October 6, 1905.] 



SCIENCE. 



435 



and to indicate a direct and simple derivation 

 of the desired relationship. 



Wheatstone's bridge consists, essentially, of 

 two circuits in parallel through which an elec- 

 tric current can flow. Let these circuits be 

 represented by ABD and ACDj Fig. 1, and 



Fig. 1. 



let the currents through the two branches be 

 denoted by I and F. Since the fall of poten- 

 tial from A to D is the same whichever path 

 is considered, there must be a point C on one 

 circuit, which has the same potential as any 

 chosen point B of the other. If one terminal 

 of a galvanometer is joined to B and the other 

 terminal is moved along ACD the galvanom- 

 eter will indicate zero deflection when the 

 point C has been found. Since B and C have 

 the same potential, the fall of potential from 

 J. to 5 is the same as from A to C, or in 

 terms of the currents and the resistances, 



ip=rQ 



where P and Q are the resistances of AB and 

 AC, respectively. 



Similarly for the other part of the circuits 



iR = rx. 



Dividing one equation by the other gives 

 P:Q::R:X 



as the relationship of the resistances when the 

 bridge is balanced. In the usual method of 

 iising the Wheatstone bridge three of these 

 resistances are known and the value of the 

 fourth is easily computed from the above rela- 

 tion as soon as a balance is obtained. 



In teaching ' Mance's method ' the attempt 

 has been made to deduce directly the expres- 

 sion for the resistance of the cell similarly 



to the above deduction for the Wheatstone 

 bridge. Some three years ago a careful search 

 of the literature was made, with the result that 

 no direct and simple explanation of the meth- 

 od could be found, while the best authorities, 

 German, English and American, either made 

 statements which are absolutely false or 

 passed over the subject in silence. 



The flrst edition of Maxwell, published a 

 few months after Mance's original paper, gives 

 the method as follows (the italics are my 

 own) : 



The measurement of the resistance of a battery 

 when in action is of a much higher order of diffi- 

 culty, since the resistance of the battery is found 

 to change considerably for some time after the 

 strength of the current through it is changed. In 

 many of the methods commonly used to measure 

 the resistance of a battery such alterations of 

 the strength of the current through it occur in 

 the course of the operations, and therefore the re- 

 sults are rendered doubtful. 



In Mance's method, ivhich is free from this ob- 

 jection, the battery is placed in CD and the gal- 

 vanometer in BG. The connexion between A and 

 D is then alternately made and broken. If the 

 deflexion of the galvanometer remains unaltered 



Fig. 



we know that AD is conjugate to BG, whence, 

 Qli = PX, and X, the resistance of the battery, is 

 obtained in terms of known resistances P, Q, R. 

 •:;■ * * jj^ ^i-jjg jj-iethod of measuring the resist- 

 ance of the battery the current in the hattery is 

 not in any loay interfered with during the opera- 



