EXTINCTION ANGLES. 121 
It is of interest to plot the value? derived from equation (6) for different 
values of < and 6. From the graphical relations thus obtained most of the 
conclusions in the following pages will be derived. 
In Fig. 73, curve V, the rate of increase in intensity of light is given for 
the special case of 6 = 0, where simply the upper nicol is turned and the 
crystal plate has no effect on the polarization of the waves from the lower 
nicol. In this case 
2/i=I+COS 2<f> (lO) 
From the curve it is evident that the rate of decrease in intensity with 
increase of <f> is very slow at first, but increases rapidly and reaches a flexion 
point at 45, after which the intensity decreases with decreasing rapidity to 
its minimum value o at 90. 
In case the nicols are crossed f < = - J , the rates of increase for differ- 
ent values of K are given by the reduced equation 
2/1 = #(1-0)8 40) = 2 # sin 2 26 (n) 
which defines a curve similar in aspect to the foregoing, except that <f> is 
replaced by 26 and the factor K tends to reduce all values proportionately. 
The curves I to IV of Fig. 73 represent the relative intensities for values of 
K =I > it li and o respectively. The greatest possible intensity is thus 
attained when K = i, 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 = o, i. e., when the 
distance between the two emergent waves is a whole number of wave- 
lengths. 
In Figs. 74-78 intensity curves are drawn to show the relative intensity 
of the emergent light for different positions of the crystal plate (6 usually 
I 5'> 3' 45'. and i) with the principal plane of the lower nicol and for 
different positions of the upper nicol (<f> ranging from 88 to 92). The 
heavy curve in each figure is the relative intensity curve of the crystal alone 
- 
(nicols crossed, </> = - and 6 ranging from 2 to +2). Only this narrow 
2 
range of intensities is considered, since in general it represents about the 
order of magnitude of the probable error of a single determination made 
in the usual manner. 
In each of the figures the unit ordinate division represents 0.025 P 61 " cen * 
of the total intensity and the unit abscissa division 10' of arc. 
In Fig. 74, K is considered equal to i or sin 2 2-d(y' a') = i, which obtains 
A 
when the one wave is any odd number of half wave-lengths ahead of the 
second on emergence from the plate; in Figs. 75-78, the relative intensity 
curves are drawn for /C = , \, \, and o, respectively. 
It is not difficult to grasp the meaning of these curves, as the following 
example will 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 
birefrigence that for yellow light the faster waves after emerging from the 
plate will be precisely half of a wave-length ahead of the slow waves (K= i, 
