THE EQUILIBRIUM OF FLUIDS. 155 



and since, in the transfer of the fluid to A's surface, its particles 

 move over spaces of the order Sa only, the alteration which will 

 thence be produced in V will evidently be of the order 



and consequently the value of V will become 



k being a quantity which remains finite when 8a vanishes. 



In establishing the preceding results, n has been supposed 

 greater than 2, but p the density of the fluid within B and the 

 quantity of it condensed on A's surface being still determined by 

 the same formulae, the foregoing value of V ought to hold good 

 in virtue of the generality of analysis whatever n may be, and 

 therefore when n is a positive quantity and Ba is exceedingly 

 small, we shall have without sensible errors 



Conceiving now P' to represent the density of the fluid con- 

 densed on A 1 a surface, 4?ra 2 P' will be the total quantity thereon 

 contained, which being equated to the value before given, there 

 results 



and hence we immediately deduce 



2 + n 



" 



Moreover as Q represents the total quantity of redundant fluid 

 in the entire sphere A, the quantity contained in B is 



