Ui 



line integral of f?j along this circle amounts therefore to inr . S?x', 

 this line integral also amounts to 2jtr . '>/, so that we get: 



We shall further assume the length of the bar to be large with 

 respect to its diameter, in which case the intluence of the magnetisation 

 at the extremities in the determination of the field intensity inside 

 the bar in case of longitudinal ujaguetisation will be small, so that 

 we may assume 



Inside the bar the following ei|iuititins hok! 

 25., = (1.0/ -f i h-a ƒ;/ 



The change of the magnetic induction within the bar in conse(|ncnce 

 of the twisting auionnis to 



ZiiV= i A-m.n./ 



AQ5„= I krit -C"»," 



In the same way we have for the magnetisation : 



W, = x. .pi" -f ^ /;m.r-)/ 



m,^=zx . .5/ f h km .p," 



Also outside tiie nuignclic induclion changes in consec|neiU'e of 

 the twisting. (_)n account of ilie change of 'S,, the (|uantity of 

 magnetism will namely ciiange at the extiemities of the bai' which 

 will give rise to a change of strength of the field outside the bar. 

 If there was no ii'on inside the solenoid, and if this was infinitely 

 long, the change of the magnetism at the extremities would not 

 give rise to an induction current at all, because every quantity of 

 magnetism sends its induction lines tiirough the windings lying on 

 eitlier side, and the sense of rotation of the induced electric force 

 is directed for the windings on one side opposite to that on the other 

 side. We commit an error on account of the presence of the ii'on 

 inside the solenoid in as much as the magnetic induction inside 

 the iron does not change in the same way as that outside it. As 

 we have, howe\er, assumed that as far as the magnetic induction 

 inside the iron is concerned, we may disregard the magnetism at 

 the extremities, we may also leave this error out of account. 



In order to calculate the induction impulse, we must therefore 

 integrate the just mentioned amounts u\' L '^ij and A 55^ inside the 

 bar over the surface which is surrounded by every circuit, and then 

 sum up over all the circuits. 



We cx[)licitly exce[)ted (§ 2 above) movements of the current 



23 



Proceedings Ruyal Acad. Aiusterdam, Vol. XV 111, 



