114 On the Molecular Constitution of Crystals. 



the crystal grows, the same form will be retained (fig. 14). Such 

 a crystal will be liable to modification in the same manner as 

 those already discussed, and thus all other forms may be built 

 up in this manner. 



We have thus seen that on these three hypotheses it is pos- 

 sible to explain all forms ; the cubical gives rise primarily to the 

 cube, and by means of decrements to all others except the tetra- 

 hedron. And here we may mention a fact strikingly confirma- 

 tory of these views, namely, that there is not a single instance in 

 nature of a a-ysfal exhibiting the tetrahedral form, or that of any 

 of its hcmihedral derivatives, and possessed of cubical cleavage. 

 The tetrahedral gives rise to that solid and all others by its mo- 

 difications, and the dodecahedral in like manner gives rise to all 

 forms; and thus any crystal may have any cleavage. 



As regards cleavage, it takes place in every case in whatever 

 direction the least resistance is met with ; thus where each mole- 

 cule has six poles the cleavage is cubical, because such a division 

 separates each atom from one other only, whereas the dodecahe- 

 dral cleavage would separate each atom from two others, and the 

 octahedral from three, as is at once evident on inspection of 

 fig. 5. 



In like manner, in the tetrahedral arrangement the cleavage 

 is parallel to the faces ; for it is evident (fig. 3) that such a divi- 

 sion would separate each molecule from three others, whereas 

 the only other cleavage which it could possibly undergo, namely 

 that parallel to planes on the edges, would separate each mole- 

 cule from four others. Lastly, where the poles are eight in 

 number, and the formation dodecahedral, the cleavage planes are 

 parallel to the faces ; for by division in such directions we over- 

 come the resistance of two poles in each molecule, while if we 

 divided the crystal by planes parallel to the faces of the cube, 

 we should separate each atom from four others ; if by planes 

 parallel to the faces of the octahedron, from three others. 



These three formations occur in the other systems also, and 

 give rise to corresponding cleavages ; but as some of the poles 

 arc stronger than others, in those systems particular cleavages 

 are eminent. 



We have now reviewed all the different forms of the first system : 

 it only remains to speak of hemitrope and twin crystals. 



Dana has satisfactorily shown that these will arise from the 

 accidental union of two molecules at the middle points between 

 two or more poles; an account of his theory first appeared in 

 the American Journal of Science for 1836. He was certainly 

 the first person who fully investigated this part of the subject ; 

 but justice compels me to add, that his ideas were directly bor- 

 rowed from Sir David Brewster, who some years before, in an 



