the Use of Nicol’s Prism. 321 
a homogeneous medium and use Fresnel’s formule, we find 
the rotation is about ‘005 in the case of an ordinary Nicol. 
I have calculated from Neumann’s theoretical formule for 
refraction at the surface of crystals what the rotation would 
be in the case of light entering the Nicol and exciting only 
the extraordinary wave, and find it is less than with a homo- 
geneous medium. In the case of light leaving the Nicol 
there are two reflected waves, so the formule would pro- 
bably be very complicated. I think we may safely assume 
that the rotation is less than ‘Ola, and may therefore be 
neglected. In the case of a flat-ended Nicol the incidence is 
nearly direct, and the rotation may obviously be neglected. 
Owing to the circumstance that this rotation is negligible, 
the whole of this investigation applies without alteration to 
the case when the Nicol is used as an analyzer, and the light 
is consequently incident on the spar. In this case we have to 
find the position of the plane of polarization that only the 
ordinary wave may be excited, and the formula for the rotation 
is the same as in an isotropic medium. 
Weare nowin possession of a convenient formula for ex- 
pressing the position of the plane of polarization in terms of 
the direction of the emergent light relative to fixed planes in 
the Nicol. We shall apply this formula to the discussion of 
the error in measuring arotation. This part of the investiga- 
tion would be very short if we confined ourselves to the first ap- 
proximation. A number of com- Fig. 2. 
plications are introduced by the 
necessity of retaining the syuares 
and products of small quantities. 
The figure represents a portion 
of the sphere of unit radius. Let 
A be the axis of rotation, 
N P the principal plane, 
P’ the emergent wave-normal, 
P’« the plane of polarization. 
Draw AP, and P’P perpen- 
dicular to the principal plane. 
This fixes Py, which has hitherto 
been arbitrary within certain 
limits. A and P’ are fixed in 
space, while N and P> are ro- 
tated round A. 
For simplicity, suppose the 
circle-reading is zero when P’ K 
lies on AP,. Then 6=P AP” is the reading at any time. 
Produce A P’ to meet N Py in K, 
