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HARVARD
UNIVERSITY
LIBRARY
LONDON:
PRINTED BY GILBERT AND KIVINGTON, LIMITED,
KT. JOHN'S HOUSE, CLERKENWELL ROAD, E.C,


PREFACE.
This book has been compiled because of a
strongly felt want of a complete text-book upon
the subject of Theory and Analysis of Ornament,
the Author having been asked by his own and other
students, why he did not write a book more in
advance of the teaching of the present time. The
study of Ornament has made such rapid progress
during the last twelve years, that those books which
were previously quite efficient have become obso-
lete. So far as the Author's knowledge extended,
there seemed a very large demand for books of an
explanatory nature, as applied to the work of
elementary and technical schools. This work is
published with the object of more completely
developing the various sections of the subject
hitherto dealt with. The arrangement is such as
A
2


Introduction.
to present the entire subject in the simplest and
most easily to be understood form.
The present Minute of the Education Department
on Science and Art, encouraging technical work in
the schools, promises great results ; and the Author
has endeavoured to produce a book of practical
use to teachers, in their preparation for the tuition
and examination of schools.
François Louis SCHAUERMANN.


CONTENTS.
CHAPTER
PAGE
FIRST PART.
1.—Theory and Analysis of Ornament .
II.-Order, Form, Relief, Colour . .
III.—Monumental and Decorative Art .
.
1
.
.
·
·
SECOND PART.
First Section.
1.-Fundamental Notions . .
II.-Size, Quantity
III.-Extent-Co-ordinated .
IV.- Measure and Graduation . .
SECOND SECTION.
Linear Extent and Delineation
I.--Straight Line and Rectitude . .
II. & III.-Curvity and Curved Lines
IV.–Figurative Elements
V.- Æsthetical Affections
VI.-Delineations.
Third Section.
Superficial Extent and Plane Surfaces . .
1. Fundamental Forms of Superficial Extent :
II.--Generation of the Fundamental Plane Surfaces.
III.-Fundamental Dominant Lines of Plane Surfaces
IV.-Fundamental Forms of Plane Surfaces . .
56
59
66


Contents.
CHAPTER
V.-Harmonical Lines of the Fundamental Forms .
VI.–Variation in the Fundamental Forms ' . .
VII.-Polygonal Plane Surfaces . . .
VIII.—Polygonal Figures and Lines Derived from
them . . . . .
IX.-Derived Polygons . . . . . .
X.-Derived Polygonal Plane Surfaces . .
XI.--Rhombical Elements and Cuneiforms of Poly-
gons . . . . . . .
XII.-Assembled Polygons . . . . .
XIII.—Derivative Polygonal Declinations . : : 102
FOURTH SECTION.
Extent and Corporeal Forms .
I.-- Followed or Linear Forms .
II.- Declined Forms . .
III.-Spheroidal Forms . .
IV.-Varied Forms . . . . .
.
.
.
.
. 107
. 110
: 111
. 11:
. 112
.
.
FIFTH SECTION.
Regularity and Symmetry
1.-Symmetry . . .
.
.
.
.
.
. 116
. 117
THIRD PART.
Order and Disposition in Ornament and Forms. 130
FIRST SECTION.
Unlimited Dispositions . .
1.-Order of Disposition in Series .
Il.–Ranges . . . . .
III.—Conjugations of Ranges . .
IV.–Varied Dispositions . .
.
.
.
.
.
.
.
. 132
. 132
. 137
. 141
. 151
.
.
SECOND SECTION.
Multiplied Dispositions . .
I.-Networks . . . . .
.
.
.
.
. 156
. . 156


Contents.
CHAPTER
PAGE
167
II.-Grouping of Circles
III.--Repartitions
·
THIRD Section.
Agglomerated Dispositions
.
.
.
.
179
·
. 181
.
.
·
181
·
..
FoURTH SECTION.
Figurative Dispositions .
I.-Linear Dispositions .
II.- Peripherical Dispositions
III.—Orbicular Dispositions .
IV.-Radiated Dispositions .
V.-Pennate Dispositions .
VI.- Palmated Dispositions.
VII.-Curved Dispositions ,
VIII.-Branched Dispositions :
IX.- Assembled Dispositions .
18+
184.
185
·
·
·
·
·
.
.
189
190
.
·
.
.
.
.
Fifth Section.
Co-ordinated Dispositions
Sixth Section.
Constructed Dispositions
.
.
.
.
194
.
FOURTH PART.
Developments and References .
1.- Application of Quadripartitions
II.—Partitions of the Coat-of-Arms.
III.-Imbrications . . . .
IV.-Compartments and Adjustments
.
.
.
.
.
.
:
195
195
201
202
204


LIST OF ILLUSTRATIONS.
1. Greek Scroll with Acanthus Leaf.
2. Oak-leaf Bracket.
3. Flemish Renaissance Panel (in time of Holbein).
4. Louis XVI. Astronomical Panel.
5. Flemish Renaissance Panel.
6. Panel from Nature.
7. Modern Renaissance Panel.
8. Flemish. Renaissance Panel.
9. Egyptian Capital.
10. Japanese Rail.
11. Cinquecento Capital.
12. Louis XIV. Pane!.
13. Japanese Rail.
14. Greek Scroll and Acanthus-leaf Panel. .
15. Modern English Panel.
16. Italian Capital.
17. Cinquecento Bracket.
18. Greck Scroll and Acanthus Leaf (larger scale).
19. Japanese Rail (larger scale).
20. Japanese Rail (larger scale).
21. Bold Specimen of Italian Scroll-work.
22. Byzantine Panel.
23. Louis XIV. Panel (larger scale).
24. Elizabethan Panel.
25. Egyptian Scroll Panel.
26. Perpendicular Gothic Window.
27. Modern English Panel.
28. Louis XVI, Flower Panel.


THEORY AND ANALYSIS OF
ORNAMENT.
Part X.
CHAPTER I.
1. DIAPERED forms are productions of the artist,
and are in contradistinction to those produced by
nature. Forms produced by nature bear the mark of
a first creative power; whereas, the diapered forms,
produced upon those original forms, are the pro-
ductions of the human brain assisted by certain tools
employed, which are themselves in turn the pro-
ductions of mechanical skill. The two things
necessary to bring about or carry out the artist's
work, are material and industry. Industry is,
then, the “ways and means” by which the artist
brings about the productions of his art. Nature
furnishes the raw material, art produces form,
in the raw material, necessary to the wants of man,
both artistic and useful.
2. The artist's work can easily be distinguished
from that which shows mere mechanical skill.
Mechanical skill can be recognized as proceeding ·
from practice in a certain art or industry; the
artist's work indicates a higher inherent power, but
can easily be distinguished from an untutored pro-
duction of the brain.


2 Theory and Analysis of Ornament.
The diapered form, independently of its beauty
and usefulness, is a compound of three elements, viz.,
material to be used, mode of manipulation, and,
thirdly, its relation to art.
The material to be worked furnishes its plastic
and decorative qualities.
The types depending on art are form and decora-
tion. Form is the result of particular modifications
wrought in the material by the workman, and is
necessary to the satisfying of the ästhetic taste of
the worker. Decoration is an addition made to the
first form, as produced by the artisan, and is the
work of the artist.
The following table should be carefully studied,
as giving the principal forms and types as brought
into existence by the artist or mechanic. The
mechanic's work must be acknowledged as a very
necessary adjunct to the complete production of the
diapered forms produced by the inborn genius of
the artist himself.
FORMs.
Modelled
( Modelled (plastic).
Turned (ceramic).
(i.) Forms.
Blown (glass works).
(Plastic.)
(Hammered (brass ware).
Carved
(Carving (carving).
(ii.) Forms.
Sculptured (sculpture).
Chiselled (toreutic).
(Schipture.) ( Engraved (glyptic).
(iii.) Assembled forms (joinery, iron-foundry, &c.).
(iv.) Built or added forms (construction, architecture).
(v.) Weaved forms (weaver's trade, basket trade).
DIAPERED FORMS.
3. Materials produced by nature are peculiarly


Theory and Analysis of Ornament.
n
S
adapted to the manipulation of the artist, and the
latent qualities afford the genius in man an op-
portunity to exercise its powers of producing
decorative forms and types so pleasing to the mind
and necessary to the true enjoyment of nature.
Man sees the raw productions of nature, and,
concurrently with sight, springs up a desire to
beautify, which desire calls forth an inherent talent
capable of being more highly developed in those
whose natural qualifications are those of an artist
apart from or above those of the mechanic.
The following table should be carefully studied, as
giving the different modes of decoration.
(I.) The illuminated, painted or enamelled de-
coration ; which refers to the modelled, carved,
assembled, builded and weaved, diapered forms.
(II.) The modelled or sculptured decoration ;
which refers to the first four, viz., modelled, carved,
assembled and constructed forms.
(III.) The engraved and carved decoration ;
which refers to modelled, carved and assembled
forms.
(IV.) The embroidered decoration, which refers
exclusively to the weaved forms.
ORNAMENTATION.
4. Form and decoration are so closely allied that
the one naturally forms part of the other; that the
blending of the two makes one quality, viz., that of
ornamentation. Under the generic name of orna-
ment, we must consider the numberless variety of
drawings, forms, reliefs, coloured prints, &c., by
which man has surrounded himself, and which
B 2


Theory and Analysis of Ornament. 5
nces
vey
Carull,
at that age, the decorations being principally the
productions of those monks possessed of artistic
ability, and who were almost the sole representatives
of the refining influences of education. In the
Middle Ages the artisan was employed for carrying
out the work of genius as dictated by it, and it is no
less now the labour of the mechanic that supplies
the apparatus for the artist's use, by which he can
transform nature and convey correctly the produc-
tive forms of one country to another, however far
apart upon the face of the earth.
Nature has two distinctive characteristics ; those
perceptive and those conceptive—those in actual
being and those that we can conceive as possible,
to understand which, we must conceive four
worlds.
1. Existing world (the actual universe).
2. Historical world (world of names and events).
3. Fabulous world (mythological world).
4. Ideal world (imaginary world).
To the existing world belongs the actual universe,
the physical formations, moral and political govern-
ments, &c.
The historical world is that which records events
and tells of the great movers in those events, with
their epochs.
The fabulous world is that which is full of imagi-
nary gods, beroes and heroines.
The ideal world is that where beings exist only
in imagination, and who are, with imaginary objects,
treated as having real existence.
The artisan or the artist has a limited horizon,
he must confine himself and his art to things


6
Theory and Analysis of Ornament.
17
ms
strictly terrestrial, leaving for the philosopher a
separate field for the exercise of his learning
and study. The artist must have reality in his
model, that is to say, his conceptive powers must
be limited to those objects that can be imagined as
forming a part or parts of the existing universe,
yet his imaginative powers must not be so much
circumscribed as to injure his form, type or picture.
He must leave telescopic worlds and microscopic
nature free from his portrait or diapered form or
type.
The theologian, the moralist, the poet and other
learned men may treat of the actual universe, and
yet seek further by the aid of telescope, microscope
and imagination to embellish their works; but in
material forms the true artist will confine himself
to the copy of real nature, and any introduction to
his world must be actual and not imaginative phe-
nomena. The painter artist has a world even less
limited than that of the sculptor or carver. The
painter finds many of his finest touches from the
clouds as governed and tinted by the varied con-
ditions of the atmosphere ; but as the sculptor or
carver cannot diaper light or colour, his world is
necessarily more limited tban that of the landscape
painter.
6. Form may really be said to have a threefold
existence, viz., natural, diapered and ästhetic : the
natural form being that in which nature produced
it ; the diapered form a result of the artist's skill ;
and the æsthetic form that produced under varied
degrees according to the imaginative powers of the
artist.


Theory and Analysis of Ornament. 7
DO I
The technical mode of decoration must be strictly
applied in ornament for producing a thorough
harmony; ornament wrongly or carelessly applied
to the diapered forms produces discord, and is
therefore repulsive to the aesthetic eye of the art
critic. The æsthetic eye sees in the natural form
the diapered form or type produced, and fancy
adds ornamentation to be carried into effect by
the industrial application of skill. The natural
artist, upon first contemplating original form,
perceives every geometrical figure, geometry
forming, as it were, a most important constituent
of his brain-power; therefore geometry must be
cultivated for the complete reproduction of objects
of nature in diapered forms or types.
7. As all objects in nature possess peculiar
powers of motion under the heads generation, pro-
gression, concatenation, variation, &c., the artist's
mind must associate these powers with geometry as
necessary to the successful delineation of his work.
Suppose for instance, that the artist diaper the
form of a horse ; for the true reproduction, his
diapered form must bear out the notion of move-
ment, and the prominent features of the diapered
form must convey an idea of the exercise of the
five senses.
The abstract, rational science called Kinematics,
is the power of transforming or reproducing, in the
diapered form, the true compositions of varied
motion. Thus the idea of motion, in the abstract,
enters into combination with geometry in the
mind of the artist.
The idea of motion, independent of the


8
Theory and Analysis of Ornament.
es
YS
notion of actual movement, combines with
geometry, and this combination being correctly
delineated produces, in the diapered form, the
nearest approach to actual life. In short, all the
attributes of life must be as correctly copied as
possible, and be projected as prominently in the
figure as art can produce in the way of actual
creation.
The ideas of motion and swiftness must not
be associated with the idea of strength. The
practical kinematic plies his skill upon the basis of
motion and swiftness, but it remains for the genius
of the artist to convey the notion of existing
strength. Thus, the idea of equilibrium, separate
from the ideas of strength and motion, combines
with westheticism, and shows by the neces-
sary use of the words balancing, ponderation,
proportion, &c., the æsthetic determination of
forms.
The idea of equilibrium, apart from the idea of
motion but associated with the idea of strength, or
rather the idea of occult and permanent endeavour
or stability, is the basis of operation by the mecha-
nical architect. The idea of disposable or exhaustive
strength is the basis of operation by the mechanical
engineer.
It must be realized by the student, that the idea
of strength hides itself behind higher ideas which
become indefinite in ordinary logic as produced
by scientific construction. Where language is
employed to explain, scientific construction conveys,
by expressive metaphors, the idea of strength,
activity, attraction, intensity, energy, &c.


Theory and Analysis of Ornament. 9
The following table must be studied in order
fully to grasp the meaning of the foregoing
remarks.
PURE GEOMETRY.
Analytic geometry (Kinematics) = The artisan's
mechanics. '
Descriptive geometry (Statics) = The architect's
mechanics
Dimensive geometry (Dynamics ).- The engineer's
mechanics.
8. Every motion, instinctive or derived, contains
two or more elementary parts, viz., simple motion
and movement in straight or circular lines, which
may really be reduced to two simple motions,
or technically speaking, Helicoidal and Volubilial
motions.
The three geometric elements, having the property
of constant juxtaposition (slippery relief on incrusta-
tion), are, the straight line, the circular line and the
spiral line.
The straight line, the circular and spiral lines, are
the fundamental, simple and irreducible elements of
geometry.
The rectilinear, circular and helicoidal motions
are the three fundamental, simple and irreducible
elements of kinematic or theoretical geometry as
applied to motion.
The two rectilinear motions, circular and transla-
tory, can be continuous or alternative, i.e., constantly
directed one way, or alternately directed over a
plane surface; thus, from the four elementary
motions, which form the basis of industry in the


Theory and Analysis of Ornament
in
surfaces, specifications, &c., together with motion
upon planes, may be estimated with great exactness.
Among the different properties of figurative
extent are lines and surfaces geometrically deter-
mined alike in plane surfaces as in solids, the
geometrical lines being employed in every case as
determining the extent or volume of the figure in
question.
These two kinds of geometry may again be
classed as elementary or euclidian, and modern or
general geometry. These divisions in geometry
inust be recognized in order that the student may
grasp the full reason why science must be applied
to art, mechanical or inherent, for the full develop-
ment in production.
11. Now, instead of accepting, indefinitely, the
dogmatic as adhered to, generally, by teachers and
lecturers, we will consider the subject as a whole.
A full acquaintance with the following paragraphs
will assist the student in grasping the meaning
without encumbering his mind with the sub-divi-
sion.
Four heads : Analytic, Synthetic, Descriptive,
Dimensive.
Pure geometry, as established by the Greeks and
adopted as classical in our schools, places before
the eye of the student, logical strictness and perfec-
tion : it teaches demonstration, concatenation, and
subordination of proportion; it teaches also the
laws of definition and classification geometrically
considered. Such logical foundations constitute
the real establishment of geometry as a science.
Geometry, studied under the four heads given


12
Theory and Analysis of Ornament.
above, leads the mind to admiration of the broad
field for expressed exactness opened by its study.
No science is more adapted to the establishinent of
logic, the science being logic itself, and where logic
exists, the mind endowed with it must manifest its
capability for applying it to objects more or less
artistic. The practical artist is, in his works, an
illustration of the useful application of pure
geometry.
ANALYTICAL GEOMETRY.
The mathematician applies the science of algebra
to the working out and proving of the truth of
problems in geometry, and consequently truths are,
by analytical geometry, proved, as relating to
questions based upon the science of geometry, and
to which that science must be applied for perfect
elucidation.
Descriptive geometry is the application of special
and artificial methods, viz., the methods of projec-
tions, as applied to frames and solids.
By descriptive geometry we understand the theory
of intrinsic composition of forms, and the defini-
tion of different particularities of the lines and
surfaces. This statistical contemplation of the
forms of extent is not at all subordinated to a
particular drawing method, nor to a spiral ter-
minology.
The geometric, like all other forms, might be
described by ordinary language, and might be drawn
up by the usual artifices of the drawing art.
The ideas of generation and description are so
closely allied that analysis does not separate the
e
S


Theory and Analysis of Ornament.
13.
ideas advanced under each head, yet it is necessary
to distinguish the two orders of perceptions, as the
one goes to the root of the science and separates
the parts so as to give explanation to their generic
independence, the other explains the simultaneous
presence of their dispositions. Perhaps the dis-
tinction is vague, and the language employed must,
of necessity, be somewhat vague also; yet a study
of the matter will throw light upon the somewhat
clouded expressions, for geometry is a science well
adapted to prove its genuineness in its own un-
uttered language. When the science of geometry
is applied, as it must be, to the true production of
nature, the artist may apply under the several sub-
divisions, and yet keep aloof from the idioms or
rubrics of the science, simply applying the abstract
to the correctness of his art.
12. Geometry, as taught by mathematicians, forms
an important branch of the general system of mathe-
matics, which contains the three following theories:-
1. The theory of numbers.
2. The theory of figures.
3. The theory of sizes.
Pure mathematics are absolute and rational, and
most perfect examples of form and construction, and
form the secret of pre-eminence in the scientific
art-roll.
The perfection of the mathematician has proved
his license to intrusion into the artistic world, either
to the damage or benefit of the latter (?), and the
exactness of his calculations presents a formidable
critique upon the work of the artist and compels him
to stoop to criticism.


14
Theory and Analysis of Ornament.
13. The teacher of geometry employs, of necessity,
a rude method of drawing, and the science he teaches
admits of dogmatic sanction of the clumsy and
inartistic method called linear drawing. Linear
drawing may be classed as an intrusion upon the
artist's freehold. The student in geometry requires
ruler and compass, and upon their use depends
the success of his linear drawing; the artist sup-
plies these necessities by the natural and artistic
effort of his brain.
The student in mathematical geometry can, with
the help of the ruler and compass, produce neatly-
effected work, yet he must admit that his produc-
tions are chiefly the result of the instruments he
employs.
The careful student in geometry carries, in his
work, the power of imposing upon the unartistic
world—he is deemed, by a credulous public, an
artist, whereas his productions are by no means
resulting from artistic genius. Until art has passed
through, or proved itself above this sham, the artist
must be in constant rivalry with the pretentious
linear drawing student.
That the cause of true art must ultimately
triumph is certain : as a consequence, theoretical
education in art must assert superiority over those
who have passed by the preliminary education and
taken their first step half-way up the ladder, from
which they cannot rise nor will their bigotry admit
of descent.
The student will perceive that the science of
geometry is only shown in its true beauty when
applied to art productions.


