388 ON MAGNETS. 



410. Ellipsoid. This is also the case with a homogeneous and 

 isotropic ellipsoid, one of whose axes coincided with the direction of 

 the uniform field during magnetisation ; it is merely necessary to 



replace the factor -TT by a coefficient L which depends on the form 



of the ellipsoid (357). 



The maximum magnetisation I , and the fraction which deter- 



m 



mines the maximum residual magnetisation, have values which are 

 connected with those which correspond to the sphere by ratios 

 depending on the form of the ellipsoid. 



The law of distribution is still known, and the poles are at a 



distance from the centre equal to - of the semi-axis parallel to the 

 magnetisation. 



We might in like manner obtain a uniform magnet with a 

 circular disc magnetised perpendicularly to a plane, or parallel to 

 a diameter (357). 



411. Anchor Ring. A simple case, which can be easily realised 

 experimentally, is that of a body bounded by a closed tube a 

 torus or anchor ring, for instance in which the magnetisation 

 would be everywhere parallel to the axis. The magnet may then 

 be regarded as formed of simple solenoids closed on themselves 

 (371). The external action of the system is always exactly null. 



412. Cylinder. To the preceding examples, all of which repre- 

 sent finite volumes, which can be exactly realised, we may add that 

 of a homogeneous and isotropic unlimited circular cylinder placed in 

 a uniform field perpendicular to the axis ; the magnetisation is then 

 represented by the expression 



1 = Z F. 



I + 2TTK 



These cases seem to be the only ones in which the distribution 

 of magnetism can be theoretically determined, at least when the 

 coefficient k is not independent of the magnetising force. 



413. ANY GIVEN MAGNETS. EXPERIMENTAL METHODS. The 

 problem of magnetisation for a body of any given form can only be 

 attacked experimentally by the study of its external actions ; we have 

 already had occasion to remark that our knowledge of the external 

 field of a magnet can teach us nothing about the internal distribution 

 of magnetism ; it only enables us to determine the distribution of the 

 fictive layer, equivalent to the real magnetisation. 



