272 



CRYSTALLIZATION. 



adjacent holes to touch it, as indicated by the dotted circles. Above 

 these four more may be placed in the openings a b c d, so as to touch 

 it — making twelve in all. If the pile be completed, we shall get a 

 four-sided pyramid, of which each side is an equilateral triangle, as 



represented in Fig. 2. It will be seen that, in these triangular faces, each 

 ball (except,of course, those forming the edges) is touched by six others. 

 Again, if we start with such a triangle, as in Fig. 3, where each ball 

 is touched by six others, we can place one ball — the shaded one — so as 



Fig. 3. 



to rest on three others, and can then place six more round it and touch- 

 ing it, as indicated by the dotted circles. In three of the triangular 

 holes between the shaded ball and the dotted balls touching it we can 

 place three more, so as to touch the shaded ball— again twelve touch- 



