380 Mr. Airy on Laplace’s Investigation of the 
point out those parts of the investigation which appear to me 
to be unsatisfactory, and to state them in the form to which, as 
I conceive, the objections will not apply. 
It may perhaps be thought an arrogant attempt in me to 
correct at once the errors of the two most distinguished analysts 
of the age. On a mathematical subject, however, in which the 
value of an assertion depends entirely on the proofs by which 
it is supported, it is at least allowable for any one to give the 
reasons which have led him to a conclusion different from that 
at which another has arrived. For the transcendent powers of 
Laplace, and for the analytical skill of Mr. Ivory, I have the 
most profound admiration ; in particular the investigations of at- 
tractions given in the Mecanique Celeste, I consider as the most 
wonderful theory in the whole compass of mathematical science. 
But I am induced by this very circumstance to think, that the 
efforts of mathematicians are well directed when they endeavour 
to correct any errors which may have crept into such abstruse 
investigations. That a theory so complicated should be free from 
defects, is hardly to be expected ; and the discussion of the faults 
which are to be ascribed only to inadvertence, or oversight, will 
always serve to display more clearly the excellencies which are 
the offspring of nothing but genius and labour. 
The attraction of a spheroid im any direction is made by 
Laplace to depend on the function V, which expresses the sum 
of the products of every particle, into the reciprocal of its distance 
from the attracted point. If 56 be the radius of a sphere, r the 
distance of the attracted point from its center, this sum for the sphere 
is — , (Liv. II. No. 12. and Liv. III. No. 6.) and for a spheroid, 
the attracted point being supposed exterior to it, 
