562 BELL SYSTEM TECHNICAL JOURNAL 



Fig. 2 having the impedance kjl and containing an e.m.f. Ee—*''j2. 

 Similarly circuit 3/4 will be replaced in Fig. 2 by a branch having the 

 impedance kjl. As the current reaching circuit 3/4 will divide 

 equally between the two ends of the line and the part reaching the be- 

 ginning of the line will be further attenuated by the factor e'f' the 

 termination k in Fig. 1 is to be replaced by the receiver in Fig. 2 which 

 indicates only e~'*''l2 of the current flowing through it. Substituting 

 these values in the expression for the galvanometer current in a bridge * 

 we find for the crosstalk current 



FY 

 AT = — z^e-'^yx 



1 



_ ^ 

 64 



or approximately 



EY 



A/„ = rz^ 6"^"^^ as Y is very small. 



"^ 16 



This Is the current at the end corresponding to the transmitting 

 station. At the other end the attenuation factor will be that corre- 

 sponding to transmission over the entire length of line / — making the 



crosstalk 



FY 



It will be noticed that the crosstalk at the farther end of the line is 

 independent of the position of the admittance unbalance, while the 

 crosstalk at the transmitting end of the system will diminish as the 

 point of unbalance is moved farther from this end. In one case 

 the wave must traverse the entire distance between terminal stations; 

 in the other it must travel down the line to the point where it is carried 

 across from one circuit to the other and then back from this point to 

 the beginning of the line where the crosstalk is received. 



The mutual impedances between the four conductors composing the 

 two circuits may be treated in a manner similar to that which has been 

 employed for the admittances between these conductors. Assume that 

 any four mutual impedances are added and then divide them into 

 four components, of which three may be shown to give rise to no 

 crosstalk. The remaining component is the mutual impedance un- 

 balance Z/4 and the crosstalk due to it may be found as follows. 

 The circuit is shown by Fig. 3, which may be replaced by the trans- 



1 Maxwell I, §347. 



