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THE
CABINET-MAKER AND UPHOLSTERER'S
GUIDE:
BEING A
COMPLETE DRAWING BOOK;
IN WHICH WILL BE COMPRISED
TREATISES ON
GEOMETRY AND PERSPECTIVE,
as applicable to the above branches op MECHANICS ;
The Definitions and Problems explained in the most plain and familiar Terms, with much new matter introduced, and ihe Diagrams
rendered at once entertaining and practically useful. The whole Illustrated by a Series of Instructive Examples, and
XVUlMEEROirS ENGRAVINGS.
TO WHICH IS ADDED, A
COMPLETE SERIES OF NEW AND ORIGINAL DESIGNS
FOB
HOUSEHOLD FURNITURE, AND INTERIOR DECORATION,
In the most approved, elegant,and modern Taste,
BEAUTIFULLY ANDCORRECTLY COLOURED,
PROM THE ORIGINAL DRAWINGS ;
And accompanied with Vsi^nl and Practical Instructions for the Manufacture of the same.
INCLtDING ,
PL.1NS, PROFILES, AND A SCALE TO EACH, WITH THE MOUIiDINGS ENIiARGBD, FOH ASSISTING THE
WOKKMAN ; VIZ.,
Drapekies, Curtains, Beds, Canopies, Cornices.-^Chairs and SpFAs for Drawing-Rooms, Parlodrs, Libraries,
Halls, &c. — Ottomans, Seats, Chaise-Longue,— Writing, Wohkj Dressing, Library, and Card Tables. — Side
boards, Celerets, Book-Cases, Secretaires, Commodes, WabCrobes. — Vases, Tripods, Candelabras, Lustres,
Girandoles, Lamps, Mirrors, Pier Glasses, Chandeliers, CattiNEY Ornaments, Screens, &c. &c.
comprising likewise,
INSTRUCTIONS AND EXAMPLES IN THE ELEMENTAllY PRINCIPLES
OP
ORNAMENTAL FOLIAGE, &c.
Enabling the Student to draw with facility and correctness in this so generally useful branch Of the Att ; with numerous
Original Compositions, adapted for Tablets, Friezes, &c. for the use of Carvers— Painters — Modellers — Masons —
Smiths, &c. and all the various workers in Metals, &c.

By GEORGE SMITH,
VphoUierer and Furniture Draughtsman to HIS MAJESTY ; Principal of the Drawing Academy, Brewer Street, Golden
Square ; and Author of various Works on the Arts of Design and Decoration.

LONDON:
PUBLISHED BY JONES AND CO.
TEMPLE OF THE MUSES (Late Lackington's), FINSBURY SQUARE;
AND MAY BE HAD OF ALL BOOKSELLERS.
1828.


YALE


INTRODUCTION

Historical View of the Origin ofthe Art in this Country. — First Specimens introduced
iy the Norman Invasion. — Ornaments derived from Cathedrals and Ancient
Edifices. — Mr. Cotman's Work. — Reign of Richard II. — The Norman and Saxon
Style superseded by the florid Gothic during the Reigns of Henry I, II, and III. —
Distinguishing Feature of the Taste from this period to the Reign of Elizabeth. —
Progressive Improvement continued. — Age of Louis XIV- — The old system super-
sede/jl by the Arabesque Style. — Importation into England. — Continued to the early
part of George III. — Messrs. Chippendale's and Ince's Works. — A total revolution
in Taste, introduced by the Messrs. Adams. — Improved by Mr. James Wyatt. —
Perfection in Ornament, S^c. reserved for the present time. — Effect produced by
Mons. Denon's Work. — The Author's flrst Work on Furniture and Design super
seded by later Improvements. — By what Cause Produced — Intended Object arid
Plan of the Present Work,
IN a w^ork treating wholly of Domestic English Furniture, it
can scarcely be considered irrelevant, to precede it with a short
historical view of the earliest style, variations, and progressive
improvements that have taken place up to the present period.
As far as research so remote, can enable us to form any judg
ment on this subject, the Norman invasion of our island appears
to have afforded the earliest specimens of what constituted the
Domestic Furniture of that warlike age.


iv INTRODUCTION.
It is probable that in proportion as their manners were simple,
and luxury was unknown, their Domestic Furniture would com
prise utility, divested of ostentation. No doubt the conqueror
and his nobles brought with them the taste of their country ; for
in the very few specimens that time has spared of the style of that
age, we can only distinguish the bold projecting mouldings on the
legs supporting their tables and seats, and wherever ornament
was adopted, it appears to have corresponded with those used in
their cathedrals ; examples of which may be seen in Mr. Cotman's
accurate drawings, made from the ancient edifices, and from which
it is evident that their artists were not unacquainted with the
Grecian elegance of composition.
From this period to the reign of Richard II, the Baronial
castle alone offers any example of domestic furniture. The same
siniple style seems to have been followed, but withthe addition of
more enrichment.—During the reigns of the three first Henrys,
the Norman and Saxon architecture gave place to the pointed
and florid Gothic, changing in a great degree the feature
of domestic furniture. The taste of these times down to the
reign of Elizabeth, is distinguishable in the light spiral columns
in the backs of chairs, the spiral twisted column in the legs of
their tables, the variety and beauty of their turned mouldings, and
in an excessive use of ornament, no way to be compared in ex
cellence with what preceded.
From this period, and during the fifteenth and sixteenth
centuries, under Louis XII, and Francis I, of France, at which
time some distinguished artists existed, and until the age of Louis


INTRODUCTION. v
XIV, the taste in decoration appears to have progressively
improved. At this period, the whole system seems to have given
place to a style completely Arabesque, although blended with much
grandeur peculiar to this taste, and brought to great perfection by
the artists then employed in its manufacture. — The importation
of it into England changed the whole feature of design, as it re
lated to household furniture, in our houses and mansions. This
taste continued almost unchanged through the reign of George II,
and the earlier part of George III. The elder Mr. Chippendale,
was, I believe, the first author who favored the public with a work
consisting of designs drawn from this school, with great merit to
himself, however defective the taste of the time might be. To
this work succeeded that of Mr. Ince, in the same style. From
this period to the time of Messrs. R. and J. Adams^ the same
species of design continued, with little or no alteration, until the
researches of these scientific Gentlemen in architecture and orna
ment, in Rome, Dalmatia, and other parts of Italy and Greece, were
made public. A complete revolution in the taste of design imme
diately followed ; the heavy pannelled wall, the deeply cofl'ered
ceiling, although they oflfered an imposing and grand eflFect, gave
way to the introduction of a light Arabesque style, and an orna
ment highly beautiful. But the period for the introduction of not
only a chaste style in architecture, but likewise of ornament (and
which extended itself to our domestic movables), was reserved
for the late Mr. James Wyatt, whose classic designs will carry his
name to posterity with unimpaired approbation. Here it would
appear almost unnecessary for invention to have gone further, but


vi INTRODUCTION.
perfection, it appears, was reserved for the present period, in
relation to ornament and domestic embelUshment. In the year
1804j Mons. Denons' grand publication, detailing the antiquities
of Egypt, becarae public. The novelty displayed throughout
these fine specimens of art, caUing to recollection so distant a
portion of ancient history, gave rise and life to a taste for this
description of embelUshment. At this period, the author was
induced to lay before the public, a Collection of Designs for
Domestic Furniture. This work, however highly appreciated at
the time, has become wholly obsolete and inappUcable to its
intended purpose, by the change of taste and rapid improvements
which a period of twenty years has introduced. The travels of
scientific men — the publications within the last twenty years — ^the
Elgin marbles, all alike detailing the perfection of Grecian archi
tecture and ornament ; the beautiful specimens contained in Sir
William Gell's work on the Remains of Pompeii — the inexhaustible
resources for beautiful outline in the Vases of SirWilliam Hamilton,
if no other causes had existed, would surely have been sufficient
to account for the present elegant and refined taste. In this
highly improved state of the fine arts, a work on domestic
furniture, comprehending every iraprovement to the present day,
may be considered necessary as well as acceptable to the tratle,
and has induced the author to compile this volume, containing,
not only a large cox,l,ection of original, designs, in the
various schools of the art, but also to add to it instructions in
drawing, suflBcient to make any one a draftsman in his own person.
For this purpose, a portion of GEOMETRY is of the greatest


INTRODUCTION. vii
consequence, and scarcely to be dispensed with ; the knowledge
it gives of the power of lines is without limit, and the assistance
it affords in the practice of Perspective, great and extensive. —
PERSPECTIVE DRAWING is of equal use to everyone, who
would wish to place the object of his invention under the most
intelligible and natural position before a spectator, and renders a
treatise on it a necessary appendage to such a publication.
Some works on domestic embellishment have lately been
published, wholly in outline; this kind of design may answer ex
tremely well for the architect, but is of little use to those who cannot
readily make out all the projectingpartsfromaplan; this, perspective
will accomplish, and a design made out under its rules, will not only
give a natural and pleasing representation of any object, but convey
all its projecting and receding parts with clearness to the observer.
ORNAMENTAL DRAWING is Ukewise an acquirement every
Artisan ought more or less to be acquainted with, and is of pecuUar
advantage to the Cabinet-Maker and Upholsterer, in the embel
lishment of his designs. Instructions, therefore, in this elegant
branch of Art, should forra a coraponent part of the DRAWING
BOOK, so as to become of general use.
With an experience of forty years devoted to the study of
these subjects, both in theory and practical application ; and
having been honored with the patronage of HIS PRESENT
MAJESTY, as well as the most flattering testimonies from
Mr. Thomas Hope, and other individuals, distinguished by
their researches, and liberal patronage of the Arts ; the
Author trusts he may without presumption, promise to produce


vm

INTRODUCTION.

a Work at once creditable to his own labors, and combining
whatever is of real utility to those connected with the Cabinet-
making and Upholstery trade — a work, in short, the most complete
in itself, and superior to any that has hitherto appeared on the
same subject.
Our vessel now launched, may she encounter prosperous
gales during her voyage over the extensive tract she is destined
to sail ; and that her freight may prove extensively useful, as well
as beneficial, is the sincere wish of the author,

GEORGE SMITH.

41, Brewer Street,
Golden Square, London,
April 8, 1826.


CABINET-MAKER AND UPHOLSTERER'S
GUIDE,
§•0. Sj-c.

GEOMETRY,
Should commence with the definition of terms, and first with that of
points, proceeding next to define the nature of lines, angles, surfaces and solids.
I cannot agree with some authors who conclude Euclid's definition of
the point to be useless, inasmuch as the thing in itself is self-evident.
There are many reasons for adopting a different opinion ; first, a series
of points constitute a line, a series of lines produce a surface, and a series of
surfaces generate a solid.
There are in perspective, points of intersection, points horizontal,
station points, points of distance, and vanishing points, &c. each requiring
explanation to render them familiar to the mind, as they pass under con
sideration in practice.
A POINT, is that which is without parts or magnitude — is the least part
of matter, and thus called a physical point.
For example : — such is the poiat made by the compasses, pencil or
ink, as the point A, in Geometry, Plate 1. a scries of points put together,
in length form right or curved lines, such are the lines figured AiV, 5jr.
A line of points a b, tig. 6, supposed to move from a towards c, will in
its course downwards, generate a plane abed.
The mathematical point, is the least object possible to be conveyed to
the imagination, and consequently invisible ; it is without dimension, but is
the beginning of every invisible length.


2 GEOMETRY.
Given point, is a point proposed to be set in some place, whether de
noted by compasses or pin. For example: the point B, fig. a a, is a point
given, for this reason, that on that spot is placed a pivot.
Point of intersection, is a point where many lines cross or meet each
other. For example : the point G, fig. 1, is the point of intersection,
because the walls H G D, E F C, meet together at the point G.
Horizontal points, are points equally distant from the centre of the
earth ; such are the points h h h, fig. 2, and a series of such points constitute
the entire surface of the globe. N.B. Their use will be explained in de
scribing the horizon in perspective.
Point of incidence, is a point where one line meets or touches another
line or superfice, and there makes an angle. Example : the point I, in fig.
I A, is the point of incidence, because it is the point where the right line
K I, meeting the right line L M, makes there an angle.
Point of contact, is where a right line touches a curved line, in such
manner, that being produced or extended it will not cut the curve, or it is a
point where two curved lines meet together vi^ithout cutting. Exaraple : the
point N, fig. 2, is the point of contact ; because it is the place where the
right line O N touches the curve, and being prolonged or extended to P, it
does not cut the curved line N Q R ; for the same reason the point Q is the
point of contact.
Station point, is a point where we would place a staff, or the foot of any
mathematical instrument in surveying. Example : the point T, fig. 3, is a
station point; because it is the place on which we would put the instrument
O, N.B. this also will be further explained in the perspective.
Point of distance, or extent, is a point or any other mark observable
in some part of an object to be measured. Example : the crossed arrows
in the building at V, fig. 3, serve as a point of distance ; because the mark,
or point V, is one of the points necessary towards enabling us to ascertain
the inaccessible height, X W. LINES.
A line, is a length without breadth.
The mathematical or intellectual line, is that which we imagine to pass
from one object to another without being visible. Example : the line A B,


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GEOMETRY I.
DEFINITIONS. OF POINTS

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GEOMETRY. 3
"fig. 1, or the line C D, fig. 2, are each mathematical lines ; because supposed
to be invisible.
The physical or visible line, is that made by the motion of a physical
point, and which is drawn with the ink, pencil or any other material.
Example : the line E F, fig. 3, is a physical or material line ; because it
is made by something rendering it visible.
A right line, is that which is equally comprised between its extreme
points. Example : the line G H, fig, 4, is a right Une, because its points
are equally disposed betwixt the extremities G and H, neither rising
nor descending one more than another ; so that if we view this line G H,
from its extreme as at G, that first point G, shall cover all the other
points which we suppose to be contained from G to H, for generating the
right line G H. Remark, that a right line is the shortest distance betwixt
one point and another.
The extremities of lines are points; Example : the extremities of the
line N, fig. 5, are the points I K.
Indefinite or indeterminate line, is a line drawn of any length we
choose, being at liberty to make it more or less extended. Example : the
line L M, fig. 6, is an indefinite line, beeause it is supposed not to be deter
mined, being at liberty to make it longer or shorter at pleasure.
The definite or given line, is tbat contained in a certain length. Ex
ample : the line O P, fig. 7, Geometry, Plate 2, is a determinate line,
because its limits are from O to P.
Perpendicular line, is a right line, which falling on another right line,
makes the angles on each side equal. Example : the line Q R, fig. 8, is
perpendicular upon the line S T, because falling on the line S T, it makes
the angles R Q S, R Q T, both equal to right angles ; for the same reason
the pillar A, fig. A, is said to be placed perpendicular or plumb to the horizon
or ground B, because it makes right angles with the horizon ; remark also,
that a line charged with a plummet at one of its extremities, as at N, fig. N,
makes a perpendicular line, called by workmen a plumb line.
Inclined iine, is that which, falling on another line or on some plane, is
neither perpendicular nor horizontal to the line or plane on which it falls ;
but is slopwise. Example : the line V U, fig. M, is inclined in respect to
the line W X.


4 GEOMETRY.
Parallel right lines, are such as being in the same plane, and drawn apart
the one from the other indefinitely, will never meet. Example : the right
lines ab, c d, ef, fig. 9, are parallel lines, because, being in the same plane
and drawn apart, they will never meet or cut each other. Lines are in
general called parallel lines, or simply parallels, being such as are equally
distant from each other in their extent : thus the curved lines g h, i k, fig.
10, are called parallels, because the smaller curved line i k, is equally distant
in its course with the longer line g h.
Ordinate lines, are lines parallel to another line serving as a base to a
parabolic figure. Example : the lines o o, y z,w x, v u, s t, fig. 11, are called
ordinate lines, for this reason, that they are parallel to the line P Q, the base
of the parabola P Q R.
Horizontal Line, called likewise the line of apparent level, is that which
touches or cuts at right angles, a line tending to the earth's centre. Ex
ample : The line N, N, fig. 12, is an horizontal line, because it cuts at right
angles the line C D, tending to the earth's centre at D, and aU lines which
are parallel to the line N N, such as M M, L L, in the same figure, are called
horizontal lines.
Level Line, is that which is drawn horizontally, by an instrument called
the level. Example : the line Q R, fig. 13, is termed a level line, inasmuch
as it is level with the horizon, being drawn along the lengthened side, S T Oi
the level V, adjusted horizontally by the plumb line U.
Diagonal Line, or simply a diagpnal, is a right line, which being drawn
in a square or parallelogram, from one angle to the opposite, divides them into
two equal parts. Example : in the square W, X, Z, Y, fig. 14, the line
W Y is a diagonal, because it passes from the angle X, W; Z, to the opposite
angle X, Y, Z, and divides the square W, X, Y, Z, into two parts, or equal
triangles. W, X, Y, and W, Z, Y. The same applies to the parallelogram
W, X, Y, Z in the same figure.
Line of sight or visual ray, is a line formed by the eye in viewing an
object, either by means of stakes, the quadrant, or other instruments. For
example: the line A B, Geometry, Plate 3, in fig. 15, is the line of sight
or visual ray, because it is formed by the eye in viewing the object C,
through the telescope D.
N. B. This Une is of great use in perspective.


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GEOMETRY.

ANGLES.

A plain angle, is the inclination of two lines, the one towards the other,
and indirectly touching in a plane or surface. Example : the two lines,
CD, ED, fig. 16, PLATE 3, form an angle C D E, because the two lines,
C D, E D, touch indirectly at the point D ; that is to say, the two lines
which are drawn on the same plane do not form one right line, and therefore
form the angle C D E. Remark, that the middle letter in all triangles ex
presses the angle ; D therefore is the angle forlned by the two lines C D,
and D E, likewise the angle of any figure is generally expressed by a single
letter, as D.
Right lined angle.— The angle, A, B, C, fig. 17, is a right lined angle,
because it is formed by the two right lines, A B, A C.
Curvilineal angle, is an angle formed by two curved lines. Example :
the angle C D E, fig. 18, is curvilineal, because it is formed by the two
curved lines, CD, ED.
Mixtilineal angle, is an angle formed by a curved and a straight line.
Thus : the angle F G H, fig. 19, is a mixed angle, being formed by the
straight line, F G and the curved line H G.
N. B. The lines forming any angle are called its legs.
An angle is said to be less than another, wheu its legs are more inclined «
to, or nearer each other ; let there be two lines, A B, A C, fig. 20, meeting
in the point A. Now ifyou imagine the legs A B, A C. to be moveable on a joint
at A, it is easy to comprehend that the further they are opened or parted
from each other, the greater will be the angle between them ; and, on the
contrary, the nearer they are brought together, the more they will incline to
each other, and so the angle betwixt them will be less, as D E.
The angle of a polygon, or figure of many angles, is that formed by any
two sides of the figure. Example : the angle, K, fig. 21, is the angle of a
polygon, because it is made hy the two sides I K, K L, of the pentjigon,
IKLMN. External angle, is that angle which has its point without the figure- ^x-
ample : the angle, N M L, fig. 21, is an external angle, because its ppint is
without the figure, IKLMN.


6 GEOMETRY.
Internal angle, is that which carries its point within the figure, such as
the angle N O I, in the pentagon I K L M N, fig. 2 1 .
All angles are measured by an arc of a circle, containing a certain
number of divisions or degrees of the whole circle. In order to have a clear
idea of which, we shall proceed to lay down the divisions, as settled by geo
meters, in dividing the circle's circumference, and at the same time furnish in
structions for inaking such divisions, before we commence describing figures
cf many angles.
The circle by all geometers is divided into 360 parts, otherwise termed
degrees. Thus the circumference of the circle, A B C D E F G H, fig. 22,
PLATE 4, is supposed to be divided into sucli k number of parts or degrees.
It is evident the divisions will be less in a small circle than in one more
extended. Thus the circle, abc defg h, though smaller, contains the same
number of degrees as the larger circle, in consequence of both generating from
the same central point S.
The line A B, dividing the circle into two equal parts, the arc ABC
will necessarily contain 180 degrees, the half of 360, and is called a semi
circle. The line C D, perpendicular to A B, and passing through the circle's
centre at S, will divide it into four equal parts, of 90 degrees each, four
times ninety making the whole number 360. If the arcs A C, C B, B D,
D A, are subdivided at E, G, H, and F, the circle will then be divided into
?eight equal parts, of forty-five degrees each ; eight times forty-five, making
the whole number 360, as before.
The semicircle, ABC, fig. 23, PLATE 4, represents the protractor in a
Case of Instruments, (of the whole of which, with the latest improvements,
and their proper uses, a description will be given in course of the work),
the outermost line ABC, being gradated from A to C, into ] 80 equal
parts or degrees. The angle A I D, is found to contain forty-five of these
degrees, and is the side of an octagon. The angle E I F, is found to contain
sixty degrees, and is hence the side of a sexagon. The angle G I H, is found
to contain seventy-two degrees, and is therefore the side of a pentagon. The
angle A I B, contains ninety degrees, and becomes the side of a square.
The angle KIL, contains 120 degrees, and furnishes the side of a triangle
and thus - may be laid down the angle of any figure, from ten degrees
and upwards, to within one degree of 1 80, when it becomes a straight line.


PLATE XLV.

IF.

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GEOMETRY.

To divide tke circle into 360 parts or degrees.
Let the line A B, fig. 22, PLATE 4, be the proposed diameter of the
circle, to be divided into two equal parts at S, and describe the circle A C
B D, on A, with any opening of your compasses, greater than A S, as A A.
Describe two arcs at 1 1, then on B. With the same opening of the compasses,
describe two other arcs K K, cutting the arcs 1 1 at L L ; through their in
tersection, draw the line C D, which passing through the centre S, will be
perpendicular to A B, and the circle will then be divided into four equal parts ;
on A and C, with any radius A i, more than half A C, describe two arcs,
cutting each other at k ; and draw the line k S, indefinite to /; on B and C,
describe two other arcs with the same radius, cutting each other at m, and
draw m S, indefinite to o, which will then subdivide the arcs A C at E, C B
at G, B D at H, and D A at F. The circle by this process becomes divided
into eight equal parts. Next proceed and divide any one of these eight
parts, as A E, into three equal parts atjoja, and these three parts again into
three other equal parts, and you then have nine divisions in an eighth part
of the circle : divide the remaining parts into the same proportions, there
will then be 72 divisions round the circle, of five degrees each, equal in
the whole to 360. To obtain the degrees, divide any one part, as M, into
five parts, and each other part into a like division ; the whole circle will
then be divided into 360 equal parts or degrees.
The use of the circle so divided, is to enable the student to lay down
an angle of any number of degrees he may require, whether for the triangle,
pentagon, sexagon, octagon, or any other figure of many sides.
A right angle, is that which is made by a right line, falling perpen
dicularly on another, or which contains in its opening the fourth part of the
circumference of a circle, described from its point, or which contains 90
degrees out of 360, the circle's whole circumference.
Example : the angle ABC, fig. 24, PLATE 3, is a right angle, be
cause the line A B, falls perpendicular on B C, at the point B ; or because
the angle contains in its opening the fourth part of a circle, described from
the point B of the angle ABC.
Remark, the right angle is ordinarily called by workmen a square angle.


8 GEOMETRY.
for instance ; the angle DEF, fig. 25, is a square angle, because it is made
by means of the square G.
An obtuse angle is greater than' a right angle, or that which
contains more in its opening than a quarter of a circle. Example : the
angle H I K, fig. 26, is obtuse, because it exceeds the right angle, L I K,
or because it contains in its opening more than 90 degrees, or more than a
quarter of the circumference of a circle^ described frcftn the point I of the
angle H I K. Workmen call the obtuse angle, a full angle, because it is
more open than the square angle V,
An acute angle is less than a right, angle, or that which contains
betwixt its lines less than the quarter of a circle, or less than ninety degrees.
The angle MNO, fig. 27, is acute, because it is less than the right angle
P N O, as it contains between its two legs, less than 90 degrees, or a quarter
of the circumference of the circle described from its point N : the acute
angle is termed by workmen, a lean angle, Isecause it is less than the square
angle X. "' .^ TRIANGLES.
A triangle, is a plain figure bounded by three lines, and containing as
many angles. Example : the triangle ABC, fig. 28, PLATE 5, is a plain
triangle, because it is bounded by the lines A B, B C, and C A.
The triangle ABC, is likewise called a right lined triangle, because
its lines are all right or straii.
Mixed triangle is that which has two of its sides curved, or sometiraes
only one, such are E and F, fig. 29 and 30.
EquilateraFtriangle, is that which has its three sides equal ; thus G, fig.
31, is an equilateral triangle,- because its three sides HI K, are all equal.
A right angled triangle, is that which has one right angle. The triangle
L M N, fig. 32, is a right angled triangle, because M is a right angle Of 90
degrees. Observe that in all right angled triangles, the line opposite the right
angle, is called its hypothenuse ; the line L N, is the hypothenuse of the
right angled triangle L M N.
Scalene triangle, fig. 33, is one which has its three sides unequal; the


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GEOMETRY 9
triangle GHI, fig. 33, is a scalene triangle, because its three sides are of
different lengths, the side O I, being longer than that of G H, and the
side G H longer than H I.
Isoscele triangle, is that which has only two sides equal. The triangle
DEF, fig. 34, is an isoscele triangle, because the two sides D F aad D E,
are of the same length ; but it is possible for the side F E to be longer than
either of the two sides D F, D E.

FIGURES.
A square, is a figure in which the four sides are equal, and the four
angles are right angles. The square A B C D, fig. 35, is termed a perfect
square, because its four sides are equal, and the four angles equal. The square
likewise, in practical geometry, is termed equilateral square, right angled
square, and parallelogram, because it has its four sides equal or of the same
length, its four angles are right angles, and its opposite sides parallel.
The long square, has its four angles right angles, but all its sides are not
equal. E F G H, fig. 36, is a long square, because its four angles are right
angles, and its four sides are not equal, having two sides longer than the
other two ; this long square is sometimes called oblong square, right angled
parallelogram, or simply rectangle.
Rhomb, is a figure, having four equal sides, but not equal angles; KLMN,
fig, 37, is a rhomb, for the reason that the four sides are equal, and because
its four angles are unequal^ jhavuig the two angles K L M and K N M
obtuse, and the other two opposite angles N K L and N M L acute.
The Rhomb, is sometimes termed lozenge, and sometimes equilateral
Rhomb.
Rhomboid, is a figure wjiich has its angles, .gs likewise its opposite sides,
equal betwixt themselves, being neither equilateral nor rectangular. O P Q R,
fig. 38, is a Rhomboid, beca»se its twp opposite sides, O P Q R, which are
parallels, are longer than the other two sides P Q, O R, which are equal
and parallel betwixt themselves, and the four angles are not right angles.
The opposite angles O P Q and O R Q are obtuse, ^d the two other oppo
site angles POR, P Q R, are acute.


10 GEOMETRY.
Trapezium, in general, is another square figure, besid^r" the preceding
parallelogram. AB CD,, fig. 39, is a trapezium, because it is a square
figure, or of four sides, and which has not all its sides parallel.

Polygonal, or many-sided figures,
Are such as are composed of more than four right lines ; the pentagon
is a many-sided figure, being right lined, and having five sides and five
angles, such is fig. A, Plate 6.
The hexagon, or sexagon, fig. B, the octagon fig. C, and all figures
having their sides as well as their angles equal, are included under this
term, as also all irregular figures of any number of sides whatever.

Arcs, and their summits
An arc is a portion or part of the circumference of a circle, being neither
one half nor one fourth of the whole ; the dotted part D E, fig. D, of the circle
I F G H, is an arc, because it is less than the fourth, I F, of the circumfer
ence ; the remaining part I H G F is also an arc, because that part is greater
than the fourth or half of the circumference.
Summit of an arc, in general implies the central point of the arc ; such
is K, fig. E, because it is in the middle of the arc L K M ; summit of an arc,
is also the point where an arc would touch a line. As regards the line
O P, the summit of the arc O K P is the point K, because it is the point
where the arc touches the lirle O P.

Planes, and super/ices.
A Plane, in general signifies a space or superfices, bounded by one or
more lines, such are the figures R, S, T. In relation to these figures the
space included within their lines is called a plane. Remark, that all figures
having right lined or curved sides, whether regular or irregular, are planes
when considered as possessing length and breadth without thickness.


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GEOMETRY. 11
There are convex and concave superfices or planes, such are the figures
V, being convex, and W; concave surfaces.
Parabolic superfice or plane, is a space terminated by a right line and
by part of an oval, such is a c, fig. X.
Plane or section of a body, is a superfice or flat section, made by a
line ; the section d, of the globe E, fig. Y, by which we see the two super
fices F, and G, is what is called a plane or section, because those two super
fices are made by one and the sarae section, which is without thickness.
Surface, or superfice, the air, space, extent, &c. are all synonymous ;
names serving to express the space contained within the boundaries of any
figure. Ellipsis or oval.
An ellipsis or oval, is a plane figure bounded by a curved line, falling into
itself, which is not uniform or circular in any part, but varying continually ;
being described by two points, called its foci. The further' these points are
asunder, on which the ellipsis is described, the more it is drawn out or
lengthened. The periphery or circumference, is the curved line that bounds the ellip
sis A "B C D, fig. X, Plate 7.
The centre of an ellipsis, is the point E, where any two diameters at A
C, or B D, intersect or cross each other.
Diaraeter of an ellipsis, is any right line, as B D, or G F, passing through
the centre, and terminated by the periphery^
Transverse diameter, is the longest line, such is A C.
Conjugate diameter, is the shortest line, for example, B D.
Ordinates, are right lines drawn parallel to the conjugate of any diame
ter, such are H I, and K L. Plan or Draught.
A plan or draught, in general signifies a space or superfices, bounded
hy one or raore right lines.
In drawing and design we distinguish three kinds of plan or draught.
1st. The Ichnographic Plan (geometrical, or simple plan,) is that
which represents by lines and angles, the space or figure, that is to contain


12 GEOMETRY.
some elevated body to be erected above the ground. Example : the plan
Y, is an ichnographic plan, because it represents in plain lines the outline,
or ground plot, occupied by the building Z.
2nd. The Orthographic draught or elevation, is the simple representa
tion of the height of a body, building or other object, with its component
parts, without reference to its substance. The figure Z is the orthographic
draught or elevation, from the plan of the church Y,
Scenographic draught, is that which represents some object with
all its parts entire; that is, the height, length and depth. The figure
A is a scenographic representation of the church Z, because it may be con
sidered as showing an object complete in all its dimensions.
PRACTICAL GEOMETRY.
Problem 1.
From a given point A, (fig. 1, Plate 8,) to let fall or draw a line A D,
that shall be perpendicular to a given indefinite line B C.
On A, with any opening of the compasses, for example, A E, describe
an arc of a circle, cutting the line B C in E and F; on the two points E and
F, with the same radius describe two other arcs, intersecting or cutting
each other at G ; a line drawn from the point A to G, will be a perpendicular
line to the given one B C, making on each side an angle of 90 degrees at
H and I. APPLICATION.
By the aid of this problem in geometry, the Upholsterer, Paper-Hanger,
Decorater, &c. can obtain as many perpendicular lines on the walls of an apart
ment, whether for the hanging of paper, silk, or the laying out in decorative
pannelling ; in this example we suppose the workman is required to place an
ornamental pilaster on the wall of a drawing room at a point a. Beneath the
point a, draw a line b c, at any distance on the wall, and parallel with the
cornice or floor of the apartment ; with any radius a d ow. a, describe an arc
of a circle, cutting the line b c ditd and e ; on rf and e with the radius d h and
eg, more than half ^ e, describe two arcs intersecting each other at/, then a





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PRACTICAL GEOMETRY. 13
line drawn from a . through /, will be a perpendicular to the line h c, to
which all the other upright lines on the wall raust be made parallel.
To prove if the line ha perpendicular, stick a pin or nail in the wall
at the point a, to which attach a plumb line, suffering it to remain at rest at
i ; if the line drawn on the wall be a true perpendicular, it will fall into the
line or string a i, and be concealed by it.
Problem 2, Plate 8.
From a given point A, (fig. 2, Plate 8,) on a given line B C, to erect
a perpendicular A F to that line.
Set off any measure from A, as A e and A rf on the line B C, then on rf
and e, with any opening of the compasses more than half B C, describe two
arcs intersecting each other at g ; a line drawn from A through the intersec
tion at g, will be a perpendicular to the line B C.
APPLICATION.
In a room having its end semicircular, or terminated by the arc of a
circle, it is required to take the ground plan for a carpet, or the sweep of
the wall at top for the window cornices.
In that part of the room frora whence the bow coraraences or springs,
draw a line frora A to B, which subdivide for a centre as at C, from C set
off any space on each side, as C e, and C rf; next take any radius more than
half rfe; then on the points rf and e describe two arcs intersecting at/,/;
proceed next and draw a line from C through/ until it cuts the arc or sweep
line of the bow at D, which will give the true depth, whether a semicircle or
only the portion of one. Problem 3.
To raise a perpendicular B C, fig. 3, Plate 8, at the end of a given
line A B.
Set one foot of a pair of bow compasses any where above the line A B, as
at D, and open them until they extend to the end of the line at B, and
sweep the arc e B/at pleasure, cutting the given line A B, in e ; draw a
line frora e through the central point D, and continue it at pleasure, until

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14 PRACTICAL GEOMETRY.
it cuts or intersects the arc B g, at/; draw a line from B through / towards
c, which line will be a perpendicular to A B; the angle c B/in this case
forming an angle of 90 degrees. APPLICATION.
In drawing or design, this problem is extremely useful, either for
laying down the ground plan of rooms or of buildings : for exaraple, the line
W X, being the given width of a roora, suppose, fifteen feet, and the length
W Y, twenty-five feet, the walls being at right angles or perfectly square,
a perpendicular niust be raised as before stated, at the point X, and a line
drawn parallel to it from the point W, on each of which lines is to be put down
twenty-five feet, the length of the room, as W Y, and X Z, then by drawing the
line Y Z, the plan will be completed, the four angles W, X, Y, Z, making
an angle of 90 degrees each ; consequently each line will be perpendicular
to that adjoining it ; this problem is of great use throughout the whole of
geometrical or perspective drawing, and in whatever relates to cabinet
work, wherein square angles are required.
Problem 4, Fig. 1, Plate ix.
To raise a perpendiculai line, m b, fig. 1, at the end of a given line
m a, by means of a scale of feet. Rule : having made a scale df feet, as at
A, take three of those feet in the compasses, and setting one foot of the in
strument on the point m., of the given line m a, with this opening strike
the arc rf rf; proceed next and take four feet from the same scale, and lay it
down on the line m a, from mto o; lastly, take five -feet in the compasses
from your scale, and setting one foot of the instrument on the point o, strike
an arc intersecting the other arc in the point e, the intersection thus gained
will give a point, through which to draw the perpendicular liue m b, from m
as required. APPLICATION.
This mode of raising a perpendicular is very useful in the various branches
of mechanics. The builder by this mode readily constructs a square, enabling


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PRACTICAL GEOMETRY. 15
him to lay down his ground plan ; for by taking three rods, viz. one of three
feet, another of four feet, and another of five feet, and fastening them together,
as in the diagram. Problem 4, fig. 2, a square will be readily constructed,
by which any angle, that should he a right or square one may be proved.
The paper-hanger, by this problem, is also able to construct an instrument
which will enable him readily to rule all his perpendicular lines, without
the use of the plumb line, excepting where it may be necessary to ascertain
the true level on which the square is placed, in which case a plumb line
may be attached to the upright edge of the square, as at P, fig. 2, Problem
4, which will always regulate the true level of the square, the plumb line
concealing the edge of the square when perpendicular.
Problem 5, Fig. 1.
To make an angle equal to any right lined plane angle given; BAC,
fig. 1, Plate 9, is the given angle, and D E, fig. 2, the line given; it is re
quired to makeat the point B, on the line D E, fig. 2, an angle equal to the angle
BAC. Rule : with any radius or opening of the compasses at discretion,
on Aj fig. 1, the vertex or point of the given angle BAC, describe the arc
of a circle a b, cutting the legs, or two sides of the angle in the points a and
b; proceed next to fig. 2, and on the given line D E, at the point D, place
one leg of your compasses, having in them the sarae opening as in fig. 1, and
describe the arc of a circle rfe; raake rf e equal to a b ; and lastly, draw D F>
through the point e. The angle E D F, will then be equal to the angle
BAC. APPLICATION.
Frora this problera we learn to lay down the angle of any room, &c. on
paper, a plan of which may be required, whether the walls be right angled,
that is to say square, or otherwise. Again let it be required to measure the
internal angle C B D, fig. 3 : coraraence by setting off equal raeasures on the
ground frora B to C, and from B to D, say five feet on each side, and draw
the chord line ef, which will be found five feet nine inches in length, or
otherwise, according to the measure first made use of; then having drawn


16 PRACTICAL GEOMETRY.
B D, fig. 4, indefinite as to length, or at pleasure ; proceed to make a scale
of equal parts, see E, under the diagram, fig. 3, which represents seven feet,
from this scale take five divisions, or parts, in the opening of your compasses,
and placing one foot of the instrument on the angular point B, fig. 4, describe
the arc ef, cutting B D, in / then on / with an opening equal to five
feet nine inches, taken from the scale, describe an arc cutting DC, at e ,
lastly, draw B C, and you will have an angle C B D, equal to the one
measured, C B D, fig. 3. Remark : the length of the sides or lines will not
make any difference in the angle. Problem 6.
To bisect a right lined plane angle B AC, fig. 1. Plate 9. Rule : with
any opening of the compasses, on the vertex or angular point A, describe an
arc, rf c, at discretion, cutting both legs, A C and A B, of the angle BAC
in the points rf and c ; then on rf and c, with the same, or any other radius
or opening in your compasses, describe two ares intersecting each other
at E ; lastly, from A, draw the line A F through E, which will bisect the
angle A B C as required.
Or a right angle may readily be divided into two parts after this raan
ner : On the vertex B, of the right angle A B C, fig. 2, with any opening
of the compasses, describe the arc A C, cutting the line A B in A and B C
in C, on A and C ; with the same, or any other radius in the compasses,
describe two arcs intersecting at D ; lastly,, draw the line D B, through E,
which will divide the angle equally, as required. — By this problem the
workman is enabled to find the true mitre for returning his moulding, either
as a Cabinet-maker, or Joiner, &c. with truth and expedition, whether the
angle be an internal or external one, for the right angle bisected is the true
mitre, and by which all the mouldings will exactly meet and fit at the
angles. Problem 7.
To trisect a right angle, ABC, Plate 9. Rule : with any radius at dis
cretion on the vertex B, of the right angle ABC, describe the arc or quadrant.


PRACTICAL GEOMETRY. 17
A D E C. Then with the same radius in the compasses on A and C, describe
the arcs B D, B E, cutting the quadrant AC at the points D and-E. Lastly,
draw the lines B D and B E, by which means the right angle ABC, will
be trisected.

APPLICATION.
This problem is of great use in perspective, enabling us with ease and
facility to lay down the vanishing point for the angle of a sexagon, on the
horizontal line ; its use wUl also be shown in laying down the line of chords,
as on the sector, in a case of instruraents. Pro^BLem 8.
To construct an equilateral triangle ABC, Plate 9, on a given line
A B. Rule : On A and B, with an opening of the compasses equal to the
iine A B, describe two arcs intersecting each other at C, draw the lines A C
and B C, and the equilateral triangle is then constructed.
This problem is useful in finding the side of any polygonfeil or mahy-sided
figure, and will be exemplified in the construction of a pentagon, hexagon,
&c. &c. it is also of use in trisecting a right angle, as A B E in problem 7.
Problem 9, Plate x.
Ona right line E F, fig. 2, Plate 10, to make a triangle similar to
another triangle BAC, fig. 1, by means ofa scale of feet.
Let a scale of feet or equal parts be made as rf e, under fig. 1. Now
the sides B A and A C, fig. 1 , may represent the walls of a room whose
sides are not square, but of which a plan is required. Begin and measure
the space from A to B, which will be found to measure 8 feet 6 inches ; next
proceed and measure the side A C, which will be found to contain 6 feet ;
then a chord line being drawn from B to C, it will contain 6 feet 3 inches,
more or less as it may happen ; now to lay down a similar triangle for the
purpose of making the plan required, draw the line E F, fig. 2, indefinite ;
and from the scale of feet rf e, take six divisions which set off from E to F ;
next take 8^ divisions from the scale in the compasses, and, placing one leg
H


ts PRACTICAL GEOMETRY.
m the point E, describe an arc^; lastly, take 6^ divisions from the scale,
or 6 feet 3 inches, in the compasses, and placing one limb on F, describe an
arc cutting the other arc ^r at D ; draw the lines F D and D E, and the
triangle DEF, fig. 2, will be exactly similar to the one measured BAC,
fig. 1. For if the triangle DEF, fig. 2, was cut out, and the point E laid on
the point A, fig. I, the one triangle would be found exactly covering the other.
Problem 10, Fig. 1.
To construct a square G H I K, on a given line G H, Plate 10, fig. 1 ;
on either extremity of the line G H, as H, raise a perpendicular H I (by
problem 3), raake H I, equal G H ; then with a radius equal to G H, in the
compasses, on G, describe an arc of circle, at pleasure, and on I, with the
same radius, describe another arc intersecting it at K ; lastly, draw G K and
K I, which will complete the square. Case 2.
Another mode of constructing a square with equal truth may be used;
let G H, fig. 2, be the line given on which to construct the square G H I K ;
on G and H, with the radius G H in the compasses, describe two arcs inter
secting each other at M ; next bisect or equally divide the arc G M (by
problem 11), that is by taking any opening in the compasses more than half
the space G M, and placing one leg of the instrument in G, and again in M,
describe two arcs intersecting each other at n and o; a line drawn through
the intersecting points will divide G M into two equal parts at P ; then on
M, with a radius in the compasses equal M P, describe two arcs inter
secting H I, at I, and G K, at K, draw H I, G K, and K I, and the
square will be completed. APPLICATION.
The construction of the square is of general use in drawing ; in a per
fect square each side becoraes the tangent to a circle inscribed within it.
An elegant and ready mode of constructing an octagon, is obtained by first


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PRACTICAL GEOMETRY. 19
making a square, half of one of the diagonals of which, when laid down
on the sides, frora each corner, will cut off the true sides of an octangular
figure. Problem 11.
To bisect a given right line L M.
Rule : with any radius in the compasses, more than half the given line
L M, Plate 10, place one leg in the points L and M, and describe two arcs
intersecting each other at N and O. Through the two intersections N and O,
draw the right line N O, which will divide the given line L M, into two
equal parts at the point of intersection Q ; after the same manner, the arc
of a circle may be divided as L P M, in the point P.
From this problem an elegant and certain mode is obtained for dividing
any given line into two equal parts, without guess or reference to repeated
trial by the compasses ; we have likewise by the same means, four lines per
pendicular to each other, and consequently generating at the point Q, four
right angles, containing ninety degrees each, and forraing the centre of a
circle to which L M, N O, become the diameters.
Problem 12.
To trisect a given line Q R, Plate 10.
With any radius at discretion in the compasses, on Q and R, describe
two arcs intersecting each other at S and T, draw the lines Q T and R T,
through the intersection at I, each of which bisect or divide (by problem 11),
into two parts, at V and U, draw S V and S U, cutting Q R, in the points
e and/; the line Q R will then be truly trisected.
APPLICATION.
The division of a line after this manner being the most correct, is
at the same time elegant. It is useful in the construction of polygons, oi
figures of more than four sides.


20 PRACTICAL GEOMETRY.
Problem 13.
To find a right line that shall he equal to the circumference of a circle.
A B C D is the given circumference of a circle, for which a line is re^
quired that shall be equal to it.
Rule : divide the diameter A C, of the circle A B C D into eight equal
parts or divisions, prolong the diameter A C, towards E indefinite, and set
six of the same parts from C to F, making in the whole fourteen parts from
A to F. Through the point C, and on the line A E, draw the right line
G H, perpendicular to the right line A E at pleasure, it will then be parallel
to the circle's diameter D B. From the point F, as a centre, with the dis
tance F A in the compasses, describe the arc I A K, then the line I K, in
respect to its length, will equal the circumference of the circle A B C D.
To prove the truth of this problem, divide C D, which is one quarter
of the whole circle, into sixteen equal parts, by subdivisions ; that is to
say, divide the quarter C D first into two parts, next divide each of the parts
so divided into two parts also, you have then the quarter or quadrant divided
into four parts ; proceed and divide these four parts into two each, and
you have eight parts ; and lastly, divide the eight parts into two each, and
sixteen is the produce for the arc C D ; these divisions carried round the
circle would divide it into sixty-four equal parts. Take four of these divi
sions in the compasses, which place on the line G H from C, aud continue
it eight times, until you finish at K, making then thirty-two parts : C K
being half the line, I K will give sixty-four parts for the whole, and thus
the line I K shall equal the circumference of the circle A B C D.
This problem is of use to all mechanics who desire to know the con
tents of an exterior or interior spherical surface ; whether the same be a
plain curved wall, the inside or outside of a dome.





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PRACTICAL GEOMETRY. 21
t,..;; Problem 14-
To find a right line that shall he equal to a determined curved line.
D F E, fig. 1, plate 10, is the given curved line. Take any small measure
in your compasses, so that the curve contained in the portion thus takeu, shall
not visibly vary from a straight line, carry this measure round the arc or
curve D F E, from D unto E ; the curve in this diagram will be found to contain
this measure thirty-two times, or otherways according to its extent. Proceed
and draw the right line G H, fig. 2, indefinite, and from G set off thirty-two
such divisions towards H; by which raeans the line will equal the true length
of the curve.
This problem will be found of as great use as the one preceding it ;
from it we can obtain the contents of the surface of a wall, being the seg
ment of a circle ; also the raised ceilings of rooms or beds, partaking of
the same form. Problem 15.
Through a given point C, fig. 3, plate 1 0, to draw a Une that shall be parallel
to a given right line A B.
A B is the given right line, C the given point.
Through the point C draw a right line at pleasure, of any inclination,
cutting the given line A B in E ; take any opening in the compasses, and
setting them on E, describe an arc ff; which is the opening or measure of
the angle C E A, made by the line C E ; with the same opening of the com
passes on C, describe an arc at pleasure g hj transfer the measure of the
Arc ff, on the arc g h, or make g h equal toff; by which means the two
angles will be equal ; a line drawn from C, through the point g h, will be
parallel to the given line A B.
Problem 16. Plate U.
Where the parallel lines are very long, the following raethod is to be
preferred., 1


22 PRACTICAL GEOMETRY.
A B is the given line, and C the given point.
Take the distance from the given point C, to the given line A B, in the
compasses as C A, and assuming any point E, towards the epd of the line
A B ; describe with this radius, an arc as D ; apply a ruler from the point
at C, to the top of the arc at D, and draw C D ; then shall that line be
parallel to the given line A B. APPLICATION.
The use of these problems is general, and will be found essentially so
in the practice of perspective; from them we have the construction of the
parallel ruler; of great utility in the making of plans, when unprovided
with a drawing board or T square, and in every instance wherein parallel
lines are required.
Suppose two plain rulers, e f 'And gh, (fig. I, plate II,) to be joined
together by two upright pieces of metal, so as to forra four right angles,
as at A, B, C, D, and consequently the raetal pieces be perpendicular ;
then it follows that the four angles being equal, the two rulers must like
wise be parallel.
Again ; admit these two upright pieces of metal d c,h a, fig. 2, to be so
fixed, as to be capable of motion backward and forward by means of pivots,
rivetted at the parts o, o, o, o, then it will easily be imagined, that these two
rulers may be compressed, or divided the one from the other, continually at
equal angles, as may be seen in the figure, wherein the angle a equals the
angle c, the angle h equals the angle d, consequently the moveable rulers ef,
g h, must be parallel.
From the same problem we have the construction of the bevelled square
N G, fig. 3, used by architects and others for drawing inclined lines, that are
intended to be parallel one with the other ; in perspective also it is of the
greatest uSe in laying down angles for points on the horizontal line, and
for casting of shadows, whether from geometrical figures, or objects put into
perspective, wherein all the shadows flow parallel. To the Joiner and
Cabinet-maker its use is familiar for setting the mitres, whether full or acue.
Suppose ABC, fig. 3, to be a plain T square, on the centre of which at
N, a ruler or another T square E F G, be fixed by a thumb screw, so as to lie


PRACTICAL GEOMETRY. 23
moveable at pleasure ; and conceive the fixed stock A B of the T square
A B C to be placed on one edge of a perfectly square drawing board H, all the
angles of which I, K, L, M, are right ones, and consequently the sides per
pendicular the one to the other ; then the moveable square, which at first was
parallel and exactly covering ABC, may be inclined at any angle that maybe
required, as at N. Now imagine the square ABC to be moved along the
edge of the board as at I M, it will in its motion downwards, produce a
series of lines R O, R P, R Q, parallel the one to the other, every angle
at R being equal. Problem 17.
Any angle which is conta.ined in a semicircle is a right angle.
ABC, fig. 1, plate II, is the semicircle given. From A draw the line A B
of any inclination at pleasure, touching the circle's circumference at B ; from
B draw the line B C, then the angle ABC, thus formed is a right or square
angle. So likewise A b and h C being drawn, produce a right angle A 6 C ;
for all angles standing on the diameter of a semicircle, and contained within
the circumference, jwill be right angles,
APPLICATION.
From this problem we have a practical way of raising a perpendicular
at the end of a line, (see problem 3,) fpr the line dCa, fig. 2, being drawn
from d, through thepentre C, where it cuts the semicircle as at a, will pro
duce a point perpendic,ular over b, the comer of the line d b.
Mechanics also are furnished by this prpblem with a mode for ascertain
ing the truth of their -squares; for having drawn a semicircle ahd, fig 2,
with a radius equal to the length of one side. of the square as a h, and drawn
the line ad, apply the corner of the square ahd, to any point in the circum
ference of the circle as at b, and one side, on one end of the diameter as at
a; ifthe square is a true one, the third point will fall on the opposite end of
the diameter at d.


