LEWIS. THERMAL PRESSURE. 163 



claimed for it absolute accuracy, and it is probable that, except for its 

 plausible theoretical basis, it would already have given place to a more 

 accurate, purely empirical equation. If equation (16) is used in place of 

 the formula of van der Waals as the equation of condition of gases and 

 liquids, then the form of the function a must be found for each substance 

 separately from its empirical equation ; and on account of the presence of 

 this function of unknown form, it is obviously impossible at present to 

 test by experiment the validity of equation (16). 



The curve of attractive pressure may be easily plotted in diagram on 

 the PV plane. On this plane the rectangular hyperbola which, in the 

 older theory, is only of ideal significance as the limit towards which the 

 equation of condition tends as the substance approximates the perfect 

 gas, in our present theory always represents a real physical quantity, — ■ 

 the thermal pressure. If from the ordinates of this hyperbola are sub- 

 tracted the ordinates of the actual equation of condition, then, according 

 to equation (4), these differences may be drawn as ordinates of the curve 

 of attractive pressure. A general survey of many such curves will be 

 necessary in order to show what general laws govern the variation of the 

 quantity a. This task must be reserved for the future, but it may be 

 confidently predicted that interesting and useful relations will be found 

 which will give to equation (16) a specific value which it now lacks on 

 accouut of its great generality ; for the study of coincident conditions 

 shows that from the behavior of one unassociated liquid or gas we may 

 predict the behavior of any other, and therefore it seems eminently prob- 

 able from equation (16) that since /? has the same form for all substances, 

 the form of the substance a for any simple liquid or gas will be found to 

 be closely related to its form for any other simple liquid or gas. 



Notwithstanding the indefiniteness given to equation (16) by our ig- 

 norance concerning the quantity u, in one respect the equation is explicit, 

 and is again in direct antagonism to the equation of van der Waals. It 

 follows directly from our equation that the pressure of any substance is 

 greater than, equal to, or less than the corresponding pressure of a perfect 

 gas, according as the attractive pressure is less than, equal to, or greater 

 than zero. In other words, whenever the volume of any phase is greater 

 than the volume that it would occupy as a perfect gas, a is negative, 

 and the total resultant force between the molecules must be repulsive. 

 Regarding such a repulsion, which finds no place in van der Waals' 

 theory, it is true that there is little positive evidence, but what evidence 

 there is seems to indicate decidedly the existence in some cases of some 

 kind of a repulsive force. If a liquid is cooled at constant pressure, its 



