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.

ATTRACTION OF OBLATE SPHEROID. 129
and the base of the pyramid
= wq. qt = r2. cos 0. 4(. î0;
therefore by (7), its attraction in the direction AP
k. r. cos 0. P. 0 k r. cos 0.. 0.
re
Draw PN perpendicular to the plane of the equator: NO
perpendicular to AM; let AO = v, ON= y, NP = z. If
we resolve the attraction of the pyramid into two' parts,
one ii the direction AN, and the other in NP, the latter
of these will be counteracted by the attraction of another
pyramid in the same wedge, equally inclined to AR but
on the opposite side; and the former
= k. r. cos.. cos.os 0 = k. r. cos20. (. 0.
This is in the direction AN; if we resolve it into two in
the directions AO, ON, the latter of these will be 'ounteracted by the attraction of an equal pyramid, in another
wedge which makes the same angle with AM; and the
former
= k.. cos~0..( 0. cos. = I.k... sco. cos'0. Îo. 0.
Now the equation to the spheroid is
b'
PN2 = ( (AC' - CO2 - ON")
a2
b2 9
or 2 = — (2a - 2 - y2);
a2
putting for x, y, and z, their values
r. cos 0. cos (, r. cos 0. sin q, r. sin 0,
it becomes
b2S
r2.sin2 0 = - (2ar.cos. cos -r 2.os20. cos2 - r2.CS20. sin%2 );
2b2 cos 0. cos 9
* =r -. -
a (1 - e2). cos20 + sin"0
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