C. Bancs — Nuclei and Ions in Dust-free Air. 139 



If the upper inflection of the distribution curve (fig. 2) is a 

 criterion, i. e., if adiabatic cooling ceases with the occurrence 

 of identical terminal coronas for successively increasing ex- 

 haustions, the fog chamber with water-air is efficient to about 

 Sp = 31 or 32 cm , with water and carbon -dioxide to about 

 Sp = 37 cm , with alcohol and air to about 8p = 20 cm . In the 

 former case the vapor would be cooled from 20° to about 

 — 10° C. even after condensation : in the latter case to about 

 + 10°. On general principles and in view of the low tempera- 

 tures of the water particles, it would seem probable that the 

 efficiency of the fog chamber must vanish gradually. Bat the 

 appearance of the curves is such, as if the action were unim- 

 paired up to a given terminal drop in pressure. 



In every case the fog particles with the surrounding medium 

 of vapor soon reach the temperature of the air again, so that 

 additional moisture must arrive from somewhere. It has been 

 instanced above that the marked constancy of the water-coronas 

 during this period in the work done heretofore gave no evi- 

 dence of the evaporation ; while the present water and alcohol 

 coronas decrease one-half in aperture, i. e., the preponderat- 

 ing fog particles actually grow, because the exhaustion is 

 slowly but steadily incremented when the stop-cock is not 

 quite tight, the fog particles acting like very large nuclei. 

 Even if this is compatible with the evaporation of the smaller 

 particles, there is again no evidence for it. Much of the 

 moisture must therefore come from the wet cloth and the 

 water within the vessel, which are not cooled by the expansion. 



5. Size of the nuclei. — Here it may be worth while to 

 inquire into the reason why the precipitation in alcohol is 

 apparently so much easier ; or what is the same thing, into the 

 estimated size of the nucleus on which precipitation takes 

 place in these several cases. The Kelvin equation as modified 

 by Helmholtz* may be usedf for this purpose (as was done by 

 the latter and by Wilson J in the form Pr/jp^— e * T / Bs r where 

 p r and p^ are the vapor pressures at the convex areas of radius 

 r and radius infinity respectively, T the surface tension of the 

 liquid of density s, M the gas constant of its vapor at the 

 absolute temperature 6. Since p r is the ad iabatically reduced 

 vapor pressure (without condensation) in the volume expansion 

 due to the drop of pressure 8p, and p m , the normal vapor pres- 

 sure at the same temperature 6 = 273° + 4 in Table I, r fol- 

 lows from the equation. The values of 8 = p r /p x an <l r so 

 found are both given in Table I, and have been constructed in 



*Helmholtz : Wied. Ann., xxvii, p. 524, 1886. 



f Similar estimates of my own are given in Bull. U. S. Weather Bureau, 

 No. 12, 1895, p. 48. 



%C. T. R. Wilson : Phil. Trans., vol. clxxxix, 1897, p. 305. 



