1871.] L. Schwendler — Discharge of long Telegraph lines. 85 



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

 resistance including the resistance of the sending battery and dis- 

 tant 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 discharging relay 

 is of a good construction, this r can always be neglected in com- 

 parison with I. 



Therefore we have from formula (II) 



x = r. 



Or to malce the prolonging effect of the shunt a maximum, its resis- 

 tance must he equal to the resistance of the coils of the discharging relay. 

 This law will hold good for any long overland Telegraph line, 



where N = \ I (r -j- asJ-J-rasl-lr + ajl 



d 2 m _ _ 2 x (I -f. r) 2 dm dN 



' ' dx 2 N 2 " ~N" ' dx " dx 



dm 

 .'. when ■ = U 



dx 



= rjl + r 



_ d 2 m 2a( I -f r) 



and — 



dx 2 N 2 



which is always negative for a positive value of x. 



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

 nent magnetism in the closed circuit (r -\- x), no" matter by which of the two coils 

 the magnetism is produced ; thus m' must necessarily be symmetrical 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 maximum of m'. If, for instance, r is 

 taken as the coil developing w', 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- 



[£(/• + <?)+ r x j |r -f x j 



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

 maximum of m', developed by x ; just the case to be avoided as much as 

 possible. 



