422 
CR YSTA’LL 
trapezoids will be reduced to elongated hexagons, which 
will intercept twelve rhombufes parallel to the faces of 
the nucleus. This is the variety to which is given the 
name of intermediary garnet.. In the fulphure of zinc the 
regular odfahedron refults from a decrement by a range 
around the eight folid angles, compofed of three planes, 
viz. C, B, O, G, F, D, A, I, fig. 43. The fame fubftance 
a Humes alfo the figure of a regular tetrahedron, by the 
help of a decrement by one range on four only of the 
eight folid angles before-mentioned, fuch as C, O, F, A. 
This tetrahedron is remarkable by its ftrudlure, which 
prefents an affemblage of other tetrahedra with ifofceles 
faces. 
Crystals, the Molecules of which are Triangular 
Phisms. 
•Oriental. —This appellation is given to a kind of 
gem known under the names of the ruby, fapphire, and 
oriental topaz, according as it is red, blue, or yellow. It 
is fo rare to find cryftals of this gem which do not exhi¬ 
bit marks of a precipitate formation, or which have not 
been rolled, that hitherto we have had no accurate de- 
feripfion of its different varieties, nor any precife indica¬ 
tion of the nature of the particular angles of each variety. 
The cryftals from which were drawn the following re¬ 
fults, were of a form fufficiently well characterized. 
1. Primitive Oriental. —It cryftallizes in the form of a 
regular hexahedral prifm divifible parallel to its bates. 
Theory points out other joinings, parallel to the planes, 
from which it follows, that the molecula is an equilate¬ 
ral triangular prifm. The height of this prifm, fuch as 
given by theoretic calculation, is a little lefs than three 
times the height of the triangle of the bafe. 
2. Elongated Oriental, fig. 47.— Geometrical Charaftcr. Re- 
fpeefive inclinations of the triangles I A S, IBS, i39°54'. 
Angles of the triangle I A S, A = 22 0 54', I or S =2 
This form is the effedf of a decrement by a fimple range 
of fmall quadrangular prifms on all the edges of the bales 
of the nucleus. Let q cl, fig. 42, be the fuperior bale, 
fubdivided into fmall triangles, which reprelent the ana¬ 
logous bafes of fo many moleculae. The edges of the 
laminae of fuperpofition will corrcfpond fucceffively to 
the hexagons h ilmnr, ek uxyv, See. from which it evi¬ 
dently follows, that the fubtradfions take place by ranges 
of fmall parallelopipedons or quadrangular prifms, com¬ 
pofed each of two triangular prifms. 
3. Minor Oriental.—Geometrical CharaBcr. Dodecahedron 
formed of two right pyramids lefs elongated than thofe 
of the preceding variety. The triangles which correfpond 
to I A S, IBS, are inclined to each other 122° 36'. In 
each of thefe triangles the angle of the fummit is 31 °, 
and each of the angles at the bafe is 74 0 30'. The law 
from which this variety refults differs from that which 
produces the preceding, as it determines a mixed de¬ 
crement by three ranges in breadth and two ranges in 
height. 
4. Enneagonal Oriental, fig. 48.— GeometricalCharaElcr. In¬ 
clination of each fmall triangle, fuch as cqi, to the adja¬ 
cent bafe a c ip l bg e d, 122 0 18'. 'It is the elongated 
oriental the fummits of which are replaced by two faces, 
parallel to the bafes of the nucleus, with the addition of 
lix fmall ifofceles triangles cqi, Ibf vzm. Sec. the three 
fuperior of which are alternate in pofition with the three 
inferior. Thefe triangles refult from a decrement by 
three ranges of fmall quadrangular prifms on the three 
angles of the fuperior bafe of the nucleus, fuch as b, d,g, 
fig. 42, and on the intermediate angles of the inferior 
bafe. It may be readily donceived, that in the decre¬ 
ment which takes place, for example, on the angle g, the 
thr 2 ranges, which remain unoccupied between that 
angle and the correfponding edge of the firft lamina of 
fuper 'ofition, are, 1 It, the fmall rhombus g 0 ip, which 
alone forms the firft range; 2d, the two rhombufes osti-, 
pz d i ■, 3d, the three rhombufes fituated on the fame line 
1 1 
OGRAPHYj 
behind the two preceding. Cryftals of the oriental are 
found particularly in the kingdom of Pegu. 