•24 PRACTICAL GEOMETRY.
Problem 18.
To find the centre ofa circle, of which an arc only, or portion, is given
A C B, fig. 1, plate 1 1, is the given arc.
Draw the chord lines A C and C D, which may be, as in this case,
equal to half the segment A C B ; or one of the right lines might be made
longer than the other; take rather more than half one chord line as C A, in
your compasses as at/ and on A. and C, describe arcs intersecting each other
at g and g ; with the same opening, and the compasses transferred to B, de
scribe other arcs intersecting at g and g, draw right lines g g and g g, which
continue until they meet or intersect each other at H. The point of inter
section will be the centre of a circle, of which the given arc A C B is only a
portion. APPLICATION.
By this problem a centre is obtained for describing the arc of a circle,
of which wehave only three points through which it will pass, as A C B.
Let A C B be the bow end of a room, forming the segment of a circle : the
real outline of which is required to be drawn. Draw the chord A B on the
floor, which may be done by a chalked line, fastened at the extremities A and,
B, which being raised in the centre and then let fall, will give a correct right,
line ; divide A B into two equal parts, and raise a perpendicular D C, cutting
the segment at C, draw the chord lines C B and C A, by means of the chalked
line as before, which also equally divide at E and I ; next proceed and measure
(by a two or three foot rule), the chord line A C, likewise the chord C B,
which note or mark down on paper ; mark also the distance from D to C ;
then on the lines C B and C A, at the points E and I, apply your square,
and draw lines perpendicular, until they unite in a centre, as at H ; which
intersection gives a point that will be the centre of a circle, of which the arc
or bow is only a part.
In the Upholstery and Cabinet departments, this problem is not without
its use, for by the above process, the plan of a room (having its end in the


PRACTICAL GEOMETRY. 25
form of a bow, either as a semicircle, or part of one), may be taken in a
rough draught, and from the measures thus noted down, a similar plan
may easily be laid down; for instance, in London, although the measure
should be taken in any part of the country distant frora it, and a carpet be
required, it may be thus made up to fit exactly. The sweep of the wall is
also obtained, by which the window cornices can be manufactured with
out fear of want of alteration. It is to be observed that this process will
alone answer in cases where the bow or arc forms the segment of a real
circle ; in sorae cases the arc or sweep will partake of the section of a
cone ; for instance, in that, of the parabola, or flattened oval ; recourse
must then be had to means that will be explained hereafter.
APPLICATION,
The square AB C D, fig. 2, Plate 11, contains a figure representing a
block forming part of the support for a pillar and claw table, used either for loo
or dining table. The inclined corners A B C D, are parallel to the diagonals
of the square, and are always occupied by the feet forming a support for the
block on which the pillar is to be placed : to take away from the heavy effect a
square block would produce, the sides are usually curved, and in most cases
such curve becomes the segment of a circle; to obtain which, the practice
before explained must be resorted to. For example : the corners or cants
A B C D, being taken off the square, find the centre of each side, and draw
a perpendicular line through each as L M and M N, &c. The depth of the
sweep being given, place the same from e tof; draw^ / and hf, which
bisect at i and i, by problem 11., and through these intersections, draw the
lines i, i, until they intersect the line L M, at L, which will then become a
centre, from whence the curve line g f h may be described ; the line M N,
being made equal to L M ; the point N likewise becomes a centre for striking
the sweep on the side D C ; which practice made use of on the two other
sides C B, and B A, completes the whole figure of the block.


26 PRACTICAL GEOMETRY.

Problem 19, Plate 12.
*
Three lines heing given to find a fourth, that shall hear the same proportion to
the third that the second does to the first.
M N, O P, and Q R, are the three lines given, and to render the use of
this problem clear and positive, the line M N may be considered in length,
5 feet; the line O P, 2 feet; the line Q R, 5 feet 6 inches; now a fourth
line is required that shall bear the same ratio or proportion to Q R, that
0 P bears to M N.
Rule : Draw the line T V indefinite, and from T draw the inclined line
T S of any angle at pleasure. On T V, from T to X, set the measure of
the line M N ; and from T on the inclined line T S, set the measure of the
line O P to Y ; draw Y X ; then from X towards V, set the raeasure of
the third line Q R, and from Z draw a line parallel to X Y, by Problem 15,
Plate 10, (or more readily by a parallel ruler as described in Plate 11,)
cutting T S in I ; then the space on the line T S, comprehended betwixt Y
and I is the measure of the fourth line sought. This problem, part of the
sixth book of Euclid, is one araongst the many, forming the foundation of
arithmetic ; it is now introduced, as it may be of service to those, with
whora arithmetic, or the rule of three, is not familiar, forasmuch as lines will
answer the place of numbers : to elucidate which, in our application of its
use, it will be stated both ways.
For example : The line M N may be considered as the top of a sofa or
occasional table, and represent a length of 5 feet; the line O P considered
as the width, may represent 2 feet ; now another table is wanted whose
length shall be 5 feet 6 inches, the width of which shall bear the same pro
portion to such length, as exists in the table of 5 feet by 2 feet.
This may be accomplished arithmetically, by the rule of three, thus:


PI. Lill

GEOMETRY. 12

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FuHistecLij Jones & C° Aa,?'- 1826.





PRACTICAL GEOMETRY. 27
If 60 inches produce 24 inches, what will 66 inches produce.
PIKST TERM. SECOND TERM. THIRD TERM.
Stated thus, 60 : 24 : : 66
Multiply by 24 the second terra.

264
132

C 5 ) 1584
Divide by 60 or first term. < 
(12) 316|

26 Inches product.
or 2 feet 2 inches and a fraction.
Frora hence it appears that a table 5 feet 6 inches long would require
to be 26 inches and a fraction in width, to bear the same proportion as the
one 5 feet by 2 feet. To the Cabinet Maker and Upholsterer this problera
may be of great use; it can be extended in various ways, in enlarging or re
ducing designs, frora objects that are considered in good and harmonious
proportion. To prove the truth of the above problem, we shall refer to the
figure, wherein T X represents the length of the top M N, or 5 feet; T Y
represents the width of the top O P, or 2 feet; X Z represents the length of
another given top to be 5 feet 6 inches, for which a width is required that
shall be in the same proportion to 5 feet 6 inches, as 2 feet is to 5 feet; and
this we find to be Y I, and which measured by the scale placed on M N,
will be found to be rather more than 2 feet 2 inches, being the same as tbat
found by the rule of three.
This problem has been selected as of use to our present purpose ; pro
portional lines extend not only to the foundation of nurabers, but afford
ineans for laying down all the lines on the sector, proportional corapasses,
&c. &c. Problem 20.
To inscribe a triangle ABC within a circle G C H F,fig. 1.
Rule : Draw the Diameter G H of the circle through the centre S ; on
S raise S I, perpendicular to G H ; on H, with the radius H G in the com-


28 PRACTICAL GEOMETRY.
passes describe an arc, and on G, with the same radius describe another
arc intersecting it at I ; draw the lines G I and I H, the equilateral tri
angle G I H, will then be formed on the circle's diaraeter G H ; divide the
semi-diameter S G into three equal parts, each of which will contain 30 de
grees. Draw I A through the second division from the centre, and where
it intersects the semi-circumference at A, 30 degrees will then be cut off;
from A draw A B parallel to G H, until it cuts the semi-circumference at
B, then will A B form one side of the equilateral triangle. Draw A C and
C B and the equilateral triangle is compleated.
We have often occasion to circumscribe the triangle in a circle, and
particularly so in proportioning a triangular block, part of the support for a
circular loo table, also for the same description of form in the blocks for
screen standards, and for supports of work tables, &c. 8tc.
POLYGONAL FIGURES.
Problem 21.
To inscribe a pentagon or figure of five sides within a circle ABC D,fig. 2.
Rule : Draw the diameter A C, half of which divide into five equal
parts at 1, 2, 3, 4, 5. On A and C, with a radius, or opening of compasses
equal to A C, describe two arcs intersecting each other at E, draw the lines
A E and E C, from E ; then from E, through the second division from the
centre S, draw the line E/ and continue it until it cuts the semi-circum
ference A D C, in the point G; draw G H parallel to the diameter, cutting
the semi-circumference also at H, which line will pass five times round the
circle at the points G, K, B, I, and H,
It is here necessary to remark, that the intersection through the points
/and g, on A C, at G and H, as they cut the circle, must be very carefully
taken ; and further, that in passing them round the circle's circumference, the
point must invariably fall in the line of circumference, and not the least
out of it.
This mode of dividing the diameter into as many parts as the figure
possesses sides, will answer for every polygonal figure circumscribed by a
circle; there are many other modes of dividing the circle's circumference, so


PRACTICAL GEOMETRY. 29
as to obtain the sides of regular polygonal figures ; but as these figures
seldom come under the attention of the Upholsterer or Cabinet-maker, we
shall proceed only in giving the readiest rules for the formation of such of
them as may be useful in those branches, and in the first instance proceed
with the hexagon or figure containing six equal sides.
The truth i df this problem may be thus explained ; every circle con
taining 360 degrees in its circumference, it follows that one half such circle
must contain 180 degrees, and such is A D C in fig. 2. An equilateral
triangle, whose base is made by the diameter of a circle, being divided into
any number of equal parts, if lines be drawn from the top or apex of the
triangle, through the divisions on the base line, it will divide any line placed
below it, proportionally, provided that line is under the same angle, and
within the limbs of the triangle, if extended ; by the same rule, the semi-
circumference of a circle, under the base of a triangle, will be divided into
as many equal parts as are contained in the base line of such triangle.
The diameter A C, of fig. 2, is divided into 10 parts, each part con
taining 18 degrees, and numbered from the centre S; now as 36 degrees
are cut off from the centre, by a line passing from E, through the second
division at/ and intersecting the circle's semi-circumference at G ; so will
a like measure be cut off, on the other side the centre at H, by the line E g,
cutting the semi-circumference at H ; making together 72 degrees, which
is the measure of a side of a pentagon. Therefore drawing G H parallel
to A C gives the side required. Problem 22.
The circle L M N 0, fig. 3, Plate 12, is required to be divided into six
equal parts, forming an Hexagon.
Rule : To preserve a parallel form in the upper and lower parts of this
figure, begin by taking L ^ in the compasses, (the circle's radius,) and placing
one leg ofthe instrument in the point L, describe the arc qp; next proceed
and place the compasses at the point j», and describe the arc L j; again, on
s, with the compasses describe the arc t N ; and lastly, with the instrument
on the point N, describe the arc t r. You will then have six points, L, q, r,
L


30 PRACTICAL GEOMETRY.
N, s, p, which being joined together by right lines as L q, &c. completes the
hexagon. Remark, that great care must be taken to note the intersection of
each arc on the circle's circumference, as the least variation may occasion
the trouble of going repeatedly over the same ground, to make the sides
agree ; for let it be noted, that although the operation in this case is me
chanical, the calculation is raathematical, and depends entirely on a point
considered in itself indivisible.
This figure is of frequent use, and will often come before the Mechanic's
observation. The bow end of many apartments in country houses partake
of one half of this form, particularly where the gothic style is adopted ; in
Hall Lamps, the marble tops of tables, and various other instances it falls
into use. The hexagon has this singular property over all other polygonal
figures, that it will join and come together without any loss of roora ; the
cell ofthe industrious bee is thus constructed.
Problem 23.
To construct an octagon from a given side.
Rule : Let kJ, fig. 4, Plate 12, be the side given ; on k and/ with a radius
equal to the given side, describe two arcs intersecting at n ; draw the line
A C, through n, perpendicular to kj ; next proceed and divide the arc k n
into six equal parts, and on n, with the radius n m, equal to two parts de
scribe the arc m o, cutting the perpendicular A C, at o, then will the point o
become a centre for describing the circle A B C D, round which kj will
pass eight times at the points efg h ij k I.
The octagon, is a figure in such general use, that it will be needless to
say more respecting it than we have in describing the hexagon.
Problem 24.
Tn a given square E F G H, fig. 5, Plate 12, tp construct an octagon.
Rule : Draw the diagonals G E and H F, whose intersection at I will give
the centre of the square ; then on the points E, F, G, H, with the opening


PRACTICAL GEOMETRY. 31
in the corapasses E I, (equal to one half the diagonal line E G,) describe
arcs cutting the side of the square E H in Q and R ; the side E F in P and
O ; the side F G in N and M ; and lastly, the side G H in K and L : draw
the lines Q P, P 0, &c. &c. and the octagon is compleated.
This manner of constructing an octagon is considered by Geometers
the most elegant. Problem 25.
The diameter of an octagon being given to find the sides.
Rule : Let S T, fig. 6, Plate 12, be the diameter given ; bisect it at the
point O, and divide each half into six equal parts, numbered from the centre
O ; on 0 raise a perpendicular to S T, at pleasure, and set the distance O T,
on the perpendicular from O to Z ; then through T, draw the line V V in
definite, but parallel to S T : proceed, from the points w and x, (which are
betwixt the second and third divisions right and left of the centre O,) and
raise the perpendiculars w W and x U, cutting the line V V at W and U.
On T and S, with a radius in the compasses equal to two divisions
and a half, describe two arcs, cutting the perpendicular S V at X, and T V
at the point Y. Join U Y and W X, and the half octagon is completed.
This problem will be found very useful in taking the plan of any octan
gular bow end of a room, where the figure forms half of a regular octagon ;
which may be readily known, first by measuring the width or span of the
bow S T ; and next, measuring the depth O Z ; then if O Z measures
one half the whole width S T, you may be assured the octangular form
is that of a regular one, being included in one half of a square S V, T V.
This problem will also be found of use in the practice of perspective, and by
wnicn the trouble of making a geometrical plan may be avoided.


32 PRACTICAL GEOMETRY.
Problem 26.
Ellipsis or Oval.
TTie transverse or longest diameter A B, fig. 1, Plate 13, being given, to find
the centres C and D ; and the centres E and F, on the conjugate or shortest
diameter G H ; % which to construct the Ellipsis.
Rule : Divide the line A B into three equal parts, and construct on the
central division C D, two equilateral triangles C E D and D F C ; the
points or apex of the triangles will then become the centres for describing
the curved lines g h and i k; continue the sides of the triangles indefinite ;
namely, E C to i; E D to A; F C to ^; and lastly, F D to ^.
On C, as a centre with the radius C A, describe an arc inter
secting the lines F I and E o, at the points g and i; on D, with the
same radius or opening in the compasses, describe another arc intersecting
the lines F m at ^, and E w at ^. On the focus F, with the radius F g and
on E, with the same radius, describe the arcs g h and i h, which will com
pleat the ellipsis. Remark, the length and breadtk of this kind of ellipsis,
holds the proportion of three to four, or nine to twelve ; that is to say, if
the longest diameter contains four parts, then the conjugate or shortest
diameter will contain three parts, or if the longest diameter shall contain
twelve parts, then the shortest will hold nine parts >
Problem 27.
To find the foci of an ellipsis A B C D, fig. 2, Plate 13, the longest diameter
A C, and the shortest diameter B D being given.
Rule : Take half the longest diameter A C in the compasses, and on
the point B of the shortest diameter, with such radius describe an arc inter
secting A C in the points e and g ; which points will become the foci for
generating the ellipsis.
By this problera we are enabled, with a string and pencil, to describe
a true ellipsis ; for having found the foci on the longest diameter (e and


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PRACTICAL GEOMETRY. 33
g,) let two pins be fixed, then passing a packthread or line, of equal sub
stance, round these two points, connect the two ends together, in such a
manner, that they shall form a triangle, whose apex or point shall meet the
shortest diameter, as at B; then with a pencil, chalk, or any other marking
substance, held steadily in the hand to this point, proceed and move the
string towards A; it will then in its progress pass through the point/ on
wards to A, round to D and C, and finish at B, from whence it started.
Note : the further these foci are asunder from each other, the more oblong
will be the ellipsis ; and the nearer they are towards each other, the nearer
the ellipsis will approach to a circle, provided the same length of string be
made use of; but ifthe foci coincide or meet in a point, then the string will
be equally extended, and the curve so described will be a complete circle,
whereof that point is the centre. All this is easily apprehended by a
view of the figure, and may be tried by a string and two pins, as described
above. Problem 28.
To describe an ellipsis by means of ordinates, the diameters being given as before.
Rule : Let A C, fig. 3, Plate 13, be the longest, and B D the shortest
diameters given ; through the points B and D, draw lines parallel to the
diameter A C, at pleasure, and through the points A and C, draw two other
Hnes parallel to B D, meeting at the points 4,4, 4, 4; divide each half
diameter into four equal parts (or more if required), as figured 1, 2, 3, 4;
proceed and draw lines or ordinates, from B 1 to A I, and from B 2 to A 2,
and from B 3 to A 3, repeating the same in the other three quarters ; a
curve so traced, that in its progress touches the lines 3, 3 ; 2, 2; 1, 1 ; be
twixt, or in the centre of each intersection, will forra the ellipsis required.
For laying down working drawings, this mode of using ordinates is
to be preferred. Sections qf the Cone.
Every Grecian moulding owing its beautiful outline to some section of
the cone, and such outline being regulated by the particular section made ;
M


34 PRACTICAL GEOMETRY.
whether it be perpendicular to the base, parallel to the cone's axis,
more or less inclined to it, or lastly, if parallel to the sides ; it has been
thought necessary to explain the same by a diagram, shewing the different
forms made by such sections, as at fig. 4.
First, if a cone be cut directly through its axis A, and perpendicular to
its base B C, the section made will be that of an isoceles triangle as AB C,
fig. 4. Note : For the sake of elucidation, the base of the cone in this diagram
is put into perspective.
Secondly, if a cone be cut by a line parallel to its base, such section
will be a circle.
Thirdly, if a section be made by a line passing through the cone, in
tersecting both its sides, and inclined more or less to the base, such as he ;
then the section thus made, will form an ellipsis or oval.
Fourthly, if the section be made by a line parallel to one of its sides,
as at d k, the figure formed by such section will be a parabola, as d ef.
Fifthly, ifa cone be cut by a right line as^ I, perpendicular to its base
or parallel to its axis, the section made will be an hyperbola, such as
g h i. We will now proceed to give the construction of each figure produced
by the sections before raentioned, viz. that of the parabola, and hyperbola ;
a description of the ellipsis being fully described in problems 26, 27, and
28, any thing further respecting it is here unnecessary, we shall therefore
hasten to explain the construction ofthe parabola, by

Problem 29.
To describe the parabola from the cone.
Suppose the section to be made at d k, fig. 4, Plate 13 : on k, with the
radius A B, describe the semicircle B m C, which represents one half the base
of the cone; proceed and drop a perpendicular from k, until it cuts the semi-
circumference at m, which line will then measure half the width of the
parabola. Transfer this measure on a line from A ito D, and froin


PRACTICAL GEOMETRY. 35
D to B (fig. 5), the length of which line A B will be the width
of the parabola; draw A E and B F, perpendicular to A B, which
make equal to d k in fig. 4; draw EF; on D draw D C perpendicular
to A B, and divide each half, from D, into four parts as figured ;
and from each division raise a perpendicular : next, divide the lines A E
and B F, each into the same number of equal parts, numbering from the top
downwards ; draw the lines C 1, C 2, and C 3, cutting the corresponding
perpendiculars on the base; namely. No. 1 on A E, to cut No. 1 on
A D ; No. 2 on A E, to cut No. 2 on A D, and so on for all the rest ; a line
traced through these intersections will be the outline ofthe parabola.
Problem 30.
To describe the hyperbola from the cone
Suppose the section to be made at g I, fig. 4, Plate 1 3 ; continue g I until
it cuts the semi-circumference at n, represented by the dotted line I n, which
will then measure half the base of the hyperbola, and g I will be its height;
transfer this; measure twice on A B, fig. 6, that is, from A to D and from D to
B; raise perpendiculars from A, D and B as before; then on D set up the
height (^ /fig. 4), from D to C, and through C draw E F parallel to AB ; divide
A B, A E and B F as before; next set the whole height of the cone from
D to G ; then lines drawn from the divisions on the base A B to this point,
and intersecting the lines drawn to C from the corresponding divisions on
the heights A E and B F, will give points through which the form of the
hyperbola raay be traced.
Problem 31.
To-describe an eliptical arch by means of two laths of wood.
Let efg h, fig. 7, Plate 13, be a board or plane, on which the arch is
required to be drawn.
Suppose a b the width of the arch, and c d its height at the centre ; at
the central point nail down a slip of woody So that Cne edge shall pass through


35 PRACTICAL GEOMETRY.
it; take another slip, and size it to one half the length ofthe arch, ar.d from
one end of this lath, as at i, place the height of the arch as at k ; through this
point pierce a thin pivot, until its point come through the opposite side of the
lath ; if then the slip i I be raoved along the edge of the board from d
towards g, keeping the hand on the pivot at k, it will in its progress de
scribe one half of the required arch as c i a; observe, likewise, that the end
ofthe lath I, must be kept raoving up the edge ofthe perpendicular lath cm;
the other half frora d to b raay be described after the sarae raanner.
Problem 32.
To find the centre for describing a Saxon arch.
Let 0 4, fig. 8, Plate 13, be the width of the arch, which divide into four
equal parts as numbered. On No. 1, with an opening in the compasses equal
to 1, 3, describe an equilateral triangle, whose apex Q, shall be below the
line 0 4; then drop perpendiculars from 1 and 3 indefinite, and continue the
sides of the triangle until they intersect them at the points r and s, con
tinuing the same upwards at pleasure ; on Nos. 1 and 3, with the radius 1 o,
describe the two haunches of the arch, stopping thera on the lines at the
points * and v ; then on r and s, with the corapasses extended to /, describe
the remaining arcs t p and p v, and the arch required will be completed.
Proble.m 33.
To find the centres for describing a Gothic arch.
Let a 6 be the width given, which divide into eight equal parts, num
bering one half, by 1,2,3, and 4, from the centre right and left, to a and h;
draw c d perpendicular to ab; then on No. 1, with the compasses extended
to b, describe the arc d b, and pursue the same raethod for the other -half
a d, which will give the form of the arch.
The two preceding problems are applicable to various purposes ; in
laying down the lines for bed and window cornices, the diagonal ribs for
dome teasters, also the heads for bookcase doors, and Gothic blinds, &c. &c.





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PRACTICAL GEOMETRY. 37
GEOMETRICAL FIGURES.
Mouldings. Plate 1.
Mouldings partake oftwo characters, the dne after the Roman, the other
after the Greek; raouldings of the first character, have for their outline,
the quadrant or quarter of a circle, whether such outline be concave or con
vex. They are either simple in their forra, or corapounded. The outline of
the Roman scotia is an exception to this rule, its form being generated by
the segments of a circle. Grecian mouldings have for their outline a curve,
formed by a section of the cone ; such section being either perpendicular
to the cone's base, as is the hyperbola; inclined to it, but parallel to one of
the sides, as is the parabola ; or inclined to the base, and cutting both sides
of the cone, as is the ellipsis.
In Plate 13, of Practical Geometry, fig. 4, this has been fully explained;
it is, perhaps, necessary to reraark, that the sweep, generated by a conic
section, gives to the Grecian raouldings, not only their graceful outline, but a
decided preference as far as regards their use. Sir Williara Chambers, ob
serves, " that an assemblage of essential parts and mouldings is termed a
profile ; and on the choice disposition and proportion of these, depends its
beauty or deformity. The most perfect are such a.' are coraposed of few
mouldings, varied both in forra and size, fitly applied with regard to their
uses, and so disposed, that the strait and curved ones succeed each other
alternately. In every profile, there should be a predominant member, lo
which, all the others ought to be subservient, and seem made either to sup
port, to fortify, or to shelter it frora the injury of the weather; as in a cornice,
when the corona is the principal, the cyma or cavetto serves to cover it, and the
modillions, dentals, ovolo, and talon to support it. When ornaments are
employed to adorn the mouldings, some of them should be left plain, in order
to form a proper repose ; for when all are enriched, the figure of the profile is
lost. In cornices the square raerabers should not be ornaraented; neither
should the different facies of architraves, or plinths of columns partake of
any decoration ; for they are, generally speaking, either principal in the com
position or used as boundaries to other parts ; in either of which cases their
figure should be distinct, and unembarrassed. N


38 PRACTICAL GEOMETRY.
These observations, correct, in themselves, are equally to be attended to,
as well by the cabinet raaker as the builder, to whora they were originallv
addressed. The outline of the Roraan raouldings being forraed by segraents of a
circle, the first object is to find the centres for describing their curves,
whether simple or corapounded ; we shall, therefore, coraraence with the
ovolo, as being the raost siraple.
To find the centre by which to describe the ovolo or quarter round, fig. A.
Having the projection from the fillet, and the height of the raoulding given ;
take the measure of the height in the compasses, and from the extrerae pro
jection of the ovolo set back this measure by an arc as at a, which will then
become a centre for striking the outline of the moulding.
"' To describe the cavetto, fig. B.
The projection and height of the raoulding being given, as before ; proceed
and frora the upper fillet or projection, drop a perpendicular, and continue
the bottora line of the raoulding, until it intersects at b; which point becoraes
the centre for striking the cavetto.
The astragal or bead C, toay be described by taking half its height ; and
this measure set back frora the given projection will give a centre, by which
to turn the online of this raoulding.
To describe the cyma-recta, or ogee, fig. D.
The projection ofthe upper fillet from the lower one, and the height of the
moulding being given, join the extremities of both fillets by a right line,
which divide into two equal parts, then proceed and subdivide one of these
divisions into six equal parts, as nurabered in the figure; take five of these
parts or divisions in the compasses, and from the extremity of each fillet,
describe two arcs, the one right, and the other left ; and with the same radius
on the central point, describe two other arcs intersecting the former at C
and G, which points are the centres for striking the convex and concave
curves, forming the outline ofthe moulding.


PRACTICAL GEOMETRY. 39

To find tlie centres bywhich to describe the Roman scotia, fig. E.
Let A B be the given height of the mbulding between the fillets, and E B
its projection at the base; divide the height on a perpendicular line A B (drop
ped frora the edge ofthe upper fillet) into seven equal parts frora A toB; on
E, the edge ofthe lower fillet, raise a perpendicular indefinite ; and through
the third division frora the top, draw a line C i, parallel to E B, intersecting this
perpendicular at d : raake c?/equal to £?E, as shown in the figure by the dotted
semicircle; from /through the third division draw the line f g at pleasure;
the point on the third division will then become the centre for striking that
portion of the arc contained betwixt the points A and yi; and / will be
the centre for striking the reraaining portion from* h to E, which completes
the outline of the scotia.

To describe the Greek scotia, fig. F, by means of ordinates.
The height ofthe moulding being determined, let t be the projection ofthe
upper fillet, y the projection ofthe lower fillet, and s the greatest depth of the
hollow ; join t and v by a right line, which first divide into two equal parts,
through which division draw a line, parallel to the upper and lower fillets,
intersecting another line drawn parallel to f w at s; and let r be
equally distant from the line t v as is s; divide each half oi t v into
four equal parts, and the depth of the scotia into the same number of
parts, top and bottom; from each of which divisions draw lines tending
to *; frora r draw lines also through the divisions ontv intersecting the cor
responding lines tending to s ; namely, the first division from the top to
intersect the first division from t, the second from the top to intersect the
second frora t, and so on for all the rest, the same to be observed below
from V, through which points the outline of the moulding raay be drawn.
To describe the Greek echinus, fig. G, its outline being parabolic.
Let F C be the given height, and A F the utraost projection. Draw the
lines A B and B C, which raay be considered as two tangents to a parabolic^


40 PRACTICAL GEOMETRY.
curve, the one A B perpendicular to the line ofthe moulding; the other B C,
inclined to it; which inclination raay be raade frora one half, one third, or one
fourth of the whole height, of the raoulding from the base ; next divide A B
into five equal parts, and leave one for the quirk of the raoulding at top ;
through the reraaining four divisions draw lines tending to C; and frora A,
draw a line parallel to B C, intersecting the perpendicular F C at E, which also
divide into four equal parts : raake E F equal to E C, frora which point, draw
lines through the divisions on A E, figured 1, 2, 3, 4, until they intersect
each its corresponding line, drawn frora A B to C, as before described in
the preceding figure.
To find the two axes or diameters hy which to describe tke echinus moulding,
fig. H, taking the form of an ellipsis for its outline; the point C being one of
the extremities ofthe sJtortest axis.
The height of the raoulding being given, let P be its utraost projection
beyond the lower fillet ; frora this, drop a perpendicular at pleasure, and let
A be any raeasure set frora the top you please, which is to form the quirk : let
the distance B from the bottora be less than one half the whole height.
Join A C, which bisect at L, and draw B C ; frora C draw a line perpendi
cular to B C at pleasure ; and frora B through L draw another line intersecting
this perpendicular at M, which will then becorae the centre ofthe ellipsis tobe
described; through the point M draw the line IMP parallel to B C at plea
sure, upon which line the longest diaraeter raust be placed. Set the distance
C M frora A to Q, through which point frora A draw a line intersecting the
perpendicular C M at N, the length of which frora A to N will raeasure one
half the longest diameter, which must be set upon the line IMP before drawn
from the centre M equally right and left ; and lastly M C, will raeasure half
the shortest diaraeter, which raust also be repeated to K. These diaraeter.<8
being found, the foci for striking the ellipsis raay likewise be found bv pro
blera 27, Practical Geometry.


PRACTICAL GEOMETRY. 41

To describe the cyma reversa, fig. I, or ogee, by means oj ordinates.
The height and projection of the moulding being given as before, com
mence by dividing the projection into two equal parts ; through which draw a
perpendicular equal to the height, which also divide into two equal parts, as
atZ; and through this division draw a line of any inclination at pleasure,
intersecting perpendiculars raised from the ends of the raoulding as at m m.
The quirks at top and bottora being taken off; from these, draw lines parallel
to m m, each terminated by the perpendicular line kk; then proceed and
find the ordinates as before described, for the parabolic echinus, marked G
To describe the cyma recta, fig. K, hy the same means.
Having the height and projection ofthe moulding given, as before, form
the same into a parallelogram, the sides of which divide into two equal parts,
each way; through which division draw lines, nn,pp, perpendicular to
each other, intersecting in the point o; from whence the divisions must
commence for finding the ordinates, and proceed as before directed ; q q
being dividing points for those divisions placed along the line n n.
All these mouldings have been selected as being in general use, and
may be used either for the upper mouldings of cornices for windows, book
cases, &c. as D and K, where they forra a finish ; in regard to mouldings
for supporting table tops of raarble or wood, we may use in either case those
marked G H or I ; the sarae raouldings reversed, may be adopted for bases.
.,' ' Geometrical Figures, Plate 2.
In this Plate are given five various ornamental pieces, intended for
friezes, bands or raouldings, and which have been as variously used by the
ancients. The Fret or key moulding, has the highest claim to antiquity,
existing frora the earliest period araongst the Chinese and Persians,
frora whence it was carried into Egypt, and from thence into Greece, em
bellishing their buildings, as well as their vases ; it was probably coraposed
from the form of writing used araongst the Persians, where a similar orna-
0


42 PRACTICAL GEOMETRY
ment denotes a sentence. Frora the nature of its construction as to forra
or pattern, an endless variety raay be obtained, and which has been beauti
fully practised by the Etruscans on their fictile vases ; in Cabinet-work the
patterns, fig. 1 and 2, in the present Plate, executed in raetal of a mixture
of ormolu or bronze, are proper for the friezes of cabinets, bookcases, or
commodes ; in decoration their use is tastefully eraployed as bands, or in
borders ; and in every case they will not fail of producing a chaste and
pleasing effect The cabled moulding, fig. 3, as a base raoulding to Cabinet
work, either cast in raetal or carved in wood, will always produce a richness of
effect, particulariy so if executed in ormolu, and has been thus happily appro
priated on many occasions by our French neighbours. Fig. 4 and 5, pre
sent two speciraens of the antique guiloche, used by the Roraans at their
happiest period ; forming the ornament for the bands in the division of their
arched ceilings, and tastefully adopted in the torus raouldings of their co
lumns ; these forms have also been greatly used by paper-hanging designers,
and profusely so by the carpet manufacturers ; in patterns, therefore, of
such general appropriation, rules for their construction cannot but prove
acceptable. 4
To f orin the Greek Fret, fig. I .
The width of the pattern being determined, as A B, divide such space
into thirteen equal parts, and draw lines parallel to A A and B B, from
such divisions, the whole length of your intended pattern. Take one
division from the width, and repeat it on the lines A A or B B, and
draw perpendiculars throughout the whole length ; you will then have
divided your pattern wholly into small squares ; by retaining or rejecting
more or less of these little squares, the pattern is forraed, and it will thus
be dependant for its beauty in forra and use, according to the taste and ability
of the designer ; in the present design, the pattern in its length is coraposed
of two figures, the one half of the pattern occupying twelve of the squares,
the other half pattern eight squares in length : observe, that the band, or
what is called the Fret, andthe spaces between, are always equal in size; thus
the bands X, X, X, X, occupy the space each, of one of the divisions, and
the dividing spaces the sarae measure likewise^





PRACTICAL GEOMETRY. 43
Fig. 2 is constructed entirely on the sarae principles, and, therefore,
needs not a repetition ; a little practice in drawing these figures will render
any difficulty sraall, and afford rauch arauseraent.
To form the cable moulding, Jig. 3.
Divide the width E F into three equal parts, as nurabered 1, 2, 3;
then subdivide the second division into two equal parts, for a central point,
and describe the sraall circle I; this raay then be called the eye ; on the same
centre, with an opening in the corapasses, equal half the width E F, describe
two semicircles uniting at m; next proceed and set two of the divisions
from o to n, and then n will again become another centre, frora whence to
continue your circles; the whole length being gone through after this
raanner, the lines or portions of the pattern not wanted to reraain, are to
be rubbed out.

Figure 4.
This pattern is divided exactly into the same proportion ; as is seen by
the nurabers 1, 2 and 3, on the width G H; only a band is added, which the
figure shows ; the space betwixt the bands, adraits of being filled with various
ornaments agreeable to the fancy of the artist.
Figure 5.
This elegant specimen of ancient design in ornaraental decoration, is
constructed on sirailar principles, to the two figures preceding it; only the
width ofthe design or pattern I K, must be divided into five equal parts,
the central one X, forming the eye, whose centre becomes the point by
which to strike the larger and smaller circles; in this design one division is
appropriated for the band, which again has two sraall fillets taken out of it ;
this pattern, like the other two, is equal throughout, in its divisions, having
three parts between centre and centre, as is seen in the figure ; of the highly
beautiful raanner in which this pattern has been enriched by our forefathers
in decoration, the present design will give sorae idea.


44 PRACTICAL GEOMETRY.

Geometrical Figures, Plate 2.
Let A B, fig. 1, be the given height for a Greek or Etruscan shaped
vase, without including the base : in the present exaraple it is intended to
shew one half only, as the other half raust be worked by the sarae process ;
the line A B is, therefore, considered as a vertical one, and passing through
the centre of the vase ; let this line be divided into three equal parts, from
A to B, as numbered 1, 2, 3 : next give two of these parts for the height of
the belly or body of the vase, set up frora A to C ; and take one and a half of
the same parts for one half the width of the vase from C to D, from which drop
a perpendicular D E indefinite ; draw a line frora A, perpendicular to A B,
until it intersects the line D E, at F. Divide A F into eight equal parts, and
number them, beginning with the first from the centre A ; divide F D also
into the same number of equal parts, and number this line likewise, beginning
at the first division above F. Proceed and draw lines frora No. 1, above F,
to No. 1, at A ; from No. 2, on F D, to No. 2, on A F ; frora No. 3, on
F D, to No. 3, on F A, and so on for all the rest, for every number from
1 to 8 on the line F D ; which will produce an intersection of lines gene
rating points as noted by the raarks 8 x — 7x — 6x — 5x — 4x — 3x — 2x — ;
through these points of intersection, which raust be very carefully noted,
the parabolic curved line forming one half the body of the vase from D to
A, may be faithfully traced. For the remaining height of the vase (or one
part), frora C to B, let it be divided into five equal parts as numbered, and
let two parts, form the turnover, and mouldings of the upper part, as G H.
Again, divide G H into three equal parts, and give one to i k, which will
form the lipping.
Having given one and half parts, as C D, for the width of one half the
body of the vase, give two thirds of the whole height, for the utmost pro
jection of the lipping, as B L; the outline of which, as shown at L, forras an
ellipsis; the hollow necking under it m n, makes also for its outline, the
fourth ofa parabola, as shown by the nurabers ; the base A M, in height, is
equal to the upper raouldings (B O), ofthe vase, taken together, which may
be divided into five parts, and one part A X, given for the necking betwixt
the bottora ofthe vase and the plinth X M, forming the base. The width


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PRACTICAL GEOMETRY. 45
of the base at top will be found to be twice X M, and the width at M below,
may be raade a sraall portion more. The beautiful outline exhibited in all
these fictile vases (valuable remains of antient art), has resulted from their
artists' thorough knowledge of the conic sections, and of the rules of propor
tion, by which one part is raade to suit with another, in harraonious accor
dance ; an excellence only to be obtained by the sarae labour and research
as used by these antient artists.
Fig. 2 represents a vase, constructed on similar principles, but shewing a different
outline, its height a h being given as before.
Divide the whole height a h into seven equal parts, as numbered on the
line 0 o, and set off four of these parts frora d to b, which must be numbered,
beginning from d; make d e equal to three such parts, for one half the
width of the body or cup. Divide b r into the sarae number of parts, as is b d,
which nuraber likewise progressively frora b : then divide the upper height
of the vase frora d to a, into nine equal parts, and raake e d, or the shoulder
of the vase, equal to four of the parts ; the reraainder (e a) of the height
will then forra the neck : divide this height also into two equal parts at i, and
make the width of the neck (i k) equal to the sarae raeasure; draw the line
o I perpendicular to i k, and dividing / k into four equal parts, raake k o
equal to three of such parts, and divide this also into four parts : draw the
line I e ; and raake / m equal to I k ; dividing this raeasure also into four
parts : next divide m e into four parts, also e d into the same nuraber.
From these five divisional lines o k, k I, I m, m e, and e d, the ordinates as
nurabered, are to be drawn as described in fig. 1 ; and through their inter
sections the curves forming the neck and shoulder of the vase may be traced.
The sarae practice raust be used in regard to the lines d b and b r, which
will produce an outline for thc belly or body of the figure. Divide the
height ofthe neck/^ into five equal parts, and give one-fifth for the lipping
g h, which again divide into four, and give one for the upper fillet ; raake ^ n,
which is half the raouth of the vase, in diaraeter equal to one and a half parts
out of the seven, on the line o o, into which the whole height is divided. Lastly,
divide the whole height into fifteen equal parts, as on the \inep q, and make
the height ofthe base r s equal to one of these parts ; divide r* into two parts.


46 PRACTICAL GEOMETRY.
which will give t s, for the torus or base raoulding, the reraainder for the
hollow; the width * w, is equal to one-fifth the whole height, or half s a:.
These two exaraples have been selected out of raany of those beautiful
speciraens of antient art now in existence ; the sarae principles are applicable
to all of thera, and it is evident, that the change of numbers will produce, and
does account for the endless variety in shape to be found in these objects.
The principles exhibited in these speciraens were very little known, until
coraraunicated to the late Sir W. Harailton, by an Italian artist, whose great
assiduity and toil enabled him to ascertain the systera on which these valu
able reraains of the antients were constructed.
Figures 3, 4, and 5, are examples taken from the works of Sebastian
Seriio, a celebrated Italian architect that flourished in the sixteenth century ;
they are here introduced to show the advantages resulting frora a knowledge
of Georaetry, and to prove how highly its rules are to be estimated, as they
relate to the doctrine of proportion. In the exaraple, fig. 3, the propor
tion (that is to say of width to height), is as 3 to 5 ; in fig. 4, as 2 to 3, and
in fig. 5 the proportion is as 1 to 2.
We shall now proceed by giving Serlio's rule for outlining these three last
figures, and first as to fig. 3, which bears the proportion of 3 to 5. Begin by
dividing its giyen height A B into ten equal parts, and draw a line indefinite
through the seventh division at right angles to A B ; on which line set six
divisions right and left frora the centre, each equal to those on A B, as at
C and D : through the division No. 1, draw e g indefinite, and on 2, with a ra
dius equal to one division and a half, describe an arc intersecting the line drawn
through 1, at e and g, which will terrainate the outline of the vase at bottora.
On D and C, with an opening in the compasses equal Yi c or C g, describe
the arcs e i and g k : draw a line through 8, at pleasure, and on r and s, with
a radius equal to one division (7-8), describe two segments, cutting the
line 8 at Z and m, which will form the shoulder of the vase ; divide the
space 9-10, into two equal parts, and give one for the upper member, or
lipping, and make the whole width of this lipping equal to three divisions, as
no; the curved line of the neck may then be drawn by hand ; the base/> q
will be found nearly equal to four divisions, and its height equal to three-
quarters of one ofthe same.


PRACTICAL GEOMETRY. 47

Figure 4.

Let a A be the given height of the vase, which divide into 7 equal parts
as nurabered ; through the fourth division draw the line d b indefinite, and
at right angles to a k; then with a radius equal a e on e, describe the circle
abed, one half of the circumference of which divide into eight equal
parts ; draw lines frora thera, through the centre e, cutting the opposite
senii-circuraference ; also draw ordinates or lines parallel to the diaraeter
frora each of these points, as 2x.3x.5x.6x.7x. Divide the diaraeter
d b into six parts, and on e, with a radius equal to two parts, describe a
smaller circle, as shown by the figures 6, 5, 2, 1 ; this smaller circle will then
be equally divided by the lines passing from the larger one, through the
centre e; which lines will generate intersections or points in the sraaller
circle at o, o, o, o, o, a. Drop a perpendicular from each of these intersect
tions cutting the ordinates 5, 6, 7, at p,p, p, p, p, p; through these points
right and left, the curved outline, forming the bodyof the rase, maybe
drawn. The lines 2-10, and 14-6, in their progress to the centre, cut the
ordinate 3, 13, atfg; which intersection gives the widthof the neck : the hollow
curve may then be drawn by hand; the upper raoulding may be raade one-fifth
ofthe height frora rto 6; the raoulding h, one-fourth the height from e to i;
the base c k, in height is equal to one division, and may be divided into
three parts for.its mouldings ; its width being soraething raore than its height
Figure 5.
This vase although differing in shape, 'its- outline is obtained precisely
on the sarae principles as fig. 3, which raakes it here unnecessary to go ovet
the explanation again, further than to observe, that the bottora sweep of the
vase is obtained by taking a radius of one division and a half in the corapasses,
and setting it on the half space betwixt" 2 and 3, as at G, which becomes
a centre for striking the arc E I F ; the points C and D will likewise be
corae centres for striking the arcs EH and F I ; the neck M N is equal in
width to one division, the lipping o^^ to two of the sarae, which also gives
the width ofthe base Q R, and its height is equal to half its width.


48 PRACTICAL GEOMETRY.
Note : The divisions on A B are equal to those in fig. 3, but the vase
having less of these parts in width than the other, its height becomes less in
proportion, reaching no higher than the eighth division.

Geometrical Figures, Plate 3.
The globe, jig. 1, Plate 3, being given, to find the shape of the gores, so that
when applied on its surface, ihey shall be found to join each other, and
cover it exactly.
Divide one-fourth of the circle's circumference {k I, fig. 1,) into three
equal parts, and from these points, draw ordinates, or lines, parallel to the
diameter lm,as2oo, and Ipp; raake q k, right and left of the centre, equal
to half of a division, and draw the lines q e, q e : produce the line k n, indefi
nite, on which set the measure A 1, A 2, A 3, on the quadrant frora A towards n;
and through each ofthese describe arcs, as at A; 1 and 2; proceed and take
the raeasure pp frora the triangle within the circle, and transfer it on the sweep
line k n, as raarked ^jo; next take the measure o o frora the sarae triangle,
and transfer it on the arc at 2, raarked oo; then lines being traced frora the
apex 3, through these points on both sides, will give the outline or figure of
the gore, raaking a twenty-fourth part of the covering requisite for the
whole surface of the globe. Case 2.
Another raethod raay be adopted, thus : proceed and draw a right
line E F, at pleasure, which may be considered as a parallel section through
the globe, and answering to the line ofthe equator; draw another line A C,
at right angles to this line, and set the three divisions as nurabered on the
quadrant, fig. 1, from E fo A, and frora E to C ; draw A B and C D, at
pleasure, each parallel to E F, and raake the length of the line E F double
A C, which will then equal the whole circumference of the globe, fig. 1 ;
through F draw D B, parallel to A C ; next divide the line E F -into
twelve equal parts, and nuraber them as marked; and, lastly, take an opening
in the compasses equal to nine of these divisions, and setting one foot in E,


Tl.LVn.

't:;i;o vn'iT.uii fAi, i^'igtzke^ . iii

1/ "V

London. rubhstLcd by Janes & C°Aud"^ 2,\?-Z6.





