of Duplex Telegraphy. 131 



The question therefore is, which of the three branches, a 3 b, 

 or d, is the best adapted for the purpose ? 



To decide this we must remember that for station II., in ac- 

 cordance with the first condition (D = 0), a similar equation has 

 to be fulfilled, namely, 



a"d u -b"(L'i + p f ) = 0. , ", . . (V.) 



Now p l , the complex resistance of the arrangement in station 

 I., is a function of all the resistances in station I. ; and similarly 

 p", the complex resistance of the arrangement in station II., is 

 a function of all the resistances in station II. Therefore, gene- 

 rally, if in order to obtain balance, say in station I., any of the 

 three branches a 1 , V, d 1 were adjusted, p' would alter in conse- 

 quence of this readjustment, and thereby the balance in station 

 II. (equation V".) would be disturbed, mi&vice versa. In other 

 words, the readjusting in one station would interfere with the 

 balance in the other station, 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 insur- 

 mountable. 



However, examining the positions of the three branches, it 

 will be seen at once that b acts as the galvanometer-branch of a 

 bridge for auy current arriving through the line. Thus, if we 

 were to fulfil the condition 



ad-fg=0 (VI.) 



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

 dent of b* 9 and consequently any adjustment of V to reestablish 

 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 (equa- 

 tion VI.) for both the stations, the branch b would evidently be 

 the best suited for adjustmentf. Under these circumstances it 

 would then be clear that balance in either station can be obtained 

 by a single adjustment of b; and therefore we may call equation 

 VI. " the immediate-balance 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 eom- 



* -.(9+d)(a+f)_(ad-fgY 

 P a+d+f+g ¥{b) ' 



Therefore if ad—fg is very near zero, p becomes most rapidly indepen- 

 dent of b. 



t Further, it must be remarked that, even if the condition ad—fg = Q be 

 not rigidly fulfilled, still by adjusting in the branch b we have "accele- 

 rated" balance, whereas by adjusting in a or d we should, on the contrary, 

 have "retarded" balance. 



K2 



