536 CRYSTALLOGRAPHY to the whole interior. III. The various forms of crystals belong mathematically to six sys- tems of crystallization : the isometric, tetragonal or dimetric, orthorhombic or trimetric, mono- clinic, triclinic, and hexagonal. The greater part of the crystalline forms may be regard- ed as based on four-sided prisms, square, rec- tangular, rhombic, or rhomboidal in base ; and the rest on the regular six-sided prism. The four-sided prisms are either right prisms (erect) or oblique (inclined). Any such four- sided prism may have three fundamental axes crossing at the centre, one vertical axis con- necting the centres of the opposite bases and two lateral, connecting the centres of either the opposite lateral faces, or the opposite lateral edges. The six-sided prism is right, and has four axes, one vertical and three lateral. In the right four-sided prisms, the intersections of the axes are all at right angles ; in the ob- lique, one or all of them are oblique angles. A. Right or orthometric systems. 1. Isometric system : the three axes equal, and thus of one kind. The system is named from the Greek <<rof, equal, and //rpov, measure. The cube (fig. 1), contained under six equal square faces, the FIG. 1. FIG. 2. FIG. 8. regular octahedron (fig. 2), under eight equal triangular faces, the dodecahedron (fig. 3), un- der twelve equal rhombic faces, are examples of the forms. The three axes in the cube connect the centres of the opposite faces; in the regular octahedron they connect the apices of the solid angles ; in the dodecahedron, the apices of the acuter solid angles. Examples : garnet, diamond, gold, lead, alum. 2. Tetra- gonal or dimetric system : one axis, called the vertical, unequal to the other two, or lateral, and the lateral equal; the axes thus of two kinds. The term dimetric is from the Greek <Kf, twice, and /u^rpov, measure. The square prism (fig. 4) is an example. As the base is a square, the lateral axes, whether connecting FIG. 4. FIG. 5. the centres of opposite lateral faces or edges, are equal ; while the vertical may be of any length, longer or shorter than the lateral. Under this system there are square octahe- drons (fig. 5), equilateral eight-sided prisms, and eight-sided double pyramids (fig. 6), be- sides other forms. Examples : idocrase, zir- con, tin. 3. Orthorhombic or trimetric (Gr. rp/f, three times, and fiirpov) system : the ver- tical axis unequal to the lateral, and the late- ral also unequal, or in other words, the three unequal. In the rectangular prism (fig. 7, a right prism with a rectangular base), the three il FIG. T. axes are lines connecting the centres of oppo- site faces, and are unequal. In the right rhom- bic prism (fig. 8) the vertical axis connects the centres of the bases, and the lateral, the cen- tres of the opposite lateral edges. Fig. 9 rep- resents a rhombic octahedron, another form under this system. Of the two lateral axes in this system, the longer is called the macrodi- agonal, and the short- er the brachy diagonal. Examples : sulphur, heavy spar, Epsom salt, topaz. B. Oblique or clinometric systems. 4. Monoclinic system : one only of the intersec- tions oblique. This system is named from the Greek fj.6vo?, one, and nMvetv, to incline. If we take a model with three unequal axes arranged as in the trimetric system, and then make the vertical axis oblique to one of the lateral, we change the system into the monoclinic. While FIG. 9. 1 FIG. 10. FIG. 11. the right rhombic prism belongs to the ortho- rhombic system, the oblique rhombic prism and the related forms belong to the monoclinic sys- tem. Fig. 10 represents an oblique rhombic prism with its axes, and fig. 11 an oblique prism on its rectangular base, which is another form of the same system. Examples : borax, Glau- ber salt, sugar, pyroxene. 5. Triclinic system : all the three intersections oblique and the axes unequal. The forms are oblique prisms con- tained under rhomboidal faces. Examples: blue vitriol, axinite. 0. The axes four in num- ber. 6. Hexagonal system. In the regular hexagonal prism (figs. 12, 13) the vertical axis connects the centres of the bases, and the three
