POLARIZED  LIGHT FROM DIFFERENT  SOURCES.            257
the stream for which the azimuth of the first axis lies between a and a + doc, we have m (c^2) = (2<rr)~^l c^2cZa; and in the application of the formulae (16) the summation, to which 5 refers, will of course pass into an integration. We have therefore
c^2                    f^"*
£ = -—sin 2/3      ck = c^2sin2/3;
^7T                 Jo
(7=0;                  D = 0;
whence we get from the formulae (19), supposing ft positive, J' = c^2sin2/3;        J = c^2(1 - sin 2£);        /3'=45°;
while d 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 mentioned at the beginning of this paper; but the mean values represented by m 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
* See Philosophical Magazine, Vol. xxx. (1847) p. 465. S. m.                                                                                           17