158 HELMHOLTZ ON THE CONSERVATION OF FORCE. 



the latter being that in which the above unit of current developes 

 the unit of heat in the unit of time. The same law is deduced by 



Neumann, 1. c. § 9, only instead of - he has an undetermined 



constant e. 



6. When a magnet moves under the influence of a conductor, 

 towards which its potential for the unit of current is (f>, and of a 

 piece of iron magnetized by this conductor, towards which its 

 potential for the magnetism excited by the unit of current is p^, 

 we have then, as before, 



dt at 

 hence 



^ _ a\dt dt J 

 R 

 The electromotive force of the induced current due to the 

 presence of the piece of iron is therefore 



a dt' 

 If in the electro-magnet the same distribution of the magnetism 

 be effected by the current w, as by the approximated magnet, 

 then, in accordance with what has been stated in No. 4, its po- 

 tential w% towards the magnet must be equal to its potential 

 towards the conducting wire nV, when V denotes the same for 

 the unit of current: therefore % = V. Hence when an induced 

 current is excited by means of the magnetization of the piece of 

 iron by the magnet, the electromotive force is 



ldx_ IdV 



adt" a dt' 

 and, as in No. 7 we have the whole current 



/> 



ldt=^ 



R 



where V^ and V^, are the potentials of the magnetized iron 

 towards the conducting wire before and after magnetization. 

 Neumann deduces this law from its analogy with the foregoing 

 case. .. 



7. When an electro-magnet has become magnetic under the 

 influence of a current, through the induced current heat is lost ; 



