434 Prof. A. Gray : Notes on 



Thus the batteries furnish in time dt a quantity of energy, 

 over and above that converted into heat, equal to the incre- 

 ment of electrokinetic energy and the work done by the electro- 

 magnetic forces, taken together. 



Let us now consider the effect of a change of configuration 

 of the battery circuits, without change of the currents in 

 these circuits, that is allow the steady state to have been 

 resumed before the effect on the magnets is estimated. Thus 

 in dT e we have no terms depending on dy u dy 2 > • •• • But 

 inasmuch as the mutual inductances between each of the 

 battery circuits and the various molecular circuits are, we 

 suppose, altered by change of configuration, and there is 

 electromotive force of induction but no resistance in any 

 molecular circuit, we have, not merely in the present case 

 but always, 



|S{L' 7 '+2(M 7 )}=0 (9) 



Here one summation, the inner, is taken for all the battery 

 circuits (carrying current 7) and the other for all the mole- 

 cular circuits. 



If the currents 7 be of moderate amount only very small 

 changes, if any, are produced by the changes of configuration 

 — this is matter of observation. In considering, however,, 

 the influence of the presence of the magnets on the dynamical 

 value of the system, we have to take the effect, not of moving, 

 the conductors in the field, but of opening the circuits while 

 fixed in position. When this is done the effect if any of the 

 annulment of the terms XX (M77') is to be traced in change 

 of the magnets. For when the circuits are opened the tubes 

 of magnetic induction through the circuits produced by the 

 magnets are not changed (except in so far as the magnets 

 are changed by the withdrawal of the tubes thrust through 

 the molecular circuits by the battery circuits), they remain 

 in situ, none of them crosses the wires. On the other hand, 

 the tubes which the battery circuits have linked through the 

 molecular circuits shrink in and disappear, and cross these 

 latter circuits in doing so. On this view the effect of the 

 evanescence of the terms XX (M77'), in these circumstances, 

 ought to be looked for in the magnets. 



From (9) we obtain by integration 



2{LV+S(M 7 )}=S(LV), 



where y ' denotes the current in a molecular circuit when 

 the currents 7 have ceased to exist. 



If practically no change takes place in the molecular 



