﻿JS71.] L. Sclivvendler — On the general Theory of Duplex Telegraphy. 9 



acting as a Leyden jar of large capacity. In the first case the sohition 

 would be directly applicable to short overland lines (not over 200 miles in 

 length), and in the second case to submarine cables, which, if good, may 

 always be considered sensibly constant in conduction and insulation. 



Further, as a long overland line acts both as a variable conductor and as 

 a Leyden jar of sufficiently large capacity, it would then be necessary to give 

 a solution with respect to both these effects. To obtain, however, the same 

 result without rendering the problem too intricate, it will be best to sepa- 

 rate the two questions from the beginning, and afterwards combine their 

 solutions judiciously for application to the case of overland lines. 



1st Problem. What is the hest arrangement of any given duplex 

 method when the line is regarded as a variable condiwtor, hut not as acting 

 perceptibly as a Leyden jar ? 



2nd Problem. What is the best arrangement of any given duplex 

 method^ tvhen the line is regarded as a Leyden jar of large capacity, but not 

 as a variable conductor. 



The second problem may be expressed more clearly as follows : — 

 2nd Problem. What must be the distribution of condensers along a 

 given resistance, in order that the two essential conditions (I and II) may 

 be least disturbed for a speed of signalling variable between two fixed limits <'* 

 It is clear that the nature of these two problems is very different, 

 because in the first we have to deal with forces constant with respect to 

 time, while in the second the forces acting are functions of time, i. e., of the 

 * A telegraph line always acts as a condenser with capacity and conduction resist- 

 ance in each point of its entire length, while an artificial condenser, such as a Leyden jar, 

 which we are able to produce sufficiently cheaply, has only capacity but no perceptible 

 conduction resistance in each point. This is in fact the essential diiference between a 

 line and a condenser, and, therefore, in order to render their charges and discharges under 

 the same circumstances as nearly as possible equal, as is required for duplex working, it 

 will be necessary to find the law according to which to distribute a certain given system 

 of condensers along a given resistance. 



This law will clearly be a function of the signalling speed within its limits of varia- 

 tion. For instance, say the signalling speed is constant, or its range zei'o, then clearly one 

 condenser connected to any point of the given resistance would suffice ; only the mag- 

 nitude of the capacity of this one condenser would be determined by its position with 

 respect to the resistance, and in addition to this would of course be fixed by the signalling 

 speed and the known capacity of the line. 



Further, say the speed of signalling is variable between and oo , or its range is 

 infinite, then clearly only an infinite number of small condensers distributed along the 

 given resistance in the very same manner as the capacity is distributed along the line 

 would strictly answer the purpose : in fact, the condenser required in this imaginary case 

 would be nothing more or less than a second Telegraph line, identical with the one used 

 for signalling. In practice, however, the speed of signalling varies only between narrow 

 limits, and therefoi'e the number of condensers required to reproduce as nearly as possible 

 the action of the line with respect to charge and discharge, will become few, especially if 

 the best system of distribution has been determined. Until this law is known we can do 

 nothing but find it approximately by experiment, however tedious it may be to do so. 



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