Elements of crystallography after the method of Haüy : with, or without, series of geometrical models, both solid and dissected; exhibiting the forms of crystals, their geometrical structure, dissections, and general laws. According to which the immense variety of actually existing crystals are produced

Lrl*

• 55U

/z. rx. oc»o / 3i~?

ELEMENTS

OF

CRYSTALLOGRAPHY,

AFTER THE METHOD OF HAUY;

WITH, OR WITHOUT,

^etie0 of (Scometrjcal ^oDel0,

BOTH

SOLID AND DISSECTED ;

EXHfBlTlNG THE FORMS OF CRYSTALS, THEIR GEOMETRICAL
STRUCTURE, DISSECTIONS, AND GENERAL LAWS.

ACCORDING TO WHICH THR

IMMENSE VARIETY OF ACTUALLY EXISTING CRYSTALS
ARE PRODUCED.

By FREDRICK ACCUM,

OPERATIVE CHEMIST,

LECTURER ON PRACTICAL CHEMISTRY, ON MINERALOGY, AND ON CHEMISTRY
APPLIED TO THE ARTS AND MANUFACTURES J MEMBER OF THE ROYAI.
IRISH ACADEMY, FELLOW OF THE L1NN,>EAN SOCIETY, ^C.

WITH COPPEH-ELATES.

ItonOoii:

PRINTED FOR LONGMAN, HURST, REES, ORMK, AND BROWN
PATERNOSTER-ROW.

1813.

TO HIS EXCELLENCY

COUNT MUNSTER MEINHOVEL,

aiS afAJESTY*S SflNISTEH OF STATE: FOR THJE ELECTORATE OF
HANOVER; COMMISSIONER OF HIS MAJESTY^S PROPERTY,

TO THE RIGHT HONOURABLE

SIR JOHN BORLASE WARREN,

baronet; knight companion of the most honourable

ORl>ER OF THE BATH, MEMBER OF THE KING’s MOST

honourable privy council,

ADMIRAL OF THE BLUE,

commander in chief of his majesty's fleet, on the

NORTH AMERICAN STATION, &C- &C,

AND TO

SIR JOHN SAUNDERS SEBRIGHT,

baronet; representative in parliament for the county

OF HERTFORD, fifC* &C,

MY LORD,

AND

GENTLEMEN,

Permit me to offer to your Notice this
Treatise, containing the Elements of a Depart¬
ment of Mineralogy, which embraces the Sub¬
ject of one of the Courses of Lectures I had
the honour to deliver to you.

VI

DEDICATION.

The Ardour and Interest you have on all
Occasions shewn, for promoting' the Philosophy
of Chemistry and the Science of Minerals,
encourage me to make this Claim upon your
Patronage; and T am confident you will allow
me to add, that a respect for your Talents and
intellectual Virtues, is among the leading Mo¬
tives for my present A{)plication.

I have the honour to be, with the highest
respect.

My Lord,
and

Gentlemen,

Your most obedient humble Servant,

THE AUTHOR.

PREFACE.

Compton Street^ Soho.

Our earnestness in the pursuit of any study
is, in general, proportionate to the benefits or
pleasure we expect to derive from its cultiva¬
tion ; for where there is a prospect of recom-
pence in any rational way, we engage in literary
pursuits with ardour and spirit; but where there
is no such prospect, the mind is seldom active
in its exertion.

PREFACE.

Tiii

Hence the different points of \iew under
which natural bodies, and the phenomena they
present, may be studied, have given rise to
various departniewts of learning j and these have
been multiplied as the progress of mental im¬
provement, has added new sources of informa¬
tion to the sciences already established.

The general attention which of late years has
been paid to the science of minerals, cannot
have escaped the notice of the most superficial
observer.

No department of Natural History has been
cultivated with more ardour and success than
mineralogy; no branch of physical knowledge
has become more fashionable; and in none are
the votaries of science more numerous, both at
home and on the Continent.

PREFACE,

IX

It embraces a wide circle among the curious
and wealthy classes of the community; and it
is intimately connected with that enthusiasm for
travelling, and prevailing passion for exploring
the productions of nature, which characterize the
age in which we live.

When we consider how much the philoso¬
phy of the mineral kingdom has of late been
advanced and perfected, by the application of
the Theory of Crystallography, created by the
genius and industry of the Abbe Haiiy; when
we contemplate the strong and steady light
it has thrown on some of the most obscure
branches of Mineralogy,—it appears surprising
that not a single English work on the Theory
of the Structure and formation of Crystals has
appeared; whilst upon other departments of the

i

X

PREFACE.

’ science of Minerals^ several excellent works have
been published.

To remedy this defect, is the object of the
following pages.

The Treatise now presented to the tribunal
of the public, is designed, for the purpose
of initiating into the Principles of Crystallo¬
graphy, those who possess no previous know¬
ledge of it.

To accomplish this object, I have given such
an exposition of the leading facts of the Theory
as appeared best calculated to interest the mind,
and fix the doctrine in the memory, in all the
characters it is justly entitled to. I was well
aware that an attempt to exhibit the Doctrine
of Crystallography, in its whole extent, and
with all its numerous mathematical relations,

XI

PREFACE.

was an enterprise beyond my power; neither
was this the subject on which I intended to
write.

I have contented myself on the present occa¬
sion to attend merely to the development of
the general principles of the theory, and such
consequences and applications as are connected
with the science of minerals.

As it is certain however that the doctrine which
explains the production of crystalline forms, and
their metamorphoses, abounds in mathematical
and algebraic calculations, and cannot be studied
with ease and success, by such as are unac¬
quainted with the mathematics; I have, (to ren-

/

der this Treatise more generally useful) made
arrangements to accompany it with sets of

/

geometrical models, partly solid and partly dis¬
sected.

They who are in the habit of teaching, will
readily allow, that the human mind receives in¬
formation from the mathematics, with much
greater facility from demonstrations afforded by
tangible solids, than from mere designs drawn up¬
on a plane surface. It requires an eye familiarized
with the rules gf lineal perspective, to compre¬
hend the diversified and often complicated fornis
of angular polyhedra, represented by projections
of straight lines only, which must naturally cross
each other in many directions, in the representa¬
tion of crystalline bodies.

The dissected Models, are so constructed, that
they can readily be taken to pieces, and built up

PREFACE-

xm

again in various ways, to give the untutored
eye a distinct conception of the laws of that
geometry of nature which are followed by the
integrant particles of crystallisable bodies when
they combine, and of which the orderly arrange¬
ments produce symmetrical crystals^—and this
in fact constitutes the science.

It is therefore presumed, that'with the book in

hand, and by inspection of the Models, those who

s

are actually unacquainted with the mathematics,
will be enabled to .study with gi'eat advan¬
tage the Laws of Crystallography, and their
mutual relations and consequences. The student
will immediately comprehend why crystals are
always rectilineal bodies bounded by planes
and solid angles j and whence that immense
varietjf of polyhedral forms is derived, with

f

PREFACE.

xir

which the mineral kingdom has hitherto astonish*
ed the world.

It is nevertheless presumed, that the Trea¬
tise, as far as it goes, will be found complete,
and may be clearly understood without the
Models.

The numerous wood-cuts and plates in-

troduced into the work, in illustration of the

laws of the science, will render the geometrical
6

solids, superfluous to those who are familiar
with geometry and lineal perspective.

The graphic designs have been traced by
the method of projections; the entire lines re¬
present the edges or outlines of that part of
the solid immediately turned towards the ob¬
server.; and the dotted lines express tho.se
edges in the opposite part, which of course

PREFACE.

XT

the observer could not see, unless the solid was
diaphanous.

By giving this information of my intention to
supply the public with series of crystallographic
Models, I feel no solicitude as to any imputation
of private or commercial views; such attempts
are fully consistent witli the purest regard to
the public welfare. Conscious that the ad¬
vancement of science must greyly depend on
the facility with which the practical means of
study can be acquired: the reader will, I have
no doubt, think himself accommodated by being
reminded of it.

FREDRICK ACCUM.

CONTENTS

JfACi

Dedication.. , * , . t

Preface rii

List of Crystallographic Models referred to in
the Work xllii

List of Models illustrative of CrystaUography,
exhibiting the Primitive Forms of actually ex¬
isting Crystals^ and their Transitions, or Modi-
fications of Forma.liii

PART .1.

SECTION L

[ Page 1. ]

JDelinition of the Term Crystal—Nature of CrystalUsa'
tion-^-Disposition of crystallisahle Materials to as^

b

XVUl

CONTEXTS.

surae certain Forms peculiar to them in preference
to others—Symmetrical arrangement of the Mecha¬
nical Elements of Crystals—Object of Crystallo¬
graphy—Constitution of Crystalline Solids—Recti¬
lineal Interior Structure of Crystals^—Increase of
Growth of Crystals—Nature of the Process—Con¬
trasted with tlie Growth of Organic Beings—Crys¬
tallisation, according to Dr. Young, the universal
cause of Solidity.

SECTION 11.

[ Page 8. ]

Artificial Crystallisation—Conditions and Means by
which it is effected—Crystallisation of Saline Co¬
dies—Crystalline Power, or Primary Cause of the
Crystallisation of Bodies—Ratio of its Energy in
different Bodies—Process of Crystallisation as it
takes place in a Body from the Diminution of tlic
solvent Power of a Liquid, which has communicated
Fluidity to a Solid, by having combined with it

CONTEXTS.

XIX

Ciystallisation of Saline Substances—Disposition of
Crystals to extend themselves during the Process of
Crystallisation, more in an horizontal, than a vertical
Direction—More rapid growth of Crystals at the
bottom of a tall vessel, than nearer the surface—
Circumstance which influence the Crystalline Affinity
of Bodies to become efficient.—Influence of the
Form of the Vessel in which the Process takes place
—Practical Observations w ith regard to the Art of
crystallising Bodies—Water essential for the regular
Form of Saline Crystals;—is in a state of Chemical
Union with them,—and adheres to Crystalline Mate¬
rials with different Degrees of Force—Quantity, va¬
ries in different bodies—Efflorescence—Deliquescence
of Crystals, to what owing—Ratio of Crystalline
Energy in different Bodies—Advantages resulting
from it to the practical Operation of Chemistry—
Crystallisation as it takes place from the Reduction
of temperature in a crystallisable Body, which had
been rendered fluid by the action of Heat—Crys¬
tallisation of Metals and Metallic Substances—Best

b2

XX

CONTENTS*

Means of eflect*ng it—Tlieory of the Process—
Crystallisation effected by Sublimation—Bodies to
which it ■ is applicable, arc tliose which can readily
be volatilised without cliaiiging their Chemical Con¬
stitution—Practice of the Art—Theory of tlie Pro¬
cess—Crystallisation induced by Chemical Affinity
—Easy Methods of exhibiting the Operation—
Theory of the Process—Practical advantages result¬
ing from this Process, to the Art of Analysis—When
Bodies are merely suspended in a state of extreme
comminution nothing but Rest appears in some Cases
to be necessary for their Crystallisation^—Circum¬
stances which are essential to render the Forms of
Crystals regular—Effect of Time—Space or suffi¬
cient Room—Repose “Beauty and Size of Crystals
depends upon the Art of conducting the crystallising^
Process—Curious Method of obtaining large and
perfect Crystals almost of any Size, and of varying
their Shape at pleasure—Influence of certain Agen¬
cies on the Process of Crystallisation—Effect of the
Air, in promoting Crystallisation, as depending on

CONTEXTS.

XXI

the Pressure it exerts on the Crystalline Fluid
—Effect of Commotion—Electricity—The Solar
Ray.

SECTION III.

[ Page 47. ]

Terms of Crystallography—Geometrical Definitions—
Theory and Measurement of Angles—Nature of
Geometrical Solids—Crystals considered as Recti¬
lineal Bodies—Definition of the exterior Parts
of Crystals—Planes of Crystals—Edges—Solid An¬
gles—Summits—Bases—Secondary Planes of Crys¬
tals or Truncatures, &c.—Theory of Angles—Plane
Angles—Solid Anijles—An«rles with reirard to raag:-
nitude—Right Angle—Oblique Angle—Acute Angle
—Obtuse Angle—Compliment of an Angle—Subli-
ment of an Angle—Vertical or opposite Angies—
—Contiguous or adjoining Angles—Alternate An¬
gles. Triangles, or Three-sided plain Figures—
Equilateral Triangle—-Isosceles Triangle—Scalene

XXll

CONTENTS.

Triangle, Triangles with regard to their Angles—
Right-angled or Rectangular Triangle—Obtuse-
angled Triangle—Acute-angled Triangle. Nature
of Quadrangles or Four-sided plain Figures—Paral¬
lelogram—Square—Rectangle—Rhombus—Rhom¬
boid—Trapezium—Trapezoid. Nature of Polygons
or plain Figures liaving more than Four Sides—
Pentagon, Hexagon, Octagon, &c. Other Geome¬
trical Terms employed in lllustriition of the Theory
of Crystallography—Diagonal Line—Area of a
Figure—Base of a Figure—Altitude of a Figure—
Vertex of a Figure—Axis of a Figure—Upright or
Right Figures—Oblique Figures—Quantity—Com¬
mensurable Quantities —Incommensurable Quanti¬
ties—Ratio. Solid Rectilineal Figures—Regular
Solid Rectilineal Figures—Tetrahedron—Cube-
Octahedron—Dodecahedron—Icosahedron. Irregu¬
lar Solid Rectilineal Solid Figures—Pyramid, re¬
gular Pyramid—IiTegular Pyramid, &c.

CONTENTS,

XNlll

SECTION IV.

[ Page 86, ]

Admeasurement of the Solid Angles^ or the Inclination
ivhich one Plain Surfece of a Crystal makes with
another—Description and Use of the Pocket Gonio¬
meter of CarangeaUj for measuring the Angles of
Crystals—Optical Goniometer of Wollaston—mea¬
sures the Angles of crystallised Bodies even if the
Solid be very minute^ with a degree of precision
which has not hitherto been expected in Goniome-
try—Its accuracy of Performance has detected capi¬
tal Errors in the former Admeasurement of Crystals
—Application of the Instrument,

XXIV

fiONTENTS.

PART II.

SECTION I.

[ Page 96. ]

Philosophy of Crystallograpliy—Simple Bodies—Com¬
pound Bodies—ElemctiU of Bodies—Chemical and
Mechanical Analysis—Chemical Elements—Mecha¬
nical Elements—Crystalline Power, or Symmetrical
Attraction of the Mechanical Elements of Bodies
—Attempt of Newton^ Bergman^ Galiiij and Borne
de Lisle, to account for the Production of Crystal¬
line Forms—^Theory of Jlauy“Demonstrates that
all Crystals however complicated their Form may
be, contain within them, a Geometrical Nucleus,

CONTENTS.

XXV

which has an invariable Shape in each chemical
Species of Ciystalline Solid, under certain Restric¬
tions—and which may be extracted out of all of
them by a skilful Mechanical Analysis; hence the
identity of the Form may often be better established
by measuring the Angle, than from an inspection of
the whole Crystal;—the Primitive Solid may again be
dissected or subdivided, into Solids or Parts of a
less simple Nature, called Integrant Particles,—of
whicli every Ciystal is made up,—and which, by a
variation in their symmetrical Arrangements, pro¬
duce different varieties of Forms—The Theory
farther traces the I^aws of Armugement, or the
Directions followed by the Mechanical Particles of
crystallisable Bodies, by which Crystalline Attrac¬
tion combines Molecules of crystallisable Materials,
to produce all possible varieties of Crystalline Fi¬
gures,—and calculates the Mathematical Measure¬
ment, or the Determination of the Laws of Arrange¬
ment, according to which the Crystalline attraction
appears to be conducted.

XXM

CONTESTS.

\

F

i

SECTION 11.

[ Page lie. ]

Mechanical Dissection of Crystals in illustration
of their Structure—Development of Primitive
Forms—Symmetrical Arrangement of the Elemen¬
tary Parts of Crystalline Bodies—Geometrical Struc¬
ture of Crystals—Nature and Number of Primi¬
tive Forms of Crystals—Parallelopiped—Regular
Octahedron—Regular Tetrahedron—Regular Hexa-
hedral Prism—Rhomboidal Dodecahedron—Pyrami¬
dal Dodecahedron—Mechanical Analysis of the Hexa-
’ " hedral Prism of Carbonate of Lime, to develop its

internal Nucleus or Primitive Form—Dissection
of the Acute Rhomboid of Carbonate of Lime, to
extract its Nucleus or Primitive Form—Dissection
of the Pyramidal Dodecahedron of Carbonate of

f

I

CONTENTS,

xxvii

Lime to obtain its Primitive Nucleus—Further
Illustration of the Mechauical Division of Crystals
—Dissectioii of the Cube of Fluor Spar, and deve-*
lopnfient of its Nucleus—General Inferences, re¬
lating to the Mechanical Analysis of Crystalline
Solids, ill Illustration of the Theory of Crystallo¬
graphy.

SECTION Ili-

[ Page 139* '}

Mechanical Analysis of the Primitive Forms of Ciys*
tais, and Development of the Integrant Molecules of
Crystalline Bodies—Remarkable Arrangement of
some of them, in the Interior of the Primitive
Forms—Nature and Number of the Integrant Mo¬
lecules or Particles of Crystals—Further Illustra¬
tion of the Nature of the Solids called Primitive
Forms of Ciystals;—they are those bodies of a

xxviii

CONTENTS.

constant Gigometrica] Figure^ inscribed Syminetn’*
cally^ in all the Crj'stals of one and the same
SpecieSj or Chemical Composition^ unless the
Form possesses a remarkable perfection or regula¬
rity—they may be cleft parallel to their Faces to any
extent—and sometimes also in Planes^ not parallel
to their Sides—the Products obtained by this latter
Method of course differ in shape from the Primitive
Form of the Solid to which they belong—these
Solids thus obtained by the cleavage of the Primitive
Forms^ are called Integrant Molecules or Integrant
Particles of Crystals—Examples in lllustratjoii of
the Mechanical Dissection of the Primitive Forms of
Ciystals with a view to develop the Integrant Mo- *
Iccules of which they are composed~The Primi¬
tive Form therefore do not constitute the ultimate
Results to which the Mechanical Anatomy of Crys¬
talline Bodies may be carried—Mechanical Division
of the Rhomboid of Turmalin in lUustradon of the
preceding Statement^—^Division of the Hexaheclfal
Prism of Phosphate of Lime—Instances in which the

CONTENTS.

xxix

Mechanical Division of Crystals gives Integrant
Molecules of two kinds combined together through¬
out the whole extent of the Primitive Solid—Illus¬
tration of this fact—Mechanical Division of the Oc¬
tahedron considered as Primitive Form, to exhibit its
Integrant Molecules—Mechanical Division of the
Regular Tetrahedron, considered as Primitive Form
—Further Illustration of the Mechanical Division of
Primitive Forms to develop the Integrant Particles
—Mechanical Analysis of the Rhomboidal Dodeca¬
hedron, considered as Primitive Form—Analysis of
the By-pyramidal Dodecahedron, considered as Pri¬
mitive Form—Remarkable Relation which serves to
connect the Crystalline Structure of Substances,
whose Molecules are Tetrahedrons or Triangular
Prisms, with that of Substances which have, as
Molecules, simple Assemblages of Elementary
Parallelopipedons—Illustration of this Fact—Opi¬
nion of Dr. Wollaston concerning this Subject, [see
jpageSll]—Mechanical Analysis oftheCube ofFluate
of Lime, considered as Primitive Form—which

XXX

CONTENTS.

leads to a mixed Structure of Integrant Molecules,
of Octahedrons and Tetraliedrons—General Reflec¬
tions on this part of the Theory of the Structure of
Ciystals—Considerations of the Integrant Molecules
of Crystals, taken in a geometrical point of view;
—th^y are all the most Simple Solids—Susceptible of
and infinite variety in the Dimensions of their Sides—
and V alue of the Angles which terminate them—Have
all a fixed term of regularity to which they tend—
Are the ultimate products of the Mechanical Ana¬
lysis of Crystalline Bodies;—their Union constitutes
the Crystal.

SECTION IV.

[ Page 165. ]

Laws of Decrement of the Structure of Crystals—
Nature and Production of Secondary Forms—Simple
Secondary Forms—Compound Secondary Forms—

f

CONTENTS. XXxi

Decrements on the Edges—Illustration of this Law
—Production of the Rhomboidal Dodecahedron,
considered as Secondary Form—Originating from a
Cube, as Primitive Solid, according to the Law of
Decrement on the Edges—^Analytical and Synthe¬
tical Demonstration of this Statement—Further
Illustration of the Law of Decrement on the Edges,
acting parallel to the Sides of the Primitive Nu¬
cleus—Decrements on the Angles—illustrated by
analysing mechanically, an Octahedron originating
from a Cube as primitive solid—Synthesis of the re¬
production of the Octahedron moulded on a Cube,
according to the Law of Decrement on the Angles,
or the Action of which takes place parallel to the
Diagonals drawn from one Angle to the opposite
Angle of the Faces of the Primitive Solid—General
Illustration of the Effect of this Law of Decre¬
ment—Intermediary Decrements,—the Operation
of which is neither parallel to the Edges, nor to
the Diagonals of the Faces of the Primitive Nu¬
cleus, bu^ in Directions parallel to Lines placed
between the Diagonals, and the Edges of the Pri-

xxxii

CONTENTS.

mitive Solid—Illustmtion of the Action of this Law
—Mixed Decrements—Action of it to disguise the
Primitive Solid—Nature of Compound Secondary
Forms, resulting from several Simultaneous Laws
of Decrements acting at once—or from one Law
which has not reached its Limit—Examples of the
production of Secondary Forms.

CONTEXTS.

XXXIli

PxVRT III.

SECTION I.

[ Page 223. ]

Difference between Structure and Increment, as re¬
lating to the Production of Crystals—Illustration—
Singular Alterations absolutely accidental, to whicli
the Symmetry of Crystals is subject—reversed Po-

H, ,

sitions of the Faces of Crystals—Production of
Twin-Crystals—Ilemitropes—Maclcs, &c.—In or¬
dinary Crystals the Faces adjacent to each other

• ' * ''V

always form saliaiit, and never re-entering Angles
—Crystals also exist which present re-entering or
internal Angles—Instances of Crystals exhibiting
re-entering Angles—occur when One of the Two

c

XXXIV

CONTENTS.

Moieties of a Crystal presents itself in a re¬
versed Position with respect to the other half—He-
mitrope Feldspar, exhibiting Saliant and re-enter¬
ing Angles—in certain Cases the Plane of Junction
of which the Two Halves of the Crystal are joined,
is situated parallel to one of the Faces of the Nu¬
cleus, and the Assortment does not admit of pre¬
senting a re-entering or internal Angle to a Saliant
Angle—Striking Example of the Transposition of
the Faces of Crystals—Transposed Spinel, com¬
posed of the Two Halves of a regular Octahedron,
cut apparently obliquely into Two Halves, of which
One Half, appears to have turned upon the other
Half, in a Quantity equal to a one-sixth Part of a
Circle—Transposed Crystals of Oxid of Tin—Appa¬
rent Penetration of Crystals, grouped Crystals, &c.

SECTION II.

[ Page 244. ]

Electricity of Crystals—how excited—shows itself in
the Attraction or Repulsion of other Substances with

CONTENTS.

XXXV

which the Crystal is brought nearly into Contact—
considercd as connected with their Geometrical
Form and Symmetry—Electric Poles of Crystals
—their Situation—Modes of distinguishing them, &c.
—^.411 Crystals susceptible of becoming Electric,
deviate remarkably with regard to the Symmetry
of their Faces, and enable us to predict on what
Side either Species of Electricity resides—the Parts
which exhibit opposite States of Electricity differ
from each other with respect to tlieir Geometrical
Form, although they are similarly situated—while
in those Ciystals that are not electric, the simi¬
larly situated Parts correspond also in Form—if
for instance a Crystal consists of a Prism terminated
at each Extremity by a Pyramid, and these Pyra¬
mids differ as to the Kind of Electricity they are
capable of acquiring—it will be found that they
also differ in their Configuration—one consisting of
a greater Number of Faces than the other—the
Part possessing the greatest Number of Planes, be¬
comes electrified plus —the other minus —Mineralo-
gical Electrometer—Application of the Instrument
—Electricity of the Turmalin Boracite, &c.—

4

XXXVi CONTENTS.

Other Minerals possessing the Capability of becom¬
ing Electric.

SECTION IIL
[ Page g58. }

Double Refraction of Crystals—is called the Property
which they possess of presenting a double Image of
an Object viewed througli them—Means employed
for observing it—Quantity—varies from one Sub¬
stance to another—Crystallized Minerals pos^sessing
the Power of Double Refraction,

PART IV.

SJECTION I.

£ Page 266* ]

Principles of Nomendature of Crystallograpbj—Ap¬
plication of the Word Primitive—Nomenclature
of Secondary Forms considered with respect to the
Modifications which they present of the Primitive
Form-Nomenclature of Secondary Forms consi¬
dered in themselves^ and as being purely Geometrical
—Nomenclature of Secondary Forms considered re¬
latively to certain Facets^ or certain RidgeSj remark¬
able for their Arrangement or Position—Nomencla-

iXXVllI

CONTENTS*

tyre of Secondary Forms considered relatively to
the Laws of Decrement on which they depend^—
Nomenclature of Secondary Forms considered rela¬
tively to the Geometrical Properties which they pre-
jent—Nomenclature of Secondary Forms considered
relatively to certain particular Accidents.

SECTION IL

[ Page 299* ]

Amorphous Crystallisation—Crystals having no exact
and precise Determination— Ltcnlicular^ or imitating
the Form of a Lentil— 'Cylindroids^ the Prisms of
which are rounded off— Fmcimlar^Acicular^ Globulavy
&c*—Amorpliousj a Term denoting the Iasi Degree of
confused Crystallisation^ the Form of which becomes
mute to the Senses—Nature of Basaltic Columns
—Stalactites^—how formed—Are those calcareous
Concretions which resemble in their shape the com-

CONTENTS*

XXXIX

mon Icicle—^Incrustation,—how formed—Is a Con¬
cretion ill the Form of a Crust applied to the Surface
or the Interior of a Body—Tuffas,—Origin of them
— Geodes — Septarium — Pseudomorphoses,—is a
Concretion endowed with a Form foreign to its
S ub s tance—Petri facti o n s,—Obse rvation s concern i ng
themj &c.

SECTION III*

[ Page 332. ]

Table of Crystalline Forms of Minerals—Substances
which have a common Primitive Form with the same
Dimensions—Substances^ the Primitive Forms of
which are of the same kind with the same Dimen¬
sions^ respectively peculiar to each—Forms which are
found to be Secondary in different Species—Sub¬
stances which assume the Form of a Cube—Of a

RegularOctahedron—RegularTetrahedron—Rhotn-

boidal Dodecahedron—Rhomboid with Obtuse Sum-

xl

CONTENTS,

mit—Rhombokl with Acute Summits—Octahedronj
the Pyramids of which Iiave Square Bases—Octahe-
droDj the Pyramids of wliicli have Rectangular
Bases—Octahedron, tlie Pyramids of which have
Rhombic Bases—Substances which assume the Form
of a Riglit Quadrangular Prism ivith Square Bases
—x\. Quadrangular Prism with Square Bases—A
Quadmngular Prism with Rectangular Bases—The
same with Rhombic Bases—Substances which pre¬
sent themselves in the Form of an Oblique Quadran¬
gular Prism with rectangled Bases—With Rhombic
Bases—With Oblique-angled Parallelogram Bases—
Crystals which assume the Form of a Regular
Hexahedral Prism—Crystals which assume the Form
of a Pyramidal Dodecaliedron^—Forms which are
found to be Secondary, in different Species—are the
Cube—Regular Octahedron—-Regular Hexahedral
Prism—Rhomboidal Dodecahedron—and the Solid
with Twenty-four equal and similar Trapezoids.

CONTENTS.

Xli

. [ Page 341. ]

General Observations, and Reflections, on the State¬
ments, comprehending the Theory of Crystallo¬
graphy—Opinion of Dr. Wollaston concerning the
Structure of certain Crystalline Forms.

SECTION IV.

[ Page 349. ]

Tabular View of the Methodical Distribution of Mi
nerals according to the System of Ilaiiy.

LIST

OJP

CRYSTALLOGRAPHIC MODELS,

BOTH SOLID AND DISSECTED,

to in TME fVOMK,

NO.

1. Cube.

2. Cube with the solid angles truncated^ or replaced

by one facet or secondly plane.

3. Cube with the edges truncated^ or replaced by one

facet.

4* Cube, bevelled 07i the edges^ or having the edges
replaced by two facets or secondary planes.

xliv

CRYSTALLOGRAPHIC MODELS

NO,

5* Regular octahedron composed of two four-sided
pyramids put base to base,

G, Regular octahedron, having the solid angles [trun¬
cated] replaced by a secondary plane,

7, Regular octahedron, with the edges [truncated] re¬

placed by a facet,

8, Regular octahedron, having both the ^ edges and

solid angles [bevelled] or replaced by two facets,

9, Tetrahedron, considered as one of the regular

geometrical solids*

10, Regular pentagonal dodeeahedi*on, considered as

one of the regular geometrical solids,

11, Regular Icosaliedron, considered as one of the

regular geometrical solids,

IS, Right quadrilateral pyramid,

13, Triangular prism.

14, Hexahedral prism.

15, Farallelopiped, considered as one of the primitive

forms ofciystals,

16, Regular octahedroiij considered as one of the

primitive forms of crystals.

17, Regular tetrahedron, considered as primitive form.

REFERRED TO IN THE WORK. xlv

NO.

18. Hexahedral prism, considered as primitive form.

19. Rhomboidal dodecahedron, considered as primi¬

tive form.

20. By-pjramidal dodecahedron, considered as primi¬
tive form.

21. Dissected hexahedral prism of carbonate of lime.

22. Dissected acute rhomboid of carbonate of lime.

23. Dissected by-pyramidal dodecahedron of carbo¬

nate of lime.

24. Dissected cube of fluate of lime.

25. Dissected rhomboid of turmalin.

26. Dissected hexahedral prisms of phosphate of

lime.

27. Dissected regular octahedron, considered as pri¬
mitive form.

28. Dissected regular tetrahedron, considered as pri¬

mitive form.

29. Dissected rhomboidal dodecahedron, considered

as primitive form.

30. Dissected by-pyramidal dodecahedron, considered

as primitive form.

xlvi

CRYSTALI.OG11APIT1C MODET.^l

NO*

3L Dissected cube*

32* Regular tetrahedron, considered as one of the
integrant molecules of crystals*

33* Triangular prism, considered as integrant mole¬
cule*

34, Cube, considered as integrant molecule,

35* Dissected rhomboidal dodecahedron, to illustrate,
[by the method of analysis,] the production of a
secondary form from a primitive solid, according
to the law of decrement parallel to the edges,
and acting in one direction only, namely, in
breadth*

36* Dissected rhomboidal dodecahedron, to illustrate
the pi'eceding statement by the metliod of syn¬
thesis*

37* Dissected irregular pentagonal dodecahedron, to
illustrate [by the method of analysis,] the pro¬
duction of a secojidary form from a primitive
solid, according to the law of decrement parallel
to the edges, acting in two directions, namely,
in height and breadth*

REFERRED TO IN THE WORK. xlvii

NO.

38. The same solid^ constructed to prove the preceding

statement by the method of synthesis.

39. Dissected by-pyramidal dodecahedron, considered

as secondary form originating from a primitive
rhomboid; in illustration of the eflFect of the
law of decrement on the edges.

40. Dissected octahedron, considered as secondary form,

originating from a cube, in illustration [by the
method of analysis] of the law of decrement on
the angles^ or the action of which takes place in
a direction parallel to the diagonals, drawn
from one angle to the opposite angle of the faces
of the primitive form.

41. Dissected octahedron, constructed to prove tlie

same law, by the method of synthesis.

42. Farther illustration of the action and effect of

the law of decrement on the angles.

43. Illustration of the law of decrement [called in¬

termediary'll the effect of which takes place pa¬
rallel to lines situated between the diagonals and
the edges of the primitive solid.

Xlviii CRYSTALLOGllAPHIC MODELS

NO*

44* Illustration of the law^ called decrement*

45* Model constructed to show the apparently acci¬
dental alterations to which the symmetry of ciys-
tals is subject^ or the production hemitropesj
niacles; &c*

46* Model of a regular octahedron cut obliquely into
two halvesj the one of which may be turned upon
the other half in a quantity equal to one-sixth
part of a circle, and thus producing a solid
with alternate and re-entering angles, in illus¬
tration of the transposition of the faces of
crystals.

47. Model of a four-sided prism, terminated at each
extremity by a four-sided pyranj td,

48* The preceding model dissected exhibiting the
halves of two separate four sided prisms, termi¬
nated at each extremity by trihedral prisms, ap¬
parently turned half round on each other, to
form the hemitrope solid.

49. Model of two cubes grouped upon each otlicr

REFERRED TO IN THE WORK. xlix

NO.

to show the manner in which crystals are
grouped or aggregated,

50. Model of tw^o crystals [rectangular staurolitej
crossing each other at right angles.

The preceding collection of models may be subdi-
vided, for the convenience of study, into groups or
series, forming distinct and progressive lessons, in
some respect independent of each other, namely:

SERIES L

MODELS.

Nos. 1, 2, 3, 4, 5, 6, 7, 8.

Crystals considered as rectilineal geometrical solids,
—denominations of the exterior parts of crystals,
&c.

CRYSXAI-LOGRAl'Hie MODELS

SERIES IL

MODELS.

Nob. I, 5, 9, 10, 11.

Regular rectilineal geometrical solids.

SERIES III.

MODELS.

Nos. 12, 13, M.

Examples of irregular rectilineal geometrical solids.
SERIfiS IV.

MODELS.

Nos. 15, 16, 17, 18, 19, 20.

Primitive forms of crystals.

V

SERIES V.

MODELS.

Nos. 21, 22, 23, 24.

Mechanical dissection of crystals—development

REFERHET) TO IN THE WORK.

li

of the primitive forms of crystals—geometrical struc¬
ture and cleavage of crystalline solids, &c.

SERIES VI.

MODEI.S.

Nos. 25, 26, 27, 28, 29, SO, 31.

Structure of primitive forms—development of the
integrant molecules of crystals—remarkalde arrange¬
ment of some of them, in the interior of the primitive
forms.

/

SERIES VII.

MODELS.

Nos. 32, 33, 34.

Integrant molecules of crystals.

SERIES VIII.

MODELS.

Nos. 35, 36, 37, 38, 39, 40, 41, 42, 43, 44.

Laws of decrements of the structure of crystals—
Decrements on the edges—Decrements on the angles

2d

lii CRTSTAI^LOGHAPHIC MODELS, &C*

“Intermediary Decrements—Mixed Decrements, ex¬
hibiting the modes of arrangement followed by the
mechanical elements of crystallisable matter, according
to which the immense variety of actually existing crys¬
tals are produced.

SERIES iX,

MODELS.

Nos. 45, 46, 47, 48, 49, 50.

Singular alterations to which the symmetry of
crystals is subject—reversed position of the faces of
crystals—production of niacles, hemitropes—grouped
crystals—crystals penetrating each other, &c.

MODELS.

liil

M O D E L S

3;llu0tran6e of CrpgtallogtapSp,

EXHIBITING THE PRIMITIVE FOR3IS OF AC¬
TUALLY EXISTING CRYSTALS, AND THEIR
PRINCIPAL TRAN^SITIONS OR MODIFICA¬
TIONS OF FORMS.

The object in selecting the following assortment of
crystallographic models with their descriptions, is
chiefly to familiarize the student with the primitive
forms of actually existing crystalline solids, and their
metamorphoses or modifications of forms, so as to
enable him.to see at one view, what they possess in

* These models may likewise be had with this treatise, either
singly, or in sets.

liv

MODELS ILLUSTRATIVE

common, and wJiat is peculiar to each crystalline
solid.

I. THE PARALLELOPIPED, WHICH INCLUDES THE
CUBE, THE RHOMBOID, THE QUADRANGULAR
PRISM, AND ALL SOLIDS BOUNDED BY SIX-SIDES,
PARALLlV- TWO AND TWO.

1. THE CUBE.

NO.

1. Native gold.

2. Native silver.

3. Native copper.

4. Gray cobalt ore, or bright white cobalt ore.

5. Loucitc, grenatite, araphigcne, or white garnet.

6. Borate of magnesia, boracite, or cubic quartz.

7. Muriate of soda, common salt, or rock salt.

8. Aploma.

9. Sulplmret of lead, galena, or potter’s ore.

10. Sulphuret of iron, common iron pyrites, or mar¬
tial pyrites.

m; of crystallography.

f

Iv

% A "Right Tetrahedral Prism mth Square
Bases.

KO.

11. Sulphate of magnesia or Epsom salt.

12. Vesuvian, Idocrase, or brown volcanic hyacinth.

13. Meionite, or white hyacinth of Somma.

14. Wernerite, or scapolite.

15. Mesotype, stilbite, cubic zeolithe, chabasie,

or analcime.

16. Chromate of lead, or red Siberian lead ore.

17. Oxyd of titanium, or titanite.

18. Micaceous uranite, or oxyd of uranium.

3. A Right Tetrahedral Prism with Rectangular
Bases.

NO.

19. Chrysoberil, cymophane, oriental and opalescent

chrysolithe, peridot of commerce.

20. Euclase, peridot, or olivin.

21. Foliated zeolithe or stilbite.

Ivi

MODELS ILLUSTRATIVE

NO*

Apophilite*

23. Tong-state of iron and manganese^ or wolfram*

24* PhrenitOj greenish zeolite, chr_ysolite of the Cape.

4. A liigkt Tetrahedral Prism with Pkombic
Bases*

NO* j

25. Sulphate of barytes, ponderous spar, cawk of the
Derbyshire miners, baroselenito hea vy spar, or
Bologna stone

26* Sulphate of strontia, or celestine*

27. Topaz, topaz of Saxony, of Brazil, or Occidental

topaz*

28. Mica, and when in small scales and of a glittering

appearance, talc.

29. Diaspore.

30* Triphane or spodumene.

31. Arsenical pyrites, mispickel, or native arsenic

alloyed with iron.

32. Sulphuret of molybdena, molybdenite.

OF CRYSTALLOGRAPHY.

Ivii

5. A Right Tetrahedral Prism with oblique angled
Parallelogram Bases.

NO.

33. Gypsum, sulphate of lime, selenite or specular

gypsum.

34. Epidote, dclphinite, thalite, glassy antinolite of

Kirwan, arendalite, akanticonite, or strahlstein.

35. Axinite, thumerstone of Kirwan, yanolithe, violet

shorl.

6. An Oblique Tetrahedral Prism with Rectangular
Bases.

NO.

36. Borax, borate of soda, native borax or tinkal.

37. Cyanite, sappare or distbene.

7. A?i Oblique Tetrahedral Pnsm with Rhombic
Bases.

NO.

38. Amphibole, hornblende, basaltinc, or basaltic horn¬

blende, opake rhomboidal shorl.

39. Pyroxene, augite, or volcanic shorl.

10. Gramiuatite, or treraolite.

Ivih

MOBEI.S ILLUSTRATIVE

8* An Oblique Tetrahedral Prism mth Oblique-
angled Parallelogram Bases*

NO*

41* Feldspar, when of a cream colour and silky lustre;
it is called Adularia or moon stone*

42* Sulphate of copper, yitriol of copper, or native
blue vitriol*

9* A Rhomboid with Obtuse Summits*

KO*

43* Carbonate of lime, or calcareous spar*

44* TurmaHn, or electric sliorl, black shorl, cockle of
the Cornish miners; and if of a bright red
colour, rubellit*

45* Dioptase, compact green carbonate of copper, or
compact malachite or emerald copper.

46, Hock crystal, or crystallised quartz; if of a
brownish or yellowish black colour, cairngoruin
if of a yellow colour, occidental topaz, mock
topaz; if rose red, Bohenvian or Silesian ruby;
if of a light blue colour, mock or occidental sap-

OF CRYSTALLOGRAPHY.

lix

NO,

pliiroj water sapphire; if of a pale violet or pur¬
ple colour, amethyst.

47. Ruby or red silver, or antimonial sulphuret of

silver.

10. A Rhomboid with Acute Summits.

NO.

48. Telesia, perfect red corundum, sapphire, oriental

ruby of commerce, adamantine spar; if yellow,
purple, green, and yellowish green, it is called by
the jeweller oriental topaz, amethyst, emerald,
and chrysolite.

49. Oligiste iron, or specular iron ore.

50. Sulphate of iron, green vitriol, martial vitriol, green

copperas.

II. THE REGULAR TETRAHEDRON, OR TRIANGULAR
PYRAMID.

NO.

51. Triple sulphuret of copper and iron, yellow copper
pyrites, yellow or purple copper ore.

lx

MODELS ILLUSTRATIVE

i

t

IIL THE hegular hexahedral prism,

NO,

5S* Phosphate of lime, crystallised appatite, asparagus
stone.

53 Emerald, smaragd, or when of a pale green colour,
berjll or aqua marine,

54. Nepheline, or sommit.

55. Finite, or micarelle.

56. Oipyre, or leucolithe.

57. Sulphuret of mercury, or native dnnabar.

IV. THE RHOMBOIDAL DODECAHEDRON.

NO.

t

as. Garnetj pyrope of Werner, carbuncle of the an¬
cients, syrien, oriental, or noble garnet.

S9. Sulplioret of zinc, blende or pseudo galena.

OF CRYSTALLOGRAPHY.

Ixi

NO.

61. Phosphate of lead, green lead ore, or green spary
lead ore.

VI. THE REGULAR OCTAHEDRON.

NO.

62. Fluate of lime, fluor spar, or Derbyshire spar.

63. Muriate of ammonia, or native sal ammoniac.

64. Alum, rock alum, roach alum, or native super-)

sulphate of alumine.

65. Spinell, true ruby, or balas ruby.

66. Muriate of copper, sandy copper, or green copper

sand of Peru.

67. Diamond.

68. Native amalgam, or quicksilver alloyed with

silver.

69. Ruby copper ore, red copper ore, or calciform red

copper ore.

70. Magnetical iron ore, load-stone, or common mag¬

netic iron stone.

71. Native bismuth.

72. Native antimony.

Ixii

MODELS ILLUSTEATIVE

1, The Octahedron^ the Pyramids of which ha'ct
Rectangular Buses-

NO.

73. Nitrate of potash^ saltpetre^ nitre.

74. Carbonate of lead^ spatliose, or spary leatl ore,

white lead ore, glassy lead ore.

75. Sulphate of leadj native vitriol of lead.

76. Oxid of zinc or calaoiino.

77. Made or chiastolite.

78. Arragonite or Arragoa spar.

79. Shorlaceous beryll.

2. The Ociahedron^ the Pyramids of which ham Square
Bases-

NO.

80. Zircon, jargon, or mock diamond.

81. Anatase, oisanite, octahedrite, blue schorl, octahe¬

dral titanite.

