Doubly Refracting Plates and Elliptic Analyzers 9 



(6). These equations- can be transformed into a form analogous 

 to that given by Mallard, 1 involving functions of the sums and 

 differences of the orders of the plates, but the result is more com- 

 plicated and less convenient for use. 



Inverse Form. — It will be shown later (5, p. 15) that the coefficients 

 ( Q o , Q n ), ( Q ,K n ), etc., may be considered as the direction cosines 

 of a rotation of a system of rectangular coordinates. The inverse 

 theorem may therefore be written: 



Q.=( Q* Qn > QrH £„ K ) K n + ( Q , S n ) S n 

 K=( a;, Q n ) Q„+ ( a;, a; > K n + (K> s. > S n 



S~(S„, QJQ n +(S , K k yK n +(S ,S n )S n 



(9) 



3. Special Cases 



The following special cases of the general theorem will be used 

 in the applications following and are here given for convenient 

 reference. 



Initial light : 



P, Q, K , S . (10) 



After passing through one plate : 

 First Form 



P= P 



Q 1= =+Q o cos 2 (0,1) 

 -f#C sin2(o, 1) 

 K 1 = — Q„sin 2 (o, 1 ) cos 2 ttN x 



H-#C COS 2 ( O, I ) COS 2 7T A 7 , (il) 



-\-S sin 2 *r TV, 



5 1 = : H-Q„sin2(o, 1 ) sin27rA ; ' 1 

 — K o cos 2(0,1) sin 2 7T7V, 



4 S„ COS 2irN l 



1 Mallard E. Traite de Cristallographie, Paris, 1884, T. 2, pp. 169-74. 



16.S 



