274 CRYSTALLIZATION. 



We have to do, tneii, with an agency which we can not neglect In all 

 these cases the tension measnred is at a surface bounded by air, and is 

 such as tends to contract the surface. We have, then, at the boundary 

 between a crystallizing solid and the fluid, be it gas or liquid, out of 

 which it is solidifying, a certain amount of potential energy; and by 

 the laws of energy the condition of equilibrium is, that this potential 

 energy shall be a minimum. The accepted theory of surface tension is 

 that it arises from the mutual attraction of the molecules. The energy 

 will, therefore, be a minimum for a surface in which the molecules are 

 as closely set as possible. 



Kow, if you draw a surface through a heajj of balls packed so that 

 each is touched by twelve others, you will find that the surfaces 

 which have the greatest number of centers of balls per unit area are 

 all plane surfaces. That in which the concentration is greatest is the 

 surface of a regular octahedron, next come that of a cube, then that of 

 a rhombic dodecahedron, and so on according to the law of indices of 

 crystallographers. The relative numerical values of these concentra- 

 tions are as follows, taking that of the faces of the cube as unity: 



Octahedron 1. 1547 | Tetrakishexaliedron 0. 4472 



Cube 1. 0000 Eikositessarahedrou 0. 4083 



Dodecahedron 0. 7071 1 Triakisoctahedron 0. 3333 



We do know that the surface tension is exactly in the inverse pro- 

 portion to the concentration ; all that we can at present say is that it 

 increases as the concentration diminishes. 



If, then, the molecules occupy spherical spaces, the bounding sur- 

 face will tend to be a regular octahedron. 



But we have another point to consider. If a solid is bounded by 

 plane surfaces, there must be edges where the planes meet. At such 

 an edge the surfjice tensions will have a resulr.ant (see Fig. 5) tending 

 to compress the mass, which must be met by a corresponding opposite 

 l)ressure, and unless there is some internal strain there must be a cor- 

 respondent resultant of the tensions on the opposite side of the crystal. 

 Hence, if one face of a form is developed the opposite face will also be 

 developed -, and generally, if one face of a form be developed all the 



