EXTINCTION ANGLES. 127 
on the central plate can be detected at 91 41', the field is lighted up by 
0.085 P er cent instead of 0.050 per cent of the total intensity. These 
differences of intensity are of such a character that they can readily be 
observed, and the sensitiveness of any method involving the rotation of 
the upper nicol while the crystal remains stationary is, in this case at least, 
twice as great as that for which the nicols remain crossed and the crystal 
plate alone is rotated. Similar theoretical conclusions can be drawn from 
Figs. 74 and 75. 
These relations are also directly evident from the intensity formula itself. 
The plate will appear dark under crossed nicols in monochromatic light if 
the intensity of the transmitted light is below the threshold value 7 or 
A 
For white light this equation for the total intensity becomes 
= Ci'd X = I 7 W si 
For a given light source and thickness of crystal plate the integral quantity 
/ = i'd X = 7 sin 2 20 sin 2 ~ a d\ 
7 (A) sin 2 
X 
may be considered constant and 
7 = K . sin 2 20 
For small angles we may substitute the angle for its sine and obtain 
/"Tf 2 
~~ -1 /V \j 
If the plate appears dark, then 
where 7 is the threshold value or on an average about o.ooi meter candle. 
Thus if the total intensity /T = 2.5 meter candles, then the angle 0, which 
gives the threshold value / , is ( - ) =0.0 1 radians or 35'. 
\ 10 / 
If the upper nicol be rotated and the plate held stationary the intensity 
equation becomes 
Trdf-Y' a'} 
7 2 = cos 2 0-sin 26 sin 2 (0-0) sin 2 - ^ 
The intensity of the field adjoining the crystal plate is then /i = cos 2 <t>, where 
0is the angle between the polarizer and the analyzer and 6 the angle between 
the polarizer and the ellipsoidal axis 7 of the crystal plate. The difference 
in intensity between the plate and the field is then 
7 1 -/ 2 = sin 20 sin 2 (0-0) sin 2 ^ y ' ~ a/) 
