of Duplex Telegraph?/. 125 



always be considered sensibly constant in conduction and in- 

 sulation. 



Further, as a long overland line acts both as a variable con- 

 ductor 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 separate the two 

 questions from the beginning, and afterwards combine their 

 solutions judiciously for application to the case of overland 

 lines. 



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

 method when the line is regarded as a variable conductor, but not 

 as acting perceptibly as a Leyden jar? 



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

 method when the line is regarded as a Leyden jar of large capacity, 

 but not as a valuable conductor. 



The second problem may be expressed more clearly as fol- 

 lows : — 



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?* 



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

 duction-resistance 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 difference between a line and a con- 

 denser ; 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 re- 

 sistance. 



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

 limits of variation. For instance, say the signalling speed is constant, or 

 its range zero, then clearly one condenser connected to any point of the 

 given resistance would suffice ; only the magnitude of the capacity of this 

 one condenser would be determined by its position with respect to the re- 

 sistance, 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 betw.en and co , 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 be- 

 tween narrow limits ; and therefore 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 distribu- 

 tion has been determined. Until this law is known, we can do nothing 



