84 L. Schwendler — Discharge of long Telegraph lines. [No. 1, 



Thus we have — 



m = E Const 



I (r -\- x) -\-r x 



The ceasing of this magnetism, after the battery circuit has been 

 instantaneously opened at 1, must be considered as the cause for 

 producing an extra current in the closed circuit {r -f- x), which 

 extra current in its turn reproduces magnetism in the iron bar in 

 the coil r. This whole process of course occupies time, however short 

 it may be and goes on steadily. But it will lead apparently to the 

 same result for our purpose, if we suppose that the cessation of the 

 original magnetism produces instantaneously the whole extra current, 

 and that the extra current, (or better an average value of it, since it 

 is variable as regards time), is used for producing fresh magnetism 

 in the iron bar of the coil r. Under these circumstances it is 

 reasonable to take a proportional quantity of the original mag- 

 netism as the new electromotive force for producing the extra 

 current C in the circuit with the resistance r -\- cc. 



Therefore we have 



C = E Const x -*£l , 



\l(r + x)+rx\(r + x) 



and this expression multiplied by the number of convolutions, n } 

 gives us the remanent magnetism m', or as n = Const ^/r y 



m' = E Const — (I) 



J I (r ■+* x) -J- r x > (r + #) 



Now it is evident that the prolonging effect, i. e. the time during 

 which the bar of iron keeps perceptibly magnetized after the in- 

 stantaneous opening of the battery circuit, must increase with m', 

 and consequently by making m' a maximum, the prolonging effect of 

 the arrangement must also be greatest. Taking, therefore, in the 

 above expression for m' } x only as varriable, we get in the usual way 

 7~ 



J: 



I H- r 



corresponding to the maximum of m. 



* We have — 



dm __ I r* — x 2 (I + r) 



dx — N a 



(III 



