ON  A  NEW  ELLIPTIC  ANALYSER.                           201
The relative retardations of phase for the four are 0, — p, p, 0. The intensity is found by the usual formula. For the object in view, S<9 and S0 may be supposed very small. The result is
Q = (S# —. §<j) -j- cos pSffi + (sin p cos 2^S<£)^2,
where ^ is put for 6 — <f>, the azimuth of the Nicol relatively to the plate.
When the retardation given by the plate does not differ considerably from 90°, the first term in Q docs not differ greatly from Sip. The expression for Q shews therefore that it is best that ty and $, not 0 and $, should be the angles that are altered independently; that is, that of the three constructions mentioned at the bottom of p. 199, that marked (b) should be the one chosen. This is the one described at the beginning, and is that with which the trials of the working of the instrument were made, the general result of which is mentioned above.
The employment of a plate giving a retardation of about a quarter of an undulation introduces considerable chromatic variations, which we might sometimes desire to avoid. Suppose for example that we were working with light only slightly differing from plane-polarized, and did not wish to reduce the intensity by the use of absorbing media or by selecting a portion of a spectrum ; it might seern unreasonable to introduce such large chromatic variations merely to determine a small ellipticity. But in such a case we are not bound to use a retarding plate such as hitherto supposed ; we may use a thin plate of mica giving a comparatively                          "
small retardation; all that is requisite being that the retardation should be large enough to command the ellipticity of the light that we have to observe, that is, as may readily be shewn, that it should riot be less than 2-sr, where tan -or denotes the ratio of the minor to the major axis of the ellipse. With the diminished retardation, the chromatic changes which the retarding plate introduces into the light observed arc of course diminished. The expression for Q shews that in this case it would be best that the motions of the plate and prism should be mechanically independent ; but as the instrument does not lend itself to that, we must take our choice of the two other arrangements, and it may be shewn from theory that the instrument ought to work well