462 
one part of a different particle and repel the 
other parts. This polarity would explain the 
regularity of crystallization; but it is itself 
inexplicable. 
It is remarkable that crystals not only as- 
sume regular figures, but arc always bounded 
bv plane surfaces. It is very rarely indeed 
that curved surfaces are observed in these 
bodies ; and when they are, the crystals al- 
ways give Unequivocal proofs of imperfection. 
But this constant tendency towards plane sur- 
faces is inconceivable, unless the particles of 
which the crystals are composed are them- 
selves regular figures, and bounded by plane 
surfaces. 
If the figure of crystals depends upon the 
figure oftheir integrant particles, and upon the 
manner in which they combine, it is reason- 
able to suppose that the same particles when 
at full liberty, will always combine in the 
same way, and consequently that the crystals 
of every particular body will be always the 
same. Nothing at first sight can appear 
farther from the truth than this. The dif- 
ferent forms which the crystals of the same 
body assume are often very numerous, and 
exceedingly different from each other. Car- 
bonatot lime, for instance, has been observed 
crystallized in no fewer than forty different 
forms, fluat of lime in eight different forms, 
and sulphat of lime in nearly an equal num- 
ber. 
But this inconsistency is not so great as 
might at first sight appear. Romh tie Lisle 
has shown that every body susceptible of crys- 
tallisation has a particular form which it most 
frequently assumes, or at least to which it 
does most frequently approach. Bergman 
has demonstrated, that this primitive form, 
as Hauy has called it, very often lies con- 
cealed in those very crystals which appear 
to deviate farthest from it. And Hauy has' 
demonstrated, that all crystals either have 
this primitive form, or at least contain it as 
a nucleus within them ; for it may be extracted 
out ot all of them by a skilful mechanical 
division. See Plate Crystallization. 
Happening to take up an hexangular prism 
of calcareous spar, or earbonat of lime, which 
had been detached from a group of the same 
kind, he observed that a small portion of the 
crystalwas wanting, and that the fracture pre- 
sented a very smooth surface. Let abed efg h 
(fig. 1 .) be the crystal : the fracture lay ob- 
liquely as the trapezium/) s u t, and made an 
angle of 135 degrees, both with the remainder 
of the base a b c s p h, and with t u ef, the 
remainder of the side i n ef. Observing 
that the segment/) s u tin thus cut off had 
for its vertex i n, one of the edges of the base 
a b c n i h of the prism, he attempted to 
detach a similar segment in the part to 
which the next edge c n belonged ; he em- 
ployed for that purpose the blade of a knife, 
directed in the same degree of obliquity as 
the trapezium p s u t, and assisted by the 
strokes of a hammer. He could not succeed : 
but on making the attempt upon the next edge 
b c, he detached another segment, precisely 
similar to the first, and which had for its ver- 
tex the edge b c. He could produce no ef- 
fect on the next edge a b , p but from the 
next following, a It, he cut a segment si- 
milar to the other two. The sixth edge 
likewise proved refractory. He then went 
to the other base of the prism, d efg h r, 
and found that the edges which admitted 
CRYSTALLIZATION. 
sections similar to the preceding ones were 
not the edges ef, dr, g k, corresponding 
with those which had been found divisible 
at the opposite base, but the interme- 
diate edges d e, hr, gf. The trapezium 
l qy v represents the section of the segment 
which had k r for its vertex. This section 
was evidently parallel to the section p s u t, 
and the other four sections were also parallel 
two and two. These sections were, without 
doubt, the natural joinings of the layers of 
the crystal ; and he easily succeeded in 
making others parallel to them, without its 
being possible for him to divide the crystal 
in any other direction. In this manner he de- 
tached layer after layer, approaching always 
nearer and nearer the axis of the prism, till 
atlastthe bases disappeared altogether, and the 
prism was converted into a solid OX (fig. 2), 
terminated by twelve pentagons parallel two 
and two ; of which those at the extremities, 
that is to say, ASRIO, IGEDO, BAODC, 
at one end, and FKNPQ, MNPXU, ZQPX 
Y, at the other, were the results of mecha- 
nical division, and had their common vertices 
O, P, situated at the entrance of the bases of 
the original prism. The six lateral penta- 
gons RSUXY, ZYR1G, &c. were the re- 
mains of the six sides of the original prism. 
By continuing sections parallel to the former 
ones, the lateral pentagons diminished in 
length ; and at last the points R G coin- 
ciding with the points Y Z, the points S R 
with the points U Y, &c. there remained 
nothing of the lateral pentagons but the tri- 
angles YIZ, UXY, &c. (lig. 3). By con- 
tinuing the same sections, these triangles at 
last disappeared, and the prism was converted 
into the rhomboid a e (fig. 4). 
