506 Theory of Electric Discharge in a De La Rive's Tube. 



That the intermittent nature of the discharge from an in- 

 duction-coil materially determines the value of /(X<? X) — % is 

 proved by the fact that when the discharge is passed from 

 storage-cells into a tube (of small spark-length), the first 

 stage — that of spray-discharge — is absent. 



13. IV. During the rotatory discharge, the product of 

 pressure and angular velocity is constant. 



In the case of steady rotation, the moment of the electro- 

 magnetic couple on the current due to the magnet is equal to 

 the moment of the retarding forces. 



The first is proportional to the current i=fjui (say), the 

 second = j* (A x -f A 2 )nur ds, 



where w = no. of +, — ions per unit length. 



r = distance of an ion from the axis and u the velocity 

 ds = an element of length of the discharge. 

 A 1? A 2 = the retardations of +, — ions per unit velocity. 



Also, if q, g' be the velocities of the ions along the line of 

 discharge, and X the electric intensity, 



e e 



Xe = qXA 1 i. e. A x = - ; similarly, A 2 = — . 



Therefore fii = tone I - + — , j I r 2 ds. 

 But Xe(q + q')n = i; 



therefore — = v» 9 ; (6) 



/j, \ r*ds v 



XT 1 1 , t 1 



Now since p = — , p cc - , and also gc —. . 



r X ' r q q 



•'• P m «ipJs (7) from (6). 



Now j" r 2 ds is found to be practically constant when the 

 distance between the electrodes remains unchanged, 



therefore — go pat. 

 V 



ft — j =y, so long as there is rotation. 



Therefore f(epa)) = y, i. e. p<o--=8, say. 



If 7 is constant, as is practically the case for air, N 2 0, &c. 

 p&> = constant. 



