200 ON A NEW ELLIPTIC ANALYSER.
Let 9 be the azimuth of the plane of polarization of the li transmitted by the Nicol, measured from a fixed direction, <£ that of one of the neutral axes of the plate when the incident light, supposed to be homogeneous and perfectly elliptically polarized, is wholly extinguished, 6 + 80, (£ + 3$ the actual azimuths in the course of an observation. In the true positions of the plate and Nicol, the elliptically polarized light presented for observation is converted by the plate into plane-polarized, the plane of polarization having the azimuth 6. In consequence of the errors of azimuth W, S$, the light falling on the Nicol has a component polarized perpendicularly to the azimuth 6 + S0. Let us determine the intensity (Q) of this light as a function of the errors of pointing.
Let 0, E denote the neutral axes of the retarding plate, N the plane of polarization of the light transmitted by the Nicol, all in the true positions, 0', Ef} N' the same in the actual positions, P a plane perpendicular to N'. Let us take the intensity of the elliptically polarized light presented for observation as unity, which may also be taken as the intensity of the light falling on the Nicol, whatever be its azimuth, since the small loss by reflection at the surfaces of the plate is almost rigorously the same for the two components, and we are only concerned with the relative intensities. In the true positions, light of intensity 1 polarized in the plane N falls on the Nicol; and if we suppose the direction of this light reversed until it has passed through the plate, substituting in the plate acceleration for retardation, and then reverse the direction again, we shall obtain the light presented. This incident light is now to be supposed to fall on the plate and Nicol in their actual, not their true positions.
The light, whether reversed or direct, falling on the plate must be resolved into its components polarized along the neutral axes, and these again must be resolved so as to retain the components polarized in the plane P'. The four components with which we are concerned may conveniently be designated as NOO'P, NOJE'P, NEO'P, NEE'P, from their successive planes of polarization. The magnitude of each component will be got by taking the product of the cosines of the successive differences of azimuth; thus for NOOTP it is
cos (6 - </>) cos S0 cos (0 + 80 + JTT - <£ -