112 
Mr. Ivory on the expansion , &c. 
The observations that have been made, relate only to the 
foundation of the method in the Mecanique Celeste , and do 
not touch upon the general scope of the analysis, which is 
deserving of every praise. It is natural to think, that the 
theory of the figure of the planets would be placed on a 
firmer basis, if it were deduced directly from the general 
principles of the case, than when it is made to depend on a 
nice, and somewhat uncertain point of analysis. To hazard 
a conjecture suggested in the course of writing this paper, 
the theory will probably be found to hinge on this propo- 
sition, that a spheroid, whether homogeneous or heterogene- 
ous, cannot be in equilibrium by means of a rotatory motion 
about an axis, and the joint effect of the attraction of its own 
particles, and of the other bodies of the system, unless its 
radius be a function of three rectangular co-ordinates. If 
this proposition were clearly and rigorously demonstrated, 
the analysis of Laplace, in changing the ground on which it 
is built, would require little or no alteration in other re- 
spects. 
Dec. 2z, 1821. 
