Discharge in a Transverse Magnetic Field. 61 



voltage of the induction-coil, is materially affected by the 

 circumstances of the discharge. 



25. All these points seem to be capable of explanation on 

 such considerations as the following : — 



Let V be the voltage of the induction-coil j then the 

 energy supplied per unit of time by the coil will be pro- 

 portional to the V , say i V , where i is the current in the 

 circuit. 



Let V be the potential difference between the electrodes ; 

 then the energy supplied to the electrodes per unit of time 

 will be proportional to V = i'V. say. 



Therefore i Y = i'V + energy carried away by the positive 

 and negative ions, thrown oh 1 ' from the electrodes, less the 

 energy carried to the electrodes by positive and negative 

 ions reaching them (per unit of time). 



But the energy carried off by an ion =X#A. 



Therefore, 



i V =i ,/ y + Xe(lXq'\' + nq\)-ft, 



where n and N are the numbers of positive and negative ions 

 thrown off from the electrodes and occupying unit length 

 of the discharge, and X, V their mean free paths. 

 In order to find E, we may proceed as follows : 

 It can be shown that the equations of continuity in a 

 discharge-tube can be written, in the steady state, 



^LKaKq' + ynq, 



where a=A/(X*\'-/9') 



(6) 



7 



1 },.... (7) 



and n, N the number of positive and negative ions per unit 

 length of discharge, oc being measured along the line of 

 discharge. 



Therefore, we have 



N#' + nq = const. = , 

 where i is the current carried by the discharge. 



