300 CONSTITUTION OF MAGNETS. 



As the sum of the magnetic masses is always zero for any given 

 magnet, we have the equation of condition 



\pdv. 



The components of the magnetic force at the point P are 



W 



C. L, CORY. z Jj ; 



and the value of the force itself is 



These formulae are general, and apply not only to points on the 

 exterior but also to points in the interior of the magnet. 



It can be shown that, as in electricity, the sum AV of the three 

 partial secondary differentials of the potential is equal to zero for any 

 external point, and to -4^ for any point inside the magnetised 

 bodies. 



The fundamental equations are the same as for statical electricity. 

 Hence, without a fresh demonstration we may apply the theorems 

 already established, provided that these theorems do not depend on 

 the properties of conductors, and that, on the other hand, the 

 coercive force does not come into play. 



315. A MAGNET is EQUIVALENT TO A MAGNETIC SURFACE. 

 We may demonstrate directly Poisson's theorem, that the action of 

 a magnet on an external point is equivalent to that of a fictive layer 

 of a total mass equal to zero, distributed along the surface according 

 to a certain law. 



Suppose that, as a matter of fact, the masses in question are fixed 

 electrical masses, and that the magnet is covered with an infinitely 

 thin conducting surface in contact with the ground. On the inner 

 surface of the conductor a layer of opposite sign to the internal 



