348 BELL SYSTEM TECHNICAL JOURNAL 



These currents (/i and I-i) and voltages (Fi and V-^ (the subscripts 

 applying, of course, to the respective tertiaries) are given by the 



coefficient array, 



where Oi, bi, ai and 62 are constants to be determined from the boundary 

 conditions, and 



S = 2X10^^^ /^"■'''"^' +•«'"• ^''^ 



/i and /a being the impressed fields along circuits 1 and 2 respectively. 

 If we consider the two tertiary circuits as consisting of (1) the outer 

 coaxial conductors in parallel with return by tertiary path 1 and (2) 

 tertiary path t — tertiary path 2, only tertiary circuit 1 will be 

 subjected to an impressed field. Thus we will have /a = and 

 /i = Zue~'^'' (for unit sending-end current in the disturbing coaxial 

 line), where Zu is the mutual impedance, per unit length, between a 

 coaxial (in the presence of the other paralleling coaxials) and tertiary 1, 

 and 7 is the propagation constant, per unit length, for the coaxial 

 circuit. The other quantities in this array are circuit parameters 

 given as follows in terms of the series impedances Z\\, Z22 and Zu per 

 unit length and admittances an, ^22 and ai2 per unit length (subscripts 

 11 and 22 for self impedance or self admittance of circuits 1 and 2 

 respectively, and 12 for mutuals) : 



2 ~ 2\_^uZll + <Z22.2^22 + 2ai2Zl2 ± ((duZll — ^22^22) 



^' + 4(aiiZi2 + ai2Z22)(fli2Z„ + a22Zn))"''], (22) 



7i^ — fliiZii — ai2Zi2 



(23) 

 (24) 

 (25) 

 (26) 