PRACTICAL GEOMETRY. 49
describe an arc cutting the parallelogram A B C D, at the points G and H;
and witb the same opening on No. 1, describe another arc through No. 10;
then on No. 2, describe a sirailar arc through No. 11, and on 3 describe
the arc passing through No. 12. To produce all the remaining arcs, the
line E F will require to be extended both ways, to receive as many of the
sarae divisions as will be found necessary to strike the arcs right and left;
the outline of all these gores will be found exactly of the same size and
shape as that in fig. 1, as is plain by a reference to the letters in each figure.
REMARKS.
The line E F, fig. 2, is equal to the whole circumference of the globe,
fig. 1, raeasured round the line /m, and raay be called the equatorial line,
dividing the globe into two equal parts : the curved lines in the parallelogram
A B C D, are each, equal in length to one half the globe's surface, frora north
to south, or frora east to west, and are called raeridians, or lines of
longitude ; the line E F, and all lines drawn on the globe parallel to it are
called lines of latitude.
These problems are useful to the Cabinet-maker, Upholsterer, and
raore so to the decorative artist. In bedsteads having dorae teasters, the
Upholsterer, by these, finds the lines for shaping a pattern or gore, enabling
hira to cut out his covering, either for the exterior or interior surface, with
out loss or waste.
The Cabinet-raaker is also enabled to get out his veneers for covering a
dome from the base to its surarait. The decorator is readily able, by the
sarae raeans to shape the mould on which to draw his design, and which, when
applied to the part required, will be found to fit exactly.
To find the true curve or outline for the ribs of an elliptical dome.
Fig. 3, is the half plan of an elliptical dome for a bedstead ; da exQ-
presenting one quarter, and e d, e c, e b, e a, four of the ribs. To find the
outline of the rib e a, set its length on a line from Y to X (fig. A), and the
given height of the dorae, on another line at right angles to it, as from X to
W ; next^ divide each of these line" into four equal parts, as nurabered, and
Q


50 PRACTICAL GEOMETRY.
draw the lines 1 1, 2 2, &c. as ordinates, whose intersections will give
points through which to draw the curved line ofthe rib required.
Fig. B represents the curve line for the rib e 6 in the plan, and is obtained
by the sarae process. The outlines for the two other ribs e c and e d, are
got in a sirailar manner. These four moulds will answer for all the rest.
In fig. 4, A B C D represents half the teaster of a regular four post
bedstead, and D H C half the plan of an elliptical dome ; E H, E G, E F
and E C, the plan of the four ribs contained in one quarter; X W, fig. C,
is the height of the dorae above the teaster, and becomes the sarae for every
rib ; XX is the length of the rib E C ; the length of the rib E G, is shown
in fig. D ; the length and height of each are to be divided, as in fig. 3, and
the intersecting lines will give points, through which the different curves
may be traced as before. In groined teasters, where the ribs pass from
corner to corner, the moulds raay be obtained, after the sarae raanner.
To find the outline of the face moulding for a raking pediment and its returning
mitre.
A B, fig. 5, is the profile of the level raoulding, C, the rake of the pe-
diraent. Divide the face ofthe raoulding A B into any nuraber of parts; in
this case it is divided into four, and those equal ; then frora these points
on the outline, draw lines parallel to the fillet A C, such as 3 3, 2 2 and 1 1 ;
next draw the line D E on any part of the rake, and perpendicular to the
line B F ; then take the measure on the rake marked (4-0), and transfer
it frora 4 to 4, beyond the line E D ; transfer the raking lines 3-4, 2-0, 1-0,
on A B, to 3 3, 2 2, and 1-1, frora the sarae line ; then through these points of
intersection 1, 2, 3, 4, the outline, making the face of the raoulding, raay be
traced. For the return, or raitre of this raoulding, if an open pediraent as
at C, raise a line on the lower fillet, perpendicular to the level raoulding, as
at F G. Frora the points 1, 2, 3, 4, in the level raoulding at A B, draw
lines parallel to B H, intersecting the perpendicular line B i, at 4, 3, &c.
Next set the raeasures 4 4, 3 3, 2 2, 1 1, from the level moulding, on the raking
lines 1, 2, 3, 4, frora F G, as 4 4, 3 3, &c. through which points the outline
(C P) may be drawn.





PI LM

GEOMETRICAL h -. FIGURES PLATE. 4.

A ¦/ parts .

n

•n

Fig.:!.

B X
; V
'- jt-

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r;

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London, riihii'.tiefl by .Jonrs M- {'" Vin.','), li'),;(S'

^ I


PRACTICAL GEOMETRY. 51

To find the face mould of a circular pediment.
Let A B, fig. 6, be the outline of the level raoulding, which divide into
four parts, as nurabered ; frora these points describe arcs, parallel to the cir
cular fillets B B and A A : then on B, No. 1, raise a perpendicular, cutting
the upper fillet in C; and draw C D parallel to the line of thelevel mouldingNo. 1,
which make equal to the projection at A ; and from the divisions 1, 2, 3, 4,
draw lines parallel to B C, until they intersect the line C D in the points
g,f, e: next on any part ofthe pediraent, as at No. 2, draw a line (B C) per
pendicular to the curve, cutting the curve lines at o o, o o, frora which draw
tangents to each sweep, such as o A, o 3, o 2 and o 1. Make C D, No. 2,
equal to C D, No. 1 ; C e. No. 2, equal to C e. No. 1, and so on for the other
divisions, pointed out by the letters : frora these points at No. 2, draw lines
parallel to B C, and where they intersect the tangents, as at 1, 2, 3, 4, will
give the outline for the face raoulding.

Geometrical Figures, Plate 4.
The diameter of a circular loo table being given to find the proportion of a
triangular block, bearing the supports for the top.
Let I G, fig. 1, be the diaraeter of the top, and equal to four feet four inches
taken frora a scale of feet and inches; proceed and coraplete the square ABC D,
within which frora the centre C, describe the circle F G H I, which will then
be the plan of the top. In a circular table of this diaraeter, naraely, four feet
four inches, the Circle circurascribing a triangle of a fit proportion for the
block, would require a radius of twenty-two and a half inches, which raust be
taken from the scale, of which only a portion is here shown by the dotted line
K N P O. To form a triangle within this circle, divide the half diaraeter
N C into three equal parts, as nurabered frora N to C; and forra an equila
teral triangle, equal to the whole diaraeter N Q, having its apex, or point,
at E; frora E draw the line E P through the first division, cutting the arc
K N PO at P; frora P draw a line parallel to the diaraeter, cutting the op
posite portion ofthe arc at O; which line will becorae the length of one side


b2 PRACTICAL GEOMETRY.
ofthe triangle, ana by the scale be found to raeasure three feet three inches;
next draw the lines K P and K O, which will complete the remaining sides of
the triangle required. The width of the canted corners of the block under
which the supports are placed being deterrained, such width must be set frora
the apex of each angle on the sides, as frora P to k, and P to / &c. Lines
drawn frora k tof, h to h, e tog, will give the three canted corners required,
and which will be found to be one thirteenth part of thc diaraeter of the
top. To produce the curved line frora angle to angle of each cant, bisect
the line/e at n, and through this point draw a perpendicular to such line
indefinite, passing through the centre C ; then on this line, frora n, set three
inches by the scale for the depth of the sweep to p, and draw the line^ e, which
bisect also at r ,• and continue the line until it intersects C n at d, which will
becorae the centre for striking the curve e pf; the distance of which, frora
the centre C, raust be set off upon perpendiculars drawn through the centres
of the other two sides.
Note, that the depth of the sweep (three inches), is equal to nearly one-
seventeenth of the whole diameter of the top ; but it may be raade one-
eighteenth or raore, at pleasure. Remark, likewise, that the pillar, or sup
port of the top, frora the block, in its lower diaraeter, exclusive of its
ornaraental raouldings, raust not exceed an eighth of the whole diaraeter of
the top, and will, therefore, in this instance be six and a half inches.
This mode of proportion will hold good for all tables, either of a larger
)r smaller diameter, and reference may then be made to the rule of three,
as raentioned in problera 19, relating to the occasional table.

To find the outline for a console or truss bracket, by means of proportional
numbers.
This elegant support in the Corinthian entablature, having been adopted
{n sorae raeasure, as an ornaraental support for pier tables, coramodes, side
boards, &c. in household furniture, the raode of finding its outline raay not,
'.n this instance be deemed unacceptable.
In fig. 2, the console bears a proportion as regards the length to the
height, as I to 3 ; that is, if the height be I foot the length would be 3.


PRACTICAL GEOMETRY. 53
Divide A C into eight equal parts, four of which set frora A to E for the
centre or eye of the volute ; next bisect the division 4^5, on the height A C, as
at F; through which draw a line intersecting another line dropped frora E^
(equal four parts), which will then be the centre for the eye of the volute : this
being obtained, raake the circle or eye equal to one division, and construct the
lozenge square abed: bisect each side of this square ; then begin with No. 1,
and strike the arc ef; frora No. 2, strike the arc fg ; next, from No. 3, describe
the arc g h, which gives the greatest width of the volute ; and from No. 4,
strike the arc h i, completing the fourth evolution : the remaining evolutions
are gained by the inner divisions on the diagonal lines at 1, 2, 3 and 4,
which process, may be seen more at large, in architectural works, describing
the raethod for working the volute of the Ionic capital. For the sraaller
volute, divide the line B D into s.even equal parts, and give four of these
parts to the sraall volute for its height ; which again divide into eight other
parts as at X X, four of which set back from B ; draw a line parallel to
B D, on which line set four and a half parts frora the top, for the centre of
the eye, and proceed by the same principles as laid down for the larger volute.
The two volutes being thus obtained, draw a right line frora the bottom of
the larger one at e, to the extremity of the fourth evolution in the sraaller
one at k; bisect this line, as at G, frora which point raise a perpendicular at
pleasure : divide the half of this line e G, into nine equal parts, and set
back one of thera frora G to H ; this deterraines the centre for the corapound
curve, raaking the belly of the console. Draw the lines e H and H k, bi
secting each at V and W ; and from these points draw perpendiculars.
Maks W Y equal to one-ninth of the line e G, and V Z equal to one-seventh
of the line M k; the two curves, e Y H and H Z *, raay then be drawn
by hand, which will coraplete the outline of the console.
This system of proportion is applicable in making any working
drawing frora a design having this figure, where there is an opportunity of
allowing a bold projection. Suppose the height allowed for the support of
a table, having this contour or outHne, to be thirty-one inches, the projec
tion as A C, would then require to be ten inches and one-third ; this would
answer in open pier tables, but not so for inclosed coraraodes, for in such
case it would be found necessary to make the volute of an eliptical forra, in
order to avoid too rauch projection. The elegant outline prevailing


54 PRACTICAL GEOMETRY.
amongst the best reraains of antiquity, cannot be too attentively studied.
It proves that the attainment of thera was raore the effort of study, than the
effect of chance. It is to be observed, that the figure, as drawn here, ex
hibits the console as it is placed in the eorinthian entablature; but, when re
versed, raakes the truss supporting our present raoveables of taste and fashion

To find the proportion, the Top, the Mouldings, and Frieze of a Sideboard
should bear to the whole height.
A B, fig. 3, represents the usual height of a sideboard ; this height
divide into six equal parts, and give one for the thickness of the Top, with
the raouldings, and the frieze, as C D ; next divide C D into six equal
parts, and give one for the square of the Top, one and a half to the raoulding
under it, and the reraainder for the frieze. This proportion answers for all
sideboards, not having a plinth to support the legs.
To find the proportion, the Top, the Mouldings, Frieze, and Plinth with base
moulding of a sideboard should bear to the whole height.
E F, fig. 4, is the given height of a sideboard having a plinth (F G) with
mouldings, on which the supports would rest.
Divide E F into nine equal parts, and give one and a half of these parts
as E H, to the Top, with the raoulding and frieze. Divide E H into five
equal parts, and give one for the square of the top, one for the moulding
under it, and the remaining three parts will belong to the frieze. For tbe
base, give one division E G, for its whole height, which again divide into
four, and let one make the raoulding, the remainder making the plinth.
Of Mathematical Instruments.
Having now brpught the Geometry to a closCj it remains to give
a list of such mathematical instrumerits a? are generally contained in the-
larger or smaller cases, confining ourselves, however, to a description of ,
those oply, wl)o^e utility if le?ist,kno\yn amqpgst Mechanics.


PL. LVIil .

COI^STRUCTIO:^ OF SCAJLjIES &co

a &

I

Scale, of Fe^^ & Fnch&s.

7/\,f

k
V \-^
-9-1- ^
.9/ 
7«/ X?
17/ \l
X
b
I2 K
/t
1
2 cL 3
F-y.2.
J&Sf 3 7 6^
^
*:
:5
Scole. of Tenths.
h rri 0
?
e
ZO
^
9
\
\
'f
\
\
1
7
\
\
\
1
1
\
.y
1
\
\
-^
\
\
\
J
1
'
2
f
1 1
2
t t
2 n.
? /*-
J(
Jcafe of Chords
F^.4.
S3
— 1—
73
— t—
^.
-^
-^
-4^
_j.
-^
-^
i>£? <fO 70 60 JO 40 30 ZO 20 J
CU^—X  L__J.
l'?Mto'9 3 7 6
Fine. ofFeli/^ons.
Ir
T o-n^n^ P"'^^Usted by Jones Sc C°Dec.23, 18.?6,





PRACTICAL GEOMETRY. 55
These cases contain, first, a pair of corapasses, with a shifting leg ; thus
made, to allow the placing a brass drawing pen, or pencil, with its brass
holder, in place of the shifting leg : a pair of plain corapasses or dividers :
the spaaU bow corapasses : the drawing pen, having a steel pointer that screws
in and out of it: a brass seraicircle or protractor: the ivory plain scale; a
sector ; and parallel ruler.
The corapasses with the shifting leg are used in drawing circles and
arches of larger diraensions than can be performed with the sraall bow cora
passes ; as well as to admit of changing, the brass pen for the pencil holder,
as occasion may require. The drawing, or steel pen, is used for producing
straight lines, by the edge of a ruler ; the shaft, or handle, containing the
steel pointer or pin, is useful in making a fine point or dot upon paper
when wanted, and is used likewise in perspective, to fix at the vanishing
points or point of sight, where raany lines converge, and are required to be
drawn. The protractor is a seraicircle of brass, divided into 180 degrees, and
numbered each way 10°, 20", 30°, &c. for the convenience of taking off the
divisions ; the external edge, or straight side of this instrument, is called
the central line, and is chamfered down to the under side. The chief use
of this instrument is to measure, or to lay down any angle required ; see
its application in Plate 4, fig. 3, of Georaetry.
Construction op Scales, &c.
The scale of feet and inches, or plain scale, fig. 1.
This scale is used in making drawings of pieces of furniture, or other
objects, that require to be drawn sraaller than the objects themselves really are J
or otherwise, for raaking a design on a sraall scale, that shall bear the same
proportion in all its parts, as one on a larger ; for instance, one scale may have
its divisions (representing feet), each one inch in length ; another may have it
three quarters of an inch, another half an inch, and another one quarter of
an inch ; each of these divisions are supposed to be alike, and divided into
twelve equal parts ; therefore, by this scale it follows, that any object may
be drawn to a larger or sraaller size, and hold the same proportion.


56 PRACTICAL GEOMETRY.

To construct a scale of feet and inches.
Draw the line a b, fig. 1, on which set up six equal parts; frora
b, draw the line b d, at right angles to a b, on which set off as raany
equal divisions as you may think necessary ; which divisions may repre
sent feet, or any other certain measure; from the points e f g h i a,
as marked on the line a b, draw lines parallel to b d, and raise the perpen
diculars k I, \ m, 2 n, d c, numbering them progressively from k: the divi
sion b k representing one foot, must be divided into twelve equal parts
for the inches, after this manner ; divide a I into two equal parts, as at 6,
and drav/ the lines b 6 and ^ 6 ; by this raeans each half will be accurately
divided into six equal parts, as nurabered 1, 2, 3, 4, 5, 6, &c. In using this
scale, ifyou require one foot one inch, set your compasses on the line above
1, as at X, and open thera to 1 on the sarae line, in the inches ; you will
then have a raeasure equal to one foot one inch, and so on for every increase
up to 6; and again for any measure beyond 6, extend the compasses to the
points 7, 8, &c. marked on the line 6 b, until you finish at 12, raaking the
foot.

The scale of tenths, and its construction, fig. 2.
Proceed and set up ten equal divisions on a perpendicular line/c, and
through these draw lines, each parallel the one to the other; on the line/i
set off any nuraber of divisions you raay require, which raay represent feet or
any other raeasure ; frora these raise perpendiculars, as i k, I m, n o and
hg; next divide e A into ten equal parts, and drop a perpendicular from
each ; draw the inclined line 1 i, and lines frora 2, 3, 4, 5, 6, 7, 8, 9 and 10
parallel to it: the parallelogram fe k i, will then be divided into 100 equal
parts, called tenths or hundredths. The divisions I n, nh, raay each be con
sidered as a foot, an inch, or any other measure.
In using this scale, suppose you required a measure of five feet and five
tenths of a foot, begin by placing your compasses on 6, in the line I m (which is
the fifth division), and extend thera to the fifth division on the sarae Hne in the
parallelograra/e k i; you will then have the raeasure required. Ifthe divi-


PRACTICAL GEOMETRY. 57
sions il,ln,nh were inches, then the divisions in/e k i, would be the tenths
or hundredth of such inch. It is, therefore, evident by this scale, that the
foot, inch, or yard, raay be divided into 100 or 1000 equal parts. This
scale is found on the plain scale.

The scale of chords.
This scale is found on the sector, an instruraent of ivory, its two limbs
opening like the compasses, with corresponding divisions raarked on each
limb, and marked C. It will be found essentially useful in laying down
angles of any number of degrees, as well as to divide a circle into any
number of equal parts

To construct a scale of chords, fig. 3.
Draw a right line B C, and raake the line B A perpendicular, or at
right angles to it; raake B C and B A each of equal raeasure, and draw the
hypothenuse A C; this will then becorae the chord line, and is to be
divided after the following raanner ; — on B, with the radius B C or B A,
describe the arc A C ; divide this arc into nine equal parts, which number
frora the first division over C, 10, 20, 30, and so on to 90; the segraent, by
this raeans, becomes divided into 90 degrees ; each of which may again be
subdivided for the halves. Proceed and set one foot of the corapasses in C,
and opening the other to the division 10, describe an arc cutting the line
A C at ^^, this will then be the first division on the line of chords; in the
same manner lay down all the other divisions from the segraent, on to the
chord line, and likewise for the half divisions, as nurabered ^, ^^, &c. Sec.
be whole line will then be properly divided.
Draw a right line m I, fig. 4, and from I set off the first measure
on the line A C, fig. 3, above C ; proceed and take all the remaining
raeasures on A C, from C, and transfer them on the line I m, fig. 4, frora
I, until the whole are put down, you will then have a regular scale o.
chords to work from.


58 PRACTICAL GEOMETRY.

APPLICATION.
Suppose an angle of 30 degrees is required to be laid down; take
the measure 60 frora the scale, in your compasses, which set from n to o,
fig. 5 ; and on n, with this radius, describe an arc of a circle op; next
take the measure 30 from the scale, and placing the corapasses in o, de
scribe an arc intersecting the other at p, and draw n p; then will
p n o he an angle of 30 degrees. The nuraber of degrees contained
in the side of any polygonal figure being given, the circle circurascribing
it may, by this means, be accurately divided into as many equal parts as
the figure contains sides, provided the radius of the circle equals the raea
sure 60 taken from your scale ; if an octagon having eight sides of 45
degrees each is required, take 45 from the scale, which line will then
pass eight times round the circle, and so on for any other raany sided
figure. lAfte of lines.
This line is also placed on the sector, and is denoted by the letter L
on the end of each limb.
In fig. 6, q r, q t may represent the limbs, which are each equally
divided into ten equal parts ; its use is to divide any given line into an
equal nuraber of parts, and is thus performed. Let a a be a line that is to
be divided into seven equal parts; take the raeasure of this line in the cora
passes, and setting one foot on the sector, fig. &, at the division raarked 7,
open the other lirab of the sector until the opposite point 7 coincides with.
the opening in your compasses, in which situation let the sector reraain ;
then set one foot ofthe compasses on the division 1 on the sector, and^close
them until they meet at the opposite point 1 ; this measure will then be one-
seventh ofthe line a a. If a line of the sarae length (5 b) is required to be
divided ^into eight parts, then with such length in the corapasses, set one
foot on the division raarked 8, and open the sector until the compasses reach
the opposite division marked 8, as before described in dividing for 7;


PRACTICAL GEOMETRY 59
the opening at I, 1 will be the raeasure required; in this way any right line
may be divided by the sector. The line polygons.
The division of this line is likewise to be found on the sector, and is
denoted by the letters POL; half on each limb, as shown in fig. 7, where the
limbs, L M and L N are divided by the figures 4 to 12 marked on each lirab.
To divide a circle A B C D E, fig. 8, into five parts, or to construct
a Polygon, take the radius of the circle S A, fig. 8, in the compasses, and
set one foot on the division raarked 6 on the sector, and open it until the
corapasses touch the point 6 on the opposite lirab; thus let the sector re
main; next proceed and set one foot of the compasses on the division
marked 5, and contract or open thera until they reach the opposite point 5
on the instrument ; this measure in the corapasses will be the side of a
pentagon, passing five times round the circle, at the points A B C D E, as
shown in the figure : any division of the circle from 4 to 12 may be obtained
by the same raeans. The Geometrical square may be constructed by the
same process, for taking the raeasure 4, 4 frora the sector, it will pass four
times round the circle.

The proportional compasses.
These consist of two limbs or sides of ^brass lying flat on each
other, and appearing as one piece when shut These sides are raade
to turn or open upon a centre, (moveable in a grove cut through the
greatest part of their length; to this centre, on each lirab is fixed a
sliding piece of a short length, called an index, having a fine line
drawn upon -it to be set against other lines or divisions placed on one lirab
of the compasses, and sometiraes on both. There are the line of lines,
the line of circles, or otherwise polygons to be inscribed in circles,
on one lirab ; and a line of superficies or areas, and a line of solids on the
other; it is thought necessary here, only to show the side of that lirab
having the line of lines and of circles, as being the raost essential to our
present purpose. These lines are all unequally divided. The line of lines


60 PRACTICAL GEOMETRY.
from 1 to 10, and the line of circles from 6 to 20. Their uses are as
follow : —
By the line of lines, a given one may be divided into any number of
equal parts, by placing the index against I and screwing it fast by the nut ;
if the compasses are opened, the distance between the points at each end
will be equal. By placing the index against 2, and opening the corapasses,
the distance between the points of the longer legs will then be twice the
distance between those of the shorter ; and thus any line rnay be bisected
or divided into two equal parts. If the index be placed against 3, and the
corapasses opened, the distances between the points will be as three to one,
and thus a line is divided into three equal parts, and proceed in the sarae
raanner for any nuraber of parts under ten.
The numbers raarked on the line of circles are the sides of polygons
required to be inscribed in any given circle, or by which a circle may be
divided into equal parts frora six to twenty. Thus if the index be placed at
6, the points of the corapasses at either end, when opened to the radius of
a given circle, will contain a side of an hexagon, or divide the circle into
six equal parts. If the index be placed against 7, and the corapasses
opened so that the longest points be equal to the radius of the circle, then
the shorter points will divide the circle into seven equal parts, or raeasure
the side of an heptagon; again by placing the index at 8, and opening the
corapasses, the longest points will contain the radius, and the shortest points
divide the circle in eight equal parts, and inscribe an octagon ; the sarae
method raust be raade use of to obtain any other polygonal figure. The line
of superficies, and line of solids being only of use in the higher branches of
mathematics, renders the description of thera useless in this place, and for
which reason, the corapasses are shown in the plate with the lines raarked
only on one side.
The parallel ruler has been fully described with its use in Problera 16,
Plate II, Figure 1.


PERSPECTIVE.

INTRODUCTION.
Perspective is the science or art of projecting all objects on a plane
surface, giving thera the appearance of reality, or as they would appear to the
eye of a spectator, placed at a certain distance, and in a certain position in
regard to the object; and that by the aid of lines.
Perspective raay be regarded as the offspring of Georaetry ; the princi
ples on which it is founded being contained in the first, third, sixth and
eleventh Books of Euclid ; containing the doctrine of angles, circles, propor
tion and planes. This science raay be classed or coraprehended under two
heads, naraely. Theoretical and Practical ; the first of which, deraonstrates
the nature and truth of its propositions ; the second, applying thera to practice.
It may likewise be divided into rectilinear and curvilinear, either parallel or
inclined. The study of it is entertaining as well as useful, and of consider
able importance to the painter, and much more so to the architect and rae
chanic. To understand it theoretically, requires an intiraate acquaintance
with Georaetry, and Matheraatics; but the practical part may be attained
with a slight knowledge of Euclid's Elements; in which case the retention
of its rules laid down, will depend entirely on the strength of meraory and
continued practice. As the body acquires strength by the exertion of its
powers, so it is with the faculties of the mind : the inquisitive student will
not be satisfied but by demonstration, in which case he must have recourse
to the theory; while others will rest contented with a knowledge of its rules
by rote, taking them for granted, as they are laid down. In a work like
the present, it is not our intention to enter into that part constituting the
theory ; which would require an education, and a raind fitted for such a course
of study : we shall therefore confine ourselves to the practical part alone,


62 ' PERSPECTIVE.
and consider it more as an art than a science without oraitting to mention
and account for, in a farailiar way as occasion raay require, that which other
wise would belong to the theory. Neither is it intended to write a treatise
for those conversant in raathematical knowledge, to confute opinions, or to
improve a science so ably treated on, and brought to perfection by others.
Our only aim will be that of detailing inforraation in plain and farailiar
terms, endeavouring to reduce a science, that has hitherto been considered
difficult of attainment, easy in coraprehension. All raaterial objects become
perceptible to us by rays of light continually passing in right lines from all
parts of thera, entering the pupil of the eye ; and diverging under the sarae
angle until they are seated on the retina, a raerabrane or net work covering
the back part of it, and in a reversed position. How this impression is again
conveyed to the sensoriura or brain, giving it its original representation,
has eluded the researches and reasoning faculties ofthe most scientific men;
every thing already advanced araounting only to conjecture. Those who
may be desirous of entering into the nature of vision, applicable to this sub
ject, raay consult the works of Newton, Simpson, Brook Taylor, Hamilton,
Malton, &c., where they will find the whole amply treated of and largely
explained. The science of Perspective has been ably and powerfully handled by learned
men of alraost all countries ; but particularly so in Italy, Gerraany, France,
England and Holland. To render the subject as clear as possible to those unac
quainted with other branches of science, we shall in this place have recourse to
thesarae systera pursued by us in treating on Georaetry; beginning our course
with as many definitions as are necessary to a right understanding of all the
terms used in this amusing and useful department of art : we shall therefore
proceed in the first place, to define the point iri all its various acceptations ;
in the next, explain all the properties attached to lines ; and in the third
and last place, define the nature and doctrine of planes ; a very careful
reading of which is strongly recomraended previous to entering on the prac
tice ; as tending very materially to lessen the difficulties that present them
selves to the student in the coraraenceraent of this study ; and raake that a
matter of ease, which otherwise would be considered as one of difficulty.
In our progress every pains will be taken to render the subject clear and
famihar to the understanding, accompanied at the sarae tipie with such dia-


PERSPECTIVE. 63
grams and reraarks as are applicable and tend to the purpose. It would be
possible to have written extensively on this our present subject ; but as our
purpose is not to write so much for the initiated in science, or the clearing up
of difficulties with the raatheraatician, as for the inforraation of the untaught,
it would becorae foreign to the present purpose, and rendered in this trea
tise unnecessary ; a great deal of the science being raore a raatter of specu
lation than positive use. Those who wish to enter fully into the theory raay
consult the works of Dr. Brook Taylor, Harailton and Malton.
In order to a right understanding of the true principles of this
art, all objects about to be represented should be considered as placed
behind the picture or any transparent plane, such as glass; through
which a distinct view of the object on the other side would present
itself to the eye of the spectator : in this case it is evident that by keeping
the eye steadily fixed to one point, such object or objects may be faithfully
traced by the hand on the transparent plane : this, the rules of perspective
enable us to realize by the aid of lines.
The true principles of this art were very little known in this country, until
taken up in a very scientific raanner by Dr. Brook Taylor; Who is supposed
to have drawn his principles from a work written by one Guide Ubaldi, and
printed at Pesaro, in the beginning of the fifteenth century ; who first disco
vered that all lines parallel to each other, but inclined to the plane of the
picture, would converge to sorae point in the horizontal line ; such point
being gained by imagining a plane to pass frora the eye of the spectator
parallel to the side of an original object, until it cuts the picture. These
principles have since been greatly iraproved upon by subsequent writers.
Having said thus much as to its use in general, we shall now say
something how far it can be useful to those raechanics to whora our
treatise is addressed. To these the knowledge of Perspective is of the
greatest iraportance, enabling thera to show by a slight but spirited sketch,
a model of the article they design to raake. In taking orders, they will
find in this, a real advantage over others that have not the sarae acquire-
raent. That the subject has hitherto been too raatheraatically treated is well
known, but no fault can be attributed to those who have written on it ; as
few or none have thought it worth their while to treat it in a manner fitted
to the coraprehension of humble capacities. A great advantage also arises


64 PERSPECTIVE.
from a knowledge of this art, insomuch that any design can be raade and
forwarded into distant parts, either at ¦ horae or abroad, and have the sarae
effect as would be produced by a raodel. The raaster Cabinet-raaker, or
foreraan, should on no account be uninformed in this science, or neglect ad
vantaging themselves by it : they can convey their ideas better to the
artizan by a true perspective sketch in many instances than by lines; and
for the sarae reason the workraan should not be deficient, as in this instance
he would he would raore readily enter into the designs of his employer. If
therefore our explanations do not abound with technicals, but are confined
to plain and siraple terras, it is so done to render the raatter clear to the
student. Thus much for introduction ; a considerable deal raore reraains to
be said; but will come in with better effect, and more to the purpose, in de
fining singly the three essential parts constituting the whole art of Perspec
tive ; namely. Points, Lines and Planes. The greatest defect in all books
written on this subject has arisen from placing several diagrams on the
sarae sheet; the consequence has been a crossing or raixture of lines, quite
sufficient to terrify any but a hardened student from entering into the sub
ject ; much less to follow references so intermingled with those of another
object. Our plan will be different, giving the diagrams singly as the only
means of avoiding confusion. It remains now to commence with the defini
tions, and this we shall first do as regards the Points.

PERSPECTIVE, Plate A.
DEFINITIONS. Points.
Point op Sight — Is that point imagined to pass frora the eye of the
spectator, in a direct line, and at right angles to any transparent plane,
placed between hira and the object; intersecting such plane in the horizon :
such is the point s, Plate 1, Diagrara 1 : also s in Diagram 2, and D in
Diagram 3, where d efg may be considered as the transparent plane, and de
the horizon. This point is commonly called the centre of the picture, be
cause the spectator's view is equally extended right and left ofit.





PL- LXXXVIl.

Peirspective. a
DEFINITIONS.

Loniioa FuBlistei ly Jones &C° iIovVl,1826,


PERSPECTIVE. 63
Station Point — Is a point on the ground plane, generated by a perpen
dicular Hne dropt frora the eye of a spectator to his foot; such is S, in Dia
grara 1, where the line D D raay be considered as the site of the transparent
plane, and s the point of sight as explained above. Also G in Diagrara 3,
where the point is shown as dropped frora the spectator's eye to his foot.
Point op Distance — Is a point placed on the horizontal line right or left
frora the point of sight, denoting the distance frora the spectator to the
centre of the picture or transparent plane : such is S s, Diagrara 1, placed
frora s to D, right and left : s D, Diagrara 2, and S D, Diagrara 3, where
each represents the space frora the spectator to the plane ofthe picture.
Directing Point — Is a point generated by a line passing direct frora the
side of any original figure, and intersecting the plane of the picture on th«
ground. DEFG, (Diagrara 4,) and H K L M, (Diagrara 6,) are both original
figures, with the line of the picture, placed above each of thera ; iu such case
a line supposed to pass frora the side E F, (Diagrara 4), and the angular
point L, (Diagrara 6,) would intersect each of these lines at the points I and I;
such points would become directing points. A perpendicular line raised
frora either of these points would constitute what is called the Geometrical
line ; as D I, (Diagrara 4).
Vanishing Point-t-Is a point passing in a direct line frora the eye of
the spectator, parallel to any side of an original figure, and intersecting the
plane of the picture in the horizon. In Diagram 6, V- V, are the vanishing
points of the sides L K and L M ; M H and H K, of the original figure
HKLM. In Diagrara 5, s represents the station point, and S its distance set
up frora the horizon. Van, Van, are the vanishing points of the sides
L K and L M, of the figure in Diagrara 6. Dist, Dist, denote the
points of distance for the same sides, and which points are the distances
from L to V on each side of the figure, set off from the vanishing points in
Diagram 5, as shown by the arcs.
Diagonal Point — Is a point imagined to pass from the eye of the
spectator in a direct line, and cut by the plane of the picture; such line
bisecting an angle of 90 degrees, supposing the eye of the spectator to
be the vertex.


66 PERSPECTIVE.
In Parallel perspective the Point of Distance serves as a diagonal point,
because it passes in a line frora the eye of the spectator at an angle of 45
degrees. This point is used for obtaining the raitre lines for all right angled
figures in perspective, whether parallel or incHned to the Picture; Diag,
in Diagram 5, denotes the Diagonal point, bisecting the right angle a S b.
Having defined the different points made use of in Perspective, and
illustrated thera by Diagrams ; the definition of Lines and Planes falls the
next under consideration. In perspective there are- six lines chiefly to be
considered ; namely, the Ground line, the Horizontal line, the Vertical line,
the Original line, the Station, and the Vanishing line.
Ground or Base Line — is a right line passing under the foot of a spec
tator, and drawn parallel in every respect to his horizon, or the line passing
through his eye : it denotes that part of the surface upon which he is sup
posed to be stationed, when looking at any object ; such is the line C D,
fig. 1, Plate B.
On this line all Geometrical or known measures are usually placed.
Horizontal Line — is a perfect level line passing through the eye of the
spectator and bounding his view on every side : it is that line or circle
where the heavens and the earth appear to meet. A B, fig. 1, Plate B, is
the Horizontal line of the spectator standing on the ground line C D.
This is considered the principal line in perspective delineation ; as regu
lating from its fixed and deterrained position, all other vanishing lines ;
we shall, therefore, on this account, be raore particular in explaining it;
the proper understanding of which will very much assist the student in
comprehending the doctrine of planes ; a subject which has hitherto passed as
a matter of difficulty.
It may in the first place be necessary to inforra the reader that, from
the convexity of the earth's surface, every point or place on it will have a
different horizon, in regard to a spectator stationed on it.
Let EFG, fig. 2, represent an arc or portion of the earth's surface,
drawn on as large a scale as the limits of the paper will adrait: the space
from F to H raay be considered as one meridian or twelfth part of its cir
cumference, containing 30 degrees or 2085 English railes. If a spectator
be stationed at H, a tangent I m, drawn through this point will be his
horizon: if placed at F, ojo will then becorae his horizon: a line drawn


Perspective B
Definitions.

London ruTjlishcd. JJv Jones ^- ^- ' liovV !¦ lo.. 6.





PERSPECTIVE. 67
at right angles to any one of these tangents, would pass through the
centre ofthe earth, and consequently becorae the centre of gravity to such
tspectator. Suppose the spaces i H and H k, each to represent the eighth
part of this raeridional space; they will each raeasure the eighth part of 30
degrees, or 260 railes and 5 furlongs. Now although this space of ground
is literally a curved line, the angle raade by the tangent or level line I m,
passing through H, is so sraall in this nuraber of railes as to make the seg
ment iraperceptible, and appear to a spectator travelling over the whole, or
a part ofit, a straight line. If therefore the earth's curvature is iraperceptible
even in 260 railes, it must be less so in a sraaller portion, so that a traveller
continually walking over its surface, would find hiraself everywhere on a
level, and for this reason his horizon would be a straight line.
The Horizon is' either Sensible, Rational, or Visible. The Sensible
Horizon is a circle, the plane of which is supposed to touch the spherical
surface of the earth in the place of the spectator, whose horizon it is, and
frora thence continued to the sphere of the heavens : thus in fig. 3, if I iraa
gine rayself placed at/ and the ground on which I stand to be extended every
way until it reaches the sphere of the heavens, as shown in the figure by the
perspective circle I ; this plane becomes my Sensible horizon : if I travel
onward to g, my Sensible horizon will be the circle L.
The Rational Horizon is a circle whose plane passes through the centre
of the earth, parallel to the sensible horizon, and continued to the heavens : the
circle K is the Rational Horizon of the figure placed at/^- likewise the circle
M becomes the Rational Horizon of the figure at (g). The earth is so sraall
in comparison to the raagnitude ofthe sphere ofthe heavens, that the planes
of the sensible and rational horizon coincide ; that is, the distance betwixt
them, when measured in the sphere of the heavens is' insensible ; not
great enough to be discovered by observation. We raay, for the sake of
coraparison iraagine the circle H, which in this diagrara represents the
figure ofthe earth, to represent the sphere ofthe heavens; in which case the
earth would be no larger than the point M, and consequently the distance
between both horizons would be insensible, being denoted only by a single
line. To illustrate the coincidence between the sensible and rational horizons,
still farther, we have thought proper to introduce a diagrara, taken frora an
eraineijt writer on Astronoray, explaining it nearly in his own words. Let


68 PERSPECTIVE.
G, in Fig. 8, represent the earth, and H, the sphere of the heavens. If an
inhabitant of the earth stand on the point A, his sensible horizon is A L and
his rational horizon h o ; the distance between these two planes is G A,
(equal the seraidiaraeter of the earth) which is raeasured in a great circle of
the sphere oi the heaven, by the angle » G e, or by the arc i e. This arc
in so sraall a circle as H i, &c. would araount to several degrees, and conse
quently the difference between the two horizons would be great enough
to be discovered by observation. But this circle H i e, representing the
sphere of the heaven is too sraaU in proportion to that, representing the
magnitude of the earth. Now let the sphere of the heaven be represented
by the larger circle P K »j, &c.; here the seraidiaraeter of the earth G A,
measured in this circle, would amount to fewer degrees : for the arc K m,
measures a less nuraber of degrees in the circle P K m, than does ie, in the
circle H i e, &c. thereby raaking the angle K G w», less than the angle i G e.
But this angle raay araount also to raany degrees or rainutes, and consequently
be large enough to be raeasured by observation.. If we imagine the sphere of
the heaven to be still larger in proportion to the globe of the earth, so that
the half of it may be represented by a semicircle of which P L is a portion,
the distance between the planes of the sensible and rational horizons, as
measured by the angle L G 0, or by the arc L o, is less, as containing fewer
degrees than in the last supposition ; but may still be large enough to be
observed. From a view of this scherae, it appears that the larger the circle
representing the sphere of the heaven, is, in proportion to the globe of the
earth, the less sensible will be the difference between the sensible and
rational horizon ; as being raeasured by less angle. We may suppose the
sphere of the heaven so large, that the angle which should measure the
distance of the sensible frora the rational horizon would amount only to a
few minutes, or perhaps not so rauch as one second of a rainute, and conse
quently too small to be raeasured. This in fact is the case, as raentioned in
the Diagram, Fig. 3 ; therefore the difference between the two horizons
is insensible : just as it would be if the earth was a point of ncsensible
raagnitude. The Visi|)le Horizon is a circle, or plane, passing through the spectator's
eye, parallel to his sensible and rational horizons. This in perspective is
commonly called the Horizontal line, in which all lines situate on the ground
plane, or any plane parallel to it, appear to vanish and become impepc^tible.


PERSPECTIVE. 69
Suppose the circle S, fig. 4, to represent the earth; if a spectator be
stationed at n, the line c rf passing through his eye would be his Visible
Horizon; a b his Sensible, and Z m his Rational Horizon. The sarae applies
to thp figure placed at R, as denoted by the lines e / &c. Thus rauch in
explanation of the Horizontal line.
Vertical Line ; this is a right line drawn frora the spectator's eye to
his foot, and at right angles with the Horizontal and Ground lines, dividing
the picture into two equal parts; it is coraraonly caUed the central line ofthe
picture. In fig. 5, n o, represents the Horizontal line, p q, the Ground line ;
a line r s, drawn perpendicular to these, through the centre of the picture,
would becorae a Vertical line.
Vanishing Line — If a plane be imagined to pass through the eye,
parallel to the ground plane or to any plane perpendicular or inclined to it,
and continued to the picture, it will by its section thereon, generate a line.
This line so produced is called a Vanishing line.
The Horizontal is the Vanishing line for all lines and planes that are
parallel to the ground, situate either on or above it.
The Horizontal Line, H II, Fig. 6, is the Vanishing line, for the plane
A B C D, because this plane being seated on the ground, there converges
in a point, from hence called its vanishing point ; likewise the Vertical line
V V, would become the Vanishing line for the inclined planes, abed, and
c d ef; V V, their vanishing points being there seated.
Station Line — Is aline drawn from the foot of the spectator and
continued to the plane of the picture, cutting it at right angles: it is
generated by the intersection of the Vertical with the Ground plane. This
line produces the point of sight or centre of the picture. Suppose ; D E,
Fig. 7, to be the Ground line ; A B, the line of the picture ; the point S
produced to C would generate a line ; this line so produced is called the
Station Une. If the picture be placed before the spectator at S, in the
inclined position mb; ^ c, would then become the Station line.
Pl.wes.
A Plane in perspective is an imaginary surface, perfectly even in itself;
and bounded either by strait lines or circles. See this also explained
in Georaetry, page 10.


70 t PERSPECTIVE.
The picture in Perspective is always considered as a plane. If you
suppose a square of glass to be placed between the spectator and an
object, and through which he views it; this would be called the plane of
his picture. Likewise the board or canvas upon which any subject i.s
drawn raay be called the plane of the picture.
A plane raay be of any figure, and is always imagined to be infinitely
extended. In the practice of Perspective, the understanding of imaginary planes
is of considerable iraportance ; since the boundaries of all solid bodies,
whether rectilineal or curvilineal, constitute planes.
There are in Perspective five eleraentary planes necessary to be
understood : viz.
1 . Plane of the Picture — which is always supposed to be perfectly
upright, and placed at any distance between the spectator and the
object; intersecting the Horizontal and Ground planes at right angles-
This plane is always considered transparent, inasrauch as all rays from
the object to the eye of tbe spectator, are supposed to pass through it,
forming thereon the perspective representation of that figure.
2. Ground Plane, which is always considered as perfectly level and
parallel in every respect to the Horizontal plane : such is the floor or
ground on which we stand.
3. Horizontal Plane. This is a plane imagined to pass through
the eye of the spectator, extending itself to the reraotest Line* of
vision, and being in every respect parallel to the ground plane, it becomes
the vanishing plane for all objects standing perpendicular on that plane ;
whether they be rectiHnear or curvilinear, parallel or inclined to the picture.
4. Directing Plane — is a plane perfectly upright ; iraagined to pass
through the eye of the spectator, right and left, parallel to the plane
of the picture ; and at right angles with the Ground plane. In this plane
all the geometrical heights of objects are supposed to be seated.
* In this line, which terminates the plane ofthe horizon apparently to the eye, the vanishing
points of all objects, bounded by horizontal and vertical planes are supposed to be seated,
and where the objects themselves would appear to vanish and become invisible.
This applies to vertical as well as horizontal planes, the height of one diminishing \yith the
breadth ofthe other, in proportion as they recede from the eye and approach this line.





PL, LXX Vlll ,

PERSPECTIVE . C.
DEriNITIONS

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PERSPECTIVE. 71
5. Vertical Plane. This plane is also perfectly upright, and
iraagined to pass frora the spectator's eye, cutting the picture, and the three
other planes, at right angles.
All planes, standing perpendicular to the ground plane, become ver
tical planes ; and raay be placed in any position with respect to each other,
either parallel, perpendicular, or inclined. The vanishing points of all
objects in the horizontal line are generated by these planes.

EXAMPLES.
1. G H E F; (figure 9, plate C,) represents the Plane of the Picture ;
being the plane through which the spectator, (stationed in the directing
plane, R S D C,) would view the object.
2. D E FC; in the same figure represents the Ground plane; because
it passes under the foot of the spectator at M; and is parallel to the
horizontal plane A N 0 B.
3. A B N O ; denotes the Horizontal or vanishing plane ; as passing
•through the spectator's eye at I, and by its intersection with the picture
at P Q, producing what is called the Horizontal line. (See also definition
of lines page 4.) --
4. R S C D ; represents the Directing Plane, as passing through the
spectator's eye, and paraUel to the Plane of the Picture G H E F.
5. I K L M ; denotes the Vertical Plane ; caUed likewise direct, as
passing iraraediately from the spectator's eye, and continued to the plane of
the picture, cutting it and the three other planes at right angles.
Besides these already mentioned, there are others called inclined
planes ; which are neither parallel nor inclined to the Picture : such are the
sloping tops of desks; the revolving frames of Cheval dressing glasses;
the inclined roofs of houses, &c. These would vanish in a plane per
pendicular to the horizon, or otherwise into a vertical plane.


72 PERSPECTIVE.

EXAMPLES.
Fig. 10, represents a desk, the top of which I K LM, forms an inclined
plane, vanishing into the vertical Hne V S. It raay also be considered as
the folding flap ofa writing table.
Fig. 11, represents a box, with the lid or cover as turning on its hinges
or centre N O, generating thereby a plane, taking the forra of a quadrant,
as denoted by the letters T P R U. According as the top is raore or less
raised, so it would generate various inclined planes ; as shown by the letters
P Q N O, and R S N O.
Visual Rays — are right Hnes drawn frora the angular corners or
extreraities of an object, to the spectator's eye ; cutting the plane of the
picture, and forraing thereon its image or perspective representation.
Exaraple : X and W, (Fig. 12), are original objects, seen through the trans
parent plane abed, by the spectator stationed at S T. Lines drawn
frora the base and apex of the pyramid X, as also from the square W,
to the spectator's eye at S, are visual rays. These rays produce the repre
sentation of the original objects, X and W, on the plane of the picture abc d,
which are denoted by x and w; hh, raaking the Horizontal line ; c d, the
Ground line, and i i, the Vertical line.
The appearances of all objects are conveyed to the eye by raeans of
visual rays. The nearer any object is brought to the eye, the larger it
will appear ; the further it is placed from the eye, the less it wiH appear ;
making the angle raore or less extended in proportion to its distance. This is
shewn in the diagrara Fig. 13 — where the line F F, by the visuals raakes
a larger angle than the line B C, as raeasured on the seraicircle D E. The
other lines raarked F F, F F, &c. each show the variation of the angle, as
they recede raore or less from the eye.
Pyramid of Rays — are visuals drawn from every extreme point of a
rectiHneal solid to the eye ; thereby forraing a solid angle, composed of
several plane angles ; raaking together the form of a Pyramid : such are the
rays drawn from the several extremities ofthe object y. Fig. 14, to the eye
at S, making a similar figure (y) on the plane Z


PRACTICAL PERSPECTIVE. 73
Cone of Rays — are visuals pr right lines drawn frora any globular or
cylindrical object ; so called frora the rays passing from each extreme or
tangent of its surface towards the eye, and forraing thereby a figure resera
bling a cone : as is shown by Fig. 15.

PRACTICAL PERSPECTIVE.

