Attraction of Mass, and some New Gas Equations. 67 



It would have been more correct to substitute </> c =2/3 

 in the original equation, converting the latter into the 

 quadratic form 



a 3 R . T e 



an equation in which v c has the same meaning on either side, 

 and which is a special form of a general quadratic expression 

 into which we can reduce a cubic gas equation. In this 

 manner we take into account that the two extreme values 

 of v for the roots of every cubic equation are points of the 

 quadratic " Border-curve." 



I. 



In order to meet the two objections mentioned, I have 

 found it useful to introduce, apart from the factor ft, another 

 factor b. 



ft is the actual co-volume : 



b is the " theoretical " co-volume. 



Imagine an actual gas with a co-volume ft exerting at the 

 volume v and the temperature T the same pressure Tl^pt+lh 

 (pressure -f the effect of the cohesive forces) as exerted by a 

 "" perfect" gas at the same volume and temperature. If the 



number of molecules in the latter is N= — , then the number 

 in the former is 



1 v+b ' 

 with the co-volume r 



v + b 



Consequently b is the " theoretical " co-volume of 

 N molecules of an actual gas at the "theoretical" volume 

 [v + b), which at the "measured" volume v would exert 

 the pressure II of N molecules of a "perfect" gas at the 

 same temperature and volume v. The volume v contains 

 X 2 molecules of the actual gas, and we have the relations : 



N 1= -^N = ^N = i/.N, . . . (1) 

 v+b v v J 



ft = v.b, (2) 



o = v'\ft, (3) 



1ST v + b r 



(4) 



V 2 



