ELLIPSOID. 341 



Induction is therefore a constant force, which makes, with 

 the axes, angles whose cosines are respectively proportional to 

 ( 4 7T- L) A, (477- M) B, and (471-- N) C. 



Lastly, the values of 'the flows of induction across the three 

 principal sections are respectively irbc (477 - L) A, irca (477 - M) B, 

 and nab (477 - N) C. 



357. If the magnetisation is parallel to one of the axes the axis 

 a, for instance we have simply 



-IL. 



From the manner in which the layer is formed, the quantity of 

 magnetism M a , distributed on each of the halves of the ellipsoid, is 

 equal to the total charge which would exist on the principal section, 

 parallel to the two other axes, if the density were uniform and equal 

 to I ; we have then 



The magnetic moment S7 a of the magnet thus formed, is equal to 

 the product of the volume by the intensity, which gives 



4 4 



n = - irabc\ = irabc . 

 3 3 L 



The poles of the magnet, or the centres of gravity of each of the 

 two layers, are at a distance a' from the centre determined by the 

 equation 



which gives 



, ICT 2 

 a = --=-a. 



2M 3 



Thus the pole of an ellipsoid uniformly magnetised in a direction 

 parallel to one of the axes, is at a distance from the centre equal to 



2 



- of the length of the corresponding half-axis. 



