MOTION OF GASEOUS IONS IN STRONG ELECTRIC FIELDS 187 



cussed in Section lA. When (25) is inserted into (13) it is seen that 

 a, N and V enter only in the combination a/ NT. The quantity 



\Nvr' 



has the dimension of a velocity. A second such quantity is 



which arises from the Maxwellian functions under the integral sign.^^ In 

 the high field case, this quantity does not enter, that is, the velocity dis- 

 tribution functions for the molecules could be replaced by 5-functions 

 at the origin. Hence the first combination controls all velocity averages. 

 For the mean drift velocity, we can thus write 



<c.) = const Y^j^ (26a) 



This formula gives the variation of the drift velocity with the electric 

 field. It is worth while writing the result out explicitly for the two special 

 cases discussed above. The first is the case of constant mean free path, 

 a = 0, for which 



(c) = const -a'^V^' (26b) 



This is a drift velocity varying as the square root of the field or a mo- 

 bility varying inversely as the square root of the field. The second case 

 is the one of constant mean free time a = 1, for which 



(Ci) = const -ar (26c) 



This means a drift velocity proportional to the field or a constant mo- 

 bility. 



In the low field case we cannot disregard one of the two velocity 

 parameters constructed above; but now equation (13) is to be solved by 

 perturbation theory only, it then yields a drift velocity varying with the 

 first power of a/ NT. Dimensional analysis then yields the dependence of 

 the mobility on the temperature. We find 



16 Dimensional analysis is incapable of distinguishing between m and M; this 

 means that we cannot master dependence on mass by the method of this section; 

 all our "pure numbers" are actually unknown functions of m/M. 



