Unstriated Discharge and in the Arc. 283 



larger. In metallic conduction the number of electrons 

 appears to be constant, and the current is determined by the 

 electric force. In the unstriated discharge the electric force 

 remains approximately constant, and the current is determined 

 by the number of electrons sent into the gas from the cathode. 



The number of new ions formed will depend on the 

 number of electrons hitting the molecules, on the number of 

 molecules to be hit, and on the velocity of the electrons. 

 The velocity will depend on the distance through which the 

 electron has moved since the preceding collision and on 

 the electric force accelerating it. Only those electrons 

 which move through comparatively large distances will be 

 able to ionize. 



Let us denote by V x the potential difference through 

 which an electron must pass in order to have sufficient 

 velocity to ionize. Let x x be the distance corresponding to 



such a potential difference. Then #1=-^, where X is the 



electric force. According to the kinetic theory of gases * 

 the number of electrons passing through a distance as great 



or greater than x l before impact will have to the whole 



_n 

 number of impacts the ratio expressed by e *, where \ is 

 the mean free path of the electrons. Since the number of 

 molecules is proportional to the density of the gas, we may 

 indicate the total number of collisions per c.c. per sec. by 

 bn^, where S is the density of the gas and b is a constant. 



The number producing ionization will then be bn^he *, which 



may also be written bn x he *x. Since \ is inversely propor- 



tional to the density, this may be written bnfie x ? where c 



\ 

 is a constant of such value that c&= — . 



X 



Some of the electrons which do not have sufficient velocity 

 to ionize the molecules which they hit, will combine with 

 them. It has, however, been shown by the work of 

 Townsend f on the diffusion of ions that combinations do 

 not always occur with such collisions. In many cases the 

 electrons collide with molecules and again separate without 

 any permanent effect on either the molecules or the electrons. 

 In case of collisions between electrons and molecules there 

 are three possible results. The electrons may ionize the 



* Meyer's ( Kinetic Theory of Gases,' p. 408: Townsend, Phil, Mag. 

 [6] i. p. 210(1901). 



t Phil. May. [6] xxiii. p. 857 (1912). 



