POTENTIAL OF MAGNETISATION. 317 



_ V _ _ 



The first member of this equation is thus an exact differential. 

 Conversely, if the expression Adx + 'Bdy + Cdz is the exact dif- 

 ferential of a function of the co-ordinates, the components of 

 magnetisation are respectively equal to the partial differentials of 

 this function, and the magnetisation is lamellar. 



The condition of lamellar magnetisation may be expressed by 

 equations in which the function < does not appear. 



We have, in fact, 



which gives the three equations 



3A SB 



N -\ ' 



dy ox 



(12) as ac 



_ .-, __ _ y ? 



oz oy 



333. A magnetic shell is said to be complex when, the mag- 

 netisation being always perpendicular at each point, the magnetic 

 strength is not constant throughout the whole extent of the shell. 



The potential at the point P of the element d of the shell is 

 still 



and the potential of the entire shell 



the integral being extended to the whole surface of the shell. 



When a magnet can be divided into complex magnetic shells, the 

 strength of magnetisation is no longer inversely as the distance of 

 two infinitely near shells, but the lines of magnetisation are still 

 orthogonal to the surfaces of these shells, which gives the condition 



A_JB __(:_ 



(13) ~~* 