Previous to commencing the practical part of perspective, it may
perhaps be necessary in this place to furnish a few observations, accom
panied with certain rules, as regards the position of the picture, and the
distance the most advisable to be reraoved frora it, so that the object
.shall appear to the eye under the raost agreeable and natural point
of view. There is a difference between the original object and its perspective
representation, although the one is often raistaken for the other. If we wish
to see an object in its truest and raost natural form, we must place ourselves
in a line parallel to the front of it, or in other words directly facing it ;
fbr the iraage forraed on the retina (a net work covering the bottom or
back part of the eye,) from this position, will approach the nearest iu
similarity to that of the object under view ; and according as this position
is more or less in a parallel line to the object we contemplate, so the idea
of its figure will be conveyed raore or less perfect to our senses.
As the appearance of an object to the spectator's eye is formed on the
retina, so its perspective representation would be drawn on the plane of
the picture, and its appearance will depend on the position of this plane ;
which position raay be infinitely varied.
In reference to the shape and size of the picture no deterrained rule
can he laid down, as this is always at the discretion of the artist, and
regulated according to the extent of his view, and the nuraber of objects
to be introduced ; the oblong rectangle is in most cases selected, as being


74 PRACTICAL PERSPECTIVE.
ofa more agreeable and pleasing proportion than the square; such propor
tion being as 3 to 2; that is, if the length be 3 feet, the width would be
2 feet, or otherwise as occasion may require. Some objects whose altitude
is great, as church towers, columns, &c. require it in an upright position ;
whilst others, such as oblong figures, buildings, &c. require it more gene
rally lengthways. With regard to the height ofthe eye, and consequently
the height of the horizontal line, this also must be regulated according as
circumstances may require. In general it is placed equal to the height of the
spectator's eye, which never exceeds 5 feet, or 5 feet 6 inches frora the
ground, as in most cases he is supposed to be standing onthe Ground Plane.
In many instances, it is necessary to adopt or raake use of a low Horizon,
when we would see the under side of some objects, or projecting raembers
of others raore distinctly; such, for instance, as the inside of beds, the soffits
of cornices in low rooras, &c. The low Horizon is to be preferred in drawing
of any article of furniture, and may judiciously be reduced to 4 feet, par
ticularly iu the representation of chairs, sofas, &c. as the high horizon would
produce a distorted appearance in the seats.
It must not be taken for granted that any position or distance of the
picture, with regard to the spectator and the object is alike suitable ; per
spective; representations becorae distorted by placing the station point too
near the object ; although such "representations are equally as true, by the
rules of (perspective, as those which approach nearer in reserablance to the
original.' In pictures for general observation, such a position should be
chosen as an indifferent spectator would take without straining his eye, and
which raust always be regulated according to the size of the object.
ILLUSTRATION.
Let A B C D, Fig. 1, Plate D, represent a plane ; either paper or
canvas, upon which a subject is to be drawn ; and a spectator to be so
placed, as to view the sarae to the best advantage: the question is,
what position and distance he should take to view it advantao-eously
under such circurastances. It is evident in this case that the picture
A RC D, will be seen raost to advantage when the axis of the eye X


PL. L XXIX.

PERSPECTIVE. D

Fig.l.

H

LondouPjtl.shodbyJones.&C^Ou,. 10 18,>





PRACTICAL PERSPECTIVE. 75
is perpendicular, or at right angles to it ; because the picture in this instance
wiU be parallel to the retina or baok part of the eye boa.
And again if the said axis X cuts the middle of the picture at S, all
the extreme parts of the plane A B C D, equidistant frora the central point
will be equally inclined to the eye ; that is, the rays E X and F X, pro
ceeding from the points E and F, will enter the pupil of the eye at X
under the same angle ; and the appearance of these rays will be the nearest
in this instance to the centre of the retina at O ; and thus the whole picture
will be seen to the most advantage, when the seat of the eye is placed in its
centre S : see the diagram Fig. 2.
The seat of the eye being deterrained; its distance from the picture
or object under view is next to be considered. If we place ourselves
too near the object, the whole of it cannot be seen, and if too far removed
from it, the raore rainute parts cannot be distinguished. Let S, be the seat of
the eye in the picture, ABC D ; if the eye be reraoved frora it equal the
distance S E, as at X ; a ray drawn from E, through the centre or pupil at
X, will cut the axis or line S o, at an angle of 45 degrees, which woukl be
the greatest angle under which the object would be visible. For let the
point be raised to H, the line H X, passing through the pupil of the eye
would not be conveyed by the crystaline humour (tinctured blue in the
Diagram,) on to the retina, it being below it, as at V; as may be seen in
the figure. The point E, fig. 1, although visible, cannot be seen distinctly; being
too far removed from the centre of the retina ato. The points G and I, whose
distance is G S or S I from the seat of the eye at S, is not two-thirds of the
distance S X, and will therefore be a rauch better boundary for its limits,
as seen at d and c in the eye ; because the rays G X and I X, cut the axis
S X, at a less angle, and consequently bring the points d and c, nearer to
the centre of the retina at o. Again admit the extreme distance of the picture
frora the eye not to exceed the distance K S or S L ; (half the distance S X,)
the appearance then of such picture will occupy the space or diameter e f,
which space would approach nearer to a plane surface, than the curves a o b,
and cod: in this case, the figure on the picture and its iraage on the retina
will be nearly similar.


76 PRACTICAL PERSPECTIVE.
The shortest distance that can be allowed, is that, which the farthest
point of the picture is frora its centre. Let A B C D, fig. 2, represent a
picture and S its centre; tbe distance S A, set on to X, is the shortest
to be taken. Instead therefore of raaking this the distance of the picture, it
will be raore advisable to raake it twice this distance, namely the distance
of S I • as such would be a distance any person would naturally choose
in order, to see the whole without losing sight of the minuter parts ;
and which is here laid down on the horizontal line from S to K. If the seat
ofthe eye be directly inthe middle of the picture AB C D, as at s, the dis
tance s i, equal s A, will be shorter than the distance S X; and which would
in consequence make the distance s k, shorter than the distance S I ; it
will therefore be raore advisable to place the eye at S, rather than at *.
It raust here be reraarked that he who works with a short distance, will
produce a picture greatly distorted; but if he use a long distance, or one
not less than twice the distance, the farthest extreraity of the picture is from
the seat of the eye, no deformity will arise : therefore a long distance is the
most advisable to be used.
EXAMPLES. Plate I.
To delineate or find the representation of a square on the ground plane, the
length of one side a h, being known, and placed parallel to the picture.
Let G G, Fig. *1, represent the line of the directing plane, (the plane
supposed to pass through the spectator's eye, perpendicular to the horizon
as before described ; and comraonly called the Ground line.) Let H H,
represent the horizontal line ; (its height frora the ground line in this diagram
being assuraed;) S, the centre or point of sight; and D D, the points of
distance, taken at pleasure and set equally right and left frora S. Thus far
being arranged, suppose a h, to raeasure the side of a cubical or square
figure : set the length of this on the base line, and from its extremities, a and
b, draw lines or visuals tending to S ; a line frora a or b, drawn to the point
of distance D, will intersect the visuals, a S, and b S, in the points d and c ;


Pl;xxx.

LONDON Pubhshed Ijy JONES SsC April e 1826.





PRACTICAL PERSPECTIVE. 77
through these intersections draw a line d c, parallel to the base line.
This will coraplete the perspective representation of the figure ab cd. The
lines 6 D, or a D, are coraraonly called diagonal lines ; because they pass
through the opposite corners of the perspective square abed.

Figure 2,
To represent a pavement of squares in perspective, two of their sides ocmg parallel
to the picture.
I et G G, represent the ground Hne as before ; H H, the horizontal
line ; S the point of sight ; and D, D, the points of distance. Take the
raeasure of one side of a square, and repeat it any nuraber of times on the
ground Hne from a ; in this diagrara seven are shewn : frora each of these
divisions, draw visuals, tending to the point of sight, S ; a diagonal line
drawn from a or b, to the distance D, will intersect these visuals in
seven different points ; through these points draw lines parallel to the base
line G G, and the paveraent will be corapleted; as shewn by the black and
white chequers.

FlGUllE 3.
To represent a pavement of squares, hamng lozenges or rhombs, with a border
between each square.
First proceed and set off the width of the border on the ground
line, frora a, (in this diagrara left. white :) next set off the side of a square,
(here shadowed black ;) and again repeat the border, and so on for as raany
squares and borders, as you raay require. In the present exaraple there are
three squares, and four white spaces, raaking the borders; to obtain the
perspective representation of these, and their distance frora each other, as
j:hey recede frora the eye ; proceed as directed in fig. 2. For the lozenges
z


78 PRACTICAL PERSPECTIVE.
or rhombs, find the centre of each square on the ground line ; and from
these points draw lines tending to S, which will intersect the parallel sides
of all the distant squares and give their centres : lines drawn from these
to the points of distance D and D, right and left, will give the sides of the
lozenges. ^
It will be seen by the annexed Fig. A, that the
sides, making the lozenge B, are parallel to the diagonal
lines a a and 6 b, of the square A ; which Diagonals
would tend to the point of distance ; for which reason the
sides ofthe lozenge would Hkewise tend to the sarae points :
for all Hnes parallel the one to the other and araongst
theraselves would vanish into one and the sarae point.

^

/^

>8^

/*

X
Figure 4.
To find the representation of squares placed at different distances from each
other, their sides being paraUel to the picture.
The horizontal line H H, and ground line G G, &c. being assuraed as
before, let K G, be one side ofthe square to be represented, the depth of which,
K M, raay be obtained by the same process as that used in fig. 1. Suppose
another square, as O P Q R, be required, situate at a distance equal to tbe
width of one side of the square, G K L M : proceed and draw a diagonal
line from M, to the distance D, cutting the visual line G S, in O ; a line
P O, drawn through this intersection, parallel to M L, will represent its front
or nearest line ; its depth P R, raay be obtained as before directed. Another
raethod raay be adopted for obtaining the side of a square, or the depth of
any parallelograra. Set the raeasure ofthe front side A B, upon the ground
line G G : if the figure is to represent a square, then the raeasure of one side
must be set from the nearest corner B, to C, upon the ground line ; a line
drawn from this point to the distance D, will give its depth on the visual
B S, at the point d; through which a parallel line d e, raust be drawn. If
the depth ofthe figure be equal to twice its length ; the raeasure B C, raust
be repeated frora C to F, and cut off on the visual B S, at F ; the depth in
this cafee will be represented by the length B F : If three times its length.





FL: LXX XIX.

PERSPECTIVE, i"


PRACTICAL PERSPECTIVE. 79
the sarae measure may be repeated frora F to H, on the ground line, and cut
off on the visual B S, at the point H, as before directed. This raethod
raay likevv^ise be adopted for representing the distance of one figure from
another, as shewn by the tinted squares AB d e, and F G H I ; likewise
any given depth raay be obtained by this process.

° ' Plate 2.
Figure 1.
The Diameter ofa circle being given or known, to find or draw the perspective
representation of the same ; being situate on the Ground plane, and placed
parallel to the Picture.
Suppose E G, Fig, 3, to be the given Diameter ; proceed and describe
the circle E F G H ; next circumscribe this circle by the square A B C D ;
frora the corners of which draw the diagonals AC, and B D, intersecting
the circle's circuraference in the point abed; these with the four central
points E F G H, (produced by the two diaraeter lines E G and F H,) will
make eight divisions on the circle's circuraference, and becorae so raany points
through which it would pass.
It is necessary in order to obtain the perspective representation of the
circle, to find the perspective situation ofthese points on the ground plane; for
through such points the outline of the circle (forraing an elipsis) must be
traced. The Ground and Horizontal lines; the points of sight, and distance
being deterrained; transfer the circle's diameter E G, Fig. 3, on to the
ground line G G, Fig. 1 ; as denoted by the letters A and B ; and find the
perspective representation of the square A B C D, (bounding the circle's
circumference) bythe diagram,, Fig. 1, Plate 1. Through the axis c, draw
the lines ef, andg h; intersecting the sides of the square at the points e,f, g,
and/i: these will becorae the four tangent points. The four other points
on the diagonals A C and B D, may be obtained by transferring the points
a and b. Fig. 3, upon the line A B, Fig. 1 ; as denoted by the letters a and b;
frora these points draw lines tending to S, which will intersect the diagonals


80 PRACTICAL PERSPECTIVE
A C and B D, in i, k, I and m. Through these eight points on the/ground
plane, the outline ofthe circle raust be traced. /
This raethod of obtaining the representation of a circle by eight points
win answer for any circular figure of a raoderate size ; butfor circles of larger
proportion, sixteen and soraetiraes twenty or raore points are raade use of,
Figure 2.,
This Diagram shews the same Circle in perspective, with the addition of a
Triangle in the centre ; which may represent the plan ofa block for a TLoo
Table ; the Circle representing the top.
In raaking the plan, first find the proportion the equilateral triangle
e fg, (Fig. 3), should bear to the circle, by Fig. 1, Plate 4, Georaetrical
Figures; and the mode of constructing it by prob. 8, Practical *Georaetry.
This being done, proceed and draw the circle in perspective, by the
raethod adopted in the preceding diagrara. For the triangle, transfer the
distances F e and F /, in the plan, upon the line A B, at m and n, as shewn
by the dotted curved lines ; and square these raeasures perpendicularly on
to the line a b. Fig. 2, at e and /. From these points draw lines tending to
the point of distance D, until they intersect the central rajfg, at i and m.
Through the point m, draw a line parallel to A B, at pleasure. Next transfer
the points f and g, (Fig. 3,) perpendicularly on the Hne a b, (Fig. 2,) at
n and n ; fi-om which points draw visuals tending to the point of sight S,
until they intersect the line drawn through m, at o and p; which will
give the length of the parallel side : join i o and i p ; this will give the two
other sides, and complete the triangle. The vanishing points of these two
sides are found by continuing i o and ip, to the horizontal line intersecting
it at V and V- The canted corners are found by transferring the distance
F A in the plan, (Fig. 3,) on to the Hne A B, from F to o; which raust be
squared up perpendicular to a b, (Fig. 2 ;) as at h. From this point draw a
line tending to D, until it intersects the visual/^ at * ; a line drawn through
this point and terminated by the sides, i o and i p, will give the represen-
Itation of the canted corner h, in the plan ; for the corners » and k, draw


PL.L.XXVI

FERSPECTIVE. TLATE 3.

PIG. 2

London. Published bjr Jones ScC!" Novf?. 1826





PRACTICAL PERSPECTIVE. Cl
lines frora q and r, tending to V and V, until they intersect the side o p, in
s and t; lines thrown back from these, by the Vanishing points V and V,
will give the other two canted corners, and complete the perspective repre
sentation of the triangular block, as shown by the tinted figure.
Plate 3.
To find the Perspective representation ofa regular Hexagon or six-sided figure ;
one side being parallel to the picture
It is necessary to observe that the inclined sides of a regular hexagon
are parallel to those of an equilateral triangle ; for as there are six
equilateral triangles coraprised in every hexagon, whose sides are equal ;
each angle contained therein will raeasure sixty degrees ; it follows therefore
that each of the inclined sides of such triangle would be coincident to the
inclined sides of an hexagon. Knowing thus rauch, the Vanishing points
in the horizon for the inclined sides of this figure, are easily laid down.

OPERATION.
The Horizontal Line, the Station Point, and Distance of the Picture
being deterrained, the following process for finding the Vanishing points
may be adopted. Frora the Station point S, (Fig. 1,) on the Horizontal line
H H, raise a perpendicular S I, which make equal to the distance of the
picture. Through I draw the line G K at pleasure ; and on I as a centre,
with any radius at discretion, describe the semicircle XXX, which divide
into 3 equal arcs as numbered : each arc will then raeasure an angle of 60
degrees, and consequently raeasure the side of an equilateral triangle.
Through the divisions I and 2, draw lines from I, until they intersect the
Horizontal line in the points V, V. These points are the Vanishing points
for the inclined sides of the Hexagon.
Having constructed the plan of the Hexagon abc def, hy problem 22,
Practical Georaetry, coraraence by drawing the ground line G G, upon
Virhich transfer the parallel side e jrf, as at E D ; from E and D, draw
2 A


go PRACTICAL PERSPECTIVE.
visuals tending to S ; draw also the lines E B and D A, tending to V, V> and
intersecting each other at L. Through L, draw a line parallel to E D at plea-
sure. Next from E and D, draw lines tending to V, V, until they intersect
the parallel line through L at F and C ; F E D C will then represent one-half
of the figure. The other half is obtained by drawing lines from F and C, to
the respective vanishing points, until they intersect the visuals E S and D S,
at A and B. Draw the line A B, which .will coraplete the perspective repre
sentation of the original figure, as shown by the tint.
Fig. 2, is a Diagrara which shows how the preceding example may be
applied in various ways. It represents the interior of an apartraent, the
floor of which is shown as covered with a carpet, having the pattern made out
wholly of Hexagons ; at the end is represented an Hexagonal bow, making
half the plan of the Hexagon, fig. 1. Frora the centre of the ceiling is sus
pended a lantern of the sarae figure ; the Vanishing points V, V, of this
Diagrara are laid down frora the centre S, at double the distance of those in
fig. 1 ; the points of distance after the sarae ratio. The spaces e d, edjcd,
refer to the original raeasure of the side e d, fig. 1, being taken at one-fourth
the size. The raode of representing this floor of Hexagons will be shown
more at large in the following Diagrara.

To represent a floor qf Hexagons in parallel perspective.
Suppose G G, (Fig. 1, Plate 4,) to be the gronnd line ; H H, the Hori
zontal line (the height of which, in this exaraple, is taken at pleasure); C the
centre of the picture (or point of sight) ; and D, its distance. Proceed and
lay down the Vanishing points for the inclined sides, as directed in the pre
ceding exaraple. Divide the Diaraeter, df, ofthe Hexagon into two equal
parts, one of which will be the measure of one side. Take this raeasure in
the compasses, and repeat it along the line G G, right and left ofthe centre
e, as often as the width or length ofthe floor will allow. Frora these divi
sions so placed, draw visuals tending to the point of sight C, as a C, b C,
c C, &c. Next, from a, b c, &c. draw lines tending to each Vanishing point:
the intersection ofthese lines with each other as at k, k, k, &c. will give the
centre or axis of each Hexagon, throughout the whole surface of the floor.





EL.LXXVH.

PERSPECTEVE. FLATE /,

London Published by Jones 8: C° HovfT , 1826 .


PRACTICAL PERSPECTIVE. 83
Through these intersections, draw the lines I m, no, &c. parallel to the
Ground line : these will receive and limit the inclined sides of each Hex
agon, as atak,ck,kn,U p, &c. by this raeans the whole will be completed.
The figure of each Hexagon raust afterwards be denoted by stronger lines.

To represent an octagon, Fig. 2, in Perspective, two of its opposite sides being
parallel to the picture.
As every octagon has four of its sides coincident to those of a square,
andthe reraaining four parallel to the diagonals of such square; it follows,
that if two of its sides are parallel to the picture, two would be at right angles
with it, and the four other sides inclined to it at an angle of 45 degrees :
consequently the Vanishing points of an octagon would be the centre and
distance of the picture. The distance of the picture being deterrained, this
raust be set on the Horizontal line, right and left ofthe centre C, as at J) D.
These then become the Vanishing points for the inclined sides.
Having proceeded thus far and constructed the figure of the octagon
ah cd, fg h, by problera 24, Practical Geometry, transfer the- diameter of
the square containing it, on to the Ground line G G, as at A B ; and find
the perspective representation of this square as directed in the diagrara, fig. 1,
plate 1. Frora a and b, draw visuals tending to the centre C, and cutting the
line D C, iny and e ; this will represent the side opposite to a b, in the plan.
A line drawn frora the point a to the point of distance D, will, where it inter
sects the Visual A C, give the representation of the inclined side a h, in the
plan. A line drawn frora b to the opposite point of distance D, where it
cuts the Visual B C, will give the other inclined side b c. Aline thrown
back frora the pointy bythe point of distance D, will give the representation
ofthe opposite side to b c; also aline thrown back frora e, bythe opposite
point of distance, will give the representation of the opposite side to « A ;
and thus the perspective figure of the octagon will be completed. If an
octagon be required to be represented in Perspective, where no plan is
given, the method used to obtain the raeasure of one side as directed in
problem 25, Practical Georaetry, must be adopted; as shewn in the plan by
the divided line x x.


84 PRACTICAL PERSPECTIVE.
Fig. 3, shews the raethod of representing one octagon within another
by raeans of Mitre lines.
Having obtained the Perspective representation of the larger octagon as
above directed, find the axis by drawing the Diagonal lines A C and B D,
which will intersect each other at e; to this point the raitre lines frora each
corner of the octagon raust be drawn. To obtain the smaller octagon, square
up its diaraeter from the plan upon the line G G, as at r s. From these points
draw visuals to C, which wiU intersect the mitres from d, c, g, and h; at I:,
m, p, and q; this will give the representation ofthe two sides, I m and qp, in the
plan. The other sides are obtained by throwing lines from the points /, m, p,
and q, by the points of distance terminating thera on the different mitre lines,
as will be seen by inspection of the figure.
To ¦jrepresent a square of octagons. Fig. 4, in parallel Perspective.
Having drawn the Horizontal line H H, and laid down the points of
distance as before directed, take the measure of the diaraeter of an Octagon
in the corapasses, as a 6 ; and repeat it along the Ground line G G, as often
as occasion may require, Frora these divisions a, b, c, d, e,f, so placed, draw
visuals tending to the centre C. A line drawn frora « or y to the point of
distance D, will intersect these visuals in the points xxx, &c ; through these
points draw lines parallel to the Ground line G G, and the whole square will
be perspectively divided into sraaller squares. Next find the centre of each
square on the Ground line, frora which set one-half the measure of the side
of an octagon to be represented, as o o, o o, &c. which draw to the point
of sight C. These will intersect the parallel lines g h, i k, &c. at the points
PP>PP>9 9i 99} Sec* which wiUgive the measure ofthe sides, oo, o o, &c. on
all the distant squares. Lines drawn frora these points to the points of distance,
where they intersect the visuals a C, b C, and c C, &c. will give the repre
sentation of the inclined sides of each .octagon throughout the whole surface
ofthe square.





'I. i,y.\T:jj

London. Pubfahed by Jonesife C°Dec.^3,18aS.


PRACTICAL PERSPECTIVE. 85

Plate 5.
The plan and Elevation of a Cube heing given, to represmt the same in parallel
Perspective.
A B C D, No. 1, Fig. 1, is the given plan of the cube : G G, the Hne
of the directing plane or Ground line, H H, the Horizontal line ; S the
centre or point of sight ; and D, D, the points of distance. Square up the side
A B of the cube, on to the Ground line at a and b : from these points draw
visuals (a S and b S) tending to the centre S : likewise transfer the space B b,
(the distance between the side A B, and the directing Hne) frora 6 to c. A line
drawn frora c to the point of distance D, will intersect the visuals a S and
6 S, at «? and e ; through these points draw the lines e g, and fd, which will
give the perspective plan of the cube ; and likewise its distance frora the
directing plane. Frora the corners f, d, and g, raise perpendiculars at
pleasure ; also from b, raise the perpendicular b h : this line being in the
Directing Plane, is denominated an Original or Georaetrical line, and on
which line all original heights raust be placed. On this line frora b, set up
the height b i, of the Cube (equal to its width,) and draw the Visual i S ;
its intersection with the perpendiculars d and g, will give the Perspective
height of the Cube, at k and /. Frora k draw the parallel k w, intersecting the
perpendicular raised frora f, at w. Frora w, draw the Visual w n ; and
frora I draw the parallel I m, terminated by the forraer at m : this will
coraplete the representation ofthe Cube.
The Parallellopiped or Prisra opqv t s, being under the sarae Visuals
with the Cubeyrf^ Imw, but of greater height, its seat is obtained by set
ting off its Distance frora the directing Plane, upon the Ground line frora b to
W: a line drawn frora this Point will give the seat of the Prisra at o p,
and its depth by the intersection at r. Parallels drawn from p and r, and
terminated by the Visuals, will complete the plan. Frora o, p, and q, erect
Perpendiculars at pleasure. On the Original line b h, place the intended
height of the Prism as at X ; from which, draw the Visual X S : its inter-
2 b


86 PRACTICAL PERSPECTIVE.
section with the Perpendiculars at t and v, will deterraine the height of the
figure, which is completed by drawing a parallel from /, to the perpen
dicular line 0 *.

To find the Perspective representation of a Cylindrical Solid.
Let A B C D, No. 2, Fig 2, be a square inscribing the circle E F G H,
as making the plan of the Cylinder.
Transfer the Diameter A B of the square to the ground Hne, as directed
in the preceding figure ; and obtain the Perspective plan of the square and
Cylinder, by the Diagrara, Plate 2. Erect Perpendiculars frora the points a
and h, in the perspective square a bed ; and draw the Original or Directing
line IK; on which set up the height of the solid as at L. A line drawn from
L tothe Point of Distance D, will intersect the Perpendicular raised from a,
at i : this will determine the height of the upper square, in which to draw the
Perspective Circle, nopq, equalto that on^the Ground Plane. Frora %
draw the parallel i k. Prora i, and k, draw the Visuals i m and k I, intersec
ting the Diagonal lines, i I, and k m, at I, and m ; through which, draw the
parallel m I, which will coraplete the upper square. The Diagonal Points
raay be obtained by squaring up the same points frora the lower square, on
to the diagonals, in the upper one ; as shown by the dotted lines, 1, 1 ; 2, 2 ;
3, 3 ; and 4, 4. Frora the extreraities n and p, of the Ellipsis, drop the
perpendiculars n e, and p g ; this will complete the Perspective represen
tation of the CyHndrical Solid. Such figure is called the Frustrum of a
Cylinder and sometimes a truncated coluran. The perspective representation
of the column Z, is obtained thus : — Find the seat of the square Y, on
the ground plane, and the perspective circle contained in it, as before directed.
From each corner of the square so obtained, raise perpendiculars : on the
original line I K, set up its height from the ground, which draw to the dis
tance D, and where it intersects the perpendicular r a.t s ; this will deterraine
the height of the coluran. Through *, draw a parallel, * v, terminated at v by
the perpendicular frora t; and coraplete the square with the perspective
circle contained in it as before described ; this being done, join the extre
raities of the two Ellipses, as in the cylindrical solid nlaced below it, which
may be seen by inspection of the figure.


PRACTICAL PERSPECTIVE. 87
This diagram is given, to show the perspective appearance of the circle
when placed beneath or above the horizon. In chairs and tables, whose
legs are below the horizon, the raouldings will have for their outline the
curve ofthe elHpsis Y, as seen in front. For bed pillars, cheval glass frames,
standards, &c., where the upper mouldings are above the horizon ; these will
take for their outline the curve of the elipsis at W- Remark that the per
spective representation of the circle, as it approaches nearer to the Horizon
tal Hne, whether above or below it, will become raore and raore flattened,
until it faUs into the horizon itself; in which case it wiH become a straight
line ; as raay be seen in figure 4, wherein C d, the upperraost plane, is seen
raore fully than the plane C e; and again C e, raore plainly than.Cy which is
so much nearer the horizontal line H.

To find the Perspective representation of an Octangular solid.
Let A B C D, No. 3, Fig. 3, be a Geometrical Square, inscribing the
octagon EFGHIKLM. Transfer the side A B ofthe square on to the
ground line G, G, as at Y Y ; also the side E F of the octagon, as at X X :
from these draw Visuals tending to S, as Y S, X S, &c. Next transfer the
distance (A Y) ofthe Octagon frora the plane of the picture, frora Y top;
this drawn to the distance D will intersect the Visual Y S, at « ; draw the
parallel a b, and coraplete the square ab c d, as before directed : next find
the perspective plan of the Octagon, by the Diagrara, fig. 2, plate 4: frora
each angle of the Octagon so obtained, raise perpendiculars; also the
Georaetrical line Y P, frora Y, and the perpendicular line b n. Upon the
line Y P, set up the height of the figure as at N. This draw to the centre
S : its intersection with the line bn at o, will give the perspective height
of the figure. A parallel drawn frora o and intersected by the perpendiculars
eandy at q and jt), will give the paraUel face of the upper Octagon. The
remaining faces are obtained by drawing their sides to the respective
Vanishing points, D D, terminated by the perpendiculars as before
explained. The Octagonal Prisra V, being under the sarae Visuals, naraely Y S,
&c. is obtained by the sarae process. Its seat on the ground plane is


88 PRACTICAL PERSPECTIVE.
governed by that of the cylinder (before explained). Its height is deter
rained by placing it on the original line Y P, as at r, in the sarae manner as
that of the preceding example. Reraark, that this figure is likewise given
to show the difference in the outline of the Octagon, either above or below the
horizon. If you wish to represent the interior of a bow window, peculiar to
many of our old English raansions ; all the lines that are below the Horizon
will answer to the concave part ofthe ground plan at R, and all those above
the horizon will answer to the concave part of the upper Octagonal plane
at T. In what relates to the circle, the sarae applies to the octagon ; for
being circumscribed by a square, it is subject to the sarae diminution the
nearer it approaches the Horizon; and will, as the painters express it,
become more and more foreshortened, until, like the circle, it would fall into
a straight line.
No. 1, Fig. 5, represents a cubical object having a top, (5,6.7,8,)
projecting equally over the four sides.
Let A B be the raeasure of one side of the cube to be represented ;
and B C its distance frora the directing plane. Proceed and coraplete the
Perspective plan a 6 c rf, as in fig. 1, from which raise perpendiculars,
as before. From A and B, set off the projection of the top as A D and
B D, which draw to the point of sight S, intersecting the Diagonals a c and
h d, at the points 1, 2, 3, 4. On C erect a perpendicular C G; this will
becorae the Georaetrical line : on this line set up the height of the cube,
also the thickness E F, of the projecting top, which draw to the point of
distance D ; and where they intersect the perpendicular raised from 2, you
will obtain the projection ofthe top at the point 6; (the nearest to the spec
tator.) Frora 6 draw Visuals tending to the point of sight S, and where
they intersect the perpendicular raised frora 3, you have the projection on the
returning side, as at 7. Frora 6 and 7 draw parallels, and where they inter
sect the perpendiculars raised on 1 and 2, as at 5 and 8, you will have
the farthest projection: draw the Visual 5, 8, tending to the point of
sight S, and the figure will then be completed.
This Diagrara is applicable to all objects of furniture that are under
the Horizon ; whether tables, commodes, &c, that have an equal projection
of top, or mouldings round their sides.


PRACTICAL PERSPECTIVE. 89
The upper figure represents the sarae cube, having the same projection
over the top, but seen above the Horizon; the Geometrical line being
differently placed ; namely on the nearest angle of the cube. To obtain
(he projection in this Exaraple, draw the Diagonals Y V and X Z, which
Diagonals prolong at pleasure : on the Diagonal at Y, place the projection
0, which will be that nearest to the spectator ; and draw the Visual o r,
tending to the point of sight S, which will intersect the Diagonal X Z at r,
and give the furthest projection jo r. Frora o draw the parallel o g', which
by its intersection with the Diagonal X Z at q, will give the opposite
projection to o. Next let the perpendicular line from Q be continued at plea
sure towards W; on which line set up the intended height ofthe pyramidal
roof, frora Y to V; which draw to the point of distance D, and where it
intersects a perpendicular raised frora the centre or axis C, of the square
X Y Z V, will deterraine the perspective height at T. Lastly draw the
Hnes Tp, T p, and T p, which wiU coraplete the figure.
The cornices of rooras, and the projecting raerabers of all objects
seen above the Horizon raay be obtained frora this diagrara. The square
figure U, raay be supposed to represent the body of a book-case, wardrobe
or any other object ; and q o r, the projecting cornice.
Fig. 6, No. 1 and 2. These cylindrical figures are the sarae, and ob
tained by the same raeans as that of No. 1, fig. 2 ; with the addition of a
projecting meraber to each, as seen above and below the horizon. Having
constructed the cylinder W, by the process used in No. 1, fig. 2, prolong
the diagonals, corresponding to those marked m k and i I, in the sarae
figure ; also prolong the line i k, upon which, from i and k set off the given
projection, as at e ; this convey on the diagonals by the point of sight S,
at the intersections a b and c d, forming the larger square, as is shewn by
the fiffure. Next, take little more than l-7th of the line a b ; that is, run
the compasses along the Hne until the l-7th division extends a little
beyond the end of it at the point b ; this being the proportion that the
space A I, No.2, fig. 2, bears to the whole line A B. Set this measure
frora a and b to x and x; which convey by the point of sight S, on to the
diagonals a c and 6 d, as nurabered 1, 2, 3, and 4. Next draw the diaraeters,
5: 6, and 7 8 : through these eight points the circle forraing the projection
may be traced. The under curve is obtained first, by dropping perpen
2 c


90 PRACTICAL PERSPECTIVE.
diculars from a and h, equal to the giten thickness ; through which draw
the parallel line o o, which line will receive the diagonal points x, x, at 10
and 1 1 ; also the central point 7, at 9 : these draw to the point of sight
S, and wliere they intersect perpendiculars dropt frora I, 2, 5, and 6, will
give so raany points through which to trace the under curve. The pro
jection over the cylinder No. 2, is obtained by the sarae process, as may
be seen by inspection of the figure. The tinted Planes in these figures,
as also those in No. 1, fig. 2, show the squaring of the seventh points upon
the diagonals of such squares as are of equal dimensions, placed one above
another. Fig.' 7 is an octagonal prism, standing on an octagonal base, and
supporting an octagonal top.
First set off the width of the square, representing the top, upon the
ground line G G, from i to k; also the width of the square making the block,
frora I to m. Frora I and m draw Visuals to the point of sight S, and frora t
draw a line to the point of distance D : its intersection with the Visual
drawn frora I, will give the seat of the front line of the block at o ; frora
which draw a parallel line, intersecting the visual frora m, at p; this will
give the Perspective width of the square of the block. Frora o and p, raise
perpendiculars ; next set up the thickness of the block on the Georaetrical
line iX from itoq; this likewise draw to the point of distance D; and
where it intersects the perpendicular raised from o, at a, will deterraine
the thickness of the block. Next draw the square abed, as in fig. 1 ;
and the octagon contained in it, as in fig. 3, which will compleat the block.
For the Prisra, draw raitre lines frora each angle, (1, 2, 3, 4, 5, 6, 7, 8,) of
the octagon, to the centre or axis C. Next set the given diameter on the Hne
a J, at 1 and 2 (in this exaraple equal to one side of the octagonal block:)
this draw to the centre S, until it intersects the raitres 7, 8, 3 and 4, at 1 1, 12,
15, and 16, which wiU give the two sides parallel to those raarked 7 8,
and 3 4, on the block : the reraaining sides are got by throwing lines back
bythe points of distance D, D, frora 11, 12, 15, and 16, intersecting tbe
corresponding mitres at 9, 10, 13, and 14; from which intersections, the
two sides paraUel to 1-2, and 5-6, may be drawn, corapleting the perspective
plan of the prism. Frora each exterior angle visible to the eye, raise per
pendiculars, as in the prisra V, fig. 3. Next set up the height and thickness


PRACTICAL PERSPECTIVE. 91
of the top upon the Geometrical Hne i X, as at e ; frora which draw parallels
at pleasure. Likewise square up the given width frora k (on the Ground
Hne), intersecting the paraUel drawn from e aty,- and complete the square
e fg h, as before directed. Lastly, set off the given measure of the canted
side> from e to r* and frorayto * ,- which convey on the line above by perpen
diculars. Visuals drawn frora these to the centre S, wiU give the raeasure
of each cant on the back line hg, (ofthe square,) at t and v. Lines thrown
back by the points of Distance firom these intersections {t and v,) will give the
four canted sides ofthe figure, as raay be seen by inspection. By 'this
exaraple we are taught the raanner of obtaining the Perspective repre
sentation of loo Tables with their pillars and bases, when of an Octagonal
forra; it is likewise applicable in gothic designs, whether for Tables,
Candelabri, or any other object having, octagonal supports. We shall now
coraraence with the application of these exaraples, by delineating the various
articles of Doraestic Furniture in general use ; giving the perspective lines
with each example.

Plate 6.
To represent a Library or rvriting Table from a given plan and Profile.
No. 1, Fig. 1, is the scale to plan and profile, drawn f of an inch to
a foot. No. 2, shews one half of the plan of the writing Table to be projected ;
a b cd, raaking the top; ffo o, the frarae; and e, e, two ofthe legs.
No. 3, shews the profile of part of one of the ends with its moul
dings, &c.
Having drawn the Ground Hne G G, take 4 feet from the scale, which
measure set up from G G, for the Horizontal line. Next place the point of
sight on this line at pleasure ; observing to place it neither too near, nor too
far removed from the angle or nearest corner B. The point of distance raay
be placed from the point of sight at pleasure, but not less than twice the
length of the object to be represented ; as before remarked in page 75 : in
this instance it is raade longer, viz. 13 feet 4 inches ; the length ofthe table


92 PRACTICAL PERSPECTIVE.
being 5 feet. Proceed and square up frora the plan on to the Ground line the
length a b, ofthe top, at E E; also the length yy ofthe frame at F F ; and
the legs e, e, at M M : these draw to the point of Sight S. Next'set-off the
width of the table from back to front, (equal 3 feet 6 inches,) from E to I ;
which draw to the point of distance, as shewn by the dotted line raarked
Diag, the point being off the plate : its intersection with the visuals drawn
frora E, F and M, will determine the perspective width of the top and frame
ofthe table atK, and give the squares for the back legs at M; from which
draw parallels, intersecting the corresponding visuals at the other end at
K and M. For the front legs, draw a line frora the nearest corner E to the
point of distance ; its intersection with the visual drawn frora M, will
give the square ofthe leg at the corner nearest to the spectator ; which may
be squared to the- opposite visuals drawn frora F and M : this wiU compleat
the perspective plan. Frora E, raise a perpendicular E 0 at pleasure; on
which line square all the original heights frora the profile, as denoted by the
dotted lines. The height of the table being squared on to the original
line E O, as at B, raust be drawn to the point of distance ; its intersection
with a perpendicular raised frora the square of the frarae at F, will deter
raine the parallel front of the top at X , which raust be continued to
y, on the perpendicular raised frora the opposite corner F: visuals
must then be drawn from X and y, to S, intersecting perpendiculars raised
from K and K (the furthest squares,) at C and D ; draw the parallel D G,
which will complete the top. Next from Z on E O draw a diagonal as
before, tending to the point of distance, and where it intersects the
perpendicular raised frora F as before ; this will be the perspective depth of
the frarae ; which raust be squared to the corresponding perpendicular
frora F at the furthest end, intersecting it an N; this will deterraine the
length of the frame in front. Frora Z draw a visual to S, which by its in
tersection with the perpendicular raised from the square at K, wiU give
the returning side at R. . The top moulding being transferred to B ; as
shewn by the dotted line, its projection is determined by the original line E O ;
(it being in the Directing plane ;) which raust be continued to the perpendi
cular raised frora E, intersecting it at A : a visual drawn frora B and inter
sected by the perpendicular from K, will give the return. The small
raoulding at fhe bottom is found by carrying its thickness to Z, and from


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PRACTICAL PERSPECTIVE. 93
thence conveying it by a diagonal, to the corner line of the frarae ; this being
on so sraaU a scale, may in most instances be drawn by eye ; the bottom
Hne of the moulding being first obtained. Having thus completed the
frame, draw the legs at N, N, N, which is done by squaring them up
frora the tinted squares in the perspective plan. The dirainishing of the
leg being deterrained in the profile, lines raay be drawn frora the under
part of the frarae, at t t, through the dirainished part at bottom at
V V ; vvhich two Hnes will unite and meet in a point on a Hne drawn
through the centre or axis, at P. Next convey the point P, by a
parallel, on to the original line h 0, at the point p. Proceed and drop per
pendiculars from the axes of the four squares, (M, M, M, M,) at pleasure.
From p, draw a diagonal line, intersecting the axis of the nearest square
(M E,) at the point O ; this will be the perspective seat of the point P, in
the profile. From' O, draw a parallel, intersecting the axis of the farthest
square F M, at n, which gives the opposite diminishing point to O. Visuals
drawn from O and n, until they intersect the axis lines of the back squares,
wiU give the diminishing points for the back legs, at s and r. These foui
points n, O, r, s, being obtained, proceed and raise perpendiculars from
the perspective squares, F M, M E, &c. (in the plan), up to the bottom line of
the frarae, as at W, Z, R and D ; vvhich wiU give the squares of the legs at
top : frora these, draw lines to the apex points, n, O, r and s, and you have
the dirainishing lines for the legs. Frora the points, 1, 2, 3, 4, 8cc. as
conveyed frora the profile on to the original line, draw diagonals to the
point of distance ;. their intersection with the diminishing line drawn from
Z, wiU give the heights of the respective raouldings and ornaraental parts
of the leg Z ; which raay be squared on to the leg W. Those required
on the leg R, may be obtained by Visuals drawn from the corresponding
heights on the leg Z, to the point of sight; which again must be squared
over to the leg D : all that remains is then to be done by hand ; reducing
your draught as near as possible to the finished design, as shewn below at
fig. 4. Reraark that where the term diagonal is meutioned, it refers to those
lines that are drawn to the point of distance.

2d


94 PRACTICAL PERSPECTIVE.

Plate 7.

To represent a Secretaire Desk and Bookcase in Perspective^ from a given plan
and profile. -,
The figure marked B, represents the plan of the bookcase; where
W W, W W, denotes the length and depth of the lower carcase,
corresponding with the depth marked W W, in the profile C : Y W, denotes
the depth of the upper carcase, answering to Y W, in the profile. The
dotted line X X, shews the projection of the cornice round the top, being
marked with the same letter in the profile. Z, Z, Z, Z, shews the pro
jection of the base raoulding round the lower carcase, as shewn in the profile
by the sarae letters. H H, is the Horizontal line, G G, the Ground line,
and D the point of distance for the bookcase. Fig. 1. The station or point
of sight in this exaraple is placed 17 feet and half an inch (by the scale)
frora the distance D. The first thing to be considered, is the position of
the figure about to be represented, in regard to the station or point of
sight ; or in other words, the distance the nearest corner of it is from the
point of view. In the present Example the poii	 F on the ground line
G G, has been chosen as the nearest corner of the object. The next thing
to be perforraed is that of making the perspective plan (raarked E) beneath
the ground line ; with all its parts and projections, the sarae as in the
Georaetrical plan raarked B. This raay be placed at any distance below
the ground line, but in all cases the lower *uch plan is placed below the
horizon, the raore distinct wiU be the different intersections. Proceed and
draw the line a a, under fig. 1, ^at pleasure ; upon which set the length
W W, of the bookcase (in the iplan B,) from the nearest corner F ; as
frora V to b, which wUl make the 'front line of the lower carcase. Frora b
and V, draw visuals to the point of sight : next set off the depth (W W,)
of the lower carcase, frora 5 to c ; this draw to the point of distance D :
its intersection with the visual from b at e, will deterraine the perspective
depth of the lower carcase. A line squared from e toy parallel to 6 v, will
complete the plan of the lower part. Next set off the measure W Y, (in the


'J-

id





PRACTICAL PERSPECTIVE. S5
plan B) from o to g, which draw to the distance as before ; its intersection
with the visual b e at i, will determine the seat of the upper carcase : a
parallel drawn from t to i, wiU represent the front Hne. It then remains to
find the perspective projection of the mouldings, in the lower and upper car
cases ; which may be obtained as foUows : set off the projection of the
plinth, (raarked W O, in the plan B,) from b to o, and v to y ; which draw
to the point of sight : a line thrown back frora h, by the point of distance,
wiU by its intersection with the visual drawn through o, give the projection
of the plinth at I; and a line squared frora I, intersecting the visual drawn
through y, at m, will give the projection of the plinth at the furthest point
frora the spectator. The sarae process must be followed for finding the pro
jection of the cornice in tho upper part ; observing to throw the raitre back
from t; and thus the plan of the lower and upper carcases, with their pro
jections and mouldings is found perspectively. Next square up the corner
h, perpendicularly at pleasure, as at I ; which line consider as the Geometrical
line, upon which all the original heights of the figure raust be placed : in
this Exaraple the heights are squared from the profile C, as numbered,
1, 2, 3, 4, 5, 6, 7, 8. Frora all these heights on the original line, draw
visuals to the point of sight ; not the whole length, but only as far as raay
be necessary to receive the intersections of the perpendiculars raised frora
the perspective plan. Having proceeded thus far, commence by raising a
perpendicular frora t, in the plan ; this will intersect the visuals drawn frora
4, 5, 6, 7, and 8, at the points o, o, o, o, o, and thereby, deterraine the heights
of the cornice and frieze in the upper carcase. These heights squared to
the perpendicular raised frora the point i, in the plan, wUl coraplete the
frieze; and also the bottora line of the cornice in front; giving likewise the
base line of the upper carcase at K. The heights of the raembers on the
lower carcase are determined on the original line itself at 1, 2, 3, and 4 ;
frora which visuals alone are required to be drawn ; and these, as weU as the
visuals drawn from 5, 6, 7, and 8, in the upper carcase, are terminated by a
perpendicular raised from e, in the plan : thus far the body of the bookcase
is corapleted. The projecting raembers are found in the plan at the points
/ and m, for the plinth in the lower part ; and n and r, for the cornice in the
upper part. It only remains to throw raitre lines by the point of
distance, frora o, i, and F, which by their intersection with perpendiculars


93 PRACTICAL PERSPECTIVE.
raised frora n and I, in the plan, will give the required height and projection
of the cornice and plinth, as shewn by the letters s, s, s. Parallels drawn
from these intersections and terrainated by perpendiculars raised from m
and r, wiU complete the figure. The profiling of the raouldings must be
regulated by the Georaetrical elevation, and drawn by hand, as shewn in the
finished Exaraple, fig. 2. The remainder of the finishings, viz. the pilasters,
pannelling, fraraing the upper doors for glass, &c. wiU depend entirely on
the taste of the designer.
Fig. 2, shews the sarae bookcase as finished in all its parts, with the
addition of a Secretaire drawer thrown open for writing; which it was
thought proper to shew in this figure, instead of fig. I, for the purpose of
keeping the latter diagrara distinct and free from too great a raixture of lines.
In all these articles of furniture, the lower or hinged part of the fall down
front is placed about 2 feet 6 inches frora the ground, and is generally about
9 or 10 inches in depth. To shew this drawn open and let down for the
purpose of writing, commence and draw visuals by the point of sight, from
C and D. Next set off the height of the fall down front, with the depth
of the drawer when out, from D toe; this measure throw from the point of
distance ; its intersection with the visual D g, at g, will give the front
of the writing flap. This squared to the visual from C, intersecting
it at y wUl deterraine the length of the flap. To obtain the place of
the cheeks or sides, (X, X) of the drawer; set the raeasure of one of
them (generally about 9 inches), frora D to i; this raeasure thrown back
by the point of distance D, upon the visual D g, at h, wiU give the seat
of the nearest side X ; which being squared on to the opposite visual from C,
will give the seat of the furthest one at m. Perpendiculars raised from h
and m, and cut by visuals frora A and B, will deterraine their height. The
seat and height of the quadrants for supporting the fall down front, are
found after the sarae manner, as raay be seen by inspection of the figure.
Reraark, that the point of sight in fig. 2, is shewn at S ; and the distance
being the same frora it as that in fig. 1, namely 17 feet and i an inch by the
scale, could not be shewn in the picture ; but its tendency is shewn by the
dotted line marked F. In like raanner the tendency of the point of sight
in fig. 1, is shewn by the converging lines, making the top and bottom ofthe
bookcase.








