520 
PROFESSOE HENEY A. MIEES: AN ENQUIRY INTO 
ljut the doclecahedi'oii and octahedron. To i-eplace the cube or the octahedion b}- 
vicinal planes nearly coincident with them is to replace planes ol the gieatest possible 
reticular density by planes ol the least possible reticular density. And }et the 
crystal is hounded by the latter rather than l:)y the lormer. Is it not possible that 
the supersaturated ll(pud in immediate contact with the growing alum crystal 
consists of particles of alum uniformly mingled with particles of water, and that the 
act of crystallisation consists in the escape of the crater, and consecpient solidification of 
the alum ? Immediately liefore tlie act of crystallisation the alum particles in the 
solution cannot he so closely packed as those in the crystal, since they aie separated 
by particles of water; if, then, they are to he la.id down in plane layeis, and aie yet 
to find their places at once as constituent parts of the crystal structure, they will he 
laid down not along planes of great reticular density hut along vicinal planes. 
Fig. 21 gives a crude representation^' of a cubic structure in which the particles 
are so widely spaced immediately before the act of crystallisation that they solidify 
4 3 2 1 
Fig. 21. 
along the plane (025). The density in the cube face is 5'385 times as gieat as the 
density in this plane; for in the cube plane the mesh is a scjuare (side co), and in 
the plane (025) the mesh is a rectangle whose sides are a and 5-385a respectively. 
It is, of course, impossible from the constitution of a single layer of particles to 
deduce that of the solution in the neighbourhood of the crystal as a whole; and the 
refractive index presumably only gives the average constitution of a certain layer of 
the solution, thin though that layer may be. Nevertheless, the figure indicates that, 
if the crystallising particles be regarded as a shower falling normally upon the surface, 
the shower is so dense upon a growing cube face that it would leave little space for 
the escape of the solvent, whereas upon the fiice (025), although equally dense as 
measured along lines perpendicular to the plane of the diagram, it is more than fi^ e 
* The particles are only represented as circles in contact with each other, in order to make the struetme 
more clear. 
