CRYSTALL 
diere is alfo an affemblage of tetrahedra, but regular; 
that is to fay, the faces of which are equilateral trian¬ 
gles. Nay more, it is poffible that fimilar molecules may 
produce the fame cryftal line form by different laws of 
decrement. In fhort, calculation has condudfed me to 
another refult, which appeared to me ftill more re¬ 
markable, which is, that, in confequence of a fimple law of 
decrement, there may exifta cryftal which externally has 
a perfect refemblance to the nucleus, that is to lay, to 
a folid that does not arife from any law of decrement.” 
In what has been hitherto laid refpedting the decre¬ 
ments to which the lamina; of fuperpofition are fub- 
jefted, the only view has been to unfold the laws of 
flrudture. It has not been meant to afl'ert that, in the 
formation of a dodecahedral cryftal, or one of any other 
form having a cube for nucleus, the cryftallization has 
originally produced that nucleus, fuch as it is extradted 
from the dodecahedron, and made it afterwards pafs to 
the figure of that dodecahedron, by the fucceflive ap¬ 
plication of all the laminae of fuperpofition by which it 
is covered. On the contrary, it feems proved, that 
from the firft the cryftal is a very fmall dodecahedron, 
containing a cubical nucleus proportioned to its fmall 
fize, and that the cryftal afterwards increafes by de¬ 
grees without changing its form, by new layers which' 
envelop it on all fides, fo that the nucleus increafes 
alfo, always preferving the fame relation with the 
whole dodecahedron. 
This theory fets out from a principal fadl:, on which 
it makes all fadts of the fame kind to depend, and 
which are only as it were corollaries. This fadt is the 
decrement of the laminae fuperadded to the primitive 
form ; and it is by bringing back this decrement to 
fimple and regular laws, fulceptible of accurate calcu¬ 
lation, that theory arrives at refults, the truth of which 
is proved by the mechanical divilion of cryftals, and by 
obfervation of their angles. But there (fill remain new 
researches to be made, in order to afcend* a few fteps 
farther towards the primitive laws to which the Creator 
lias fubjedted cryftallization ; and which are nothing 
elfe themfelves than the immediate eifedts of his fu- 
preme will. The objedt of one of thele reiearches 
would be to explain how thele fmall polyhedra, which 
are, as it were, the rudiments of cryftaU of a l'enfible 
bulk, reprefent fometimes the primitive form without 
'any modification ; fometimes a lecondary form produced 
in virtue of a law of decrement; and to determine the 
circumftances which produce decrements on the edges, 
and thofe which give rife to decrements on the angles. 
Such is the theory by which Mr. Hauy explains the 
various cryftalline forms of the fame ful (lance. This 
theory, to fay no more of it, is, in point of ingenuity, in¬ 
ferior to few ; and the mathematical fkiil and induftry 
of ics author are entitled to the greateft applaufe. Bur 
' what we conlider as the moft important part of that 
phil.ofopher’s labours, is the method which they point 
out of difeovering the figure of the integrant particles 
.of cryftals ; becaule it may pave the way.for calculating 
the affinities of bodies, which is certainly a desideratum 
in chemiilry. This part of the fubjedt, therefore, de- 
ferves to be invelligated with the greateft care. 
■ Mr. Hauy found, that the primitive form of all the 
cryftals which lie examined may Le reduced to fix ; 
i. The parallelopipedon in general, comprehending the 
cube, the rhomboid, and all lolids terminated by fix 
fides, parallel two and two ; 2. The regular tetrahedron ; 
3. The octahedron with triangular fides ; 4. The hex¬ 
agonal prifin ; 5. Tire dodecahedron bounded by 
rhorpbs ; 6. The dodecahedron bounded by ifofceles' 
triangles. Were we to fuppofe that tliefe primitive 
forms are exactly fimilar to the form of tiie integrant 
particles : 'wjtuch corn pole them, it would follow, that 
the integrant partu !es of all the cryftals hitherto formed 
have oniy fix different forms. This fuppolition, how- 
4 
OGRAPHY. 419 
ever, is not probable ; becaufe the fame nucleus has 
been difeovered in different fpecies of minerals, and be¬ 
caufe we can eafily conceive integrant particles of diffe¬ 
rent forms combining in fuch a manner as to compofe 
nuclei of the fame figure, juft as we have feen that dif¬ 
ferent primitive forms are capable of producing the fame 
fecondary form. Still, therefore, in endeavouring to 
difeover the integrant particles of bodies, there are dif¬ 
ficulties to remove, which hitherto, at lead, have been 
infurmountable. But the theory of Mr. Hauy may be 
cpnfidered as a firft ftep towards the difeovery, and a 
Jiep in refearches of fo difficult a nature is of very great 
confequence. 
