398 BULL SYSTEM TECHNICAL JOURNAL 



Likewise, the resistance of one wire between l^nd 1 of the cal)Ie and 

 the faults is: 



i' - '') = v^,- ('") 



AppUcalion: To apply the Double Varley method, ordinary \'arley 

 measurements, V\ and V-i, are made from the two ends of the cable, 

 using bridges with ecjual ratio arms, and the loop resistance, 2r, of 

 the wires is measured. The location, x or {r — x), can be calculated 

 from Formula (9) or (10), and then converted into feet in the usual 

 manner. 



Similarly, using the Rule of Resultant Faults, it can be shown that 

 Formulas (9) and (10) also apply when only one of the wires used for 

 Varley measurements is faulty. In this case the resistance, x, of the 

 portion of the faulty wire between the distant end of the cable and 

 the fault is: 



V F 



where V is the balancing resistance for a Varley measurement made 

 from one end of the cable. This formula indicates that, w^here the 

 ordinary Varley method (Figs. 5 and 6) is used, the insulation re- 

 sistance of the "good" wire should be at least several hundred times 

 as high as the fault resistance of the faulty wire. If this condition 

 does not obtain the Double Varley method should be used. It will 

 be clear, however, that the Double Varley method may be used, if 

 desired, instead of the ordinary Varley method in cases where a wire 

 of suflficiently high insulation resistance to be a "good" wire is avail- 

 able. In such cases the sum of the Varley balancing resistances ob- 

 tained by measurements from the two ends of the cable will be equal 

 to the loop resistance and Formula (9) will reduce to Formula (1). 



The Double Varley method is workable only if the conductor re- 

 sistances of the two wires used for measurements are equal. It can 

 be shown that, if the conductor resistance of the ware having the fault, 

 AI, is rm and that of the wire having the fault, 7^, is r/, and if the normal 

 insulation resistances of the wires are equal and uniformly distributed 

 so that they may be regarded as concentrated at the middle of each 

 wire. Formula (9) becomes: 



X = r/ 



^^ 12MF + N{M -f F)-\ -f '-^-^ IMF + N{M -f F)] 



Yl±Il[_2MF + N{M ^ F)-] 



+ {rj - rm)lMF + N{M + F)] J 



