Attraction of Mass, and some New Gas Equations. 89 



A mathematical expression denning the value of the 

 Inward Pressure p lc can he verified, if correct, at the critical 

 state, inasmuch as it must give us the value of the critical 

 pressure p c . 



In this manner we can test a general expression for the 

 cohesive forces., deduced as follows. 



V. 



The cohesive forces causing the " Inward Pressure " appear to 

 folloiv a law similar to the inverse square law of mass 

 attraction. 



If c is the " Inward Pressure " at the volume 1, then at 

 the volume v, 



and 



c = x. W 



Pl=„2 



m* = x . p* 



(28) 



m being the mass of a molecule, N the number of molecules 

 at the volume v = I, hence N . m the density p. The factor x 

 is considered a constant peculiar to the nature of a gas. 

 (Compare e. g. J. H. Jeans,, ' Dynamic Theory of Gases/ 

 Cambridge, 1904, pp. 118 & 114.) 



In the following I intend to show that c is dependent on 

 the mass or molecular weight M only and x is a constant for 

 all substances. 



Without discussing how the form ^9 1 = — has been arrived 

 •at, I will here give my own deduction. 



Suppose (vide fig. 2) to be a molecule at the surface of 



Fiff. 2. 



a fluid attracted by the molecules below the surface in every 

 direction at angles between -: and 0. Let us consider 



