218 ON FARADAY'S LINES OF FORCE. 



and a the radius of the sphere. Let / be the undisturbed magnetic intensity 

 of the field into which the sphere is introduced, and let its direction-cosines 

 be /, m, . 



Let us now take the case of a homogeneous sphere whose coefficient is , 

 placed in a uniform magnetic field whose intensity is II in the direction of x. 

 The resultant potential outside the sphere would be 



and for internal points 



So that in the interior of the sphere the magnetization is entirely in the direc- 

 tion of x. It is therefore quite independent of the coefficients of resistance in 

 the directions of x and y, which may be changed from &, into k t and k, with- 

 out disturbing this distribution of magnetism. We may therefore treat the sphere 

 as homogeneous for each of the three components of /, but we must use a 

 different coefficient for each. We find for external points 



k,-k' 



and for internal points 



3k, 



The external effect is the same as that which would have been produced 

 if the small magnet whose moments are 



' mlat > 



had been placed at the origin with their directions coinciding with the axes of 

 x, y, z. The effect of the original force / in turning the sphere about the axis 

 of x may be found by taking the moments of the components of that force 

 on these equivalent magnets. The moment of the force in the direction of y 

 acting on the third magnet is 



and that of the force in z on the second magnet is 



