Velocity of Swiftly Moving Electrified Particles. 609 



corresponding to the same value for W, but also in collisions 

 with other electrons in the atom. Considering, however, the 

 rapid decrease in the chance of ionization with increasing W, 

 we may in a simple way obtain an approximate estimate, if 

 we assume that all the ionization produced by the secondary 

 rays is due to collisions with electrons corresponding to the 

 smallest value for W. This value will be the one which is 

 determined in experiments on ionization potentials; let it be 

 denoted by W r . In the same way as above we now get 



t v / a a a x '2ire 2 WNAx * r/ 1 1 \ 



1= S(A w + Aw + w k + A w+ m 1 + ■■■)— myi SIAW-qJ 



+ (w+W 1 "Q ) + -J" 



If Q is big compared with all the W's, we get approximately 



T WEFNA* 1 i . /Q \ ,. lK . 



On account of the simplifying assumptions used, the formulae 

 (34) and (35) can only be expected to indicate an upper 

 limit for the ionization. 



The minimum fall of potential P necessary to produce 

 ionization in hydrogen, helium, nitrogen, and oxygen was 

 measured by Franck and Hertz*. They found 11, 20*5, 7*5, 



Fe 



and 9 volts respectively. By help of the relation VV=— , 



J J 600 



we get from this W equal to 1'75. 10" 11 , 3-25.10" 11 , 

 1-20.10- 11 , and 1*45. 10" 11 respectively. 



The absolute number of ions produced by a rays in air is 

 determined by H. Geigerf. He found that every a. particle 

 from radium C in passing through 1 cm. of air at ordinary 

 pressure and temperature produced 2*25 . 10* pairs of ions 

 From this we get, using T. S. Taylor's J measurements of 

 the relative ionizations in air, hydrogen, and helium, that the 

 number of pair of ions produced by an a particle from 

 radium in passing through 1 cm. of one of the two latter 

 gases is very nearly the same and equal to 4 6 . 1(J 3 . 



If now in (31) we introduce the above value for AV 

 for hydrogen and use the same va ues for N, n, e, E, m, 

 and V as in section 4, we get for a rays from radium C 



* Verh. d. Deutsch. P/v/s. Ges. xv p. 34 (1913;. 

 t Proc. Roy. Soc. A. lxxxii. p. 486 (1909). 

 t Phil. Mao-, xxvi. p. 402 (1913;. 



Phil Mao. S. 6. Vol. 30. No. 178. Oct. 1915. 2 R 



