﻿222 L. Schwendler — On the General Theory of Duplex Telegraphy. [No. 4, 



of the resistances of the two arrangements, which function must be first 

 determined before we can decide what general condition makes 6' as small 

 as possible. 

 We have 



' - ' + i + r + p" 



p" being the complex resistance of Station (II). 



Put V = X 

 and^'H- l"=L 



i {L — X + p'O 



.-. c =^x-\- 7, 



I -^ Jb X '\- p 



Now c' may vary from three essentially different causes, namely : — 



1. X varies, or the position of the resultant fault alters ; 



2. i varies, or the resistance of the resultant fault alters ; 



3. L varies or the real conduction of the line alters, as may happen 



by an increase or decrease of the temperature along the whole 

 length of the line, or by the occurrence af a partial discon- 

 tinuity (imperfect joints, loose shackles, &c.). 

 These three causes may act separately or conjointly, and their total 



effect we can approximately get b}^ taking the total differential of c' with 



respect to x^ i, and L. 



dc' 



d£ 



dx 



dc' 

 dx -f -jr di •\- 



Zc' = -— S^ -f 

 dx 



di 

 d&_ 

 di 



dc' 

 dL 



dL 



Si + %. SL 

 dL 



approximately, 



which expression is perfectly true, however, for small variations S.r, 8/, 

 and hL. 



Now* 



m' xl;' N' . , , c^ / 



— — =—^-\.bc=p'-^c + oc 



but 



m' 



=" 





b' 







N' 



K' 



— 



A' 





N' 





K' 





A' 



n' 



li? 



~ 



T 



~ 



~b' 



^ 



K' 





N' 





A' 



n' 



b' 





ni' 



+ 



~b' 



m' 



A' 



= 



h' Sc' 







b' 



= 



Di' 



+ 



dc' 



in' 



