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



are applied to its ends, the difference of potentials at the ends 

 of this simple conductor and the strength of the current flow- 

 ing through it have the same numerical values 7, u, and on. 

 The resistance of this single conductor is then the same as 

 that of the complex network. 



The resistance of the network is obviously some function 

 of the resistances of the separate conductors or wires which 

 compose it, and is capable of being calculated from them. 

 Experimentally, the resistance of a complicated network would 

 best be determined by the measurement of the current- 

 strength in the anode lead and the difference of potential 

 between the source and the sink. Theoretically, it is in- 

 teresting to examine the law of distribution of currents in a 

 network, and to reduce to a function of the separate resist- 

 ances the total resistance of the whole network between any 

 two points. 



§ 2. In his larger Treatise on Electricity, Clerk Maxwell 

 has treated the general case to determine the differences of 

 potentials and the currents in a linear system of n points con- 

 nected together in pairs by % n(n—>l) linear conductors*, and 



has shown how to form the linear equations, the solution of 

 which gives the condition of the network when given electro- 

 motive forces acting along some or all of the branches have 

 established steady currents in them. 



The usual method of obtaining a solution for the distribu- 

 tion of currents is the application of Ohm's law round the 

 everal currents of the network, controlled by the condition 

 of continuity that there is no creation nor destruction of elec- 

 tricity at the junctions. 



Since the publication of the first edition of his Treatise, 

 Maxwell reduced these two sets of equations to one set by 

 the simple device of regarding the real currents in the meshes 

 of the network as the differences of imaginary currents round 

 each cycle or mesh of the network, all directed in the same 

 direction, and thus obtained by the application of Ohm's law 

 a single set of linear equations, the solution of which gives 

 the required currents in each branch. Maxwell's method is 

 as follows f: — If we have p points in space and join them 

 together by lines, the least number of lines which will con- 



* < A Treatise on Electricity and Magnetism,' 2nd edition, Vol. i. § 280 

 and § .'347. 



t This method was first given by Clerk Maxwell in his last course of 

 University lectures. It is alluded to in the second edition of his larger 

 Treatise and in the Appendix of his smaller Treatise by their respective 

 editors, Mr. W. D. Niven and Professor Garnett, to whom it was com- 

 municated by the present writer. 



