Theory of Faults in Cables. G3 



its final strength, half its final strength in 4* 7a, and -9845 in 

 14a. 



3. Now, referring to fig. 2, suppose both ends of the line 

 to be insulated, and the cable free from charge. At any time 

 £=■0 let a small charge be instantaneously communicated to 

 one end of the cable. This corresponds to working with con- 

 densers at both ends when the capacities of the terminal 

 condensers are very small, and terminal resistance negligible. 

 The charge thus communicated then diffuses itself along the 

 cable, becoming finally equally distributed. Sir W. Thomson's 

 mathematical theory indicates that the potential at any point 

 x rises in exactly the same manner as the current rises at the 

 same point when both ends of the line are to earth and a con- 

 stant electromotive force operates at one end. Therefore the 

 arrival curve of the potential at the distant end in working 

 with condensers at both ends is the same as the arrival-curve 

 of the current shown by 1, fig. 1. It is reproduced in 1, fig. 2, 

 for comparison with the curves for a fault. 



When there is a fault, or merely general loss through the 

 insulator, there is conductive connexion between the conductor 

 and earth ; consequently the charge initially communicated 

 to the beginning of the line must ultimately all escape, reducing 

 the potential everywhere to zero. Therefore, although the 

 current as shown by curve 1, fig. 1, never reaches its full 

 strength, yet, since insulation is never absolutely perfect, the 

 potential, as shown by curve 1, fig. 2, must sooner or later 

 reach a maximum and then fall to zero. As the leakage in- 

 creases, the time taken to reach the maximum decreases. The 

 maximum is reached in 10'3a, as shown by curve 2, fig. 2, 

 when there is a fault in the middle of the line of one fourth 



20a 



