THE 
PHILOSOPHICAL MAGAZINE. 
AND JOURNAL. 
23h FEBRUARY 1826. 
XIII. On the Theory of the Figure of the Planets contained in 
the Third Book of the Mécanique Céleste. By J. Ivory, 
Esq. M.A. F.R.S. 
[Concluded from p. 37.] 
II. "(HERE can be no other apology for the observations 
which I have made on the analysis of Laplace, ex- 
cept that they are true and rigorously proved. ‘And as this 
is the best apology that can be made, so I am not aware that 
any other is necessary. ‘To avoid as much as possible all 
objection and cavil, I have employed in the proof the author’s 
own mode of investigation. Speculations of this kind are at 
present entirely out of fashion, or rather they are discouraged 
and tindervalued as much as possible. ‘They seem even to be 
excluded from what is popularly called the inductive philo- 
sophy, forgetting that they form a part of the noblest and 
‘ most successful induction that, we may venture to predict, 
will ever do honour to the human intellect. What has occu- 
pied the attention of Maclaurin and Simpson, of D’ Alembert, 
Lagrange and Laplace, is now utterly condemned as useless, 
with a degree of levity that will not easily be believed. But 
the exclusive spirit which reigns so powerfully at present, 
whether it proceeds from particular interests or from narrow 
views. of science, will at length spend its force; and the dis- 
cussion I have undertaken may then contribute to place an 
important branch of the philosophy of Newton on a solid 
foundation. It follows from what has been shown, that the 
method of Laplace, when freed from series withou! con- 
vergency, and reduced to what is strictly demonstrative, + 
confined to a class of spheroids first proposed by D’Alem- 
bert. We cannot, therefore, allow that the method is per- 
fectly general, unless it were proved that the class of spheroid: 
mentioned comprehends every case in which the conditions 
of equilibrium can possibly be fulfilled. But it is greatly to 
be wished that so important a part of the system of the world 
as the theory of the figure of the planets, were deduced from 
Vol. 67. No. 334. Feb, 1826, L sure 
