THE POLARIZATION OF LIGHT BY REFRACTION. 
137 
tion x of the planes of polarization ab, cd, (Fig. 1,) is 45°; but when this is not 
the case, the general expression is 
Cot p = cot x cos (£ — i'). 
When the light passes through a second surface, as in a single plate of glass, 
the value of x for the second surface is evidently the value of p after the 1 st 
refraction, or in general, calling 0 the inclination after any number n of refrac- 
tions, and p the inclination after one refraction, 
Cot 0 = (cot p) n 
When 6 is given by observation we have 
Cot p — _y cot 0. 
The general formula for any inclination x and any number n of refractions is 
Cot 0 = (cot x cos (i — i')') n , and 
Cot p = cot x cos ( i — i'). 
And when x = 45 and cot x = 1 as in common light, 
Cot 0 — (cos (i — i')) 71 . 
Cot p = „y cos ( i — i'). 
As the term (cos (i — i'))” can never become equal to 0, the planes of pola- 
rization can never be brought into a state of coincidence in a plane perpen- 
dicular to that of reflexion, either at the polarizing angle, or at any other 
angle. 
In order to compare the formula with experiment, I took a plate of well an- 
nealed glass, which at all incidences separates the reflected from the transmitted 
rays, and in which m was nearly 1.510, and I obtained the following results. 
MDCCCXXX. 
T 
