NUCLEI IN ALCOHOL VAPOR. 115 



view, measurements of latent heat for the more common vapors at very 

 low temperatures would be desirable. 



Finally, the point at which the drop in pressure ceases to be efficient, 

 on account of the increasingly rapid inward radiation of heat from the 

 vessel, is the most serious of the outstanding errors. I have endeavored 

 to diminish it compatibly with the desideratum of a large and easily 

 adjusted fog chamber by successively increasing the bore of the exhaust 

 pipes and stopcocks; and this plan has been in the large measure suc- 

 cessful. The extent to which the error is present, as the drop in pressure 

 increases more and more, is nevertheless left unanswered. If the upper 

 inflection of the distribution curve (fig. 56) is a criterion, i.e., the occur- 

 rence of identical terminal coronas for successively increasing exhaus- 

 tions, the fog chamber with water-air is efficient to about dp = 31 or 3 2 

 cm., with water and carbon dioxide to about dp = 37 cm., with alcohol 

 and air to about dp = 20 cm. In the former case the vapor would be 

 cooled from 20 to about io C. even after condensation; in the latter 

 case to about +io. On general principles and in view of the low 

 temperature of the water, it would seem probable that the efficiency of 

 the fog chamber must vanish gradually. But the appearance of the 

 curves is such as if the action were unimpaired 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 is remarkable that the marked con- 

 stancy of the water coronas in perfectly tight apparatus during this 

 period gives no evidence of the evaporation; while the alcohol coronas 

 decrease one-half in aperture or the preponderating fog particles actually 

 grow. 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. 



80. 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 used for this purpose, as was done by 

 the latter and by Wilsonf in the form p^lp^ =z l T/Rsdr where p T and 

 p x 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), 

 R the gas constant of its vapor at the absolute temperature ($). 



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

 fWilson: Phil. Trans., vol. 189, p. 305, 1897. 



