1891.] on Crystallisation. 883 



we start with spheroids arranged as in Figure 1, with their axes 

 perpendicuhir to the plane of that figure, and place three others 

 touching that marked a ; there are two ways in which we can do 

 this. We may place the three either in the white or in the black 

 triangles. The two positions difier in such a way that you pass from 

 one to the other by turning the three spheroids as a whole through 

 180°. The relation is that of twin crystals. If a crystal wore 

 growing by addition to the face which we suppose represented iu 

 Figure 1, it would be as likely that one arrangement should be taken 

 as the other so far as the middle part of the face is concerned. But 

 a crystal built up of such alternate layers of twins v/ould have ridged 

 and furrowed faces, that is faces of extra surface-tension, except in 

 the case of hexagonal forms. For hexagonal forms are no way 

 altered by being turned through two right angles. There will there- 

 fore be a tendency for such forms to grow unless the rhombohedral 

 faces have a much less surface energy. Hexagonal forms have also 

 less surface per unit of volume than rhombohedrons, and lend them- 

 selves to the formation of nearly globular crystals, with a minimum 

 of total surface, as is often seen in pyromorphite. 



Recurring to the cube of spheres, if it be subject to a stress in a 

 direction not parallel to an edge or diagonal, we shall get an arrange- 

 ment of spheroids which will give forms of less symmetry. Also if it 

 be subject to two uniform stresses at right angles to one another the 

 spheres will become ellipsoids and may be taken to represent the 

 molecules in the most general case. The degrees of symmetry, and 

 the directions of most easy cleavage, may be woi^ked out on the lines 

 already indicated, and will be found to correspond with those observed 

 in nature. 



Bravais long ago suggested arrangements of the molecules 

 corresponding to the symmetry, and Sohncke has extended his 

 suggestions, but neither has assigned any mechanical reason why the 

 molecules should so arrange themselves. They also supposed 

 different arrangements for different kinds of symmetry. I have 

 endeavoured to give a sufficient reason for the positions taken by the 

 molecules and to show that out of the one arrangement by which the 

 molecules are packed as closely as., is possible all the varieties of 

 symmetry will arise. 



M. Curie also has, before me, pointed out that differences of 

 surface tension will determine the relative sizes of different faces ; 

 but he has not pointed out that the same principle determines that 

 the faces shall be planes, and that similar edges and angles shall be 

 similarly modified, or that the law of indices in the relations of 

 different forms is a direct consequence of it. 



We are able now, I think, to understand the interesting facts 

 brought forward by Prof. Judd in a discourse which he delivered 

 at the Eoyal Institution in the early part of this year. 



It does not matter how long a crystal has been out of the solution 

 or vapour in which it was formed, the surface tension remains 



