THE EQUIVALENT CIRCUITS OF COMPOSITE LINES IN 

 THE STEADY STATE. 



By A. E. Kennelly. 



Presented October 2, 1909; Received October 4, 1909. 



Definitions and Purpose. 



A composite line may be defined as an electrically conducting line 

 formed of two or more successive sections, each section having its own 

 length and its own particular uniformly distributed resistance, induc- 

 tance, capacitance, and leakance. Each such section, considered sepa- 

 rately, may be described as a single line. A composite line is, therefore, 

 a successive connection of single lines which differ in linear constants. 



It has been shown by the writer in a preceding paper 1 that any 

 uniform single line, operated in the steady state, either by single- 

 frequency alternating currents or by continuous currents, may be 

 externally imitated by a symmetrical triple conductor. The triple 

 conductor which can be substituted for a single line in a steady sys- 

 tem of electric flow without disturbing the potentials, or currents, at 

 or outside of the line terminals, may be defined as an equivalent circuit 

 of the line. A star-connected equivalent circuit, with two equal line 

 branches and a single leak, may be called an equivalent T ; while a 

 delta-connected equivalent circuit with two equal leaks, and a single 

 line-resistance or impedance between them, may be called an equiva- 

 lent l~l. It is the object of this paper to extend the laws of equivalent 

 circuits from single lines to composite lines, with or without loads, and 

 also to present formulas for the distribution of current and potential 

 over such composite lines. 



Important Practical Application of the Problem. 



An important application of this problem is found in telephony. 

 With given sending and receiving apparatus, the commercial opera- 

 tiveness of a telephonic metallic circuit apparently depends only on 

 the strength of alternating current, at a certain standard frequency, in 



1 "Artificial Lines for Continuous Currents in the Steady State." See 

 appended Bibliography. 



