Sir David Brewster on the Compensations of Polarized Light. 385 



Compensations between one Reflexion above the polarizing Angle, and one 



Refraction. 



Reflexion. Refraction. 



89^ ^ 22° 



89 ' 42 • 



88 59 



86 74 



83 80 



82 87 



81 89^ 



If we now compare these results with the experimental and calculated ones given 

 in my papers of 1830,* we shall find that one reflexion will compensate another 

 reflexion, or one refraction, when the inclinations of the planes of polarization 

 produced by the two reflexions are equal and opposite, or when the inclination 

 produced by one reflexion is the complement of the inclination produced by one 

 refraction ; or more generally, in both cases, when the rotations produced in the 

 plane of polarization are equal and opposite. Hence, it follows that the compen- 

 sations of polarized light are produced by equal and opposite rotations of the 

 planes of polarization. 



Now, the inclination of the plane of polarization by reflexion at any angle 

 of incidence i, is 



cos (i-\-i') 



tan == tan. x ;. ..; , 



cos (^ — J ) 



and the inclination 0' for refracted light, is cot <j} = cot x . cos (i — i'). In the 

 case of reflected light, the angles of incidence which compensate each other are 

 those where <j> has equal values ; and in the case of reflected and refracted light, 

 the one compensates the other, when -j- 0' zz 90°, or tan + cot 0' = 1, or 

 when 



cos (i -\-i') 



tan X 



cos 



;. .,, + cotar. cos (i — i') = 1. 



{i — t) ^ ' 



Now, though we shall find that at the angles of compensation in the preceding 



* Philosophical Transactions, 1830, pp. 74, 75, 78; 136, 138, 139, and 143. 

 VOL. XIX. 3 D 



