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BELL SYSTEM TECHNICAL JOURNAL 



where -S(co) = cor + (r(co) ± nir and is the phase angle of the transfer 

 impedance, provided, as we shall assume, that k is approximately a 

 constant. Whether ^ is a constant or not, B{oi) represents the 

 difference in phase between the currents at the sending and receiving 

 ends. B{<x)) is given by 



5(a;) = /coa^VMI + Vl + {R/o:L% (9) 



Fig. 5 shows B(w) and a-(co) in radians for a 500-mile length of cable 

 whose constants are: 



resistance R = 2.74 ohms per mile, 

 inductance L = 0.001 henry per mile, 

 capacity C = 0.296 microfarad per mile. 



5 10 15 20 25 



FREQUENCY IN CYCLES PER SECOND 



Fig. 5 — Phase distortion correction on long telegraph cable 



and for the frequency range, 0-25 cycles per second. The straight 

 line, cor ± mr, representing the distortionless phase characteristic is 

 not fixed except that it must pass through the origin or d= mt at zero 

 frequency. It is here chosen to pass through the origin and to have 

 the same value as the cable phase itself at / = 25 c.p.s. The dotted 

 curve representing — a{oj) then shows the departure (with the sign 

 reversed) of the cable phase from the distortionless characteristic. 



