the Attractions of Spheroids of every Description. 27 
6 . We have hitherto confined our attention to the law of 
attraction that actually takes place in nature; but before we 
conclude this discourse it may not be improper to add a few 
words on the theorem taken in the general sense in which it 
is laid down in the Mecanique Celeste .* Let n represent the 
exponent of that power of the distance according to which the 
attraction acts ; dM a molecule of the spheroid, and / the dis- 
tance of the molecule from the attracted point; then V — 
f-r i . dM, the fluent being extended to all the molecules 
in the mass of the spheroid. If p denote a radius of the sphe- 
roid and r the distance of an attracted point (situate in the 
prolongation of p) from the centre, the function V will con- 
sist of two parts one derived from the sphere whose radius is 
P ; and the other, which we shall denote separately by s, from 
the difference between the spheroid and the sphere : and if 
dm denote one of the molecules of that difference, then s = 
(£ 
idr 
. f n+l . dm : 
f .f * 1 . dm: therefore |~j = ( n -f- 1) . Jf ^ 
but retaining the same denominations as before, f= jf 1 — zrp . 
m 
1 + and 
Ids ] 
\dl] 
'~P • 7 
■2 rp . y + 
therefore 
,/ i+I . dm: 
2 rp • y + p 
and, by substituting p (1 ■— 7) + (r — />) for r-p.y, we 
shall get 
(ft) = ( M + 0 f • dm + (» + 0 ■ ( r ~0 • 
f'f~ l • dm: 
* Liv, 3 e, No. 10 . Equation (i). 
E 2 
