k' 2 = 



a Gas in an Electrical Field. 

 hF 2 



537 



*"*('♦ K® 



For small values of k' 



d- -2 loo- 4 



V 



, t, 2 32^ f t A B, 2 ) 



cosh-^- = -.-— — —7, (ordinary circular functions). 

 2 sm\# + /3 v J ' 



\ 2 



and 



- w M 1+ il?> 



"= I- 



(This is the least value of d.) 



From 



r-^+m* 



we set 



where 

 and 



i <?/*% __ 1 dtxKx + /3, fc 

 cosn— - - _^_^ 



1 l 1+ 2mN?r 



* 2 



f 1 + * Bl ^ 



£ /2 = 



32ttNi 



F 2 



h iv 



l T 2m N, 3 f 



F- 



and if k f is small. 



IxF 4 



lfe M 1+ ss?) 



Now Goldstein (Wied. 4nfe. xv. p. 277, 1883) finds that d 

 is very nearly inversely proportional to the density, while 

 Mr. R. S. Willoughs (Cav. Lab.) finds that above a certain 

 strength of current the distance d diminishes as the current 

 increases. N x will be proportional to the density multiplied 

 by some function of F, so that the formula for d will agree 



Phil. Mag. S. 5. Vol. 49. No. 301. June 1900. 2 P 



