262 



NATURE 



[December 21, 191 1 



cells of which is the habitat of a chemical molecule of the 

 substance of which the crystal is composed, and of which 

 it is the most highly organised solid form. It was shown 

 by Frankenheim and Bravais that there arc fourteen such 

 space-lattices possible, all of which exhibit the full sym- 

 metry of one or other of the seven crystal systems, the 

 cubic, trigonal, tetragonal, hexagonal, rhombic, monoclinic. 



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Fig. I. — Triclinic St ace-latlice. 



or triclinic. As a typical example of a space-lattice, and 

 the one of most general form, the triclinic space-lattice is 

 shown in Fig. i. 



But the chemical molecules, the arrangement of which 

 thus determines the crystal system, are not the ultimate 

 units, being composed of elementary atoms, and it is the 

 arrangement of these latter, the ultimate structural units, 

 which determines the class of the system. 



Quartz crystallises in the trigonal system of symmetry. 

 It does not develop, however, the full holohedral trigonal 

 symmetry, but that of the trapezohedral class of the 

 system, no plane of symmetry being present, and the three 

 digonal axes of symmetry occupying positions in the hori- 

 zontal plane midway between those of the holohedral class. 



Now in the most general case six faces are required to 

 be present by the symmetry elements in operation, when 

 one face is given as present, and they make up a double 



Fig. a.— Right Trigonal 

 Trapezohedron. 



Ftg. 3.— Left TriRonal 

 Trapezohedron. 



trigonal pyramid, of which the lower half is rotated some- 

 what with respect to the upper, screw-wise, the solid thus 

 produced being known as a trigonal trapezohedron. 



In actual fact two such trigonal trapezohedra, which are 

 the mirror-images of each other, are possible, and the two 

 solids are quite distinct, for no amount of rotation will 

 brmg either to resemble the other. That corresponding to 

 Fig. 2 is called the right trigonal trapezohedron, and that 

 NO. 2199, VOL. 88] 



represented by Fig. 3 the left variety. Thii fundan 

 fact respecting the general form of this class of tri^ 

 symmetry affords the explanation of the two varicn'-^ 

 right- and left-handed, of quartz, which mineral sliuw 

 characteristic development, in the well-known little x faces* 

 of the two trapezohedra. 



Two characteristic crystals of quartz, a ri. " ' A 



a left-handed one, are shown in Figs. 4 ;i; fi 



the small faces x are those of the rif!'^' ! 



trapezohedra respectively. Also, the 1 

 5 are those of another pair of mirror-i:: 



forms of the trapezohedral class of trigonal svnjineiry, the 

 right and left trigonal bipyramids. The other farf-s shown 

 on Figs. 4 and 5 are those of the hexagon 

 form common to both the hexagonal and ti 

 and also common to both varieties of ii.-i.ii> >-i 

 trigonal trapezohedral class ; also those of the two comple- 

 mentary rhombohedra r and r', which togeth<r make u 

 what appears to be the hexagonal pyramid terminating eai 

 end of a full} -developed quartz crystal. Alternate f.ires 

 the pyramid belong, however, to different rh'" 

 three to r and three to r' ; and they are often ch;i: 

 ally different, either in amount of development or in pi.ii>r. 

 the faces of the rhombohedron r being much more brilliant 

 than those of r'. Moreover, the quartz crystals from a 

 particular locality in Ireland show one rhombohedron only, 

 without a trace of the other. 



It will be observed, further, that the little s and x faces 

 occur replacing right solid angles on a right-handed crystal, 

 and left solid angles on a left-handed crystal. Also, if « 

 faces be absent, a good little s face is often present, and 



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Fig. 4.— Right-handed Quart*. Fic. 5.— Left-handed Quartz. 



it is usually marked by striae parallel to the edge sr, whi< 

 enable the location of the face, and its nature, to 

 recognised. 



We are next attracted by the further problem of 

 internal structure, which is the prime cause of this oui 

 ward development. The evidence afforded by cleavage 

 very emphatic, in spite of the fact that quartz cleaves on^ 

 with the greatest difficulty. Indeed, this difficulty of pro 

 voking cleavage in quartz enhances wonderfully the impor 

 ance and use of the mineral, both for scientific and indv 

 trial purposes, for it enables lenses, prisms, and plates 

 this clear, transparent mineral to be cut, ground, a 

 polished with the greatest ease, without risk of flaw. B«i 

 when a quartz crystal is heated, and then suddenly coole 

 by plunging it into cold water, it breaks up into rhoml 

 hedra closely resembling cubes, the angle of which 

 85° 46', that of the primary rhombohedron r of Figs, 

 and 5. Now it is interesting, also, that simple appare 

 cubes, really these rhombohedra, of quartz are occasions 

 discovered, quite a number having been found in the neij 

 bourhood of Bristol. 



These facts not only confirm the trigonal, as distinguish^ 

 from possible hexagonal, symmetry of quartz, but 

 indicate that the space-lattice structure present is that 

 the rhombohedron, the elementary cell of which is re 

 sented in Fig. 6. 



Thus we conclude that if each molecule SiOj were re 

 sented by a point, the points would be arranged in th* 

 form of a rhombohedral space-lattice having the angle of 

 the rhombohedron of quartz, 85° 46'. 



If we take, next, a hexagonal section of a prism of 



