324? Mr. Ivory o« the Figure of Equilibrium^ 8^c. 



1755) which cannot be enough admired for invention and all 

 the qualities of the highest mathematical genius, if we over- 

 look the too precipitate adoption of a principle seducing by 

 its great generality. But the equality of pressure seems to 

 have been first used in solving this problem by Maclaurin. 

 If we strictly appreciate what that great geometer has pi'oved 

 in his celebrated demonstration, it will be found not only not 

 inconsistent with what has been said, but to acquire force and 

 simplicity when stated according to the foregoing principles. 

 Taking any particle of the fluid spheroid, Maclaurin proves 

 that any rectilineal canal standing upon it and terminating 

 in the upper surface, urges it to move with a force equal to 

 the effort of the fluid in the difference of the polar semi-axes 

 of the proposed spheroid and a similar one, the surface of 

 which passes through the particle. (Fluxions, § 639). Now 

 this does not prove that the particle is at rest by the equal 

 pressures upon it ; but, on the contrary, that it may have any 

 position on an elliptical surface without any variation of the 

 pressures which urge it. It follows indeed that all the par- 

 ticles on the same elliptical surface are in equilibrium rela- 

 tively to that surface, that is, there is no force urging them 

 to move upon it ; but, even when this is attended to, another 

 condition is still wanting to prove the immobility of the par- 

 ticle relatively to the whole spheroid, which is, the stability, 

 both in form and position, of the elliptical surface which con- 

 tains the particle. These observations being duly weighed, 

 it is obvious that all the inferences from what Maclaurin has 

 proved, are deducible from the equality of pressure at all the 

 points in the surface of every interior elliptical spheroid, con- 

 centric and similar to the given one ; which is according to 

 Clairaut's principle. 



In his work on the Theory of the Earth, Clairaut has 

 adopted the method of Maclaurin in preference to his own 

 theory, of which he makes little use. In reality the equili- 

 brium of a homogeneous planet in a fluid state cannot, by 

 strict reasoning, be deduced from his method according to 

 the exposition he has given of it ; because the reaction of the 

 strata on the masses on which they are laid is neglected. 



Oct. 15, 1838. James Ivory. 



