﻿1874.] L. Schvvendler — On the general Thcorij of DiijpJcx Tehgraphj. 15 



and therefore rigid balance could be only attained after a series of successive 

 adjustments in both the stations, and then only, from a theoretical point of 

 view, approximately, introducing practical difficulties almost insurmount- 

 able. 



However, examining the positions of the three branches, it will be seen 

 at once that h acts as the galvanometer branch of a bridge for any current 

 arriving through the line. Thus if we were to fulfil the condition, 



a d— f g = (VI) 



for both stations, the value of p would become at once independent of 

 h* and consequently any adjustment of h' to re-establish balance in 

 station I would not affect in the slightest degree the balance in station II, 

 and vice versa. 



Thus, presupposing the fulfilment of this condition (equation YI) for 

 both the stations, the branch h would evidently be the best suited for adjust- 

 ment.f Under these circumstances it would then be clear that bakmce 

 in either station can be obtained by a single adjustment of h, and therefore 

 we may call equation VI " the immediate halance condition,''' and the 

 fulfilment of this condition, being of the greatest practical importance to 

 ensure the success of duplex working, we are justified, nay even compelled, 

 to use this relation (equation VI) as the basis for all subsequent investi- 

 gations. 



We will therefore suppose henceforth, that 



a d— f g = , (VI) 



is rigidly fulfilled for both the stations. 



But, as the value oif depends on the position of the key, which during 

 signalling moves from contact 3 to contact 4 and back, the rigid fulfilment 

 of equation (VI) necessitates at once that 



w-f-)8=:f (VII) 



not only for both the contacts 3 and 4, but also for all the intermediate 

 positions of the key. Thus supposing that w + i^ = f, «. e. the resistance 

 from contact 4 through battery to earth equal to the resistance from contact 



3 to earth, a key constructed in such a way that contact 4 is not broken 

 before contact 3 is made, and that contact 3 is not broken before contact 



4 is made, would fulfil the required condition entirely. Keys of this kind 

 can be easily enough constructed. It is true that in any su3h key, there 

 will be always a moment when the contacts 3 and 4 are simultaneous, and 

 when therefore the resistance to earth is not /, as it ought to be, but only 



^ (g + d)(a+f) (ad-fg )^ 



P— a + d + f+g r(b) 

 Therefore if afZ — fg is very near zero, p becomes most rapidly independent of h. 



f Further, it must be remarked that, even if the condition ad — fg = be not 

 rigidly fulfilled, still by adjusting in the branch h we have " accelerated" balance, whereas 

 hy adjusting in a or d we should on the contrary have " retarded" balance. 



