600 
MR. R. T. GLAZEBROOK ON THE REFRACTION OF PLANE 
Then (Lorentz, c Schlomilch,’ xxii.; Glazebrook, Proc, Camb. Phil. Soc., 18S1) we 
have the equations 
(a cos 9-\-a / cos 6,) sin 2 <j>=a' cos O' sin 3 cos 6" sin 2 <£".(l) 
(a sin 0+cq sin 6) sin cj)=a sin 6' sin sin 6" sin <f>" .(2) 
(a cos 9 — a y cos 9) sin <£ cos cf>—a' cos 9' sin cos cos 9" sin <j>" cos <j>" . (3) 
(a sin 9— cq sin 9) sin 3 $ cos </>=a' sin 9' sin 3 <f>' cos <j> 
+a"(sin 9" cos ^/'-j-tan q sin <f>’') sin 2 (/>" .... (4) 
These equations express the conditions referred to previously and enable us to 
find cq a' a" and 9 t ; 9', 9" are known from the position with reference to the axis 
of the wave front in the crystal. 
We can solve them in the general case, but for our present purpose it is sufficient 
to find the conditions that only one wave should be propagated in the crystal. Let 
us first take the ordinary wave; we may put a"=0 in the equations, and we get the 
condition 
tan 9— tan 9' cos (<£—(/>') .(5) 
by eliminating cq a' and 9 r 
This then is the condition which must hold between the position of the plane of 
polarization of the incident light and the angles of incidence and refraction in order 
that only the ordinary wave may traverse the crystal. 
If we desire to have only the extraordinary wave, put a'=0 and we obtain 
tan 9= tan 9" cos hi—<£") + .(6) 
In order to apply these formula) we must find 9' 9" and q in terms of the angles of 
incidence and refraction and constants. 
Let the intersection of the incident, reflected and refracted waves with the face of 
incidence meet a sphere, centre 0, in B (fig. 1). 
Let the inward drawn normal to the face of incidence meet the same sphere in C, 
while the face itself cuts it in A B. 
Let B I be the trace of the incident wave. B It of the refracted. 
Let the optic axis cut the sphere in X. Join B X. 
The prism used in the experiments was cut in such a way that X and It were on 
opposite sides of the arc B A, as in fig. 1. 
Let B X=/3 and let the angle A B X=X. (3 and X are known if the position of the 
face of incidence with reference to the optic axis is known. 
Draw X Y perpendicular to B It and take Y Y' an arc of 90°. Then Y Y'=— ; 
also O Y,OY / are clearly the two possible directions of vibration in the wave front 
B It. O Y is the direction of the extraordinary vibration 0 Y' of the ordinary. 
