Page:Proceedings of the Royal Society of London Vol 69.djvu/317

Rh cuprite, justifies the treatment of the ensuing discussion to a great extent by construction. Let ab (fig. 8 (a) ) be any line drawn in the face

FIG. 8.

of the cube of reference through its centre ; let co be a tetragonal axis of the cube on which, by the conditions of the case, an atom of oxygen must be situated at a distance of 1*31 from the centre of the cube, and 1-34 from c, the centre of the face. To obtain a section through a primitive octahedron of which the line ab shall be an axis, circles may now be drawn 1*92 in diameter, representing sections through atoms of copper ; their centres must be situated on ab and at such a distance from c, that the circles just touch that representing an atom of oxygen.

Using ab as a diagonal, construct upon it a square (fig. 8 (b) ) ad, and at the corners of the square as centres describe circles of the given diameter to represent atoms of copper, this will give us a section through the primitive octahedron containing the axes on which the four atoms of copper are situate. We may sometimes speak of this as the copper square.

When the construction is made, it will be found that the circles intersect to a very slight but appreciable extent. The smallness of the amount of the intersection suggests that we have not been far out in our calculation, and leads to the conclusion that some slight reduc- tion in the dimensions of the atoms of copper accompanies a change from the free state to that of combination, as indeed might naturally be expected when the loss of energy which accompanies this change is considered. On this assumption we may legitimately reduce the diameters of our circles in fig. Sb till the latter just touch. The diameters thus pass from 1'918 to T90. This is a limiting value; the atoms may be slightly smaller, for they are probably not in actual contact, but they cannot be larger.

The effect of the reduction in the diameters of the atoms of copper