148 I)R. BREWSTER ON THE ACTION OF THE SECOND SURFACES 
capable of producing an inclination of 53° or a rotation of 53° — 45° = 8°, 
and this rotation being in an opposite direction from that produced by the 
second reflexion at C, the inclination of the planes of polarization for the ray 
C S is nearly 44^°, the reflexion at C having brought back the ray A C almost 
exactly into the state of natural light. 
Without changing either the light or the angle, I cemented a prism M cd 
on the face M d, so that c d was parallel to d N, and I found that the second 
refraction at b, equal to that at A, changed the inclination of the planes of 
polarization to 53°; that is, the two refractive actions at A and b had overcome 
the action of reflexion at C, and the pencil bs actually contained light polarized 
perpendicular to the plane of reflexion. 
In order to put this result to another test, I took a plate M c N Q (Fig. 3.) of 
the same glass, which separated the pencil b s reflected at the second surface, 
from the parallel pencil A P reflected from the first surface, and I found that 
at an angle of 83°, the value of the inclination I or <p for the ray was about 3 7^°, 
while the value of I for the ray bs was nearly 55°, an effect almost equal to the 
refractive action of a plate at 83° of incidence. 
When the pencil II A is incident on the first surface at the polarizing angle 
or 56° 45', the rotation produced by refraction at A is about 2°, or the inclina- 
tion I = 45° + 2° = 47° ; but the maximum action of the polarizing force at C 
is sufficient to make 1 = 0° whether x is 45° or 47°. Hence CB is completely 
polarized in the plane of reflexion, and the refractive action at b is incapable 
of changing the plane of polarization when 1 = 0°: the reason is therefore 
obvious why the two rotations at A and b, of 2° each, produce no effect at the 
maximum polarizing angle. 
If we now call 
<p = Inclination to the plane of reflexion produced by the 1st refraction 
* at A, 
<p' — Inclination produced by the reflexion at C, 
<p" = Inclination produced by the 2nd refraction at b, 
We shall have 
l 
cos (i — {') 
Cot < p = cos (i — i') ; or tan <p = 
