138 PROCEEDINGS OF THE AMERICAN ACADEMY 



and i?2 ^^^ resistances which may be varied until no current passes 

 through tlie galvanometer. AVhen the current through the galvano- 

 meter is nothing, the ratio of the electromotive forces of the two 

 batteries is very easily found. Let HJ^ and K2 be tlie electromotive 

 forces of the two batteries, and -5^ and B^ their internal resistances. 



Kirclioff 's Second Law, when applied to the closed figure embracing 

 the resistance £^, H^, G, gives, 



JE, = (B, + 7?J (1) 



where (7 is the current traversing the circuit. 



The same law when applied to the closed figure r, B,^, B.^, G, gives 



B,= (r + B, + B,)0 (2) 



Dividing (1) by (2) 





(3) 



In order to use this formula, we must know the values of i?^ and 

 B^. These may be determined thus : Give to B., a little different 

 value, and vary B^ until there is again no current going through the 

 galvanometer. Repeat this operation with still a ditferent value of 

 B^, and there will be three different values of the ratio of the elec- 

 tromotive forces, which will give three equations to determine B^, B^, 



E 

 and —^. B. and R„ are most conveniently made large ; and in this 



case, if extreme accuracy is not needed, we may neglect B^ and B,^ 

 compared with R^ and R^. 



It is, of course, not necessary to have any resistance corresponding 

 to r ; but as it is often possible to get quite accurate results by making 

 R^ and ^2 small resistances, and then varying r by means of a 

 rheostat until no current traverses the galvanometer, a resistance r 

 is inserted in the figure. 



Tlie chief advantages of this method are : — 



1st, its great accuracy. 



2d, that the current through the galvanometer is made zero. 



3d, that the circuit does not have to be broken during the com- 

 parison. 



4th, that the resistances of the two batteries are, very readily ob- 

 tained without altering any of the adjustments, if their electromotive 

 forces are constant. 



The greatest disadvantage in this arrangement is that a large 