PRACTICAL PERSPECTIVE. 97

Plate 8.
To represent a Chiffonier commode (Fig. \,) in Parallel Perspective, shewing the
manner of representing a door open.
Let the Profile marked A be first made, agreeable to the size and pro
portion proper for such an article of furniture. From this construct the
perspective plan marked B, after the sarae manner, and by the sarae process
as that adopted for the bookcase in plate 7 ; the horizontal line H H ;
station point S ; ground line G G, and distance D, regulated as before.
The tinted circles raarked a a, in the plan, denote the place of the columns
supporting the frieze and marble top; the squares figured 1, 1, denote the
capitals : E F, shews the front Hne making the body of the comraode with
the doors : A B C D, is the plan of the raarble top. The dotted lines bb, c c
and d d, shew the front lines of the shelves in the upper part (raaking the
chiffonier ;) which are got by setting off the breadth of each shelf in the
profile, from h, (the back ofthe comraode,) and conveying them on the visual
B C, by the point of distance ; as shewn by the lines e b, f c, and g d.
The perspective plan being completed, proceed and draw the perpendicular
line G H, from the corner B, in the plan ; which consider as the Georaetrical
line, upon which to receive all the original heights frora the profile. Cora
raence by squaring, first, the height and thickness of the top i i, which being
in the plane of the picture, raust be continued direct to the perpendicular
raised frora A in the plan : this will determine its length in front. Next
square along the height (top and bottom) of the frieze k k ; which convey
by the point of distance to the perpendicular raised from the corner m in the
plan B, intersecting it at o, o. ParaUels drawn from o, o, and continued
to the perpendicular raised from /, wiU coraplete the frieze. The colurans,
shelves, &c. raay be aU obtained after the sarae raanner; as may be seen by
reference to the plate, it being needless to repeat over the sarae process a
second tirae, as such would occasion a raultitude of references which would
only tend to perplex the figure. It is thought proper in this example
tp shew one door of the commode open, and at the same tirae to de
2 E


98 PRACTICAL PERSPECTIVE.
raonstrate and lay down the principles by which it is performeo. It is
evident that every door turning on its hinges, would by its revolution,
generate a seraicircle equal in diaraeter to double the width of the
opening. This seraicircle being found perspectively, the door raay be
shewn open on any part of its seraicircuraference. Suppose the djor
to be hinged at P, and P n to be the width of the opening ; continue the
line P n, out at pleasure, upon which set off the width of the opening P n,
from ^ to q; and throw visuals by the point of sight frora n, P, and q : a
line thrown frora P by the point of distance, will by its intersection with the
visual thrown frora n, give the breadth of the half square, containing the
seraicircle, at r ; a parallel drawn frora r to t will coraplete the half square.
Draw the seraidiagonal P t. Next take little raore than one seventh of the
line q n, which convey upon the semidiagonals P r, and P t, by the point of
sight, at w and v. The seraicircle raust then coraraence from the point q, and
be traced through the points w, s, v, terminating at n. The semicircle being
thus obtained, take any point on its circumference as X, for the extent you
raean the door to be thrown open ; a line drawn frora this point to P, will
raake the bottora line of the door, which being continued to the horizontal line
will there give the vanishing point for the door, as thrown open at this angle.
A line thrown from Q, by the vanishing point, and cut by a perpendicular
raised frora X at Y, will give the upper line of the door. The point Q is
found by squaring a line frora x until it cuts the perpendicular drawn frora
P. The vanishing point for a door thrown open at any point upon the serai
circuraference of the circle raay be found after the sarae inanner ; naraely, by
joining such point with the centre where the door hinges by a line, and con
tinuing it to the horizon.
Reraark, the distance of the vanishing point in this example is two
feet two inches from the station point on the right hand, by the scale.

To represent a fiight of Bedsteps, Fig. 2, in Perspective.
In this example the profile of the steps is shown parallel to the picture,
and consequently would be Geometrical ; save and except the projections of
pHnth and nosings. First set off the measure of each tread of the steps


PRACTICAL PERSPECTIVE. 99
(being 9j inches) on the line a a, at A, B, C, and D ; which draw to the
point of sight. Next set off the width or front of the step (being 21 1 inches)
firora D to E ; this conveyed by the point of distance on tLe visual drawn
frora D, will give the perspective length of the front at F : a line squared
frora F to G, wiU coraplete the plan of the steps The lines B H, C I, and
D F, wiU in this case be the seat of each tread. The projection ofthe plinth
and nosings being the sarae, both are found as follows : set off the raeasure
of the projection from A to a, and from D to d, from which draw visuals to
S : Lines thrown from G and D, by the point of distance, where they in
tersect these visuals at g and d, will give the projection at the corners G and
D. Lines squared frora G and D, and cut by the visuals before drawn, will
give the projection of the two opposite corners at a andy ; this corapletes the
plan. In raising the elevation, coraraence by drawing the perpendicular h i,
frora A in the plan ; on which set up the height of each step frora the ground
Hue G G, as at k, I and o : these square to the perpendiculars raised frora B,
C, and D, intersecting thera at x, n, t, m and u, which will coraplete the
profile ofthe steps. Visuals drawn frora o, x, n, t, m, and u, and cut by perpen
diculars raised from H, I, and F, will represent the treads of the steps ; the
perpendiculars cut by them at z p, v q, andw s, forraing the furthest extre
mities of the risers. The thickness of the nosings are set below the top of
each step, and their projections squared up from the plan : the plinth likewise
after the same manner, as is shewn by the dotted lines. In this example, the
top of the upper step is represented as thrown up ; the principle of per
forraing which is applicable to all table tops or desks that have a sloping
elevation. On o, as a centre, with a radius equal the width o x, describe the
quadrant xb ; likewise on y, with the radius y z, describe the quadrant z c ;
and draw the visual b c. If the Hd or top be thrown up perpendicularly
on its centre, its representation wUl be the dotted plane bcoy. Butin
this instance it has been thought proper to show the top only partially open ;
for which purpose any point in the quadrant b x, raay be chosen, as at c ;
which being drawn to the centre o, will represent the nearest edge of the
lid : this being continued until it intersects a perpendicular raised from the
point of sight S, will give the vanishing point for the inclined position
of the lid ; to which the opposite edge y e is drawn. A visual drawn
from e, in the quadrant b x, to e, in the opposite quadrant c z, will represent


IvK) PRACTICAL PERSPECTIVE.
the front edge ; the nosing drawn round may be measured by those of the
other steps.
It is necessary to observe, that the more or less the lid or top is
elevated, so the seat of its vanishing point, in the perpendicular vanishing
line, will raore or less vary.

Plate 9.
To represent a chair in Perspective, its side being seen in front, and its front
being at right angles with the picture.
The back of all chairs being less than the front, it follows that the two
side rails will form inclined planes ; the one opposite in its direction to the
other> which if continued would intersect each other soraewhere below the
horizon, and terminate in the horizontal line; the one to the right hand of
the station or point of sight ; the other to the left ; biit each equaUy distant
frora it ; this is to be understood of a chair seen front ways, that is, whose
front is placed parallel to the plane of the picture.
Chairs as they are placed in apartments, generally have their bevelled
sides opposite to the plane of the picture ; the vanishing points for such
inclined sides would therefore be greatly beyond it, which sides if pro- !
duced, would intersect the horizon at so great a distance, as to render the
ase in practice inconvenient ; which can be avoided by adopting a different
practice. It is obvious then that there are two methods requisite for putting a
chair into perspective ; the one as relates to the view when taken in front,
or wnen the front of the chair is parallel with the plane of the picture ; the
other when the chair is placed with its back and front at right angles with
3t ; or in other words, when the bevelled side of the chair is immediately
oefore us.
We shall give an example both ways, and coraraence with the side
view in preference ; giving a plan and elevation, with a scale, by which the
whole is proportioned.


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PRACTICAL PERSPECTIVE. 101
In the present exaraple the plan of the chair seat is represented at
fig. 1 : the letters AAAA, denoting the square in which the seat, with its
bevelled sides A B and A B, is contained ; thus, A A denotes the front rail
of the chair and B B, the back rad ; A B, and A B, are therefore the
inclined sides of the seat rail coramon to all chairs : the spray of the front
legs are denoted by the letters bb ; those of the back by c c. The plan, fig. 1 ,
being corapleted, and the profile C, fig. 2, constructed, proceed and
transfer the depth (A A,) of the bevelled side of the chair in the plan, frora
A to B, on the ground line, fig. 3. Next set off the raeasure or spray of
the back foot (B c,) frora A to R : from R, A and B raise three perpendiculars ;
B I, to receive the heights for the front rail ofthe chair, and A I for those of
the back rail ; also R G to receive the height of the top yoak, the spray, or
any other division of the back. Transfer, or square from the elevation C,
the different heights (D D D,) of the raU and stulfing, at D D D, on the line
R G ; at 6, 6, b, on the line A I ; and at c, c, c, on the line B I ; and transfer
the spray b b, of the front seat in the plan, frora B to g.
From R, A and B, draw visuals to the point of sight : next set off the
width of the chair, (A A in the plan) from B to E ; this convey to the visual
B S, by the point of distance D, intersecting it aty Frora f draw a line
parallel to the ground line, intersecting the visual A S atg; this will cora
plete the square containing the seat of the chair.
For the bevel of the sides, set off the raeasure B A, in the plan, frora
B to g, and frora E to g, on the ground line ; which measures convey on the
visual B S, by the point of distance D, intersecting it at N and N. From
N and N, square lines across to O and O, as shewn in fig. 4. Join B o, and
fo, which wUl give the two bevelled sides, and complete the perspective plan
of the seat. These lines continued wiU receive the spray of the back legs.
Next from b, b, b, on A I, draw visuals at pleasure tending to S ; and frora
o and 0, in the perspective plan raise perpendiculars until they intersect the
visuals drawn frora b, h, h, at o, o, o, and o, o, o ; likewise frora c, c, c, on B I,
draw visuals to S, which terrainate by a perpendicular frora yat c, c, c ; draw
the lines co, co, co, and c o, c o, c o ; which wUl raake the Hnes of the side
raUs and stuffing.
To obtain the height of the back, first raise perpendiculars frora x and y,
on the visual R S ; as a; A, and y M. From K in the profile C, square the
2f


102 PRACTICAL PERSPECTIVE.
height of the back to the perpendicular R G, at L ; this draw to the point
of sight S : its intersection with the perpendiculars x k and y M, att and M,
wUl give the height of the back. The sweep of the back may be found by
dividing the height T K (in the profile, fig. 2,) into any nuraber of parts ; as
at L, L, L, L : frora these divisions draw lines until they intersect the out
line of the mould at M, M, M, M. From M, M, M, M, drop perpendiculars,
intersecting the ground line T V, at a, a, a, a. Next square the divisions
L, L, L, L, to the perpendicular line R G, as at L, L, L, L; and draw
visuals tending to S, untU they intersect the lines x k and y M at P, P,
P, P, and P, P, P, P.
Transfer the measures a, a, a, a, (in the profile,) to the ground line fig. 3,
from R to a, a, a, a, as lettered ; these convey on the bevelled lines B x and
N y by the point of sight S ; frora these intersections, perpendiculars raust be
raised until they raeet, each its corresponding line, squared frora P, P, P, P ;
by this means points will be produced, through which to draw the outline ma
king the sweep of the back : these lines form, the one an outside sweep, and
the other an inward. For the inside of the back foot, set the measure T T, (in
the profile fig. 2,) from R to R, fig. 3; this draw to the station S, intersecting
B ar at 1, and N y at 3 : perpendiculars raised from these points will give the
springing for the inside of the back leg, on the rail at 2, and on the opposite
rail at 4 ; the two sweeps raay then be drawn by hand ; the thickness ofthese
legs may be drawn near enough by the eye in small examples. For the front
legs, the sweeps are contained within the space Z Z, in tbe profile : this raea
sure is then tansferred frora B to x, and conveyed by the point of sight on the
opposite side at x. Perpendiculars raised frora these points and intersected by
a line squared frora Z Z, (in the profile) at Z Z; and by visuals drawn frora Z Z
at zz, will give points through which the sweeps may be drawn. To give
every point and line necessary to the perspective construction of such an ex
ample, would only perplex the student; raore lines are now given than has
hitherto been atterapted in other works of this kind , but we have chosen to be
thus particular in this and the following exaraple, convinced that those
who wish to learn and know the reason for that which is laid before them,
wdl not be discouraged to go through the references, although apparently
numerous. Fig. 4, is introduced for the purpose of shewing the manner of finding
the perspective representation of the seat on a larger scale.








PRACTICAL PERSPECTIVE. 103

Plate 10.
To represent an dhow chair in perspective, the front being placed parallel to th
picture.. \
Having constructed the plan and profile by scale as before, and deter
mined on the points of sight and distance ; coraraence by setting the raeasure
of the front rail of the chair (from the plan A,) on the ground line G G, as
A B ; from which draw visuals to S. Next set off the depth of the side
raU from A to g ; this conveyed on the visual A S, by the point of distance,
will give the perspective depth of the rail at C ; from which draw a parallel
line, terminating it on the opposite visual at D. Next proceed and take
half the raeasure ofthe back rail, and set it right and left frora the centre X
of the front line A B ; this convey on the back line C D, by the point of
sight, intersecting it at c andd; the line erf wiU then represent the width
ofthe back rail. Set the width of the square A (in the plan) frora A to a,
and from B to 6 ,* these draw to the point of sight S ; a line drawn from A
to the point of distance, where it intersects the visual from a, will give the
depth of the square ; this transferred to the visuals frora A, b, and B, will
coraplete the two' squares containing the front legs : join b c and q d, which
lines wUl raake the two bevelled sides, and these continued to the horizontal
line H H, wiU there give the vanishing points for the bevelled sides at V 1,
and V 2. From A, a, B, b, I and m, raise perpendiculars ; and consider the
perpendicular A H as a Geometrical line, upon which to receive the heights
from the profile B. First square or transfer the heights (x, x, x,) of the rail
and stuffing to the Georaetrical line A H, at 1, 2, and 3, which continued
across to the perpendiculars raised frora a, h, and B, wUl give the front Y
ofthe stuffing, with the two knees X, X, of the front legs. Lines drawn frora
1, 2, 3, to the point of sight S, and received by the perpendicular frora I, at
X, X, X, will make the return of the knee X, and give the plane for the scroll
of the arra at the nearest corner : lines drawn frora x, x, x, to the vanishing
point V 1, and received bythe perpendicular raised from c, wUl give the re
presentation ofthe bevelled side of the raU and stuffing : likewise a line drawn


104 PRACTICAL PERSPECTIVE
frora y, to tbe vanishing point V 2, and terminated by a parallel squared
frora w, will coraplete the seat of the chair. To obtain the place of the elbows,
setoff the distance they recede from the front line y x, (ofthe profile,) frora A
to e ; this convey on the visual A S, by the point of distance : its intersection
at r, wiU deterraine thc place of the elbows, which raust be squared across to
the lines Ic, ot, pv, and q d, intersecting thera at o o, and oo ; o o and o o
will then becorae the front lines for the upper scrolls. The depth w w, in
the profile raust next be set frora e tof; conveyed on the visual A S, and
be squared across as before raentioned; being denoted by the tinted planes.
Frora 0, o, o, and o, o, o, raise perpendiculars; next square the height y of the
elbow, and thickness z of the scroll, to the Georaetrical line A H, at 4 and 5 :
lines drawn from 4 and 5, to the point of sight, received by the perpen
dicular 1 1, and frora thence conveyed by the vanishing point V, to the per
pendicular 0 X, will give the perspective height of the elbow, and thickness
of the scroll at n and m ; and its return at g, g. Lines squared across from
n and m, and received by perpendiculars from o, o, and o, o, at n, m ; n, m,
and n, m, will give the planes for turning in the scrolls. Having thus
obtained the planes for the top and bottom scrolls ofthe two elbows, the
sweeps C, C, may then be drawn by hand. It were possible to give lines
and points, whereby the sweeps C, C, raight have been found; but this would
have occasioned rauch coraplexity of lines, and taken up rauch ofthe student's
time to very little purpose. The elbows being drawn in, proceed next with
the back ofthe chair ; first by finding its seat Z Z, in the perspective plan
below, as before directed ; the distance of which from the frontline ofthe chair
is denoted in the plan A, by A Z, and set on the ground line from A to k.
The height and thickness of the scroll of the back, raust next be squared
frora the profile B to the Georaetrical line A H, at 6 and 7 ; this convey first
on the perpendicular 1 1, by the point of sight at K, K, and thence by the
vanishing point V 1, on the perpendicular Z Y at Y; this wdl deterraine its
perspective height; which must be squared across to X : the outline sweep
of the back raay then be drawn by hand. The directions given in the pre
ceding plate for finding points to obtain the outHne of the back, will also
apply to this exaraple ; as likewise for the sweep of the elbows. The front
legs are denoted on the perspective plan by the tinted circles contained in
the squares / A a, and m 6 B ; the diameters of which will regulate the





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PRACTICAL PERSPECTIVE. 105
projections of all the upper raouldings, whose heights raust be squared from
the profile as before. The taper of the legs may be found by adopting the
process as described in plate 6, for those ofthe table: to repeat the process
here would be needless. For the back legs set off the raeasure A X, (in the
plan) from A to i, which convey on the visual A S, by the point of distance,
and square it to the bevel lines / Z and q Z, as before ; which will be seen
by reference to the figure.

Plate 11.
To represent a Grecian chaise tongue, or Sofa in Parallel Perspective.
In order to render this lesson explanatory and easy of comprehension,
it is thought necessary here to lay down the plan. A, by a scale suited to the
size the object is intended to appear. Thus, E F F E, denotes the frame or
seat of the sofa. " The dotted lines C and D, shew the head and foot scrolls ;
B, B, B, and B, shews the situation ofthe four legs ; the squares of which are
denoted by the letters E E and E E ; thus far, all will be ready for practice.
Next determine your ground line G G; also your horizontal Hne H;
likewise the point of sight S, and the point of distance (here out of the pic
ture) on such Hne. Let L, (on the ground line G G,) as squared up from the
line D in the plan, be that end of the object, nearest to the spectator.
On L raise the perpendicular line L K ; next square up the line C upon
the ground line at N, and raise the perpendicular NI ; these two perpen
diculars (L K and N I,) will receive all the original heights, (or geometrical
measures :) for this object being placed parallel to the plane of the picture,
and the front side in the directing plane, (or plane passing through the eye
of the spectator, as explained in page 70) such side would in this case be
georaetrical. Proceed and square up the points F and F frora the plan,
upon the ground line at e and e; also the squares E E, and E E, ofthe legs,
at e e and e e. On the extrerae ends, e and e, raise the perpendiculars e k and
e i, at pleasure ; these lines lirait the georaetrical length of the frarae, and
deterraine the place of the legs or feet. Being thus far advanced, proceed
and make a profile of the leg as at M ; the raouldings of which raust be
2 G


106 PRACTICAL PERSPECTIVE.
squared to the perpendicular ef, as shewn by the dotted lines. On N I set up
the heights N I and 1-2, ofthe under and upper parts ofthe rail; which square
across to the lines ei and e k, at the points y-y and g — A. On the sarae lines
set up the thickness of the stuffing at i, and draw the line i h. Next set up
the height you intend the head scroll to be. It wUl then be necessary to
draw the scroll agreeable to such outline as you mean it to take ; which
must be geometrical, and is here marked by the letters o, o, o, o, o. The
foot scroll raust also be drawn geometrical after the same raanner, as
denoted by the letters h, q, q, q. For the purpose of obtaining the scrolls
on the opposite side, which are perspectively reduced at O and P, it will be
necessary to divide the scrolls at I and K, each into a certain nuraber of
parts : the scroll I at 3, 4, 5, 6, and 7 ; the scroll K at 8 and 9. Onl draw
the lines 3 — o, 4 — o, 5- — o, and 6 — o, intersecting this larger scroll at o, o,
0, 0 : the sarae is to be perforraed as regards the lesser scroU, by squaring
the points 8 and 9, to q and q. The inside outline of both scrolls raust next be
drawn ; that at I, through the points p,p,p, p, terrainating with the seat at i :
that of the sraaller scroll atK, is to be drawn through r, finishing with the seat
at k : so far the georaetrical figure will be completed. The next point is to
obtain the width E F, (ofthe chaise longue in the plan.) Proceed and draw
visuals from N, e, e, e, e, and L on the ground line, to the point of sight S.
Next set the depth E F, of the chaise longue, frora L to Q, which convey
on the visual L S by the point of distance, intersecting it at R. This
raeasure raust be squared to the visual N S at the point T, intersecting the
visuals e S and e S, at V and V. Ou R, V, V, and T, raise perpendiculars :
viz. T O to receive the divisions 3, 4, 5, 6 and 7, (on N I,) by visuals, at
I J 2, 3, 4, 5, 6, and 7 ; R P, to receive the divisions 7, 8, 9, and q, on
(L K) at 7, 8, 9, and g- ; V and V to receive those marked i, o, on e,
and k h, on e, at s s, and x h. Lines squared frora the divisions 3, 4, 5
and 6, on T O, untU they intersect visuals drawn frora p, p, p andp, on the
front scroll, will give points through which to draw the outline of the
back scroU frora O to * ; likewise Hnes squared frora the divisions 7, 8, and 9,
on R P, until they intersect visuals drawn from q, q, q, on the foot scroll,
will givw points through which the outline ofthe footscroU P, may be drawn.
To obtain the thickness of the two scrolls, set such thickness frora L to n j
nhiclt draw to the point of distance, intersecting L S at t; which must


PRACTICAL PERSPECTIVE. 107
be squared across to the visuals e S, e S and N S, at d, x and v. On v raise
a perpendicular, intersecting the visuals drawn frora 3, 4, 5 and 6, at y,
y, y, and y. Draw visuals from p, p, p, and p : Lines squared from y, y, y,
and y, will intersect these visuals at z, z, z, and z; through which points,
the outhne raaking the thickness raust be drawn. Vi^hat has been thus
performed for the head scroU, may be done for the foot scroll ; as shewn
by the planes gr 8 w and q^ w.
The thickness of the head and foot scroUs at the opposite side is found
by raising a perpendicular from a on the visual N S, and from b on the
visual L S. Visuals drawn frora 3, 4, &c. and 8, 9, &c. will intersect these
two perpendiculars at a a, &c. and b b, &c. Lines squared frora a, a, a, and a,
— &, b, and b, and intersected by the visuals drawn from p, p, p, and p ; q, q,
and q, will give so many points, through which to draw the outline making the
thickness, as shewn by the tinted planes. For the legs B, B, B, and B, in the
plan; their perspective appearance is obtained by forming perspective squares;
as at e e and e e, V and V; the diagonals of which, will by their intersections,
produce the four axes or centers. The directions given for drawing the
turned legs of the chair in plate 10, will likewise apply to this, to which the
student is referred to avoid repetition : what else is required in any design
of this kind may be drawn by hand, near enough to answer every purpose.
Quite sufficient has been done in this example to enable the student to put
any sofa or chaise longue into perspective, the same principle extending to
all, however various in shape.
Plate 12.
To represent an occasional Table in Perspective, its front being parallel to tne
picture.
Construct the plan A A A, of the top, with the blocks B B, supporting
it; likewise' the profile E, as directed in plate 6. Make G G, the ground
Hne ; H, the Horizontal line ; S, the station or point of sight ; and let the
point of distance be placed on the horizontal line 11 feet 5 inches, (by the
scale) from the station point S. Thus far prepared, square up frora the
plan, the length (A A,) of the top, to the ground line at the points a and G j


108 PRACTICAL PERSPECTIVE.
likewise the seat of the blocks C C and C C, to c c and c c, on the same
Hne. Raise a perpendicular from G, which consider as a geometrical line,
on which to place all the original heights from the profile E; as shewn by the
dotted lines. From a and G, (on the ground line) draw visuals to S ; as also
frora c c, and e e. Next set off the width D D, (of the top in the plan) from G
to H, which convey on the visual Ge, by the point of distance; this squared to
the visual from a, will complete the perspective plan a b e G o£ the top. To
obtain the situation of the frarae under the top, as shewn by the inside plane,
the learner is referred to the table, plate 6, where he wUl find the whole amply
explained. Divide G H into two equal parts as at X : a line drawn from X to
the point of distance, will give the centre for each standard on the visual G e
at X. From the centre x of the profile E, take all the different projections
making the outline of the standard (as marked 1, 2, 3,) and set thera from
X, at 1, 2, 3, and 1, 2, 3, right and left on the ground line ; which measures
convey on the visual G e, by the point of distance, as before ; these points
squared to the visuals, drawn frora c c and c c, wiU deterraine the seat of the
projections (raarked 1, 2, 3, in the profile,) in the perspective plan,, at o,o,
o, 0, &c.
• Commence and square from the profile, the height ofthe top, and depth
of the frame under it, to the georaetrical Hne G G ; which draw to the point
of distance ; and proceed with the rest, as described in the table, plate 6. The
situation ofthe standardsj with aU. their coraponent parts are thus obtained :
square the heights (marked I, 2, 3, &c. in the profile,) to the geometrical
line G G, as denoted by the figures 4, 5, 6, &c. to 11 ; which convey on a
perpendicular raised from O in the perspective plan (corresponding with
o in the georaetrical plan), at the points t, t &c.; these square to ihe
opposite perpendicular/) w. Frora all these heights on the perpendiculars
O V andp w, draw visuals to S, untU they intersect perpendiculars raised
frora 0 0, &c. in the plan ; these will deterraine the different heights and
projections for bothjstandards, by which to regulate the outline as shewn
in the profile. The thickness of the standards at top and bottora is regulated
by the planes r, r, r,&c. on both sides; which are likevpise squared up from
the perspective plan. Figures 8 and 9, will give the situation for the stretcher
F, or tye pf the table frame. For the rest the pupil is referred to the direc
tions given in the preceding exaraples ; it is needless to go through a repe-


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Feet. J

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PRACTICAL PERSPECTIVE. 109
tion of the process, as the student will in this example find all the necessary
lines laid down, which by a little attention he will find to correspond with
those at the opposite end, either by figures or letters. The projections being
thus correctly obtained, the pattern ofthe standard, as shewn in the profile, is
to be drawn by hand, as recoraraended in the preceding lessons. The sha
dowed example below exhibits the same table divested of the perspective
lines, to give the learner a more distinct idea ofthe pattern.

Plate 13.
The plan and profile ofa circular loo table being given, to represent the same in
parallel perspective ; having a turned column on a triangular block for its
support. It will be necessary first to make a correct plan of the table ; viz. its
circular top, which must be coraprised within a square equal to its dia
meter, for the purpose of obtaining the Diagonal points on the circle ; as mar
ked X, X. Within this circle is placed the block, whether triangular or of a
square figure. If triangular as in the present instance, the raethod for
obtaining such will be found amply detailed in plate 4 Georaetrical figures,
page 51, to which the reader is referred.
The seraicircle F X G X H, denotes one half the plan of the table top ;
the sine circle within this, denotes the situation of the rail under the top ; the
dotted seraicircle K L M, bounds the triangle, in which is forraed the block. :
the seraicircle N U 0 W P, inscribes the ornaraental raoulding H, in the
profile, and the semicircle E, denotes the diameter of the pillar at G, in the
same profile.
Having inscribed the circle in a square, draw the diagonals B E and
D E, intersecting the circle at X and X : you have then four points out of
eight for obtaining the perspective circle : that is, supposing the whole of the
plan was shewn coraplete, of which arc half is only given in the plate before
us, for want of roora. As all the other references relate to the operative part
of the circle, to say any thing farther as regards thera in the plan would be
needless : we shall therefore proceed to the operation. Having as before,
2h


no PRACTICAL PERSPECTIVE.
determined the Ground Hne and the height of the Horizontal line, with .th«^
station or point of sight S ; as also the point of distance, (in this example
out of the picture,) you must first make a perspective plan at any distance
below the ground line : For the lower it is placed below the horizon, as
has been before observed, the more distinct will be the intersections of the
lines. In this species of table, the block of which is triangular, it may be
necessary to say soraething as to the choice of the point of view. It will
in all cases be raost advisable when the block is triangular, to regulate your
view so as to have the apex of the triangle to appear in front, or directly in
the centre ; by which raeans its figure will be better raade out, and convey a
more distinct idea of its form.
Let the line O O, be placed any distance below the ground line at
pleasure ; on which line lay down the width or diaraeter of the top of the
table (as taken from the plan) from A to B ; taking care that the centre F
of this line be placed perpendicularly under the station S. From A and B
draw visuals to S, and coraplete the perspective square A B C D, as shewn
in the diagrara, plate 2, page 79. Draw the opposite diagonal A D ; also
the lines F H and I G; you have then four points for turning in the elHpsis
or perspective plan of the table top. Take the distance D x, frora the plan
in the corapasses, and set it on the line A B, from A to x, and from B to ary
visuals drawn frora x and x, intersecting the diagonals A D and B C, at
X, X, X, and X, wUl produce four other points through' which the ellipsis
may be described. The measure G i, in the plan; is next set off on the line
A B from A to i, and from B to i, in the perspective plan. Visuals drawn
frora i and t, to S, wUl intersect the diagonals A D and B C at ir, r, r, and r,
and thereby produce a square circurascribing the ellipsis, making the frame
under the top of the table. The raeasure D y in the plan, is next set off on
the line A B, from A to y and from B to y; visuals drawn fromy and y,
intersecting the diagonals A B and C D, at y, y, y, and y, will give the
four diagonal points, through which to trace the inner circle :~the four
central noints are seen by the intersection of the lines I G and F H,
at w w, &c. To find the situation or place for the block gRhh P, (in the
plan,) transfer the measure I h, right and left of the centre F, on the line
A B at the points 1 and 1 : from these draw visuals to S. Likewise


PL.CXII

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HOR-  POI NT of DISTAN C E is ll(' 1 1 '" from ih e  § _P O ] NT of SIGHT by the SCALE^

HOR.

PERSPECTIV E.XIII.

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London Published bv Jones t C? Feb? 1827





PRACTICAL PERSPECTIVE. Ill
transfer the measure f g, from F to 5 and F to 6. Next take the raeasures
Fy, B h, and h o, and set thera frora B to c, frora B to d, and frora d tof;
these convey on the visual B D by the point of distance, intersecting it at
m, I and b. Lines squared frora m and / and intersected by the visuals
drawn frora 1, 2, and 3, 4, wiU give the two canted sides h h and hh; also
a line squared frora b, intersecting the visuals drawn frora 5 and 6, will
produce the canted corner e g. The points e h and g h, being joined, and
continued to the Horizontal line, will there produce the vanishing points for
the inclined sides of the triangle, of which one is shewn in the plate at V,
to which the canted side h h would tend ; the tendency of other vanishing
points being shewn by the dotted lines V and V. The square Q R S T,
and the one within raarked E are found by setting the corresponding
raeasures E O. &c. in the plan, frora F to 9, frora F to 8, and from
F to 7, which measures are conveyed on the diagonals A D and B C
by visuals as before. The intersection of the visuals 8 and 9, with
the diagonals, will give the points R and Q; likewise the intersection
ofthe visual from F, with the line squared from I, will produce the point P,
answering to P in the plan : through these points, R, Q and P, the sweep
sines ofthe block may be traced. For the pillar, the circle contained in the
square Q R S T answers to the circle N O W P, &c. in the plan, and
denotes the situation of the raoulding H in the profile, making the base of
the pillar: the inside circle E, also answers to that marked E in the plan,
and determines the greatest diameter of the pillar in the profile at G. We
have thus been particular in describing the process for obtaining the per
spective plan for a table of this kind, which being well understood, will
render other objects less difficult of comprehension. The next step is that
of putting the profile or elevation into perspective; in doing of which, the
perspective plan wUl be found of considerable service. First raise a
perpendicular from the point B in the perspective plan : this becomes a
geometrical line upon which to receive all the original heights frora the
profile, and is here raarked G G. Commence and transfer the heights 6, 7
and 8 from the profile, to 6, 7 and 8, on the georaetrical line G G. Frora 8
on the georaetrical line, square the line 8-8, which make equal to A B in the
plan below : frora 8 and 8 draw visuals tending to S ; lines drawn frora 8
and 8 to the points of distance, will intersect these visuals at 9 and 9, and


112 PRACTICAL PERSPECTIVE.
complete the perspective square ofthe top. The eight points through whi
to draw the ellipsis, are squared up from the corresponding points in the p«
spective plan. For obtaining the thickness ofthe top, a line must be squar
from 7 to 7; and for the depth of the rail, a line must be drawn frora 6
the point of distance, intersecting a perpendicular squared frora r in t
plan; frora thence squared across, and terrainated by a perpendicular squar
up from r on the opposite corner, intersecting it at a. The planes produei
the points, through which to describe the two ellipses making the thickne
of the top and depth of the rail, are squared up from the points X, X and y
in the plan ; for further instruction, the student is referred to plate 5, fig.
No. 1 and 2, page 89. To obtain the representation of the block, proce
and raise a perpendicular frora b, in the plan up to the ground line at
upon which to receive all the perspective heights forming the thickness
the block, and place for the front foot. Square from the profile to t
line G G, the heights 1 and 2; these convey on the perpendicular fn
X by the point of sight S, at h, b and h ; lines squared from these poii
determine the perspective height of the front foot, likewise the thickness of 1
block at the canted corner eg. Lines squared up frora e g, in the ph
will intersect these lines so squared, at o o, o o, and produce the cant
corner as seen in front, and give the situation of the front foot at e g. Fn
eg, 0 0, and o o, draw lines tending to the vanishing points V and V; a
square up the points h h and h h frora the plan, until they intersect th(
vanishing lines at the points p p,p p; this wUl deterraine the extremities
the block at the furthest corners ; lines drawn from o and o, to the t
vanishing points, and intersecting lines drawn frora p and p, to the sa
points, will give the two canted corners of the block at q and q. It n
reraains to find the seat of the square Q R S T (in the plan below,) on the 1
of the block above ; to obtain which, draw a line frora 2 to the point
distance, which line intersected by a perpendicular squared up from R
the ground plan, will give the front of the square at r. A line squared fr
r and intersected by a perpendicular squared up from Q, will give the pc
q above, and deterraine one side ofthe square; visuals drawn frora q and r i
terrainated by the diagonals at t and s, will give the two returning sides
the same square ; which is completed by drawing a parallel from t t
Within this square, the circle regulating the base moulding of the pi


PRACTICAL PERSPECTIVE 113
must be drawn, answering to H in the profile. Lastly, square the heights
marked 3, 4 and 5 in the profile, to the Geometrical line at 3, 4 and 5. Lines
drawn frora 3 and 4 to the point of distance, and intersected by perpendiculars
squared from u and a in the plan, will determine the perspective height of
the mouldings at u and a, answering to those marked 3 and 4 in the |.rofile.
The diminution of the pillar at 5 is found after the same manner. The
sweeps on each side of the block are drawn by hand from q, through p to q;
from p, through g to oy and from p, through r to o, on the opposite side.
The sweeps making the thickness of the block are drawn after the same
manner; the centres of which are found by dropping perpendiculars from q
and r ; intersecting r, by a line drawn frora 1 to the point of distance at w,
which raust be squared across to the perpendicular from q, at x. The paw
feet are likewise to be drawn by hand, which must depend entirely on the
taste of the draughftsman ; the guiding lines at p and p pointing out their
situation : the same may be said as to the outline of the pillar.
AU circular objects, and particularly tables, are best represented perspec
tively with the eye placed in the centre, or equaUy betwixt its two extremes ;
answering to what is terraed a central view : this has been adopted in the
present exaraple. In all cases where a circular object, as the one before us,
comes urider practice, the central point of view is recoraraended in preference
to that of a side one ; for unless the spectator places himself or takes his
station at a very considerable distance on one side of the circle, and also
takes a long point of distance, the circle wiU become very much elongated
at the furthest extreraity from him ; and vice versa, tbe nearest end will
becorae very rauch foreshortened : thus, although the block be placed exactly
in the centre, the top of the table will appear to hang over raore on one side
than the other, producing thereby a distorted appearance. These obser
vations have been deeraed necessary in order that the learner may avoid
adopting that point of view ever found to produce a bad effect.

2 1


114 PRACTICAL PERSPECTIVE.

Plate 14.
The perspective representation ofa cheval dressing glass, the front heing placed
parallel to the picture ; shewing the mode and manner of finding per
spective by the inclination of the swing frame, thrown hack in any im lined
position. Fig. A, shews one half the elevation of the cheval frarae and glass, as
seen in front. Fig. B, shews the profile of one of the standards, with the
inclined position of the swing frarae, as raarked by the letters X X.
The ground line is denoted by the letters G G ; the horizontal Hne
by the letters H H, and in this example is placed 4 feet 9 inches frora the
ground. The points of sight and distance are both placed out of the picture;
the point of sight being 7 feet 21 inches by the scale frora D on the right
hand ; the point of distance being the sarae raeasure frora D on the left hand :
this is done for the sake of shewing the object to the best advantage ; for in
all cases the further the point of view is placed frora the nearest side of the
object, and the further the point of distance is reraoved back frora the front
of it, the greater similarity wiU its appearance bear to the original. It will
be necessary first to make a perspective plan as before directed in the
preceding examples : for which purpose, the measure C a, in the front
elevation, is first set off on the ground line G G from C to a, right and left ;
likewise the measure C b, in the sarae elevation, is set frora C to h, right and
left, on the sarae line. These measures, a a and b b, are then conveyed to
the point of sight by visuals. The measure o o, in the profile B, must next
be taken and set off from a to o ; this measure being conveyed to the point
of distance, wUl intersect the visual a datd; a line squared frora d, and
intersecting the visuals drawn frora b, b, and a, at e, e, and d, will determine
by those intersections the utmost stretch of the claws of both standards
perspectively ; as also their thickness in front. The tinted planes raarked
////and gggg, denote the front and depth of the two blocks which receive
the claws, and answer to the measure marked pp in the profile : this raeasure
is set right and left of the centre X at the points p and p, and conveyed by
the point of distance on the visual a d as before, intersecting it at g and g.


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PRACTICAL PERSPECTIVE. 115
The tinted plane raarked k k shews the situation and perspective width
of the glass frarae : this is found by taking frora the front elevation the mea
sure C c, and setting it right and left of the centre C, as at c c, frora which
visuals raust be drawn as before, intersecting a line squared frora q, at k
and k. For the reraainder, the student is referred to the exaraple itself, where
he will find in the perspective plan, all the Hnes laid down, necessary for work
ing his draught. So rauch having already been detailed in the preceding
lessons as to raising the elevation from the perspective plan, as also for
obtaining the perspective heights of all objects, we have only to state that
the heights in this exaraple are all transferred as usual frora the profile and
front elevation upon the two original lines raarked F and G ; as denoted by
the figures 1, 2, 3, &c. and 1, 2, 3, &c. and carried frora thence by visuals
to the point of sight, intersecting perpendiculars raised from the corres
ponding places in the perspective plan, as wiU be seen by inspection;
G being the geometrical line for the standard at the nearest end, and F,
that of the standard at the farthest end. It now remains to lay down
the process for obtedning, perspectively, the incHned position of the
glass frarae, its swing being thrown back at any supposed inclination.
Let X X, in the profile B, be the supposed inclination of the swing
frarae : frora X and X drop perpendiculars, intersecting the ground line
at X and x. Take half the raeasure x x, and set it .right and left of the
centre X, as at x and x ; these points convey by the point of distance
onthe visual a d at m and m; lines squared frora m and m, intersecting
the visuals drawn frora c and c wUl give the seat of the top line
y X, of the glass frame at / and I ; the seat of the bottora line y x,atn and n.
From c and c on the ground line raise the perpendiculars E and E, upon
which lines transfer frora the profile, the height of the central point or
pivot upon which the glass revolves, at Z and Z ; these heights being con
veyed to the point of sight, will intersect the perpendiculars raised from
k and k, at z and z, and deterraine the height of each centre or pivot per
spectively. Next transfer from the profile B, the upper and lower heights,
X and X upon the perpendiculars E and E at W and W, Y and Y : these
heights convey by the point of sight on the perpendiculars raised from I and
I; n and n, intersecting them at y and j;, y and x: lines drawn from x
through z to x, and frora y through z to y, will represent the inclined position


118 PRACTICAL PERSPECTIVE.
of the glass frarae, which is completed by squaring lines from x ana x, top
and bottom. The banding forraing the face of the frarae, is placed on the
perpendicular E, as at V, and conveyed frora thence bythe point of sight on
the inclined line x x ; the sarae raeasure wiU answer for the three other
sides. The divisions comprising the ornaraental parts of the stretcher, are
taken frora the front elevation, and placed on the ground Hne, right and
left of the centre C, at r r and s s; frora thence conveyed on the Hue k k, by
visuals drawn to the point of sight, and then carried by perpendiculars upon
the line of the stretcher, as raay be seen by inspection.
The vanishing point of all inclined planes, supposing such planes to be
placed in front of the spectator, as in the present example, is seated in a
perpendicular raised upon the horizontal line from the station point ; and is
found by a line drawn frora the point of distance parallel to the inclined
position of the glass frarae, and continued until it intersects such perpen
dicular : in this instance the vanishing point for the incHned plane of the
glass would be at a considerable distance above the horizontal line, being 30
feet by the scale ; and therefore the present process is adopted as saving
rauch trouble and inconvenience to the learner.
The incHned Hne frora D, is drawn parallel to the inclined position of
the glass frame X X, and would, if continued, intersect a perpendicular
raised on the station point, at a distance of 15 feet above the horizontal line,
which would be one half the required distance of the vanishing point ; the
point D being only half the real distance frora the point of sight, as before
observed. Every object moveable on a centre, will by its evolution round its own
axis, describe a circle: it follows therefore that the inclined position of aU
doors and box-lids thrown open ; dressing-glass fraraes, wheel-spokes, &c.
may be found perspectively on the circumference of an ellipsis, such being the
perspective representation of a circle ; but this would be attended with more
trouble and time than the process adopted in the present instance.
To elucidate the foregoing observations, two diagrams are added, the one
geometrical and the other perspective ; shewing the method of finding the
position of an inclined surface perspectively, as observed above.


PRACTICAL PERSPECTIVE.

ll

Fig 1 1^

.TF

Fig. 2

The learner raay suppose A B, Fig. 1, to represent the edge of a glass
frame, or any other object, as raoveable on its pivot or axis C, round which it
revolves. It is therefore evident, that if the frarae be turned on its centre, it
win by its evolution describe the dotted circle A E B F. If the same frame
be removed from its perpendicular position A, to the points, its position will
then be inclined, as shewn at h g ; for being revolved on its centre or pivot
C, the bottom edge of the frarae would rest atg, and make the angle g- C B,
equal the angle A C /«; therefore let the frame be moved into any position;
whether perpendicular, inclined, or horizontal, it would still describe a circle :
consequently its top and bottora edges would be liraited by the periphery of
a circle. Fig. 2. Shews the circle A E B F, fig. 1, as represented perspec
tively, the sarae forraing the ellipsisaftcrf: parallel with it, is shewn another
elHpsis efg h, as produced frora the sarae circle. In both these eUipses the
lines k k and 1 1 represent the two upright edges of the glass frame, as placed
in the inclined position h g, fig. I . It will be seen in this diagram that the
sides of the glass frarae converge frora the bottom to the top edge, which
being continued, would fall into a point situated in a plane perpendicular to
the horizon ; which perpendicular, as we have before observed, would be
raised on the point of sight.
The student has now before him three different modes of effecting the
same end, viz. the mode laid down in the Example, plate 14; secondly, the
method of finding a vanishing point into which the sides of the glass would
2 K


ug PRACTICAL PERSPECTIVE.
converge, by a line drawn from the point of distance, parallel to the inclined
position of the frame, whatever such may be, until it intersects the per
pendicular raised from the point of sight ; and, lastly, the mode as here
shewn in fig. 2.
We shall conclude the present treatise with some PreHminary Observa
tions on Angular Perspective, as applicable to objects of furniture ; and
explain its principles by an example, shewing a four post bedstead as placed
in an inclined position with respect to the plane of the picture; giving at
the same tirae instructions for laying down the Hnes, vanishing points, &c.
for the same.

ANGULAR PERSPECTIVE.

Preliminary Observations.

Hitherto the practical part of Perspective in this treatise has been
confined to a parallel view of the f bject with re pect to the plane of the
picture ; this being considered the most eligible position as regards house
hold furniture in general ; first, as conveying a more lively and correct
representation of the object to the individual to whom the design is offered ;
and secondly, by the addition of a plan and profile, accorapanied with a
scale of feet and inches, enabling the workman to ascertain correctly, every
geometrical raeasure, as regards height, depth, and projection of breaks
and mouldings. There is no method in practice, that can be applied with more
success than parallel perspective for the delineation of furniture designs ;
which therefore in this instance is strongly recommended. Inclined per-


PRACTICAL PERSPECTIVE.

119

spective, which is raore generally practised amongst architects, is chiefly
applicable in delineating views of detached buildings with their surrounding
scenery; colonnades, porticoes, &c. and all subjects wherein picturesque effect
is required ; and which parallel perspective would fail to produce. We have
nevertheless, in order to render the present treatise complete and generaUy
useful, given one exaraple in this branch of the art; with instructions,
showing how far angular perspective may in some cases be successfully
applied in delineating objects of household furniture.
The difference between parallel and inclined perspective, consists in
the position of the object under view, with respect to the plane of the
picture ; as is exemplified and iUustrated in the annexed diagrara.
Let the line P P, re
present the plane of the pic
ture ; S, the station point, or
spot where the spectator is
supposed to stand to view
the objects A and B. The
object A is said to be placed
parallel to the picture and to
the spectator; as having its
front face a b parallel to the
plane PP, and its side face be
at right angles to it ; the va
nishing point of such side
would in this instance be in
the centre of the picture, or
that point immediately opposite the eye ofthe spectator ; as shewn at C.
The figure B is said to be inclined to the picture ; its sides d a and d c
being neither parallel to the plane P P, nor at right angles to it: the
vanishing points for the sides d a and d c, as produced by the lines S V and
S V, would cut the picture at angles equal to the angles which the sides d a
and dc would make with the plane PP; as shewn bythe arcs eyand^A;
ef being equal to a b, and g h equal to c C.
The figures D and E, are perspective representations of the objects
A and B, as both would appear to the eye of a spectator stationed at S


120 PRACTICAL PERSPECTIVE.
shewing the difference in appearance betwixt a parallel and inclined position
of the object : s becomes the vanishing point for the return side t, of fig D,
as squared up from the centre C : v and v are the vanishing points for the
sides o and x, fig. E, as squared up from the points V and V. When one face
of the object, as a h, is coincident with the plane of the picture ; that is,
directly in the line of it, such face would be drawn geometrically, and conse
quently may be raeasured by scale.
This branch of perspective may be generally appHed to all objects,
approaching in their dimension and form to that ofa square ; that is, iu any
figure wherein one side does not raaterially exceed the other ; as in chairs,
bedsteads, pedestals for sideboards, &c.: it raay also be successfully applied
to all articles of furniture, taking either a triangular, octagonal, or circular
form ; such as tripod stands, candelabra, loo-tables, &c. When the object
is required to be shown in angular perspective, it is always advisable to
place the station point at a much greater distance than perhaps would be
requisite in parallel perspective; for by placing the station point too near
the object, the vanishing points for its sides will be brought proportionally
near also, and cause them to converge too suddenly ; giving the object a
distorted appearance, and consequently conveying an incorrect idea of it to
the spectator. In the example now given, a very distant station is made choice of;
which producing vanishing points proportionally distant, tend to give
the object a more natural and agreeable appearance to the eye, but which
would be found nevertheless very inconvenient in raost instances for
drawing articles of furniture ; such vanishing points being so far removed
out of the picture or off the paper, as to require boards of larger diraen
sions to be made use of, in order to receive them. Having said thus much,
we shall now proceed to explain the principles of this branch of perspective,
and iUustrate the foregoing observations by the foUowing example;
(representing a four-post bedstead, as such would appear to the eye when
inclined to the picture).


