360 MINERALOGY Pyra mids. There are two closed forms. (1) The rhombic pyramids (figs. 110, 111), bounded by eight scalene triangles, whose lateral edges lie in one Fig. 110. plane, and form a rhom bus. They have eight polar edges (four acute and four more obtuse) and four lateral edges. The angles are six rhom bic, the most acute at the extremities of the longest axis. (2) The Fig. 112. Fig. 113. rhombic sphenoids (figs. 112, 113) are bounded by four scalene Sphen- triangles, with their lateral edges not in one plane, and are hemi- oids. hedral forms of the rhombic pyramid. They are of very infrequent occurrence. Prisms. The open forms, again, are rhombic prisms bounded by four planes parallel to one of the axes, which is indefinitely ex tended, and may be longer than the lateral, as in fig. 114, or shorter as in fig. 115. They are divided into upright (as in the above figs.) and horizontal prisms, according as either the principal or one or other of the lateral axes is supposed to become infinite. For the latter form the name doma or dome has Domes. been used ; and two kinds, the macro- dome (fig. 116) and the brachydome (fig. 117), have been distinguished. Pinacoids. Rhombic pinacoids also arise when one axis becomes =0 and the two others are indefinitely extended ; and so we .. have macropinacoids (fig. 118) and & brachypinacoids (fig. 119), the qualifying term thus designat ing the axis to which the faces of the dome or pinacoid are parallel. In deriving these forms from a primary, a particular rhombic pyra mid P is chosen, and its dimensions determined either from the Fig. 114. Fig. 116. Fig. 117. Macro- and brachy- diagonal. angular measurement of two of its edges, or by the linear pro portion of its axes a : l> : c, the greater lateral axis b being assumed equal to 1. To the greater lateral axis the name macrodiagonal is given, to the shorter that of brachydiagonal ; and the two principal sections are in like manner named macrodiagonal and brachydiagonal, according to the axis they intersect. The same terms are applied throughout all the derived forms. They conse quently mark only the position of the faces in respect to the axes of the fundamental crystal, and frequently of necessity without reference to the relative magnitude of the derived axes. By multiplying the principal axis by any rational number m, Fig. 118. 119. greater or less than 1, a series of pyramids arise, whose general sign Derived is mP, and their limits are the prism and pinacoid ; the whole series forms. being contained in this formula, OP .... mP .... P .... mP .... oo P, which is the fundamental series, the lateral axes always remaining unchanged. From each member a new series may, however, be developed in two directions, by increasing one or other of the lateral axes. When the macrodiagonal is thus multiplied by any number n greater than 1, and planes drawn from the distance n to the polar edges, a new pyramid is produced, named a macropyramid, with the sign inPn, the mark over the P point ing out the axis en larged. When ?i = oo, a macrodome results, with the sign mPoo . If the shorter axis is multiplied, then brachy- pyramids and brachy- domes are produced, with the signs inPn and mPoo . So also from the prism oo P, on the one side, originate numerous macroprisms ooP, with, the limiting macro- pinacoid coPoo ; on the other, numerous brachy- with the Fig. 120. prsms limit form oopoo , or the brachypinacoid. In figs. 120, 121 the two domes are shown in their relation to the primitive pyramid. M Fig 122. Fig. 123. Fig. 124. The pyramids seldom occur independent, or even as the pre dominant forms in a combination ; sulphur, however, is an excep tion. Prisms or pinacoids usually give the general char acter to the crystal, which then appears either in a columnar or tabular or even rectangular pyramidal form. The determination of the position of these crystals, as vertical or horizontal, de pends on the choice of the chief axis of the fundamental form. In the topaz crystal (fig. 122) the brachyprism and the pyramid are the predominant elements, asso- Fig. 125. Fig. 126. ff d ciated with the prism, its sign and letters being ooP2(Z), P(o), ooP(3f). Fig. 123 of stilbite is another example, the macropinacoid ooPoo or M being combined with the pyramid P(? - ), the brachypinacoid ooPoo(T), and the basal pinacoid OP(P). Another instance is fig. 124 of a lievrite crystal, where the brachy prism and pyramid combine
Fig. 127.