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MR. R. T. GLAZEBROOK ON DOUBLE REFRACTION 
faces of tlie rhomb. Let the normals, drawn in directions making acute angles with 
each other, meet in Rj R, R 3 a sphere centre O. Then R : Ro=Ro R S = R S R 1} and if 
the optic axis meet the sphere in S, SR 1 = SRo=SR 3 . 
Fig. 2. 
Let P Q be the points in which the normals to the two faces, P Q, of one of the 
prisms meet the sphere. Let us take the plane R x R 3 as plane of x y, the internal and 
external bisectors of the angle R x Ofh as axes of x and y respectively, the axis of z 
being perpendicular to the plane, x y. Then R 3 and S lie in the plane, z x. 
Let 
PR 1= ^ 
PR 3 =0 3 
R 1 R 3 =2/a 
Oy 0. 2 y are known from experiment. Let a. /3 y be the direction angles of 0 P. 
Then from triangles P x R : P x R 3 
cos 0i —cos a cos p-J-sin a sin y cos PafRj 
cos d> = cos a. cos p,—-sin a sin y cos PaR x 
cos or. 
cos 0 t + cos 0 2 
2 cos y 
6 l + 0., 6 X — 0o 
COS —COS - 
cos y 
Prom triangles P y R x P y R 3 
cos 61 = cos /3 cos ^+/xj + sin ft sin cos P 2 /R 2 
cos 0o=cos fi cos pj+sin ft sin l^—y'j cos P?/Ro 
cos 9. 2 — cos 9 X — 2 cos /3 sin y 
( 1 ) 
