Wellisch — Experiments on Active Deposit of Radium. 285 



The results show that the application of either a positive or 

 a negative potential is without any decided effect on the dis- 

 tribution of the active deposit. In the experiments described 

 in the previous paper approximately the same value was 

 obtained for the deposit on the central rod as in the above 

 series ; however, the assumption was there made that the 

 neutral particles were distributed on the central rod and the 

 case in the proportion of the areas exposed. This assumption 

 is not justifiable ; it is in fact easy to obtain a theoretical ex- 

 pression which will give approximately the relative distribu- 

 tion on rod and case which results from the process of dif- 

 fusion. 



Let us consider a cylindrical condenser of infinite length, 

 the radius of the inner electrode being #, and that of the 

 outer o. 



Let g be the number of deposit particles that are produced 

 per cc. per second in the gas as a result of the disintegration of 

 the emanation. 



Let n be the number of deposit particles present per cc. in 

 the gas at a region distant r from the axis. 



Let D be the coefficient of diffusion of the deposit particles. 



Then, if there be no applied electric field, we will have, 

 using cylindrical co-ordinates, as the equation for the steady 

 state 



d*n 1 dn\ _ _ 



di* rdr~~ q (1) 



->( 



The solution of (1) is given by 



n= - 1-r 2 +C l log r + C 2 (2) 



4D 



where C x and C 2 have yet to be determined. 



Inasmuch as the deposit particles adhere to the exposed 

 solid surfaces, the concentration in the gas will be zero in the 

 vicinity of the metal, i. e. n — for r = a and r = b. 



We deduce V = JL . y ~ 0> 



4D log b — log a 



and C =X "' lQ £ h ~ V lo £ a 

 2 4D log b — log a 



The concentration at any place r is then given by 



)gb—b^\o{ 

 g b— log a 



(3) 



n=- iLr 2 + .*_. b * ~ a * log r + <Z a' logb-Vloga 

 4D 4D log b — log a 4D log b— log a 



