OEDEE OE CHAEACTEES. 107 The order in which the characters will he given in the following descriptions of minerals :— The system of crystallization to which the mineral belongs. The angular elements used in computing the mutual inclina tions of the faces of the crystal. The letters and symbols by which the simple forms are denoted. Enumeration of liemihedral forms. The angles between normals to the faces. These angles are the supplements of the angles between the faces as they are usually given. It happens not unfrequently that forms occur, the faces of which could not be shown in the figures, without increasing their number enormously, and that the situation of such faces is not capable of being clearly described in words. In every case*of this kind we have added a map ot a sphere to the surface of which the faces of the crystal are referred, by radii drawn perpendicular to the respective faces. This sphere is called tho sphere of projection, and the extremity of a radius drawn perpendicular to any face is called the pole of that face. The map for crystals belonging to the cubic system is given m fig. 28. As the dots on the maps, corresponding to the laces on the figures, are marked by corresponding indices or letters, the reader will, after a little practice, be able easily to perceive the relation of the maps to the figures, and, when once accus tomed to observe the crystalline forms on the maps, lie will ex perience as little difficulty in tracing the relative positions of the faces as on the solid figures he has been accustomed to consult. The maps given in this work exhibit, respectively, all the faces which we arc aware of having been hitherto observed on the crystals of each separate mineral, and, being records of all that is at present known of crystalline forms, they may for a long time be consulted by the mineralogist as standard figures. Simple forms that have been observed in nature without any additional faces, and the principal combinations of simple forms which have been observed. The lists of combinations are sometimes abbreviated. Thus enpr.d.z.t is used to denote com binations of the forms e, n, ■p, r with each of the forms d, z, t; and enpr..d.z.t to denote that the forms e, n, p, r have been observed in combination with each and with all of the forms d, z, t. The letters denoting liemihedral forms have accents placed over them. When two or more liemihedral forms have E G