the vertex of the pyramid with a force proportional to its distance from the vertex.
The proper mathematical interpretation of the stated force law in crystals shows its perfect identity with the Newtonian law of gravitation, Fig. 18. according to which every particle of the universe attracts every other particle, with a force proportional to the product of the masses, and inversely as the square of the distance. Thus, the symmetry, beauty, and definiteness displayed in the infinite variety of crystal forms have necessarily impressed themselves upon the observing mind, ever since the remote period of the dawn of the natural sciences, as the silent carriers of a law of profound influence upon the nature of substances. That this law, in obedience to which the planets are swept through space, should also regulate the position of the tiny crystal molecule, is a striking instance of the truism, in accordance with which the essences of things are not affected by their magnitude, and without which the human mind could not conceive the interaction of the forces of Nature.
The stated law also governs the interaction of electrical masses. Now, the only reason why it applies to the ultimate particles of a crystal Fig. 19. is their tetrad arrangement. Hence the tetrad grouping of the ultimate particles, and therefore crystallization, is caused by an agent which acts like electricity. Very probably it is electricity itself, as is evidenced by the electrical properties of certain crystal forms, which appear to establish an intimate causal connection between the structure of crystals and this agent. This is illustrated in many so-called hemimorphic forms: these are forms in which opposite ends of a crystal, instead of being bounded by faces of the same form, are bounded by faces belonging to different forms. This phenomenon occurs in