9 J 



CONDENSATION NUCLEI. 197 



Let the whole apparatus be contained in a closed vessel containin<>- 

 only watei- vapor. 



We lia\"e then the convex water-air meniscus depressed heidw tlic 

 level of the llat surface in the lar<»'e vessel to a depth //. such tlial 

 (/ir/i =- -iT'/-. where t/ is the acceleration due to <i-ravity. f the density 

 of the H(iui(l ( IV = 1 in the present case), T is the surface tension, and 

 /• the radius of curvature. Thus the pi'cssure of the vai)()r in contact 

 Avith till' meniscus nnist he oreater than that over the flat surface by 

 that (hie to the weiii'ht of a colunni of water vapor of Iieii>ht A. the 

 ])ressui'e at the toj) of the cohunn beiuii' that re(|uired for e(juilibi-ium 

 over a Mat surface at the given temperature. This iiu-reased pressure 

 must, moreover, be the pressure necessary for equilibrium o\-er the 

 curvetl surface; distillation from the one surface to the other would 

 otherwise take place, resultin<i' in a continuous cii'culation. To find 

 this pressure y>., p^ being that at the flat surface we have (/jj=(/fj<//i, 



dp 



P 



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

 obeyed, this gives 



9 Pi 9 fti 

 R being the constant in the e(juation pr^=Rf, t l)eing the absolute tem- 

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

 tively. 



But h = ST/rr/, thus 



log,B=log.^-l 2T 



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

 which water vapor nnist have in order that it nuiy be in e(iuilibriuui 

 in contact with a drop of any size. The e(]uilibrimn is obviously 

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

 suj)ersaturated condition is maintained; if too small it will evaporate 

 completely. The possession of a charge of electricity by the drop or 

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

 be stal)le if its size be less than a certain limit, (lej)ending on the nuig- 

 nitude of the charge or tlie ([uantity of dissolved substance. Let us 

 consider the case of electi'itication. We may inuigine the water s\u*- 

 face in one limb of a U tube in an ai'rangement like that described 

 above, to l)e uniforndy charged with electricity by holding a vei-y 

 short distance above it a parallel conducting surface maintained at a 

 different potential. It is immaterial whether the water surface be 

 flat or curved ; a tension of 2 tcg"^ dynes per square centimeter will be 

 exerted on the end of the colunni, ff being the charge per s(juare centi- 

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



