918 



holds good not only for each part separately, but also for the parts 

 mutually, that the energy is zero for every position of the dipoles. 

 The coercitive-force thus becomes again a third of the magnetisation 

 of saturation, for other divisions into two groups a much smaller, 

 even a negative value being found. 



There are still many other divisions into groups conceivable, which 

 perhaps ma}' be of interest when another direction of the exterior 

 field is chosen. So e. g. the division into three groups. In the case 

 exclusively treated here where the field is parallel to the edge of 

 the cube, they appeared to yield a greater value for He than that 

 calculated below. 



4. We shall take the y-axis in the direction of the exterior field, 

 the .{•- and z-axes along the two other edges. For an arbitrary division 

 into two halves the dipoles of which are directed parallel to the 

 xy-plane, and form angles -|- y and — <r with the y-axis, we can 

 indicate the energy as follows. Every dipole may be decomposed 

 into a y-component p co.^: fp and an .^-component p sin 'f for the one 

 and — p sin (p for the other group. The y-components form a com- 

 plete cubic lattice and their mutual energy is consequently zero. 

 In consequence of the exterior field Hg each dipole has an energy 



P 

 pHgCOStp and so the dipoles together an energy of ~ He cos (p per 



a' 

 unity of volume. Also the magnetical energy of the o^-dipoles and the 

 y-dipoles is zero on account of the cubic arrangement of these latter. 

 The mutual energy of all .r-components thus remains to be calculated. 

 In order to determine this we imagine the .I'-components of the 

 dipoles of the second group inversed in sign. 



Then all are directed in the same way and their mutual energy 

 is zero, (f now we inverse the dipoles again then only the mutual 

 energy of the two groups becomes different in sign. The energy sought 

 for of all dipoles together is thus equal to twice the mutual energy 

 of the two groups. We shall now calculate this with the help of (2). 



Call the potential caused by unit-poles placed in the first half V, 

 then the energy of a magnet with moment — p sin (p in the field 

 of the first group the dipoles of which have a moment psimp is 

 according to what preceded 



Ox 



or per unity of volume 



sill* rp - — . 



2d' dj;» 



