﻿8 L. Schwendlor — On the general Theori/ of Duplex Telegrapliy. [No. 1, 



Further if ^ cannot be always kept rigidly equal to zero (on account of 

 unavoidable variations in the system) we should at least have : — 



— = D as small as possible (HI) 



and if P cannot be always kept rigidly equal to Q, we should at least 

 have : — 



P — Q = S as small as possible (IV) 



p, P and Q being functions of the resistances and electro-motive forces 

 of the system, which are known so soon as the particular duplex method has 

 been selected. 



The general problem which is to be solved for duplex Telegraphy may 

 now be clearly stated as follows : — 



D and S are two knoivn functions wJiicli must he rigidly equal to zero 

 when no variation in the system occurs ; and which for any given variation 

 in the system must he as small as possible, and approximate rapidly towards 

 zero as the variation in the system hecomes smaller and smaller. 



Thus the solution of the problem for any given duplex method will 

 always be a question of the Minima and Maxima Calculus. 



Having then ascertained the best arrangement for each duplex method, 

 the methods can be compared inter se, and that method will be best and 

 should be selected for use which for any given variation in the system gives 

 the least absolute magnitude to the functions D and >S'. 



If we suppose, however, that the particular duplex method is not given, 

 the problem to be solved becomes more general, but would still be entirely 

 within the limits of the Variation Calculus, furnishing no doubt a very 

 interesting and important application of that most powerful mathematical 

 instrument. The general solution would at once determine the best method 

 possible, after which special solutions would give the best arrangement for 

 that best method. 



It is, however, not my intention to endeavour to solve here the 

 duplex problem in this most general form. To be able to indicate so 

 general and desirable a solution is by no means identical with being able to 

 effect it. The task before me is far more simple, since, as already pointed 

 out, I shall investigate each duplex method separately to determine its best 

 quantitative arrangement, and ultimately compare the different methods to 

 ascertain their relative values. 



To do this, the question may be attacked in two different ways, depend- 

 ing on the purpose for which the solution is required. 



Namely, either the solution is to be made when considering the line as 

 a variable conductor only, but not acting perceptibly as a Ley den jar ; or 

 the line is to be considered as constant in conduction and insulation, but 



