292 



THE ELECTRIC TELEGRAPH. 



, r 2 r 3 = 0. 

 r, r a 



This is, therefore, the relation which must be established 

 between the four sides r l9 r 2 , r 3 , and r 4 before the condition 

 can be fulfilled that the intensity of the current in the bridge 

 a b is null. 



The way in which this system is applied for the measure- 

 ment of resistances will be explained directly. Before we 

 come to that, however, there is a case worth considering 

 which often occurs in testing cables or conductors whose 

 ends have different temperatures that of a foreign electro- 

 motive force in one of the branches of the system. With 

 cables, this arises mostly from earth currents or from electro- 

 motive force between the earth plates ; in other instances, 

 from thermo-currents. 



Let the four resistances A, B, C, and D (Fig. 138) be 

 adjusted so that the current in the balance a b is inappre- 



ciable, while the inten- 

 sities of the currents due 

 to the battery E, inserted 

 between the points c and 

 d in the several branches, 

 are increased or dimi- 

 nished by the current of 

 the element, E t , set up in 

 Fig. 138. the side C. If the inten- 



sities of the currents in the circuits under these conditions 

 are a, |3, 7, , and c, and R the resistance of the battery 

 between c and d, 



a y = 



ft I = 



y 3 = 



Aa 3(3=0 



C y D ft = E' 



2) 

 3) 

 4) 

 5) 

 6) 



By eliminating (3, S, and c with the aid of 1), 2), 3), and 4), 



