﻿14 L. Schvvendler — On tlie general Theory of Duplex Telegrajpliy, [No. 1, 



H'lgid fulfilment of the first condition^ i. <3., D = 0. 

 For station I, we have D' = 



which equation can only be satisfied by A' = 



since the other factor of D' cannot become zero for quantities larger than 

 or smaller than go . Then substuting for A' its value, we have 



a' d'—bl (L' 4- /) = • (V) 



or balance in station I, when that station is sending and station II is at 

 rest, must be rigidly established. 



Therefore, if balance in station I is disturbed, say by Z' varying or by 

 any other cause* external to i'', we must have means of conveniently re- 

 estabUshing balance without delay. This of course could always be done 

 by altering either all the branches, «/, h', and dl, or any two of them, or 

 only one of them ; but it is clear that so long as the variation of L' 

 which disturbs the balance does not exceed certain limits, balance may be 

 regained by altering only one of the three branches available, and as this 

 will also be more convenient in practice than altering two of the branches, 

 or all three simultaneously, we shall make the suf)position that : — 



' Balance is re- established hy an appropriate re-adjustment of one of 

 the three available branches. '^ 



The question therefore is, which of the three branches, a, Z>, or </, is 

 the best adapted for the purpose ? 



To decide this we must remember that for station II, in accordance 

 with the first condition ( D = 0), a similar equation has to be fulfilled, 

 namely 



a'' d"— b'' (L" + p') = (V") 



Now p the complex resistance of the arrangement in station I, is a 

 function of all the resistances in station I, and similarly p the complex resis- 

 tance of the arrangement in station II, is a function of all the resistances 

 in station II. Therefore, generally, if in order to obtain balance, say in 

 station I, any of the three branches a\ h', d' were adjusted^ p> would alter 

 in consequence of this re-adjustment, and thereby the balance in station II 

 (equation V") would be disturbed, and vice versa. In other words the re- 

 adjusting in one station would interfere with the balance in the other station, 



* Causes of disturbance to balance external to L' are inappreciable in practice and 

 therefore may be neglected from the beginning. 



t Finally, when the best resistance arrangement has been found, the resistance of the 

 different branches will be expressed in terms of L, and therefore to keep the best arrange- 

 ment when L varies between any two given limits will involve necessarily a simultaneous 

 alteration of the resistance of all the branches. 



If, however, the variation of L is small in comparison with L itself, an alteration of 

 one branch for the purpose of re-establishing balance is justified, and would be absolutely 

 correct if the variation of L were infinitesimal. 



