F. E. Wright — Measurement of Extinction Angles. 357 

 The condition that the entire light be transmitted is 



or (1 - K) cos 20 + K cos 2(0 - 20) = 1 



which is satisfied if both = and 0=0. 



In case either 9 or be given, the problem of finding the 

 particular disposition of upper nicol or crystal plate for which 

 the intensity of the transmitted light reduces to a minimum 

 or maximum, involves the first partial differential quotients of 

 the function 2I X (equation 6) after either or 0. If be 

 given, the point in question is determined by 



5 2 V =4K sin 2(0-20) = O 



O V 



.'. = 20 or = ti— 20 



The second partial differential quotient shows that for the first 

 value of the intensity is a minimum, while for = 7r — 20 the 

 intensity is a maximum. This relation is of importance in cer- 

 tain of the methods described below. 

 If be given and is the variable, 



-^ — '-= — 2 (1— K) sin 2<£ — 2 K sin 2 U — 2$) = 



From this equation we find 



. , K 2 sin 2 40 



sin 2 20 = 



(1-K) 2 + 2K (1-K) cos 40 + K" 



a complicated expression which for K=l simplifies to 



sin 2 20 = sin 2 40 and this equation 



is satisfied for = 20 



0= 7T _ 2(9 



It is of interest to plat the values given by the equation for 

 different values of and 0. 



2l 1 =l4-(l-K) cos 20 + K cos 2(0-20). ' (6) 



In fig. 2, curve V, the rate of increase in intensity of 

 light is given for the special case of = 0, where simply the 

 upper nicol is turned and the crystal plate has no effect in the 

 polarization of the waves from the lower nicol. In this case 



2l 1 = 1 + cos 2cf> (10) 



From the curve it is evident that the rate of increase is very 

 slow at first, but rises rapidly and reaches a flexion point at 

 45°, after which the intensity increases with decreasing rapid- 

 ity to its maximum value at 90°. 



