12G Mr. L. Schwendler on the General Theory 



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

 different, because in the first we have to deal with forces con- 

 stant with respect to time, while in the second the forces acting 

 are functions of time, i. e. of the signalling speed. (The forces 

 in this case are proportioned to the true currents.) The latter 

 problem being far the more intricate, and for my special purpose 

 only of secondary importance, I shall begin with the solution of 

 the first. 



Solution of the first Problem for any given Duplex Method. 



What is the best arrangement of any given duplex method when 

 the line is regarded as a variable conductor, but not as acting per- 

 ceptibly as a Ley den jar? 



I. The bridge method*. 



This arrangement for duplex working is based on the well- 

 known method of comparing electrical resistances^ "Wheat- 

 stone's bridge;^ and the figure (p. 127) gives the general dia- 

 gram when this method is applied for duplex working. 



/3 is the internal resistance of the signalling- battery. 



1/ the "measured conductor "f resistance of the line when 

 measured from station I. ; 







• V—l'+ - 



but find it approximately by experiment, however tedious it may be to 

 do so. 



It has also been proposed to use Ruhmkorff's coils for balancing the 

 effect of charge and discharge. This method, however, I believe must be 

 always much inferior to the one of using condensers, inasmuch as the 

 strength of a voltaic induction-current scarcely depends on the speed of 

 signalling, while the charge and discharge of a line, it is well known, is 

 not at all an inconsiderable function of the signalling speed. 



Therefore if the strength of the induction-current had been adjusted to 

 balance the charge and discharge of the line for a certain signalling speed, 

 the balance would be considerably and at once disturbed if the speed 

 varied even slightly ; and since so long as hand signalling is used a certain 

 variation in the speed of signalling will always exist, this method will prove 

 a failure, or at all events will render fresh adjustments more frequently 

 necessary than when condensers are used. 



* Dr. W. Siemens mentions this in Pogg. Ann. vol. xcviii. p. 122 (1856). 



Mr. O. Heaviside (Phil. Mag. 18/3, vol. xlv.) states that Mr. Eden, of 

 Edinburgh, claims to have suggested this method at about the same time 

 as Mr. Stearns, of Boston, U.S.A., took out a patent for it. 



t Generally these measured values 1/ and L" will be different from each 

 other, especially for long overland lines. They can become equal only 

 under two conditions — either if the resistance of the resultant fault (i) is so 

 great that the total conductor resistance of the line (7 1 + l" = l) can be neg- 

 lected against it, or for any magnitude of i if the latter has a position in 



the middle of the conductor, i. e. when Z' = £"=:?• 



