312 CONSTITUTION OF MAGNETS. 



the filament were defined by the ratio 



dm _ d(al] 

 ~~~~ ~ 



and we may write 



y ^S*p* 



'i. J / 



328. SOLENOIDAL MAGNETS. A magnet is said to be solenoidal 

 when it may be divided into simple solenoids terminating at the 

 surface or closed upon themselves. There is no free magnetisation 

 in the interior of the magnet ; the distribution is entirely superficial. 



The volume density p being zero, we have 



(8) + + = 0. 



Conversely, if the condition (8) is satisfied, the density is zero at any 

 point in the interior, and the magnet is solenoidal. 



329. MAGNETIC SHELLS. A simple magnetic shell is a magnet 

 formed of two infinitely near equidistant surfaces, charged with equal 

 and opposite uniform magnetic layers ; or is a magnet formed of 

 two infinitely near but not equidistant layers, always equal and of 

 opposite signs, and such that the density at each point is inversely 

 as their distance. 



If h be the thickness of the shell at a point, and o- the density of 

 the layer, the product Jvr must be constant ; it is called the magnetic 

 power of the shell. 



We may also define a simple magnetic shell as being an infinitely 

 thin plate, the magnetisation of which is perpendicular at every point 

 to the surface, and its intensity inversely proportional to the thickness. 



If < be the magnetic power of the shell we have 



That portion of the shell which corresponds to an element dS, 

 may be regarded as an infinitely small magnet, the moment of 

 which is 



