244 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1953 



such a decomposition even in the presence of molecular agitation. Thence 

 a generalized form of (47) may be derived containing essentially the 

 same terms. Finally, all but the first two spherical harmonics are dropped 

 and two equations analogous to (63) and (64) are obtained. In fact, it 

 is found that equation (63) is maintained entirely. An extremely compli- 

 cated reasoning is required, on the other hand, to find the generalization 

 of (64). The result is 



/i(c) = 



SkT dfo 



Combining (63) and (141) we find 



(141) 



' I , 3fcr\ dfo m 



/ I - cos x\ + W]dE^^M'^'''^ 

 ,\ ar(c) / / 



and hence 



/o(c) = exp 



— m / 



c dc 



M 



/ I — cos x \ 



\ aric) I 



+ fcT 



(142) 



This is the so-called Davydov distribution which is a generalization 

 containing within itself the Maxwellian distribution as well as the high 

 field distribution (65). 



The mean energy and the drift velocity of electrons may be calculated 

 from (63) and (142). They are obtainable from the literature and will 

 not be discussed here any further. Equipartition of the energy exists at 

 all field conditions. 



Part IV — Diffusive Motion of Ions 



IVA. diffusion for mean free time models 



It was proved in Section IC that if there are spatial inequalities in the 

 distribution of the charge carriers then a smoothing out process sets in 

 which can be described as diffusion. This derivation of principle can be 

 supplemented for "Maxwellian" molecules by an explicit computation 

 of the two components of the tensor (24), that is an evaluation of the 

 integral (23). We shall do this by following the method of Maxwell^* 



