HELMHOLTZ ON THE CONSERVATION OF FORCE. 15/ 



according to the notation before made use of, these are, Aldt 

 in units of heat, or ahldt in mechanical units, where a is the 

 mechanical equivalent of the unit of heat. The vis viva gene- 

 rated in the path of the current is al^Rdty that gained by the 



dY 

 magnet is l—rrdt, where V represents its potential towards the 



CLt 



conductor through which the unit of current passes. Hence 



aMdt=al^Kdt + l^,dt, 

 consequently 



A IT 



^_ a dt 



R 



1 ^V 

 We can distinguish the quantity — -7- as a new electromotive 



tZ CLv 



force, that of the induced current. It always acts against that 

 which moves the magnet in the direction which it follows, or 

 which would increase its velocity. As this force is independent 

 of the intensity of the current, it must remain the same, when 

 before the motion of the magnet no current existed. 



If the intensity be changeable, the whole induced current 

 during a certain time is 



where V^ denotes the potential at the beginning, and V^^ at the 

 end of the motion. If the magnet comes from a very great 

 distance, we have 



1 



/ 



Ut=-^, 



independent of the route or the velocity of the magnet. 



We can express the law thus : — The entire electromotive force 

 of the induced current, generated by a change of position of a 

 magnet relative to a closed conductor, is equal to the change which 

 thereby takes place in the potential of the magnet towards the 



conductor, when the latter is traversed by the current . The 



•^ a 



unit of the electromotive force is here regarded as that by which 



the arbitrary unit of current is generated in the unit of resistance. 



