174 Mr. L. Schwendler on Testing Telegraph Cables 



or balance in the galvanometer is established. According to the 

 two laws of Kirchhoff, we have eight independent equations be- 



tween these different resistances and their respective intensities; 

 viz. : — 



A-B -G=0, 

 C-D-G = 0, 

 F-H-P=0, 

 B-H-Q=0, 

 Q-P+C=0, and 



aA+gG- dD=0, 

 //Q+pP-AH=0, 

 gG + cC-qQ-bB = Q. 



By eliminating seven of the intensities, with exception of F and 

 G, and the latter developed, we have 



G = F 



q(dh—ap)-\-{p + q-\-h) (bd— ac) 



' {p + q + h){g(a + b + c + d) + (a + d){b + c)} + q{p + h)(a + d+q 



Supposing now F > 0, i. e. E > 0, we have to put, in case G = 0, 



q(dh — ap) -\-(p + q-\-h){bd—ac)=0 } 



which equation gives the required general relation between the 

 different resistances if balance is established; and it is evident 

 that generally, when q, h, and p are definite quantities and larger 

 than zero, the above equation is different from the simple law of 

 Wheatstone's diagram. Reverting now to fig. 2, and calling 

 the resistance of the fault in o' ¥ x , the resistance of the fault in 

 o n F y , and oc and y their respective distances, expressed also in 

 resistances and measured from the same end I of the cable, we 



