with Electron Currents in Different Gases. 435 



ions are apparently liberated. According to Bohr's theory 

 the last named effect is either illusory or is a secondary 

 phenomenon. For the present we shall assume for simplicity 

 that the only effect influencing the motion of the electrons 

 at the critical equipotential surface is the loss of kinetic 

 energy. We propose to defer the consideration of the more 

 complicated case, in which positive ions are liberated, until 

 later, when we hope to be able to submit further experimental 

 results bearing on the question at issue. 



Turning to equation (3), and keeping to the case of parallel 



1 dV d 2 V 

 planes, since i is the same everywhere, we see that — j- -t-j 



V CIX (XX 



must have the same value on each side of the critical equi- 

 potential surface. Since v vanishes at the critical surface, 



•4.1 dY d ' Y 1 ' U T> , dY • * f 



either -=- or -r-» must also vanish. But -r- is not zero tor 

 dx dx z dx 



V<V], and if ^- were not continuous, there would be a 

 dx 



finite charge on a surface in the gas. and this would not be 

 in equilibrium under the forces to which it is subjected. 



dV . . . d 2 V 



Thus — — must be continuous at the critical surface and —7-5 



dx ax- 



must vanish for V^Vj. Considering the solution for 



dV 



V< V 1? we see from (6) that the value of -j— at the critical 



surface (since C = in this region) is given by 



(j_X) =(2a)HV ,. . 



(16) 



Since U vanishes at this surface C in (15) is equal to 

 2aY^\ and 



dJJ 



w 



Thus 



here 



(2a)fc + C' = V 1 *F(y ) -Vi*FW, 



(17) 

 (18) 



F(*)«i- 



15 



.5/2 



4- c 4 — 

 + 18 



2^ 

 891 



,11/2 



+ . ... 



+ / !y l^7 (8n-2) 2 



ln + 2 



3'y< 



+ .. 



(19) 



