238 Dr. Brewster on the laws of polarisation , &c. 
vj> = the angle of the forces. 
7T = the angle B,EF. 
a = the angle CEF. 
A = the arch FC, or the angle CAF, or the azimuth on the 
great circle BGC passing through the poles of no 
polarisation. 
D = the arch FE, or the declination or distance of the 
point E from the same great circle. 
f = half the difference of the angles at the base or at the 
diagonal of the parallelogram of forces. Then 
1. When the two axes are B,C in the plane passing 
through the diameters of no polarisation, we have 
Cos. 9 = Cos. A x Cos. D. 
Cos. (p = Sin. A x Cos. D. 
2. When the two axes are C,A in a plane perpendicular to 
the plane passing through the diameters of no polarisation, 
Cos. 9 = Cos. A x Cos. D. 
a = 90° — D. 
Then we have, in general, whether the axes are A,C or B,C 
Cos. a = 11 
COS. 7 T = 
Tang. 6 
Tang. D 
Tang. <p * 
When B,C are the two axes, either both positive or both 
negative, $ = 2 7 +Z. 
When A,C are the axes either both positive or both ne- 
gative, 4 1 = 2 (l8o° — u) = 2 a. 
When B,A are the axes either both positive or both ne- 
gative, ^ = 2 ( 180 — -w) = S 7T 
When B,C are the axes, the one positive and the other 
negative, 
