376 



COMPARISON OF RESISTANCES. 



As a particular case, if the sum of the resistances a^ and b l 

 is constant, and is taken equal to y, the equation reduces simply 

 to 



(39) 



Let us consider the nine branches arranged as. in Fig. 198 ; 

 a' and V are the two resistances to be compared ; AB and PQ 

 two cylindrical and homogeneous wires ; the end C of the wire 

 of the galvanometer may slide along PQ ; two contacts insulated 

 from each other, but kept at a constant distance, and communicating 

 respectively with the two ends of PQ, may be displaced along the 



Fig. 198. 



wire AB. The slider A l 'B l has a double contact and is placed first 

 in a position such that the needle of the galvanometer is almost at 

 zero, and the adjustment is effected by displacing the point C. 

 Formula (38) gives the ratio of the two resistances a' and ', and 

 it reduces to formula (39), if the resistance y of the portion of the 

 wire comprised between the contacts A 1 and B I} is equal to the 

 entire resistance of the wire PQ. 



976. This arrangement has been realised by Sir W. Thomson 

 and Mr. Varley in the form represented by Fig. 199. Each of 

 the wires AB and PQ is replaced by a series of equal coils, 

 connected end to end, and arranged in a circle on two dials 

 denoted by the same letters. The first series is formed of 101 



