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LOADED TELEGRAPH CABLES 393 



As can be seen from formula (4), the real part of the propagation 

 constant, as, the attenuation constant of the cable, involves all four 

 of the cable parameters, but on account of the fact that the inductance, 

 leakance and the various components of the effective resistance 

 predominate in influence at different points in the frequency range it 

 is possible, by methods of successive approximations, to obtain a 

 reasonably good set of values of these quantities. 



The imaginary part of the propagation constant, 13s, is to a close 

 approximation, given by 



^s = sp-{CL. (7) 



From this it follows that the time of propagation of a sinusoidal wave 

 of voltage or current over the cable is given by 



T = s 4CL, (8) 



and knowing the time of propagation and the capacity at any fre- 

 quency the inductance of the cable at this frequency can be easily 

 computed. Since the resistance and leakance have only a slight 

 effect upon the time of propagation, this is the most direct method of 

 determining the average inductance of the cable. 



Measurement of Attenuation 



The attenuation constant of the cable is determined by measuring 

 the values of voltage received at one end of the cable, due to various 

 values of voltage of constant frequency impressed at the other end. 

 The impressed voltage may be either sinusoidal or square top in 

 shape, the latter being preferable for the reason that, at the low 

 frequencies and high voltages required, it is difficult to obtain a wave 

 form from an oscillator sufficiently free from harmonics to enable an 

 accurate determination of the fundamental component to be made. 

 Square top reversals of any frequency and amplitude can be easily 

 obtained by means of a relay actuated by an oscillator, and the 

 amplitude of the fundamental component can be accurately computed. 



At the receiving end, for the frequencies of particular interest, 

 the arriving voltage is practically sinusoidal, since the harmonic 

 components are eliminated by the higher attenuation of the cable for 

 such frequencies. This voltage is measured by terminating the cable 

 in an impedance which is very large compared to the characteristic 

 impedance of the cable, and measuring the potential drop across all 

 or part of this impedance by means of a vacuum tube amplifier in 

 the output of which is a thermocouple and meter. The advantages 

 of the high imi)edance termination are, first, that by reflection it 



