82 Prof. G. KirchhofF on the Measuring 



If from the resistance of a wire (determined by one or the 

 other of the methods mentioned) we wish to ascertain its con- 

 ductivity, and an error of the order of the ratio of the thick- 

 ness of the wire to its length is inadmissible, the currents at 

 the place of junction of three branches of the conducting 

 system must not be regarded as linear ; therefore the theory 

 of current-distribution in non-linear conductors must be em- 

 ployed. 



Of the resistance of a non- linear conductor (taken strictly) 

 one can only speak on the assumption that the part of its sur- 

 face through which electricity flows consists of two surfaces, 

 within each of which the potential is constant. The difference 

 of the values of the potential in these two electrode surfaces 

 (as they may be called), divided by the amount of electricity 

 which flows through the one or the other in the unit of time, 

 is then a constant of the conductor, which is even called its 

 resistance. We must here take into view a more complicated 

 case — namely, that instead of two electrode surfaces more of 

 them are present, of which, however, each is again a surface 

 of equal potential. 



Let n be the number of electrode-surfaces, Pj, P 2 , . . . P„ the 

 potential- values in them, and J 1} J 2 , . . . J n the quantities of 

 electricity which flow through them in unit time into the con- 

 ductor. If these intensities, between which the relation 



Ji + J 2 + ... + J„ = 

 must subsist, be given, the quantities P up to an additive con- 

 stant are determined ; namely, calling this c, 



P x = c + a n J ± + a 12 J 2 + . . . + a ln J n , 



P 2 = C + «21 Jl + a 22^2 + • . • + a 2n J n , 

 Prc= C + a n iJi + Cl n 20 2 + • • • + ttnn^ n j 



where the quantities a designate constants of the conductor — 

 constants which, however, by the way, are not independent of 



n( n ~— 1 ) 

 one another, but can be reduced to -^ — - reciprocally inde- 

 pendent quantities. 



Let it now be assumed that n = 4, that electrode surfaces 1 

 'and 4 are connected to the poles of a battery, and surfaces 2 

 and 3 to the ends of a wire (one of the wires of a differential 



pared a similar method with Thomson's and found it superior to the latter ; 

 the differential galvanometei used by him, however, was not so arranged 

 that the windings could be displaced ; and in consequence of this he had 

 to forego some essential advantages offered by the method recommended 

 in the text. 



