MOTION OF GASEOUS IONS IN STRONG ELECTRIC FIELDS 209 



rary device of a ^, 17, ^ coordinate system we find for ^: 



m t(c) m t(c) \ dc. ^ dc 



,. dh\, (MV sin^c fd% d% d^\ 

 ' dc4 "^ \m) 4t(c) XdcJ' "^ ac/ "^ dc.-') 



, (M\ 2(1 - cos x)' - sin' x / 3 , d , d 



47(c) r ac. ' '^ dcy ' "• dc, 



Cx dh Cy dh Ci 

 C dCx C dCy C 



' dcj 



If the last term is evaluated exactly terms of the order (M/mY are 

 added to the first derivative terms in h{c). They are obviously negligible. 

 Finally integration over x yields the following form for equation (68) 



dhic) ,^. ilf/l — cosx\(. ( w-Lf \ 



... , . - cos x\ Y^ , Sh ,\ (M\ / sin' x\ 2 V ^''^ ncx\ 



ikf /I — cos 



+ 



1 /iW^\ / (I - cos x)(l - 3 cos x)\ V 



4 \m)\ ^) / ihi ''' dcidcu 



When equation (70) is considered up to linear terms in M/m it yields 

 a 5-f unction about the drift velocity (c,) which results from the implicit 

 equation 



/ V m //I — cos x\ (n^\ 



{Cz) = ifT a / ( -^^ ) (71) 



M / \ t{c) /c^{e,) 



The 5-function takes here the aspect of a non integrable function which 

 in a special case can be seen to equal 



hf^{cl + 4 + (c.- (c.))T"' 



When normalization is imposed on such a function it is made to vanish 

 everywhere except at the point corresponding to the drift velocity. 



The square terms in M/m are necessary to gain information about the 

 functional form of h(c). Since the region in velocity space in which h is 

 appreciable is still small we may take a as constant in that region. A 

 further simplication results from order of magnitude considerations 

 on c: 



