Page:Proceedings of the Royal Society of London Vol 69.djvu/316

300 are brought just into contact. Considering the want of exactitude in our knowledge of the specific gravity of silver sulphide, the requisite amount of rotation may be obtained by construction, the errors attendant on this method lying within the errors of observation. Let

FIG. 9.

the centres of two octahedral elements be projected on a plane, which cuts the two rectangular axes on which they lie at 45, and is parallel to the third, i.e., parallel to two of the diagonals of the cube of refer- ence. Then let each octahedron be supposed to rotate through a, complete circle, the centres of the paired atoms will then project into an ellipse which may be used as a kind of directrix. The spheres representing the paired atoms will always project as circles. Find the point on the ellipse at which the centres of two circles representing the silver atoms must be situated so as just to touch. The angle which a line joining one of these points to the centre of the octahedron makes with that joining the centres of the two octahedra is that sought. In the case* of silver sulphide it amounts to 21 52'.

Thus, while preserving the dimensions we had previously obtained for the atoms of silver and sulphur, we arrive at a structure which completely explains the cleavage of silver sulphide, and satisfies the conditions of symmetry imposed by the system to which it belongs.

Gryrohedry has not yet been described in silver sulphide, but it has been discovered in cuprite by Professor Miers. To this mineral we turn therefore with particular interest.

The molecular weight of cuprite, Cu 2 0, is 142 -6, its specific gravity has been determined with most discordant results; we select that given in ' Watts' Dictionary of Chemistry,' viz., 5-749 at 4 C. The molecular volume obtained from this is 24-8043, and the edge of the cube of reference measures 5*3. The diameter of an atom of copper in the metal itself has been previously determined as 1-918, that of oxygen on a somewhat doubtful basis, as 1-851.

Our want of certitude regarding the precise specific gravity of