Mathematical tracts on the lunar and planetary theories, the figure of the earth, precession and nutation, the calculus of variations, and the undulatory theory of optics.

352 UNDULATORY THEORY OF OPTICS.
139. The nature of the light in the reflected ray may
then be generally expressed by saving that it is elliptically
polarized: and in the first case by saying that it is circularly polarized. Wherever after this we speak of common
polarized light we shall for the sake of distinction call it
plane polarized light. From the investigation of the second
case it appears that Fresnel's rhomb, by proper adjustment
of position with respect to the plane of polarization, is capable of producing elliptically polarized light of every degree
of ellipticity. We will therefore suppose that the circularly
or elliptically polarized light is produced by Fresnel's rhombl.
For use, it is convenient to have it mounted in a frarne
which, without stopping the light, admits of its turning round
the axis HI fig. 33: this frame may be placed on the board
in fig. 24: then the light plane-polarized by A is by the
rhomb converted into circularly or elliptically polarized light
and emerges from the end DC opposite to the analyzing
plate B in fig. 24. If the mounting be graduated so as to
determine the angle made by the plane of polarization with
the plane of reflection, then when this angle is o, 900, 180~,
270', the plane polarized light is not altered: when it is
45~, 135~, 2250~, 315~, the emergent liglit is circularly polarized: when it has any other value, the light is elliptically
polarized.
140. Now it is evident that circularly polarized light
may be resolved into two vibrations parallel and perpendicular
to any arbitrary plane, and that the magnitudes of these
vibrations are always the same. Consequently this light,
when examined only by the analyzing plate B, shews no sign
of polarization (96). This is experimentally true. But
if elliptically-polarized light is resolved in the same way,
neither of the resolved parts ever vanishes, though their
magnitudes vary: and therefore when examined with the
analyzing plate it will appear to be partially polarized.
This is also true.
' We shall hereafter mention another contrivance which produces nearly but
not exactly the same effect, and which has been used more extensively than
Fresnel's rhomb.