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.

DIFFERENCE OF RETAIRDATIONS IN BIAXAL CRYSTALS. 373
Hence
sin - sin m nearly, and sin n= sin n nearly:
v v
and therefore the difference of retardations is
T. C. a3
- sin m. sin n.
2v
This as before we shall call I.
PROP. 35. A plate cut from a biaxal crystal (as in
Prop. 34) is placed between the polarizing and analyzing
plates: to investigate the intensity of the light in different
points of the image seen after reflection from B.
163. Let q/ be taken now to represent the angle made
by the plane of polarization of either ray with the plane of
first polarization, and the expression of (155), which is founded on no supposition except that the planes of polarization
of the two rays are perpendicular to each other, will apply
to this case. The intensity of light is therefore
a2 {cosa - sin2o. sin (20 + 2a). sin2 -.
Conceive fig. 36 to be the projection of the directions of the
rays and planes on a sphere (or rather on the tangent plane
to a sphere) of which the eye is the center and whose radius
is r. Let A, B, thus represent the optic axes, P any ray
under consideration, DE the plane of first polarization. Put
B3 for the angle made by the plane passing through the
optic axes of the crystal with the plane of first polarization.
Let PQ bisect the angle APB: then, by (124), PQ represents the plane of polarization of one ray, and therefore
PQA = p +,g.
A P BP
Also sin m = - nearly, sin n = - nearly,
r r
and therefore
T. C.a'
I=.AP. BP,
2vr2