﻿Cubic Crystals with Theoretical Atoms. 763 



A Cubic Crystal. 



If we now attempt to build up a solid by placing such 

 planes one above the other, a possible way is to place an 

 exactly similar plane above this one with all axes reversed, 

 making the odd planes like fig. 6 and the even planes like 

 fig. 7. A different formula applies to the distance between 

 the planes, for, in adjacent atoms « = 7r, whereas in the 



plane a= , and we do not get a perfect cubic crystal. 



It is evidently necessary to seek further for the proper 

 arrangement in a cubic crystal. All three principal planes 

 of atoms mutually perpendicular to each other should be 

 identical in character, a condition which cannot be secured 

 when the axes of all atoms in one plane lie in the same plane. 

 Fig. 1 shows an arrangement of the axes in a cubic crystal* 

 that satisfies all the required conditions. All axes of rotation 

 lie along some long diagonal of the cube, and a plane of 

 atoms parallel to any face of the cube is similar to all other 

 such planes parallel to any face. A study of the figure 

 shows that the axes of any two adjacent atoms along an 

 edge of the cube lie in the same plane, namely the plane 

 through the two atoms and through the centre of the cube 

 to or from which the axes point. Moreover, the angle 

 between the directions of the axes of rotation of every two 

 adjacent atoms in the whole structure is the same, equal to 

 cos -1 -J = 70° 31 /, 7, being the angle between any two ad- 

 jacent long diagonals of the cube. We have to study only 

 four different sorts of cubes shown in figs. 8 to 11 from 

 which the complete structure may be built. The lower left 

 front corner cube in fig. 1 is like that shown in fig. 8 ; the 

 next adjacent cube to the right in the front row is like 

 fig. 9 ; and the cube immediately above this is like fig. 10, 

 and the one just back of that, being the central cube in 

 fig. 1, is like fig. 11. Fig. 8 shows axes of all atoms point- 

 ing towards the centre, and fig. 11 all away from it. Fig. 9 

 shows four axes pointing to the centre of an adjacent cube 

 on one side, and four towards the centre of the corresponding 

 cube on the opposite side ; while fig. 10 simply reverses the 

 directions of these arrows. In each of these figures any 

 two adjacent axes of atoms along an edge of the cube lie in 

 the same plane, namely, a plane containing the two diagonally 



* Since this paper was communicated it has been found that the axes 

 of rotation of atoms in the odd planes parallel to the hexagon tig-. 12 

 should all be reversed in direction. 



