UNIFORM MAGNETISATION. 367 



spheres, disseminated in a non-conducting medium, equal ellipsoids 

 turned in the same direction. If the body thus constituted " were a 

 homogeneous sphere, and it were made to turn without displacing its 

 centre of gravity, and without any change either in the external 

 forces or in the function V, the magnitude and directions of the 

 magnetic forces in this body would nevertheless change. As this 

 particular case has not yet been met with, we shall for the present ex- 

 clude it from our researches." (Memoire surla theorie du magnttisme, 

 "Me'm. de 1'Institut pour 1821-22," Vol. v., p. 278.) 



For the reasons which we have already developed in electricity 

 (215), there must in this case be three principal axes of magneti- 

 sation. If we place each of these axes successively in the direction 

 of the field, we shall have between the coefficients , #, k" of sus- 

 ceptibility, and the coefficients ju, //, p" of permeability, the ratios 



When the body is directed in any manner whatever in reference 

 to the field, we may substitute for the true field three fields whose 

 directions are rectangular and parallel to the principal axes, and 

 consider the real magnetisation as the resultant of these three 

 magnetisations. 



This superposition is evidently legitimate in all cases of dia- 

 magnetic, or of slightly magnetic bodies ; it is only a consequence 

 of the principle of the proportionality of the magnetisation to the 

 magnetising force. 



385. UNIFORM MAGNETISATION. If the surface of a body is 

 such that uniform magnetisation in a certain direction produces a 

 certain constant force, and we place it in a uniform field, the force 

 of which is parallel to this direction, it will acquire a uniform 

 magnetisation, since the magnetising force will have the same value 

 at all points, and that, without its being necessary to make any 

 restriction on the magnitude of the coefficient k. The magnetising 

 force F being the sum of the strength of the field <, and of a force 

 CI due to induced magnetisation, which is evidently proportional to 

 the intensity of the magnetisation, we shall have 



and therefore 



