198 CONDENSATION NUCLEI. 



Avoiild have ocoiipied in (he absence of the charge through a distance 

 2 TTff - r/, and there will be a corresponding diminution in the satura- 

 tion A'apor pressure. The vapor pressure necessary for equilibrium 

 over a charged drop is now given by the e(|uation 



where p.^ is the saturation vapor pressure over a flat, uncharged sur- 

 face, p.^ that necessary for equilibrium at the same temperature in 

 presence of the drops, and e is the charge on each drop. In an at- 

 mosphere saturated with resjDect to a flat uncharged surface a drop 

 carrying a charge e would be in stable equilibrium if its radius were 

 such that the two terms on the right-hand side of the above equation 

 w^ere equal, i. e., when )'^=e-/H')7r T. If the density of the vapor were 

 increased the drop would become larger, the equilibrium remaining 

 stable until the vapor pressure reached the maximum value corre- 

 sponding to the above equation. To find this we have on differen- 

 tiating 



p dr Rt \ r' 2 nr^ ) 



The maximum vapor pressure in contact with the drops occurs 

 when y'^ = ^r/4 n T, and has the value given by 



Pi 2 Rtr 



If the j5ressure of the vapor be increased beyond this limit the 

 unstable condition is reached, and the drop increases in size so long as 

 the supply of vapor is unlimited. In most cases the final size of the 

 drops would be determined by the amount of vapor initially present, 

 and the number of drops among which the water is distributed; 

 unless they are very numerous, and, therefore, very small when full 

 grown, they will grow until the vapor is not sensibly supersaturated ; 

 it will only be in very rare cases that the final size of the drops is so 

 small that equilibrium will be reached while the vapor is at all con- 

 siderably supersat ui'ated. 



It is easily seen that the l)ehavior of drops containing dissolved sub- 

 stances will be quite similar. If we start with very small drops, there 

 is for a given size of drops a certain vapor pressure corresponding to 

 equilibrium ; if we increase the density of the vapor the drop grows, 

 the equilibrium remaining stable, until a certain size is reached, after 

 which the drops suddenly grow to their full size. The theory of con- 

 densation on ions or other nuclei has been treated by J. J. Thomson " 

 and by Langevin and Bloch.'' 



" J. J. Thomson, Conduction of Eloctrioity throujih Gases, p. 149. 

 6 Bloch, Recherehes sur la conductibilite electriyue de I'air produite par le 

 phosphore et sur les gaz recemment prepares (Paris, 1904). 



