1 871. J L. Schweudler — Discharge of long Telegraph lines. 83 



netism produced in r by closing the battery circuit, would be 

 greatest. On the other hand, if the resistance of the shunt b 

 were taken as infinitely small, then, (though there would be the 

 best possible channel for an extra current), no such current could 

 be established, because no original current would pass through r, 

 and therefore no magnetism in r could have been developed. 

 Knowing, therefore, that for b = oo and for b = o the extra current 

 is = 0, it follows that there must be one or more values of b 

 between these limits, for which the extra current is a maximum. 



However, the function, by which this extra current, or better the 

 remanent magnetism in r, is expressed, is of such a nature, that it 

 has only one maximum, and this can easily be calculated, since 

 all the laws determining it are perfectly known. 



In diagram 2 we will designate by r the resistance of the 

 bobbin producing the magnetism (which in the discharging ar- 

 rangement represents the resistance of the coils of the discharging 

 relay) ; and for brevity we may suppose that the whole resistance 

 between the points p and q through r is used for producing 

 magnetism. 



Suppose also — 



n the number of convolutions in r ; 



x the resistance of the bobbin acting as a shunt to r, and ex- 

 tending between p and q ; 



E the electromotive force producing the original current ; 



/ the resistance between the points p and q through the battery 

 E, including the resistance of the battery ; 



thus the current C which passes through r, when 1 is closed is— 



C = E - 



I (r -f ®\ + r x 1 



and consequently the magnetism m, developed in r by C is : 



M = C» = E 7- ; r , 



I (r + x) -i r x 

 and, supposing the conductivity of the wire, filling the given space of 

 bobbin r, constant for any diameter whatever, and neglecting the 

 thickness of the necessary insulating covering of the wire in com- 

 parsion with its diameter, we may substitute for n the value n - 

 Constant v' r. 



