﻿J874.] L. Schwendler— 0;j the General Theory of Duplex Telegraph/. 225 



These expressions follow from tlie general formulco by fulftlliiig the 

 regularity equation (VIII) for both stations, and in addition the balanee 

 conditions. 



Multiplying now G' by ^ g' and G" by -/ g"^ we get 

 P' = ^" ^3' 



4 g"-\-d' 



/* 



4 ^ + e 

 the magnetic moments of the two instruments in Nos. (I) and (II) Sta- 

 tions respectively ; and, considering that* 



li! jjif' i 



g' + g" 9' + g' ~Q 

 where Q = (^' + V) {g" + I") + i {q' + / + Z' -f- I"), we may write the 

 two above expressions as : — 



The first expression has clearly an absolute maximum with respect 

 to g' ^ and the second with respect to g\ but these two maxima cannot be 

 simultaneously fulfilled, and do not therefore represent a solution in this 

 particular case. But if we consider that during a duplex signal both the 

 instruments g' and g" are in circuit, while during a single signal, though not 

 both the instruments yet certainly their equivalent in resistances are in 

 circuit, it will be clear why simultaneous maxima of the two single expres- 

 sions are not possible. It represents simply the more general case to which 

 the question belongs of making the magnetic moments of two instruments, 

 connected up in the same single circuit, maxima. In this case it is well 

 known we can do nothing more than make the sum of the magnetic mo- 

 ments a maximum, and here therefore we must do the very same. 



Adding then we get 



"^ ~4 Q 



w 



4 „. /'* 



l)ut g"^ =*b" (f' on account of balance in Station (II) 

 This can be easily shewn by substituting for /*', ^i", c/ and r/ theii^ actual A^alucs. 



