Mr maxwell, ON FARADAY'S LINES OF FORCE, 58 



in the same circuit. There is therefore an electrical effect which is equal at every section of the 

 circuit. If we conceive of the conductor as the channel along which a fluid is constrained to 

 move, then the quantity of fluid transmitted by each section will be the same, and we may 

 define the quantity of an electric current to be the quantity of electricity which passes across 

 a complete section of the current in unit of time. We may for the present measure quantity 

 of electricity by the quantity of water which it would decompose in unit of time. 



In order to express mathematically the electrical currents in any conductor, we must have 

 a definition, not only of the entire flow across a complete section, but also of the flow at a given 

 point in a given direction. 



Def. The quantity of a current at a given point and in a given direction is measured, 

 when uniform, by the quantity of electricity which flows across unit of area taken at that point 

 perpendicular to the given direction, and when variable by the quantity which would flow 

 across this area, supposing the flow uniformly the same as at the given point. 



In the following investigation, the quantity of electric current at the point (.ryar) estimated 

 in the directions of the axes x, y, x respectively will be denoted by a^ h.^ Cj. 



The quantity of electricity which flows in unit of time through the elementary area dS 



= dS {la.^ + mh^ + nc^, 



where Imn are the direction-cosines of the normal to dS. 



This flow of electricity at any point of a conductor is due to the electro-motive forces 

 which act at that point. These may be either external or internal. 



External electro-motive forces arise either from the relative motion of currents and 

 magnets, or from changes in their intensity, or from other causes acting at a distance. 



Internal electro-motive forces arise principally from difference of electric tension at points of 

 the conductor in the immediate neighbourhood of the point in question. The other causes are 

 variations of cnemical composition or of temperature in contiguous parts of the conductor. 



Let P2 represent the electric tension at any point, and X2 Y^ Z-^ the sums of the parts of 

 all the electro-motive forces arising from other causes resolved parallel to the co-ordinate axes, 

 then if aj, ^2 72 be the effective electro-motive forces 



Oj = X2 — , 

 ax 



dy 



ry dp., 



1- (A) 



dz 



Now the quantity of the current depends on the electro-motive force and on the resistance 

 of the medium. If the resistance of the medium be uniform in all directions and equal to k.^, 



as = Asffla, /Sa = ^2625 72 = hc» (B) 



but if the resistance be different in different directions, the law will be more complicated. 



These quantities 02 (i^ 72 may be considered as representing the intensity of the electric 

 action in the directions of xyz. 



