116 Mr. L. Schwendler on the General Theory 



This result might, of course, have been anticipated from the 

 special solution, since equation (VIII.) gives only a relation be- 

 tween the branches, quite independent 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 in- 

 struments. 



Maxima Magnetic Moments. — By definition we have 



S=P-Q 



for both stations ; and as it has been proved before quite gene- 

 rally that S = if A = {i. e. if rigid balance in the station for 

 the outgoing 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 moment 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 



and 



G'= 



E" 



V'-M" 



in station I., 



G"= 



E' 



= 4 " 



, , in station II.* 

 g' + c' 



These expressions follow from the general formulae by fulfilling 

 the regularity equation (VIII.) for both stations, and, in addi- 

 tion, the balance-conditions. 



* For balance in station II. the current passing through station I. is 

 But ^//'=4'" on account of a = d=g=fm each station ; 



Kutn"=4g"(g"+b"). 

 and dividing by b" we get 



h" 

 .-. G' = E — ii\ 



G'= E ' 



4 „ , a" 2 

 v + - — 



But g" 2 = b"c" on account of balance in station I. ; 



.\G'=_ . 



E" fx' 



4 g c 



