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THE 
 
 CABINET-MAKER AND UPHOLSTERERS 
 
 GUIDE: 
 
 BEING A 
 
 COMPLETE DRAWING BOOK; 
 
 IN WHICH WILL BE COMPRISED 
 
 TREATISES 
 
 ON 
 
 GEOMETRY AND PERSPECTIVE, 
 
 AS APPLICABLE TO THE ABOVE BRANCHES OF MECHANICS ; 
 
 The Definitions and Problems explained in the most plain and familiar Terms, with much new matter introduced, and the Diagrams 
 rendered at once entertaining and practically useful. The whole Illustrated by a Series of Instructive Examples, and 
 
 NUMEROUS ENGRAVINGS. 
 
 TO WHICH IS ADDED, A 
 
 GOMPLETE SERIES OF NEW AND ORIGINAL DESIGNS 
 
 FOR 
 
 HOUSEHOLD FURNITURE, AND INTERIOR DECORATION, 
 
 In the most approved, elegant, and modern Taste, 
 BEAUTIFULLY AND CORRECTLY COLOURED, 
 
 FROM THE ORIGINAL DRAWINGS ; 
 
 And accompanied with Useful and Practical Instructions for the Manufacture of the same. 
 
 INCLUDING 
 
 PLANS, PROFILES, AND A SCALE TO EACH, WITH THE MOULDINGS ENLARGED, FOR ASSISTING THE 
 
 WORKMAN; viz. 
 
 Draperies, Curtains, Beds, Canopies, Cornices.— Chairs and Sofas for Drawing-Rooms, Parlours Libraries 
 Halls, &c— Ottomans, Seats, Chaise-Longue.— Writing, Work, Dressing, Library, and Card Tables.— Side- 
 boards, Celerets, Book-Cases, Secretaires, Commodes, Wardrobes.— Vases, Tripods, Candelabras Lustres 
 Girandoles, Lamps, Mirrors, Pier Glasses, Chandeliers, Chimney Ornaments, Screens, &c. &c. 
 
 comprising likewise, 
 
 INSTRUCTIONS AND EXAMPLES IN THE ELEMENTARY PRINCIPLES 
 
 OF 
 
 ORNAMENTAL FOLIAGE, &c. 
 
 Enabling the Student to draw with facility and correctness in this so generally useful branch of the Art ; 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, 
 
 Upholsterer 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. 
 
 ACTON PLACE, K1NGSLAND ROAD. 
 
 1826. 
 
INTRODUCTION 
 
 Historical View of the Origin of the Art in this Country. — First Specimens introduced 
 by 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 Style superseded by the florid Gothic during the Reigns of Henry I, II, and III.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- 
 seded 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, 5fc. reserved for the present time. — Effect produced by 
 Mons. Denon's Work. — The Author's first Work on Furniture and Design super- 
 seded by later Improvements. — By what Cause Produced — Intended Object and 
 Plan of the Present Work. 
 
 IN a work 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 
 simple style seems to have been followed, but with the 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, chano-ino; 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 Avork 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 coffered 
 ceiling, although they offered an imposing and grand effect, 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 moveables), 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 
 
 c 
 
vi INTRODUCTION. 
 
 perfection, it appears, was reserved for the present period, in 
 relation to ornament and domestic embellishment. In the year 
 1804, Mons. Denons' grand publication, detailing the antiquities 
 of Egypt, became public. The novelty displayed throughout 
 these fine specimens of art, calling to recollection so distant a 
 portion of ancient history, gave rise and life to a taste for this 
 description of embellishment. 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 inapplicable 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 Sir William 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 improvement to the present day, 
 may be considered necessary as well as acceptable to the trade, 
 and has induced the author to compile this volume, containing, 
 not only a large collection of original designs, in the 
 various schools of the art, but also to add to it instructions in 
 drawing, sufficient 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 projecting parts from apian; 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 likewise an acquirement every 
 Artisan ought more or less to be acquainted with, and is of peculiar 
 advantage to the Cabinet-Maker and Upholsterer, in the embel- 
 lishment of his designs. Instructions, therefore, in this elegant 
 branch of Art, should form a component 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 
 
viii INTRODUCTION. 
 
 a Work at once creditable to his own labours, 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, 182G. 
 
THE 
 
 CABINET-MAKER AND UPHOLSTERER'S 
 
 GUIDE, 
 
 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 point made by the compasses, pencil or 
 ink, as the point A, in Geometry, Plate 1. a series of points put together, 
 in length form right or curved lines, such are the lines figured Ax, 5x. 
 
 A line of points a b, fig. 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 without cutting. Example : 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 breath. 
 
 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. 
 
GEOMETRY I 
 
 DEFINITIONS. 
 
 OF POINTS 
 
 \ 
 
 London, Published bv Jones SC" April 3. 1826 
 
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 line, 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, because 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 that 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 gTound 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 line, 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 a b, c d, e f, 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 a\ 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 all 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 of 
 the level V, adjusted horizontally by the plumb line U. 
 
 Diagonal Line, or simply a diagonal, 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 N 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 line is of great use in perspective. 
 
Fig- 10 . 
 
 2 . 
 
 London. Published by Jones X: C° April 3.182S 
 
I 'I WAY 
 
 LnncouPiiMisM bv Jau<-s ft C« JuIt 23 182G 
 
GEOMETRY. 
 
 5 
 
 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 formed 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, C D, E D. 
 
 Mixtilineal angle, is an angle formed by a curved and a straight line. 
 Thus : the angle FGH, 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, when 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 if you 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 by the two sides I K, K L, of the pentagon, 
 IKLMN. 
 
