§ Mr. Ivory on the Method of computing 
theorem, it may be remarked, is merely laid down by the 
author, and the truth of it confirmed by a demonstration ; it 
does not arise naturally in the course of the analysis ; and 
the reader of the Mecanique Celeste is at a loss to conjecture 
by what train of thought it may have been originally sug- 
gested. It may be doubted whether the theorem was intro- 
duced for the sake of demonstrating a method of investigation 
previously known to be just from other principles ; or whe- 
ther it preceded in the order of invention, and led to the me- 
thod of investigation. But however this maybe : after having 
studied the Dart of Laplace's work referred to with all the 
i 
attention which the importance of the subject and the novelty 
of tiie analysis both conspire to excite, I cannot grant that the 
demonstration which he has given of his proposition is conclu- 
sive. It is defective and erroneous, because a part of the ana- 
lytical expression is omitted without examination, and rejected 
as evanescent in all cases ; whereas it is so only in particular 
spheroids, and not in any case on account of any thing which 
the author proves. Two consequences have resulted from 
this error; for, in the first place, the method for the attraction 
of spheroids, as it now stands in the Mecanique Celeste , being 
grounded on the theorem, is unsupported by any demonstra- 
tive proof ; and, secondly, that method is represented as ap- 
plicable to all spheroids differing but little from spheres, 
whereas it is true of such only as have their radii expressed 
by functions of a particular class. 
In a work of so great extent as the Mecanique Celeste , 
which treats of so great a variety of subjects, all of them 
very difficult and abstruse, it can hardly be expected that no 
slips nor inadvertencies have been admitted. On the other 
