Discharge of long Overland Telegraph Lines, 25 



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



c = E 7r-rVr-' 



l\r + x) + tx 

 and consequently the magnetism m developed in r by C is 



wo? 



m = b?i = .L 7 t — ■ — r— — ; 

 l[r + x) + rx 



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 



comparison with its diameter, we may substitute for n the value 



n— constant Vr, 



Thus we have -^ X\/r 



m = E const v . 



l(r + x) -f rx 



The ceasing of this magnetism after the battery circuit has 

 been instantaneously opened at 1 must be considered the cause 

 for producing an extra current in the closed circuit (r + #), 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 instanta- 

 neously 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 magnetism as the new elec- 

 tromotive force for producing the extra current C in the circuit 

 with the resistance r-\-x. 



Therefore we have 



C'=E const. 



x V 



-j l(r + x) +rx] [r -f x) ' 



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

 gives us the remanent magnetism m! 3 or, as n= const. y/r 9 



xr 



Wl' = E COnst. -7-77 : y- f -r. . . . (I.) 



{l(r + a?)+rx\(r + x) v ; 



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

 during which the bar of iron keeps perceptibly magnetized after 

 the instantaneous opening of the battery circuit) must increase 

 with ?7i' ; and consequently by making m 1 a maximum the pro- 

 longing effect of the arrangement must also be greatest. Taking, 

 therefore,- in the above expression for m f 3 x only as variable, we 



