106 PROCEEDINGS OF THE AMERICAN ACADEMY. 



Thus in Figure 6 the current at the sending end is 0.065617 ampere. 



The current at junction 3 will be 0.065617 X Sm J'°^}^ = 0.029409 

 J sinh 1.7586 



ampere. 



At the nth leak, the ratio of ongoing to arriving line current is 



h-i sinh 2 (n- 1)6 

 I n sinh 2 n6 ' K l) 



The current escaping at the nth leak is : 



, _ , cosh (2 n - 1)6 _ , cosh (2 n - 1)6 

 in-< n g - e g - ^ Q - e m g — ^——^ 



,cosh(2n-l)^ ' 



= e ^ cosh^cosh2m^ am P ereS ' (18) 



Line grounded at Far End. (Figure 5.) 



Sending-End Resistance. 



The sending-end resistance at the nth junction with the far end 

 grounded is : 



R g = To tanh L 2 a = r tanh 2 n6 ohms. (19) 



In the case represented by Figure 5, for m = 5, R g = 1436.1 X 

 0.94235 = 1353.3 ohms. As we ascend the line from junction to 

 junction, the resistances are in proportion to the hyp. tangents of the 

 angles of those junctions. 



The sending-end resistance at and excluding the nth leak is: 



„, .sinh (2 n — 1)6 . ,_. 



y "-* c M h(2.-2)» 0hmS ' (20) 



The sending-end resistance at and including the nth leak is: 



„, .sinh (2 n — 1)6 



R '°.» = r °' C osh 2 n6 ° W (21) 



When n is indefinitely increased, (20) becomes: 



R'^o^ro'* ohms, (22) 



and (21) becomes: 



fl'a,°c = r 'e-o ohms. (23) 