 External angle, is that angle which has its point without the figure. Ex- 
 ample : the angle, N M L, fig. 21, is an external angle, because* its point is 
 without the figure, IKLMN. 
 
 E 
 
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. 21 . 
 
 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 making such divisions, before we commence describing figures 
 of many angles. 
 
 The circle by all geometers is divided into 360 parts, otherwise termed 
 degrees. Thus the circumference of the circle, ABCDEFGH, fig. 22, 
 PLATE 4, is supposed to be divided into such a 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, a b c d e f g 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 D, will divide it into four equal parts, of 90 degrees each, four 
 times ninety making the whole number 3C0. 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 KI L, 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 180, when it becomes a straight line. 
 
adon. Fublislied Try Jones tc C° J£ajl9. 1627. 
 
GEOMETRY. 
 
 7 
 
 To divide the 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 I I 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 at p p, 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. 
 
GEOMETRY. 
 
 for instance ; the angle D E F, 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 from 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 M N O, 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, because 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 strait. 
 
 Mixed triangle is that which has two of its sides curved, or sometimes 
 only one, such are E and F, fig. 29 and 30. 
 
 Equilateral triangle, is that which has its three sides equal ; thus G, fig. 
 31, is an equilateral triangle, because its three sides H I K, are all equal. 
 
 A right angled triangle, is that which has one right angle. The triangle 
 LMN, 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 
 
GEOMETRY 
 
 9 
 
 triangle G H I, fig. 33, is a scalene triangle, because its three sides are of 
 different lengths, the side G 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 
 D E F, fig. 34, is an isoscele triangle, because the two sides D F and 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 ABCD, 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, having the two angles K L M and KNM 
 obtuse, and the other two opposite angles N K L and NML acute. 
 
 The Rhomb, is sometimes termed lozenge, and sometimes equilateral 
 Rhomb. 
 
 Rhomboid, is a figure which has its angles, as likewise its opposite sides, 
 equal betwixt themselves, being neither equilateral nor rectangular. O P Q R, 
 fig. 38, is a Rhomboid, because its two 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 OPQ and O R Q are obtuse, and the two other oppo- 
 site angles P O R, P Q R, are acute. 
 
 F 
 
10 
 
 GEOMETRY. 
 
 Trapezium, in general, is another square figure, beside the preceding 
 parallelogram. A B C D, 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 Jigures, 
 
 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 line 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 plane? 
 when considered as possessing length and breadth without thickness. 
 
1AT1 
 
 GEO ME T]RX 
 
 Desuiition's J'oti/w/is or 7jianu Sided -Fiqwes . 
 
 lonccc. PicMisfaea try Janes %z C° Sep^lS 1327. 
 
1 ciuJdii PttUuM t\v- Janro & CT.fnh- -2 18~.(>. 
 
GEOMETRY. 
 
 SI 
 
 There are convex and concave superfices or planes, such are the figure* 
 V, being convex, and W, concave surfaces. 
 
 Parabolic superfice or plane, is a space terminated by a right line an^ 
 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 s. 
 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 same 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. 
 
 Diameter 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 
 by one or more 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 on a, describe an arc 
 of a circle, cutting the line b c at d and e;on</ and e with the radius d h and 
 eg, more than half d e, describe two arcs intersecting each other at /, then a 
 
f.AT K XI. IX 
 
 PRACTICAL GE ()>'[ ET BIT, VMI, 
 
 /Wv. /. 
 
 ////. /. 
 
 II I 
 
 b — 
 
 Apnticaiien 
 of 
 
 I'rob. Z. 
 
 J 1 / //. 2 
 
 JFio. 2 . 
 
 C 
 
 3 
 
 i) 
 
 l> 
 
PRACTICAL GEOMETRY. 
 
 i3 
 
 line drawn from a through /, will be a perpendicular to the line b c, to 
 which all the other upright lines on the wall must be made parallel. 
 
 To prove if the line bs 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 d on the line B C, then on d 
 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 from whence the bow commences or springs, 
 draw a line from 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 d; next take any radius more than 
 half d e; then on the points d and e describe two arcs intersecting at f,f; 
 proceed next and draw a line from C through f, 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 from e through the central point D, and continue it at pleasure, until 
 
 G 
 
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 e 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 example, the line 
 W X, being the given width of a room, suppose, fifteen feet, and the length 
 W Y, twenty-five feet, the walls being at right angles or perfectly square, 
 a perpendicular must 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 perpendicuku 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 of 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 d d ; proceed next and take four feet from the same scale, and lay it 
 down on the line m a, from m to 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 line ??i 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 
 
Pi. .VI K I. 
 
PRACTICAL GEOMETRY. 
 
 15 
 
 him to Jay 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 be 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. I. 
 
 To make an angle equal to any right lined plane angle given; BAG, 
 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 theline D E, fig. 2, an angle equal to the angle 
 B A C. Rule : with any radius or opening of the compasses at discretion, 
 on A, fig. 1, the vertex or point of the given angle BAG, 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 same opening as in fig. 1, and 
 describe the arc of a circle de; make d 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 
 B A C. 
 
 APPLICATION. 
 
 From this problem 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 : commence by setting off equal measures on the 
 ground from B to C, and from B to D, say five feet on each side, and draw 
 the chord line e f, 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 e f, cutting B D, in f, 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 A C, fig. 1. Plate 9. Rule : with 
 any opening of the compasses, on the vertex or angular point A, describe an 
 arc, d c, at discretion, cutting both legs, A C and A B, of the angle B A C 
 in the points d and c ; then on d 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 man- 
 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 A C 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 will also be shown in laying down the line of chords, 
 as on the sector, in a case of instruments. 
 
