130 



Prof. P. O. Pedersen on the 



when (the electric field) X has a given value, but the 

 calculations are extremely complex, and the resulting 



Fio- 1. 



& 



formula for the relation between i; a, p, X is not of a 

 form to which Townsend's measurements can be applied." 

 He therefore assumes that the number of electrons n x 

 varies continuously with the distance x from the cathode 

 and thus obtains an approximate solution. 



The exact solution is, however, quite simple and may be 

 given a form to which Townsend's measurements may 

 easily be applied. The deduction of this solution may 

 therefore, perhaps, be of sufficient interest to be given 

 here. 



3. Let L be the mean free path of the electron ; then 

 the probability s that a- new collision results in ionization 

 is determined by 



where 





(3) 



(4) 



The electrons coming from A (see fig. 1) fall into two 

 groups 1 and 2. In the first we shall reckon the electrons 

 whose initial free path is greater than / and which will 

 thus ionize at the first collision. The second group includes 

 the electrons whose initial free path is less than l : of these 

 the first collisions which occur between x = and a = l will 

 not result in ionization. 



The number of ionizations which take place in the space 

 element between the planes x and x + dx, and which is 



