POLARIZED LIGHT AT THE SURFACE OF A UHIAXAL CRYSTAL. 599 
ordinary spectrum, and again observed the deviations; each of these observations was 
repeated five or six times and the mean taken. I then altered the angle of incidence 
by about 6° and made similar measurements. 
In this manner I obtained a series of observations of angles of incidence ranging 
from 30° to 85°, with the corresponding deviations for both ordinary ana extraordinary 
waves. 
Let us call <j> the angle of incidence, <f>' that of refraction for the ordinary wave, 
<f>" for the extraordinary. From the observations the values of <// and </>" are easily 
determined by means of formulae given by Professor Stokes (Brit. Ass. Beport, 1862) 
and used by me in the paper already referred to. 
If i be the angle of the prism xfj, \Jj' the angles of emergence from and incidence on 
the second face, and D the deviation, we have 
\Jj=D-{-i—<p 
tan^ - ;- ^ - =tan tan — cot 
A A A A 
(f> 
and these equations give us <£'. 
cf>" of course is found in the same manner. 
I obtained thus a series of values of </>, (j>, and <j>" ; now, of course, since ft refers to 
the ordinary wave, if y be the ordinary refractive index of the light used we should 
have S r- 7 7 — u, a constant, and this was found to be the case within small limits of 
sm <p 
error, showing that I had succeeded in quenching the same light throughout. 
The value of /x was P662. 
The values of were also tabulated, and, of course, varied very slowly. 
When this table had once been constructed, it was sufficient for the future to 
observe the angle of incidence ; for knowing and /x, </>' is at once given by the 
formulae sin </>'=sin (fx/fi and <j>" by interpolation from the table. Thus the observations 
with the sugar-cell reduced to determining the angles of incidence at which the dark 
bands in the spectra coincided. 
Each of these was determined five or six times and the mean taken. 
We must now return to the theoretical considerations which enable us to express 
the azimuth of the plane of polarization of the incident light in terms of the angles of 
incidence and refraction and the position of the plane of polarization in the crystal. 
Let us consider a plane-wave incident at an angle (j>, let <j/, cj/' be the angles of 
refraction for the two refracted waves respectively. The incident, reflected and 
refracted waves cut the plane face of incidence in the same line, let 9, 9 /} 6' and 9" be 
the angles between this line and the directions of the electric displacement in the 
incident reflected and refracted waves respectively. 
Let a, a /} a' and a" be the amplitudes of the electric displacements in these directions. 
Let q be the angle between the extraordinary wave normal and the corresponding ray. 
MDCGCLXXXII. 4 H 