 Problem 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 polygonal or many-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. 
 
 On aright line E F, fig. 2, Plate 10, to make a triangle similar to 
 another triangle B A C, fig. 1, by means of a scale of feet. 
 
 Let a scale of feet or equal parts be made as d 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 d 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 
 
IS 
 
 PRACTICAL GEOMETRY. 
 
 in the point E, describe an arc g ; 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 g at D ; draw the lines F D and D E, and the 
 triangle D E F, fig. 2, will be exactly similar to the one measured B A C, 
 fig. 1. For if the triangle D E F, fig. 2, was cut out, and the point E laid on 
 the point A, fig. 1, 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), make 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 ] 1), 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 becomes the tangent to a circle inscribed within it. 
 An elegant and ready mode of constructing an octagon, is obtained by first 
 
London. Mblished ~bj Jones k C? Jtayl9.]& 
 
PRACTICAL GEOMETRY. 
 
 19 
 
 making a square, half of one of the diagonals of which, when laid down 
 on the sides, from 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 forming 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 f; the line Q R will then be truly trisected. 
 
 APPLICATION. 
 
 The division of a line after this manner being the most eorrect, 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 AB 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, and 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. 
 
PRACTICAL GEOMETRY. 
 
 21 
 
 Problem 14. 
 
 To find a right line that shall be equal to a determined curved line. 
 
 D F E, fig. t, plate 10, is the given curved line. Take any small measure 
 in your compasses, so that the curve contained in the portion thus taken, 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 means 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 10, to draw a line 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 f f; 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 h; transfer the measure of the 
 arc ff, on the arc g h, or make g h equal to f f ; 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 11. 
 
 Where the parallel lines are very long, the following method is to be 
 preferred. 
 
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 end 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 g h, (fig. 1, plate 11,) to be joined 
 together by two upright pieces of metal, so as to form four right angles, 
 as at A, B, C, D, and consequently the metal 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, b 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 b equals the angle d, consequently the moveable rulers e f, 
 •7 It, 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 shadow's 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 be 
 
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 may be 
 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 contained in a semicircle is a right angle. 
 
 ABC, fig. 1, plate 11, 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 b 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, will 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,) for the line dGa, fig. 2, being drawn 
 from d, through the centre C, where it cuts the semicircle as at «, will pro- 
 duce a point perpendicular over b, the corner of the line d b. 
 
 Mechanics also are furnished by this problem with a mode for ascertain- 
 ing the truth of their squares ; for having drawn a semicircle abd, fig 2, 
 with a radius equal to the length of one side of the square as a b, and drawn 
 the line a d, apply the corner of the square abd, 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 ; if the 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 of a circle, of which an arc only, or portion, is given 
 A C B, fig-. 1, plate 11, 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 f 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 we have 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 
 tioor, 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 from 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 some 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 A B 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 R 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 to f; draw g f and h f, 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. 
 
 K 
 
2f> 
 
 PRACTICAL GEOMETRY. 
 
 Problem 19, Plate 12. 
 
 Three lines being given to find a fourth, that shall bear the same proportion to 
 the third that the second does to the first. 
 
 M N, 0 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 measure 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 1 is the measure of the fourth line sought. This problem, part of the 
 sixth book of Euclid, is one amongst the many, forming the foundation of 
 arithmetic; it is now introduced, as it may be of service to those, with 
 whom 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: 
 
GEOMETRY. 12 
 
PRACTICAL GEOMETRY, 
 
 27 
 
 If 60 inches produce 24 inches, what will 66 inches produce. 
 
 FIRST TERM. SECOND TERM. THIRD TERM. 
 
 Stated thus, 60 : 24 : : 66 
 
 Multiply by 24 the second term, 
 
 264 
 132 
 
 C 5 ) 1584 
 
 Divide by 60 or first term. < 
 
 (12) 316* 
 
 26 Inches product, 
 or 2 feet 2 inches and a fraction. 
 
 From 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 problem 
 may be of great use ; it can be extended in various ways, in enlarging or re- 
 ducing designs, from 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 that 
 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 numbers, but afford 
 means for laying down all the lines on the sector, proportional compasses, 
 &c. &c. 
 
 Problem 20. 
 
 To inscribe a triangle ABC within a circle G C H Y,fig. 1. 
 
 Rule : Draw the Diameter G H of the circle through the centre S ; oo 
 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 diameter 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. &cc. 
 
 POLYGONAL FIGURES. 
 Problem 21. 
 
 To inscribe a pentagon or figure of five sides within a circle ABC Y),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 fi, and continue it until it cuts the serai-circum- 
 ference ADC, 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. 
 
 Tt is here necessary to remark, that the intersection through the points 
 / and^, on A C, at G and H, as they cut the circle, must be very careful! v 
 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 of 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 j 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 f y 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, jig. 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 t in the compasses, (the circle's radius,) and placing 
 one leg of the instrument in the point L, describe the arc q p; next proceed 
 and place the compasses at the point p, and describe the arc L s ; 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 mathematical, 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 room : the 
 cell of the industrious bee is thus constructed. 
 
 Problem 23. 
 To constmct an octagon from a given side. 
 
 Rule : Let kj, fig. 4, Plate 12, be the side given ; on k and j, 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 k j 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. 
 
 In a given square E F G H, fig. 5, Plate 12, to 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 compasses 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 O, &c. &c. and the octagon is corapleated. 
 
 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 1*2, be the diameter given ; bisect it at the 
 point O, and divide each half into six equal parts, numbered from the centre 
 0 ; 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 oroblem 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 20. 
 Ellipsis or Oval. 
 
