204 
SPHERICAL ELEMENTS OP CRYSTALS. 
Formation 
the tetrahe- 
dron; 
and the octo- 
hcdroir. 
brought as ing the elementary particles to be perfect spheres, which, by 
sibte wMlfCm altraciion, have assumed that arrangement which brings 
the solids. them as near to each other as possible. 
Instance. One The relative position of any number of equal balls in the 
lamina dispos- ^ * 
ed to break in same plane, when gently pressed together, forming equilateral 
lines at 60°. triangles with ««ch other, (as represented perspectively in 
£g. 4.) is familiar to every one ; and it is evident, that if balls 
so placed were cemented together, and the stratum thus formed 
were afterwards broken, the straight lines in which they would 
be disposed to separate would form angles of 60 '’ with each 
other. 
of If a single ball were placed any where at rest upon the pre- 
ceding stratum, it is evident that it would be in contact with 
three of the lower balls, (as in fig. 5,) and that the lines join- 
ing the centres of four balls so in contact, or the planes touch- 
ing their surfaces, would include a regular tetrahedron, having 
all its sides equilateral triangles. 
The construction of an octohedron, by means of spheres 
alone, is as simple as that of the tetrahedron. For if four balls 
be placed in contact on the same plane in the form of a square, 
then a single ball resting upon them in the centre being in 
contact with each pair of balls, will present a triangular face 
rising from each side of the square, and the whole together 
will represent the superior- apex of an octohedron ; so that a 
sixth ball, similarly placed underneath the square, will complete 
the octohedral group, fig. 6. 
The octohe- There is one observation with regard to these forms that 
samVVii'ctlier appear paradoxical, namely, that a structure which, in 
besran on the this case, was begun upon a square foundation, is really intrin- 
foimditfion of . , , • , • , ... 
four or of sicaliy the same as tliat which is begun upon the triangular 
tiirte spheres ; gyj jp 
we lay the octohedral group, which consists of 
six balls, on one of its triangular sides, and consequently with 
an opposite triangular face uppermost, the two groups, consist- 
ing of three balls each, are then situated precisely as they 
would be found in two adjacent strata of the triangular arrange- 
and i.< r.?r.:n ment. Hence, in this position we may readily convert the 
convcrtibif to ii,(o aj-cgular tetrahedron, by addition of four more 
balls 
