3 ° 
Mr. Ivory on the Method of computing 
In this formula the expression under the sign of integration is 
a finite quantity* depending on the nature of the molecules ; 
and thus the case of nature is the point where the reasoning 
of Laplace ceases to be exact. 
The equation last investigated, although it has a finite form 
ought nevertheless to be equivalent to the equation (C) which 
is expressed in an infinite series. To bring this matter to the 
proof, I observe that both the equations will be accurate 
whether p reaches exactly to the surface of the spheroid, or 
only nearly to that surface : for all that the reasoning sup- 
poses is that p differs only by the small quantity a .a .y from 
a ; that the attracted point is in the surface of the sphere of 
which p is the radius ; and that the shell of matter spread 
over the surface of the same sphere is every where so thin as 
to contain only one molecule in the depth. Suppose then u'to 
denote a rational and integral function of s/ 1 — {L 2 . cos. % d, 
V i — [L 2 . sin. to' ; and let a . a . v denote the thickness of the 
molecule dm ; then dm = a . a . p 2 . u' . d\d . da d; consequently, 
on account of the formula ( E ) , the equation last found will 
become 
and in like manner by valuing the several terms of the equa- 
tion ( C ) we shall get 
i V -I ‘ a . 
dV 
dr 
— . a 2 — u . a 
3 
2 7T . u : 
2 
* Art. 3. Equat. (E). 
