276 CRYSTALLIZATION. 



terior of a mass, the question of cleavage suggests itself. In dividing 

 a crystal we create two new surfaces — one on each piece, and each with 

 its own energy. Tlie division nuist tlierefore take place most readily 

 when that surface energy is a minimum. Hence the jmncipal cleavage 

 of a crystal made up of molecules having their motions comprised within 

 spherical spaces will be octahedral. As a fact, we tind that the greater 

 part of substances which crystallize in the octahedral, or regular sys- 

 tem, have octahedral cleavage. But not all; there are some, like rock 

 salt and galena, which cleave into cubes, and a very few, like blende? 

 have their easiest cleavage dodecahedral. These I have to explain. I 

 may however first observe that some substances — as, for instance, 

 fluor-spar — which have a very distinct octahedral cleavage are rarely 

 met with in the form of octahedra, bnt usually in cubes. In regard to 

 this, we must remember that the surface energy depends upon the 

 nature of both the substances in contact at the surface, as well as on 

 their electrical condition, their temperature, and other circumstances. 

 The closeness of the molecules in the surface of the solid determines the 

 energy, so far as the solid alone is concerned; but that is not the only 

 — though it may be the most important — factor conducing to the result 

 It is therefore quite possible that, under the circumstances in which 

 the natural crystals of fluor were formed, the surface energy of the 

 cubical faces was less than that of the octahedral, although when we 

 experiment on tliem in the air, it is the other way. This supposition 

 is confirmed by the well-known fact that the form assumed by many 

 salts in crystallizing is affected by the character of the solution. Thus 

 alum, which from a. solution in pure water always assumes the octa- 

 hedral form, takes the cubic form when the solution has been neutra- 

 lized with potash. 



To return to the cubic and dodecahedral cleavages. If we suppose 

 the excursions of the jiarts of the molecule to be greater in one direc- 

 tion than in the others, the figure within which the molecule is comprised 

 will be a prolate spheroid ; if less, an oblate spheroid. Now, as already 

 explained, the .spheroids will be packed as closely as jiossible if the axes 

 are all paralled and each is touched by twelve others. Xow suppose 

 the spheroids arranged as in Fig. 0, with their axes perpendicular to 



Fig. 6. 



the plane of the figure; place the next layer in the black triangular 

 spaces, and complete the pyramid. The three faces of the pyramid 