82. Harmatome, cross stone, white cruciform hyacinth,

staurotide, staurolite, or granatite.

83. Molybdate of lead, yellow lead ore.

NOTICE

1 Ij Old Compton-Streetj Sotso.

Those Jndividmh zs)bo are desirous of receiving
ike Models enumerated in the preceding pages^ (or Sets
of them )y will have the goodness to favour the Author
with their Orders, either in a direct way^ or through the
medium of their Booksellers.

London^ March J4th^ ISIS*

errata,

Sis line IS, for ** afnoresce,” read “ elHorcscc,”

Sa, — 14, for “ 3,” read “ 41,”

64 , IG, for “ put t,”

104, — If, for ” course,” read causs',’*

110, — IG, for “ coutalwff,” read contaiu,”

111 , — 10, for sulphurate,” read “ sulphuret*”

114, — 3, for “aimalyt’ical,” read “aualytical.”

IS!, — 3, for divni-aioO,”^ read division,”

130 , — 10, for “ Crystal,” read ** Crystals.”

159 ^ „ g, for €6,” read " 50,”

I 64 j _ 10, dele the Tvords “ dlfFprcuce between structure and dec re-

lueut,” &c,

sll, — 4, for fl 35 r,” read " B r, & A.”

£3S, — 6, for “ FieldspJir,” read “ Feldspar,”

S4f, -- 8, for " obl^ue,” read “ obliquely,”

3 ;J0, — 17, dele tbe word or,”

342, — !>, for “ tetrahedron,” read letrahedroas,^

344, ^ ts, dele the words ” lU order,”

1 >

.>

M ^ / r\ : M .1* / i f

ELEMENTS •

r ,:a

h

. ’ . - i u**! »!< In ? i ^ * r>

CRYSTALLOGRAPIiy.

r ■ '. ■ ' . I '' ■ - • I. /

.i;« >' :

^ PART L ' *

• : ♦ • . . I i ■■■

* »"** ' . ^ 'll

SECTION I. '

I i/ 1 . • ' I

DEFINITION OP THE TERM CRYSTAL.
NATURE OF CRYSTALLISATION-OB¬

JECTS OF CRYSTALLOGRAPHY—CON-

* 8TITUTION OF CRYSTALLINE SOLIDY-

4. INCREASE OR GROWTH OF CRYSTALS
, CONTRASTED WITH THE GROWTH OF

ORGANIC BODIES. . .

-/1 *■} '■ r -L '•< *>

The name Crystal, is given to those
polyhedral bodies, produced by nature and
the operations of chemistry, which possess a
regular geometrical form, and rectilineal
interior, structure. .

\

B

3

PROCESS OF

Crystallisatioit is the process by
which crystals are produced. It expresses
the separation of the integrant particles of
crystallisable bodies from a fluid, with which
they were combined, so as to unite by
virtue of their crystalline attraction into
rectilineal solids.

The mineral kingdom presents a varii tv
of crystallised bodies, which, on account
of their beautiful forms, have at all times
attracted the attention of mankind, and
chemistry or the chemical art is also ca¬
pable of causing a vast number of saline
and other substances to assume symme¬
trical forms.

Observation has shewn that every sub¬
stance in crystallising has a tendency to
assume a peculiar figure. Common salt
crystallises in cubes, Epsom salt in six-
sided prisms, alum in octahedrons, sugar-
candy in oblique four-sided prisms with
wedge-shaped summits. But the crystal¬
line form in any crystallisable material
is liable to be altered by circumstances af¬
fecting the crystallising process, and hence

CRYSTALLOGRAPHY.

3

the geometrical forms, which the same
identical substances present, often bear no
such resemblance to each other as would
seem to indicate their relation. There are,
nevertheless, a certain number of figures
peculiar to every cry stall isable body, and
the crystals of that substance assume one
or the other of those forms, and no other.
Common*''sait^ for example, when it has
assumed its true crystalline shape, presents
itself in the form of cubes; it is also met
with in octahedrons, dodecahedrons, or
some figure appertaining to those solids.
Sugar-candy usually crystallises in oblique
four-sided prisms, and it likewise occurs
in cubes and in six-sided prisms, with
wedge-shaped summits variously modified;
alum crystallises in octahedrons, but it also
occurs in cubes.

This however is not all. When we pe¬
netrate into tlie interior structure of crys¬
talline solids, we become convinced that
their mechanical elements are disposed in
symmetry according to laws Avhich have
their measure and their value. Their state

B

o

4

OBJECTS OF

V'>*'

f •«

of aggregation is absolutely geometrical,
and appears as if it had been atfected by
instruments saided by skill and intelli¬

gence.

To explain these laws of crystalline ar¬
chitecture is the province of Ciiystallo-
cuAFHY. It is the business of this de¬
partment of knowledge to elucidate to
what the forms of crystals and their meta¬
morphoses are owing; or, in other words,
to account for the production of that im¬
mense variety of crystalline figures,,.with
which the mineral kingdom, and the labo¬
ratory of the chemist, have hitherto asto¬
nished the world. This science has, in
our own time, been so successfully culti¬
vated, that it has given the most dignified
aspect to the philosophy of minerals. It
enables us to calculate wdth the fewest
possible data, simple in the extreme, yet
inatheraatically certain the geometrical
Ibrras of crystals, with a like degree of ac¬
curacy, as astronomers attain in calculat¬
ing the motion of the heavens. They who
have been in the habit of examining crys-

CRYSTALLOGRAPHY.

5

talline substances niust have noticed, that
when their forms are well determined, they
always constitute angular polyhedral bodies
bounded by planes. w ! .-.i'.

Hence those soft outlines and that round¬
ness of figure which is so j characteristic in
the subjects of organic beings, and which,
in fact, constitutes their elegance of formsj
indicates on the contrary, among crys¬
tallised .substances, a want of perfection.
The characteristic of true beauty in these
substances of nature undoubtedly is tlie
sti’aight line. ,ir ‘ i . , t

The term rectilineal structure, therefore,
has been chosen to express the arrangement
of the small solids which combine geome¬
trically to form crystals,,in oppositiofl to
the term of organization, which denotes • the
more complex mechanism of vegetable
and animal substances. And this distiuc-;
tion is the more essential in the science of
Crystallography, for otherwise a column,
of basalt, which indeed is a symmetrical
rectilineal solid, might be considered as a,
crystal; which in reality it; isi,not,:,for.

6

ACGMENTATIOir OF

it does not possess a rectiiineal mterior
structure.

The increase or giowth of a crystal, is
exceedingly diiferent from the growth of
organic beings; it does not take place by
the expansion of its particles, and it pro¬
duces no advantage to the individual itself;
no state of its existence can be deter¬
mined as the period of its perfection.
The magnitude of a crystal can only be
increased by the mechanical or chemical
application of new matter; its increase as
well as its change of' form, is the result of
simple combination of external materials,
aided by molecular attraction.

In the vegetable and animal kingdoms
each individual constitutes a whole, pos¬
sessing a determinate form and structure,
stamped on it by a peculiar power as a
living being, which grows by appropriating
different materials for its subsistence, and
converting it into its own substance. All
its dimensions are thus increased, its vari¬
ous parts uniformly preserve the same pro¬
portion, and they continue to perfonn their

CP.Yi5^TAJ.S.

T

functions. It lives, continues its species,
and dies. In the mineral kingdom it is
otherwise. The arrangement of the sub¬
jects of this department of nature, are
passive; they are merely acted on by me¬
chanical and chemical agencies, and possess
no power of changing that action.

According to Dr. Young*, a more or less
perfect crystallisation is the universal cause
of solidity. We may imagine that when
the particles of bodies are disposed without
any order, they can afford no strong re¬
sistance to a motion in any direction ; but
when they are regularly placed in cer¬
tain situations with respect to each other,
any change of form must displace them in
such a manner, as to increase the distance
of a whole rank at once, and hence they
may be enabled to co-operate in resisting
such a change.

T

• Natural Philosophy, vol. i. p. § 28 .

8

ARTIFICIAL

'' '■ c 1 i ^ 3 i I ‘ • i '

4

I. ; <ii i I . : • ■*' i i ,- -

••I 1 ?' - ■ ’»<» ’ t '1 ' ' i, ■ *! t t - ■ j

. : ‘ ' Ui it ^ M < j '1 r. ' » '*

i t ■»♦ H ■ r ^‘ .Jilt- ’ ' J. ■ , i

r '-[ ‘uu-,, SECTION-IT.

^ . _ s I > “ ■ I ‘

ARTIFICIAL • CRYSTATLISATIOBT^—CON-
'• !l>ITIONS AND MEANS iBYt WHICH IT IS
EFFECTED-CRyS,i'ALL^SATION OF SA¬
LINE. BODIES-CRYSTALLINE POWER,

OE PRIMARY CAUSE OF THE CRYSTAL-
" LISATION OF SOLIDS—'RATIO OF ITS
■'ll energy in DIFFERENT BODIES.

■ I • ' •

j jTo cause a body to crystallise, it is in
the first place necessary to I'educe ifito the
most complete state of disintegration, i Its
integrant , particles must be placed at a
distance from each other, by the interpo¬
sition of a fluid, in which .they have full
liberty to move, and which opposes no
resistance to a S3nnraetrical arrangement
being assumed, b^^^yirtue of the crystalline
or attractive power with which the particles

- - . CRYSTALLISATION.

9

are enducedand secondly, it is essential,
that the fluid which keeps the integrant
particles at a distance, should be gradually
abstracted, or cease to keep them asunder,
to enable the particles fully and freely to
exercise their reciprocal affinities. For the
particles of crystallisablc bodies cannot
come into contact and form crystals, as long
as the forces of the attraction existing be¬
tween them, and.the fluid with which they
are combined, is superior or greater than the
natural attraction or crystalline .power' ex¬
isting among the particles themselves;

From this simple exposition it is easy
to conceive, that crystallisation is ope¬
rated solely by virtue of the attraction
existing between the integrant particles of
bodies, which tends to bring them together,
and make them adhere to each other. And
as crystals assume the forms of geometrical
solids, we are led to imagine that their
integrant particles have a form peculiar to
them, and they ecjually induce ustto be¬
lieve that the polyhedral figures i belong to

10 CRTSTALLISATIOJf EFFECTED

the particles of crystallisablc bodies, having
unequal sides, or some faces of greater ex-^
tent than others; these particles must have
a tendency to approach and unite by those
faces which are the most extensive. Sup¬
posing this, it will be easy to conceive that
when the particles are made to approach
each otlier, they will unite by those taees
which are best adapted to each other, or
which bear the strongest relation.

It cannot be doubted, that every crystal-
lisable substance has its proper and pecu¬
liar mode of crystallising; or, which is
the same thing, that it has its elementary
mechanical particles of a determinate form,
different from tliat of every other. This
unquestionably is the hrst cause of the re¬
markable differences that exist between the
crystals obtained. But the great varieties
of forms that appear among crystallised
bodies, are evidently owing, as will be shewn
hereafter, to the different geometrical modes
of arrangement in which the particles are
aggregated upon each c^her.

BY A PREVIOUS SOLUTION.

The processes by which crystallization is
aoconiplislied by art, are the following:

Cri/stalIisatio7i, as it takes place in a body
from the dimmution of the solvent pozeer of
a liquid which has communicated fluidity to a
solidf by having combined with it.

By the term solution is understood in
•chemistry, that operation in which a solid
body, combines with a fuid in such a man*
ner, that the compound retains tlie duid
form, and is permanent and transparent.

Perfect transparency and permanent
suspension of the solid are marks of perfect
solution, by which it is distinguished
from simple mixture or mechanical dif¬
fusion.

This process, no doubt, is nothing else
than an effect of the opKiration of chemical
affinity, exerted between the fluid and the
body which is to be dissolved. Thus,
when common salt is thrown into water,
the salt may be considered as acted on by
two forces. The cohesive or corpuscular

12

ART OF

attraction of its particles on the one hand
tends to preserve it in a solidistate; and its
affinity for water, on the other hand, to
bring it into a state of solution. The latter
force, however, prevails. The chemical
affinit}’^ being stronger than the corpus¬
cular or cohesive attmctions of the par¬
ticles of the salt, a compound is produced,
in which the particles of salt and water are
no longer distinguishable by the eye, nor
separable from each other by any mechani¬
cal force. -

In the solid, when thus dissolved, the
molecular or cohesive attraction, though
overcome by a counteracting power, must
nevertheless still be considered as existing,
and as constantly tending to re-unite the
integrant particles which are dissolved.
For, if we expel or evaporate by heat, a
Sufficient portion of the fluid which re¬
moved the particles of the dissolved body
beyond their 'sphere of mutual attraction,
the particles t of the solid become approxi¬
mated, i they, are brought within the limits
of their mutual affinity, they combine.

CRYSTALLISING BODIES.

13

and the solid re-appears. And if this ab¬
straction of the fluid is accomplished gra¬
dually, and so as to leave the elementary
moleculae time to arrange themselves, if we
may use the expression, to present them¬
selves suitably to one another, the crystal¬
lisation is regular; while, on the contrary,
too speedy an abstraction of the separating
fluid will force them to come tofsether
suddenly, and, as it were by the first faces
that oft’er, in which case the crystallisa¬
tion is irregular, and the figure of the
crystal difficult to be ascertained. And if
the abstraction be altogether sudden, the
body will ever form only a concrete mass,
which will have scarcely any crystalline
appearance.

The art of crystallising substances is
chiefly built on these fundamental trul hs.

Hence the method of effecting the crys¬
tallisation of such bodies as require a pre¬
vious state of solution, and among which
the class of salts hold a distinguished
rank, consists in heating the saline solution
so as to dissipate gradually part of the

14

ART OF

water by evaporation. It is thus that
chemists proceed for obtaining crystals of
sulpliat of potash, muriate of potash, &c.

The figure of the crystal has very little
regularity, if the water be evaporated too
hastily, as by boiling; but by keeping the
saline scdution in a gentle heat, very beau¬
tiful and very regular crystals are con¬
stantly obtained in a longer or shorter
space of time; and there is scarcely any
salt which may not be made to assume a
very distinct fonn by this process, if it be
skilfully conducted.

^ s

AW crystals extend themselves more in a
hoj'iaoDtal than a vertical direction, and ac¬
quire a much taster growth at the bottom
of a tall vessel than nearer tiie surface.
This curious fact will admit of a simple ex¬
planation ; tlie integrant niolecwlae, being
denser than the solution from which they
are separated, fall diown^ and augment by
their continual accretion the expanding
crystals belo^v. There are other circum¬
stances which materially influence the co-
liesive affinity of dissolved solids, in deter-

CRYSTALLISING BODIES.

15

mining it to become efficient; of this kind
is the refrigeration of the fluid.

This process is successfully employed
for such saline bodies as are more soluble
in hot water than in cold. It may readily
be conceived, that a salt of this kind must
exhibit this phenomenon, since it ceases to
be equally soluble in water, of which the
temperature is diminished ; so that the
portion, which remained dissolved only by
means of the higher temperature, willwpa-
rate by degrees as the liquor cools; and
when this is completely cooled, it will re¬
tain in solution only such a quantity as
cold water would dissolve. It is the same
with this second process, as with the first.
The more slowly the water cools, the more
will the saline moleculse be enabled to
approach each other by those faces which
are most suitable, and a very regular crop
of crystals will be obtained. For this rea¬
son a certain degree of heat must be kept
up for some time under saline solutions,
diminishing it gradually.

It must be observed, that all the salts.

16

AiiT or

which maybe made to crystallise in this man¬
ner, are also much more soluble in general
than those, for which the preceding method
is employed : and as they are dissolved at
first in boiling water, if this be suddenly
cooled, it will let fall in a shapeless im^s
all the salt that was dissolved by means of
the boiling heat: on the contrary, if the
solution be placed, while very hot, on a
sand-bath, or in a warm place, and care be
taken to conduct the refrigeration slowly,
the crystallisation will be very regular.
Such is the mode of obtaining sulphate of
soda, nitrate of pot-ash, carbonate of soda,
carbonate of pot-ash, muriate of ammonia,
&c. in beautiful crystals.

A third method of crystallising saline sub¬
stances, is by subjecting them to spontane¬
ous evaporation. For this purpose, a saline
solution is exposed to the temperature of the
atmosphere in capsules of glass or shallovv
stone ware basons, which must be covered
with paper or gauze, to prevent any dust
from falling into the liquor, without hinder¬
ing its evaporation. For this operation, a

CRYSTALLISING BODIES.

17

separate chamber or garret should be cho¬
sen, and used for no other purpose. The
solutiop^.i^jd^ft exposed to the air, till
crystaH^^^e, perceived in it, which some¬
times 00;^ take place in less than four,
five, pi* tijx.jtHyeeks, or even longer with
some salts. This process usually succeeds
better than either of the others for obtain¬
ing crystals very regular in their figure, and
of considerable bulk. It ought to be em¬
ployed in general for all salts, if time would
allow, because it is the means of having
them perfectly pure.

On some occasions a combination of these
processes may be advantageous, particu¬
larly for obtaining crystals of very deli¬
quescent salts. The solutions of.these
bodies being briskly evaporated, are ex¬
posed immediately to a great degree of
cold; but this method never aflbrds any
but irregular crystals, and sometimes con¬
crete masses.

The form of the vessel, and the plunging
of foreign bodies into saline solutions, have
also much influence on crystallisation.

18

ART OT

Both of these circumstances aflTect the figure
and growth of the crystals, and produce in
it a very great variety; for this reason
threads, glass rods, slips of metal, or little
sticks, are placed with advantage in the cap¬
sules or basons, in which the crystallisa¬
tion is performed, with a view to obtain
regular crystals. In this case the ciystals
are precipitated on the threads, and as
the surface on which they repose has very
little extent, they have commonly the
greatest regularit}^ of figure, while in attach¬
ing themselves to the oblique, irregular, un¬
even sides of the vessels, they are always
more or less irregular.

The plunging of foreign bodies into sa¬
line solutions, has frequently another ad¬
vantage ; they actually determine the forma¬
tion of the crystals, which would have been
much slower without their presence. Thus
a piece of wood, or a stone, thrown into a
saline solution, becomes a base, on wliich
the solution readily deposits crystals. Other
circumstances effecting the crystallising j'u’o-
cess of bodies, will be mentioned hereafter.

1 =

1

CRYSTALLISING BODIES.

19

AVe sliall form some idea of the process
of crystallisation effected by means of a
previous state of solution, if, after having
dissolved a quantity of a crystallisable salt,
for instance, nitrate of ammonia, alum,
nitrate of potash, or sulphate of soda [Glau¬
ber’s salt], in water, we observe what takes
place whilst the solution is suffered to cool;
after having been previously evaporatt^d to
saturation*, or better till a drop, when
placed upon a cold body, shows a dispo¬
sition to crystallise; or at farthest till the
evaporation has proceeded to such a degree,
that a saline pellicle begins to appear on
the surface of the liquor, which phenomena
are proofs that the cohesive attraction of the
particles of the salt is obtaining a supe¬
riority over the solvent power of the hot
water, and that the solution when left un¬
disturbed will crystallise.

* The term saturation in this case implies that the
combination in which a bod^ is combined with the
largest quantity of another substance; hence, when
water has dissolved the largest quantity of salt which
it can dissolve, it is said to be saturated.

c 2

- p —:

20

ART OP

We shall find upon the bottom and the
sides of the vessel, when the solution has
become cold, small heaps of salt deposited,
which gradually increase in size by the ac¬
cumulation of new particles, and if these
masses of salt be examined by a lens, it
will be seen that they consist of groups of
minute solids, or crystals possessing deter¬
minate geometrical forms.

All crystals deposited from water, con¬
tain a quantity of that fluid. It is termed
their. Water of Cr]fstallisation, and is essen¬
tial to the regularity of their form. It
gives them their transparency and density,
those qualities being always lost when this
winter is evaporated. Different saline
bodies contain dift'erent quantities of water
of crystallisation. There are some which
contain more than half their weight; as
sulphate of soda, carbonate of soda, nitrate
of ammonia, the triple sulphate of alumine,
&c.: others have but a small portion, as
sulphate of potash, nitrate, and muriate of
soda, &c. The proportion of water varies
according to the nature of the salt that is

CRYSTALLISING BODIES.

21

crystallised, and appears to be in an in¬
verse ratio to the force of its crystalline
power. Thus sulphate of potash, which re¬
quires a large quantity of water to counter¬
balance the cohesive force of its particles,
contains but little water of crystallisation,
whereas sulphate of soda, which is readily
soluble in water, holds more than half its
weight of water. This water appears to be
in a state of chemical combination with the
salt, and not simply interposed between its
cr3’stalline laminas. The affinity however
which it exerts is but feeble, at least in those
salts into the composition of which it enters
largely, since a considerable proportion of
it is driven off by simple exposure to the
air, and such salts are said to affloresce^ be¬
cause they abandon their waters of crystal¬
lisation by mere exposure to a dry and
Avarm atmosphere, and thus lose their
transparency, their volume, and in time
their form, as sulphate of soda, &c.

Those salts on the contrary, Avhich hold
their water of crystallisation very strongly
combined, and eagerly attract more on ex-

\

ART OR

posure to a damp atmosphere, become li¬
quid or deliquiate. The pi'operty is called
deliquescence. Tor instance, nitrate of -am¬
monia, &c.

^ The cohesive attraction is therefore to be
considered as the sole cause of the crystal¬
lisation of solids. It is exerted between
the integrant particles of bodies. (See p. 9 )
It essentially depends on two conditions
only: one of which is, that the moleciilsc of
bodies should be in the state of disintegra¬
tion; and the other, that they should be kept
in suspension in a liquid capable of aban¬
doning them to the crystalline attraction
which solicits them towards each other. In
short, every thing in the process of crystal¬
lisation, is regarded as passing in the same
manner as if, the force of gravity being null,
and the liquid ivas not coerced by the sides
of any surrounding matter, and as if the
crystal itself remained isolated in the liquid.

But the particles of different bodies, no
doubt, possess different degrees of crystal¬
line powers, or to arrange themselves sym¬
metrically.

CRYSTALLISING BODIES.

23

Thus the integrant particles of carbonate
of lime may be considered as possessing a
very high degree of crystalline energy, for
not only are very beautiful large crystals
of this substance extremely abundant, but
the^^ are met with in the mineral kingdom
with all the leading geometrical characters
of calcareous spar, even when mixed with
a very large portion of foreign ingredients.
Thus the acute rhomboids of calcareous
spar, which are found at Fontainbleau, con¬
tain more than two-thirds of their weight
of granular quartz: the principal angle of
pearl spar are nearly the same as that of
calcareous spar, although, in many in¬
stances, the carbonat of lime in this mineral
amounts to no more than about a third of
its weight, the remainder being oxyd of
iron and manganese; again, in the bitters-
path the carbonat of lime preserves nearly
its essential crystalline character, though
mixed with almost half its weight of carbo¬
nate of magnesia, for the value of its geo¬
metrical angle differs little from that of the

24

ART OF

:’o2

primitive figure of the characteristic angle
of carbonat of lime. On the other hand,
the crystalline affinity of sulphuret of cop¬
per is probably but small, and therefore
the minuteness of its crystals, and their
comparative rarity.

Hence also, when two solids are dis¬
solved in one licjuid, they may be separated
from each other by their different crystal¬
line energies. That solid whose particles
possess tlie greatest crystalline tendency
will separate first, and the other, which is
less disposed to crystallise, may be after¬
wards obtained by reducing the quantity,
or temperature of the solvent. The sepa¬
ration, iiowever, of the two solids from
each other, is seldom, if ever perfect, on
account of their mutual affinity for each
other.

When nitre and common salt, for cx-
ampie, exist together in the same solu¬
tion, after separating most of the nitre by
its greater disposition to crystallise, there
still remains a portion of it in the saline so-

CRYSTALLISING BODIES. 25

lutioii. Tiie crystals which we obtain at first,
are not pure nitre, but consist of that salt,
combined with a portion of common salt.

Observation and experiment have shown,
that those salts that arc permanent in the
air, have the strongest degree of crystalline
power. In those which are elTlorcscent this
force is considerably less, and* it is the
weakest of all in those that deliquesce on
exposure to the air. Now if two salts of
the first class are dissolved together in the
same quantity of water, provided they do
not decompose each other, and especially
if their ratios of solubility are different, al¬
though they ai*e rendered more soluble by
their mutual affinity, yet the whole quan¬
tities of them, may be obtained again in
a crystalline state without leaving any
uncrystallisable fluid. Thus equal parts
of nitrate of potash and sulphate of pot¬
ash, though soluble Avhen mixed together
in less water than would have been ne¬
cessary for both in a separate state, af¬
ford by evaporation successively and
in proportion to their solubility, first, sul-

ART OF

S6

pliate of potash, and then nitrate of potash,
■without leaving any portion of it in the
nncrystallisable liquid. But on the other
hand if nitrate of soda and sulphate of soda
are subjected to the same experiment,
both of which have only a slight tendency
to crystallise and are of jiearly equal
solubility, only a small quantity of sul¬
phate of soda will separate by crystallisa¬
tion, all the nitrate and the remainder of
the sulphate remaining liquid and uncrys-
tallisablc. When the mutual action of
the two salts is sufficient to effect a double
decomposition of them, it is necessary to
take into consideration the solubility of the
new formed salts, in order to make a correct
estimate of the quantity of uncrystallisable
residue, or of their crystalline powers; and it
is by taking thus advantage of the supe¬
riority of the affinity of cohesion over that
of different bodies, that we are able to pro¬
cure in a separate state many saline bodies
in the difficult art of analysis.

It is unnecessary to expound this subject
to a greater extent. A summary chemical

CRYSTALLISING BODIES. 27

view of it would involve a minuteness of
detail altogether unsuitable to the purpose
of this work.

CrijstaUisation as it takes place from the
rednction of temperature, in a body which has
had fluidity communicated to it, by the action
of heat.

There are some classes of Ijodies which
are not soluble in water, but nevertheless,
are capable of assuming crystalline forms.
Such, for instance are the metals; some in¬
flammables, and a vast number of chemical
compounds.. •

These substances when returning to the
solid state after having been fused, undergo
a regular crystallisation ; they are made to
crystallise by being previously fused, which
in fact, is a solution by means of caloric.

If we melt a ladle full of bismuth, anti¬
mony, zinc, sulphur, or muriate of lead,
and allow it to cool slowly, and quietly, till
a thin crust has formed on the surface, and
then by means of a jwinted iron, make two

28

ART OF

small opposite apertures through the crust,
and quickly pour out by on^, the fluid por¬
tion as carefully and with as little motion of
the mass as possible, whilst the air enters by
the other aperture, there will appear on re¬
moving the upper crust by means of a chis-
sel, when the vessel has become cold, a cup
shaped concavity studded with cr3'stals,
very brilliant, and more or less regular, ac¬
cording to the magnitude of the quantity of
massemploj'cd, the tranquillity and slowness
with which it has cooled, and the dexterity
with which the fluid central portion, at the
moment before it commenced to solidity,
was decanted from the crystallised part.
The same effect will be produced by fusing
the substance in a crucible, which has a
hole in its bottom, lightly' closed by an iron
rod or stopper, which is to be drawn out,
after the vessel has become removed fi om
the fire, and the surface of the licpiid become
congealed. Or the substance when melted,
may be poured into a deep plate or dish,
placed in a slanting position, which is sud¬
denly inclined in the opposite direction.

CRYSTALLISI^TG BODIES. 29

when the mass begins to congeal; by tliis
means the superior portion which is fluid,
is made to run olF, and a cake studded
over Avith crystal is obtained. Sulphur,
bismuth, siilphuret of antimony, and
muriate of lead, are easily crystallised in
this manner.

The conversion of water into ice, is a
process of crystallisation arising from the
abstraction of caloric, by the combination
of which, water presents itself in a state of
fluidity; its natural form being ice, hence it
passes into the solid state at 32*^ at the loss
of caloric. When water is suftcred to freeze
very slowly and Avithout agitation, small
needle-shaped crj'stals are observed on its
surface, shooting out from each other at an
angle either of 60 or 120® ; these crystals
gradually accumulate, they cross each other
in all directions, and lastly, form one uni¬
form solid mass of ice. A similar crystal¬
line arrangement is observable in new
fallen snoAv, the flakes of Avhich present
stars with six radii. If a piece of fistu-

tr

30

ART OF

lous ice, containing water in its internal
parts, be broken, and tiie water besiiftered
to run out, tlie external cavity wlien ex¬
amined by tlic microscope, will be found
studded with beautiful triangular or hexa-
hedral prisms, curiously interlaced, and
grouped upon each other.

1

CrystaUiHdtion effected by mhlimat'mu

Crystallisation effected by nteans of sub¬
limation, is applicable to those bodies
which are readily volatilized without chang¬
ing their chemical properties on exposure
to a moderate heat. To illustrate this fact,
take any quantity of benzoic acid, put
it into a Florence flask, and aj)ply a
gentle heat to the bottom of the flask
by means of a lamp. The benzoic acid
will be volatilized in the form of white
vapours, -which again condense within
the upper part of the vessel in a beauti¬
ful cr3'stalline form. In these cases, the
caloric acts as ordinary liquids with re-

CRYSTALLISING BODIES.

31

spect to a salt which they hold in so¬
lution.

It is the retiring of the substance at first
interposed between the particles, which
removed them to a distance from each
other, so as to permit them to tipproach
insensibly nearer to each other b}'^ vir¬
tue of their molecular attraction, and to
unite under geometrical forms, when such
withdrawing is made slowly enough to give
them time to assume the arrangements
which accord with the laws of crystalli¬
sation.

Crystallimtion as it takes place by the
exertion of ^chemical affinity.

The mutual approach of the integrant
particles of crystallisable bodies held in
solution by a liquid, so as to approach and
to present regular angular forms, may likc-
Avise be effected, by presenting to the fluid
another bo<ly which has an affinity su¬
perior to that of the crystalline solid itself,
and therefore weakens its affinity, and

32

ART OF

effects a decomposition. In illustration of
this principlCf the action of alcohol upon
most of the saline solutions may be ad¬
vanced. If we make a very concentrated
solution of nitrate of potash, alum, siilpiiatc
of copper, or sulphate of magnesia in
water, and pour into it copiously, alcohol,
the salt held in solution by the water be¬
comes instantly precipitated in the form of
exceedingly rniiiute crystals, by virtue of
the alcohol combining with the water by
which the salt was dissolved.

If we spread on a plate of glass a few
drops of a dilute solution ofnitrate of silver,
and place in contact wdth it a copper or
brass ware, and lot the whole*remain un¬
disturbed in an lioriiiontal position ; a bril¬
liant crystallisation of metallic silver will
make its appearance upon the glass next
the piece of copper ware, and this arrange¬
ment of crystals will extend gradually till
the whole quantity of fluid is evaporated.
In this case the copper or brass unites to
the oxigen of the oxid of silver dissolved in
the nitric acid, which holds it in solution;

CRYSTALLISING BODIES.

33

and as this takes place, the silver becomes
precipitated in the metallic state, assuming
a kind of arboriform arrangement, whilst
the nitric acid unites to the copper.

If a piece of phosphorus be suffered to
remain immersed for about twelve hours,
in a solution of sulphate of copper, the
phosphorus will gradually become enve¬
loped in a coat of extremely brilliant and
crystalline metallic copper, impervious to
air. Because the phosphorus has a stronger
affinity for oxigen than copper; it there¬
fore de-oxidizes the solution of this metal,
and the copper re-appears in its metallic
form.

The precipitation of silver in a metallic
state may be effected by suffering phos¬
phorus to be immersed, for a few days, in a
solution of nitrate of silver. The whole of
the metal will be precipitated on the phos¬
phorus in fine dendritic crystal. The ra¬
tionale of this experiment is analogous to
the former.

The metallic precipitation of lead, com¬
monly called the lead tree, may be ex-

D

34

AET OF

hibited in the following manner. Into a
quart decanter, nearl}^ hllcd with water
that has been boiled, put half an ounce of
acetate of lead leduced to powder, shake
the mixture, and suffer it to stand undis¬
turbed for two or three days; then decant
the clear fluid from the insoluble residue;
reject the latter, and after having rinced
the decanter with water, return into it the
clear solution. If now a ball of zinc be sus¬
pended in the middle of the fluid, by tying it
to a thread affixed to the stopper, and the
vessel be then set in a place where it can¬
not be disturbed, the zinc soon becomes
covered with a moss-like substance, being
metallic lead, which increases gradually, and
shooting out brilliant crystallised plates of
metallic lead, which place themselves in a
kind of symmetrical arrangement resembl¬
ing a tree or shrub. The zinc has a greater
affinity than lead has for oxigen, it there¬
fore deprives the oxid of lead of it, which
being thus reduced to the metallic state,
can no longer remain united to the acetic
acid in which it was dissolved, but must

CRYSTALLISING BODIES.

35

become precipitated upon the zinc, and in
so doing places itself, by virtue of its mole¬
cular attraction, into such a symmetrical
arrangement, as the disposition of its par¬
ticles is best adapted to assume.

Crystallisation effected by a previous state
of comminution and suspension in a f ind.

From the experiments of Mr. Watt, it ap¬
pears, that in order to obtain bodies in the
form of crystals, a previous solution is not
always necessary, but that an extreme me¬
chanical divisions and suspensions in a fluid
is in some cases sufficient, so that the dis¬
united particles have full liberty to approach
each other very gradually and without
starts. Mr. AVatt persuades himself, that
in this manner petrified wood is almost
daily formed, in which, though crystallisa¬
tion does not actually take place, a very
perfect arrangement is indicated by the in¬
timate union of the silicious matter of which
it is composed, and that in this manner are
produced other depositions which approach

D 2

to a crystalline structure, although the ma- ^
terials of which they are composed are vir¬
tually insoluble in water-

i

Circumstances which are essential for the
production of zirell formed crystals.

In order that the form of crystals may be
regular, three circumstances are required;
time, a sufficient space, and repose.

Time causes the superabundant fluid to
be slowly dissipated, and brings the inte¬
grant particles nearer to each other by insen¬
sible concentration, and without any sud¬
den shock. The integrant parts therefore
unite according to their constant laws and
form a regular crystal. Indeed it is a gene¬
ral rule that the slower the formation of a
crystal, the more perfect is its form; it is
also larger, harder, more transparent and
regular.

Space^ or sufficient room, is likewise a ne¬
cessary condition for obtaining beautiful
and regular crystals. If nature be restrained
in her operations, the products of lier labour

CRYSTALLISING BODIES. 37

will exhibit symptons of tliis state of con¬
straint. It may be asserted, that nature
forms her productions according to all the
circumstances which can influence her pro¬
cesses.

A state of repose in the fluid is absolutely
necessary to obtain very regular forms.
Uninterrupted agitation opposes all sym¬
metrical arrangement; and in this case the
crop of crystals obtained, will be confused
and indeterminate.

«

Method of obtaining large and perfect
crystals of almost any size.

We are indebted to Le Blanc* for an
ingenious method for obtaining large and
perfect crystals almost of any size, and for
varying their shape at pleasure, by causing
them to be formed, or grow under certain
circumstances. The process is as follows.
Let the salt to be crystallised be dissolved

* Journal de Physique, tom. iv. p. 300 .

38

ART Of

ill water, concentrate the solution slowly by
evaporation, to such a degree that it shall
crystallise on cooling, which may be known
by suffering a drop of it to cool on a plate
of glass or other substance. This being
' done let the solution be put aside, and when
perfectly cold, pour off the liquid portion
from the mass of crystals at the bottom, and
put it into a flat bottomed vessel. Alter
having stood for some da3's, solitary crystals
will be formed.

This being done, crystals will begin to
form at some distance from each other,
which gradually increase in size; select the
most regular of these, and place them into
a flat bottomed vessel at some distance
from each other, and pour over them a
quantity of the concentrated liquid obtained
by evaporating a solution of the salt, till it
crystallises on cooling. Alter the position
of every crystal once at least every day,
with a glass rod, that all the faces may be
alternately exposed to the action of the
lic^uid: for the side on which the crystal
rests, or is in contact with the vessel, never

)

CRYSTALLISING BODIES. 39

receives any increment. The crystals will
thus gradually grow or increase in size.
When they have grown to such a size that
their form can easily be distinguished, let
the most perfect ones be selected, or those
having the exact shape Avhich we wish to
obtain; and put them separately in a vessel
filled with a portion of the same liquid, and
let them by turned in the manner directed
several times a-day. By this means they
may be be obtained of almost any size we
wish. When the crystal has continued in
the liquid for a certain time, the quantity of
salt held in solution becomes so much dimi¬
nished, that the liquid begins to act upon
the crystal and redissolve it. This action is
first perceptible on the angles and edges of
the crystal; they become blunted, and
gradually loose their shape altogether.
Whenever this begins to be perceived, the
liquid must be poured off, and a portion of
new liquid put in its place; otherwise the
crystal is infallibly destroyed. They may
be made to grow in length or breadth; par¬
ticularly if they are of a regular form.

40

ART OP

They will grow in length if they be made to
lay upon their sides, and in breadth, when
they are placed upon their bases. Crystals
may thus be produced of an extraordinary
size and beauty.

Influence of atmospheric pressure on the
process of crystallisation.

The access of air has an import influence
on the process of crystallisation. If a sa¬
turated solution of salt whilst hot be put into
a vessel from which the air is excluded, it
does not crystallise even when cold. But if
air be admitted, the crystallisation immedi¬
ately commences and proceeds with rapidi¬
ty. This fact may be shown in the follow¬
ing manner.

Make a concentrated solution of sulphate
of soda, or Glauber’s salt, by adding por¬
tions of it gradually to water kept boiling,
till this fluid dissolves no more; (an ounce
and a half of water, will thus dissolve two
ounces of salt): pour the solution whilst
boiling hot into common medicine phials.

CRYSTALLISING BODIES.

41

previously warmed, and immediately cork
them, or tie slips of wetted bladder over
the orifice of the phials; so as to exclude
the access of common air from the so¬
lution. This being done, set the phials by
in a quiet place, without shaking ; the solu¬
tion will now cool to the tempei’ature of the
air, and remain perfectly fluid, but the mo¬
ment the cork has been drawn, and atmos¬
pheric air becomes admitted, it begins to
crystallise on its upper surface, the crystal¬
lisation shoots downward in a few seconds,
like a dense white cloud, and so much heat
becomes evolved, as to make, the phial
A'ery sensibly warm to the hands. When
the crystallisation is accomplished, the
whole mass is so completely solidified, that,
on inverting the phial, not a drop of it falls
out.

The explanation of this phenomenon as
given by Mr. Murray*', is as follows.

When the saturated solution of the salt is
enclosed in the vessel, and the pressure of

* System of Chemistry, vol. i. p. 87.

42

ART OR

the atmosphere excluded, the particles in
solution may be conceived as placed at dis¬
tances too great to admit of the attraction
of cohesion being asserted, so as to cause
them to unite and crystallise. But when
the pressure of the air, or any equivalent
pressure, is brought to act on the surface of
the fluid, its particles, as well as the parti¬
cles of the solid contained in it, are forced
nearer to each other; the distances between
them are lessened; the attraction of cohe¬
sion is exerted, and the crystallisation com¬
mences. 'i’he small crystals that are thus
formed at the surface, afford solid points
from which other crystals are formed, and
this proceeds rapidly through tlie whole
fluid.

Singular ej^ect of commotion; and other
agencies which effect the crystallising process
of saline bodie^.

Although the entire absence of external
motion, (as stated page 37), is peculiarly
favourable for the production of well formed

CRYSTALLISING BODIES.

43

crystals, the crystallising process may be
promoted in some instances by a slight dis¬
turbance or commotion of the fluid. This
is particularly the case with the solution of
those salts that are much more soluble in hot
than in cold water, and have but a feeble
crystalline power.

It has been observed, that in general the
effect produced, depends upon a particular
agitation produced in the liquid, rather than
upon a rapid motion impressed upon all the
mass. For we may succeed by striking
lio;htlv with the bottom of the vessel the ta-
ble Avhich supports it, or by striking against
the interior parts of the said bottom with a '
glass tube, or feather. Sir Charles Blagden
has noticed that of all the exciters of crys¬
tallisation, that which most rarely fails in
its effect in such cases, is a small piece of
wax with which the interior parts of the
vessel are struck in some points inferior to
the upper surface, so as to generate a spe¬
cies of tremulous motion. If water be suf¬
fered to cool without the least agitation,
and very slowly below the freezing point,

44

AET OP

it does not congeal; but at the instant
the vessel is agitated, there will be seen a
crust of ice at the part of the vessel situated
beneath the wax. We may conceive that,
in this case, the agitation of the liquid, at
the same time that it assists the saline parti¬
cles in disengaging themselves from the
aqueous particles, which still oppose a small
obstacle to their re-union, will occasion a
variety of different motions in the former,
whence will result for a certain number
among them, the positions ivhich give the
greatest advantage to crystalline affinity.

It has been remarked also, that a little
crystal of salt, placed in a solution of the
same salt, favours the crystallisation; be¬
cause the moleculse which compose this crys¬
tal having already the respective positions
necessary to satisfy the aggregation, solicit
those in their vicinity to motions the most
favourable to the action of the same force;
and this disposition is communicated regu¬
larly to all those which would make an
effort to crystallise. The presence of a
small piece of ice, which is placed in like

CRYSTALLISING BODIES.

45

manner in water that is already below the
degree of congelation, becomes as it were a
rallying point for all the moleculai which
have a tendency towards this union, and
effect the congelation.

The electric state of the atmosphere it ap¬
pears influences the crystallisation of saline
bodies. This is particularly observable in
the laboratories of chemists, when large
quantities of saline solutions are made to
crystallise. It frequently happens, that so¬
lutions which yields no crystals after having
been sufficiently concentrated, and left to
stand undisturbed for some days, suddenly
deposit the most abundant crop of crystals,
during or immediately after a thunder
storm.

Efecf of light on the 'production of crystals.

A very singular property may be ob¬
served in saline bodies which may be re¬
ferred to crystallisation, but is likewise in
some measure remote from it, because it
does not depend upon the same causes.

This is the property of.jrising along the
sides of the vessels which contain the solu-
tiori. It IS known by the name of saline
vegetation. Tims, if a solution of muriate of
ammonia or prussiate of potash previously
evaporated to the point of crystallisation,
be left undisturbed in a shallow vessel from
which the light is excluded, tins salt crys¬
tallises most effectually at the illuminated
part, it rises over the margin of the vessel,
and appears to be solicitous of the rays of
light, and the crystallisation may thus be
determined at pleasure towards any part of
the vessel by the mere admission or ex¬
clusion of light, &;c. Camphor possesses
this property in a high degree. This sub¬
stance rises by insensible evaporation in
half filled vessels, and constantly attaches
itself in a crystalline form at the most en¬
lightened parts of the vessels.