 The 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 GH; by 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 anclDFC; 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 k; F C to g; and lastly, F D to h. 
 
 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 h, and E n at k. On the focus F, with the radius F g and 
 on E, with the same radius, describe the arcs g h and i k, which will com- 
 pleat the ellipsis. Remark, the length and breadtk of this kind of ellipsis, 
 holds the proportion of three tc 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 problem we are enabled, with a string and pencil, to describe 
 a true ellipsis ; for having found the foci on the longest diameter (e aud 
 
GEO M E1TRY. 13 
 
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 f 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 if the 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. 
 
 T o 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 
 lines 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, I ; be- 
 twixt, or in the centre of each intersection, will form the ellipsis required. 
 
 For laying down working drawings, this mode of using ordinates is 
 to be preferred. 
 
 Sections of 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 ; 
 
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 A B 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 be ; 
 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, if a cone be cut by a right line as g 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 mentioned, 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 of the 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 k 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 to D, and from 
 
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 of the parabola. 
 
 Problem 30. 
 To describe the hyperbola from the cone 
 
 Suppose the section to be made at g I, fig. 4, Plate 13; 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 (g I 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 may be traced. 
 
 Problem 31. 
 
 To describe an eliptical arch by means of two laths of mood. 
 
 Let efgh, 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 wood, so that one edge shall pass through 
 
36 
 
 PRACTICAL GEOMETRY. 
 
 it; take another slip, and size it to one half the length of the arch, and 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 moved 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 
 of the lath /, must be kept moving up the edge of the perpendicular lath cm; 
 the other half from d to b may be described after the same manner. 
 
 Problem 32. 
 To find the centre for describing a Saxon arch. 
 
 Let o 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 o 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 them on the lines at the 
 points t and v; then on r and s, with the compasses extended to t, describe 
 the remaining arcs t p and p v, and the arch required will be completed. 
 
 Problem 33. 
 To find the centres for describing a Gothic arch. 
 
 Let a b 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 b; 
 draw c d perpendicular to a b; then on No. 1, with the compasses extended 
 to b, describe the arc d b, and pursue the same method 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. 
 
. I XXV 
 
 GEOM ETR I I'AL P 10. I J LATE \ . 
 MOUl L) IN U.S. 
 
 Elt/inctil Echinus 
 
 It cud 
 
PRACTICAL GEOMETRY. 
 
 37 
 
 GEOMETRICAL FIGURES. 
 Mouldings. Plate 1. 
 
 Mouldings partake of two characters, the one after the Roman, the other 
 after the Greek; mouldings 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 form, or compounded. 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 remark, that the sweep, generated by a conic 
 section, gives to the Grecian mouldings, not only their graceful outline, but a 
 decided preference as far as regards their use. Sir William 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 as are composed of few 
 mouldings, varied both in form 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, 1o 
 which, all the others ought to be subservient, and seem made either to sup- 
 port, to fortify, or to shelter it from 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 members should not be ornamented ; 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 then- 
 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 maker as the builder, to whom they were originalh" 
 addressed. 
 
 The outline of the Roman mouldings being formed by segments of a 
 circle, the first object is to find the centres for describing their curves, 
 whether simple or compounded ; we shall, therefore, commence with the 
 ovolo, as being the most simple. 
 
 To find the centre by which to describe the ovolo or (piarter round, fig. A. 
 
 Having the projection from the fillet, and the height of the moulding given ; 
 take the measure of the height in the compasses, and from the extreme 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 moulding being given, as before ; proceed 
 and from the upper fillet or projection, drop a perpendicular, and continue 
 the bottom line of the moulding, until it intersects at b; which point becomes 
 the centre for striking the cavetto. 
 
 The astragal or bead C, may be described by taking half its height ; and 
 this measure set back from the given projection will give a centre, by which 
 to turn the ouline of this moulding. 
 
 To describe the cyma-recta, or ogee, fig. D. 
 
 The projection of the 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 numbered 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 of the moulding. 
 
PRACTICAL GEOMETRY. 
 
 39 
 
 To find the centres by which to describe the Roman scotia, fig. E. 
 
 Let A B be the given height of the moulding between the fillets, and E B 
 its projection at the base; divide the height on a perpendicular line A B (drop- 
 ped from the edge of the upper fillet) into seven equal parts from A to B ; on 
 E, the edge of the lower fillet, raise a perpendicular indefinite ; and through 
 the third division from the top, draw a line C i, parallel to E B, intersecting this 
 perpendicular at d : make d f equal to dE, as shown in the figure by the dotted 
 semicircle; from f 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 h; and f will be 
 the centre for striking the remaining 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 of the moulding being determined, let t be the projection of the 
 upper fillet, v the projection of the 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 t v at s; and let r be 
 equally distant from the line < t; as is s; divide each half of 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 s; from r draw lines also through the divisions on t v 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 from t, and so on for all the rest, the same to be observed below 
 from v, through which points the outline of the moulding may be drawn. 
 
 To describe the Greek echinus, fig. G, its outline being parabolic. 
 
 Let F C be the given height, and A F the utmost projection. Draw the 
 lines A B and B C, which may be considered as two tangents to a parabolic, 
 
40 
 
 PRACTICAL GEOMETRY 
 
 curve, the one AB perpendicular to the line of the moulding; the other B C, 
 inclined to it: which inclination maybe made from one half, one third, or one 
 fourth of the whole height, of the moulding from the base; next divide A B 
 into five equal parts, and leave one for the quirk of the moulding at top ; 
 through the remaining four divisions draw lines tending to C; and from A, 
 draw a line parallel to B C, intersecting the perpendicular F C at E, which also 
 divide into four equal parts : make E F equal to E C, from which point, draw 
 lines through the divisions on A E, figured 1, 2, 3, 4, until they intersect 
 each its corresponding line, drawn from A B to C, as before described in 
 the preceding figure. 
 
