MINERALOGY 367 is that the twin axis corresponds with that normal of the brachy- diagonal which is situated in the plane of the base. In pericline, a variety of albite, these twins appear as in fig. 198, where the two crystals are united by a face of the basal pinacoid P, whilst the faces of the two brachypinacoids (M M Fig. 196.
Fig. 198. Fig. 197. and Af) form edges with very obtuse angles (173 22 ), re-entering on the one side and salient on the other. These edges, or the line of junction between J/and At , are also parallel to the edges formed by these faces and the base, or those between M and P. In this case also the twins are occasionally several times repeated, when the faces appear covered by fine strife. Cause of the Formation of Twins and Hemitropes. It has been shown above that the relative position of the molecules of crystals is determined by a polarity in the molecules themselves. This polarity must exist along three lines which intersect in the centre 1 i, ^ t ^ ie mo ^ ecu ^ es J an( l unlike poles must attract each other. It has growth, been supposed that compound crystals result from a reversion of the original polarity of the molecules of a crystal, after it has at tained a certain size. Heat and electricity, resulting from move ments in strata, might occasion such reversion during the forma tion of a crystal, and this would suffice for the explanation of hemitropes, though not directly of geniculated crystals, and still less of intersecting twins. Twins have accordingly been divided into " paragenetic " and "metagenetic." The first term is applied to the ordi narily occurring twins, in which the compound structure is supposed to have had its beginning in a nucleal compound molecule, or to have been compound in its very origin. In metageuetic twins the crystal was at first simple, but afterwards, through some change in the material furnished for its increase or possibly induced in itself, it received new layers, or an extension in a reversed position. Fig. 201. Fig. 203. Eutile occurs in crystals like fig. 173, but with a bend at both extremities, instead of one only. Here the middle portion of the crystal is supposed to have attained a length of half an inch, and then it became geniculated simultaneously at both extremities ; indeed, in this mineral such geniculations are frequently repeated until the ends are bent into one another, and produce short hexa gonal prisms with central depressions or even vacuities. The re peated twinning which produces striation, as in calcite and the felspars, and the peculiar rippled structure of amethyst, are ascribed to a similar operation, acting in an oscillatory manner. Certain intersecting twins in the cubic system may be explained simply through excessive or undue accretion of molecules along cer tain lines. At page 351 it was shown how the three-faced octahe dron (fig. 39) was formed through an accretion of molecules upon the faces of the octahedron along axes joining the centres of its faces (those which connect the solid angles of the cube). It was also shown that when through this accretion two faces of the triakis- octahedron (fig. 199), adjacent along the edge of the octahedron, rose into one plane the rhombic dodecahedron resulted. If now accretion still goes on along the same axes, so that the trihedral pyramid rises above the level of the dodecahedral planes, fig. 200 results. This is the twin of the three-faced tetrahedron (fig. 201). Fig. 204. Fig. 206. Fig. 208. If the accretion is still along the same axes until the lateral edges of the adjacent pyramids fall into the same line, fig. 202 results; and this is the twin of the simple tetrahedron (fig. 203). Here accretion upon the faces of a complex holohedral form has produced a twin of a simple hemihedral form. Again, starting from the six-faced octahedron (fig. 204), there is produced by the same process first fig. 205, the twin of the six- faced tetrahedron (fig. 206), and ultimately fig. 207, the twin of the three-faced tetrahedron (fig. 208). 2. Departure from Regularity on Account of Undue Accre tion in certain Directions. Distortion of Crystals. The Distor- laws of crystallization should produce crystal forms of tions. perfect symmetry ; these laws, however, are subject, not only to the influence of other laws, but also frequently to disturbing influences which are subject to no law. Abso lute symmetry, therefore, is very uncommon, crystals being generally so distorted and disguised through interference during their formation that either familiarity on the one hand or skill on the other is necessary for their recognition. As the magnitude of the angles may vary somewhat, even this guide may sometimes perplex. Hence it is necessary to be familiar with such departures from symmetry ; and some of the more common are here noticed. In the cubic system a cube (fig. 26), lengthened or shortened Of cube, along one axis, becomes a right square prism (fig. 209), and if elongated in the direction of two axes is changed to a rectangular prism (fig. 7). Cubes of pyrites, galena, fluor-spar, &c., are generally thus distorted. It is very unusual to find a cubic crystal that is a true symmetrical cube. In some species the cube or octa
hedron (or other monometric form) is lengthened into a capillary