RESIDUAL WATER NUCLEI. 129 



ing by mutual destruction per second. Here c is negative for generation 

 and positive for absorption. If a is zero, 



dn/dt = cn + bn 2 

 or 



n 



where the nucleation n and n occurs at the times t and t , respectively. 

 If 6-0, 



if c = o, the equation reverts to the preceding case, where dn/dt = bn 2 . 

 Hence when c becomes appreciable, 



dn/dt c 



= -f- b 



n 2 n 



or the usual decay coefficient increases as n diminishes, becoming 

 infinite when n = o. This is precisely what the above tables have brought 

 out. The value of b does not appear, except when n is very large. Since 

 6 is of the order of io~ 6 , if c is of the order of 3 X io~ 2 (as will presently 

 appear), c/n will not be a predominating quantity when n is of the order 

 of io 6 (c/w = 3X io~ 8 ); but it will rapidly become so as n approaches 

 the order of io 4 (c/n = 3 X io~ 6 ), which again is closely verified by the 

 above data. 



Finally, if the decay bn 2 is temporarily ignored and if the ions are 

 supposed to be absorbed with a velocity K at the walls of the cylindrical 

 fog chamber of length / and radius r, 



I . 2 XT . K . n = I . nr 2 . en or K = cr/ 2 



if c = 3 . 5 X i o ~ 2 , r 6 cm. , K = o . i cm/sec. , which is not an unreasonable 

 datum. It is not improbable, however, that absorption occurs within 

 the fog chamber in view of the presence of water nuclei. Finally, if the 

 ends of the fog chamber be taken, 



v- r r 



'a(i+r//) 



quite apart from the effect of internal partitions. Hence K estimated 

 at o. i cm. /sec. is an upper limit. 



Again, if dn/dt= a + bn 2 + cn, the conditions of equilibrium are 

 modified and become (since dn/dt = o) 



a = en + bn 2 



where a measures the intensity of radiation. It no longer varies with n 2 . 

 Thus 



2& V 



The complicated relation of n and a was not suspected in my earlier 

 work, where distance effects due to X-rays were observed. 



