380 Professor G. D. Liveing [May 15, 



the surface energies. What we can assert is that greater concentra- 

 tion means in general less surface energy. 



Hence when the molecules are spherical the bounding surface 

 tends to be that of a regular octahedron. 



But we have another point to consider. Since the solid must be a 

 closed figure, there will be edges where the bounding planes meet 

 each other. At these edges the surface tensions will have a resultant 

 tending to compress the crystal, and there must be a corresponding 

 resultant pressure on the opposite side. It follows from this that if one 

 pair of faces are developed on one side of a crystal a parallel pair must 

 in general be developed on the opposite side, and if one face of a form, 

 be it cube, octahedron, or other form, be developed, all the faces of 

 that form will, as a rule, be developed. 



But there is yet another point to be taken into account. The sur- 

 face energy may become less in two ways ; one by reducing the tension 

 per unit of surface, and the other by reducing the total surface for 

 the same quantity of matter. When a liquid separates from another 

 liquid, as chloroform from a solution of chloral hydrate by adding an 

 alkali, or a cloud from moist air, the liquid assumes the form which 

 for a given mass has the least surface, that is the drops are spherical. 

 If you cut off the projecting angles, and plane away the projecting 

 edges of a cube or octahedron, you bring it nearer to a sphere, and 

 diminish the surface per unit volume. And if diminution of the 

 total surface is not compensated by the increase of the surface 

 energy on the truncations, there will be a tendency for the 

 crystal to grow with such truncations. The like will be true in 

 more complicated combinations. There will be a tendency for such 

 combinations to form provided the surface energy of the new faces is 

 not too great as compared with that of the first formed faces. 



But it does not always hapj)en that an octahedron of alum 

 developes truncated angles. This leads to another point. To pro- 

 duce a surface in a homogeneous mass requires a supply of energy, 

 and to produce a surface in the interior of any fluid is not easy. Air 

 may be supersaturated with aqueous vapour, or a solution super- 

 saturated with a salt, and no cloud or crystals be formed in the 

 interior, unless there is some discontinuity in the mass, specks of 

 dust or something of the kind. 



When solid matter separates from a solution, a certain amount of 

 energy is available from the change of state, and supplies the surface 

 energy of the new solid. The amount of this available energy is 

 proportional to the mass of solid separated. But since the surface 

 varies as the square of the diameter, while the mass varies as the cube 

 of the diameter, the amount of energy available when the mass is very 

 minute may be insufficient. In fact, a very small mass of solid might 

 be squeezed into liquid again by its own surface energy. It will be 

 easier to add to a surface already formed, even if that surface be one 

 of less energy than that of the new solid, than it is to break the con- 

 tinuity of the fluid. Hence we find that crystals often form on the 



