﻿1874.] L. Schwendler— 0;j the general Theory of Duplex Telcgmphy. 19 



tained in y' have to fulfil two condition equations, namely the immediate 

 halance (equation VI) and the balance (equation Y). 



Substituting for m' its value, and remembering that 



a + g 

 on account of the immediate halance condition (equation VI), we get 



^ a' + g' "^ b' 



But 



a^ (g' + d') 



; ; — = P 



a 4- g 



the complex resistance of station I (the expression for p has become thus 



simple on account of the immediate balance condition VI). 



Further 



a'd' ,, 



(on account of balance in station I, being established, equation V). 



Thus we have 



y --=?' •\- P" + ^' 

 for station I. 



And similarly 



y"=p' + p"+L" 

 for station II. 



Therefore the rapid approximation of hoth the functions D and S tO' 

 wards zero in hoth stations is obtained, if we make the complex resistances p' 

 and p" maxima. 



Now the form of p shews at once that it has a maximum for 



(a + = (g + d) 

 which, in consequence of equation (VI), gives at last 



a = g = d = f (VIII) 



From the development of this result it will be clear that the relation 

 expressed by equation (VIII) must hold for either station independent of L. 



All that now remains is to determine h, and further to fix the abso- 

 lute magnitude of any one of the branches. Before doing this it is however 

 necessary to enquire what the other factor of S, namely G, becomes in 

 consequence of fulfilling the regularity condition as expressed by equation 



(vni). 



The current which passes through the receiving instrument to produce 

 "single" as well as " duplex" signals is at balance expressed by 



G = E. — ^^ X const. 



(a + g) I L (a + g) + 2 a (g + d) I 



which expression has a maximum for either a or y. 



