THE STRUCTURE OF THE NUCLEUS. 51 



Unfortunately, this theoretically very pi-omising method breaks down on 

 experiment. For, let a small exhaustion be made adiabatically at the mean pres- 

 sure jt?, and the mean absolute temperature, 6. Then in the modified form of 

 Kelvin's equation for water (density = 1), let the logarithm be expanded. If J" is 

 the surface tension of water, p' its vapor pressure, the I'adius of water nucleus will 

 be, approximately, 



where It is the gas constant of water vapor and f5 denotes increments. If the con- 

 densation takes place near the freezing point, as in the above expei'iments, we may 

 write Sp /f' — .076^0. Again, for the occurrence of adiabatic expansion 6d/d = 

 {{y—^)/y)Sp/p. After substituting both results in equation (1) 



where dp is an adiabatic increment of pressure, applied to the moist air at d and p. 

 Using this equation for water particle of the order of dimensions estimated above at 

 d = 273° and^ = 76 cm., an exhaustion of but 1/10 millimeter is in question. Now 

 I satisfied myself in special experiments that exhaustion as small as 1 cm. would be 

 perceptible in color changes of the coronas, particularly 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 otlier than those based on measurements of coi'onas 

 will be applicable for the determination of the aV)solute dimensions. 



Pursuing this subject, I found tnat the coronas of benzol following the initial 

 fogs are all noi'mal, relatively large particles being precipitated at once. Hence, if 

 m be the mass of benzol condensing, computed for given exhaustions as in § 16, and 

 if d be the diametei- of the benzol particles found by measuring the coronas, then 

 n = Qm/nd^. The number of nuclei active in different methods of nucleation may 

 thus be found by a few exhaustions, compared with the more prolonged observation 

 necessary for water vapor. Unexpected difficulties were encountered in the use of 

 benzol, however, whereas the method led to a satisfactoiy issue for water vapor, as 

 will be detailed in the next chapter. 



