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.

382 UNDULATORY THEORY OF OPTICS.
are accurately known. Quartz has been mentioned as an
exception to the common laws of uniaxal crystals. It appears that the phenomena which it exhibits may be perfectly represented by supposing the Ordinary ray to consist
of elliptically-polarized light whose greater axis is perpendicular to the principal plane, and the Extraordinary ray to
consist of elliptically-polarized light whose greater axis is
in the principal plane: these two rays having also the difference* mentioned in (141): and the ellipses being changed
to circles when the direction of the rays coincides with the
axis of the crystal. It is also necessary to suppose that
the axis of revolution of the spheroid (prolate for quartz)
in which the Extraordinary wave is supposed to diverge
(115) is less than the radius of the sphere into which the
Ordinary wave diverges. For these investigations we must
refer the reader to the Cambridge Transactions, Vol. Iv.
PnoP. 38. In every case where the interposed crystal
resolves the light into two rays polarized in planes at right
angles to each other, on turning the analyzing plate 900 the
intensity of the light at each point is complementary to what
it was before.
175. This is seen from the expression of (155). On
putting 90~ + a for a, the expression becomes
1- -cos 2q. cos (2( + a) - sin 2 (. sin (( + 2a).os —,
which added to that in (155) snakes a~. Thus if in one
case there is black, in the other there will be white: if in
one there is an excess of red at any point and an absence
* The crystal is right-handed or left-handed according as the Ordinary or
the Extraordinary ray is of the first of these kinds. Sometimes (as in macled
quartz, or amethyst) the two species of quartz are mixed: the optical phonomena which the mixture presents are very remarkable. It is to be observed
(as a consequence of what is stated in the text) that in the direction of the
axis the two rays, circularly polarized in opposite ways, are transmitted with
different velocities: no mechanical theory has yet been formed which will completely account for this. (See however Mr Tovey's papers in the Philosophical
Magazine.) It is remarkable that several fluids (as turpentine, sugar and
water, &c.) possess this property, and even the vapour of turpentine: and apparently in all directions.