308 CONSTITUTION OF MAGNETS. 



Integrating between the limits p = h and p = *Jr 2 + /z 2 , we get 

 / h \ 



/= 27T ( I ) : 



we shall have therefore, for the action of the two layers, 



h 



Two cases are particularly interesting those in which one of the 

 two qualities h and r is very great in comparison with the other. 



When the cylinder is very long, the ratio - is very small, and the 



h 



value of R tends to zero. The real force which then acts in the 

 cavity is reduced to the action of external masses. An infinitely 

 thin cylinder with any base will clearly give the same result ; this 

 will also be the case if we imagine in the magnet a section made by 

 any surface parallel at each point to the lines of magnetisation, and 

 if we suppose an infinitely thin interval between the two separated 

 parts. h 



When the cylinder is reduced to a flat disc, the ratio - is very 

 small, and in the limit the value of R becomes 



R = 4 7Tl. 



The components of this force parallel to the axes are 



These values will agree also with the case of an infinitely 

 thin section made in the magnet perpendicular to the lines of 

 magnetisation. 



If the cavity is in the form of a sphere, the sides will be covered 

 with two equal and contrary layers distributed like layers of gliding ; 

 the action R of this layer on any point in the interior is constant, 

 parallel to the magnetisation, and is expressed by 



