CRYSTALL 
lamina, the axis of the cryftal will be fo much the 
longer as the commencement of the decrement on the 
fuperior angles fhall have been retarded. This difference 
of epochs becomes fenfible by infpeCting the dodecahe¬ 
dron, fig. 2, which is one of the refults of the mechani¬ 
cal divifion of the prifm. It is there feen that the pen¬ 
tagonal laminae, of the fummits, fuch as AOIRS, de- 
creafe only by their edge R S, which correfponds to the 
inferior angle b df fig. 4, while, by their upper parts, 
they continue to envelop the cryftal without experienc¬ 
ing any decrement towards that fide ; fo that it is only 
on the laminae mod diftant from the axis, as that corre- 
fponding to p su l, that the two decrements take place at 
the fame time. The refult which we have explained is 
general; that is to fay, that, whatever may be the angles 
of the primitive rhomboid, the fecondary folid will al¬ 
ways be a regular hexahedral prifm. 
Amphitrigonous Iron Ore. — Fig. 50 reprefents 
this cryftal in a horizontal projection, and fig. 51 in per- 
fpective. Mine de fcr a faces, Daub, and De l’lfle. 
Geometrical CharaQer. RefpeCtive inclination of the tri¬ 
angles gen, ged, See. from the fame fummit 146° 26' 33“; 
of the lateral triangles bgu, bgq, to the adjacent penta¬ 
gons., fuch as gutmn, iS4°45'39 w - 
This form is that under which the iron ore of the ifland 
of Elba rnoft commonly appears. It refults from a de¬ 
crement by two ranges on the angles, to the fummits of 
a cubic nucleus which produces the ifofceles triangles 
gen, ged, ned, fig." 50 and 51, and of a fecond decrement 
by three ranges on the lateral angles cbp, crp, ers, See. 
which produce the triangles mnr, rnk, ugb, qgb,Scc. 
Thefe two decrements ftop at a certain term, fo that there 
remain faces parallel to thofe of the nucleus, viz. the 
pentagons gutmn, k dn k l. See. fig. 50. 
The firft decrement is the fame as that which pro¬ 
duces the rhomboidal iron ore. The fecond has this 
property, that, if its effeCts were complete, it would give 
a dodecahedron of ifofceles triangles, or compofed of two 
right pyramids united at their bafes. In the cafe of any 
other decrement by two, four, or more, ranges, the faces 
of the dodecahedron would be fealene triangles. The 
triangles of the fummits are frequently furrowed by ftrise, 
parallel to the bafes gn, dn, gd, of thefe triangles, and 
which point out the direction of the decrement. 
Analogical Calcareous Spar, fig. 52.— Geometri¬ 
cal Character. Inclination of any one imeh, of the trape¬ 
zoids of the fummits to the correfponding vertical trape¬ 
zoid ecpg 116 0 33' 54"; angles of the fame trapezoid, 
i — 114 0 18' 56"; e =2 75° 31' 20"; m or k S5 0 4' 52". 
Angles of the trapezoid eh og, e—yc?-, 0— 127 0 25' 53"; 
g = 67°47' 44"; h — 74°46' 23"; of the trapezoid cegp, 
e=6o°; p— 98° 12'46"; c or g 100° 53' 37". 
Geometrical Properties. 1. In each vertical trapezoid the 
triangle ceg is equilateral. 2. The height ex of this tri¬ 
angle is double the height p x of the oppofite triangle 
cpg. 3. In the trapezoid eh 0g and the others fimilarly 
fituated, the angle keg is a right angle. 4. If the diago¬ 
nal gh be drawn, the triangle heg will be fimilar to any 
one a of, fig. 4, of thofe which would be produced by 
drawing, in the primitive rhombus, the two diagonals bf 
ad. 5. If in the trapezoid emi h, or any other fituated 
at the fummits, the diagonals ei, mh, be drawn, the height 
e l of the inferior triangle me k will be double the height 
il of the fuperior triangle m. ih. 6 . The triangle m ih is 
fimilar to half of the rhombus of very obtufe fpar, di¬ 
vided by the horizontal diagonal; and the triangle meh 
is fimilar to half of the rhombus of the acute (par, di¬ 
vided in the fame manner. 
The numerous analogies by which this variety is con¬ 
nected with different cryftalline forms, whether we con- 
fider certain angles formed by planes, as the angle h eg 
of 9b 0 , the angle ceg of 6o°, or certain triangles obtained 
by drawing the diagonals of the trapezoids, have induced 
the name of analogicalfpar. It is derived from three other 
varieties, viz. very obtufe fpar by the trapezpids t in ih. 
