Theory of Faults in Cables. Gl 



end is reduced, the loss of current through the fault being- 

 greater than the increase in the current leaving the sending 

 end. Another effect is to increase the speed at which signals 

 can be made through the cable. A cable may be considered 

 electrically as a long cylindrical condenser, or as a conductor 

 having a great number of condensers of small capacity con- 

 nected at equidistant points to it on the one side and to earth 

 on the other. When an electromotive force is applied at one 

 end, to establish a permanent current in the circuit these con- 

 densers have to be charged, an operation requiring time for 

 its fulfilment; and before the current can cease when the elec- 

 tromotive force is removed, the charge must be got rid of : 

 in fact, the current results from the discharge of the cable's 

 electricity. If there is a fault, the discharge of the cable is 

 facilitated; for there is not only a smaller quantity of electri- 

 city to be discharged, but more paths are open to it. Similarly 

 the charging of the cable is facilitated, as will be seen by sup- 

 posing the cable when uncharged to contain two exactly equal 

 and opposite charges. Let one of these discharge itself. The 

 cable will then become charged Avith the other; and since the 

 discharge of the first is facilitated, the charging of the cable 

 by the second is also facilitated. With a fault, a smaller 

 quantity of electricity is required in order to produce the per- 

 manent state of electrification when an electromotive force is 

 applied at one end of the line than when there is no fault ; 

 therefore, other things being the same, a given fraction of the 

 final permanent state is more quickly reached in the former 

 than in the latter case. Similarly the effect of a given signal 

 is more rapidly dissipated in the former than in the latter case; 

 and consequently from both these causes signals can be packed 

 more closely together when the cable is faulty ; or, in other 

 words, the speed of working can be increased with equal 

 legibility. 



2. Before proceding to the mathematics of the subject, I 

 give some of the calculated arrival curves in simple cases. 

 Referring to fig 1, suppose in the first place the cable is per- 

 fectly insulated and free from charge, and that both ends are 

 to earth. At a given time £ = 0, introduce a constant electro- 

 motive force E at one end P of the cable. Then the well- 

 known curve of arrival of the current at the distant end Q is 

 represented by curve 1. Time is measured to the right, and 

 current strength upwards. The unit of time is 



ckl 2 . ckP 



10/r 2 * eXyj 42-86' 

 where I is the cable's length, and c, k its capacity and resistance 



