of a Stream of Light passing through a Crystalline Plate. 85- 



and neglecting the products of the /*'s with one another, and with 7* 

 and d. since such products will introduce terms that we shall not 

 require, we have 



Hence if p n , q n , r n , s n denote the coefficients of sin n ilv n in p, 3, r, *- 

 respectively, and [ ] rt denote the coefficient of sin^jv" in the expres- 

 sion within tbe vinculum, the equations that determine these quan- 

 tities are 



(1) If n = 2m 



= R 2 m, say, 



= S 2wt , say, 

 and from the first and third of these equations, we have, unless 



zm 0, 



Avhich relations hold whatever m may be. 

 (2) If n 



0, 



= T 2m+ i, say, 



= 0, 



and from the second and fourth of these equations 



and when wi>0, <? 2tft+ i = 0, so that r 2m+1 = > 2 ;j+i (w>0). 



