the Attractions of Spheroids of every Be scrip Hon, S3 
mend the following observations to the notice of such mathe- 
maticians as may devote some part of their attention to the 
cultivation of this important branch of physics. Although the 
analysis which Laplace has traced out for the attractions of 
spheroids must be allowed to be very ingenious and masterly, 
yet still there are some considerations which cannot but lead us 
to think, that it falls short of that degree of perfection which it 
is laudable to aim at. And in particular the coefficients of the 
several terms of the expansion are, in his procedure, formed one 
after another, beginning with the last term : so that the first 
terms of the series cannot be found without previously com- 
puting all the rest. This is no doubt an imperfection of some 
moment: and it can only be removed by deducing every term 
of the series immediately from the radius of the spheroid, and 
enabling the analyst to calculate any proposed coefficient in- 
dependently of all the rest by a process, as easy at least as in 
the investigation of Laplace. It is also to be observed, that 
in the application of this method we are not limited to such 
spheroids as do not differ much from spheres ; we may ex- 
tend it to all spheroids provided their radii be expressed by 
functions of the kind so often mentioned : it would therefore 
be extremely desirable to deduce in this way all the known 
formulas for ellipsoids, and elliptical spheroids of revolution, 
which would bring the whole theory of attractions under one 
uniform analysis. 
MDCCCXH. 
F 
