MOTION OF GASEOUS IONS IN STRONG ELECTRIC FIELDS 181 



K(c)j gp(c) = expansion coefficients which result when /i(c), gr(c) are 

 expanded in Legendre Polynomials about the field direction. 



LAx) = A set of functions of the scattering angle defined in (48). 



( ) = the quantity in pointed brackets is to be averaged. 



{s, v) = abbreviation for {w^P, (cos d))\ the average is taken over /i(w). 



[s, v] = A normalized correction to (s, v) contributed by fir(w); see 

 equation (155). 

 A special convention will be adopted to distinguish velocities before 



and after a collision: 



c'j C = velocities before the collision. 



c, C = velocities after the collision. 



When used in this fashion the twelve components of the four vectors 

 above satisfy the four identities: 



mc' + MC = mc + MC (7) 



mc'' + MC' = mc' + MC' (8) 



The same convention is to apply to other vector quadruples, such as 



u, U, u', U' 

 For the velocities in the center of mass system we use 



y' = c' — C = relative velocity before the collision. 

 Y = c — C = relative velocity after the collision. 

 In consequence of (7) and (8) the t's obey the relation 



y" = y' (9) 



The multiple integrations occurring in the theory are of the following 

 two types. Either they are over the three components of a velocity in 

 a Cartesian velocity space; we shall denote such integrations by 

 dc, du, dU', etc. Or they are proper ''collision" integrations which classi- 

 cally have the form 



yhdhde 



where h is an impact parameter and e an azimuth. In most cases these 

 integrals depend on extraneous factors for their convergence but this 

 fact is usually disregarded for convenience; we shall follow this habit by 



