Moleadar Constitution of Crystals. 1 13 



For if any two of these spheres become united by two of their 

 poles, they will evidently, from the mutual action of all the poles, 

 assume such a position as shown in fig. 8 ; and a third molecule 

 would be attracted in a similar position, while a fourth would 

 attach itself to the three poles. A, B, C, by its three poles a, b, c 

 (fig. 9). We have now a tetrahedron formed, and by precisely 

 analogous reasoning we can continue the process of formation. 

 It will be observed that a fifth molecule, if attached, will be in 

 the same plane with three others, and will only touch two ; a 

 result to the necessity of which 1 have already adverted when 

 speaking of Dr. \Yollaston^s hypothesis. 



If a tetrahedron be thus formed, and if a row of molecules 

 along each edge lose their polarities in each consecutive layer, 

 each additional layer of particles will be deficient by a row, and 

 faces will appear replacing the edge of the crystal tangentially ; 

 such faces, it is well known, belong to the cube. We have now 

 a compound foi-m consisting of a cube and tetrahedron. [Vide 

 Plate 11. figs. 10 and 11.) 



If each layer be deficient by one molecule at each corner of 

 the faces, planes will appear truncating the corners of the tetra- 

 hedron, which will of course belong to the octahedron. In like 

 manner, if two or more rows be omitted, the hemiikositetrahedron 

 will be formed. And if the same occurrences take place after 

 an octahedron has been formed, the holohedral forms of these 

 solids will be obtained. 



It is well known that crystals in the first system are liable 

 to three distinct cleavages, which would evidently indicate 

 three distinct formations j two we have already investigated, 

 namely the cubical and tetrahedral ; we will now endeavour to 

 show under what circumstances spherical molecules will assume 

 the form of a dodecahedron, and will then proceed to prove that 

 these three formations will give rise to three distinct cleavages, 

 the directions of cleavage being in every case parallel to the faces 

 of the solid itself, an instance of agreement which is strongly 

 suggestive of truth. 



If the spherical molecules have eight poles situated in the 

 same relative positions as the corners of a cube, they will, if under 

 no disturbing influence, assume the form of a dodecahedron ; 

 for if any sjihere attract eight others, they will be arranged as 

 shown in PI. I. fig. 12, all the poles of each sjihcre having the same 

 ])Osition as regards the eye ; for it is evident, that, if after union 

 they have any other position, the mutual actions of all the ])oles 

 will cause them to rotate on each other till they have that definite 

 position ; these eight will be attached simultaneously, and imme- 

 diately six others will be attached to them, as shown in fig. 13. 

 We have flow a dodecahedron formed ; and it is evident that as 



