On the Intimate Structure of Crystals. 



301 



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 



Y 2 



