1 64 



NATURE 



[March 30, km r 



by Miers and Ostwald as the " inetubtable " conditiun, 

 usually yields well-formed individual cryxtalii suitable for 

 study and measurement, whereas crystallisations from more 

 stronjjly supersaturated solutions, those in the " labile " 

 condition, invariably take the character of skeletal, tree- 

 like, or acicular forms, very beautiful, but unsuitable for 

 crystal measurement. The extraordinary fact was then 

 referred to that germ-crystals of all common crystalline 

 substances are constantly floatinf* about in the air, and 

 that by falling into metastable solutions of their own or 

 similarly constituted (isomorphous) substances are able to 

 set them crystallising. Indeed, metastable solutions are 

 entirely dependent on such intrusions of germ-crystals, for 

 labile solutions are alone capable of spontaneous crystallisa- 

 tion. ^ 



The great diversity of habit of the crystals of the same 

 substance was next discussed, and a striking instance given 

 in the three common forms of calcite, carbonate of lime, 

 namely, the rhombs of Iceland spar, the scalenohedral 

 (pyramidal) dog-tooth spar, and the long prismatic form 

 of calcspar terminated by rhombohedra. Totally dissimilar 

 specimens of all three were exhibited, and others still more 

 remarkable, from the same mine, were projected on the 

 screen, so unlike as to be apparently the crystals of quite 

 different substances. Yet the faces present were geo- 

 metrically the same, but developed to different extents, in 

 all three, and inclined at angles of precisely the same 

 value. It was shown how this diversity of habit had 

 delayed the discovery of the laws of crystallography, and 

 the historic sequence of events, from the seventeenth 

 century onwards, was briefly outlined, until in 1784 the 

 main laws were enunciated by the Abbe Haiiy, especially 

 the great law of the constancy of the angles of the crystals 

 of the same substance. 



The natural classification of crystals into seven styles of 

 architecture or crystal systems, according to the geo- 

 metrical disposition of their faces, was then discussed, and 

 shown to depend on the presence of a greater or less 

 number of planes and axes of symmetry, this external 

 configuration being due to the regular homogeneous 

 character of the internal structure. It was shown that 

 this latter is of the nature of a space-lattice, each unit cell 

 of which is occupied by a chemical molecule. The 

 chemical molecules are thus the regularly arranged bricks 

 of the crystal edifice. Some remarkable examples of 

 crystals of the various seven systems were exhibited, both 

 in the form of natural mineral crystals of large size, and 

 of artificial crystals, some of considerable size and others 

 grown under the microscope, photographs of many such 

 crystals taken in the act of growth being exhibited on the 

 screen. 



The grouping of crystal faces in " forms " or sets having 

 an equal value with respect to the symmetry, and the mode 

 of distinguishing the faces by their' " indices," symbols of 

 three or four figures (inversely proportional to the lengths 

 of the axes cut off by the face) enclosed within brackets, 

 was explained. The simple or " rational " nature of 

 these indices, the low numbers, i, 2, 3, and 4 vastly pre- 

 dominating, and being often the only numbers involved, 

 was emphasised, thus demonstrating the important law of 

 rational indices. 



It was shown in the second lecture that these external 

 regularities are entirely the consequence of the internal 

 homogeneity and structural symmetry of the molecular 

 arrangement in one or other of the fourteen space-lattices 

 referred to in the first lecture. The remarkable work of 

 Sohncke, Schonflies, von Fedorow, and Barlow was then 

 discussed, whose joint labours had indicated 230 types of 

 hoinogeneous structure, represented by point-sy sterns, and 

 which include 165 involving the property of mirror-image 

 symmetry and 65 Sohnckian assemblages of points which 

 do not, but clusters of which latter, if each cluster be re- 

 presented by a single point, give us the 14 space-lattices. 

 The interesting fact was brought out that the space-lattice 

 represents, in all the simpler cases, the arrangement of the 

 molecules, while the detailed point-system represents the 

 plan of distribution of the atoms. 