 To find the two axes or diameters by which to describe the echinus moulding, 
 fig. H, taking the form of an ellipsis for its outline ; the point C being one of 
 the extremities of the shortest axis. 
 
 The height of the moulding being given, let P be its utmost projection 
 beyond the lower fillet ; from this, drop a perpendicular at pleasure, and let 
 A be any measure set from the top you please, which is to form the quirk : let 
 the distance B from the bottom be less than one half the whole height. 
 Join A C, which bisect at L, and draw B C ; from C draw a line perpendi- 
 cular to B C at pleasure ; and from B through L draw another line intersecting 
 this perpendicular at M, which will then become the centre of the ellipsis to be 
 described ; through the point M draw the line IMP parallel to B C at plea- 
 sure, upon which line the longest diameter must be placed. Set the distance 
 C M from A to Q, through which point from A draw a line intersecting the 
 perpendicular C M at N, the length of which from A to N will measure one 
 half the longest diameter, which must be set upon the line I M P before drawn 
 from the centre M equally right and left; and lastly M C, will measure half 
 the shortest diameter, which must also be repeated to K. These diameters 
 being found, the foci for striking the ellipsis may likewise be found dv pro- 
 blem 27, Practical Geometry. 
 
PRACTICAL GEOMETRY. 41 
 
 To describe the cyma reversa, Jig. I, or ogee, by means of ordinate?. 
 
 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 
 at 7; and through this division draw a line of any inclination at pleasure, 
 intersecting perpendiculars raised from the ends of the moulding as at m m. 
 The quirks at top and bottom being taken off ; from these, draw lines parallel 
 to m m, each terminated by the perpendicular line k k; then proceed and 
 find the ordinates as before described, for the parabolic echinus, marked G 
 
 To describe the cyma recta, fig. K, by the same means. 
 
 Having the height and projection of the 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 oj 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 form a finish ; in regard to mouldings 
 for supporting table tops of marble or wood, we may use in either case those 
 marked G H or I; the same mouldings reversed, may be adopted for bases. 
 
 Geometrical Figures, Plate 2. 
 
 In this Plate are given five various ornamental pieces, intended for 
 friezes, bands or mouldings, and which have been as variously used by the 
 ancients. The Fret or key moulding, has the highest claim to antiquity, 
 existing from the earliest period amongst the Chinese and Persians, 
 from whence it was carried into Egypt, and from thence into Greece, em- 
 bellishing their buildings, as well as their vases ; it was probably composed 
 from the form of writing used amongst the Persians, where a similar orna- 
 
 o 
 
42 
 
 PRACTICAL GEOMETRY 
 
 ment denotes a sentence. From the nature of its construction as to form 
 or pattern, an endless variety may 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 metal of a mixture 
 of ormolu or bronze, are proper for the friezes of cabinets, bookcases, or 
 commodes ; in decoration their use is tastefully employed 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 moulding to Cabinet- 
 work, either cast in metal or carved in wood, will always produce a richness of 
 effect, particularly 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 specimens of the antique guiloche, used by the Romans at their 
 happiest period ; forming the ornament for the bands in the division of their 
 arched ceilings, and tastefully adopted in the torus mouldings 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. 
 
 To form the Greek Fret, Jig. 1 . 
 
 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 formed, and it will thus 
 be dependant for its beauty in form and use, according to the taste and ability 
 of the designer ; in the present design, the pattern in its length is composed 
 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, and the 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 same measure likewise. 
 
PRACTICAL GEOMETRY. 
 
 43 
 
 Fig. 2 is constructed entirely on the same principles, and, therefore, 
 needs not a repetition ; a little practice in drawing these figures will render 
 any difficulty small, and afford much amusement. 
 
 To form the cable moulding, fig. 3. 
 
 Divide the width E F into three equal parts, as numbered 1, 2, 3; 
 then subdivide the second division into two equal parts, for a central point, 
 and describe the small circle /; this may then be called the eye ; on the same 
 centre, with an opening in the compasses, 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, from whence to 
 continue your circles; the whole length being gone through after this 
 manner, the lines or portions of the pattern not wanted to remain, are to 
 be rubbed out. 
 
 Figure 4. 
 
 This pattern is divided exactly into the same proportion ; as is seen by 
 the numbers 1, 2 and 3, on the width G H; only a band is added, which the 
 figure shows ; the space betwixt the bands, admits of being filled with various 
 ornaments agreeable to the fancy of the artist. 
 
 Figure 5. 
 
 This elegant specimen of ancient design in ornamental decoration, is 
 constructed on similar principles, to the two figures preceding it ; only the 
 width of the 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 small 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 manner in which this pattern has been enriched by our forefathers 
 in decoration, the present design will give some idea. 
 
44 
 
 PRACTICAL GEOMETRY. 
 
 Geometrical Figures, Plate 2. 
 
 Let A B, fig. I, be the given height for a Greek or Etruscan shaped 
 vase, without including the base : in the present example it is intended to 
 shew one half only, as the other half must be worked by the same process ; 
 the line A B is, therefore, considered as a vertical one, and passing through 
 the centre of the vase j 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 from 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 from 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 from No. 1, above F, 
 to No. 1, at A ; from No. 2, on F D, to No. 2, on A F ; from 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 marks 8x — 7 x — 6x — 5x — 4 x — 3x — 2x — ; 
 through these points of intersection, which must 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), from 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, asBL; the outline of which, as shown at L, forms an 
 ellipsis; the hollow necking under it m n, makes also for its outline, the 
 fourth of a parabola, as shown by the numbers ; the base A M. in height, is 
 equal to the upper mouldings (B O), of the vase, taken together, which may 
 be divided into five parts, and one part A X, given for the necking betwixt 
 the bottom of the vase and the plinth X M, forming the base. The width 
 
(G-3EOM1ETMICA3L F I(&1T]RIE § a HI o 
 
 T he &tomctricol Jlethod.used iy (h&JEtruscans fc Greeks, for oiidincinq their Vases. 
 
