38 TIIK STRUiTUISK OF THE NUCLEUS. 



Tlie foloi's of tables 9 and 10 correspond very nearly, except that the former is 

 one exliaiistiou ahead of the other. This clearly corresponds to the double nuclea- 

 tion (nuclei added in each of the first two successive exhaustions) in the first case. 

 Taldell shows the apparently intense nucleating efficiency of the sulphur flame, 

 and nearly 8 exhaustions are needed to bring out the first corona. This series is 

 thus five exhaustions ahead of table 10 and four exhaustions ahead of table 9. 

 Apart from this the coromxs, if minor differences .>f tint be neglected, may readily 

 be placed. In table 1-2, the colois agree with table 9 up to the tenth, after which 

 the former skips one corona and is in advance of the latter. 



VALUES OK THE NUCLEATION COKUECTEU. 



IC. Amount of precijyitation. — In the preceding tables the limits of the 

 nucleation N are defined between isothermal and adiabatic conditions. The actual 

 case (apart from experimental difficulties) is neither the one nor the other, because 

 of the accession of heat received from the pi-ecipitated water. The rigorous equa- 

 tion for this is, I believe, known, but the computation may be made sufficiently close 

 and perspicuously by the following method of successive approximation. 



Let 3 and s' be the original and final absolute temperatures, corresponding to 

 the pressures yj and/ and the densities p and p'. Then approximately 



l=(fT""''=(;0'"- ... (•). 



Let She the entropy (per gram) of a mixture of vapor and liquid in the ratio 



ofa;/(l-a;). Then 



^ = CMgS + '/■a?A 

 if ir is the temperature of the mixture, r the latent heat of evaporation, C the spe- 

 cific heat of the liquid, and natural logarithms are used. Since 6'= 1, and the 

 mixture is initially all vapor expanding adiabatically, IgS + r/B = IgS' + Vx'/b', 

 which with the approximate e(iuation (1) becomes 



where 1 — x' is the quantity of water piecipitated per gram of mixture, if the heat 

 thus evolved is neglected. Since at 20^ S == 293° /• = 589, / = 582, y=\A, 

 p'/p = 58/76, therefore x' = 949 and I — x' = .050, where /' is introduced under 

 the assumption that the cooling reaches 0°C., in equation (1). 



The next approximation is an allowance for the heat evolved. The saturated 

 air at 20° contains 17.2/10'' grams of moisture per cub. cm. or .0142 grams of 

 moisture per gram of air. The amount of water condensed is thus .050 X .0142 = 

 710/106 grams, and the heat evolved 710/106 x 590 = .419 calories p.-r gram of 



saturated air. 



But from equation (1) 5' = 271.2 and since the specific heat of air is .237, about 

 .237 X 21.8 = 5.17 calories are absorbed in the adiabatic e.xpansion of one gram of 

 air. The available .419 calories due to condensation will heat this, .419/.237 = 

 1.77'= S", which is the correction to be added to S'. 



The data for computing .r' are nowS = 293°, S'= 271.2 + 1.8 = 273°, /• = 582, 

 /•'=: 589, whence 



