KENNELLY. — EQUIVALENT CIRCUITS OF COMPOSITE LINES. 41 



r„ = 55.92 ohms per loop km. (90 ohms per loop-mile) ; g n = 

 /,, = 0.70 X 10~ 8 henry per loop km. (1.126 millihenry per loop-mile) 

 c„ = 0.049,7 X 10~ 6 farad per loop km. (0.08 X 10 -6 farad per loop-mile): 

 values which correspond to 



r = 27.96 ohms per wire km. 



/ = 0.35 X 10" 8 henry per wire km. 



c = 0.099,4 X 10" 6 farad per wire km. 



Substituting the above values in (1), (2), and (3), we obtain at <u = 

 5,000 radians per second : 



a„ = a = 0.117,976,6 /46° 47" 26" hyps per loop km., or per wire km. 



0„ = 6 = 5.898,83 /46° 47' 26" hyps for both the double line and the 



single line. 

 *,, = 474.755 \43° 12' 34" ohms for the loop circuit. 

 z = 237.377,5 \43° 12' 34" ohms for the single line. 



The equivalent l"l and T of one wire are indicated at ABGG' and AOBG 

 in Figure 4. The architrave impedance AB is 6,736.96/156° 51' 15" 

 ohms, which is also the receiving-end impedance of each line, exclud- 

 ing the receiving instrument Z r ; because, if we ground the line at B, 

 the current which will flow to ground at B will be the impressed poten- 

 tial at A divided by this architrave impedance. 



The equivalent circuits of the loop line are indicated at ABB" A" 

 and AOBB'O'A' (Figure 4). The former is a rectangle of impedances, 

 and the latter an I of impedances. It will be seen that the rec- 

 tangle ABB" A" is merely a doublet of the single line n, ABG'G; 

 while the I, AOBB'O'A' is merely a doublet of the single line T, 

 AOBG. The receiving-end-impedance of the loop-circuit is evidently 

 2 X 6,736.96/156° 51' 15" = 13,473.92/156° 51' 15" ohms, excluding 

 the receiving instrument Z r . 



Since, then, the equivalent circuits of metallic-circuit or loop-lines 

 are mere doublets of those for their component single wires, and the 

 latter are easier to think about and discuss, we will confine our atten- 

 tion to the latter. 



