MINERALOGY 363 repeated, are linear, or, with diminishing size in the individual, acicular. Fig. 139. Fig. 140. Duplex Twins and Ifemitropes. Though closely related, formed crystals. un der the operation of very similar laws, and to a certain extent passing into one another, these are not the same. In the first case a plurality of individuals must be present ; in the second this is not necessary. In fig. 140 two individuals evidently intersect one another; in figs. 141, 142 one individual may be supposed to have been bisected in a certain direction, and the two halves reattached, but in a position differing in some definite manner from their relative position before the separation. Fi Fig. 142. Varieties There are four varieties of true twins: those of apposition, of of twins, intersection, of partial or completed interpenetration, and of in corporation. The first is exemplified by spinel, as in fig. 143 ; the second by Fig. 145. Fig. 146. staurolite, as in fig. 144; the third by calcite, as in fig. 146, and by blende, as in fig. 145, where the two individuals of iig. 143 may be supposed to have been forced vertically into one another ; and the last by quartz, as in fig. 147. The following are the laws of union of twins. 1. The face of Laws of union of twins, termed the "face of composition," must be either twinning, a plane which does occur in the mineral twinned, or which can occur in accordance with the fifth law of symmetry. A face of Fig. 147. Fig. 148. union in twins is also a face of union in hemitropes of the same mineral. 2. From the above it results that the axes of the united crystals are either parallel (fig. 148) or inclined (fig. 149). The former generally occur among hemihedric forms ; and the two crystals are combined in the exact position in which they would be derived from or would reproduce the primary holohedral form. The class with oblique axes occur both in holohedric and in hemihedric forms; and the two individuals are then placed in perfect symmetry, in accordance with law 1. Twins are generally recognized by having re-entering angles (figs. 150, 151); but sometimes the crossed faces coincide in one plane, when the combination appears as a single individual (figs. 152, 153). The line of union may then be im perceptible, or it may be disclosed by the intersection of two sets of striae (figs. 154, 155), or by some physical diversity in the char acters of the two faces. The formation of twin crystals may be again, or many times, repeated, forming groups of three, four, twenty-four, or more. When the faces of union are parallel to each other, the crystals form Fig. 149. Fig. 150. Fig. 151. rows of indeterminate extent. When they are not parallel, they may return into each other in circles, as in rutile ; or form bouquet or rosette groups, as in chrysoberyl (fig. 156) ; or stellate groups, as in calcite (fig. 157) and in cerussite (figs. 158, 159). Fig. 152. Fig. 153. When the crystals are of different size, greater complexity results; but a number of minute crystals are frequently arranged upon a larger at those points where the angles of a single large crystal would protrude. Occasionally a simple form is twinned with a
more complex one, as in chabasite (fig. 160).