406 BELL SYSTEM TECHNICAL JOURNAL 



and since, for a testing current of very low frequency, C2 and x are 

 proportional to D, while (Ci + C2) and r are proportional to T: 



a 



and we may write; 



C, + G 

 F ' T 



= .T, 



\\'hen the bridge is balanced to the value R, with wires 1, 2, 3 and 4 

 connected together at the distant end, the amount of unbalance 

 between wires 1 and 2 is measured. Assuming that F is the only 

 unbalance present, and that the conductor resistances of wires 1 and 

 2 are equal : 



Rr.^F 



and therefore; 



D = ^T. (12) 



Application: The same general requirements set down for the short 

 cable method must be met to secure accurate results with the long 

 cable method. While Formula (12) has been developed specifically 

 for non-loaded cable, it is clear that it applies also to loaded cable, 

 provided the effective series impedances of the wires, including the 

 loading coils, are very low compared to the effective shunt impedances 

 of the wires. A testing frequency of three or four cycles per second 

 is sufficiently low to satisfy this requirement on telephone cables up 

 to a repeater section in length. If, however, the cable is only a few 

 miles in length, the effective sensitivity of the bridge may be too low 

 for satisfactory results. 



In general, the long cable method is suitable for locating, with 

 reasonable accuracy, series resistance unbalances ranging from about 

 10 ohms to several thousand ohms. A well insulated bridge and a 

 fairly sensitive galvanometer are desirable, especially when workmg 

 with faults of low resistance. 



An essential requisite for accurate results is that the resistance of 

 the fault remain constant while a set of measurements to determine 

 Ro and Re is being made. In the application of the method, therefore, 

 the bridge voltage used should be as low as practicable. Bridge volt- 

 ages of, say, 100 volts for measuring Rq and six volts or less for measur- 

 ing Re are usually satisfactory. In this connection it can be pointed out 

 that if measurements Roi and R02 are made from the two ends of the 

 cable it is unnecessary to measure Re since {Roi + ^^02) will equal F 



