of Duplex Telegraphy. 121 



at once that the fulfilment of the immediate balance condition is 

 required also in order to have the greatest possible constancy in 

 the signalling current. Thus, when investigating the question 

 of maxima currents, we are justified in presupposing the rigid 

 fulfilment of the immediate balance for both stations, i. e. 



ad—gf=0. 



Further, as it has been shown before that the fulfilment of the 

 regularity-condition 



a=:d=g=f 



for both stations does make the effect of the disturbances still 

 smaller, we have only to investigate the current at balance, and 

 to show that the condition of maximum current becomes iden- 

 tical with the regularity-condition, whence it would follow that 

 the duplex method under consideration is perfect in every con- 

 ceivable respect. 



The question to be solved stands, therefore, as follows : — 

 Two signalling currents, the expressions of which are known, 

 have to be made simultaneous maxima, while the different variables 

 are linked together by four condition equations. 

 Thus 



the current which produces single and duplex signals in sta- 

 tion I. ; 



G»=E'|>f", 



the current which produces single and duplex signals in sta- 

 tion II. 



a'd'-2>' c '=0, . . (1) 1 



balance in /, station I. ; 



a"d"-b"c"=0, . (2) 

 balance in g n , station II. ; 



a'di-g>f = 0, . (3)1 



a»d»-g«f = 0, . (4) J 

 immediate balance in both stations. 



Condition equations. 



Now d is a function of p" ; but, on account of equation (4), p n 

 is independent of b" ; thus c' is also independent of b". In the 

 same way it follows that c" is independent of b' ; thus b ! and W 

 can be explicitly expressed at once, and from the four condition 

 equations we haye 