SECTION IIL

TERMS OF CRYSTALLOGRAPHY-GEOME¬
TRICAL DEFINITIONS-THEORY AND

MEASUREMENT OF ANGLES~NATURE
OF GEOMETRICAL SOLIDS.

In every science or art there are many
terms which require to be frequently men¬
tioned, if these were described as often as
they occur, it is obvious that a great loss of
time would follow, and no advantage would
be gained in perspicuity, because these de¬
scriptions w’ould continually divert the
mind from the leading object. And this is
the more essential in a science founded on
the principles of geometry and the mathe¬
matics.

All crystals with regard to their shape
may be considered as rectilineal solids, com¬
posed of planes, edges, and solid angles.

The planes of crystals, are those surfaces

I

48 GEOMETRICAL DEFINITIONS.

which lie evenly between their bounding
lines, anrt with which a straight line drawn
in any direction shall coincide in every
point.

The edges of a crystal, are formed by the
junction of two planes or faces, under deter¬
minate angles.

The mlid angles of crystals, are produced
by the coincidence of two or more planes in
one point. Every crystal also has two op¬
posite ends; if the ends of a crystal termi¬
nate in solid angles, they are called mmmitsi
an^ if in surfaces, they receive the name of
bases. The planes or faces, upon which the
crystal is supposed to stand erect, is simply
denominated the base*, and the lines by
which it is circumscribed, are called the
edges of the base. The faces interposed be¬
tween the two bases are called lateral-faces,
and the lines by w’hich the faces unite are
called lateral edges.

The faces whicli compose the summit, are

* It may be any dde or face at discretion.

GEOMETRICAL DEFINITIONS. 49

called accuminating faces, or faces of the
terminal pyramid, and the edges By which
they join, are named the edges of tlie py¬
ramid.

If an edge, or solid angle, be wanting, or
as if it were, cut off, by presenting a new
face, the edge or angle is said to be trun¬
cated, or replaced by a secondary plane.
And if it be cut off so as to present two
planes or faces, joining each other, it is said
to be bevelled or replaced by two secondary
planes. Fig. 1* represents a cube.

* Model, No. 1.

N. B. The Models referred to in this rcork, may be
had at Messrs. Accum and Garden^ Compton Street^
Soho.

* Model, No. 4. t Model, No, 5.
£ 2

GEOMETRICAL DEFUSTITIONS.

Fig. 4* represents the cube Fig. 1^ becel^
led; because the edges of the solid are
replaced by two secondary planes.

Fig. 5-f- is a regular octahedron, composed
of two four-sided pyramids, put^base to
base.

THEORY OR ANGLES.

53

Fig. 8* is the octahedron Fig. 5, trun¬
cated on all the edges and solid angles.

8

Theory of Angles.

If two straight lines lean or incline to¬
wards each other, they will at last meet,
which place of meeting is called an angle.

A plane angle is therefore the opening
or corner, made by the mutual inclination
of two straight lines, which are not in the
same direction, but meeting in a point as
Fig. 9.

* Model, No. 8.

54 THEORY or ANGLES.

A

The lines A B, and B C, which form the
angle, are called the legs or sides, and the
point B, where they meet or touch, is
called the vertex of the angle, or the an¬
gular point.

A solid angle is that which is made by
more than two plane angles, applied close
to each other, at the same point, so that
two of them are not in the same plane.

If we draw Fig. 10 upon pasteboard or
any'other pliable matter, and cut the lines

MEASUREMENT OF ANGLES. 55

half through, and then tgrn up the parts,
they will form a solid angle at the point
where their vertices meet each other.

Measurement of Angles.

The measure of every angle is an arc
of a circle, whose centre is the angular
point; hence to determine the value or
measure of angles, the circumference of
a circle is the standard of comparison.
This circle, of whatever size it may be, is
supposed to be divided into 360 equal
parts, called degrees; each degree is again
subdivided into 60 equal parts, called
minutes, and every minute is subdivided
into 60 seconds; and hence the measure of
an angle is said to be so many degrees, mi¬
nutes, &c. as are contained in its measur¬
ing arc. Degrees are marked by mi¬
nutes by and seconds by Therefore an
angle of 45 degrees, 15 minutes, and 7 se¬
conds, is written in this manner, 45° 15' 7"-

56 MEASUREMENT OF ANGLES.

To measure the value of an angle, we
describe a circle round the angular point
as a centre, and according to the number
of degrees, minutes, and seconds, cut olf by
the sides of the angle, so many degrees,
minutes, and seconds, the angle is said to
contain. For instance

If from two points in the circumference
of a given circle, as E and F, Fig. 11, lines
are drawn to the centre as E C and F C ;
there is made an angle at the centre C,
which is greater or less according to the
number of degrees on the arc E D F, but
of course it will be the same in a small
circle as in a large one; because the lines
will have the same inclination to each
other; via. A D B is a semicircle, whose

MEASUREMENT OE ANGLES. 57

centre is C; the arc A E D F G B, contains
ISO degrees, half 360, the whole circum¬

ference.

From the middle point D, of the arc A

D B, wliich is 90 degrees each way, from

A and B, if the line C D be drawn, it will
be perpendicular to A B; for A C D, and

D C B are each a fourth part of the whole

circumference, or half the scmi-circum-
ference of the circle; these angles are
therefore said to be of 90 degrees.

If the arc A D be bisected in E, and
E C be drawn, the angles ACE, and E C
D will be each of 45 degrees, half A C D

58

f

DIVISION OF ANGLES.

bisected in d, and a d is again bisected in e,
and d 5 is also trisected at/‘and g; where¬
fore AT), a d are each a fourth; ED, e d
an eighth; B F, 6 jf a sixth; and F D,
f d, a twelfth part of their respective
circles; and the angles A C D, a C d;
E C D, e C d, &c. are the same in both.
From which it is obvious, that angles may
be formed or measured by a circle of any
radius; and also that equal arcs of the
same, or of equal circles, or that an equal
number of degrees in a circle of any radius,
will form equal angles at the centre.

Division of Angles.

A '

Angles are of various kinds and denomi¬
nation. With regard to their magnitude
they are divided into right, oblique, acute,
and obtuse angles.

A right angle is that which is formed by
the meeting of two straight lines, which do
not incline to each other, but which are so
placed that either of them is perpendicular
to the other. Thus when one straight line,

/

a, stands upon another line, Fig. 12, so
as not to lean more to one side than to the
other, both tlie angles which it makes with
the other line are called right angles, be¬
cause their measuring arc is equal to 90
degrees.

If either side of a right angle be drawn
out beyond the vertex, there is necessarily
produced another right angle. And con¬
sequently if both sides are produced, there
will be generated four right angles. Thus
ABC, Fig. 13, is a right angle; if when
A B or C B be drawn towards D or E,
there is made another angle C B D, or
ABE; and if both are produced, E B D
is a fourth right angle.

60

DIVISION OF ANGLES.

|C

E

Oblique angle is a common name for any
angle that is not a right one, and it is either
acute or obtuse.

An acute angle is that which is less than
a right angle, or less than 90 degrees. See
Fig. 14.

14,

An obtuse angle, Fig. 15, is that which is
greater than a right angle, or whose measure
exceeds 90 degrees.

/

DIVISION OF ANGLES

61

Namely, if the line C B, Fig. 16, meeting
A B in the point B, falls on this side of a
perpendicular, B D, at that point; this
angle ABC, being less than the right angle
A B D, is called acute.

But if the line B E, Fig. 17, falls on the
other side of the perpendicular B D; the
angle A B E is obtuse.

3 S 5

Complement of an Angle. The differ¬
ence C B D, fig. i6, between an acute
angle ABC, and a right angle A B D, is

62

DIVISION OF ANGLES.

called the complement of the angle A B C.
Hence the complement of an angle of 50
degrees is 40 degrees, because 40 degrees
is what it wants of a right angle or 90®.

And if either side of an obtuse angle, as
A B, Fig. 17, be produced, the angle E B F
is the complement of the obtuse angle, or
its deficiency to two right angles, A D B,
D B F, or 180 degrees. Hence the com¬
plement of 100 degrees is — 10 degrees
a negative quantity. The complement to
180 degrees is usually called the suhlement^
that is to say, idaat it wants to a semi-circle
or 180 degrees, to distinguish it from the
complement to 90 degrees, properly so
called. Therefore tlic sublement is the dif¬
ference of two right angles or semi-circles,
and complement of an angle, expresses its
deficiency from a right angle or 90 degrees.

Angles have other denominations which
are given to them only from their situation,
in respect to each other, yet still retaining
the general appellation of right, acute, or
obtuse, namely, ,

DIVISION OP ANGLES.

63

\

Vertical or opposite angles. If two lines, A B
and C D, Fig. 18, cut and cross each other,
there are made four angles, at the point E
of their mutual intersection; either two of
these angles, A E D, C E B, or A E C,
and DEB, touching at their vertices only,
arc called vertical or opposite angles.

■ Contiguous or adjoining angles. Any
other two, as A E C, A E D, or AEG
and CEB, and having one side C E, or
A E, common to both angles, are called
contiguous or adjoining angles.

Altej'nate angles. If a line crosses or
intersects two lines, there are made eight
angles. A, B, C, D, &c. Fig. 10, of which
C and F, also E and D, between the two
lines, one on each side of the cutting line,
are called alternate angles.

64

DIVISION OF ANGLES.

C and E, also D and E, are called in¬
ternal angles on the same side.

E and A F, and B C, and G or D, and
H, are called internal and opposite angles
on the same side.

Triangles.

The fewest number of right lines that can
include a space arc three, ■which form a
figure called a triangle, or three cornered
figure. Triangles therefore are those plane
figures which are contained by three
straight lines, and which consequently
have three sides and angles, from whence
they take their names.

Any side of a triangle which is opposite
to any angle, is said to subtend that angle.
Thus A B, Fig. 20, subtends the angle C

NATURE OF TRIANGLES. 65

and A C ; subtends the angle B, and B C ;
subtends the angle A.

B

Triangles are of various kinds; they are
distinguished first, with regard to their
sides, and secondly, with regard to their
angles.

An equilateral triangle^ is that which has
all its sides equal to one another, as
Fig. 21.

An isosceles triangle is that which has
only two sides equal, as D E F. Fig. 22.

F

66

JfATUUE OF TRIANGLES.

22 .

A scalene triangle is that which has all
its sides unequal, as G H I. Fig. 23.

G

Triangles, with regard to their angles,
are either right angled, obtuse, or acute.

A right aiigled, or rectangular triangle^ is
that three-sided figure which has in it one
right angle, as A B C, Fig. 24, containing
or measuring 90 degrees.

NATURE OF TRIANGLES.

67

The side opposite to th.e right angle is
called the htfpotlienuse, and the other two
sides the legs.

The side which stands upright is called
the perpendicular, and the other the base.
Thus A C is the hypothcnuse, B A the
perpendicular, and C B the base.

The angles opposite to the two sides are
both acute.

The three angles of every right lined tri¬
angle are equal to two right angles; that is
to say, the angles ABC, Fig. 25, taken to¬
gether, arc equal to a semicircle or 180
degrees, viz. two right angles of 90 degrees
each, because the three arches described
on the angular points, as shown by the
dotted lines, arc equal to a semi-circle, or
180 degrees.

68

WATUUE OP TftlANGLES.

An obtuse angled triangle. Fig. 26, has in
it one obtuse angle, or an angle, which
is greater than 90 degrees.

The other two angles are acute, or less
than 90 degrees.

An acute angled hiangle. Fig. 27, is that
which has all its three angles acute, or
less than 90 degrees. See Fig. 27.

Isosceles ox scalene triangles, it is obvious,
may be either right-angled, obtuse, or
acute.

Oblique-angled triangles. All triangles

NATURE OF QUADRANGLES. 69

that are not right angled, Avhether they are
acute or obtuse, are in general terms called
oblique angled triangles.

Quadrangles or Quadrilaterals,

A quadrilateral is a plane figure, compre¬
hended by four right lines, and having con¬
sequently also four angles; hence the names
quadrangle.

The term quadrilateral comprehends the
following particular species of geometrical
figures; namely, parallelogram^ square^ rect¬
angle, rhombus, rhomboid, frapezhm, and
trapezoid.

Parallelogram. This name is given to
every quadrilateral right-lined figure, whose
opposite sides are parallel to each other.
It is immaterial whether the angles are
right angles or not.

70 STATURE OF QUADRASTGLES.

Fig. 28 is a pavalielogram.

28.

A square is a parallelogram which has all
its sides equal to one another, and whose
angles are right ones, as Fig. 29.

29.

A rectangle is a parallelogram ■which
has all its angles right angles, but has not
all its sides equal. It is also called an
oblong, being longer than broad. See
Fig. 30.

30 .

NATURE OF QUADRANGLES. 71

A rhomhus, or lozenge, is a parallelogram
whose sides are all equal, but whose angles
are not right angles, as Fig. 31.

A rhomboid is a parallelogram which has
its opposite sides equal to one another,
but all its sides are not equal, nor its angles
right ones. See Fig. 32.

Trapezium. Every other four-sided
figure besides those mentioned before, are
called trapeziums.

72

NATURE OF POLYGONS.

Fig. 33 is a trapezium.

Consequently every irregular quadrangle or
quadrilateral, which is not a parallelogram,
is a trapezium.

A trapezoid has only one pair of its sides
parallel, as Fig. 34.

Polygons^ or figures having more than four

sides.

Figures bounded by more than four
straight lines, are called polygons, signify¬
ing many sides. If their sides and angles
are equal, they are called regular polygons;

NATURE OF POLYGONS. 73

if unequal, they are called irregular poly¬
gons.

The names of these figures are derived
to them from the number, of their sides,
namely,

A pentagon is a polygon that has five
sides.

A hexagon has six sides.

A heptagon has seven sides.

A octagon has eight sides.

A notiagon has nine sides.

A decagon has ten sides.

A duodecagon has twelve sides.

A quindecagon has fifteen sides.

These eight are the most essential. When
they have a greater number of sides, it is
usual to call them polygons of sixteen sides,
of seventeen sides, and so on. To specify
every polygon would be infinite.

A diagonal is a right line drawn between
any two angles that are opposite, is a poly¬
gon, as A C, Fig. 35.

74

GEOMETRICAL DEEINITIONS.

In parallelograms the diagonal is usually
called the diameter^ because it passes
through the centre of the figure.

A C, and B D, Fig. 36, are the two dia¬
gonals; E the centre where they intersect
each otlier.

The area of a figure is its measure or su¬
perficial contents, viz. the quantity of space
contained within its bounds, expressed in
an^'^ known measure.

The base of a figure is called the side on
■which it is supposed to stand erect ; it is
generally applied to the low'er side.

geometrical DEEINITIONS. 75

The altitude of a figure is called its per¬
pendicular height from the base.

The vertex of a figure is the angular point
in which two or more lines, forming an
angle, meet, and touch each other.

The axis of a figure is called the line
drawn from its vertex to the centre of the
base.

An upright, or right figure. If the axis
of a figure is perpendicular to the plane
of its base, it is called a right or upright
figure.

An oblique figure, is, when its axis is in¬
clined to the base.

Quantity; denotes whatever may be mea¬
sured or numbered, estimated or compared,
in respect of more or less. It is of two
kinds, viz. commensurable, and incom¬
mensurable.

Commensurable quantities* are such as have
a common measure or aliquot part, that is,
such quantities as may be measured or di¬
vided into the same equal parts, or into parts
of the same magnitude, without leaving a
remainder. Thus two quantities are com-

76 GEOMETRICAL DEFINITIONS.

mensurable when some determinate quan¬
tity may be found, which, being taken or
multiplied, a certain number of times is
equal to either, without deficiency or ex¬
cess. Thus a foot and yard are commen¬
surable, there being a third quantity which
will measure each, viz. an inch, which
taken twelve times make a foot, and thirty-
six times a yard.

Incommensurable quantities are such as no
other quantity can measure, i. c. there can¬
not be found any determinate quantity,
how small soever, which, being multiplied,
will be equal to each of the other; but
that there will be a deficiency or excess in
one or the other. Any two quantities
whose proportion to each other can be ex¬
pressed by numbers, are commensurable;
two quantities, whose ratio cannot be ex¬
pressed in numbers, are said to be incom¬
mensurable to each other.

Multiple; that quantity is called a mul¬
tiple in respect of another quantity, when

it contains exactly, or is equal to the other,
being taken any number of times; then

NATURE OP SOLItl, &C.

the less is said to measure the greater.
Thus a foot is a multiple of an inch, of
itwo, three, four, or six inches. A j-ard
is a multiple of a foot, or of an inch,
&c.

Ratio ; is a mutual habitude or relation of
quantities of the same kind, in respect to
more or less.

Quantities arfe said to have ratios to one
another, which being multiplied, can exceed
each other.

A plane rectilineal Jigure is a superficies
or space, bounded by straight lines only,
and having but two dimensions, namely,
length and breadth.

A solid rectilineal figure is a body bound¬
ed by plane surfaces only, and having three
dimensions, namely, length, breadth, and
thickness.

Regular solid rectilineal figures are
those, whose sides are all equal, and which
may be so included tvithin a sphere or circle,
that each angle shall touch the internal
surface of the circumference of the circle.

m

78

NATURE OF SOLID

Of these bodies there can be no more than
five, namely:

1- The tetrahedron. Fig. 1 and Fig. 6,
Plate II.* is a regular solid, contained under
four equal and equilateral plane triangles.
It may be considered as a pyramid stand¬
ing on an equilateral triangular base.

A figure drawn upon pasteboard or card,
similar to Fig. 37, having the lines cut
half through, folded up, and glued to¬
gether, will form a complete tetrahedron.
The superficies of this regular solid, it must
be obvious, is equal to four times the area
of the base.

V

EECTILINEAL FIGURES. 79

2. The cube. Fig. 3, Plate II. *, is a solid
contained under six equal square planes.

If we draw a figure upon card or paste¬
board, like Fig. 38, and cut the lines half
through, and then turn up the parts £ind
glue them together, we shall form a cube.
It will thus be conceived that this regular
solid is a body contained under six equal
square planes, and that its solidity is equal
to three dimensions, multiplied by each
other, and that its superficies is equal to six
times the area of its base, or one of its
sides.

1

s

* Model, No. I.

80

IfATtTBE OF SOLID

3. The octahedron. Fig. 5, PI. II.*, is a
solid, contained under eight equal and equi¬
lateral triangles. This regular solid may be
conceived as consisting of two quadrangular
pyramids put together base to base. Fig.
39, being drawn upon stiff paper or paste¬
board, cut half through in the lines, folded
up and glued together, will show in a
tangible manner that the octahedron is
composed of eight equilateral triangular
pyramids, or of two quadrangular pyramids
joined at their bases; and further, that the
superficies of this solid is equal to eight
times the area of one triangle, and that its
solidity is equal to the solidity of the eight
composing pyramids, or to two triangular
ones.

* Model, No. 5.

RECTILINEAL PIGURES.

81

4, The dodecahedron'^ is a regular solid,
composed of twelve equal pyramids, meet¬
ing in a point at the centre of the solid;
the base of each pyramid being an equila¬
teral pentagon, and eeiual to each other.
The superficies of this body is therefore
equal to twelve times the area of one pen¬
tagon, and the solidity is equal to the soli¬
dity of the twelve composing pyramids.

If Fig, 40 be drawn upon a playing card
or stiff paper, and the lines be cut half
through, folded up, and glued together, the
several pentagons will form a regular do¬
decahedron.

40.

* Model, No, 10.

I

82

KTATURE OF SOLID

5. The icosahedron* is a regular solid,
made up of twenty pyramids, whose sum¬
mits meet in a point at the centre of the
body: the base of each pyramid being an
equilateral triangle and equal to each other.
The superficies therefore, is equal to twenty
times the area of one triangle, and the
solidity equal to the solidities of the twenty
composing pyramids. If Fig. 41 be drawn
upon pasteboard, and the lines be half cut
through, and then folded up, it will form
an icosahedron.

The latter two regular solids of the geo¬
meters, namely, the regular dodecahedron
and icosahedron, can not exist among crys-

* Model, No. II.

RECTILINEAL EIGURES.

83

tailised bodies, for reasons which will be
pointdS out in the seo^uel of the work.

Irregular rectilineal solids, are called those
bodies which have more than four sides
composed of straight lines, and the sides
of w hich are unequal: of these there are a
vast variety, for instance,

A pyramid is a solid figure contained
wdthin, or bounded by a number of planes,
whose bases may be a triangle, square, or
any polygon, and whose faces are triangles
terminating in a point, called the summit
or vertex of the pyramid.

When the figure of the base is a quadri¬
lateral, it is called a quadrilateral pyramid,
as Fig, 42.*

* Model, No. 19.
0 2

1

A pyramid is cither regular or irregular,
according as the base is regular or irre¬
gular.

A pirisni is a solid figure contained under
a number of planes more tlian four, of
which the two oj^posite ones, or ends, are
equal and parallel to one another, and all
the other parallelograms. Prisms are deno¬
minated according to the number of the

I’hus when the
ends are a triangle, the prism is called a
triangular prism. Fig. 2, Plate II. * When
it is a square, it is called a square prism;
when a hexagon, a hexagonal prism. Fig.
7, PI. II.* Hence the denomination of
prism, comprehends also the cube and
tik' parallelopipedon, the former being a
square prism, and the latter a rectangu¬
lar one,

A parallelopiped, see I^late II. Fig. 4, as
stated, is a prism, (or as it is sometimes,

llECTILIKfEAI, FIGURES.

85

though improperly, called an oblong cube),
contained under six quadrilateral figures,
whereof every opposite two, are equal and
parallel to one another.

86 CEOMETUTCAL ADMEASUREMENT

SECTION IV.

ADMEASUREMENT OF THE ANCLES
OF CRYSTALS.

Pocket Goniometer.

The pocket goniometer, contrived by
Carangeau for measuring the solid angles
or the inclination, which one plane surface
of a crystal makes with another, consists of
a protractor or semi-circular scale of de¬
grees, A A, Fig. 43, and a small pair of
compasses or nippers, B B B B, destined to
receive the crystal.

The protractor has a hollow centre at
t, lying in the direction of that diameter,
Avhich terminates the graduation. The
centre c of the pair of compasses is made
moveable like those of the common propoi'-
tional con>passes, so as to permit the legs
B B, and B C B, to be considerably length-

OF THE ANGLES OF CRYSTALS. 87

ened or shortened, when the two pieces are
applied to each other. The fixed leg B B,
is represented as beneath the moveable one
B C B, or radius, measuring 90 degrees, and
the lower end of the centre pin which could
not be shown in the wood cut, is made to
fit the hole or centre C in the protractor
precisely at the same time that tlie stud or
projecting piece of brass, being admitted
into the long perforation a of the leg B B,
the piece becomes steadily attached to the
protractor or semi-circle, as is seen in Tig.
43, The instrument is neatly executed in
brass or silver.

88 GEOMETRICAL ADMEASUREMENT

The application of this instrument is
obvious. The crystal to be measured is
applied between the pair of compasses,
which being thus set, arc applied to the
protractor A A, and the value of the angle
may of course be read olF at the fiducial
edge of the leg B C B.

Let us suppose, foi’ the sake of illus¬
tration, that we wish to measure on a crys¬
tal the angle formed by two adjoining
planes. We know that this angle is equal
to that of two lines drawn from one and the
same point of the edge which joins these
planes, with the condition that they are
perpendicular to this ridge and laid down
on the same planes. In order to have this
angle, we shall arrange the instrument so
that the portions of the two legs may leave
no light between them and the planes in
question, and at the same time their edges
may be perpendicular to the edge of junc¬
tion. In this case, the faces which em¬
brace the crystal are tangents to the two
planes whose incidence w’e seek for. This
being done, we shall seek on the circum-

OF THE ANGLES OF CRYSTALS. 89

ference of the protractor, the degree which
the edge or index line marks, or the angle
which this line forms with that which
passes by the centre c and by the zero
point, which angle is equal to that formed
by t!ie two portions of the arms, since it is
opposite to it at the summit. In the sketch
43 it is shown as giving 90 degrees.

It is an advantage to be able to shorten
the legs at pleasure, to avoid the obsta¬
cles w'hich would render the operation im¬
practicable, and which might be occasioned
eitlier by the matrix to which the crystal
adheres, or from the adjoining crystals.

But notwithstanding much ingenuity has
been bestowed on this instrument it is not
sufficiently accurate for the performance
for wffiich it is applied; it may never¬
theless be used in many cases where no
gieat accuracy is required, and ite porta¬
bility and cheapness render it an object of
value to the cultivator of mineralogy.

90 GEOMETRICAL ADMEASUREMENT

Optical Goniometer of Dr. Wollaston.

We are indebted to Dr. AYollaston for the
invention of a goniometer, which is entirely
optical. Its action consists in employing
a ray of light reflected from the surface,
instead of the face itself; and thus accord¬
ingly, for a radius of l-50th of an inch we
may substitute either the distance of the
eye from the crystal, which would naturally
be about twelve or fifteen inches, or, for
greater accuracy, we may by a second me¬
thod substitute the distance of objects seen
at a 100 yards or more from us.

The instrument consists of a circle (Plate
IV.) graduated on its margin, and mounted
on a horizontal axle supported by an up¬
right pillar. This axle being perforated,
admits the passage of a small axle through
it, to which any crystal of moderate size
may be attached by a piece of soft cement
or shoe-makers^ wax, with its edges or in¬
tersection of the surfaces horizontal and
parallel to the axis of motion. . This posi-

OF THE angles OF CRYSTALS. 91

tion of the crystal is first adjusted, so that
by turning the small axle each of the two
surfaces, whose inclination is to be mea¬
sured, will reflect the same light to the eye.
The circle is then set to zero, or 180 deg.
by an index attached to the pillar that
supports it. *

The small axle is next turned till the fur¬
ther surface reflects the light of a candle
or other definite object to the eye; and
lastly, (the eye being steadily hept in
the same place), the circle is turned by
its larger axle, till the second surface re¬
flects the same light. This second sur¬
face is thus ascertained to be in the same
position as the former surface had been.
The angle through which the circle has
moved is in fact the supplement to the in¬
clination of the surfaces; but as the gra¬
duations on its margin are numbered ac¬
cordingly in the inverted order, this angle
is correctly shown by the circle without
requiring need of any calculation. It may
be here noticed that it is by no means neces-

92 GEOMETRICAL ADMEASDREMEXT

sary to have a clean uniform fracture; for
since all those small portions of a crystal¬
line surface that are parallel to one another,
though not in the same plane, glisten at
once with the same light; the angle of an
irregular surface may be determined nearly
as well as when the reflecting sm faces arc
actually in the same plane. In this
method (of taking the measure of an angle),
when the eye and candle are only ten or
twelve inches distant, a small error may
arise from parallix. But such an error may
be rendered insensible, even in that mode
of using the instrument, by due care in
placing the crystal, and ivhen the surfaces
are sufficiently smooth to reflect distinct
images of objects, these errors may be
entirely obviated by another mode of using
it.

For this purpose, if the eye be brought
within an inch distant of the reflecting sur¬
face, the reflected image of same distant
chimney or other object may be seen be¬
neath its true place, and if by turning the

OM TH]6*'^i^NGLES OF CUYSTALS. 93

small ax.!e,niay be brought to correspond
apparently’witb the bottom of the house, or
with some other distant horizontal line. In
this position the surface accurately bisects
the angle which the height of that house
subtends at the eye; then by turning the
whole circle and crystal together, the other
surface, however small, may be brought
exactly into the same position, and the angle
of the surfaces may thus be measured with
a degree of precision that has not been
hitherto expected in geometry.

a b, Plate IV. is the moveable circle of
the goniometer, graduated on its margin or
edge; c, the axle of the circle; d d a
milled head by which the circle is turned ;
e e, the small axle with its milled head f
for turning the crystal without moving the
circle; a- y, a brass plate supported by the
limb g, and serving as a vernier or noxius ;
h, the extremity of a small spring by which
the circle is stopped at 180® without the
trouble of reading off; i a joint having
two centres of motion, the one horizontal.

94 GEOMETRICAL ADMEASUREMENT

the other vertical, for adjusting the posi¬
tion of the crystal; k, a sliding wire with
a milled head, m afiixed to the universal
joint i L

The crystal being attached, by means
of a little of shoemakers* cement, to the
sliding wire k at the point «, in the centre
of all motion, with one of its surfaces as
nearly parallel as may be to the milled
head is next rendered truly parallel to
the axis by turning the sliding wire k, till
the reflected image of a horizontal line is
seen to be truly horizontal. By means of
the central axis, e e the second surface is
then brought into the position of the first;
and if the reflected image from the surfac-e is
found not to be horizontal, it is rendered
so by turning the milled head /c, and since
this motion is parallel to the first surface it
does not derange the first adjustment.

The accuracy of this instrument is such,
that several errors in former observations
may be corrected by it; Dr. Wollaston
has coi rected one in the common Carbonate

OF THE ANGLES OF CRYSTALS. 95

of lime. The inclination of the surface of
a primitive crystal of this kind, is stated at
104® 28' 30", but which Dr. Wollaston
has determined to be 103 deg.

96

ELEMENTS OP BODIES.

S

PART 11.

SECTION 1.

PltlLOSOPTIY OP CRYSTALLOGRAPHY-

ELEMENTS OF BODIES-CHEMICAL

AND MECHANICAL ANALYSIS-CRYS¬

TALLINE POWER, OR SYMMETRICAL
ATTRACTION OP THE MECHANICAL
ELEMENTS OF BODIES—ATTEMPT OF
NEWTON,, BERGMAN, GAIIN, AND
ROME DE LISLE, TO ACCOUNT FOR
THE PRODUCTION OF CRYSTALLINE
FORMS—THEORY OF IIAUY.

All bodies in nature, with regard to the
manner in w'hich they may be examined
and the properties which they exhibit, pre¬
sent themselves to our observation either as
simple or compound bodies, each having

ELEMENTS OF BODIES. 97

certain habitudes peculiar to itself. Where
the matter which constitutes the substance
of our globe, as well as what enters into the
composition of organic beings, and the at¬
mosphere, of one kind, it would be nothing
more than a lifeless mass, destitute of all
other action than that occasioned by im¬
pulse and gravity.

Simple bodies are called those of which
all others are composed, and which resist
further analysis ; whereas compound bodies
are such, as can be analysed into bodies of
a less simple nature.

The ancients believed many bodies to
be simple, which the superior skill and
knowledge of modern chemists have most
assuredly decomposed; and there is no
reason to believe that in any one case has
chemical analysis been able to procure the
real elements or simple constituent parts of
substances. A chemical element, there¬
fore, does not so much signify a body that
is absolutely undecomposable, as one that
has not yet been resolved. In all proba¬
bility the number of simple bodies will

H

(

98 ELEMEItfTS OF BODIES.

Dot remain long without alteration. We
cannot pretend to say that the bodies now
called so, are really simple in themselves,
or that they arc not formed of other ele¬
ments still more simple. AVe can only
affirm, that in all the experiments of the
science, these bodies are found to act as if
they were simple; that they cannot be
decomposed by any of our methods ; that
they resist every species of analysis, and
can only be combined with other bodies, or
be made to undergo various syntheses.
When it was ascertained that many na¬
tural substances are compounded of dif¬
ferent principles, or other bodies still more
simple, methods were successively employ¬
ed to separate the principles from each
other. The name of analysis was given
to the art of effecting this separation ; an
expression which, since its adoption by
chemists, has been received in every branch
of human knowledge to denote the sepa¬
rations and decompositions, even in the
order of our sensations and our ideas.

Now natural philosophy and chemistry

t

ELEMENTS OF BODIES. 99

furnish us two modes of attaining the final
results of the division or analysis of bodies.

Without entering into useless metaphy¬
sical discussions on infinit}', we may sup¬
pose any substance whatever reduced to
the finest and most imperceptible particles
which the mind can imagine; these minute
solids, or least possible cpiantities of a
body, are called integrant particles, or
mechanical elements of bodies.

Yet these elements of physical division,
may be still very compound in another
point of view, and undergo another species
of analysis, effected by chemical agencies.
When the latter is also carried to its ulti¬
mate point, we obtain the, chemical ele¬
ments of bodies. By the term mechanical
elements^ we therefore understand that
physical solid which occupies the smallest
portion of space which Ave can conceive;
whereas the term chemical element expresses
such a body as cannot be decomposed
into a body of a less simple nature. For
instance, a mass of common salt is made
up of a vast multitude of particles posses-

II 3

100 MECHANICAL AND CHEMICAL

sing the same chemical properties, and
these particles are the integrant particles of
the salt. They may be further decomposed
or analysed by chemical means, into parts
possessing very different properties, namely
muriatic acid, and soda, two substances of
very different habitudes, and these are the
chemical elements of the salt. With the
latter substances crystallography has no¬
thing to do, it is not possible to ascertain
their forms.

The integrant particles of bodies, both
with regard to their forms and the manner

® ,...W '

in which they'v'adl^cfre to each other, are
proper objects of a'dme^ureraent, and ma¬
thematical caloulafio!f^vijij.The case however
is widely differ^nt'^with the chemical ele¬
ments, or those of which the integrant mo-
leculse of conipoimd bodies are composed;
the mode of their combination is not capable
of being explained by geometrical calcula¬
tion. It is the aggregation of the integrant
particles alone which interests the crystallo-
grapher. For these particles, how minute
soever we suppose them to be, cannot be

ELEMENTS OE BODIES.

destitute of magnitude; they must have a
certain length, breadth, and thickness, and
therefore must possess some particular
shape. Besides all this, it is very con¬
ceivable that the particles of every parti¬
cular body, may have a shape peculiar to
themselves, and differing from the shape of
the particles of every other body. Thus
the particles of A may have one shape,
those of B another, and those of C a third ;
and if the particles of bodies have length,
breadth, and thickness, we cannot avoid
conceiving them as composed of an inde¬
terminate number of still more minute par¬
ticles or atoms. Now the crystalline at¬
traction of two integrant particles for each
other, must be the sum of the crystalline
attractions of all the atoms in each of these
particles for all the atoms in the other:
but the sum of these attractions must de¬
pend upon the numljer of attracting atoms,
and upon the distance of these atoms from
each other respectively; and this distance
must depend upon the figure of the par¬
ticles.

n

t ■

103 MECHANICAL AND CHEMICAL

For it is obvious, that if two particles,
one of which is a tetrahedron and the
other a cube, and which contain the same
number of particles, be placed at the same
relative distance from a third particle, the
sum of the distances of all the atoms of the
first particle from all the atoms of the third
particle, will be less than the sum of the
distances of all the atoms of the second
particle from those of the third. Conse¬
quently, in this case, though the apparent
distance of the particles be the same, their
real distance is different; and of course the
cube will attract the third particle more
strongly than the tetrahedron; that is, it
will have a greater crystallisable power for
it, than the tetrahedron.

And if the particles of bodies differ from
each other in ligure, they may differ also in
density and in siise: and this must also
alter the absolute force of the crystallisable
power, even when the distances and the
figure of the attracting particles are the
same. The first of these two circum¬
stances indeed may be considered as a

ELEMENTS OF BODIES.

103

diiFerence in the mass of the attracting
bodies, and therefore may be detected by
the weight of the aggregate; but the
second, though also no less a variation in
the mass, cannot be detected by any such
method, though its effect upon the strength
of affinity or power may be very con¬
siderable.

There is no doubt that, upon the suppo¬
sition that such differences in the figure,
density, and size of the attracting particles,
really prevails, and it is in the highest de¬
gree probable that they do exist.

It is certain that crystallisation is effected
between the integrant particles of bodies
only, for these are the solids that are sus¬
pended in the fluid from which crystallisa¬
tion is about to happen.

These particles which are held together,
whether they be of the same nature or of
a different nature, continually tend to form
bodies of a polyhedral, constant, and deter¬
minate form.

I’his beautiful law of nature, by which
she impresses on her productions a constant

CRYSTALLOGRAPHY OP

104

and regular form, appears to have been
unkuo^v'n to the ancients, and when che¬
mists began to discover that almost all
bodies of the mineral kingdom effected
regular forms, they ascribed the fact to a
peculiar kind of polarity inherent in the
bodies.

This explanation however is too hypo¬
thetical to be received as a satisfactory
account of the process of crystallisation.
It assigns moreover a course, the existence
of which we cannot prove.

The sehoolraen, in order to account for
the multifarious forms of crystal, had re¬
course to the microscope, with a A'iew of
extorting from nature the secrets of element-
ary forms, caliing in the assistance of this
instrument to trace the origin of crystals.
In this case however, the microscope reveals
nothing beyond what may be discovered by
the unassisted eye. The smallest particles
of a crj'^stal which we can perceive by the
aid of optical instruments are crystals, or
parts of crystals, already formed according
to cei'tain geometrical laws, and these

EOME DE LISLE, &C. 105

merely differ in their dimensions and struc¬
ture from those whose augmentation has
arrived at its limit. They also denomi¬
nated crystals after the resemblance more
or less rude, which they thought they per¬
ceived between them and known bodies;
hence the name of crystals in the form of
tombs, stars, diamonds, crosses, wedges,
knife blades, &c.

The lirst attempt to account for the pro¬
duction of crystals in any manner ^at de¬
serves the name of philosophical, was by
Newton: according to him and the theory
of Boscowich, the aggregation of the par¬
ticles of which crystals are composed is
produced by the attraction wdiich Newton
had proved to exist between the particles
of bodies, and which acts as soon as they
are brought within a certain distance of
each other. The regularity of the figures
he explained by proving, that the particles
of bodies, whilst in a state of solution in a
fluid, must be arranged in the liquid at
equal distances, or in regular ranks and
files. The consequence of which, as they
are acted upon by a power which at equal

106

CRYSTALLOGRAPHY OF

distances is equal, at unequal distances nn-
equal, will be crystals of determinate figure.
In the crystallisation of salt or other bo¬
dies, the water which held the salt in solu¬
tion removed the particles of the salt to
a certain distance from each other, to break
down the attraction of aggregation existing
between them; each particle became sur¬
rounded by a number of particles of water,
and when the quantity of the solvent
became diminished by evaporation, the
particles of the salt came, nearer to each
other, their attraction towards the water
became diminished, whilst the attraction of
the particles of the salt towards each other
became consequently increased; they there¬
fore separated from the fluid, and arranged
themselves orderly in groups according to
certain laws, which have their measure and
their value. And as the particles, Avhich
compose the same body, have the same
form,’ the aggregation of any number of
those particles must produce, if their
arrangement by undisturbed, masses of de¬
terminate figures or groups of crystals.

107

ROME DE LISLE, ScC.

Such is the theory of Newton; it is worthy
of the luminous and acute mind of its
author. Still, however, there remain va¬
rious phenomena respecting the production
of the infinite variety of forms which re¬
quire to be explained.

Gahn, a German philosopher, hav¬
ing broken a crystal of calcareous spar,
found that it afforded rhomboidal frag¬
ments, and that the whole crystal ap¬
peared to be composed of small rhomboids.
Jiergman soon afterwards seized upon this
idea of his pupil, and as he combined a
knowledge of geometry with chemical sci¬
ence, endeavoured to trace all the observed
forms of crystals to a few simple or primary
ones. In the instance of calcareous spar,
he demonstrated that its numerous modifica¬
tions may possibly result from one single
figure, the rhomboid, by the accumulation
of which, in various Avays, cr^’stals of the
most opposite forms may be produced.
This theory he extended to crystals of every
kind, and he explained the difference of
exterior figure from the super-position of
planes, Avhich he calls the constituent parts

108

CEYSTALLOORAPHY 01

of crystals, variously piled around a crys¬
talline nucleus of a constant form, but in
each case according to certain laws of de¬
crease, and that the primitive form may be
discovered from the arrangement of the
laminae, of which the crystal is com¬
posed.

About the same period with Bergman,
or immediately afterwards, Rome de Lisle
pursued still farther the tlieory of the struc¬
ture of crystal. He was the first who
pointed out that this department of know¬
ledge was, perhaps, one of the most inte¬
resting objects of mineralogical science.
He endeavoured to reduce the diversity of
crystalline forms to a general or primitive
type. He classed together, as much as he
was able, crystals of the same nature;
he described the various modifications
under which that form appeared to be
masked ; and, lastly, he explained the pro¬
duction of the principal crystalline figures
derived from a primitive form. To the de¬
scriptions and figures of the primitive
forms he added the mechanical admeasure-

ROME DE LISLE, ScC.

109

ment of the principal angles, and demon¬
strated that these angles are constantly
the same in each variety. It mast be ac¬
knowledged however, that the j^riinitive
forms of Rome de Lisle were assumed en¬
tirely gratuitously, and not the result of
any experimental analysis. His method
was to frame an hypothesis, and then to
examine its coincidence with actual appear¬
ance; on this principle any form might
have been the primitive one, and any other
have been deduced horn it. If i>ersuasion
was the sole object of philosophy, Rome
de Lisle would have been a powerful phi¬
losopher, but philosophy must convince,
demonstrate, and wrest consent, however
violently opposed. An enemy must not
be able to make use of the same arms, or
deduce the same proofs to establish a con- *
trary opinion, nevertheless such would be
the case with Rome de Lisle's principle,
for any form, according to his system, may
become the primitive, and any other may
be deduced from it; his primitive forms
were imaginary, and not the result of ana-

110

BASIS OB TUB

lysis ; and they were selected merely from
their supposed simplicity.

Basis of the Theory of Jlaiiy.

Of a different nature from what has been
so far stated is the theory of crystallography
adv^anced by the Abbe Ilaiiy. This philo¬
sopher, by a happy discovery, has actually
demonstrated, where Rome de Lisle merely
imagined. lie has developed the primitive
form of crystals by mechanical analysis,
and has established a real, instead of an ar¬
bitrary, though descriptive, system of crys¬
tallography. He has also shewn, that all
crystals, however compUcated their form
may be, contains within them a primitive
geometrical nucleus, which has an invaria¬
ble form in each chemical species ofcrystal-
lisable material.

Accordingly, by dissecting an hexahe-
dral prism of calcareous spar by sections
parallel to each other, as will be shewn
presently, we may reinoye successively all
the lamina; in wMch it is enveloped, till we

THEOllT or HAUY.

Ill

^ 4 *

come to a geometrical solid, which repre¬
sents a perfect rhomboid.

By separating the eight solid angles of a
cube of Fluor spar, Ave obtain an octahe¬
dron : sulphate of Barytes produces an
upright prism with rhomboidal bases ; feld¬
spar an oblique-angled pai’allel-opipedon;
the ber}'!!, an upright hexahedral prism;
blend or sulphuret of zinc a dodecahedron
with rhomboidal faces; Elba iron ore, a
cube, &c. The solids thus obtained arc
called the primitive forms of crystals. The^'
are enumerated page 118.

