236 Mr. J. J. Thomson on the Electric and Magnetic 

 or they may also bo written 



«=^G( 2 -0-K^/- 7 ?)); 

 *=g(<—0-K^O> | ' ' (4) 

 7 = w (pte ~ ^ ~ q (" ~ ^) ' 



Comparing these expressions with those given by Ampere 

 for the magnetic force produced by a current, we see that the 

 magnetic force due to the moving sphere is the same as that 

 produced per unit length of a current whose intensity is 

 fie \/ p 2 + (f + r 2 , situated at the centre of the sphere, the direc- 

 tion of the positive current coinciding with the direction of 

 motion of the sphere. The resultant magnetic force produced 

 by the sphere at any point is rw/xesine/ p 2 , co being the velo- 

 city of the sphere, and e the angle between the direction of 

 motion of the sphere and the radius vector p drawn from the 

 centre of the sphere to the point ; the direction of the force is 

 perpendicular both to the direction of motion of the sphere 

 and the radius vector from the centre of the sphere to the 

 point; and the direction of the force and the direction of motion 

 are related to each other like translation and rotation in a 

 right-handed screw. 



It may be useful to form a rough numerical idea of the 

 magnitude of the greatest magnetic force which could be pro- 

 duced by a moving charged sphere. The greatest value of the 

 force =■ fiKY aa / p 1 , where a is the radius and V the potential 

 of the sphere. Now if F be the greatest electric force which 

 can exist without discharge, the greatest value of V is Fa. 

 According to Mr. Macfarlane's experiments F is, roughly 



speaking, about 3 x 10 12 , /xK=-^ — ttvzoI substituting these 



values, the greatest value of the magnetic force becomes 



9 2 8 . Now - cannot be greater than unity ; so the greatest 



value of the force is &>/3x 10 8 . If the sphere were attached 

 to an arm of such length that it described a metre in each 

 complete revolution of the arm, and if the arm were to make 

 100 revolutions a second, co would equal 10 4 , and the greatest 

 magnetic force would be 1/3 x 10 4 = '000033. Prof. Rowland, 

 in his experiments on the magnetic effects of electric convec- 

 tion, measured a magnetic force only about one tenth of this. 



