Mr maxwell, ON FARADAY'S LINES OF FORCE. 71 



surface, and that the induction through the surface should be the same whether deduced 

 from the external or the internal potential. Putting x = r cos 0, we have for the external 

 potential 



p = [ir ■{■ A~\co%Q, 



and for the internal 



p,= Br cos Q, 



and these must be identical when r = a., or 



The induction through the surface in the external medium is 



k dr,^, k 

 and that through the interior surface is 



These equations give 



and .-. -;(7-2^) = - B. 

 k k 



. k — fC _, 3k ^ 

 ^ = -1 T' ^> B= — -, /. 



ih + k Zk + k 



The effect outside the sphere is equal to that of a little magnet whose length is / and 

 moment ml, provided 



ml= — rrO' !• 



2k + k 



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 equivalent 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 field 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 ccyix are represented by a,)8i7i, 

 then, if as a first approximation we regard 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 



