Page:Proceedings of the Royal Society of London Vol 69.djvu/311

Rh are thus related cannot readily be arranged so as to give a stable structure, which will satisfy the conditions of cubic symmetry.

Let us then regard the two atoms, which form a pair, and which we may speak of as the paired atoms, to be approximated to each other as in fig. 2, and next let one such molecule be placed over

FIG. 3.

another similar one, but inverted, so that the paired atoms form the corners of a square, and the unpaired atoms rest upon them imme- diately over the centre of the square (fig. 3). The resulting figure is that of an octahedron, and might be regarded as the crystalline element from which other forma could be built up. Within certain limits determined by the relative dimensions of the paired and un- paired atoms, such a primititive octahedron might possess the " regular " character, i.e., lines obtained by joining the centres of the atoms, or by drawing common tangent planes to their surfaces taken in threes, would be that of a regular octahedron. This would ob- viously be the case if the atoms were all of equal size, but it might also be if the unpaired atoms were larger than the paired atoms, but more closely approximate. Yet such an octahedron could not by itself be regarded as satisfying the requirements of cubic symmetry, for of the three rectangular axes which may be imagined to be drawn from the centre of the figure through the centres of the atoms, one, that which passes through the unpaired atoms, differs in its properties from the rest, inasmuch as it passes through two atoms of different kind to the other four.

It might be possible to uphold the view that jn a chance distribu- tion of such octahedra as many might be found with their single axis on one crystallographic axis as on another, but few crystallographers, I presume, would be prepared to admit that the exigencies of cubic symmetry could be so easily satisfied.

It is possible, however, to arrange our octahedra into groups which are completely symmetrical. In the case of regular octahedra, there would appear to be but one way of doing this. We may imagine three rectangular axes, the " tetragonal " axes of the cubic system : on each of these a primitive octahedron may be supposed to be placed, so that the axis passing through the unpaired atoms may coincide with one of the semi-axes of the rectangular system; and the other