of Relativity in Electromagnet ism. 415 



in relative motion. The following point laws are partly 

 known from the Maxwellian theory. They can be easily 

 verified and found in agreement with the! differential 

 equations. 



When two electrons move relatively to each other the 

 passive one is acted upon by the force 



v 1 q 2 v- 



^l-^sia'y)* 



(1) 



Here r x si°'nifies a unit radius vector drawn from the active 



to the passive electron ; q is the charge of the electron, y is 



the angle which the direction of motion makes with r, u is 



l-i Vjl 

 the velocity of motion, and s = l— -j. 



Of two moving fictitious magnet-poles of unit strength the 

 passive one is acted upon by the force 



r* I 1 £ sin 2 7 V 



Further. when an electron and a unit magnet-pole are 

 moving relatively to each other, the force on the passive 

 electron is 



sq 



whereas the force on the passive magnet-pole is 



F = VriU— ■? Ti. . . . (4) 



r 





Here as elsewhere the radius vector is always drawn to 

 the passive system. JXow an inspection of these four funda- 

 mental equations shows that the choice of the passive one of the 

 two systems in relative motion is arbitrary; i. e., a moving 

 magnetic pole exerts exactly the same force on a " resting " 

 electron as a moving electron on a " resting " pole, and we 

 can at once conclude that with any distribution of magnetic 

 and electric masses in the two systems, the force exerted by 

 A on B is the same as that exerted by B on A. This proves 

 the validity of the third law of Newton and implies the 

 principle of relativity. 



