DETERMINATION OF THE COEFFICIENTS OF MAGNETISATION. 377 



In like manner, the coefficient of magnetisation of an anisotropic 

 medium in a determinate direction is the longitudinal magnetisation 

 which an infinitely thin cylinder would acquire, parallel to this 

 direction, in a field equal to unity. 



394. We see also that to determine the coefficient of magneti- 

 sation of highly magnetic bodies such as iron, we cannot make use of 

 the external action produced by spheres or by elongated bodies in a 

 direction perpendicular to the field. For the ratio of the magneti- 

 sation to the force is respectively equal to 



II 21 



ATT I ATT 2 



1+ r I+ -^ 



ATTK ATtk 



according as the body is a sphere, a disc, or a very elongated 

 ellipsoid of revolution. These ratios differ too little from the 

 approximate values obtained by making k infinite, to allow us to 

 deduce the coefficient k with any degree of precision. 



On the contrary, with elongated bodies parallel to the lines of 

 force, the magnetisation tends to become proportional to /, and 

 independent of the shape of the body. 



395. DISPLACEMENT OF BODIES IN A MAGNETIC FIELD. 

 ATTRACTIONS AND REPULSIONS. The potential energy of an 

 infinitely small dielectric sphere (178) in a field is 



2 47T 2 



This expression represents also the energy of an infinitely small 

 magnetic sphere, and even of any volume element of a homogeneous, 

 isotropic substance, whose coefficient of magnetisation, positive or 



negative, is very feeble ; we have then = /, and W = -uk > 



ATT 2 



For a very small displacement, the variation of energy is 



" 



If the body is magnetic the coefficient k is positive, the energy 

 diminishes when the body approaches points where the absolute 



