﻿of a Balanced Alternating-Current Sndge. 1031 



component parts and the possibilities of various bridge con- 

 nexions and measurements analysed, using only elementary 

 algebraic transformations. 



When one or more branches of a bridge contain parallel 

 paths, quicker results may be obtained by using admittances 

 in place of impedances. Let, for example, the branches 1 

 and 4 contain ohmic resistances only, Jet branch 3 contain 

 an impedance r s +ja>Ij 3t and let branch 2 consist of a 

 capacitive susceptance jcoC a in parallel with a resistance r 2 . 

 We then have, according to eq. (1), 



(f 3 +>L s )/fi 4>C ) = ^ 4 . . . (34) 



or V? 2 / 



r 3 +>L 3 = r 1 ?' 4 /?'2-f>r 1 >' 4 C„. . . . (35) 



Equating the real and the imaginary parts, eqs. (19) and 

 (20) are obtained. 



Fig. 2. 

 A 2 



Gal van ometer 







Zm 



1 'WsAAAAAA, *P± VvVWVWV^ 



A, . '. A3 



I — vwvWvv^ VVVC^VVV 



e 



Note, — Fig. 2 shows the diagram of connexions of 

 Maxwell's mutual inductance bridge (item 2 in the table). 

 At first sight it does not seem possible that fig. 2, with 

 its two separate circuits, could be a particular case of 

 fig. 1 which has one circuit only. In order to explain 

 the transformation of fig-. 1 into fig. 2, intermediate 

 diagrams of connexions are shown in figs. 3 and 4. In 

 fig. 3, the impedances Z 2 and Z 4 are assumed to be very small, 

 otherwise the connexions are the same as in fig. 1 for the 

 case of a single path in branch 2. In other words, the points 

 0, B, and A 2 are electrically close to each other. In fig. 1 

 the limiting assumption is made that Z 2 = Z 4 = 0, and the 

 three points are brought together. Under these conditions 



