268 Dr. C. Barus on Spontaneous Nucleation and 



surface-tension, p and cr the densities of liquid (solution) and 

 vapour, Kelvin's equation asserts 



^— p oo =2Tcr//or, nearly, if p replaces (p — a). 



The present liquid, however, is a solution and its vapour-pres- 

 sure, p xi lies below the normal value for the pure liquid. 



Furthermore, as the large drops grow at the expense of 

 the smaller, the vapour-pressure for capillary reasons alone 

 would decrease in the former case and increase in the latter 

 case. At the same time, however, the larger drops becoming 

 more dilute, increase their vapour-pressure, while the smaller 

 drops becoming more concentrated decrease it- correspondingly. 

 The second group of influences therefore tend to counteract 

 the effect of capillarity. It is quite conceivable that a state 

 of I equilibrium may eventually be reached in which the 

 drops, large and small, will all have the same vapour- 

 pressure (namely, that of the free surface of the liquid), 

 that further evaporation will thereafter cease and the droplets 

 persist, however small. 



In fact, after the lapse of time the preceding equation will 

 be replaced for a given drop by 



/r/-y„ = 2T' < r/pV, 



since the pressure, tension, size, and density of the droplet 

 of solution have all changed by evaporation. 



If the more concentrated droplet of radius r 1 now persists, 

 yy y/ =p oo , the vapour-pressure at the flat surface of the original 

 solution. Hence 



2>.-y»=2*TypV. 



For the case in which a solid is dissolved its mass remains 

 fixed within each suspended drop while the water alone 

 evaporates. When a gas like HC1 or H 3 N is dissolved the 

 same will also probably be true, for the receiver is filled to 

 the full partial pressure with the gas in question. Hence 

 p' may be expressed in terms of p, or if c = r' 6 /r rd , 



whence finally, if &p =p co —p'^ , 



2<rTI(l + (p-l).c).8p. 



For dilute solutions, /> = !, and the last equation is simply 

 r' = 2crT/8p. 



Hence the nuclei produced by shaking dilute aqueous 



