j\Ir. FoRSTER on the Molecular Formation of Crystals. 499 



found in crystals of spinel, a mineral in which the cleavage is octahedral. We 

 must, accordingly, show how it may take place, on the hypothesis which 

 explains the octahedral formation. A plane joining the three poles A, B, C, 

 (Fig. 10) is evidently parallel to a face of the octahedron of which the mole- 

 cule forms a part. Hence, if two such molecules be united by two points equi- 

 distant from three such poles, they will each become the origin of a crystal ; 

 and since they will naturally assume a symmetrical position with regard to each 

 other, A opposite A', &c., these two crystals, of which they are the origin, will 

 be similarly situated. Also, since each crystal prevents the other from growing, 

 except in a direction away from itself, they will together make up only one 

 crystal. Thus, the halves of two crystals similarly situated are evidently the 

 same as the halves of the same crystal rotated on eacli other through 180°. 



Crystals are also found in which the cleavage is octahedral, and composition 

 has taken place parallel to a face of the cube : such are some crystals of 

 diamond. These forms will result if two molecules, such as in the last case, 

 unite at a point of equilibrium between four poles. We have seen that the 

 dodecahedron of the first system may be built up of molecules having eight 

 poles; and I have stated that the molecules, as they unite, will occupy such a 

 relative position that the poles will be disposed symmetrically. Although that 

 is unquestionably the normal position of equilibrium, yet there is evidently 

 another position in which two such spheres may unite by two poles, namely 

 one 180° remote from this. Such is a position of unstable equilibrium ; but it 

 is one which, if nothing occurs to destroy it, will become the basis of a crystal. 

 Two such molecules will be the germs of two crystals, which, from the peculiar 

 circumstances under which they are formed, together exhibit the parts of one 

 crystal : they will be united by a plane parallel to a face of the octahedron, and 

 will exhibit the dodecahedral cleavage. Crystals of blende are found of this 

 formation. We might also have two such spheres united by two points inter- 

 mediate to four poles, the lines joining which would form a face of a cube ; and 

 if these molecules became the centres of formation, we would have a crystal 

 with dodecahedral cleavage, and hemitropism on a cubic face. Such a crystal, 

 however, could not be distinguished by the eye from an ordinary cube. In 

 fact, there are certainly twelve positions in which two such molecules might 

 unite and be in equilibrium. Tlie question is then merely one of probability as 

 to which combination may most readily take place. Those combinations whicli 



