Dec. 20, 1883] 



NA TURE 



187 



Potassic iodide, KI, 

 Sodic chloride, NaCl. 

 Sodic bromide, NaBr. 



Sodic iodide, Nal (anhydrous above 40° C.)- 

 Ca;si_ chloride, CS.Cl. 

 Plumbic sulphide, PbS. 

 Argentic chloride, AgCl. 

 When we have named lithic chloride, crystallising above 15° 



Pi-n/, 



in octahedra, we have mentioned most of the compounds con- 

 sisting of two elements in equal proportions known tu us in a 

 crys-.alline state. 



Mercuric sulphide, Hg . S, which crystallises in six-sided 

 prisms, is an apparent exception, but if we were guided 

 by the gaseous volume of mercury in determining its 

 atomic weight, we should have to write the compound 

 HgoS. 



Other apparent exceptions are : — 



Zincic oxide, ZnO, crystallising in six-sided prisms. 

 Cadmium sulphide, CdS ; and 



Glucina, GO, crystallising in minute six-sided prismatic 

 crystals. 



Now three out of our five possible kinds of internal symmetry 

 have three axes or directions at right angles to each other, in 

 reference to which they are disposed in the same symmetrical 

 manner, and two kinds, the first and second, admit of a very 

 symmetrical arrangement of two kinds of particles in equal 

 numbers (see Figs. 2 and 3). Snrely this coincidence is very 

 significant, and at lea t suggests the probability that when a 

 compound consists of two kinds of chemical atoms in equal num- 

 bers, these atoms are symmetrically placed according to either 

 the first or the second kind of internal symmetry. 



We ol)serve next that the third and fourth kinds of symmetry 

 (Figs. 4 and 5) readily lend themselves to the symmetrical 

 arrangement of particles of two kinds present in the proportion 

 I : 2. For, as already pointed out, these two kinds of sym- 

 metry may either of them be produced by piling up layers 

 of spheres placed triangularly in contact (see plan d), and 

 spheres of two colours present in the proportion of 2 : i can 

 be arranged in a most symmetrical manner in layers of this kind 

 (see plan e). 



As to what varieties of position of bi-coloured layers of this 

 kind with respect to one another are possible, consistent with 

 great symmetry, we have concluded that, apart from the ques- 

 tion of arrangement of colour, there are but two, viz. the third 

 and fourth kinds of symmetry (Figs. 4 and 5) ; but taking colour 

 into account a greater variety is possible. Thus a little con- 

 sideration shows us that, while all the possible ways of depositing 

 the second layer produce a practically identical result, a choice 

 of six different equally symmetrical results is presented in de- 

 positing the third layer, in all of which the spheres of the less 

 numerous colour form files of sphere, in contact running through 

 the layers, and three of which belong to the third kind of sym- 

 metry and three to the fourth. 



To specify these : We may have the less numerous spheres of 

 the third layer placed with respect to those in the second and 

 first :— 



(I) So that the three spheres of each of the files just above 

 alluded to range in line, the lines joining their centres forming 

 a series of parallel straight lines crossing the planes of the layers 

 obliquely. This arrangement belongs to the third kind of 

 symmetry. 



(2 and 3) So that the centres of these three spheres, when 

 joined, form a slightly obtuse angle ; a different result being 

 produced as the angle is made to the right or to the left. This 

 pair of arrangements belongs also to the third kind of symmetry. 



(4) So that the less numerous spheres in the third layer are 

 vertically over those in the first. This a'rangement belongs to 

 the fourth kind of symmetry. 



(5 and 6) So that, as in (2) and (3), the tri,jlets of spheres 

 form a system of equal obtuse angles, but the angles now being 

 very obtuse. There are here, as in (2) and (3), aright-handed and 

 a left-handed arrangement. These belong to the fourth kind of 

 symmetry. 



The deposition of the third layer, by the necessities of sym- 

 metry, determines the deposition of succeeding layers, and it 

 follows therefore from the above that six different equally sym- 

 metrical arrangements of spheres of two colours present in the 

 proportion 2 : I are possible in the third and fourth kinds of 

 symmetry. 



As to (l) the parallel files of the less numerous spheres cross- 

 ing the first three layers will extend through subsequent layers. 



As to (2) and (3) every three continuous layers will display 

 the less numerous sphere centres placed to form the same 

 angles as are presented by the triplets in the first three layers, 

 and consequently these sphere centres lie on spirals which are 

 right-handed or left-handed as the case may be ; the less numer- 

 ous spheres in the fourth layer being vertically over those in the 

 first, those in the fifth over those in the second, and so on. 



As to (4) the less numerous spheres in the fourth layer must 

 lie vertically over those in the second, those in the fifth over 

 those in the third, and so on; and thus the files of spheres in 

 contact running through successive Jayers form a series of similar 

 zigzags. 



As to (5) and (6) the sphere centres, as in (2) and (3), lie 

 either on right-handed or on left-handed spir.als ; in this case 

 the less numerous spheres in the seventh layer being vertically 



