THE 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[FIFTH SERIES.] 



SEPTEMBER 1885. 



XXVII. Problems on the Distribution of Electric Current 9 in 

 Networks of Conductors treated by the Method of Maxwell. 

 By J. A. Fleming, M.A., D.Sc. (Lond.), Fellow of St. 

 Johns College, Cambridge, Professor of Electrical Tech- 

 nology in University College, London*. 



[Plates VI. & VIL] 

 §1. FF any number of points in a plane be joined together 

 -S- by linear conductors such as metallic wires, we 

 have an arrangement of conductors which is called a Network. 

 If at any point in the network a current of electricity be 

 allowed to flow in and is drained off at some other point by 

 conductors, called respectively the anode and kathode con- 

 ductor, then, after a short period, depending on the self and 

 mutual induction coefficients of the various conductors, the 

 total quantity of electricity arriving by the anode will distri- 

 bute itself throughout the network and settle down into a 

 steady flow. When this is the case there is a certain definite 

 difference of potential between the anode or source-point and 

 the kathode or sink-point, and there is also a certain definite 

 and constant strength of current in the anode conductor and 

 in every mesh or branch of the network. Call a and 7 the 

 potentials of these source- and sink-points, and x the strength 

 of the current in the anode lead, that is the whole quantity 

 of electricity flowing per second through the network, then 

 (7— a)/x measures the resistance of the network. We can 

 imagine the network replaced by a single linear conductor or 

 wire of such sort that if the anode and kathode conductors 



* Communicated by the Physical Society : read June 27, 1885. 

 Phil. Mag. S. 5. Vol. 20. No. 124. Sept. 1885. R 



