496 Mr. FoRSTER on the Molecular Formation of Crystals. 



If each sphere have eight poles, situated in the same relative positions as 

 the corners of the cube, they will, if under no disturbing influence, assume the 

 form of the dodecahedron ; for if any sphere attract eight others, they will be 

 arranged as shown in Fig, 13 ; that is, their centres will occupy the same posi- 

 tions as the corners of a cube, but also their poles will all have the same posi- 

 tions as regards the eye, for their mutual actions will cause the spheres to turn 

 on the points of mutual contact till they have such an arrangement. These 

 eight will be attached simultaneously, and immediately six others will become 

 attached to them, as shown in Fig. 14. It is evident that as the crystal grows, 

 the same form is retained (Fig. 15). Such a crystal will be liable to modifica- 

 tion in the same manner as those already discussed, and thus all forms may be 

 built up. With regard to the cleavage of such a crystal, it is easily deduced 

 by referring to the principles already made use of The three possible planes 

 of division in this formation are planes replacing an angle, replacing an edge, 

 and parallel to a face. It is evident that the last is the natural one, for it sepa- 

 rates each particle from two others, while that replacing an edge divides each 

 particle from three ; that replacing an angle, from four others. 



We have now reviewed all the forms of the first system, and have endea- 

 voured to show under what circumstances the different cleavages will take 

 place. 



We have now to consider the other systems. As I have already said, 

 Dana has shown how the forms in these systems will arise from the molecules 

 being spheroids or ellipsoids, the length of whose axes and the position of 

 whose poles are in every case given by the length and obliquity of the axes of 

 the crystal ; but, as in the case of the first system, he has given but one forma- 

 tion for each of the other systems. We have already seen that this leaves 

 unexplained the cleavage in the first, and the same is true for the others also. 

 He considers the molecule in the second or dimetric system to be an ellipsoid 

 of revolution with six poles, as in the first system. This will easily explain the 

 prismatic and basal cleavages, but it will not account for the octahedral. 



It is to be remarked, that in this, and every system except the first, we can. 

 not expect that any poles will have the same strength except those of the same 

 kind. We find, accordingly, that from the inferior strength of two of the 

 poles, cleavage will exist in one direction only, or, as is often the case, may be 



