MOTION OF GASEOUS IONS IN STRONG ELECTRIC FIELDS 



201 



glance what averages can or cannot be obtained, and what the relation- 

 ship is between the high field and the general averages. 



For this reason we limit ourselves at present to the high field averages 

 obtainable from (49) . For the special case under discussion this equation 

 system takes the form 



(2, + 1) zyiiiM) (c-p, (cos &)) 



ar I 



= K^ + s + l)(c*~'P^i (cos t?)) 



(51) 



+ (^^ + l)(s - ^)(c'"'Ph-i (cos t?)> 



that is we have a system of linear relations connecting the averages 

 (c'P, (cos ??)). The connection between these averages is made apparent 

 in Fig. 9. Each average {cPy (cos t>)) is marked in this figure as a dot in 

 an s-i'-plane if s is integer. The equations (51) connecting these averages 

 are shown as lines with different equations leading to the same dot shown 

 in different outline. These equations generally have the shape of a V; 



Fig. 9 — Interconnection established by the Boltzmann equation among the 

 averages l^c*F, (cos «?)); case of constant mean free time. 



