CRYSTALLOGRAPHY. 
415 
stfcribed it to the forms of the particles themfelves; and 
this Teems to be the real folution of the problem. For, 
fuppofing that all particles have the fame form, they 
muft of courfe pofiefs the fame polarity; and therefore 
every cryftal muft have the fame form. It is impoftible, 
then, to account for the different forms of cryftals, with¬ 
out fuppofing that the particles which compofe them 
have alfo different forms. And if the particles of bodies 
have different forms, their regular aggregation muft pro¬ 
duce cryftals of various ftiapes ; and therefore their po¬ 
larity, which is merely a fuppofition founded on this 
difference in the appearance of cryftals, cannot be ad¬ 
mitted. Suppofe, for inftance, that eight cubic parti¬ 
cles were regularly arranged in water, and that by the 
gradual evaporation of the liquid were to approach, and 
at laft to combine, it is evident that the cryftal which 
they would produce would be a cube. Eight fix-fided 
prifms would alfo produce a fix-fided prifm: and eight 
tetrahedrons would form a very different figure. But it 
will be afked, if the figure of cryftals depends entirely 
upon the form of the particles that compofe them, how 
comes it that the fame fubftance does not always cryltal- 
lize in the fame way, but prefents often fuch a variety of 
forms, that it is fcarcely poflible to reckon them > We 
anfwer, that thefe various forms are fometimes owing to 
variations in the ingredients which compofe the inte¬ 
grant particles of any particular body. Alum, for in¬ 
ftance, cryftallizes in octahedrons; but when a quantity 
of alumina is added, it cryftallizes in cubes; and when 
there is an excefs of alumina it does not cryftallize at all. 
If the proportion of alumina varies between that which 
produces octahedrons and what produces cubic cryftals, 
the cryftals become figures with fourteen (ides; fix of 
which are parallel to thofe of the cube, and eight to 
thofe of the oCtahedron ; and, according as the propor¬ 
tions approach nearer to thofe which form cubes or octa¬ 
hedrons, the cryftals aft time more or lefs of the form of 
cubes or octahedrons. What is ftill more, if a cubic 
cryftal of alum be put into a folution that would afford 
octahedral cryftals,, it paffes into an odtahedron: and, on 
the other hand, an octahedral cryftal put into a folution 
that would afford cubic cryftals, becomes itfelf a cube. 
It is known that cubes of fab-ammoniac and oCtahedraof 
marine fait have been found in urine. (See Chemistry, 
vol. iv. p. 365.) But whence happens it that marine 
fait cryftallizes in oCtahedra, and not in cubes, and that 
fal-ammoniac cryftallizes in cubes, and not in oCtahedra? 
Fourcroy is of opinion, that thefe forms are owing to 
the prefence of uric. This he proves by the following 
experiment: Marine fait, or muriat of foda, exceedingly 
pure and in perfedt cubes, having nothing in common 
with human urine, to which it never belonged, lince it 
arofe from fpring-water evaporated, was difl'olved, with 
an equal part of cryftallized uric , in five times its weight 
of diftilled water. The folution was put into a porce¬ 
lain capfule, which was covered with paper to prevent 
the accefs of foreign bodies, and was left to fpontaneous 
evaporation. In a few weeks there were formed octahe¬ 
dral cryftals exceedingly regular, and of a reddifti brown 
colour. Sal-ammoniac, or muriat of ammonia, treated 
in the fame manner, cryftallized in cubes, though it 
Cryftallizes in general in odlahedra. “ It is a fad then, 
fully proved,” fays he, “that uric, diffolved in the fame 
water as the two falts above-mentioned, modifies and re¬ 
veries their natural form by combining with each of 
them, and by penetrating the laminae of their cryftals. 
To it, therefore, is due the odahedral form affumed by 
marine fait, with which human urine has been faturated.” 
Another circumftance which contributes much to vary 
the form of cryftals, is the different degree of concentra¬ 
tion to which their folution has been reduced, and the 
rapidity or flownefs with which they are formed. For it 
is too evident to require illuftration, that when cryftals 
are depofited very rapidly they muft obftrud one ano¬ 
ther,, and mix together fo as very much to obfeure the 
natural regularity of their form. But, independent of 
thefe accidental circumftances, Mr. Hauy has fhewn that 
every particular fpecies of cryftals has a primitive figure, 
and that the variations are owing to the different ways in 
which the particles arrange themfelves. Of this theory, 
which is exceedingly ingenious, and very futisfadlory, wei 
ft)all give the following view. 
