CONDENSATION NUCLEI. 197 



Let the Avhole apparatus be contained in a closed vessel containing- 

 only water vapor. 



We liave then the convex water-air nienisciis-depressed Ix'low the 

 level of the tlat surface in the large vessel to a (lei)th //. such that 

 (jirJi ^ L?'r /', Avhere </ is the acceleration due to gravity, ir the density 

 of the li(juid {w = 1 in the present case) , T is the surface tension, and 

 /' the radius of cur\ature. Thus the pressure of the vapor in contact 

 with the meniscus nuist be greater than that over the fiat surface by 

 that due to the weight of a column of water vapor of height h. the 

 pressure at the lop of the column being that required for e(|uilibrium 

 over a flat surface at the given temperature. This increased pressure 

 nuist, moreover, be the pressure necessary for equilibrium over tlie 

 curved surface; distillation fi'om the one surface to the other would 

 otherwise take j^lace. resulting in a continuous circulation. To find 

 this pressure />., p^ being that at the flat surface we have <lj)=gpdh^ 



g J p 

 p being the density of the steam. If we assume Boyle's law to be 

 obeyed, this gives 



9 Pi iJ Pi 



R being the constant in the equation pr^llt, f being the aljsolute tem- 

 perature, Pj, p., the density of the vapor at the two surfaces respec- 

 tively. 



But h = 2T/rr/, thus 



log,^=log/~i- . ^ 



We have thus the means of calculating the pressure, or the density, 

 which water vapor nuist have in order that it may be in equilibrium 

 m contact with a droj) of any size. The equilibrium is obviously 

 unstable; a drop, if too big for equilibrium, will grow so long as the 

 supersaturated condition is maintained; if too small it will evajxirate 

 completely. The possession of a charge of electricity l)y the drop or 

 the existence of a dissolved substance within it will cause the drop to 

 be stable if its size be less than a certain limit, depending on the mag- 

 nitude of the charge or the quantity of dissolved substance. Ijct us 

 consider the case of electrification. We may imagine the water sur- 

 face in one limb of a U tube in an arrangement like that described 

 above, to be uniformly charged with electricity by holding a very 

 short distance above it a parallel conducting surface maintained at a 

 different potential. It is immaterial whethei- the water surface b(> 

 flat or curved; a tension of 2 ttc^ dynes per s<iuare centimetei- will be 

 exerted on the end of the coliunn, ff being the charge per sc^uare centi- 

 meter. This will raise the electrified surface above the level which it 



