THE LOCALISATION OF BKEAKS AND FAULTS. 443 



at both ends, the insulation resistance at 1st min. and the true 

 CR. If the true CR is not known the approximate CR can be 

 used. In fault testing L may be taken as the observed CR or 

 the apparent CR as worked out by a localisation test. 

 Again, by division of (6) by (5), we obtain 



i = AJ^^:A (9) 



This is the mathematical expression for Murphy's theorem, 

 which may be stated as follows : — 



The N.R.F. position divides a cable into two parts, the 

 resistances of which are inversely as the square root of the 

 differences between the true and observed CR's from the two 

 ends. 



Dividing the line resistance in proportion to the ratio (9), we 

 obtain the distance of the N.R.F. from the A end in another 

 form approximately 



J> = ^1=7 (10) 



and the distance from B end approximately 



L 



<1 = - 



^Vi^' 



(11) 



The last two formulse are useful to find the position of the 

 N,R.F. from the observed CR's at both ends and the true CR 

 without it being necessary to know the insulation resistance. 

 If the true CR is not known, the approximate CR may be used. 

 In fault testing, L may be taken as the observed CR or the 

 apparent CR as worked out by a localisation test. 



For example, suppose we have from tests on a good cable 

 CR observed from A end = 8,320 

 „ „ „ B „ =8,485 



The true CR on the splice list is 8,500 ohms. We shall find 

 the position of the N.R.F. most conveniently by formula (10) 

 or (11) as the insulating resistance is not given. 



Distance (p) from A = — ' — -j^^ = 1,900 ohms. 



^^ 1 + V12 