EXAMPLES of COMPOUND SECONDARY 
FORMS. 
Prismatic Calcareous Spar, fig. i.-— Spatk calcaire 
en prij'me hexaedre, Daubenton Tab. Miner, edit. 1792^.15, 
No. 6. De l’lfie Gryflallograplde, tom. i. p.514, var. 10. 
The bafes of this prifm are produced in confequende of 
a decrement by a fingle range on the angles of the fum¬ 
mit fbaf, g af bag, dex, dec, c c x, fig. 4, of the pri¬ 
mitive form. The fix planes refult from a decrement by 
two ranges on the angles b df fxg, beg, dfx, dbc, cgx, 
oppofite to the preceding. Let a b df, fig. 49, be the 
fame face of the nucleus as fig. 4. The decreafing edges 
fituated towards the angle of the fummit a will fuccef¬ 
fively correfpond with .the lines hi, k l, & c. and thofe 
which look towards the inferior angle d will have the 
pofitions pointed out by ran, op, &c. But, in confe- 
quence of the firft decrement taking place by one range, 
we prove that the face which refults from it is perpen¬ 
dicular to the axis; and calculation (hews, in the like 
manner, that the fecond decrement, which takes place by 
two ranges, produces planes parallel to the axis, and 
thus the lecondary folid is a regular henahedral prifm. 
To difplay farther the ftrudfure of this prifm, let 11s re¬ 
mark, that in the production of any one abenih, fig. 1, 
of the two bafes, we may confine ourfelves to confider 
the effedf of one only of the three decrements which take 
place around the folid angle a, fig. 4, for example, of 
that which takes place on the angle b af fuppofing that 
the laminae applied on the two other faces, fagx, bage, 
do not decreafe but to afiift the refult of the principal 
decrement, which takes place in regard to the angle baf 
But here thefe auxiliary decrements are altogether fimi- 
lar to that the effedf of which they are fuppofed to pro¬ 
long. The cafe will be totally different if we apply the 
fame obfervation to the decrements which are effedled 
by two ranges on the inferior angles b df, dfx, fxg, See. 
and which produce the fix planes of the prifm. For ex¬ 
ample, if wm confider the effedf of the decrement on the 
angle dfx, it is neceffary alfo that the laminae applied on 
the faces afdb, afxg, fig. 4, Ihould experience towards 
their lateral angles afd, afx, adjacent to the angle dfx , 
variations which fecond the effedf of the generating de¬ 
crement. But here thefe variations are intermediary de¬ 
crements by ranges of double moleculae. 
To conceive a better idea of thefe variations, let us re¬ 
fume the face abdf fig. 49. The variations in quefiion 
will take plaae parallel to the lines ce, rx,gz, vy, Sic. 
that is to fay, by one range of double moleculae, and in 
fuch a manner that there will always be two laminae on 
a level at their edges in the diredtion of the height. By 
this it is evident why the laminae taken from the prifm 
by the firft fedtions are trapeziums, fuch as plus, fig. i, 
in which the affortment of the fmall compofing rhom¬ 
bufes will be the fame as on the trapezium usop, fig. 49. 
We may in the like manner aflign the reafon of the dif¬ 
ferent figures through which the laminae, fucceffively de¬ 
tached, before arriving at the nucleus, are obliged to 
pafs. But this detail would lead us too far. Every thing 
is included in the effedf of the principal decrements: that 
is to fay, in the prefent cafe, of thofe which take place 
on the fuperior and inferior angles, or parallel to the ho¬ 
rizontal diagonals ; and after the firft lamina of fuperpo- 
fition, the figure of the cryftal is given according to this 
fingle condition, that the initial faces be prolonged fo' as 
to interfedf each other. 
The prifm is fufceptible of varying in the length of 
its axis compared with its thicknefs, which depends on 
the different epochs at which the decrements commence, 
or are fuppofed to commence. For example : if we fup- 
pofe that the decrement, which takes place towards the 
inferior angle, adts alone at firft on a certain number of 
laming; 
