ON THE CONDITION OF EQUILIBRIUM OF 

 A SYSTEM OF MUTUALLY ATTRACTIVE 

 FLUID PARTICLES*. 



THE generally received theory of the Equilibrium of Fluids, 

 (due in its present form to Euler,) assigns one condition as 

 necessary and sufficient in every case. Mr Ivory conceives, 

 that when a fluid is acted on by forces arising from the mutual 

 attraction of its particles, a second condition is requisite for 

 equilibrium, and has developed the considerations which have 

 led him to this result, in several papers published in the Phil. 

 Trans., and also in the Phil. Mag. The authority of Mr Ivory 

 on any point of mathematical physics is very great : his decision 

 on one to which he has long directed his attention, would be 

 almost final, were it not opposed to the views of Euler, Laplace, 

 and Poisson. The object of this paper is, to examine how far 

 Mr Ivory, in a paper published in the Phil. Mag. Vol. xni. 

 p. 321, has demonstrated the necessity of the subsidiary con- 

 dition in question. The writer feels it unnecessary to express 

 the diffidence with which he attempts to consider so difficult 

 a subject; he regrets also his inability to discuss Mr Ivory's 

 views more at large than the present limits would permit. 



In the paper just mentioned, Mr Ivory states the principal 

 steps of the investigation by which Clairaut was led to the con- 

 dition of equilibrium of a fluid acted on by forces directed to 

 fixed centres ; and proceeds to consider the modifications re- 



* Cambridge Mathematical Journal, No. VII. Vol. n. p. 18, November, 1839. 



