498 Mr. FoKSTEE on the Molecular Formation of Crystals. 



deiitly occur if the molecules have eight poles — two at the extremities of the 

 principal axis of the molecule, and six round the circumference of a circular 

 section through its centre. If these six poles are stronger than the two others, 

 the cleavage will be basal ; if not, lateral ; and if they all have the same 

 strength, both cleavages will coexist. 



We have thus shown how the primary forms of the rhombohedral system 

 may be produced. The secondary forms can, of course, be explained on the 

 same views. Thus, the dodecahedron can be easily deduced by means of de- 

 crements from either the rhombohedron or the hexagonal prism ; and thus it 

 may have either cleavage, and may be found in combination with either of 

 these forms. The didodecahedron may be obtained in a similar manner. The 

 hemihedral forms of these solids are of course deduced in the same manner as 

 the holohedral. The cause of their occurrence in general we have already 

 explained. 



In the fourth, or trimetric system, where the crystallographic axes intersect 

 at right angles, and are all unequal, the molecule is evidently an ellipsoid. If 

 the poles are situated at the extremities of the axes of this ellipsoid, the form 

 produced will be a prism with a rectangular base. As the poles are iiulike, it 

 is evident that cleavage may exist in such a form parallel to any of the faces. 

 There is, however, another cleavage, namely, parallel to all the lateral faces of 

 a prism, having a rhomboidal base ; and this will arise if the lateral poles are 

 situated at the extremities of equal conjugate diameters. Dana has explained 

 the formation of both these prisms. 



The secondary forms can be easily deduced in a manner precisely ana- 

 logous to that in which we have deduced those of the other systems. 



The formations of the two remaining systems take place in precisely analo- 

 gous ways. To enter into an explanation of all the combinations could only 

 prove tedious. I shall, in conclusion, show that the phenomena of hemitrope 

 forms and twin crystals are in strict accordance with, and can be readily 

 explained by, the hypotheses which I have advanced ; and further, that some 

 of them can be explained on these views, which were quite unintelligible on 

 Dana's hypothesis. 



One of the best known cases of hemitropism in the first system is where 

 one half of an octahedron is rotated on another, through an angle of 180", the 

 plane of separation being parallel to an octahedral face. Such combination is 



