33 COMPARISON OF RESISTANCES. 



parallel, and finally by the two resistances in series; if a , a, a', 

 aj and a 2 are the swings which correspond to the various 

 experiments, and p the resistance from the principal circuit to the 

 galvanometer, we have 





From this is deduced, for the ratio of the resistances, the dif- 

 ferent values 



a a, i i i i 



-?-I I~ J - + ----- : 

 a aa 1 a 2 a a 



^ 



r ^0_j !_^ IJ* 



a a' a a 2 



937. DIFFERENTIAL GALVANOMETER. A differential galvano- 

 meter may be used in various way to measure resistances. The 

 battery, of electromotive force E, and of resistance /o, is closed by 

 two branches A and B ; one of them contains the resistance r 

 and one of the coils g of the galvanometer, the other the coil g', 

 and a standard resistance r 1 . The principal current I and the 

 currents i and /' in the two branches, give the ratios 



' '" ' __ E-I,. 



I 



+ 



g+r g' + r' g+r g' + r' 



If k and k' are the factors respectively proportional to the 

 galvanometric constants of the two coils, the deflection 8 of the 

 needle may be expressed by the formula 



whence putting 



r+ r'}, 



