386 ON MAGNETS. 



direction to the force which produces it ; it follows that the induction 

 of a magnet on itself always tends to diminish the magnetisation, and 

 acts like a demagnetising force. 



The apparent magnetism, or that whose effects we can observe, 

 arises from the superposition of these two magnetisms. Hence 

 the determination of the intensity, and of the distribution of the 

 apparent magnetism, generally presents great difficulties. 



The problem is simplified when the demagnetising force is 

 proportional at each point to the rigid magnetism at this point ; the 

 law of distribution is then the same as if this secondary effect of 

 induction did not take place. 



In particular, when the rigid magnetism is uniform, the apparent 

 magnetism will itself be uniform, if the secondary inductive action is 

 constant in the interior of the magnet. 



This condition is realised, as we have seen above, for a uniformly 

 magnetised sphere ; and also for an ellipsoid with a uniform magneti- 

 sation parallel to one of the axes, and for a straight unlimited circular 

 cylinder, magnetised perpendicularly to the axis. 



408. Let us first consider a sphere. Let I be the rigid, I' the 

 induced, and \ the apparent magnetisation ; the demagnetising force 



is then (355) equal to - irl v and we have 



From which we deduce 



i r-i 



For an ellipsoid magnetised parallel to one of the axes, the 

 demagnetising action has the value IjL, I 1 M, or I 1 N, according to 

 the axis along which it acts (356). It is 471-^, or Try i - e 2 I x for a 

 disc, according as it is magnetised transversely or parallel to a 

 diameter (357). For an elongated ellipsoid of revolution, it is 2i?\ 



b*/2a V 



if the magnetisation is transverse, and 4^11 ^ ( * -r i ) if the mag- 

 netisation is longitudinal (357). ' ^ 



This latter expression tends towards zero as the ratio - gradually 



diminishes. The demagnetising force would be still smaller for a 

 long cylinder (373). 



