KENNELLY. — EQUIVALENT CIRCUITS OF COMPOSITE LINES. 43 



the same type of line. This is for the reason that in the unsteady 

 state, or period of current building prior to the formation of the steady 

 state here discussed, there is neither wave reflection nor discontinuity 

 of wave propagation at the junction BC, when the surge resistance or 

 impedance z is the same on each side thereof. 



In order, however, to simplify the transition to complex cases later 

 on, we may pause to consider the following case of two sections, with 

 different a but the same z. 



Zi = 100 km., r x = 20 ohms/km., ^ = 2X 10~ 5 mho/km. 

 X 2 = 100 km., r 2 = 10 ohms/km., g 2 = 10 -5 mho/km. 



Whence ai = 0.02 hyp/km., z x = 1000 ohms ; 



a 2 = 0.01 hyp/km., z 2 = 1000 ohms. 



Merger Equivalent Circuits of Composite Lines. 



Figure 6 shows the two lines at AB and CD respectively. It also 

 shows the n and T equivalent circuits of AB at A"B"G"G" and 

 A'OB'G', likewise of CD at C"D"G"G" and C'OD'G'. If we connect 

 the sections together at BC, into a composite line AD, we virtually 

 connect together some one pair of the combinations of equivalent cir- 

 cuits V[ AB V\ CD , T AB 1 CD , V\ AB J CDi T AB Y\ CD . The first two combinations are. 

 shown at ABCDGGG and A'OBCOD'G'G'. If we merge together the 

 two elements of any such pair by known formulas, 3 we arrive either at 

 the equivalent I~l, ADGG; or the equivalent T, AODG, of the com- 

 posite line. 



The equivalent l~I or T of a composite line, computed by the merging of 

 the lis or Ts of the component sections, may be called the " merger Y\ " 

 or "merger T" of the line, to distinguish them from the n or T com- 

 puted directly from the composite lines by the formulas to be presented 

 later. The latter may be called, for distinction, the " hyperbolic l~l " 

 or T. For a given degree of precision, it will be found much easier to 

 compute the hyperbolic l~I or T of a composite line than to compute the 

 merger n or T. In all the examples given in this paper the equiva- 

 lent n and T of the various composite lines considered have both been 

 derived hyperbolically, but have also been checked by the merging 

 process. 



s "The Equivalence of Triangles and Three-Pointed Stars in Conducting 

 Networks," A. E. Kennelly, Electrical World and Engineer, Vol. 34, No. 12, 

 Sept. 16, 1899, pp. 413-414. 



