﻿Motion of Electrons in Argon and in Hydrogen. 1047 



distribution of the velocities of agitation about the mean. 

 In pure argon the velocity corresponding to /fc = 340 may be 

 taken as a lower limit to the velocity at which a large loss 

 of energy occurs in a collision. This velocity is the velocity 

 due to a potential fall of 12*6 volts, and is a lower limit to 

 the ionization potential. 



The increase in Xx 10"' from 1*54 to 179 in pure argon 

 when ux 10~ 7 changes from 13*6 to 11*5 may be due to a 

 small quantity of impurity remaining in the gas. It will be 

 noticed that the mean free path / changes from *118 cm. to 

 *20 cm. with this change in u, so that the effect of an 

 impurity would increase as u diminishes, since the proportion 

 of the total number of collisions in which there is a 

 considerable loss of energy increases. 



11. The mean free paths of the electrons are much longer 

 in argon than in nitrogen or hydrogen. When moving 

 with a velocity of 12*6 x 10 7 cm. per sec, the values of I are 

 •147 cm. in argon, '029 cm. in nitrogen, and *035 cm. in 

 hydrogen, the gases being at one millimetre pressure. If 

 the molecules were elastic spheres of the radius a- which is 

 obtained from the viscosity of argon, the mean free path of 

 the electron in argon at a millimetre pressure would be 

 •0286 cm. 



With the range of velocities of agitation given in the 

 table, the free path I in argon increases rapidly as the velocity 

 diminishes, and much longer free paths would evidently be 

 obtained if experiments were made with higher pressures 

 and smaller forces. With the amount of pure argon at our 

 disposal we were unable to make reliable experiments with 

 values of Z/p less than '105, which gave £ = 95. 



The free paths given in the tables for the velocities 

 11*5 x 10" cm. per sec. and 12*6 x 10 7 cm. per sec. are 

 probably too large, as may be seen by considering the effect 

 of a large increase of I for a comparative^ small reduction 

 in Mj on the relation connecting W with Z, u, and /. If the 



Zel 



formula W= x 0"815 be taken as giving accurate values 



mu ° ° 



of I corresponding to the mean velocity of agitation u when 

 a large change in u produces a small change in /, the 

 numerical factor must be increased when a small reduction 

 in u produces a large increase in /. The correction depends 

 on the distribution of the velocities of agitation about the 

 mean velocity u s and the rate of change of the mean free 

 path with the velocity. When these two factors are taken 

 into consideration, it is found that in the case of argon, 