 Sebas(j° Scrlw's ■Method . 
 
 a. 
 16 
 
 ccnaon . PabTislied "by Jone 9 8c C?An^25. 1826 . 
 
PRACTICAL GEOMETRY. 
 
 45 
 
 of the base at top will be found to be twice X M, and the width at M below, 
 may be made a small 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 made to suit with another, in harmonious accor- 
 dance ; an excellence only to be obtained by the same 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 b into seven equal parts, as numbered on the 
 line o o, and set off four of these parts from d to b, which must be numbered, 
 beginning from d; make dc equal to three such parts, for one half the 
 width of the body or cup. Divide br into the same number of parts, as is b d, 
 which number likewise progressively from b : then divide the upper height 
 of the vase from d to a, into nine equal parts, and make e d, or the shoulder 
 of the vase, equal to four of the parts ; the remainder (e a) of the height 
 will then form the neck : divide this height also into two equal parts at i, and 
 make the width of the neck (i k) equal to the same measure; draw the line 
 o I perpendicular to i k, and dividing I k into four equal parts, make k o 
 equal to three of such parts, and divide this also into four parts : draw the 
 line I e j and make I m equal to Ik; dividing this measure also into four 
 parts : next divide m e into four parts, also e d into the same number. 
 From these five divisional lines o k, k I, I m, m e, and e d, the ordinates as 
 numbered, 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 same practice must be used in regard to the lines d b and b r, which 
 will produce an outline for the belly or body of the figure. Divide the 
 height of the neck f g 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 ; make gn, 
 which is half the mouth of the vase, in diameter 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 line p q, and make 
 the height of the base r s equal to one of these parts ; divide r s into two parts, 
 
 p 
 
46 
 
 PRACTICAL GEOMETRY. 
 
 which will give t s, for the torus or base moulding, the remainder for the 
 hollow; the width s w, is equal to one-fifth the whole height, or half s x. 
 
 These two examples have been selected out of many of those beautiful 
 specimens of antientart now in existence ; the same principles are applicable 
 to all of them, 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 specimens were very little known, until 
 communicated to the late Sir W. Hamilton, by an Italian artist, whose great 
 assiduity and toil enabled him to ascertain the system on which these valu- 
 able remains of the antients were constructed. 
 
 Figures 3, 4, and 5, are examples taken from the works of Sebastian 
 Serlio, a celebrated Italian architect that flourished in the sixteenth century ; 
 they are here introduced to show the advantages resulting from a knowledge 
 of Geometry, and to prove how highly its rules are to be estimated, as they 
 relate to the doctrine of proportion. In the example, 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 given height AB 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 from 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 terminate the outline of the vase at bottom. 
 On D and C, with an opening in the compasses equal D o 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 I and w, 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 p q 
 will be found nearly equal to four divisions, and its height equal to three- 
 quarters of one of the same. 
 
PRACTICAL GEOMETRY. 
 
 m 
 
 Figure 4. 
 
 Let a k be the given height of the vase, which divide into 7 equal parts 
 as numbered ; 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 from them, through the centre e, cutting the opposite 
 semi-circumference ; also draw ordinates or lines parallel to the diameter 
 from each of these points, as 2x. 3x. 5x. 6x. 7x. Divide the diameter 
 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 smaller 
 circle at o, o, o, o, o, o. Drop a perpendicular from each of these intersec- 
 tions cutting the ordinates 5, 6, 7, &t p, p, p, p, p, p ; through these points 
 right and left, the curved outline, forming the body of the vase, may be 
 drawn. The lines 2-10, and 14-6, in their progress to the centre, cut the 
 ordinate 3, 13, at f g; which intersection gives the width of the neck : the hollow 
 curve may then be drawn by hand ; the upper moulding may be made one-fifth 
 of the height from i to 6; the moulding A, 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 something more than its height. 
 
 Figure 5. 
 
 This vase although differing in shape, its outline is obtained precisely 
 on the same principles as fig. 3, which makes it here unnecessary to go over 
 the explanation again, further than to observe, that the bottom sweep of the 
 vase is obtained by taking a radius of one division and a half in the compasses, 
 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- 
 come centres for striking the arcs E H and F I ; the neck M N is equal in 
 width to one division, the lipping o p to two of the same, which also gives 
 the width of the 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, fig. ] , Plate 3, being given, to find the shape of the gores, so that 
 when applied on its surface, they 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 I m, as 2 o o, and 1 p p; make 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 k 1, k 2, k 3, on the quadrant from k towards n; 
 and through each of these describe arcs, as at k 1 and 2; proceed and take 
 the measure pp from the triangle within the circle, and transferit on the sweep 
 line k n, as marked/) p; next take the measure o o from the same triangle, 
 and transfer it on the arc at 2, marked oo ; then lines being traced from the 
 apex 3, through these points on both sides, will give the outline or figure of 
 the gore, making a twenty-fourth part of the covering requisite for the 
 whole surfece of the globe. 
 
 Case 2. 
 
