384 Professor G. D. Liveing [May 15, 



the same, and it must grow on its old faces if replaced in the same 

 medium. 



Also if it have any part broken off, 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 to a 

 minimum, i. e. to replace the broken surface by the regular planes of 

 less surface energy. 



The formation of what have been called " negative crystals " by 

 fusion in the interior of a mass, is due to the same principle. If 

 the mass is crystalline in structure the surfaces of least energy 

 will be most easily produced in the inside as well as on the outside. 



We see a very similar result in the development of crystalline 

 form by the action of solvents, as of acids on metals. The substance 

 acted on must be crystalline in its molecular arrangement internally, 

 though its external figure may have been derived from the shape of 

 the vessel or other cause. If this is the case, and if the acid is not 

 so strong as to dissolve the metal rapidly, there must be a tendency 

 for those parts of the surface for which the energy is greatest to be 

 most easily removed. The result is to leave a crystalline form with 

 surfaces of minimum energy, as we see in Widmanstatt figures, a tin 

 plate acted on by dilute aqua regia, and many such cases. 



In fact, the solution of solids in liquids is very closely and directly 

 connected with the surface tension. One of many facts connected 

 with crystallisation is that the same substance in one crystalline form 

 may be soluble in a liquid in which it is not soluble when it has 

 another crystalline form. It is probably the low surface energy of 

 one form of crystals of sulphur which makes them insoluble in carbon 

 disulphide, and this low surface energy may be an electric effect. It 

 is not difficult to understand that the same molecules may give rise to 

 crystals of different degrees of symmetry, according to the orientation 

 of the axes, and the orientation of the axes may very well depend on 

 the distribution of the mass within the molecule, or the molecules may 

 in one case contain a greater number of chemical atoms than in the 

 other. With different crystalline forms of the same kind of sub- 

 stance we shall in general have different surface energies, and a 

 surface of great energy will be attacked by a solvent when one of 

 less energy will resist it. 



I pointed out that the law of symmetry, the development of all the 

 faces of any form, and the similar modification of all corresj)onding 

 edges and angles, is in general necessary in order to give equilibrium 

 under the action of the surface tensions. But we often find crystals 

 with only half the modifications required for symmetry. In such 

 cases the surface tensions must produce a stress in the interior tending 

 to deform the crystal. When the crystal was in process of formation 

 there was necessarily equilibrium, and there must have been a 

 pressure equal and opposite to this effect of the surface tension. 

 There are various ways in which we may suppose that such a force 



