468 SUBMARINE CABLE LAYING AND KEPAIKING. 



the current through the fault is greater when taking the " free " 

 than the " earth." To make the current equal in both readings, 

 Mr. Kingsford added a resistance to the line while taking the 

 "free," but pointed out that in case of a high-resistance fault 

 near the distant end, the added resistance might be so high as 

 to interfere seriously with the sensitiveness of the test. In 

 that case the battery power would have to be altered. Dr. 

 Kennelly afterwards showed [The Eledridon, Feb. 12, 1886), 

 that if the added resistance is put in the battery circuit instead 

 of in the line this difl&culty is overcome and only half the 

 amount of resistance is required (assuming an even bridge and 

 battery of negligible resistance). There is also no subtracting 

 of the resistance from the result afterwards as must be done 

 when it is in the line. Hence it is a simpler operation to add 

 he resistance to the battery circuit, and this is usually done. 



To find what this resistance must be, we have to make a 

 few trials. First, take the ordinary test without any resistance, 

 from which we obtain the approximate value of .a- by the well- 

 known formula : — 



a; = Ex/(F-E)(L-E), . . . . (1) 



where E is the earth reading, F the free reading, and L the 

 copper resistance of the whole cable. The test should be taken 

 with one direction of current only, zinc to line, and balancing 

 to false zero. 



By equating the currents through the fault in the two read- 

 ings, a formula is obtained for the approximate resistance to 

 add, namely, 



(F-x) {a-vx) , 

 2(L-^) °^"^«- 

 This assumes an even bridge being used ("ft" being the resis- 

 tance of one arm) and the battery resistance small in com- 

 parison with the rest of the circuit. 



A second pair of readings is then taken, inserting the resis- 

 tance so obtained when taking the "free," and cutting it out 

 when taking the " earth." This gives a more correct value for 

 a'. Then using the new values of x and F in the above formula 

 a nearer estimate of the resistance to be added is obtained. 

 The resistance is then altered accordingly and a fresh pair 

 taken. 



After one or two pairs there is very little change to make ia 



