COIL BRIDGE. 367 



which shows that the absolute or relative sensitiveness is greatest 

 at the centre of the wire and is null at the extremities. 



Thermoelectrical currents are greatly to be feared in wire bridges, 

 and we should carefully avoid touching with the fingers any of the 

 metal pieces of the apparatus. 



968. The wire bridge may also be employed in two different 

 ways, either by substitution or by the comparison of ratios. 



The method of substitution is the most exact, and it requires 

 no knowledge of auxiliary resistances. The two resistances to be 

 compared b and b l are placed successively at Q, and the positions 

 x and x 1 of the roller which correspond to equilibrium are deter- 

 mined. We have then 



a + x 



b' b + / - x b l + / - x 1 b b l (x x-J ' 



This equation gives the difference b b-^ as a function of the dif- 



ci 

 ference x x l of the readings, and of the ratio . 



If we wish to eliminate this ratio, it is sufficient to interchange 

 the resistances a' and b'. The two new readings y and y give 

 then 



- l -x-x l y-y l 



or 



If the resistance a be chosen, so that the positions x and y 

 are near the ends of the scale, we might measure a difference twice 

 the resistance of the wire. 



When the difference b - b l is greater than the length of the wire, 

 it may be determined by a series of experiments with intermediate 

 resistances r^ r 2 ,. . . r n , such that the successive differences of two 

 of them are directly measurable, as well as those of the first with b 

 and of the last with b lt and we shall have 



969. In order to compare the values it is necessary to know the 

 values of a and b as a function of the unit of length of the wire, 

 of which they form in some sort the prolongation. Let us count 



