60 THE SCIENTIFIC PAPERS OF 



same, whilst the further end is to earth. We have then by means 

 of Ohm's law, the following equations : 



1. c = 



2. a^ 



3. bi = 



s . ?/ 



Z . 



By eliminating z and y the resistance x is found by the 

 following expressions : 



2=^1+' (VIII.) 



c-bf, Ib c-a\ 



= a. (1- A / _ ] 



a-b \ V a c-b/ 



x /a c-b 



= Vj -^r a 



! -a) (c- a). 



If the cable was not perfectly well insulated before the fault 

 under consideration appeared, the values a, b, and a 1} b v supply 

 the means for determining approximately the resistance y of the 

 previous leakages. This resistance 7, together with the final readings 

 of insulation 2 , b, gives the place of the fault as follows : 



In all these measurements the battery power must be so regu- 

 lated as to keep the polarisation at the faulty place uniform. 

 This is to be accomplished by determining preliminarily the place 

 of the fault, then by regulating in the final measurement the 

 number of cells so as to send from each side an equally powerful 

 current through the fault, taking care not to take the observations, 

 till the polarisation has reached its maximum. We attach con- 