O G R A P H Y. 423 
fiht, Sec. metaftatic fpar by the trapezoids emdc, ehog, 
olit.z, Sec. and the prifmatic fpar by the trapezoids bdek, 
cegp, See. which are confequently parallel to the axis. 
It often happens that the trapezoids ivi e li, f i h f; See. 
are feparated, by an intermediary ridge, from tlie verti¬ 
cal trapezoids cegp, go zr, Sec. In that cafe the trape¬ 
zoids edme, geko, See. are changed into pentagons. It is 
here fuppofed that the cryftal is brought back to the moil 
fyrnmemc figure, that is to fay, having-its furface com¬ 
pofed only of quadrilaterals,- as fometimes happens. This 
variety is found in Derbylhire. 
Icosahedral Sulphure of Iron, fig. 53.— Pyrite. 
ferrugineitfe polyedra a vingt faces triangulaires, Daub, and 
De l’lfie.— Geometrical CharaEler. RelpeCtive inclinations 
of the ifofceles triangles P L R, PSR, i26°52'n"; of 
any one PN L of the equilateral triangles, to each adja¬ 
cent ifofceles triangle PT. R or L N K 140° 46' 17". An¬ 
gles of the ifofceles triangle PLR, L 2= 48° 11'.20"; P 
or R — 65° 54' 20". 
This variety refults from a combination of the law 
which produces the octahedron originating from a cube, 
with that which takes place for the dodecahedron with 
pentagonal planes. The firft law gives birth to the eight 
equilateral triangles which correfpond with the folid an¬ 
gles of the nucleus, and the fecond to twelve ifofceles tri¬ 
angles, fituated, two and two, above the fix faces of the 
fame nucleus. The icofahedron of the fulphure of iron 
has been confounded with the regular icofahedron of geo¬ 
metry, which differs from it very fenfibly, fince all its 
triangles are equilateral. It is demonftrated by theory, 
that the exiftence of the latter icofahedron is as impof- 
fible in mineralogy as that of the dodecahedron; fo that 
among the five regular polyhedra of geometry, viz. the 
cube, the tetrahedron, the octahedron, the dodecahe¬ 
dron, and the icofahedron, the three former only can 
cxift-there, in confequence of the laws of cryftallization. 
It is not uncommon, therefore, to find them among cryftals 
of various kinds of minerals. The icofahedron of the 
fulphure of iron is much lefs common than the dodeca¬ 
hedron. It is found in folitary cryftals. 
Polynomous Petunze', or Feld-spath, fig. 54.-— 
Spat/i etincelant ou fcldfpatk en prifme a dix pans avec des 
J'ommcts a. deux faces,et quatre faccttes, Daub. Gcomet. CAa- 
ra£l. RefpeCtive inclination of tire narrow planes onkm , 
c fhg, to the adjacent planes on each fide, 150°; of the 
planes ctFg, Po??zN, to thofe contiguous to them by the 
edgestF, PN, 120°; of the heptagon pGcldez to the 
enneagon BzebnoPrs, 99° 41'8"; of the trapezium 
dafe both to the plane nbafliilk and to the heptagon 
pGtcdez, 135 0 ; of the facet deab or A Bzp to the 
fame heptagon, 124“ 15' 15". 
This form, fuch as it is given by the mechanical divi¬ 
fion of fecondary cryftals, is that of an oblique prifm of 
four planes, fig. 56, two of which, fuch as GOAD, 
RBHN, are perpendicular to the bafes A D NH, 
OGRB. The other two, viz. BOAH, RGDN, 
make, with the former, angles of 120° at the ridges O A, 
RN, and angles ot 6o° towards the oppofite ridges B H, 
G D. Theie planes are inclined to the bafes at the 
place of the ridges GO, BR, in" 29' 43", and at the 
oppofite ridges 68° 30' 17". This form is at the fame 
time that of the moleculas. Theory (hews that the two 
parallelograms GOAD, OGRB, as well as their pa¬ 
rallels, are equal in extent; and that the parallelogram 
BOAH, or its oppofite, R GD N, is double each of the 
preceding ; which may ferve to explain the roughnefs 
of the feCtions made in the direction BOAH, when 
compared with thofe obtained in the directions of thq 
(mail parallelograms, and which are always extremely 
fmooth and brilliant. Moreover, if the diagonal OR 
be drawn, it will be found perpendicular to O A and 
RN; or, what amount? to the fame, will be fituated 
horizontally, by (uppofing that the ridges O A, BH, 
See. have a vertical pofition. 
The polynomous petunze prefents the mod compli, 
cated. 
