( *»’) 
current have a velocity superior by a small value only to that of 
the medium through which they move. 
§ 3. Wilson and Martyn calculate the velocity of the rotating 
discharge very nearly in the following manner. 
If X is the electric intensity parallel to the axis of the cylinder, 
positive and negative ions will have the velocities k x X and — k 2 X 
in the direction of that intensity. Say that the positive ions move 
downward with the velocity 
k x % .(42), 
and the negative ones upward with the velocity 
v t = k,X .(43) 
The mechanical force acting on each ion is equal to the product 
of the magnetic intensity, the charge of the ion and its velocity. 
Thence we conclude that the velocities with which the positive and 
negative ions resp. move laterally, are 
u x z=k x 'HX. . . .(44) 
= k^HX .(45) 
Positive and negative ions will be able to follow the same path 
only when it is inclined, the part near the anode being in advance. 
Let « be the angle which the discharge makes with the axis. This 
angle will appear to be very small. 
If V x is the velocity of a positive ion in the direction of the 
discharge and V the lateral velocity of the discharge, the true velocity 
of the positive ion will be at the same time the resultant of the 
velocities v x and u x and of the velocities F, and U. 
We must have therefore 
(46) 
u 1 =y-V 1 sina .(47) 
And if the negative ions move upward in the direction of the 
discharge with the velocity F 2 we must likewise have 
v,=z-V,cosa .(48) 
and 
V,dna .(49) 
Prom the four last equations we obtain 
( 50 ) 
