Radium, Thorium, and Actinium in Electric Fields. 363 

 X b X 25 • • • \i are the real positive roots of the equation 

 J (\&) = 0. 



Let c be the radius of each of the central disks EF 

 and GH. 



The number of neutral atoms reaching EF or GH 

 per second is 



-**»$) \ r= rdr=^ I 1 JlA^|) tanh(M . 

 \dzhjr=o o n= i V Ji(X^) 



The total number of neutral atoms generated in the 

 cylinder EFHG is 2iic 2 lq, and the ratio of the number 

 reaching the central plates to the number generated between 

 them is 



an expression which depends only on the dimensions of the 

 containing vessel. 



This series converges rather slowly. From the first twelve 

 terms the result found for the vessel with the ebonite ring- 

 was 0*993. A second determination, made by giving c 

 a very slightly different value, was 0*989. Hence all but 

 about one per cent, of the neutral atoms formed in the volume 

 EFHG reach the plates EF and GH. The error introduced 

 is therefore negligible, and has been neglected in all sub- 

 sequent calculations. 



In the case of the apparatus described by Henderson, for 

 which 2h — 11*5 cm., 2c = 7'0 cm., and 21 = 3 cm., values 

 calculated were 0*965 and 0*952. Values of J 1 were obtained 

 from a table given by Wilson and Peirce *. 



IV. Experiments with Radium B. 



Previous investigators on the distribution of radium and 

 thorium active deposits in electric fields have neglected the 

 part played by the disintegration of Pa A into PaB and ThA 

 into ThB. It will be shown subsequently that if the per- 

 centage of PaB which is initially positively charged at the 

 end of the recoil path in a particular gas, and also the efficiency 

 of recoil of PaB from PaA from the surfaces of the electrodes 

 are known, then the percentage of PaA initially positively 

 charged in that gas may be calculated from the results of 

 experiments in which the gas is mixed with radium emanation. 



* Wilson and Peirce, Bull. Amer. Math. Soc. iii. p. 153 (1896 7). 



