354 Mr KELLAND, ON THE TRANSMISSION OF LIGHT 



of the angles which their common direction makes with the optic 

 axes suggested (apparently) that the same Theorem approximately held 

 when wave was put for ray, and normal to front for direction, &c., 

 and thus a Theorem which is in no way connected with the result, 

 does from the circumstance of its close analogy to the true one, give 

 correct results, or nearly so. 



3. Let ^C be the direction of one ray in the crystal ; BE a normal 

 to its front ; CG perpendicular to BA ; (p the angle of incidence ; 

 <p' the angle which BE makes with the normal to the plane surface 

 of the crystal ; BC makes Q with the same ; T the thickness of the 

 plate. (Note at end.) 



Then if v be the velocity before incidence, v the velocity perpen- 

 dicular to the front after refraction, 



v' sin (p' 

 V " sin (^ ' 



and the ray has moved perpendicularly to its former front through a 

 space 



= BG = CBcos((p - 6) 



2' 



= ^ cos (0 - 6), 



cos 9 ^^ 



T v' 



since r = BC; also -r — -k is the velocity along BC; 



cos cos (0 - ) •' ° 



.•. time of describing BC = A — ;r^; 



therefore the space which the wave would describe in the same time 

 in air, is 



Tv 



—, ;; cos (0 — d>'), and the retardation is 



vcosO ^ ^'^ 



^, {f {cos (e -.')}- cos (0-0)} 



