34 PARTICULAR CASES. 



so that the total flow of induction which traverses the great circle, 

 perpendicular to the magnetisation, is expressed by 



356. ELLIPSOID. Consider a homogeneous ellipsoid, the axes of 

 which 2#, 2$, zc, are taken as axes of the co-ordinates. Denoting by 

 L, M, N, known functions of the axes, the potential of this ellipsoid 

 at a point in the interior, the co-ordinates of which are x, y, z, is 



P = - - (L* 2 + M/ + N* 2 ) + const. 



s 



If the ellipsoid is uniformly magnetised in a direction which 

 makes, with the axes, angles whose cosines are /, m, , the com- 

 ponents of the magnetisations are 



A_B_C 

 1 } 



/ m n 



and the state of the ellipsoid may be considered as being produced 

 by the superposition of these three magnetisations, respectively 

 parallel to the axes. The potential in the interior is 



and the values of the components of the force parallel to the axes are 

 X=-AL, Y=-BM, Z=-CN. 



The interior magnetic force of a uniformly magnetised ellipsoid, 

 is therefore constant in magnitude and direction, and makes, with 

 the axes, angles whose cosines are respectively proportional to AL, 

 BM, and CN. 



The components of the induction parallel to the axes are 



