ON FARAD AYS LINES OF FORCE. 217 



The expression for the potential, the middle of the line joining the poles 

 being the origin, is 



We* + 1* - 2cr cos Vc 2 + r 1 + 2cr cos W 

 From this we find as the value of P, 



and the moment to turn a pair of spheres (radius a, distance 26) in the 

 direction in which 6 is increased is 



Ic-lc J/Vfc 3 . 



^~ O O _ i / ;: Sill Zi \J 



This force, which tends to turn the line of centres equatoreally for diamagnetic 

 and axially for magnetic spheres, varies directly as the square of the strength of 

 the magnet, the cube of the radius of the spheres and the square of the dis- 

 tance of their centres, and inversely as the sixth power of the distance of the 

 poles of the magnet, considered as points. As long as these poles are near each 

 other this action of the poles will be much stronger than the mutual action of 

 the spheres, so that as a general rule we may say that elongated bodies set 

 axially or equatoreally between the poles of a magnet according as they are mag- 

 netic or diamagnetic. If, instead of being placed between two poles very near 

 to each other, they had been placed in a uniform field such as that of terrestrial 

 magnetism or that produced by a spherical electro-magnet (see Ex. vin.), an 

 elongated body would set axially whether magnetic or diamagnetic. 



In all these cases the phenomena depend on k k', so that the sphere con- 

 ducts itself magnetically or diamagnetically according as it is more or less 

 magnetic, or less or more diamagnetic than the medium in which it is placed. 



VI. On the Magnetic Phenomena of a Sphere cut from a substance whose 

 coefficient of resistance is different in different directions. 



Let the axes of magnetic resistance be parallel throughout the sphere, and 



let them be taken for the axes of x, y, z. Let k lt k t , k,, be the coefficients of 



resistance in these three directions, and let k' be that of the external medium, 



VOL. I. 28 



