﻿224 L. Schwendler — On the General Tlieory of Ditplex TelegrapTiy, [No. 4, 



The fulfilment of the immediate balance condition is therefore no longer 

 an assumption made to afford convenient and quick means of adjustment 

 when balance is disturbed, but, as has been proved, is necessary in order to 

 reduce the effect of any disturbance whatever to a minimum. 



Supposing now the fulfilment of the immediate balance, we have 

 __ {g -\-d){a + f) 

 ^a+d+f-i-g 

 which again has a relative maximum for 



g + d== a + f 

 whence it follows, in consequence of equation (VI), that 



a = d=f=g (YIII) 



represents the general solution of the problem. 



This result might of course have been anticipated from the special 

 solution, since equation (VIII) gives only a relation between the branches, 

 quite independently of i. It remains now to determine the magnitude of one 

 of the branches, and to this end we have to consider the magnetic moments 

 of the receiving instruments. 



Maxima Magnetic Moments. By definition we have 

 S=F—Q 

 for both stations, and as it has been proved before quite generally that 

 S = if A == 0, i. e., if rigid balance in the station for the out-going 

 current be established, we know at once that at or near balance the currents 

 which in one and the same station produce single and duplex signals must 

 be identical, and need therefore express the magnetic momenfj in each station 

 for one current only, by presupposing balance in both the stations. 

 The currents which at or near balance produce the signals are 



*^' = T'7- + -? in station (I), 



U" 



fX 



'^' *''" = -4-7t7 " " (">• 



* For balance in Station (II) the current passing through Station (I) is 



n" 



h" 



"but ^* = »|/" on account ofa — d==g=fm each Station 



b" . 



7'' 



but w" = 4 f/* {g" -f b") 

 and dividing by b" we get 



