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



ment is obtained when X. = 1 and when //, = oo — that is to say, 

 when c is equal to d (the resistance to be measured), and when 

 a and b are equal and as large as convenient. When these 

 arrangements are made, the maximum value of y, or the 

 change in the difference of potential between the terminals of 

 the condenser brought about by depressing the key, is, when 

 c is nearly equal to d, 



Y=iez or=|.^; .... (7) 



and this is the quantity to be inserted in equation (3). 



The sensitiveness is evidently directly proportional to the 

 electromotive force of the cell : but it is independent of its re- 

 sistance; i. e. a high- resistance is measured with as great pro- 

 portional accuracy as a low one. But it must be remem- 

 bered that when the resistance to be measured is great, the re- 

 sistances a and b should be as great also ; if they are not as 

 great as d, the sensitiveness falls off very appreciably. But, 

 as said before, there is really no limit to the sensitiveness of 

 the method ; for the size of the condenser and the length of wire 

 on the galvanometer may be increased to any extent. 



Practical Details. 



The condenser I have used is a small standard one with the 

 dielectric of mica; and it has a capacity of slightly over one 

 micro-farad. The galvanometer is a Thomson astatic by 

 Elliott, with a resistance of about 7000 ohms. The two branches 

 a and b of the resistance-coils, forming the equal arms of the 

 bridge, were 1000 ohms each, being the largest resistance 

 conveniently available in the box of resistance-coils used. But 

 when the resistance to be measured is large (say over 500 

 ohms) it is better to have a and b greater than this ; and they 

 may then be made of Muirhead's carbon-paper (fig. 4). A strip 

 2 feet long by half an inch broad will have a resistance of about 

 14000 ohms ; and the galvanometer terminal B may be con- 

 nected with its middle so as to divide it into two halves repre- 

 senting a and b. Exact equality in the two arms is not essential, 

 as it is easy (and, indeed, generally advisable) to eliminate any 

 errors of this sort by a method analogous to double weighing. 

 Connect a and b to a commutator in such a way that it is easy 

 to interchange them end for end (see fig. 4), and balance the 

 resistance d by the coils c ; then interchange a and b and 

 balance again ; this time we may require an amount c'. Then 

 it is easy to see that d= *j(cc f ), whatever the ratio of a to b ; 

 for in the first case we have d :c = a:b, and in the second 

 d : c J = b : a. If c and d are nearly equal, their arithmetic 



