378 THE ELECTRIC TELEGRAPH. 



and, when the currents of the bridge system are balanced, 



7" = K + * 

 From these two equations the distances are 



expressed in units of resistance. These values are reducible 

 to units of length by dividing them by the average resist- 

 ance n of one knot ; and they become L x and L y knots 

 respectively, 



d L , E + ~ 



(p+r)n 



Generally, the branch resistances r and p may be made 

 equal to each other, facilitating the calculation with the above 

 formulae, which then become 



Z-K l + K, 



*==__ and y =--- 



in resistance, or 



,.-=* an, *-*+??;' 1 



in knots. 



Another way of doing the same thing is by making the 

 resistance between a and b some power of 10, and inserting 

 in the side a d a set of resistance-coils, R. The ends of the 

 cable are connected immediately to the points b and d y which 

 are joined also by the ends of the galvanometer-coil G, as 

 before ; x and y being the two ends of the cable from the 

 fault in opposite directions, and no current deflecting the 

 needle of Gr on closing the battery circuit, we have the bridge 

 equation 



JL = = x ^y. 



