Page:Proceedings of the Royal Society of London Vol 69.djvu/318

302 must next be represented in the section shown in fig. 8. The correc- tion is readily made by a slight enlargement of the atomic volume of oxygen, the diameter of this becoming 1-89.

We are now in a position to determine the amount of rotation which the primitive octahedra must undergo so that the centres of the atoms of copper may be situated in the face of the cube of reference.

Mr. Harold Hilton, Fellow of Magdalen College, has kindly sup- plied me with the following solution, in place of my geometrical con- struction.

Let A (fig. 10, a) be the centre of the group of the six octahedra, each of which consists of four copper and two oxygen spheres. Let D be the centre of one of the inner oxygen spheres, MiMiM 3 M 4 the centres of the four copper spheres in the same octahedron ; and let D', M' correspond to D, M in a neighbouring octahedron. Let the centre of the square MiM 2 M 3 M 4 be U. Let the radii of the copper and oxygen spheres be r\ r% respectively.

The centres of all the copper spheres of the six octahedra lie on a sphere with centre A. Let AD, AD' meet this sphere in H, H' (fig. 10, b), and let the great circles MiM/ HH' meet in K; MI, MI' being the centres of two copper spheres (from different octahedra) which touch.

FIGK 10.

Then we have from symmetry

HK - JHH', MjK = And hence readily

HK = T

AMi

sn ! AM X