THE VARIATION OF ANGLES OBSERVED IN CRYSTALS. 
521 
times more open as measured in the plane of the diagram. [With vicinal laces of the 
sort actually observed, the difference is, of course, very much greater; for example, a 
vicinal plane (OM) in the cubic lattice inclined at 0° 30' to the cube face has a 
rectangular mesh whose sides are a and 114a (about), and the density in the cul )e 
face is therefore about 114 times that in the vicinal plane.] Although the plane (025) 
has a comparatively open structure, the successive layers of particles parallel to this 
plane are far more closely packed than successive cube layers, as is clear from tlie 
figure (lines 1, 2, 3, 4). The black circles represent the particles which, at a given 
moment, bound the ciystal; the plane 'which ^Dreceded it is represented by shaded 
circles whose centres lie on the line 1, and the set of particles in the act ot 
crystallising is represented by dotted circles. 
If we are to speculate concerning the arrangement of the material in layers further 
removed from the surface of the crystal, Ave may perhaps suppose that along lines 
normal to the surface (the arrows of fig. 21) the particles are even as closely packed 
as along an edge of the cube. Each successive layer is then formed as the crystal 
solidifies by the particles immediately behind those of the newly solidified layer 
slipping sideways into their places. 
Further, in the case contemplated, each dotted circle in the figure may be talren 
to represent a line of particles pei’pendicular to the plane of the clraAAung, Avhich are 
packed as closely as the particles along a cube edge in tlie crystal, i.e., as closely as 
the horizontal lines of particles. The act of crystallisation Avill then consist in the 
deposition of such lines all parallel to tlie cube edge, but so widely spaced as to lie in 
a vicinal plane (Oli). This corresponds with the fact that tlie vicinal planes, though 
they vary in inclination, ahvays belong to well defined zones; in tliis instance they 
will lie in the cube zone, and sodium chlorate possibly affords an example of vicinal 
planes of the sort depicted in fig. 21. 
The determinations made above enable us to compare the weight of material 
contained in a given volume of the crystal Avith the Aveight of the same material in 
the same volume of the solution ; that is to say, the density of the substance in the 
crystal AAuth its density in the immediate neighbourhood of the crystal, ignoring tlie 
solvent. Thus for alum: — Taking the specific graAuty of the crystallised salt to he 
1-72, then 100 cub. centims. of the solid Avill contain 172 grammes of alum; and 
100 cub. centims. of a solution containing 9'3 per cent, alum, and of specific gravity 
1-048, Avill contain 9-74 grammes of alum. The density of alum in the crystal is, 
therefore, about I7f times that in the adjacent solution. 
For sodium chlorate: — Specific gravity of the crystallised salt = 2-289; 100 cub. 
centims. of the solid Avill contain 228-9 grammes of sodium chlorate; and 100 cub. 
centims. of a solution containing 47-73 per cent, of the salt Avill contain 65-27 grammes 
of sodium chlorate. The density of sodium chlorate in the crystal is, therefore, about 
3^ times that in the adjacent solution. 
For sodium nitrate :—Specific gravity of tlie crystallised salt = 2-244; 100 cub. 
A"OL. CCII. - A. 3 X 
