166 TRANSACTIONS OF THE [APR. 1, 
their original intensities, which is also the relation between the 
constants of the partially polarized beam. 
If we let a and 6 represent the original amplitudes of vibration 
in the two images, then the intensities of these images are re- 
presented by a? and b? respectively. The proportion of polariza- 
tion is evidently the difference between these intensities 
divided by their sum. If w is the angle which the transmitting 
plane of the Nicol makes with the direction of vibration of the 
more intense of the two beams, say a?, then the intensities of 
the two images as seen through the Nicol will be, by the law of 
Malus, 
a cos? w and 6? sin 7w. (1). 
Hence for the position of equality we have, 
a’ cos? w — b* sin *w. (2), 
9 
aa sin? w 
or i ie eos? w (3) 
If we call the degree of polarization in the original beam p, 
we have 
ae—b? 
P = qe (4) or, from (3) 
___ sin?w—cos*w cotw—sintw __ ___ egg 2 w, (5) 
P = gn2w+cokw — — 1 
Hence, when the position of the Nicol which produces equality 
in the images has been found, the amount of polarization is im- 
mediately given by (5). 
Cornu, in discussing the instrument, shows in addition, that, 
when the principal sections of the partially polarized beam are 
not known, the degree of polarization may still be found by tak- 
ing one set of readings in any position whatever of the axes of 
the double prism, and then rotating the whole instrument 
through an angle of 90° and taking a second set of readings. 
The degree of polarization can then easily be shown to be given 
by the formula 
p =sin (wz—w,) 
In this work, however, we are not concerned with this last 
formula, since the principal sections were always known. 
Waly 
ADJUSTMENT OF THE INSTRUMENT. 
Since the series of experiments here considered were all made 
upon horizontal surfaces, and since the polarization of the 
emitted light is always in a plane normal to the surface, but one 
adjustment of the instrument was necessary, viz., that of bring- 
