Radium, Thorium, and Actinium in Electric fields. 371 



Let ns consider the activity accumulating on the anode. 



It receives by diffusion half of the neutral A atoms, i. e. 



1 — a v 



— - — . Of these, - (1 — a) free themselves by recoil, and 



br 



— (1 — a) of them are initially positively charged and are 



drawn to the cathode. The neutral atoms return to the 

 anode by diffusion. Hence the total number of atoms 



left on the anode is ^fl — ^)(1 — a). The rest of the 



atoms resulting from the decay of the emanation reach 

 the cathode. It is readily found that 



2 Pl -br 



a =^br- 



Since b is obtained by multiplying the experimental values 

 given in column 3 by 0*93, and r is obtained by dividing 

 the value found for the efficiency of recoil found in air 

 by the same number, then br and hence the above equation 

 are independent of the experiment in which 93 per cent, was 

 obtained for RaB in air. The values of a calculated from 

 this equation are given in column 5. 



VII. Thorium Emanation. 



To test the theory given for the distribution of the active 

 deposits, exposures were made with thorium emanation 

 mixed with various gases, using the vessel shown in fig. 1. 

 The relative difference in mass of the isotopes of RaA or of 

 RaB is so small that we may assume that for each group 

 of these isotopic atoms the percentage positively charoed 

 the coefficient of diffusion, and the efficiency of" recoil are- 

 identical. Hence it is easily shown that p 2 , the value of 



? for thorium emanation, is given bv 



c + d to 



p 2 c= a -|- b(l — a) 1 1 — s + -^ J. 



It is to be noted that p 2 , owing to the terms involving s, 

 depends on the size and the type of testing vessel used and 

 also on the pressure of the gas. The values of p 2 found by 

 experiment and by means of this equation are given in 

 columns 6 and 7. It was assumed that the coefficient of dif- 

 fusion of the A-atoms is inversely proportional to the square* 



