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BELL SYSTEM TECHNICAL JOURNAL 



hyperbolic errors for different frequencies of testing potential showed 

 that this error decreased with frequency, the optimum value of 

 frequency being zero. This relation is shown in Fig. 7, where the 

 maximum errors at different frequencies for a 60-mile length of 19- 

 gauge, non-loaded cable are plotted. However, with zero frequency, 

 the sensitivity to unbalance for an impedance bridge network is also 

 zero, increasing as the frequency increases. 



Z 4 6 8 10 12 U 16 18 20 

 Frequency of Testing PrtenUal in Cycles per Second 



Fig. 7 — The maximum hyperbolic error for various frequencies of testing potential. 



The problem, then, was one of selecting a frequency which would 

 be low enough to make the hyperbolic errors negligible for all cases 

 of lines as regards length, gauge, and loading, and at the same time 

 provide a sensitivity which would be sufficient to permit an accurate 

 balance of a bridge. From this standpoint it may be observed that 

 for a decreasing frequency of testing potential the maximum rate of 

 decrease of hyperbolic error appears at about four cycles as shown by 

 Fig. 7. A computation of the hyperbolic error for measurements made 

 at four cycles on sixty miles of cable gives results as follows: 