If, after coming to the last subdivision,
Ave Averc to attempt to proceed in the same
manner in other directions, we should break
the crystal instead of dividing iK

But the solid w^hich forms the nucleus
may also be subdivided in a direction pa¬
rallel to its faces, and sometimes in other
directions. The same is the case Avith
respect to the enveloping matter, Avhich-
may be cleft by sections parallel to the faces
of the original crystal; so that the detached
parts are similar to each other, differing
only in bulk, which keeps diminishing

112

BASIS OP THE

in the ratio as the division is continued.
In most instances the dissection of the pri¬
mitive form and the enveloping layers, may
be continued in the parallels of the same
planes only to any extent, and in no other
direction, and this dissection of course can¬
not alter the form. But some of the pri¬
mitive forms and their enveloping layers
are farther divisible in planes that are not
parallel to the faces of the crystal, and
when this is the case a solid is obtained
which dilfers from the primitive crystal to
which it belongs, and these solids thus pro¬
duced by different methods of dissections,
are called by Haiiy integrant molecules of
crystals. See page 16'1.

The quantity of matter superposed to
the primitive form is not placed indiscri¬
minately; the arrangement is always per¬
fectly geometrical, the layers of particles de¬
crease regularly by the substraction of one
or more rows of particles either from its
edges, or its angles, or in other directions of
the faces of the nucleus, and always in a
geometrical order. See Laws of decre¬
ments, page 165.

THEORY OF IIAUY,

113

The production of all possible forms of
crystals therefore arises from certain laws
of arrangements of the layers of parti¬
cles surrounding what Haiiy calls a pri¬
mitive form or nucleus, which is always one
of the solids before stated; and this nu¬
cleus originates from the assemblage of a
certain number of integrant moleculse
possessing a constant form.

And as the order, according to which the
enveloping matter becomes aggregated,

may be interrupted, whether the form may
be complete or not, new figures will be pro¬
duced, always regular and symmetrical, and
which must be varied as the arrangement
of the particles are itself multiplied.

The layers of moleculse, the substraction
of which determine the decrements, is a
kind of unity to which we may refer the
structure of all crystals; so that we are at
liberty to adhere to the data which it fur¬
nishes, in the application of calculation to
every possible crystalline form. To know
aftenvards if this unity be divisible or if it

X

has fractional parts, is a matter of observa¬
tion or annalitical calculation.

Such is the basis of the system of Haviy.
It is similar in this to other theories, that
it sets out from a principal fact, on which it
makes all facts of the same kind depend,
and which are only as it were corollaries.
This fact is the decrement of the lamiiu^
super-added to the primitive form; and it is
by bi'inging back this decrement to simple
and regular laws, susceptible of accurate
calculation, that the theory arrives at results,
the truth of which is proved by the mecha¬
nical division of crystals, and by the obser¬
vations of their angles.

To the Abbe Hatiy is also due the scheme
of simplifying the calculation of forms, by
expressing according to algebraic formula;,
the different laws of decrements which
determine the modification of crystalline
forms. So far, as they are the result of
calculation and measurement, we may ad¬
mit the laws of calculation; for whenever
the supQT-position or substraction of simp]a

TIIEOIIY OF HAUY.

or compound inolecula;, around a nucleus,
shall hy calculation give a series of planes
and angles, which corresponds exactly to
the angles and planes measured on natural
crystals, it will amount to no more nor less
than a demonstration of the rule or ar¬
rangement of the mechanical elements
which have combined in the formation of
the crystal.

Il6 MECHAWICAL DISSECTIOST

SECTION IL

MECHANICAL DISSECTION OT CRYSTALS

-DEVELOPMENT OF THE PRIMITIVE

FORMS OF CRYSTALS—SYMMETRICAL
ARRANGEMENT OF THE ELEMENTARY

PARTS OP CRYSTALLINE BODIES-

STRUCTURE OF CRYSTALS-NATURE

and number op primitive rORMS.

The term mechanical division of crystals
is given by the Abb6 Haiiy, to the opera¬
tion of which we are enabled to perform,
as it were, the anatomy of cr 3 'sta]s to deve¬
lop their geometrical structure. Lapida¬
ries and jewellers, who cut and polish
stones, have at all times noticed that these
substances may be split more easily in
some directions bj" fissures than in others,
and that crystals can be cleft in certain di¬
rections only^ to afford smooth and brilliant
surfaces and regular formed portions. We

OF CUYSTALLINE BODIES.

say cleft or splits and not sawed or cut, as
the sections of crystals are not to be obtain¬
ed by slow and continued efforts, but by
sudden shocks or blows, resembling the art
of cleaving stones. It is this which con¬
ducted Haiiy to the theory he has esta¬
blished; namely, that if dexterously
divide in the direction of the natural joints
or laminae, the most complex crystal, we
at last obtain a geometrical solid or nucleus,
which observation has shown is constant in
all the crystals of the same species, or che¬
mical composition, and even in those whose
external forms are most strongly con¬
trasted.

The diversity of primitive forms ought
therefore to be regarded as a certain indi¬
cation of a difference in nature between
two substances, and the identity of primi¬
tive form indicates, identity of composition,
unless the nucleus is one of those solids
which have a marked character of regu¬
larity ; such as the cube, the regular octa¬
hedron, &c.

118

PRIMITIVE FORMS

The primitive solids hitherto discovered?
are the following geometrical solids.

Viiimitvce forms of crystals.

1. The parallelopiped, Tig. 4, 1^1.
II*

2. The regular octahedron, Tig. 5 ,
PI. Il.f

3. The regular tetaiiedron, Fig-
6, PJ. ll.t

4. The regular hexahedral prism.

Fig. 7, PI. II. §

5. The riiomboidal dodecahedron,

Fig. 3, PL II.II

6. The pyramidal dodecahedron,
composed of two hexahedral pyramids, put
base to base, Fig. 9> Pb U.f

A few examples will render the mecha¬
nical division of crystals obvious.

* Model, No, 15.
+ Model, No. 17.
jl Model, No. 19.

t Models No, 16,
h Model, No. 18,
!I Models No. 20,

OF CEVSTALS.

119

Let Fig. 44,*’ represent a regular six
sided prism, which the mineral kingdom
presents in one of the varieties of carbo-
rates of lime or calcareous spars.

If w'C attempt to split this solid with the
blade of a knife, assisted by the blow of a
hammer, we become convinced that among
the six edges in, nc, cb^ ah, of the superior
base, three only w-ill yield to the mechanical
division. Let i n, represent one of these
edges. The division is made accord!ng to a
planep s u t inclined at an angle of 45°, both
to the base abenc h, and to the plane in ej.
Then the two edges b c, and a A, will admit

^ Model. No. 2L

120 MECIlASriCAL DISSECTIOS

of being cleft jjrecisely similar to tlie pre¬
ceding ; but the other three, ’which are
intermediary, if struck with the knife,
resist splitting, and if broken by a greater
blow the fracture and the surfaces of the
detached portion, instead of being smooth
and polished, will be dull, rugged, and un¬
even. If we proceed to the dissection of
the contours of the inferior base of the crys¬
tal, we find here also that three edges only
can be cleft by the knife in the same degree
of obliquity; but here they arc precisely the
reverse of those of the upper base; namely
the intermediate ones. The dotted plane
l(j[y z represents the sections. The dissect¬
ed model, No. 21, shews the sections itself.
By extending the division farther by cuts,
as exhibited in this model, we find that
six new planes are developed. These in the
natural crystal possess a vitreous lustre,
which indicates that they coincide with the
geometrical joinings or layers of particles,
the assemblage of which constitute the
prism.

If we continue to make sections on the
model still farther, to detach successively

or CRYSTALS.

121

la 3 rer after layer, parallel to the former cuts,
and consequently to each other, we ap¬
proach nearer and nearer to the axis of the
crystal; and when the faces of the original
form have been obliterated; a regular sym¬
metrical solid, presents itself, which is the
nucleus of the crystal, and which in this
case is an obtuse rhomboid. A E I 0 K
represents this rhomboid * in its due posi¬
tion, in Fig. 44, with regard to the circum¬
scribed prism.

* Hauy gives the name of rhomboid to a parullelopi'
pedon a e, Fig, 45j terniinated by six rhombuses equal
and similar.

In every rhomboid two of the solid angles such
as u e opposite to each other, are formed by the
junction of three equal plane angles. Each of the
other six solid angles is formed by a plane angle equal
to each of the preceding, and by two other angles of a
diiferent measure^ but equal to each other. The points

122 MECHANICAL DISSECTION

The dissected model No. 21, will render
what has been stated obvious. 31y detach¬
ing at the upper or lower extremity, the
three first sections which there present it¬
self, the six cunci-form slices will offer to
view six trapeziums; by again removing
three more slices from both extremities, the
prism becomes converted into a solid, ter¬
minated by twelve pentagons parallel two
and two. The six faces of which are the
remains of the six sides of the original
prism, and the other six are the intermedi¬
ate one produced by dissection.

Fig. 46^ exhibits the pentagonal dodeca¬
hedron, as produced from the six sided
prism, which there is represented as inscrib-

« e are therefore the summits^ and the line a c the
axis* In any one whatever of the rhombuses a h df^
■which compose the surface^ the angle contiguous to
the snmmltj is called the superior angle i the angle cf,
the inferior anglei and the angles h and/, are the late^
ralangles. The sides a 6, uf are the edges;

and the sides h d, df the inferior edges ; hfh the hori^
tontal diagonaly and a d tlic ohltque diagonaL
^ See Model; No. SL

OP chystals.

123

ed in the original solid, that the process
by which it is obtained may be better con¬
ceived.

By making six more sections upon the
model, always parallel to each other, name¬
ly, three at the upper, and three at the
lower base, the faces of the prism dimi¬
nish in height, and in proportion as the
sections are multiplied and kept always
parallel to each other, the external sides of
the original solid have disappeared, the
prism will be converted into the acute
rhomboid, which represents the nucleus of
the original solid.

124 MECHANICAL DISSECTION

Now, in a like manner, all the crystalline
forms of calcareous spar, even those that
differ most from the six sided prism, if dis¬
sected in the direction of their laminae, will
produce a rhomboid, which is precisely
similar to that obtained from the before-
mentioned solid; and it is singular to see a
nucleus issue from varieties of forms wdneh
do not present any common point of resem¬
blance that seem to indicate their rela¬
tion.

For instance. Let us place by the side
of each other, calcareous spar, in the form
of a regular six sided prism. Fig. 44.*
Calcareous spai', in the form of a rhom¬
boid. Fig. 47.i‘

if

* Model, No. 91.

+ Model, No. 99,

OF CRYSTALS. ISfO

And calcareous spar in the form of a py¬
ramidal dodecahedron with isosceles trian¬
gular faces, Fig. 48.*

We can scarcel}'^ perceive how three
varieties of calcareous spar or carbonate of
lime, so dissimilar at first sight, and so fo¬
reign to each other, with regard to their
exterior forms, should contain concealed
within them one and the same shaped
nucleus. This however is the case, and
the fact may be proved, by penetrating

* Model, No. §3.

126 MECHANICAL DISSECTION

into the exterior structure of these solids,
namely :

To dissect the pyramidal dodecahedron,
Tig. 48,* it is only necessary to make one
cut through the edge E 0, 01; a second
through Eli; a fourth, through O 1,1 K;
a fifth through 13 K, G H; and a sixth
through E O. This being done, the nu¬
cleus will be obtained, as is obvious at first
sight from the figure which exhibits the
nucleus or primitive rhomboid within the
pyramidal dodecahedron in its proper posi¬
tion. See also model. No. 23.

To dissect the crystal of calcareous spar,
Ihg'. 47,T ''^diich itself is a rhomboid some¬
what acute, all that is necessary to be done,
is, to direct the cuts parallel to the six
extreme edges in such a manner, that each
of them may be equally inclined to the
planes it cuts into; namely, we have to
make sections upon the edges S T, S IT,
S N, on one hand, and S T, S U, S N, on

* Model, No. 23.

+ Model, No. 22.

Wfi

OP CRYSTALS

127

the other; in such a way, that the cutting
planes are equally inclined upon the faces
which they cut. The first section will lay
open six pentagonal faces r, r, r, r, r.

49.

parallel to the faces of the nucleus, and it
is easy conceived that by continuing the
cuts alwaj's in the same directions, and
parallel ta each other, until the internal
faces of the rhomboid have been oblite¬
rated, -we shall have a new rhomboid, which
will be the nucleus or primitive form.*
There are a vast number of varieties of
calcareous spar which bear no resemblance

* See Model No. 22.

MECHANICAL DISSECTION

to each other, but all of them contain, con¬
cealed within them, a nucleus precisely
similar to that under consideration.

If we attemjit the anatomy of a crystal
belonging to another species of mineral, the
nucleus w ill be chanojcd. In such substance
it will be a cube, in another a rectano-ular
prism, wdth rhomboidal bases, here it Avill
be a dodecahedron with rhomboidal planes,
there a pyramidal dodecahedron with isos¬
celes triangular faces. For example, let 13
D E N M L, Fig. 50,* represent a cube

OF CRYSTALS.

129

this cube by sections parallel to its faces, it
will resist of being cleft by cuts in that
direction, and if a gi’eater force be employ¬
ed than is necessar^r to split the crystal, no¬
thing but irregular fragments will be obtain¬
ed. But if the cuts be directed in the
line gf. Fig. 50, parallel to the diagonal line
B E upon one of its faces and at an angle
of about fifty-four and a half, we shall
accomplish the object, the solid angle I g
h f will become detached, and the part
obtained will be a triangular pyramid, and
the new face presented, will be an equilate¬
ral triangle g/ A, Fig. 51, shows the clevage
of this crystal, d c, b f the angles to be cleft.

If we continue the divisions further and
further upon the eight solid angles, d cbf,

K

130 MECHAWICAL DISSECTIO?f

&c. Fig. 51, the cuts will be first replaced
by eight equilateral triangles, and when the
sections intersect each other, the equilateral
triangular faces will disappear, and become
changed into hexagons, Fig. 52.

And when nothing more remains, of the
faces of the original cube, an octahedron with
equilateral faces will make its appearance,
which in this case is the nucleus contained
in this species of mineral, e, inscribed into
Fig. 53, exhibits this nucleus in its due
position.

53.

The dissected model No. 24, will palpably

OF CiiySTALS.

131

illustrate the mechanical diversion of this
crystal, and the position of its nucleus.

It is not ahvaj^s necessary to dissect a
crystal in order to reduce it to its primitive
form or nucleus. Because in ’certain in¬
stances, crystallisation at once produces the
nucleus, whereas again certain mineral pro¬
ductions are very rarely met with in the
primitive form. There exist, for example,
crystals of calcareous spar which differ in
no respect from the rhomboid which we
extract out of the regular hexahedral prism.
Fig. 44, page 119j and from the other va¬
rieties we have mentioned, and there arc
natural crystals of octahedral fluate of lime,
but these instances are rare. It frequently
happens also, that among the faces of a se¬
condary crystal there are some which are
parallel to those of the primitive nucleus.
Thus we meet with varieties of carbonate
of lime which are exactly similar to that of
Fig. 54, (see p. 132,) in which crystallisa¬
tion has left hextagonal faces, situated like
those which we obtain by dividing the six
sided prism, represented Fig. 44. In such

K 2

132 MECHANICAL DISSECTION

cases the route is, as it were, traced out
before hand, previous to arriving at the
nueleus.

Before we leave this subject we shall
advance one example more, in illustration
of what lias been so far stated, with regard
to the mechanical division of crystals, and
the development of the primitive forms.
For example;

If we endeavour to split some hexahedral
prisms of corundum in a direction, either
perpendicular or parallel to their axes, we
meet with a very considerable resistance:
the crystals may, indeed, be broken in these
directions; but the rugged and irregular

OP CRYSTALS.

133

Surface of the broken parts^ clearly proves
that the direction in which the crystal¬
line laminae have been deposited one up¬
on another has not been followed. The
regular hexahedral prism of this mineral
cannot therefore be considered as the form
of the nucleus of the crystal; and, con¬
sequently, is not the primitive form of the
crystals of this substance. If, in order
to discover the direction of the crystal¬
line laminae, a variety of crystals be ex¬
amined, some will hardly fail to be met
V with, which, on their solid angles, formed
by the junction of the sides of the prism,
with the planes of the extremities, present
small isosceles triangles. These are some-
times greater, and sometimes smaller, and
form solid angles, of 122° 34', with the
extreme planes of the crystal. They are
in some instances, real faces of the crystal,
but most frequently they evidently are the
effect of some violence on that part. The
smoothness and brilliancy of these small
faces, in the latter case, shew that a piece
has been detached in the natural direction

134 MEClIAlflCAI, DISSECTION

of crystalline larainse. It is, indeed, much
less difficult to separate a portion of the
crystal at those angles, than at any other
part; and in following the natural direction
of the faces, with a little patience and dex¬
terity, all the crystalline laminae may be
detached, and progressively increase the
size of the triangular face. Tins operation,
however, cannot be done indiscriminately
on all the solid angles of the crystals, but
only on the alternate ones at the same
extremity, and in a contrary direction to
each other. As to the other angles, they
may be broken, but it is impossible to
detach them. When, instead of the solid
angles of an hexahedral prism, small trian¬
gular planes are met with (which frequently
happens, whether caused by violence or
otherwise), they are always placed in the
direction above mentioned. If by follow¬
ing this indication of nature, we continue
to detach the crystalline laminse, we shall
at last cause the form of the hexahedral
prism to disappear totally, and in place of
it, a rliomboidal parallelopiped will be

OF CRYSTALS. 135

obtained, of which the plane angles at the
rhombs, in this case will be 86° and 94° ;
the solid angles at the summit will measure
84^ 31'; and that taken at the reunion of
the basis will be 95° 29'.

We can split this parallelepiped only in a
direction parallel to its faces; it will still
consequently preserve the same form,
which is that of the nucleus of this sub¬
stance, and its primitive form. It is,
therefore, by a modification of the rhom¬
boid al parallelopiped that nature has
formed the regular hexahedral prism, which
this substance presents.

Thus the application of general laws, to
ascertain constant characters, after they
shall have been fully verified, may be very
simple and general; and hence the follow¬
ing facts have been deduced ; namely, that
the small solids or primitive forms of crys¬
tals, in all those which belong to the same
species, that is to say, which agree in their
chemical constitution, have one invariable
geometrical form. They accurately corres-

136 MECHANICAL DISSECTION

pond with each other in their shape, and
the dimensions of their angles. But it is by
no means true, as has been hastily asserted,
that everif species has a peculiar primitive
form. Thus muriate of soda, sulphuret
of lead, sulphuret of iron, boracite, &c.
have the same primitive form; namely, a
cube, and a^;e besides composed of the same
integrant moleculaj, which is also a cube.
In a like manner fluate of lime, alum, dia¬
mond, bismuth, ruby copper, spinell,
antimony, &c. afford, by calculation and
mechanical division, a regular octahedron
for their primitive figure, composed of regu¬
lar tetrahedral integrant particles. With the
exception however of these nuclei, which are
regular geometrical solids, [see page 117],
and therefore unsusceptible of any variation
in their dimensions, it may be affirmed that
no two nuclei of different species or dis¬
similar substances, have precisely the same
dimensmis ; thus the primitive form both of
calcareous spar and tourmaline is an obtuse
rhomboid, but in the former the obtuse

OF CKYSTALS. 137

angles are = 105*^ 5', while in the latter
they are = 113^ 34'.

Those regular geometrical forms, although
they belong to dilferent species, may be con¬
sidered as the limits at which nature arrives
by different ways, while each of the figures
placed between these limits, seems to be
confined to one particular chemical com¬
pound only. ' ,

In the magnesian carbonate of lime, or
bitter-spar, which is a different chemical
compound, the primitive form is well known
to be a regular rhomboid, as well as that of
carbonate of lime, and so nearly resembling
it, as to have been hitherto supposed the
same.; differs from this quantity by 1(7
in the measures *of these crystals; for that
of the magnesian carbonate is full 106?*^.

The primitive angle of i ron-spar Dr. Wol-
laston has found still more remote fi-om that
of the common carbonate of lime,, which it
exceeds by nearly two degrees. This philo¬
sopher has examined various specimens,
some pure white, others brown, some tran¬
sparent, others opake.

138 DISSECTION OF CRYSTALS.

Dr. Wollaston believes that it is not un¬
likely, that when substances which agree so
nearly in their primitive angle, are intermix¬
ed in certain proportions, they may each
exert their crystalline power; and may oc¬
casion that confused appearance of crystal¬
lisation with curved surfaces, known by the
name pearl-spar present. And although he
has not made any accurate comparative
analyses w’hich may be adduced in support
of the hypothesis, that mixtures are more
subject to curvatures than pure chemical
compounds; but it is very evident from the
numerous analyses that have been made of
iron-spar by other chemists, how extremely
variable they are in their composition, and
consequently how probable it is, that the
greater part of them are to be I'egarded as
mixtures; nevertheless it is also possible,
that there may exist a triple carbonate of
lime and iron as a strict chemical com¬
pound.

ANALYSIS OF PEIMITIVE SOLIDS. 139

SECTION III.

MECHANICAL ANALYSIS OF THE PRIMI¬
TIVE FORMS OF CRY'STALS-DEVEL-

LOFMENT OF THE INTEGRANT PAR¬
TICLES OF CRY'STALLINE BODIES ; RE¬
MARKABLE ARRANGEMENT OF SOME
OF THEM, IN THE INTERIOR OF THE

PRIMITIVE FORMS-—NATURE AND

NUMBER OF THE INTEGRANT PARTI¬
CLES OF CRYSTAL.

From what has been stated in the pre¬
ceding sections it becomes obvious, that
the name of immitive form has been given
to those solids of a constant figure, which
are contained symmetrically each, in all the
crystals of one, and the same species or
chemical composition, unless it is one of
those forms which possess a particular cha¬
racter of perfection and regularity, (see page
117 and 135,) and which may be extracted
out of them by a skilfhl mechanical division.
All crystals, it is true, are not susceptible

140

ANALYSIS OF

of mechanical dissections, but those which
refuse to l^e clett, the theory seconds by
various indications the cleavage, and con¬
sequently determines tlie primitive form,
from theoretical calculations of certain exte¬
rior vestiges which the crystal presents. For
instance those strite that are observable on
the faces of many secondary crystals, when
the operations of nature have not attained
the perfection of which they are capable, fre¬
quently indicate, by their directions, the pro-
gressof crystallisation, or the direction of the
component laminae ; they therefore assist us
in catching by analogy, the form and posi¬
tion of the nucleus, which otherwise might
escape observation. Nevertheless, these
indications require to be used with caution,
for it sometimes happens that the surface of
the nucleus itself is striated. This sino-u-
larity seems to be the effect of an imperfect
decrement, which experiences such great
interruptions, that .the faces resulting from
it, sensibly coincide with the primitive
faces. In like-manner, it is not impossi¬
ble, that the faces of a secondary crystal

I

PRIMITIVE SOEIDS. 141

may have striae, in a direction different
from that which ought to result from the
progress of the decrement. But there are
cases in which the striae are so palpable, as
to show plainly the mechanism of the
structure.

The relations which serve to connect the
different original crystals of one and the
same substance with a common or pri¬
mitive form, are founded on the laws of
structure (which will be explained pre¬
sently,) whose tendency is to determine the
number and arrangement of the planes or
layers of particles which compose the sur¬
face of each crystal. From a necessary
consequence and acquaintance with the
progress of these laws, it becomes merely
requisite to have our eyes on the primitive
form, and tlie value of the 'decrements
which its angles or edges undergo, in order
to represent the polyhedron resulting from
it, and to see in.what manner in idea we
may effect the metamorphosis of the nu¬
cleus from which this polyhedron is. de¬
rived.

142

ANALYSIS OF

But the nucleus or primitive form of' a
crystal, is by no means the ultimate result
to which the mechanical anatomy of these
bodies may be carried. It is a character
common to all primitive forms, to be divi¬
sible by successive sections, parallel to their
different faces, and sometimes also in other
directions. The products obtained, will
be solids of different forms, from those of
the primitive, from which they originated.
These solids have received the appellation
of integrant moleculae, or integront ■par-
tides of ci'ystah.

When the nucleus is a parallelepiped,
that is to say, a solid bounded by six faces
two and two alike, as for instance, the
cube, and the rhomboid, which can be
divided by blows in a direction parallel to
the six faces, it is evident that the figure of
the integrant particle is itself a parallelopi-
ped, similar to the nucleus, and differing
from it only in bulk, which continually de¬
creases in the ratio as the subdivision is
carried further.

It may however happen that the primi-

PRIMITIVE SOLIDS.

143

tive parallelopiped, is farther divisible bj
planes, not farallel to its external faces, but
diagonally, or in other directions; for in¬
stance, let us conceive that A A K H, &c.
Fig. 55,* the central figure in this page,

represents the rhomboid of turmalin, and
that it admits of divisions, as it ac¬
tually does, parallel to the six rhombuses
which terminates the crystal, and with the
help of planes, each of which passes by an

^ Modelj No, £5.

144

ANALYSIS OF

oblique diagonal A O, by the axis A A',
and the edge A O, comprehended between
the same diagonal and the axis. These sec¬
tions will detach six irregular tetrahedrons,
which have been figured separately around
the primitive central rhomboid, in positions
analogous to those which they had when
joined in one body, in such a manner, that
we may follow as it were with the eye, the
anatomy of this solid. These six irregular
tetrahedrons represent the moleculae of the
substance, of which this crystalline solid is
the primitive figure.

Let us take another example; for in¬
stance, the regular hexahedral prism of
phosphate of lime; the division of this pri¬
mitive solid, gives for integTant moleculae
equilateral triangular prisms, as may be
perceived by inspecting Fig. 56.

PRIMITIVE SOLIDS.

145

We there see one of the faces of the
prism divided parallel to its six sides, and
consequently into equilateral triangles, each
of which is the base of a small triangular
prism, which represents the integrant mo-
leculae *.

In some cases the mechanical division
yields particles of different figures combin¬
ed together throughout the whole extent of
the primitive solid; the crystal in this case
affords products of a mixt structure, but
this division does not invalidate the
theory.

The analysis of the octahedron will illus¬
trate this fact. In this solid the sections by
planes, parallel to its faces, give in succes¬
sion to the ultimate point to which the di¬
vision is carried, moleculae, of two different
forms, namcijs tetrahedrons and octahe¬
drons; but every probable reason occurs to
reject the octahedron, and to adopt the most
simple solid, namely, the tetrahedron, as

♦ Model, No. 26 .

L

AUALXSIS OP

the true integrant particle. So that, in
whatever manner the octahedron is direct¬
ed, it always gives solids of two kinds
without ever arriving to unity. The divi¬
sion of the primitive form of fluate of lime,
which may easily be cleft by twenty-four
sections, as shewn by the dotted lines
Tig. 57 and likewise through the centre

will illustrate this analysis. The result will
be six octahedrons and eight tetrahedra.
The equilateral triangles a aaa represent
each, one of the exterior faces of the tetra¬
hedra, the three others are lost in the solid,
where they unite in a common point, and

PRIMITIVE SOLIDS. 147

are confounded with the centre of the
crystal.

The division of the regular tetrahedron,
as primitive form, likewise leads to a mixt
structure of a similar kind, namely, tetra¬
hedrons, leaving octahedral vacuities *.

The analysis of the rhomboidal dodecahe¬
dron gives as results, tetrahedrons, the faces
of which are, without doubt, equal and
similar isosceles triangles. These by being
taken in groups of six, form rhomboids
of a bulk proportional to their own*!-, so
that this solid may be conceived as being
itself immediately composed of four rhom¬
boids, and in the last analysis of twenty-
four tetrahedrons, without leaving any va¬
cuities between them. For as the dodeca¬
hedron has eight solid angles, each foi’med
by three planes, the assemblage of which
forms four rhomboids, which have for ex¬
terior summits the four angles.

With respect to the division of the pyra-

L 2

* Model, No. 28.

+ Model, No. 29.

148

ANALYSIS or

inidal dodecahedron, composed of two six-
sided pyramids, with isosceles triangular
faces, put base to base, we cannot extract
the moleculae, which compose this solid,
without dividing it in directions different
from those which would be parallel to
the faces. The tranchant plane in this
case ought to pass by the axis and by the
ridges, contiguous to the summits, whence
irregular tetrahedrons result as integrant
particles*.

Such is the structure of the primitive
solids of crystals. There is a remarkable
relation w-hich serves to connect the crys¬
talline structure of substances, w'hosc mole¬
cule is the tetrahedron or triangular prism,
with that of substances, which have, as
primitive forms, simple assemblages of ele¬
mentary parallelopipcdons. This connec¬
tion consists in the tetrahedral or prismatic
moleculoe, being always assorted in such
a manner, in the interior of the primitive

* Model, No. 30.

PRIMITIVE SOLIDS.

149

form and of secondary crystals, that on
taking them by small groups of twos, fours,
sixes, or eights, they compose parallelopi-
pedons, so that in reality the ranges sub¬
tracted by the effect of decrements are
nothing else, as well as the whole crystal,
than sums of these parallelopipedons.

That we may comprehend how this takes
2 )Iace, let A B D, D, &c. Fig. 58,*

be one of the basis of a regular six-
sided prism, subdivided into small tri¬
angles, which are the basis of so many in¬
tegrant moleculae. It is evident, that any
two given triangles adjoining the other, such

^ Modely No, 26,

150

ANALYSIS OF

as A p i, A O, i, Sec. compose a rhombus,
and consequently the two prisms to which
they belong form by their union a prism
with rhomboidal basis, which is one of the
kinds of parallelopipeds.

There is no crystal from which a nucleus,
in the form of a parallelopiped, may not
be obtained, if we confine ourselves to six
sections, parallel two and two. In a great
number of substances this parallelopiped
is the ultimate product afforded by the
mechanical division. But in some mine¬
rals it can be further divided by sections
made in different directions of its faces, the
moleculas of course thence resulting differ
from that of the parallelopiped. The follow¬
ing example will illustrate this statement.
Let a c h s 71 0 , Fig 59, be a cube, having

PRIMITIVE SOEIDS.

151

two of its solid angles, o, s, situated on the
same verticle line. This line will be the
axis of the cube, and the points a and s
will be its summits. Let it be supposed
that this cube is devisible by sections, each
of which, such as a h n, passes through
one of the summits a, and by two oblique
diagonals a //, an, contiguous to this sum
mit. This section will detach the soli^
angle i; and as there are six solid angles,
situated laterally, viz. *, hy c, r, o, n, the
six sections will produce an acute rhom¬
boid, the summits of which will be con¬
founded with those of the cube. Fig. 60,*

* Model, No, 31 -

152

AKALl'SIS OF

represents this rhomboid existing in the
cuboj in such a manner, that its six lateral
solid angles, b,d,f\p,g, e, correspond to
the middle of the faces achi^ crs A, h i n s,
&c. of the cube.

Besides, it may be proved by theory,
that the cube results from a decrement
which takes place by a single range of
small rhomboids, similar to the acute
rhomboid, on the six oblique ridges ab, ag\
ae, sd, if, sp. This decrement produces
two faces, one on each side of each of
these ridges, which makes in all twelve
faces. But as the two faces, which have
the same ridge for their line of departure,
are on the same plane by the nature of the
decrement, the twelve faces will be reduced
to six, which arc squares; so that the se¬
condary solid is a cube.

Suppose that the cube, Fig. 59, admits,
in regard to its summits a, s, two new divi¬
sions similar to the preceding six, that is
to say, one of which passes through the
points c, 0 , and the other through the
points h, n, r. The first will pass also

2

PllIMITIVE SOLIDS,

153

thi’ough the points h, e, and the second
through the points d,f, p. Fig. 6‘0, and 61,
of the rhomboid, from which it follows, tliat
these two divisions will detach each a regu¬
lar tetrahedron huge or dsfpf Fig. 6l,*

jT

61 .

so that the rhomboid will be found convert¬
ed into a regular octahedron e/j Fig. 62,-jf

which will be the real nucleus of the cube;

* Model, No. 31.

+ See tlie same Model, No, 31, which will render
obvious w!)at relates to this subject. •

154

ANALYSIS or

since it is produced by divisions similarly
made, in regard to the eight solid angles
of the cube.

If we suppose the same cube to be divi¬
sible, throughout its whole extent, by sec¬
tions analogous to the preceding, it is
clear that each of the small rhomboids of
which it is the assemblage, will be found,
in like manner, subdivided into an octa¬
hedron, with two regular tetrahedra ap¬
plied on the two opposite faces of the
octahedron.* Indeed, in whatever man¬
ner we proceed to subdivide either the
cube, the rhomboid, or the octahedron, we
shall always have solids of two forms, that
is to say, octahedra and tetrahedra, without
ever being able to reduce the result of the
division to unity. But the moleculai of a
crystal being necessarily similar, it appears
probable, says Ilaiiy, that the structure is,
as it were, interspersed with a multitude of
small vacuities, occupied either by the
water of crystallisation, or by some other

* See Model, No. 31.

PRIMITIVE SOLIDS.

155

substance, so that, if it were possible to
carry the division to its limits, one of the
two kinds of solids in question would dis¬
appear, and the whole crystal would be
found composed only of moleculse of the
other form.

This view is the more admissible, as each
octahedron being enveloped by eight tetra-
hedra, and each tetrahedron being equally
enveloped by four octahedra,* which ever
of the forms we imagine to be suppressed,
the solids that remain will join exactly by
their edges; so that, in this respect, there
will be continuity and uniformity through¬
out the whole extent of the mass.

The manner in whicli each octahedron
is enveloped by eight tetrahedra may be
readily conceived, if we take care that in
dividing the cube (Fig. 59) only by the six
sections, which give the rhomboid, we may
depart at pleasure from any two, a s, o A,
c «, i r, of the eight solid angles, provided
that these two angles be opposite to each

* Model, No. 27.

156

AKAL^SIS or

m i

other. But if we depart from the angles
a s, the I'homboid will have the position
shewn, Fig. 6l. But by departing from the
solid angles 0 , A, these angles will beeoine
the summit of a new rhomboid. Fig. 63,

composed of the same octahedron as that
of Fig. 62, with two new tetrahedra ap¬
plied on the face.s b df^ e g p. Fig. 63,
which were unoccupied on the rhomboid of
Fig. 6l. Fig. 64, and Fig. 65,

64.

M-.:

5

PRIMITIVE SOLIDS.

157

represent one, the case in which the two
tetrahedra repose on the faces d b e, f g p,
of the octahedron; the other, that in which
they would rest on the faces bfg, d e p.
It is thence seen, that whatever may be
the two solid angles of the cube assumed
for the points of departure, we shall always
have the same octahedron, with two tetra¬
hedra, contiguous by their summits to the
two solid angles in question; and as there
are eight of these solid angles, the central
octahedron will be circumscribed by eight
tetrahedra, which will rest on its faces. The
same effect will take place, if we continue
the division always parallel to the first sec¬
tions. Each face of the octahedron, then,
however small we may suppose that octa¬
hedron to be, adheres to a face of the te¬
trahedron, and reciprocally. Each tetra¬
hedron then is enveloped by four octahe-
dra. This structure is that of fluor spar.

By dividing a cube of this substance we
may, at pleasure, extract rhomboids, having
the angles formed by their planes equal to

158

AXALTSIS OF

✓

120o or regular octahedra, or tetrahedra,
equally regular. There are a small num¬
ber of other substances, such as rock crys¬
tal, carbonate of lead, &c. which being
mechanically divided beyond the term at
which we should have a rhomboid or pa-
rallelopipedon, give also parts of various
different forms assorted together in a man¬
ner even more complex than in fluate of
lime. These mixt structures necessarily
occasion uncertainty respecting the real
figure of the integi'a! moleculas which belong
to the substances in question. AVe have,
however, observed that the tetrahedron is
always one of those solids which concur to
the formation of small rhomboids or paral-
lelopipedons that would be drawn from the
crystal by a first division. On the other
hand, there are substances, which, being
divided in all possible directions, resolve
themselves j3nly into tetrahedra. Of this
number are garnet, blend, and tourma¬
line.

In short, several minerals are divisible
4

PRIMITIVE SOLIDS.

159

into right triangular prisms. Such as the
apatite or phosphate of lime, the primitive
form of which is a regular right hexahedral
prism, divisible parallel to its bases and its
planes, from which necessarily result right
prisms with three planes, as may be seen
by inspecting Fig. 66, which represents
one of the bases of the hexahedral prism
divided into small equilateral triangles,
which are the bases of so many moleculae,
and which, being taken two and two, as A ip
p k, C I G &c. form quadrilateral prisms
with rhombuses for their bases.*

By adopting then the tetrahedron in the
doubtful case, we reduce, in general, all
forms of integral moleculse to three, re¬
markable for their simplicity; viz. the pa¬
rallelepiped on, which includes the cube;
the triangular prism ; and the teti’ahedron.

This simplicity may furnish a reason for
the preference given to the tetrahedron in

* Model, No. S6.

160

ANALYSIS OF

fluor spar, and the other substances of which
we have spoken. The Abbe Haiiy, however,
forbears deciding on this subject, as the
want of accurate and precise observations
leaves to theory nothing but conjectures
and probabilities.

But the essential object is, that the dif¬
ferent forms to which the mixt structures
in question conduct, are assorted in such a
manner, that their assemblage is equiva¬
lent to a sum of small parallelopipedons,
as ^ve have seen to be the case in regard to
fluor spar; and that the laminre of super¬
position, applied on the nucleus, decrease
by subtractions of one or more ranges of
these parallelopipedons; so that the basis
of the theory exists independently of the
choice wdiich might be made of any of the;
forms obtained by the mechanical division.

By the help of this result, the decrements
to which crystals are subject, ■whatever be
their primitive forms, arc found brought
back to those which take place in sub¬
stances where this form, as w'ell as that of

INTEGRANT PARTICLES, &C. l6l

the molccultSj are indivisible parallelopipC’
dons; and theory has the advantage of
being able to generalize its object, by con¬
necting with one fact that multitude of
facts which by their diversity seem to be

little susceptible of concurring in a com¬
mon point.

Integrant pa^'ticles of Crystals.

The forms of the integrant particles of
crystals, as far as experiment and observa¬
tion have gone, may be reduced, as stated
page 159, to three, namely,

1. The regular tetrahedron, the
simplest of the pyramids, Fig. 1, Ph II.*

2. The triangular prism, the sim¬
plest of the prisms. Fig. 2, PI. Il.'f- and,

3. The cube, the simplest of the solids,
whose faces arc six in number, and pa¬
rallel two and two, Fig. 3, PI. II. %

* Model, No. 32. t Model, No. 33.

t Model, No. 3t.

V

l62 INTEGRANT PARTICLES

These geometrical solids, which perform
the office of the integrant molecuUe, arc all
the most simple, namely, those with four
sides, the least number possible to contain
a solid, those with five, and tliose with six.
They are all susceptible of an infinite
variety in the dimensions of their sides,
and in the inclination of the faces which
terminate them, although all have a fixed
term of regularity toward which they tend.
Thus the cube sometimes presents itself as
a rhomboid, with an acute or obtuse sum¬
mit, or as a parallelopipcd, or as a right or
oblique quadrangular prism, with a square,
rectangular or rhombic base. In some
cases the triangular prism is merely isos¬
celes, in others it is equilateral, and in this
last case the relation between its height
and the side of its base is various. The
tetrahedron undergoes analogous results; it
is sometimes regular, at others irregular.
And if these figures, says Hau 3 % are not
those of the true integrant molecules em¬
ployed by the mechanism of nature in the
structure of crystals, they deserve at least

OF CEYSTALS.

163

to supply their places in our limited con¬
ceptions. With such slender means nature
composes forms in an indefinite number,
and sufficient to establish a theory which
embraces so many extended results.

Since the integrant particles are the last
products of the crystal which preserves ah
exact proportion of its chemical composi¬
tion, they constitute the ultimate results to
wliich the mechanical analysis can be car¬
ried. And although the further practical
analj'sis of these bodies is out of our power,
yet we can form a very correct idea, and
indeed it may be demonstrated, that by a
further mechanical subdivision, were it
possible, their forms would not change.
Tlie integrant particles thus exhibited are
therefore the representative of the last pro¬
duct obtained by mechanical analysis, and
their union constitutes the crystal.

In a geometrical point of view they may
be pronounced'as containing the minimnm
of space under tlie maxiiMim of surface,
whence tlie primary forms of crystals
which are its first results, comprehend the

M 2

16'4 INTEGRANT PARTICLES, Scc.

maximum of space under the minimum of
surface, provided the inclination of tlie
planes be equal.

A table exhibiting the crystalline forms
of minerals, which have a common j)rimi-
tive form with the same dimensions, &c.
wilt be given at the end of this work. See
table of crystalline forms.

s

LAWS OE DECREMENT OE THE STRUC¬
TURE OP CRYSTALS—NATURI^^ AND
PRODUCTION OE SECONDARY EORMS,
SIMPLE AND COMPOUND——^DECRE¬
MENTS ON THE EDGES-DECREMENTS

ON THE ANGLES-INTERMEDIARY" DE-

C R E M E N T S- jM IX T DEC R E ME N T S-

DIFFERENCE BETWEEN STRUCTURE
AND DECRESIENT, &C.

IN the jireccding section it has been
stated, that the nucleus is the sj^nnuetrical
solid, which constitutes tlic primary fornu
arisins; from the union of the inteo:rant
particles, and constituting the first result
of their composition; now netwidary forms
are called all those which differ from the
primitive; they originate from the addition
of similar particles enveloping a primitive
solklj and piled round it according to cer-

166 LA^VS OF DEC REiM ENTS OF

tain laws. They are of two kinds, namely,
simple and compound. The former originate
from a simple law of decrement; the latter
are produced by the action of several laws
of decrement acting at once, or from a
single law, which has not attained its
limit.

In speaking of those solids we shall sup¬
pose them situated always in such a man¬
ner, that the line which may be considered
as their axis has a vertical position, and
then the faces parallel to this axis will
themselves bear the name of vertical faces,
whereas horizontal faces are called those
which are perpendicular; and the name
oblique faces those which are inclined to¬
wards it.

The laws of architecture or peculiar
modes of arrangements of the particles,
according to which are produced these
forms by virtue of those regular coverings
of crystalline laminae, which disguise under
such various forms one and the same primi¬
tive figure, are called laics of decrease or
laws of decrement of the structure of crystals,

THE STRUCTURE OF CRYSTALS. l67

and the layers of particles superposed upon
the nucleus receive the name of iamineE
of superposition.

Observation and the calculus have
shewn, that these laminse superposed to
the nucleus, gradually decrease in num¬
ber, sometimes on all the sides of the
nucleus at once, in consequence of the
substraction of one or more of their layers,
sometimes on particular sides only, so that
the abstractions of the particles have, for
the limit of their departure or origin, some¬
times all the edges, sometimes certain
sides, and sometimes the angles, sometimes
lines situated between the edges and the
angles of the nucleus, and it is the deter¬
mination of these laws of diminution, whe¬
ther partial, or total, or modified according
to certain geometrical rules, which disguise
the nucleus under such various forms, and
which give rise to such infinite variety of
crystalline solids met with in nature. The
hnvs of diminution or decrement which
have been observed are the following.

l68 DECREMEWTS ON THE EDGES.