It was also shown how recent work had confirmed the 

 law of Haiiy as to the constancy and specific nature of the 

 crystal angles of any one substance, and that in the cases 

 of the isomorphous series of Mitscherlich, composed of 

 analogously constituted compounds, which were at first 

 NO. 2 161, VOL. 86] 



!>upposed tu be identical in their cryfttal morphok>gy, ti. 

 crystalit of the different men»ber« of the -•;•■- -1.... .• 

 but real differences in their angles, 

 differences in their other prop<,*rties. .Mo: 

 eiices conform to a definite law, for they follow i 

 of progression of the atomic weights of the inif-rch 

 chemical elements which give rise to the - 

 dimensions of the structural-unit molecular 

 space-lattice also conform to this law. 



'ihe optical properties of crystals may, in gen 

 represented by an ellipsoid, the three rectangular 

 which are proportional to the three different r 

 indices afforded along those directions^'and the po- 

 which varies with the symmetry. Crystals of the rhombk, 

 monoclinic, and triclinic systems have such a triaxiai 

 ellipsoid, but it becomes an ellipsoid of revolution for 

 crystals of the tetragonal, hexagonal, and trigonal systems, 

 and a sphere for a cubic crystal. This property thus at 

 once enables us to discriminate between these three groups 

 of crystal systems, which are characterised, respectively, 

 by three indices, two indices, and one index of refraction. 

 The directions of the three axes of the ellipsoid are identical 

 with the crystallographic ones in a rhombic crystal, but 

 only one axis is coincident with a crystal-axis in a mono- 

 clinic crystal, and no axes are coincident in a trii linii 

 crystal. 



Such an ellipsoid with three unequal rectangul.> 

 must possess two circular sections symmetrically situated, 

 and directions perpendicular to these sections are the well- 

 known optic axes of " biaxial " crystals, more or less 

 comparable to the single axis of no double refraction of 

 " uniaxial " crystals, which are characterised by an 

 ellipsoid of revolution. It is round these two optic axial 

 directions that the well-known spectrum-coloured rings 

 and dark hyperbolic " brushes " are visible in convergent 

 polarised light, thus forming the biaxial analogue of the 

 circular spectrum-rings and black rectangular cross of a 

 uniaxial crystal such as calcite. Many of these phi?nomena 

 were projected on the screen with the projection polari- 

 scope, including the Mitscherlich experiment showing the 

 crossing of the optic axial plane of gypsum as the crystal 

 becomes warmed by the heat rays accompanying the beam 

 of convergent light. 



The concluding lecture opened with a description of the 

 remarkable " liquid crystals " discovered by Lehmann, 

 substances of complicated and elongated chain-like chemical 

 constitution, the molecules of which set themselves, by 

 virtue of their inherent directive force, in shapes resembling 

 crystals, which display double refraction and rotate th> 

 plane of polarisation. Mobile crystals of para-a2ox>- 

 anisol in the form of rotating drops, of the ethyl ester of 

 para-azoxy-benzoic acid, and of para-azoxy-phenetol in the 

 shape of rounded crystals showing interference bands, were 

 exhibited on the screen with the Zeiss projection micro- 

 scope, and also spherulites of cholestery! acetate, beautiful 

 star-like apparitions breaking out all over the field, exhibit- 

 ing colours and a dark cross in polarised light. The mobile 

 crystals were instantly deformed on touching the cover- 

 glass, but as instantly recovered their shape on removing 

 the pressure. 



The conclusion arrived at from experiments of this 

 nature was that the molecular directive force of crv'stal- 

 Jisation, temporarily discarded as unnecessary by the geo- 

 metricians for the building up of homogeneous structures, 

 is reinstated as a fact which cannot be ignored. There 

 can be no doubt that in these mobile crystals the chemical 

 molecules are constantly arranging themselves in space- 

 lattices, although the substance may be as mobile as water. 

 The fundamental importance of the space-lattice, its 

 formation by the chemical molecules as its structural onits, 

 and its influence in determining the crystal system, are 

 thus again strongly emphasised. 



It was proved by various optical devices that crystals of 

 quartz exhibiting characteristic little facets on certain 

 right-hand solid angles invariably rotate the plane of 

 polarisation to the right, while other crystals on which 

 these faces are only developed on the left-hand solid angles 

 rotate the polarised rays to the left. It was further proved 

 that this was due to an oppositely right-handed and left- 

 handed helical arrangement of the atoms composing the 

 molecules in the two cases, and that there are equal 

 chances in nature for the formation of either. The re- 



