62 LEAKAGE IN ULTRA-VIOLET LIGHT [CH. vi. 



field applied, as well as the absolute strength of the 

 magnetic field. 



The calculation is so simple that it may be given 

 here : 



Let figure 9 show the zinc and the gauze facing 

 each other, close together, with a gradient of 

 potential (V - V)/d = E between them ; and let a 

 magnetic field of density H (which letter is, in this 

 case, to represent M times the intensity, for brevity 

 of writing) be applied normal to the paper. 



Then the motion of a charged particle detached 

 and propelled from the origin into the region between 

 the plates, provided that the plates are in vacuum 

 so that there is no resisting medium to interfere, 

 will be taking the axis of x as a perpendicular to 



the plate .. ^ TT . 



mx = &e iiey 



my = Hex 



the initial values of x, y, x, and y, being all zero. 

 The solution of these equations, under these initial 



conditions, is /, 7 , x 



x = a(l -cos ot) 



y a(bt sin bt) 



Era , 7 TT e 

 where a = TT9 and b = H . ; 

 He ra 



and from these we see that x is oscillatory in accord- 

 ance with a versine, ranging from to 2a and back ; 

 while y is both oscillatory and progressive, com- 

 pleting its period in a time -=--, and increasing in 



every such period by the amount 2-n-a. In other 

 words, the equations represent a cycloid traced by 

 the rim of a circle of radius a rolling on the zinc 

 plate. 



