150 Mr. Ivory on the figure requisite to maintain , &c. 
c = Y a 9 - (1+ a?) 
*y = a /( i — mO = iq ( 1 — f- 9 ) 
(i + *.>') = <* {i + i? (i — f* 2 )}* 
Such is the method of investigation for which we are in- 
debted to Legendre and Laplace in its fundamental prin- 
ciples : for, when all the operations necessary for applying 
it extensively and readily are fully explained, it becomes a 
great branch of analysis. The result is no more than an 
approximation, both on account of the quantities omitted, 
and because no attention is paid to one of the conditions of 
equilibrium. Considering the near approach of all the planets 
to the spherical form, the method of calculation may be 
deemed sufficiently accurate for determining the figure of 
the fluids that cover their surfaces ; but it is not the less 
necessary to place the physical theory on a clear and sure 
foundation. As the subject is usually treated, there is an 
obscurity, and a want of evidence, arising from the incon- 
sistency between the hydrostatical theory and what is proved 
by M’Laurin, which is extremely embarrassing, but which 
entirely disappears, when we take into account all the phy- 
sical conditions requisite to maintain the equilibrium of a 
homogeneous fluid mass that revolves upon an axis. 
J. IVORY. 
November z, 1823. 
