Attraction of Mass, and some New Gas Equations. 71 



The critical point thus forms the point of intersection of 

 three curves belonging to the equations (A) or (B), (C), 

 and (14). 



The equality of the critical pressure and critical " Inward 

 Pressure " accounts for the disappearance of the phenomena 

 of surface-tension and of the latent heat of vaporization at 

 the critical state. For the attraction is compensated by the 

 thermic pressure, and the transference of a molecule from 

 the interior of the fluid towards the space over its surface 

 does not require work done against a force p lc . This equality 

 can be deduced entirely independently of the preceding, as 

 will be shown presently. But it is as well to point out that 

 it demands that the principle of the equality of action and 

 reaction applies to the cohesive forces as to all other forces*. 



According to the preceding, we should get in a p.v.t.-system 

 a series of cubic and quadratic curves in vertical planes. 

 Every equal-pressure line cuts the two curves of each plane 

 in their points of intersection, denoting the volumes of the 

 saturated vapour and its liquid. At the critical point the 

 equal-pressure line cuts through the point of intersection of 

 three curves. 



1 T? T 



Subtraction of — ^ =- — '- — - (equation 14) from equation 

 (C) for the critical state leads at once to 



P° + ^ = -v7> (Cl) 



a similar equation to equation (C), and naturally affording 

 the same values for the vertex of its curve for which -^ = 0. 



We have not so far considered the influence of the tem- 

 perature on the relative values of b and /3 in respect of v. 

 Still such an influence must exist, and is bound to affect the 

 increase of II with increasing density. If we compress 

 the same gas at different temperatures from the volume 1 

 and the total pressure 11 = 1, it is clear that the same com- 

 pression causes a greater pressure-increase at the lower than 

 at the higher temperatures. For /3 at the lower temperature 

 is relatively and absolutely greater than at a higher tempe- 

 rature. A change of density at lower temperatures causes 

 greater changes of II than at higher temperatures. 



Our equations (A), (B), and (0) do not allow for this 



temperature influence. Their solution causes the temperature 



factor to divide out. But it is here that the introduction of 



the factor b, the "theoretical co-volume," proves most useful. 



* Vide Kara, Phil. Mag. vol. xxxi. 3an. 1916, p. 35. 