Theory and Analysis of Ornament. 15
CO
14. Science may be said to be knowledge logically
organized, and logical organization is based on the
concatenation of propositions. Logic reduces the
initial notions as much as possible, thus covering
much important matter and difficult questions under
a few words, questions the solutions of which can-
not be arrived at but by logical argument. Those
geometrical propositions, logically formed, can be
stated thus :-
1. To reduce the fundamental notions as much
as possible under the dogmatic form of axioms,
definitions and postulates.
2. To satisfy logical rigour by giving demon-
stration to all that is susceptible of it.
All geometrical teaching is founded upon the
foregoing method, assisted by numerical calcula-
tion, applied to geometrical sizes, and propositions
in illustration.
Geometry, as a science, does not admit of exercise
in what has been described as “ Mathematical Joy."
The logic applied, and the application required in
the solution of its problems, take up the whole
attention of the student, who must bend his efforts
to his work, leaving no spare time or energy for
devotion to the work of pure art; in other words,
did artistic ability exist, it is destroyed or
negatived by the arduous work of the student in
geometry.
Before the intervention of measuring and count-
ing and mechanical linear drawing, the first
principles of geometry were acknowledged to be
abstract ideas, which predominate in all branches of
mathematics. True artistic study can produce the


16
11
Theory and Analysis of Ornament.
es
same result, although the artist does not, for be
must not undertake to plunge too deeply into the
maze of abstract ideas, figures or measurements;
his mind supplies spontaneously much that the
geometrical student acquires by hard study. In
short, the student in geometry is one being, and
the artist another.
15. The materials, of the science of geometry,
are sizes or mathematical quantities, conceived in
all simplicity, classified and constructed upon the
general principles of order and form.
If, in the attempt to study art, the student in
geometry isolates the susceptible forms or figures
of mathematical propositions, he leaves the world
of human conditions, and plunges into a maze of
logical abstractions. The attempt results in
failure.
The work of the artisan preceded the science of
geometry, therefore, Science may be called “a
knowledge of knowing.” Its place is in the rear of
poetry, art, history, moral and philosophical com-
positions, thus showing that science is only regu-
lated argument upon facts established. Science
cannot be maintained but by profound study of
truths recognized, and following the rules strictly
laid down under the terms assiduous and disciplined
application.
16. Geometry may be looked upon as suddenly
springing up from a latent existence, and as
suddenly presuming to govern the arts. The pre-
sumption is, that as art existed without practical
geometry, science presumes a right to govern
the arts.
ea
US


Theory and Analysis of Ornament.
All that was produced by moral activity, now
forms objects for special and necessary culture.
Methods and systems have been arranged to pro-
perly develop the intellectual faculties, and the
earlier the mind is called upon to learn those
methods and systems so as to become acquainted
with the field, the sooner can the matured
mind be brought to grapple with the facts
hidden underneath. Science, then, developed
by education and intellect; it is inborn in man,
and its full development depends upon the
strength of brain-power assisted by applica-
tion; and the more advanced one becomes in
scientific knowledge, the further away does he
remove himself from the real sentiments of life.
The scientific mind sees order and neatness in
everything in creation, it detects disorder in every-
thing that has passed under manipulation; and
although removed from the real sentiments of life,
it finds a world of thought and beautiful reverie as
a result of study and appreciation of the beautiful
which is always present in God's creation. This,
then, is the rule of science, and under this rule
there is no place but for organized activity. The
humble artisan and the busy mechanic must sub-
mit themselves to the guidance of men who are
scientifically capable of directing their efforts.
However distasteful to the worker, such a
situation must be considered as an unavoidable con-
dition of modern life. The art student goes into
the past for his lessons, he takes the great masters
of by-gone ages for his guides, his deductions from
their works are brought into actual contact with


18
Theory and Analysis of Ornament.
and made to bear upon modern ideas; and
such a blending of the past and present cannot
but be productive of greater perfection, and
that this perfection should reign supreme should
not be looked upon with dissatisfaction, but rather
rejoicing, seeing that science adds to the com-
fort and blessings of all living under its bene-
ficent sway. When we extol the cause of this, we
must not be led away to forgetfulness that much
is due to the artisan, much improvement has been
made as the result of skill, exercise and persever-
ance, and, in many cases, great inventions have been
made by the mechanic; yet it must be acknowledged
that where the mechanic's mind has attained to
such scientific perfection, he has been assisted by
an inborn artistic nature which would have quali-
fied him for a place among the artists, had he
been allowed to follow the dictates of nature
rather than been led off to a mere mechanical
exercise of his faculties. The world cannot rest,
science must have its sway, and however much the
mechanical mind revolts, its masters and best pro-
fessors of mechanical skill must acknowledge the
power of the scientist. Should it be so ? Yes,
unless pride bars the advance of progress so neces.
sary for meeting the enormous requirements of a
thickly-populated world.
CHAPTER II.
ORDER, FORM, RELIEF, COLOUR.
17. The idea of form corresponds with the
natural, diapered or inventional, which have three


Theory and Analysis of Ornament. 19
dimensions. We will call the “ Fixing of Limits,"
“Extension of Form; " the figure ending in out-
lines or lines of delineation. This figure is the
representation ; the image or the drawing of a
diapered form, or it may be termed a purely inven-
tional figuration.
18. The idea of order governs the constitutive
parts of form, that is, it implies a diagram or
plan of disposition of purely intelligible type of real
form.
The idea of order is more particularly the idea of
arrangement of parts distinguished only by analysis ;
it constitutes the disposition of asthetic form and
ornament, and consequently the law of monu-
mental art.
19. The notion of Form has two acceptations.
1. The abstract, figurative and geometrical
form.
2. The ästhetic or concrete and the expressive
form.
All particular forms are diapered or described-
1. By geometrical types based upon terms of
geometrical exactitude.
2. By picturesque types, for the definitions of
which are employed numerous arbitrary metaphors,
which explain forms in nature as well as in art.
The idea of abstract form, at first purely geo-
metrical, contains particular points of view :
1. Material, or corporeal forms.
2. Ideal, configurative and enveloped forms,
which embrace the most showy points of material,
organized or diapered form.
The notion of concrete form contains the material,
IS
.
02


20 Theory and Analysis of Ornament.
it also contains the special points of view of organ-
ized form, of diapered and, in fact, all æsthetical
form.
20. The following table arranges the different
accepted notions of form and shows their order of
mutual dependence :-
ÆSTHETIC Form.
Monumental, Plastical, Picturesque, Decorative,
Ornamental.
Diapered Forms.
Organized Form.
Assembled.
(Morphology of
Built.
Animals and
Weaved.
Vegetables.)
Material.,
Envelope Form.
Carved.
Diapered Form.
Modelled.
(Organized Form.)
(Minerals.)
Material Forms.
ABSTRACT FORMS.
21. The abstract form is more particularly geo-
metrical, when it can be defined by the rigorous
methods of mathematical science. The abstract
plan of construction must be distinguished from the
concrete or æsthetical.
The abstract disposition depends on the intellect
strictly defined by scientific theory. Scientific
theory must be acknowledged as the spirit of art.
The æsthetic disposition depends on sentiment.
It is the object of chief appreciation which depends
upon tact and artistic imagination; it is particularly
the collective genius of mankind and the special
genius of individuals. It is obtained by nicely
balancing the particularities of form, size, relation
and proportion. These can be regulated and classed


22 Theory and Analysis of Ornament.
the ornamental, together with multiplied figures and
motives.
Permutation is an operation by which things of
the same class can be arranged one with the other.
Such are the rational foundations of the syntactic or
science of order, i.e. exclusively logical and mathe-
matical developments.
24. Order is Form in discontinuation.
Form is Order in continuation.
The idea of order intervenes for architectonic
determination to appear in reality on the combina-
tion and arrangement of materials. This is the ab-
stract or artificial bond which binds discontinuation
and determines groups or architectonic compositions.
This relation is more or less essential or homo-
geneous, accidental, or heterogeneous, according to
the degree of independence, of unity, or individuality
of each of the terms.
The determination or exact combination does not
take away the beauty of idea though logically and
mathematically formed ; on the contrary, exact com-
binations become soft and moving by the express
intervention of the æsthetical causes of variation,
and are made the base of disposed form and
ornament. Combination is as essential in material
as it is in the individual. By combination of
material, high buildings are reared, and a multiplica-
tion of edifices makes a city; man populates, and
combination enacts laws, elects rulers, and thus the
town and its occupants are an example of combina-
tive power : untie the knot or disintegrate the
atoms, and the individuals stand apart, lacking
order as a result of a lack of combination.


Theory and Analysis of Ornament. 23
The superior idea of order, which is the spirit
of artistic humanity, has not yet been drawn up
methodically. To logical and mathematical science
we will add the architectural; these are not only
positive but rational and ästhetical.
Following the method of an eminent philosopher,
M. Cournot, we will classify as follows:
ORDER AND FORM.
Order purely intelligible. Phenomenal order.
Mathematical Science. Architectural.
Logic,
Materials of Institution. I
Signs of Convention.
|
Language. | Algorithmy. |
Signs of Institution.
Draught. | Drawing.
Logic, mathematical and architectural meta-
physics have for their object the pure ideas of ab-
stract nature. Æsthetics have for their object the
sensible ideas of human nature. Each and all these
sciences have, for their general organ, language;
indeed language in a general and abstract sense is
the principal instrument employed in conveying
logical expressions. Mathematical science has for
its object, the theory of numbers and their applica-
tion to the theory of sizes; its particular instrument
is algorithmy. Draught has for its object the pro-
perties of extent, while drawing treats of archi-
tectural science.
If we turn back to the last table, we shall see that
architectural science employs, in different degrees,
drawing, draught, algorithmy and logic. Arith-
metical geometry employs draught, algorithmy and
logic, only. All these numerated sciences have
multiplied proportions common to them. Archi-


24 Theory and Analysis of Ornament.
tectural science is so complicated, so many ideas
intervene, that only the practical man can over-
come its complexity.
25. Real Form is characterized, in its in-
dividuality, by shades immediately perceived. We
will treat these shades as so many units; they can
be grouped systematically, or used in logically con-
structing other forms.
If the codification of these objects were scientifi-
cally realizable, they could be theoretically defined
and classed with other scientific and positive
theories, susceptible of perfection.
All that belongs to art would, then, form a
systematic and regular doctrine, which would pre-
side over the whole system of Forms. It would
substitute a uniform method of combinations and
deductions for the occult power of invention, which
has added so materially to the world of thought and
enhanced the particular and collective genius of the
artisan, giving him a false position as viewed from
the standpoint of pure art.
If my plain speaking, in defining mechanical and
comparing it with the natural productions of the
artist, has been thought somewhat egotistical, I must
plead my excuse in a desire to show, that while there
is a certain combinative principle, there is never-
theless such variance that the two must be con-
sidered as having entirely separate existences. As
we proceed it will be seen that I shall bring both
art and science as proof of the assertions made at
the commencement of this book; also, as we go on
we may consider ourselves as being doomed to
follow a regular and systematic line of thought, and
IS
ka


Theory VAN
ат
man
Te
and Analysis of Ornament. 25
to give explicit obedience to certain laws, which tend
to curtail freedom and subject us to the dictates of
sentiment. The tendency of art is to escape from
a categorically pre-conceived programme, as the
result of a want of formulæ to define, and geo-
metrical method to limit it.
26. One man may remain primitive, taking
naturally what of nature presents itself without
questioning the giver or the manner of bestowing ;
he is content to see himself surrounded by
nature and his desire reaches no further than
to be able to distinguish, by name, one thing
from another; logic and mathematics are no part
of his existence. Another man, from his earliest
being, calls for assistance in primitive distinction,
yet, not being satisfied, an inborn inquisitiveness
prompts him to seek the why and the wherefore :
here logic plants her foot, followed by mathematical
reasoning, to be perfected by a desire for a re-
production, &c., &c. Here follow the arts and
sciences.
As the tilling of the soil presents itself as the
first duty or man's first natural employment, so
does formations upon that surface occupy the mind
naturally born to become nature's student. Archi-
tecture is one of man's first studies, and archi-
tectural science cannot be pursued to efficiency
without calling in the aid of kindred arts.
As one science is, in a great measure, governed
by or dependent on others, so is architectural art in
alliance with logic and mathematical science; they
are necessary to its solidarity. The fundamental
ideas of the three sciences mentioned are the same,
red


26 Theory and Analysis of Ornamentan
re
.
though essentially different in their results accord-
ing to the groove one choses for his special employ-
ment.
The Aristotelian logic, taught in our schools,
is the highest order of philosophical criticism, and
that alone produces æsthetic architectonic science
in true perfection.
We will go back to M. Cournot's theory for all
that concerns philosophical developments of logic
and the sciences, but for what concerns the archi-
tectural we must confine ourselves more particularly
to study the past with the present. We will choose
a study familiar to so many, as an illustration.
Music. The first elements in music are sounds.
Sound, considered as homogeneous sizes, is sub-
jected to variations, and these variations are
the results of vibration. Vibration, reduced
to numbers, is the mathematical material of
acoustics as a branch of physics, these being
ail which intrude into this science. Sounds
are, with the æsthetical particularities which
follow them, the real materials of musical art.
When the instrument, as a result of handicraft,
is considered in connection with acoustics,
mathematical and experimental science claims a
place in such construction, the combination of
the three being necessary to produce the result
as an unit.
Logic, mathematics and architecture may, to the
philosopher, be three sciences of co-equal importance
and equally important one to the other, which
is but natural, seeing that the philosopher's art is
an abstract one, weighing and judging the pro-
in


Theory and Analysis of Ornament. 27
ceedings of humanity. But the artist, who has
personal experiences, only finds, in his inborn
artistic nature, precepts, indications and prescrip-
tions which guide him to the completion of his work.
27. The idea of order and form has been ex-
plained in the preceding chapters, yet it will be
taken up again as we proceed.
28. The idea of order and the notion of form
once well understood by the help of tables and signs,
notations and figures, will remain a fixed element in
the mind, forming a source of supply when necessary
as we pass on to other categories of art work.
Colour and relief are necessary elements in a work
of art.
The idea of relief is correlative to the idea of form,
but the idea of order is foreign. All the particu-
larities of forming and modelling adhere to and
command each other without having an abstract
and independent bond. The idea of size and
quantity, according to the æsthetic sense, mingles
with the idea of proportion and measure.
A work of art contains the idea of proportion
which exists between the projections and the reliefs
of the same form. The particularities of relief and
modelling must not be considered as units or as
different elements to be grouped or combined
systematically, as is the case with different forms
and colours. Again, the power of modelling or
sculpturing correlatively with the faculty to con-
ceive or imagine space, belongs to certain privileged
races. The Greeks possessed this faculty to a
great extent, while the Semitic races were utterly
lacking in it.


Theory and Analysis of Ornament.
N
in
29. The sensation of colour is purely effective ;
it has not in itself any representative virtue.
Sensation distinguishes colours and gives them
specific names as a result of its distinct character
and special qualification. Exact demonstration in
small numbers serves for comparison, to which it
adapts desinences, a mode of flexion, position and
syntax, by which means we can express, in language,
all the best varieties of decoration.
When we look upon colour in nature, or when
we conceive the philosopher's optical phenomena,
we raise scientific questioning of a theory con-
cerned with the solar spectrum, which furnishes
images always the same in themselves. In all
other types the elements are chosen and compared
in an arbitrary manner, seeing that there is no
other bond that unites them but the frame of
human invention.
Out of this property of form that pervades the
solar spectrum, and which is produced in a
manner always identical, theories arise to mea-
sure the number of vibrations peculiar to each
colour, and count and measure by refraction that
which is produced by those colours. But all this
scaffolding of science, strong though it seems,
does not show how the accident of colour is
bound up with the swiftness and vibrations of
ether; or in what proportion it exists in every
luminous ray. We will no more introduce the
solar spectrum in this work, but we will and must
use the colours generated from that system, as an
all-important element in art, i.e., the colouring or
coloured materials, but not the purely figurative,


Theory and Analysis of Ornament. 29
phenomenal images, which may be considered as
simple appearances only. We must accept the
colours as they are in their substantial and tangible
reality, with all their cortège of sensible and
phenomenal particularities, and use them without
putting them under scientific analysis—unimportant
here.
The theory of colour is immediately bound up
with the notion of form. The extent of colour and
the form of separate delineation, determine the
sensations of harmony and contrast of colour which
would otherwise depend upon physical and physio.
logical theory, useful and interesting in itself, but
not necessary to proof in the course of reality. The
notion of form is not only inseparable from decora-
tive notion, but it contains substantial and material
qualities-colouring and coloured properties.
30. The notion of colour is bound up in the
notion of form and the two are bound to the idea of
order. Let us take, for example, a palette ; here we
have distinct elements in the abstract considera-
tion of order; here, a number of colours, which
establish variety in combination, two by two, three
by three, and these again present themselves under
our powers of sensorial impression.
We may agree that relief is necessary to order
and form, and also a necessity in order, form and
colour, for nicely determining and specifying.
The particulars of colour are subordinate to order
and form, as are also the particularities of relief to
form.


30
lan
Theory Van
.
and Analysis of OrnamentCHAPTER III.
MONUMENTAL AND DECORATIVE ART.
31. Ornament is constituted by a harmony of
conditions, which can be shown in four parts.
Relief and colour form the basis of Decorative
Ornamentation, when the relief and colours are
fixed by form, and are distributed strictly according
to the idea of order. .
The idea of order is specialized in ornamentation
and becomes a disposition.
The idea of form is specialized in ornamentation
and becomes a motive.
32. Decorative art is determined in three parts,
viz., Form, Relief and Colour.
The essential foundations of decorative art are
Relief and Colour, which are stronger than Form.
Decorative art is an extension of decoration,
which, at first, belongs to diapered forms, and has
taken up a strong position wherever architectural
art has become developed. An ornament is more
particularly decorative where colour and relief are a
lesser part than the form, surpassing it in luxuriance
only.
Diapered forms which depend upon decorative art
are the modelled and carved and the assembled and
weaved forms.
33. Monumental art is governed by conditions
of Form and Order.
Of monumental art, diapered, modelled and
carved, constructed and superposed forms, the
monumental stands highest. Modelled and carved


Theory and Analysis of Ornament. 31
forms, in conjunction with diapered forms, con-
stitute the ornamental.
Therefore modelled and coloured decorations,
with other modes, constitute, only in combination,
the ornamental. Order has a special growth in
ornamental form, and, as such, is an all-important
factor of the whole. Order, as a growth in orna-
ment, proves itself above logic; the one becomes a
reality while the other remains as existing only in
conceptive form, being, however, essential to true
harmony and artistic ornamentation.


32
Theory and Analysis of Ornament.
Part XI.
DEFINITION AND ANALYTICAL
MATERIALS.
This part is divided into five sections, treating
of-(1) fundamental notions; (2) linear extent
and delineation ; (3) superficial extent and plane
surfaces; (4) extent and corporeal forms; and (5)
regularity and symmetry.
FIRST SECTION.
FUNDAMENTAL NOTIONS.
CHAPTER I.
NUMBER.
34. There are two fundamental acceptations of
the word number.
1. Concrete, which is bound up with objects.
2. Abstract, which is conceptive and applied
to objects in a logical form, susceptible of different
uses in the reunion of groups.
35. Theory touches the very essence of number,
and must therefore be treated as having three im-
portant applications.
1. Its employment for designing quantities
from cardinal numbers.
2. Its employment to measure and continue
sizes and to form correct ideas of quantity and
measure.
Im-


Theory and Analysis of Ornament.
33
3. Its employment to indicate or fix order from
cardinal numbers.
The idea of number is logic employed to deter-
mine numerical and conventional signs therefore ;
it must be considered as an alphabetical idea of
abstract numeration, an esthetical contemplation of
things. It might be called a mental guess, under
the ideas of unity, plurality, simplicity, &c. I will
give the term “Indetermination " to the abstract
idea of number, for by this term alone is it ex-
pressive of actual signs.
36. Number known, ideas follow; united ob-
jects existing under different numbers, give the
relation of nuinbers. Under Arithmetic and Mathe-
matics the relations are determined, and they have
or bear the name of proportion, such, for example,
being fractional numbers. But, under æsthetic
view, they are distinguished in three kinds of re-
lation, viz., multiple, determined and undetermined.
This idea of numerical relation pertains to
concrete notion of disposition; it is the one which
characterizes rhythm in ornamental disposition, the
composition in ornamental forms, and ordinance in
monumental art. In multiple relations, the number
of a series is sometimes twice, sometimes three or
four times the number. In the determined relations,
the numbers are fixed and determined, but have no
proportion between them. In undetermined re-
lations the particular numbers are not certain
or correctly discernible, and a vague eurhythmy
presides as a balancing power in particular
numbers.
The idea of order united with that of quantity,
IS


34
Theory and Analysis of Ornament.
forming a unity, gives the esthetic notion of
rhythm, which has remarkable interpretations in
the musical and poetic arts, as also in monumental
art. After rhythm, which is special, comes accord,
which rules the co-existence of the different parts,
ordered or disordered, and blends them in superior
unity. It is eurhythmy or accord which rules the
ordinance of an edifice or poem and forms the par-
ticular rhythms and constitution of the work.
CHAPTER II.
SIZE, QUANTITY.
ded por-
37. Mathematically considered, the idea of size
is an idea of homogene, susceptible of being divided
by thought into such divisions that we should like
to have similar or identical parts : the divided por-
tions may grow indefinitely. With the notion of
size springs that of measure. When size is known
and determined, it may be taken as a term of com-
parison or unity. Size thus expressed in number
has the name of quantity.
Size also determines form and extent. In Archi-
tecture, mathematical quantities do not operate so
much as æsthetic quantity. Figures and forms are
turned into one changeable and movable unity,
which is intermixed with the specific graduations
corresponding with the extent of man's natural
grasp of the nature of objects. From this we may
distinguish two fundamental acceptations of the
word size, viz., Mathematical and Architectural. A
third acceptation is found, æsthetically, mixed with
e


