Ionization and Radiation of Gas Molecules. 245 



distance; of course the same relation must exist between the 

 potential difference XZ, on the electrodes, and the ionizing 

 potential V. 



Let 7 be the probability of the ionization of the gas 

 molecule due to an inelastic collision. Then the probability 

 of the emission of light will be equal to 1 — y. 



Suppose that rc electrons set free by some external cause 

 (for instance, by photoelectric effect) are made to travel 

 from the cathode towards the anode plate. After having 

 passed the fall of potential V they will inelastically collide 

 with the gas molecules and produce n Q y new pairs of ions. 

 Therefore in the electric field there will be n (l + y) electrons, 

 and after a new series of collisions the number will be increased 

 to n (l + 7) 2 , and so on. 



It is obvious that the total number of electrons reaching 

 the positive plate will be equal to 



Ml +7)*' (1) 



In Prof. Townsend's theory* the same quantity is denoted 

 by the expression 



n e al , . . (2) 



where a is the number of ions which an electron produces 

 by collision in going through a centimetre of the gas. The 

 numerical values of a were experimentally determined over 

 a wide range of gradient X and pressure p by Prof. Townsend 

 and his pupils. These values can be easily obtained from the 



curves, representing — as a function of — . 



By means of the expressions (1) and (2) we can write an 

 equation for the determination of 7, 



lognat(l + 7 )=^a (3) 



This equation may be considered in a slightly modified 

 form 



a =7 1 °g nat ( 1 +r)» 0) 



which determines a as a linear function of X. This formula 

 holds good only when the above-mentioned limitation is 

 made for the " ionizing distances." With increase of X the 

 " ionizing distances " are diminished and become comparable 

 with the mean free paths of the electrons. In this case after 



* J. S. Townsend, " The Theory of Ionization of Gases by Collision." 



