33 2 COMPARISON OF RESISTANCES. 



The resistances r and r being very near, we have sensibly 

 D = 



so that, if the resistance of the battery is very feeble compared 

 with that of the galvanometer, the sensitiveness is proportional 

 k 



We may examine what should be the resistance of the galvano- 

 meter with a given channel so that the sensitiveness is a maximum. 

 If we replace the wire used, by a wire of another diameter m times 

 as small, we should replace the constant k by m*k (731) and g 

 by m*g y which amounts to replacing 



_* by k ( ___ | 



But this latter expression is a maximum for 



r 

 3' 



that is to say, when the resistance of each of the coils is the third 

 of the resistance to be measured.* 



When this condition is realised, we have 



-dr 



The deflection A which the branch containing the resistance r 

 would of itself give, the other being cut, is 



P+g+r 4 r 

 consequently 



939. When the resistances to be compared are very small, they 

 are put successively as shunts on the coils of the differential 



* WEBER. ZurGalvanometrie.GottingerMemoiren, Vol. x., p. 65. 1862. 



