the Double Refraction of Quartz. 469 
which express a circular vibration, (from right to left, or from left to right, according 
to the sign of the second p,) the result was 
S=a= +c 
from (19.), and 
es=a'+ 2D 
from (20.); which showed that D-=- —C, since the values of s, corresponding to the 
same circular vibration, ought to be equal. The transition from this simple case to that 
of a ray inclined at a given angle ¢ to the axis, was easily made, by taking into ac- 
count the doubly refracting structure of the crystal. This was done by supposing 
€ and » parallel to the principal directions in the plane of the wave, and by chang- 
ing a’, in equation (20.), into a’—(a*—b*) sin *¢; and thus the fundamental equa- 
tions (1.) and (2.) were obtained. 