Theory and Analysis of Ornamentaz
. 35
the architectural size; this is also mixed, geome-
trically, with mathematical size.
38. Mathematical, architectural, and aesthetic
acceptations of the word quantity correspond to or
with the three acceptations given of size. These
ideas given of size, measure, unity and quantity,
constitute the basis of the science of sizes, which is
an important part of the general system of Mathe-
matics. Architecturally considered, each quantity
or quality embodies its own measure, and forms
unity as producing the one impression of unity.
Adopt the test of mensuration, and you will find
unity in size, and that number takes the place of
extent.
39. Mathematical quantity is, then, determined
and fixed, and is reduced, in regular method, by
numbers. Architectural quantity is, on the con-
trary, the object of particular determinations which
suffer variation following the quantity.
CHAPTER III.
EXTENT-CO-ORDINATED).
40. Geometricians distinguish two kinds of
quantities, the one permanent, which is called extent ;
the other successive, which is called duration
All that which refers to extent is the object of
immediate intuition, and the notions which result
from it participate in the firmness which is essential
to it. All that concerns duration is the object of
perceptions whose intensity is changeable ; those
elements and their co-ordination being engraved on
2


36 Theory and Analysis of Ornament.
m
the mind, we can henceforth recognize them in-
stinctively and finally as necessary to the creation
of works artistic.
41. The notions of extent and duration lead us to
the idea of space and time, whose forms rule all that
happens in the spheres of phenomenal and sensible
things. The notions of extent and duration im-
plicate the idea of continuity which is suggested by
the contemplation of form and extent of movements
in space. The idea of continuity, which is inherent,
leads us, by logical necessity, to the institution of
mathematical science, and, by an æsthetical necessity,
to the institution of architectural science. The one
is built on the idea of homogeneous discontinuity,
the other upon the artisan's particular genius and
the collective genius of mankind in general.
Space has three dimensions, time has but one.
The three dimensions in extent possess changeable
quantities, but all that which denotes duration has
but one dimension. Following the proportion of
three dimensions, we arrive at the three fundamental
determinations, viz., quantity, size and extent, or
linear quantity, superficial quantity and corporal
quantity.
42. We conceive, in the idea of mathematical con-
tinuity, that linear extent and lines are involved
in Linear Element; that superficial extent and the
surfaces are involved in the superficial element, and
that corporal extent and space are involved in the
solid element. These conceptions are, however,
exclusively mathematical.
These elements may be said to accent works of
art. Real and corporal forms exist in extent, but
ms


Theory and Analysis of Ornament.
37
bave no important place other than that they
harmonize the condition of specific co-ordinations,
as essential to the ideal nature of form, and con-
formable to the æsthetical co-ordinations of extent.
All directions, orientations and oblique positions
are composed of fundamental co-ordinations, and
implicate them, even absolute as they appear.
CHAPTER IV.
MEASURE AND GRADUATION.
43. The idea of order and quantity is what deter-
mines rhythm. The idea of order, with the idea of
quantity, determines proportion. In the first case,
discontinuity is real. In the second, the ideas of
quotiety and quantity are sometimes separate and
sometimes assembled; for example, we do not count
corn-grains but measure them.
Measure may, then, be looked upon as an unity,
and is called the unity of measure. Quantity is,
however, the proportion of unity of measure. The
proportion of sizes is measure, and the proportion
of numbers is rhythm. The complicated propor-
tions may be fixed in three measures, thus, the sub-
ject is round when its dominant is circular; long,
· when its dominant is linear; oblong, when its
dominant is oval.
In the prosodic quantity, it is necessary to
account for the very nature of the subject, which
has, for an enveloped form, a circle or an oval;
for the position or orientation of the subject, the


38
па
Theory and Analysis of Ornament.
vertical or horizontal. It is also necessary to
account for the real size, or graduation, which
modifies the accentuation of forms.
44. Graduation, or the notion of graduation,
embodies the aesthetic measure of size, and is of
changeable extent, comprised between limits upon
and under. It is necessary to distinguish three
distinct and fundamental graduations, viz., personal,
monumental and ornamental.
Tlie personal is the normal graduation which
extends to the size of man; the monumental is
adapted to the exigences of locomotion and cir-
culation, and depends principally upon man's eye.
Normal graduation is somewhat abstract, it is a
contraction of the object to within mental sight.
45. The ideas of measure and graduation regu-
late the expansion and development of form and
ornament, necessary for detail, and to form con-
cordance in general harmony. This metric
rigorously and geometrically engenders the mono-
tony which characterizes the academic art of the
past century. Since artists have left this rigidity
and called to their assistance tools, as for example
the ruler and compass—these constitute a machine
similar to the successive parts of a drawing or
composition governed by geometrical lines-faith
has been slower, feeling a secret despair. We
should, then, hold fast to the ideas that seem rapidly
becoming extinct.


40 Theory and Analysis of Ornament.
spirals, changeable in size, circular curvity, spiral
curvity and declined curvity.
CHAPTER I.
STRAIGHT LINE AND RECTITUDE.
47. The perfect quality of a straight line is rec-
titude. A straight line is the abstract image of
linear continuity and only changeable as to its size.
The straight is still the unity of direction, it indi-
cates order and situation.
To form a correct idea of a straight line, we must
distinguish the straight edge which limits spaces and
forms.
An ideal line of rectitude is absolute, as being
founded upon reason.
In edge-lines, rectitude is relative, the impression
being changeable as belonging to the phenomenal
world.
In the stripe line, the figuration is relative, the
impression being absolute for the kind of materiality;
this gives to this line an apparent and sensible
breadth, which is, necessarily, imposed. Rectitude
may have a tendency to pre-occupy the mind, we
may instinctively take the image at first sight, which
would be pretext in reality, and, in its dispositions,
totality. We get from either or both sides the idea
of a straight line or æsthetical idea of lectitude.
The first is absolute; the second is changeable.
Motion is found under most circumstances, and
this is particularly essential to artistic work.


Theory and Analysis of Ornament. 41
48. The metaphysical consideration of the
straight, that pretends to add transcendant and
sovereign qualities to the abstract idea, confers by
that means an operative virtue from which, where
the notion of rectitude exists, comes all the apparent
and actual qualities of artistic work.
CHAPTER II.
CURVITY AND CURVED LINES.
49. It is necessary to distinguish two things in
curved lines, viz., the line or draught, which is
mixed with the linear element, and that remarkable
quality of curvity. Curvity has the quality of con-
tinuation, and it requires a mathematical expression
-size. In architecture, curvity is a particular
quality which changes; yet, still, architectural
quantity of the curvity can be uniform or variated
from one point to another, or un-uniformly variated
from the starting to the arriving point.
A line possesses uniform curvity in all its parts
and belongs to circumference, and so, in variation,
it is one with the bend or the rolling according to
the degree of intensity of variation. A curved line,
coming from the left side, can become more and
more variated till the rolling is most accentuated.
If a curved line be divided into segments,
curvity is more sensibly impressed; with necessarily
small curves, it appears in progressive, modified
form, and varies in the direction of each seg-
ment. This small curviture can be seen if the


42
Theory and Analysis of Ornament.
rou
segment be denoted by a regular accumulation of
points.
Curvity, in a circumference, is uniform, each of its
segments forming an equal radius from a centre, and
in this case the curve corers a strictly uniform line
of points.
50. We have a distinct impression of curves in
every point of a curved line, rolling in any way,
but we mentally associate them in one curved and
interminable line—the circumference.
Each of the segments of a curvity has linearly a
direction determined according to the next segment
and corresponding with the entire line.
Curvity being subdivided into segments, and each
one being uniform in the circumference, rays, from
the centre to the points in each segment, will be
equal, and their being so proves the uniform nature
of each segment in the circumference. By the
angle formed at the centre, by any two rays, or
radii, can be determined the extent of the curve.
As in the circumference of a circle all lines from
that circumference to the common centre are equal,
therefore, any two of those lines may enclose
a segment, small or large, yet uniform with
the regular rolling line forming that circumfer-
ence..
51. After a circle, the simplest curve is the
spiral, which is uniform in its composition. The
spiral has a double curved line which necessarily
embraces the three dimensions of space. Straight,
circumference and spirals are clear and definite
ideas, upon which we can base our conceptions of
curvity and curved lines.
үе


Theory and Analysis of Ornament.
43
We will now pass on from these fundamental and
uniform lines to the equally fundamental but va-
riated lines; from the straight, and the arc, to the
bent, and from the bent to the rolling lines; from
the spiral to the voluble and declined spirals, i.e. to
spiral rollings in space.
52. Lines are formed by the combination of
two fundamental movements, the rectilineal or
translatory, and the circular or rotatory movements.
1. The rectilineal movement is that made by a
ruler and can only be a straight line.
2. The circular, or that line made by a compass
and which must, necessarily, be circular.
3. Two rectilineal movements make a number
of lines.
4. Circular, rectilineal movements make bent
lines, spirals, rolling and declined spirals, and a
number of geometrical lines, as spirals, conchoid,
cycloid, &c., &c.
5. Conic sections can be made by combined
rectilineal and circular movements with determined
lengths and fixed points.
6. Two circular movements make an epicycloid
or trochoid, and all curled curvities resembling
starred polygons.
. 53. We will now treat of Descriptive Geometry
and of the description of forms, i.e. the specification
of different particularities which characterize them,
holding each other by an abstract bond, contained
in its construction. There are three kinds of affec-
tion for the linear form.
1. The analytical elements, or those which refer
to the nature of lines.


44 Theory and Analysis of Ornament.
2. The figurative elements, or those which refer
to variated lines.
3. The æsthetic affection, viz., those introducing
accent and agreement, and which are subordinate to
the general form of lines.
These peculiarities hold together as a part of the
solid construction, and are expressed by real form,
and constitute a product of art.
54. Lines are, in their fundamental specification,
unlimited. We will give here some examples of
segments of straight lines, arcs and curvities.
1. Straight lines are changeable only in size.
2. Arcs, of uniform curvity, are changeable both
in size and curvity.
All arcs of uniform curvity form parts of a cir-
cumference. All arcs coincide when their radii are
equal. The size of an arc is dependent upon two
particulars, linear extent and curvity.
As an abstract figure, a circle is always a circle,
the absolute size counting for nothing but a
subject, i.e. real form, and is subordinate to
graduation.
All that has been said of circles can be applied to
arcs and, indeed, to all curvity. In an arc the
curvity can be short or long. When short, it is
accentuated; when long, it is feeble.
3. Curved lines. The curvity of a line being
varied, and a product of a straight line becoming
more accentuated by rolling, points out or indicates
a variety of solid lines of motion.
55. There are three distinct parts in a curved line.
1. The extremity, or starting-point, where the
curvity is least.


46
Theory and Analysis of Ornament.
Those joined and continued by a starting-point and
a summit (d).
3. Those even and symmetric curved lines
called the handles, which are of two kinds or forms :
the curved lines joined (Fig. 1) and continued by
the summits s'f"''''; and those continued lines
joined by starting-points (c). They follow the
accent of the primitive curved line. The handles
or curved lines being continued and joined by the
summits give rise to three kinds: the first is quite
rectilinear, with a small circularity, or the hyper-
bolical or angular handle (f), the branches being
undefined.
The second is curvilinear, with a small rectitude,
or parabolical oval handle (f').
000000
00
Fig. 2.
The third one, which arises from the first and
second, has the elliptical or rounded handle (f").
The branches are oval and ended.
4. The oval or closed curved lines (Fig. 2) which
are even and symmetrical when the two curved lines
are different but directed the same way (9), or even
and symmetric when they are constructed by the
turning of the constitutive varied curved line
(h). This regular form of oval can be made
by joining two curved lines or handles (i). Those


Theory and Analysis of Ornament.
47
two handles being different give rise to a number
of ovals, and establish continued transition of the
oval (j).
5. Closed or curved ovals can be even or uneven
or quartered. Ovals are even when the four curved
lines forming them are different (l). This form is
intermediate between the regular and the irregular
oval. The even oval is determined by the diagonal
turning of a varied curved line; the symmetry there
is diagonal (1). When the oval is quartered it pre-
sents the regular, typical form, and is then composed
by the turning and joining of an even symmetrical
handle, or by the quartered turning of a simple
curved line (j).
The form (m) (Fig. 1) is composed regularly by
the repetition and joining of a curved line, whose
symmetry is diagonal, preserving the transition from
the oval to the circle.
57. The draught of a curved line is quite inde-
pendent of the construction of open or closed curved
lines.
58. A curved line, whose curvity is varied by
rolling round a real or imaginary point, produces a
rolling ; and this rolling can also be conceived as a
backward draught, i.e. starting from a real or
imaginary point. Here we conceive a line growing
up linearly at the same time that it forms a rolling
round this point, in such a way that, while the line is
developed, the bend suffers variation, decreasing and
progressive.
The most simple idea that can be gained of such
a graduation is, to imagine that a straight line turns
round a point, incessantly moving, while the moving


Theory and Analysis of Ornament.
49
len
If in such determined delineation we notice all
these remarkable points, the parts of lines situated
between them do not contain other variations
than those relative to the bend; these are the
straight and the bent lines, and the arcs. If we
isolate all these linear segments of delineation,
we break continuity, and produce discontiguous
delineation.
We must, then, consider it of importance that we
form a correct idea of continuity and discontinuity,
of contiguity and discontiguity.
Linear continuity is maintained by joining in-
o=4,YAXI
Fig. 3.
flections and bucklings. The angular branches and
tactions break the continuity but preserve con-
tiguity. Tactions and crossings are the result of
discontiguity.
Conjugated straight lines. Two lines can be
either crossed or cut, which determines a crossing-
point (1 and 2) or contiguity, one touching the
other at their extremities. This determines linear
angulation and a summit (3); or, like a branch, one
line reaching the other in its course, being con-
tiguous by one of its extremities, which produces
particular and complete angulation, that is, when the
two lines meet together and form a right angle (5).
When the two lines are separate, they have a
parallel conjunction (6).


50 Theory and Analysis of Ornament.
Two conjugated arcs. Two conjugated arcs
following their reciprocal positions, determine-
1. A joining-point, when the arcs follow each
other yet forming a break or curvity between
them; though these lines may join, a long line
may be imagined that would contain both of them,
Fig. 4 (1).
2. An inflection occurs when the two arcs are
joined linearly, having their cavities directed back-
wards or directed from concavity to convexity, and
reciprocally. At the point of inflection (2) an in-
version is formed in the cavity.
3. The extremities of two contiguous arcs deter-
ma
Fig. 4.
mine curvelined angulations, at the point of con-
tiguity, or at the angular point. These angulations
are of three kinds, corresponding to the three
fundamental conjugations. .
The first one, Fig. 5 (1), where the two arcs have
their convexities set back to back ; the second,
where the two arcs have their concavities set face to
face (2); the third, where the two arcs are turned
the same way. If the arcs are equal, they produce
thus two even or symmetrical angulations. The
separation of the arcs is quite determined, and,
if we conceive these two movable arcs round the
angular point, a fixed form is apparent between all ;
as (1) and (2) the joining of the two arcs, and (3), an


Theory and Analysis of Ornament. 51
idea of their inflection. The angles (1) and (2)
possess an axis of symmetry, or a linear diameter
(2'); (3) has a diameter, but it is curvilinear,
caused by the junction of the normal line (3'), by
the centres of a series of parallels (3''), or by
the centres of a series of oblique lines (3''). If
instead of looking at the angulation, we follow the
course of the line, we get, in each angular point, a
turning-point.
"A "A" AV U V
Fig. 5.
4. Contact or taction (Fig. 6). Two arcs, one
touching the other at their extremities, can be
equal (2) or unequal (1). If they are equal, they.
give a particular figure (2), symmetrical or
quartered, when the arcs touch one another at
their centres of figure. We can conceive that these
two figures (1) and (2) are determined by the cross-
ing of the two arcs, inflected at the point of contact,
or by the joining of two appointed angulations.
Two arcs, being unequal, give rise to a particular
form of contact, which is inside (3), the arcs being
directed the same way. This particular form may
be considered as a result of the intersection of two
arcs, and where one cuts the other at the point of
taction.
♡
X
Fig. 6.
I 2


52 Theory and Analysis of Ornament.
5. Crossing two arcs (Fig. 7), where one cuts the
other in a point, determines a crossing-point (1) and
three kinds of curvilinear angulations (1') (1") (1'').
Two different or equal arcs (Fig. 6) can also be
cut in two points when the convexities are turned
back to back, Fig. 7 (2). If the arcs are unequal
and turned in the same way, they produce a
figure (3).
m xx xx xx x
CS
Fig. 7.
6. Branchings (Fig. 8). Two arcs meeting at
extremities produce a branching (1). If the arcs
join together, they form a branching-point, a join-
ing-point, a point of inflection, and a point of con-
tact (2). The branchings of the figure (1) contain
the forms of angulation.
7. Two arcs are discontiguous, or separated
(3), and are yet alike, being symmetrical or
parallel.
0 VN
) )
Fig. 8.
60. Two conjugated curved lines (Fig. 9).-
Figures produced by curved lines are varied by
the accent of curvity, although it may not widely
differ from the preceding one ; but starting from the


Theory and Analysis of Ornament. 53
curvity, two curved lines or figures appear individu-
ally. These figures are rolling or curling.
The curl determines a closed figure (Fig. 9) and
a crossing-point, (1) and (2). In the case of regu-
larity, the curl has an axis of symmetry which
passes by the crossing-point (2). As rolling is a
mode of figuration belonging to linear continuity,
it gives rise to different forms. The course of a
straight line can be stopped by a round or oval
curl (3); so also the course of an axis (4)
By means of this intervention of inflection they
pass from convex angulation to a curl, by two
inflections, which meet at the crossing-point or
curling (5), or from the crooked angle to the curl
nV8018808
Figs. 9, 10, 11.
by one inflection (5''). They pass from the concave
angle to the curl by four inflections (5'). It is
necessary to distinguish both curling and inter-
sections.
CHAPTER IV.
ASTHETICAL AFFECTIONS.
61. These affections are of two kinds, linear and
figurative. They are linear when subordinated far
from the pace of the line and introduce variety
by discontinuity. They are figurative when they
determine ornamental delineations in engrailing,
lacing, twisting, &c.


54 Theory and Analysis of Ornament.
62. For restoring the pace of a line of form (1),
we determine some attractive points which follow
their approaching, and interrupt the very law of
form. These points, bound by straight lines,
determine a polygonal line which, in the limit of
our perception, is equal to a perfect line. They
substitute discontinued variation for continued varia-
tion. This discontinuity is realized by the artisan
in carved, turned and hammered forms. These dis-
continued variations are so many accents, so many
marks, from which the figure is determined and which
presents to the mind a real subject which reveals the
handiwork of the artisan.
CHAPTER V.
DELINEATIONS.
63. There are two kinds of delineations.
1. Delineations of profile and outlines of form.
2. Simple delineations.
Profiles and outlines of form are the conventional
and abstract delineations, which have no existence
independent of form. The fundamental disposi-
tions are the joinings, inflections, and angula-
tions. The joinings are the starting-points, which
represent linear construction. The inflections are
not reduced to a point; they can be either short
or long, so that two curved lines are abruptly
drawn closer or otherwise, that a straight line
may separate them. All the particulars which
characterize extent and linear form are found in the
simple delineations with accentuations infinitely


Theory and Analysis of Ornament. 55
varied, though they may arise from the technical
mode of decoration. These delineations constitute
the drawing of ornament and form.
In ornamentation these particulars, in their
essential and proper nature, give rise to a number
of dispositions, although without any accession of
æsthetical ideas or abstract principles of monu-
mental co-ordination.


