of homogeneous Ellipsoids. 34,7 
leave no room for perfecting the theory of the attractions of 
ellipsoids in both these respects. It consists in shewing that 
the expressions for the attractions of an ellipsoid, on any ex- 
ternal point, may be resolved into two factors ; of which, one 
is the mass of the ellipsoid, and the other involves only the 
excentricities of the solid and the co-ordinates of the attracted 
point: whence it follows, that two ellipsoids, which have the 
same excentricities, and their principal sections in the same 
planes, will attract the same external point with forces pro- 
portional to the masses of the solids. This theorem includes 
the extreme case, when the surface of one of the solids passes 
through the attracted point : and by this means the attraction 
of an ellipsoid, upon a point placed without it, is made to de- 
pend upon the attraction which another ellipsoid, having the 
same excentricities as the former, exerts upon a point placed 
in the surface.* Le Gendre has given a direct demonstra- 
tion of the theorem of La Place, by integrating the fluxional 
expressions of the attractive forces ; a work of no small diffi- 
culty, and which is not accomplished without complicated cal- 
culations.^ In the Mecanique Celeste , the subject of attractions 
of ellipsoids is treated by La Place after the method first 
given by himself in the Memoirs of the Academy of Sciences, £ 
founded on the theory of series and partial fluxions. It was 
in the study of La Place's work, that the method I am about 
to deliver, was suggested ; and it will not be altogether un- 
worthy of the notice of the Royal Society, if it contribute to 
simplify a branch of physical astronomy of great difficulty, 
and which has so much engaged the attention of the most 
eminent mathematicians. 
* Acad, des Sciences de Paris pour 1 7 8 3. -j- Ibid. 1788. J For 1783. 
