On the elementary Particles of certain Crystals. 67 
_ It may further be observed, that the proportion of the 
height to the base of such a prism must depend on the ratio 
between the axes of the elementary spheroid. 
The Cube. 
Although I could not expect that the sole supposition of 
spherical or spheroidical particles would explain the origin 
of all the forms observable among the more complicated 
erystals, still the hypothesis would have appeared defective, 
if it did not include some view of the mode in which so 
simple a form as the cube may originate. 
A cube may evidently be put together of spherical par- 
ticles arranged four and four above each other; but we have 
already seen that this is not the form which simple spheres 
are naturally disposed to assume, and consequently this hy- 
pothesis alone is not adequate to its explanation, as Dr. 
Hooke had conceived. 
Another obvious supposition is, that the cube might be 
considered as a right-angled rhomboid, resulting from the 
union of eight spheroids having a certain degree of oblate- 
ness (2 to 1) from which a rectangular form might be de- 
rived. But the cube so formed would not have the proper- 
ties of the crystallographical cube. It is obvious, that, 
though all its diagonals would thus be equal, yet one axis 
parallel to that of the elementary spheroid would probably 
have properties different from the rest. The modifications 
of its crystalline form would probably not be alike in all 
directions as in the usual modifications of the cube, but 
would be liable to clongatioy in the direction of its original 
axis. And if such a crystal were e'ectric, it would have 
but gne pair of poles instead of having four pair, as in the 
erystals of boracite. 
There is, however, an hypothesis which at least has sim- 
plicity to recommend it, and if it be not a just representa- 
tion of the fact, it must be allowed to bear a happy resem- 
blance to truth. 
Let a mass of matter be supposed to consist of spherical 
particles all of the same size, but of two different kinds in 
equal numbers, represented by black and white balls; and 
Jet it be required that in their perfect intermixture every 
black ball shall be equally distant from all surrounding 
white balls, and that all adjacent balls of the same deno- 
mination shall also be equidistant from each other. I say 
then, that these conditions will be fulfilled, if the arrange- 
ment be cubical, and that the particles will be in equilibrio. 
Fig 14 represents a cube so constituted of balls, alternately 
E2 black 