Theory and Analysis of Ornament2022
ece
. 57
3. The label or linear space.
4. The angle or angular space.
The superficial size or plane surface is homo-
geneous and uniform. An uniform and declined
curvity is not the same as a plane surface, for a
number of plane surfaces can be held within the
limits of the form which contains them. This
essential uniformity in superficial extent necessitates
the idea of co-ordination,
1. The plan. The harmonical, co-ordinate lines
of the plan, are the horizontal and the vertical.
These correspond with the two dimensions of the
plan. Oblique and diagonal lines also participate in
the fundamental dimensions of the plan. Oblique
lines have two fundamental positions. Horizontal,
vertical and oblique lines determine four systems
which cut the plan into quadrilateral segments,
when combined two and two, three and three,
and so on. It is this harmonical decomposition
of the plan which gives a particular quality to
monumental decoration.
2. The circle. Suppose superficial extent to be
contained in a point, and then suppose this point to
extend uniformly, then the correct idea of a circle
is formed. The harmonical, co-ordinated lines of
circular space, are those striking off from the point
and cutting the infinity of concentrical circumfer-
ences which fill the whole circular space. These
concentrical circumferences liinit the circular space,
although in itself unlimited. The rays from the
.centre cut the circular plan into angular spaces or
sections. These two systems of co-ordinated lines,
reunited, cut the circular spaces into four-cornered


58
Theory and Analysis of Ornament.
СОЦе
and curvilinear segments, which are the segments
of the wreaths, determined by the system of con-
centrical circumferences.
3. The label. Superficial extent, being reduced
to a straight line, is indefinite, although limited.
The co-ordinated lines of the label are those that
run parallel to the head straight line, also the trans-
verse straight. These two systems of co-ordinated
lines cut the label into four-cornered segments,
like those of the plan.
4. The angle. In angular space, the super-
ficial extent is declined from the opening to the
summit of the angle, wbere this extent comes to
nothing. It is necessary to know, by angle, the
superficial space which lies between the two oblique
straight lines, or the space formed by the fold of a
straight line.
66. In order to value the sizes, mathematically
or architecturally, we must reduce them to unity of
measure or appreciation.
The unity of measure, for valuing sizes, is the
square.
The unit of appreciation, for the contemplation of
sizes, is the circle.
67. In architecture, where the elements so
differ, analogy is held as necessary to distinguish
the two methods of appreciation. .
Applying the general method of appreciation to
the fundamental forms or spaces-i.e. to the label
and circle only—we shall arrive at an exact defini-
tion of what delineation of a plane surface means.
All circles described and united within the limits of
the label are equal, Fig. 12 (1). This is an artificial


Theory and Analysis of Ornament. 59
method, for we have immediate perception of linear
and uniform extent, as the unnecessary aid to the
true artist.
This is also artificial when applied to the angle,
yet it has the advantage of placing before the eye
the essential quality of the angle, that is, its deline-
ation (2), (3). If the angle is either acute or obtuse,
A 3
OOOOo
Fig. 12.
the declination of the space is continued, i.e. uni-
lateral or collateral.
CHAPTER 1I.
GENERATION OF THE FUNDAMENTAL PLANE SURFACES.
68. The architectural unity of appreciation of
plane surfaces is the circle, where the extension goes
round an actual or vertical point. The extension of
size is, determined by combination of circular ex-
tent and linear translation, the centre of extent
going over all the points of the headline. The head.
line is the head-point. These are the irreducible
and last foundations of the generation of forms.
We conclude that the correlation from the superficial
extent to the linear is absolute. A proportion esta-
blished between the circular extent and the head-


60
I
Theory Va
.
and Analysis of Ornamentline is what determines the fundarental form of the
plane surfaces.
The general terms of this proportion are-
I. A fixed circle and a headline; the form of
the circle is then determined by the translation of
the circle, following the course of the line.
II. A changeable circle, whose size changes har-
monically with the form of declination and a head-
Fig. 13.
line; the form of extent is then determined by the
· translation of the circle in all successive points of
the line.
I. A fixed circle and a headline.
69. Straight headline. The straight headline,
being indefinite, is, by the translation of the circle
or the label, indefinitely symmetrical in all its parts,
and is thus uniform. This is the third fundamental
form of superficial extent. If a straight line be
finished, we can have a figure, equally finished, and
ended at its extremities by a circular form, Fig 13 (1).
Circular headline. The circumference being closed,
we get a circular label; the arcs being finished, we
get some figures finished and ended at the extremities
by a circular form (2), by the closing of the arcs.
Curved headline. The bent line being finished,
we get the figure (3). The handle will give the
figure (4)


Theory and Analysis of Ornament.
61
Further explanation is unnecessary upon this
subject of the mode of generation, applied to simple
lines, composed or composite, i.e. to handles, ovals,
ovates, undulated lines, either turned back, buckled
or polygonal. Æsthetically finished plane lineary
surfaces are segments of indefinite lineary plane
surfaces; the full arc is a finished plane cir-
cular surface; therefore it will be seen that we
must not confound physical with æsthetic termina-
tions. The extremities of lines are physical termi-
nations as opposed to harmonic.
2000a
Fig. 14.
Lin ear plane surfaces are composed of rectangular
segments, with æsthetic ideas of centre and circle
overruling the notion of lines.
II. A variable circle and a headline.
70. Straight headline. Taking a fixed circle and
passing its centre over every part of the headline,
the decreasing circle gives a correct idea of what is
termed a declined plane surface, presenting, at the
same time, angular declination. Again, take a
straight line as a declinator, and recline it to the
headline, or part of the arc, and you have exhibited
specimens of rectilineal, raised and sharp angula-
tion, Fig. 14 (1), (2), (3).
We must form ideal circles at all points of the


62
Theory and Analysis of Ornament.
declinator. We must also realize the idea of tangent
circles, which are the essential types of declination.
In Fig. 14 (1), the declination is regular, and shows
the ordinary rectilineal angle. In (2), the de-
clination is rapid and the appointment accentuated.
In (3), the declination is slow and hesitating,
and the plane surface is stronger than the angular
declination. Order of forms should, therefore, be
1, 2, 3. In these figures the declination is pro-
longed, although following the inclination of the
envelope-line. The declination changes the type,
for if the angles be very open, the declination is
blunt (4), (5), (6).
This declination becomes symmetrical or re-
current, and goes by each side of the headline.
These declinations belong to the horizontal order,
conforming with the second type of a straight line
(symmetrical at every point). The first belongs to
the vertical order, and conforms with the first type
of the straight line (a successive line from one
point to another).
Following their graduation, these declinations are
forms or desinences. These desinences give detail
to form and impart degrees of accent.
71. Arched headlines. The progression of a
circle following an arc determines a particular form
of angular declination—circular or hooked (7).
From this declination we must distinguish two
fundamental forms.
1. The angular declination, where the figure
ends in nothing, and the headline going as far as
the summit of the angulation.
2. The oval declination, following the head-


Theory 1
63
and Analysis of Ornament.
line at the extremity of which, rays, a circular plane
surface, goes round the desinences. In angular
declinations the headline can either be a straight
line or an arc.
The series of circles is indefinite on the open side
of the handle, but finished near the summit, in a
fixed point where the circle is osculatrix of the
curvity. The oval desinence is more or less
accentuated, and changes from the arc of the circle
as far as the angular desinence.
Though the handle may be hyperbolic, parabolic
or elliptic, and the headline curved or straight, we
es
Fig. 15.
get (Fig. 15) the figures (1), (2), (3), (4). The
elliptic form (3) is half an oval. The curved form
(4) has an inflecting point.
With obtuse angulation, we get oval declinations,
resembling the handle of a basket.
All the forms of plane figures are synthetically
made up of the following elements.
1. The circular extension.
2. Linear prolongation, either uniform, recti-
linear or curved.
3. Angular declination, rectilinear or curved,
straight or bent.
4. The angular declination, rectilinear, straight
or bent. Angular declination is physically finished,


64
Theory and Analysis of Ornament.
and its plane figure is of the same form in all its
parts. The oval declination is harmonically finished,
and its plane figure is composed of circular extension
and angular declination.
CHAPTER III.
m
a
8
FUNDAMENTAL DOMINANT LINES OF PLANE SURFACES.
72. Extent, being essentially uniform in all its
parts, is harmonically composed of two dimensions ;
all fundamental forms of extent, and segments of
them, participate, at all points, in its essential
nature, and depend, in a general way, upon the
two principal dimensions, length and breadth.
These two dimensions determine the plan. Seg.
ments of the plan are simple plane surfaces, whose
actual dimensions are determined. These segments
are, generally, polygonal.
If in a plane surface one dimension overrules the
other, we get a third form of superficial extent, or
label. The segments of a label possess a funda-
mental character, viz., linear prolongation following
the course of the line. This is a particular kind of
plane surface, uniform in all its points, but where
a dimension is reduced the other grows up slowly,
and is the circular space for immediate contem-
plation in all the successive points of the headline.
In the label, the plane surface is indefinitely
symmetrical from both parts of the point under
consideration.
We will imagine, by proportion to the dimension,
which characterizes the label, that the space is not


Theory and Analysis of Ornament.
65
uniformly divided, but goes on decreasing from one
extremity of the line to the other until it ends in
nothing, and we get here a fourth form of super-
ficial extent, or angular declination. All segments
of this extent possess angular plane figures.
73. Spaces being theoretically undefined and of
homogeneous composition, an architectural deter-
mination is fixed for imagining the existence of
harmonic segmentation in these spaces. Each of
these gives rise to particular and proper segments,
which participate in its fundamental nature.
1. Segments of the plan. The extent of the
plan being sub-divided by harmonic lines, gives
rise to polygonal, four-cornered segments, the
dominant line being in the plane surface.
2. Segments of the circle. The circular space
being reduced, regularly or irregularly, in segments,
by straight lines, polygons are produced. The
dominant line is circular.
3. Segments of the label. Linear space being
separated by straight lines, we obtain four-cornered
segments. Their dominant line is linear.
4. Segments of angles. Angular spaces pro-
duce proper triangular segments. The dominant
is angular.
Resuming the fundamental forms of extent, it is
necessary to conceive the following correlations,
viz. :—To rectangular space corresponds arranged
repetition, or simultaneous order, correlative to the
system of lines and network which bind the different
points of extent.
To circular space corresponds circular order, cor-
relative to regular repetition of points round a centre.


66 Theory and Analysis of Ornament.
To linear space, or label, corresponds uniform
linear order, i.e., indefinitely symmetrical form on
both sides of each point.
To angular space, or angle, corresponds successive
linear order, i.e., everything on one side and in the
way of the line, or from one point to another.
CHAPTER IV.
FUNDAMENTAL FORMS OF PLANE SURFACES.
74. Combining the fundamental modes of genera-
tion of plane surfaces with the diagrams, we obtain
18 n 9
Oh Oh Oh
Fig. 16.
Fig. 17.
linear prolongation, and declination of the simple or
compound lines which form the plan of disposition,
and numberless figures which are proportional to
the following fundamental forms (Figs. 16 and 17).
1. The circle. Absolute unity or fundamental
bases of forms are entirely centred in a head-point; its
length varies with the ray of extension, Fig. 16 (1).
2. The angular oval. Starting from the circle,


Theory and Analysis of Ornament.
67
we conceive the declined fluxion of a plane surface.
Following a head-line, coming from the head-point
and finishing at the other extremity, following also
the form of delineation, which can be rectilinear,
sharp or swollen, we get the three principal forms of
the angular oval (2) (3) (4).
These angular declinations form desinences for
the plane surfaces. If we take a head arc, or a
curved line, instead of a straight line, we get the
fourth form of the angular oval, i.e., the curved or
broken oval (5).
3. The oval proper. If starting from a circle
we conceive the declined fluxion of the plane sur-
face, following a head straight line, coming from
the head-point and harmonically finishing at the
other extremity, i.e., forming at the extremity of
the head-point, from whence it arises, a new circle,
we get the oval properly so called (6) (7) (8),
which, at the joining of the angular oval possesses
a higher character of unity, i.e., harmonized form
The unity of angular ovals consists in an actual
ending of the plane surface. The circular exten-
sion of the extremities of the headline can pass,
together or separately, by all the kinds of size. If
the circle of desinence be small, the proper line is
inclined towards the angular oval. If the headline
be an arc or a curved line, we get the curved
oval (9).
4. The oval. Starting from the circle, we con-
ceive the oval fluxion as going symmetrically on each
side of the head-point, following a diameter, we get
the oval, Fig. 17 (1) in its quartered form, and
possessing a centre of figure, and two head-points
F2


68
Theory and Analysis of Ornament.
in uneven 0
1
I
.
which are symmetrical with it. If the circles of
the extremities are reduced to a point, we get the
angular oval (2).
5. The hooked line. The straight line and the
arc, being in uniform composition, are symmetrical
or even.
The curved line, being infinitely varied from one
point to another of its course, is an uneven or un-
symmetrical line. If, then, we conceive a circle at
one of its extremities, and the declined fluxion of the
plane surface following the course of the line, we
shall be able to determine two distinct forms,
Fig. 17 (3) (4).
In (3) the size of the space is declining from the
starting point to the desinence; in (4) the size of
the space is declining from the point of desinence
to the starting-point. If the circle of the extremi-
ties were reduced to a point, we should get hooked
lines, with a regular desinence. If the headline
became rolling, declination would take place, ex-
clusively, from the starting-point to the desinence.
The Ionic style is a remarkable example of this
form.
a rem
CHAPTER V.
HARMONICAL LINES OF THE FUNDAMENTAL FORMS.
1. Harmonical lines of a circle. The circle
possesses two systems of harmonical lines, viz., the
rectilinear rays coming from the centre, and the
concentrical circumferences which limit the exten-
sion of circular space.
2. Harmonical lines of the oval. The har-


Theory and Analysis of Ornament.
69
monical, co-ordinate lines of the oval are, the
principal centre and a headline, i.e., the centre of
extension and a prolonged line. If we wish to
mark the lines of radiation, we will trace a tangent
on a point of a headline, then the normal line which
will cut the next oval, and, at this point, trace a
new and normal line which will cut the third oval,
and so on ; we shall thus get curved lines coming
from the principal point, producing a palmated
harmony. We have, then, the harmonical lines of
the oval and circle; some of which are curved lines
Fig. 18.
Fig. 19.
of changeable declination, and some concentrical
lines which are handles of declination of curvity-
also changeable-depending harmonically on the
handle-envelope of the oval, Fig. 18 (1) (2).
The form of the oval being essentially changeable,
this harnionic sub-division is essentially a subject of
tact and artistic feeling
It is necessary to conceive that, starting from
the circle subdivided harmonically, the head-point
comes successively in all parts of the headline,
carrying away with it all the lines of the primitive
network which do not modify the general co-ordi-


70
Theory and Analysis of Ornament.
nation of the form. The fluxion or the declination
of the parts is not thus harmonically equal at
what makes the essence of the oval, as a result
of the uniform mechanical movement, Fig. 19 (1)
(2).
But if we choose the head linear line and propor-
tion the oval, we notice that that oval is determined
by the successive transfer of a circle of extent,
changeable in all points of the headline. The
harmonical lines are the head-
line, or virtual, and some sym-
metrical branches on each side
of it. The harmonic lines are
subordinate to the centre.
The branches have their con-
cavity turned towards the axis.
The curvity of these nerves
varies with the curvity of the
Fig. 20.
outlines, the outline being recti.
linear like the nerves.
By this second sub-division, the plane surface
(Fig. 20) is pennate with a propension at the
palmation, i.e., at the occult convergence of the
nerves on a secret point (1) (1').
3. The harmonic rays of the hooked line. The
course of a hooked line being linear, it is necessary
to conceive that the successive centres are multiplied
and separated in proportion with the curved line,
and with intervals which follow, in this variation, the
laws governing the declination of the head curved
line. Here we get (Fig. 21) the headline and
those embracing it, together with the nerves which
cut them. The nerves on the side of the cavity,
DIVE
CH


Theory and Analysis of Ornament.
71
and those on the side of the concavity have their
curvity turned the same way.
75. We now pass from the consideration of the
hooked lines to that of the forms and pennate
sub-divisions which are correlative to the oval or
Fig. 21.
angular declination. In oval declination, at the
point of ovalation, stands a centre of palmation ; and
following the curvity of the branches, two collateral
series of curved and rectilinear rays follow in a
Fig. 22.
slanting direction towards the occult convergence.
In the angular and convex declination, the collateral
nerves of oval declination follow the laws of declina-
tion, except in the palmation of the summit. In
convex declination the collateral nerves follow the
laws of variation of nerves in the oval. In recti-
linear declinations, the nerves are rectilinear or
curvilinear, but parallel.


72
Theory and Analysis of Ornament.
From this we see that transition, which joins the
circle and label, is continued, passing by the oval to
the angular and oval declinations. These three
diagrams should be noticed :-
1. The radiated disposition which is subordinate
to the head-point.
2. The pennate disposition which is subordinate
to the head-line.
3. The palmated, which is subordinate with a
headline and point, and, therefore, is in connection
with the others mentioned.
CHAPTER VI.
VARIATION IN THE FUNDAMENTAL FORMS.
11.
76. All forms have two dimensions of extent.
Three minor cases arise from these two, viz. :-
1. The two dimensions are equal.
2. The longitudinal dimension is the greater.
3. The transversal and longitudinal are equal.
The types corresponding to these three cases are
the circle, the oval, and the ovate. The two dimen-
sions in a circle are equal; the shape is concen.
trated entirely in a point. In the ovate the
dominant dimension is longitudinal, and it is by this
dimension that the oval shape is susceptible of
determined orientation, straight or overturned, i.e.,
equal to vertical order, or slanting in every degree,
and then reduced to a determined disposition. In
the oval, the dominant dimension is transversal,
and equal to horizontal or symmetrical order.
A circle faintly depressed on one side, forms an


Theory and Analysis of Ornament.
73
oval whose determined dimension is longitudinal and
the sense vertical. A circle depressed on two of
its parallel sides, becomes an oval whose dominant
dimension is transverse and the sense horizontal.
An oval lengthened on one side only becomes an
ovate.
Angular or oval declinations, straight or bent, are
forms lengthened and measured by the circle, the
oval or the ovate form.
If the curved declination becomes rolling, the
unity of shape would be a circle, containing a cen-
tral pole or point around which turns the line, while
the curved lines possess poles which exist linearly.
leas
001098
Fig. 23.
The head-point of a circle implicates a number of
axes or rays crossing the point and terminating at
the outline. The two head-points of an ovate pos-
sess the variations of the circle; the headline can
be either straight, arched, bent, polygonal, or
broken. The oval participates in both circle and
ovate forms, suffering all their variations in their
determined dimensions. In the diagram, the head-
line can be rectilinear or curvilinear, uniform or
varied, &c.
77. The variations, which belong particularly to
the outline, remain stationary in the, properly called,


74
Theory and Analysis of Ornament.
plane surface. There are two ways to draw, viz.,
by designing all the parts of the outline by hard
lines, and by following the whole outline by an un-
interrupted line. In the first, we show the accent
without losing the integrity of shape ; and, in the
second, we lengthen the continuity and neatness
of the touch. An outline may implicate a plane
surface, real or imaginary, implicit or explicit.
When the plane surface is real, it is the outline
which is implicit or explicit, and the modes of
ornamentation, following these conditions, shall
vary.
CHAPTER VII.
POLYGONAL PLANE SURFACES.
ro.
78. The essential character of polygonal plane
surfaces is that they are segments of plane sur-
faces, i.e., portions cut out of the superficial extent.
The number of segments which form the outline is
indefinite ; and the segments, multiplied indefinitely,
pass insensibly from a rectilinear to a curvilinear
outline.
What strikes the sight are figures of touch,
or described polygons, in the rectilinear outline.
Here it is necessary to notice segments of straight
lines, which meet together end to end, forming
equal and unequal angulations at every point. Ac-
cording to the number, length and inclination of
these segments, together with their general co.


Theory and Analysis of Ornament. 77
no
three variable, angular desinences. The absolute
form is the trigon, which has three equal angles and
desinences. Every triangle, whose domination is
a circular halo, if not absolute or trigon, is an
irregular form. In the case where this form would
be symmetrical, or isosceles, the impression should
not be less dissonant, the type of the isosceles being
angular, raised or elliptical. This form is, essen-
tially, regular; the trigon has its angles equal as
well as its sides, it is a central figure, which has no
absolute orientation ; it envelopes a regular straight
line. The natural lines of a trigon are (Fig. 25) the
heights (2), the rays (3), the apothegms (4); the
SO-
Ø
A
A
A
A
Fig. 25.
figure (5) is the inscribed trigon, and figure (6)
has all these particularities.
82. If we establish a correlation between the base
and the height, it is that the height is determined by
the two rampings of the triangle. Every inclined
line being relative, having two absolute directions,
the horizontal and the vertical; and further, these
two rampings and these two inclined lines being of
equal inclination and length, give a view of the
vertical, which is their normal, absolute line.
Between the isosceles triangles, the geometrical
form is the rectangular isosceles triangle. If we
trace a series of isosceles triangles, whose heights
and lengths are rigorously determined, starting
from a base equal to the number 8, and giving the


78
Theory and Analysis of Ornament.
00
> 00 00 00
Orics
heights successively 1, 2, 3, 4, : : : raised from that
base, we should get the following list (Fig. 26):—
Base. Height. Sides.
4:123
4:469
Pythagoras' isosceles triangle.
5.656 Rectangular isosceles triangle.
6.403 Egyptian triangle.
8 6 7.211
8 7 8.062
83. Applying to a few isosceles triangles of
different forms the general method of the inscrip-
tion of tangent-circles (Fig. 27), we will consider
what constitutes harmony, beauty and unity in that
triangle, among others.
(1). Rectangular isosceles tri.
angle-abrupt bilateral declination.
(2). Trigon—abrupt and divided
in three part declinations.
(3). Declination greater in
height.
Fig. 26. (4) and (5). Declination more or
less accentuated in height.
(6). Declination in height quite decided, the
declination on the base disappearing.
(7), (8), (9), (10). Bilateral declination more and
more prolonged.
(11). Declination exclusively ramping and pro-
longed horizontally, all vertical declination dis-
appearing.
The artifice of the inscription of circles has the
advantage of showing how a form more or less
favourably follows its graduation or actual size.
When we say that the horizontal or vertical has
disappeared, we mean that they are more or less
mo


Theory and Analysis of Ornament79
un
.
0-
eclipsed. The erasure is seen in the preceding
figures, but we must understand that if the figures
were greater, that which remains, after the in-
scription of the circles, would be perceptible and
should leave a shade of indecision which would
render the image not clear.
If the isosceles is ramping, or on the contrary
raised in only one vertical declination, we have
Fig, 27.
two types, and we get æsthetical determinations
quite distinct and heterogeneal; for example-in
architecture the pediment, and in the particulars
of ornament, the obtuse or acute desinences.
II. FOUR-CORNERED SURFACES.
84. Quadrilaterals are regular or irregular
segments of the four fundamental shapes of ex-
tent, the plan, label, circle and angle. If they are
segments of the plan, the dominant is the plane


80
Theory and Analysis of Ornament.
surface circumscribed by the quadrilateral figure;
if they are segments of the label, the dominant is
linear; if segments of a circle, the dominant is
circular ; if the segments at the angle, the dominant
is angular. Quadrilaterals have four sides, equal,
unequal or varied, and are submitted to a plan of
construction or to a diagram of symmetry which
gives rise to eight kinds of forms (Fig 28).
1. The irregular (1), unsymmetrical quadrilateral,
or those without an axis.
m
OOO
Fig. 28.
2. The irregular (2, 2), unsymmetrical trape-
ziums, or those having no axis.
3. The regular (3) and symmetrical trapezium,
having an axis.
4. The variable and symmetrical corners
(4, 4', 4'), according to angle, with an axis.
5. The parallelogram (5), whose symmetry is
diagonal, and with axes.
6. The quartered lozenges, whose symmetry is
diagonal, with two axes.
7. The quartered rectangle, whose symmetry is
diagonal, with two axes.
8. The square with the symmetry, four axes.
The quadrilateral has its four sides unequal and


Theory and Analysis of Ornament. 81
articulated under unequal angles; the parallelo-
gram has its sides equal 2 and 2, and parallelly arti-
culated under equal angles 2 and 2 ; the middle form
between the quadrilateral and the parallelogram
being the trapezium, which has two parallel sides.
The two particular forms of the trapezium are the
rectangular trapezium, and the isosceles or symme-
trical trapezium. The rectangle and lozenge are
particular kinds of parallelograms: the sides of the
lozenge are equal, so also are the angles 2 to 2.
The sides of the rectangle are unequal, but the
angles are equal and straight. The absolute shade
iu
.
MB HABH
B
AT
Fig. 29.
of the movable lozenge is the square, which has
its sides and angles equal. Symmetrical lozenges
have their middle shade between the quadrilateral
and the lozenge, their composition being varied
according to the angles; an acute angle, an obtuse
angle, two obtuse or two acute angles opposite the
shade of the corner, is midway between the irregular
quadrilateral and the lozenge. The above examples
show the narrow correlation which exists between
the rectangle and the lozenge. The natural lines
are the diagonals, which join the summits, and the
medium which joins the middles of the opposite sides.