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PRACTICAL PERSPECTIVE. 121

Plate 15.

To represent a four post bedstead and furniture in inclined perspective, the sarr.e
being placed in any angular position.
In the delineation of an object in Angular Perspective, it is requisite
in the first instance to find the vanishing points in the horizon to which
the sides of the object would converge ; also to lay down the points of
distance, the same serving to cut off all original measures on the vanishing
lines, as respects length or breadth ; it will therefore be necessary before we
commence with our instructions in the present example, to lay before the
student the method and process of finding these different points, frora any
angular position of the object; which being well understood in the first
instance, will render this branch of perspective less difficult of attainment.
As the vanishing points, and points of distance, made use of in this exaraple
of the bedstead, could not be shewn in the plate for want of roora, the
method for laying thera down is shewn in the diagram, fig. 1 ; where H H,
denotes the horizontal line ; C S the distance of the picture, as set up per
pendicularly from C to S ; the sarae being one sixth ofthe original distance of
the station point for the bedstead, as set up frora C on the horizontal line
below. Let abed, be the plan of an original figure, as inclined to the parallel
line G G; its inclination being shewn by the angles ech and fc d. Frora
the station point S, lay down the angle g S h, equal to the angle eeb in the
original figure A ; also from S, lay down the angle i S h, equal to the angle
fed, in the same figure. From S, through h and k, draw the lines S V
and S V : V and V, wiU then become the vanishing points for the sides a b,
d c, and a d,b c. Bisect the angle k^ hatl ; a line drawn from S through
I, will produce the diagonal point at m. The distance 1 — S, laid down on the
horizontal line frora V, will produce the right hand point of distance at E; the
distance 2 S, laid down from V, will produce the point of distance 2. on the
left hand. The picture is then prepared for practice ; having the two
vanishing points, \ and - for the sides of the object, with the two points of
distance " and .f, for the purpose of cutting off on the vanishing lines
2 L


132 PRACTICAL PERSPECTIVE.
e— I and c~2, any original raeasure of length or breadth. The diagonal
point m, serves as a vanishing point for any diagonal or raitre line in the
plan A, and by raeans of which, all mitres are projected. Transfer frora c
on the Hne G G, the side c b of the fig. A, at e; likewise the side cdatf,
on the same line; these measures conveyed on the vanishing lines c — I
and c — 2 by the points of distance, will give the perspective length and
breadth of the figure, at o and p : lines drawn frora o and p to the points
Vand V, intersecting each other at r, will produce the plane c o r p, which
plane will be the perspective representation of the plan A. From c, o, p
and r, raise perpendiculars at pleasure: on the perpendicular raised from
e, set up the intended height of the object, as at g ; which draw to the
yanishing points as , before, intersecting the perpendiculars from o and p^
at s and t : the figure is then completed. We shall now coraraence with
the application of this diagram in the example of the bedstead. Having
laid down the vanishing points, &c. agreeable to the inclined position
of the bedstead, proceed and raise a perpendicular O G, frora the point
O, which consider as a geometrical line. On this line set up all the
original heights ; viz. the height of the rail at 1 and 2 ; the height of
the foot board and bedding, at 3; the height of the bolster, at 4; the
height of the bedpillars and teaster frarae, at 5 and 6 ; aqd that of the risers
on the laths at 7. Frora O, 5 and 6, draw lines to the respective vanishing
points : next take six feet frora the scale, which set off from O to 6, on the
right hand of the georaetrical line ; and set off 7 feet frora O to 7, on the
left hand of the sarae line : these raeasures being conveyed on to the
vanishing lines O V and O V by the points of distance, will deterraine the
length and width ofthe bedstead at a and b. From a and b, draw lines to the
vanishing points, intersecting each other ate; and from a and i, raise up
perpendiculars until they meet the vanishing lines 6 V and 6 V at e and f;
a e and bf wiU then represent the two extreme corners of the bedstead. The
situation of each post on the ground is thus found : take 4j inches from the
scale for the diameter, which set off on the ground Hne from O to/>,right and left
from 6 to p, and frora 7 to p : these raeasures convey on the vanishing lines
O V and O V by the points of distance, at y, y, y, and-y. Lines drawn frora
y, y, &c. to the vanishing points, intersecting each other at z, s, &c. will
produce the perspective squares ayz, yO y z. zyb, and dzyc. Thus much


PRACTICAL PERSPECTIVE. ' 123
being done, proceed next with the teaster.; first by drawing the line TT
through the point 6, upon which line, set off the breadth of the teaster lath,
viz. 3^ inches, from 6 to r, right and left ; from T to r and from T to r ;
these measures convey on to the vanishing lines 6 e and 6 f by the points
of distance at s, s, s, and s; and square them down on the lines 5 v and 5 v
at u, u, &c. Liues drawn from u, u, &c. as also frome, *; s, s ; and s,f, to
the respective vanishing points, intersecting each other at t and w, will
complete the teaster frarae of the bedstead ; and perpendiculars squared up
frora the planes a y z, y o y z, Slc. terrainating with the plane of the teaster,
wiU give the representation of each post, considered as a square body. For
the side and foot rails of the bedstead, the ornaraental parts of the pillars,
&c. the learner is referred to the plate. The bolster is found by setting off
the measure of its diameter (9 inches) from p to m, which must be conveyed
on the vanishing line atg, as before, by the point of distance, and from thence
drawn to the right hand vanishing point, intersecting the line c b at h: lines
squared up from g and h, and cut by the lines drawn from 3 and 4, will give
the planes A and B, in which to draw the two ellipsis forming the ends of the
bolster ; which raust be joined by lines drawn to the right hand vanishing
point. The bedstead being thus completed, the furniture may be designed
and drawn in according to fancy ; which in this example is shewn on one
side only ; the other side, shewing the frame of the bedstead, with the pattern
of the bed pillars. The inside vallance is shewn on one side at f—t.
Fig. 2, shews the plan of the bedstead, drawn to a scale reduced, J
'the size ofthe perspective example. The distance of each vanishing point,
and point of distance in this example, as set off on tbe horizontal line from
the centre C, is as follows. Ft. In.
Station point  20 2 upwards frora C
Right hand vanishing point . 19 8"\
heft hand Ditto ... 20 7 f the horizontal line
Right hand point of distance . 8 4 T from the centre C
Left hand Ditto ... 87)
In concluding this portion of the drawing book, it may be proper to
furnish such hints and observations as wiU assist the learner, uot only in his
studies, but atthe sarae time point out to hira the course he may persue with


124 PRACTICAL PERSPECTIVE.
the greatest advantage to himself My chief aim in compiling this treatise
has been, to render the practice of perspective familiar and comprehensive
to those for whose use this work is designed ; to comprise theresult of many
years study and practice in as small a compass as the subject would possibly
admit of; lo illustrate its principles by the most easy and simple examples ;
and to convey the instructions given with each example in the plainest
language. This I have endeavoured to do to the best of my abilities ;
how far I have succeeded in the undertaking, raust be left to the 'udg
ment of the reader. The science of Geometry is made the corner stone
Ol my structure : the principles of this science the student is strongly
advised to make hiraself acquainted with ; and first with the definitions ; not
contenting himself with a mere reading, but to use every endeavour and all
possible raeans to imprint thera on his meraory; so as to have them present
at all times, as occasion may call thera into use.
Although this raay appear dry, and be attended with sorae difficulty in
the first instance, yet once obtained, will render the practical part of Geometry
not only more pleasant, but much more easy in the attainment.
Throughout the whole of this treatise, every endeavour on the Author's
part has been used to render the science easy of coraprehension, and at the
sarae time amusing, as far as the nature of the subject would allow. Much
original matter has been given in this treatise, especially in the practical
part; and every information afforded which the Author's many years expe
rience and reading have enabled him to offer,
He who would cultivate his vineyard, must labour I He wno would reap
the fruits of an harvest, raust sow ! and he who would seek to gain diamonds,
must be content to search and dig for thera ! The sarae reasoning appHes
to all those who wish to acquire knowledge ; they raust not only read, but
digest what they peruse, and enure themselves to private study if they wish
to learn and excel in any science ; unattainable without such resolutions.
A slight reading will answer well in the first outset : a closer reading is
recomiriended for the second, and a still closer reading for the third. If the
student can be prevailed upon to make use of this exertion, the reward
he will ultimately receive, will be more than commensurate to the anxiety,
pain, and trouble experienced in the trial. The pupil in this case is
recommended to copy each diagram on a larger scale, and if he can be


PRACTICAL PERSPECTIVE. 125
reconciled to encounter the trouble of writing out the instructions on paper,
he will find an advantage more than equal to the time bestowed on the
labour; as this will tend to imprint them more firmly on his meraory:
in addition to w^hich, the written instructions being thus before the student,
will render a reference to the work less irksorae, and where the references
are raany, less perplexing.
This practice is recoraraended by the Author, frora the advantages it
has afforded to his pupils in their tuition ; and inasmuch as it has been
observed and followed, so have his scholars improved and benefited by it.
In the study of Perspective, the same course raust be pursued as is here
recommended with regard to the Geometry ; the pupd commencing first with
the definitions, which should be well imprinted on his memory; proceeding
next with the practical diagrams, which will then be the easier understood; and
having made himself thorough master of these, together with their use,
he will be enabled the better to apply them in working the practical examples
which follow.
He whose disposition would lead him not only to learn, but to excel or
attain preeminence in any art or science, must first raake himself master of
the principles on which that art or science is founded ; without which, either
his failure in the knowledge of it must follow, or his progress in the study of
it be greatly retarded. Perspective as an art, is the offspring of geometry;
its principles depending on, and entirely to be drawn from it. To expatiate
and enlarge on the utility of these two sciences, with the connection and
relation they bear to each other, would occupy and require more room than
can be allowed in this place : it only remains to observe, that the doctrine of
angles, as laid down in the first part of the geometrical treatise, (see pages
5 and 6) if weU digested and understood in the first instance, will be found of
essential service in facilitating the knowledge of this most useful department
of mechanical drawing perspective. By the doctrine of angles we are enabled
to find the trae place of any vanishing point to which the side of an object
would tend ; either in the horizontal, or on a perpendicular plane.
In the Geometrical definitions, the learner will find that frequent refer
ence is made to their use in perspective: (see pages 1, 2, 4, &c.) All lines
tending to the point of distance, either in parallel or incHned perspective,
answer to the diagonal Hnes of a square in Geometry : This is quite
2 M


126 PRACTICAL PERSPECTIVE.
sufficient to shew the accordance and relation, existing between the two
sciences.
In fraraing the perspective exaraples, as applicable to objects of furniture,
attention has been paid to give such only as would be really useful, and at
the sarae time pleasing and interesting ; being fuUy aware, that in most in
stances, it is necessary to lead the mind, and encourage it in the pursuit
of science, by a judicious selection of objects. We shall conclude this
treatise with offering to the student the following directions, as regards the
utensils necessary for his practice.
In commencing with the study of Geometry or Perspective, it is neces
sary that the learner provide himself with a case of raathematical instruments,
a drawing board, a T square and a parallel ruler. The case of instruments
should consist of a pair of dividing compasses ; a pair of corapasses with
shifting limbs, the one for a pencil, the other for ink; a drawing pen with
steel point, and a pair of bow corapasses for the purpose of striking sraaller
circles ; and these also adapted to receive a shifting limb for pencil or ink, as
occasion raay require : ' In addition to these, raay be added a plain scale,
as described in Geometry, page 55. These instruraents are all that are
necessary for the student in this departraent of drawing ; the sector, pro
portional compasses, &c. being more in use ainongst those who practice in
the higher branches of mathematics.
The drawing board should be made with a shifting pannel, to receive on
it the drawing paper, whicn is first damped over with a wet sponge. It is
necessary to be observed, that one side of the drawing paper is to be pre
ferred to the other, as being less defective. In the manufacture of all drawing
paper, that side destined by the maker, for receiving the artist's performance,
has on it a covering of size, which the other side does not possess ; and which
therefore may be found defective : this is known by holding the paper before
the Hght, in which case, the water-mark with the maker's name, raust invari
ably read backward ; this is the side to be wetted and placed next to the
shifting pannel ; after which the paper should be notched at the four corners,
and, with the pannel, placed in the frarae ; the whole being secured by two
shifting battens : the fair side of the paper will then offer itself, and when
dry, be ready for use. The structure of the drawing board for this purpose


PRACTICAL PERSPECTIVE.

127

Fig.f. A

wiUbeeasie* understood, by reference to the annexed wood-cut, (fig.l,)
which represents it with its front face upwards ; shewing a fraraing
all round, equal to two inches.
Figure 2, shows a section of
the sarae board ; the upper
face A, Fig. 1, being denoted
at B ; by which may be seen,
the manner in which the loose
pannel is made to fit into the
frame. The size ofthe board
for general use, should mea
sure 18 inches by 2 feet, in
cluding the outside frame.
The T square having a stock,
into which is affixed the blade
or staff, fitted exactly at right
angles to it, should be raade
of a length proportionable to
that of the board in use. fn
many of these squares, the stock is raade to consist of two parls ; the one
attached to the blade as a fixture, the other moveable on a centre or
pivot ; and both secured by a thumb screw in such manner, that when the
raoveable part of the stock is placed at the edge of the drawing board, the
other half with the blade attached to it, becoraes moveable ; and may be
adapted to any inclination, or set to any angle at the discretion of the stu
dent. (See its use further explained in pages 22 and 23.) The parallel ruler
is also of indispensable utUity in the practice of geometrical and perspective
drawing : its length should not be less than 15 inches for general use. Its
construction aid use has been already described and demonstrated : (seepage
22, Practical jeoraetry.)

Il2. Jr

Iti.
Ji

¦¦¦ill Fig. 2. B.


128 ORNAMENTAL DRAWING.

ELEMENTS OF ORNAMENT,

DRAWING IN GENERAL.

Preliminary Observations.

Ornamental drawingeonstitutes a very essential part in the qualification
of those artisans for whose use this work has been composed ; viz. that
of the Upholsterer and Cabinet-raaker : and as no design can be considered
complete in which this elegant and useful branch of drawing is wanting, so
the present work could not be considered as complete in' itself, or as a
whole, without a treatise on the subject ; combining every information which
such a branch of Art would require. It has therefore been thought neces
sary by the Author to lay down such rules and precepts, as are really
necessary and useful for this purpose, offering the result of raany years prac
tice and experience.
This part of our work opens a wide field for great and continued grati
fication ; for without ornamental embellishraent, the two sister arts (Geometry
and Perspective) appear undressed ; but with the assistance of ornamental
drawing, what is taught in the two former branches, is heightened, realized
and brought to perfection by the latter. It is quite possible to delineate a
design correctly in perspective ; but how often, for want of practice in the
ornamental branch, are such designs deficient in good drawing : it is on this
ground, that he who would perfect himself and become a correct draughtsman,
should make himself proficient in this fascinating, elegant, and useful depart
raent of drawing. It remains now to point out the direct road in which the
student raay travel ; not only with advantage to himself, but with a promise
of reward at the end of his journey.


ORNAMENTAL DRAWING. 129
It is a usual practice with many parents to send their sons to be taught
Perspective Drawing only, whilst they are totally ignorant and unacquainted
with that which should precede such instruction : nothing in this instance can
be more erroneous in principle, and nothing worse in practice : it would be
quite as consistent to put a youth to the learning of Matheraatics without a
previous instruction in Geometry ; and to teach him the science of
Algebra, without a previous knowledge of the four fundamental rules in
Arithmetic. The Author from many years practice in teaching, has invariably
found it of the greatest advantage to the pupil, to perfect him previously in
Ornamental Drawing.
The first object of the pupd is to gain a freedora of hand for sketching,
and to attain a thorough acquaintance with every line in all its circuravo-
lutions and bearings; and this can only be achieved by continual practice.
This mode has all along been considered as the raost conducive in the end
towards producing perfection of outline in drawing ; added to which, a double
advantage is obtained ; naraely, that of designing ornaraent tastefully, and
drawing that ornament more correctly when subject to the laws of per
spective. Taking this view of the subject, a treatise on Ornamental Drawing
wUl not be considered as an unnecessary appendage to this work. What
we have to detail on the subject will be laid down in a plain and farailiar
raanner, such as will meet the comprehension of the learner.
It would be a loss of time to give a youth an ornamental lesson to copy,
without first instructing him in the leading principles by which it is produced .
for without proper attention be paid in this instance, he will produce a faulty
drawing, and in raost cases a very imperfect copy ofthe original.
As Ornaraental Drawing therefore forras an essential qualification
both to the upholsterer and the cabinet-raaker, it should be practised and
be well understood previous to the study of Perspective.
Perspective as applicable to furniture drawing, differs in sorae raeasure
frora the practice of it in Architecture ; the one being alraost wholly confined
to straight lines ; whereas the other is in a great raeasure coupled with lines
that are curved, or on the sweep. By the rules of perspective, the planes
which inscribe all eUiptical curve lines are produced; and by the
sarae rules, certain points are found in those planes, through which the
outline of such curves may be traced ; but without a previous practice in
2 N


130

ORNAMENTAL DRAWING.

ornamental drawing, these lines will ever be at variance with truth. To
obviate this difficulty, the system of drawing various curved lines is here
recomraended; and which may be practised jointly with the study of
geometry : our system therefore coraraences with a series of siraple and
corapound outlines, as coraprised in plates CX. and CXI. the same having
been carefully studied and wholly adapted to ornaraental composition ;
and to which reference will occasionally be made in the subsequent
examples. It is here necessary to advise the practitioner to make use
of a soft lead pencil, with which the outlines now given should be lightly
sketched in.
As a great degree of fluency in this department, depends on the wrist,
the Author would recommend the following system. Let a common slate
be made, use of as a drawing board, on which with a piece of prepared
pipe clay inserted in a port crayon (sold at aU colour shops), let the pupil
practice the examples given ; supporting his wrist on a bridge, (constructed
as shewn in the wood cut,) so that the point ofhis crayon will only touch the
slate. This may feel some
what irksome at the first, but
the practitioner will soon be
reconciled to it; and the
advantage obtained by it, will
be experienced, when using
the pencil or pen without aid
of the bridge : the freedom
also with which the crayon of pipe clay will pass over the slate, will intui
tively and imperceptibly give a freedora to his hand ; and of this he can only
be convinced bythe trial. We shaU now commence with the series of exam
ples given in this treatise. ,





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ORNAMENTAL DRAWING. 131

Plate CX.

The outlines in this plate, as well as in those which follow in plates CXI,
XX, CXXI, and XXI, are properly termed elementary; consisting of outlines
simple, and compound; in theraselves, the foundation of every speciesof orna
mental composition. These outlines, varied in their form, must be practised
by the learner, until he finds his hand capable of drawing thera fluently and
with freedom. This will be greatly facilitated by copying thera on an enlarged
scale, whether on the slate with the pipe clay crayon as before noticed, or
otherwise with a piece of common chalk on a flat board, as the learner may
find the most agreeable to hiraself The outUnes contained in the present
plate, have been selected as the most essential for the learner's practice in
the ornamental department, but may nevertheless become useful in other
branches of drawing.
Fig. 1 and 2, partake of the outline, coraraon to the head and foot scrolls
of every Grecian couch.
Fig. 3 and 4, exhibit the same species of outline reversed ; and here
introduced for the purpose of educating the hand to the practice of drawing
the same outline both ways.
Fig. 5 and 6, may also be considered as elementary, being the first
sweep Hnes of all continued scroUs; and therefore drawn right and left
also. Fig. 7, is the first elementary outline in a foliage leaf; being that
part where the leaf makes a folding over at its extremity : the learner
should also exercise his hand in drawing this outline both ways, viz. right
and left. Fig. 8, exhibits the outline for one half ofthe tulip flower; and Fig. 9,
is the two halves put together. This species of ornament is much used for
the ends of cornice poles. I
Fig. 10, shows the outline for a scroll which is commonly adapted to thfe
same use.
Fig. 11, exhibits the outHne of the Archer's bow ; is often used as an
ornamental finish in its simple forra, but more frequently adorned with foliage.


132 ORNAMENTAL DRAWING.
This outline has been rauch used forthe cornices of windows, as also in those
of bedsteads : it has likewise been much used as an ornamental back for
side- boards, &c.
Fig. 12, is the outline of Fig. 10, reversed.
Fig. 13, is what is comraonly called in architecture the Vitruvian scroll:
this ornaraent is chiefly applicable to the decoration of friezes or borders, and
is sometimes used as an ornamental gallery for cabinet work.
Fig. 14, exhibits the outHne of a portion of the circle, when drawn per
spectively. The exterrial face of all circular objects, such as colurans. Sec.
when seen below the eye, partake of this outline.
Fig. 15, shows the outHne of a portion of the perspective circle, when
viewed sideways, or removed to the right or left hand ofthe spectator.
Fig. 16, pourtrays that portion of the perspective circle, as being the
most distant from the spectator.
Fig. 17, exhibits the outUne of the upper part ofthe perspective circle,
when drawn in a perpendicular position.
Fig 18, is the outline of the perspective circle when coraplete : the flat
surfaces of all circular objects partake of this outline when seen below the eye.
These various outlines of the circle are here given, as being considered
raost essential for the pupil's practice ; so that in exercising his hand, he may
draw such outHnes with more truth and facility, as they occur in the practice
of perspective drawing. These five simple forras being well studied and
practised by the hand, wUl save the student rauch trouble, and enable him
to draw many of his sweep lines in perspective, without the aid and
necessity of finding the points for the same in a perspective plane, whether
above or below the horizon.

Plate CXI.
The outlines in this plate are compounded more or less from those given
in the preceding plate : for instance,
Fig. 18, will be seen to partake of the outlines
raarked 8 and 9 in the preceding plate. It is chiefly
used in ornamental work to fill up the vacant space
betwixt two scrolls as rising one out ofthe other: thus, as in the wood cut.





PL .CXI

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ORNAMENTAL DRAWING. 133
Fig. 19 : — the sarae ornament reversed.
Fig. 20 : is compounded of the oUtHnes numbered 1, 5, and 6 in pl-ito
CX. This combination of leaves is greatly used in the composition of
foliage. Fig. 21, exhibits a portion of what is commonly called in ornamental
decoration a foliage leaf; and where five of these are combined together,
it is called a palm ofthe leaf, as bearing a similitude to the palm ofthe hand,
which has five fingers. This species of leaf is tastefully adopted in the
decoration of the Corinthian capital.
Fig. 22, is the same outline drawn the reverse way.
Fig. 23, may be considered as denoting the three principal fibres con
tained in the palm of a leaf : and partakes nearly of the outlines, 1 and 6.
Fig. 24 : — This spiral outline is chiefly used as a model for the truss
bracket : it admits of being ornamented in various ways.
Fig. 25, is a palm of leaves corapounded of Figs. 21 and 22. The
projecting part, separating each leaf is termed a pipe, and its upper part (or
hollow) is termed its eye. This leaf is greatly used amongst carvers in the
composition of foliage.
Fig. 26, is a combination of Fig. 24 and a portion of Fig. 4. This
composition oi outHne when cloathed with foHage, is applicable to the pur
poses of decoration in various ways ; it is sometimes made use of as the
outiine ofa supporting bracket for the upper shelves of a chiffonier.
Fig. 27, is denominated the honeysuckle fan ornament ; and is com
pounded of a portion of Figs. 2 and 4.
Fig. 28, forms the outline of all truss supports, whether for sideboards,
commodes, Ste.; admitting of great enrichment.
The straight lines drawn through figures 1, 2, 3, and 4, plate CX ; as
also through Figures 18, 19, &c. CXI, are intended to guide the student
in drawing the respective outlines ; the inclination ofj«which must be regulated
accordingly. In copying these figures, the pupil should commence from the
top, as in Fig. 1, and complete the upperraost sweep, in which he will be
guided by the space it occupies upon the straight line : he will then proceed to
draw the bottom sweep in continuation, from the point where the upper one
terminates, until it crosses the straight line at bottom, which must be his guide
also in this instance : his eye enabling him to judge of the proportion.
2 o


134 ORNAMENTAL DRAWING
the two curves bear to the staight line, which a Httle practice will make him
master of What has thus been said of Fig. 1, will also apply to the rest of
the outlines on these two plates.
It is here necessary to remark, that as all varied outline owes its birth
and perfection to simple outline, so the first cannot be too much considered.
By a correct knowledge of outline, we are enabled to give elegance to those
forms to which they are intended to be applied ; whether as objects of
furniture or ornamental decoration. In plate CXI, almost every variation
which outline is capable of receiving, is given ; at least as much as is neces
sary to the present purpose.

Plate XX.
Consists of a collection of leaves in outline, ranged into four divisions :
in the first or uppermost range, the leaf is drawn as a simple outHne only,
in regard to its width and height. The leaf adjoining, being produced from
the preceding outline, is divided into nineteen parts, forming so raany
smaUer divisions of the leaf; and these are pointed at their extremities.
The third leaf partakes of the sarae form, but divided only into thirteen
parts, being rounded instead of pointed at their extremities. The fourth
leaf in this range is of the same species as the preceding, but divided into
seventeen parts, and rounded at each extremity, vrith the addition of an
inner band partaking of the same form.
The second range contains, first, a leaf in simple outline ; the adjoining
leaf has the same outline, but is varied by an inner line being drawn, which
forms a band. The two remaining leaves in this row are ofthe same contour,
or outline as the preceding, having nine divisions within each ; the fourth
being varied by a hollow separation between each division. ,
The third row in this plate consists of outlines for such leaves as are
principally adapted for the enrichment of mouldings ; having the Ovolo,
Grecian Echinus, Cima Recta, Cima or Reversa, for their contour or
outline. The fourth and last series in this plate consists, first, of a leaf, having
twenty-one divisions for its detail ; tbe leaf adjoining has the same number


'^^

P1:XX.

L :ii: .A V £ c?

Elaih-nt.s of Ornament, exanplMcd itv the forms and method of drairiiu> divers Jcinds of leaves, e/nploi/ed
ill tliat braneh of Art.

Lfl)ndon, Publiflied \>-.- Jones S- Q? \.vi\ ^3 1826





ORNAMENTAL DRAWING. 135
of parts, but is varied by having a division or space between each part, with
the addition of a fold over at the end of every division ; forming what is
termed amongst carvers, a lipping. The third leaf in this range is the same
in contour as the preceding, being divided into nine parts, with a division
between each part. The nine principal parts represent the honej'suckle
when in bud; the space betwixt each part denotes the flower when in
blossom. The reraaining leaf offers the sarae outline, but is varied in its detail ;
having eleven divisions, inwardly scrolling at their several terrainations.
This species of leaf is universally termed, the Greek honeysuckle.

Plate CXXI.
In this plate are given examples of three different species of leaf;
consisting, first, ofthe simple outHne of each leaf; and secondly, the same
outline filled up with the detail; forming altogether what is termed a foliage
leaf. It will readily be seen that these leaves are compounded from similar
forms given in plates CX and CXI. These different species of leaf enter
more or less into aU ornamental composition, and are here purposely intro
duced, as being es.sential to the student's practice.
The ornaraental speciraens given in this plate are variously used in de
corating tbe Corinthian and Composite Capitals in Architecture ; and are
frequently adopted for decorating the friezes of rooms, &c. : and they often
form the principal embellishment of enriched mouldings, pateras, &c. It must
be observed that these leaves, and all ofa similar kind, are subject to a par
ticular system, as regards the arrangement of their parts ; each leaf, consisting
of seven divisions; three forming the leafage on each side, right and left,
the seventh or uppermost raaking the turn over.
In the two first examples, each division of the leaf consists of five smaller
divisions, and beingdivided after this raanner itis then calledahand or palra of
the leaf. The third exaraple in this plate consists also of seven principal divi
sions, each of which are again subdivided variously ; the two lowerraost hands
consisting of seven parts, the next of nine parts, and the two above these of
six parts; four of which only are seen distinct. The turnovers in the three


1.% ORNAMENTAL DRAWING.
examples are divided, each alike into nine parts. It now reraains to furnish
the practitioner with sorae instruction as to the raanner in which he must
proceed, in copying the examples given in the two foregoing plates, with
correctness and ease to hiraself
Coraraencing with the first figure in plate XX, let him proceed and
draw a line across his board as a base line ; on which line a perpendicular
raust be raised, and which may answer for the centre or stem of the leaf
Let hira next proceed and lay down half the width of the leaf, right and left ;
after which let the height of the leaf be set up on the perpendicular line,
before drawn : the sweeped outline denoting the form of the leaf, may then
be carefully drawn by the hand ; the eye correcting any irregularity that may
Occur in the drawing. The outside form being correctly drawn in, will serve
as a guide for drawing the inside band. The perpendicular dotted line wiU
then serve as a guide for drawing in the stem. The learner will next proceed
to copy the same outline as regards the second figure, observing to draw the
inner sweep line but faintly with the pencil ; in the leaf before us, it is
dotted. Upon this dotted line, right and left, must be noted as raany smaller
divisions, whether equal or unequal, as it is proposed the whole leaf shall
consist of; marking each division by a dot on the faint line : curved lines must
then be drawn from these respective points in gradation towards the base
and stem of the leaf; and again joined by a reversed sweep from the
point of each curve.
The third leaf exhibits the same outline in its contour, but varied in its
divisions. In this species of leaf each division is rounded • and it is thus
called a reeded leaf. The instructions given for copying the preceding leaf,
will apply to this also.
The fourth leaf in this series, takes a similar outline, and is divided
nearly after the same raanner ; the variation consists in the terminations
being raore rounded, with the addition of a hoUow or flute within each
division : it is drawn after the sarae manner as those precedng it.
In the second range of leaves, the second example is produced from the
first ; the third is produced from the second, and the fourth frora the third.
These leaves are all subject to one and the sarae outline as to their outside
forra ; being varied in their detail at the pleasure of the artist.


PL. CXXI.

OMIOJMnBn TAJL IDJR.A^WjLK'G 1.E Al^TE S ^ II ,

L'ablulicd Vy Jones ;¦ C?/\pr-i: 21. 16?e





ORNAMENTAL DRAWING. 13>
The third range in this plate shows the inanner of drawing the outline
lor the strap leaf The dotted lines point out how the leaf is divided, when a
repetition is required : these divisions form the centre and extremity of each
leaf^ and are repeated on the base Hne for as many leaves as are required.
In the fourth range, the two first leaves are both under one outline, the
secondbeing a slight deviation from the first; the same is to be observed ofthe
two last. What has been said before, as to the drawing of them, renders
any further directions unnecessary. The student by repeated practice in
copying, wdl soon findhimself in a capacity to overcome every difficulty, as to
producing a correct imitation of any example which may be placed before
him. It may however be necessary to advise the practitioner to commence
filling in the detail of each example from the lowermost point, and to
proceed upwards; carefully copying one side of the leaf first. The
different heights may then be transferred to the opposite side by the aid of
a T square,, admitting that the paper be laid down on a drawings board.
Whatever can be achieved by the eye without having resource to the aid of
compasses and square- is- rather to be recommended) as accustoming the
pupil to copy more readily from the- original : nevertheless the usage of these
helps is not altogether to be denied ; particularly when more than ordinary ac
curacy is required. It may also be necessary to remark, that a soft le&,d pencil
should always be used, and that with great lightness when sketching in the
rough outline, so that any raistake may the more easily be rubbed out, and
a cleaner and better surface be retained on the paper. If we have been
somewhat particular in this first part of our treatise, it is with a view of
rendering directions less necessary in what is to follow.
In Fig. 1, Plate CXXI, which represents in simple outline, fig. 2; the
base line should first be drawn ;. afterwards the centre or perpendicular line :
thC' base, line will i^eceive all the widths, the perpendicular the heights,
The outside sweep line, with the turn over ofthe leaf must then be drawn i
afterwards, the distance of each' pipe frora the centre line in Fig. 2, must be
set off right. and left from the centre ia fig. 1; as also the termination o a
of the first palm at bottom,, together with the width of the stem.
Next proceed and set up the height of the first palm of leaves on the
perpendicular line ; then the second, and lastly the third. The height and
width of each palra or hand of leaves being thus denoted, the outline com-
2 p


138 ORNAMENTAL DRAWING.
prising them maybe drawn after the manner shown in the example : this
completes the orthographic elevation of the leaf in simple outline. The mode
of procedure now laid down, should be pursued by the practitioner in copy
ing from any original object which may be placed before hira ; inscribing
such object, first in siraple outline ; dividing such outHne afterwards into
parts or sections, and such sections to contain the detail of the smaller
parts.

Plate XXI.
In this plate are given five different examples, intended as designs for
Pateras ; shewing the manner of dividing them into simple outline, and the
mode by which they may be varied.
The pupU in reference to the first figure, must commence and draw a
line across his board cr paper, which may be considered as the central line
of the Patera. Upon any part of this line as a centre, he wiU then with hi.^
compasses describe the circular outline which is to form the utmost boundary
of his figure, as shown by a dotted semicircle in the example. This semicir
cular iine may then be divided into eight equal parts: lines drawn from these
points to the apex, wiU determine the centre or stera of each leaf Another
seraicircle raust then be described within the first, which will regulate the
extent of the intermediate leaves, generally called the tongue leaf. Within
this is inscribed a third circular line, comprising the outline of what is
termed the rose of the Patera; and wilhin this again is described a fourth
circle, regulating the turning, or eye of each leaf in this portion of the figure
A smaller circle is then described, comprising that part ofthe ornament
called the eye of the Patera. It will bo seen that one half the range of leaves
in this Patera are drawn quite plain, forming a mere outHne. Tbe variation
of the above outline is exhibited in the lower half, each exterior leaf
having a band or list around it, with the central line formed into a stem.
For drawing in the foliage, the pupil must be guided by his eye and hand.
With respect to the second figure, it is subject to the same law as
regards the drawing of the first ; its extreme outline being first defined, and
then that of the smaUer circles within it; hut instead of eight parts, this


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'lUul.s- of leavis in torimiu/ Rosa-, futirtis , ki ive





ORNAMENTAL DRAWING. 139
Patera has its half or semicircle divided into four only. Having been fully
explicit and particular in describing the first figure, it becomes unnecessary
to go over the same ground again ; we shall therefore leave the student to
his own exertions, with the copy to guide him in the progress of his work.
The third or centre Patera, in this series, from its pattern, is termed
spirally involved ; inasmuch as the stems of the leaves composing its foliage,
have a tendency, one tp follow the curve of the other, from the centre or
apex. The whole circmnference of this Patera is divided into eight parts,
four of which regulate the eyes dividing each leaf, and the remaining four
their stems.
This species of Patera is freqaently termed a bosse, and is greatly used
in our cathedrals, as forming a finish for supporting the extremities of
several arches when joined together ; or rather the crowning to a centre in
which they would terminate. They are as varied as they are richly deco
rated. In this example four circles only are necessary, for limiting the
outHne of the foliage and its component parts. The outermost circle serves
for the outline of the patera and the extreme limits of each leaf; the second,
for the eyes and the turn overs of fhe leafage ; the third, for the eyes in the
lower range of palms, and the fourth for the rosette or centre. After what
has been before said, the student is supposed to be capable of following the
example placed before hira, raaking use of his own judgraent, taste, and
perseverance in drawing the details. — The two remaining Pateras are alike
subject to the same rule for drawing them ; the principal lines defining their
parts, being laid down in the examples, will afford sufficient assistance to the
pupil in copying them with correctness.

Plate CXXII.
In this plate are given four different designs for Ornamental Com
position, combining every description of sweep and variation of outline that
can be introduced into ornamental decoration. The two first examples are
compositions, displaying the manner in which leaves are capable of being
decorated, and that in various ways. The third example exhibits an assem
blage of ornament adapted as a centre ; frora whence a continuation is


140 ORNAMENTAL DRAWING.
supposed to be madie, both from the right and the left hand. The fourti
exaniple is a compiotdition from various oi^tiamental fragments discovered at
Porapeii ; intended likewise as the central part of a frieze ornament.
All theste eiibiples are here given solefy" for the purpose of practice
in copying, and shoiild be drawn on an enlarged scale ; observing the sarae
rules as to dividing them into p'arlls for theif simple outHne, as is detailed in
th6 p^e'c^ding plates.
With these examples we shall conclude aU we have to offer on the
sddre ef outline ih Oi'namental Draw'ing, convinced that enough has already
been given for the practice of the learner ; at least as much as is sufficient
fof the present purpose. If the student can so far perfect himself in drawing,
as to copy corfectiy all the eiampfes here given in this treatise, there is
every promise of his sacceeding, w'hen th'ose of a more difficult nature are
pkced before him.


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SHADOWING. 141

SHADOWING.

Previous to entering upon the practical part of this section of the work.
it wiU becorae necessary to say something as to those laws which regulate
the various gradations of light and shade.
Without perplexing the mind of the reader with the theory, or the
various opinions of writers on this subject, it wiU be quite sufficient to our
present purpose, simply to consider light as being subject to, and capable
of being reflected from other bodies, or refracted by the interposition of
other mediuras ; the raateriality or immateriality of its nature appertaining
more to the inquiring mind of the Philosopher, than to the tasteful genius
of the Artist. To explain the progress nf Hght, and the effect of it as pro
ducing shade frora solid bodies, is aU that is needful or can be any way
useful in this work.
The rays oi light as proceeding frora the Sun, the great luminary of our
system, are universally in their passage through space projected in straight
lines ; but these straight lines in their passage are subject to interruption,
and are broken or divided frora their regular course, by the rarity and density
of the different mediums, or atmospheres through which they have to pass :
this in raatheraatics is what is termed refraction of light ; the theory and
demonstration of which belongs exclusively to optics.
• It raay however be necessary to state, that this refraction of rays pro
duces what is comraonly termed daylight ; that is, the light we experience
wheu the Sun is concealed frora our view by the density of the atraosphere.
In this case the shadows from solid objects, are mellowed and rauch penum-
brated ; being scarce definable at their extremities, and in opposition to those
as cast from objects opposed to the direct rays of the luminary ; the shadows
of which are determined and opaque. We shall here consider the rays of
light as proceeding direct from the luminary, uninterrupted by any interme
diate mediura ; and thus faUing with their full brilliancy on such objects as
are intended for shade, or from which shadows are to be cast.
2 Q


142 SHADOWING.
It raust Hkewise be observed, that as the diaraeter of the Sun's body
greatly exceeds that of the earth, and his distance frora us bemg so
imraense ; the shadows of all solid bodies wiU be found to flow in a parallel
direction : this raay be seen by any observer under a clear sunshine, when
the shadows, as cast frora the iron railings before a dwelling house, wiU be
projected from each bar, the one perfectly paraUel to the other.
The rays of Hght faUing on solid objects, such as are opaque, or whose
surfaces are not penetrable by light ; such rays are diverted frora their direct
course, and fly off in other directions ; in which case they are termed reflected
rays ; and this reflection of rays, as they illuminate objects already m shadow,
come more especially under our notice.
This win be understood more fully
by reference to the annexed diagram,
where we may suppose A to represent
the luminary ; B, a ray of light issuing
frora it ; C, the point on the solid body,
(D) where this ray would fall ; which
ray would in this case be interrupted
in its progress and fly off in the
direction, E. Now we say, the angle
of reflection (E C G,) is equal to the angle of incidence (B C F) ; that
is, the angle made by the falling ray B, with a perpendicular dropt
from the luminary at A, will equal the angle the reflected ray would
make with a perpendicular raised from the point C : this serves to explain
the reason why objects in shadow are illuminated by means of light reflected
fi-ora other bodies opposed to them. Suppose I to represent the ceiling of a
room : B, the direction of the light issuing through a window ; impinging
on the floor at C, and from thence reflected in the direction E : It is eviden"
that this reflected ray, or coUection of rays, would illuminate the ceiling at H ;
it would again be reflected from H at an equal angle (as shewn by the Hne
H «) untU interrupted again by the floor or sorae other adjacent object ; and
this reflection would be carried on incessantly, until darkness succeeded to
light. From this cause is to be attributed, the floating light existing in all
apartments ; and from being weU conceived and understood, has been
sometimes ably and beautifully managed by painters both in oil and water


SHADOWING.

143

colors. From the same cause,
that side of a solid object, the
most in shade, would be illumi
nated and rendered less dense,
by the light reflected from the
illurainated side of sorae other
object opposed to it. The an
nexed diagram will serve to
explain what we have now said,
Suppose S to represent the lu
minary; A, a solid body, having
its side G, in shade, frora whence the shadow H, on the ground is projected.
Suppose B to represent another solid body, having its front or illuminated
side opposed to the shadowed side G, of the solid A ; now the ray of light
frora S would irapinge, or strike on the block B at the point C, frora thence
be reflected downward by an equal angle to the ground at D, and again be
reflected from D by an equal angle, until it impinges or strikes upon the side
(G) at E ; which portion ofthe face would instantly become illuminated, losing
part of its shade, and leave the shadow cast from it on the ground„the
darkest. The shadow on the ground in its turn, would be again iUuminated
at its extreraities by raeans of the reflected light from C ; leaving that part
of the shadow which is nearest the solid, the darkest. We have thus been
minute and particular in explaining this interesting branch of painting, being
a subject little treated of, in works of this kind ; the theory of which may be
found in the 13th, 14th, and 15th Propositions of the 1st book of Euclid.
The Author would recommend those who wish for further information on this
head, to a Work recently pubHshed, entitled " Sciography, or Examples fot
Shadows, with Rules for their Projection, by Joseph Gwilt;" and also to the
Works of Sir Joshua Reynolds, Fuseli, and others.


144 PROJECTION OF SHADOWS.

PROJECTION OF SHADOWS.

Plate CXXIH.
Shadows, as they are projected by the Sun, vary in their length according
as the luminary changes its situation in the heavens at the different hours of
the day. Those Shadows which are projected the soonest after sun rising, or just
before the time of his setting, will become the most lengthened ; and be gra
dually foreshortened, each in proportion as the Sun appears to approach
or recede frora the meridian; or in proportion as. the surface of our planet
would be opposed to him in her diurnal revolution round her own axis.
Shadows as projected from the Sun, will vary also in their length according
to the particular raonth of the year in which the earth's surface may be
opposed to the luminary in her annual revolution. For the Sun as seen from
ouf earth will appear to rise and set in different points of the horizon at
different periods ofthe year ; hence it is that his height at noon, is so much
higher in summer than in winter This also accounts for the difference
we find in the length of the day at the different periods of the year. The
first Exaraple in Plate CXXIII. wiU serve to elucidate what we have to say
by way of explanation on this subject. In the exaraple now before us, we
have here supposed the tirae of the Sun's rising to take place at a little before
five o'clock in the raorning ; that is, at the time when his light would become
perceptible to us above the eastern point of the horizon.
The figure of a man is here represented as placed under the centre of
a semicircle, or immediately under the angle of a quadrant ; which is
elevated above him at pleasure, and is divided into six equal parts, answering
to so many hours of the natural day. Now supposing this half, or quarter
circle to denote the Sun's daily path in the heavens, the figure as opposed
to it will then appear to receive the effect of light from the luminary, casting
his own shadow on the ground ; which, supposing tbe figure tobe stationary


^VTE cxxin.

SHAJDOWS
FjXUTjp. J '^

J\i?l

' ih«t. L.oQdoii. rubljshfid hy Jones t- C? SepT.''7,18i'7.





