326 Mr. J. C. M‘Connel’s Notes on 
In the first position the plane of polarization is P’ AN X. 
In the second position let it be P’ K. 
Mr. Glazebrook finds P/KA=5° 3’. 
The angle, however, that we wish to find, is the angle through 
which the plane of polarization has been turned about the 
direction of the ray, viz. AP’ K, and this, of course, is not 
equal to 90°—P’ K A. 
After I had written the greater part of this paper, I found 
that the ground had been already traversed by Sande Bak- 
huyzen (Pogg. Ann. exlv. p. 259, 1872). His investigation 
is considerably longer than mine, and he only examines the 
case of the ordinary Nicol. He obtains results of the same 
general form; but he falls into at least one serious error; so 
his numerical values are quite different. Instead of assuming, 
as I have done, that the rotation of the plane of polarization 
on refraction out of the crystal is negligible, he uses a com- 
plicated formula, giving directly the position of the plane of 
polarization of the incident ray in which only the extraordinary 
ray is excited in the crystal. This formula he has apparently 
deduced from a formula given by Neumann (Pogg. Ann. xli. 
p- 11). And itis here that the error occurs. He has not 
paid sufficient attention to Neumann’s explanation of how 
the quantities in the formula are to be measured. He puts 8 
for w; whereas he should put @—a for w. Making this cor- 
rection in his equation (5), we find all the terms in the deno- 
minator are of one sign, and the value of tan A is consider- 
ably diminished. We find, too, that 90°—A is practically the 
same as the angle between the plane of incidence and the plane 
of polarization in the crystal, which is what I have assumed. 
In this very same operation Bakhuyzen falls into another 
mistake. He is considering the case of light emerging from 
the Nicol, while he uses the formula for light entering the 
crystal. Hven with glass this would have been wrong; but 
with crystal the cases are totally distinct, for when light is 
refracted out of the crystal there are two reflected rays instead 
of only one. 
It may not be out of place here to describe a simple method 
for testing the necessary adjustment, which I lately found 
convenient. In my arrangement (fig. 5) the source of light 
was an illuminated slit A, whence the light passed through a 
lens B, placed so that the slit was at its principal focus. Thus 
a parallel beam of Jight fell on the polarizing Nicol C. To the 
Nicol circle I attached a plane mirror D as nearly as possible 
at right angles to the axis of rotation. Between B and D, I 
interposed a lens EH at a distance of half its focal length from 
D. An image of the slit is thus formed at a on the surface 
