36 Mr green, ON THE LAWS OF THE EQUILIBRIUM OF FLUIDS. 



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

 over spaces of the order ^a only, the alteration which will thence be 

 produced in V will evidently be of the order 



n — 2 n 



and consequently the value of V will become 



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



In establishing the preceding results, ti has been supposed greater 

 than 2, but p the density of the fluid within S and the quantity of it 

 condensed on ^'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 w is a positive quantity 

 and hi is exceedingly small, we shall have without sensible errors 



v;^m^m«'--* ' 



Conceiving now P' to represent the density of the fluid condensed 

 on A's surface, 47ra^P' will be the total quantity thereon contained, which 

 being equated to the value before given, there results 





-y/TT 



(I) 



and hence we immediately deduce 



fn + V 



n — 4 -p 



2~ 



m 



Moreover as Q represents the total quantity of redundant fluid in the 

 entire sphere A, the quantity contained in B is 



