MR. R. T. GLAZEBROOK ON PLANE WAVES IN A BIAXAL CRYSTAL. 307 
Section V. —Determination of the Values of the Principal Indices.—Angle between 
the Optic Axes. 
Our next step is to determine the values of the refractive indices on Fresnel’s 
theory. 
It has been shown (Section III.) that the principal plane of the first prism cuts the 
plane C AC' in a line inclined at an angle of 2° 31' 58" to 0 A, and makes with that 
plane an angle of 1° 12' 4". 
Let us consider the intersection of this plane and the plane B C, B' C'. 
Eig. 6. 
It will be a line, M O M', say, inclined at 1° 12', or rather less to C O C'. 
Take 0 A, O B, O 0, as axes of x, y, z, and let g a , gj„ g c be the principal refractive 
indices, and therefore the semi-axes of the surface of w r ave slowness. 
The sections of the surface of wave slowness on Fresnel’s theory by the plane 
B 0 C are a circle of radius g„ and an ellipse axes gi, g c in the directions of 0 C, O B 
respectively. 
Hence the values of the radius vector in this direction given by experiment— i.e., 
the values of the refractive indices for light traversing the crystal in this direction— 
are g a , and the radius vector of an ellipse axes gi, g c , inclined at about 1° 12' to gi,. 
To determine which of the experimental values of g is in this direction we require 
to find L M, L being the point of intersection of M M' and A C'. 
From the triangle C' L M, since C' is a right angle, 
cos C'LM= tan C'L cot LM 
Whence 
LM = S7°28'4" . . , . ..(1) 
And if 0 P / be as before normal to the face P, of the first prism, 
LP,= 67° 27' 25" [Section III. (8)]. 
MP =20° 0' 39" 
2 r 2 
Whence 
(2) 
