CONDITIONS OF SENSITIVENESS OF WHEATSTONE's BRIDGE. 349 



If the two diagonals are interchanged, as the battery and the 

 galvanometer each brings its own resistance, the denominator A 

 acquires a new value A', such that 



(28) A' - A = (R - r) [(a + b) (a + b') -(a + a) (b + b'}\ 



Suppose that the product (a b'} (a - b) is positive, so that we 

 have at once 



a>b' and a'>b, 

 or 



a<b' and a'<b. 



As the ratio ab' = a'b may be considered as almost satisfied, 

 these two conditions amount to supposing that the four resistances 

 a, a', b, b' are arranged in order of increasing or decreasing magni- 

 tudes that is to say, that the two summits A and B (Fig. 184) 

 are the points of junction, the one of the two largest resistances, 

 and the other of the two smallest. 



In this case, if R>r, A'>A, and the first arrangement is better 

 than the second; the contrary would be the case for R<r. Hence 

 this rule : 



The maximum sensitiveness is obtained when in Wheatstone's 

 bridge the diagonal which connects the summits where the two 

 greatest resistances and the two least separately terminate, is formed 

 of that one of the branches, the battery or the galvanometer, which 

 itself has the greatest resistance. 



In practice, the galvanometer has generally a higher resistance 

 than the battery. 



954. Let b be the resistance to be measured, b' the standard 

 resistance which is compared with it, and suppose we adjust so that 

 a balance is obtained, a and a' being arbitrary resistances. If a = # ', I 



b' = b ; but we may make any ratio we like between a and a', so that 

 the condition of equilibrium corresponds to the same ratio between 

 the branches b and b'. 



If we follow out the analogy of resistances and of weights, we 

 may call Wheatstone's arrangement a balance, while the resistances 

 a and a are the two arms of the beam. It must, however, be 

 observed that the conditions of weighing are here reversed; the 

 resistances to be compared b and b' are here proportional to their 

 respective arms when equilibrium is attained. 



