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.

308 UNDULATORY THEORY OF OPTICS.
2 r bX 2- 27r
=cos- (vt-B).. cos (pa +qy')-cos (p +cqy")}.À 2wq b À bX
C)w bXS 2w 4 2(a
sI —(vt-B). b). {bs T
-sin-( -).. {sin b -(p+qy')-sin -b(px+qy")}.
Let the integrals of the terms within the brackets (with
respect to x and between the proper limits) be P and Q:
then the coefficients of
cos - (vt - B) and sin (vt - B)
X À
bX bX
are respectively P and - Q,
2 7rq 2 rq
î): X2
and the intensity of the light is;(Po + Q2).
81. Ex. Let the aperture be a parallelogram whose
sides are 2e and 2f in the direction of v and y. Ilere:? - -f, y = +f:
2., - 2,.
cos - (pmx + qy') - cos - (px + qy")
bX bX
= cos (px - qf) - cos- (pox + qf)
bX bX. 27 2wr
= 2 sin 1 px. sin b qf,
the integral of which is
bX 2 r 7r
- -. sn -qf.cos -px;
7rpJ bX bx
which fior om = - e to a= = + e gives P = 0. Also
sin b - (p; + qy')- sin (px + qy")
bX bX