436 



SCIENCE. 



[N. S. Vol. XXII. No. 562. 



Hon, so that we may ascertain its resistance for 

 any given strength of current, so as to determine 

 how the strength of current affects the resistance. 



A glance at Fig. 2 will show that in Mance's 

 method the battery is joined in series with 

 P, Q and R, and no two points having the 

 same potential can be found on this circuit. 

 The effect of closing K is to short-circuit P 

 and Q, thus closing the battery through R 

 alone, which frequently is not very large. 

 Often the current from the cell is changed 

 from a few ten-thousandths of an ampere to 

 several tenths, and this larger current flows 

 through the hey from A to D. Thus it is 

 readily seen that the points A and D are not 

 at the same potential, and that the current in 

 the cell is subject to considerable variation. 



Lodge^ pointed out this error in Maxwell 

 and gives a very clear exposition of the meth- 

 od, but does not deduce any formula, con- 

 cluding with the words : 



T have entered into this matter at some length 

 because the slip in Maxwell is getting repeated in 

 other books, and it is well to get clear on the 

 subject. 



Had all later writers read this admirable 

 account the present paper would be unneces- 

 sary. But even after this clear exposition 

 Maxwell has gone through two editions with 

 the only result that the last paragraph quoted 

 above now reads: 



In this method of measuring the resistance of 

 the battery, the current in the galvanometer is 

 not in any way interfered with during the opera- 

 tion, so that we may ascertain the resistance of 

 the battery for any given strength of current in 

 the galvanometer so as to determine how the 

 strength of the current affects the resistance. 

 [Which is meaningless.] 



However, the makers of books have kept on 

 as though nothing had been said, and some 

 have fallen into a more grievous error in the 

 attempt to deduce a formula for this method 

 from its analogy with Wheatstone's bridge. 



A standard English work written in 1887 

 says: 



In the Wheatstone bridge diagram, if the bat- 

 tery be placed in the X arm so as always to send 



^0. J. Lodge, PUl. Mag., 1877, Vol. 3, p. 515. 



a current through the galvanometer, then, by the 

 principle of the bridge which we have already 

 explained, when P:Q=:R:X, the opening or clos- 

 ing of the key can have no influence on the cur- 

 rent in the galvanometer, inasmuch as the two 

 jwints A and D are at the same potential. This 

 is the principle of Mance's method, in which ad- 

 justments are made of P, Q and R until the cur- 

 rent in the galvanometer remains the same, 

 whether the key is open or closed. 



One of the largest and best German trea- 

 tises, written in 1893, puts the matter more 

 explicitly. 



But as no current can flow through the bridge 

 {AD, containing the key) the potential at A is 

 the same as at D, and the fall of potential over P 

 is equal to that over Q and the fall of potential 

 over R is equal to that over X. So then if there 

 is no current through the bridge the same cur- 

 rent, i, flows through the entire circuit BAG, and 

 the current i' flows through the entire circuit 

 BDC, and 



iP — i'Q, iR = i'X, P:Q = R:X, 



from which the desired resistance is obtained. 



Of still more recent date are two American 

 manuals, excellent in many respects, which 

 follow the example set by the older books. 

 One of these, written in 1898, puts the matter 

 thus: 



If the cell, X, is placed in the branch CD of the 

 bridge, and a key, K, inserted in place of the bat- 

 tery in the branch AD, there will, of course, al- 

 ways be a current through the galvanometer, and 

 its needle will be deflected. But if, on making 

 and breaking the key K, there is no change in this 

 deflection, A and D must have the same potential; 

 otherwise some of the current would have gone 

 through AD when the key was closed and so a 

 different quantity would have gone through the 

 galvanometer. If, however, A and D have the 

 same potential, 



P:Q::R.X. 



* * * Under this condition no current flows 

 through the branch containing the key K. 



The other book, written only last year, is 

 simply another echo. 



The adjustment consists in finding such a point 

 of contact. A, that opening and closing the bridge 

 does not alter the galvanometer reading. Then 

 A and D are at the same potential, and the re- 



