Middle of the Nineteenth Century. 223 



in the earlier part* of the memoir, he calculated the induced 

 currents in various particular cases. 



But having arrived at the formulae in this way, Neumann 

 noticedf a peculiarity in them which suggested a totally 

 different method of treating the subject. In fact, on examining 

 the expression for the current induced in a circuit which is in 

 motion in the field due to a magnet, it appeared that this 

 induced current depends only on the alteration caused by the 

 motion in the value of a certain function ; and, moreover, that 

 this function is no other than the potential of the ponderomotive 

 forces which, according to Ampere's theory, act between the 

 circuit, supposed traversed by unit current, and the magnet. 



Accordingly, Neumann now proposed to reconstruct his 

 theory by taking this potential function as the foundation. 



The nature of Neumann's potential, and its connexion 

 with Faraday's theory, will be understood from the following 

 considerations : 



The potential energy of a magnetic molecule M in a field 

 of magnetic intensity B is (B . M) ; and therefore the potential 

 energy of a current i flowing in a circuit s in this field is 



where S denotes a diaphragm bounded by the circuit s ; as is 

 seen at once on replacing the circuit by its equivalent magnetic 

 shell S. If the field B be produced by a current i' flowing in a 

 circuit s', we have, by the formula of Biot and Savart, 



1 *' 



curl 



* 1-8. It may be remarked that Neumann, in making use of Ohm's law, 

 was (like everyone else at this time) unaware of the identity of electroscopic 

 force with electrostatic potential. t 9. 



