CONDITIONS OF SENSITIVENESS OF WHEATSTONE's BRIDGE. 351 



Of six quantities a, a, b, b', r, R, the resistance b to be measured 

 is the only one given a priori ; R and r are completely arbitrary; the 

 three other resistances a, a, and b' are connected to b by the con- 

 dition of equilibrium. 



Suppose that b', r, and R are given with b ; the resistance a is the 

 only unknown quantity, the ratio of a' to a being known. The value 

 of a, which corresponds to the minimum of the values of K and 

 H is defined by the condition 



equation (29) and the condition of equilibrium of the bridge give 

 directly 



" -*T" 



The least values of K and of H are then 

 ST 



957. If b, R, and r are alone given, which in practice is the 

 usual case, it remains to choose 0, and the ratio of the two arms of 

 the beam. Whatever b' is, it is clear that the best values of a and of 

 a should first satisfy the preceding conditions, which give the 

 minimum K x and H r Hence we may regard b' as the only inde- 

 pendent quantity, and investigate that value which makes the 

 quantities K x and H 1 a minimum. 



The expression of K x shows that the absolute error is smaller 

 the smaller is b', but in practice this fact is only of secondary 

 importance. 



Putting 



ST 



we may write 



_ i 



1= 7 



