3^2 Sir J. J. Thomson on the Mobility of 



once the electron has become attached to a molecule it stays 

 so for a time which is large compared with its life as a free 

 electron ; for the sake of simplicity we shall suppose that 

 when once the electron is attached to a molecule it reaches 

 one of the parallel plates and is removed from the field before 

 it gets free again. 



Let X be the electric force between the plates, k x the 

 mobility of the electron, then /c x X is the velocity of drift of 

 the electron : we assume that this is small compared with V, 

 <the velocity of the electron due to thermal agitation. We 

 shall suppose that when an electron collides with a molecule 

 the chance of its uniting with it and forming a negative ion 

 is 1/n. 



We shall first calculate the expectation of an electron 

 traversing a distance x parallel to the electric force without 

 becoming attached to a molecule. 



The time taken by the electron to traverse this distance is 

 w/JciK, and in this time, since V is assumed to be large com- 

 pared with ^X, it passes over a space which is approximately 

 Wx/kiK. We shall write a for V/^X, so that this space is 

 <equal to olx. 



The expectation of the electron travelling over this space 

 without a collision is e~ aX ' x , where \ is the mean free path o£ 

 the electron, and this is the expectation that it should pass 

 over this space without making a collision and without 

 uniting with a molecule and becoming a negative ion. 

 The expectation that it makes one collision, but no more, in 

 passing over the space x ma} r be found as follows. The 

 expectation that it passes over a distance f without a collision 

 is e~ a ^ x ; the expectation that it should make a collision 

 between £ and £-f^f is ctd^jX ; and the expectation that it 

 should make the rest of the journey without a collision 

 is e -*(*— OA. Hence the expectation that it makes but one 

 collision, and that between f and f + d%, is 



e- a ^ x (ad^X)€-< x ~^ x or ^e- ax l x ad%. 



Hence the expectation that it makes one and only one 

 collision in the whole journey is 



I 



e -ax/X«dZ o] . e -a*/X ax/x 



The expectation that this collision does not result in 

 recombination is (n — l)/n. Hence the expectation of the 



