456 BELL SYSTEM TECHNICAL JOURNAL 



the general form 



RcD+jXcD = A -}-jB, (3) 



where A and B are real quantities, one of the adjustable impedances 

 will appear in A and not in B, while the other will appear in B but 

 not in A. 



Consideration of equation (2) shows that if adjustable standards 

 consisting either of both components of Zbc or of both components of 

 Zad, are chosen, and if the impedances of the two remaining arms 

 are selected so that their ratio is either real or imaginary, but not 

 complex, then equation (2) reduces to the form of equation (3). No 

 other combination will meet the requirement taking equation (2) as 

 it stands. Since for the general case there is no essential difference in 

 the resulting type of bridge whether Zad or Zbc is used as our ad- 

 justable standard, this means that there is really only one method of 

 adjustment, namely the use of both components of one adjacent 

 impedance. 



However, if it is realized that parallel components may be used 

 instead of series components for the standard, then equation (2) may 

 be rewritten as follows: 



RCD +jXcD = (RaD -i-jXAD) (RbC +JXbc){GaB - JBab) (4) 



where 



Gab — JBab = Yab = -^ — • 



^AB 



From this it follows that Gab and Bab may be used as the adjustable 

 standards, by making the product ZabZbc real or imaginary. 



Thus there are two methods of adjustment possible, either the two 

 series components of an adjacent arm or the two parallel components 

 of the opposite arm. 



Having chosen the adjustable standards, there remain in each case 

 two arms, adjacent in one case and opposite in the other, which have 

 fixed values. These impedances must meet certain definite require- 

 ments, as already stated. 



For the case of adjustment by an adjacent arm, that is, by Zad, 

 equation (2) may be written in the form 



RcD + jXcD = 1^ {Rad + JXad). (5) 



^ab 



Then in order that this equation fulfill the requirements expressed by 

 equation (3), the vector ratio of the fixed arms must be either real or 



