198 CONDENSATION NUCLEI. 



would have occupied in the absence of the charge through a distance 

 2 TtG -A/, and there will be a corresponding diminution in the satura- 

 tion vapor pressure. The vapor pressure necessary for equilibrium 

 over a charged dro]) is noAv given bv the equation 



where />i 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 respect 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 eqiuition 

 Avere equal, i. e., when r^=e-/lC;r 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" J 



The maximum vapor ])ressure in contact with the drops occurs 

 when r^ = e-/A: n T, and has the value given by 



If the pressure 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 dro])s 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 (mly be in very rai'e cases that the final size of the drops is so 

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

 siderably sui)ersaturated. . 



It is easily seen that the behavior of drops containing dissolved sub- 

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

 is foi" a given size of drops a cei'tain vapor pressure corresponding to 

 eiiuilibriuin ; if we increase (he density of the va])or the di'op grows, 

 the ('(luiiibrium reinainiiig stable, until a certain size is reached, after 

 which (he (h"oi)s suddenly grow (o their full size. The (heory of con- 

 densa(i()n on ions oi- other nuclei has been treated by J. ,J. Thomson" 

 and by Langeviu and Hloch.'' 



« J. J. Thomson. roTidiietion of Electricity through Gases, p. 14!). 

 6 Bloch, Recherclics sur la coiiductihilite electrique de Tiur itroduite par le 

 phosi)hore et sur les guz rOoeuimeiit prepares (I'aris, 1904). 



