Modified Form of Wheatstone's Bridge. 



61 



moreover, the disadvantage of a sliding contact. It may, 

 therefore, be worth while to give some details of its use. 



In Wheatstone's Bridge, let (S and 7 (fig. 1) bo nearly 

 equal resistances permanently mounted. Let b and c be the 



Fig. 1. 



coils to be compared, B a resistance-box in parallel with the 

 higher of the two. Let b n c t be the resistances of the con- 

 nexions of b and c. Put 



6B! _ , 

 c + R'" C; 

 then 



(c'+c,) 7 =(& + &,)/3. 



If c and R be interchanged with b and B has to be altered to 

 B' for balance, putting 



cK' „ 



then 

 Hence 



b^i'-v+'fi 



(e" + b,)l3=(b + c l )y. 



(&,/3-<yy)(/3-7) 



2 V/3 



7 / 



+ 



Wy 



The second term, on the right-hand side, is of the second 

 order of small quantities ; and as j3 and 7 should be within 

 Yoqq of one another, while the resistance of the copper strip 

 and mercury-cup connexions is very small, it may be 

 neglected. Therefore, 



-(£ + ?> 



put7=/3(l + S), where S is small. Hence 



6=c'(l + 8) + c"(l-8)=-°^' + |(c'-c"). 



