354 The Followers of Maxwell. 



Ampere's reasoning rests on the assumption that the mag- 

 netic field produced by a current is in all respects of the same 

 nature as that produced by a magnet ; in other words, that only 

 one land of magnetic force exists. This principle of the " unity 

 of magnetic force" Hertz now proposed to supplement by assert- 

 ing that the electric force generated by a changing magnetic 

 field is identical in nature with the electric force due to electro- 

 static charges; this second principle he called the "unity of 

 electric force." Suppose, then, that a system of electric currents 

 i exists in otherwise empty space. According to the older 

 theory, these currents give rise to a vector-potential a, , equal 

 to Pot i ;* and the magnetic force H t is the curl of a t : while 

 the electric force E! at any point in the field, produced by the 

 variation of the currents, is ai. 



It is now assumed that the electric force so produced is 

 indistinguishable from the electric force which would be set 

 up by electrostatic charges, and therefore that the system of 

 varying currents exerts ponderomobive forces on electrostatic 

 charges ; the principle of action and reaction then requires that 

 electrostatic charges should exert ponderomotive forces on a 

 system of varying currents, and consequently (again appealing 

 to the principle of the unity of electric force) that two systems 

 of varying currents should exert on each other ponderomotive 

 forces due to the variations. 



But just as Helmholtz,f by aid of the principle of conser- 

 vation of energy, deduced the existence of an electromotive 

 force of induction from the existence of the ponderomotive 

 forces between electric currents (Le. variable electric systems), 

 so from the existence of ponderomotive forces between variable 

 systems of currents (i.e. variable magnetic systems) we may 

 infer that variations in the rate of change of a variable magnetic 

 system give rise to induced magnetic forces in the surrounding 

 space. The analytical formulae which determine these forces 



* a = Pot /3 is used to denote the solution of the equation V'a + 47r = 0. 

 fCf. p. 243. 



