154 HELMHOLTZ ON THE CONSERVATION OF FORCE. 



When the solderings are of different temperatures, it follows 

 from equations (1) and (2), that 



that is to say, with the same intensity of current both the force 

 which generates and which absorbs the heat increases with the 

 temperature, in the same proportion as the electromotive force. 

 I am thus far unacquainted with any quantitative experiments 

 with which either of the inferences might be compared. 



VI. Force-equivalent of Magnetism and Electro-magnetism. 



Magnetism. — Through the attractive and repulsive forces 

 which a magnet exerts upon other magnets, or upon soft iron, 

 it is capable of generating a certain vis viva. As the phaenomena 

 of magnetic attraction may be completely deduced from the 

 assumption of two fluids which attract or repel in the inverse 

 ratio of the square of the distance, it follows, without going 

 further than the deduction made at the commencement of this 

 memoir, that in the motions of magnetic bodies the conservation 

 of force must take place. For the sake of the following theory 

 of induction, we must consider a little more closely the laws of 

 these motions. 



1 . Let m^ and m^^ be two magnetic elements, referred to a unit 

 which, at the distance 1, repels an equal quantity of a similar 

 magnetism with the force 1. Let the opposed magnetisms 

 be distinguished by opposite signs, and let r be the distance 

 between m^ and m^^ the intensity of their central force is 



the gain of vis viva during the passage from an infinite distance 



to r IS ' — ^'. 



r 



2. Let US call this quantity the potential of the two elements, 



and extending the term potential to magnetic bodies as in the 



case of electricity, we obtain the gain in vis viva during the 



motion of two bodies whose magnetism does not change, for 



instance of steel magnets, when we subtract from the potential 



at the end of the motion its value at the commencement of the 



motion. The gain of vis viva during the motion of magnetic 