82 Theory and Analysis of Ornament.
These lines are axes of symmetry. In Fig. 29, (4)
(4') form a lozenge or rectangle ; (5) (5') reunite the
diagonals and mediums; (6) (6') show the inscribed
figure; (7) (7') unite the inscribed figure and
the diagonals; and (8) (8') unite or show all the
peculiarities. The square participates of the rect-
angle, and the lozenge is the absolute form
between the quadrilaterals.
85. The dominant of the square is the circle.
The dominants of the rectangles, lozenges and
corners are even ovals, quartered for rectangles
and lozenges, and even for the corners. The
dominant is even for an open space, i.e., the oval
implicates the rectangle, and the rectangle implicates
O
KODOM
Fig. 30.
the oval, or the oval dominant which determines the
æsthetical appreciation of the rectangle. The oval
and the rectangle each have two axes, an oval with
undefined axes, and an uncertain form whose
dominant is a circular space; but if the axes become
plainer, the dominant becomes linear. In the two
cases the forms are extreme, one condition being
exaggerated to the detriment of the other, which
suffers for the want of development. This co-
existence of two different conditions determines the
variety of ovals and rectangles. In the lozenges,
angular desinences are most impressive; if these are
prolonged, the oval also is prolonged, and is less


Theory and Analysis of Ornament.
83
adapted to the form. The corners and ovate figures
have varied forms; the abside and desinence can be
varied in every point, as the figure is lengthened or
otherwise.
ENTAGONS.
ns are
III. Pentagons.
86. Pentagons are of three kinds, regular, semi-
regular and irregular (Fig. 31). The irregular
pentagon has sides and angies unequal and no axis
of symmetry. The semi-regular pentagon has lines
and angles equal, and the figure is symmetrical in
proportion to an axis.
Fig. 31.
The regular pentagon (3) is a centred figure, and
has for its dominant a circle, or circular arcola.
The mid-regular pentagon (2, 2') is an even figure,
and has for its dominant the lengthened ovate or
elliptic; a regular pentagon has for its dominant a
plane surface, the circle and the angular desinences.
IV. HEXAGONS.
87. The hexagon (Fig. 32) can be regular or
absolute (1); in this case it has six axes of
symmetry, three angular and three transversal ; its
dominant is the circle. The semi-regular hexagon
has two forms (2) and (3); the first has its sides
equal and three angular axes; the second has its
angles equal and three transversal axes; their
G 2


84
Theory and Analysis of Ornament.
dominant is the circle. The quartered hexagon is of
two forms, one rectangular, the other rhomboidal
(4) (4'); their axes are quartered, one angular, the
other transversal; and their dominant is the oval.
The diagonal hexagon has several axes, or a circle
of symmetry (5) (5'). The even hexagon has an axis
of symmetry, and an ovate dominant (6) (6') (6")
(6'''). Lastly, we have the irregular hexagon (7).
0000000
Fig. 32.
V. OCTAGONS.
88. The number eight can be separated into mul-
tiples as, 8 = 4 x 2, or 8 = 8 x 1. We get six
distinct octagons (Fig. 33). The regular octagon
(1) has eight axes of symmetry, four angular and
four transversal, and has for its dominant the circle.
The semi-regular octagon (2) (3) is of two forms,
one having two angular and two transversal axes,
the other four angular axes; its dominant is the
circle. The quartered octagon is of two kinds, one
having a transversal axis, the other an angular axis
(4) (5); the dominant is oval. The even octagon is
of two forms, one having a transversal axis (6'), the


Theory and Analysis of Ornament. 85
other an angular axis (6); the dominant is ovate.
The diagonal octagon has a number of axes, or a
circle of symmetry (7). Lastly, we have the
irregular octagon (8).
00000
00.00
Fig. 33.
an
89. We could extend this analysis and employ it
for polygons of a greater number of sides ; it will
be sufficient to remark,-
1. That a polygon of an uneven number of sides
has but three forms, viz., a regular and centred, which
has as many axes as there are unities in the number
of sides; a semi-regular or even form, which has an
axis of sympathy, and whose dominant is an oval ;
and the irregular or undetermined form
(Fig. 34). Fig. 34 shows, successively,
the semi-regular forms of the polygon
of 3, 5, 7, 9, 11 sides.
2. That the multiples of uneven
numbers give rise to resolved forms, and
out of these forms rise a submultiple of
axes, some even, some irregular.
3. That every even or multiple
Fig. 34.
number gives rise to a number of figures,


Theory and Analysis of Ornament.
87
is the rudimentor, being the simplest of all figura-
tion. These points determine a direction.
Four lines in a quadrilateral, bound by the out-
ward distances, form a lozenge, or trapezium,
&c., and the distances which bind the opposite
points, or outward distances, are diagonals. Five
points are placed in a straight line, determining
a real or imaginary figure, like a T-form trapezium,
cross, or polygon, &c. A number of points dis-
tributed in a straight line determine a real or
imaginary figure. If the form is real, we get,
Fig. 35.
successively all the varieties of polygonal figures.
If the figure is imaginary, the different arrangements
of points are specified by number and situation. It
is what appears in a coat of arms.
In the repetition of the figures it is necessary to
consider number and situation. Upon situation
depends the particular arrangement (Fig. 35),
because numbers can be arranged diversely. Gene-
rally, the arrangements of points are designed and
specified : 1st, by a series which indicate number and
situation; 2nd, by the usual figures, determined as
the cross and the chevron ; 3rd, by the geometrical


88 Theory and Analysis of Ornament.
figures, such as the straight line, triangle, hexagon
&c.
92. A determined number of disseminated
points give immediately a proportional or corre-
DAV
DODO
ooloo
o oo
Fig. 36.
lative number of distances. When the number
of points increase, the number of distances
which bind them increase most rapidly-so three
points give three distances; four points six
straight lines ; five points ten straight lines, and


Theory and Analysis of Ornament.
89
so on. All these straight lines are sides and
diagonals of polygonal figures. A distribution of
points is symmetrical when the distances are equal,
i.e., symmetrically placed; it is regular when the
distances are equal, as cut by points equally distant
one from the other. This regularity is given in the
circular arrangements of the points, from which
polygons are or can be formed.
93. Three points, regularly separated, determine
the trigon ; four points, the tetragon ; five, the
pentagon; six, the hexagon; and so on, following
the ordinary series of numbers.
The trigon can occupy four distinct positions (Fig.
36) :-
1. Based on one side.
2. Stood on the point.
3. Turned to the right.
4. Turned to the left.
It can also occupy several inclined positions, in all
of which the triangle is sensibly deformed, the base
or point prevailing according to position, and main-
taining the integrity of the line. The lozenge gives
rise to three distinct figures : stood on the point ;
cross or lengthwise; and stayed on the side, when the
figure is undecided and forms a parallelogram. The
rectangle has two positions : the square stood on the
side, or on the point; this latter represents a lozenge.
The hexagon has two positions as well as the octa-
gon: the first represents the parallelism of the
lines and the rectangular directions; the second is
only a centred figure, when it is necessary to count
the number of sides for determining the polygon.
The pentagon can be easily deformed in each of the
1ca


90
Theory and Analysis of Ornament.
Ca
Ssa
four cases indicated (Fig. 36), but it is necessary to
notice that the changing of position alters only the
regularity of form, without giving it a new aspect.
The pentagon and other polygons are figures of
uneven number of sides, essentially centred.
94. The heptagon, nonagon, decagon, and
polygons of a greater number of sides, are cen-
tred figures, the natural sense of which is the
regularity of the distribution of the sides in pro-
portion to the centre, or following circular order.
CHAPTER IX.
DERIVED POLYGONS.
95. The trigon has no derived figure, nor has
the square more than two crossed diagonals. The
eight principal polygons, viz., the pentagon, the
hexagon, the heptagon, the octagon, the nonagon,
the decagon, dodecagon and pentedecagon, have
some starred derived polygons of different kinds, as :
The pentagon, a continued starred figure (Fig.
38).
The hexagon, a starred figure formed of two
trigons regularly crossed or intersected (Fig. 37).
The heptagon, two continued starred polygons
(Fig. 40).
The octagon, a star formed of two squares
crossed, and of a continued star (Fig. 39).
The nonagon, a star of three intersected trigons,
two continued starred polygons (Fig. 42).
The decagon, a star of two intersected pentagons


Theory and Analysis of Ornament.
91
-a continued starred polygon—a star formed of two
continued starred polygons intersected (Fig. 41).
Fig. 37.
Fig. 38.
Fig. 39.
Fig. 40.
Fig. 41.
Fig. 42.
Therefore we get the following table :-


92
Theory and Analysis of Ornament.
Polygons.
Crossed
Polygons.
Continued
Polygons.
Starred and inter-
sected Polygons.
Hexagon
Pentagon
Octagon
Heptagon
Decagon
Nonagon
From each figure are derived some stars
having a number of submultiples and semi-regular
polygons; thus, from the dodecagon are derived the
following stars :-
1. From the intersection of three squares, a
star with six obtuse points and a semi-regular
polygon.
2. From the intersection of four trigons, a star
with four points.
3. From a starred' dodecagon, a star with six
points, with straight angles turning inward, and a
star with four points.
In general, if we take two points on a circum-
ference divided into equal parts, and we join them
by a straight line, and then draw a perpendicular line
through the middle of that line, all the points of this
perpendicular on both sides being joined with the
points of division of the circumference, we design all
the possible varieties of polygonal forms, between
which are placed the figures mentioned before, these
being connected with geometrical modes of genera-
tion.
INSCRIBED OR CONCENTRICAL POLYGONS.
96. All polygons can be mutually inscribed,
whether they correspond by their lines of diagram,
ca
m


Theory and Analysis of Ornament. 93
or whether they are derived one from the other by
the regular junction of points taken on the outline.
Fig. 43.
CHAPTER X.
DERIVED POLYGONAL PLANE SURFACES.
97. Parallelograms, lozenges, rectangles and tri-
gons are decomposed into small elements of equal
*
W
KU
XXX
EXON*
KUR
Fig. 44.


94
Theory and Analysis of Ornament.
forms. This decomposition is established by
the sub-division of the sides in a like propor-
tion.
If the lozenge is trigon, it is decomposed like a
trigon, into elements of the same form; the square
rectangle and the square are decomposed into ele-
ments of the same form. This subdivision shows
that the figure is a combination of harmonical net-
work. From the hexagon we obtain a trigonal
network which is or can be decomposed into six
. Fig. 45.
trigons and three trigonal lozenges. Polygons,
trigons, squares, the pentagon, hexagon, &c., have
each their own proper net-work, constructed on a
uniform type, the centred polygonal net-work. This
net-work is determined by polygons inscribed paral.
lelly one in the other, with uniform or varied inter-
vals, and intersected by lines coming from the centre.
These net-works may be considered as projections
in the plan of pyramids, whose faces are cancelled
conformably with the net-works of the infinite plan.


Theory and Analysis of Ornament.
97
figure into corners, which have for an angle that
in the centre of the polygon, and for opposite
angles, successively, all the angles of the generator
polygon and some starred polygons derived from
them.
We have, then, for each polygon a finished
****
Fig. 51.
series of angles. If we conjugate two and two the
angles between them or with the angle of the
centre, we obtain lozenges and corners (Fig. 51).
CHAPTER XII.
ASSEMBLED POLYGONS.
100. From the preceding examination we con-
clude that, on the reverse, some polygonal figures
are assembled, and hence determine some composed
figures. Two triangles or four triangles will deter-


98
Theory and Analysis of Ornament.
mine a quadrilateral. From isosceles triangles can
be described convex polygons, and from corners or
lozenges can be described starred polygons. But
for synthetic composition, a condition is absolutely
necessary : it is that the figures have angles in such
a way that, assembled round a particular point,
their sum may be equal to four right angles, i.e.,
placed side by side they do not leave any space,
On this condition we arrange round the same point
Fig. 52.
a certain number of equal figures, when the angle
of the figure is an exact fraction of four straight
angles, or if those angles together form a sum equal
to four right angles.
We can place round a point six trigons, six or
three trigonal lozenges, three hexagons. The paral-
lelograms, the rectangles and the squares are
arranged four together, round a point (Figs. 52
and 41).
"O


Theory and Analysis of Ornament.
99
For the different figures the fundamental assem-
blages are as follows:-
Fig. 53.
Fig. 54.
1st. 2 hexagons and 2 trigons (Fig. 53).
2nd. 2 dodecagons and 1 trigon (Fig 54).
Fig. 55.
Fig. 56.
res
3rd. 1 hexagon, 2 squares and 1 trigon (Fig. 55).
4th. 1 dodecagon, 1 hexagon and 1 square (Fig
56).
Fig. 57.
Fig. 58.
5th. 2 octagons and 1 square (Fig. 57).
6th. 2 lozenges and 2 squares (Fig. 58).
7th. 2 rectangles and 2 squares (Fig. 59).
8th. 2 lozenges and 2 rectangles (Fig. 60).
9th. 1 decagon and 2 pentagons (Fig. 61).
H
2


100 Theory and Analysis of Ornament.
10th. 1 pentedecagon, and i decagon, and 1
trigon (Fig. 62).
Fig. 59.
Fig. 60.
A hexagon surrounded by six squares and six
trigons gives a dodecagon. The reunion of the
dodecagon with the trigon is equal to the
assemblage of the four figures of the hexagon,
the square, the trigon, and the trigonal lozenge.
Fig. 61,
Fig. 62.
The sixth assemblage is changeable, according to
the accent of the lozenge. The seventh is change-
able, according to the proportion of the rectangle.
The eighth is changeable, by the simultaneous
variation of a lozenge or a rectangle.
These eight assemblages can
be repeated indefinitely upon
the whole surface of the plan.
The ninth assemblage is
finished, and composed of a de-
cagon with a crown of penta-
Fig. 63.
gons. The tenth assemblage is


Theory and Analysis of Ornament101
Innan
.
equally finished, and composed of only four figures,
a pentedecagon, a decagon and two trigons.
We can arrange around the same point a dode-
cagon, a mid-regular octagon whose axes are trans-
versal, and an isosceles triangle. (See Fig. 63.)
101. The polygons derived by the prolongation
Fig. 64. Fig. 65. Fig. 66. Fig. 67.
of the angles can be assembled, and give rise to
combinations infinitely varied. We shall take,
for example, some of the figures derived from the
hexagon and from the octagon
Fig. 68.
Fig. 69.
Fig. 70.
Fig. 71.
For the hexagon we join two hexagons and two
hexagonal stars (Fig. 64); 1 hexagon, a star and 1
dodecagon with three inward-turning angles (Fig.
65); 1 hexagon, a hexagonal pearl and a rose with
six hexagonal projections (Fig 66); 1 hexagon, a
rose with seven assembled hexagons, 1 pearl with
four assembled hexagons (Fig. 67).
For the octagon, we join 4 octagons with two
rose


IO2
102 Theory an
VAN
and Analysis of Ornament.
inward-turning angles (Fig. 68); 2 octagons and
2 stars with four points (Fig. 69); 1 octagon, the
starred octagon of two squares, and the polygon with
16 sides with four projections (Fig 70); 1 starred
octagon, 2 octagons, and ultimately a square (Fig. 71).
This assemblage, reduced to the star and to the two
octagons, gives a final disposition, composed of
the star and 8 octagons, circularly distributed; but
with the aid of the insertion of a square, the assem-
blage becomes indefinite, and applicable all along
the extent of the plan.
CHAPTER XIII.
DERIVATIVE POLYGONAL DECLINATIONS.
102. It is necessary to conceive the outlines of
polygonal figures as formed by two means: the
first, similar in its linear course, treats of lines which
follow each other under any inclination; the second,
resembling the diagram of disposition or circular
order, considers the sides or angular folds as regu.
larly divided around a point or centre.
I. General construction of the polygonal delinea-
tions. The irreducible and last elements of the
polygonal delineations are the angles and the sides
or segments of straight lines.
Those segments follow each other by making
angles between them. The segments are change-
able in linear sign and the angles are changeable in
angular sign, &c. It is necessary to consider,
separately, the angles and segments which fix the
limits of these angles. All segments can be uniform


Theory and Analysis of Ornament. 103
or varied, which would give rise to four modes of
generation of polygonal declinations.
1. Equal segments and equal angles. Starting
from a fixed segment, or from a fixed angle, then
tracing or repeating successively the segment and
the angle, we obtain, generally,
two kinds of polygonal figures ;,
regular convex polygons, or
continued starred polygons.
If, for example, it be the one in
the octagon, we should get the
Fig. 72.
convex octagon; if the angle
is the one in the starred pentagon, we should get
the starred pentagon.
Equal Segments and Varied Angles.
2. If the uniform segments follow each other by
reclining under angles, successively smaller and
smaller or greater and greater, we obtain a declined
polygonal outline, which inscribes or circumscribes
a bent line (Fig. 72). The angles can be varied in
Fig. 73.
every way, whether uniformly or by a regular
declination, or by a varied way, the angles being
equal two and two, &c., &c.
3. Equal angles and varied segments. The
segments regularly decreasing in size while they


Theory and Analysis of Ornamentan
. 105
octagon and hexagon (Fig. 75). Starting from the
octagon, if we abate two opposite folds, we get (1);
if we abate the four folds we get (2); if, taking the
middle points of the sides, we abate the eight angles,
we get (3) ; if we only abate 2 and 2 we get (4). The
figure (5) is obtained from (2) by the re-abatement
of all the angles turning inwards ; (6) is obtained
from (3) by the re-abatement of the angles two in
two; and (7) is obtained from (3) by the re-abate-
ment of all the angles. The figure (8) is made
from (7) by the re-abatement inside the projecting
Fig. 75.
angles; and (9) is obtained from (7) by the re-
abatement of the straight angles turning inwards.
Starting from the hexagon, and taking the middle
points of the sides, by abating the angles we get
the figure (1); abating them only two and two, we
get (2). Separating the sides in three equal parts,
and abating the angles, we get (3), (4), &c. From
the dodecagon, and generally every other polygon,
we obtain infinitely varied figures; but the detail
would be too tedious, and not absolutely neces-
sary.
103. If after having divided the sides of the
figure into two parts, we prolong the outline in
a straight line, we get a series of broken lines,


Theory and Analysis of Ornament.
111
CHAPTER II.
DECLINED FORMS.
109. These forms are produced by the declined
progression of a generating line following a headline.
The generating and head lines are equal to the
preceding, only the principle of declination inter-
venes for the determination of the forms. So,
taking a straight headline and a circular generating
line, and guiding the progression by a straight
inclination of the headline, we obtain a cone, whose
volume declines from the opening of the angle to
the summit. The progression taking place along
a curve or arc, every other condition being the same,
we get an ovoid form. If starting from a circular
generating and from a spiral headline, and the pro-
gression be declined instead of being uniform, we
get instead of a cylindrical serpentine a conical
serpentine.
SYMMETRY IN THESE TWO CLASSES OF FORMS.
110. Symmetry in solid forms refers to a point
or a straight line, or one, two or three plans which
are rectangularly cut. By the point, a number of
plans pass arranged in every possible way. By the
straight line pass an equal number of plans, but all
these plans containing the straight line are directed in
the same way. Thus the sphere and the regular poly-
pedrons have centres of symmetry; the cylinder,
the cone, the prisms, the pyramids, &c., have centres
of symmetry. The ovoids and the ovaloids have
one, two or three plans of symmetry.
From that and that which concerns the cylindri-
CO


Theory and Analysis of Ornament.
113
as
lowing arcs or curved lines; but if, instead of
these simple lines, we employ varied declining
lines, which should contain a number of funda-
mental affections of the lines, we should obtain
a number of varied forms, in general, such as the
diapered forms, the essential parts of the vases
parts of architecture, &c., &c.
According to the relative situation of the head
and generating lines, and the reciprocal nature of
their form, we obtain the elements of certain forms
essentially different. For example, taking for the
head a straight line, for generating a circle, and for
declining or profile a curved line, according as that
curved line turns its concavity or convexity on the
side of the headline, we obtain a conical, convex,
or open form. In the torns we get these two sys-
tems of curvity; in the ordinary cylinder all the
sections, perpendicular or slanting to the headline,
are curved lines. All the sections, on the contrary,
which pass by the headline, or are parallel to it, are
straight lines.
From that we distinguish three kinds of curved
surfaces :-
1. Those which have all their curvities in the
same way, starting from the same point, as the
sphere, the oval, and generally the convex surfaces.
2. The curved surfaces which have their cur-
vities always in the contrary way, as the torns,
the serpentine, and generally the inflected sur-
faces.
3. Those surfaces simply rounded, or having
curvity only in one way, as the cylindrical or conical
surfaces.


