Intelligence and Miscellaneous Articles. 483 



current of the intensity m in absolute measure, ds would be acted 

 on by a certain force from the pole P. Let y be the component of 

 that force along the direction of the motion ; the elemental law 

 given by Neumann is the following : — 



eds=— evy, 



v designating the velocity of the element ds, and e being a constant. 

 Let us consider what takes place in the time dt for the entire 

 circuit. Let E be the resistance ; the elementary current produced 

 will be, according to Ohm's law, 



i dt= — — Luydt, 

 the symbol 2 extending to the entire circuit B. 



But we have v = -j~, dw representing the element of the trajec- 

 tory of ds ; therefore 



which gives the following enunciation : — 



The differential current is equal, except a factor, to the sum of the 

 elementary work of the forces to which the pole is subjected on the part 

 of the elements of a current 1 supposed to traverse the circuit B. 



Integrating between the corresponding limits, we get 



Zydw (A) 



fiX.-jf 



It follows that, for a given circuit, the first impulse of the galva- 

 nometer is proportional to the work which would be necessary to 

 produce the relative motion of the pole and the circuit supposed to 

 be traversed by the current 1. 



If we wish to pass to the case of the true magnet, it suffices to 

 consider any number of poles ; and it is seen, by a series of sum- 

 mations, that the theorem applies in the case of any distribution as 

 in that of a single pole. 



We have now to estimate the work as a function of the data of 

 experiment. 



Let Y be the potential, relative to the circuit, of any pole P, and 

 jj, the magnetism of the pole ; the work in order that the system may 

 pass from one state to the other, taking into account this pole only, 

 is equal to the corresponding variation of the quantity /jY ; let it 

 be fx(V 1 — V ). "We shall therefore have, by substitution in equa- 

 tion (A), 



Y idt =-k 



-^ M Y-Y ), 



the summation here extending to all the poles of the arrangement*. 



* This equation agrees with the calculation given by G. Wiedemann, /. c. 

 vol. hi. p. 80. 



