58 



THE STRUCTURK OF THE NUCLEUS. 



5. Number of particles. — It is uext in order to indicate the difficulty en- 

 countered in endeavoring to find the number of nuclei initially present from the 

 data found for the initial diameters d^ =■ 44/10*' and iJ^ = 154/10*. The data 

 available for benzol in Landolt and Boernstein's tables (pp. 336 and 348), are nut 

 sufficiently harmonious to lead to a solution. If, as above, 1 — x' is the mass of 

 precipitate from 1 gram of saturated vapor, after adiabatic cooling from the absolute 

 temperature ^ to - ', 



It is therefore necessary to know both the variation of specific heat O, and of latent 

 heat, /■, with temperature, and the whole question depends on the character of this 

 variation. Since /■ from liegnault's data is very nearly constant within the 20" in 

 question (/• = 109 to 107), it will facilitate computation to regard it so and to 

 compute (kc/d^ from a; = (s/r) (^S — CMgS) for the adiabatic process in question, 

 S being the entropy of the mixture. Hence, with S and Cas variables, 



dx_ _ . S-C-(lgS+i ) ^ aC^ , 



d^ ~ r r dB »■• 



From the observations of de Heen and Deruyts, between 10° and &0°,dC/dB may 

 be estimated as .028, nearly at 0° centigrade. Furthermore, for s =z 293°, ,v = 1, 

 ?■= 109, C= .31 ; 5'= 271, 6"=.37, S= 2.46 (computed). Hence at 3'= 27 r\ 

 (/ic/ds = —.0341 and at S = 293°, dx/ds = —.0437, or the amount of vapor within 

 the mixture shoidd increase markedly with fall of temperature in both cases, which 

 is directly contrary to the experiments. If 6" is considered constant, dx/ds will be 

 positive for the given interval, and precii)itation must therefoi'e occur on cooling, as 

 observed ; but it is obvious that results so obtained ai'e quite arbitrary. 



In the absence of compatible data, an estimate might be made by assiiming 

 the masses precipitated to be inversely as the latent heats of the vapors. The 

 results are equally meaningless. 



Narrow fog stratum between hemispheres of clear air. 



