Discharge in a Transverse Magnetic Field. 55 



The third term of (4) will then be of the form 



C/(«)(?i-N) 2 6>, 



the other terms (depending on the velocities) being neglected. 

 Here C is a constant depending on the form of the various 

 stream? of discharge, and a the angular coordinate defining 

 the position of the stream, whose equation of motion is given 

 by (4), provided n and N are constant throughout the 

 discharge, observing that in this case, alone, 6 will be the 

 same for all points. In any case, if w = N, the equation of 

 motion is of the form 



I0+n6=§Kpids 



= the couple acting on the discharge due to the magnetic 

 action of the electromagnet, 



here 



since 



I =§(m 1 + m 2 ) n ds p' 2 , 



jb = 0, in the steady state. 



But this couple == §Mi, where M is the total magnetic 

 strength of induced magnetism (Phil. Mag. Oct. 1908). 

 Therefore we have 



where 



/*=(A 1 + A 2 )nj , / 



ds. 



This is the same equation as was obtained in a previous 

 paper by identifying the discharge (which is in the form of 

 fig. 1) with an electric current. 



14. If the number of positive particles is small in com- 

 parison with that of negative particles, the number of the 

 latter will not necessarily be constant throughout any stream 

 of discharge. In this case, putting n = and considering 

 the motion of a small element of a discharge, we have, 

 when the steady stage is reached, 



B0 = Hs£ or 0=3^, ... . (5) 



where B is a function of p, a, defining the position of the 

 element of the discharge considered. This completely 

 explains the twists described in para. 10. 



Comparing figs. 8 and 11 with figs. 9 and 10, one might 

 be led to suppose that the twist is independent of the direction 



*' 