 Another method may 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 of the equator ; draw another line A C, 
 at right angles to this line, and set the three divisions as numbered on the 
 quadrant, fig. 1, from E to A, and from E to C; draw A B and C D, at 
 pleasure, each parallel to E F, and make 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 £ F into 
 twelve equal parts, and number them as marked; and, lastly, take an opening 
 in the compasses equal to nine of these divisions, and setting one foot in E, 
 
PRACTICAL GEOMETRY. 
 
 49 
 
 describe an arc cutting the parallelogram A B C D, at the points G and H; 
 and with the same opening on No. 1, describe another arc through No. 10; 
 then on No. 2, describe a similar 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 
 same 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. I, 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, measured round the line Im, and may 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, from north 
 to south, or from east to west, and are called meridians, 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 
 more so to the decorative artist. In bedsteads having dome teasters, the 
 Upholsterer, by these, finds the lines for shaping a pattern or gore, enabling 
 him to cut out his covering, either for the exterior or interior surface, with- 
 out loss or waste. 
 
 The Cabinet-maker is also enabled to get out his veneers for covering a 
 dome from the base to its summit. The decorator is readily able, by the 
 same means 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; d a e re- 
 presenting one quarter, and e d, e c, e b, e «, 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 dome, on another line at right angles to it, as from X to 
 W ; next, divide each of these lines into four equal parts, as numbered, and 
 
 Q 
 
50 
 
 PRACTICAL GEOMETRY. 
 
 draw the lines 11, 2 2, &c. as ordinates, whose intersections will give 
 points through which to draw the curved line of the rib required. 
 
 Fig. B represents the curve line for the rib e b in the plan, and is obtained 
 by the same process. The outlines for the two other ribs e c and e d, are 
 got in a similar 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 dome above the teaster, and becomes the same for every 
 rib ; X X 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 may be obtained, after the same manner. 
 
 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 moulding, C, the rake of the pe- 
 diment. Divide the face of the moulding A B into any number of parts; in 
 this case it is divided into four, and those equal; then from 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 from 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, from the same line ; then through these points of 
 intersection 1, 2, 3, 4, the outline, making the face of the moulding, may be 
 traced. For the return, or mitre of this moulding, if an open pediment as 
 at C, raise a line on the lower fillet, perpendicular to the level moulding, as 
 at F G. From the points 1, 2, 3, 4, in the level moulding at A B, draw 
 lines parallel to B H, intersecting the perpendicular line B i, at 4, 3, &c. 
 Next set the measures 4 4, 33, 2 2, 1 1, from the level moulding, on the raking 
 lines 1, 2, 3, 4, from F G, as 4 4, 3 3, &c. through which points the outline 
 (C F) may be drawn. 
 
K 
 
 GEOMETRICAL FIGURES PLATE 4 
 
PRACTICAL GEOMETRY. 
 
 51 
 
 To find the face mould of a circular pediment. 
 
 Let A B, fig. 6, be the outline of the level moulding, which divide into 
 four parts, as numbered ; from these points describe arcs, parallel to the cir- 
 cular fillets B B and A A : then on B, No. i, raise a perpendicular, cutting 
 the upper fillet in C; and draw C D parallel to the line ofthelevel moulding No. 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 of the pediment, as at No. 2, draw a line (B C) per- 
 pendicular to the curve, cutting the curve lines at o o, o o, from which draw 
 tangents to each sweep, such as o A, o 3, o 2 and o 1. Make C D, No. 2, 
 eq.ual to C D, No. ] ; C e, No. 2, equal to C e, No. 1, and so on for the other 
 divisions, pointed out by the letters : from 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 moulding. 
 
 Geometrical Figures, Plate 4. 
 
 The diameter of a ciradar 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 diameter of the top, and equal to four feet four inches 
 taken from a scale of feet and inches ; proceed and complete the square A B C D, 
 within which from 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 diameter, namely, four feet 
 four inches, the circle circumscribing a triangle of a fit proportion for the 
 block, would require a radius of twenty-two and a half inches, which must 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 diameter 
 N C into three equal parts, as numbered from N to C ; and form an equila- 
 teral triangle, equal to the whole diameter N Q, having its apex, or point, 
 at E; from E draw the line E P through the first division, cutting the arc 
 K N PO at P; from P draw a line parallel to the diameter, cutting the op- 
 posite portion of the arc at 0 ; which line will become the length of one side 
 
b2 
 
 PRACTICAL GEOMETRY. 
 
 of the triangle, ana by the scale be found to measure 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 determined, such width must be set from 
 the apex of each angle on the sides, as from P to k, and P to f y &c. Lines 
 drawn from k tof, It to h, e to g, will give the three canted corners required, 
 and which will be found to be one thirteenth part of the diameter of the 
 top. To produce the curved line from angle to angle of each cant, bisect 
 the line f e at n, and through this point draw a perpendicular to such line 
 indefinite, passing through the centre C ; then on this line, from n, set three 
 inches by the scale for the depth of the sweep to p, and draw the linepe, which 
 bisect also at r $ and continue the line until it intersects C n at d, which n ill 
 become the centre for striking the curve e p f; the distance of which, from 
 the centre C, must 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 made one 
 eighteenth or more, at pleasure. Remark, likewise, that the pillar, or sup- 
 port of the top, from the block, in its lower diameter, exclusive of its 
 ornamental mouldings, must not exceed an eighth of the whole diameter 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 
 or smaller diameter, and reference may then be made to the rule of three, 
 as mentioned in problem 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 
 in some measure, as an ornamental support for pier tables, commodes, side- 
 boards, Sec. in household furniture, the mode of finding its outline may not, 
 in this instance be deemed unacceptable. 
 
