of Duplex Telegraphy. Ill 



Now the first relation that we shall introduce is 



w=/3=f 



for both stations, which may be called most appropriately " the 

 key equation" 



The introduction of this relation at the outset is quite justified ; 

 for say that S' = D'=0 is rigidly fulfilled in station I. when sta- 

 tion I. is sending and the key in station II. is at rest, and sup- 

 pose the electromotive force in station II. equals (the electro- 

 motive force of all elements annulled and only their resistance 

 /3 !f left), then, moving the key in station II. from its rest con- 

 tact to its working contact, the regularity condition S'=D'=0 



would be (i. e. balance in station I.) at once disturbedif w" + /3 ,/;> f l 



during the motion of the key, even if no variation in the line 

 took place. Thus it is paramount to have w+/3=f for each 

 station during the movement of the key *. 

 But if, for instance, in station I. 



w'+0 = f, 

 it follows that 



Hence, substituting its value for a 1 and reducing, we get more 

 simply 



s'=¥+'-™-> &■) 



but as 



N' ~ AW 

 m! 



* To fulfil the key equation most exactly during the movement of the 

 key, I have constructed a key (constant-resistance key) based on the fol- 

 lowing principle. During the first movement of the key (up or down 

 stroke) a force is stored up in a spring before the contacts are changed, 

 which force finally causes the change in these contacts ; for this reason the 

 two principal contacts of the key coexist only for an almost infinitesimal 

 time, the length of which is moreover independent of the signalling speed. 

 Thus for this key w-\-f=fi is fulfilled in all positions except one, when it is 



— - — , but for such a short time that the error cannot have any disturbing 



influence whatever. 



f \]/' is the proportion of the total current arriving at point 1 (diagram), 

 which passes off through the instrument g' when the key of station I. is 

 at rest. Then \J/', being a r function of a', b', d\ g', is also a function of 

 fl cf)' is the proportion of the total current arriving at point 1 (diagram), 

 which passes through the instrument #'when the key of station Lis sending ; 

 thus, besides being a function of a', b', d', and g', it is a function of w'-\-fi' 

 instead of/'; and as (j)' and ^/ f are otherwise quite similar functions, they 

 become identical if we make f = w'-h3'. 



