242 Dr. J. A. Fleming on the Distribution of 



Pi = L 1 a? 1 + M 12 a? 2 , &c. 



If E is the impressed electromotive force in the circuit or 

 mesh arising from some cause, battery, thermopile, dynamo 

 machine, &c, which would produce a current independently 

 of magneto-induction, then, if R be the total resistance 



round the mesh, and x the cyclic current, Ra? is the electro- 

 motive force required to overcome the resistance of the circuit, 

 and B — R# is the electromotive force available for changing 

 the electric momentum of the circuit. 

 Accordingly, by Lagrange's equation, 



dt dx' 



where T is the electrokinetic energy. As T does not contain x> 

 that is to say it is a function of currents, not quantities, the 

 last term disappears, and we have 



. d dT 

 Jii — iia? -j. — -, 



or 



dt dx 



The electromotive force is therefore expended in two 

 things : first, overcoming the resistance R ; and, secondly, 

 increasing the electromagnetic momentum p. Now if there 

 is no electromagnetic momentum, we have seen that the 

 cyclic equations are of the form 



where H is the dissipation function of the system, and W is 

 the acting electromotive force concerned in overcoming the 

 resistance of the circuit. 



• . d& 



If, then, we substitute for R# in equation J— -, we have 



dx 

 as the general equation for the electromotive force in any 

 mesh or cycle x, 



d <JT ,<JH 



<M dx dx 



This most important equation is Maxwell's general equation 

 for determining the current x in any circuit when the dis- 

 sipation function, and kinetic energy, and impressed electro- 