I. Decrements on the Edges.

To render what has been stated more
obvious, let us proceed to illustrate by the
methods of synthesis and analysis, the pro¬
duction of secondary'forms. AVe shall for
that purpose take the rhomboidal dodeca¬
hedron, Tig. 66, and Fig. 8, Plate 11.^

which indeed ranks among the primitive
forms, but it also presents itself occasion¬
ally as a secondary solid, and in this case
it has, for a nucleus, sometimes a cube,
sometimes an octahedron. Let us sup¬
pose the nucleus to be a cube.

^ No, 35*

DECREMENTS ON THE EDGES. l69

To prove tliis Ijy analysis it will be ne¬
cessary to cut off successively the six
solid angles as S II T, &c. Tig. 06’, com¬
posed of four planes each, by cuts passing
through the minor diagonals of the faces.
These sections will successively lay open
six squares A I, 0 1, E 0 O T, 10 0 1,
See. which will be the faces of the cube*.
This cube being evidently an assemblage
of integrant particles of the same form, it
will be necessary that eacli of the six py¬
ramids resting on its faces be itself com¬
posed of cubes equal to each other, as
well as to those which constitute the primi¬
tive nucleus. This condition will be ful¬
filled, if w^e suppose that each of the faces
of the cube supports a series of decreasing
laminm eomposed of cubical particles,
every one of which exceeds that immedi¬
ately above it by one row of particles on
each of its six sides. This arrangement is

* Model, No. 35.

represented by Fig. IjPl. III.ivhere it may
be seen, that the last Ia 3 'er or plate of parti¬
cles is reduced to a single cube, marked s.
In the figure only three of the {[uadrangular
■pyramids are shown as suj>eradded to the
nucleus, it is easy to supply the other py¬
ramids mentaly. On examining the figure
attentively, we shall find that it lias been
traced on the supposition that the cubic nu¬
cleus has on each of its edges seventeen
ridges of molecules; whence it follows,
that each of its faces is composed of two
hundred and eighty-nine facets of mole-
culae, and that the whole solid is equal to
four thousand nine hundred and thirteen
molcculaj. On this h^^pothesis, there are
eight laminae of superposition, the last of
which is reduced to a simple cube, whose

edges determine the numbers of molecules
w'lucli form the series fifteen, thirteen,
eleven, nine, seven, five, three, one, the

DECREMENTS ON THE EDGES.

difl’erence being two, because there is one
course in breadth, substracted from each
extremity.

Now it is easy to conceive that the dif¬
ferent series will produce the triangular
fkces O S I, O E S, I 0 0 O T, 0 T I,

&c. Fig. 1, Plate III. and Fig. 66, page
l68, of these pyramids by the diminishing
edges of the lainiiiffi of superposition, which
arc obviously found on the same place; so
that they are alternately re-entei ing and
salient. But there are six pyramids, and
consequently twenty-four triangles. And
as the diminution is uniform throughout
the extent of the adjacent triangles upon
the contiguous pyramids, it results that the
triangles, taken two by two, form a rhom¬
bus. The surface of the solid will there¬
fore be composed of twelve equal and
similar rhombi, that is to say, this solid will
have the same form as that which is the
object of the problem.

In explaining this structure of a crystal,
or the production of a secondary form, from a

Id

172 DECREMENTS ON THE EDGES.

solid, although the representation
in the Fig. 1, PL III .* be such as shew the de¬
crement of the laniinm, by rows of particles
visible to the eye, or of such a size as re¬
sembles quadrangular flights of steps rest¬
ing on the six faces of the cube, it is ob¬
vious, if we substitute for this kind of
coarse masonry, which possesses the ad¬
vantage of speaking to the eye, the indefi¬
nitely delicate architecture of nature, the
number of laminje may be so immensely
great, and the minuteness of their cubical
particles so beyond comparison small, that
the depressions or channels of tlieir edges
will be altogether imperceptible to our
senses, and the surfaces will appear perfect
planes, and this is what takes place in the
crystals produced by the band of nature.

Such is an example of the production of
a simple secondary form, from a primitive
solid, by superposition of laminae accord-

* And also in the Model, No. 36.

DECEEMEISTTS OST THE EDGES. 173

ing to a certain law of decrement, and to
enumerate the result, we say that this
rhomboidal dodecahedron is produced in
virtue of a diminution by a single row of
ranges of moleculiE, parallel to all the edges
of the eubic nucleus. A crystal which has a
cube foi' its primitive figure may therefore
liavc a (hjdccahcdronfor its seeondary form.
To prove this by synthesis, it is only neces¬
sary to rear a series of cubical laminm on
each of the six sides of the cubic nucleus*,
in such a manner that each layer decreases
in surface on all the six edges, by the value
of one row of cubical particles of which it
consists, and thus continuing the super¬
structure until the last layer or apex is re¬
duced by the progressive route of the de¬
crement to a single cube.

In the figure, Plate III. Fig. 1,T the ratio

^ Model, No.se.
f And also in tlie Mode!, No. 56.

N. B* Any number of small cubes, [and also trian¬
gular prisms, or tetrahedrons,] calculated to imitate

2

174 D]lCREME>fTS ON THE EDGES.

of the decrement is represented as eqiial to
one row of particles, substracted from the
breadth of the superposed laminae, there¬
fore the height of the pyramid is equal to
half its length of one of the sides of its
base. For the second laminae is less by one
range in every direction than the first, and
the third is less than the second, and so on.
And as the sections are to be smooth, the
joints as stated already, must form one in¬
clined plane, therefore the ranges and even
the particles at the joints must not encroach
on each other; and hence it follows that
the number of ranges successively sub¬
stracted from each laminae can never be
incommensurable. Hence the theory de¬
monstrates that the existence of a regular
dodecahedron is not possible by virtue of
any law of decrement. And indeed it
does not exist in mineralogy.

artificially, the structure of the quadrangular pyramid
under considenition, may be had, with tliis treatise.

DECREMENTS ON THE EDGES. IJq

If the decrement in breadth, as it is
called, or parallel to the sides of the primi¬
tive form, [as in the case just cited,] where
the effect of the decrement is in the direc¬
tion of the breadth, is more rapid, that is
to saj, if it consists instead of one, of, 2,
3, 4, or more rows of particles, less than,
the inferior laminre, then the pyramids
produced on the nucleus by this decrement
being more flattened, their contiguous faces
can no longer be found two by two in the
same plane, the surface of the secondary
crystal will then be composed of twenty-
four distinct isosceles triangles all inclined
together.

Besides all this, the decrements of the
lamime of superposition may be considered
as taking place not merely in hreadih^ but
also in height, and the ratio, or coj7imon
difference of this latter, like the former,
may also vary from 1, 2, 3, 4, 5, to 6, or
more rows of particles, in wliich case the
height will be to the breadth of the py¬
ramid as 1.1, 1.^, 1.^, l.j*, l.j, l.gj
<5cc. and it not unfrequently happens that

176 DECEEMEBrTS ON THE EDGES.

these two kinds of decrements arc nnited
in the same crystal. Tlic dodecaticelron,

67

with pentagonal faces*', is an example of
the combination of these two kinds of de¬
crements; it results from a diminution of
square plates on a cubical nucleus, by t\vo
rows in breadth, on two of the sides of the
nucleus, and by two rows in height on the
two other sides, and as the decrements by
two rows in breadth tend to produce a
more inclined face, than the decrements by
two rows in height, each pile of superposed
lamina; will terminate not in a single cube,
but in a range of cubes, or supposing the

* Model, No. 37.

DECREMENTS ON THE EDGES* 177

cubes infinitely small, instead of termi¬
nating in a point, it 'will terminate in a
ridge or wedge-shaped summit* And the
whole solid will be bounded by twelve
equal and similar pentagonal faces, on ac¬
count of the regularity of the nucleus and
the symmetry of the decrement-

Tliese two kinds of decrement actually
exist in the following example, taken from,
the sulphuret of iron with pentagonal
faces*. This dodecahedron has a cube
for its nucleus, at the extraction of which
we should arrive by causing the cutting
planes to pass through the diagonals O I,
O E, A E, A I, &c. Fig. 68, which inter-

» Model, No. 37.

N

178 DECREMENTS ON THE EDGES,

cept the angles opposite to the basis,
whence it appears, that the portions super-
added to the nucleus, instead of being py¬
ramids as in the dodecahedron with rhom¬
boid al faces, are a species of wedge, re¬
sulting, as stated, from two decrements,
the one through two ranges in breadth pa¬
rallel to the two opposite edges O I, C E,
of the corresponding face A E, O I, of
the nucleus; the other through two ranges
in height parallel to the other edges E O,
A I of the same face, by which we see that
each decrement acts upon the different
faces of the cube, according to three di¬
rections respectively perpendicular, or so
as to cross each other at right angles.

On considering attentively Irig. 2, PI.
III.*' where we have rendered sensible to
the eye, the distinction of laminae of su¬
perposition, and the moleculae of which
they are the assemblage, it will be seen
that the progress of the decrement in breadth^
which contributes, for exam pie, to the for-

* Model, No. 38.

DECIlEMEIfTS ON THE EDGES. 179

ination of the additional part I O, jo and
which takes place parallel to the edge O I
and to its opposite, being more rapid than
that of the decrement in height, which is
made parallel to the edge 0 1 , and to op¬
posite, the two faces that spring from the
former must be more inclined than those
which are produced by the second; in
such sort, that each pile of decreasing la-
mince no longer terminates in a point but
in an edge f qi* moreover each trapezoid,
such as 0 p 5 i, Fig. 68 , page 177, what
results from the decrement in breadth being
upon the same plane with the triangle
G H in consequence of this that the decre¬
ment in height, which determines the latter,
is only the repetition in a contrary direc¬
tion of this decrement in breadth, the ag¬
gregate of the two figures forms a pentagon
■p 0 f i qi whence it follows, that the
secondary solid is terminated by twelve
equal and similar pentagons, by reason of

* Model, No. 38.
N %

180 DECREMENTS ON THE EDGES.

the regular figure of the nucleus, and of
the S 3 unmetry of the decrements.*

If it be supposed that the decrements
act according to two other laws, one of
which is always the inverse of that which is
combined with it, in such manner, that
there shall be three, four, &c. ranges sub-
stracted in breadth, and as many in height,
the result will still be a dodecahedron of
twelve equal and similar pentagons. It is
very evident that all these dodecahedrons
difier either from one another, or from the
proceeding dodecahedron, by the measure
of their angles. A multitude of new po¬
lyhedrons may be constructed, in illustra¬
tion of this fact, by simply piling cubes in
different ways, and according to the value
of the decrement we wish to produce.

Besides all this, the decrement may not
take place on all the edges but only on one
or tw'o of them, whilst no decrement at all
takes place on the others, the result of
which must be secondary forms very dif¬
ferent from each other: or the retrench-

* Model, No. 37,

DECREMENTS ON THE EDGES.

ment of the laminae may cease to be added
before they have reached their smallest

' l y* i v

possible size, the consequence of which
will be a secondary form, again different.
Thus, in the example given in illustration
of the synthesis of the structure of the
dodecahedron by virtue of a deci’ement,
by one range of small cubes on the eight
edges of a cubic nucleus, page 173; if the
superposition of the laminae had ceased
before the pyramids were completed, the
crystal would have consisted of eighteen
faces, six squares parallel to the faces of
the nucleus, and twelve hexahedrons pa¬
rallel to the faces of the secondary dodeca¬
hedrons. See Fig. 60.*

1S2! DECREMENTS ON THE EDGES,

We sliall conclude that which regards
the law of decrement on the edges^ by an
example drawn from the pyramidal do¬
decahedron, whose faces are scalene tri¬
angles, Fig. 70, which, as we have said

p. 125, is one of the varieties'of carbonate
of lime; here the nucleus is a rhomboid,
which also comprehends the cube, tlie axis
of which, that is to say, the line pass¬
ing through the two solid angles A A,
composed each of three equal obtuse
angles, must be situated vertically, that

DECREMENTS ON THE EDGES.

this rhomboid may be presented to the
eye under its true aspect, it results that
symmetry does not require as whh respect
to the cube, that the decrements operating
on any one E O, of the edges of one of the
faces, as A E O I, for instance, should be
repeated on the opposite edge A I, since
this latter which is contiguous to one of
the summits, has in some measure a mode
of being different from the other; it is
enough that all what takes places with
regard to the edge E O, obtains equally
in respect of the five others, O I, 1K, K G,
G H, H E, similar situated. One may
judge solely from an inspection of Fig.
70*, that these six borders or edges
which are common to the nucleus, and to
the secondary crystal, serve as lines of de¬
parture to so many decrements, which in
this case take place only with respect to
them, without any relation to the upper

.' 11 ^

184 DECREMENTS ON THE EDGES.

edges. That is to say, six in the upper
part, and as many in the lower, and all
these triangles will be scalene, on account
of the obliquity of the parting lines. The
figure on the plate facing the title of this
work will illustrate this kind of arrange¬
ment. It represents only the kind of upper
pyramid added to the nucleus, which being
thus partly uncovered, enables us to compre¬
hend more easily the progress and effects
of the decrement by two courses. The
salient and re-entering alternatives that are
formed by the laminie of superposition to¬
wards their decreasing edges, being no¬
thing as to sense in the crystal produced by
nature, the position line c s will represent
one of the edges contiguous to the summit,
such as it will be seen on the same crystal;
the difference between the geometrical sum¬
mit- s of the dodecahedron, and the phy-

* Model, No, 39.

DECKEMENTS ON THE EDGES. 185

sical summit S, vanishes by reason of the
extreme minuteness of the particles. In the
design, each edge of the nucleus has been
divided into ten; whence it follows that
every face is an assemblage of a hundred
small rhombs, which are the external facets
of as many molcculae. This construction
requires but eight laminse of superposition
for each of the same faces; and these
laminae being united together, three and
three, in the places which correspond to
the upper edges of the nucleus, form kinds
of decreasing envelopes which are succes¬
sively genei’ated, and the last of which is
composed of eight small rhomboids.^' If
we consider the position of the line e s,
which represents one of the terminating
edges, composed of all the solid angles
which are contiguous to it, we shall remark
that the geometrical summit s of the do¬
decahedron is situated above the physical

* Model, No. 39.

186 DECREMENTS ON THE EDGES.

aummit S, but this difference is considered
as nothing, on account of the extreme mi¬
nuteness of particles.

What we have said as to incTements as¬
sumed by the laminae of superposition to¬
wards their upper edges, in continuing to
envelop the crystal on this same side, is
a consequence of this general principle,
namely, that the portions of laminae, situ¬
ated out of the reach of the decrement,
extend, by mutually retrieving themselves,
in such a manner as to avoid the re-enter¬
ing angles which seem excluded by the
cr^^stallisation, at least in solitary crystals.
But we may abstract these simply auxiliary
variations, as the effect of decrements only
determines the form of the secondary crys¬
tal. It is even sufficient to take the decre¬
ments at their origin, in order to have as
many planes; and these again being after¬
wards extended in idea until they meet,
lead to the complete form of the polyhe¬
dron wMch they tend to produce. Hence
it is thus that we confine ourselves to the

4

DECREME^fTS ON THE ANGLES. 187

consideration of the initial effect of decre¬
ments, in calculation of which the progress
is always much more simple and expedi¬
tious than that of reasoning.

2. Decrements on the Angles.

Independently of the decrements which
take place parallel to the edges of the faces
of the nucleus, others occur in different
directions, namely.

Decrements on the angles are called-those
arrangements or decreases of the laminae of
superposition, of which the lines proceed in
a direction parallel to the diagonals of the
faces of the primitive nucleus.

This decrement, wdiich therefore has
angles for the points of departure, and the
action of which takes place parallel to the
diagonals drawn from one angle to the
opposite angle of the faces of the primitive
nucleus, follows the same laws as the
former, and will readily be understood from
the following example.

faces of a cubic nucleus, subdivided into a
multitude of little squares which will be
the faces of so many moleculas.

The ranges or rows of these particles
may be considered in two different direc¬
tions, namely, in the direction of the edges,
as the files lying in the line an qw s, &c. and
also in the direction of the diagonals of the
ranges, one of which is represented hy ah c
d efi &c. another by nt I m p o, and a
third by qv kuxy Zf the only difference is,
that here the moleculi® of the ranges pa¬
rallel to the edges, are simply placed side
by side, instead of which those that com¬
pose the ranges parallel to the edges, touch

DECREMENTS ON THE ANGLES. 189

each other by one of their/aces, the former
being parallel to the diagonals, are as if
dove-tailed into each other, they touch by
a ridge only, hence the faces produced by
virtue of^ the decrement are no longer
simply striated as in the decrease on the
edges, but are full of small points, which
being all on a level, and escaping the eye
from their minuteness, present the aspect
of a plain surface.

To illustrate this law of decrement let it
be understood, that the same substance,
which has a cube for its nucleus as a pri¬
mitive form, may appear under the shape
of a regular octahedron, and also under
the form of a pentagonal and rhomboidal
dodecahedron; and no case of decrement
on the edges can possibly produce an octa¬
hedron from a cubical nucleus; on the
contrary, if we actually dissect a regular
octahedron moulded on' a cube we shall
perceive, that the primitive nucleus is so
situated with regard to the octahedron,
that each of the eight solid angles of the

190 DECKEMENTS ON THE ANGLES.

former correspond with the centre of the
triangular faces of the latter*. A fact
wholly irreconcileable with the law of de¬
crement on the edges. To extract the nu¬
cleus of this octahedron, it is therefore
necessary to remove the six solid angles of
the octahedron by cuts perpendicular to
the axis, passing through the same angle,
and therefore jjuraiiel to the faces of the
cube-f-.

* Model, No. 40.

+ Model, No. 40.

DECREMENTS ON THE ANGLES. IQl

To explain this law more fully we shall
here again adopt the synthetical method,
and run over the series of laminae of super¬
position, indicating the auxiliary variations
which they undergo, and which assist the
effect of the decrement, to which every
thing may be refi rred. Let A E, O I,
Eig. 73,* be the superior base of the nu¬

cleus subdivided into eight3’^-one small
squares, or facets of moleculac, which will
be the basis of so many cubes, of which the
primitive cube is composed. What we are
about to say relative to this base may
equally be applied to the five other faces of
the cube.

* Model, No. 41, ■will fully explain the synthesis of
this crystal.

192 DECREMENTS 0,N THE ANGLES.

Fig. 74, represents the first lamina

of superposition, "which must be placed
above A E, O I, Fig. 73j io such a man¬
ner that the point e answers to the c,
the point 4 to the point a of 73, the point
b to the point o, and the point i to the
point i. We see, in the first place, by this
arrangement, that the squares E e, A
0 0 , I *, Fig. 73, remain uncovered, which
is the initial effect of the law of decre¬
ment alluded to.

We see moreover, that the edges Q V,
P N, L C, F G, Fig. 74, project by
one row beyond the edges E A, E O, 0 1,
X A, Fig. 73, which is necessary, that the
nucleus may be enveloped towards the
same edges, and that the solid may increase

DECREMENTS ON THE ANGLES. 193

as usual in the parts to Avhich the decre¬
ment does not extend.

The superior face of the second laminae
will be similar to B K, II D, Fig. 73,

B

and it must be placed above the preceding,
in such a manner that the points e", a", i",
0 ", may answer to the points e, d, i.
Fig. 74, leaving the squares, which have
their external angles situated in Q, S,
R, P, V, T, M, G, &c. and continuing
to effect the decrement by a row. We
also see here that the solid increases suc¬
cessively towards the analogous edges at
E A, E 0, A I, O I, Fig. 73> since
between B and FI, for example. Fig. 75,
there are thirteen squares instead of there

194 DECREMENTS ON THE ANGLES.

being only eleven between Q Y and L C,
Fig. 74; but as the effect of the decre¬
ment confines more and more the surface
of the laminae in the direction of the dia¬
gonals, nothing else is wanted than to add
towards the unchanging edges a single
cube, denoted by B, K, II, or D, Fig.
75, instead of the five, which terminate the
preceding lamina along the lines Q V,
P N, L C, F G, Fig. 75.

The great faces of the lamina of supei-
position, which were hitherto octagons,
Q V, G F, C L, N P, Fig. 74, having
reached tlie figure of the square B K, H D,
Fig. C 75, will, after passing this point,
decrease, so that the following laminae will
have for its great superior face, the square
B' K' ir D', Fig. 76, which is less by

DECllEMENTS ON THE ANGLES. 195

one row in every direction than the square
B K, H D, Fig. 75; we shall dispose the
first above the second, so as to make the
points c', A', g\ Fig 76, answer to the

pointsc,/, A,g, Fig. 75. Figs.77,78,79,and
80, represent the four laminae which ought

successively to rise above the preceding,
with this condition, that the similar letters
correspond as above. The last laminae
will be reduced to a single cube. Fig. 81,
o 2

196 DECREMENTS ON THE ANGLES.

f

and which ought to rest on that repre¬
sented by the same letter. Fig. 80.

It follows from what has been said, that
the laminse of superposition, when applied
on the base E A 1 O, Fig. 73, produce,
by the assemblage of the decreasing edges,
four faces, which, issuing from the points
E, A, I, 0, are inclined towards each
other under the form of a pyramidal sum¬
mit.

We must now remark, that the edges in
question have lengths which commence by
increasing, as we may observe by in¬
specting Fig. 74> and Fig. 73, and then
proceed to diminish, as we may judge by
the following figures. Hence it results, that
the faces produced by the same edges go
on enlarging from their origin to a certain
point; and when past this, they begin to
contract themselves so as to constitute
two triangles joined base to base, or a qua-
drilater. We see, Fig. 24, one of these
quadrilaters, and in which the inferior
angle o is blended with the angle 0

DECREMENTS ON THE ANGLES. 197

of the nucleus, Fig. 82, and the diago-

s

nal t X represents the edge H K, Fig. 76,
of the laminae B K H D, which is the
most extensive in the direction of this same
edge. As the number of the laminae of
superposition producing the triangle t o
Fig. 82, is less than that of the laminae
constituting the triangle t o .r, and as there
is here only a single lamina which precedes
the lamina B K H D, Fig. 76, while there
are six which follow it as far as the cube z.
Fig. 81, inclusively, the triangle t s x. Fig.
82, composed of the aggregate of the bor¬
ders of these last laminae, will be much
higher than the inferior triangle t o x, as
expressed by the figure.

198 DECREMENTS ON THE ANGLES.

The surface of the secondary solid will
therefore be formed of twenty-four quadri¬
laterals, disposed three and three around
each solid angle of the nucleus; but as, in
decrements by a simple range on all the
edges, the faces produced on both sides of
each edge are on the same plane; so in
decrements by a range on all the angles,
the faces which originate in the three sides
of each solid angle, such as O, Fig. 72,
page 190 , are on a level so as to form but
one face: and since the cube has eight
solid angles, each composed of three plain
angles, the secondary crystals will have
eight faces, which, on account of the re¬
gularity of the nucleus, will be equilateral
triangles, i. e. the secondai*y crystal will be
a regular octahedron. One of these tri¬
angles is represented at Fig. 83, Z N I C
so as to

"L

DECREMENTS ON THE ANGLES. 199

enable us to judge, at a single glance, of
the arrangement of the cubes which concur
in forming it.

This level of faces produced by subtrac¬
tions of a range from both sides of the
same edge, or around the same solid angle,
is a general result of the crystallisation
which takes place for any primitive form
whatever.

The circumstance just considered, and
which occurs in muriate of soda, sulphu-
ret of iron, sulphuret of lead, &c. affords
a new example of a form which, although
primitive in certain species, performs in
others the function of a secondary one.
Theory thus b’aces the limit that separates
objects which the eye would be tempted to
confound.

If the decrements had not their complete
effect, that is to say, if tliey stopped short
of the limit where the faces they produce
incline to unite in a point, some faces pa¬
rallel to those of the nucleus would remain
on the secondary crystal. The first would
then have fourteen faces, namely, six

200 DECREMENTS ON THE ANGLES.

ranged like those of a cube, and eight
situated like those of a regular octahedron.*
Nothing is more common in crystals of
sulphuret of iron, than this modification,
to which Haiiy has given the name of
cubo-octahedral sulphuret of iron. Here
the remark again occurs which we made
with respect to decrements on the edges.
If we confine our consideration to the im¬
mediate effects of decrements on the angles
of two opposite faces, for example, on those
of the bases A E O I, A' E' O' I', Fig. 73,
and if we subsequently imagine the eight
faces to which these decrements give exist¬
ence, are prolonged between the bases to
the point of intersecting each other, the
result will always be a regular octahedron,
supposing that the decrements obtain their
limit.

If the law' of these decrements followed a
more rapid course, viz. if more than one
course was subtracted, then the three tra¬
pezoids S T 0 X, Fig. 82, of which three

♦ Mode), No. 42.

- DECEEMENTS ON THE ANGLES. 201

would be formed around the same solid
angle, could no longer be on a single plane;
they would incline towards each other, and
the secondary solid would have twenty-
four faces which would also be trapezoids,
but with angles of a different measure.

Let us now choose for a primitive form
the rhomboid represented by Figure 84,

A

which differs from the cube in being a little
more acute.

Suppose that the laminte which adhere
over all tlie faces of this rhomboid decrease
solely on the angles contiguous to the sum¬
mits A, O, and that this decrement takes
place by two ranges; then, instead of
twenty-four faces no more than six will be

202 IJJTiillMEDIAllY MECKEMENTS.

formed ; and if we conceive them prolong¬
ed until they meet, they will compose the
surface of a very obtuse rhomboid, which
will be the secondary form.

Fig. 85 represents this rhomboid with

85.

f

O'

its nucleus. We there see that its summits
A, O', are blended with those of the primi¬
tive rhomboid, which are the parting
limits of the decrements, and that each of
its faces, such as A e o corresponds with
one of the faces A E O 1 of the nucleus, in
such a manner that the diagonal which *
passes by the points e, *, is parallel to that
which goes from E to I, and has merely a
more elevated position.

Observation shows that this result is
realized by crystallisation in a variety of
oligiste or specular iron ore, which bears
the name of binary specular iron ore.

IWTERMEDIARY DECREMENTS. 203

The decrement on the angles, like those
on the edges, are susceptible of many va¬
riations with regard to height or in breadth,
and the effects thence resulting may be
calculated, but on this subject it is unne¬
cessary to speak.

3. Intermediarif decremaits.

There are certain crystals in which the
decrements are neither parallel to the edges,
nor to the diagonals of the faces of the pri¬
mitive nucleus, but in directions parallel to
lines situated between the diagonals and
the edges.

For example, let ah de^ Fig. 86, repre-

86 .

f/h e

/

''A.

€ -

d

1 1

sent the face of a cube, divided into a mul-
3

2104 INTERMEDIAET DECREMENTS.

titude of little squares. The decrement call¬
ed intermediary, in this case does not effect
the cubes in the directions of the diagonals
a d, or e h, but it takes places according to
lines situated between the diagonals a d,
and c b, namely, in directions represented
hy / C) hi g, or in any other imaginable
direction, and this happens when the ab¬
stractions are made by ranges of double,
triple, &c. particles. Fig. 87 exhibits an

instance of the subtractions in question j
and it is seen that the raoleculae which
compose the range represented by that
figure are assorted in such a manner as if •
of two there were formed only one ; so that
we need only to conceive the crystal com¬
posed of parallelopipedons having their
bases equal to the small rectangles abed,
e df g,h gi I, &ic. to reduce this case under
that of the common decrements on the
angles. This particular decrement is uu-

INTERMEDIARY DECREMENTS. 205

common, it follows otherwise the same
laws.*

It is a general rule therefore, that in all
cases the lamina decrease in arithmetical
progression, and its rates or the number of
ranges is always commensurable.

We have seen that in the case of a decre¬
ment by one range round one and the
same solid angle, O, Fig. 72, the three
faces produced were always on a level, and '
that in this case we might confine ourselves
to the consideration of the effect of the
decrements with respect to one of the
plane angles, which concurred to the for¬
mation of the solid angle, by supposing
this effect to be prolonged above the adja¬
cent faces. In this case the decrements
which take place on these latter faces, are
i;eckoned as intervening in a subsidiary
manner, in order to favour the action of
the principal decrement.

In general, whenever a solid angle of the

* Model, No. 49, will be sufficient to illustrate the
action of the law of decrement, called intermediary.

4

i '■ \ ^

INTEllMEDIARY DECREMENTS,

primitive form undergoes decrements which
tend to give rise to a facet in its place,
whatever be the law of that to which we
refer the production of this facet, there are
always auxiliary decrements, the concur¬
rence of which is necessary in order that
the facet in question may be properly pro¬
longed. Now, when this decrement, which
we consider in preference, takes place by
two or more ranges, the auxiliary decre¬
ments which form a continuity with it fol¬
low a law entirely peculiar, namely.

Let A A, Fig. 88, be any given paralle-

88 .

lopipedon, which undergoes a decrement
by two ranges on the angle E 0 I, or its

INTERMEDIARY DECREMENTS. 207

base A E O I. It is evident, that the
edges of the laminie of superposition will
have directions h c, r s,* parallel to the
diagonal, which goes from E to I, and si¬
tuated in such a manner that there will be
on the edges O E, O I, two ridges of mo-
leculaj, comprised either between the term
of departure O and b c, or between b c and
r s. But as we have said, the laminae ap¬
plied on tlie adjacent faces I O A' K,
Fi O A' H are lineally disposed like b g, r t.
For since the lower edge of the first lami¬
nae, applied on A E O I, coincides with

* We must conceive that the subtractions, which are
here represented on the quadrilater A E O I, take
place successively on the different laminse of superpo¬
sition. The distances between each of these laminae
and the succeeding one being tlie same with that which
exists between the lines 6 c, r and all the rest simi¬
larly situated, we may, for the sake of greater conveni¬
ence, refer the whole, as we do in the present instance,
to the quadrilater A E O I, as a kind of scale which
gives the measurements of the subtractions operated by
the decrement on the corre.sponding laminae.

308 INTERMEDIAUr DECREMENTS,

6 e, and as the height of this lamina answers
to a ridge of a moleculae, we may, with a
little attention, conceive that the plane
beg, which in one part also coincides
with b c, and in another is removed from
the base A E O I in a quantity measured
by a ridge O g- of a molecule, is necessa¬
rily parallel to the face produced by the
decrement It is the same with the plane
r t s; from which it follows, that if we
suppress the part situated above r t s we
shall have a solid, on which the facet r t s
will represent the effect of the decrement
under consideration.

We may now observe, that the direc¬
tions c g, s t, of the laminfB ap]ilicd to
the face I O A' K, (and the same may be
said of the face E O A' H), in virtue of
the auxiliary decrement, are no longer pa¬
rallel either to the edges or to the diagonal,
but are situated between both. A fortiori,
the defect of parallelism will take place,
if we suppose that the decrement on the
angle E O I of the base proceeds by three,
four, or more ranges. Decrements of this

MIXED DECREMENTS. 209

kind are called intermediate; and we con¬
ceive that they may be referred to an infi¬
nity of different directions, according as
they are more or less removed from the one
or other of their limits, which are the paral¬
lelism with the ridges and the parallelism
with the diagonals.

We see by these details, to which we
could give a much greater latitude, that
the intermediate laws, the existence of
which is in other respects hitherto confined
to a trifling number of cases, produce
forms equally simple with those which ori¬
ginate from the ordinary laws, and that
their theory even leads to results which
would deserve to be followed and developed
as a simple object of curiosity.

4 . Mixed Decrements.

It may happen that each lamina of su¬
perposition exceeds the following by two
ranges of particles in breadth or parallel
to the edges, and that it may at the same
time have an altitude triple that of a single

p

9 ^' 1 '

!i»l

DECREMENTS.

molecule, or by three ranges in breadth
and two in height In this case, therefore,
the decrement, whether it takes place on
the angles or on the edges, varies according
to laws, the proportion of which cannot
be expressed but by the fraction two-thirds
or three-fourths. It may happen, for ex¬
ample, that each lamina exceeds the follow¬
ing by two rows parallel to the edges, and
that it may at the same time have an alti¬
tude triple that of a simple molecula.
Fig. 89»* represents a vertical geometrical

section of one of the kinds of pyramids
which would result from this decrement;
the eflFect of which may be readily con-

* Model, No. 44,

MIXED DECREMENTS.

211

ceived by considering that A B is a hori¬
zontal line, taken upon the upper base of
the nucleus ; b a z r, the section of the
first laminse of superposition ; gf e n, that
of the second; and d c p o the third. The
theory of this law may easily be referred
to that of decrements, in which there is
only a single range substracted in one of '

the two directions. It occurs but rarely.

Haiiy has only met with mixed decrements
in some metallic crystals.

In what has been so far stated we have
confined ourselves simply to the considera¬
tion of those forms which depend upon a
single law of decrement, and what pro¬
duces simple secondary forms.

The name, compound secondary forms^
is given to those which proceed from seve¬
ral simultjmeous laws of decrement, acting
at once, or from a single law which has not
attained its limit; and which of course has
left on the secondary crystal, faces parallel
to those of the primitive nucleus.

Let us suppose, for example, that th*

p 2

212

MIXED DECREMENTS.

' law which gives the octahedron originating
from the cube, Fig. 72, page 190, is com¬
bined with that from which results the do¬
decahedron with pentagonal faces. Fig.
68, page 177* The first will give rise to
eight faces, which will have as centres the
solid angles of the nucleus, and it is easy
to see that each of these faces, for instance
that whose centre coincides with the solid
angle O, Figs. 67, p-175, and 68, p. 177,
will be parallel to the equilateral triangle
whose sides would pass by the points p, .s, i.
In the same w^ay the face whose centre will
be confounded with the angle o, will be pa¬
rallel to the equilateral triangle, whose
sides would pass b}'^ the points s, n, p; but
the second law produces faces situated like
pentagonals cut by the sides of the tri¬
angles p s #, Slip. Now the sections of
these triangles on the pentagon # O s O' n,
reduce the latter into an isoscele triangle,
which has for its base the line t n, and
whose two other sides pass, the one by the
points tf .s, the other by the points n, s. It
is the same with the other pentagons;

IDEAS OF BUEE.

213

whence it follows that the secondary solid
will be an isosahedron terminated by eight
equilateral triangles, and twelve isoscele
triangles.

Such is the nature of the decrements of
the structure of crystals, which account for
the metamorphoses which these bodies pre¬
sent ; and the truth of which is rendered
legitimate by the mechanical division of
crystalline bodies, and the geometrical cal¬
culation of their angles.

From what has been stated with regard
to the laws of decrement, the problem
which must be proposed to discover the
generation of each of the forms of crystals
may therefore be expressed thus;

A secondary crystal being giveUf as well
as the figure of its nucleus^ and that of its
integrant particle, being likewise given, sup¬
posing moreover that each of the laminae,
that will be added to the nucleus, does not
project so far or overlaps by the preceed-
ing in certain parts, by a quantity equal to
one, two, three, &c. ranges of moleculae, to
determine among the dijferent laws of decre~

\

214

IDEAS or BUEE

ments, the law from which a dmilar form to
that proposed will remilt^ with respect to the
mmiber^ the figure, and the disposition of its
faces, and the measure of both its faces and
solid angles.

Before we conclude this subject we shall
transcribe some ingenious speculations ad¬
vanced by the Abbe Bue6j* concerning the
question why the same crystallisable ma¬
terial is induced to crystallise in such vast
varieties of forms, for this question has not
been treated by the Abbe Haiiy.

First causes, says the Abbe Buee, are not
the object of this discussion. IJe states
the question thus:—Why does the same
subject ci ystallise in such a variety of forms,
ai^vays symmetrical and always tcrniiiiatcd
by planes?

“ The solution of this question seems to
require three conditions:

“ ist. That the particles of the substance
dissolved in the fluid all leave the state of

* Nicholson’s Journal, vol, ix. October, 1804.

CONCERNING CRYSTALLISATION. 215

rest at the same instant, to form the crys¬
tal by their aggregation.

“ 2clly. That, while these particles are in
the act of drawing near to each other, no
foreign power shall imprint on them
any other motion than a common mo¬
tion, whether it be in a straight line,
or rotary round their common centre of
gravity.

“ 3dly. That the particles all arrive at the
state of rest at the same instant, which
takes place when the act of crystallisation
is finished. The second condition is neces¬
sary, and infers the first and third. The
natural consequence of these conditions
will be, that the aggregation of the parti¬
cles will only take place conformably to a
law acting equally on all of them, whatever
the law may be.

“ Since they all leave the state of rest at .
the same instant, they are in equilibrio
previous to that instant. Since they all
arrive at the state of rest at the same in¬
stant, they are in equilibrio after that in¬
stant; but when particles that are acted

216

IDEAS OF BUE6

upon by no other force than that which
they exercise on each other, arc in equili-
brio, they are in the closest possible union
that concomitant circumstances will per¬
mit. If the particles were in cquilibrio
previous to their leaving the state of rest,
something must have obstructed their ap¬
proach. Let us suppose that something to
be the interposition remains equilibrium is
maintained. But this can only be the case,
inasmuch as the whole of the particles of
the interposed substance are in cquilibrio
with the whole of the particles dissolved
and about to leave the state of rest, which
in the future I shall call the proper particles.
If by any cause which acts uniformly on
the whole surface of the dissolvinjj fluid
any of the interposed particles are sub¬
tracted, the proper particles must cease to
be in equilibrio. A step toward aggrega¬
tion will immediately take place, and the
equilibrium will be restored. A further
subtraction will produce a further step to¬
ward aggregation, and a consequent equi¬
librium ; and these operations will be re-

CONCERNING CRYSTALLISATION. 217

peatcd so long as the cause of subtraction
continues, and the longer its duration the
larger will be the resulting crystalline
mass.

“ If the above mode of reasoning be ad¬
mitted, it will suffice to apply the laws of
equilibrium to deduce the laws of crystal¬
line forms. The laws of equilibrium to
which I allude, are those of the equilibrium
of fluids, which certain modifications I
shall presently state. According to these
laws, that the preceding conditions may
take place in the formation of a crystal, it
will be necessary that they take place in the
formation of each and every part of it,
whatever may be the figure or the small¬
ness of those parts. They must also take
place in those last crystals which contain
the least possible number of particles; and
as these particles are in equilibrio, and in
the greatest possible state of proximity to
each other which circumstances will per¬
mit, it must follow, to fulfil all the condi¬
tions, that these particles form a syrame-

218

IDEAS OF EUEE

trica] polyedron. This peculiar disposition
of llie crystalline particles constitutes the
modification, to which I alluded, in the*
laws of the equilibrium of fluids ; it being
necessary in this case to take the number
of crystalline particles into account, which
is not the case when treating of the par¬
ticles of a fluid.

In a fluid, the particles and their reci¬
procal distances are supposed infinitely
small; but the crystalline particles and
their distances to each other must be sup¬
posed finite. This material difierence will
necessarily cause a difference between the
forms of their aggregates. Those formed
■with the particles of a fluid will be bounded
by curved lines; the crystalline aggregates,
on the contrary, will be terminated by
straight lines; and when these straight
lines are not too small, the boundaries will
be sensibly rectilinear.

“ To ascertain what the power is that
holds the particles in the state of rest,
though not in close contact, is not the

CONCERNING CRYSTALLISATION. 210

question ; but the form of the polyhedrons
which they produce. The closer adhesipn
"of the particles to be obtained by the sub¬
traction of caloric, sufficiently demon¬
strates that the particles are not in close
contact with each other, and the constancy
of the crystalline forms equally proves that
they are in equilibrio.

“ We shall now proceed to the construc¬
tion of a crystal with these crystalline par¬
ticles. That the constancy of the form in
the large crystal be preserved, the particles
must be in equilibrio. That the equili¬
brium be preserved, the forces that solicit
the particles to motion must mutually de¬
stroy each other. That the mutual destruc¬
tion of those forces be effected, these forces
after having been decomposed into other
relatively parallel to three axes perpendi¬
cular to each other, and having a common
point of intersection, must each meet in its
direction another force equal and diame¬
trically opposed to it. This will be ob¬
tained if the similar particles are arranged
on straight lines parallel two and two at

S20

IDEAS or BUEi

equal opposite distances from the common
centre, and bisected by lines passing
through that centre; but if tlie particles*
are thus arranged, they must produce sym¬
metrical solids bounded by planes; and
they are thus arranged : for if a foreign
force, an excess of caloric for example,
does not impede the free arrangement of
the particles in the formation of the crystal,
their exterior disposition will follow as
much as possible their interior arrange¬
ment ; but their interior arrangement must
be on straight lines, or the crystal would
cease to be homogeneous; their exterior
disposition will therefore be on straight
lines.

As the circumstances giving rise to the
approach of the particles may be in the
highest degree variable, it must follow as
the forms produced may be diversified in
the extreme. This is the answer I should
submit for the solution of the question pro¬
posed.

“ When speaking of the approach of the
proper particles, I said that it might be

1 '

C02JCERT!fING CRYSTALLISATIOIf.

occasioned by the subtraction of certain
interposed particles which obstructed the
^ approach of the proper particles. The for¬
mer are generally water, caloric, or any
fluid elastic or not. Tlieir exit may per¬
haps make place for others, such as light,
electricity, &c. &c. But the essential point
is, that whatever these particles may be,
they are in perfect equilibrio with the pro¬
per particles, otherwise they would become
perturbing forces.

“ hlence it follows, that not only the in¬
tegrant particles of the crystals, but all
those that are mixed with them, the che¬
mical or component particles and even the
vacuities, must follow the same laws. It
also follows, that if each species of particle
(even the chemical) that enters into the
formation of the crystal be separately con¬
sidered, each species will have its distinct
symmetrical and polyhedral form. The
forms will penetrate each other, while the
particles will not only not penetrate, but
not even touch each other. All forms
would stand in the same predicament as

222

IDEAS OF BFEE.

the regular octahedron, which contains, as
has been shewn by the Abbe Haiiy, six
I’egular octahedrons and eight regular tetra¬
hedrons, each tetrahedron containing one
octahedron and four tetrahedrons. It will
further follow, if the chemical electments
can be looked upon as particles which are
not in contact with each other, that we
may from thence mathematically determine
chemical affinities.

STRUCTURE AND INCREMENT. 223

PART in.

SECTION I.

DIFFERENCE BET WEEN STRUCTURE AND
INCREMENT, AS RELATING TO THE
PRODUCTION OF CRYSTALS-SINGU¬

LAR ALTERATIONS ABSOLUTELY AC¬
CIDENTAL, TO WHICH THE SYMMETRY
OF CRYSTALS IS subject; reversed
POSITIONS OP THE FACES OF CRYS¬
TALS-PRODUCTION OF TWIN-CRYS¬

TALS, HEMITROPES, MACLES, &C.

In the preceding development of the
theory of crystallography, we have supposed
that the component laminae of crystals origi¬
nally of one and the same species, issue from
one common nucleus, undergoing decre¬
ments subjected to certain laws, upon which
the forms of these crystals depended.

