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.

SUPPOSED HETEROGENEOUS. 151
And from the equation
12 + m2 + n2= 1,.f+g h2 1
or 28-+;-;=1 or f2 + h2_2e(f2+g)}=l
a ~y 'y
we get 2 =f2 +g h2 - 2E(f2+g);
c2 C2
but c=- e =f+g +h-e;
y-. j2 =g2 + g 12 + g2 ) h.; 72=f+g + - 2)#e
(f2 + g+h'
a..d a /(f2 +g2 + h).(f + e2 + h2)~'
Also, since a2 - 7y = as - c2 = 2c2e,
f2.+g2 + g2 +
2 ho... = /( +'2 + 2) h
(f y1+ go + +g~
46. Now, the co-ordinates of A' (Prop. 20.) = la, mb, nci
fa ga ho
or = -,, -. The distance of this point, therefore,
a a y
from the axis of the spheroid
- / \f2 a2 g 2 ) = (
- a at)>
And, as this point is within the spheroid whose semi-axes
are a and y, its attraction towards the axis, by (19),
= 5-ïp (1 - - (f + g):
3 5 a
hence, its attraction in tle direction of x
f 4i7r a
c-p. ( 1 — e).*-.f
LErr 2 ct{