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.

320 UNDULATORY THEORY OF OPTICS.
position of the crystal. But between the properties of the
two rays a remarkable relation can be found. When the
rhombohedrons are in similar positions, O will produce only
an ordinary ray. When the first is turned 90~, E will produce only an ordinary ray. Consequently, on turning the
crystal 90o, E bas the same properties which O had before
turning it. Again, when the rhombohedrons are in similar
positions, E will produce only an extraordinary ray. On
turning the first through 90", O will produce only an extraordinary ray. Consequently, on turning the crystal 90~,
O has the same properties which E had before turning it.
This shews clearly that the two pencils have properties of
the same kind with reference to two planes passing through
their direction and moving with the crystal; and that the
two planes are at right angles to each othêr. If a plane
passing through the direction of the pencil and the shorter
diagonal of the rhombic face be called the principal plane*
of the crystal, then we may assert that the properties of the
Ordinary ray possess the same relation to the principal plane
which the properties of the Extraordinary ray possess to
the plane at right angles to the principal plane. This is
commonly expressed thus: the Ordinary ray is polarized in
the principal plane, and the Extraordinary ray is polarized
in a plane perpendicular to the principal plane.
95. There are some crystals which possess the property
of separating common light into an Ordinary and an Extraordinary pencil, and then absorbing one of them. Thus
certain specimens of agate, and plates of tourmaline cut parallel to the axis, allow the Ordinary pencil to pass, and
nearly suppress the Extraordinary. This however is only
true when the plates have a certain thickness: for, when
they are very thin, the Ordinary and Extraordinary pencils
are seen to have equal intensities. But the method of
exhibiting polarized light which is most extensively used
in experiments is, to reflect common light from unsilvered
glass or any other transparent substance, solid or fluid.
It is found that if the tangent of the angle of incidence
* This term will be used hereafter in a more general sense.