DR. CAMPBELLS MEMORANDA OF 1907 AND 1912 



561 



give rise to crosstalk. The second admittance is added between the 

 conductor 3 and conductors 1/2 and subtracted between conductor 4 

 and conductors 1/2. This does not destroy the symmetry of circuit 

 1/2, and it can in consequence not give rise to crosstalk. The third 

 admittance {a — h — c -\- d) j^ \s added in the same way as the second 

 with an interchange of circuits. It will also not give rise to crosstalk. 



Crosstalk due to the added admittances, a, h, c, d, must therefore be 

 due to the last component (a — b -\- c — d)l4: = F/4 where Y is 

 what we may call the direct admittance unbalance. 



In order to determine the crosstalk occasioned by this admittance 

 unbalance F, when the electromotive force E is impressed upon one 

 of the circuits, we may proceed as follows: 



The circuits are connected as shown by Fig. 1. This is equivalent 



Fig. 1. 



to the bridge of Fig. 2. For if the unbalancing admittances F/4 were 

 removed circuit 1/2 would be clear. Then as the e.m.f. E acts through 

 an impedance k upon a line whose impedance is k, the potential 

 difference at the sending end of the line would be E/2 and in traversing 

 a distance x this would be attenuated by the factor g— i'^. The im- 



Fig. 2. 



pedance of each end of circuit 1/2 at the point x will be k and therefore 

 the entire circuit with its two ends in parallel will have the impedance 

 k/2. We may therefore replace circuit 1/2 of Fig. 1 by a branch in 