Examples of Primitive Forms. 
The primitive form is that obtained by feftions made 
on all the fimilan parts of the fecondary cryftal ; and 
tliefe feftions, continued parallel to themfelves, condudt 
to a determination of the form of the integral molecule, 
of which the whole cryftal is an affemblage. This re¬ 
quires certain confiderations that relate to the moft de¬ 
licate point of the theory, which we lliall now explain. 
There is no cryftal from which a nucleus in the form 
of a parallelopipedon may not be extracted, if we con¬ 
fine ourfelves to fix feCtions, parallel two and two. In a 
multitude of fubftances this parallelopipedon is the Lift 
term of the mechanical divilion, and confequently the 
real nucleus. But there are certain minerals where this 
parallelopipedon is divilible, as well as the reft of the 
cryftal, by farther feCtions made in the different direc¬ 
tions of the faces ; and there thence neceffarily refults a 
new folid, which will be the nucleus, if all the parts of 
the fecondary cryftal, fuperadded to this nucleus, are 
fimilarly fituated. When the mechanical divilion con¬ 
ducts to a parallelopipedon, divilible only by fections 
parallel to its fix faces, the molecuhe are parallelopipe- 
dons fimilar to the nucleus ; but, in all other cafes, their 
form differs from that of the nucleus. 
Let achsuo, fig. 35, be a cube, having two' of its 
folid angles a, s, fituated on the fame vertical line.' 
This line will be the axis of the cube ; and the points a 
and s will be its fummits. Suppofe this cube to be divi- 
fible by leCtions, each of which, fuch as a/m, paffes 
through one of the fummits a , and by two oblique dia¬ 
gonals ah, an, contiguous to this fummit. This feCtion 
will detach the l'olid angle i; and as there are fix folid 
angles, fituated laterally, viz. i, h, c, r, 0, n, the fix fec¬ 
tions will produce an acute rhomboid, the fummits of 
which will be confounded with thofe of the cube. 
Fig. 36 reprefents this rhomboid exifting in the cube, 
in fuch a manner that its fix lateral folid angles, b , d,J, 
p, g, j 'e, correfpond to the middle of the faces achi, 
ersh, bins, &c. of the cube. But geometry fhews that 
each of the angles, at the fummits bag, dsf psf, See. 
of the acute rhomboid, are equal to 60", from which it 
follows that the lateral angles abf, agf. Si c. are equal 
to 120 degrees. Befides, it is proved by theory, that 
the cube refults from a decrement which takes place by 
a lingle range of fmall rhomboids, fimilar to the acute 
rhomboid, on the fix oblique ridges ah, ag, ae, sd, sf, 
sp. This decrement produces two faces, one on each 
fide of each of thele ridges, which makes in all twelve 
faces. But as the two faces, which have the fame ridge 
lor their line of departure, are on the fame plane by the 
nature of the decrement, the twelve faces.,will be re¬ 
duced to .fix, which are legumes ; fo that the lecondary 
folid is a cube. This refult is analogous to that of the 
very obtufe calcareous fpar before-mentioned. 
Let us now fuppofe that the cube, fig. 35, admits, in 
regard to its fummits a, s , two new diviiioqs fimilar to 
the preceding fix, that is to lay, one of which pail'es 
through the points c, i, 0, and the other through the 
points h, n, r. The firft will,pals alfo through the points 
h,g, c, and the fecond through the points d.,f,p, fig. 36 
