318 Mr. J. C. M‘Connel’s Notes on 
The phenomenon in its simplest form may be described 
thus:—If the emergent ray be parallel to the long edges of 
the prism it is polarized in a plane perpendicular to the prin- 
cipal plane of the prism, 7. e. to the plane containing the optic 
axis and the normal to the face. If the ray be inclined to this 
position but still lie in the principal plane, then the new plane 
of polarization is as nearly parallel to the old one as is con- 
sistent with its containing the new ray. This indeed is 
obvious from symmetry. But now let the ray lean out of the 
principal plane: there is a marked change in the plane of 
polarization. It has been twisted about the ray, and the angle 
of twist is nearly one third of the angle of deviation. From 
this explanation it is easy to see in a general way how the 
error arises, and also how it may be eliminated by taking 
readings in the two opposite positions of the Nicol. 
There is another important point that is apparent on the 
face of the matter. If the direction of the ray coincide with 
the axis of rotation, the ray will not move relatively to the 
prism when the prism is turned, and the rotation measured 
by the circle will be identical with the actual rotation of the 
plane of polarization. We shall find, moreover, that to the 
second order of approximation the final error depends entirely 
on the angle between these two directions (see equation 8). 
It is independent of any reasonably small errors in the adjust- 
ment of the Nicol in the circle. 
In a Nicol’s prism used as a po- Fig. 1. x 
larizer, it is the second half of the | 
prism that determines the plane of | 
polarization of the emergent light. | 
If the optic axis of the spar in the | 
first half be not accurately parallel to 
the axis in the second half, the effect | 
is not to turn the plane of polariza- | 
tion, but merely to mix a little ordi- / 
nary light with the emergent polarized ) 
light. 
The figure represents a portion of [Ss 
the sphere of unit radius. 
X is the optic axis. N the normal 
to the face. 
So XN is the principal plane. 
P’ is the wave-normal of the emer- 
gent light. FP 
()’ is the wave-normal of the inter- xX 
nally incident light. 
Draw Q’Q, P’P perpendicular to XN produced. Join XQ’. 
x P 
