194 



PROPAGATION OF ELECTRICITY. 



of the two conductors between the points A and B. This is 

 obviously a general relation. 



Thus the resistance of a series of successive cylindrical conductors 

 is the sum of the resistances of all the conductors. 



In conclusion, let us take the case of a conductor of any given 

 shape terminated at its ends by equipotential surfaces kept at 

 potentials V 1 and V 2 ; the current is proportional to the difference 

 v i ~ V 2 f tne potentials, and the number by which this difference 

 must be divided to give the strength of the current represents the 

 resistance of the conductor. The number thus obtained is the 

 resistance of the cylindrical conductor, which for the same difference 

 of potential would give the same current. 



208. KIRCHHOFF'S LAWS. Let us suppose linear conductors, of 

 various materials and different sections, to be joined to each other 

 in a complicated manner, the division of the current among these 

 various conductors must satisfy the two following conditions, which 

 follow directly from Ohm's law. 



Fig. 51. 



i st. If several conductors terminate at the same point, the sum of 

 the currents, counted from this point, is zero. 



For, since there can be no accumulation of electricity at the point 

 in question, the quantity of electricity brought by one set of con- 

 ductors must be equal to that which passes away by the others in the 

 same time; so that if we give the positive sign to the currents 

 proceeding towards the point, and the negative sign to those which 

 pass away, we must have 



(3) 3*/-o. 



2nd. If several conductors form a closed polygon, the sum of the 

 products of the resistance of each conductor, by the current which 

 traverses it, is zero. 



Imagine a series of conductors of resistances r v r^ r^, r n , 



which form the successive sides of a closed polygon (Fig. 51); let 



