Mr. FoRSTER on the Molecular Formation of Crystals. 4J»7 



eminent. Thus, iu the second system, we have cleavage parallel to the termi- 

 nal plane only, because the poles at the extremities of the longer axes are the 

 weakest : we have also cleavage parallel to the faces of the prism. When the 

 contrary is the case, both these cleavages occur when the poles are six in num- 

 ber : but we have seen that the octahedral formation occurs in the first system 

 when the poles are twelve in number ; and it is easily seen that it will also 

 occur in the second system under similar circumstances. 



The arrangement of the poles is shown in Fig. 16 : the poles, as in Fig. 8, 

 lie six and six on ellipses which are four in number, and inclined to each other 

 at the same angles as the faces of the octahedron which they imite to form. If 

 any number of such ellipsoids unite by the poles A, B, C, D, they will be dis- 

 posed as shown in Fig. 17, which is a section in the plane of these poles : 

 another ellipsoid will become attached by its terminal poles (a, b, c, d) to the 

 four poles d,d',d",d"' : another will be attached opposite to it, and thus an 

 octahedron will be formed. It is easily seen that the cleavage will be parallel 

 to the faces of the octahedron ; for, as in the formation of the first system, that 

 cleavage will separate each molecule from three others; while the prismatic 

 cleavage would separate each from four others. The poles are also of the same 

 kind, taken in this manner, three and three, and accordingly all the cleavages 

 will take place with the same facility. 



It is evident that the tetrahedron will also be formed in the same manner. 



We thus see that four molecules may first unite, as in Fig. 17, or three, as 

 in Fig. 18, it being merely a matter of accident which result takes place. We 

 have in the first case proved that the resulting form is the octahedron, and in 

 the second the tetrahedron : thus we have a simple explanation of a fact which 

 at first sight appears singular, that under the very same conditions we may 

 have either the holohedral or the hemihedral form. 



Thus we may have the tetrahedron of the second system ; and by means of 

 decrements we can readily explain the dioctahedron and hemidioctahedron. 



In the third, or rhombohedral system, the rhombohedron will be formed, 

 if the molecule be an ellipsoid of revolution, and the poles are placed at the 

 extremities of three equal conjugate diameters. This Dana has explained. 

 The rhombohedral cleavage will also take place under similar circumstances ; 

 but we have two other cleavages, namely, that parallel to the faces of the hex- 

 agonal prism, and that parallel to the base of the prism ; and these will evi- 



