﻿2i) L. Schwendler — On tJie general Theory of Duplex Telegraphy. [No. 1, 



The maximum of G, with respect to a, it will be seen, contradicts the 

 regularity condition, since a = g = d could only satisfy 



■^ = « 



d a 



if d were negative, a physical impossibility. 



However, the maximum of O with respect to g, gives 



|| = L(a=-g^) + 2ag(d-g)=0 



which is satisfied by 



a = g = d 



This is a fortunate coincidence and speaks well for the Bridge method. 



Now substituting for a and d their value g in the expression for the 

 current G, we get 



^ E 1 



G = — - -= — X const. 



4 L_+ 2g 



and this expression multiplied by .^/g gives the magnetic effect of the receiv- 

 ing instrument, namely : 



E a/2" 



M = - ^ ^ X const. 

 4 L -{- 2g 



which has an absolute maximum with respect to g for 



L 



Further substituting in the balance equation (V) 

 a = d = sf ==: — 



we get ^ =" 6 ' (^^^ 



We have therefore the following two equations by which the problem 

 is generally solved 



a=-g=:d = f= "1^ (Ylii) 



^-=1 = -^ (i^) 



by L being understood the measured conductor resistance of the hne 

 from that station for which the best resistance arrangement is to be 

 calculated. 



General Results. 



1. The branches of the bridge with the exception 

 of the one lying opposite the line must be equal to each 

 other and severally equal to half the measured con- 

 ductor resistance of the line. 



