52 THE SCIENTIFIC PAPERS OF 



at, the sheathing works, the insulation resistance gradually 

 decreases, and the instrument would very soon be too sensitive. 

 It could be made less sensitive, it is true, but in resorting to this 

 it would no longer be possible to appreciate correctly the value of 

 the resistance of the last coil added to the cable. 



It was, therefore, necessary to resort to a means of maintaining 

 the original degree of sensitiveness of the measuring instrument, 

 while the total resistance gradually decreases. 



For this purpose the coils of the sine galvanometer employed are 

 surrounded by an additional coil of comparatively few turns, 

 through which the current of a constant small battery continually 

 passes. 



The insulation current passes through the wire of the instru- 

 ment, but is counteracted by the current in opposite direction 

 in the outer coils, which is so regulated by means of a resist- 

 ance coil, that no deflection of the galvanometer needle can be 

 observed. 



In adding to the length of the cable, the resistance coil in the 

 outer circuit of the instrument has to be diminished by stopping 

 till the equilibrium of the needle is restored ; and the value of the 

 alteration of the resistance coil being known in units, this number 

 has only to be multiplied by the fixed proportion of the relative 

 power of the outer and inner coil upon the needles to produce 

 the correct result. 



If W (Plate 1, Fig. 2) represents the resistance of the inner coil, 

 TFi, the resistance coil put into the inner circuit, m, the number of 

 cells of the battery of the inner circuit, w, the resistance of outer 

 coil, w u the resistance coil put into the outer circuit, n, the number 

 of cells of the outer battery circuit, and k, the number indicating 

 the proportion of the effect of the outer and inner coil on the 

 needle, we have, 



w+w^ 



k = (W+Wjn' 



If instead of W l the unknown resistance x of the cable is intro- 

 duced into the circuit, and the resistance u\ altered (to V) till the 

 needle is perfectly at zero, when to make the equation quite general 



