si sin 0{) cos (j> = 



S' sin & cos yfr' cos ((/>'— i|r') + terms in S", 

 forms which may sometimes be useful. 



(18) 

 (19) 



