Fig. 22.—Measured Crystal of Topaz.
Besides these four more highly symmetrical systems or styles of crystal architecture, a fifth, the monoclinic system, characterised by a single plane of symmetry and one axis of digonal symmetry perpendicular thereto, has already been alluded to, and a typical crystal illustrated in Fig. 15. A sixth, the rhombic system, perhaps in some ways the most interesting of all, and certainly so optically, possesses three rectangular axes of symmetry, identical in direction with the crystallographic axes, and three mutually rectangular planes of symmetry, coincident with the axial planes and intersecting each other in the axes. The lengths of the three crystal axes are unequal, however, and herein lies the essential difference from the cube. A very typical rhombic substance is topaz, a crystal of which, about three millimetres in diameter, is shown very much enlarged in Fig. 22. Every face on this crystal has been actually investigated on the goniometer, and the interfacial angles measured.
Fig. 23.—Measured Crystal of Copper Sulphate.
Lastly, there is the seventh, the triclinic system, in which there are neither planes nor axes of symmetry, but, even in its holohedral class, only symmetry about the centre, each face having a parallel fellow. Sulphate of copper, blue vitriol, CuSO4.5H2O, shows this type of symmetry, or rather lack of it, very characteristically, and a crystal of this beautiful deep blue salt, measured by the author, is represented in Fig. 23.
Hence, we have arrived logically at seven systems of symmetry or styles of crystal architecture, distinguished by the nature of their essential axes of symmetry, and the planes of symmetry which may accompany them. Now the full degree of symmetry of each system may be reduced to a certain minimum without lowering the system, and in all the systems but the triclinic there are several definite stages of reduction before the minimum is reached, each stage corresponding to one of the thirty-two classes of crystals. Thus in the cubic system there are four classes besides the holohedral, in the tetragonal six, in the hexagonal four, in the trigonal six, in the rhombic and monoclinic two each, and in the triclinic one.
PLATE IV.
Fig. 24.—Octahedra of Potassium Cadmium Cyanide.
