516 Mr. 0. J. Lodge on a Modification of Mance's 



matter whether these variations are simple changes of resist- 

 ance or the introduction of new electromotive force. 



By ascertaining, then, whether the insertion or removal of 

 batteries at r has any effect on a galvanometer at g, one can 

 observe whether the relation ac = bd is or is not fulfilled, and 

 can change one of these resistances until it is. For the case 

 when a, b, c, and d are simple metallic conductors, this is 

 Wheatstone's method of comparing their resistances. 



Again, reciprocally, when this relation is fulfilled, no change 

 in g can affect the current through the battery in r ; and 

 therefore, if this battery in r is the only electromotive force in 

 action, a change in the resistance of g does not affect the cur- 

 rent at all anywhere. Hence a galvanometer in, say, d will 

 show a constant deflection whether the resistance of g is or 

 co , whenever ac = bd ; and this is Thomson's method of mea- 

 suring the resistance of the galvanometer d. 



Further, from what has been said, there is no objection to 

 an existence of electromotive force in any or all of the con- 

 ductors, provided it remains constant; for it will be equally pos- 

 sible to observe whether changes in r (of any sort) have any 

 effect on the current in g ; and if not, then ac—bd, as before. 

 For the case when d is a battery of constant electromotive 

 force, this is Mance's method of determining its resistance. 



But it must now be observed that although changes in r 

 may have no effect on the current in g, they must affect very 

 essentially the current every where else, and therefore through 

 the battery d. This battery ought, then, to preserve its electro- 

 motive force constant in spite of variations taking place in the 

 strength of its current — a thing which no known battery is 

 capable of doing. The electromotive force of every battery is 

 really a function of the current it is producing and of the time 

 it has lasted. In cells called constant the dependence of elec- 

 tromotive force on current and time is only slight ; but in 

 none does it disappear. 



This fact that the current * and consequently, to some extent, 

 the electromotive force of the battery are made to vary by the 

 process of measuring its resistance, constitutes a great appa- 

 rent defect of the method ; but it is an irremediable defect, and 

 is not peculiar to this particular method. It is in fact impos- 

 sible to measure the resistance of a battery without varying 

 the strength of the current passing through it, by any method 

 founded, as all our methods are, on a measurement of current 

 or of difference of potential. In other words, just as it is im- 



* Professor Clerk Maxwell, in describing this method (' Electricity and 

 Magnetism/ i. p. 411), says that a the current in the battery is not in any 

 way interfered with during the operation j" but this must be a mistake. 



