﻿Energy of a. Particles on passing through Matter. 685 



It is very interesting to observe that this equation is o£ 

 the same type as that derived by Bohr in his second paper 

 on the motion of a particles through matter, although derived 

 on quite different assumptions. The meaning of some of the 

 constants is, of course, quite different. 



§ 4. Comparison with Experiment. 



Substituting accepted values of the physical constants we 

 have from (4) 



5-84 xlO- 36 



x — 



[E,-(-Y,)-E«(-Y)] 



for air at 15° 0. and 760 mm. pressure, assuming the number 

 of electrons in the fictitious air molecule to be 144. 



"We substitute numerical values in expression (4) for log 6, 

 term by term, 



log 2m = 2-30 log M 2 X 9-0 x 10" 28 = - 61-58. 



The remaining two terms are more difficult to evaluate, as 

 the values of the ionization and resonance potentials are 

 not completely known, and we are treating with average 

 values for air. The order of magnitude of these quantities 

 is, however, fairly well established. We will choose values 

 of this order of magnitude which give the best agreement 

 with experiment. 



Assuming 4 electrons for which Q = 200 volts = 3*18 X 

 10 -10 erg and 10*4 electrons for which Q=15 volts 

 = 2-38 x TO" 10 erg, 



-2^1ogQ,= -2-3 [ ~ lo gio 2'38 x 10-" 



+ Ii 7 4 log3 ' 18xl0_1 °l =23 ' 75 ' 

 For values of the resonance potential which are near the 

 ionization potential the terms (l — Qf+^/Q^) will be practi- 

 cally zero. Hence we need only concern ourselves with 

 those few resonance potentials which are considerably lower 

 than the ionization potential. We shall probably not be far 

 wrong if we set % t (1 — Q^ +1 )/Q ( p = 2 for each set of electrons. 

 Then log b= -61-58 + 23*75 + 2-0= - 35*83, 



log 6 s =-71-66, 



corresponding to a value of b 2 =7'5 X 10~ 32 approximately. 

 Thus the velocity equation of the u particle becomes 



ar = 7'79 x 10~ 5 [Et(- Y )-Ei(-Y)]. 



