Electric Currents in Networks of Conductors. 241 



tribution of the currents in, and the resistance of, the network 

 will be affected by them during the time taken by the cur- 

 rents to become steady. 



In those pages of his Treatise in which Clerk Maxwell 

 worked out his splendid dynamical theory of electromagnetism, 

 he starts with the explanation of the methods Lagrange and 

 Hamilton employed to bring pure dynamics under the power 

 of analysis, and the results of Lagrange are embodied in the 

 equation 



X=- d -- d l 



~dt fa dx> 



in which X is the impressed force tending to increase the 

 variable %, and T denotes the visible energy of the system of 

 bodies at that instant. 



This equation establishes a relation between the kinetic 

 energy of a material system at any instant, the force im- 

 pressed upon it in a certain direction, and a quantity called a 

 variable, which expresses the state or condition of the system 

 with respect to that direction. Maxwell, by a process of ex- 

 traordinary ingenuity, extended this reasoning from materio- 

 motive forces, masses, velocities, and kinetic energies of gross 

 matter to the electromotive forces, quantities, currents, and 

 electrokinetic energies of electrical matter, and in so doing- 

 obtained a similar equation of great generality for attacking 

 electrical problems. 



In the electrical problem the variables are the quantities of 

 electricity x, y, z, &c. which have from the beginning of the 

 epoch flowed past any points, and the analogues of the velo- 

 cities are the fluxes of these, x, y, 0, &c, or the currents. 



The electrokinetic energy is measured by the quadratic 

 expression 



T=^L 1 ^i + iL 2 a? 2 + . . . M 12 #i# 2 + , &c, 



where the coefficients L x , L 2 , M 12 are functions of the geome- 

 trical variables, but into which the electrical variables do not 

 enter. 



If now, as before, x ly x 2 represent the imaginary like-directed 

 currents round each mesh of a network, in which currents 

 are beginning to flow, then 



dT , dT k 

 — r- and — r , <fcc. 

 dx\ dx 2 



represent the electrokinetic momenta of these circuits. De- 

 note them by p ly p 2 , &c, and accordingly 



