Mr. Ivory on the Attractions 
34> 6 
determining the attractions of round bodies (or such as are 
generated by the revolving of a curve about a right line which 
remains fixed) when the attracted point is situated in the com- 
mon axis of the circular sections :* and he employs this me- 
thod to compute the attractive force of a spheroid of revolution 
on a point placed in the axis.'f Maclaurin was the first who 
determined the attractions of such a spheroid generally, for 
any point placed in the surface, or within the solid. The me- 
thod of investigation, invented by that excellent geometer, is 
synthetical, but original, simple, and elegant, and has always 
been admired by mathematicians. When the attracted point 
is placed without the solid, the difficulty of solving the pro- 
blem is greatly increased ; and it was reserved for Le Gendre 
to complete the theory of attractions of spheroids of revolu- 
tion, by extending to all points, whether without or within 
the solid, what had before been investigated for the latter case 
only. X La Place took a more enlarged view of the problem ; 
he extended his researches to all elliptical spheroids, or such 
solids whose three principal sections are all ellipses ; and he 
obtained conclusions with regard to them, similar to what 
Maclaurin and Le Gendre had before demonstrated of 
spheroids of revolution. In this more general view of the 
problem, the investigation is particularly difficult, when the 
attracted point is placed without the solid. The method of in- 
vestigation, which La Place has employed for surmounting 
the difficulties of this last case, although it is entitled to every 
praise for its ingenuity, and the mathematical skill which it 
displays, is certainly neither so simple nor so direct, as to 
* Sect. 13, Prop. 91. f Prop. 91, Car. 2. 
1 Acad, des Sciences de Paris, Savans Et rangers, Tom. X. 
