36 BELL SYSTEM TECHNICAL JOURNAL 



ments of conductor for a given transposed cable can be found and 

 the calculated values of ho and hi may be used to plot a correction curve. 



If, for a given transposed cable, a correction curve is calculated as 

 outlined above, it will be found to have the general characteristics 

 shown diagrammatically in Figs. 4 and 5. Fig. 4 is for the case 

 where the faulty conductor enters the measuring station in the outer 

 layer and Fig. 5 for the case where the faulty conductor enters the 

 measuring station in the inner layer. In the lower half of each figure 

 the total errors are separated into their component parts. In either 

 Fig. 4 or Fig. 5 the total error curve can be assumed to be made up of 

 two factors, a hyperbolic error similar to that shown in Fig. 2, and a 

 straight line error due to the fact that the two halves of the cable do 

 not have the same unit capacitance. The latter error would be 

 present in such a cable even though its length were insufficient to 

 cause a hyperbolic error. Such a division can be made because the 

 constants of the inner and outer layers do not differ enough to affect 

 the hyperbolic error appreciably. It is not possible to plot a general 

 family of curves of the type shown in Fig. 3 due chiefly to the fact 

 that the location of the transposition point and the difference in total 

 length of different cables constitute a double variable. The need for 

 a correction involving the double variable has been met by the develop- 

 ment of open location equipment and methods which reduce this 

 error to a negligible magnitude for the lengths and types of lines 

 encountered in practice. The rigid treatment is, however, that out- 

 lined in formula (2). 



The amount of the hyperbolic error can be calculated closely 

 enough using the average constants of the inner and outer layers. 

 The size of the straight line error due to the different capacitances of 

 the inner and outer layers is found as follows: 



Let Ci and Co represent the adjacent and far end capacitances per 

 unit length and Di and Do the respective lengths of these sections. The 

 total conductor capacitance is then DiCi + D^Co. If D is the location 

 of the fault and D is less than D^, that is, the fault is in the half of the 

 cable adjacent to the measuring station, the bad wire capacitance is 

 DC\. The apparent location is 



DCi 

 DiCi + AC2 

 and the correction is 



D DCx 



Dy + D2 DiC\ + D2C2 ' 



Similarly when the trouble occurs beyond the transposition point, 



