MOTION OF GASEOUS IONS IN STRONG ELECTRIC FIELDS 241 



The analogous result for sin x was obtained by the computing group 

 of Bell Telephone Laboratories 



f sin' X d(^) = 0.511 

 Jo 



/ sin' X d(jf) = 0.261 



which gives 



/sin' X^ _ 1 



\~7-/ 



= --0.772 (130) 



Ta 



We may now rewrite the major results of Section III A for the polariza- 

 tion force. From equation (117) we get 



, . _ 0.9048 /I ^ 1 E 



(131) 



This formula may be found in the literature.^^ What is new about (131) 

 is the realization that it is exact at high as well as low electric field. 



The formula for the total energy needs no discussion for a special 

 model ; it does not involve the angular distribution law when written in 

 the form (122). Thus we would obtain, for instance, for an ion travelling 

 in the parent gas that its total energy is obtained by doubling its ap- 

 parent energy observable in the drift and adding to this the thermal 

 energy %kT, 



For the partition of the high field component of the energy in the 

 three coordinate directions we have two formulas, formula (58) parti- 

 tions the entire field contribution of the kinetic energy, formula (60) only 

 its random component. The first formula gives 



e,:ey:e^ = M:M:{M + 6.73m) (132) 



Formula (60) gives 



e,:ey:e* = (ikf + m): (M + m): (M + 3.72m) (133) 



It is convenient to apply the general formulas also to the case of con- 

 stant mean free time, coupled with the assumption of isotropic scattering. 

 This combination of assumptions represents, strictly speaking, an im- 



" The formula is equation (3), p. 39 of Reference 2, in the limit X = 0; or also the 

 last unnumbered equation on p. 919 of Reference 6. 



