tem 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 materially 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 particles 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 proceeding with their further discussion we cite some instances of crystallization 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
| Fig. 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
