THE PROBLEM OF CRYSTALLIZATION. 



47 



tern being subject to the gravity of the earth, they assume certain 

 definite relative positions which determine the magnitude of the slope. 

 In order to insure the same slope, the particles need not necessarily be 

 perfectly alike, but the average size and shape of a limited number of 

 them, chosen at random, should be uniform throughout. It is clear 

 that the nature of the support must influence the slope of the heap, for, 

 resting on a polished surface like a plate of glass, the slope is less than 

 when supported on a rough surface, as a wooden floor. Generally, in 

 a heap of gravel the slope is different from that of a heap of grain, 

 inasmuch as the dimensions and shape of the grain-particles differ ma- 

 terially from those of the gravel-particles. Bearing in mind that the 

 magnitude of each of the particles is very small, when compared with 

 that of the heap, and therefore their number very large, we have then 

 considered a state of aggregation of particles, assuming certain definite 

 outward forms, these being dependent upon known causes, which we 

 can readily modify at will, so as to produce forms with stated slopes. 

 Mechanically, this may be said to be entirely analogous to the problem 

 of crystallization. There also we have states of aggregation of parti- 

 cles occurring in definite regular shapes of infinite variety, depending 

 upon the nature of the substance and the nature of the force active 

 between the ultimate particles, and the problem of crystallization is 

 solved when the nature of the ultimate particles and of the force 

 which holds them in their relative positions in the crystal has become 

 known to us. 



These are the actual questions under consideration, and before pro- 

 ceeding with their further discussion we cite some instances of crvstal- 

 lization of substances, rendered familiar to us, either through their 

 utility in the arts and industries, or the recognized value they have by 

 reason of their rarity and beauty. In Fig. 1 a crystal of diamond is 



Fia. 1. 



Fig. 2. 



Fig. 3. 



represented ; the beauty and value of this gem are greatly enhanced 

 by the cutting process ; the remarkable property of cleavage, which 

 all crystals possess to a greater or less extent, is well developed in the 

 diamond, and skillfully utilized in its cutting. The form shown in 

 the figure occurs at the Cape, and has a yellow tinge ; the bluish-white 



