64 THE SCIENTIFIC PAPERS OF 



cable, the end B of which is to earth, and A C the electro-motive 

 force E of a battery, one pole of which is in connexion with A, the 

 other pole being to earth. Then, according to the laws of Ohm, 

 supposing the cable to be of equal section and conductivity 

 throughout, the curve of the electro-motive force at any point 

 along the line is indicated by C B. 



In 1849 (see " Poggendorff' s Annalen"), Werner Siemens proved 

 that when a current is sent through a submerged cable, a quantity 

 of electricity is retained in charge along the whole surface, being 

 distributed proportionally to the tension of each point. Thus, the 

 tension of the electricity on any small intermediate given length, 

 d x of the conductor at the distance x from A may be represented 

 by y; the quantity of electricity d q t by which the outside cylinder 

 d x is charged according to the formula given previously for in- 

 duction in cables is : 



This quantity of electricity d q has to pass through the resistance 

 of section x in order to arrive at d x. 



The resulting current develops d q in the time d t, and we have 

 accordingly the equation 



., Edt Er*ir\ f} . 

 aq= -= - at 

 x x 



r* ir\ 



By equating these values of d q, a differential equation is 

 obtained : 



y . 2 ITT dx Er* ir\ , , 



~ 



by substituting for y its equivalent : 



E : ~l : l-x 



l-x) 

 I 



