On Polarization of Light by Refraction. 



231 



The last column but one was calculated by the formula cot ^ = cot 

 X. (cot 58° 40')=*. The differences on an average amount only 

 to 36'. 



In determining the quantity of polarized light in the refracted pen- 

 cil, we must-follow the method already explained for the reflected 

 ray, mutatis mutandis. The principal section of the analysing rhomb 

 being now supposed to be placed in a plane perpendicular to the 

 plane of reflexion, the quantity of light Q' polarized in that plane, 

 will be 



Q'=l-2 cos^'^, 

 the quantity of transmitted light being unity. But, 

 Cot <p=cot X cos{i - i'), 

 cos' 9 

 and as cot 9 = -=—^ — and sin^ (p + cos- (p = l, we have the quotient 



and the sum of sin* 9 and cos^ <p to find them. Hence 



(cot X cos {i — i'))'^ 



COS^ 9= , , / -7-. TTTT 



1-f (cot a; cos (i — I ))- 

 and by substituting this for cos^ 9 in the former equation, it becomes 



(cot X cos (i — i')Y 



Q!=l 



1 + (cot a; cos {i — i'))'- 



