140 PROCEEDINGS OF THE AMERICAN ACADEMY 



Dividing (1) by (2) 



E., (r + B,) (6 + E, + R.,) 4- li;S ^ ' 



wliich is the formula required. 



NO. XV.— OX A NEW METHOD OF MEASURING THE RE- 

 SISTANCE OF A GALVANIC BATTERY. 



By B. 0. Peirce, Jr. 

 Presented, March 14, 1877. 



Of the many known methods of measuring the resistance of a galvanic 

 battery, only two, those of Mance and Tiiomson, are found to give 

 accurate results. A third method, which seems to work well in prac- 

 tice, is this : — 



A known resistance (r), a galvanometer of known resistance (G^), 

 and the battery whose resistance is to be measured, are joined up in 

 a simple circuit. The battery is shunted, and the deflection of the 

 galvanometer needle is noted. This shunt is now removed, and the 

 galvanometer is shunted, so that it gives the same deflection as before. 

 A knowledge of the ratio of the resistances of the shunts gives the 

 resistance of the battery by means of a simple formula. Let E be the 

 electromotive force of the battery, and B its resistance, and let ^S* and 

 G be the resistances of the shunts. In the expressions that follow, 

 Cff, Csi ^'^d Ca denote currents passing through the galvanometer and 

 the two shunts respectively. 



When the battery is shunted, the whole current in the circuit is 



8^ r -}- G 



Kirchoff 's Laws give 



(7 = Cff -I- C; and (T^ . ^ = Ga{r + G) 



therefore 



C^G,^A±L^r_0) ^2) 



o 



