a Gas in an Electrical Field. 



533 



wher 



cosh e/l X + " - I • 



C09n 2 ~ sn(Xa + £,*)' 



B 



2 + 



k 2 



s/NtJSr 



Before discussing the nature of the solution we shall con- 

 sider the case when an electric current is passing. We shall 

 suppose that the current is due to the bodily transference of 

 the free atoms, while the molecules have practically no bodily 

 motion. 



Fixing our attention for the moment on the positive 

 group :— 



Let pi be the pressure, p x the density, so that p v 



_ P\ 



and let m, be the group velocity. Then the hydrodynamical 

 equations are 



d^i . u (K _ __ J_ 5 log Pi _ e_ B% 

 ^t ! d# km ~§x 



and 



a* 



For a steadv state 



Hence 



dpi - o _ d"i 



i mu \ 2 i 



and ^ 1 m 1 =B X , 



where N x and B x are constants. 



Similarly for the negative atoms wo have 



/3 3 W 2 = B 2 . 

 Hence the electrical density at a point is 



^(pi-p»). 



and the electrical current is 



= £(Pi"i-p 2 " 2 ) = ^(Bi-B^ = ysay. 



