152 PROCEEDINGS OF THE AMERICAN ACADEMY. 



that is, the tendency of a substance to escape from a phase is greater, 

 the greater the thermal pressure and the less the attractive pressure. 

 Now equation (5) applies to any phase of any pure substance, solid, 

 liquid, or gaseous. In some cases a small change in pressure will cause 

 a very great change in both /? and a ; in others, a very small change in 

 both. The change in (B relative to that in a will sometimes be werj 

 great, sometimes very small. In general, the function \jj depends, not 

 upon the absolute, individual magnitudes of /? and a, but only upon their 

 difference ; and we may conclude from the very universality of equation 

 (5) that it is true not merely when fB and a are changed by a change in 

 the external pressure, but that in general a change in y8 or a, no matter 

 how caused, will affect the quantity \p only as it changes their difference 

 jB — a, and that any change in (B accompanied by an equal change in a 

 has no effect on xp since one neutralizes the other. This will be a neces- 

 sary postulate in the development of the following theory. 



Let us consider a system composed of a liquid or solid phase and its 

 vapor, under such circumstances that the latter obeys the laws of a per- 



feet gas. By equation (1), if we replace — by — , the molecular volumes, 



R T o-i ^1 



and write v^ = -yj- where R is the gas constant, T the absolute tem- 



-* 1 

 perature, we obtain 



dF\_v^ dP, _ P^ dP, _ dP. 



dP, ~ V,' '''■' dP, ~ RT ' ''''' P, ~ /RT^' ^^^ 



This equation expresses the very remarkable result that the change in 

 vapor pressure is to the total vapor pressure as the change in the exter- 

 nal pressure upon the solid or liquid phase is to the pressure which that 

 phase would exert if it should behave as a perfect gas. This may be 

 presented in diffei'eut form by the aid of equation (4) as, 



dPi _d(/3^- as) 



Pi (R 



V2 J 



(7) 



In attempting an explanation of these relations let us consider first a 

 case in which the change in a^ is negligible compared with the change in 

 ySs- That is, /Jg changes while ao remains constant. Since the attractive 

 forces remain constant, it might be predicted a priori that the vapor pres- 

 sure would be proportional to (Sn , the thermal pressure, especially if the 

 kinetic point of view is adopted ; for the vapor pressure is believed to be 



