306 CONSTITUTION OF MAGNETS. 



strength of magnetisation is constant in magnitude and direction 

 throughout the whole extent of the magnet ; the differentials of the 

 components A, B, C are null, and the equation (6) gives 



there is magnettem therefore on the surface only. 

 The potential reduces then to 



or, if ^Sj_ is' the projection of ^S, on a plane perpendicular to the 

 magnetisation, 



All the elements of volume* being magnetised parallel to each other, 

 the magnetic moment of the whole, is equal to the sum of the 

 moments of all the elementary volumes ; we have, then, 



or = \Idv = I \dv = vl. 



Thus, the magnetic moment of a uniform magnet is equal to the 

 product of the volume by the strength of the magnetisation. 

 The expression for the surface density 



or = I cos Q 



shows that the external action of a body magnetised uniformly is 

 equivalent to that of two layers of gliding (157) that is to say, 

 of two layers which would result from the superposition of two 

 homogeneous magnetic masses of densities p equal and of opposite 

 signs, of which the positive part has been displaced parallel to the 

 magnetisation by a quantity 8 such that p8 = I. 



We have said (308) that we may explain the action of the 

 earth by an infinitely small magnet placed at the centre, or by 

 two layers of gliding ; we see that we may also suppose the earth 

 uniformly magnetised; this latter condition being equivalent to 

 the two others. 



