Mr. Ivory on the Method of computing 
l.* Conceive a spheroid which differs hut little from a 
sphere, and also a point or centre in the middle ; let p denote 
the radius of the spheroid drawn to an attracted point in the 
surface : then the whole spheroid will consist of two parts, 
viz. a sphere of which the radius is p, and a shell of matter 
spread over the surface of the sphere every where so thin as 
to contain only one molecule in the depth. The function V 
( which, in the law of attraction that takes place in nature, is 
the sum of all the molecules of* the attracting body divided by 
their respective distances from the attracted point), relatively 
to the whole spheroid, will be determined by seeking its value, 
ist. relatively to the sphere ; 2dly, relatively to the shell of 
matter. 
Produce the radius p without the surfaces of the spheroid 
and sphere, till the distance from the centre be r; then the 
value ofV, relatively to the sphere, for the attracted point 
situate at the extremity of r, will be — . (tt denoting the 
periphery when the diameter is unit) ; and, making r = p, it 
will be y . p 2 , for the point in the surface at the extremity of 
p. Again, let dm be one of the indefinitely small molecules 
in the difference between the spheroid and the sphere ; and 
let jf denote the distance of the same molecule from the at- 
tracted point in the surface at the extremity of p ; then the 
value of V, relatively to the shell of matter spread over the 
surface of the sphere will be =J ~ 9 the fluent being extended 
to all the molecules in the shell, those on the outside of 
* Mec. Celeste, Liv, 3, No. 10. 
•}• Liv. 2d, No. 12. 
