Method of Measuring Battery Resistance. 517 



possible to measure any resistance whatever without the pas- 

 sage of a current through the resisting body, although it is 

 quite easy to measure an electromotive force without any cur- 

 rent circulating through the electromotor, so, although a 

 current of constant strength is sufficient to give a measure of 

 the resistance of a homogeneous conductor, such as a metallic 

 wire of uniform material, or a homogeneous liquid, or anything 

 else which contains no internal electromotive force, yet a vari- 

 able strength of current is necessary to determine the resis- 

 tance of an electromotor. 



And the reason of this is apparent, viz. that the opposition 

 experienced by a current in passing through an electromotor is 

 of two kinds — one due to the proper ohmic resistance, the other 

 due to the electromotive force : and with only one strength of 

 current it is no more possible to tell how much of the opposi- 

 tion is resistance and how much is electromotive force, than 

 it is to obtain the values of two unknown quantities from one 

 equation. We may either take two measures of the strength 

 of current and then eliminate one of the unknown quantities 

 algebraically, or we may use a contrivance (like Mance's 

 method) by which one of them (viz. electromotive force) is 

 eliminated electrically ; but two strengths of current are just 

 as essential in the latter case as in the former, as also it is 

 just as necessary that the two unknown quantities shall remain 

 constant. It is possible that the resistance, as well as the 

 electromotive force, of a battery does not accurately fulfil this 

 condition, but that it varies to some extent with the current ; 

 in so far as it does this, however, it is not a definite thing, and 

 is incapable of accurate measurement. 



I have entered into this matter at some length because the 

 slip in Maxw T ell is getting repeated in other books (cf. Cum- 

 ming's admirable c Introduction to the Theory of Electricity,' 

 p. 162) ; and it is as w r ell to get clear on the subject. 



The difference of potential required to force a current of 

 strength C through an electromotor of resistance R and internal 

 electromotive force e is 



E=RC±e. 



Various methods may be applied to measure E and C ; but 

 no observation of a single value of E and C can determine R 

 unless e is known. Another observation with a different value 

 of E and C must be made ; and then e can either be eliminated 

 directly, or one can employ an indirect means of effecting 

 its elimination, provided it remain constant. (If it does not 

 remain constant, and if the law of its variation is unknown, no 

 amount of experiments can eliminate it.) It is true that a 



