34 COMPARISON OF RESISTANCES. 



The coefficient A^ of e^ in the value of i\ contains then simply 

 the combinations pi and pi together of conductors which 

 leave the simple circuits of which r^ and r^ form part at the 

 same time. The coefficient A'f, in the expression of / 2 obviously 

 contains the same combinations. 



Moreover, these combinations are respectively of the same sign, 

 for in any residual circuit, the portion of the current t\ which 

 arises from e 2 is of the same sign as that portion of the current 

 which results from <?j ; hence AJ = A\. 



Thus when a network of linear conductors is complete, the 

 intensity of the current sent through a branch r lt by the electro- 

 motive force of another branch r 2 , is equal to that of the current 

 which will be sent through the conductor r 2 by the same electro- 

 motive force placed at r r 



In particular, if the coefficients AJ and AJ are zero, the current 

 in each of the conductors r^ or r 2 is independent of the electro- 

 motive forces which the other contains. These two conductors, 

 as well as the corresponding sides of the network, are then said to 

 be conjugate. 



The electrical conditions of two conjugate conductors are 

 independent of each other ; if we change, for example, the electro- 

 motive force, or the resistance of the conductor r lt or even if 

 the system is suppressed, the general distribution of the currents 

 in the network is modified, but the current in the conductor r 2 

 does not change, at any rate if the regime is stationary. 



In the case of a variable regime, on the contrary, changes in 

 the intensity of the current in the other branches give rise to 

 electromotive forces of induction, the reaction of which is felt on 

 the conjugate conductor of that which has been modified. 



946. We ruay mention here a remarkable property which has 

 been demonstrated by M. Thevenin.* In any system of conductors 

 traversed by permanent currents, let us consider two points A 

 and A' the potentials of which are V and V. If these two points 

 are connected by a new conductor r, the difference of potential 

 tends to produce a current in this conductor, but the original 

 equilibrium is restored by introducing at the same time an electro- 

 motive force - E in the contrary direction equal to V - V^ in 

 absolute value, and the current is zero in the conductor r. If p 

 is the total resistance of the original system between the points A 

 and A', if we now introduce in the conductor r an electromotive 



* THEVENIN. Comptes rendus, Vol. XCVIL, p. 159. 1883. 



