Forces acting upon the 'Poles of the Electric Arc. U73 



Take the case of discharge between two large parallel 

 electrodes A and G close together (that is virtually between 

 two infinite parallel plates). Let the dotted line B represent 

 a thin uniform sheet o£ negative ions which has started at 

 the cathode C and is on its way to the anode A. Let the 

 initial pressure of the gas between A and be " j»/ J and let 

 the conditions be such that the field between A and is 

 sensibly uniform ; also assume the motion of B to be viscous,. 

 i. e. steady on the average. The drag of B on the gas is 

 constant and calls into existence a constant difference of ( 

 pressure pi — p 2 between AB and BC, due to the transfer- 

 ence of a small amount of gas from right to left through B. 



Fia-. l. 



B 



Since the electrodes are large and the distance AC short, 

 there 'is no eddying, and the momentum of the drag is passed 

 straight on to that of static pressure without any appreciable 

 amount taking the form of motion of gas in the process. 



At the beginning of B's journey close to C, p± will be 

 equal to p, and the whole change in static pressure will 

 occur in p 2 . Hence will feel the whole of B's drag as a 

 suction, while A will be unaffected. 



As B travels across, p^ rises above p while p 2 approaches p 

 until, when B is close to A, p 2 ~p and the whole change of 

 static pressure occurs in p { . Tne momentum imparted to 

 the gas is thus returned wholly to C at the start and wholly 

 to A at the finish, and divided between A and C in varying 

 proportions on the journey. But the process is symmetrical, 

 and, if the whole journey is taken into account, it will be seen 

 that half the drag momentum is received by A and half by C, 

 the resultant force on each being directed towards the left. 

 As, moreover, half the drag is also felt by A as electrical 

 reaction and the other half by 0, these being forces directed 

 towards the right, it follows that A and will be separately 

 in equilibrium when the whole journey of the ions is con- 

 sidered. This argument holds equally when the discharge 

 takes the form of a constant current between A and C 



