If the looped lines are both in good condition and free from leakage, the current sent out on line r will be exactly equal to the current received back on line 2; and as these currents will have equal but opposite effects on the galvanometer needle, no deflection of the latter will be produced.
If, however, there is leakage, the current received on the galvanometer will be less than the current sent out, and the result will be a deflection of the needle proportional to the amount of leakage.
The galvanometer being so adjusted that a current of definite strength through one of the coils gives a definite deflection of the needle, the amount of leakage expressed in terms of the insulation resistance of the wires is given by the formula.
Total insulation resistance of looped lines = 2 R(D/d - 1); in which R is the total resistance of the looped wires, including the resistance of the two coils of the galvanometer, of the battery, and of the two resistance coils r and r' (inserted for the purpose of causing the leakage on the lines to have a maximum effect on the galvanometer.
Two receiving instruments, a siphon recorder and a mirror galvanometer, are shown; one only is absolutely necessary, but it is convenient Cable to have the galvanometer ready, so that in case of accident to the recorder it may be at once switched into circuit by the switch s.