114
Theory and Analysis of Ornament.
car
113. The superficial extent has two dimensions
and two co-ordinations; the corporeal extent has
three dimensions and three co-ordinations. A
dimension predominates, or is harmonically lost
in giving the circle; again a dimension pre-
dominates, the two others being lost or distinct,
or the three dimensions are lost harmonically in
the sphere. The fundamental forms of the linear
extent are the plan, circle, label and angle; the
fundamental forms of corporeal extent are the cube,
sphere, and the prismatical parallelogram. The seg-
ments of the fundamental forms of extent which are
superficial are the triangle, the quadrilaterals, and
polygons. The dominant of the plane surfaces are
circular, quadrangular, linear and angular; the
dominant of extent are cubical, spherical, prismatical
or linear, polyhedrical or pyramidal. In general
the regular polygons correspond to the regular
prisms, the regular pyramids, and the spherical
polyhedrons. The starred polygons correspond to the
prisms and pyramids with sides, and to the starred
polyhedrons which are produced from the ordinary
polyhedrons by diagonal plans, as well as to the
starred polygons which spring from the ordinary
polygons by diagonal lines. The circle corresponds
with the cylinder and the cone or the sphere.
The outlines of the plane surfaces correspond with
the surfaces of the solids.
114. All the preceding theoretical considerations
belong to elementary and general geometry.
115. In the arts and handicrafts the surfaces and
forms are diapered directly, and plainly, by model-
ling or sculpture. The mode of manutention is


Theory and Analysis of Ornament.
115
0
more or less definite, according as the form is
more or less definite; but all the mechanical im-
provements given to the tools, or engines, do not
add anything to the notion of the form. It is not in
the industrial improvement of the mode of elabora-
tion that the development of the art of form lies;
on the contrary, this improvement, which is quite in
the economical sense, and organized for a rapid,
abundant production, is really prejudicial, though it
assists the power of invention and creation.
1 2


116
Theory and Analysis of Ornament.
FIFTH SECTION,
REGULARITY AND SYMMETRY.
116. A drawing, whether it be touch, delineation,
figure-form or ornament, is simple, composed,
complex or composite.
A drawing is simple when we can separate
it, still keeping a form, or when it is the starting
points of compositions or arrangements, or when
this form is always found in definite drawing. It is
composed when we can distinguish distinct parts
which assist in its formation, but so united that we
cannot separate them without breaking the unity of
form. It is complex when it is formed of different
parts, and the bond which unites these different
parts is apparent. It is composite when the parts
determining it are of different sorts, and the part
is prominent or dominant.
117. A form is regular or irregular. It is regu-
lar when it is constructed in accordance with an
apparent law, when we can distinguish regularity in
the arrangement of the disjoined parts, and when
we can conceive a barmonical bond in the arrange-
ment of its different parts artificially separated or
only distinguished by analysis.
The idea of regularity has two distinct accepta-
VIL.


Theory and Analysis of Ornament.
117
a
tions, according to what they depend on. The
harmonical bonds which unite the different parts
of the disposition, and which consist in a regular
declination, are:-
1. The position following the curved line.
2. The size of the parts.
3. The accentuation of form, which is of a
special nature, and does not depend upon the idea
of a developed law, for which could be substituted
sensible and immediate form.
A regular form can be symmetrical, declined,
or varied, so that the ornamental regularity is
separately or conjointly determined-
1. By the symmetry.
2. By the declination.
3. By the variation.
CHAPTER 1.
SYMMETRY.
118. A "form, whatever it may be, has its con-
stituent parts referred to a diagram, also its
geometrical plan of construction, or this form is
repeated in proportion to a geometrical diagram of
disposition. Accordingly as the parts of a figure or
disposition are assembled at a point, line or plan,
the symmetry differs.
The solid forms of uniform constitution have all
their parts drawn up in a point, as in the poly-
hedrons and spheres; in the straight line or axis, as
the prisms, pyramids, cylinders and cones; in one or
several plans, as the sphere, cube, ovoids, &c. Let


118
U1012
Theory and Analysis of Ornament.
us now .examine the different cases of symmetry
without separating them from the forms which con-
tain them.
119. Seeing the forms in their formal unity and
in the integrity of their image, we are obliged to
distinguish them, and to define them, in the follow-
ing manner: a form is uneven, even, diagonal
or quartered, revolved or radiated, ternary or
senary.
1. Uneven forms. A form is uneven when it has
neither axis nor centre of symmetry. An uneven
form is regular or irregular; the regularity con-
sisting in a progressive and harmonical variation
XTO AO in
..
X
Fig. 76.
of what constitutes the essence of form : for ex-
ample, a curved line is regular because there is a
continued change and progressive modification in
the curvity. An uneven form is simple or com-
pound, being simple when its principle of unity holds
entirely to its essential nature; thus a curved line
is a simple form, because there is continuity in
the declination of the curvity. An even Greek
parallel is complex, because the parts which
compose it are different and form each a unity or
simple form. To speak correctly, it is not a form
but a disposition.
2. Even forms. A form is even when it has an
axis of symmetry which separates it into two equal


Theory and Analysis of Ornament. 119
parts, and these correspond by turning. The
arcs, handles, ovals, straight angulations, isosceles
triangles, &c., are even forms, and the simplest of all.
Generally, symmetry separates the object into two
parts, places in the middle the unique parts, besides
those which are repeated, and which form a sort of
equilibrium, giving order, liberty and beauty to the
object. (Fig. 76.)
XX ASXF
9 8 7 . Fig. 57.
3. Diagonal forms. A diagonal form is con-
structed by reference to a point : it has its halves
placed in the inverted way in proportion to one of
the straight lines, which pass by the centre or sym-
metrical point. In general, a diagonal form is
*** 0-0 0-X
Fig.178.
determined by the doubling of an uneven or even
form; it bas always a figure which repeats itself by
invertion, Fig. 77 (6), (7), (8), (9).
4. Quartered form. The two even and diagonal
symmetries together determine the quartered sym-
metry. A quartered form has two symmetrical
axes which are crossing at the point of the sym-
metrical centre. (Fig. 78.)


120 Theory and Analysis of Ornament.
There is a straight symmetry in cross and
diagonal figures (symmetry at cross-wise). The
straight, the cross-wise, the rectangle, lozenge, oval,
&c., are forms as well quartered as are those of
diagonal compositions.
5. Quarternary form. A form is quarternary
*11** *83* *
Fig. 79.
when it has four symmetrical axes crossing or
radiating at a point. (Fig. 79.)
6. Ternary or Senary form. A form is ternary
or senary when it has three symmetrical axes which
cross at a point or which radiate from this point in
number three or six (Fig. 80). A senary form has
for form-envelope a hexagon or a circle. A
ternary form has for form-envelope a trigon or a
circle. The quarternary, ternary, senary, quinary
0
e
*
A
*
*
Fig. 80.
forms, &c., are forms whose pieces are circularly
turned down; so also is the quartered form, but this
last implicates two axes rather than a centre and rays,
in the case where the number of pieces is uneven,
or the multiple of an uneven, and a centre and axes
in the case where the number is even, or the
multiple of an even number.
7. Revolved form. A form is revolved when it


Theory and Analysis of Ornament.
121
has all its parts circularly arranged round a real or
imaginary point, and turned in the same way (Fig.
81). A revolved form is an uneven one if the
number of pieces are uneven ; the imaginary point
is then a centre of disposition, seeing that the
figure has neither axis nor symmetrical centre. A
revolved form is of diagonal symmetry if the
number of pieces is equal or even, the centre of
disposition being then a symmetrical centre by
which passes a number of axes. Generally, a
diagonal form is one composed of two pieces.
8. Radiated form. A form is radiated when
the symmetrical axis is an indefinite number too
Fig. 81.
great for counting. The simplest figure is the circle
which has a number of axes.
120. Every even, uneven, diagonal, or quartered
form has a degree, the idea of the figure-envelope
which contains it, and which can be an irregular
figure, or more particularly the isosceles triangle, the
quadrilateral, triangle, or the circle. Every revolved
and radiated form (i.e., every form circularly con-
structed round a point) implicates a figure-envelope
the image of a regular polygon, from the trigon to
the circle. For seeing the question in all its gener-
ality it is necessary to consider two very important
points :-
1. The different positions which a determined
form can occupy.
2. The reciprocal positions or conjugations of


122 I 22
Theory and Analysis of Ornament.
two identical or different positions of a determined
forni.
ns
I. POSITIONS OF THE FORMS.
121. 1. Radiated forms. A radiated form, hav.
ing more than four axes of symmetry, and whose
form-envolope is a polygon of more than eight sides,
or a circle, is not susceptible of direction, and remains
indifferent.
2. Revolved forms. A form revolved of one piece
is uneven ; a form revolved of two pieces is uneven
and diagonal; a form revolved of three pieces, having
for form-envelope a triangular outline, can occupy
eight positions, as the triangle. A revolved form of
four pieces, having for form-envelope a quadri.
lateral, can occupy four positions.
3. Quarternary and ternary forms. A quar-
ternary form, which has four axes of symmetry, and
for form-envelope an octagonal or circular outline,
can occupy two positions. A quarternary form or
senary form, which has three symmetrical axes, can
occupy eight positions, as : an axis being horizontal,
the points turned on the right or on the left; an
axis being vertical, the point turning up or down;
and an axis being oblique, in two positions, on the
right or on the left, can get a point turned in one
way or in the other.
4. Quartered forms. A quartered form, or one
with two axes, has two positions if the form-
envelope is a square ; or four positions, one hori.
zontal, the other vertical, and the other two oblique,
if the form-envelope is a lozenge or a rectangle.
5. Diagonal forms. A diagonal form, having a


124 Theory and Analysis of Ornament.
2. The reciprocal positions. The two forms being
considered only for their directions, the conjugation
two and two of these directions determines the
reciprocal positions.
3. The reciprocal situations. A form occupying a
determined place, the second form, which is con-
jugated, occupies a different place, which is, with the
first one, in a relative situation whatever it may be.
It is the reciprocal position which determines the
sort of conjugation, the number of directions or
the kind of form determining the varieties of the
conjugation pertaining to this form; and the
reciprocal situation determines the figure or actual
form of the conjugations; and more, they obtain
varied images, according as the two forms may
remain different, or separated by an interval, what-
ever it may be, or are touching one another.
1st. Uneren forms. Taking for example the
rolling, and putting together the different positions
of this form, we obtain from them six sorts of
definite conjugations :-
1. The uneven conjugation, where the two pieces
have not any definable relation.
2. The revolved conjugation, uneven or unsym-
metrical, but regular, because the points are cir-
cularly corresponding together by proportion to an
axis or curvilinear diameter.
3. The followed conjugation. Two forms being
repeated, the distances of the corresponding points
are all equal and parallel between them, i.e., these
distances are directed in the same way and follow-
ing a linear head-line (Fig. 82). This conjugation
is equal to its precedent; in one case the forms are
01


Theory and Analysis of Ornament. 125
circularly followed, in the other, they are linearly
followed.
4. The diagonal conjugation. Two forms being
diagonally repeated, or in situation reciprocally
contrary, have all the distances of the correspond-
ing points equal and are crossed in the middle by
the same point which is the symmetrical centre
(Fig. 84).
5. The conjugation in the wrong way. Two forms
being symmetrically repeated by proportion to an
axis have all their corresponding points equally
distant from this axis. The distances are all
parallel and crossed in their middle by the
symmetrical axis which is perpendicular to them
(Fig. 83).
6. The contrary conjugation. Two forms being
AA A CATA
Fig. 82.
Fig. 83.
Fig. 84.
Fig. 85.
repeated and contradicted, have their corresponding
points equally distant, but those distances are not
all directed in the same way; they are sometimes
parallel, sometimes crossed in a changeable manner
and in different places (Fig. 85). It is necessary to
observe :-
1. That a followed conjugation is uneven, i.e.,
has neither axis nor symmetrical centre.
2. That a conjugation in the wrong way is even,
i.e., has a symmetrical axis.
3. That a diagonal conjugation is diagonal, i.e.,
it has a symmetrical centre.


126
Theory and Analysis of Ornament.
nin
4. That a contrary conjugation is uneven, but
has a transversal axis or a diameter which separates
the figures in two equal parts as quantity, and
superposable by moving and turning. Each of the
conjugations is, for situation :-
1. Separated (Fig. 56).
2. Contiguous (Fig. 87).
3. Crossed (Fig. 88).
6 89 90e G9
Fig. 86.
They can be defined simply and briefly by saying
of a form that it is followed, even, diagonal, or
contrary; and more, add that each of them is
separated, contiguous, or crossed.
CrOS
oo
oo
or
do
Fig. 87.
To construct these different conjugations, it is
necessary to place the initial form in proportion
with the square touch.
on sa ora
Fig. 88.
2nd. Even forms. An even form has its axis
vertical or horizontal; if the position of the axis is
oblique, the form can be considered as uneven.
The symmetrical axis can occupy some positions
and directions which are changeable: we obtain, by


Theory and Analysis of Ornament.
127
the reciprocal combination of those positions and
directions and following the relative situation of
the parts, the following conjugations :-
123. I. Axes are parallel, straight or oblique.
1. Directed in the same way (Fig. 89).
2. Directed in the opposite way (Fig. 90).
Kran
C ba
Fig. 89.
Fig. 90.
wro
ms
The first follow in the wrong way if the forms
are directly corresponding, a; the second follow
and alternate if the forms are obliquely following
one another, b, c. The first is an even form, the
second an uneven form. The third conjugation, d,
where the axes are turned in the contrary way,
is always diagonal, whatever the relative situation
may be.
Fig. 91.
Fig. 92.
II. Axes are in prolongation.
1. Directed in the same way (Fig. 91).
2. Directed in the opposite way (Fig. 92).
In the first case the conjugation is followed, and is
an even form; in the second, it is the backward
conjugation, and a quartered form.


Theory and Analysis of Ornament.
129
A
one with the other, the conjugation is then in the
opposite way; and if the forms are crossing by the
centre of the figure, we get a quarternary form.
When the axes are oblique the one with the other,
we get the symmetrical or opposite conjugation.
5th. Revolved forms. Revolved forms are uneven
or diagonal. Uneven revolved forms of more than
five pieces are almost indifferent, and determine
the followed and opposite conjugations. The
revolved form of three pieces determines all the
conjugations of the uneven form; the simplest,
the opposite conjugation, being regularly crossed,
determines a senary form
6th. Ternary and Senary forms. One of these
forms which has less than four symmetrical axes,
gives rise to the followed and reciprocal conjuga-
tions. A ternary form, or one with three axes,
which has a triangular form-envelope, must be con-
sidered as even. A senary form which has a
hexagonal or circular form-envelope, gives rise to
two followed and opposite conjugations.
7th. Radiated forms. A radiated form can only
be submitted to the followed conjugation, or to the
principle of repetition ; it is and remains indifferent
in every situation, being exclusively constructed by
reference to a centre. In general, and considering
all the forms as having at least three axes, a radiated
form of 3, 5, 7, 9.... pieces is even; a radiated
form of 6, 10, 24 . . . pieces is quartered; a
radiated form of 4, 12 ... pieces is quarternary;
a radiated form of 8, 17. ... pieces is radiated.
.


130
Theory and Analysis of Ornament.
Part #fx.
ORDER AND DISPOSITION IN ORNAMENT
AND FORMS.
ud
124. Generally, the differences in the modes of
construction of the ornaments have importance
only by their relation to the proper genius of
mankind, and their neatness and logical or geome-
trical strictness are not the measure of superiority
of one style or another. This appears from the
following brief comparison of three particular styles
of ornamentation.
1. Japanese ornamentation is disjoined without
regular co-ordination. It is composed of forms
taken from Nature, arts, and society. All these
forms, which have very accentuated profiles, are
mixed in confusion. It is the habit of these people
to give the forms of ornamentation neatness
and precision, which are the modes of perception
and consisting in the immediate determination of
forms in plane surfaces and under a correlative
graduation.
2. The ornamentation of the Asiatic is regular
and continued upon all surfaces. It is a multi-
plied and luxuriant ornamentation, which is not
strictly disorderly, but which yet is not quite
orderly.
On


Theory and Analysis of Ornament.
131
3. The ornamentation of the Greek, or more
generally the classical ornamentation, is essentially
ordered and regular. This ornamentation is con-
tained and distributed under the form of ranges,
which follow the great lines of edifices.
CLASSIFICATION OF DISPOSITIONS.
125. Forms and ornamentation regularly con-
structed have all their varieties divided in two
classes.
FIRST CLASS : UNLIMITED DISPOSITIONS.
1. Order. Dispositions in series.
2. , Multiplied dispositions.
3. , Agglomerated dispositions.
SECOND CLASS: LIMITED DISPOSITIONS.
1. Order. Figurative dispositions.
2. „ . Co-ordinate dispositions.
3. „. Constructed dispositions.
S.
K
2


Theory and Analysis of Ornament. 135
tion has a period, or a changeable cut, with a
number of forms (Fig. 101).
00000000000000000nm
Fig. 103.
Four forms give a period of eight elements; one
form being repeated four times, another twice, the
other two occurring only once. This cut is com-
UUU00000000000000
Fig. 101.
posed of two periods, which is equal to an alterna-
tion of the two groups (Fig. 102).
The disposition can be infinitely varied. Thus
the recurration Fig. 103 is varied by taking for
000000000000000000
Fig. 105.
one of the forms the symmetrical grouping, taken
from the intercalation one composed of eight
sections. The recurration Fig. 104 is composed
0008000000000000
Fig. 106.
of five elements, two of which are repeated three
times, and one twice. In Fig. 105 we have
three elements, one of them being repeated three
times, and one twice.


