6 Mr. Ivory on the Method of computing 
deduced in a manner admirably simple, when the complicated 
nature of the question is considered. 
In order to give a succinct view of the plan of analysis pur- 
sued by Laplace, we must begin with observing that he does 
not seek directly an expression of the attractive force, but 
that he investigates the value of another function from which 
the attractive force in any proposed direction, may be derived 
by easy algebraic operations. This function, which in the law 
of attraction that obtains in nature, is the sum of all the mole- 
cules of the attracting solid, divided by their respective dis- 
tances from the attracted point, he expands in all cases into a 
series, containing the descending powers of the distance of 
the attracted point from the center, when that point is without 
the surface ; but the ascending powers of the same distance, 
when the attracted point is within the surface : and the ques- 
tion is, to determine the coefficients of the several terms of 
the expansion. In the first place, it is proved that every one 
of the coefficients satisfies an equation in partial fluxions, first 
noticed by the author himself, and from the skilful use of 
which, all the advantages peculiar to his method are derived. 
Laplace next lays down a theorem, which, he affirms, is true 
at the surfaces of all spheroids that differ but little from 
spheres ; hence he deduces the value of an expression, which 
is the sum of all the coefficients sought respectively multiplied 
by a known number ; and, what is remarkable, the value 
alluded to, is found to be proportional to the difference be- 
tween that radius of the spheroid which is drawn through the 
attracted point, and the radius of the sphere nearly equal to 
the spheroid. The circumstances we have now mentioned, 
suggest an elegant solution of the problem, and one that has 
