1 86 



NATURE 



\_Dec. 20, I < 



PROBABLE NATURE OF THE INTERNAL 

 SYMMETRY OF CRYSTALS 

 COME studies pursued by the writer as to the nature of mole- 

 cules have led him to believe that in the atom-grou]iings 

 which modern chemistry reveals to us the several atoms occupy 

 distinct portions of space and do not lose their individuality. 

 The object of the present paper is to show how far this con- 

 clusion is in harmony with, and indeed to some extent explains, 

 the symmetrical forms of crystals, and the argument may there- 

 fore in some sort be considered an extension of the argument for 

 a condition of internal symmetry derived from the phenomena of 

 cleavage. 



If we are to suppose that crystals are built up of minute 

 masses of different elements symmetrically disposed, it is natural 

 t ) inquire in the first place uhat very symmetrical arrangements 

 of points or particles in space are possible. 



It would appear that there are but Jive, which will now be 

 described. 



If a number of equal cubes are built into a continuous mass 

 (Fig. i), a system of points occupying the centres and angles of 

 these cubes will furnish an example of one of these symmetrical 

 arrangements. In this system each point is equidistant from 

 the eight nearest points, and if a number of equal-sized spheres 

 be stacked on a base layer arranged so that the sphere centres 

 when joined form a system of equal squares, a side of w hich 

 bears to the diameter of the spheres the ratio 2 : ^^,'3 (see 

 plan a), the sphere centres in such a stack will also furnish an 

 example of this first kind of symmetry (Fig. 2). 



A second kind of synmietry will be presented if one-half the 

 pomts in the first kind be removed so that we have only those at 

 the cube centres, or only those at the cube angles. In this 

 system each point is equidistant from the six nearest points, and 

 if equal-sized spheres be stacked upon a base layer, arranged so 

 that the sphere centres when joined form a system of equilateral 

 triangles, a side of which bears to the diameter of the spheres the 

 ratio v'2 : I (see plan l>) ; and if the layers be so placed that 

 the sphere centres of the fourth layer are over those of the first, 

 those of the fifth over those of the second, and so on, the sphere 

 centres in such a stack will also furnish an example of this second 

 Ivind of symmetry (Fyr. 3). 



A third kind of symmetry will be presented if again one-half 

 the points be removed, i.e. so that when cubes of two colours 

 arranged in such a way that each cube is surrounded by cubes of 

 the other colour are used (see Fig. i), we have only the points 

 at the centres of the cubes of one colour. In this system each 

 |ioint is equidistant from the twelve nearest points, and if equal- 

 sized spheres be stacked upon a base layer in which the spheres 

 are in contact, and whether they form a square pattern (see 

 plan (-), or a triangular one (see plan </)— prrvided that, if tri- 

 angular-pattern layers be employed, the sphere centres in the 

 fourth layer must be over those in the first, those in the fifth 

 over those in the second, and so on— the sphere centres (the 

 arrangement being tlie same in either case) will furnish a second 

 example of the third kind of symmetry (Figs. 4 and 4a, the 

 latter showing a stack with the angle removed to display the 

 triangular arrangement). 



A fourth kind of symmetry, which resembles the third in that 

 each point is equidistant from the twelve nearest points, but 

 wh:ch is of a widely different character from the three former 

 kind,, is depicted if layers of spheres in contact arranged in the 

 triangular pattern (plan d) are so placed that the sphere centres 

 of the third layer are over those of the first, those uf the fourth 

 over those of the second, and so on. The symmetry produced 

 IS hexagonal in structure and uniaxal (Figs. 5 and 5a). 



A fifth kind of symmetry, and this completes the number of 

 very symmetrical arrangements possible, resembles the second 

 kind of symmetry in that each point is equidistant from the six 

 nearest points, and bears the same relation to the fourth kind 

 (Fig. 5) as the second (Fig. 3) bears to the third (Fig. 4) ; that 

 IS to say, it may be regarded as produced by the insertion of 

 additional points in positions midway between points arranged 

 in the fourth kind of symmetry. It is depicted if triangularly 

 constituted layers identical with those depicting the second kind 

 . f symmetry (plan /-) are deposited in the following way (Fig 6): 

 -—First place three layers as though to produce the second kind 

 of symmetry; then place the fourth with its sphere centres over 

 those of the second layer ; then the fifth so that the third, fourth, 

 and fifth, like the first, second, and third, are in the second kind 

 of symmetry ; then the sixth with its sphere centres over those 



of the fourth and second ; and then the seventh, so that the fifth, 

 sixth, and seventh layers are also in the second kind of sym- 

 metry ; and so on. The symmetry produced is, like the last, 

 hexagonal in structure and uniaxal. 



The writer believes that every one of the various symmetrical 

 forms presented by crystals can be shown to be consistent with 

 the subsistence of an arrangement of the atoms of the crystallising 

 compound in one or other of these five kinds of symmetry at the 



Plan a. 



y V^ V_y V_7 



oooc 



"^ )00 



oooc 



■\ n\ r\ r\ 



Fig. 4. PLin c. 



lime 'f/wn cryslallisation begins ; and proposes to show that a 

 relation subsists between the atomic composition of very many 

 bodies and their crystal forms in harmony with this conclusion, 



To proceed then to facts, we notice first that, as a rule, com- 

 pounds consisting of an equal number of atoms of two kind» 

 crystallise in cubes. 



The following may be mentioned : — 

 Potassic chloride, KCl. 



Potassic bromide, KBr (sometimes elongated into piism.s, 

 or extended into planes). 



