CRYSTALLOGRAPHY. 
mity of the edges lf,dc,bm, readily yield 
to this division by a knife stnick in the pro- 
per direction ; but that the other three, those 
which are intermediate, fd,ch, and m I, 
cannot be divided in a similar manner ; and 
if broken by a greater force, the fracture, 
instead of being polished like the others, 
is rugged and uneven. If we repeat the 
experiments at the under extremity of the 
prism, we shall find here also that segments 
of three only of the edges can be detached ; 
but these edges, instead of being the cor- 
responding one with those devisable at the 
upper extremity, that is, lf,cd,hm, are 
the intermediate ones f d, c d, b m, are the 
intermediate ones df, c b, and m 1. 
The six divisions compose so many tra- 
peziums. Three of these are represented 
in fig. 6, namely, the two which cut off 
the edges If, c d represented by the dotted 
lines pp, o o and a a, k k, and that which 
cuts off the inferior edge df, and which 
is marked by the dotted lines nn, ii. 
Each of these trapeziums will have a 
smoothness and lustre, from which it can be 
perceived, that it coincides with one of the 
natural joinings, the assemblage of which 
form the prism. The prism cannot be di- 
vided in any other directions than these. 
But if the division be continued parallel to 
the first segments, it necessarily happens, 
that on one hand the surfaces of the bases 
of the prism become narrower, and that 
on the other hand the heights of the sides 
diminish; and at the point at which con- 
tinuing the section, the bases disappear, the 
prism will be changed into a dodecaedron, 
with pentagonal faces (fig. 7) ; six of which, 
ooiOe,olkii,&c.are the remains of the 
sides of the prism, and the other six, E A 
loo, OA Kii, &c. are the immediate re- 
sults of the mechanical division. 
In this, and the two succeeding figures, 
the hexaedral prism, which circumscribes 
the solid extracted from it in the division, 
is stilt represented to shew better the pro- 
gress of the operation. 
Beyond this point, the planes at the ex- 
tremity preserve their figure and dimen- 
sions, while the lateral planes continue to 
diminish in height, until tlie points o, k of 
the pentagon olkii coinciding with the 
points i, i, and also the other points simi- 
larly situated having a like coincidence, 
each pentagon is reduced to a simple tri- 
angle, as is represented in fig. 8. 
Lastly, by continuing the section the 
triangles are made to disappear, so that 
there remains no vestige of the surface of 
the original prism ; but in place of it we 
have the obtuse rhomboid E A I O (fig. 9), 
which is therefore the nucleus, or primitive 
form. 
This discovery of the method of dividing 
a crystal was made by Hauy, in examin- 
ing a crystal of calcareous spar which had 
been detached from a group of which it 
formed a part. He observed that the frac- 
ture had happened at one of the edges of 
the base of the prism, and that its surface 
was perfectly smooth and regular. At- 
tempting to detach a segment in a similar 
direction from the contiguous edge, he 
could not succeed, but the one next to it 
was easily divided ; and proceeding in this 
manner, he was able to effect the mecha- 
nical division of the crystal in the manner 
already explained. Struck witli the impor- 
tant result of the experiment, he applied 
tlie same method to other crystalline forms 
of the same substance, and obtained from 
them the same result ; the crystal, whatr 
ever was its figure, being by this mechani- 
cal division converted into a rhomb. Thas 
in the dodecaedron, composed of two six- 
sided pyramids Joined by the base, the pri- 
mitive form may be obtained at once by 
making a first section, on the edges E O, 
O I, fig. 10 ; a second, on the edges I K, 
G K ; a third, on G H, EH; a fourth, on 
O I, I K ; a fifth, on G K, G H ; and lastly, 
a sixth, on E H, E O ; and the result is, that 
these edges become the same with the la- 
teral edges of the primitive form, as may 
be perceived from mere inspection of fig. 11, 
which represents this primitive form des- 
cribed in the dodecaedron. He then ap- 
plied it to other crystalline substances, and 
found, that from these also, by discovering 
the joints by which the laminae composing 
the crystals were united, a certain primi- 
tive form might be extracted. That of 
fluor spar, is an octaedron ; and that of the 
heavy spar, a prism with rhomboidal bases ; 
of corundum, a rhomboid somewhat acute ; 
of beryl, a hexaedral prism ; and of the 
elba iron-oar, a cube. Each of these forms 
is constant with regard to the species, and 
is that from which all the forms of the va- 
rieties, often extremely numerous, are de- 
rived. The latter are denominated by 
Hauy, secondary forms. Sometimes, though 
rarely, the primitive and secondary forms 
are the same. 
It is not every crystallized substance, 
however, that admits of this mechanical 
analysis. But with regard to those that 
have lutherto refused it, Hauy has re- 
