917 



For the case of the cubic lattice tlie analogous general method is 

 impracticable for the reason mentioned above, but it is clear that 

 also there we must And the combination of deviations, which 

 most easily leads to an unstable position of the magnets. This 

 combination must serve in calculating the coercitive-force, and it 

 will yield for this quantity a smaller value than all other virtual 

 displacements. Led by the analogy of the above mentioned simple 

 case we shall examine those combinations of displacements, in which 

 the dipoles of the lattice are distributed over two equal groups, 

 which show an opposite displacement. Further it will be favourable 

 in order to get unstability if the magnets with opposite deviations 

 are placed as alternately as possible. 



We can obtain a division into two groups by starting from a 

 plane through three arbitrarily chosen points of the lattice and 

 then using the system of parallel planes which contains all points. 

 The dipoles lying in such planes can be assigned in a systematic 

 way to each of the groups. The most obvious method is to count 

 the planes alternately to the first and to the second group. Let the 

 chosen planes divide the three edges of the elementary cube, respec- 

 tively in /, m, and n parts. The dipoles on the .r-axis will belong 

 alternately to the two groups, when / is odd, but all to the same 

 group if / is even. From this it follows that in principle there are 

 possible only three divisions into groups i. e. dipoles along three, 

 along two or only along one axis belonging alternately to different 

 groups. These divisions can be obtained by starting respectively 

 from the octahedron, the rhomb-dodecahedron or the cube-plane. 



In the same way we can examine the distribution of the points 

 of the central cubic lattice, by paying attention to the question 

 whether the dipoles lying on three of the cube-diagonals belong or 

 do not belong to different groups Here the two last cases appear 

 to be identical. Consequently there are only two possibilities, which 

 belong respectively to the octaeder and the rhomb. -dodecahedron plane. 

 When we consider the distributions of the plane-centred cubic lattice 

 we can take three diagonals in the sides which meet in one corner. 

 Then the first and the third case are identical and belong to the 

 octahedron-plane, the second case belongs to the cube-plane. 



With each of the lattices mentioned we meet with a way of 

 the de\iatioMs that will yield no sharper ci-ilerion for the stability 

 than the deviation in parallel of all dipoles. These are the distri- 

 butions that belong to the octahedion-plane. For it is evident that 

 for each half separately the equivalency of the three directions 

 of axes still exists. Analogous to what has been discussed sub 1 it 



