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VIII. Alternating Currents in Concentric Cables. 

 By W. A. Price, M.A* 



Fig. 1. 

 B PA 



§1 ■ i ■ 1 



O 



AOB is part of an infinite electrical conductor possessing 

 resistance and capacity, the inductance being negligible. The 

 characteristic differential equation is 



d 2 u du 



d^ i=pri ~dV 



p being the resistance, and 7 the capacity per unit of length. 

 At A, B are inserted equal alternating electromotive forces 

 in the same phase, each represented by 2E sin cot, so that there 

 is no current at the middle point of AB. The distance AB 

 is 2 L. At any point P distant x from the potential due to 

 the electromotive force acting at A is 



|] g-a(L-x) gm { w t — a(L — x)) 



where 



■=\/T> 



and the current at P due to this force acting at A is 



E a 

 -— -e-«< L -*>[sin { w t — a(L— #)} + cos {(ot—a(L— a?)}]. 



The current at P due to the electromotive force acting at 

 Bis 



— =.-e-*V>+d[sm{a>t--a(L+a:)}+ cos {cot-a(L + x)}] 



acting in an opposite direction to the first. 



The potential at P due to the electromotive force acting 

 at B is 



Ee~< L+x ) sin {cot— a(L+%)}. 



Then the resultant potential at A is 



E {sin cot + e~ 2aIj sin (tot — 2«L) } ; 

 the potential at is 



2Ee- aL sin{cot—aL); 



* Communicated by the Physical Society : read April 9, 1897. 



