528 BELL SYSTEM TECHNICAL JOURNAL 



potential and the axial electric force at any point x in i. Then Vi is 

 analyzable into three parts (F,,, Va, Fi) and £»• into three parts 

 (£i„ Eijji) due respectively to the primary system t, to the secondary 

 system j, and to the arbitrary impressed field; that is.^o 



Vi = Vi. + Vii + Fi, (77) 



Ei = Ei. + Eii + U (78) 



In particular, at the secondary wire j the potential F,- and the axial 

 electric force Ej are analyzable in accordance with the equations 



F,- = F,v + Fyy + F^, (79) 



E,- = E,v + £,/ + //. (80) 



In the present subsection, the problem to be dealt with is the calcu- 

 lation of Fjv and Ejv, namely the potential and the axial electric force 

 at any point x in the secondary j due directly to the currents and 

 charges of the primary system tt. 



The n wires of the primary system tv will be numbered 1, 2, 3, • • • w. 

 The letters h, k, r will be employed generically: each may denote 

 any one of the designation numbers 1, • • • n — as h in equation (81); 

 or each may run through the whole set 1, • • • n — as in equation (91). 

 (It is hardly necessary to remark that j is not a member of the set 1, 

 • • • n, in the notation of this Section (III), where j always designates 

 the secondary wire.) 



The current at any point x in any wire h of the primary will be 

 denoted by Ik = h{x); and the charge on wire h, per unit length, 

 by Qh = Qk{x). 



The potential Vh and the axial electric force Eh at any primary 

 wire h are analyzable in the manner expressed by the equations 



Vh = Vh. + F,y + Fh, (81) 



Eh = Eh. + Ehj + fh, (82) 



in accordance with the general equations (77) and (78) respectively. 

 It will be found convenient to call Vh. the 'systemic potential' and 

 Eh. the 'systemic axial electric force' at wire h, since Vh. and Eh. 

 are due only to the system tt of which his a. member, and do not include 



20 Regarding the use here of double subscripts, it will be noted that the first 

 subscript designates the line or the wire where the effect occurs, and the second the 

 wire or the system of wires which produce the effect. Thus, Vi. is the potential 

 produced in line i by the whole primary system tt; the contribution of any one 

 wire h would be denoted by Fa. 



