276 Dr. R. A. Lehfeldt on the 



motion. Another charge e 2 is located at the point (r, 0, 0), 

 and has the velocity V 2 with components (u 2 , v 2 , w 2 ). Then 

 the first charge exerts on the second a force F, which has 

 components in the x and y directions, but not in z } and its 

 components are 



-r, _ _ e A i\e 2 v 2 Tj , _ e Y v x p 2 u 2 



where the charges are expressed in electrostatic units and c is 

 the velocity of light. The reaction exerted by e 2 on e 1 is not 

 equal and opposite to this, because the momentum of the field 

 must be taken into account if we wish to apply Newton's laws 

 of motion. That is of no consequence for the present purpose, 

 however, as the laws just stated enable one to calculate the 

 forces and hence the motions, whether of the conductors as a 

 whole or of the electrical charges within them. 



Now it is of assistance to regard this action as taking place 

 in two stages, and say that the movement of the first charge 

 produces a magnetic field, and that this field acts on the 

 second charge, causing a mechanical force. 



Calling the magnetic field H, we may define it as a vector 

 of the value 



XT _ Wl 

 J-J-a? — k- 



in the direction of x and without components in the other 

 directions, and can then say that the field H acts on the 

 charge e 2 moving with velocity (u 2 v 2 iv 2 ) with the force 

 components 



F r = + ?f^ and F.= -§^, 



c c 



i. e. with a resultant force e ^ ™ 2 Vt * perpendicular to the 



c 

 plane containing the field and the velocity, and proportional 

 to their vector product. 



The signs occurring in the above equations may be deter- 

 mined by the well-known " right-hand screw " and " three- 

 finger " rules. 



It is, of course, open to dispute whether the above state- 

 ments form a complete account of the action of one moving 

 electron on another, since that action is not directly accessible 

 to experiments ; it might be proposed to employ the " ration- 

 alized current element,''' consisting of the system of lines of 

 force produced by a moving electric charge, in addition to 

 the charge itself. But again this is unnecessary here, as we 



