the Active Deposit of Radium, 



429 



atoms situated in the gas charge up both positively and 

 negatively in appreciable numbers when the density of 

 ionization exceeds a certain amount; the atoms thus charged 

 act then as nuclei of condensation and build up aggregates 

 of active particles when these are present in sufficient 

 quantity. 



There is of course a possibility that both the aggregation 

 and the charging-up may be conditioned by the presence in 

 the gas of foreign nuclei such as traces of dust particles, etc. 

 Against this view, however, is the fact that practically 

 identical results were obtained in different series of experi- 

 ments, when in every instance great care was taken to 

 exclude foreign matter. Such matter might, however, have 

 been introduced on the insertion of the electrode. It should 

 in this connexion be mentioned that when the emanation had 

 decayed so that the saturation current was in value between 

 5'0 x 10" 9 and 10~ 9 ampere, the number of charged particles 

 for any given amount of emanation, although small, was 

 subject to irregular variations. 



Coefficient of Diffusion of the Active Deposit of Radium, 



6. An expression was given in Section 3 for the amount 

 of active deposit present in the gas contained in a cylindrical 

 vessel when a steady state is established such that the 

 production of fresh deposit from the emanation is balanced 

 by diffusion to the surface. This expression is, however, 



only approximate as it neglects 

 the diffusion to the top and bottom 

 of the cylinder ; inasmuch as the 

 exact expression comes out with 

 surprising simplicity, it seems 

 desirable to present here the exact 

 theory. 



Let ABCD represent a longitu- 

 dinal section of the closed cylinder 

 (without any central electrode). 

 Let q be the number of active 

 deposit particles produced per c.c. 

 per second from the emanation. 



Let the axis of the cylinder be 

 taken as the axis of z, and let the 

 origin be midway between top and 

 bottom. 



Let 21 be the height of the 

 cylinder and b its radius. 

 Using cylindrical coordinates we have as the equation of 



Fif 



