(9) 

 (10) 



for the Measurement of a particular Besistance. 285 



Equating (4) to zero, we get 

 2 _ gc{K(c +/) + */} 



~ R(R+# + c) " , 



Equating (6) to zero, we get 

 Bq(R + ff)Q+/) 



~ (a + <r)(B+/) / 



Substituting for c in (9), we find 



ga(R+g)(a+f ) f Ra(B + ?)(«+/) ] *., 



a+ff + t (a+g)(B+/) / y/ an 



J Ba(B+fr)(«+/) |* H ' • ^ ; 



I (a+gW+f) S +B+& 



the positive signs before the radicals only being taken, as a and 

 c are essentially positive. 



After reduction, all the factors being retained, this expres- 

 sion takes the form 



W _ gff ^+A jpia+f)(a+g)-a(K+f)(Ti+g)} =0. 



Hence we have 



°&±2)=0, and ,.a = 0; 



a+g 



or 



or 



c?-gf=0, and /. a= */gf; (12) 



(R— a)(/#-Ra) = 0, and /. a = R or &. 



On examining equation (11), it will be found that the latter 

 two roots refer to the equation when the negative signs are 

 taken before the radicals. 



From equations (9) or (10) we see that, when a = 0, c=0; 

 and, again, when a = \/fg, 



-v 



u+f~ (ld) 



Substituting these values in equations (5), (7), and (8), it 

 appears that a = and c = neither give a minimum nor a maxi- 

 mum, but that a= Vfg and c= \/ ^- , always give a 

 maximum value for Gr. •' 



This leads to a very simple rule for the adjustment of the 

 bridge, because, no matter what the resistance to be measured 

 may be, the resistance a should have a perfectly definite value, 