So unexpected a result induced him to 
make the same attempt upon more of these 
crystals ; and he found that all of them could 
be reduced to similar rhomboids. He found 
also, that the crystals of other substances 
could be reduced in the same manner to 
certain primitive forms; always the same in 
the same substances, but every substance 
having its own peculiar form. The primitive 
form of fluat of lime, lor instance, was an oc- 
tahedron; of sulphat of barytes, a prism with 
rhomboidal bases; of feltspar, an oblique- 
angled parallelopiped, but not rhomboidal ; 
of adamantine spar, a rhomboid, somewhat 
acute; of blende, a dodecahedron, with 
rhomboidal sides ; &c. 
These primitive forms must depend upon 
the figures of the integrant particles composing 
these crystals, and upon the manner in which 
they" combine with each other. Now by 
continuing the mechanical division of the crys- 
tal, by cutting off slices parallel to each of 
its faces, we must at last reduce it to so small 
a size that it shall" contain only a single inte- 
grant particle; consequently this ultimate 
figure of the crystal must be the figure of 
the integrant particlesof which it is composed. 
The mechanical division, indeed, cannot be 
continued so far, but it may be continued till 
it can be demonstrated that no subsequent di- 
vision can alter its figure ; consequently it 
can be continued till the figure which it as- 
sumes is similar to that of its integrant par- 
ticles. 
Hauy has found that the figure of the in- 
tegrant particles of bodies, as far as experi- 
ment has gone, may be reduced to three ; 
namely, 
1. The parallelopiped, the simplest of the 
solids, whose faces are six in number, and pa- 
rallel two and two. 
2. The triangular prism, the simplest of 
prisms. 
3. The tetrahedron, the simplest of pyra- 
mids. Even this small number of primitive 
forms, if we consider the almost endless diver- 
sity of size, proportion, and density, to which 
particles of different bodies, though they have 
the same figure, may still be liable, will be 
found fully sufficient to account for all the 
differences in cohesion, and heterogeneous 
affinity, without having recourse to different 
absolute forces. 
These integrant particles, when they unite 
to form the primitive crystals, do not always 
join together in the same way. Sometimes 
they unite by their faces, and' at other times 
by their edges, leaving considerable vacuities 
between each. This explains why integrant 
particles, though they have the same form, 
may compose primitive crystals of different 
figures. 
Mr. Hauy has ascertained, that the primi- 
tive forms of crystals are six in number; 
namely, 
1. The parallelopiped ; which includes the 
cube, the rhomboid, and all solids terminated 
by six faces, parallel two and two. 
2. The regular tetrahedron. 
3. I he octahedron with triangular faces. 
4. The six-sided prism. 
5. The dodecahedron terminated by- 
rhombs. 
6. The dodecahedron with isosceles trian- 
gular faces. 
Each of these may be supposed to occur as 
the primitive form or the nucleus in a variety 
of bodies ; but those only which are regular, 
as the cube or the octahedron, have hitherto 
been found in any considerable number. 
But bodies, when crystallized, do not al- 
ways appear in the primitive form; some of 
them indeed very seldom affect that form, 
and all of them have a certain latitude and a 
certain number of forms which they assume 
occasionally as the primitive form. Thus 
the primitive form of fluat of lime is the octa- 
hedron ; but that salt is often found crystal- 
lized in cubes, in rhomboidal dodecahedrons, 
and in other forms. All these different forms 
whicha body assumes, the primitive excepted, 
have been denominated by Hauy secondary 
forms. Now what is the reason of this lati- 
tude in crystallizing? why do bodies assume 
so often these secondary forms ? 
To this it may be answered: 
1st, r I hat these secondary forms are some- 
times owing to the variations in the ingre- 
dients which compose the integrant particles 
ot any particular body. Alum, for instance,, 
crystallizes in octahedrons ; but when a quan- 
tity of alumina is added, it crystallizes in 
cubes ; and when there is an excess of alumina, 
it does not crystallize at all. If the propor- 
tion of alumina vary between that winch 
produces octahedrons and what produces 
pubic crystals, the crystals become figures 
with fourteen sides, six of which are parallel 
to those of the cube and eight to those of the 
octahedron ; and according as the proportions 
approach nearer to those which form cubes or 
octahedrons, the crystals assume more or less 
of the form of cubes or octahedrons. What 
is still more, if a cubic crystal of alum 
is put into a solution that would afford octa- 
