TITK STUtlOTUKE UF THE NTCLKtrs. 



1 3:1 



respondiug r.-ulii he similarly aoceiituatfd c/c' = r'-Y/--^ and (■,/(•',=;/•', ^/z', 

 where /■' and r\ are the final I'adii. Hence, after reduction, since ij = \, 



'■'f(er^/r'^) = 2'ra^r\f{< 



V>-\')- 



If the diops in both dilute solutions are initially, /. r., immediately after shakinir, of 

 the same average size, r'-^ = /■^■\ and the e(|uati(>n is tlius a relation hetween r' and 

 /•'j, the radii of the nuclei for the two given solutions. Tlie results accentuate the 

 need of observations on the vapor pressure of concentrated solutions. 



47. The ineclianisin ge)ie)'(tlize<l. — In connection with the simple mechanism of 

 § 44 for producing nu(dei of a startling degree of sraallness l)y mere shaking, nuclei 

 which may or may not be without electrical charge, the (piestion naturally arises 

 whether the mechanism may not be sufficient to account for nuclei in the presence 

 of satui'ated vapor, in general. 



Suppose, therefore, that such chemically powerful agencies as the X-rays or 

 Becquerel rays, or ultra-violet light, or the electric glow, etc., on being passed 

 through a saturated vapor, produce in that vapor a new chemical synthesis, in 

 degree however small (since the insignificant vapor pressure of a few hundred nuclei 

 per cub. era. is alone in question), soliiMe in the liquid from which the vapor arises. 

 Then immediately around the new molecule there will be a region of vanishing 

 vapor pressure. The new molecule, whether it be ionized or not, will therefore 

 grow by condensing vapor, until further growth is arrested by the increment of 

 vapor pressure due to the preponderating surface tension which accompanies con- 

 tinued dilution. In other words, the critical diameter is again reached. 



The relations here involved are peculiar and need a more detailed elucidation. 

 If vapor pressure increases with increasing convexity, for capillary i-easous, but 

 eventually decreases again as 



\ 



\ 

 \ 



a 



Fig. ZO. 



a result of the concentration 

 I'eached on evaporation, to a 

 value nearly zero or at least be- 

 low the normal vapor pressure 

 at a flat surface, it follows that 

 as the size of the drop continu- 

 ally decreases the vapor pressure 

 at its surface must pass through 

 a maximum. The accompany- 

 ing diagram, figure 20, is an 

 attempt to lepresent the case 

 graphically by making the vapor 

 pressures the ordinates and the 

 radii of the given droplet of so- 

 lution, the abscissas. The line 

 ab indicates the normal vapor 



pressures. All particles whose sizes correspond to the abscissas between s and h, 

 therefore, evaporate in the lapse of time, those lying near the maximum m, fastest, 

 those lying near s or h with proportionate slowness, while the latter are also lost by 



radJM 



Fk;. 2o.— Diagram Showing the Kklation of Vapor Pressure 

 TO THE Radius of the Nucleus for Different Sirengths of 

 Soi.t-noN. 



