700 



SCIENCE PROGRESS 



The complexes are piled in vertical columns in such a 

 manner that the faces which do not carry a small sphere are 

 in contact. The general arrangement in the complexes persists 

 in the resulting structure, each small sphere being in contact 

 with three large ones. The close-packing of the structure is 

 then somewhat increased by compressing the columns slightly 

 and so shortening their height ; after this slight distortion the 

 small spheres touch four large ones instead of three, as in the 

 initial arrangement. Figs. 2 (a) (b) and (c) show the resulting 

 structure in plan and elevation. The small and the large 

 spheres alternate regularly in the vertical columns (fig. 2, c) 

 and by geometrical partitioning these columns they may be 

 divided into segments each consisting of two consecutive layers, 

 as shown in fig. 2 (b). The shortening of the column as 

 described does not lead to any considerable distortion. 



Fig. 2. 



Next the vertical columns are placed in contact side by side 

 and it is found that, in order to secure the closest possible 

 packing, half the columns must be raised slightly with respect 

 to the rest ; the walls of the columns then interlock. A further 

 slight distortion increases the closeness of the packing and 

 would appear to render it as close as possible — i.e. to give a 

 minimum of interstitial space. As already explained, this 

 interstitial space is merely a geometrical feature ; no separation 

 of space into two kinds, enclosed and unenclosed, as in a 

 system of spheres, is to be regarded as obtaining in the actual 

 crystal. Indeed, the conditions supposed to prevail are more 

 closely represented if the spheres used are deformable and the 

 assemblage they form is compressed so as to distort them into 

 polyhedra and annul the interstitial space altogether. 



The arrangement arrived at is shown in plan in fig. 3. It 

 has now to be shown that this assemblage corresponds in 



