On Polarization of Light hy Refraction. 229 



The above expression is of course suited only to the case where 

 the inclination 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 a; cos {i—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 1st refraction, or in general, calling d the inclina- 

 tion after any number n of refractions, and <p the inclination after 

 one refraction, 



Cot ^ = (cot (p)" 



When & is given by observation we have 



Cot 9 = y cot ^. 

 The general formula for any inclination x and any number n of re- 

 fractions is 



Cot ^ = (cot lT cos (i — i'))", and 



Cot {p= V cot j; cos (i — i ). 

 And when a?=45 and cot x— 1 as in common light, 

 Cot ^ = (cos {i—i')Y. 



Cot(p = A/ COS (i — i'). 



As the term (cos {i — i')Y can never become equal to 0, the planes 

 of polarization can never be brought into a state of coincidence in a 

 plane perpendicular to that of reflexion, either at the polarizing an- 

 gle, or at any other angle. 



In order to compare the formula with experiment, I took a plate 

 of well annealed glass, which at all incidences separates the reflect- 

 ed from the transmitted rays, and in which m was nearly 1.510, 

 and I obtained the following results. 



