126 INCREASE OF INERTIA [CH. XIL 



this second method of treatment is not only simpler 

 but that it is adequate to existing knowledge, enabling 

 numerical results to be obtained which are singularly 

 concordant with experimentally measured results. 



In any case an indication of the mode of attack 

 can be suggested thus : 



The magnetic force due to motion is proportional 

 to the speed of the motion. The secondary electro- 

 static force due to the motion of this magnetic field 

 is likewise proportional to the same speed.* Hence 

 the disturbance of the original uniform electrostatic 

 field will be of the second order, u 2 /v 2 ; and when- 



*The value of the magnetic force at any point P, with polar 

 coordinates r f 6, due to a charge e flying with speed U, is 



TI _ 



and is in rings round the line of motion u. It is not shown in the 

 diagram because it is perpendicular to the paper, through P. 



Q 



FIG. 17. 



The electric force generated or induced by motion across this 

 magnetic field which is necessarily at right angles to the direction of 

 motion is fiRu ; and in this case is therefore equal to 



This is the secondary or induced E.M.F., to be superposed at every 

 point on the primary or direct electric force of the charge itself along 

 the line eP, namely e/Kr 2 ; and it is in the direction PQ, being perpen- 

 dicular both to the magnetic field and to the motion. So the ratio of 

 the induced to the original E.M.F., at every point in a direction 0, 

 reckoned from the charge and axis of motion, is 



sin 0, which equals sin 0. 



In consequence of this the original direction of the stationary 

 electric field, eP, is displaced or tilted into a position such as eQ. 



