of Duplex Telegraphy. 137 



However, the maximum of G with respect to g gives 

 |? =L(a*-,f) + 2^-^=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 



G= j =. — x const. : 



4L + 2y ' 



and this expression multiplied by V ' g gives the magnetic effect 

 of the receiving-instrument, namely 



E Vn 

 M = tt-ttt x const., 



which has an absolute maximum with respect to g for 



L 



Further, substituting in the balance-equation (V.) 



L 



9 



a = d=g=~, 



NVC S et 0=^ (IX>) 



We have therefore the following two equations by which the 

 problem is generally solved : — 



a=g = d=f=\, (VIII.) 



*-i-» m 



by L being understood the measured conductor resistance of the 

 line from that station for which the best resistance -arrange- 

 ment is to be calculated. 



General Kesults. 



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 conductor resistance of the line. 



2. The branch lying opposite the line should be equal to the 

 sixth part of the measured conductor resistance of the line; and 

 only in this, the smallest of all the branches, should readjustment of 

 balance be made. 



Nos. 1 and 2 necessitate the alteration of all the branches if 

 L, the measured conductor resistance, alters within wide limits. 

 A determination of L will therefore be required from time to time. 



