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.

RETARDATION OF RAYS IN UNIAXAL CRYSTAL. 359
PROI. 31. A plate of Iceland spar (or other uniaxal
crystal, except quartz) is bounded by planes perpendicular
to the axis of the crystal: light is incident nearly in the
direction of the axis; to find the position of the fiont, and
the velocity perpendicular to the front, of the ordinary and
extraordinary waves: and the retardation of each produced
by passing through the plate.
150. First, for the extraordinary ray. In fig. 34 let
AB be the normal to the front of the incident wave, or
the direction of the incident ray: BC the normal to the
front of the extraordinary wave, which is not generally the
same as the direction of the extraordinary ray: CD the direction of emergence parallel to AB: i the angle of incidence made by AB, i' the angle of refraction made by BC:
v the velocity before incidence, v' the velocity of the extraordinary wave perpendicular to its front: T the thickness
T
of the plate. The time of describing BC is, —; the
v cos%
space which the wave would in the same time have deTv
scribed in air is -,. But since the front of the wave, cos
at incidence was perpendicular to 4B at B, and at emergence perpendicular to CD at C, the whole space which
the wave really has advanced is
BE -=T cos (i - i')
COs Z
and therefore it has been retarded by a space in air
equal to
i -,O (- cos t.cosi'-st. sin t
cosi i v
131. Now sini'= -sini. For if GH be a position of
v
the front before incidence and BK after entrance, GB and
HK must have been described in the same time, and therefore GB: HK (or sin i: sin i'):: velocity of incident
wave: velocity of extraordinary wave perpendicular to its