94 Barns — Geometric Sequences of Coronas, etc. 



If the change of pressure to pass from a given to a succeeding 

 corona, or to any recognizable change of corona, be determined 

 by two successive exhaustions, the particles of the first corona 

 are the nuclei of the second, and consequently the radius of 

 the former should be determinable absolutely. With this 

 datum for the particles of one corona, Tables I and III would 

 furnish the diameters of all. 



Unfortunately this theoretically very promising method 

 breaks down on experiment. For, let a small exhaustion be 

 made adiabatically at the mean pressure, p, and the mean abso- 

 lute temperature, 6. Then in the modified form of Kelvin's 

 equation for water (density = 1), let the logarithm be expanded. 

 If T is the surface tension of water, p' its vapor pressure, the 

 radius of water nucleus will be approximately, r=2T/R0 

 (Pp' ' /P '~^JP/P)) (1)> where R is the gas constant of water vapor 

 and 8 denotes increments. If the condensation takes place 

 near the freezing point, as in the above experiments, we may 

 write hp' /p' = -O76S0. Again, for the occurrence of adiabatic 

 expansion S6/6 = ((y — l)/y)8p/p. After substituting both 

 results in equation (1) rhp — 2Tp/R0('2l70 — 1), where hp is 

 an adiabatic increment of pressure, applied to the moist air 

 at 6 and^>. Using this equation for water particle of the order 

 of dimensions estimated above at 6 = 273° and p = 76 cm , an 

 exhaustion of but 1/10 millimeter is in question. Now I sat- 

 isfied myself in special experiments that exhaustion as small as 

 l cm would be perceptible iu color changes of the coronas, par- 

 ticularly in the case of certain higher orders ; but the small 

 change corresponding to *01 cm is out of the question. I do not 

 see, therefore, that methods other than those based on measure- 

 ments of coronas will be applicable for the determination of 

 the absolute dimensions. 



Pursuing this subject, I found that the coronas of benzol fol- 

 lowing the initial fogs are all normal, relatively large particles 

 being precipitated at once. Hence, if m be the mass of benzol 

 condensing, computed for given exhaustions as in § 5, and if d 

 be the diameter of the benzol particles found by measuring the 

 coronas, then JV = 6m/ird s . The number of nuclei active in 

 different methods of nucleation may thus be fouud by a few 

 exhaustions, compared with the more prolonged observation 

 necessary for water vapor. Care must be taken, however, to 

 make allowance by the same method for those nuclei which I 

 recently found* are spontaneously generated by benzol. I will 

 soon be ready with data bearing on all these questions. 



Brown University, Providence, *R. I. 



* Science, Jan , 1902. With regard to subsidence of nuclei it is well to 

 remember that'the same fine clay subsides in water very gradually, but in ether 

 almost tempestuously. A like condition of things may hold for nuclei in relation 

 to the vapors of water and benzol, etc. There is a distinct tendency to agglom- 

 erate in the latter case and not in the case of water. 