Happening to take up an hexangular prifm of calcare¬ 
ous fpar, or carbonat of lime, which had been detached 
from a group of the fame kind of cryftals, he obferved 
that a fmall portion of the cryftal was wanting, and that 
the fracture prefented a very frnooth furface. Let abode 
fgh, in the Cryftallography Plate I. fig. 1, be the cryftal; 
the fradture lay obliquely as the trapezium psut, and 
made an angle of 135°, both with the remainder of the 
bafe abespk and with fury, the remainder of the fide 
inef. O'oferving that the fegment psut in thus cut off 
had for its vertex in, one of the edges of the bafe abenih 
of the prifm, he attempted to detach a fimilar fegment 
in the part to which the next edge cn belonged, employed 
for that purpofe the blade of a knife, directed in the fame 
degree of obliquity as the trapezium psut, and affifted 
by the ftrokes of a hammer. He could not fucceed : but, 
upon making the attempt upon the next edge b c, he de¬ 
tached another fegment, precifely fimilar to the firft, and 
which had for its vertex the edge be. He could produce 
no effedt on the next edge ap- but from the next follow¬ 
ing, ah, he cut a fegment fimilar to the other two. The 
fixth edge likewife proved refradtory. He then went to 
the other bafe of the prifm defghr, and found, that 
the edges which admitted fedtions fimilar to the preced¬ 
ing ones were not the edges cf, dr, g k, correfponding 
with thofe which had been found diviliblc at the oppo- 
fite bafe, but the intermediate edges dc, hr, gf. The 
trapezium Iqyv reprefe'nts the fedtion of the fegment, 
which had kr for its vertex. This fedtion was evidently 
parallel to the fedtion p s u t ; and the other four fedtions 
were alfo parallel two and two; Thefe fedtions were, 
without doubt, the natural joinings of the layers of the 
cryftal. And he eafily fucceeded in making others pa¬ 
rallel to them, without its being poflible for him to di¬ 
vide the cryftal in any other direction. In this manner 
he detached layer after layer, approaching always nearer 
and nearer the axis of the prifm, till at laft the bales dif- 
appeared altogether, and the prifm was converted into a 
folid, O X, fig. 2, terminated by twelve pentagons, pa¬ 
rallel two and two; of which thofe at the extremities, 
that is to fay, ASRIO, IGEDO, BAODC, at one 
end.andFKNPQ^MNPXU, ZQPXY, at the other, 
were the refults of mechanical divifion, and had their 
common vertices O, P, fituated at the center of the 
.bafesofthe original prifm. The fix lateral pentagons 
RSUXY, ZYRIG, &c. were the remains of the fix 
fides of the original prifm. 
By continuing fedtions parallel to the former ones, the 
lateral pentagons diminifhed in length ; and at laft the 
points R, G, coinciding with the points Y, Z, the points 
S, R, with the points U, Y, &c. there remained nothing 
of the lateral pentagons but the triangles YI Z, UXY, 
&c. fig. 3. By continuing the fame fedtions, thefe tri¬ 
angles at laft difappeared, and the prifm was converted 
into the rhomboid ae, fig. 4. So unexpedted a refult in¬ 
duced him to make the fame attempt upon more of thefe 
cryftals; and he found that all of them could be reduced 
to fimilar rhomboids. He found alfo, that the cryftals 
of other fubftances could be reduced in the fame man¬ 
ner to certain primitive forms ; always the fame in the 
fame fubftances, but every fubftance having its own pe¬ 
culiar form. The primitive form of fluat of lime, for 
inftance, was an odtahedron; of fulphat of barytes, a 
prifm with rhomboidal bales ; of field-fpath, an oblique 
angled parallelopiped, but not rhomboidal; of adamant¬ 
ine fpar, a rhomboid, fomewhat acute; of blende, a do¬ 
decahedron, with rhomboidal fides ^ and fo on. Thefe 
muft therefore be confidered as the real primitive forms of 
the 
