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.

INTENSITY OF LIGHT PASSING THROUGH A HOLE. 261
Expanding,
sin20
ZG= r-cos O. z + 2 + &c.
2r
z2
If z be so small, and r so large, that -will never exceed
a fraction of À, (or even if it amounts to several multiples
of X), the terms after the second may be omitted. Then
the disturbance produced by one little wave is
c.Îz 27r
ZG sin (v t -r + cos. z):
and the sum of all the disturbances is
cJ. sin- - (v t - r + cos 0. z).
In the integration we shall produce no sensible error if we
put r for ZG, and this makes the sum
C 7nr
-fsin (v t - r + cos 0.).
r X
Integrating, it is
-cX 2Tr
-2rrco cos - (vt - r + cos. z):
27rrcos6 X
and taking this from z= -b to z = +b, the disturbance
at G is
eX 27r 27r
x { cos- (v - r - cos. b) - cos- (vt - r + cos 0. b)
2 rr cos 0 X X
cX. 2r. b. cos. 2r -
= -.-sin.'.sin-(vt-r).
7rr cos0 X
This represents a vibration whose maximum is
cX 27rbcosO. sin
7rr cos 0 X
25. We shall now proceed to compare the values of
this expression for different values of 0.