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.

336 UNDULATORY THEORY OF OPTICS.
includes the sphere. If the spheroid be prolate, as in
quartz, uniaxal apophyllite, &c., the extraordinary ray is
always more refracted than the ordinary ray. The normal to the front of the wave is always in the plane of
incidence.
117. A compound prism which produces great angular
separation of the two rays is thus constructed. Let a prism
A be cut from Iceland spar with its' edge parallel to the
axis, and another prism B of equal angle with its edge
perpendicular to the axis, and let them be placed as in
fig. 31. Thle vibrations parallel to the plane of the paper
will furnish the ordinary ray of A and the extraordinary
ray of B; that is, this wave will be most refracted by A
towards C, and least by B towards D, and it will therefore on the whole pass towards C. In a similar manner,
the wave produced by vibrations perpendicular to the paper
will be least refracted by A towards C, and most refracted
by B towards D, and it will therefore on the whole pass
towards D. If the prisms be cut from quartz, the separation is in the opposite direction; it is smaller also, as
the prolate spheroid of quartz differs less from a sphere than
the oblate spheroid of Iceland spar.
PIOP. 24. To investigate the law of double refraction
in biaxal crystals.
118. By biaxal crystals are meant those in which a2,
b2, e2, are all different. Our limits will not allow us to
go through the whole of this investigation, and we shall
merely give the principal steps, referring for details to the
Memoirs de l' Institut, 1824; the Annales de Chimie, 1828;
and the Cambridge Transactions, Vol. vi. p. 85.
119. The first thing to be done, as in (108), is to
find two directions in the front of a plane wave in which a
displacement produces a force in the same direction, neglecting that force which is perpendicular to the front. As
we shall only have to calculate the forces in the directions
possessing this property, we shall at once resolve the whole