of Duplex Telegraphy, 113 



in the line resistance*, we have at once 



8c', the total variation of the line resistance, may be either 

 positive or negative ; and supposing that Sc 7 contains its sign, 

 we have 



#'= -to 



m'Y' 



T 



to be made as small as possible. 



Now in case of the line being perfect (i= go), oV = c>L (a 

 constant with respect to the different resistances of each arrange- 

 ment, as was the case in the first solution). At present, 

 however, 8c 1 is a function of the resistances of the two arrange- 

 ments, which function must be first determined before we can 

 decide what general condition makes 1 as small as possible. 



We have 



p f ' being the complete resistance of station II. 

 Put 



l f =x 

 and 



Z' + Z" = L, 



. ' i(L— x + p") r 



~~ i + h—x + p ,J 



Now d 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 of a partial dis- 

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



These three causes may act separately or conjointly ; and their 

 total effect we can approximately get by taking the total differen- 



* The variations in c may be due~ to variations in the line, or to varia- 

 tions in the duplex arrangements. In the latter case they may be due 

 either to an alteration of temperature in the station ; and then the effect can 

 be only small — or to an accident (wire or connexion breaking) ; and then 

 the influence will become so great that nothing short of actual repairs 

 could help. Thus practically the problem has only to be solved for varia- 

 tions in the line. 



Phil. Mag. S. 4. Vol. 49. No. 323. Feb. 1875. I 



