﻿232 L. Schwendlcr — Oti the General Theory of Duplex Telegraphy. [No. 4, ' 



Thus it follows generally that a ^= d =: g represents a maximum of 

 the currents, and this, in consequence of the immediate balance, gives at 

 last 



a=d=g=f 

 the known regularity condition, which thus has also to hold good in order 

 to make the two currents Q' and G" simultaneous maxima. 



The first prohlem for the Bridge Method has therefore now been gene- 

 rally solved, and the results are expressed by the following formulae : 



=H(y" 



where 



o o 



When .the insulation is perfect (» = oo) the results revert to those 

 originally obtained in the special solution, viz : — 



a = d = f=g = w + /5 

 ^ 2 



It will be clear that the given solution fulfils the following conditions 

 which are necessary and sufficient to place Duplex Telegraphy on a par 

 with Single Telegraphy. 



i. Any variation in the resistance of the line has the least possible dis- 

 turhing effect on the receiving instrument. 



ii. Any disturbance can he eliminated hy a single adjustment ill the b 

 tranoli without disturbing balance in the distant station. 



iii. 3£aximum magnetic moment of the receiving instrument* 



iv. Maximum current. 



There seems to me to be no other method that can fulfil all these con- 

 ditions simultaneously, and the " double balance'^ method must therefore 

 be pronounced perfect in every conceivable respect. I am convinced that if 

 the general problem of duplex working were investigated by means of the 

 Variation Calculus, the double balance method would come out as the final 

 and only solution.f 



* I have called this method the " double balance" method, since there are two 

 balances to be fulfilled in each station, namely, balance in the h branch for the arriving 

 current and balance in the g branch for the oiitgoing current. 



t The double balance method was introduced on one of the important Bombay-Cal- 

 cutta main lines in June last. Since then this duplex method has been working so 

 satisfactorily and with such regularity and speed, even during the worst time of the 



