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.

RINGS PRODUCED BY UNIAXAL CRYSTALS. 363.,..,.. f27I-2 7r 27r/1
a. sin ç. sin (b + a). sin { (v t - V) + -.
The sum of these represents the displacement produced by
the wave that enters the eye. Adding them, and expanding
sin (vt - X) +, — we find for the coefficient of
2,r1
a. cos.jcos (+ c+a) + asn. sin. sin ( + a). cos -,
2rand for the coefficient of cos - (vt - x),
a sin 0. sin (b +a a). sinThe sum of the squares of these coefficients is to be taken
for the measure of the intensity {as in (17) and (23)}. This
sumn is
a2. cos2. 0. cos(p + a) + a2 sin2p. sin~ ( + a)
27rl
+ 2 asin p. cos r. sin ()( + a). cos (p + a).cos
9.
or-1 + cos2.cos(2 + 21 a
+ sin 2>. sin (2p + 2a).cos —
or a2 {cos2a - s sin (2 + 2a). sin2
156. This gives the intensity of the light that enters
the eye in a given direction, or the brightness of one point
of the visible image. To determine what point of the image
it is, we have only to remark that this ray makes the angle
i with the ray that passes in the direction of the axis, in
a plane that is inclined < + a to the plane of analyzation
(supposing that we look in the direction of the ray's motion),