On the elementary Particles of certain Crystals. 63 
from its novelty. But I have since found, that it is not 
altogether so new as I had then supposed it to he; for, by 
the kindness of a friend, I have been referred to Dr. Hooke’s 
Micrographia, in which is contained, most clearly, one 
essential part of the same theory. 
However, since the office of a Jecturer is properly to dif- 
fuse knowledge already acquired, rather than to make 
known new discoveries in science, and since these hints of 
Dr. Hooke have been totally overlooked, from having been 
thrown out at a time when crystallography, as a branch of 
science, was wholly unknown, and consequently not ap- 
plied by him to the extent which they may now admit, I 
have no besitation in treating the subject as I had before 
designed. And when I have so done, I shall quote the 
passage from Dr. Hooke, to show how exactly the views 
which I have taken have, to a certain extent, corresponded 
with his; and I shall hope that, by the assistance of such 
authority, they may meet with a more favourable recep- 
tion. 
The theory to which I here allude is this, that, with re- 
spect to fluor spar and such other substances as assume the 
octohedral and tetrahedral forms, all difficulty is removed 
by supposing the elementary particles to be perfect spheres, 
which by mutual attraction have assumed that arrangement 
which brings them as near to each other as possible. 
The relative position of any number of equal balls in the 
same plane, when gently pressed together, forming equila- 
teral triangles with each other (as represented perspectively 
in fig. 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 an- 
gles of 60° with each other. 
If a single ball were placed any where at rest upon the 
preceding stratum, it is evident that it would be in contact 
with three of the lower balls (as in fig. 5.), and that the 
fines joining the centres of four balls so in contact, or the 
planes touching their surfaces, would include a regular te- 
trahedron, 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 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 tri- 
angular face rising from each side of the square, and the 
whole together wil! represent the superior apex of an octo- 
hedron ; 
