176 Mr. L. Schwendler on Testing Telegraph Cables 



o n , where in reality no fault exists ; but as W, the resistance at 

 which balance in the galvanometer is established, must evidently 

 be the same in both the formula?, the balance would not be 

 affected by moving the two faults from o' o ft to o ; and for this 

 reason we may call that imaginary fault whose position is ex- 

 pressed by formula (2) : — 



The resultant fault of the two real faults. 

 By eliminating W from both the equations, we have, by put- 

 ting for a. its value, y—z z—x 



~T~ = ~F7' • ( 3 ) 



*-y i-X 



which is a very simple and interesting relation between the two 

 real faults and their resultant fault v : see fig. 5 . 



Fig. 5. 



y 



As ^- and =r- are the relative conductivities of the faults in 



F 



F 



o 1 and o", and calling in future the product of relative conduc- 

 tivity and distance from the resultant fault the moment of a fault, 

 we may define, according to equation (3), the position of a re- 

 sultant fault as follows : — 



The resultant fault is that point for which balance of the mo- 

 ments of all faults is established. 



The resultant fault of a cable is therefore a point similar to 

 the centre of gravity ; and we may infer directly that all for- 

 mulae which give the positions of the centre of gravity are appli- 

 cable for the position of the resultant fault, substituting only for 

 weight conductivity. 



But it will be better to find the general formula for the posi- 

 tion of a resultant fault directly, without referring to such ana- 

 logy. If we develope z from equation (3), we have 



F, +F, 



(4) 



by the aid of which we can calculate the position of the re- 

 sultant fault for any number of real faults, if their positions and 

 resistances are known. Supposing a cable having n faults, of 



