PARTICULAR CASES OF MAGNETISATION. 387 



Hence the shape of thin plates, or of very long cylinders, 

 is that best fitted for obtaining permanent magnets, for the de- 

 magnetising force is then the least possible. These are, in fact, 

 the shapes which have been adopted in practice. Experiment 

 shows, moreover, that the influence of temper is then far less than 

 in the case of short and thick magnets. Coulomb had already 

 observed that tempering has but a very slight influence on the 

 magnetic rigidity of a steel wire. 



409. PARTICULAR CASES OF MAGNETISATION. Sphere. It 

 follows from the preceding discussion that a solid homogeneous and 

 isotropic steel sphere, placed in a uniform magnetic field, will acquire 

 a uniform temporary magnetisation, and will then retain a uniform 

 residual magnetisation. 



The expression for the temporary magnetisation will be of the 

 form 



I- k F 



w 4 : ' 



I+-7JV& 



in which the coefficient k must be regarded, not as a constant 

 quantity, but as a function of the intensity F of the true field ; the 

 fraction by which the force F must be multiplied to get the magneti- 

 sation I, tends in fact to become inversely as F that is to say, 



equal to -=!, as F increases, since the magnetisation tends towards a 



maximum I . 



In like manner, the residual magnetisation is a fraction of the 

 temporary magnetisation ; a variable fraction, and one which tends 



towards a limiting value , since the residual magnetisation has a 



maximum, and is then , a fraction of the maximum temporary 



, , m 



magnetisation. 



In all cases the law of distribution is the same ; the density at 

 every point is equal to the perpendicular projection of the magneti- 

 sation that is to say, proportional to the abscissa of the point 

 measured from the centre along the diameter, parallel to the 

 magnetisation. The linear density measured along the same axis is 

 also proportional to the abscissa. The moment of the sphefre is ul lt 



the total mass of each of the layers -, the distance of the poles is 



4a .2 4 * 



, and each pole is - of the radius from the centre. 



3 3 



C C 2 



