180 TRANSVERSAL VIBRATIONS. 



in which a and a' denote (as before) the angles which the 

 planes of polarization form with the plane of incidence, be- 

 fore and after refraction. This law was discovered experi- 

 mentally by Sir David Brewster : it is a necessary conse- 

 quence of the theory already given, and is deduced by a 

 process exactly similar to that of the preceding article. 



When the refracted ray meets a second surface parallel 

 to the former, and emerges into air, the azimuth of the plane 

 of polarization of the emergent ray will be given by the 

 formula 



cot a" = cot a f cos (r - i) ; 



wherefore, since cos (r - i) = cos (i-r), we have, for the 

 change of the plane of polarization, produced by transmission 

 through a plate bounded by parallel surfaces, 



cot a" = cot a cos 2 (i - r). 



