kennelly. — equivalent circuits of composite lines. 73 



Conclusions. 



Any composite line of any number of sections, with or without loads 

 of any kind, operated in the steady state either by a direct current, or 

 by an alternating current of one frequency, has the same receiving-end 

 impedance from each end ; so that, if one volt be applied to each end 

 in turn, the current strength received at the other end will be the 

 same. 7 



The equivalent circuits of such lines may always be computed either 

 for the D. C. or A. C. case by the formulas given in this paper. That 

 is, any such line may always be replaced by one delta connection or by 

 one star connection of impedance, without disturbing the electrical 

 conditions outside of the line. 



Notation Employed 



a, a //} a lt a 2 , a 3 .... attenuation-constants of a single line, of a 



loop-line, and of different sections of a 

 composite line (hyps, per km.). 



c, c /; , c x , c 2 , c 3 linear capacitance of single line, loop-line, 



and sections (farads/km.). 



8, 8 A , 8 B , the hyp. angles. of points on a line (hyps). 



G, G g , G gA , ... G f , G fA , ... the sending-end admittance (D. C. conduc- 

 tance) of a line, the admittance beyond a 

 point on the same, when the far end is 

 grounded, and when the far end is free 

 (mhos). 



9> 9/^ 9^ 9* 9* - - • ' linear conductance of single line, loop-line, 



and sections (mhos/km.). 



g' = \/R' conductance of leak of a T (mhos). 



g"=l/R" conductance of leak of a n (mhos). 



y conductance of a leak load (mhos). 



i, i A , i P ....... current strength, at the sending-end, and at 



a point on the line (amperes). 



j v- 1 



l, l ifl l l} l 2 , l 3 linear inductance of single line, loop-line, and 



sections (henrys/km.). 

 L, Li, L 2 , L 5 length of a line and of sections (km.). 



7 An exception should be noted in the case of any part of the composite 

 line not obeying Ohm's law, as, for example, a fault in the insulation; so that 

 the current through the fault is not proportional to the potential at the same. 



