1891.] on Crystallisation. 381 



side of the vessel, or at the top where the liquid meets the air. But 

 it is easiest of all to add to a surface of the same energy as that of 

 the crystal. The additional energy required will then be only for 

 the extension of the surface. This explains why dropping a crystal 

 into a supersaturated solution starts crystallisation. Large crystals 

 grow more readily than small ones because the extension of surface, 

 that is the addition of energy, for a given addition of mass is less in 

 the former. Also it is easier to add to the faces already formed than 

 to develop new faces. 



While speaking of the difficulty of creating a new surface in the 

 interior of a mass, the question of cleavage suggests itself. It is 

 plain that in dividing a crystal we create a new surface on each of the 

 two parts, each with its own surface energy. The division must there- 

 fore take place most readily where that surface energy is a minimum. 

 Hence I infer that the principal cleavage of a crystal made up of 

 molecules for which the vibrations are comprised within spherical 

 spaces will be octahedral. As a fact, we find that the greater part of 

 substances which crystallise in what is called the regular system, 

 have an octahedral cleavage. But not all ; there are some which 

 have a cubical cleavage such as rock salt and galena, and a very 

 few like blende have the principal cleavage dodecahedral. These I 

 have to explain. 



I may, however, first observe that some substances, like fluor spar, 

 which have a very distinct octahedral cleavage, are rarely met 

 with in octahedral crystals, but usually in the cubic form. In regard to 

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

 of both the substances which meet at the common surface, their 

 electrical state, their temperature, and other circumstances. It is a 

 well known fact that the form assumed by a salt on crystallising is 

 affected by the character of the solution. Thus, alum, which from a 

 solution in pure water lakes the octahedral form, from a solution 

 neutralised with potash takes the cubic form. It is therefore quite 

 possible that, under the circumstances in which the natural crystals 

 of fluor spar were formed, the surface energy of the cubical faces was 

 less than that of the octahedral, although when we experiment upon 

 them in the air it is the other way. The closeness of the molecules 

 in the surface of the solid will determine the surface energy so far 

 as the solid alone is concerned ; but though this may be the most 

 important factor of the result, the molecules of the fluid in contact 

 with the crystal have their effect too. 



But to return to cubic and dodecahedral cleavages. If we suppose 

 the excursions of the parts of the molecule to be greater in some one 

 direction than in the others, the figure within which the molecule 

 vibrates will be a prolate spheroid ; if it be less, an oblate spheroid. 

 Now if such spheroids be packed as close as possible, each can be 

 touched by twelve others, and they can be packed just as the spheres 

 were, provided their axes be all parallel. It matters not what the 

 orientation of the axes may be so far as the closeness of packing goes. 