PROJECTION OF SHADOWS. 146
will vary in length as the sun appears to travel onward towards its meridian
at the point 12 in the semicircle. At five o'clock in the morning the sun
will have arrived at the point V ; in this case, a line drawn from 5, being
prolonged and passed over the head of the figure, will extend to the point
V on the ground : the line A V will then denote the length of the shadow,
as cast from the figure at that period of the day. A line drawn from
the point 6 on the quadrant, and continued over the head of the figure, until
it intersects with a line drawn from his foot, at the point 6, will give the
length (A 6) of the figure's shadow at six o'clock in the morning ; and so on
for all the rest, until the sun attains its meridian or greatest height at twelve
o'clock, when it would be situated directly over his head, and in that case
cast no shadow. The quadrant on the other side, if divided after the same
manner, will enable us to obtain the length ofthe shadows, as they would be
projected by the sun in the opposite direction, at the corresponding hours
after raid-day. It will be necessary to observe that the lines from the foot
ofthe figure, as denoting the length of his shadow at the different hours ofthe
day, and numbered 1, 2, &c. are here drawn in different directions, for the
purpose of shewing the length of each shadow distinct ; which if represented
by perfect horizontal lines, would be confounded and run one into the other,
and present one uniform line in length.
It now remains to lay down such rules as are necessary for the casting
of shadows, previous '>^ which it may be useful to say something as to the
material to be made v-^i of in tinting, generally termed China or Indian ink,
which is of various q*%lities. The best is that which is found to rub smoothly
W'ithout grittiness, and is strongly scented with musk, the same giving a brown
and mellow colour to the ink. The pupil must here observe that a tint
produced from Indian ink alone, will always appear lighter when dry than
when wet, and therefore deceive the student as to the effect he wishes to pro
duce in his drawing ; in this case it will require to be often repeated, until
the proper depth of tint is obtained. This inconvenience may in some measure
be obviated by making use ofa raixture of sepia, (an article to be procured at
any of the wtour shops) which partakes of a rich brown tint, and wiU give a
decided tone, retaining the same force when dry as when wet ; this will
tend to reraove the defect experienced in the use of Indian ink alone, and
give at the sarae time a soft and mellow effect to the drawing.
2 E


146 PROJECTION OF SHADOWS.
The brushes necessary for use are of two kinds, the one commonly
termed the camel's hair pencil, the hairs of which are of a soft nature, and
generaUy of ablack colour; the other is termed the sable pencil, as being
manufactured frora the hair of the sable, the hairs being of a firmer texture,
and generally of a red colour. The camel's hair pencil is sold from one
penny and upwards, according to the size and quality; the sable hair pencil sells
from eight pence and upwards : of the two, the sable is to be preferred,
being ofa more durable nature than that of the camel's hair. In choosing
the one or the other, the brush should be first dipped into water, then drawn
through the mouth without much pressure, no more than wiU just conduce to
bring the hairs all to one point ; if when thus drawn to a point, the brush
be applied to paper and gently moved backward and forward, the hairs
not dividing but adhering closely to each other, the brush may then
be considered as one of a good quality. Hair pencils are manufactured
of various sizes, beginning with one small enough for the finest, enamel
painting, and finishing with a size sufficient for the largest pictures. As far
as concerns our present purpose, brushes, such as are confined within the
duck or goose quill, will be found to be quite as large as wiU ever be
required; especially for single objects of furniture. In shadowing the
interior of rooms, wherein a large body of tint is required, a brush confined
within a swan quill may be of use.
The rubstone is an article also necessary in drawing, as used for
the mixing of Indian ink tint ; it has three hollow reet ^tacles for tint, besides
a shelving groove, in which the ink is generally rubbv 1. The three hollow
receptacles serve for mixing up three different degrees of tint from the same
co(our, before the process of tinting is comraenced upon. To elucidate
what we now recoraraend, the student is referred to the Exaraple marked A,
in Plate CXXIII.
No. 1, Exhibits a tint coraposed of Indian ink and a sraall portion of
sepia, which being raixed very light, is termed a first tint.
No. 2, Exhibits the first tint as strengthened or made deeper, by the
addition of a little more ink and sepia; it is then denorainatei the second
tint. No. 3, Exhibits the second tint as strengthened still further by a larger
addition of the two colours before raentioned, and is then terraed the third


PROJECTION OF SHADOWS. 147
gradation of tint. These three gradations of tint are almost aU that are
necessary for general effect of shade : but where a strong and decided effect
is required, a fourth tint may be used by deepening No. 3, with a stronger
proportion of Indian ink and sepia ; this we shaU have occasion to notice in
the fourth Exaraple. Having thus given araple instruction as to the raixing
of tint in all its variety of tones, we now proceed to practice j
referring our student to the second Example, which represents a cubical
block a b c d e f g. In this Example the lurainary is supposed to be
inclined to the front face (a d ef) of the figure ; in which case the shadow
cast from it on the ground, would fly off at some angle, more or less as the sun
is inclined in regard to the object which it illuminates ; this inclination or
seat of the luminary is denoted by the angle k fi, as raeasured by the arc
p q. The next point to be attended to, is the sun's declination ; or rather
its precise situation in the heavens in its daily course from east to west, as
explained in the first Example ; which in the present example is denoted
by the angle c g I, measured by the arc m n.
The student must first deterraine the sun's inclination as fk, which
being done, lines raay be drawn parallel to this from g and h, at pleasure;
The sun's declination being next determined by the angle m c n, lines parallel
to such raust be drawn from the points d arid c, where the rays of the luminary
would strike the object; their intersection with the incHned lines y A and
g I, at the points k and Z,will determine the utmost projection ofthe shadow at
kl. A line drawn from I paraUel to e f, until it cuts the inclined line from
h, at 0, will give the shadow of the side opposite to a de f All the inclined
Hnes, denoting the sun's inclination and declination, may be drawn as to
their parallelism by raeans of the T square with its moveable haunch or
shoulder. The outline ofthe shadow being denoted by faint pencil lines, the
pupil will commence his tinting by washing over the whole figure and cast
shadow with the tint No. 1, Exaraple A. Next, with the tint No. 2, he will
proceed and wash over the return side def g, and also the cast shadow;
leaving the front face ade fand the upper surface abed in the first tint.
Thirdly, with the tint No. 3, he must observe to wash over the cast shadow
only. He may next with the same tint wash over a portion ofthe shadowed
side of his object, commencing upwards from d c, and soften it into the
original tint by passing his brush sHghtly into pure water, and then as quickly


148 PROJECTION OF SHADOWS.
as possible, proceed and draw the tint downwards. He must again dilute his
tint in water and draw the last degree of shade downwards, until it gradually
mellows into the tint originally laid on : this is what is called in painting,
softening off, or rather penurabration of shadow; that is, allowing sorae
reflection of light, either directly or indirectly, to fall on your object in shade,
by which the uniforraity and flatness is counteracted. It will be sufficient
to say that the shadow on the ground is to be managed after the same
raanner, observing to keep the darkest part of the shadow close to the bottom
edge of the object ; by which raeans a brilliancy and force will be given to
the object which it wou.ld not attain without.
Example 3. This object has a capping or projection ACD; the
sarae casting a shadow B E on the cubical block underneath it. The depth
of this shadow is regulated by the sun's elevation, and would be deeper
raore or less, according to the tirae of day in which it is projected. The
sun's elevation (or declination) is denoted by the dotted Hne A B, and
determines the depth of the shadow as projected frora the capping A C, atB ;
which must then be squared across to E. The whole of the figure raay
then be washed over with the first tint No. 1, as before directed; after which
with No. 2, pass over the cast shadow B E, with the soffit or under part
ofthe projecting cap ACD; and also the return side F. Then proceed
with the third tint, and pass over the cast shadow B E with the soffit of the
projection A C, leaving that of the projection G D. Again with the sarae
tint, pass it under the projection on the solid at g h, and soften off as shewn
in the Example. Lastly, with the third tint, made a small degree darker, pass
over the shadow B E, and again over the return side at g h: the figure will
then have attained its proper effect. These two Examples although slight in
themselves, will be sufficient to give the student an insight into the raanner
in which shadowing is raanaged and effected; and enable hira to
comprehend more clearly what will be offered to hira in the next plate. A
coraplete and coraprehensive dissertation on the laws of shadow raight have
been here given, with the whole process laid down for projecting them ; but
as this is a matter of more concern to the architect, we have only retained
and explained so much as could be of real use to those, interested in perusing
or studying the present work.
Example 4. Exhibits four truncated columns, and shews the process


PROJECTION OF SHADOWS. 149
of shadowing all objects that are round or cylindrical. In this Example are
displayed the different gradations of tint, necessary for giving to a cylindrical
body the full effect of rotundity. All turned legs of tables, supporting piUars,
bedposts, pedestals, &c. as partaking more or less ofa cylindrical forra, will
require to be shadowed after the raanner here laid down.
Having prepared a tint equal to the tone of No. 1, (Exaraple A,) cora
raence with the column No 1, and with this tint in your brush pass it down
the shaft, in width equal to a? a? j turning it suddenly off at a until it reaches
the base at b : the tint so passed down must then be immediately softened off
at both edges, right and left. The same tint must then be passed over the base
raoulding and the return side of the plinth, as likewise over the shadow cast
on the ground. You will next proceed and strengthen your tint to the tone of
No. 2, and with a sufficient quantity in your brush, pass it down .the shaft
of the column over the preceding tint, as before, and likewise over the base
raoulding ; only not so broad as a: ^r : this must again be softened off at both
edges ; observing not to cover the tint first laid on entirely, but to leave a
portion reraaining : your coluran will then be brought to the effect of No 2.
You will then with a tint equal to No. 3, pass over the shaft and base of the
coluran direct frora the right hand edge, keeping it to the breadth of c d;
which must be softened off towards the left hand, leaving a portion of the
second tint uncovered : your coluran will then be brought up to the effect
of No. 3.
This will be found sufficient for most subjects of a cylindrical forra ; but
where a greater strength of effect is required, the tint No. 3, a little
strengthened, raay again be passed down from the right hand edge of the
shaft to the breadth ofcf, and softened off as before ; which wiU bring it to
the effect of No. 4. The»student will remark, that a weak tint is passed
down from the left hand edge of the column, and softened off; leaving a small
portion of light on that part ofthe column where the sun's rays are supposed
to strike direct : by this raeans a greater effect of rotundity will be produced.

2 s


150 PROJECTION OF SHADOWS.

Plate CXXIV.

In this plate are given four different objects of furniture; shewing the
raode and raanner of projecting the cast shadows from the same on a
horizontal plane, and also on one perpendicular.
Example 5. Let A represent the general plan ofa pedestal sideboard,
the same shewing the situation of the four console supports of the pedestals
at a b, c, and d. Fig. B "represents the sideboard as shewn perspectively,
and Fig. C the georaetrical profile of its depth. It is required to give to this
object its proper proportion of light and shade, and to project the shadows
as cast frbm it on the wall and ground ; and Hkewise to project the shadows
from the console supports on the front faces of the pedestals, so as to give
to the whole an embodied effect, and convey to the eye a lively representation
of what the original piece of furniture would be when executed. To cast
the shadows by exact rule from every part of this figure, would require the
aid of a great nuraoer of lines, and tend to render the process perplexing ;
to avoid which, we have chose to confine ourselves to a few only of the
principal lines, as being sufficient for the purpose required, and all that are
necessary for general use.
The student, by the aid of these lixamples, will be enabled to project the
cast shadows for alraost any piece of furniture ; the same being applicable to
every case that may occur, either to the Upholsterer or Cabinet-maker, as a
draughtsman. The first thing to determine on, is the sun's inclination, or seat
on the ground with regard to the object as opposed to it : this raust be laid
down in the plan, as shewn by the parallel line k%n, i I and eg. Frora the
intersection of these lines at m, I and g, on the waU line W W, perpen
diculars are raised to the base or ground Hne G G, on which the sideboard
or original object is placed; as ats, v, and u. From these points, radial lines
are drawn to the station or point of sight S ; which give the sarae points
perspectively on the waU line at w, and w. The next thing to be considered
is the sun's declination ; or otherwise its particular ascension or descension at
some precise period of the day: In design this is entirely arbitrary,
depending on the judgment ofthe artist. It would argue want of taste to


fl,. CXXIV.

SMAIS OWS ,

1

F.vttmp. J .

-T

TT

'' ."

a i

Fjcamp . tf.

[C i e

'"Tf"

J^xcanp. 8.

_Lon3on. F\i>bshe4 "by Jones &: C''A-QdI1.16l'7.





PROJECTION OF SHADOWS. 1,51
represent the shadows of too great a length, as supposing the sun to
be elevated very little above the horizon ; as well as to raake thera too
narrow, by considering the sun as near its meridian, or point directly over
our head. In these Examples, the middle course is adopted; the sun's
declination being deterrained by the Hne x y in the profile C. The point
where the ray would strike the wall at y, would be the geometrical depth of
the shadow as cast from the overhanging ofthe sideboard top and rail : this
must be squared across to the georaetrical line X at o. Frora this point a
radial raust be drawn to S, intersecting the back line of the sideboard atp, and
from thence squared across until intersected by a perpendicular raised from
w at Z. A radial must then be drawn from a on the frieze line, towards the
point of sight, intersecting the back line of the pedestal at b. A line drawn
frora h to z, will give the sun's declination perspectively ; to which all the
lines projecting the shadows from the pedestals on the wall raust be drawn
parallel; viz. those drawn frora the several projections of the top and rail ;
these are intersected by a perpendicular raised frora w, as will be seen by
inspection of the figure. The points 1 and w, 2 and w, being each joined by
lines, will give the sun's inclination, or seat on the ground, perspectively ;
which being continued to the horizontal line, will there raeet in the point V,
v/hich then becoraes the vanishing point for all shadows cast on the ground by
such inclination. The intersection of the line x y in the profile with the back
line of the truss, at v, will give the shadows frora the over-hanging of the rail,
upon the front faces of the pedestals. This being squared across to the geo
metrical line X as before, and from thence conveyed by the point of sight on
the back line ofthe truss at n, wdl give the depth of the shadow perspectively;
which must again be squared across on the pedestals, until intersected by per
pendiculars raised frora o and q in the plan. The outline ofthe shadows as pro
duced by the truss supports, may then be drawn by band from the points already
obtained. Soraetimes in large subjects it is necessary to find a number of points
for obtaining such outline ; but in the present instance this would be attended
with a great loss of time, and is not requisite in designs on a small scale.
Example 6, Exhibits a pier table in perspective, the plan of profile of
which are here given as in the last Example; — denoted by A and C. The
inclination of the rays of light from the luminary are here denoted by the pa
rallel lines a, b, c, d and e; which are marked by single letters only, to avoid


152 PROJECTION OF SHADOWS.
repetition where so rauch has already been said in the previous Example.
The declination of the rays of light is denoted in the profile C, by the line
X y. Having projected your shadows geometrically frora the plan and profile,
proceed and transfer thera on to the perspective figure, as directed in the
preceding Example. As it is not necessary to repeat the process in this
Figure,. the learner is referred to the Hnes as laid down in the same, which,
with the instruction already given in the previous Exaraple, will be quite
sufficient for hira as a guide.
Example 7, Is the perspective representation of a lady's escrutoire.
The plan below shews part of the depth, of the carcase.
a a shews the thickness ofthe two ends.
b b denotes the depth of the secretaire drawer when fully drawn out.
d denotes the fall down front of the drawer when in a horizontal position
for writing. The shadows in this as iu the preceding Examples are projected on the
plan by the sun's supposed inclination, and those on the profile by the sun's
declination. The sun's rays, passing frora the upper shelf would strike on
the back surface of the object at 1, which would be the depth of the cast
shadow. The same ray passing from the second shelf, will give the depth of
its shadow on the back surface at 2. The shadow from the side of the secre
taire drawer is shewn at 3. The shadow on the doors of the bookcase from
the overhanging of the desk is shewn at 4. Coraraence by squaring these dif
ferent points (1, 2, 3, 4,) across to the georaetrical line G. The shadow
cast on the bookcase frora the overhanging of the desk in the perspective
figure, would be equal to its georaetrical depth, inasrauch as it falls on the
front face of the bookcase, which in itself is georaetrical. This shadow is
intersected at d by a Hne squared from the correspondent point c, in the
plan. A line drawn frem e to d, will represent the declination of the sun
perspectively. The shadows cast frora the shelves, would be conveyed per
spectively frora the georaetrical line, to the back line of the figure by the
point of sight, and from thence squared across, until intersected by Hnes
drawn paraUel to e d, frora / and g. A line squared across from 3, until
intersected by the inclined Hne drawn frora h, will give the shadow as cast
from the side of the secretaire drawer oii the frame containiug the pidgeon
holes and small drawers.








PROJECTION OF SHADOWS. 153
For the rest the student is referred to the Example.
Example 8. Shews an upright ended chaise longue as drawn in per
spective, of which the shadow from the cheek on the back is required. In
the plan A, the places occupied by the pillow and bolster are denoted at b
and c, from which are drawn lines parallel to the sun's supposed inclination
or seat on the ground, untU they impinge on the back ; as will be seen by
inspection of the figure. What has been already discussed in the previous
Examples, wiU render it unnecessary to say more as regards this ; we shall
therefore refer the student to the figure, no way doubting but by this time
he will be enabled to shadow such simple subjects without further aid or
instruction. It wiU be sufficient in Examples either of chairs or tables, to
represent the shadow as cast frora the legs, by a mere touch of the brush as
shewn in this Example.

Plate CXXV-
It wiU now be requisite to draw the pupU's attention to the nature of
drapery in its outline, which consists of a composition of folds, either broken
or forraing a continuity one over the other ; and this will arise more or
less according to the material used. It is almost impossible to make
the folds hang in a graceful form where callicoes are used, stiffened as they
generally are by high glazing. This is in some measure remedied by the
use of woollen of a slight texture, and next to this material, that of undressed
moreen ; but the most perfect material that can be raade use of for producing
gracefulness of folding drapery, and which is raostly used in France, is that
of silk ; which, governed only by its own weight, will fall into those natural
diversified folds, known amongst painters, as broken. We have in this
plate brought the effect of drapery as near as possible, to the latter remark ;
and such as wetted Hnen when suspended would produce. This is done
to give the student a freedom of hand in the shadowing of drapery.
Having premised thus much, we shall now proceed with the subjects
given in this Plate; referring to fig. A, as an outline, first to be drawn.
Fig. B, exhibits thesame outline as under the first degree of shadow or tint ;
2 T


154 PROJECTION OF SHADOWS.
which tint, if in Indian ink, must be mixed up with the addition of a little
Sepia, as before mentioned.
Fig. C represents the same drapery as under the second degree of tint,
leaving a portion of the first tint uncovered ; and fig. 4 is the same object
under a slill stronger degree of tint, leaving a portion uncovered of both
first and second tints : but should the pupil wish to give a more deterrained or
higher effect to his drawing, he is at full liberty to darken this, his last tint ;
taking care to place his darker touches only where the folds of his drapery
are the closest collected together ; what has been thus far said as to tinting
the drapery, will regulate also the tinting of the fringe.

Plate CXXVI.
Fig. 1, in this plate displays the outline of a foliage leaf, taken from
an Example ofthe Corinthian capital, as existing in the remains of the arch
of Titus, at Rome. The outline of the leaf must first be correctly drawn
with a black lead pencil, agreeably to the directions given in page 135 ;
the same outline may afterwards be drawn in ink with a quill pen, omitting
those lines which denote the principal fibres as issuing frora the stem.
Fig. 2, which represents the same leaf under its first tint, wUl give the
pupil an idea of the manner in which he must work in his shades.
Fig. 3, shews the leaf in its second stage of tinting.
Fig. 4, offers the same Exaraple under its last gradation of tint, shewing
out the leaf with its full effect.
Having prepared the three tints necessary for use as before directed,
let the tint for figure 2, be laid on with a fuU brush, washing in the broad
shade frora the turnover, together with the shadow cast frora the outside of
the leaf The shades appertaining to the leaves, must then be laid on each sepa
rately, as shewn in the Example.
Proceeding next to figure 3, with your second degree of tint, pass over
the broad shade at top, observing to omit tinting aU the projecting parts,
such as the stems and fibres of the leaves under this shadow ; this may be ob
served in the parts marked 1, 2, 3, 4, Sic, throughout the Example. By this


PLATE CXXn.

SmAlJ)fj)W';lN(&„

7-^'^Tint

^r, . hil^h.-Aed "bv Jonej I'v C? 5ep7r2-il8r ^





PROJECTION OF SHADOWS. nS
process we are taugnt to detach or raake such parts appear to project, as we
know such to stand the one before the other. In passing over the other
parts of the leaf, the pupil will place his second shade over the first equal
only to one-third of its breadth, when he may proceed and soften or
penurabrate it towards the edge of the first shade. The same is to be
observed as regards the shadow cast frora the outside of the leaf, which
raust be so shadowed as to leave a portion of the first tint remaining.
With a moderate share of attention and perseverance the student will soon
be convinced of the reason by which our practice is enforced.
Fig. 5, represents the leaf under its full effect of light and shade, as
produced by the power of tint. It will be necessary to inform the pupil, that
the third or last degree of tint raust be laid over that of the second, precisely
after the same manner as directed above ; taking care throughout to leave a
portion of the first and second tints visible. A spirit and brUliancy may be
given to the drawing by a judicious use of dark and spirited touches, placed in
such situation where we know thatlight would be totally obscured by projec
tion ; or where one part (as is the case with ornament in general) would be
deeply undercut, and so produce a powerful effect by the opposition of shade
to light. We shall now leave the student to make use of his own abilities,
merely stating, that without an active exertion he can expect to reap but
little advantage.

Plate C.
In this Exaraple the pupil will observe that the general outline comprising
the whole of the foliage is first drawn ; which outline is again divided into
distinct parts, (here shewn by the dotted lines,) each comprising the detail of
the foliage : and the whole to be raeasured from the perpendicular dotted line.
What has already been said in the previous Exaraple as regards light and
shade in the shadowing of foHage, will likewise apply to this ; naraely that
of. laying on the shades with the first tint generaUy, as shewn in the second
Exaraple in this plate, observing that the pen lines in the outline Exaraple
be left out in all parts excepting in the outline forra of the leaves^ and the
larger turn overs.


156 PROJECTION OF SHADOWS.

Plate CVI. •
The first subject in this plate exhibits the sarae ornament under its
second gradation of tint, to effect which, the pupd is referred to the
directions given with Plate CXXVI. With respect to the finished Example
in this plate, the pupil is required to raake use of his own abilities, as he
raust by this tirae have acquired sufficient knowledge to follow his copy
without the necessity of any further direction.
These Examples are given, as tending to shew the power of light and
shade, with respect to all subjects delineated on a plane surface, giving them
the appearance of a positive projection.
In leaving a portion of the three tints uncovered one under the other,
consists the art of giving a softness of effect to the drawing, and of gaining
a transparency, as has been before observed.

Plate XIV.
The two subjects given in this plate shew in some raeasure, how far, by a
judicious corabination of forms, a tasteful design in ornament raay be produced;
this is what is terraed in art, composition ; that is, an assemblage of parts
so arranged and put together, as to form a pleasing and agreeable whole.
Either of the two designs in this plate are well calculated for the decoration
of friezes ; whether in those belonging to appartments, or in those of cabinet
furniture. Sufficient effect of light and shade is exhibited in these two subjects to
enable the learner to shadow such, or similar designs, if what we have before
enforced be well studied. We shall here close all we have to say, as relates
to drawing, together with the effect produced by mechanism in the management
of light and shade, and conclude our instructions with giving necessary direc
tions for the choosing of colours, and for compounding the various tints
produced from mixing one body with the other ; this branch of the art is
comraonly termed Colouring.


.SlHUlii il) VVMA' I

i'irii-t Tin/

JEILEMJilN-TS OF 0:R_r>'Ai4MWTs.l.








ELEMENTS OF FOLIAGE
COMPOSITION .

Desi^nM hi ¦ & Smith,

i-OJJDOJM. Pab^ b,- JOSES .tCMayfc

-Unaraved b^ Neele^-352 Strand.





COLOURING. 157

COLOURING.

There are, properly speaking, but three priraitive colours ; viz. blue,
yellow, and red. These colours by a mixture one with tlie other, will pro
duce three other distinct colours ; viz. green, by the mixture of blue and
yellow ; purple, by the mixture of red with blue ; and orange, by a mixture
of red and yellow. These various hues will be seen by reference to fig. 1,
in the diagram.

Plate CXXVII.
Red, blue and yellow, blended together, will produce more or less as the
blue predominates, a dense black, but when mixed in a lighter degree, the
tint so produced is called neutral : thatis, partaking of raany shades of colour,
but exhibiting no one in particular. This tint is used for putting the general
effect of light and shade into drawings intended for colour : it becomes a
proper tint for shadowing all objects that are intended in themselves to
appear white; viz. drapery or curtains of muslin, white silk or dimity, in
furniture drawing; and lillies, white roses, &c. in flower painting.
Besides the three primitive colours, and those resulting from the mixture
of them one with the other, there are other colours of a vegetable, mineral, or
earthy origin, all useful of their kind ; such are the umbers and siennas
(burnt and raw), the yeUow and Roman ochres ; vei^iUion, Venetian red, and
carmine ; madder brown, indigo, &c.
It is usual with many persons when purchasing colours to choose a box
containing perhaps from twenty-four to. thirty cakes, each of a different tint;
a practice not to be recomraended. Those already enumerated are all that are
likely to be brought into use in colouring either drapery, .or cabinet furniture ,
or any other subject confined to the two branches of Upholsterer and
2 u


158 COLOURING.
Cabinet-maker. It remains therefore to give some instructions fo our pupil
as to the art or raanner of mixing the different colours one with the
other, so as to enable him to produce the different tints in all their variety of
tone, such as may be requisite for his use.

Plate CXXVII.
No. 1, Is gamboge mixed up as a light wash, and is the first tint to be
laid on in any subject intended to be coloured yellow ; whether drapery, or
ornamental work when represented as gilt.
No. 2, Is the same colour (gamboge) worked deeper.
No. 3, The same colour worked still deeper.
No. 4, Is gamboge in its full colour.
No. 5, Is Prussian blue, washed in light, and answers for the first or
ground tint, in any subject intended to be coloured blue.
No. 6, The same colour made a slight degree darker.
No. 7, Ditto made still darker
No. 8, Ditto in full colour.
No. 9, Carmine worked Hsrht.
No. 10 and II, Are tints from the same colour, but strengthened in
mixing. No. 12, Is carmine in its full colour.
These being all primitive colours it remains next to proceed with the
different tints produced by the mixing of one with the other.
No. 13, Is gamboge with a smaU portion of carmine, and in this state
becomes a shadowing tint for curtains or drapery, when tinted yellow ; as
also the first shadowing tint for any thing intended to represent gold.
No. 14, Is gamboge with more carmine added.
No. 15, Ditto with a larger addition of carmine.
No. 16, Ditto with a still larger proportion of red.
The three last tints are made use of, in working up the shadows of any
subject that is coloured yellow.
No. 17, Is gamboge mixed up with a little Prussian blue.
No. 18, Is gamboge with more blue added.

< 


COLOURING. 159
No. 19, Is produced by the addition of more blue.
No. 20, Is the sarae, mixed up with a greater proportion of the blue ;
and then becoraes a full grass green
The manageraent of these tints in colouring raust be after the same man
ner as those preceding.
No. 21, Is Prussian blue, with a small portion of carmine, and makes
when thus raixed, the first tint of purple, commonly called lilac.
No. 22, Is Prussian blue with a further addition of the red.
No. 23, Is the same blue with a still further addition of the red.
No. 24, Is blue and carmine, each in its full mixture, producing the
purple in its full colour.
It now remains to point out such other mixture of tints as are necessary ;
together with the different substances of which they are composed.
No. 25, This tint is produced by washing over the part to be coloured,
first with a tint of gamboge ; which, when dry, is glazed over with a tint of
vermilion : the colour so produced is called scarlet.
No. 26, Is produced by a deeper wash of the gamboge first laid on,
and glazed over with a deeper tint of vermUlion.
No. 27, Is produced by a faint wash of crome in the first instance, and
afterwards, when dry, glazed over with a faint wash of carmine.
No, 28, Is produced by a wash of the crome in its full colour; the
same when dry being glazed over with carmine in its deepest tint.
No. 29, Is coraposed of a light mixture of burnt umber, and burnt
terra de sienna, producing a warra drab colour.
No. 30, Is produced by a stronger mixture of the same colours ;
raaking a rich and warm brown. This colour may be used in different
degrees of strength for shadowing such objects as are tinted with No. 29.
No. 31, Is produced by a light mixture of yellow oker, with a little
burnt terra de sienna added.
No. 32, Is yellow oker deepened in tone, with burnt sienna and
umber. These two tints may be used in colouring any article of cabinet furniture
intended to represent oak.
No. 33, Is Indian ink, mixed up with a portion of carmine, producing
a purplish tint, and will be found serviceable as a first wash for all cabinet
work, intended to be coloured as in rosewood.


l&O COLOURING.
No. 34, Is carmine mixed up with raw sienna, burnt sienna, and a small
portion of blue ; this mixture produces a mellow warra tint, .approaching
to a marone, and is used in the shadowing of objects coloured as rosewood.
No. 35, Is a mixture of carmine, gamboge, raw sienna, and burnt
umber, and may be used for strengthening the shadows of aU objects worked
up, with the tints 15 and 16.
No. 36, Is the same mixture with a larger portion of the< burnt umber,
and is used in painting the shadows cast on any object coloured as gold ; and
alsc for representing the deeper folds and recesses in yeUow drapery.
No. 37, Is produced by a slight wash of Hght red : in this state it
becomes the first or ground colour to be washed over any part of a design,
intended to shew as mahogany.
No. 38, Is the same tint deepened with burnt umber, and in this degree
of force is used as a shadowing tint for all objects coloured with No. 37, aud
for giving the imitation ofthe curls and veining of the wood.
No. 39, Is used for heightening the deeper shadows ; and is composed
of the preceding tint No. 38, with the addition of more umber and burnt
sienna ; or the shadows may be strengthened by using the tint No. 36.
No. 40, Is produced by a mixture of carmine with burnt umber, and
may be used as a ground tint for colouring rosewood objects, which may
again be heightened by using the tint No. 34.
No. 41, Is Venetian red with blue, and becomes, when the red prevails,
a warm drab. This colour is useful as a ground for curtains, &c. whose
trimmings are intended to be either blue or gold.
No. 42, Is Venetian red with Prussian blue, producing a grey tint;
curtains, &c. when- coloured -with this tint, should have their trimmings of
scarlet. No. 43, Is a mixture of Venetian red and blue; both colours being
used strong in tint, but the red the most prevalent. This colour when used
for curtains, may have its trimmings of gcld or blue.
No. 44, Is compounded of Venetian red aud blue, the latter, being
predominant; producing, by the mixture of the two colours, a deep grey.
The mixture so produced may be used as a shadowing tint' for curtains or
draperies whose ground tint is No. 42.


COLOURING. 161
No. 45, Is a mixture of Indigo, raw terra de sienna and carmine or
lake, producing what is terraed a neutral tint. The neutral tint is rauch used
amongst artists, in painting landscape scenery or subjects of architecture.
In the former, this tint is varied in its raixture or tone according to that
portion of the landscape over which any positive colour is to be placed. Thus,
this tint should partake raore of the blue or grey tone, for sorae portions of
the clouds and distant objects in the landscape ; it should be raixed up with
raore of the red where rocks and warra fore ground occupy a place in the
picture, and again this tint should partake raore of the yellow when used as
a shadowing tint for the green of trees.
No. 46, Exhibits this tint, the red being the prevailing colour.
No. 47, The same mixture used light, the yellow being predominant.
No. 48, The sarae tint lightly raixed, the blue holding the pre
ference. No. 49, Is a mixture of Venetian red, crome and flake white.
No. 50, Is what raay be terraed a lavender tint, and is corapounded of
flake white, carmine and Indian ink.
There are raany other tints to be produced in water colour painting by
the raixture of one transparent colour with another ; and again there are
others that can only be obtained by a mixture of body colour ; such are the
peach blossom and salraon colours, as No. 49 ; the lavender tint. No. 50, and
raany varieties of the drab, but as these will fall more to the lot of the
decorator, than to the artist or draughtsman, they are not insisted on in this
work: to mix these colours in body, would require personal instruction and
rauch experience ; they are subject to many difficulties in the mixing, as being
affected either by the too great heat or coldness of the atmosphere.
After having given such araple directions for the raixing of transparent
colours, and producing all their variety of tint, it only reraains to offer
instructions as to the raanner of disposing them in any drawing that is
intended for colour.
It raust be observed in the laying on of colour, or in colouring any par
ticular subject, as drapery or curtains, that the brightest tint of each colour
should be first laid on, and that very weak, scarcely exceeding the whiteness
of the paper on which it is laid ; and let it be further observed that the tint so
laid on is to answer for all the high lights of the projecting parts ; for exaraple,
2 X


162 COLOURING.
in the component parts of drapery ana curtains, or the folds of such. As cer
tain portions of such folds have their upper parts wholly exposed to the rays
of light, and are generally ofa round figure, in such case, that part the most
opposed to the light would offer a tint highly under illumination, and of course
be fainter and brighter in its appearance than those parts receding from it;
the full colour being alone exhibited by those parts the most under the influ
ence of shade : upon this principle consists the necessity of gradation of tint
in colouring; on the successful application of which, depends raore or less
the realization of those appearances we see in nature.
Let it here be impressed upon the student's attention, that in laying on
his tint, he be careful not to cover either the first, the second, the third or
the fourth tint entirely, but to leave a portion of each visible, reserving hi.*-
darkest tints for those parts the most removed from the effect of light ;
which in the end will give life and spirit to his drawing. With this we shall
conclude the instructive portion of our work, convinced of the aid it will
afford in rendering the assistance of a raaster raore effective, which at all
times cannot but be of service, inasmuch as explanation by word of raouth
is often better understood than much reasoning on paper. With an earnest
desire that his Hmited knowledge raay prove of service to his friends and
students, the author here consigns thera to their own studies, trusting the
helps he has afforded thera throughout the whole of the work may be found
real and beneficial.
He has not withheld any thing however trivial, that could be of real
service ; and he has studiously endeavoured in plain and distinct terms to
elicit what he wished others to comprehend as well as himself Having said
thus much, the remaining portion wUl henceforth consist in explanatory
descriptions of the different designs of furniture introduced throughout the
work, together with their uses, mode of raanufacture, &c. We shall first
commence with those of decoration, as they are exhibited in the plate".,
offering such remarks as the change of fashion and times have occasioned.


INTERIOR DECORATION.

INTERIOR DECORATION.

In the earliest period of the anna-s of mankind we find sufficient proofs
of the existence of a taste for architectural and ornamental erabelHshment.
Not to go further back than the period in which architectui-e flourished
araongst the Egyptians, we find in the ruins of their teraples, their
catacombs and obelisks now existing, many exa,raples of ornaraental deco
ration, evidently the work of hands, superior in talent to the coramon idea
hitherto entertained of their knowledge in works of art. The variety and
beauty displayed in the capital of the columns in the remains of the great
temple now existing at Apollonopolis Magna (or Edfou) in upper Egypt,
exhibit as much taste in their design, as excellence in their workmanship.
Whether the Hindoos derived their taste for architecture and orna
mental embellishment frora the Egyptians, or the Egyptians from the Hindoos,
can be but of little raoraent at this period : it is sufficient that we observe in
tlie works of both nations an accordance and sirailarity as to the disposal of
their parts into iraposing and gigantic masses. Amongst the ancient Greeks
we find decorative painting and sculpture carried to a great degree of elegance
in almost every instance ; as may be seen in the ornaments belonging to
their teraples, their vases and other works of art. To these succeeded the
decoration of the Etruscans, a Grecian colony, visible in the reraains
of their public and private buildings, baths, &c. lately discovered at
Porapeu and Herculaneum. Frora the era of this people, we pass on to the
time in which the arts of design flourished amongst the Roraans, when decora
tion raay be said to have reached its zenith ; and here we have abundant exam
ples in their altars, vases and candelabri ; in the baths, of Titus, Nero, and
Dioclesian; and likewise on the walls of the catacombs at Naples and its


164 INTERIOR DECORATION.
neighbourhood. Passing from thence to modern times, we have to notice
the style of decoration practised in the 15th and 16th centuries, in the times
of Leo X. and Julius II. when Michael Angiolo, Raffaelle, and other
eminent raen of genius flourished, whose works may be seen in the Vatican
and palaces of modern Rome ; and likewise in raany of those in the neigh
bouring states of Italy, as also in various parts of France. However rauch
we raay adraire and becorae prejudiced in favour ofthe light and airy style
reigning throughout, and alraost peculiar to the whole of the Grecian orna
ment, we cannot but feel a sensation of pleasure and gratification in con
templating the breadth, freedom and raanly boldness of effect displayed
in the ornamental productions of this age. The works of Jean le Pautre,
who flourished in the age of Louis XIV. of France, (although this period
was productive of a bad style) are distinguished by their variety and peculiar
happiness of invention. It raay not be paying an exaggerated encoraiura
to our neighbours the Franks, when we assert the superiority of their
inventive faculty in the ornamental parts of design. We have however in
the present day many decorative artists, (natives of our own soil) of great
merit, some of whora possess uncommon versatility of talent ; performing
equally well both in oil and distemper colour, the three branches of deco
rative art; viz. figure, landscape, and ornamental painting in all its variety;
as the numerous works of Mr. R. Jones (who stands at the head of his
profession) sufficiently testify. Amongst the raany proficients in this
departraent of art we must not omit to raention Mr. R. Nelson, whose
abilities entitle him to great praise, and to whom the Author feels hiraself
indebted for raany valuable practical hints. Several others raight be here
enuraerated, but we shall close this article by raerely intiraating that the
present work will contain speciraens of all the different styles of decoration,
such as may be found useful to the decorative artist of the present day ; the
same being selected from remains handed down to us, of the Greek,
Etruscan, Roraan and Saracenic or Gothic styles. Speciraens wiU likewise
be given of that of the Franks in the age of Louis XIV, together with the
present prevaUing taste now in vogue in our own island Great Britain ; all
of which wUl be noticed in the descriptive account accompanying each
design.


INTERIOR DECORATION. 165

Plate XXVIII.
In this plate are given four different designs for corner ornaraents in the
Grecian style, intended each as a finishing for the four angles of the com
partments in a room where the walls are divided into panels. These
ornaraents are worked in various ways ; soraetiraes carved and finished in
gold ; on other occasions painted in oil or disteraper, as representing the
effect of basso relievo ; and frequently executed by the French in a style
which they terra Rehauss^e D'or : which is done by a species of hatching in
gold on a dark ground, where the gold itself forms the high light; or where
such species of hatching in gold is relieved by dark shadows on a light ground.
There is extant a print after one of the old masters, heightened in gold after
this raanner on a brown ground, and which is comraonly called the golden
print; it is now extreraely scarce. A very chaste style of decoration consists
in making the ground or panels of the room of an even light colour ; for
instance, a very pale drab, a peach blossora, a stone colour, &c. ; the storie
colour decreasing in force to almost a white, and approaching nearly to a
cream colour. In all these cases the style of the panel raay be of a sirailar
colour as the ground, but worked darker for the purpose of giving the
appearance of projection to the panel itself A gold raoulding placed round
the walls under the cornice above, over the dado or plinth below, as well
as up the angles, internal and external of the apartraent, will in this case
make the finish. Where the corner ornaraents are carved and gilt, the straight
raouldings betwixt them forming the panels raust be of gold also. In cases
where the ornaraents are painted, the raouldings apparently parting frora them
should be painted also ; which may then be relieved from the ground by a dark
line underneath, and a light one above : the sarae is to be observed in
relieving the ornament. It is necessary to state, that this species of orna
mental decoration is alone to be adopted in drawing rooras and boudoirs.
The ornaraent in the middle of the plate wiU answer as a central ornament
in decoration ; whether upright or horizontal, in carving or painting in relief

2 Y


166 INTERIOR DECORATION.

Plate CXXXIIL
The four designs given in this plate, and nurabered 1, 2, 3 and 4, are
intended as corner pieces for the decorative panels of drawing rooms.
The observations given in the description of plate XXVIII. will render
further explanation on the subject before us unnecessary : they are intro
duced for the sake of variety, and to assist the decorator in selecting or
choosing from the whole. It is not intended that the designs throughout this
work should be copied or adopted precisely as they are here given ; if they
afford hints and materials for composition to the artist, it is all the author has
aimed at. Nos. 5 aud 6, are intended as designs for the decorating of
friezes, either in painting, carving, or casting in metal.

Plate LXXXV.
In this plate are given three designs for ornaraental PUasters, intended
to be painted in disteraper or oil, and subject as to colour, to the same rules
as laid down in plate XXVIII. It may be observed that the ornaments on
these Pilasters are often painted in a variety of colours, and thus called
Arabesque ; such are the Pilasters in the Vatican at Rome. The situation
which these Pilasters generally occupy in apartments is the space between the
ornamented panels. Rooms when decorated with such an arrangeraent of
ornament, will always present a pleasing and imposing effect; particularly
when executed with taste by the artist, as regards light and shade.

Plate LXXXVL
In this plate is exhibited a portion of that side of an apartment appro
priated to the chimney ; the same shewing the chimney-piece, with its glass
and ornaraented frarae above, which should be finished entirely in Or, Matt
and burnished gold. On the external Angles, marked A A of the chimney


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INTFRIOR DECORATION. 167
breast, are to be fixed gUt mouldings. In handsome apartments, the base,
and surbase raouldings of the dado, raarked A A, are frequently finished
in gold. A gold moulding to suit, should be carried round the roora
under the lower raeraber of the cornice at top ; and over the upper
raember of the dado at bottom. The internal angles should have a
double moulding, the reverse of those that are on the external angles ofthe
chimney breast. A portion for the decoration of the panels, right and
left of the chimney breast, with their ornamental corners is likewise
shewn in this plate, together with the profile for the glass frarae.

Plate XXXIX.
Four designs for raouldings fully enriched are given in this plate,
which raay be used for various purposes : viz. for the cornices of windows,
in which case they are intended to forra the upper raouldings, and should be
carved and finished in gold ; or, where the expence becoraes an object, the
ornaments may be procured in composition. These mouldings on a sraaller
scale raay be accoraraodated for cabinet furniture, and raay be either cast in
raetal or carved in wood. The Greek frett, and Italian gmlloche, of which
we have given exaraples in plate XL. may be as variously applied in
Decoration : for example, the frett may be adopted to ornaraent the frieze
of an entablature ; or it may form the border round the soffit or ceiling of
an apartment, either in stucco or in painting. In many cases it forms a
beautiful border surrounding panels.
The guUloche is peculiarly adapted for soffit decoration, and raay
when cast in metal be used with great advantage in Cabinet work ; it may
likewise be used with good effect in the ornamenting of glass frames.


lb» INTERIOR DECORATION.

Plate CXLVII.

EGYPTIAN DECORATION.
This plate and the three that follow it, offer in theraselves specimens
ofthe different styles of decoration in use araongst the antients, but adapted
to our raoderii English apartraents. We shall coraraence with the
style of the earliest known period in which painting was practised, viz. that
of the Egyptian ; and although there exists not at the present tirae a vestige
of any of their private buildings or Palaces, yet we have sufficient speciraens
stUl existing in their teraples, grottos, &c. frora whence a style after their raan-
nier may be drawn: this has been successfully attempted by the elder
Piranese in his design for a coffee-room at Rorae, as shewn in his works ;
but it is too close a copy of a style and manner which in all its parts is
raassive and colossal. We have in this plate endeavoured to preserve the
character of the Egyptian style without following its heaviness ; adopting
the design for a library, of which the draught before us forras the entrance
side. The casing for the doors is copied frora the doorway or entrance as seen
in most ofthe Egyptian temples, than which, no form can excel it for beauty.
Vitruvius has followed the same outline in most of his doors and windows,
and we find the same form still existing in the remains of many of the
Grecian temples at Athens. The colour for the walls of such a room may be
that of a warm stone, or what is otherwise termed a drab colour ; round
which may run a style or margin of a deep blue, the ornaraental decoration
on which should be of raised gold : the frieze also should be worked after
the sarae raanner. The four angles of the roora raay receive a raoulding in
the form ofa palm tree stalk, and crowned with a palm foliage, spreading itself
on each side the angle. Over each door-way in this design are paintings,
the subjects representing two out of the ten plagues of Egypt ; the other
two pictures raay represent the portraits of Cleopatra and Antony. The
bookcase will be seen to partake of the general forra and character of the
Egyptian temple, before the pUasters of which are placed bronzed figures


INTERIOR DECORATION. !69
of Osiris and Isis and other Egyptian Deities : all the other embellishments
in this apartment should partake of a simUar character. The doors being
deeply thrown back, may have their jambs fitted up for the reception of
books ; and it would likewise be advisable to cover the doors themselves
with sham books. Under the hand of an intelligent and clever Artist, a room
might be fitted up after this manner, possessing a light, yet imposing effect ;
although we are fully aware that this taste has been anathematized as
barbarous, arising chiefly frora the very injudicious manner in which it
has been adopted.

Plate CXLVIII.

GREEK DECORATION.
Notwithstanding the ruin and desolation which the Grecian states
have undergone during the lapse of . ages, and by the hands of bar
barians, who have from time to tirae raade theraselves raasters of that part
of the world; we have still sufficient proof left of their refined taste in what
relates to Architecture and Ornamental Sculpture, as seen in those chaste and
raagnificent structures, their teraples. Amongst the Greek Artists, we find
their taste for design exhibited not only in their larger works, but extended
even to the smallest vessels in domestic use ; and although we have no
existing remains of any portion of what constituted their private buildings,
yet it may be presumed that their Princes and Nobles resided in palaces
and mansions suitable to their rank and taste.
The nuraerous remains of sculpture in columns, pilasters, mouldings,
panels and other portions of decoration, many of which have been brought
over to this country, are the only grounds on which we can hazard a conjec
ture as to what raay have formed the feature of the interior decoration of
their houses. In the absence therefore of other information, we have
ventured to give in this plate a design of what raay be terraed an apartment
decorated after the Grecian taste ; compiled from the raaterials already
2 z


INTERIOR DECORATION. 171
style or border surrounding it, such style being painted in a deeper tone
of the same colour. It is evident that these Artists were not unacquainted
with the science of perspective, whiih the effect produced in the original
painting from whence this design has been composed fully proves, added to
which, in the original, there reigns throughout the whole, a Hghtness and a
fantasy of design, highly pleasing to the eye.

Plate CL.
OMAN DECORATION.
As with the Grecian states, so it fared with the Roman Capitol ; no
mark or vestige being left remaining of any of the splendid palaces and
mansions which existed during the Augustan age, or that embellished Rome
under the reigns of her Emperors. It is from the many fine sculptured
candelabra, raarble vases, statues, consoles, pUasters and panels found
araongst their ruins that we are alone enabled to form any idea of the
magnificent arrangement and decoration oi their apartments. The present
design pourtrays one side of a large dining room, with its decoration ; the
same consisting of Corinthian pilasters, the spaces between which are raade
out with ornamented panels. The centre of the side is occupied by a niche
intended to receive either a single or a group of figures ; or otherwise a
glass, having a side table under it; the whole of which arrangement of
decoration with the candelabra placed between the pilasters, we mav venture
to term after the manner ot the Roman costume.

Plate CLI.
GOTHIC DECORATION.
With the destruction of the great Western Empire by the northern
hordes, vanished all the remains of private grandeur, as raised bv the


172 INTERIOR DECORATION.
luxury and great wealth of the Greek and Roman princes and nobles.
And here a long blank ! a dreary wilderness of space intervenes, under
which every thing relating to art, learning and literature becarae dormant.
What formed the style or character of the habitations, the palaces or resi
dences of these barbarians we are unacquainted with. Suffice it to say
that from this general ruin, arose a species of architecture drawn
from the intersection of the Roraan arch, the one crossing the other
at an angle of 45 degrees ; this intersection when made by semicircles,
was found to produce the pointed or lancet shaped arch. On the
other hand, when the height of the arch became less than its span,
then such diagonal arch becarae eliptical and rauch flattened ; this
species of arch was the earHest in general use in England, and both the one
and the other, viz. the lancet and eHptic forms were caUed Gothic, however
improperly; which have nevertheless been brought to very great per
fection, the proof of which maybe seen in many of our antient cathedrals.
In this plate is offered a design after the Gothic style ; a style well suited
for country residences. It has been a great mistake with most persons who
have supposed, that because the buUding partook of this peculiar style, that
the furniture was designed after the same fashion ; the contrary of which is
proved to be the case ; for in those days the furniture for domestic use was
raassive and heavy, consisting chiefly of bold and highly relieved mouldings,
with other members partaking ofthe round and cable form. Many of the
ornaments used about their meubles may be called Arabesque, and in some
cases they partook very much of the grotesque.


INTERIOR DECORATION. 173
Plate CLII.
DECORATION OF THE AGE OF LOUIS XIV.
The subject of this Plate exhibits a speciraen of the taste that prevaUed
in the age of Louis XIV. and displays the style of decoration used during
that period, in the best houses -of the nobUity and gentry in France.
We generally find the walls of most of their apartraents divided into
corapartraents and ornaraented with pilasters, painted frequently in iraita-
tion ofthe finest raarble; and sometiraes panelled out, and decorated with
richly carved ornament. The mouldings around the panelling on the walls
were usually of a very bold projecture, and wholly enriched. Most of this
species of decoration was executed in Norraan oak, and would frequently
be partially gilt ; and the interior panelling, if not left in the plain oak,
w^as generally filled up with the finest Coblentz tapestry.
If we refer to the Meubles or Garniture of these apartraents, we shall
find thera to partake of the sarae boldness of forra and enrichraent of
detaU, as displayed in the architectural erabellishraent of the rooras. In
most of their tables, the tops were of the finest and variegated raarbles,
around the edges of which would be fixed a bold projecting raoulding of
brass, chased and gilt; and the frieze or rail under the raoulding was fre
quently enriched with finely executed ornaraents in Or Molu. The pillars or
supports to these tables were soraetiraes of a turned forra, and richly decorated ;
at other times the supports would be composed of grotesque chimera figures
and foliage ornaraent associated together : a plinth, either of fine raarble,
or of wood, wholly carved and gilt, would form the base for this enriched
table ; the back ground of which was universally fitted up with silvered
glass. The chairs, sofas, candelabra, tripods, glass-fraraes, &c. each, and
all partook of the same splendid style of enrichment ; and although there
raight and did exist, a bad taste in fhe design and arrangeraent of raany of
the parts coraposing the whole of this style of decoration, yet it has never
been surpassed by any other taste for richness and splendour of effect. It is
alike suitable to the kingly palace, as it is to the raansion of the nobleraan ;
but is no ways answerable to the dwellings of persons of sraall fortune. This
3 A


174 INTERIOR DECORATION.
style of decoration has lately been introduced by Messrs. PhUip and
Benjamin Wyatt, in the building newly erected for Mr. Crockford in St.
James's Street ; in direct opposition to the chaste Grecian taste of the late
Mr. Jaraes Wyatt, his late Majesty's surveyor-general. As this raansion
is solely appropriated to nightly purposes of pleasure, perhaps such a taste
may be in unison wilh the wasteful transfer made of property in such esta-
blishraents. From the extravagant expence attending it, such a style of
decoration cannot be recomraended, except in instances wherein property
would justify its adoption. Plate CLIII.
The style of decoration exhibited in this plate raay properly be termed
French, inasrauch as it was first introduced into this country by certain
French artists, brought over frora France by Messrs. G. and F. Echardts ;
who not only engaged in their service the raost erainent decorative painters,
but also those excelling in the flower and landscape departments. These
efforts, although aided at the tirae by English property, yet the expence
in execution was found too great for general use; nevertheless the taste
was not altogether lost on our native artists, who, iraproving upon the lessons
of their' neighbours, have succeeded in producing a sirailar effect at a rauch
less expence ; for what before was only effected by the hand, has now
been accoraplished by the art of printing.
A different style of decoration has lately been introduced from France
by the raanufacture of a coraposition of paper into every species of ornaraent
whether for the waUs of an apartraent or interior decoration in general. This
species of raanufacture has been called Papier Mach6, which in fact is nothing
raore than paper reduced to paste, and then forced into raoulds of the forra re
quired. In this instance we now excel our inventive neighbours in the execu
tion ofthe sarae article; the English raanufacture being raore durable as well
as raore iraitative of real carved work, frora its sharpness of edge and depth
in cast. But with respect to the elegance and phantasy of design in paper
decoration, the French offer patterns very far superior to all others ; this may
be accounted for frora the great inventive faculties of sorae of their first rate
artists, being men who have acquired and possess a taste for the beautiful, and


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HOUSEHOLD FURNITURE. 175
have been foremost in furnishing raaterials for all the inventive and orna
mental decorations necessary to the erabelHshment of the houses of their
principal nobility and gentry. These observations wUl render it unnecessary
to go into a lengthened explanation of the plate before us ; it wUl be sufficient
to observe that the whole of the decoration in this plate is supposed to be the
effect produced by the hand of the artist, and executed either in oil or disteraper
color, aided only by mouldings in gold where the pannel would require it.
It will be easily seen by coraparison, how far the one style excels the other.
The age of Louis XIV. offers heaviness with grandeur ; but the present
style, drawn from the Greeks, although it offers only to our view a few but
well chosen ornaraents (putting expence out of the question), wUl always
afford to the eye of taste a continued gratification.

