426 MEASUREMENT OF ELECTROMOTIVE FORCES. 



The same test is then made for each of the elements. The 

 differences of potential v and V Q , before and after opening the 

 battery, will also give 



whence 



r 



As an experimental verification, it is clear that the total electro- 

 motive force and resistance of the battery should be respectively 

 equal to the sum of the values obtained for the different couples, 

 which requires that we have 



or, more simply, 



V = 2?' , 

 V =2z;. 



A couple has no useful effect in the series unless its electro- 

 motive force is greater than the fall of potential produced by the 

 resistance it introduces that is to say, if the difference of potential v 

 is positive, and we have 



e>E 



The mere sign of v would thus enable us to discriminate the 

 couples which are in bad order, without its being necessary to 

 open the circuit. 



If all the elements are of the same kind, they have the same 

 electromotive force, and only differ in resistance. We may then 

 put E = ne, and the preceding condition becomes 



From this it follows, that if the internal resistance of an element 

 is not less than the nth part of the total resistance, which is simply 



