On the Intimate Strmture of Crystals. 299 



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 

 VOL LXIX. Y 



