the Ions in Gases at Low Pressures. 549 



Eliminating x we have : — 



,^=^(xe-mf) 



dt" m \ dt )• 



The solutions of these equations, if x, y, dx/dt, dyjdt all 

 vanish when t = 0, is expressed by 



*=zp{ 1 -° o8 Gs h ')}- 



The equations show that the path of the particle is a 

 cycloid, the generating circle of which has a diameter equal to 

 2Xw?/gH 2 , and rolls on the line x = 0. 



Suppose now that we have a metal plate AB exposed to 

 ultra-violet light, placed parallel to a larger metal plate CD 

 perforated so as to allow the light to pass through it and 

 fall upon the plate AB. Then, it CD is at a higher electric 

 potential than AB, all the negatively electrified particles 

 which start from AB will reach CD if this plate is large com- 

 pared with AB, the particles travelling along the lines of 

 electric force. Let us now suppose that a uniform magnetic 

 force equal to H, and at right angles to the electric force, acts 

 on the particles ; these particles will now describe cycloids and 

 will reach a distance 2X?n/fH 2 from the place from which 

 they start, and after reaching this distance they will again 

 approach the plate. Thus if the plate CD is distant from AB 

 by less than 2X»j/?H 2 , every particle which leaves AB will 

 reach CD provided CD stretches forward enough to prevent 

 the particles passing by on one side. Now the distance 

 parallel to y through which the particle has travelled when it, 

 is at the greatest distance from AB is TrXm/^H 2 : hence if CD 

 stretches beyond AB by this distance at least, all the particles 

 will be caught by CD and the magnetic field will produce no 

 diminution in the rate of leak between AB and CD. If, on 

 the other hand, the distance between the plates is greater than 

 2X?m/(?H 2 , then a particle starting from AB will turn back 

 before it reaches CD : it will thus never reach it, and the rate 

 at which CD acquires negative electrification will be diminished 

 by the magnetic force. Hence, if this view of the action of 

 the magnetic field is correct, if we begin with the plates 

 very near together and gradually increase the distance be- 

 tween them, we should expect that, at first with the plates 

 quite close together, the rate at which CD received a negative 

 charge would not be affected by the magnetic force, but as 



Fkil May. S. 5, Vol. 48. No. 295. Dec. 1899. 2 Q 



