HOMOGENEOUS FLUID AT LIBERTY. 521 



satisfactory when no cause of motion emanates from the fluid itself, and all the forces 

 in action depend merely on the place of a particle. But if the fluid in question consist 

 of attracting- particles, will there not come into play the attraction of every additional 

 stratum upon all the fluid contained within it, of which force no mention is made by 

 Clairaut ? The only cause assigned for the pressure of the stratum upon the fluid 

 below it, is the action of forces foreign to the matter of the stratum ; the attraction 

 of the stratum is inherent in that matter ; the two causes of motion are distinct 

 from one another, and their different eff*ects ought to be separately considered. The 

 procedure of Clairaut, although it is unexceptionable when the forces in action 

 depend only upon the position of a particle, seems chargeable with omission when 

 applied to fluids consisting of particles that act upon one another by attraction or 

 repulsion. 



The initial body of fluid H K I is assumed to be in equilibrium ; the equilibrium 

 will not be disturbed by the pressure of the stratum o n I, which acts with equal in- 

 tensity at every point of the surface H K I ; but if the fluid consist of attracting- 

 particles, the attraction of the stratum o n I upon all the particles contained within 

 it may alter the form of the mass H K I, and the equality of pressure upon the 

 changed figure no longer existing-, the equilibrium will be destroyed. This argument 

 has greater weight, because in the procedure of Clairaut it is not the attraction of 

 one stratum only which is neglected, but the sum of the attractions of all the suc- 

 cessive strata, that is, no account is made of the attraction of a stratum of a finite 

 thickness upon the particles within it. 



It may perhaps be alleged that the attraction of a stratum upon the interior fluid 

 is incomparably smaller than the forces which urge the particles of the stratum 

 itself, and therefore that the first force may be accounted as nothing in respect of 

 the other. Now the question is not about a comparison of forces different in degree, 

 but whether the stratum attracting the particles within it in all directions, has power 

 to move them and thereby to cause an alteration of figure. The procedure of 

 Clairaut, by making every stratum exert a constant pressure upon the fluid below 

 it, leaves every particle of that fluid at liberty to obey the smallest impulse ; and an 

 equilibrium cannot subsist unless the attraction of the stratum be either absolutely 

 zero, or cause a pressure urging every particle with equal intensity in all directions. 

 If the stratum be bounded by concentric spherical surfaces, or by elliptical surfaces 

 that are similar to one another and similarly posited, Newton has proved that the 

 attraction of the stratum has no power to move the particles within it. Must these 

 important propositions be extended, tacitly and without examination, to all strata, 

 whatever be the bounding surfaces ? If one bounding surface be spherical and the 

 other elliptical, or if both be elliptical but dissimilar, will the attraction of the stra- 

 tum be ineffective to move the interior particles ? The plain truth is that Clairaut 

 has not attended to the attraction of the stratum, and consequently the application 

 of his theory is limited to fluids consisting of particles that have no action upon one 



