The Brazilian twinning law of quartz, according to which the plane of twinning is parallel to a pair of faces of the second order hexagonal prism {11̄20}, appears capable of explaining all these varieties of right and left-handed twins, the interpenetration of the intimate kind shown in Fig. 85 (page 215) usually resulting in sectorial portions of space being occupied by each kind, the surfaces of junction of oppositely optically active parts being, however, very varied in their distribution and character. Where they happen to be more or less horizontal, a plate cut perpendicularly to the axis to include both kinds would show Airy’s spirals in convergent polarised light, as may readily be demonstrated by such a plate, one of several, in the author’s collection. Where they are oblique, a plate cut at right angles to the axis would, as we have seen experimentally, afford the black, white and spectral ribbon bands in parallel polarised light. Where, however, the mode of interpenetration is still more intimate, we have the rapidly alternating laminæ of the two varieties, right and left-handed, building up the beautiful structure of amethyst in thin layers. A section-plate of such an intimate blending of the two varieties, cut as usual perpendicular to the axis in order that any phenomena of optical activity shall be exhibited at the maximum, affords no indication whatever of optical rotation, the two varieties simply neutralising each other’s effects, and the plate behaves as an ordinary uniaxial crystal, affording in convergent polarised light a black cross like calcite, complete to the centre. In parallel polarised light it shows of course the laminated structure, but the tendency to remain dark under crossed Nicols is shown by the fact that the tints exhibited by the laminations are slates, greys, and even black, when the Nicols are crossed, the delightful other colours only making their appearance when the analysing Nicol is rotated. Thus the simple law of Brazilian twinning is quite capable of explaining the whole of the phenomena exhibited by composite crystals of the two varieties of quartz, and such an explanation is the one accepted by von Groth, in the excellent description of quartz in the last edition of his _Physikalische Krystallographie_. [Illustration: FIG. 96.—Plan of Amethyst Crystal. ]