26 M. L. Schwendler on an Arrangement fur the 



get in the usual way 



-Vtt? (IL 



l + r 



corresponding to the maximum of m. 



In the application to a long overland line, /represents the line 

 resistance, including the resistance of the sending battery and 

 distant receiving relay, while r is the resistance of the coils of 

 the discharging relay. 



In order to weaken as little as possible the signalling current 

 by the introduction of such a discharging relay, we take naturally 

 r (its resistance) only so great that a given electromotive force 

 (as is generally used for signalling through the line) will work it 

 with safety through the given line resistance ; and if the dischar- 

 ging relay is of a good construction, this r can always be neg- 

 lected in comparison with I. 



Therefore we have from formula (II.), 



x = r. 



Or, to make the prolonging effect of the shunt a maximum, its 



* We have 



dm' _ lr- — x\l-\- r) 



where 



N = {Z(r+a?)+ra?}{r-f x] ; 



d 2 m' __2x{l+r) __2 dm dN m 

 N dx dx ' 



' dx 2 





N 2 



dm' 

 dx 



= 0, 





x — r 



«/. 



l+r 



d 2 m! 



~dW 



= - 



2x(l+r) 



N 2 * 



and 



which is always negative for a positive value of x. 



The function m' (formula I.) is to be considered as representing the re- 

 manent magnetism in the closed circuit (r+x), no matter by which of the 

 two coils the magnetism is produced ; thus m' must necessarily be symme- 

 trical as regards r and x. But having selected one of the two coils by 

 which m' (the remanent magnetism) is to be produced, it is at once fixed 

 which of the two coils must be taken as variable in order to find the maxi- 

 mum of mf. If, for instance, r is taken as the coil developing m', while x 

 acts as shunt only, neither producing extra current nor magnetism, then 

 the shunt x must be taken as variable, and not r, since otherwise factor 



{l{r+so)+rx\{r+ %) 



would have to be differentiated, giving that value of r which represents a 

 maximum of mf developed by x — just the case to be avoided as much as 

 possible. 



