POLARITY 313 Gustav Rose and by Hankel) is associated with pyroelec- tricity (see MINERALOGY, vol. xvi. p. 376). It is worthy of FIG. 1. Tourmaline. FIG. 2. Electric Calamine. note that the crystalline polarity and the physical (electric) polarity occurring in the same substances are both of the kind not inverted by reflexion in a mirror. As an instance of the same kind of crystalline polarity of a somewhat more complicated character, also associated with pyroelectricity, we may take boracite. The crystals of this mineral exhibit combinations of the cube, the rhombic dodecahedron, and the tetrahedron, as __, -^ shown in fig. 3. If four lines are drawn corresponding to the four dia gonals of the cube, it will be observed that at the two ends of each of these axes the crystal is differently developed. (In the figure one of these axes is in dicated by the dotted line.) These axes, therefore, resemble the single axis in tourmaline and electric calamine, and are also axes of pyroelectricity, the end at which the tetrahedral face is situated being the antilogous pole. 1 Scheelite, apatite, ilmenite, and fergusonite are examples FIG. 3. Boracite. FIG. 4. Ilmenite. FIG. 5. Apatite. of crystalline polarity of the second kind. Figs. 4, 5, and G are representations of forms of ilmenite, apatite, and fergusonite. Crystalline polarity of both kinds no doubt depends on the arrangement of the molecules and on their structure; it manifests itself by the occurrence of hemihedral or hemimorphic forms. A crystal may have a polar structure although these external marks of pol arity are absent, just as the faces parallel to planes of cleavage do not appear on every crystal. Another kind of contrast between the two complementary hemihedral forms of the same substance may be mentioned here. 1 Upon some crystals of boracite the faces of both tetrahedra occur. They can, however, be easily distinguished from one another. The faces of the tetrahedron represented in the figure are smooth and shin ing, while those of the opposite tetrahedron are rough and usually much smaller. It has been suggested that boracite is only apparently regular, and that each crystal is really a group of eight pyramids with their apices in the centre of the group. For a full discussion of the relation between pyroelectricity and crystalline form the reader is referred to a series of papers by Professor Hankel in Trans. R. Saxon Soc. of Sciences, 1857-79. FIG. G. Fergusonite. Marbach observed that different specimens of iron pyrites (and also of cobalt glance) have very different thermoelectric characters, differing indeed from one another more than bismuth and antimony. Gustav Rose showed that these thermoelectrically opposite kinds are also crystallographically opposite. There is indeed no geometrical difference between two opposite hemihedral forms in the regular system, but Rose detected a differ ence in the lustre and striation of the faces of the two kinds, and by examining the rare cases in which the two opposite pentagonal dodecahedra or tetragonal icositetrahedra occur on the same crystal proved that the one surface character belongs to the one, the other surface character to the other of the two complementary hemihedra. Enantiomorphism.- A figure having polarity of the first kind gives a mirror image resembling itself in form and in position ; a figure having polarity of the second kind gives a mirror image resembling itself in form but not in position the poles being inverted. A figure the axis of which has both kinds of polarity will therefore give a mirror image not superposable to the figure itself, because the polarity of the second kind is reversed while that of the first kind remains unchanged. The figure and its mirror image are enantiomorph, as well as polar. We can construct a figure which is enantiomorph to its mirror image but not polar. Imagine a muff so made that in one half the fur lies the one way, and the opposite way in the other half (fig. 7, where the arrow-heads indicate the lie of the fur). In which ever way we put our hands into this muff one end will be wrong ; the muff in the figure has, in fact, two right- hand ends. It has therefore no polarity ; the two ends are exactly alike. But there are two ways in which such a non-polar muff could be made with two right-hand ends as in the figure, or with two left-hand ends, and these two forms are enantiomorph. A helix or screw has similar properties (compare fig. 8 with fig. 7) ; if uniform it is non-polar, but is either right- or left-handed. Hence the property which each of two enantiomorph bodies pos sesses has been called by Sir William Thomson "helicoidal asymmetry." As we have crystals exhibiting polarity of both kinds, so we have also enantiomorph crystals, indeed the word enantiomorph was first used by Naumann to express the relation between such crystals. The crystallographic theory of enantiomorph crystals has been very fully worked out. We may divide them into two groups (1) those in which the helicoidal asymmetry depends on the presence of tetartohedral forms of the regular or of the hexagonal system, and (2) those in which it depends on the presence of hemihedral forms of the rhombic system or hemimorphic forms of the monoclinic system. In the first group the asymmetry seems to be produced by the manner in which the molecules, themselves sym metrical, are arranged in the crystal. In the second group the molecules themselves appear to have helicoidal asym metry. This is shown by the action of these substances on polarized light. We shall take examples from each group. If we allow a solution of sodium chlorate to crystallize we find that the crystals, which belong to the regular system, are of two kinds enantiomorph to each other. These are represented in fig. 9. The enantio- morphism dependvS on the combination of the tetrahedron XIX. 40 Fig. 7.
Fig. 8.