THE 

 LONDON, EDINBURGH and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE, 



[FOURTH SERIES.] 



JUNE 1857. 



LIV. On the Motion of Electricity in Wires, 



By G. KiRCHHOFF*. 



I HAVE attempted to establish a general theory of the motion 

 of electricity in an infinitely thin wire, by assuming- certain 

 facts which are observed in constant currents, and in currents 

 whose intensity alters but slowly, to be universally valid. I will 

 here develope this theory, and show its application to some cases 

 of a simple nature. 



I picture to myself a homogeneous wire possessing the same 

 thickness throughout and of circular cross section. In the axis of 

 this wire I take a fixed point and a variable one; the portion of the 

 axis between both points I call s. Through the changeable point 

 I permit a transverse section to pass, and call the polar coordi- 

 nates of a point of this section, with reference to a system of or- 

 dinates whose origin is the centre, p andA|r. I will calculate the 

 electromotive force which tends to separate, in the direction of 

 the length of the wire, the two electricities in the vicinity of the 

 point determined by s, p and -yjr. This force is partly derived 

 from free electricity, partly from the induction which takes place 

 in consequence of the alteration of the strength of the current in 

 all parts of the wire. With regard to the first portion, we may 

 make use of the electrostatic law of Coulomb. Let V be the 

 potential of the free electricity with reference to the point under 

 consideration ; that is to say, the sum of all the single quantities 

 of free electricity, each divided by its distance from the point. 

 The quantities of electricity are here to be referred to a mecha- 

 nical unit ; the unit of electricity shall be that which, acting 

 * Translated from Poggendorffs Annalen, 1857, No. 2. 



Phil. Mag. S. 4. Vol. 13. No. 88. June 1857. 2 E 



