CRYSTALLOGRAPHY. 
maik«(I, that tlieir surface striated in a 
certain direction, or tlie relation subsist- 
inc among the diflerent secondary forms 
of the same substance, afford indications 
vvliicli lead to the determination, with at 
least mgeh probalrility, of their piimitive 
forms. 
Such is the process, by which Hauy es- 
tablishes what he names the “ Primitive 
Form of Crystals,” and which he defines, 
‘‘A solid of a constant form, inserted sym- 
metrically in all the crystals of the same 
species, and the faces of which observe the 
directions of the layere which compose 
these crystals.” The primitive forms hi- 
therto observed, are reduceable to six : the 
parallelopipedon, which includes the cube, 
the rhomb, and all the solids which are ter- 
minated by six faces parallel two and two ; 
the tetraedron ; the octaedron ; the regular 
hexaedral prism ; the dodecaedron, with 
equal and similar rhomboidal planes ; and 
the dodecaedron with triangular planes. 
Hauy carries the division of crystals still 
further, however, than the primitive forms. 
The solid which constitutes it, is not the last 
term of the mechanical analysis ; it may 
always be still farther subdivided parallel 
to its different faces, and sometimes even 
in other directions. All the enveloping 
matter is equally divisible by sections pa- 
rallel to the faces of the primitive forms j 
and the only limit to this possible division 
is that placed by the composition of tlie 
substance. The calcareous .spar, to take it 
as an example, may be reduced to a particle 
beyond which the division cannot be car- 
ried, w'ithout resolving it into its elements, 
lime and carbonic acid ; or at least it may 
be reduced to a particle, beyond which, if 
its minuteness allowed us to operate upon 
it, it is demonstrable its figure would not 
change. To these last particles, the result 
of the mechanical analysis, Hauy gives the 
name of integrant particles, and their union 
constitutes the crystal. Their forms, so far 
as experiment has been carried, arc three ; 
the tetraedon, the simplest of the pyramids ; 
the triangular prism, the simplest of prisms ; 
and the parallelopipedon, the simplest of 
solids, which have their faces parallel, two 
and tw'o. There is little doubt tliat it is 
between these that the attraction of cohe- 
sion is immediately exerted. 
The piimitive forms, and tlie figures of 
the integrant particles, being determined, it 
remains to complete the theory of the 
structure of crystals, to shew by what ar- 
rangements the secondary forms, in other 
words, the actually existing crystals, arc 
produced. 
I'he nucleus of the crystal is the symme- 
trical solid which constitutes its primitive 
form, arising from the union of the integrant 
particles, either by their faces or their 
edges; and the additional matter, which 
forms the crystal, consists of layers of these 
particles superadded to that nucleus, and 
arranged on its faces ; and to account for 
the formation of the crystal under a figure 
different from that of its primitive form, 
these layers, as they recede from it, are 
supposed to decrease, in the space they 
occupy, from the regular abstraction of one 
or more ranges of the integrant particles. 
This decrease may take place in various 
modes; and according to these, different 
figures of crystallization will be produced. 
Thus, to take the simplest example, let 
us suppose the primitive form is a cube ; it 
is easy to conceive, that on each of its six 
sides may be reared a series of decreasing 
layers, or laminae, composed entirely of 
cubical particles, each layer diminishing on 
each of its edges by one row of the minute 
cubes of w'hich it consists. The laminae 
thus decreasing as they recede from the 
base on which they rest, until the apex 
consists of a single particle, it is obvious, 
that on each side of the cube a four-sided 
pyramid will be formed. Two of these are 
represented, (fig. 12.) A BC D, G B C G. 
We shall thus have, then, six four-sided 
pyramids, and of course 24 triangles, such 
as A B C, BCE, C E G, &c. But since 
the decrease is uniform on all the sides, as 
from the line B C to A, and fiom the same 
line to E, it must also be uniform fi om A 
to E ; it is obvious, therefore, that the side 
A B C of the one pyramid will be found 
exactly in the same plane as the side BCE 
of the adjacent pyramid ; so that the entire 
surface of these will be the rhomb A B E C. 
The case must be the same with all the 
others. The 24 triangles will therefore 
be reduced to twelve rhombs, and the 
figure w'ill be a dodecaedron, very re- 
mote from the primitive form. Now a 
crystal of this figure, and having this primi- 
tive form, would be resolved into that form, 
merely by cutting oft' the six solid angles, 
by sections, in the direction of the small 
diagonals of the sides, which go to the for- 
mation of these angles. We .should thus 
successively uncover six squares, which will 
be the faces of the primitive cube. 
In explaining the structure of a crystal, 
although the representatiori in the figure bq 
