﻿218 [No. 4, 



On the Genebal Theobt or Duplex Telegeapht. 



By LoTJis Schwendlee. 



(Continued from page 21.) 



The first part of this investigation concluded by giving the best rela- 

 tions between the resistances of the different branches of the Bridge 

 Arrangement, under the limiting supposition, however, that the line used 

 for duplex working was perfect in insulation, or more generally that the real 

 conduction resistance of the line could be neglected against the resistance 

 of the resultant fault.* 



It now remains, therefore, to investigate if the simple relations given 

 are generally true ; or, if not, what they become in case the line has an ap- 

 preciable leakage. In fact this is clearly the case of practical importance, 

 since all overland lines, especially long ones, even if constructed on the best 

 known principles, will always have a very considerable leakage, i. e., the re- 

 sistance of the resultant fault (i) will generally be by no means very large 

 in proportion to the real conduction resistance (L) of the line. 



In order to obtain the best general solution of the problem, we must 

 conduct the investigation with great caution, that is, we must be careful 

 not to introduce beforehand any relation between the different variables, 

 however convenient, that is not necessarily a consequence of the paramount 

 condition to be fulfilled for Duplex Telegraphy, i. e., Regularity of Signals. 



Thus it will be seen that the present general investigation must be 

 conducted somewhat differently from the special one given in the First Part. 



It must, however, be understood from the beginning that whatever the 

 best relations may be, which should exist between the different resistances 

 of the Bridge Method, when used on an imperfect line, these relations must 

 revert to the special ones given before if we put i= co , and this fact affords 

 a certain check upon the correctness of the new relations to be found. 

 General solution of the first prohle7n for tJie Bridge MetJiod. 



The diagram (Fig. 1) given in the First Part represents the general 

 case, and to it therefore I shall refer in the present paper. 



The general mathematical question which is to be solved for Duplex 

 Telegraphy has been stated as follows : — 



Regulaeity op Signals. D and S are tivo functions loliich must he 

 rigidly equal to zero when no variation in the system occurs ; and which for 



* For a definition of the terms, " resultant fault," " real conduction," " measured 

 conduction," " real insulation," " measured insulation," &c., which will be of frequent 

 occurrence ia this paper, see my Testing Instructions^ Part XL Section I. 



