1891.] On the Theory of Electrodynamics. 529 



The final result is 



T = \d-r (Fx 



where F, = F+, G, = G+, H t = H+ 



a* a?/ az 



H -I 



To obtain the components PQR of the electric force we assume, 

 following F. E. Neumann and von Helmholtz, that the principle 

 involved in Lena's law is applicable to the element as well as to the 

 circuit as a whole. This is the same principle as flows from Maxwell's 

 dynamical theory, and is justified, if we assume that T is the energy 

 function of an actual dynamical system. To the kinetic part of the 

 electric force so determined the electrostatic part must be added, 

 giving in all the components 



p <ZFj d V .". dGi d\ -p eZHj d\ 



dt dx dt dy dt dz 



The conduction current is given by 



a (!, V lt M7j) = (P, Q, R), 



where a is the specific resistance. The total current is 



*-L v^ 

 dt 1 di 



where (/, g, /<>= (P, Q, R). 



The vector potential FGH is connected by definition above with 

 nvw by the equations of potential 



V 2 (F,G,H) = -4,r( W , V ,;); 

 while the characteristic equation of V is 



/df dg dh 

 \dx dy 



The equations of electric propagation are involved in these results. 



