214 Sir J. J. Thomson : Further 



portion Ou is due to the particles which acquired their charge 

 after they had left the electric field, but before they had 

 quite passed through the magnetic field, their vertical 

 deflexion being due to the part of the magnetic field which 

 stretches beyond the electric. The portions u/3 near a are 

 due to particles which got their electric charge shortly before 

 they left the electric field, while the portions fiy further 

 away from a. are produced by particles which got charged at 

 an earlier stage in their career. 



Let us now consider the effect on the shape of the lines of 

 a want of uniformity in the electric or magnetic fields. 

 Since the lines are straight when the fields are uniform, the 

 different particles which produce a line must all be moving 

 with approximately the same velocity. Let this velocity 

 be v 9 then if the particle acquired its charge at a distance £ 

 from the photographic plate, y the vertical displacement at 

 the plate due to the magnetic field is given by the equation 



e f * 

 ?/ = - — 1 xHdx, 



J mv Jo 



where H is the magnetic force at a distance x from the 

 plate. 



Thus dy _ j_ m 



where H| is the value of H at £. 



Similarly, if z is the horizontal displacement due to the 

 electrostatic force, 



mv 



e r§ 

 -a 1 #?X » dx. 

 'Jo 



where X is the value of the electrostatic force at a distance . 

 from the photographic plate* 

 We have, therefore, 



d§~mv** : *' 



and so 



dz X fc e 



And thus the tangent of the angle which the tangent to the 

 curve makes with the horizontal represents the variations in 

 the ratio of the magnetic to the electric forces. Take, for 



