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 0F OBLATE SPHEROID. 131
dw 1 - v2
and d- =2 2kb (1 - ) cos2.. 1 - - v 2
dv 1-2e+2ev2
= 2kb.( - e).cosP. 'C. (1 - v e 2e. (1 - + 2ev4), nearly,
3 4ev3 2eS'\
and w=2b(l -e).cos~2.Îo. v —+2et 2 - -+ —
which, from v= -, to v= +
= 4kb (1 - e) cos. * 2 + 15)
\S 15 /
=...~ (1 - e) co.ep. S. (1 + ~ e)
Skb 8
- -- c( -)cosP.-(1 +-e)
3 ô
8kb 3
3 5
du skb b
3 5
therefore ouchintegrC at C; ten th attraction of th given spheroid
4kb7r 3
1on E in a direction parallel to the radius CW is equal
to the attraction of th seller spheroid in thee ame dicular to the
plane of the equator, and a spheroid be described concentric, similar, and similarly situated to the given spheroid,
touching EC at C; then the attraction of the given spheroid
on E, in a direction parallel to the radius CW, is equal
to the attraction of the smaller spheroid in the same direction on the point C.
13. Suppose both spheroids divided into wedges by
planes passing through EC: let EGHB, CKDL, be the
sections of both, made by one plane; and ERSb, CTdV,
the sections made by another plane very near the former.
Draw EF parallel to CD, and let the angles GEF, HEF,
KCD, LCD, be all equal. Let the angles gEF, hEF,
kCD, ICD be also equal to each other, and very nearly
9-2