F. E. Wright — Measurement of Extinction Angles. 359 



77\ 



Iii case the nicols are crossed (<£ = — ), the rates of increase 



for different values of K are given by the reduced equation 

 21,= K (1 + cos 40) = 2K sin 2 20 (1 1) 



which defines a curve similar in aspect to the foregoing except 

 that <j) is replaced by 20 and the factor K tends to reduce all 

 values proportionately. The curves I— IV of fig. 2 represent 

 the relative intensities for values of K=l, 1/2, 1/4 and 

 respectively. The greatest possible intensity is thus attained 

 when K=l, i. e., when the waves, after emerging from the 

 crystal plate, are an odd number of half wave lengths apart 

 (in opposite phase) ; the intensity is zero for all positions of 

 the plate when K=0, i. e., when the distance between the two 

 emergent waves is a whole number of wave lengths. 



In figs. 3-6, intensity curves are drawn showing the relative 

 intensity of the emergent light for different positions of the 

 crystal plate (6 usually 0°, 15', 30', 45', and 1°) with the prin- 

 cipal plane of the lower nicol, and for different positions of 

 the upper nicol ((/> ranging from 88° to 92°). The heavy curve 

 in each figure is the relative intensity curve of the crystal 

 alone (nicols crossed, $ = 90°) and 6 (ranging from — 2° to + 2°) 

 The narrow range of intensities only is considered, since in 

 general it represents about the order of magnitude of tlie prob- 

 able error of a single determination made in the usual manner. 



In each of the figures the unit ordinate division represents 

 •025 per cent of the total intensity and the unit abscissa division 

 10' of arc. 



77 



In fig. 3, K is considered = 1 or sin 2 2 . — d(y l — a 1 ) = l, which 



X 



obtains when the one wave is any odd number of half wave 

 lengths ahead of the second on emergence from the plate ; in 

 figs. 4, 5, 6 and 7, the relative intensity curves are drawn for 

 K=3/4, 1/2, 1/4 and respectively. 



It is not a difficult matter to grasp the meaning of these 

 curves, as the following example w r ill show : let it be required 

 to find the percentage of light which emerges from the nicol 

 in the case of a mineral plate of such thickness and birefring- 

 ence that for yellow light the faster waves after emerging from 

 the plate v T ill be precisely one half wave length ahead of the 

 slow waves (K = 1, Hg. 3), the direction of extinction of the 

 plate to make an angle of 30' (0 = 30') with the principal plane 

 of the lower nicol, and the principal plane of the upper nicol 

 to include an angle of 89° 10' with the lower nicol (<£ = 89° 10') 

 On the 30' curve of fig. 3 the ordinate for 89° 10' is '104 and 

 the relative intensity is therefore *104 of 1 per cent of the 

 total intensity. 



