74 
Mr. Ivory on the Attractions of an 
suppose R to be a function of £ only, without zs ; then, as. 
before. 
B 
( /) i _ iKW+l 
•+3 J <V‘ 
2.4.6 
21 
but if R be a function of the most general kind, then it must 
be reduced to this form, viz. 
R i+3 = M (o) + (1— [x /2 ) f . M (?) . cos. ©' + &c. 
4- (1— p/ 2 )*. N^. sin. zs' - }- &c. : 
and the several parts that will consist of must be sepa- 
rately computed, as in the analogous case already considered. 
The same process will apply when the attracted point is within 
the surface. 
11. To complete the plan of this discourse, it remains that 
we apply the theory laid down in it to the case of the ellip- 
soid. Let the semLaxes be k, k', k", the first being the least 
of all the three; and let x, y, z, respectively parallel to the 
same axes, be three co-ordinates of a point in the surface : 
then will the equation of the solid be 
F t -r pr — 1 • 
put x — R[j/ ; y = R . V 1 — p/ 2 . cos. zs' ; and z = R . y / 1 — p.' 2 . 
sin. zs'; then by substitution, 
, (i-(t n ) cos V , (1— y^sin. V'7 
K IF F - “ + W ] = 1 - 
farther, let e = ~ ; /= — ; and s = p / 2 4- * ( 1 — p/ 4 ) cos. 'zs' 
4 -/. (1— p/ 2 ) . sin. V; then R= and if this value of 
R, or the radius of the ellipsoid, be substituted in the general 
