MINEKALOGY 359 faces on the angles, or ooP, P, 2P2. Fig. 95 is a similar form, the upper part of the pyramid being replaced by the pinacoid. In some crystals the lateral edges of the prism are replaced by the Fig. 95. Fig. 96. Fig. 97. second prism ooP2 (fig. 96), producing an equiangular twelve-sided prism, which always represents the combination ooP, o>P2, and cannot occur as a simple form. Figs. 97, 98 are combinations in this Rhombo- hedral forms. Fig. 98. Fig. 99. system seen in beryl. An example of a more complicated combina tion is seen in fig. 99, of a crystal of apatite, whose sign with the corresponding letters is ooP( J/), ooP2(), OP(P), *P(r), P(x), 2T(z) P2(a), 2P2(s), 4P2(rf). Hexagonal minerals frequently crystallize in those series of henii- hedral forms that are named " rhombohedral," from the prevalence in them of rhombohedrons. These (figs. 100, 101) are bounded by Fig. 100. Fig. 101. six rhombi, whose lateral edges do not lie in one plane, but rise and fall in a zigzag manner. The principal axis unites the two trigonal angles, formed by three equal plane angles ; and in the most common variety the secondary axes join the middle points of two opposite edges. When the polar edges form an angle of more than 90, the rhombohedrons are named obtuse ; when of less than 90, acute ; fig. 102 represents the first, fig. 103 the second. Hexagonal scaleno- hedrons (fig. 104) are bounded by twelve scalene triangles, whose lateral Fig. 102. Fig. 103. edges do not lie in ono plane. The principal axis joins the two hexagonal angles, and the secondary axis the middle points of two opposite lateral edges. The rhornbohedron is derived from the first order of hexagonal pyramid by the hemihedral development of its alternate faces. Its general sign should therefore be ; but on several grounds it is found better to designate it by R or mR, and its complementary figure by - mR. When the prism or pinacoid arises as its limiting form, they are designated by ooR and OR, though in no respect changed from the limiting forms ooP and OP of the pyramid. The scalenohedron is properly the hemihedral form of the dihexagonnl pyramid, but is more easily understood as derived from the inscribed rhombohedron mR. If the halves of the principal axis of this be multiplied by a definite number n, and then planes be drawn from the extremities of this enlarged axis to the lateral edges of the rhombo- "hedron, as in fig. 105, the scaleno hedron is constructed. It is now designated by mUn (the n on the right here referring to the chief axis), and the dihexagonal prism in this series by oo R?i (for merly 7/iR 11 and ooB"). The combina tions of rhombo hedral forms are very numerous, several hundreds having been de scribed in calc-spar alone. Among the most common is the prism in com bination with a rhombohedron, as seen in the twin crystal of calc- spar (fig. 106), with the sign Fi g- 104 - Fig. 105. oo R, - R, the lower half being the same form with the upper, but turned round 180. In fig. 107 the rhombohedron ?Rhas its polar Fig. 106. Fig. 107. edges replaced by another rhombohedron -fanK its lateral edges bevelled by the scalenohedron complex combination of five forms is represented in the crystal of calc- spar fig. 109, its sign, with the letters on the faces, being R 5 (y), and in fig. 108 mRra. A more Fig. 108. Fig. 109. R 3 (r), R(/ ) ), 4R(m), ooR(c,. Tetartohedral combinations are seen most distinctly in rock-crystal. IV. Right Prismatic or Rhombic System. This system Right is characterized by three unequal axes, all at right angles prismatic to each other. Any one of these may be assumed as the s y stem - chief axis, when the others are named subordinate. The plane passing through the secondary axes, or the base, forms a rhombus, and from this one of its names is derived. As prismatic forms are most frequent (the prism standing vertically on the rhombic base), it is best defined as the right prismatic. This system comprises only a few varie ties of forms that are essentially distinct, and its relations
are consequently very simple.