But here it is only a conception, adopted
3 .

224

DIFFERENCE BETWEEN

to make us more easily perceive the mutual
connections of the form in question. Pro¬
perly speaking, a crystal in its entire state
is only a regular group of similar moleculse.
It does not commence by a nucleus of a
size proportioned to the volume which it
ought to acquire, or, what comes to the
same thing, by a nucleus equal to that
which we extract by the aid of mechanical
division ; and the laminae which cover this
nucleus are not applied successively over
each other in the same order in which the
theory regards them. The proof of this is,
that among crystals of different dimensions
which are frequently attached to the same
support, those which can only be distin¬
guished by the microscope are as complete
as the most bulky; from which it follows,
that they have the same structure, viz.
they already contain a small nucleus pro¬
portioned to their diameter, and inveloped
by the number of decreasing laminae ne¬
cessary, in order that the polyhedron
should be provided with all its faces. We
do not perceive these various transitions

STRUCTURE AND INCREMENT. 225

of the primitive to the secondary forms,
which ought to take place if crystallisation
constructed as if by courses, the species of
pyramids* superadded to the nucleus, in
eoins from the base to the summit. This
however is only generally true; for it some¬
times happens, in artificial crystallisation,
(and it is very probable that we may say
as much of that of natural bodies), that a
form, which had attained a certain degree
of increment, suddenly undergoes varia¬
tions by the etfect of some particular cir¬
cumstance. We must therefore con¬
ceive, for example, that from the first
instant a crystal, similar to the dode¬
cahedron with rhomboidal planes derived
from the cube (sees' page l68, &c. Figure
65), is already a very small dodecahe¬
dron, which contains a cubical nucleus
proportionally small, and that in the fol¬
lowing instance this kind of embryo in¬
creases without changing its form, by nevv
strata which envelop it on all sides; so
that the nucleus increases on its part,

226 DIFFERENCE BETWEEN

always preserving the same relation with
the entire crystal.

We shall make this idea apparent, by a
construction relative to the dodecahedron
now mentioned, and represented by means
of a plain figure. What we shall say of
this figure may easily be applied to a
solid, since we may always conceive a plain
figure, like a section made in a solid. Let
E R F N, Fig. 90, be an assortment of
small squares.

90 . eC

0

T

L.A,r

G

Tt

«_

1

!t

1

—

is

in which the square A B C D, composed of
forty-nine imperfect squares, represents the

STRCrCTURE AND INCREMENT. 227

section of the nucleus*, and the extreme
squares R S, G A, I L, &c. that of the
kind of steps formed by the lamina? of su¬
perposition. We may conceive, that the
assortment has commenced by the square
A B C D, and that different piles of small
squares are afterwards applied on each of
the central square; for example, on the
side A B, in the first place, the five squares
comprehend between I and M, afterwards
the three squares contained between L and
O, and then the square E. This progress
corresponds with that which would take
place if the dodecahedron commenced by
a cube proportioned to its volume, and
which afterwards increased by an addition
of laminae continually decreasing.

But on the other hand, we may ima-

* This section is that which would pass by the points
s », Fig. 66, page 168, of the dodecahedron, and by the
centres of the ridges E O, A I, &c. of the nucleus.

338

DIFFERENCE BETWEEN

giae that the assortment had been at first
similar to that which is represented bjr
Fig. 91,

in which the square abed is only com¬
posed of nine moleculre, and bears on each
of its sides only a single square e nf or r.
If we refer, in imagination, this assortment
to the solid of which it is the section, we
shall easily judge that this solid had for its
nucleus a cube composed of twenty-seven
molecules, and of which each face, com¬
posed of nine squares, carried on that of'
the middle, a small cube, so that the decre¬
ment by one range is already exhibited in
this initial dodecahedron.

This assortment, by means of an appli¬
cation of new squares, will become that

3

STRUCTURE AND INCREMENT. 229

of Fig. 92, in which the central square
ah c d

./

is formed of twenty-five small squares,
and carries on each of its sides a pile of
three squares, besides a terminal square'
e n f or r. Here we have already two
laminae of superposition instead of one
only. Finally, by an ulterior application,
the assortment of Fig. 92, will be changed
into that of Fig. 90, where we see three
laminae of superposition.

These different transitions, of which we
are at liberty to continue tlie series as
far as we please, will give an idea of the
manner in which secondary crystals may
increase in volume by preserving their

230

REVERSED POSITIONS OP

form; from which we may judge that the
structure is combined with this augmenta¬
tion ; so that the law, according to which
all the laminae applied on the nucleus
when it has attained its greatest dimensions
decrease successively, was already, as it
were displayed in the growing crystal.

Singular alterations absolutely accidental
to which the symmetry of crystals is subject ;
reversed positions of their faces ; production
of hemitropes or macles,

WE have hitherto considered crystallisa¬
tion as impressing on its results the charac¬
ter of the greatest possible perfection, and
producing nothing but isolated forms, ex¬
empt from every salient angle that could af¬
fect their purity and symmetry. It remains
for us to describe certain accidents which,
under the appearance of exceptions or
anomalies, still possess a latent tendency
towards the same laws to which the struc¬
ture is subjected, when nothing deranges

THE FACES OF CRYSTALS. 231

their progress or disturbs their har-
mon}’'.

The forms of crystals are subject to va¬
rious kinds of alterations absolutely acci¬
dental. Namely, in certain cases some of
the faces of a crystal are nearer to, or
more distant from, the centre than in others
which belong to the same species, in such
a way however as constantly to preserve a
certain character of symmetry. In several
cases these variations only fall on the di¬
mensions of the faces, and not on the
number of their sides. In other cases, the
faces themselves, or some of them at least,
change their figure by the increase or dimi¬
nution of the number of their sides.

In ordinary crystals, the faces adjacent
to each other always form salient, and
never re-entering angles. But crystalline
forms also exist which present these last
angles; and Rom6 de LTsle was the first
who observed, that this effect took place
when one of the two moieties of a crystal
was in a reversed position with respect to

the other. A very simple example will en¬
able us to conceive this reversed position.
Let us suppose that B d, Fig. re¬

presents an oblique prism of hcmi-trope
field-spar with rhomboidal bases, situated
in such a manner that the faces A D d a,
C D d c, are vertical, and B D are the
acute angles of the base; and the latter
proceeds in a rising direction from A to C.
Let us besides suppose, that the prism is
cut into halves, by means of a plane which
should pass by the diagonals drawn from

THE FACES OP CRYSTALS. 233

B to D, and from b to d, and that the half
situated on the left, remaining fixed, the
other is reversed without being separated
from the former. The crystal will be pre¬
sented under the aspect which w'e see in
Fig. .94,* where the triangle 6' d' c', which

was one of the halves of the lower base,
Fig. 93, is now situated in the upper part
Fig. 94, and forms a salient angle with the
fixed triangle A B D, while the triangle
B D C, Fig. 94, which was one of the

» Model, No, 45.

234

REVERSED TOSITIOKS Of

halves of the superior basCf Fig. 93, is
transported into the lower part, Fig. 94,
and forms a re-entering angle with the fixed
triangle a h d.

AVe can easily conceive that the plane of
junction D Ji b d of the two halves of a
rhomboid, is situated like a face produced
in virtue of a decrement by one range on
one or other of the ridges A a, C c, Fig.
93; and thus the manner in which these
two halves join, is in strict relation to the
structure.

Now if we imagine a secondarv form,
which has for its nucleus the same prism,
and if we suppose that it has been cut in
the directions of the plane D B d, and
that one of its halves is a’cversed in such a
manner, that the half of the nucleus which
corresponds with it, assumes the same posi¬
tion as in the preceding case, the assort¬
ment might be such that there is still a re¬
entering angle on one hand and a salient
angle on the other, which will result from
the mutual incidences of the faces produced
by the decrements,

In certain cases the plane of junction,
on which the two halves of the crystal are
joined, is situated parallel to one of the
faces of the nucleus, and the assortment
does not admit of presenting a re-entering
angle opposed to a salient angle.

The Abbe Haiiy has given to these re¬
versed crystals the name hemi-tropes, de¬
noting one-half reversed. Roni6 de LTsle
calls them macks. But this name being
already applied to a very common species
of mineral, Haiiy thought proper to avoid
the double application of the term.

The transimecl spinel, exhibits striking
example of the transposition of the faces of
certain crystals. The primitive form of the
spinel or true ruby, is a regular octahe¬
dron, Fig. 95 , composed of two four-sided

rru#

M 4

pyramids applied base to base, with equi¬
lateral triangular faces- Now, if we con¬
ceive that this solid be cut obliquely
from e. to g, iFig. 96)’^ into two halves,

A,

96. '

\

\

! ■ - ...

/.

^ s

as shown by A B, Fig. 97> and that one-

) /

half of the crystal, for example B,had turned

* Model, No. 46.

THE FACES OF CRYSTALS. ^37

Upon the other half A, in a quantity equal
to a sixth part of a circle; the crystal would
present itself as shewn, Fig. 98,* exhibit¬

ing a solid with alternate salient and re¬
entering angles.

The ores of tin, also present some very
singular liemi-tropc crystals. The so called
twin crystal of oxide of tin, is very com¬
mon It consists of a four-sided prism,
terminated at each extremity by a four-
sided pyramid q-, which, by a transposition

^ Modely No, 46.
+ Model; No, 47.

338 KEVERSED POSITIONS, SCC.

of the parts, presents itself as shown,

Fig. 99-

In this instance it appears as if an
oblique section had been made, and the
two portions had turned half round on each
other, so as to form at each extremity two
re-entering angles*.

Another accident, extremely common, is
the manner in which grouped crystals are
inserted into each other. This kind of ap¬
parent penetration is subject to so many
diversities, that frequently, among crystals
of the same groupe, we do not find two re¬
lative positions resembling each other.
But although, in general, the positions in
grouped crystals are infinitely variable, we
find, on a closer examination, that they are

* Model, No. 48.

PENETRATION OF CRYSTALS. 239

subjected to certain laws always analogous
to those of the structure; and that these
crystals, instead of being tumultuously
precipitated on each other, have in some
measure concerted their arrangement.

I^et us also on this occasion choose a
very simple example. Let A C, Fig, 100,

be a cube, and M N r an equilateral trian¬
gular facet, produced in the place of the
angle A, in virtue of a decrement by one
range round this same angle.

Let us suppose a second cube modified
in the same manner, and affixed to the
former by the facet which results from the
decrement indicated by 3VI, N, r. We shall

240 PENETKATIOK' OP CRYSTALS,
thus have the assortment represented by

Fig. 101

We may now conceive that one of the
two cubes, that, for example, which is
placed below, is increased in all its dimen¬
sions, except at the places where the other
forms an obstacle to it. In proportion as
this increment becomes more considerable,
the upper cube will be more and more en¬
veloped in the inferior one, and it may
even finish by being entirely masked or
concealed by it.

^ Model, No. 49.

PENETRATION OF CRYSTALS. 241

AVe observe crystals effectually sunk into
each other at various depths; but which
have always a plane of junction situated
like a face produced by a decrement, in
such a manner that the two structures fol¬
low their ordinaiy progress, each on its
own part, the length of this same plane,
which serves as their respective limit. The
Abbe Haiiy having divided cubes of fluate
of lime inserted into each other, remarked,
that the laminae of each, extended without
interruption, until suddenly stopped by the
common plane of junction.

The example now quoted relates to a
very simple and very regular law of decre¬
ment. But frequently the laws which de¬
termine the plane of junction are more or
less remote from this simplicity, and there
are a few which are somewnat extraor¬
dinary.

When two prisms cross towards the mid¬
dle of their axis, there are two planes of
junction, which unite, crossing each other
as is the case in the mineral called stau-

R

243 PENETRATION OF CRYSTALS,

rolite. Fig. 103*,

h

If the two prisms a a and b h cross each
other, as in Fig. 103, at riglit angles, the
mineral receives the name of rectangular
staurolite. If the two prisms cross each
other oblique, as Fig. 103, it is called

* Mode}, No. 50.

PENETRATION OF CRYSTALS. 243

oblique angled staurolite. In Fig. 103, the
prisms intersect each other at an angle of
60 ^^; and it may be demonstrated, that the
planes also have positions analogous to
those which would be determined immedi¬
ately by the known laws of decrement.

R 2

344 ELECTllICITy OP CRYSTALS.

SECTION 11.

ELECTRICITY OF CRYSTALS AS CON¬
NECTED WITH THEIR GEOMETRICAL
FORM, AND CRYSTALLINE SYMMETRY
—ELECTRIC poles; THEIR SITUA¬
TION, AND MODES OF DISTINGUISH¬
ING THEM, &C,

THERE appears to exist a singular re-
Jation between the forms of such crystals
as possess the capability of becoming elec¬
tric by heat or friction, and their crystal-
.line symmetry. All those crystalline bodies
as arc susceptible of becoming electric by
heat or friction, Haiiy has observed, devi-

i

ELECTRICITY OF CRYSTALS. 245

ate remarkably with regard to the symme¬
try of their faces.

The parts in which the two eleetricities
reside, though similarly situated at the two
extremities of the cr 3 'stal, differ materially' in
their configuration; one of them undergoes
decrements, whieh are evanescent upon the
opposite part, or to which decrements cor¬
respond that are subjected to another law;
which may enable an observer to predict
beforehand, simply from the inspection of
the crystal, on what side either species ot
electricity Avill be found, Avhen the crystal
shall be submitted to the test of expe¬
riment.

The electrical state of minerals is either
ipliis or minus, [positive or negative.] Haiiy
has found, that each of the minerals has al¬
ways at least two points, of which one is the
seat of positive, or plus, and the other that
of negative, or minus electricity. To these
points, which are always placed in two op¬
posite parts of the mineral, Haiiy gives
the name of electric poles. To distinguish

346 ELECTRICITY OF CRYSTALS.

these poles one from the other, a very simple
apparatus has been adopted. It consists of
a needle of silver or of brass, terminated at
its extremities by two globules. This needle,
like the common compass needle, is move¬
able upon a pivot, or stem, having a very
fine point, and at the bottom a broad base
or foot. This stem with the needle are in¬
sulated by placing them upon a cylindrical
support of resin. To use this apparatus
we place a finger of the left hand upon the
foot or base of the upright stem, and taking
into the right hand a stick of sealing wax
which has been rubbed, present it, during
a second or two, at a small distance from
the stem; this being done, we withdraw first
the finger, and afterwards the stick. Thus
will the needle be found electrified minus;
in such manner that, according as we
bring near to one of the globules, the ne¬
gative or the plus pole of a crystal elec¬
trified by heat, the globule is attr^icted or
repelled. The electricity of the needle will
be preserved a quarter of an hour or

ELECTRICITY OF CRYSTALS. 247

longer, and we may, Avliile generating it,
render it either very sensible or very weak,
(according as it may be required for the
experiment proposed) by varying the dis¬
tance between the stem and the stick of
sealing wax.

The tourmalin^ being the first in which
the property of becoming electric by heat
was traced, and which crystallises usually
in nine-sided prisms four sides, terminated
by three, six, nine, or more sided pyra¬
mids. "When this crystal is at the ordi¬
nary temperature, it is only susceptible
of being electrified by friction, and in that
case the part rubbed always acquires posi¬
tive electricity. But if a tourmalin be
gently heated, it becomes electric; and if
its two extremities be afterwards presented
alternately to the little globe, we shall ob¬
serve that the one attracts and the other
repels that globe, from which we may as¬
certain the poles wherein the respective
electricities reside. That side which ter¬
minated by the pyramid is positive, the
3

248 ELECTRICITY OF CRYSTALS.

other negative, AVhen the crystal is of a
large size, flashes of light may he seen
along its surface. Now it may be con¬
ceived that the tourmalin, having only its na¬
tural quantity of electfiicity, 'svhich is alone
acted on, if its positive pole iS, turned to¬
wards the globule, it will be in the same
case as if it were solicited singly b}^ a quan¬
tity of positive electricity whose force was
equal to the difterence between the forces of
its two poles, arising from the diflerent dis¬
tances at which they act: therefore the glo¬
bule wall be repelled. Similar reasoning
will prove that, on the contrary, attraction
ought to be evinced, if the tourmalin is
presented to the globule by its negative
pole.

But if the needle were not insulated, it
is easy to conceive that the presence of
either of the poles of the tourmalin would
generate, in the globule nearest to that
pole, an electricity contrary to its own;.
whence it follows that the globule w'ould, in
this case, be constantly attracted.

ELECTRICITY OF CRYSTALS. 249

If one of the poles of the tourmalin be
presented to light bodies, such as grains of
ashes, or saw-dust, each grain, becoming in
like manner a slight electric body, whose
part turned towards the pole which acts
upon it has acquired a contrary electricity
to that of such pole, will be carried towards
the tourmalin. Having arrived at contact,
it will generally remain applied there ; for
the tourmalin, which is a non-conducting
body, not being able to communicate its
electricity to the light body, all will con¬
tinue in the same state as before. It often
enough happens, however, that some of
these grains are repelled as soon as they
have touched the stone. This effect obtains
when the minute bod}' has met with some
ferruginous or other conducting particles,
situated at the surface of the tourmalin.
In such case, if it be supposed for example
that this particle possessed negative elec¬
tricity, a portion of its electricity will pass
to the contiguous part of the little body,
which is occupied by the positive electri¬
city, and will unite or restore the equili-

•.4

250 ELECTRICITY QP CRYSTALS.

brium. Then the negative electricity which
enveloped the other part of the little body
finding itself in excess, that body will be
entirely in the negative state; whence it
must follow, that the conducting moleculae,
which is in a similar state, will repel it.
Hence we see in what manner those au¬
thors must be understood, who assert, that
the tourmalin is attracted and repelled in¬
differently by its two ends, without pro¬
ducing those constant effects of attraction
on one side, and repulsion on the other,
which we have ascribed to it. These latter
effects only take place with a tourmalin
placed opposite a body which is already
itself in a certain state of electricity. The
others, which are variable, have respect to
the case where the bodies on which the
tourmalin acts were previously in their
natural state.

In a tourmalin the electric densities di¬
minish rapidly in departing from the extre¬
mities, so that they are nothing, or next
to nothing, in a sensible space situated to¬
wards the middle of the prism : of conse-

ELECTE-ICITY OF CRYSTALS.

quence, tlie centres of action are situated
near the extremities. It may be rendered
perceptible to a certain degree, by moving
a tourmalin to and fro that has one of its
faces opposite one of the globules of the
little needle: we shall observe that this
globule has a marked tendency towards one
point of the crystal; but when it corres¬
ponds with the mean part, so that the two
centres of action are each equally remote
from it, we shall not find any motion, ex¬
cept a mere fluttering or vibration given
to the globule.

Two electrical crystals of tourmalins pre¬
sented one to another, mutually attract by
tlie poles animated with contrary electri¬
cities, and repel mutually by the poles
which shew the same kind of electricity.

If we lieat two tourmalins, and after hav¬
ing laid one of them across upon a flat
piece of cork, floating on the surface of
water, we select one of its poles, and to it
present successively the two poles of the
tourmalin. When the poles thus brought near

§52 ELECTRICITY OE CRYSTALS.

to one another have different electricities,
we shall see the floating tourmalin move
towards the other, and follow it in all its
motions. If, on the eontrary, the neigh¬
bouring poles are solicited by opposite
states of electricitieSj the floating tourmalin
will turn about to present itself to the other
by the contrary pole, and then approach
to it in virtue of the electric attraction.

The tourmalin begins to evince electri¬
city when it has arrived at a certain eleva¬
tion of temperature [of about F.]

But among bodies of this species there
exist some to which we need only, as it
were, shew fire, that they should manifest
their electricity. If the tourmalin be more
and more heated, there will be a terra
where it will cease to yield signs of the
electricity. It often happens that after
having withdrawn it from the fire, we are
obliged to leave it to return of itself to a
moderate temperature, that it should have
any action upon the little bodies which are
presented to it. But it w'ould seem that

ELECTRICITY OF CRYSTALS. 253

beyond the term where its electricity has
become insensible through the action of too
strong a heat, there is another where its
effects are reproduced in an inverse sense.
We have caused the foci of two burning
glasses to fall upon the extremities of a
tourmalin, and have observed that each
pole, after having acquired its ordinary
electricity, would next cease to act, and
lastly would pass to the opposite state; so
that the attraction, after having become
zero, would give place to repulsion, or re¬
ciprocally.

If a tourmalin be broken at the moment
when it manifests its electricity, each frag¬
ment, however small it may be, has its two
moieties in two opposite states, in like
manner as the entire tourmalin; which must
at first appear very singular, since this
fragment, supposing for example it were
situated at one of the extremities of the
crystal still whole, would then be solicited
only by a single kind of electricity. This
difficulty may be happily resolved by

S54 EIECTRICITY OF CETSTALS.

i

the help of a very plausible hypothesis
similar to that advanced by Coulomb with
regard to such magnetic bodies as present
the same singularity, that is to say, by
considering every integrant particle of a
tourmalin to be itself a little tourmalin
provided with its two poles. It hence re¬
sults that in the entire tourmalin there will
be a series of poles alternately plus and
minus; and such are the quantities of free
electricity which appertain to these differ¬
ent poles, that in all the half of the toarma-
lin yet unbroken, which manifests the plus
electricity, the plus poles of the integrant
raoleculae are superior in force to the minus
poles in contact with them; while the con¬
trary obtains in the half which manifests
the minus electricity: whence it follows
that the tourmalin is in the same state
(speaking generally) as if each of its halves
were only solicited by quantities of plus or
minus electricity equal to the diftt;rences be¬
tween the fluids of the neighbouring poles.
Now, if the crystal be cut at any place

ELECTRICITY OP CRYSTALS. 255

whatever as the section can only take place
hetmen two moleculae, the part detached
will necessarily commence with a pole of
one kind, and terminate with a pole of a
contrary nature.

In the variety of the tourmalin, which
Haiiy calls isogone, the shape of which is
that of a nine-sided prism, terminated at
one end by a summit having three faces,
and at the other by a summit having six
faces; and experiments prove that the first
summit is the seat of minus electricity,
while the second manifests plus.

Of all the crystals that exhibit this cor¬
relation between the exterior configuration
and the electric agency, the most remark¬
able are those which appertain to the mi¬
neral named horacite or borate of magnesia^
whose form is, generally, that of a cube
truncated, or incomplete on all its edges,
and farther bevelled, that is to say, mo¬
dified by facts corresponding to the solid
angles. Here the two electricities act ac-

256 ELECTRICITY OP CRYSTALS.

cording to the directions of four axes, each
of which passes through two opposite solid
angles of the cube. In one of the varieties
which Haiiy calls defective^ one of the two
solid angles situated at the extremities of
the same axis is entire, the other has given
way to a decrement or facet. Now minus
electricity is evinced at the angle which has
not undergone any alteration, and plus at
the facet which supplies the place of the
opposite angle ; thus making eight electric
poles, four positive and four negative.

AVe may no\v ask whether, in the midst
of the imposing apparatus of our artificial
machines, and of that diversity of pheno¬
mena which it presents to the astonished
eye, there is any thing more calculated to
excite the interest of philosophers than
these little electrical instruments executed
by crystallisation, than this combination of
distinct and contrary actions, confined
within a crystal ivhose greatest dimension
is probably less than a twelfth of an inch ?

ELECTRICITY OF CRYSTALS. 257

Of the series of crystals of the mineral
kingdoms which become electric simply by
heat, the following are the most conspi¬
cuous :—Borate of magnesia, Brazilian
topaz. Tourmalin, Phrenite, Crystallised
Oxide of zinc, or Electric Calamine, Si-
berite, Lepidolite, Kaupolite.

s

258

DOUBLE REERACTION.

SECTION in.

DOUBLE REFEACTIOIf OF CRYSTALS.-

MEANS EMPLOYED FOR OBSERVING

IT-MINERALS POSSESSING THE POWER

OF DOUBLE REFRACTION.

WHEN a ray of light passes obliquely
from one medium into another of a dif¬
ferent densityj it is bent out of its straight
course, and assumes a new direction. This
deviation which is called refraction^ is sub¬
jected to a constant law.

Certain substances have the singular pro¬
perty to solicit the ray which penetrates
them to divide itself into two parts which
follow two different directions. This is
called double refractiori; hence objects seen
through them appear double.

' .4

DOUBLE REFRACTION. ^59

When the refraction is simple, we only
perceive a single image of an object seen
through two faces of the solid employed on
this occasion, whereas, if it were double,
we might in the same case see two images
of the object. This property was first no¬
ticed by Erasmus Bartholinus, by looking
at the image of a line, through a trans¬
parent rhomboid of carbonate of lime
which came from Iceland, and hence called
Iceland crystal, or double refracting spar.

If a ray of light be received perpendicu¬
larly upon a plane surface of this crystal,
one part of it passes through without alter¬
ing its direction; another part on the con¬
trary is refracted in a plane parallel to the
diagonal, joining the two obtuse angles of
the crystal, so that objects seen through it
appear double. This property no doubt
depends on the particular arrangement of
the crystalline laminae composing the crys¬
tal. In order to obtain this effect with
most of the crystals endowed with the pro¬
perty in question, we must choose two
faces of the crystal inclined towards each

8 2

260 DOUBLE REFRACTION.

other, whether we employ a crystal given
by nature or a piece cut by the lapidary.

The quantity of double refraction, or,
what comes to the same thing, the opening
of the angle formed between each other by
the rays, by means of which the eye sees
the two images, varies from one substance
to the other, every thing else being con¬
sidered according to the nature of the sub-
stances themselves.

In the zircon, for instance, the double
refraction is very strong, whereas it is
much less perceptible in the emerald. Be¬
sides, this quantity varies in every sub¬
stance, from various causes. In general it
increases or diminishes, according as the
rcfrangent angle, or that which is formed
between each other by the two faces,
through which we view objects, is more or
less open.

But there is another cause of variation,
which is combined with the foregoing, and
which depends on the position of the re-
frangent surfaces relatively to the faces of
the primitive form; and such is the indu-

DOUBLE REFRACTION. 26i

ence of this cause, that under two equal
refrangent angles dilferently situated, we
may have distances evidently unequal be¬
tween the images of the same object, and
there is even a limit at which the effect of
the double refraction becomes null, e.
the two images are then confounded into
one.

This limit takes place, for instance, in
rock crystal or quartz and in the emerald,
when one of the faces which belong to
the refrangent angle is perpendicular to
the axis. It takes place in sulphate of
barytes, when one of the same faces being
parallel to the axis, is at the same time
parallel to a plane which should pass by
the great diagonals of the bases of the pri¬
mitive form.

There is a second method employed for
observing the double refractive power.
It consists in taking a pin by the point,
and presenting it against the window at a
certain distance from the eye, against
which we keep at the same time the
mineral applied by one of its faces. By

\

262 DOUBLE KEFRACTION.

making the pin assume various positions,
we shall find that there is one in which we
see two distinct images of the pin parallel
to each other, and generally prismatic
(irisies). Then, if we gently turn the
pin until it is perpendicular to its first posi¬
tion, we shall see the two images approach
by degrees, until they fall upon one and the
same line, in such a manner, however, that
one of the two heads will frequently exceed
the other. We may also make use of a
card on which we have traced a line with
ink of a good tint.

When the double refraction is not con¬
siderable, it may happen that the two
images touch each other. But, upon at¬
tentively examining the head of the pin,
we can distinguish at this place as it were
two small circles which intersect each other:
and besides, we shall observe that the same
colour which edges on one side the prisma¬
tic band reappears on the line of the mid¬
dle part, where the same series recom¬
mences.

The separation between the images is

DOUBLE REFRACTIOlf.

263

more sensible, the distance between the
object and the eye and all other circum¬
stances being alike, when the diaphanous
body used in the experiment is of a greater
thickness. And if we suppose this thick¬
ness, in its turn, to be constant, and the
object removed from the eye, the two
images will be more and more removed
from each other, at the same time that they
will be diminished in distinctness.

The following is a third advantageous
process for short-sighted people. Place a
lighted candle at a certain distance in a
dark room. Having afterwards made a
a hole in a card with the point of a pin,
apply it to one of the faces of the stone,
so as to make the hole correspond to a
point of this face; then having approached
with the eye the opposite face, seek the
position proper for enabling you to per¬
ceive the flame of the candle. You will
then have the two images distinct and well
defined, because the effect of the hole
made with the pin is to dismiss the kind

264

DOUBLE REFEACTION.

of irradiation •which dazzles them, when
we employ the stone by itself.

If a ray of light 'vvhich has suflbred
double refraction from one crystal be re¬
ceived by another crystal, placed in a simi¬
lar and parallel position, there is no divi¬
sion of the image.

But if the second crystal be placed
that its planes of perpendicular refraction
are at right angles to those of the first
crystal, there then is a new phenomenon,
and that part of the ray which before passed
through the ordinary refraction, renroves
the extraordinary one. And reciprocally,
that which underwent the ordinary refrac¬
tion suffers the extraordinary one.

If the second crystal be moved gradu¬
ally round in the same plane, when it has
made a quarter of a revolution, there will
be four divisions of the ray, and they will
be reduced to two in the half of the re¬
volution, so that the refractive power de¬
pends upon the relation of the arrangement
of the particles of the crystal with regard
to the rays passing through them. »

• DOUBLE REFRACTION. 265

The minerals, which possess the power
of double refraction, are the following:

Iceland spar, sulphate of lime, sulphate
of barytes, sulphate of strontia, quartz or
rock crystal, zircon, emerald, corundum,
euclase, arragonite, feldspar, peridote, sul¬
phur, carbonate of lead, sulphate of iron.

266

PRINCIPLES OF NOMENCLATURE

PART IV.

SECTION I.

PRINCIPLES OF CRYSTALLOGRAPHIC NO¬
MENCLATURE-—APPLICATION OF THE

WORD PRIMITIVE-SECONDARY FORMS

CONSIDERED WITH RESPECT TO THE
MODIFICATIONS WHICH THEY PRE¬
SENT OF THE PRIMITIVE FORM-SE¬

CONDARY FORMS CONSIDERED IN
THEMSELVES, AND AS BEING PURELY

GEOMETRICAL-SECONDARY FORMS

CONSIDERED RELATIVELY TO CER¬
TAIN FACETS, OR CERTAIN RIDGES,
REMARKABLE FOR THEIR ARRANGE¬
MENT OR POSITION-—SECONDARY

FORMS CONSIDERED RELATIVELY TO
THE,LAWS OF DECREMENT ON WHICH
THEY DEPEND, &C.

IF the language of mineralogy has been
SO long defective, from the bad choice of
specific expressions, the almost total defici¬
ency of names with respect to the varieties

OF CRYSTALLOGUAPIiy. 267

of crystallisation has left a void, which was
no less an inconvenience. There was no
exception, except with respect to a small
number of these varieties, the forms of
which were so simple that they would sug¬
gest as if of themselves the epithets of cu¬
bical, octahedral, dodecahedral, &c. which
ought to be added to the names of the
species. The more compound forms were
indicated by definitions, the length of
which was in some measure proportional
to the number of the facets; or, if it was
wanted to abridge these definitions, by
borrowing them from a resemblance be-
tween the crystal and some familiar object*,
this was done with so little rationality, that
it would have been desirable for the honour
of the comparison if such names were less
known.

Convinced of the necessity of introduc¬
ing the utmost precision into this part of

* The following are examples of this kind; nail¬
headed calcareous spar, dog-toothed calcareous spar, &c.

268 PRINCIPLES OP NOMENCLATUEE

mineralogical language, so much neglected
hitherto, Haiiy has attempted to designate
the various crystalline forms by simple and
significant names, taken from the characters
of these forms, or from the properties which
result from their structure, and from the
laws of decrement on which they depend.
We shall here present the readers with the
series of these names, under the form of
a methodical system. We hope that those
who peruse it with attention will find an
assistant for engraving these names on their
memory, by connecting them with consi¬
derations which are easily classified in the
mind. They will perceive that, by a kind
of economy of language, extremely useful
in such cases, the same name is frequently
applicable to varieties taken in different
species. It is true that on one hand the
word which serves to designate such a va¬
riety might also serve another variety of the
same species. For example: Haiiy denomi¬
nates binaryy a form which depends on a de¬
crement by two ranges. How supposing this
decrement to take place on the edges, it is

3

OP CRYSTALLOGRAPHY. S69

possible that another variety of the same
substance may be owing to a decrement
which takes place by two ranges on the
angles. But in this case the system will
present for the latter another name bor¬
rowed from a different consideration. The
inconvenience just mentioned is common
to all nomenclatures, and seems unavoid¬
able. Thus, in the language of botany,
one variety will bear the name of crassi-
foUa, or of rotundifolia, while another va¬
riety of the same species shares with the
first the character which has served to dis¬
tinguish it. The essential requisite is, that
the method should be copious enough to
furnish at least to all the known wants of
science. It is presumed that, by means of
this attempt, a great part of the forms
which shall be discovered in future will
be found to have been named beforehand;
and as to those which require new names,
we shall have at least a system from which
to designate them. In all descriptions of
researches, it becomes easier to go forward
when the route is traced.

270 PRINCIPLES OP NOMENCLATURE

Principles of the Nomenclature.

The primitive form of any given sub¬
stance is always designated by the word
primitive added to the name of the species.

Examples :— Primitive zircon, primitive
carbonate of lime, primitive sulphate of lime,
&c.

We may consider secondary forms :—

1. With respect to the modifications of
the primitive form, when the faces of the
latter are combined with those which re¬
sult from the laws of decrement.

2. By themselves, and as purely geome¬
trical forms.

3. With respect to certain facets or cer¬
tain ridges remarkabte by their assortment
or their positions.

4. With respect to the laws of decre¬
ments on which they depend.

5. With respect to the geometrical pro¬
perties which they present.

OP CRYSTALLOGRAPHY, 271

6. Finally, with respect to certain parti¬
cular accidents.

1. Secondary forms considered with respect
to the modif cations which they present of
the primitive form.

The crystal is called,

Fyramidated (pyramid ^), when the pri¬
mitive form being a prism, has on each of
its bases a pyramid which has as many
faces as the prism has sides.

Example: Fyramidated phosphate of
lime.

Prismated (prismi), when the primitive
form being composed of two pyramids
joined at their bases, these pyramids are se¬
parated by a prism.

Ex. Prismated zircon, prismated quartz.

Semi-prismated, when there is only the
half of the number of ridges situated
around the common base, which are inter¬
cepted by faces.

373 PRINCIPLES OF NOMENCLATURE

Example. Semi-prismated sulphate of
lead.

Based (basi)., when, the primitive form
being a rhomboid, or an assemblage of two
pyramids, the summits are intercepted by
facets perpendicular to the axis, and per¬
forming the function of bases.

Ex. Based carbonate of lime, based sul¬
phur.

Pointed ('epoijitS)y when all the solid
angles of the primitive form are intercepted
by solitary facets.

Ex. Pointed mesotype.

We shall also use the terms Unpointed
(bisSpointe) f tripointed (triSpointS) ^ qua-
dripointed (quadriSpointS) ^ according as
each solid angle may be intercepted by
two, three, or four facets.

Ex. Tripointed analcime, quadripointed
sulphuret of iron.

Marginated (emarginS), when all the
ridges of the primitive form are each of
them intercepted by a facet.

Ex. Marginated garnet.

OF CRYSTALLOGRAPHY.

273

We shall also use the term hi-marginated,
tri-marginated, as each ridge is intercepted
by two or three facets.

Example. Tri-marginatcd garnet.

Peri-hexahedral, peri-octahedral, peri-de¬
cahedral, peri-dodecahedral, when the pri¬
mitive form being a prism with four sides,
is changed by the effect of decrements into
a hexahedral, octahedral, decahedral, or
dodecahedral prism.

We also denominate peri-dodecahedron a
crystal, the nucleus of which being a regu¬
lar hexahedral prism, has its six longitudi-
nal ridges intercepted by as many facets.

Ex. Peri-hexahedral sulphate of copper,
peri-dodecahedral emerald.

Pecurved (raccourci), when the primi¬
tive form being a prism with rhombic bases,
the longitudinal ridges contiguous to the
grand diagonal are intercepted by two
facets, which make it appear diminished in
the direction of its length.

Ex. Recurved sulphate of barytes.

T

274 PRINCIPLES OF NOMENCLATURE

Retreated (rStrSci), when the primitive
form beiog a prism with rhombic bases, the
longitudinal ridges contiguous to the small
diagonal are intercepted by two facets
which make it appear diminished in the
direction of its breadth.

Example* Retreated sulphate of barytes.

2. Secondary forms considered in themseheSj
and as being purely geometrical.

The crystal is called,

Cubical., when it presents the form of the
cube, which in this case is always se¬
condary.

Ex. Cubical fluate of lime.

Cuboidal, when its form differs a little
from the cube.

Ex. Cuboidal carbonate of lime.

Tetrahedral^ when it presents the form of
the regular tetrahedron, as a secondary
form.

Ex. Tetrahedral sulphuret of zinc.

OF CEYSTALLOGRAPIIY. 275

Octahedral, when it presents the form of
this solid, as secondary.

Example. Octahedral muriate of soda,

Frismatic, when it has the form of a
straight or oblique prism, the panes of
which are inclined one hundred and twenty
degrees among each other.

o o

Ex. Prismatic carbonate of lime, prisma*
tic feldspar.

Dodecahedral, when its surface is com¬
posed of twelve triangular, quadrangular,
or pentagonal faces, all equal and similar,
or solely of two measurements of different
angles.

Ex. Dodecahedral quartz, dodecahedral
zircon, dodecahedral sulphuret of iron.

If the dodecahedron had not all its faces
of the same number of sides, it would be
.sufficient to bring them to this aspect in
imagination, by varying its dimensions.

Icosahedral, when its surface is com¬
posed of twenty triangles, of which twelve
are isosceles, and eight equilateral.

T 2

276 PiillfCIPLES OP JfOMENCLATUIlP

Example! Icosaliedral sulphuret of iron.

Trapezoidal^vihen its surface is composed
of twenty-four equal and similar trape¬
zoids.

Ex. Trapezoidal garnet.

Triaconta/iedral, when its surface is com¬
posed of thirty rhombuses.

Ex. Triacontahedral sulpliuret of iron,

Eimmconiahedralj when its surface is
composed of ninety laces.

Ex. Enneacontahedral idocrase.

'BivhomboidaU when its surface is com¬
posed of twelve faces, which being taken
by sixes, and lengthened in imagination
until they intersect, would form two differ¬
ent rhomboid.s.

Ex. Birhomboidal carbonate of lime.

We say trirhomhoidal in the same man¬
ner.

Ex. Trirliomboidal carbonate of lime.

Biform, triform, when it contains a com¬
bination of two or three remarkable forms;

such as the cube, the rhomboid, the oc-
taliedron, the regular hexahedral prism.
See.

Example. Triform sulphate of alumine.

Cubo-octahedral, cubo-dodecahedral, cubch
tetrahedral. See., when it contains a combi¬
nation of the two forms indicated by these
expressions. ,

Ex. Cubo-octahedral fluate of lime, cubo-
dodecahedral sulphuret of iron, cubo-tetra-
hedral gray copper.

Trapezian, when its lateral surface is
composed of trapezia situated on two rows
between two bases.

Ex. .Trapezian sulphate of barytes.

Ditetrahedral, i. e. twice tetrahedral,
I when its form is that of a tetrahedral prism
' with dihedral summits.
f Ex. Ditetrahedral grammatite.

I JDihexahedral, when it forms a hexahe¬
dral prism with trihedral summits.

Ex. Dihexahedral feldspar.

277

OF CRYSTALLOGRAPHY.

278 PRINCIPtES OF NOMENCLATURE

'We say in the same manner, dioctahe-
dral, dukcahedral, didodecahedral.

Example. Dioctahedral topaz, diclecahe-
dral feldspar, didodecahedral phosphate of
lime.

Trihexahedral^ ietrahexahedral, pentahex-
ahedral, heptahexahedral, when its surface
is composed of three, four, five, sev’^en rows
of facets ' disposed in sixes the one above
the other.

Ex. Trihexahedral nitrate of potash,
pentahexahedral quartz, heptahexahcdi'al
nitrate of potash.

We also say in the same manner, trido-
decahedral.

Ex, Tridodecahedral sulphureted anti-
monial silver.

Trioctahedral.

Ex. Trioctahedral sulphuret of lead.

Bigeminated, when it presents a combi¬
nation of four forms, which, taken by twos,
are of the same species.

Ex. Bigeminated carbonate of lime.

4

OF CRYSTALLOGRAPHY.

Amphihexahedral, i. e. hexahedral in two
ways, when by taking the faces according
to two different directions, we have two
hexahedral contours.

Example. Amphihexahedral axinite.

Sexdecimal, wlien the faces which belong
to the prism or to the middle part, and
those which belong to the two summits, are
the former six in number, and the latter
ten in number, or vice veisd.

Ex. Sexdecimal feldspar.

In the, same manner we say octode-

cinal. 'ifSl..

>af.

Ex. Octodccimal feldspar.

•’17

Sexduodecimal.

Ex. Sexduodecimal carbonated lime.

Octoduodecimal.

Ex. Octoduodecimal sulphuret of copper.

Deciduodecimcd.

Ex. Deciduodecimal feldspar.

'Peripolygonaly when the prism has z,
great number of sides.

-'■#14

* J M ■

\my^'

280 PRINCIPLES OF NOMENCLATURE

Example. Peripolygonal tourmaline.

Supercomposite^ when the form is very
much compounded.

Ex. Super composite tourmaline.

Aniienneahedral, i. e. having nine faces
on two opposite sides, is a name peculiar to
a variety of the tourmaline, in which the
two summits arc of nine faces, and the
prism of twelve sides; whereas, generally,
the prism is enncahedral.

Prosenneahedral, i. e. having nine faces
on two adjacent parts, is another variety
of the tourmaline, in which the prism and
one of 'the two summits have each nine
faces.

Recurrent, when, on taking the faces of,
the crystal by annular rows, from one ex¬
tremity to the other, we have two numbers,
which succeed several times, as, four, eight,
four, eight, four.

V Ex. Recurrent oxid of tin,

R^uidifferentj when the numbers which

OF CRYSTALLOGRAPHY.

281

designate the faces of the prism and those
of the two summits, which in this case differ
from each other, form the commencement
of an arithmetical series, as, six, four, two.

Example. Equidifferent amphibole.

Convergent, when in the foregoing case
the series is sensibly convergent, as, fifteen,
nine, three.

Ex. Conversient tourmaline.

Unequal (impair), when the numbers
which designate the panes of the prism and
the faces of the two summits, considered
as different from each other, are all three
unequal, without being in other respects in
progression.

Ex. Unequal tourmaline.

Upper-oxidated, i. e. acute to excess, is a
variety of carbonated lime, which contains
the combination of two rhomboids; the
one acute, which is the inverse; the other
incomparably more acute.

Spheroidal, is said of the diamond with
forty-eight bombated faces.

282 PRINCIPLES OP NOMENCLATURE

Plano-convex, is the diamond with some
plane and some curvilinear faces.