136
nan
Theory Va
.
and Analysis of OrnamentFig. 106 is composed of four elements; it can
be considered as derived from a recurration of
three elements, of which one would be repeated
twice, and which would be cut in the intervals by
the repetition of the fourth form.
By combining two and two and by intercalation
of two sorts of arrangements, we obtain a great
variety of ranges (Fig. 107).
UVODOPU00000000000
Fig. 107.
The combination of an alternation of two forms,
with a repetition of a group of three forms, gives
Fig. 108.
128. The inevitable idea of number has a
variable and relative importance to the mode of
arrangement. In simple and uniform repetition
the number is unlimited. In the alternation it is
necessary to distinguish the parity and imparity,
but only when the series is limited enough to be
000000000000000000
Fig. 108.
appreciated at once. Alternation being correct, and
finished, produces an uneven number of elements;
it is then that a finished disposition is contained in
the second class of dispositions. But if the series is
sufficiently prolonged in order not to have to count
the elements, the idea of number is nil. In inter-
calation, if the group of one and the most important
element is composed of a great number, the inter-


Theory 137
Vl
Amen
.
and Analysis of Ornamentcalary form should be insufficient; it would be
repeated and the disposition be reduced to an
alternation of groups. Still, the idea of number
is secondary, and the essential idea which
intervenes in this case is the one of measure or
quantity. The number, very far from being an
active and direct principle of harmony, is, on the
contrary, quite subordinated to the aesthetical con-
ditions of this harmony. In the periodical repeti-
tion it is necessary to maintain the whole period,
only, if these were too many, the continuation or
line becomes indefinite. In the recurration, which
is a disposition relatively complicated, the necessity
to maintain the symmetry is still more rigorous;
it is in this disposition that the ideas of number
expressly intervene, as well as symmetry, gradua-
tion, size, quantity, and æsthetically the ideas of
relief and colour, whose different particularities
show the different accents of the whole dispositions.
CHAPTER II.
RANGES.
129. The repetition and line of a form determine
ranges, where it is necessary to recognize two parts,
the headline and the composing forms. We dis-
tinguish two kinds of forms: the linear forms or
touches, and the superficial forms or plane figures.
Generally, considering the relative situation of
forms, they can be separated, continued or
crossed in the simple ranges, and articulated con-
jointly, or separated, continued or crossed in the


138 Theory and Analysis of Ornament.
composite ranges. These ranges are divided into
two general classes : the marginal ranges, or those
only upon one side of the headline, and the diame-
trical ranges, whose parts co-exist on both sides of
the headline.
I. Marginal Ranges.
130. The marginal and lateral ranges have no
axes of symmetry. They contain two varieties :-
a
cecce
-
000000000001
oooooooooooo
--
-
-
-
---
-
Fig. 109,
1st. The uneven ranges, equal to the lateral order,
or upon only one side, left or right. These ranges
are determined by the followed repetition of an
6262626 KKAS
m 10000000
Fig. 110.
uneven form, and by the followed repetition of an
oblique even form. They can oocupy four posi-
tions, viz. two situations, above or below the head-
line, and two directions, to the right or to the left
(Fig. 109).
2nd. The even or straight ranges, equal to the
m
.
van


Theory and Analysis of Ornament.
139
vertical order, i.e., from top to bottom. These
ranges are obtained by the followed repetition of a
straight even form, and by the backward repetition
of an oblique even form. These ranges can occupy
two positions, the one on the top and the other
under the headline, as in Fig. 110.
II. DIAMETRICAL RANGES.
131. The diametrical, collateral ranges have
symmetrical axes which are
confounded with the head-
line. They contain four varie-
ties.
ใด ป°
1st. Contradicted ranges.
These are determined by the
contradicted repetition of an "eccococo
A-
uneven form, by the following
N
or alternate repetition of an GEGERECR
even form whose axis is hori.
Fig. 111.
zontal, and by the constructed
repetition of an oblique even form. These ranges
can occupy four positions, which are reduced to two
when the continuation is unlimited; the difference of
one position from the one which is symmetrical, or
backward, consisting only in the moving of the form,
the two symmetrical positions would be confounded
by the removing, lengthwise, of the interval of a
form (Fig. 111).
2nd. Diagonal ranges. These are obtained by
the followed repetition of a diagonal form, a
revolved, even or quartered form obliquely placed
at its axis. These figures can occupy two posi-
tions (Fig. 112).
In


Theory and Analysis of Ornament.
141
The alternate ranges can occupy only one position
(Fig. 113).
4th. The opposite or straight ranges are-
1. Even when the range is obtained by the
following repetition of even form, or of a backward
form whose symmetrical axes are confounded with
the headline; these ranges can be directed on one
side or the other.
2. Quartered, when the range is obtained by the
followed or reciprocal repetition of a quartered form.
3. Centred, when the range is obtained by the
followed repetition of a radiated form. The quar-
tered or radiated ranges cannot occupy more than
one position (Fig. 114).
CHAPTER III.
CONJUGATIONS OF RANGES.
132. By combining the positions, or different
directions of the ranges two and two, we obtain
conjugations similar to those of the conjugations of
isolated forms.
Generally the conjugation is (1) followed, when
the ranges are parallelly repeated ; (2) returned,
when the ranges are symmetrically repeated; (3)
diagonal, when the ranges are diagonally inverted;
and (4) contradicted, when the ranges are contra-
dicted.
The conjugations are, for the reciprocal situation,
(1) straight or directly corresponding; (2) alter-
nated, when forms of a range are corresponding to
the intervals of the other; and for reciprocal correla-


Theory and Analysis of Ornament.
145
nate, when the juxtaposition is produced by the
retardment of a form, one of the labels being
changed in the longitudinal way of an interval of
form ; and it is half alternate when the juxtaposition
is immediate, between the straight and alternate
juxtaposition, the moving being reduced to the
fraction of interval.
2
သာသာ
သ
Fig. 140. Fig. 141.
Fig. 142.
Hence, and taking for example the linear and
geometrical figuration, or composed arcs of a
circle, we obtain six conjugations : A (Fig. 143), }}
(Fig. 144), c (Fig. 145), D (Fig. 146), E (Fig. 147),
and F (Fig. 148).
The conjugation A is obtained by the lateral con-
jugations of two even foliages; by alternate con-
ccc
ССС
DO
Fig. 143.
Fig. 144.
jugation of two diagonal even ranges; by the
straight conjugation of two diagonal even foliages;
by the half alternate conjugation of two diagonal
incomplete ranges; and by the straight conjugation
of two uneven ranges with longitudinal turnings.
The conjugation B is obtained by the conjugation
of two ranges with lateral turning; by the conjuga-


146
Theory and Analysis of Ornament.
tion of two uneven ranges with alternate juxta-
position ; by the conjugation of two even ranges
with straight juxtaposition; by the conjugation of
two incomplete ranges with half-alternate juxta-
position ; by even and half
alternate ranges with straight
juxtaposition; by diagonal
conjugation of two straight
uneven ranges and of two
alternate even ranges ; and
Figs. 145, 146. by the conjugation, backward
and longitudinal, of two uneven ranges, even and
incomplete with alternate juxtaposition.
The conjugation c is obtained by the lateral back-
cccccccccc
coco
00000
B
Fig. 147.
Fig. 148.
ward conjugation of two half-alternate, even and
alternate incomplete ranges; and by the diagonal
conjugation of half alternate uneven and straight
incomplete ranges.
The conjugation D is obtained by the lateral
and straight backward juxtaposition of incomplete
ranges; by the diagonal and half alternate juxta-
position of incomplete ranges; by diagonal and
alternate juxtaposition of incompelte ranges; and


Theory and Analysis of Ornament. 147
by the juxtaposition of a longitudinal and half
alternate turning of u neven ranges.
The conjugation E is obtained by straight juxta-
position with a lateral turning of uneven ranges ;
and by the straight juxtaposition with longitudinal
turning of incomplete ranges.
The conjugation F is obtained by juxtaposition
with lateral and half-alternate turning of uneven
ranges; by followed and half-alternate juxtaposi-
tion of uneven, even and incomplete ranges; and
by juxtaposition with longitudinal and half-
alternate turning of even and incomplete ranges.
Uuuoo
FF FFA
PRIVACE
Cyff $
ŏo
Fig. 149.
2. Diagonal ranges. Two diagonal ranges de-
termine the followed and backward conjugations,
which can be straight, alternate and half alternate,
distinct, contiguous or crossed. By conjugating
the diagonal ranges obtained from a revolved or
quartered form, we should obtain the same ranges,
but particularly the backward conjugation; alternate
or intersected, determines an alternate diametrical
range. Two diagonal ranges obtained from a
simple diagonal form being conjugated backward
and of half-alternate juxtaposition determine an
even marginal range.
3. Alternate ranges. The alternate ranges being
L 2


148 Theory and Analysis of Ornament.
mine
conjugated, determine the followed and backward
conjugations, whose correlation of position can be
straight, half alternate, or alternate. The half
alternate crossed conjugation is alternate diametri-
cal, g (Fig. 150). The alternate followed conjuga-
tion and the straight and backward conjugations
are quartered diametrical, D.
0XXXXXX
mm
-
لا
لا
لا
Fig. 150.
4. Opposite or straight ranges. Two even diame-
trical ranges determine the followed and backward
conjugations. The followed conjugation is even
diametrical if the juxtaposition is straight; it is
contradicted, diametrically, if the juxtaposition is
alternate. The backward conjugation is diagonal
diametrically, if the juxtaposition is straight, half
alternate or alternate (Fig. 151).
Two quartered diametrical ranges, or centred


150 Theory and Analysis of Ornament.
These two dispositions, simple and varied by
inclination of forms on the headline, being doubled
in the same way by superposition or intercalation,
determine the following dispositions :-
1. Straight superposed disposition.
2. Alternate superposed disposition.
OOOOO
OOOO
O O Q Q
TO1070
Fig. 154.
Fig. 155.
II. COLLATERAL DISPOSITIONS.
The two dispositions, up and down, being con-
jugated backward, determine the four distichous
ranges :-
ဝဝ၃ ဂဝဝဝ်ဓဝ
bobobbo 0000000
Fig. 156.
Fig. 157.
1. Straight opposite disposition (Fig. 156).
2. Straight face to face disposition (Fig. 157).
3. Alternate opposite disposition (Fig. 158).
4. Alternate face to face disposition (Fig. 159).
These diagrams, simply figurative, have a real or
imaginary axis. If the axis is real, its form can be
varied; it is then a delineation. We have supposed


Theory and Analysis of Ornament.
151
hitherto that the ranges are uniform and composed
with only one form; it is necessary now to examine
ဝဝဝဝှိုဝ၃ဝဝ
όόόόόόόόό
Fig. 158.
boooooooo
OOO 000999
Fig. 159.
the different positions given by the conjugation of
varied forms, i.e., composed of different forms.
CHAPTER IV.
VARIED DISPOSITIONS.
le
136. The five fundamental rhythms, combined
two and two, and referred to in the six preceding
diagrams, determine ninety dispositions.
To avoid dwelling too long on this paragraph, we
shall limit our examination by the two following
conditions : by taking for example only the different
combinations and ranges having at most three
different forms, and referring to the construction in
only one diagram of the straight, opposite disposi-
tion. We shall thus get the following arrange-


154
nanien
Theory and 11
.
Analysis of Ornamenteven, period of disposition is of the same number ;
if it is uneven, a period of disposition is of a double
number. Removal gives two varieties. (Fig. 165.)
O O O O O O O O O O
Fig. 165.
. 7. Alternation recurrence has a period of four
elements if recurrence is of three forms, and a
period of eight elements if recurrence is of four forms.
Transposition gives three varieties. (Fig. 166.)
O O O O O O O O O
Fig. 166.
8. Intercalation period gives a period of three
forms if the cuttings of the two composing ranges
are of three forms. Generally, if the periods are of
the same number, they determine in disposition an
000099 999
OOOOOOOOOO
Fig. 167.
equal period ; if there is discordance, the composed
period is of 12, 18. ... &c., elements. By trans-
posing the period, six forms are produced from the
dispositions. (Fig. 167.)


Theory and Analysis of Ornament.
155
9. Intercalation recurrence produces a period of
four elements if intercalation has a period of four
elements; and a period of twelve if the period of
intercalation is only of three elements. Transposi-
tion gives three varieties. (Fig. 168.)
O O O O O O O OOO
Soooo
Fig. 168.
10. Period recurrence has a cutting of four ele-
ments if the period is of four forms ; and a cutting
of twelve elements if the period is of three forms.
Transposition gives three varieties. (Fig. 169.)
O O O O O O O O O O
Fig. 169.
The dispositions repetition alternation, repetition
recurrence, and alternation recurrence are the
simplest and most regular.


156
Theory and Analysis of Ornament.
SECOND SECTION.
MULTIPLIED DISPOSITIONS.
All the possible diagrams of plane co-ordinated dis-
positions have for their essential basis the theory
of networks.
CHAPTER I.
NETWORKS.
137. When points are disposed in a regular
manner on the whole extent of a plan, they form
immediately real or imaginary lines which bind them
together in finished or indefinite lines, crossed, and
regularly bound, and determining points regularly
disposed. These points and lines determine net-
works. Moreover, the points determine distances,
and these distances are straight lines, and together
they determine polygonal spaces, which are seg-
ments of the plan.
For determining networks we start indifferently
from the distribution of points, from the crossing of
the straight lines, or from the repetition of polygons.
The networks can be seen under a triple point of
view : 1st, points ; 2nd, lines; 3rd, meshes.


Theory 1 . 157
Ana
ате
and Analysis of OrnamentI. GENERATION BY POINTS.
138. A series of points placed in line can be put
near another similar series in two ways. The first,
where the points are directly corresponding and .
©
..-Q.....- -.-.---
0--0--0 -e..
on..........
@--
0 0 --0-0--o-o-o
--0-0--0-0-0-0-0-
od 0...66-6--@---
i
B
.
-23
0.0-0-00
0.- B.--0--0--0
Fig. 170.
Fig. 171.
following lines perpendicular to the headline; this
is the straight repetition (Fig. 170). The second,
where points change places on the right or left
side and correspond to the intervals ; this is the
-OT
0-6 0-0 0 0
- 0:40:-!
q7..0.0-0.6..
* 66-6-6.
Fig. 172.
Fig. 173.
alternate repetition (Fig. 171). Distances can be
smaller, or of the same size, or even greater than the
intervals of points on the range. From the regular
seed-bed of these points come horizontal, vertical or
oblique lines (Figs. 172, 173); or four systems for


Theory and Analysis of Ornament.
159
1. Parallelograms. The centres of figures deter-
mine the same network; the diagonal lines deter-
mine a network equally parallelogramic, but not of
the same form (Fig. 176).
2. Lozenges. The centres of figures determine
HARTA
Fig. 176.
Figs. 177, 179.
the same network ; the diagonal lines determine a
rectangular network (Fig. 177).
3. Rectangles. The centres of figures determine
M17
Fig. 178.
the same network; the diagonal lines determine
the lozenge network (Fig. 178).
4. Square. The centres of figures determine the
same network, and the diagonal line determines a
squared network (Fig. 180).
All these networks can be varied in every degree,


160
namn
Theory and Analysis of Ornament
following the uniform separations; and varied in
every system, following the similitude or diversity
of separations from one system to the other.
Class II. SENARY NETWORKS.
141. All the networks of this class are determined
by three systems of lines, the third crossing the
two first ones in their intersecting points. The
elenientary meshes are the scalens and the isosceles
triangles and trigons. In all the networks of
this class it is necessary to distinguish between the
ecess
CA
*
Fig. 180.
Fig. 181.
isosceles networks, whose mesh is isosceles, and the
diagonal networks, whose mesh is trigonal.
These first two classes of networks are reduced to
three principal systems :-
1. Trigonal network, with trigonal mesh (Fig.
181).
2. Squared network, with squared mesh (Fig. 180).
3. Isosceles and conjugated networks, with
rhombical mesh, or lozenge with rectangular mesh
(Fig. 179).
Class III. DisjoinED NETWORK.
142. If we consider only the joining of polygons,
e COns


Theory and Analysis of Ornament.
161
we obtain, with the polygonal figures, at first the
networks described above, and then the disjoined
networks.
EFTE
Fig. 182.
1. Lozenges. Assembled lozenges give, by fol-
lowed juxtaposition, the ordinary network where
the lozenges have all the same direction; by juxta-
position backwards, the lozenges have two direc.
IIIIII
Fig. 183.
tions; by centred juxtaposition, the network has
three directions, a varied network by combination of
three first juxtapositions; and also the juxtaposi-
tion determined by three lozenges assembled in
point and in side (Fig. 182).
2. Rectangles and Squares. The rectangle and
the square determine the followed and rough juxta-
position (Fig. 183).


162 Theory 102
and Analysis of Ornament.
3. Trigon. The juxtaposition of trigons is fol-
lowed and turned, and contains a particular case
and varied groupings of the different networks of
trigonal lozenge.
If we do not pay attention to this condition of
perfect juxtaposition we get other arrangements
which depend on the relative position of figures.
Fig. 184.
Fig. 185.
Fig. 186.
1. Lozenges. The lozenges placed alternately
one way and the other determine the followed
grouping, which is the same as the juxtaposition
of a lozenge and a square (Fig. 184).
Fig. 187.
Fig. 188.
Fig. 189.
2. Rectangles. Two rectangles whose positions
are contradicted give the combined network of a
rectangle and a square assembled (Fig. 185).
3. Square. The two positions of a square, placed
on the point or side, determine the contradicted
grouping (Fig. 186). The followed positions of


Theory and Analysis of Ornament. 163
res
the square, with removal, give a figuration equal
to that of grouping two conjugated squares (Fig.
187).
4. Hexagon. Like the square, this form has the
contradicted grouping and the followed grouping,
which coincide with the juxtaposition of a trigon
and a hexagon (Figs. 188 and 189).
5. Trigon. The figuration obtained equals the
juxtaposition of the trigon with the hexagon, con-
jugated, i.e., one being given, the other is not
arbitrary (Fig. 190).
Fig. 190.
Fig. 191.
Fig. 192.
6. Octagon. We obtain figures analagous to the
preceding (Figs. 191 and 192).
All the forms of juxtaposition that we can refer
to polygons are very simple.
CLASS IV. COMPOSED POLYGONAL NETWORKS.
143. The condition of perfect juxtaposition, with
only one polygon, is produced by a hexagon whose
juxtaposition follows the position, disjoined for lines
of network, and polygonal because the figure has
more than four sides. The network of a hexagon
and succeeding networks (Figs. 193, 194, 195, 196,
M 2


164
A2
Theory and an
.
Analysis of Ornament197) are constructed on the type of the trigonal net-
work. The network of the square and such like
(Figs. 198, 199, 200, 201, 202) are constructed from
the type of square network.
1. Hexagon (Fig. 193).
17:
Fig. 193.
2. Hexagon and Trigon (Fig. 194).
Fig. 194.


168 Theory and Analysis of Ornament.
are continued, following the complete network of
lozenge and square (Fig. 203).
II. LOZENGE, LOZENGE-RECTANGLE.
The example chosen contains a lozenge of four
trigons, a lozenge of two trigons, and a rectangle
of two squares. This disposition has two assembled
groups of lozenges composed of nine tangent circles,
or even groups of lozenges and hexagons (Fig. 204).


Fig. 204.
Fig. 205.
III. Hexagon, SQUARE, Trigon.
This disposition results from a grouping of
hexagons composed of seven circles (Fig. 205).
IV. Hexagon, TRIGON, RECTANGLE.
This disposition results from hexagons composed
of nineteen circles.
Hexagons, trigons and squares could be composed
of a number of circles (Fig. 206).
V. HEXAGON, SQUARE, LOZENGE.
This disposition is the result of a varied group.


Theory and Analysis of Ornament. 169
ing composed of three circles in trigon and seven
circles in a hexagon.


10
Fig. 206.
Fig. 207.
VI. DODECAGON AND TRIGON.
The agglomeration results from a complete
grouping of hexagon, rectangle, trigon, or grouping
of hexagons and two circles in line, &c. (Fig. 207).
VII. DODECAGON, HEXAGON, SQUARE.
VIII. DODECAGON, HEXAGON, SQUARE, TRIGON.
This agglomeration results from a complex and
discontinued grouping
of dodecagon and Re
o
trigon (Fig. 208).
As to the other
polygonal networks,
we can add equal
circumferences fol-
lowing the line of
network or the sides
of polygons; but
such arrangements
leave variable inter-
Fig. 208.


170 Theory and Analysis of Ornament.
vals. Following the figure the interval is smaller
than the circle of grouping for the trigon, square,
Fig. 209.
and pentagon ; equal for the hexagon ; and greater
and greater for every other polygon, as heptagon,
octagon, nonagon, &c., &c. (Fig. 209).
CHAPTER IJI.
REPARTITIONS.
145. The theoretical and general notions once
established, the application to ornamentation soon
results. This application is explained in the three
following categories.
1. Ornamentation by separated forms and placed
with order, following the points of networks. These
repartitions are varied according to the different
rhythms of ranges, and determined by isolated op-
position of forms in each of the head-points of the
network.
2. Ornamentation by rays or separated and
directed ranges, following the harmonical lines of
plan, which determine three systems of rays or
ranges—the horizontal, vertical, and oblique or
diagonal.


