Theory of Faults in Cables. 67 



when z is very small ; so that for a fault of small resistance 

 the same results follow as before for its effect on the propor- 

 tional amplitude. 



7. Since the proportional amplitude is increased by the 

 fault for the same speed, a higher speed is obtained with the 

 same proportional amplitude. Thus, with the ends of the 

 cable to earth, as in paragraph 5, if V-\ is the value of n when 

 there is no fault, then, to have the same proportional amplitude 

 with a fault of resistance zkl in the centre, we must increase n 

 to n 2 , so that 



4z 



/ 1 1 y 



Now the speed is inversely proportional to r, and therefore 

 directly proportional to n 2 ; therefore the percentage increase 

 in the speed is 



<3-0- 



100! 



For W! = 8, 9, and 10 we shall find rc 2 =9*7, 10-7, and 11-7, 

 and the increase in the speed 47, 41, and 37 per cent., if 

 z= 32~> which would make the greatest possible received cur- 



* E 



rent 9ir 



For a fault of no resistance, z=0, and 



With %=8, 9, and 10 this gives n 2 =10'2, 11-3, and 12'4 ; 

 and the increase in the speed is 62, 57, and 53 per cent. These 

 values of n^ namely 8, 9, and 10, are chosen on account of 

 their nearness to the values in the working of long cables. 

 The corresponding values of t are 2*10, 1*66, and l*34a. 



8. When a natural fault, or local defect in the insulation 

 is developed in a cable, it tends to get worse — a phenomenon, 

 it may be observed, not confined to cable-faults. Under the 

 action of the current, the fault is increased in size and reduced 

 in resistance, and, if it be not removed in time, ends by stop- 

 ping the communication entirely. Hence the directors and 

 officials of submarine-cable companies do not look upon faults 

 with favour, and a sharp look-out is kept by the fault-finders 

 for their detection and subsequent removal. But an artificial 

 fault, or connexion by means of a coil of fine wire between 

 the conductor and sheathing, would not have the objectionable 



F2 