3. Secondary forma comidered relatively to
V certain facets, or certain ridges, remar
able for their arrangement or position.

Tlie crystal is called,

Alternate, when it has on its two parts,
the one superior and the other inferior,
faces w'hich alternate among each other, but
which correspond on both sides.

Example. Alternate quartz.

Bisalternate, when in the foregoing case
the alternation takes place, not only among
the faces of one and the same part, but
also among those of the two parts.

Ex. Bisalternate carbonate of lime, bis¬
alternate quartz.

Blhisalternate, when there are on both
sides two orders of bisalternate facets.

Ex. Bibisalternate sulphuret of mer¬
cury.

OF CRYSTALLOGRAPHY.

283

Annulary, when a hexaheclral prism has
six marginal facets ranged in form of a ring
around each base.

Example. Annulary emerald.

We say the same of an octahedral prism
with eight marginal facets around bases.

Ex. Annular oxide of tin.

Monostic, when a prism of any given
number of panes has, in the contour of
each base, a row of facets in number dif¬
ferent from that of the sides, -and which
may be all marginal, or some marginal and
others angular.

Ex. Monos tic topaz.

Distic, when in the same case there arc
two roM's of facets around each base.

Ex. Distic topaz.

Subdistic, when among the facets ar¬
ranged on one and the same row around
each base, two are surmounted each by a
new facet, which is as it were the rudiment
of a second row.

284 PRINCIPLES OF NOMENCLATUEX

Example. Subdistic peridot.

Plagihedraly when the crystal has facets
situated in a slanting direction.

Ex. Plagihcdral quartz, plagihedral zir¬
con.

Dissimilar, when two rows of facets, si¬
tuated the one above the other, towards
each summit, have a defect in symmetry.

Ex. Dissimilar topaz.

Squared (encadr6 ), when it has facets
which form kinds of squares around faces
of a simpler form already existing in the
same species.

Ex. Sijuared fluate of lime.

Slighthj prominent (promhnde), \t

has ridges which form a very slight emi¬
nence.

Exi Slightly prominent sulphate of
lime.

Zonary, when it has around its middle

or CRYSTALLOGRAPHY.

285

part a row of facets, which form a kind of
zone.

Example. Zonary carbonate of lime.

Apophanous, i. e. manifest, Avhen certain
facets or certain ridges present some indi¬
cation useful for ascertaining the position
of the nucleus, whicli would otherwise be
difficult to find out, or even to determine,
either in point of direction or the measure¬
ment of the decrements.

Ex. Apophanous feldspar, apophanous
sulphuret of antimoniated silver, apophan¬
ous gray copper.

Blunted (emoussS), when it has facets
which intercept, and render as if blunted,
some parts which would otherwise be
sharper than the rest.

Ex. )31unted axinitc, blunted carbonate
of lime.

Contracted, is a dodecahedral variety of
carbonated lime, in which the bases of the
extreme pentagons undergo a kind of con-

\

386 PRiisrciPLEs or rroMENCLATuuE

traction, in consequence of the inclination
of the lateral faces.

Dilated, is said of another dodecahedral
variety of carbonated lime, in which the
bases of the extreme pentagons undergo a
kind of dilatation, in consequence of the
inclination of the lateral faces.

Acuteangled, is a variety of carbonated
lime in a hexahedral prism, the solid an¬
gles of which are intercepted by very sharp
triangular facets.

Defective, is a variety of borated mag¬
nesia, in which four solid angles of the
primitive cube arc intercepted by facets,
while the oj)posite angles remaining un¬
touched, are subject to a kind of defect.

Superahtmdant, is another variety of bo-
rated magnesia, in which the solid angles
which were untouched in the defective va¬
riety, are intercepted each by four facets,
in such a way as to make a superabundance
where there was a delect.

The crystal is called,

Unitary^ when it undergoes only a single
decrement by one row.

Example. Unitary telesia.

If there are two, three, four decrements
by one row, we say bisunitary, triunitary,
quadriunitary.

Ex. Triunitary peridot, bisunitary carbo¬
nate of lime.

Binary, bibinary, tribinary. See. in the
case of one, two, and three decrements by
two rows.

Ex. Binary oligist or specular iron, bibi¬
nary feldspar.

Ternary, biternary, &c. in the case of
one, two decrements, &c. by three rows.

Unibinary, if there are two,decrements,

1

288 PRisrcirLES of nomenclatuke

the one by one row, the other by two;
uniiernaryi if there is one by one row, and
the other by three; hinoternarij, if there is
one by tw'O, and the other by three, &c.

Example. Uniternary carbonate of lime,
binoternary carbonate of lime.

The nomenclature in all the foregoing
expressions, as well as in those which fob
low, makes an abstraction of the faces j>a-
rallel to those of the nucleus, which exist
most frequently in the secondary crystal.

Among the forms in which the nucleus is
entirely disguised, some have names bor¬
rowed froni different considerations; and
those which remain are so few in number,
that I thought it unnecessary to complicate
the language by employing a particular
designation for them.

In order to avoid confounding the words
which express the decrements with those
which indicate the number of the faces, we
may remark, that the former have llieir
termination in hedral, as dodecahedral, or
in al, as octodecagonal, wdicreas the others
end in ary.

OF CRYSTALLOGRAPHY. 289

Equivalent, when the part visible (expo-
sant) which indicates a decrement is equal
to the sum of those which indicate the
others.

Example. Equivalent sulphat of iron.

Subtractive, when the part visible relative
to a decrement is less by unity than the
sum of those which indicate the others.

Ex. Subtractive pyroxene.

Additive, when the part visible relative
to a decrement exceeds by unity the sum
of those which indicate the others.

Ex. Additive sulphat of copper.

Progressive, when the parts visible form
a commencement of arithmetical progres¬
sion ; us one, two, three.

Ex. Progressive tourmaline.

Disjointed, when the decrements form an
abrupt leap, as from one to four or four to.

SIX.

V

290 PRINCIPLES OF NOMENCLATURE

Example. Disjointed sulphuretted anti-
monial silver.

Partial^ when there is some part which
remains without decrements, while the.
other parts similarly situated undergo
them.

Ex. Partial sulphuret of cobalt.

Subdouble, when the part visible relative
to a decrement is the half of the sum of
the other parts visible.

Ex. Subdouble topaz.

We say suhtriple, subquadruple. See. in
the same way.

Ex. Subtriple sulphat of copper.

• The three parts visible (exposaus) w'hich
compose the indication of an intermediary
decrement, count as one only, which is
equal to their sum.

\

Doubling, tripling, quadrupling, when
one of the visible parts is repeated twice,

4

OF CKYSTALLOGllAPHY.

291

thrice, or four times in one series which
would otherwise be regular.

Example. Doubling peridot, quadrupl¬
ing peridot.

Identical, when the parts visible of the
simple decrements, to the number of two,
arc equal to the terras of the fraction re¬
lative to a third decrement which is
mixed.

Ex. Identical gray copper.

IsonomouH, i. e. equality- of laws, when
the parts visible wliicli indicate the decre¬
ments on the edges being equal, those
which express the decrements on the angles
arc equal also.

Ex. Isonomous sulphat of copper.

Mixed, when the tc)nn results from a
single mixed decrement.

Ex. Mixed telesia.

Pantogejious, i. e. deriving its origin from
all the parts, when each ridge and each
solid angle undergoes a decrement.

IT 2

393 PRINCIPLES OF NOMENCLATURE

Example. Pantogenous sulpliat of bary
tes.

Biferous, i. e. which carries twiccy when
every ridge and every solid angle under¬
goes two decrements.

Ex. Piferous gray copper.

Surrounded (entourS)y when the decre¬
ments take place on all the ridges and on
all the solid angles around the base of a
prismatic nucleus.

Example. Surrounded sulphat of bary-
tes. HI

Opposite, when a decrement is made by
one row, and another is intermediary.

Ex. Opposite oxid of tin.

Synoptic, when the laws of decrement
present as it were the picture of those which
take place with respect to the whole of the
other crystals, or at least with respect to
the greatest part.

OF CRYSTALLOGRAPHY.

293

Example. Synoptic feldspar.

Retrograde, is a variety of carbonat of
lime, the expression of which contains two
mixed decrements, which are such that the
faces resultino; from them seem to retro-
grade, by throwing themselves backward,
on the side of the axis opposite to that
which looks towards the face on which
they originate.

Ascending, when all the laws of decre-
*ment have an ascending course, setting out
from the angles or lower edges of a rhom-
boidal nucleus.

Ex. Ascending carbonat of lime.

.5. Secondary forms considered relatively to
the geometrical properties which they pre¬
sent.

The crystal is called,

Isogonous, i. e. equality of angles, when
the faces which are on parts differently

294 PRINCIPLE OF NOMENCLATURE

situated, form equal angles between each
other.

Example. Isogonous cymophane.

Anamorphicj i. e.form turned upside dozmy
when we cannot give it the position most
natural to it, without that of the nucleus
being as it were turned upside down.

Ex. Anamorphic stilbite.

Tlhomhiferous, when certain facets are
true rhombuses, although, from the man¬
ner in which they are cut by the adjoining
faces, they do not appear at the first
glance to be of a symmetrical figure.

Ex. Rhombiferous quartz.

^qidascis, w'hen it has the form of a
rhomboid the axis of which equals that of
the primitive rhomboid.

Ex. Equiaxis carbonat of lime.

Inverse^ when it has the form of a rhom¬
boid the salient angles of which are equal
to the plane angles of the primitive rhom¬
boid, and vice versa.

OF CRYSTALLOGRAPHY. 295

Example. Inverse carbonat of lime.

Metastu.’lc, i. e. transferred, when it has
plane angles and solid angles equal to those
of the nucleus which are thus transferred to
the secondary form.

Ex. Metastatic carbonat of lime.

Contrasting, when it has the form of a
very acute rhomboid, in which an inversion
of angles similar to that which takes place
in the inverse presents a kind of contrast,
in so far as it resembles in another part
a very obtuse rhomboid.

Ex. Contrasting carbonat of lime.

¥ersisting, is a variety of carbonat of
lime in which certain faces are cut by the
adjoining faces, 'so that they preserve the
same measurements of angles which they
would have had without that, except that
these angles have other respective po¬
sitions.

Ex. Persisting carbonat of lime.

I

296 PniNCIPLKR OF NOMENCLATURE

Analogic, when its form presents s(^veral
remarkable analogies.

Kxample. Analogic carbonat of lime.

Farado^ial, wlien its structure presents
singular and unexpected results.

Ex. Paradoxal carbonat of lime.

Complex, when its structure is compli¬
cated by laws not very common, as when it
is produced by decrements some mixed and
others intermediary.

Ex. Complex carbonat of lime.

6. Secondary forms considered relatixehj to
certain particular accide^ds.

The crystal is called,

Transposed, \vhen it is composed of two
halves of an octahedron, or of two portions
of another crystal, one of which seems to
have turned upon the other in a quantity
equal to a sixth of its circumference. See
page 356'. Model, No. 46,

OF CRYSTALLOGRAPHY. 297

Example. Transposed spinel, transposed
sulplmret of ^inc.

Ilani-trope, i. e. one half reversed., when
it is composed of two halves of one and
the same crystal, one of which seems to be
reversed.

Ex. Hemi-trope feldspar. See page 232.
Model, No. 45.

Rectangular, a particular name given to
the staurotide or staurolite, composed of
two prisms which cross at right angles.
See page 242. Model, No. 50.

Obliqueangled, a particular name given
to the staurotide, composed of two prisms
which cross at an angle of sixty degrees.
Sec page 242, Fig. 103.

Sexrndiaitd, a name given to the stauro¬
tide, composed of three prisms which cross
so as to represent the six radii of a regular
hexagon.

Cruciform, a name given to the harma-

398 PRINCIPLES OP NOMENCLATURE,&;C.

tome, composed of two crystals which form
a kind of cross.

Triglyphoiis, when the strife considered
on three faces united around one and the
same solid angle, are in three directions
perpendicular to each other.

Example. Triglyphous sulphuret of iron.

Getnculated, when it is composed of two
prisms which unite by one extremity, form¬
ing a kind of knee.

Ex. Geniculated oxid of titanium.

SECTION U.

AMORPHOUS OR CONFUSED CRYSTALLI¬
SATION-BASALTIC COLUMNS-STA¬

LACTITES—INCRUSTATIONS—TUEEAS

-GEODES-SEPTARIUM-PSEUDO-

MORPHOSES—PETRIFACTIONS, &C.

When the crystalline moleculse dissemi¬
nated in a liquid experience obstacles
which affect their tendency to re-unite* in
conformity to the laws of their mutual af¬
finity, the forms which result from their ag¬
gregation have no longer that regularity
which belongs to an exact and precise de¬
termination. Their edges are blunted,
their faces are curved, their pyramids are
obliterated. Hence the crystals called /ew-
ticular, or which imitate the form of a len-

300 AMORPHOUS CRYSTALLISATION.

ti]; cylindroids, the, prism of which is
rounded oiF.

Scopiform^ or fascicular^ consisting of
laterally aggregated needle-liRe and capilli-
form crystals,* diverging from a common
center. Thus we have scopiform aggre-
I gated crystals of red antimony ore, zeolite,
striated red cobalt ore, and capiiliform py¬
rites, &c.

Acicidarf or similar to needles. Elon¬
gated equally thick prisms, adhering late¬
rally, or in the direction of their length,
present this appearance. It occurs often
very distinctly in sulphate of barytes, and
in the rnurio-carbonate, or white lead ore.

In a roWi which is best characterized by
comparing it to a string of pearls. The
axis of all the crystals lying in one direc¬
tion, so as to form a single series.

Globular. A casual aggregation consist-

AMORPHOUS CRYSTALLISATION. 301.

ing mostly of flattened prisms, which oc¬
curs sometimes in cubical or octahedral
pyrites.

Rose-like consists of thin or flattened
prisms, on whose lateral planes others are
assembled, whichj^b}' crossing each other in
different directions, give to the aggregation
a rose-like appearance.

If a multitude of small indeterminable
crystals are so intimately connected with
each other that they form only one body,
we then consider this body as a particular
being, and hence the substances which we
call striated, Jibrous, &c. and which are
formed by the junction of an infinite num¬
ber of crystalline needles, sometimes pa¬
rallel, sometimes divergent, and at other
times crossing in different directions.

The appellation amo7'phous has been
given to substances which present, as it
wmre, the last degree of confused crystal¬
lisation, and the vague and indefinable form
of which is, as it were, mute 'to the eye of
the observer.

302

BASALTIC COLUMNS.

Basaltic Columns. The natural columns
which form the giants' causewa}" in Ii’e-
land, and Tingal's cave in the isle of Staffa,
together with the rock on which Edinburgh
castle stands, and part of the hill, in the
suburbs of that city, called Arthur's seat,
are all a very compact variety of that class
of rocks called basalt; this rock is in
many instances separated into numerous
distinct but irregularly shaped columns,
consisting of from three to nine sides.*

The two most striking instances of this
columnar structure are the giants’ causeway
in Ireland, and Fingal’s cave in the isle of
Staffa. The columns of the giant’s cause¬
way rarely consist of more than six sides,
and are sometimes separated by veins of
red ochre; the columns of Staffa often
have eight or nine sides.

* A similar appearance is observable in a mass of
clay or starch that has been gradually dried; and in the
interior of a mass of block tin: often also in common
sand-stone that has been exposed to a suiBcient degree
of heat.

BASALTIC COLUMNS.

303

Tlie separate columns of both places are
articulated or disposed to separate trans¬
versely so as to form a flat concave and
flat convex surface exactly corresponding
with each other : and these articulations or
transverse fractures sometimes occur so fre¬
quently in the same column, that the
distance between two of them in many in¬
stances does not equal the diameter of the
column.

The diameter of these basaltic columns
varies from three inches to three feet.

In the general appearance of a mass of
columnar basalt, there is great regularity;
but the regularity of form in these instances
is very different from the effect of crystal¬
lisation, it exhibits internally no symme¬
trical arrangement, the measure of no angle
being fixed. Hence it seems that the sym¬
metry is to be ascribed merely to the mutual
separation occasioned by the contraction
of the mass, and these columns cannot be
classed among crystallised bodies.

Stalactites. The water which f.lters into

304

STALACTITES.

the fissures of stones situated in the arched
part of subterranean caATties, or which
oo^es through the lax and porous texture
of these vaults, arrives at the surface, after
dissolving certain stony molecules or be¬
coming combined with it in various ways.
The drops w hich remain suspended from the
arch during a certain time, undergo a soli¬
dification, which commences on the exter¬
nal surface; and the stony molecules which
the liquid gets rid of, exerting their attrac¬
tion on each other, and attracted at the
same time by the side of. the vault w'hich
they adjoin, fonn in this place an initial
tube, or kind of small ring. This rudiment
of tube increases and grows longer by the
addition of other drops, which succeed to
the first, conducting new molecules w'hicU
the orifice of the tube attracts iu its turn.
Sometimes this tube preserves the form of
a hollow cylinder, similar to a quill. But
frequently it increases in size, and is en¬
veloped with concentric layers, the matter
of w'hich is furnished by the liquid which
descends along the external surface. It

STALACTITES.

30 j

then becomes a thick cylinder or cone; and
sometimes tlje molecules hollowed out by
the drops which thus flow into the interior
of its canal, finish by obstructing it entirely.
These different modifications are peculiarly
sensible in bodies which belong to carbo¬
nate of lime.

But a part of the liquid, on falling from
the arch upon the ground, forms there other
depositions composed of strata generally
undulated, or protuberances, the figures of
which vary ad infinitum. Lastly, the
liquid which flows along the lateral par¬
titions gives rise to bodies, the form
of wdiich ive might compare to that of a
drop of congealed water. Hence Sta¬
lactites are called those bodies which are
formed in the arch of the vault; and sta-
lagviites those which originate from the
falling of the liquid on the ground. It is,
however, much more convenient to call
both stalactites, as it is sometimes difficult
to distinguish between the two kinds of
formation, when the bodies under consi-

X

306

INCRUSTATIONS.

deration have been removed from their ori¬
ginal position.

Incrmtatiom. lii the preceding con¬
cretions, the aggregation of the mole¬
cules depends more especially on the eva¬
poration and chemical changes of tlie liquid
wliich has dissolved them. Other concre¬
tions, which have been called tufas^ and
sinters, proceed from similar causes, and
sometimes likewise from a kind of preci¬
pitation only of the molecules originally
suspended in the liquid. The latter aie
frequently deposited on tlie surface of
different organized bodies, particularly on
those which belong to the vegetable king¬
dom, and sometimes cover the inside of cer¬
tain bodies, such as sewers or dfains.

Thus, if water impregnated with calca¬
reous matter or other materials, remains
long in contact with extraneous substances,
an earthy incrustation takes place, that
soon excludes the incrusted substance
from view; which thus in common Ian-

guage, is said to be petrified: the shape,
that is, remaining the same; but the sub¬
stance in appearance converted into stone.
In this manner are formed the so called
incrustations or petrifactions of birds' nests,
moss, leaves, branches of trees, &c. If
the process be. carried on for a sufficient
length of time, and the incrusted body be
of a perishable nature, as in the case of
vegetable matter, the whole of this is re¬
moved by gradual decay, and the remain¬
ing mass is entirely earthy: but its form,
and the circumstances of its situation, will
generally serve to shew its origin.

The warm springs of St. Philippe in
Tuscany contain a great proportion of cal¬
careous matter, which they deposit so com¬
pactly round substances immersed in them
as to be employed for the purpose of ob¬
taining casts, and models, &c. AVith this
view hollow moulds being suspended in
the water, the earthy particles are depo¬
sited in them; and the deposition, when
removed from the mould, preserves the

X 2

308

OSTEOCOLLA.

exact iinpression of it. I'licse incrustations
are very delicately, but veiy firmly com¬
pacted; and of a whiteness c(iual to that
of Carrara marble. It is said that there
are springs of the same kind near Guanca-
Velica in Peru; and that many vases and
statues, &c. are placed in the Church of
Lima, which have been formed from such
depositions as those of St. Philippe.

Osieocolla. The substance so called by
the earlier mineralogical writers, from its
resemblance to a mass of agglutinated
bones, is nothing more than a calcareous
deposition that has taken place round small
branches and twigs of trees. In many in¬
stances the vegetable substance has been
removed, and its place supplied by the de¬
position of fresh earthy matter; seldom
however entirely; for in making a trans¬
verse section of any of the branches of such
a mass, there may be generally observed
the trace of a longitudinal cylindrical ca¬
vity; which shews that the deposition ori-

TLOS FERRI. 309

ginally took place on something that has
been subsequently removed.

The beautiful mineral called 'Flos Ferri
is a stalactite. It is met with at Schem-
nitz in Stiria in the clefts of sparry or white
iron ore; from which circumstance, and
the delicacy of its general appearance, it
has received the above appellation: but it
contains no iron. Count Bournon has con¬
jectured that its form is the effect of subli¬
mation ; the direction of the coralloid
branches being too wavy and uncertain to
have proceeded from stalactitic deposition.
A transverse section of this substance shews
a delicate instance of a fibrous radiated
texture: the branches are often of a silky
lustre externally, owing to an aggregation
of very minute crystals, superficially^ in¬
vesting them.

Local circumstances, and the degree of ce¬
lerity with which stalactitic deposition takes
place, vary the appearance of the effect
produced; and hence those grotesque ac-

310

STALACTITKS.

cumulations which have been described as
representing the forms of various animate
and inanimate substances: as the fancied
figures of lions, &c., in some of the caverns
near Iluxton, and in other parts of Derby¬
shire. In the quarries of the island of An-
tiparos these depositions have been carried
to a great extent: an account of the fan¬
tastic shapes of which is given in extrava¬
gant terms in a letter written to Kircher,
inserted in his Mundus Subterraneus A
passage in Plin}' is applicable to this j)art
of the subject:—“ Inter plurima alia Italia;
miracula, ipsa marmora in lapicidinis cres-
cere auctor est Papirius Fabianus, natura;
rerum peritissimus: exeinptores (|uoque af¬
firmant compleri sponte ilia montium ul-
cera-f*.” The latter circumstance is often
affirmed of the quarries of Antiparos.

When water which has dissolved earthy

* Vol. I. p. 122—130.

+ Nat. Hist. lib. xxxvi.

GEODES.

311

substances is introduced into a subter¬
ranean cavity of small dimensions, where
it can remain, the stony molecules in-
cnist the sides of this cavity, which is
generally of a round form, and sometimes
end by studding it with crystals. This is
what has been called geode. Some of
these bodies contain a solid and moveable
nucleus, or a pulverulent earthy matter* :
of this description also are certain pieces
of silex found in marl. Sometimes also
the geode is entirely filled with a matter
which may be distinguished by the naked
eye from that of which it is itself com¬
posed.

The Septariuni belongs to this class.
'J'his substance is an indurated marl, con-
taining numerous veins of carbonate of
lime, which divide it into distinct parti¬
tions and hence the term septariuni: some-

* It is probably from this that the term geode is de¬
rived, i. e. a body which contains earth.

312

SEPTAUIUM.

times the transverse sections of these parti¬
tions are nearly of a square form; and as
they then i*esemble the surfaces of dice, the
substance has been called in consequence
Jjudus Helmoutii; Van-helmont having par¬
ticularly described it.

The septnrimn occurs in distinct and flat¬
tened spheroidal nodules; sometimes in
larger and irregularly shaped masses.

In the former instance the veins of cal¬
careous carbonate are opacpie and of a
white colour; and so distributed as to be of
the greatest dimensions at the centre, from
whence they gradually diminisli towards
the circumference of the nodule, but ter¬
minate within it. From this distribution
Mr. Playfair draws a ver}' strong argument
in support of Dr. Hutton’s theory of geo¬
logy ; since, as in this case, “ the matter
with which the veins are tilled could not
have been introduced by infiltration from
without, or in any other way; the only sup¬
position left for explaining the singular
structure of the fossil is, that the whole mass
was originally fluid; and that in cooling

SEPTAIIIUM.

313

the calcareous part separated from the rest,
and afterwards crystallised

The argument is, I think, incontrovert¬
ible in the particular instance; but in
many instances of the massive and irregu¬
larly shaped Ludus, the veins are neither
disposed in the same manner, nor are they
of the same colour and opacity: on the
contrary, they possess that kind and degree
of transparency and colour, which is cha¬
racteristic of those varieties of carbonate
of lime, that have unquestionably been de¬
posited from water, as in stalagmites, &c.:
and besides this, there are internal marks
of a periodical formation of the vein, both
from its stratified character, and the differ¬
ence of colour in the different correspond¬
ing strata.

AVater, impregnated with carbonic acid,
in penetrating through marble, lime-stone, or

* Playf. Illust. pp. 30, 31.

/

314

STALACTITES.

chalk strata, very commonly becomes im¬
pregnated in its passage with particles of the
calcareous carbonate; which it subsequently
deposits, either by simple exposure to air,
or upon the surface of extraneous bodies
with which it comes into contact: and
thus forms stalactites.

Calcareous amorphous masses. The
most familiar instance of the deposition
of a calcareous matter from water is that,
which takes place on the inner surface
of vessels employed for the purpose of
boiling water impregnated with a calcareous
carbonate. 'f'he incrustation separated
from the sides of Carfax conduit, in Oxford,
(at the time of its removal, about twenty-
five years since) was nearly an inch in
thickness; and of a distinctly sparry struc¬
ture. There is, in the Oxford collection,
part of a wooden duct that served to con¬
vey the water from this conduit: the trans¬
verse section of it is of a square form, and
it is worthy of observation that the calca¬
reous incrustation, w'hich is of a stratified
4

DEPOSITIONS.

315

appearance, is of equal thickness on every
one of the four surfaces: by which it ap¬
pears, that a deposition of this kind is not
mechanical.

The substance called Agaric Mineral is a
stalactitic deposition of carbonate of lime,
frequently met witli in the clefts of calca¬
reous strata, particularly such as are of a
porous texture; in some instances it ad¬
heres to the sides of the cleft with the re¬
semblance of a fungus (agaricum): and
hence its name.

It may also happen that a substance
may be incrusted with crystals of a differ¬
ent nature, by being as if moulded along
with them. For instance, we are ac¬
quainted with crystals of metastatic carbo¬
nated lime incrusted with quartz, and
sometimes the silicious envelope remains
empty after being separated from the crys¬
tals which it concealed.

J^seudomorphoses. There exists another
kind of concretions which we call pseudo-
morphoses, i. e. bodies which have a false

316

PSEUDOMORPHOSES.

and deceitful figure ; because the substances
which belong to this order present in a
very remarkable manner foreign or strange
forms, which they have in some measure
obtained from other bodies which had re¬
ceived them from nature.

When the type of this apparent trans¬
formation is a shell, it happens frequently
enough that the shell still covers in whole
or in part the substance, which is as if
moulded into its interior'^, and then no¬
thing appears simpler than the explana¬
tion of the fact, by the introduction of a
liquid charged with stony molecules into
the cavity of the shell; and this observa¬
tion leads to a similar explanation of the
formation of the kinds of nuclei modelled
into shells, which we meet with isolated
and stripped of every envelop.

Sometimes the shell itself has been pe¬
netrated by another matter generally silice¬
ous, which has been substituted for the

♦ De L’Isle Crystall, tome ii. p. 161 .

PSEQDOMORPHOSES.

317

cartiIasi nous substance of which this shell
liad been partly composed*; and it may
happen in this very case that the interior
of the shell has remained empty. It is no
longer, properly speaking, a. pseudomor-
phosis. It is a fossil which has merely
become more stony than it was before.

This last kind of modification takes place
ec{ual]y with respect to the bones and to
the other solid parts of animals which are
found immured in the bowels of the earth;
i. e., they may pass to an almost entirely
stony state, by the help of a substance
which supplies the place of their cartilagi¬
nous part.

The case cannot be the same with veget¬
able productions as with shells. They

* We know that shells, as well as the bones of ani¬
mals, are formed of two substances; the one calcare¬
ous, which is not susceptible of putrefaction; the other
cartilaginous, membranous, or fleshy, which may be
destroyed by the joint action of air and water.

318

PSEUDOMORPHOSES.

have no testiido, or envelope, which can
exist after the destruction of the interior
substance, and serve as a mould to a stony
or other substance foi' receiving an impres¬
sion of their form. If we supposed that
one of these productions, such as a portion
of the branch of a tree, were entirely de¬
stroyed, so that the cavity which it occu¬
pied in the bowels of the earth remained
empty, Ave could conceive that a stony
matter might afterwards fill this cavity and
there be modelled to it. In this case the
new body would resemble externally the
branch of a tree; it would have the appear¬
ance of knots and wrinkles, but its inside
Avould not present any trace of organiza¬
tion, and it Avould only be, as it were, the
statue of the vegetable production, Avhich
it would have displaced.

What is generally called petrified wood is
a much more faithful imitation of real
wood. On a transverse section we distin¬
guish the appearance of concentric layers,
which in the living tree must have pro-

PSEUDOMORPHOSES.

319

ceeded from its increasing in thickness; all
the principal lineaments of organization are
preserved to such a degree, tha t they some¬
times serve to enable us to recognize the
species to which the tree belonged which
has undergone petrifaction.

Among the different explanations which
have been given of this phaenomenon,
that which seems to be most generally ad¬
mitted, although not exempt from objec¬
tions, consists in supposing that the stony
matter is substituted for the vegetable in
proportion as the latter is decomposed;
and because the substitution takes place
successively, and as it were molecule by
molecule, the stony particles, in arranging
themselves in the places rendered empty
by the disappearance of the ligneous par¬
ticles, and by moulding themselves into the
same cavities, take the impression of the
vegetable organization, and copy the traits
of it precisely.

The mineral kingdom also has its pseu-
domorphoses. We find some substances

320

PETRIFACTIONS.

of this kingdom under crystalline forms,
which are only borrowed; and it is proba¬
ble that, in some cases at least, the new
substance has been substituted gradually
for that which has ceded its place to it, as
we suppose takes place with respect to
petrified wood.

The various pseudomorphic bodies im¬
print their form on the matter which sur¬
rounds them, and frequently also the im¬
pression serves as a cell for an organic sub¬
stance which is simply in a fossil state, or
which has received a certain decree of
alteration only. This takes place in parti¬
cular with respect to the ferns and other
plants of the same family, the form of
which is moulded on a schistous matter, as
we shall afterwards more fully detail.

Petrifactions .—We generally denominate
petrifactions all the variously modified sub¬
stances which we have mentioned, even
those which only present impressions of
animal or vegetable productions. Dau-

PETEITACTIONS.

321

benton applies tins term only to bodies
which, in their natural state, being partly
stony and partly cartilaginous, such as
shells, have become entirely stony.

As we merely purpose to mention a few
examples of the modifications in question,
and not to unite them methodically under
one and the same point of view as several
authors have done, we shall confine our¬
selves to the enunciation of some of them
in speaking of the substances which have
formed their secondary matter, and shall
adopt the nomenclature to this method of
classifying.

, We ought not to omit that there are also
pseudomorphoses, which arise from the sub¬
stitution of a metal in the room of an or¬
ganic body. Sulphuret of iron presents
several examples of this kind of metal¬
lization.

By referring to all that lias preceded, we
may define in the following manner the
difterent concretions of which we have'
given, the description:—

PETiai'ACTlONS.

r)‘2'2

Stalactite .—^Thc term stalactite is applied
particularly to those calcareous concretions
which are fbriiied on the roofs of natural
caverns, and which resemble in their shape
the common icicle.

Tlie matter of the stalactite, as has been
already stated, is conveyed by water that
has penetrated the c<mtigu6us strata ; and
in its deposition assumes Various appear-
ances according to accidental circum¬
stances.

If the water oo^eS through very slou'ly,
some fiine elapses before a drop is formed
of sufhe-ient size to fall by its own weight;
and, in this interval, some of the calcareous
particles arc separated from the water, and
adhere to the roof. In this manner succes¬
sive particles arc separated and attached
to each other, until a stalactite is formed.

When the formation is rapid, the texture
is comparatively loose, and of an earthy
appearance: and this is particularly the
case with those stalactites that are formed
from recently constructed arched buildings,

PETRIFACTIONS.

323

as bridges, or cellars; where the stalactite
is made up of thin concentric cylinders,
like a roll of fine cinnamon. In other in¬
stances the substance is completely sparry ;
and, often, very closely resembles the trans¬
parent part of the quill of a bird's wing;
and not unfrequently terminates in a
spherical assemblage of small pointed crys¬
tals. If the percolation of water contain¬
ing calcareous matter is too rapid to allow
time for the formation of a stalactite, the
earthy matter is deposited from it after it
has fallen from the roof upon the floor of
the cavern ; and in this case the deposition
is by some called a stalagmite: an unne¬
cessary verbal distinction adopted by some
writers merely for the convenience of de¬
scription. Stalagmites are commonly, at
least in the early stage of their formation,
of a mamillary shape: by gradual accumu¬
lation they become conical.

In some instances the separation of the
calcareous matter takes place both at the
roof and on the floor of the cavern; and,

Y 2

324

PETRIFACTIONS.

in the course of time the substance of
each deposition increasing, they both meet;
and form an irregular but continued pillar.

The incrustation is a concretion in the
form of a crust applied to the surface or to
the interior of a body. To this we may
refer the geode, which is a concretion in
the form of an envelop, spherical or nearly
so, sometimes empty and sometimes con¬
taining a nucleus.

O

The pseudomorphosis is a concretion en¬
dowed Avith a form foreign to its substance,
and for which it is indebted to its mole¬
cules filling a space formerly occupied by
a body of the same form.

With petrifactions Mineralogy has no
farther concern than as far as minerals ap¬
pear in extraneous forms, having by a sub¬
stitution of particles assumed the figure of
animal and vegetables substances.

In a geological vicAv, these bodies arc

PETRIFACTIONS.

325

highly interesting. They are justly consi¬
dered as the medals of antiquities which
serve to form the history of our globe
They are not mere geological curiosities
thinly scattered here and there. The most
internal parts of continents, now many
hundred miles from the sea, and moun¬
tains of the greatest height equally distant,
not only contain such bodies as are exclu¬
sively the inhabitants of the sea, but seem
even composed of them: immense mineral
strata are to be found in most parts of Eu¬
rope full of them; and other remains of
life and vegetation are not less abundant in
others.

Though most organized bodies that are
found buried in the soil, or in strata, are
commonly called petrifactions; yet those
only ought to receive this appellation which
have by some chemical process changed
their animal or vegetable natures, and ac¬
quired that which is peculiar to the mineral
kingdom.

Besides the difference in respect to the

326

PETRIFACTIONS.

various kinds of organic bodies, which are
now found imbedded in strata, they differ
gfeatly with respect to tlie state which they
arc in; some being still in their natural
and original state, as most of the osseous
remains of hot-blooded animals; the re¬
mains of some of the cTustaceous creatures,
and some shells. Others are charred, or
converted into coal, ds most vegetable sub¬
stances found in the strata accompanying
pit-coal. Some are changed into calcare¬
ous spar, or carbonate of lime, as most
shells. Others into different kinds of agate
and flint, as most woods; and others again
are changed into pyrites, or sulphuretted
metals.

No part of mineralogy, it must be con¬
fessed, is less understood than this. The
greater part of what pass under the name
of petrifaefionis, are either merely impres¬
sion's, or nudlci, or incrustations, so that
any general 'doctrines, founded upon 'com¬
mon observations, would be very liable to
be etroneous. We'do not recollect having

PETIIIPACTI,QNS.

327

seen any osseous Remains of hot-blooded
animals, tiiat had lost their natural struc¬
ture and assumed a lapideous texture; their
cells and pores are filled with stony and
pyriticai matter: but in general they are
cither in their natural and original state, or
they have lost the connecting medium of
the calcareous matter, and are decompf)sed.
But shells, crustaccous animals, and litho-
phyta, the common productions of the sea,
though often found in tlieir natural state or
decomposed, are generally real petrifac¬
tions. They are usually calcareous, though
their moulds and impressions are often sili¬
ceous, and likewise their perforations and
vacuities. The siliceous, we venture to af¬
firm, are the inverse of the calcareous.
Thus the entrochites in a calcareous state
are what mechanics call female screws^ hav¬
ing the worm within a hollow cylinder;
whilst those that are siliceous are male
screvus, having the worm round the outside
of a solid cylinder. The first is the real
shell converted into carbonate of lime,

328

PETEirACTIOAS,

coniinouly called spar, or with a sj)athous
texture; the latter, the mould formed with¬
in the cavity of it.

Vegetables are found merely charred, or
penetrated with bitumen, or else wholly or
partially changed into coal; often likewise
so completely penetrated with siliceous
matter as to form a solid siliceous mass;
but we believe they are never converted into
a calcareous body.

There are two things further to be consi¬
dered relative to organic remains, which, as
far as petrifactions are to be consulted as
the records of past events, arc worthy of
deep attention. First, that of a far greater
part there are now no similar species exist¬
ing; and secondly, that of those which do,
the greater part do not now exist in the
countries in which they are found. If we
go back to a remoter period than that when
the alluvial and superficial covering of tlie
eartli was deposited, to that period at which
the greater part of our stratified rocks were
formed, we shall find that almost another

PETRIFACTIONS. 3^9

creation then existed, of which our present
strata have been the cemeteries.

Of the myriads of beleninites, cornua
ammonis, encrinites, &c. &c. which are to
be seen in them, none now are ever found
in our seas, or the seas of other parts of
the world.

Some naturalists so far extend the opi¬
nion, of most of the inhabitants of the
seas of that remote period being now ex¬
tinct, that they will hardly^ admit there is a
single fossil shell wdiich will bear a strict
comparison with any species now living.
It is the same with the vegetable world.
Though there are many fossil species very
similar to species still in existence, yet few
we believe will bear a nice examination.
In the same argillaceous and sand-stone
strata, in w'hich we find some plants of the
fiiix tribe, very similar to those now grow¬
ing near the spot where these lie buried, we
find others, of whose original we cannot
form the smallest idea, which we are
certain cannot be found in the neighbour-

330

rETRIFACTIOJSIS.

hood, and which most resemble some plants
of the tropics.

If we descend to times which approach
nearer our own, and examine the alluvial
strata, we find the remains of animals in
in their natural state, which likewise are
not, and most probably never were, inha¬
bitants of the countries in which they are
now met with.

There is still another general and very
interesting observation to be made with re¬
gard to these substances, namely, that they
are generally found in the middle and lower
heights of the earth. In the middle heights
of our globe petrifactions arc still very rarej
but they increase in variety and number,
as vre approach the lower places, and are
at length accumulated in immense tjuanti-
ties in the lowest parts of Secondaiy oi
Stratified Mountains.

We also observe, that the organic re¬
mains found in the middle heights ol
mountains are totally changed into stone,
but the more we descend into the lower

PETRIFACTIONS.

331

places, the more these bodies appear unal¬
tered, or approach to their original state.
It is likewise observed, that the higher
places afford different genera and species
of petrifactions from those tound in the
lower strata.

JeOKMS OF MINERALS,

333

NAMES OF
THE SL’BSTABCES,

Sulpliuret of iron
Arseniate of iron
Oxid of tin,,«, t.... i. ^,

Gray cobalt....

Phospbate of manganese

Aploine .... *.

Atnpliigene or Leucite ..

FOEMS OF

THE IKTEOBANT MOLECULE.

1

Cube.

Trregukr tetrahedron.

II. REGULAE OCTAHEDEO^^

Regular tetrabedroa.

Float of lime.'

Muriat of ammonia..

Alum or sulphiit of ahiminc ,.

Spinellc..

Muriate of copper.

Diamond... - ^

Native amalgam....

Ruby, or red oxide of copper
Magnetic^ or oxidulated iron.,

Native bismuth... j

Native antimony ..... Irregular tetrahedron.

334

TABLE OE CllYSTALLlME

III. REGULAR TETRAHEDRON.

NAMES OF

FORMS OF

THE SUBSTANCES. THE INTEGRANT MOLECULE.

Copper pyrites
Gray copper .

Regular^tetrahedron.

IV. RHOMBOIDAL DODECAHEDRON.

Garnet. .

Sulphuret of zinc or Blond .,

( Teb'ahedron with isosceles
' triangular faces, all equal
L and similar.

II. Substances, the Primitive Forms of which only are of
the same Kind, with Dimensions respectively peculiar to
each.

I. RHOMBOID.

1. With obtuse summits.

Carbonat of lime.

Tourmaline ' .

Rock crystal or quartz

Rhomboid.

Irregular tetrahedron.

forms or minerals.

335

na‘mes of

F0HM3 OF

THE SUBSTANCES*

THE i NTS OH ANT MO LHC OLE.

Chilbasie..

Dioptase ...* • • •

Sulpliuret or red silver ore

I

RhoinboidaL

2, }¥ith acute summits.

Conuidum.

Oligist or specular iron
Sulphate of iron ___

I

Rhomboid.

iL OCTAHEDRON.

I

I, Pp^amids with square basest

Zircon..

Harmatome.

Anatase

Molybdate of lead

Mellite ....

Tungstate of lime
Oxid of tin .. *. *

1

> Irregular tetrahedron.

2 . Pyramids with Rectmgtthr bases.

Nitrate of potash .
Carbonate of lead
Sulphate of lead *

1

V Irregular tetrahedron.

336 TABLE OF CRYSTALLINE

FORMS 0 ¥

TliE INTEGRANT MOLECULE*

NAMES OF
THE SUBSTANCES,

0%id of Zinc.

Arseniate of copper,,
Mack or Chiastolite

Arragonite.

Shorlaceous Beril . *.

Irregular tetrahedrofi*

3. Pyramids with rhombic base^.

Sulphur..... *. .4-^

Red sulphuret of arsenic,,,,, I

Blue carbonat of copper.f irregular

Silicco akareous lianite • ^ |

Carbonate of soda.i

Sphene p-,* ^

IIL EIGHT OtfAOHANGULAR PRISM.

L EIGHT OR OUADRANGULAR PRISM,

1, IVifk square bases.

Sulphate of magnesia
Vesuvian or Idocrase

Mesotype.

Chromat of lead ,,.,
Oxid of titanium ,.,,
Parauttene ....

IsosceksTectangle-triangti'
lar prism.

2. With rectangular bases

HA>IES OF
T-HE SUBSTANCES

Crysoberil or cyraophane ,,,

Euclase
Peridot*

Prehnite

Ferugioated tungsten

Apophilite.* * *

Anhydrous sulphate of lime*, 7 Isosceles rectangle triangu-
Caicareous tungsten . ^ ^ prism*

Prism with rectangular
r bases.

3* f¥itk rhombic hoses»

Suipbat of barytes.. , * + i Scalene-rectangle-triangu-

Sulpliat of strontian.* * * J lar prism.

Staurotide ***** . y

„ * f Isosceles-rectanele-triangu-

.r lar pnstn.

Triphane ..J

Topaz...

Mica.*..

Talc..*.>Prism with rhombic

Arsenical iron , * * *...

