74f Mb maxwell, ON FARADAY'S LINES OF FORCE. 



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

 origin, is 



1 1 



\,\/c'+r^-9, cos Qcr \/c''+r^+2 cos Qcri ' 



From this we find as the value of P, 



■: ^ 3s = - 18 — / sin 20, 

 dO c* 



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



9 is increased is 



k-k' M'a'b^ . ^ 



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 distance 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 magnetic 

 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. VIII.), an elongated body would set axially whether 

 magnetic or diamagnetic. 



In all these cases the phenomena depend on k — k', so that the sphere conducts itself 

 magnetically or diamagnetically according as it is more or less magnetic, or less or more 

 diamJignetic 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 a?, y, ss. Let k^, k^, k^, be the coefficients of resistance in these three 

 directions, and let k' be that of the external medium, 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 I, m, n. 



Let us now take the case of a homogeneous sphere whose coefficient is A;, placed in a 

 uniform magnetic field whose intensity is II in the direction of a?. The resultant potential 

 outside the sphere would be 



