XXI. On Laplace’s Investigation of the Attraction 
of Spheroids differing little from a Sphere. 
By GEORGE BIDDELL AIRY, M.A. 
FELLOW OF TRINITY COLLEGE, OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 
AND CORRESPONDING MEMBER OF THE NORTHERN INSTITUTE. 
[Read May 8, 1826.] 
Ly two papers printed in the Philosophical Transactions for 
1812, and in a third in the Transactions for 1822, Mr. Ivory has 
objected to some parts of Laplace’s investigation of the attrac- 
tion of spheroids differing little from a sphere. That there are 
difficulties in that theory cannot be denied, but that Mr. Ivory 
has pointed out correctly the errors from which the obscurities arise 
appears to me quite doubtful. After considering the subject at- 
tentively, I have come to the conclusion, that in the part to which 
Mr. Ivory has most strongly objected, Laplace’s investigation 
may, by a slight alteration, be made free from error; but that an 
assertion of Laplace which Mr. Ivory has admitted without scruple, 
is absolutely unsupported by any demonstrative evidence what- 
ever. The result of my examination is however the same as 
that of Mr. Ivory’s; namely, that the method of Laplace may 
be applied without error, when the elevation of the spheroid 
above the sphere can be expressed by a rational function of «, 
/1—n?.cos », and ,/1—z?. sin», and that it is not demonstrated 
for any other case. In the present communication I propose to 
Vol. Il. Part I. 3C 
