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.

CRYSTALLINE PLATE CUT IN ANY DIRECTION. 379
of X on another.) For I being considerable, a very
small variation of X will make A vary by 27r:
and thus, for the various rays included in every
2 7r I
small portion of the spectrum, cos - will have
all its values, positive and negative, and the sum
of all these values will be =. The intensity of
light will therefore be 1 sin2 2 0x incident light, a
proportion which is the same for all the colours.
On turning the plate round in its plane, 1> will
vary fromn 0 to 360, and the light will disappear
four times. It will be greatest when / = 45~,
135~, &c.
(2) Colours may however be produced by crossing two
plates of very nearly the same thickness cut in the
same manner from the same crystal. For let I be
the retardation of the Ordinary above the Extraordinary ray in the first, I' that in the second; I'
will be very nearly equal to I. And, the plates
being at right angles to each other, the Ordinary
ray of the first will be the Extraordinary ray of
the second. I' therefore will be the acceleration in
the second plate of the same vibrations for which
I was the retardation in the first: and therefore
the whole retardation is I - ', and the brightness
is noF
-sin2 oi1 -cos - — ),
or a2 sini2 2. sin2 - )
This may be so small that r(I- ) may differ little
(not more than a fraction of wr or a small multiple
of r-) for differently coloured rays, and then there
will be vivid colours.