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.

COLOURED RINGS OF POLARIZATION. 357
147. The general explanation may be given thus. From
experience*, as well from the theory of Prop. 22, &c., it
appears that, whatever be the nature of light incident on a
doubly refracting crystal, the two rays which it produces
are polarized, one in one plane, and the other in the plane
perpendicular to the former. That is, the vibrations of the
incident ray are resolved into two sets, one in one direction and the other in the direction perpendicular to that,
which produce waves that describe different paths; and one
of these forms the Ordinary ray and the other the Extraordinary ray. And from the theory of (108) it appears
that these two sets of waves will pass through the crystal
with different velocities, and therefore on coming out of the
crystal will be in different phases. Their union therefore
will produce a kind of light not necessarily plane-polarized,
or not necessarily polarized in tlie same plane as before
passing through the crystal: and therefore their capability
of reflection at the analyzing plate is, generally, restored.
But, as the positions of the two planes of polarization, as
well as the difference of velocity of the two rays, will depend upon the direction of the paths through the crystal,
the nature of the light produced by the union of the two
emergent streams will vary as the directions vary; and consequently the intensity of the light coming to the eye after
analyzation will vary with the direction of the ray. Thus
bright patches or curves of different intensity will be seen.
The difference of phases, it may be easily conceived, is
generally a function of X, and thus the form or size of
the curves may be different for differently coloured light.
From the mixture of these differently sized and differently
coloured curves, curves will be produced in which the mixture of colours is different at almost every point, as in the
fringes of interference and in Newton's rings.
148. We have supposed here that neither plane of
polarization of the rays in the crystal coincides with the
plane of polarization of the light reflected from A. But
* Quartz is the only well established exception to this rule. It appears
that neither the ordinary nor the extraordinary ray of quartz is strictly plane.
polarized.