﻿1044 Prof. Townsend and Mr. Bailey on the 



values of Z/p up to 16, as indicated by the scale at the top of 

 the diagram. Taking p as unity, the curves for argon show 

 that as the force increases, k increases rapidly and attains 

 the value 340 when Z is 1*6 volts per centimetre, and after 

 a diminution to 310 at 5 volts per centimetre, k rises again 

 to 325 at 9 volts per centimetre and remains constant at 

 that value for the larger forces. 



9. The mean free path I of an electron may be obtained 

 from the formula for the velocity W : 



7,p1 



W=— x-815 (4) 



mu 



This formula for the velocity of the electrons is obtained 

 from Langevin's more general formula for ions or electrons 

 when the velocities of agitation are distributed about the 

 mean velocity u according to Maxwell's law, u being the 

 square root of the mean square of the velocities of agitation. 



It is difficult to determine the distribution in the case of 

 electrons moving under an electric force, and according to 

 Pidduck's * calculations the factor '92 is more correct than 

 '815, but the exact value of the numerical factor is uncertain, 

 as the mean free path depends on the velocity of the electron. 

 The general conclusions obtained from the experiments as to 

 the relative lengths of the free paths in different gases or 

 the variations of the free paths with the velocity do not 

 depend on the value attributed to the numerical factor in 

 the formula, and as the value *815 has already been used 

 in previous calculations, it is desirable to retain it for purposes 

 of comparison. 



The effect of a collision on the velocity of an electron may 

 be shown by calculating the coefficient of elasticity / by 

 Pidduck's formula. This method was adopted in the earlier 

 researches on the motion of electrons in air f, and in those 

 on oxygen, hydrogen, and nitrogen which were published 

 recently J. 



It is simpler, however, to give the proportion of the 

 energy of an electron which is lost in a collision, as this 

 quantity is found directly from the experimental results. 

 The loss of energy of an electron in a collision may be 

 estimated approximately from elementary considerations. 



* F. B. Pidduck, Proc. Lond. Math. Soc. vol. xv. pp. 87-127 

 (1915-16). 



t J. S. Townsend and A. T. Tizard, Proc. Koy. Soc. A, lxxxviii. 

 p. 336(1913). 



% Phil. Mag. Dec. 1921. 



