324 Sir J. J. Thomson on the Mobility of 



interval by a flash of Rontgen rays. If d is the distance 

 between the plates, it is evident that no charge at all will be 

 received until T = d/k{X., and that apart from the loss by 

 recombination all the negative ions will have reached the 

 plate when T = d/k 2 X, where k 2 is the mobility of the negative 

 ion, k x that of the electron, and X the electric force between 

 the plates. When T is between these limits the charge 

 which reaches the plates can be readily calculated by the 

 aid of the preceding expression. Let us consider the case 

 of a negative particle which takes the whole time T to get 

 across, travelling through a distance x as an electron and 

 d — x as a negative ion. We have 



X CI X m 



All the molecules which reach this distance x without 

 combining will be in time to give up their charge to the 

 plate, while those which combine before reaching this 

 distance will be too late. Thus the charge Q received by 

 the plate will be the charge carried by those electrons which 

 travel this distance without combining, and this by the 

 preceding expression is equal to 



_^ (d~k 2 XT) 

 Nee ^ ^1— V*i) J 



where e is the charge on an electron and a = V/&iX. 



We see that Q is a function of T, of the electric force, 

 of the distance between the plates, of the pressure (since 

 X and the / :'a vary inversely as the pressure), and of the 

 temperature through V. 



Let us consider how Q varies when any one of these 

 quantities changes, the others remaining constant. 



Variation of Q with T. —Considered as a function of T, 

 Q is zero until T = d/k 1 X. and becomes constant when T 

 equals d/k^K ; between these limits it varies as e'* , where 

 fjL = Yk 2 /n\{k l — k 2 ). 



The graph representing the relation between Q and T is 

 shown in fig. 1. By means of the points P and Q we can 

 determine L\ and k s , while fju can be determined by the 

 equation 



log(Q 1 /Q 3 )=/t(T 1 -T 2 ), 



where Qi and Q 2 are the values of Q corresponding to the 



