some New Equations derived therefrom, 23 



Thus the pressure P from the exterior on the gas plus the 

 " Inward Pressure n P : is the total pressure II, i. e., 



p+p 1= =n. 



It will be seen that I introduce two separate factors 

 b and yS, the latter of which is used in place of van der 

 Waals' factor b. 



b is the volume of N molecules filling a volume (f> = (Y + b) , 



TT R ' T 



at a pressure 11= - v . 



is the volume of Nj molecules filling the volume V at 

 the same temperature and pressure. Consequently b is a 

 constant, /3 sl variable ; for the smaller Y is (i. e. the greater 

 the compression) the less the number of molecules required 



tt R- T 



to exert a pressure 11 = v . 



Hence the inverse value of the volume V at any pressure 



T? T 1 1 



11= - ^x-is not the density^, but the density , v ,, , which 



as b is a constant increases less rapidly than the volume V 

 decreases, 



For large values of Y (i. e. small value of II), Y will be 

 almost equal to = (Y-+-&), X x almost equal to N, and 

 J3 almost equal to b. 



For small values of Y these factors deviate considerably. 



Introduction. 



I. 



According to van der Waals, the (i Inward Pressure " ~P 1 

 supports the pressure P from the exterior, and the total 

 pressure a gas thus bears is 



n=p+p : = J 



Y-6> 

 a 



or considering P x =^, 



p, a _ R.T 



+ Y 2 ~Y-6 - 



Evidently II is made equal to the pressure of a "perfect" 

 gas of the same temperature at the volume (V — b). 



