320 CONSTITUTION OF MAGNETS. 



- $0 the value of this potential at the point O of the surface where 

 the function * is a minimum ; during the transformation the potential 

 at P will have diminished by the product of 477 by the sum of the 

 magnetic powers of all the shells between the points P and O that 

 is by 4 Tr^p- <>()), and this quantity must be added to the new 

 potential at the point P to give it the value which it originally had. 



At any point M of the resultant superficial shell thus formed, the 



magnetic strength is equal to the sum / d& of that of the shells which 



have been superposed there ; it is therefore equal to * - $ , calling 



- < the value at this point of the original potential of magnetisation. 

 Consequently, the potential of all the layers on the point P is equal 



to 



If the point P is not surrounded by closed shells, the potential at 

 this point has diminished by 4?r (& p - <1> ) during the transformation 

 the original value of this potential was therefore 



Let us now suppose that there are closed shells ; only those which 

 comprise the point P need to be taken into account. Let $ x be the 

 value of 3> on the largest of them. The sum of the magnetic powers 

 of the open shells from the point O to the point P is 3^ 3> ; that 

 of the closed shells which comprise the point P, and which have not 

 been displaced by the preceding transformation, is equal to & p - $ r 



The potential at the point P is then 



or 



It will be seen that the closed shells do not modify the expression 

 of the internal potential. 



The external potential is not changed by the transfer of the shells 

 to the surface ; it is expressed by 



(16) 



