USE OF GALVANOMETERS OF HIGH RESISTANCE. 423 



to be compared are closed by a constant resistance of 30,000 to 

 40,000 ohms, inserting a shunt if necessary. With mirror instru- 

 ments the electromotive forces are proportional to the deflections. 

 The method is equivalent to the use of an electrometer (868), 

 and the electromotive forces thus determined are those which 

 correspond to open circuits, or, at any rate, to currents so weak, 

 and of such short duration, that their polarization may be entirely 

 neglected. 



1018. The method may also be applied to measuring any 

 given difference of potential between two points on the path of a 

 current, when the resistance s which separates them, is not of the 

 same order of magnitude as that of the galvanometric circuit. If, 

 as above (867), g is the resistance of the wire containing the gal- 

 vanometer, R that of the circuit outside the points touched, I x and I 

 the intensities of the principal current before and after the intro- 

 duction of the galvanometer, the difference of potential V observed 

 by the galvanometer is V = Is = tg, and the original difference Vj = 1^. 

 We have further 



The two currents I and Ij are sensibly equal, as well as the dif- 



ferences of potential V and V 1} if the ratio - is very small in 



g 

 comparison with unity. 



Let us suppose even, in a more general manner, that the re- 

 sistance s contains an electromotive force e, in the same direction 

 for instance as the current, and let E be the total electromotive 

 force. The intensity of the primitive current is 



and the difference of potential at the two points in question is 



v.-v-,. 



When the galvanometer is introduced, we have 



