258             ON  THE  COMPOSITION AND  RESOLUTION,  ETC.
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 Nicol's 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 (27T)"^1 cos^2 ada multiplied by the mean value of c^2. Hence we have from the formulae (16)
^ = im(o^2);       .5 = 0;       C = Jm(c^2);       £ = 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 f , and light independent of the former, of the same intensity, polarized at an azimuth zero. This result may be com-pared with one of Professor Dove's experiments.
If a rotating crystalline plate, cut from a doubly refracting crystal in a direction not nearly coinciding with the optic axis or one of the optic axes, and not sufficiently thin to exhibit colours in polarized light, be substituted for the rotating Nicol's prism, since the plate is too thick to allow of the exhibition of any phenomena depending on the interference of the oppositely polarized pencils, the effect will be just the same as in the case of the Nicol's prism, only the intensity of each stream will be doubled.
In applying the formulae of this paper to experiments in which one part of an optical train is made to revolve rapidly, it must be understood that the other parts of the train are at rest, or at least do not revolve with a velocity nearly equal to the former. Otherwise, particular phenomena will be exhibited depending on the simultaneous movements of two or more parts of the train, as appeared in Professor Dove's experiments ; and in the calculation of these phenomena it will not be allowable to substitute for the stream of light emerging from the polarizer, or first revolving piece whatever it be, the streams of common and elliptically polarized light to which, for general purposes, it is equivalent.