Effects of Moving Charged Spheres. 291 



needle began to vibrate sufficiently to make observations 

 difficult. 



The following is the method used in taking a series of 

 readings : — The motor was started, and the time of 2500 

 revolutions of the axle determined. The spheres were then 

 charged ; two elongations of the needle on one side of the 

 zero-position were read, and one on the other side ; the 

 electrification was then reversed, and similar readings taken. 

 Sometimes the readings were not taken until the needle 

 had come nearly to rest, and its new equilibrium position 

 estimated. This was repeated until about ten reversals had 

 been made. The speed was then again determined. The 

 average of the deflexions, and the average of the two values 

 of the speed were taken as representing the series. The 

 needle-constant was determined before and after a number 

 of series. 



An attempt will be made in the following to compare the 

 results obtained with the results expected from theory. From 

 reasons which will appear later, this comparison can be 

 regarded only as approximate, and is given merely to show 

 that the observed results are of the right order of magnitude. 

 Rowland's method of using the experiment to determine v, 

 the ratio of the units, will be used. 



The magnetic force produced by a moving charge, </, 

 travelling at velocity v, is * 



H = 



P 2 ' 



where p is the radius-vector drawn from the charge to 

 the point at which II is measured, and e is the angle 

 between p and the direction of motion. This expression 

 holds only in case the velocity v is small compared with 

 the velocity of light. This may also be taken as the mag- 

 netic force produced by a moving charged sphere, the charge 

 being supposed concentrated at its centre. The force acts 

 in a direction perpendicular to p and to the direction of 

 motion. 



The magnetic force at either the upper or lower needle, 

 due to one of the spheres at any point in its path, is found as 

 follows : — 



The two sets of spheres revolve in two parallel circles, 

 distant b from each other. The plane of revolution is taken 



* J. J. Thomson, Phil. Mag. xi. p. 236 (1881) ; Heaviside, 'Electrical 

 Papers/ vol. ii. p. 505. 



