p 



MOTION OF GASEOUS IONS IN STRONG ELECTRIC FIELDS 199 



From (41) and (42) it is seen that this is actually the product of two 

 independent integrals if the angular distribution 11 (x) is independent 

 of the velocity of encounter c' . The first integral is then identical with 

 the one arising from the second term in (47), and the second is a collision 

 integral having no connection with the velocity distribution. Even if 

 this is not the case, the second integral is still a dynamic average which 

 can be evaluated as a function of c' previously to any knowledge of 

 /i(c'). We express this by introducing the abbreviation 



Ib,v = V-\Py (cos k) 



Using (41) and (42) we see that 7s. ^ is the following function of x 



"'^^ '' + " ^' (48a) 



m -\- M cos X \ 



VM^ + m2 + 2Mm cos x / 

 which, for the particular case of equal masses, takes the simple form 



Is Ax) = cos' \x p. (cos ix) (48b) 



With this definition the integrated equation (47) reads 



f I L^il^ \ kXcV^' dc = ''^''+^V^ f h,.Mc'^' dc 



Jo \ aTic) I 2v — \ h 



•(c) 



2v -\- 6 Jo 



or in terms of averages 



{2v + 1) ( ^^ c'P. (cos ^)) 



\ aric) I 



(49) 

 = K^ + s + 1)(c'"'Pk-i (cos ^)) 



+ (^ _|_ 1)(5 _ v){(r^Fv-x (cos t?)) 



I believe that equation (49) contains all possible derivable relations 

 between averages as special cases. Some of the most notable ones are 



