MOTION OF GASEOUS IONS IN STRONG ELECTRIC FIELDS 249 



Having introduced moments in the manner described earlier we arrive 

 at the inhomogeneous version of (49) or (86) 



Hs + ^ + l)ls - 1, V - 1} + (y + l)(s - y){s - 1, ^ + 1} 



-(2. + 1)(1 - {Is,.)){s +l,v] = -{2v + 1)(1, l)(s, v) (154) 



+ v{s + 1, V - 1) + (v + l){s + 1, ^ + 1> 



Here the curly brackets {s, v} are normalized moments over ^(w) defined 

 as follows 



{s,v} = ^ / qMw'P, (cos t?) dvf (155) 



The equations (154) show that the quantities {s, v] are numbers, the 

 variable density gradient nk having been eliminated by the definition 

 (155). The system does permit that arbitrary amounts of the pointed 

 averages be added to the curly ones. This indeterminacy is removed by 

 the supplementary condition (18) which, in the present notation reads 



{0, 0) =0 (156a) 



The connectivity of the equation system (154) is the same as that of 

 (86). Hence it will have the same properties as that earlier system. We 

 may, therefore, reduce it in the manner followed previously and get 

 inhomogeneous versions of the equations (87), (88) and (89). They read 



{4,01 = -|<4,1) + |(1, 1X3,0). (157a) 



-f (2,0) -^(2,0) +10(1,1)^ 

 112{3, 01 - 3!7, 01 = 4(7, 1) - 4(1, 1)(6, 0) 

 + f (5,0) + il?(5,2) 



-^-|?(1,1)(4,1) 



_1^^3,l) + ^^3,3) (^^«^) 



+ *|?(1,1)(2,0)-^(1,1)(2,2) 



