114 PROCEEDINGS OF THE AMERICAN ACADEMY. 



Thus in Figure 9 the receiving-end resistance is 1436.1 X 1.422 = 

 2042 ohms. 



The voltage at junction n is : 



e n r = e m £ 20(n-m) = €q e 2n» v0 J ts< ( 6 Q) 



At the distant end, or junction 0, it is : 



e O r = e m £- L > a = e m e.- 2 ™ 9 volts. (70) 



At the wth leak, it is : 



£ (2n— 1)9 



cosh 6 



<nr = *m ^ n ~ m) = «o ^T^IT volts. (71) 



The current strength at the sending end, or junction m, is : 



I m r n = — amperes. (72) 



To 



At junction n it becomes : 



Inr = Im e 2 *^^*) = I c 2n ° amperes. (73) 



At the receiving end it is: 



I oro = ^5 e -L 2 a = e jn e -2m0 = J m e -2m9 ampe reS. (74) 

 T T 



At any leak the ratio of ongoing to arriving line current is 



in — l,r 



*nr b 



— t—29 



(75) 



General Propositions. 



Equal Increase of Receiving-End Resistance due to Resistance inserted 



at either End of Line. 



When a resistance a is added to the line at the sending end, the send- 

 ing-end resistance is obviously increased by a ; but the receiving-end 

 resistance is increased by a cosh La = a cosh 2 mO ohms. Comparing 

 this result with formula (42), it is evident that a resistance <r adds 

 a cosh 2 m6 to the resistance of an artificial line, or a cosh La to that of 

 a smooth line, whether it be added at the sending or receiving end. 

 Thus, if to the sending end of the artificial line in Figure 5, a resistance 

 of 750 ohms be added, the sending-end resistance will be increased 

 to 2103.4 ohms, and the voltage at the end A of the artificial line will 



