86 Bancs — Geometric Sequences of the Coronas of Cloudy 



If in two experiments beginning with two different nuclea- 

 tions, N 9 and JV' , the same corona or N is reached for differ- 

 ent times, t and t', and different numbers of exhaustions, n 

 and n', of the same ratio, y, then JV=JV'' and therefore after 

 reduction if for brevity JV =1 and n ~0, h = (n—n' — n )/t , —nt). 

 If two identical coronas are reached, the n may be eliminated 

 so that o=(?i 1 —n i )/((t / —nt) 1 — (f — nt) 2 ), where the first identi- 

 cal coronas are seen for JV V n 19 t v and JV\, n\, t\, and the next 

 for J¥„ n„ t„ and JV\, n\, t\. The plan is therefore to obtain 

 an even number of identical coronas in cases of Tables I and 

 II, and then to compute o from equidistant groups in the way 

 suggested. Found thus, h is constant for a given table, but 

 varies for the different parts of Table II, for reasons not yet 

 clear. Inasmuch as a correction of Table I is here alone aimed 

 at, it is not necessary to insist on very accurate values, and 

 b = *10, a mean value agreeing with the corresponding experi- 

 ments with the drum below, will be taken. In this way the 

 values JVi (isothermal, y — '764, t = 1*6 min.) and JV & (adia- 

 batic, y = '825, t = 1*6 min.) were computed.* 



5. Corrected value of N. — The true value of the number of 

 nuclei lies between N- Y and N&, nearer the latter. The actual 

 value, .zV, can be neither one nor the other chiefly because of 

 the accession of heat received from the precipitated water. 

 The rigorous equation would be somewhat complicated ; but 

 the computation may be made sufficiently close and perspicu- 

 ously by the following method of successive approximation. 



Let 6 and 6' be the original and final absolute temperatures 

 corresponding to the pressures p and p and the densities p 

 and p' of the air. We have nearly (0'/0) = {p/p) ft-Wr = 

 (p'/py~ 1 (1). Let S be the entropy per gram of a mixture of 

 vapor and liquid in the ratio of x/(l — x). Then S= C\n6 

 + rx/0, if C is the specific heat of the liquid, r the latent heat 

 of evaporation. Since C— 1, and the mixture is initially all 

 vapor expanding adiabatically, the last equation leads bv the 

 aid of equation (1) to x = (0' /r'){?/B + \n6/0% where \-x r 

 is the quantity of water precipitated per gram of mixture if 

 the heat thus evolved be neglected. Since at 20°C, 6 = 293°, 

 d' = 271-2°, r = 589, r' = 582, 7 = 1.40, p /j) = y = 58/76, the 

 result is x' — '949 and 1—x' = -050 grams. 



The next approximation is an allowance for the heat evolved. 

 The air at 20° contains 17/10 6 grains of moisture per cub. cm., 

 and the amount of water condensed is thus 710/10 6 grams, the 

 heat evolved "419 calories per gram of air. Since the specific 



* I have since repeated all these results under better conditions; but the dif- 

 ferences need not be instanced here. In case of intense nucleation such as is 

 produced by the sulphur flame, it may require ten exhaustions of the above order 

 y before the initial fogs dissolve into coronas. 



