EXTRA CURRENT. 529 



The integral of this equation determines the induced current 

 which traverses the two branches. Observing that the current i is 

 defined by the permanent state, we shall have for the time t' after 

 opening the circuit, 



- e 



P 2 



This current in the rectilinear branch is in the opposite direction 

 to the primitive current. 



The total quantity of induced electricity is 



EL r' 



m - 



If the needle of a galvanometer placed on a rectilinear wire abuts 

 against an obstacle which prevents it from obeying the permanent 

 current, this needle will be driven in the opposite direction by 

 the induction current, when the principal circuit is opened. This 

 method was used by Faraday. 



550. If we regard the problem in all its most general forms, 

 we may propose to determine the division of the currents in the 

 cases in which the conductor is made up of a network of wires 

 forming polygons of any given form. 



Let us suppose that a portion of the network is made up of a 

 polygon whose sides are A 1? A 2 , A 3 ..... Let z\, / 2 , z 3 ---- be the 

 intensities at a given moment of the currents which traverse the 

 various branches; r lt r 2 , /* 3 .... their resistances; Ej, E 2 , E 3 the 

 electromotive forces contained in each of them; L 15 L 2 , L 3 ---- 

 their coefficients of self-induction; M 1>2 , M 1-3 , M 23 ... the co- 

 efficients of mutual induction of each branch on another part 

 of the circuit, in which the intensity of the current is /'. For 

 each side of the polygon we have an equation, such as the 

 following, relative to the side A l : 



from which is deduced for the contour of this polygon, 



M M 



