572 PHENOMENA OF INDUCTION IN NON-LINEAR CONDUCTORS. 



The arc KM' being equal to a$ or 2aO, the magnetic moment 

 T3 of the element of the helix at M' is zmadO. The magnetic 

 moment GT of the corresponding magnet at M is given by the ratio 



CT 7 2ma 



Observing that we have 



r MO 



r' M'K 20sin<9' 

 it follows from this that 



m 



4 a 2 sin 3 



The magnet TS at the point M is parallel to the magnetisation 

 of the helix at M' ; it makes therefore the angle 6 with the radius 

 vector of the perspective curve. 



The calculation of the force at A would be very complicated, but 

 it is evident that the portions of the curve corresponding to the first 

 part BM' of the helix are predominant. From the direction of the 

 elementary magnets on the perspective curve, we see that the action 

 on the point A will have a vertical component, another directly 

 opposite to the velocity of the pole, and a third directed towards the 

 centre of the circumference which it describes. The entire system 

 is then equivalent to a small magnet placed behind the point O, 

 perpendicular to a radius of the disc, which makes a certain angle 

 from the opposite side of the motion with the radius corresponding 

 to the pole, the magnetisation being in the direction of the motion if 

 the pole in question is a north pole. 



If the plane was unlimited, this magnet would be at a distance 

 from the axis greater than that of the pole ; but the action of the 

 edges is to bring it more and more towards the centre in proportion 

 as the radius diminishes. We thus find all the peculiar features of 

 Arago's experiments, among others the fact that the radial component 

 is centripetal so long as the pole is away from the edges, and that it 

 becomes centrifugal as it approaches them. 



588. If the pole describes any given curve parallel to the plane, 

 we should obtain in the same way, by the trail of corresponding 

 magnetic images, the magnetisation at each point of the perspective 



