hexagonal prisms, and can build up a quartz crystal by the fortuitous concourse of atoms. I should like also to have suggested and explained the possibility that a right-handed crystalline molecule thus formed may, in natural circumstances of high temperature, or even of great pressure, become changed into a left-handed crystal, or _vice-versa_. My watch, however, warns me that I must not enter on this subject. [Illustration: FIG. 19.] § 52. Coming back to mere molecular tactics of crystals, remark that our assemblage of rounded, thoroughly scalene, tetrahedrons, shown in the stereoscopic picture (§ 36, Fig. 13 above), essentially has chirality because each constituent tetrahedron, if wholly scalene, has chirality[24]. I should like to have explained to you how a single or double homogeneous assemblage of points has essentially no chirality, and how three assemblages of single points, or a single assemblage of triplets of points, can have chirality, though a single triplet of points cannot have chirality. I should like indeed to have brought somewhat thoroughly before you the geometrical theory of chirality; and in illustration to have explained the conditions under which four points, or two lines, or a line and two points, or a combination of point, line and plane, can have chirality: and how a homogeneous assemblage of non-chiral objects can have chirality; but in pity I forbear, and I thank you for the extreme patience with which you have listened to me. FOOTNOTES: [1] See foot-note on § 22 below. [2] The holes in the cylinders are bored obliquely, as shown in Fig. 4, which causes them to remain at any desired position on the cord and allows them to be freed to move up and down by slackening the cord for a moment. [3] ‘On the Homogeneous Division of Space,’ by Lord Kelvin, _Royal Society Proceedings_, vol. lv, Jan. 18, 1894. [4] Similar curves are said to be parallel when the tangents to them at corresponding points are parallel. [5] See foot-note to § 12 above. [6] ‘On the Division of Space with Minimum Partitional Area,’ _Philosophical Magazine_, vol. xxiv, 1887, p. 502, and _Acta Mathematica_ of the same year. [7] A. Levy, _Edinburgh Philosophical Journal_, April, 1822; Whewell, _Phil. Trans. Royal Society_, 1825; Miller, _Treatise on Crystallography_. [8] I call any geometrical figure, or group of points, _chiral_, and say that it has chirality, if its image in a plane mirror, ideally realized, cannot be brought to coincide with itself. Two equal and similar right hands are homochirally similar. Equal and similar right and left hands are heterochirally similar or ‘allochirally’ similar (but heterochirally is better). These are also called ‘enantiomorphs,’ after a usage introduced, I believe, by German writers. Any chiral object and its image in a plane mirror are heterochirally similar. [9] _Philosophical Magazine_, vol. xx, 1885, second half year, p. 469, and _British Association Report_, 1885, Aberdeen, p. 896.