202 
SPHERICAL ELEMENTS OF CRYSTALS. 
Fluor spar 
the most con- 
venient for ex- 
J )eriments of 
facture. 
Neither the oc- 
tohedion nor 
tctiiiliedron 
can be arrang- 
ed in slah'e 
equilibrium, 
The substance which most readily admits of division by 
fracture into these forms is fluor spar j and there is no diffi- 
culty in obtaining a sufficient quantity for such experiments. 
But it is not, in fact, either the tetrahedron or the octohedron, 
which first presents itself as the apparent primitive form ob- 
tained by fracture. 
If we form a plate of uniform thickness by two successive 
divisions of the spar, parallel to each other, we shall find the 
plate divisible into prismatic rods, the section of which is a 
rhomb of 72 ° 32' and 109 ° 28' nearly ; and if we again split 
these rods transversely, we shall obtain a number of regular 
acute rhomboids, all similar to each other, having their super- 
ficial angles GO“ and ] 20“’, and presenting an appearance of 
primitive molecule, from which all the other modifications of 
such crystals might very simply be derived. And we find, 
moreover, that the whole mass of fluor might be divided into, 
and conceived to consist of, these acute rhomboids alone, which 
may be put together so as to fit eaeh other without any inter- 
vening vacuity. 
But, since the solid thus obtained (as represented fig. 2.) 
may be again split by natural fractures at right angles to its 
axis (fig. 3.) so that a regular tetrahedron may be detached 
from each extremity, while the remaining portion assumes the 
form of a regular octohedron ; and, since every rhomboid that 
can be obtained, must admit of the same division into one 
octohedron and two tetrahedrons, the rhomboid can no longer 
be regarded as the primitive form j and since the parts into 
which it is divisible are dissimilar, we are left in doubt which 
of them is to have precedence as primitive. 
In the examination of this question, whether we adopt the 
octohedron or the tetrahedron as the primitive form, since ^ 
neither of them can fill space without leaving vacuities, there 
is a difficulty in conceiving any arrangement in which the par- 
ticles will remain at rest : for whether we suppose, with the 
Abbe Hauy, that the particles are tetrahedral with octohedral 
cavities, or, on the contrary, octohedral particles regularly 
arranged with tetrahedral cavities, in each case the mutual 
contact 
