THE LOCALISATION OF BREAKS AND FAULTS. 431 



Hence the ratio between the quantities on the actual and ex- 

 tended cables is, by (5) and (6), 



DKE 



whence q^ DK 2r /-yx 



Q cl R^ 

 Referring to Fig. 247, the quantity {g) on the actual cable is 

 equivalent to the area between E and e (shown shaded), and the 

 quantity (Q) on the extended cable when to earth is equivalent 

 to the area of the whole triangle between E and 0. The ratio 

 between the capacities of these cables is equal to the ratio be- 

 tween their respective lengths, or, what is the same thing, their 



respective resistances — that is, as —. 



The ratio between the quantities of charge upon each Is 

 equivalent to the ratio ^ multiplied by the ratio of the mean 



potential acting respectively on each. The mean potential 



E 

 on the actual cable by formula (2) is — (2 - n), and on the 



E 

 extended cable - . The ratio between them Is therefore 2—%, 

 2 



and the ratio of charge on each is 



i^|.(2-..) = 72(2-7z) .... (8) 



Whence i \/ ^ Q /r^^ 



^ = 1-V1-^ (9) 



The ratio -^ is found from (7), in which it will be noticed 



that the factors D, d and R are observed and the others are 

 linown. 



Having thus determined n, the position of break from the 

 testing end is : — 



Distance of break x = 'Rn. . . . (lO) 



The derivation of the formula for distance of break is some- 

 what long, but the author has considered it best to show all 



