THE STKUCTURK OI' THE NUCLEUS. 57 



taken. The curve and table then show the marked spontaneous evolution of 

 particles by the breakdvwn of the h)fus after about In exhaustions. 



Again, since — o fi — (\ -| U) log //, where // will not differ materially from 

 the value for water under the same exhaustions, put — log ;// = .087. Hence, since 

 ^=2 min., i = 2.6 iu the first [)art of table 1, and ^ =:: 2.0 in the second part. 

 These values are enormously large as compared with those found for water (/; — .1) ; 

 and since the diffusion velocity of nuclei in benzol is actually smaller than in water 

 vapor, these large coefficients are either an indication of the efficiency of removal 

 by shaking (for which there is no collateral evidence), or more probably of removal 

 by subsidence. 



In fact, the equation teniporai-ily accepted is incomplete since it does not in- 

 clude the production of nuclei by shaking, i.e., the horizontal streamei', a, in figure 

 3. Put therefore JV— N^ (io^C' + '''"°8-''+ c), where N^^c is the constant number 

 of nuclei conti'ibuted by each shaking and again removed by the subsequent 

 exhaustion, after 3=00 or is very lai'ge. Since Nd^ = dl, if N^ = 1, the result- 

 ing equation is 



dl = d^ (10=(. + '>oio«.^t.) (1) 



where '/„ is the initial and d the final diameter of the cloud particle of the order, z. 

 When z = c», d^ = D^ == dl/c, and is therefore given in figure 3, curve II, by the 

 results following a, as I) = .0042. With this substitution, equation (1) becomes, 

 on differentiation and reduction, 



_ 6 (log d) ^ log>' .J _ ,/3 //)3) (1 + l,t)^ (2) 



oz 3 



whei-e b is the only unknown quantity. When Z> = o, the above value of y8 is re- 

 produced. The first member of (2) may somewhat crudely be taken as the change 

 of log d, for a unit or single change of the oi'der, z. The correction, 1 — J V(.0042)3, 

 is constructed graphically and the mean value for the interval between two suc- 

 cessive observations is found from the curve, which naturally shows rapidly varying 

 rates. The corrected value for water, log y = .00866, must be accepted in the 

 absence of a better factor. The results of the computation for h then appear as 

 follows : 



Table i (i), Table i (2), 



z= 7-8 /> - .15 cui./min., ^ = 5-6 /^ = 1.4 cm./min. 



8-9 2.4 6-7 i.o 



9-10 3.0 7-S 2.5 



lo-ii 5.0 8-9 2.5 



9-10 4.1 



so that removal is faster as the particles are larger. This is a natural consequence 

 of the sichsidence of cloud particles, whereas the removal of nuclei by diffusion 

 would show the contrary effect. To bring out the latter, thei-efore, very long time- 

 intervals between the obsei'vations are, as a rule, the indispensable requisite, par- 

 ticularly when the cloud [.articles are so huge as here in the case of benzol and in 

 the final observations with water vapor. The same result reappears from a new 

 point of view iu § T. 