Theory and Analysis of Ornament.
171
3. Ornamentation by squares and stripes crossed.
These crossings are determined by combination two
and two, three and three, four and four, of the
different systems of stripes, horizontal, vertical, or
oblique.
The squares, ranges or rows, and separated forms
being combined in every possible manner, determine
maps of ornament which we call tapestry.
146. At first the points are placed at random and
cover the surfaces; these surfaces are destitute of
order and represent Nature. Each of them having
Fig. 210.
been under man's manipulation, it is then exclu-
sively decorative. Stuffs or kinds of decoration in
colour imitate them; they dispose or separate the
seed-bed by being in contact with diagrams of
disposition. The diagrams are of several kinds :
here are the principal.
1. Diagrams determined by square network,
rectangles or lozenges. The points are placed
following the points of network, or following the
centres of meshes, every touch disappearing.
2. Diagrams determined by networks disjoined,


Theory and Analysis of Ornament.
173
ranges are alternations in the great network, and
the diagonal ranges are repartitions.
2. Following the trellis-work and the varieties of
this network. The figure 215 is a series of repar-
3.-.-.-.-.
LV--..---
...........................“
-.-O
.....................
.
O................
Fig. 212.
Fig. 213.
Fig. 214.
titions or ranges, the oblique ranges being uniform
and the horizontal alternations. The figure 216
is a figured or poised repartition, and it is com-
posed of hexagonal repartition centred by trigonal
**
o...
....
......
.
.......
.
--
--
-
-
ó...
...
citi....
..
Fig. 215.
Fig. 216.
Fig. 217.
repartition. All the rows are intercalations two and
one. The figure 217 is a repartition figured and
composed of a polygonal, trigonal, and hexagonal
network, whose hexagons are centred by a trigonal
network; the ranges are alternately repetitions


174 Theory and Analysis of OrnamentVale
.
and alternations. These three figures are analo-
gous.
II. REPARTITION OF THREE Forus.
148. 1. Following the square network and
varieties of this network. The figure 218 is a
...O..
O
0.0.0
.0.
•
O
0
O
.0·.0.0.0
.
.0
.0 •
.0
.0
• 0.0.0.0.0.
0:00
0.0.0.0
0.0.0
0.0.0.0
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s..........
20.6•ỏ, vỏ •
O.O
• 0 .
O.O .O
. 0 .0 .
0
0
O
.
-
0
0
0
O
0
0
0.0.0.0 ,
0.0.0.0.0
.
.........
O
Fig. 218.
Fig. 219.
Fig. 220.
figured repartition whose rows are all alternations,
or three alternations resulting from the combina-
...0
o . o.
• • •
...0...
o . o. o .
•
.O.
• O.O.O
.
O
O.O.O.O .O.
.O .O .
0.0.0.o .o .
0.0...0. o'.
Q.O.G.O.O.
O
•0.
.
O
0
0
oOoOoOoOoOo
OOOOOOOOOOO
OOOOOOOOO
•
OOOOO.OOOOOO
Oo •
oooOOOOOOOO
.0.0.0.0.0.0
..•°•@.0.0.0
0.0.0.0.0.
.•°•..
0.0.0.0.0.
.0..0.0
0.0.0.0.0.
.0.0.0.0
@
.O
0.00.6
••• O •••••
0.0.0 .o.o .
a ..
..
..
...
•
..0.0...
0.0.0.0...
Fig. 221.
Fig. 222.
Fig. 223.
tions two and two of three forms. The figure 219
is a figured repartition of which all rows are recur-
rences. The figure 220 is a figured repartition, all
of whose straight rows are alternations. The inter-
calary and alternate ranges are repetitions. The
figure 221 is a figured repartition which has all its


Theory and Analysis of Ornament175
nan
.
straight rows alternately one alternation and one
intercalation, its diagonal rows being alternately one
alternation and one repetition. The figure 222 is a
repartition by series or ranges, the vertical alter-
nately repetitions and alternations, and the hori.
.
• • o
ooo @ o Ooooo
A
.
o . o
O. @ o
o o
o
o
.
0.0
'o.o @oooo:
...oooooo
• oo •
.
• o
0.
0
.
O ooOOo oo
0
0
.
0
0
ooooooo
.
.
.
.
.
.
.
0 0 . 0 . 0 .
. ©
...
o
• oo
• oo • "
O
o
Fig. 224.
Fig. 225.
Fig. 226.
zontal recurrences. The figure 223 is a reparti-
tion by series. All the horizontal and vertical
rows are recurrences, the diagonal ranges being
..
o.
o
O
. . .0 .0 ..
OOO OOO OO.
0..
..00.
0
0
0
0
0
OO.OOOO.O
0
0
0
0
0
0
0
0
0
.
.
Oo.OO..
..OO.OOO
.
•
•
•
•
io · ©.o.oo
Fig. 227.
Fig. 228.
Fig. 229.
from left to right alternately alternations and re-
petitions, and from right to left repetitions.
2. Following the trellis network, and varieties of
this network. The figure 224 is a figured discon-
tinued repartition, determined by the summits, the
SILIIT


176
Theory and Analysis of Ornament,
middle of the sides and the centre of the mesh. The
figure 225 is a figured repartition, trigonal; a form
is placed at the summits, another at the centres, and
the third at the triparted sub-division of sides. All
the rows are intercalations. The figure 226 is in
series; all the rows are alternations or repetitions.
This figure can be considered as ordered following
a trigonal lozenge network; one form placed at
the summits, another following the middle of the
sides, and the third at the centres.
.
?
31
X!
2.-..
--
--
Qa6ó-e....
Fig. 230.
Fig. 231.
The figure 227 is in series ; the horizontal rows
and the oblique from left to right are recurrences;
the other oblique rows are alternations and repeti-
tions in alternate succession. The figure 228 is
figured ; all the rows are periods or a repartition
following the summits of trigonal network, then
alternately from trigon to adjacent trigon,
and are the repetitions of the second and third
form. The figure 229 has its horizontal rows
alternately alternations, repetitions and periods of
three and one ; the oblique rows are alternately
alternations and recurrences.


Theory and Analysis of Ornament.
177
III. REPARTITION OF Four Forms.
149. 1. Following the square and correlative
networks. The figure 230 and the figure 218 have
intercalated a fourth form, following the centres ;
all the diagonal rows, in 230, are recurrences.
The figure 231 is a mixed repartition with quartered
symmetry ; all the straight rows are alternations.
2. Following the trellis and correlative networks.
The figure 232 is analogous to the figure 231, all the
rows being alternations. The figure 233 is a figured

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Fig. 232.
Fig. 233.
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varied seriations resulting from the intercalation of
two series, one periodical, the other repeated.
IV. REPARTITIONS OF FIVE FORMS.
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150. The figure 234 is a figured repartition. The
horizontal and vertical rows are following in order
of recurrence, the rows being of three kinds : re-
currence of three forms, repetition of one form, and
alternation of two forms. The diagonal rows are
alternately one recurrence of four forms, one alter-
e
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178 Theory and Analysis of Ornament.
OS-O... A.
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nation of two forms, and one recurrence of three
forms. These diagonal
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current succession.
The figures 235, 236,
237, 238, 239 are squares,
whose abatements should
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Fig. 234.
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Theory and Analysis of Ornament.
179
THIRD SECTION.
AGGLOMERATED DISPOSITIONS.
151. This order of dispositions contains :-
1. Hypothetical or real agglomeration of atoms,
molecules or particles, which constitute the material
in its different specifications.
2. Composition of organized tissues or materials
of organism, which constitute the tissues or bodies
of the animal and vegetable world.
3. Natural or artificial agglomerations, deter-
mined by joining distinct elements, without any
bond other than the external cause constituting
them.
From the indefinite agglomerations to the de-
finite or figured dispositions there is a continued
passage preserved by indefinite or uncertain
groupings. Hence the three terms: agglomera-
tions which are indefinite; uncertain groupings;
and definite dispositions. These last form a dis-
tinct class, supplying itself by the principle of unity
or individuality which separates and determines
the individuals which compose it. This principle
of unity is organization in the case of living
beings, and composition or ästhetical elaboration
in the case of artistic works.
Uncertain groupings are portions or limitations
N 2


180
Theory and Analysis of Ornament.
of indefinite agglomeration, and constitute a
form-envelope independent of the inner arrange-
ment. These limitations are analogous to
material forms; and both are specified by the
conditions of an inner symmetry and regularity
correlative to the form-envelope. The form-enve.
lopes being brought into contact with the abstract
and geometrical forms essential to the uncertain
groupings and definite dispositions, a tree can
present a pyramidal configuration as well as a heap
of sand or a constructed pyramid.


Theory and Analysis of Ornament.
185
vern
ovals and circles. They have a real or imaginary
head-centre which governs the outline; and they
have not angular summits.
Marginal or diametrical ranges, instead of being
constructed by proportion of the straight headline,
can be by circular headline, i.e., a circumference.
Continued marginal ranges go either way; straight
marginal ranges have their axes directed externally,
or from the centre of circumference. Continued
diametrical, even or alternate, diagonal or contra-
dicted ranges go either way. Straight, quartered,
alternate or centred diametrical ranges have their
rectilinear headline bent, following the circum-
ference, and the axis perpendicular to this headline
coinciding with rays. Starting immediately from a
circumference, we can virtually find 1, 2, 4...8
... middles; we can also suppose 3, 6, 12 ... or
more. The case of only one middle is a ring; two
middles are directly opposite, and placed at the extre-
mities of the diameter; four middles at extremities
of two crossed diameters; six middles at the ex-
tremities of three diameters or six rays, and so on.
We can also divide the circumference in uneven
numbers of middles, 3, 5, 7 . . . &c.; only one or
two different middles for the arc, two or four
different ones for the oval, are the first division
adapted, naturally and simply, to the constitutive
symmetry of these figures.
CHAPTER IV.
RADIATED DISPOSITIONS. .
156. This class contains all the dispositions at


Theory and Analysis of Ornament. 187
COL
corresponding on both sides by straight, opposite
and alternate symmetry. These pennate forms
are articulated under angles which are, generally,
acute, and which determine a principle of general
unity; if the angles were straight they would have
a quartering centre which breaks the unity, because
it introduces two horizontal and vertical axes where
the vertical line prevails.
One portion of even, straight, alternate, dia-
metrical range can be considered as a pennate dis-
position. There is not, however, the declination of
size of compound forms; it is an essential declina-
tion which gives unity to disposition by making it
finished though it seemed indefinite.
Then, pennate disposition is determined by one
headline, one form-envelope and the principle of
declination, which has reference to size of forms,
to their inclination, and to their form and their
accentuation.
CHAPTER VI.
PALMATED DISPOSITIONS.
158. Palmated dispositions have a point or head-
centre and a headline which co-exist. The form-
envelope changes with co-ordination of disposition,
and with co-ordination of symmetry. It is necessary
to distinguish palmated dispositions from angular
desinences, and full inside palmated dispositions
from inside desinences and full outside dispositions.
Palmated dispositions are even or uneven. In the
first case the headline is an axis, the starting-


188
Theory and Analysis of Ornament.
25
point a radiating centre, and the figure-envelope
a symmetrical outline. The figure-envelope is,
generally, a handle or oval. It is necessary to
distinguish three principal varieties in this class
of dispositions: (1) Digitate disposition, when
all composing forms are of the same form, gener.
ally rectilinear; declination is only relative to the
respective size of forms. (2) Palmated disposi-
tions, properly so called, where declination is in
size, then inclination of accent and variation in form
of integral parts. And (3) Palmated dispositions
where composing forms are continued under a
radiating centre; in this case the point of insertion
is inside the figure-envelope, which is either poly-
gonal or oval, or rather an open arc or handle.
Two other varieties are also contained in this
order :-
1. Uneven palmated dispositions, which have no
rectilinear symmetrical axis, but an imaginary head-
line, on both sides of which the forms follow the
same or two different declinations.
2. Spread disposition or acanthus, which has a
symmetrical axis and imaginary centre, if it is the
diagram of every acanthus of ornamentation.
CHAPTER VII.
CURVED DISPOSITIONS.
159. Curved dispositions come from pennate and
palmated dispositions; they are realized by articula-
tion of forms following a curved headline. These


Theory and Analysis of Ornament.
189
dispositions have neither symmetry nor centre.
By supposing a real curved line, this headline
subordinates the forms on either side, or both at the
same time; and the declination being traced from
starting-point to sunmit there are six principal dis-
positions, as :-
1, 2. Forms articulated in convexity of the head-
line, and declined in one way or the other.
3, 4. Forms articulated in concavity of the head.
line, and declined in one way or the other.
5, 6. Forms articulated on both sides of the head-
line, and declined in one way or the other.
According as the curve is rolled more or less,
they have curved, long, hooked and round disposi-
tions.
ca-
CHAPTER VIII.
BRANCHED DISPOSITIONS.
160. Starting from declined polygonal delinea-
tions, or from a single touch, and symmetrically
repeating the successive branches, we get branched
dispositions, very varied, simple or compound,
following the mode of symmetry and uniform
number of successive parts. To this class of dis-
positions we can add the nerves of leaves or sub-
division of composed leaves, plane figurations of
trees, &c. The essential unity of this class of dis-
positions consists in declination of size or number of
integral parts, which are placed one on the other.
This declined ramification has, however, an actual
end, though we may conceive au indefinite sic-


190
2022
Theory and Analysis of Ornament.
cession. In a word, it is necessary to distinguish
the physical from the theoretical termination.
Closed figures, like polygons, circles, ovals, have
theoretical and physical limit.
CHAPTER IX.
ASSEMBLED DISPOSITIONS.
161. The essential unity of these dispositions is
in the diagram, forms generally being distinct and
Fig. 240.
isolated one from the other. The unity of form
surpasses the unity of grouping, and generally re-
mains distinct. That, however, does not stop the
articulation of parts, the one in proportion to the
other, or altogether in proportion to a figurative
diagram. Groupings of leaves on the branches
belong to this class.
162. Combined by syncretism, combination, con-
jugation, articulation, &c., these important definitions


192
Theory and Analysis of Ornament.
FIFTH SECTION.
CO-ORDINATED DISPOSITIONS.
163. This order contains all dispositions refer-
ring to the superficial extent of plane surfaces and
superfices of solid definite forms. All plane surfaces
with rectilinear outline, without radiating centre,
such as rectangles, lozenges, squares, &c., are
limited portions of multiplied dispositions. Poly
gons with circular dominant lines have outlines,
radiating axes, inscribed and derived figures, with a
proper centre, which governs all the system,
The diagrams of polygons are analogous to the
diagrams of circles; as :
1. Centred network.
2. The trellis networks.
In all these networks we can put the diagonal of
meshes, which forms three sorts of rows:-
1. Circular rows.
2. Radiated rows.
3. Spiral or diagonal rows.
Such are the essential foundations of disposition
co-ordinated of circles and regular polygons.
164. Generally, all the rounded and regularly-
constructed forms have lines of curvity or repartition,
which are joined to them. These lines of repartition
are the same as those of the plan, but changed by


Theory and Analysis of Ornament.
193
Sare
continuity or curvity inherent in the corporeal form.
Let us make use of these considerations with a few
kinds of surfaces.
1. A cylinder is capable of development; its sur-
face being the portion of a plan, its lines of reparti-
tion must be of three kinds_vertical, horizontal,
and oblique or diagonal. It results that the dis-
positions in series on the cylinder are :-
Rows following straight lines
Rings following circles.
Spirals following spiral lines.
2. A cone is capable of being developed, and its
surface is a portion of a circle; the lines of reparti-
tion are convergent straight lines, circles, and spiral
declined lines. The divided dispositions are the
same as those of circles.
3. Spheroidal surfaces. A sphere is not capable
of being developed, but its curvity being uniformi,
the lines of repartition determine uniform networks
like those in the plan. The sphere, like polyhedrons,
cannot be an aesthetical form.
4. Inflected surfaces. The lines of partition are
identical with the preceding; the only difference
consists in those lines which are abstract imagina-
tions, having opposite curvity.
165. All the indefinite dispositions of the first
class have their analogies in every disposition that
we can apply to forms or definite surfaces, as well
as to plain networks ; we can distinguish in these
repartitions crossing-points, lines and meshes, and
the ornamentation of surfaces is the same as plain
ornamentation.
cal


194
Theory and Analysis of Ornament.
Sixth SECTION.
CONSTRUCTED DISPOSITIONS.
lat
166. The disposition of this order results from
juxtaposition of definite solid elements, whether
these may have a determined form referring to the
grouping in which they occur or not; or, on the
other hand, the co-ordinated disposition may result
from the grouping of distinct elements.
Generally, the agglomerations, groupings and
constructions of a number of objects or materials,
brought in contact, determine definite disposition,
according to one or several of the following
conditions:-
1. The number of objects is limited.
2. The objects have definite forms, and are
correlative one with the other.
3. A headline determines the grouping or
organization.
4. The will and power of man, put in work,
juxtaposes materials.
The arrangement of foliages, branches, bouquets,
garlands, wreaths, &c., is contained in this order of
dispositions.


Theory and Analysis of Ornament.
197
Range 14 (see Fig. 241) is obtained by alterna-
tion of two quartered and even forms.
Range 15 the same as 14.
Range 16 by alternation of quartered and re.
volved forms.
169. These ranges are the result of the repetition
of close forms of the sixth class.
By following the continued delineations, it is
easy to see that the ranges are intersecances, deter-
mined by the conjugation of the forms shown in
Fig. 242.
Denticulation 1 (Fig. 242) is even marginal,
wherefrom are two figures or positions.
&23&srs
Fig. 243.
are uneven
Denticulations 2 and 3, 8 and 9, are uneven
marginal, wherefrom are four positions.
Denticulations 4 and 5 are diametric alternate,
wherefrom are two positions for each of them.
Denticulation 6 is diametric diagonal, wherefrom
are four positions.
Denticulation 7 is diametrical contradicted,
wherefrom, are four positions.
From these figures, which combine two and two,
and are intersected, we may determine a number
of ranges, in which are contained the preceding
examples.
These denticulations are themselves determined
by the conjugation and repetition of the small
number of forms shown in Fig. 243.


Theory and Analysis of Ornament. 199
Map 1 (Fig. 245) is obtained by followed repeti-
tion of a quartered form and the straight abate-
ment of range 1 (see p. 195, and Fig. 241).
Map 2 by followed and turned abatement of
range 4.
Map 3 by followed and turned abatement of
range 3.
Map 4 by followed abatement of range 5.
Fig. 245.
Map 5 (Fig. 246) is obtained by followed abate-
ment of range 6 or 8 (Fig. 241).
Map 6 by returned abatement of range 6.
Map 7 by followed abatement of range 7.
Map 8 by followed and turned abatement of
range 8.
Fig. 246.
Map 9 (Fig. 247) is obtained by followed abate-
ment of range 10 (Fig. 241).
Map 10 by followed alternate abatement of
range 11.
Map 11 by followed alternate abatement of
range 12.


200 Theory van
.
Nan
and Analysis of OrnamentMap 12 by returned or alternate abatement of
range 13.
Map 13 (Fig. 248) is obtained by abatement of
range 14 (see Fig. 241).
Map 14 by abatement of range 15.
Map 15 by abatement of range 16.
Map 16 by alternate abatement of range 16.
12
10
Fig. 247.
The repartitions being conjugated two and two
by intersecance, we should get, for example, Fig.
249, obtained by intersecance of repartitions 6 and
Fig. 248.
13; or on the contrary, these repartitions could
be divided into two, as No. 7, which is composed
of two repartitions (Figs. 250 and 251). The
Fig. 249. Fig. 250. Fig. 251. Fig. 252.
figures 250 and 252 conjugated by intersecance,
produce repartition No. 16.


204 Theory and Analysis of Ornamentnan
.
tions (Fig. 255); 3, the segment being even,
simple or varied, and the lozenge being a square, we
get the third form of imbrication, the one of four
directions (Fig. 256); and 4, the segment being
even or uneven, simple or varied, and the lozenge
being trigon, we get the fourth form of imbrication,
the one of three directions (Fig. 257).
This form is analogous to the third one, and
can be conceived as constructed by the successive
and return abatement, in two directions of a revolved
form inscribed in the square. The three forms of
imbrication, with one, two, and three directions, are
corresponding to the three moods of juxtaposition
of lozenges.
CHAPTER IV.
COMPARTMENTS AND ADJCSTMENTS.
175. All the denticulations, varied as they are,
are reduced to three fundamental linear elements:
uneven touches, even touches and diagonal touches,
whose forms or figures can be very different.
These touches succeed regularly in a straight line
and follow the different moods of conjugation
to determine the denticulations. The crossing
of these denticulations, following the lines of net-
works, determines trilateral or quadrilateral meshes,
whose outlines are formed by fundamental touches.
Taking, for example, 1, of even form, an arc which
would be the fourth part of a circumference, and
inscribed, following the diagonal of a square ; 2, of


Theory and Analysis of Ornament.
205
uneven form, a curved line inscribed in a rectangle ;
3, of a diagonal form, two arcs joined by inflection;
then constructing the figures following the four
quarters, determined by the axes which are cut at
right angles, we obtain the following meshes :-
I. MESUES OBTAINED FROM EVEN FORM.
176. Two rounded forms are conjugated, i.e., are
implicated. The networks which result from them
have thus two sorts of meshes; the last two
forms are also conjugated.
The third form, which is diagonal, determines a
network with mesh of one kind. The fourth form,
which is even, determines network with mesh of one
kind. If the even form were oblong, i.e., inscribed
in a rectangle, it would be an uneven form.
II. MESHES OBTAINED FROM UNEVEN FORM.
177. The two first forms are of quartered sym-
metry, and are both conjugated in one uniform net-
O oooooo
Fig. 258.
work (Fig. 259, 1) analogous to one of Fig. 245, 1.
The next two forms are even, and separately
determine two varieties of imbrication with one
direction; but they are also conjugated, and deter-
mine conjointly a network or varied imbrication,
with two kinds of meshes (Fig. 259, 2) analogous
to the figure 256. The fifth form is diagonal, and
determines a network with mesh of one kind.


Theory and Analysis of Ornament.
207
III. MESHES OBTAINED FROM Diagonal FORM.
178. The figures obtained by the quartering of
diagonal touch are only four. These figures are
o
♡
♡
Fig. 261.
round if the touch is inscribed in a square (Fig.
261), and oblong if the touch is inscribed in a rect-
angle (Fig. 262).
Fig. 262.
1, l' is quartered; it determines
The first form
Fig. 263.
one adjustment or uniform network, composed of
only one sort of mesh (Fig. 263).
The second form 2, 2' is even ; it determines two



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