﻿Energy of a. Particles on passing through Matter. G87 



at first in inverse proportion to the velocity. A time will 

 come, however, when the term in a' 2 will become important, 

 the value of y> will then begin to fall off rapidly to zero at a 

 finite value of V, which may be called the critical velocity 

 Y c . For the ratio (p 2 + a 2 )/a 2 = 2mV 2 /Q must not be less 

 than unity. When it is equal to 1, y> = 0. 



Then Y e 2 = QJ2m = 8*8 x 10 15 . 



The critical velocity V e =9'4x 10 7 cm /sec. 



The same results should hold for positively charged 

 hydrogen atoms, which should cease to ionize a gas of 10 volts 

 ionization potential at velocities less than about 10 8 cm./st c, 

 equivalent to about 5000 volts. This point has been discussed 

 by Sir J. J. Thomson *, who has dealt with the problem of 

 the ionization produced Ivy moving electrified particles along 

 somewhat the same lines as that followed in this paper, by 

 assuming that a definite amount of energy is necessary to 

 remove an electron from an atom. It appears from experi- 

 ment that positive rays cease to ionize only when their 

 energy is less than 1000 volts. This is not surprising, since 

 at these low velocities the velocity of the election itself 

 probably plays an important part, 



§ 5. Conclusion. 



From the figures given in Table I. it will be seen that the 

 theory developed in this paper gives good agreement with 

 experiment in air for a particle velocities which are not too 

 low. It has already been pointed out that both Bohr's and 

 the present th"ories lead to equations of the same type (4). 

 In both cases constants of the proper order of magnitude 

 give good agreement. These constants are adjustable, but it 

 should be pointed out that their orders of magnitude are 

 fairly well known, and hence they are adjustable only within 

 narrow limits. It seems a little surprising that practically 

 the same results should be arrived at, starting from such 

 different assumptions. It is possible that these views might 

 be assimilated when more is known about the actual 

 mechanism of the transfer of energy from a particle to 

 electron. 



Unfortunately the exponential integral which occurs in the 

 final equation of motion is of such a character that a certain 

 amount of variation in the values of the constants employed 

 does not materially affect the agreement with experiment. 

 It is thus impossible to decide definitely by appeal to experi- 

 ment which of the two points of view adopted is the more 

 correct. 



* Thomson, 2nd Solvay Congress, 1913. 