HOUSEHOLD FURNITURE.

WINDOW CURTAINS.
Plate II. No. 1.
This plate contains two designs for window curtains for drawing-rooras :
in both designs, the cornices supporting the drapery are intended to be
carved and finished in gold. The curtains with their draperies are supposed
to be made up, either in plain coloured sattin or daraask, of which there are
two kinds ; the one being composed of silk altogether, the other being a
mixture of silk and worsted; which last, although it raay happen to be cheaper
than the other, it will when cleaned or dyed, shrink considerably more.
In addition to these there is another material greatly in use, called
Merino damask, much of which is manufactured at Norwich, and raakes
up very beautifully, not requiring a lining.' Drapery will ever give
consequenee to an apartment, and although it raay for a time be in disuse
from the caprice of fashion, it will always be adopted wherever a good


176 HOUSEHOLD FURNITURE. ,
taste prevaUs ; economy may render the plain vaUance necessary, but it never
can be introduced with a view of producing abetter effect; and withal when
the brass rods and large rings, &c. are added, the saving becomes very doubt
ful. In alraost every design as appHcable to doraestic furniture, there arises
a necessity for using a variety of colours, inasrauch as a gay and more lively
effect is produced by the contrast ; but if we refer to a raore chaste style
of colouring, and particulariy so as regards curtains, it will be found in the
use of one colour alone, such tint predorainating throughout the whole : two
other tints raay be used, but the three raust be of one stock, each varying from
the other only by a darker or lighter gradation of the sarae tint. Where
drabs are entirely used, a modest or quaker-like appearance wiU ensue,
but nevertheless the general effect will be pleasing and in true taste.

Plate XXXIIL No. 4.
The observations raade on the designs in the preceding plate 2, wUl
apply'likewise to the two designs exhibited in this ; which being likewise
intended for drawing room decoration, what becoraes necessary in the one
wiU be found equaUy so in the other.

Plate XXXVII. No. 6.^
We have in this plate given a design for the decoration of a single win
dow, wherein drapery hasbeen dispensed with; the sarae being intended for a
drawing roora : as such, the raaterials should be of the sarae quality as before
recomraended for such rooras. The cornice is carved and gilt, and in design
after the style and raanner used in France during the lifetirae of Louis XIV-
The vallance or raantle is gathered into flutes, frora each of which raay be
suspended a tassel. This style of curtain has soraething handsorae and rich
in its appearance ; it is soraetimes termed petticoat, and at other times
Jiammercloth drapery, to the latter of which it carries a strong resemblance. [
A vallance of this kind suits better, when] used for the parlour,
library, or bedchamber.


HOUSEHOLD FURNITURE. 177

Plate CXLIV-
This design is intended for the windows of a dining roora, in which
case we would recoraraend the raaterial to be either of fine cloth. Merino
daraask, or of raoreen.
It is obvious that with a slight addition of drapery for the pier, the
present design may be well adapted for two windows, and would then forra
a handsorae arrangeraent. Plate XCV.
The style of window decoration exhibited in this plate is siraUar in taste
to that which prevaUed in England about the period when Queen Elizabeth
was on the throne ; the sarae continuing in use afterwards until superseded
by a taste for drapery, first introduced into this country frora France. It
is a style certainly well adapted for rooras that have but little blank
space or dead light above the windows, and raay in such case be indiscrimi
nately used for any apartment, changing the costly material for that which
is less expensive.
The valance in this design is supposed to be of buckram covered with
velvet, and ornamented with a material of the sarae kind, but darker colour;
cut into ornamental devices at pleasure, which are afterwards to be sewed
or otherwise fixed on : tassels are suspended at equal distances throughout
the whole extent of the valance; behind' which, a deep and rich buUion
fringe is suspended from the lath.

Plate XCVI.
A design, shewing the style and manner of fitting up the curtains and
drapery to a circular headed window : its enrichments wUl entirely depend
on the apartraent it is appropriated to, for this window is equally to be
3 B


178 HOUSEHOLD FURNITURE.
found in the parlour as well as library. The valance behind the drapery is
supposed to be gathered all over into puckers, such as we see used in the
linings of jewel boxes, drawers, &c.; and when made with silk, pro
duces not only a rich, but beautiful back ground for that purpose. When
eantonier taUs can be admitted, as in this design, a finish is theh made to the
window, which raakes any other addition unnecessary. The taste or system
of using bronzed raetal or its iraitation on a gold ground, is but a bad taste
at best, and much on a par with the contrast of black against white.

Plate CXXIX.
The cornice in this design should be wholly in gold (that is to
say, gilt,) and where carving cannot be afforded, coraposition raay be
used. To this cornice is attached what is properly terraed a stone drapery,
from its existing in raost of the antique feraale statues at Rorae, and forming
that portion of the vestment attached to each shoulder by a button, and which
falls down on the breast into folds sirailar to those in the present design. This
design is intended for a drawing roora, frora the enrichraent of the cornice and
great depth of the drapery : but with a plain japanned or painted cornice,
and less depth of drapery, the sarae design may be adapted for any other
apartment, and its materials varied also.
Plate XII. No. 3.
A design for the curtains and drapery of a Venetian window. These
windows are well adapted for the general |distribution of light into all
apartments. A pole cornice is introduced in this design, which may be
manufactured in metal, the ends and centre ornament being carved and gilt.
The observations on the articles in Plates II. and XXXIII. in regard to
the materials to be used, wUl apply equally to this, and render further ob
servation needless.


HOUSEHOLD FURNITURE. 179

Plate XIX. No. 5.

In this design the two windows are furnished with a drapery in conti
nuation over the pier ; the central arrangement of the drapery being con
siderably raised above that of the two ends. The cornice may be of metal ;
the ends and centre ornaments being carved and finished in gold.
This arrangement of drapery and curtains being intended for a drawing
room, the observations on Plates II. , XXIII. &c., wUl equally answer for
this.

Plate CXI.
This design exhibits a drapery adapted for two windows and a pier, to
suit with that shewn in Plate XXXVIII, ; the cornice in this design may
be of oak, and richly carved ; or it may be finished in gold. The curtains,
&(*., may be of rich damask, with gold trimmings, and in this case, the
design would be suitable for many parts of such a palace as Windsor
Castle.

Plate XI. No. 2.
Displays an arrangement for curtains and drapery for three windows,
the drapery being continued over the piers. The cornices are intended to
be carved and gilt, that in the centre being the highest elevated. This
design being intended for a drawing room, the drapery and curtains should
be made of the material before noticed in Plate II. Printed callicoes may
answer extremely well for secondary apartments, or for those in houses of
persons of small fortune; but they are not at all suitable for those of
persons of rank and splendid income. Muslin curtains are introduced in
the present design, as well as many of those preceding ; they serve to break
the strength of the light, without entirely secluding the cheering effect
produced from the solar rays.








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HOUSEHOLD FURNITURE. 181

BEDS.

Under this article it may be requisite to make a few observations as
regards the three kinds of bedsteads in general use : — 1st, That of the four
post bedstead, comraonly so called. 2dly, The smaller four post or field
bedstead ; and, 3dly, That of the canopy or French bedstead. With
respect to the sofa bedsteads, &c. as they are no ways introduced or noticed
in the present work, a description would only tend to lengthen this article,
without adding any thing interesting to the work.
In a cliraate so variable as that of Britain, where the transitions are so
sudden from cold to heat, and from wet to dry, &c. one uniform system, both
as regards dress as well as the fitting up of our apartments, has been
found the most beneficial and conducive to health ; and in point of comfort
the old English four post bedstead with its curtains and drapery, will
always be found to claim a preference before any other, although it does
not follow from hence, that it is necessary to close the curtains so effectually
as to exclude the free ingress and egress of fresh air ; — and no form of bed
stead can offer so much comfort as to warmth. In very small rooms, such
bedsteads may be found objectionable, but in apartments that are not less
than fifteen feet square, they are in this climate to be preferred. The ad
vantage this kind of bedstead possesses over all others, consists in its con
struction, by which the curtains surrounding the whole may with facility be
drawn back close to the head, leaving the front and sides open at pleasure.
For general domestic use, this bedstead for the reasons above stated, stands
the foremost. '2nd. The next species of bedstead which comes under the description
of English furniture, is what is termed the field or tent bedstead ; the
teasters of which partake of various forms, and in raany cases adraitting
of much taste and elegance in design, accompanied with lightness of
effect. Formerly the curtains adapted to this kind of bedstead became in
themselves too close a covering, excluding very much the free course of
air; but they are now so adapted> that the curtains on each side can be
3 c


182 HOUSEHOLD FURNITURE.
partially drawn aside to the head and foot : — in general they are never used
except in small apartments. Theprincipal bedrooms in cottages, small villas,
&c. raay be appropriately furnished with such beds.
3rd. A frequent intercourse of late years with our neighbours the French,
has brought into general use the couch or rather canopy bedstead, over
which is suspended a curtain, supported either by a single pole from the
wall, or by a small teaster, otherwise termed a canopy — the same being
variously ornamented. The furniture for this species of bedstead is in
general thrown loosely over each end of the couch. A great degree of
elegance may be pourtrayed in this kind of bedstead, inasmuch as the
couch itself admits of a great display of decoration, together with the use of
the finest woods in its manufacture. In state apartments as well as in large
recesses in first rate rooms, this style of furniture may be used to great
advantage ; and in dressing rooms, nurseries, as well as in apartments where
one or more beds are required, this species of bedstead and hangings in its
simplest form, is in general to be recommended.

Plate V.
A design for a four post bedstead and furniture, suitable for a spacious
sleeping apartment; its dimensions in width being six feet, its length
seven feet, and its altitude adapted to a room of ten feet six inches in
height. Although the furniture is represented by a plain tint of colour in
the present design, yet the material of which it is made, may be supposed
to be of a chintz pattern, lined with a plain blue, this material being most
congenial to English costume. The cornices supporting the valances may
be of mahogany and enriched with carved ornaments. The footboard,
headboard and foot pillars together with the rails, are intended to be
manufactured of the same material ; the turned pillars and crowning of tbe
foot and head boards may likewise be decorated with ornaments carved out
of the solid wood.


HOUSEHOLD FURNITURE. 183

Plate LXX.
This Plate offers a design for a four post bedstead, &c, of similar dimen
sions to the one before described, having its teaster covered inwardly, and
surmounted by an oval dome ; and the cove surmounted by a moulding,
and decorated with ornaments in gold. The pillars, whicb may be of
mahogany, are surmounted on the front and sides by three enriched carved
cornices, which support a drapery consisting of nine festoons, behind which
a range of drapery in plain flutes serves as a back ground, as well as for
an inside valance.
The drapery and curtains may be raanufactured either of silk, of chintz, or
Merino daraask, and the whole will then form a bedstead and hangings
suitable for a state apartment.

Plate CXVII.
A design is here given for a four post bedstead with head and footboard ;
from the teaster of which rises three semicircular cornices, all of which may
he manufactured of mahogany, together with the ornaments attached to them.
This bedstead has likewise an additional teaster rising from each angle,
the same terminating in a small circular block in the centre; and thus
forming by the intersection of its ribs, what in architecture would be termed
a groined arch. The whole effect of this design in execution would no
doubt look light and airy ; it is a design, suitable for the principal sleeping
apartments in the mansions of our opulent gentry. The furniture, as in
the article last described, may be either of silk. Merino damask, or of
printed calico, and may be triramed with fringe, tassels and rope. The circular
pedestal in this design may be of mahogany : its use is for receiving une pot
de chambre. On the other side ofthe bedstead a similar pedestal is placed,
intended for une table de nuit ; and both pieces of furniture may have
marble slabs for their tops.


184 HOUSEHOLD FURNITURK

Plate CXXX.
In this design, the expence of cornice with its ornaments, &c. has been
dispensed with; the whole embellishraent consisting in the wreaths and shells
necessary for supporting the festoons. These ornaraents may either be
carved, or be substituted by those cast in metal. — The furniture may be of
chintz or calico, and the bedstead of mahogany. The base valance in
this design may be of buckram covered with plain calico or velvet,
and decorated with velvet ornaments. The inside teaster valances, are also
intended to be plain and of buckram, covered with calico after the same
manner and to suit in shape the base valance, but ornamented with tassels
8tc. as fancy may dictate.

Plate XLIII.
This Plate contains five various designs for the foot pillars of bedsteads ;
in height they are rather more than 9 feet. Three of the patterns would
require a scantling of mahogany, 6 J inches square, the other two requiring a
scantling of only 5 I inches ; all these pillars are alone fitted for first rate
bedsteads, and should be supported on French casters. It will be necessary
that the wood should be carefully selected both as to quality and soundness,
and the carving put into competent hands — the plain surfaces on the
pedestals of the three first designs may be overlaid with veneers of a choice
figure.

Plate XCVII.
The field, or as they are sometimes terraed tent bedsteads, are so much
in common use as to render a description of them alraost unnecessary; we
shall therefore confine what we have to say in a small compass*,


HOUSEHOLD FURNITURE, 185
The design offered in the present Plate, and which is intended for an
apartment of a superior kind where a display of show and dress becomes
necessary, is more peculiarly calculated for the smaller apartment on the
principal floor of a mansion. The ornamental cornices supporting the
drapery, maybe executed in composition and japanned in colours to suit
the pattern of the furniture, where expence is considered an object. In regard
to the furniture, what has already been observed on the designs in the
previous plates, will likewise answer for the one before us. This description
of bedstead is generally intended for the use of single persons, but will
very well supply the place of a four post bedstead in the principal sleeping
apartment of the small villa or cottage orn6.

Plate CXIII.
A design is here given for a field bedstead and furniture, of a more
simple construction than that last described; expence being altogether
avoided in this coraposition, so far as relates to a bed somewhat above that
in coramon use : — in an object so familiar, it would be needless to enter
further on its description. — The more ornamental style of French bed will
therefore close what we have to say on this article of doraestic comfort, and
first with that numbered

Plate XIII.
This description of bedstead and furniture, with its decorations, &c. is of
foreign invention, and goes back to a period of very early date ; — it is nothing
more than a refinement on the hurable bed of our ancestors, and its use is
more prevalent in France and over the continent, than in this country.
The frame of the bedstead in the present design is supposed to be manu
factured of the finest mahogany and highly polished, and finished with
Or molu ornaments, when required. The curtain covering the whole at night,
is suspended by a pole from the wall above, and again by poles placed over
3 D


186 HOUSEHOLD FURNITURE.
each end ofthe couch, so as to keep the curtains a sufficient distancefrom the
party when sleeping ; as shewn in the plan below. The details given in the
plate, render further description unnecessary, we shall therefore pass on to

Plate LX.
Which exhibits a design for the same species of bedstead and hangings,
in its more expensive style. The dome or canopy, as an appendage to this
bedstead, forms a principal feature ; and the whole thus arranged, is suit
able for the principal or state apartment in the mansion of the nobleman or
gentleman of fortune. The richest materials will of course be requisite to be
used for such an article of elegance ; such as silk for the furniture, and the
finest woods for the bedstead.

CHA IRS, SOFAS, &c

There is scarcely any article in the whole range of the Upholstery
branch, that admits of more variety in taste and design, than that of chairs
and sofas. From the earliest periods of human civilization, and amongst
various nations, they have been in use as an article of furniture. In the hiero
glyphic paintings which have been discovered in the torabs of the kings, at
Thebes in Egypt, representations may be seen of different superb ornamented
elbow chairs, and the same of couches ; and designs drawn from these remains,
and given by the Author in a former work, have been successfully manufac
tured at various periods. But for simplicity of form, beauty of outline,
and delicacy as to substance, no chairs can be said to surpass those of the
antient Greeks, and which they could only have effected by the use of
metal. The best speciraen of chair after this taste was one, designed some
years back for furnishing of the drawing rooms of Henry Baring, Esq., and
manufactured for hira hy the Author. A similar style of chair may likewise


FOUR-POST. BEDSTEAD.
& FURNITURE. I.

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Pub^ by JONGS i. CO April 15.1826.





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HOUSEHOLD FURNITrjRE. 187
be seen in the drawing rooms at the house of Alexander Copeland, Esq.,
in Great George Street, Westminster; manufactured some years since by
Messrs. Oakley and Evans. With respect to the style and fashion displayed
in this article of furniture in England, and especially that of the present
day, much cannot be said by way of praise or encomium ; the patterns which
have lately been produced, offering in themselves rather a melange or
mixture of all the different styles associated together : — for instance, it is
not uncommon to find a parlour chair made with turned front feet, the
back feet of which will be strictly Grecian, and the yoke for the back
partaking of the same style, but supported by Roman columns. The
necessity for economy urged by many at the present day, is in itself
sufficient to check and weaken the spirit for design, and thus we see nothing
but a monotony of character in this article of furniture. In some few
instances we witness a lavish of expence displayed in the production ofthe
furniture, designed in the style and after the manner of that which prevailed
in the age of Louis XIV. of France ; an example of which is given in Plate
CXLVI. (see the design marked French) : here we have magnificence, but
not taste ; an elaborate display of ornament, but no beauty in general
outline — those who possess a strength of fancy for this species or style of
furnishing, may have his, or their taste amply gratified by a visit to Crock-
ford's Gambling-house in St. James's Street, which is wholly furnished after
this manner. We now proceed with our descriptive catalogue ofthe chairs,
contained in the present collection of designs, beginning with

Plate IIT.
The two designs contained in this Plate are wholly fanciful ; the one oii
the left hand being after that of the French school, and the other parjily
Grecian. They are both intended for furnishing the drawing room, the
frames being manufactured in rosewood, vi'ith the ornamental parts finished
in gold. The backs in both the designs are fitted with loose frames,
which may be stuffed and covered with the same material as the seat ;
a stuffed back will at all times give a consequence to the appearance of the
chair, and at the same time adds to its comfort.


188 HOUSEHOLD FURNITURE.

Plate CXLVI.
Contains two designs for antique chairs ; the first being a French
pattern, and after the taste of the age of Louis XIV. Of this design we
have already spoken and made reference, which will render any additional
observations unnecessary ; further than it is intended for the same apartment
as those described in the preceding Plate, and should be wholly of rose
wood, or altogether gilt. The other design is copied from an original chair
brought over from India and executed in ivory, being now in the possession
of Sir George Talbot. — The whole of the ornament is exquisitely carved,
and beautifully finished. This design is given to show the variation of
style as regards the taste of different countries : — It is a chair not altogether
adapted for ease on account of its form, nevertheless there is a considerable
display of merit in the original composition.

Plate CXLIII.
In this plate are two designs for chairs, after the style of the florid
Gothic ; they are intended to be executed in oak, which at all times is the
most suitable material for this style of work. Gothic furniture should never
be introduced but where the architectural style of the building is after the
same taste :¦— In all other instances its adoption becomes an anomaly.

Plate LXVIII.
* Two designs are here given for fauteuil or lounging chairs, intended eitheif
for the drawing room, the dining parlor, or library ; their covering varying
according to the apartment they are destined for. This description of chair
has its frame of mahogany or rosewood ; — of mahogany when it is destined
for the parlour or library, and of rosewood when appropriated for the
drawing room. These chairs are calculated for indulgence, being adapted
chiefly for the luxury of the wealthy, and comfort of the infirm.


HOUSEHOLD FURNITURE, 189

Plate XXXII.
Contains two designs for hall chairs ; the one on the left hand of the
Plate, to be executed in oak, and that on the right hand in mahogany.
Further observation on articles of such common usage would be needless
in this place, the parts being plain by inspection.

Plate CXIX.
The two first designs, intended as patterns for the backs of chairs, and
appropriated for the dining room, have the Grecian outline for their back,
finishing with a broad and hollow yoke. Roth the backs are intended for
stuffing, and covering with leather.
The two designs underneath are intended as patterns for the backs of
drawing room chairs, to be executed wholly in rosewood as before
stated. The first design partakes of the Grecian style, the central part
being stuffed, the frarae enriched with carving, and the yoke orna
mented to suit. The last design may properly be styled English, and is
wholly fanciful as to the arrangement of its parts.

Plate XXXVIII.
This design for a sofa is intended for the library; the frarae tobe manu
factured wholly of mahogany, and the ornamental parts carved out of the
solid wood : — the back cushions, together with the two bolsters, pillows, and
seat cushion, to be covered with green morocco leather. The ends of this
sofa partake of the Dolphin form for their outline, the whole of which
figure is made out into carved foliage ornament. The graceful outline
which this figure offers, has occasioned its introduction for this article of
domestic use. 3 E


]90 HOUSEHOLD FURNITURE

Plate CXXXVII.
A design for a sofa, intended for the drawing room ; the frame to be
executed in rosewood, and all the enrichments carved out of the solid.
The covering for the seat, the back cushions, bolsters, &c. may be raade up
out of printed colico, Merino damask, or silk, as occasion may require.
Plate LXXXI.
Two different designs for tete a tete seats. In France this description
of seat is very common as an article of indulgence ; it takes its name from its
being intended for the accommodation of two persons. This article of
furniture is very useful in small apartments, where the recesses on each
side of the chimney breast are generally too contracted in width, to admit
either sofa or chaise longue. As to their material, their decoration, and
covering, it will be the same as that of the sofas in the room for which
they are intended to be placed. Plate XCIV.
The first design in this plate represents a seat commonly termed a
Chancelier, from the resemblance it bears to the seat or cushion on which the
Chancellor of England is seated in the House of Lords, which in its
original form is made to imitate a wool sack. The present design in some
measure differs from it, inasmuch as a bolster is made to run down the
whole length of the middle, having cushions or pillows resting on each side.
This description of seat is appropriated for occupying the central
situation of spacious apartments, and should be covered en suite with tbe
curtains, sofas, and chairs in the room. The second design represents an
ottoman, which is a species of seat generally without ends or back ; but in
this figure a deviation is made. The ottoman here given, is intended
for occupying the left hand side of a chimney breast, having a framed


HOUSEHOLD FURNITURE. 191
upright back to receive the cushions which are placed against it. Being
placed in a recess, the cushion at one end is supported by the wall, and the
cushion at the other end, by the projecting breast of the chimney. The
covering &c. should be regulated as described in the preceding articles : — for
the rest, reference may be made to the plan underneath.

Plate X.
Exhibits two designs for chaise longnes, both of which are adapted
either for the drawing room, dining parlour, or the library at pleasure ; the
covering being suited to the apartment for which they are designed.
If intended for the dining room or library, the covering may be of
morocco leather, and the frames mahogany ; if used for the drawing
room, the frames should then be manufactured of rosewood, and the
materials intended for the covering, to accord with and be the same as
that of the window curtains.

Plate CXXXVI.
This elegant chaise longue as to its design, may be considered as wholly
Grecian, and is best adapted for the drawing room, or boudoir ; in which
case, the frame may be wholly of rosewood, and the seat and ends
covered either with silk. Merino damask, or linen. If appropriated for
the state apartment, the frame might then be finished entirely in gold.

Plate IX.
Six designs are given in this plate for patterns for chair legs, shewing
a part of the seat rail to each. These legs being much enriched with
carved work, are best suited for drawing room chairs ; and in that
case, they should be virrought entirely in rosewood, or have some of their


192 HOUSEHOLD FURNITURE.
parts in gold. This plate also contains four various patterns for the sup
porting feet of sofas and chaise longues, shewing part of the foot rail, and
scroll end of each.
What has been said in respect to the chair feet, will also apply to these
as regards their designation.

Plate CIV.
This Plate contains four different ideas for the scroll ends of sofas,
shewing the profile of one end, part of the rail, and one leg, in each design.
Agreeable to the fashion of the present day, the frames would require to be
made of rosewood, and the carved ornaments to be worked out of the solid ;
but we are not prevented from making use ofa mixture of gilding whenever
the other finishings of an apartment may require it.

Plate LXXIV.
Three designs are here given for music stools ; one shewing its frame
as worked in mahogany, and the other two as executed in rosewood, with
their ornamental parts in gold, the covering of each seat being of morocco
leather : — underneath each design is given a plan of its pillar and block, with
a scale.

Plate CXXXI.
This Plate contains six different designs for foot stools in profile,
intended as appendages to the furniture of the drawing room. They are
variously got up and ornamented ; some being manufactured of rosewood,
some altogether finished in gold, and others partly in rosewood with gold
ornaments. The covering for this article raust be regulated by the rest of
the furniture in the apartment.





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194 HOUSEHOLD FURNITURE.
towards producing good work, viz. that of patience, if they are not alto
gether so quick and fanciful as the French on that which relates to design.
Some years back many of these artizans worked in several of our cabinet
manufactories, but have since emigrated almost all of thera into the musical
establishments of Messrs. Broadwoods, Muzio Clementi, Stodart and others.
If we refer to the artists who have excelled in their designs for furniture
we shall find but few to notice amongst our own countrymen. Mr. Thomas
Hope stands the foremost on the list, as being best acquainted from his
travels, with the costume of foreign countries, and as possessing a very
refined and classic taste. Mr. Thomas Chippendale (lately deceased), and
knoAvn only amongst a few, possessed a very great degree of taste, with
great ability as a draughtsman and designer. Except a few secondary assis
tants in this branch of design, we have now none of any consequence ; unless
we take into the account some few of our best architects, whose efforts at
best can be but limited, arising chiefly from a want of knowledge as to the
proportion and distribution of the component parts of cabinet furniture ;
and which alone can only rest in the individual who is well acquainted
with the practical part of the whole.
If we refer on the other hand to foreigners resident in this country,
we may reckon at the head of this department Mons. Doileau, who was
formerly eraployed in the decoration of Carlton Palace. This gentleman,
in addition to his unrivalled taste in decorative painting, possesses a light,
an airy, and classic style of design for household articles of comfort; and be
has never been surpassed by any raodern artist in his designs for ornamental
plate or articles for casting in Or molu. The late Mr. Bogaert, in addition to
his merits as a carver, was also equally happy in his designs for furniture and
other branches of interior decoration. There are other artists, as well
foreigners as English, of -considerable merit, who practice in the decorative
branches of design ; but as they are no way connected with the manufac
turing department, nor with that of making designs for furniture, we shall
avoid enlarging any further on the subject, and pass on to the descriptive
portion relating to cabinet furniture, — the last series in this cur work.


HOUSEHOLD FURNITURE. 19S

TABLES.

Plates XXIV. and CXVIII.
These two plates exhibit three different designs for occasional or sofa
tables, intended as meubles for the drawing room ; in which case they
may be executed wholly in fine rosewood, or they may have a portion of
their ornamental work in gilding or Or molu. If intended for the library or
dining room they should be manufactured of mahogany, and the* orna
mental parts carved in the solid wood. In plate XXIV, each design is
accompanied with a profile of its standard, the parts of which may be
measured by the scale given j and in plate CXVIII. is given one half the
plan of the table.

Plate XLII.
In this Plate are given two designs for loo tables, intended for drawing
rooms, as being much enriched with carved work ; and which may be manu
factured either of solid rosewood, king wood, or of other fancy woods of
equal beauty. If intended for the dining room or library, this species of
table should be manufactured wholly of mahogany with a lesser portion of
carved work. A plan of each block on a reduced scale, is given at the
bottom of the plate.

Plates XXVII. and LXIV-
The designs given in these two Plates are intended as tables for
occupying the piers between the windows of the drawing room, and in these
cases should haye mirrors placed over them. The lower design in Plate
XXVII. is represented as having its sides inclosed, the panels of which on


1% HOUSEHOLD FURNITURE.
the outside are intended to be filled up with quilled silk ; and those on
the inside as well as the back, with silvered glass. The intent of this
arrangement is to produce a reflecting effect from the china objects of
ornament which are usually placed in such situations.
In Plate LXIV. is given a design for a console table, with a portion of
the glass frame shewn over it, after the style of Louis XIV., accompanied
with a geometrical profile and a scale.

Plate LXXXIII. .
The first subject in this plate is intended for the use of female artists,
as well as to answer the purpose of a pier table. When used in drawing
rooms, this table may be so adapted, as with a rising frame at the back to
admit the influence of heat from the fire place, and at the same time afford a
riser for the female artist to place her copy on : — the small drawers on the
right and left hand of the table, are intended to contain all the apparatus
and materials necessary for drawing, and that in the centre for the reception
of drawing paper. The second subject in this plate exhibits a design for
a writing table with a sliding screen at the back, which may be raised up or
lowered at pleasure, and should be filled with plate glass.

Plate VIII.
Contains two designs for ladies' work tables, which may be either ol
rosewood, fine mahogany, or of any other fancy woods. The table in the
second design is furnished with a backgamraon board, and a sliding cover,
divided either for draughts or chess. A profile and plan is given with
each table.


HOUSEHOLD FURNITURE 197

Plate XXVI.
In this Plate are given two designs for articles of Cabinet furniture,
both of them adapted for occupying the boudoir : — they may be considered
of French origin. The first design contains a secretaire drawer, adapted
to the height for writing, together with a sliding frame intended as a desk,
under which is an open space for paper, &c. The upper desk is so propor
tioned in its height, as to be equal to the position requisite for a person to
write or read when standing ; it has sliders right and left of it, for holding
candles or other articles.
The second design forms an ornaraental table, either for the boudoir
or drawing room : — the tops of such tables are generally of the finest Parian
marble ; sometimes they are composed of a mixture of scarce and valuable
stones inlaid and cemented together, and in this case are termed tesselated.
Where such table tops are known to be genuine, they are alraost invaluable;
but the craft and artifice of dealers in this article too frequently impose
on our faith, by substitution. Plate XXXVI.
The first design in this Plate is that of a dressing table, having the
central portion of the top occupied by the wash-hand bason; on each side
of which and under hinged covers are contained the water caraffs, the
tumblers, tooth brush trays. Sec, as shewn in the plan : — one ofthese sides is
fitted up with two trays, the one over the other, which are intended to
contain combs and other small articles, necessary in dressing. The dressing
glass is intended as a fixture at the back, after the manner of those in the
French toilette tables : — these tables may be manufactured either in maho
gany or rosewood. The second design exhibits a toilette table, wholly
intended for dressing ; it contains three drawers which are fitted up with
various divisions for combs, brushes, and various other articles necessaiy
for the toilette : this table, like the one preceding, has its dressing
glass fixed to the back, and may be manufactured of woods ofthe same
description. 3 G


198 HOUSEHOLD FURNITURE.

Plate LIX.
This design is intended as a double wash-hand table, and is vvholly
after the French taste. The top containing the basons, &c. is intended to be
of marble, and the frame under it to be made ofthe finest figUred mahogany,
which in the inside is lined throughout v, ith lead. This table is supported
by four truss shaped legs, resting on a plinth; the ornamental parts of which
may be of raetal, either lacquered or gilt : a plan and scale is added, by which
the parts may be measured. ' ^
Plate CXXVI.
The design in this Plate is intended as a dressing table for the principal
bedchamber, and should be manufactured of the finest wood : — the drawer
under the top is wholly fitted up to contain the necessary dressing apparatus,
with watches, trinkets, and other bijoux appertaining to female use. The
drawers above are intended for the reception of papers and other articles, over
which is fixed the dressing glass. This plate likewise contains a design
for a circular wash-hand stand, accorapanied with a plan.

Plate CXXXII.
Contains two highly ornamental stands for the reception of hand-
basons and ewers, and other articles necessary for daily lavations. This
article of furniture may either be made of mahogany or rost^wood ; if of
the latter, the whole of the orriaraentaf parts may be executed of metal,
such as the masks and tails Of the Dolphins with the shell ornaments sup
porting the base ; as well as the gallery round the centre sbelf^ and the rings
attached to the swans heads. The sarae may be said as to the ornamental
parts in the design for the larger stand, snch as the ornaments round the
frieze, the foliage on the truss supports, the paw feet. Sec.


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HOUSEHOLD FURNITURE. 201

Plate LXIII.
Exhibits four designs for the backs of sideboards, to be placed on
the level surface of the top against the wall ; answering for an ornament as
well as a guard. [They forra a substitute for brass rods, the panels sometimes
being fitted up with looking glass, as noted in these designs.

Plate XVII.
This Plate contains six various' designs for legs, as supports for side
boards. The four first are intended to be turned ; the two last to be shaped
and carved, as shewn by the profile and front view of each design.

Plate XXIX.
The two designs in this Plate are denominated running sideboards
and sometimes vulgarly termed dinner waggons. Their use is for the
purpose of bringing the dinner at once from the hall into the dining room
at one opening of the door ; and likewise for receiving and carrying away
such dishes and plates as have been used. In small families, they answer
the purpose of a dumb waiter when the attendance oi a footman is
not required. The profile and scale given with each design, will render their
construction plain to the workman.

Plate LV.
These articles of furniture which belong to the dining parlour should
be executed in mahogany, and the ornamental parts carved out ofthe solid.
The insides are lined with lead to receive the beer and ale jugs»f or at other
O H


202 HOUSEHOLD FURNITURE.
times to ice the wine intended for use after dining. A plan of each is
given, by which it will be seen that there is sufficient space in each cooler
for ten decanters or bottles.

Plate CVII.
Contains two designs for cellarets or stores for win,e, to be placed
underneath the sideboard. This article is so familiar as to render descrip
tion almost needless: — ^it will be sufficient to observe, that they appear
to most advantage when manufactured wholly of mahogany; as well the
ornaments as the body itself. ' By the plans given with each, it will be seen
how much the square plan has the advantage over that which is shaped in
point of accommodation ; the one containing twelve decanters, whereas the
other will only contain eight. The spaces noted a, a, a, a, in the first plan
are intended for the reception of bottles, placed horizontally ; and the two
spaces in the second plan are likewise for the same purpose.

Plate LXXX.
Exhibits a design for a lady's secretaire, having shiffonier on the top,
with silvered plate glass at the back. The lower part is inclosed by doors, the
panels of which are fitted up with an ornamental metal guard and covered
behind with silk, which may either be plain as in the present design, or
otherwise gathered into neat plaits. The decorative enrichments in this article
of furniture should be executed in or molu, and the case itself, of rosewood
or fine mahogany as fancy may dictate. The secretaire drawer is fitted up
as usual for the purpose of writing. The plan shews the situation of the
columns ; the profile giving the heights, the projection ofthe mouldings*, &c.
Plate VI.
This ejpgant piece of drawing roora furniture is intended for the
end of an«apartment, to be placed opposite the chimney piece ; or in


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204 HOUSEHOLD FURNITURE.
fitted up for writing ; and at other times fitted up to contain the whole of
the apparatus necessary for dressing : — the other drawers are intended for
linen. The second design being considerably higher, is intended both for
clothes and linen. The frieze is made to draw out, and forms a depository
for jewellery, papers, &c.

Plate XC.
In houses of first rate dimensions, the best apartments of which are
generally very spacious, and thereby capable of .admitting furniture on an
enlarged scale, an opportunity is afforded for giving a design out of the
common routine. The present plate exhibits a design for a wardrobe
adapted for an apartment of such ample dimensions ; affording much con
venience as regards accommodation for an extensive assortment of clothing,
as well as producing considerable efiect from the distribution and proportion
of its parts, which in such pieces of bedchamber furniture is generally very
heavy. The central division of the present design is wholly intended for
sliding tray shelves; — the parts connecting the centre with the ends, are
fitted up with drawers, and the two butside wings are intended for the pur
pose of hanging up dresses that would otherwise be injured if folded together.
The heights in this design may be taken geometrically from the front ele
vation; the perspective making little variation, and certainly none but what
the intelligent workman can make allowance for : — the plan and scale will
guide him as to the proportions.

Plate XXXI.
With respect to the design in this Plate we have only to observe that
the ends are intended for the same purpose as those in the one preceding,
for receiving the habilliments de nuit. The proportions may be obtained
from the elevation and scale as before mentioned


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HOUSEHOLD FURNITURE. 205

Plate CVIII.

This design for a lady's dwarf wardrobe is of similar dimensions to that
in the preceding Plate, but rs different as to the arrangement of the
parts. The central part being screened by folding doors, is intended to be
fitted up inside with sliding shelves up to one half its height, and the other
half to be occupied by drawers. The two wings are intended for hanging
up dresses, as before stated

Plate CL
The two designs in this plate are for box dressing glasses, so termed as
having a case placed beneath the glass, which is generally occupied by three
drawers. They are for the most part manufactured of mahogany; and
are intended for first-rate apartments, when executed of rosewood: — the
profiles in this plate will be sufficient to give the geometrical heights and
projectians.

Plate XV.
The placing a glass over the chimney piece will always hold the prefer
ence to the fixing of this mirror in any other situation in the room. The walls
of our apartments on the chimney side cannot be said to be properly furnished
without the addition of a glass ; for pictures make but an indifferent sub
stitute. There reigns throughout a cheerfulness, a gaiety, and what the French
would term a Jt ne scais quoi, in regard to the effect of a glass^ as to induce
us to consider the apartment as lifeless that does not contain it. We have
in this plate given two designs for this elegant and pleasing article of
domestic embellishment with a section of each frame, and the mouldings,
on an enlarged scale. With respect to the style and manner of their
3 I


206 HOUSEHOLD FURNITURE.
execution we shall forbear saying any thing, further than when executed
wholly in gold, the general effect will not only be the most chaste, but also
the most imposing in its appearance.

Plate LXI.
Drawing room fire screens. Two designs are here given for this useful
and elegant appendage to the furniture of the drawing-room. In the first
design, as much variety has been displayed in the form of the mount as such
would consistently admit of. In the second, the idea of the banner has
been adopted, with the addition of a Grecian ornament as a finish for the
upper part, from which is suspended silk tassels and line. The standards
in both designs may be executed either of mahogany, rosewood, king-wood,
or of zebra-wood ; and the ornamental parts finished in gilding : — or they
may be carved out of the solid wood.

Plate CXXXVIIL
Screen libraire. In the nobleman or gentleman's library, the bookcase
screen will not only be found a useful appendage, but at the same time will
form a portable and ornamental library of itself. The idea as given in this design
was suggested from the use that a portable bookcase would be in the library
or drawing room, the want of which hitherto has been supplied by tbe open
chiffonier. Here we have an article of furniture serving the purpose of a screen
in cold weather, the front of which when elevated or sliden up, discloses a small
but select library. The panel of the rising front may be filled either with silk, as
shown in the plate, or it may be fitted with transparent plate glass, shewing
the books when down ; and although we have in this instance an elevated
screen securing us from the heat when raised up ; yet we are not altogether
shutout from a view ofthe cheering fire. This elegant piece of furniture may
be constructed of any of our fancy woods, according to the apartment it may
be destined for.


HOUSEHOLD FURNITURE. 207

Plate XXIII.
This plate offers a design for a library bookcase, a, piece of furniture
familiar to almost every one. In the present design, columns are introduced
in the lower part after the French taste ; and the panelling of the under
doors is varied from the usual manner : — ^various patterns for dividing the
glazed doors in the upper part are also given. The ornamental parts, such
as the caps of the columns, the corners of the door panels. Sec, are given
on an enlarged scale ; a correct plan, with a scale for the same, and likewise
a scale for the enlarged parts, being added : — the mechanic will therefore
find no difficulty in the construction of this very useful article of furniture.

,, „ Plate XLL,
This design is intended to occupy a principal situation in the spacious
library or study. In the composition of this ornamental piece of furniture,
the Grecian style has been adopted ; and at the same time, every attention
been bestowed in its construction, to render it as a whole, and in all its
parts, useful as well as elegant. The whole af the ornamental embel
lishments are given on an enlarged scale in so ample a manner, together with
a plan of the bookcase; and a scale as well for the elevation as forthe
enlarged parts, as to render further observation unnecessary, the whole being
plain by inspection.

Plate XCVIII.
A design is here offered for a dwarf bookcase, divided into four equal
parts, each being inclosed by a single door ; having the panels filled with
trellis wire work, which may be either backed with silk or not at pleasure.
The ornamental parts, such as the busts, and the foliage cups forming the
supports for the pilasters, may be of bronzed metal. This description of





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212 HOUSEHOLD FURNITURE
like covering would spring :— it would also be continued up each angle of
the sides as well as in the division of every gore formed in the tent roofing.
In many cases the upright angles are finished at the top with a bow and
two tassels, as in the present design. From a rich rosette in the centre of
the roof, will be suspended two handsome large tassels, and frequently an
ornamented valance or drapery would be continued round the walls, sus
pended from the upper part of the sides frora whence the tent roofing would
spring ; the same being decorated with fringe or tassels as taste or fashion
may dictate. Every appearance of architectural decoration is avoided in
fitting up such an apartment, the architraves round the doors and windows
being either removed or wholly covered with the furniture chosen ; and this
will extend to the glasses over the chimney piece and elsewhere, if more
than one be introduced.
The furniture to be introduced into a room of this kind, should in itself be
of a light cast : — the chairs raay be of rosewood with cane seats and cushions ;
or the light stained chairs with coloured straw seats, as imported from
France are very appropriate. Ottoman seats with cushions at the back may
range round the walls of the apartment. A rosewood loo table should occupy
the centre space of the floor, which in the present design partakes of the
octangular forra : — dejune tables, amd light chiffoniers are adraissible; and,
where a recess is formed, it may be occupied by an escritoire with an orna
raental French clock placed on the top: — We are not so restricted by taste
or fashion, as not to admit into such an apartment, such articles as will be
essential to our comfort as well as pleasing to the eye ; taking care, agreeably
to the Latin motto, to associate in our choice the Utile cum Dulce.

^








Fl. l.X\ IV

LoTidon 1 Vl-^icKed lyr Jones & C^ Sep".?. 13J?f?

ib


INDEX
TO THE PRINCIPAL MATTERS.

N.B. The figures refer to the number of the page.
Angle of a polygon, explained, 5. Right angle in a semicircle, its application for trying the
truth of a square, 23.
Angles, definitions of the various kinds, 5, 6. To make one angle equal to another, and its
application, 15. To bisect an angle, 16. To trisect a right angle, and its application,
16, 17. To lay down an angle bythe orotractor, 7. To lay down an angle by the scale
of chords, 57.
Angular perspective, ^rdvaaiii2i.rj remarks, 118. Difference between parallel and inclined, illus
trated, 119. In what respect applicable, 120. Method of laying down the vanishing
points, and points of distance, 121.
Arc of a circle, definition of, 10. Summit of an arc, defined, 10. To find a centre for describing
the arc of a circle, 24. Its application for laying down the plan of a bow, 24, 25.
Arch eliptical, rule for describing it by means of two laths of wood, 35. To find the centres
for describing the Saxon arch, 36. To find the centres for describing the Gothic arch, 36.
Axis, or diameter of an ellipsis, defined, 11.
Bed-steps, to represent a flight of, in perspective, 38.
Bedstead, to represent a four post, in angular perspective, 121.
Bedsteads, various kinds described, 181, 182.
Block, triangular ; rule for finding the proportion of such for a loo table of any given diaraeter,
and for laying down the plan of the same, 51. Method of representing the sarae perspec
tively, 80.
Block, quadrangular ; manner of laying down the plan geometrically, 25.
Bookcase, to draw the same in perspective from a given plan, 94.
Bookcases of various kinds, described, 207, 208.
Cable molding, rules for forming it in all its varieties, 43.
Cavetto, rule for describing it, 38.
Centre of an ellipsis, defined and explainedjv^ 11. Centre of the picture in perspective,
explained, 64.
Centre of a circle, method of finding such whereby to describe any given arc, 24.
3 L


214 N D E X.
Chair, to draw the same perspectively, with its side parallel to the picture, 113. To represent
the same in perspective, with its front to the picture, and the method for finding the vanishing
points for the bevelled sides, 101.
Chairs of various kinds described, 186 — 188.
Chaise longue, to represent the same in paraUel perspective, 105.
Cheval glass, process for obtaining its perspective representation, 114. Mode for finding the
inclination of the swing frame perspectively, 115. Diagrams for elucidating the same, after
three different methods 116 — 117.
Chords, scale of, explained, 57. Its construction laid down, 57. Its application and use, 58.
Chords, line of on the sector, its use explained, 57.
Chiffonier commode, to draw the same in paraUel perspective, with the method for representing a
door open, 97.
Circle, division of, 6. Process laid down for dividing the circumference, 7. Its use for
laying down angles, explained, 7. To find the centre of a circle from an arc g^ven, 24.
To describe the arc of a circle which shall pass through three given points, 24. To divide
the circle into three psirts for the triangle, 27. Into five parts for the pentagon, 28. Into six
parts for the hexagon, 29. To draw the perspective representation of the circle, 79, 80.
Circumference of a circle, to find a right line, whose length shall equal it, 20. The application and
use of the problem explained, 20.
Circamference ofthe ellipsis, defined, 11.
lours, tints in all their varieties produced by the mixture of the primitives, one with the other,
157. A list of the different tints, with the process laid down for producing them, 158 — 160.
Process for laying them on, detailed, 161. '
Columns, process for shadowing of, detailed, 149.
Compasses, for dividing, described, 55. Compasses with shifting legs and points, 55.
Compasses, proportional, their use explained, 59, 60.
Cone, definitions of its various sections, 33, 34. Problem for describing the parabola, 34, 35.
Problem for describing the hyperbola, 35.
Cone of rays, defined, 73.
Console or truss bracket, to find the outline of the same by means of proportional numbers, 52, 53.
Corner ornaments for interior decoration, described, 165,
Cube, to represent the same in parallel perspective, 85. To represent tbe same with a projecting
top, 86.
Cylindrical solid, to represent the same perspectively, 86. The application of the diagram, 87.
How to throw out a projecting member from a round object, 89.
Cyma recta, to find the centre for describing it, 38. To describe the same by means of
ordinates, 41.
Gyma reversa, rule for describing it by means of ordinates, 41.
Decoration, interior, observations on its origin, rise and progress amongst the ancients, and its
Tadual improvement to the present time, 164. Observations on decorative painting, 165.
The difi'erent styles described, viz. — Egyptian, 168. Greek, 169, Etruscan, 170. Roman,
171. Gothic, 171, 172. French, 173. English 174.
Definitions, geometrical — of points, 1, 2. Of lines, 2 — 4. Of angles, 5 — 8 Of triangles, 8, 9.