on Ionization Currents. 



Positive Currents. 



129 



Magnetic 



Air 0-002-3 mra 



Air 0-002 -3 mm 



Hydrogen 0'01 mm 



Field. 



Electric force = 25 



Electric force = 10 



Electric force = 25 







•0109 



•0118 



•0280 



324 



•0104 



•0114 



•0238 



567 



•0104 



•0114 



•0219 



1107 



•0106 



•0111 



•0173 



1593 



•0104 



•0105 



•0138 



1987 



•0106 



•0089 



•0125 



2600 



•0104 



•0077 



•0105 



An estimate of the order of magnitude of the mass of the 

 ions may be made as follows : Sir J. J. Thomson* has pub- 

 lished the theory of ions moving under the action of electric 

 and magnetic forces. In order to apply this theory to the pres- 

 ent problem, let the axis of z lie in the plane midway between 

 the two plates and in the direction of the magnetic field H, and 

 let the axis of X be parallel to the elective force X. Thus all 

 the ions will be produced very near the plane y z. Suppose 

 that one of the ions starts from the origin of coordinates at the 

 time t = 0, with the initial velocity components iv , v , w par- 

 allel to the axes of x, y, z, respectively. According to the the- 

 ory, at the time t this ion will be found at the point x, y, z 

 given by the equations 



* = (tt-"°K (1 



w 



— (1 — cos wf ) h sin mi 



Wn 



y 



where w = 



(1 — cos tot) 



X / X\ 1 



sin wt 



w Q t, 

 He 



It appears from these equations that the distances x of the 

 ions from the plane midway between the plates does not 

 increase indefinitely. Its maximum value depends upon the 

 initial velocity and the field strengths, increasing in general as 

 X increases and as H diminishes. If the initial velocity is 



small compared with the ratio ^, this maximum distance 



becomes 



H' 



2mX 



eH 5 



* Conduction of Electricity through Gases, 2d edition, §§ 55-58. 



