226 BELL SYSTEM TECHNICAL JOURNAL 



The impressed voltage V is propagated to the left-hand end of dx. 

 Letting Va be the voltage across circuit a at this point, it will be 

 shown that Va would be balanced except for the effect of interaction 

 crosstalk which is excluded from consideration for the present. Desig- 

 nating the wires of circuit a as 1 and 2, the balanced voltage Va causes 

 charges Q\ and Q2 per unit length on these wires in the length dx. 

 These charges are affected by the presence of other wires in the length 

 dx and they are usually unbalanced. There will be equal and opposite 



or balanced charges ± — ^ on each wire and unbalanced equal 



charges on each w^re. Since the direct crosstalk is defined 



as the effect of balanced charges and currents, only the balanced 

 charges should be considered in computing Ve- Letting Qa = ^ 

 or the balanced charge on wire one per unit length, then: 



Vtt ^^ > a^a i a^a^ai 



where Ca is equal to the "transmission capacitance" per mile, i.e., 

 the capacitance used in calculating «„ the attenuation constant and 

 Za the characteristic impedance of circuit a. 



The above expression for Qa includes the reaction of charges in the 

 disturbed circuit. This reaction should not theoretically, be included 

 at this time, since, for convenience in calculation, the disturbed circuit 

 is assumed to have the impressed voltages Vm and Ve but no crosstalk 

 currents or charges as yet. The effect on Qa of charges in the disturbed 

 circuit, is, however, usually small compared with the effect of charges 

 in various tertiary circuits. 



Designating the conductors of circuit & as 3 and 4, Ve is the difference 

 of the potentials of the electric field at 3 and 4 caused by the balanced 

 charges per unit length on 1 and 2. Therefore: 



where pis, etc., are the potential coefficients. 



For c.g.s. elst. units, pis = 2 log — where 513 and ru are the distances 

 indicated by Fig. 32. Therefore: 



Ve = VaC„{pl3 - P23 " pH + p2^) = VaCapab- 



The capacitance Ca may be obtained from measurements on a short 

 length of a multi-wire line. Its value is, however, only a few per cent 



