278 CRYSTALLIZATION. 



cupying the wliite triangles is iu the position of a twin to that occupy- 

 ing the black triangles. So far as the central parts of the layer are 

 concerned, it will make no difference in which of these ways the mole- 

 cules are packed. It is only at the edges that the surface tension will 

 be affected. If the form growing be a rhombohedron, a succession of 

 alternating twins will produce a series of alternating ridges and fur- 

 rows in the rhombohedral faces, which will give rise to increased sur- 

 face tension, which will tend to i^revent the twinning. On the other 

 hand, a hexagonal form and its twin, formed in the way indicated, are 

 identical, and we have in this faet a cause tending to the production of 

 hexagonal forms. This tendency is increased by the fact that, for a 

 given volume, the total surface of the hexagonal forms is in general 

 less than that of the rhombohedral. Indeed, such forms lend them' 

 selves to the formation of almost globular crystals, as is well seen in 

 pyromorphite and mimetite. 



If the spheroids be arranged with their axes in other positions than 

 those we have been discussing, or if the molecules occupy ellipsoidal 

 spaces, they will, when packed so that each is touched by twelve oth- 

 ers, give figures of less symmetry. The results may be worked out on 

 the lines indicated in the foregoing discussion, and will be found to 

 correspond throughout to the observed facts. 



Bravais long ago proposed various arrangements of nudecules to 

 account for crystalline forms, and Sohncke has extended them to 

 further degrees of complication in order to account for additional facts 

 in crystallography. But neither of them has given any reason why 

 the molecules should assume such arrangements. To me it seems that 

 only one arrangement can be spontaneously assumed by the molecules, 

 and that the varieties of crystalline form depend on the dimensions of 

 the ellipsoids and the orientation of their axes. Curie also has indi- 

 cated that the development of combined forms, as those of cube and 

 octahedron, will depend on the surface tensions in the faces of these 

 forms, but he has not indicated how the surface tension is connected 

 with the crystalline arrangement, or why the energy of a^ cubic face 

 should be greater or less than that of an octahedral face. 



We are now in a position to understand the interesting facts brought 

 forward by Prof. Judd in a discourse delivered at the Eoyal Institution 

 early this year. However long a crystal has been out of the solution 

 or vapor from which it was formed, its gurface tension will remain 

 unaltered, and when it is replaced it Avill grow exactly as if it had not 

 been removed. Also, if any part be broken off it, the tension of the 

 broken surface will, if it be not a cleavage face, be greater than on a 

 face of the crystal, and in growing, the laws of energy necessarily cause 

 it to grow in such a way as to reduce the potential energy — that is, to 

 replace the broken surface by the regular planes of less surface energy. 

 The formation of "negative crystals" by fusing a portion in the interior 

 of a crystalline mass is due to the same principle. Surfaces of least 



