Velocity of Swiftly Moving Electrified Particles. 605 



and the probability that the j3 particle will penetrate through 

 a sheet of greater thickness without suffering a single de- 

 flexion for which -v/r > r is consequently given by W = e~\ 

 where \= fcoA.r. Substituting for A.i' from the formula 

 (18) and using the same notation as above, we get 



iV(l-0»)AT 



Considering 2 as a constant we get from this, using the 

 expression (25) for AT, 



^_ n 2 f d(3 rr / 1 - (l-/9 2 )a\ n * / S v 



where S as above denotes the last factor in the expression (28) 

 for the range R. We have consequently 



\\ 



r = K (sTl) ' (29) 



where S is approximately proportional to the range of the 

 emergent rays, and K a constant. 



The formula (29) gives an estimate of the number of 

 13 particles left in the peak of the velocity distribution of the 

 emergent rays, and may be compared with the ionization 

 measured in Varder's experiments. It will be seen that W 

 depends to a very high degree on ??, and therefore on the 

 atomic weight of the absorbing substance. As mentioned 

 above, S is for these fast rays approximately proportional to 

 n, and the exponent in (29) is therefore proportional to u. 

 It' aluminium was used as absorbing substance Varder found 

 that the ionization was approximately proportional to the 

 range of the emergent rays, while for paper it decreased 

 more slowly, and far more rapidly for silver and platinum. 



For aluminium we have n=13 and -2 = 18 for /3 = 09. 



Putting the exponent in the expression for W equal to 1, we 

 get in this case t = 0'30 and </> approximately equal to 80°; 

 this is an angle of the right order of magnitude. For paper 

 the exponent in (29) will be halved and for platinum will 

 be more than five times larger than for aluminium, for the 

 same values of t and (p. 



In connexion with the calculations in this section, it may 

 be of interest to remark that the approximate agreement 

 obtained between the theory and the measurements seem> to 



