STREAMS OF POLARIZED LIGHT FROM DIFFERENT SOURCES. 415 



time. So far as relates to the stream for which the azimuth of the first axis lies between a and 

 a + da, we have tn (c 2 ) = (2ir)~'c s da; and in the application of the formulae (16) the summa- 

 tion, to which 2 refers, will of course pass into an integration. We have therefore 



A=— da = cfi; B= — sin 2/3 / da = c 2 sin 2/3; C = 0; D = ; 

 2W 2tt •/„ 



whence we get from the formulae (19), supposing /3 positive, 



J' = c* sin 2/3; /= c 2 (l - sin2/3) ; /3' = 45°; 



while a remains indeterminate. Hence the mixture is equivalent, not to common light alone, 

 but to a stream of common light having an intensity equal to c 2 (1 - sin 2/3), combined with a 

 stream of circularly polarized light, independent of the former, having an intensity equal to 

 c 2 sin 2/3, and being of the same character as regards right-handed or left-handed as the original 

 stream would be were the ellipse stationary. The result of supposing /3 negative is here 

 assumed as obvious. 



22. Suppose that a polarizing prism and a mica plate, which produce elliptic polarization, 

 are made to revolve together with great rapidity. The stream of light thus produced will be 

 equivalent to the former. The only difference is that in the former case c was supposed 

 constant, whereas in the case of actual experiment it will be subject to the fluctuations men- 

 tioned at the beginning of this paper; but the mean values represented by Ml will not be 

 affected when these fluctuations are taken into account, and therefore the same formulae will 

 continue to apply. Hence, if the polarization be circular the rotation will make no difference; 

 if it be plane, the light will appear completely depolarized ; in intermediate cases the result 

 will be intermediate, and the light will be equivalent to a mixture of common light and 

 circularly polarized light. The reader may compare these conclusions of theory with some 

 experiments by Professor Dove*. 



23. As a last example, let light polarized by. transmission through a Nicol's prism be 

 transmitted through a second Nicol's prism, which is made to revolve uniformly and rapidly 

 while the first remains fixed. 



Let a be the azimuth of the plane of polarization of the second NicoPs prism, measured 

 from that of the first, c the coefficient of vibration in the stream transmitted through the 

 first prism. The stream passing through the second prism is made up of an infinite number 

 of independent streams such as that whose intensity is (27r) _I cos 2 ada multiplied by the 

 mean value of c 2 . Hence we have from the formulae (16) 



^|m(c ! )i 5 = 0; C = im(c 8 ); D = 0; 



whence, taking the intensity of the original stream as unity, we have 



or the light is equivalent to a mixture of common light having an intensity ^, and light 



See Philosophical Magazine, Vol. xxx. (1847) p. 465. 



