Page:Proceedings of the Royal Society of London Vol 69.djvu/315

Rh which 6 molecules would occupy must have a length of 6'318, or 0*429 in excess of that obtained from the molecular volume. Silver sulphide consequently does not possess the structure described in Case I, and Case II may be shown to be impossible, unless the dimen- sions of the constituent atoms be taken as 2*192 for the diameter of silver, i.e., 0'02 in excess of our previous determinations, and that of sulphur as 2'434, which is 0*03 in excess, and in this calculation the edge of the cube is determined from the maximum specific gravity instead of the mean.

It is of course possible that atomic volumes actually do vary to the extent this would indicate, but there would seem to be no apparent reason why silver, which retains with remarkable constancy the same atomic volume in the free state and in combination with the haloid elements, should undergo an increase in dimensions on combination with sulphur : it would therefore seem likely that the arrangement of the atoms in silver sulphide is gyrohedral. It has been asserted that the edge of the cube obtained when the atoms of silver sulphide are arranged according to Case I, measures 6'318, while that of our cube of reference obtained from the molecular volume is only 5*89. To transform the larger cube into the smaller, we may first push in towards the centre of the cube the outer atoms of sulphur (fig. 7, A), till

FIG. 7.

the point midway between them and the inner atoms lies on the centre of the face of the cube of reference. In this way we shall have reduced our deduced cube to the dimensions of that obtained from observation. This operation also fixes for us the relative position of the sulphur atoms. But by thus causing the atoms of sulphur to approach, we have at the same time caused the atoms of silver to diverge from each other in the manner shown in fig. 7, B, which is a section taken through two rectangular axes of a primitive octahedron. The atoms of silver are now much too wide apart to permit of the diagonal of the square figure which they form being brought into coincidence with a line drawn parallel and equal to the edge of the cube of reference. The requisite space for them on the face of the cube must be found by rotating the primitive octahedra, till the paired atoms at the corners