﻿18 L. Schwendler — On the general Theory of Duplex Telegraphy. [No, 1, 



m' b' 



since rr-, = — 



k — A — r 

 m 



and xb' = -;■ 



n 



Further if we call I' the value of h which in station I establishes rigid 



balance for any given values, a', d' and L', we have 



A' = b.' 8L' 



where 8 L' is the variation of L' which throws the balance out, and which 



variation may be either positive, zero or negative (Si' shall contain the 



sign in itself). 



Further substituting 



m' \!/' 



and ^' = a' 



n 



The expression for S' may be written as follows : — 



F' 



S' = p' oc G { i — 1 > = G' F 



^ ^ 81/ ^ 



f 

 which is the best form of S' for our purpose. 



The function 8' consists of two factors, namely, of G' which, at or near 

 balance, is proportional to the current by which duplex and single signals in 

 Station I are produced ; and of F' which at balance = O. 



Therefore to make S' as small as possible when balance is disturbed, we 

 can only do so by making F' as small as possible, which is evidently the 



case for y' = ■ a maximum. Further 



P' P' 



S' = G' F' 

 and since at or near balance 



P' a G' 

 it follows that 



D' = F' 



i. e. the 1st condition is also fulfilled by 



m' i//' 

 y = — 7-7- a maximvm, 

 ^ b' 



Our problem for station I would therefore be most generally solved if 



we make the function y' a maximum, remembering that the variables con- 



