326 COMPARISON OF RESISTANCES. 



932. When the resistances r and r' are very great in reference 

 to the circuit, and very different from each other, we may facilitate 

 the comparison by the use of shunts. 



If p is the resistance of the battery up to the binding screws 

 of the galvanometer, g that of the galvanometer, m and m' the 

 shunts placed in the galvanometers with the resistances r and r ', 

 / and /' the corresponding resistances, we have 



/ x \ 

 (9) E = mi ( /> + + r ) =mir 



\ m / 

 or sensibly 



consequently 



r m'i' 



(i) - = r. 



r mi 



If one of the resistances is so great compared with the other 

 that the use of shunts is not sufficient to get deviations which are 

 measurable, and within the limits of the scale, the electromotive 

 power is modified by taking a variable number of identical couples. 

 The numbers of the couples in the two cases being n and ', we 

 have 



n mir r n m'i' 



n' m'i'r ' r' n' mi 



In observing the large resistance the shunt is usually suppressed, 

 and only one couple is taken for the small one, this gives n' = i, m = i ; 

 in this case the ratio of the resistances is given by the simple 

 expression 



(n) = nm' . 



-*' * 



This is the way in which the resistance of the insulating envelope 

 of a telegraph cable is usually measured ; the cable being immersed 

 in a vessel of water, one of the ends is insulated and the other is \J 

 connected to the water through the battery bf the galvanometer. 



933. When the resistances are so great that the fall of potential 

 from one end to the other can be directly measured, the same current 



