214 



ON FARADAY 8 LINES OF FORCE. 



Suppose this uniform field to be that due to terrestrial magnetism, then, 

 if k is less than k' as in paramagnetic bodies, the marked end of the equi- 

 valent magnet will be turned to the north. If k is greater than k' as in 

 diamagnetic bodies, the unmarked end of the equivalent magnet would be turned 

 to the north. 



III. Magnetic Jield of variable Intensity. 



Now suppose the intensity in the undisturbed magnetic field to vary in 

 magnitude and direction from one point to another, and that its components 

 in x, y, z are represented by a, /3, y, then, if as a first approximation we re- 

 gard the intensity within the sphere as sensibly equal to that at the centre, 

 the change of potential outside the sphere arising from the presence of the 

 sphere, disturbing the lines of force, will be the same as that due to three 

 small magnets at the centre, with their axes parallel to x, y, and z, and their 

 moments equal to 



7, _ /' l- _ z-' /- _ /-' 



A/ A/ . 1/1 A/ Ay 



2k + k' aa ' ZT+Z"* 2k + k' 



The actual distribution of potential within and without the sphere may be 

 conceived as the result of a distribution of imaginary magnetic matter on the 

 surface of the sphere ; but since the external effect of this superficial magnetism 

 is exactly the same as that of the three small magnets at the centre, the 

 mechanical effect of external attractions will be the same as if the three magnets 

 really existed. 



Now let three small magnets whose lengths are l lt I,, /,, and strengths 

 TO,, 7H,, TO,, exist at the point x, y, z with their axes parallel to the axes of 

 x, y, z ; then resolving the forces on the three magnets in the direction of X, we 

 have 



da 



(fa 



da 



