316 CONSTITUTION OF MAGNETS. 



implicitly assumed that we placed the point P in an infinitely thin 

 slit perpendicular to the lines of magnetisation : the term 473-! is the 

 force which must be added to the external actions in order to have 

 the value of the true force in the interior of the cavity. 



We may further observe that if the intensity of magnetisation is 

 finite, the magnetic power ^> of the shell is an infinitely small 

 quantity ; for any external point at a finite distance from the contour 

 of the shell the value of the force is infinitely small, while in the 

 interior of the shell the force has a finite value 473-!, directed along 

 the perpendicular and in an opposite direction to that of the mag- 

 netisation. 



331. LAMELLAR MAGNETS. A magnet is said to be lamellar 

 when it may be divided into simple closed magnetic shells or into 

 open shells with their edges on the surface of the magnet. 



Let < be the sum of the magnetic powers of the shells which we 

 meet in going from a given point to a point whose co-ordinates are 

 x,y, z, along a line of force drawn in the interior of the magnet. 

 This quantity 3? is a function of the co-ordinates independent of the 

 line joining the two points ; it has a constant value on the whole 

 surface of a shell, but varies from one shell to another. 



The lines of magnetisation are, by definition, at right angles to 

 the surfaces of the elementary shells, and the strength of the mag- 

 netisation at each point is inversely as the perpendicular distance dn 

 of two consecutive shells. We have then 





332. POTENTIAL OF MAGNETISATION. The function < has 

 therefore, taking into account the sign, the same properties in 

 reference to magnetisation as the potential in reference to external 

 forces. Hence, by analogy, we may call the function -& the 

 potential of magnetisation. The components of magnetisation along 

 the axes of the co-ordinates, are respectively equal to the corre- 

 sponding partial differentials of the function < : 



From this we deduce 



(i i) MX + >dy + Cdz = 