Sulphuret of molybdena , *,,,

Diaspore.*....* Isosceles triangular prism*

338

TABLE OF CRYSTALLINE

4. With'oblique-angled parallelogram bases.

NAMES OF
THE SUBSTANCES.

Sulphat of lime.

Epiclote.

Axioitc.. • •.

FORM OP

THE INTEGRANT MOLECULE.

Prism with oblique-angled
paraiielogram bases.

IV. OBLIQUE QUADRANGULAR PRISM.

1. With rectangled bases,

Borat of soda.. Prism with rectangled bases.

2. With rhombic bases.

Hornblende

Actinolite.> Prism with rhombic bases.

Gram mat it e. )

Augite. Oblique triangular prism.

3, With oblique-angled parallelogram bases.

Feldspar.

Disthene.

Sulphat of copper

Prism with oblique-angled
parallelogram bases.

340 TABLE OF CRYSTALLINE FORMS, &C.

IL REGULAR OCTAHEDRON.

NAMES ON THE SUBSTANCES* fRIMITlVE FORMS*

Muriat of soda ,,

Sulphuret of lead
Sulphuret of iron
Oray col^alt.

ii

Cube*

Ill. REGULAR HEXAHEDRAL PRISM.

Carbonat of lime...

Sulphuretted aiitimoniated

silver ....

Corundum...

Phosphat of lead *..

Mica...*.,

Sulpliuret of molybdena .., *

Obtuse rhomboid.

Acute rhomboid*
Pyramidal dodecahedron.
Straight prism with rhom
bic bases*

IV* RHOMBOIDAL DODECAHEDKON-

float of lime ,.,
Oxidulaled iron
Spinel.

Regular octahedron*

GENERAL OBSERVATIONS 5 &C. 341

V* SOLID WITH TWENTY-FOUR EQUAL AND SIMILAR
TRAPE20IDS,

KAMES OP SUBSTANCES.

Muriate of ammonia

Garnet.* * ♦,,

Amphigene.

Analdtne.*, *

Regular octabedron*
Rhomboidal dodecahedron.

Sulphwret of iron

General Observations, and ReJlectio7is, 07i the
Statements, comprehending the Theory of
Crystallography.

Since the printing of the preceding
sheets, Dr. Wollaston, in a paper read be¬
fore the Royal Society, has endeavoured to
shew, that the original moleculae of crys-
tallisable matter are probably spherical.

342 GENERAL OBSERVATIONS ON THE

Assuming this statement, the constitution
of those crystalline solids which yield by
mechanical dissection, solids of two kinds,
namely, tetrahedrons and octahedrons, (see
page 146), may be more satisfactorily ex¬
plained, than if we imagine, that the ori¬
ginal inolecuUe of those substances arc
tetrahedron; because the former solids can
arrange themselves into tetrahedrons or oc¬
tahedrons, and the vacuities they leave are
of a much smaller bulk than when the for¬
mer crystalline solids are formed of tetra¬
hedral or octahedral molecula?.

Dr. Wollaston has extended this idea,
which he stated, as originally in part point¬
ed out by Dr. Hooke, to the formation of
crystalline bodies, and endeavoured to
show the laws of arrangements, according
to which crystalline forms would be ]>ro-
duced of spherical moleculie, or sometimes
of flat spheroids. The above statement Dr.
Wollaston observed is perfectly gratuitous.
It wovdd not become us to anticipate the
summary detail of this hypothesis. The

THEORY OF CRYSTALLOGRAPHY. 343

paper to which we allude, no doubt, will
be laid before the public by Dr. Wollas¬
ton himself, through the medium of the
Philosophical Transactions.

We have now made a hasty^ tour thro ugh
the fertile field of crystallography. It is a
rich field, the cultivation is merely com¬
menced, and which waits for more favour¬
able times, and a greater number of la¬
bourers to reap from it an abundant
harvest.

We have seen to what all the different
metamorphoses of crystals belong under
w'hich the primitive form is presented in
secondary crystals, whether simple or com¬
pound. Sometimes the decrements are per¬
formed at once on all the edges, as in the
dodecahedron with rhombic planes, or on
all the angles, as in the octahedron origi¬
nating from the cube. At some times,
take place only on certain edges or certain
angles. At others tliere is an uniformity
between them, so that there is only a single

344 GENERAL OBSERVATIONS ON THE

law of decrement by one, two, three ranges
or more, and which acts on different edges
or on different angles. Sometimes the law
varies from one edge to another, or from
one angle to another; and this is what
happens in particular when the nucleus has
not a symmetrical form, as when it is a
parallelopipedon, the faces of which differ
by their respective inclinations, or by the
measurements of their angles. In some
cases the decrements on the edges corres¬
pond with the decrements on the angles to
produce the same crystalline form. It also
happens sometimes that the same edge,
or the same angle, undergoes successively
several laws of decrement which succeed
each other; and even further, there is a mul¬
titude of cases in which the secondary
crystal has faces parallel to those of the
primitive form, and which are combined
with the faces produced by the decrements,
and give rise to new, in order to modifica¬
tions.

With such diversity of laws, sometimes

THEORY OF CRYSTALLOGRAPHY. 345

solitary, and sometimes marching as it
were by groups round the same primitive
fomi, the number of ranges subtracted was
in itself very variable; if, for example,
there were decrements by twenty, thirty,
forty, or more ranges, as may be imagined,
the multitude of forms which might exist
in each species of mineral would be capa¬
ble to overwhelm the imagination, and the
study of crystallography would present an
immense labyrinth, which, in spite of the
clue furnished by theory, could with diffi¬
culty be unravelled. But the power which
produces the subtractions seems to have a
very limited action. These subtractions
are most frequently formed by one or two
ranges of raolecul 0 e. Haiiy found none
which went beyond six ranges ; but such is
the fertility which is united with this sim¬
plicity, that, by confining ourselves to de¬
crements by one, two, three, and four
ranges, and abstracting those which are
mixed or intermediate, we find that the
rhomboid is susceptible of eight millions

346 GENERAL OBSERVATIONS ON THE

three hundred and eighty-eight thousand
six hundred and four possible forms of the
same substance, and even this number may
be much extended in consequence either of
intermediary or mixed decrements being
taken into account.

In order to have a still more accurate
idea of the power of crystallisation, we
must add to this facility of producing so
many different forms, in commencing with
a single figure, that of attaining one and
the same form by different structures. The
rhoinboidal dodecahedron, for instance,
which we obtained by combining cubical
molecules, exists in the garnet, with a
structure composed of small tetrahedrons
with triangular isoscele faces, as we shall
find under the head of this mineral sub¬
stance; and Haiiy has found it in a species
of fluate of lime, where it is also an assem¬
blage of tetrahedrons, but regular, and
the faces of which are equilateral triangles.
Some attempts at the dissection of primi¬
tive crystals seem to announce, that the

THEORY OP CRYSTALLOCTEAPHY^ 347

tetrahedron, with triangular faces, is the
most frequent primitive form of the parti¬
cles ; to these may also be joined, in thought,
the triangular prism and the parallelopi-
pedon. Tetrahedrons, arranged in a great
many different mannei’s, give every possi¬
ble form, as may be seen by the artificial
generation of parallelopipcdons, from la-
mi nje by every kind of superposition, of
octahedrons, of dodecahedrons, of rhom¬
boids, &c. It is evident then, that the te¬
trahedron may be supposed the only pri¬
mitive form of the particles, generating
every other form, as well in the nuclei as in
the secondary and external crystallisations.
In this probable hypothesis, which is con¬
sistent with the simplicity and economy of
natui'e, the constant and given forms, both
of the nuclei and in the secondary crystals
of the same substance, depend only on the
respective disposition, or the particular ar¬
rangement of the primitive particles among
themselves. It is in the disposition, and
the arrangement of these particles, which

348 GENERAL OBSERVATIONS, &C.

always takes place in the same manner in
the same substance, that the geometric cha¬
racter of each substance consists; and this
character, or that limited disposition of
particles, depends on the proper or chemi¬
cal nature of bodies.

CLASSIFICATION OF MINEKALS, &C. 349

SECTION IV.

TABULAR VIEW OF THE METHODICAL
DISTRIBUTION OF MINERALS ACCORD¬
ING TO THE SYSTEM OF HAUY.

Preliminary Obseixations.

THERE is no one who has seriously at¬
tended to the study of mineralogy, without
feeling at the same time the necessity of
establishing divisions among the substances
of this department of nature, so as to re-?
move the numberless difficulties which
would otherwise oppose the acquisition of
knowledge. The aim of these arrangements
consists in such a disposition of bodies as
places those nearest each other which have
similar properties, and others remoter, as
their habitudes differ.

350 CtASSIFTCATIOJSf OT MINERALS

The first notions which men adopted
from necessity concerning tlie diflerent
properties of iniiiera) substances may be
regarded as the early sketches of arrange¬
ment. In the time of Pliny, stones were
even then distinguished from salts, from
bitumens, and from metals, and a di^'ision
into four classes already existed. The
electric property of amber, the combusti¬
bility of bitumen, and the attraction of
iron by the magnet, were known: already
the stones formed distinct groups. The
marbles and gems were separated, the
heavy and the light, the hard and the soft
mi uerals were d iv ided. Anti q ui tj' h owever
did not possess one single true notion, nor
one positive idea of the methods, or classi¬
fication of natural histoiy, their advantages,
and their necessity.

It was in the eighteenth century alone,
that the denominations of kingdoms in na¬
tural bodies were adopted, that the mineral
kingdom was jiarticularly admitted, that
mineralogical metliods were imagined, and
the distinctive properties or characters ex-
3

ACCORDING TO HAUY. 351

amined with a view to class and distinguish
these different kinds of bodies.

It was natural, at first, to take for the
characters of classification such properties
as are the most apparent, the 7nost sensible,
and the most easy observed by the senses:
or at least such of them as arc most cha¬
racteristic of the substances to which they
belong; and that mineralogical methods in
particular should be founded on what are
called external characters, that is to say, on
the striking properties only which minerals
present to our senses, and which may be
observed without causing them to undergo
any material alteration.

In running over the different arrange¬
ments proposed successively, and which
have been more or less established on the
external or obvious characters, which the
senses'could discover, it was observed that
the distinctions admitted would be insuffi¬
cient to discriminate the substances of the
mineral kingdom, and that they were more
adapted to appropriate and to separate

352 CLASSIFICATION OF MINERALS

similar bodies from each other, or to con¬
found for a long time the art of regularly
and unequivocally characterising minerals,
with the mere routine of knowing tliem at
sight.

This singular pretension, which has done
much injury to the progress of rnineralogi-
cal science, is exhibited more particularly
in some systems, w'hich consider minerals
only with regard to Home of their proper¬
ties. The authors, in framing their sys¬
tems, have wished to draw, from a few
single considerations, an order and distri¬
bution which they pretend is natural for
the relative disposition, and a classification
which they assert is easy to distinguish mi¬
neral substances from each other.

Instructed by the insufficiency of this
proceeding, and guided by a light less
deceitful and uncertain, again others have
happily perceived that no single collection
of external properties can be of use to
establish real distinctions, that it is neces¬
sary to discriminate carefully the system,

ACCORDING TO HAUV. 353

which by common characters only seeks to
arrange these compounds with each other,
from that artificial method, of which the
aim is to teach the memis of distinguishing
them unequivocally and without error.
They have associated and compared not
only the obvious or striking characters,
but all the individual apparent or sensible
properties, and in opposing and contrast¬
ing the totallity of them ivith each other,
they have established characters, proper to
distinguish these bodies with more success.
They have given a kind of portrait, by de¬
composing in some measure all the features
of their physiognomy, and those outlines
which have the strongest resemblance are
then considered as answering the intended
purpose.

However advantageous such a proceed¬
ing may be, it is nevertheless evidently re¬
ducible to a clear analysis of the external
properties of minerals only; whatever may
be the facility it affords of distinguishing
each kind of mineral by reducing it to its

A A

354 CLASSIFICATION OF MINERALS

just value, we must by no means forget
that it cannot be applied for disposing
these liodies in a natural order, that it can
never serve to indicate their intimate nature
or composition, and that it is not capable
of answering its* own peculiar object, unless
a faithful enumeration of all the properties
of each individual be given, and tliat
otherwise we should constantly be in
danger of confounding the mineral com¬
pound ; and hence the method pursued
can only be considered as an approxima¬
tion to truth. It is indeed an excellent
table, by the help of which we may find
the object intended to be studied, but
which can never dispense us from the ne¬
cessity of investigating their properties and
internal nature. If we are desirous of
knowing the’bodies we examine, and par¬
ticularly determine the uses to which they
may be successfully applied, recourse must
be had to their chemical habitudes, that is
to say, to the relations which they bear to
other substances, on or from which they

ACCORDING TO HAUY. 355

are capable of producing or receiving some
peculiar observable changes.

It was undoubtedly because the study
of the external characters of minerals soon
convinced mineralogists that the mode of
proceeding just stated was far from con¬
ducing to the exact knowledge of mine¬
rals, and that it was only capable of giving
false ideas and producing errors respecting
their nature, that the project was adopted
of classing mineral substances according to
their chemical composition or intimate
nature. I’liis happy thought, which forms
the only real foundation and solid basis of
the science, which, from the mere art or
routine of distinguishing and naming these
bodies, elevates it to a true science, has
much engaged the attention of chemical
mineralogists, who have successively la¬
boured to extend, to improve, and to com¬
plete it. And this great object is not yet
terminated, notwithstanding the numerous
researches which liave been made, and are
daily making, without intermission, in this
department of knowledge.

A A 2

356 CLASSIFICATION OF MINERALS

The chemical examination of minerals,
that is to say, the nature of their composi¬
tion, it is true does not yet enable us to
compare the nature and characters of all
the minerals hitherto known, so as to ar¬
range them in a discriminate series, by the
order of their composition, or so as to form
a chemical arrangement, perfect in its
structure. Each individual has not, and
cannot be analyzed; this w ould be im¬
practicable, and were it not, it would be
without utility, but when the analysis of a
mineral has been effected, we have reason
to presume that a similarity of composition
w’ill exist in other specimens which agree
with it closely in its external properties or
characters.

It must be obvious, that the methodical
distributions of minerals, whatever steps
may be taken, cannot be so absolute and
determinate as those which belong to ani¬
mals and vegetables. Minerals, not being
organic bodies produced by egg’s or seeds,
are not themselves so determinate and con¬
stant, and thus the great and essential dif-

ACCORDING TO HAUY.

357

ference of arranging them into classes,
genera and species, so useful in the vegeta¬
ble and animal kingdom, strictly speaking,
is lost in mineralogy. And although mine¬
ralogists do by no means agree concerning
the best modes of arranging minerals,
even those who have most decidedly re¬
jected the chemical system of classifica¬
tion, have admitted that the class and
genus in mineralogy can be founded only
on chemical principles, hence the ores, the
stones, the salts, and the inflammable
fossils, form distinct classes; and each metal
and each earth gives rise to a genus. No
other principle, no other chai*acter, or set
of characters, can be substituted without
rendering mineralogy an assemblage of the
most vague, arbitrary, and fluctuating
science; and hence this proceeding of fixing
the higher divisions is well founded, and
universally admitted.

The chief difficulty which offei’s itself
affects what is called the species. In the
animal and vegetable kingdom, the species

358 CLASSIFICATION OF MINERALS

is fixed by an invariable character. A
certain organization and form are trans¬
mitted from one individual to another, with
the combining the same succession, each
plant and animal constitutes a Avholc, pos¬
sessing a determinate form; each individual
exhibits an essential difl'erence capable of
definition, and on this the species of the
plant or animal is founded, and perma¬
nently fixed. In the general assemblage
of properties there is no such thing as an
imperceptible gradation from one to an¬
other. The individual of each, not liable
to be placed under variations of circum¬
stances at their formation, when the cha¬
racters are fixed, are not liable to be much
disguised in structure or form, and any
alteration, when produced, being abso¬
lutely confined to the individual, is soon
lost.

In the mineral kingdom each substance
cannot thus be considered as an individual,
and the species therefore cannot be deter¬
minate, arising from chemical combina-

ACCOEDING TO IIAUy, 3o9

tion, and that combination being liable to
be influenced by various circumstances,
while there is a power counteracting these
and preserving uniformity, the individuals
are liable to be almost indefinitely di^'er-
sified in their properties, and must pass in¬
variable into each other.

In the system of Haiiy, the chemical
composition of minerals is said to be pro¬
fessedly taken into view, in forming the
arrangement, the species is determined
from one character, namely, the integrant
molecule; and hence Haiiy defines the
species, “ A collection of bodies, of which
the integrant moleculae are alike, and com¬
posed of the same elements united in the
same proportion.” This latter condition
being added, he generalizes the definition,
and extends it to substances which, having
their integral moleculae of the same form,
differ essentially in the principles of which
these moleculae are composed^; the form

r

* Traite de Mineralogie, tom. I. p. 169 ,

360 CLASSIFICATIOK OF MINEKALS

of the integrant particle therefore being the
basis of the specific distinction.

But as it is impossible to extend the
system of the integral molecule to all mi-
neralSf there are mineralogists who re¬
proach it with the difficulty of finding the
directions of the cleavage, in many cases,
the trouble of calculating them, See, We
should no longer*' use the microscope, the
telescope, nor the chronometer, for they
also are very difficult to execute. Let us
content ourselves with dressing, sleeping,
and eating, convinced that without the
pendulum and the telescope the stars will
continue their course, and bring back the
hours of sleep and the restoration of our
powers.

The last objection which has been made
against the system of Haiiy, says this phi¬
losopher, and ito yrhich I shall pay any
attention is that which is stated thus: “ We

* Clienevix. In the Philosophical Magazine,
voL 36 -

ACCOEDIJTG TO HAur. 36l

must abandon the French system for that
of the external characters, as the integral
molecule cannot be observed in all mine¬
rals." One of the great advantages of the
system of M. Haiiy, one of its principal
beauties, is to follow nature, and to speak
as she does. Where she has finished her
work in the highest manner of which it is
susceptible, M. Haiiy does the same ; and
if she produces a mineral endowed with all
the characters which, according to us, com¬
pose the most perfect state, it is classed
and defined as such. If she has been
sometimes less rigorous in impressing her
mark of perfection, the system follows the
same course; while the method of external
characters renders equally the honours of
rigorous classification to sapphire and to
the alumina of Plalle. To say that we
should make no use of an excellent system,
because cases occur where it is unavailable,
is to say to a patient. Lie not on a feather
bed; for, if you are deprived of it, you will
be reduced to the necessity of sleeping on
a board. It is to tell a man in health not

362 CLAssiriCATi03sr of minerals.

to take nourishment, for if the provisions
become deficient he could no longer eat.

The following is the methodical distribution
of Mmerah adopted in the French School
of Mitieralogp.

DIVISION I.

MINERAL SUBSTANCES WHICH ADMIT OF
SPECIFIC DISTINCTION.

CLASS I.

ACIDIFEROUS SUBSTANCES, COMPOSED OF AN
ACID UNITED TO AN EARTH, OR TO AN
ALCALI, OR TO BOTH.

ORDER I.

Combinations of earths with acids.

CLASSIFICATION OF MINERALS. 363

GENUS I.

LIME.

SPECIES*

Carbonate of lime.

Phosphate of lime,

Fluate of lime,

Sulphate of lime,

Nitrate of lime,

Arseniate of lime.

VARIETIES.

Carbonate of Lime united to different sub-
stanceSi so as to preserve its structure^ or
some of its principal characters.

Aluminiferous carbonate of lime,
Ferriferous carbonate of lime,

Siliceous carbonate of lime.

Magnesian carbonate of lime,

Hj-’dro sulphurised, or foetid carbonate of
lime,

Bituminous carbonate of lime.

3

364 CLASSIFICATION OF MINERALS

GENUS II.
BARYTES.

SPECIES.

Sulphate of barytes.
Carbonate of barytes.

GENUS III.
STRONTIA.

SPECIES,

Sulphate of strontia,
Carbonate of strontia.

GENUS IV.
MAGNESIA.

SPECIES.

Sulphate of magnesia,

CLASSIFICATION OF MINERALS. 365

Borate of magnesia,
Carbonate of magnesia.

ORDER II.

Combinations of alcalies with acids.

GENUS 1.

POTASH.

SPECIES.

Nitrate of potash.

GENUS II.

SODA.

SPECIES.

Muriate of soda,

t- .

•I

J

1

V

L'l!

I

366 CLASSIFICATION OF MINERALS.

Borate of soda.
Carbonate of soda.

GENUS lU.
AMMONIA.

SPECIES.

Muriate of ammonia.

ORDER III.

Comhinations of earths and ahaliea mth
acids.

GENUS 1.

ALUMINE.

SPECIES.

Sulphate of alumine and potash,
riuate of alumine and potash.

CLASSrrrCATION of MINEEALS. 367

CLASS II.

NON ACmiPEEOXJS SUBSTANCES, OR MINE¬
RALS EXCLUSIVELY COMPOSED OP EARTHS,
EXCEPT %VHEN UNITED SOMETIMES TO
AN ALCALI. *

SPECIES*

rHyaline
I Agate

Quartz ■{ Resinitc
Jasper

^^Pseudom Orphic

Zircon,

Telesia,

Cymophane,

Spinel ruby,

Topaz,

* This class has no orders nor genera, but is only a
series of individual species.

368 CLASSIFICATION OF MINERALS

Emerald,

Euclase, ,

Amphigene,

Idoci'ase,

Me'ionite,

Feldspar,

Corundum,

Pleonaste,

Axinite,

Turmaline,

Amphibole,

Actiite,

Pyroxene,

Staurotide,

Epidote,

Garnet,

Sphfene,

Wernerite,

Diallage,

Anatase,

Dioptase,

Gadoleite,

Lazulite,

Mesotype,

Stilbite,

CLASSIFICATION OF MINERALS.

CLASS III.

COMBUSTIBLE SUBSTANCES.

ORDER I.

Simple combustible substances.

' SPECIES.

Sulphur,

Diamond,

Anthracite.

ORDER II.

Compound combustible substances.

SPECIES.

Bitumen,

CLASSIFICATION OF MINEKALS. 371

Pit-coal,

Jet,

Amber,

Mellite.

CLASS IV.

METALLIC SUBSTANCES.

372 CLASSIFICATION OF MINERALS.

CLASSIFICATION OF MINERALS. 373

ORDER II.

Substa}ices immediately ox idable and reducible
by heat.

GENUS.

MERCURY.

SPECIES.

Native mercury,

Argentiferous mercury,

Sulphuret of mercury.

Muriate of mercury,
Hydrosulphuret of mercury.

ORDER III.

Substances which are oxidable, but not imme¬
diately reducible by heat.

I. SUBSTANCES CONTAINING DUCTILE AND MALLE¬
ABLE METALS.

374 CLASSIFICATION OF MINERALS.

GENUS 1.

LEAD.

SPECIES.

Native lead, (volcanic)
Sulpliuret of lead,
Arseni ate of lead.
Chromate of lead,
Caibonate of lead,
Phosphate of lead.
Sulphate of lead.
Muriate of lead,
Murio-sulphate of lead.

GENUS II.
NICKEL.

SPECIES.

Arseniate of nickel,
Oxid of nickel.

CLASSIFICATION OF MINERALS. 375

GENUS HI.
COPPER.

SPECIES*

Native copper,

Sulphnret of copper,

Grey oxicl of copper,

Red oxid of copper,
Muriate of copper,

Blue carbonate of copper,
Green carbonate of copper,
Arseniate of copper,
Sulphate of copper.

GENUS IV.

IRON.

SPECIES*

Oxid of iron,

Oligistous or specular iron,
Arseniate of iron,

376 CLASSIFICATION OF MINERALS.

Sulphate of iron,
Carbonate of iron,
Chromate of iron.

GJENUS V.
TIN.

SPECIES.

Oxid of tin,
Sulphuret of tin.

GENUS VI.
ZINC.

SPECIES.

Sulphuret of zinc,
Sulphate of zinc,
Carbonate of zinc.

CLASSIFICATION OF MINERALS. 377

II. SUBSTANCES CONTAINING METALS NOT POSSESS¬
ING DUCTILITV AND MALLEABILITY.

GENUS VII.

BISMUTH.

SPECIES.

Native bismuth,

Sulphuret of bismuth,

Oxid of bismuth.

GENUS VIII.
COBALT.

. SPECIES.

Arseniate of cobalt.
Grey oxid of cobalt.
Black oxid of cobalt.

378 CLASSIFICATION OF MINERALS.

GENUS IX.
ARSENIC.

SPECIES.

Native arsenic,

Oxid of arsenic,
Sulphuret of arsenic.

GENUS X,
MANGANESE.

SPECIES.

Oxid of manganese.

GENUS XI.
antimonV.

SPECIES.

Native antimony.

CLASSIFICATION OF MINERALS. 379

Swlphuret of antimony,

Oxid of antimony,

?Iydrosulphuret of antimony.

GENUS XII,

• URANIUM.

SPECIES,

Oxid of uranium,
Oxidulated uranium.

GENUS XIII.

MOLYBDENA.

SPECIES.

Sulphuret of molybdena.

380 CLASSIFICATION OF MINEHALS.

GENUS XIV.
TITANIUM.

SPECIES.

Oxid of titanium,
Siliceo-calcareous titanium.

GENUS XV.
TUNGSTEN.

SPECIES.

Feruginated tungsten,
Calcareous tungsten.

GENUS XVI.
TELLURIUM.

SPECIES.

Native tellurium, united to different metals.

CLASSIFICATION OF MINERALS. 381

GENUS XVII.

CHROMIUM.

SPECIES. '

Chromeate of lead,

Chromate of iron.

f

t

■t

\

V

\

I

»f

. M

382 CLASSIFICATION OF MINERALS.

DIVISION 11.

SUBSTANCES WHICH DO NOT ADMIT OF
SPECIFIC DISTINCTION.

I. DOUBTFUL MINERALS, OR SUBSTANCES NOT YET
SUFFICIENTLY KNOWN TO HAVE A PLACE IN
THE SYSTEM.

■■

Ainianthoide,

Aplome,

Arragonite,

Coccolithe,

Diaspore,

Ecume cle Terre,

Emerald of France,
Eeldspar, apyrous,

Jade,

Koupolite,

Lfepidolithe,

Lime, sulphate anhydrous.

CLASSIFICATION OF MINERALS. 383

Lime, sulphate quartziferous,
Madreporite,

Malacblithe,

Micarella,

Petrosilex,

Scapolite,

Radiant spar,

Schistous spar,

Spin there.

Tourmaline,

Triphane,

Zeolite, efflorescent,

Zeolite, yellowish radiated,
Zeolite, red.

II. AGGREGATES OF DIFFERENT MINERAL SUB¬
STANCES USUALLY DENOMINATED COMPOUND
ROCKS.

ORDER I.

Aggregates considered as of primitive forma-
tiott, and which bear more partictdarly the
name of rocks.

384 CLASSIFICATION OF MINERALS.

Feldsphathic rock,
Quartzose rose.
Amphibolic rock.
Micaceous rock,
Talcous rock.
Calcareous rock,
Jadeanrock,
Petrosiliceous rock,
Cornean rock,
Serpentinous rock,
Argillaceous rock.

ORDER II.

Aggregates generally considered secondary
or tertiary in their formation^ and which
seem to owe their ori^n to sediments^ and
their hardness to desiccation.

Clay,

Calcariferous clay or marie,

CLASSIFICATION OP ailNERALS. 385

Argilio-ferriferous poiishablc limestone, or
secondary marble, ■

Calcaritei'oiis sulphate of lime, commonly
called jilaster stone.

VARIETIES.

Potter's clay,

Puller’s clay,

Lithomargic clay,

Oclireous clay.

Schistous clay.

ORDER III.

Aggregates composed of fragments aggluti¬
nated posterior to the formation of the
substances to which they have belonged.

Quartz-agate breccia.

Calcareous breccia.

386 CLASSIFICATION OF MINEKALS.

Agglutinated arenaceous (juartz, or grit,
Tripolian alumineferous quartz. Tripoli,
Recomposed granite, commonly called grit
of the coal mines.

III. SUBSTANCES MODIFIED BY SUBTERllANEAN
FIDE,

CLASS I.

1 . VOLCANIC PRODUCTS,

LAVAS :

Substances which have undergone igneous
Jiuidity.

ORDER I.

Lifhoidal lavas, viz. having the appearance
of stones.

CLASSiriCATIOST OF MINERALS. 387

GENUS.

Basaltic lithoidal lavas,
Petrosiliccous lithoidal lavas,
Feldspathic lithoidal lavas,
Arnphigenic lithoidal lavas.

ORDER IT.

Vitreous lavas^ having more or less a vitrijied
appearance.

ORDER III.

Scoriated lavas, resembling more or less the
scoria of forges.

VARIETIES.

Obsidean vitreous lava,
c c 2

388 CLASSIPICATIOlir op minerals.

Enamdled vitreous lavaj
Pearled vitreous lava.
Pumiced vitreous lava.
Capillary vitreous lava.

CLASS II.

TIIERMANTIDES :

Substances which indicate only traces of the
agency of subterranean heat.

VARIETIES.

Cementing thermantidc,

Tripolian thermantide,

Pulverulent thermantide.

CLASSIFICATION OF MINERALS. 389

CLASS III.

PRODUCT OF SUBLIMATION.

Sulphur,

Muriate of ammonia,

Sulphuret of arsenic,

Oligistous iron, &c.

Nt B. These admit of specific distinction^ and have a
place in the method; hut considered with reference to
volcanic produclSy are only mrious sublimates.

CLASS IV.

DECOMPOSED LAVAS.

Having suffered more or less decomposition by
the attacks of acidosulpkureous vapours or
by the action of the aUnospkere,

390

CLASSIPICATTOSr OF MINERALS,

VARIETIES.

Aluminiferous decomposed lava.
The alum stone of Tolfa.

CLASS V.

VOLCANIC TUFAS.

Products of muddy eruptions, cementations,
and agglutinatwns, by the Immidprocess.

CLASS VI.

SUBSTANCES FORMED IN THE INTERIOR OP
LAVAS POSTERIOR TO THEIR FLOWING.

VARIETIES.

Mfesotype,

Analcime,

Mineraiogktil Chests^ Chtmieal Preparations and ApparatuSj

MANrFACTL'RED SOr,D

BY ACCUM AND GARDEN,

OFEEAI’IVJS CHEMISTS? COMPTOS'-STREET, SOHO, EOWDON.

MhVERJLOGlCAL AND CHEMfCAL CHESTS.

The Chemical .apparatus and Bottles contained in the following
Chests are arranged in such a manner, that thej may he seen
atone View ’when the Chest and Drawers are open; they arc
besides so packed that they can readily be to Ken out, and
wdieii replaced fU in such a way» that the ’^vbolej when Uie
Chest is locked, may be turned upside dowTi wnlhout Risk of
receiving injury*

Pocket Mincralogicfd Blotrptpe Apparatus . £3* to £4,

This small mineralogical case contains Dr, Wollaston’s hlo’w-
pipCj a double niagnifier, platina foil, a blow'pipe forceps, two
bottles of fluxes, a steel graver, lest tubes, and the most essen¬
tial re*ageiits necessary for the immediate examination of mine¬
rals, In the study of mineralogy, the pocket blowpipe appara¬
tus, which joins to the convenience of a small size, and the facility
of being easily transportable, is of singular advantage* It
enables the mineralogist to expose instantly, to the action of a
most yiolcnt heat, the substances he may meet willi in his
travels, &:c*

Mhieralogical Travelling Chests .. .£7, 7s* to £13^ 13s.

Though the blowpipe assay is usually sufllcieul to furnish ge¬
neral notions concerning the substances of the mineral kingdom,
those who study mineralogy as a science, arc not content with
this kind of analysis, because it docs not uflbrd the summary in¬
formation they require. By alwaijs operating on siual) frag-
ments, the results obtained are loo minute to enable the operator
to determine quantities with accuracy- By the applicalioti of
the re-agents contained in this chest the general nature of any
mineral may he easily and quickly ascertained,

Alineralogical Laboi'atorks .£10* IGs, to £25*

This portable laboratory contains a complele collection
of the most approved apparatus and instruments necessary for
carrying on the analysis of mineral substances of all kinds. Ft
forms a compamo?t to Accum*s Manual of Anal^ticoI Mineralo^j^i
intended to faciHiaU the pruclkal analysis of metaltie ores,

i

iccum Crysfd /1 ogi 'aphy.

FIML

^Up*

I

I

I

irruRi's ,

Fi.iu IK

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0

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393

earthsj ittojiesy and other subjects of the mineral kingdoms ; in *
Tols. A drawing and full description of the inineralogical
laboratory may be seen in the Philosophical Magazine, No. eWii.
1811.

Portable Chemical Laboratories, for carrying on a general
Course of Chemical Experiments .£30. to £80.

Since chemistry has changed its appearance; since its instru*
meats of experiments have been perfected, and acquired new
forms, new paths for exploring the productions of nature have
also been opened, the art of experimenting has been simplified,
and become more familiar and easy. Experience has thus
shown, that however varied the objects of research may be, and,
however numerous and different the products to be obtained
may appear, the operator is now enabled to perform, at a trifling
cxpence, his processes in the closet with more precision and
perspicuity than could formerly be done in the regular labora¬
tory fitted up with costly instruments. The numerous processet
of degestions, the sublimation of salts, the solution of earthy,
metallic, and other bodies, the concentration of saline liquids,
the desulphuration of metallic ores, the processes of distillation
by the naked fire or the sand-bath, and even the production of
gases, and fusion of earthy fossils with alcalies, may be accom¬
plished, at a trifling expence, by the help of the portable la¬
boratory.

Packed Goniometer, described page 86.

Wollastons Eejltctive Goniometer, described page 90.
Mineralogical Electrometers, described page 246.

Pocked Magnifiers for examining Minerals,

Improved Lamp Furnaces, £3. 3^. to £5. bs.

The lamp-furnace, as it is perhaps not very properly called, is
one of the most convenient means of applying the brilliant flame
of an Argan’s lamp to the purposes of experimental chemistry.
By means of it a vast number of chemical operations may be
performed with great speed, precision, and perspicuity. Indeed
the lamp-furnace may be useu for almost every one of the opera¬
tions of chemistry in the small way, which require a temperature
not exceeding a dull red heat. The processes of digestion, the
sublimation of salts, the solution of earthy and metallic bodies,
the concentration of liquids, all the multifarious processes of
distillations by the sand-bath, and by the naked fire, the produc¬
tion of gases with the pneumatic apparatus, may commodiouslj
be accomplished, at a trifling expence, ou the table, with the
help of this instrunieat.

D B

394

Moveable Universal Furnace, . .. . to £8, 8s*

Among the whole grotip of app^iratus rksigncd for jipplyiiig
heat to bodies, this furnave undoubtedly is for tJie purposes of
experimental chemistry the most useful, however mimerouB and
different the operations to be performed may be. It may be used
with perfect safety in a room, and is therefore well calculated,
not only for those operators who have no access to the !abora*
tory, but also for lecturers on chemistry. A very large number
of chemical processes may be carried on in this furnace coniino-
diously and at a cheap rate.

CHEMICAL APPARATUS.

Universal Furnace—Table Lamp Furnaces—Chemical Lamps
—Spirit LampS'—^Blowpipes with Plalina Jets, Platina Spoon,
Forceps, and Foil—Chemical Thermometers—Pneumatic Tables
with Assortments of BelLGIasses, Cylindrical Receivers, and De¬
ll age rating Jars—^Detonating Tuhes’—Bel LG lasses raounled with
Stop-Cocks, Bladders, &c,—Glass Retorts with long Necks for
procuring Gases—Eudiometers—Graduated Cylindrical Jars, di-
Tided into Cubic Inches and Decimal Parts—various sized Gas
Bottles, plain and tubulated—Cast-Iron and WroughMron Re¬
torts, with Conducting Tubes—largo Bladders, with Slop-Cocks
—A i r-Holders—A pparatus for i mpregnating Fl u ids wi Ih Gases—
Pneumatic Mercurial Troughs, Nests of Cylindrical Air-jars
adapted for the Mercurial Trough, plain and graduated^—Gl^s
and Earthenware Retorts, plain and tubulated, with correspoiKl-
ing Glass Receivers—Balloon Receivers—Small Copper Stills and
Refrigerators-—Glass Alembics—ditto of pure Silver, with Glass
Capital—Earthenware and Black-lead Crucibles, round, trian-
gular, and Skittle-shaped, with Stands and Covers for ditto—
Specific Gravity Bottles—Steam Baths for drying Precipitates—
Delicate Scales, and corresponding Weights—Common Hand-
scales, and Piles of Weights for ditto—Galvanic Batteries, with
Apparatus, for the Decomposition of Water—Glass, Porcelain,
Earthen, and Stoneware Funnels, plain and ribbed—Glass Funnels,
with long Kecks,for charging Retorts—Glass Jars, in Sizes,plain
and with Lips, for decanting or precipitating fluid, and for stir¬
ring mixtures—^Iron Standards, with Sliding Rings for support¬
ing Retorts, Flasks, Basons, and other Vessels—Filtering Stands
and Filtering Frames^Test Tubes and Stand—Earthenware
Basons, wiUi Spouts, in Sizes—Flasks, Assay Jars, Matrasses,
and Bolt-heads—Hand-mortars of Porcelain Biscuit—^Iron Mor¬
tars, in Sizes—Graduated Glass Measures, from two Ounces to
one Pint Capacity—Florence Flasks, and Stands for ditto—vari¬
ous sized Iron Boilers and Pans—^Adoplers of Glass and Earthen¬
ware—Steel Spatulas—a small Silver Spatula—a ditto of Platina
—Glass and Enamel Rods, for stirring Acid and corrosive Mix-

4

395

turcs—Capillary Tubes—Metal and Glass Syphons—Steel Anvils
—Iron Ladles—Glass, Silver, and Earthenware Spoons—Sockets
and Joints, for connecting Stop-Cocks, &c.—Tubes of Safety,
and Hydrostatic Funnels—circular Pieces of Metal, and Plates of
Glass, for covering deflageratiiig Jars, &c.—Copper Delibe¬
rating Ladles—Writing Diamonds—Masks, to defend the
against Accidents in Chemical Operations—Barometers—Elec¬
trical Machines—Double-barrelled Table Air-Pumps—Hidro-
static Balances, and Nicholson’s Hidromelers—Burning Lenses—
Gazometers—Portable forge and Blowpipe Tables, with double
Bellows—Freezing Apparatus—Flasks and Globes, for weighing
Gases—Calorimeters—Leslie’s Differential Thermometer—Metm
Reflectors—Agate and Steel Mortars—Blast Furnaces—very de¬
licate Balances and corresponding Weights, &c.

CHEMICAL PREPARATIONS.

ACIDS.

Sulphuric Acid, pure and common—Nitric Acid, pure and
common—Nitroas Acid—Muriatic Acid, pure and common—Oxi-
rauriatic Acid—Tartaric Acid, and all the rest of the Known
Acids.

EARTHS.

Silex—Alumine—Magnesia—Barytes—Strontia—Lime,

ALCALIES.

Potash, pure and common—Soda, pure and common—Ammo¬
nia, pure and common.

METALS.

Iron Filings and Wire—Copper, pure and common, and Cop¬
per Clippings—Granulated Zinc—Lead Foil—Silver Leaf and
Wire—Gold Leaf and Wire—Tin Foil and Filings—Platina Foil
and Wire—Qucksilvcr—Bismuth.

TESTS.

Red Cabbage Tincture—Litmus Tincture—Turmeric Tincture
—-Brazil Wood Tincture—Tincture of Galls—Papers stained
with these Tinctures—Alcohol, pure and common—Solution of
Oxid Arsenic—Solution of Acetate Barytes—Solution of Sulphate
Silver—Barytic Water—Hidrosiilphurct Lime—Lime Water—
Solution of Acetate Lead—Solution of Muriate Bismuth—Solu¬
tion of Muriate Barytes—Solution of Muriate Gold—Solution of
Muriate Tin—Solution of Muriate Lime—Solution of Muriate
Platina—Solution of Nitrate Lead—Solution of Nitrate Barytes
—Solution of Nitrate Silver—Solution of Oxalic Acid—Solution

aofs

of OxRlatc AmmonU^—Sululionof Pru^siate Potash—Solution of
Prtissiate Lime—Solution of Pru^isiato Mercury — Solution of
Soap in Alcohol—Solution of Sulphate Silver—Solution of Suc¬
cinate Soda^Polished PlHtc» of Copper, Iron, and Zinc — Sul¬
phate of Iron—Stroiilia Water.

CLt7XE9<

Vitrified Borax—Vitrified Phosphoric Acid — Dried Phosphate
—Dried Carbonate Soda—White Plux — Black Plux^Crude
PltiX'^-Powder Green Glass,

SALTS, SALINE COftSPOUNDS, SiC*

Carbonate Ammonia, pure and common—Carbonate Barytes
native—Carbonate Potash, pure and common—Carbonate Soda,
pure and common—Carbonate Strontia, native^—-Muriate Am¬
monia—Muriate Lime—Muriate Stfontla—it rale Ammonia- —
Nitrate Barytes—Nitrate Copper—Nitrate Lead-—Nitrate Mer¬
cury—Nitrate Stronliji — Oxi-uiuriatc Potash—Sulphate Iron —
Sulphate Potash—Sulphate Magnesia—Suh-carbouate Magnesia.

OXIOS,

Ox id of Manganese—Bed Ox id of Lead—Red Ox id of Mcr-
cury—Black and Red Ox id of Irou—Browu Ox id of Copper-™
White Oxid of Tin,

SULTiniHCTS.

Sulphurel Iron^Svilphuret Auimoma — Sulpliurct Lime—Sul-
phurct Potash.

MlSCELL.iNROtJS ARTICLES,

White Marble—Phosphorus—Sulphuric Ether- — Sulphur —
Naptha — Oil of Turpentine—boiled Ltnt-.seed Oil—Spirit Varnish

Paris Plaster—Windsor Loam—Stourbridge Clay — Lint-seed
" cal—Slips of Bladder—Common Lute, for closing Glass
Vessels, in preparing all common distilled Llrjuors—Lute for
confining Acid and corrosive Vapours—Fire Lute to join the
Covers of Crucibles, so as to keep them Air-tight, at a strong
Heat—Fire Lutes' for coating Glass and Earthenware Retorts—
Cement for stopping Cracks In Iron Vessels intended to bear a
lied Beat—Resinous Cement for fixing Tubes, &c. into Glass
Vessels, to be Air and Water tight—Varnish for closely fitting
Bladders and Bags to Stop-Cock's, and for rendering the joinings
of small Glass Apparatus Air-tiglit, and every other Article cm-^
I>loyed in the Pursuits of Operative aud Experimental Chemistry.

A Descriptive Catalogue^ exhibUing the Prices of
the above Articles^ may be hud at iVo, 11^ Old Compiott
Street^ Soko.

J. O, 8AIUailIt>,