Wheatstone's Bridge for measuring a given resistance. 115 



vary), so that the galvanometer may be affected the most by any 

 slight departure from the balance which occurs when a:b=:c:d. 



The nature of this problem may be more easily understood from 

 the following considerations : — 



1. If b y c, d, e, and /are given, then there is only one value 



be 

 of a which will produce a balance, viz. a= -j* 



2. But if c, d, e } and / are given, but not b, then there is an 

 infinite number of pairs of values of a and b which will produce 

 a balance by satisfying the relation a:b = c: d; and one parti- 

 cular pair will constitute the best arrangement, by which is meant 

 that the galvanometer will be most sensitive to any slight depar- 



a c 

 ture from the equality of t and -^ when those particular values 



of a and b are used. 



3. And if only d, e, and / are given, then for any value we give 

 to c there is a pair of values of a and b which constitutes the 

 best arrangement for that value ofc; and there will be a parti- 

 cular value of c which, with the corresponding values of a and 

 b, will be the best arrangement for the given values of d, e, and/'. 



In order to find what functions a, b, and c must be of d, e, and/ 

 to constitute the best arrangement, it will be first necessary to 

 find the best values of a and b when c, d, e, and / are given. 

 This I now proceed to do. 



It is well known, and may be easily proved by KirchhofFs 

 laws, that the current passing through the galvanometer is re- 



12 