 In fig. 2, the console bears a proportion as regards the length to the 
 height, as 1 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 from 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 from E, 
 (equal four parts), which will then be the centre for the eye of the volute : this 
 being obtained, make the circle or eye equal to one division, and construct the 
 iozenge square abed: bisect each side of this square ; then begin with No. I, 
 and strike the arc e f ; from 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 method for working the volute of the Ionic capital. For the smaller 
 volute, divide the line B D into seven equal parts, and give four of these 
 parts to the small 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 from the top, for the centre of 
 the eye, and proceed by the same principles as laid clown for the larger volute. 
 The two volutes being thus obtained, draw a right line from the bottom of 
 the larger one at e, to the extremity of the fourth evolution in the smaller 
 one at k; bisect this line, as at G, from which point raise a perpendicular at 
 pleasure : divide the half of this line e G, into nine equal parts, and set 
 back one of them from G to H; this determines the centre for the compound 
 curve, making the belly of the console. Draw the lines e H and H k y bi- 
 secting each at V and W ; and from these points draw perpendiculars. 
 Make W Y equal to one-ninth of the line e G, and V Z equal to one-seventh 
 of the line H k ; the two curves, e Y H and H Z k, may then be drawn 
 by hand, which will complete the outline of the console. 
 
 This system of proportion is applicable in making any working- 
 drawing from 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 outline, 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 commodes, for in such 
 case it would be found necessary to make the volute of an eliptical form, in 
 order to avoid too much projection. The elegant outline prevailing 
 
 R 
 
54 
 
 PRACTICAL GEOMETRY 
 
 amongst the best remains of antiquity, cannot be too attentively studied. 
 It proves that the attainment of them was more 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 corinthian entablature; but, when re- 
 versed, makes the truss supporting our present moveables of taste and fashion 
 
 To find the proportion, the Top, the 3Iouldings, and Frieze of a Sideboard 
 
 should bear to the whole height. 
 
 t 
 
 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 mouldings, and the frieze, as CD; next divide C D into six equal 
 parts, and give one for the square of the Top, one and a half to the moulding 
 under it, and the remainder 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 moulding 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 the 
 base, give one division EG, for its whole height, which again divide into 
 four, and let one make the moulding, the remainder making the plinth. 
 
 Of Mathematical Instruments. 
 
 Having now brought the Geometry to a close, it remains to give 
 a list of such mathematical instruments as are generally contained in the 
 larger or smaller cases, confining ourselves, however, to a description of 
 those only, whose utility is least known amongst Mechanics. 
 
PRACTICAL GEOMETRY. 
 
 55 
 
 These cases contain, first, a pair of compasses, 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 compasses or dividers: 
 the small bow compasses : the drawing pen, having a steel pointer that screws 
 in and out of it : a brass semicircle or protractor : the ivory plain scale ; a 
 sector ; and parallel ruler. 
 
 The compasses with the shifting leg are used in drawing circles and 
 arches of larger dimensions than can be performed with the small bow com- 
 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 many lines converge, and are required to be 
 drawn. 
 
 The protractor is a semicircle 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 Geometry. 
 
 Construction of Scales, &c. 
 
 The scale of feet and inches, or plain scale, jig. 1 . 
 
 This scale is used in making drawings of pieces of furniture, or other 
 objects, that require to be drawn smaller than the objects themselves really are '> 
 or otherwise, for making a design on a small 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 smaller 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; from 
 b, draw the line b d, at right angles to a b, on which set off as many 
 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, 
 us marked on the line a b, draw lines parallel to b d, and raise the perpen- 
 diculars k I, 1 m, 2 n, dc, numbering them progressively from k: the divi- 
 sion b k representing one foot, must he divided into twelve equal parts 
 for the inches, after this manner; divide a I into two equal parts, as at G, 
 and draw the lines b 6 and k 6 ; by this means each half will be accurately 
 divided into six equal parts, as numbered 1, 2, 3, 4, 5, 6, &c. In using this 
 scale, if you require one foot one inch, set your compasses on the line above 
 1, as at X, and open them to 1 on the same line, in the inches; you will 
 then have a measure 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, making the 
 foot. 
 
 The scale of tenths, and its construction, jig. 2. 
 
 Proceed and set up ten equal divisions on a perpendicular line f e, and 
 through these draw lines, each parallel the one to the other; on the line fh 
 set off* any number of divisions you may require, which may represent feet or 
 any other measure ; from these raise perpendiculars, as i k, I m, n o and 
 h g ; next divide e k into ten equal parts, and drop a perpendicular from 
 each; draw the inclined line 1 i, and lines from 2, 3, 4, 5, 6, 7, 8, 9 and 10 
 parallel to it: the parallelogram f e k i, will then be divided into 100 equal 
 parts, called tenths or hundredths. The divisions I n, nh, may 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 afoot, begin by placing your compasses on 6, in the line / m \\ Inch is 
 the fifth division), and extend them to the fifth division on the same line in the 
 parallelogram f e k i ; you will then have the measure required. If the divi- 
 
PRACTICAL GEOMETRY. 
 
 57 
 
 sions i 1,1 n,n h were inches, then the divisions in f eki, would be the tenths 
 or hundredth of such inch. It is, therefore, evident by this scale, that the 
 foot, inch, or yard, may 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 instrument of ivory, its two limbs 
 opening like the compasses, with corresponding divisions marked 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, Jig. 3. 
 
 Draw a right line B C, and make the line B A perpendicular, or at 
 right angles to it; make B C and B A each of equal measure, and draw the 
 hypothenuse A C ; this will then become the chord line, and is to be 
 divided after the following manner ; — on B, with the radius B C or B A, 
 describe the arc A C ; divide this arc into nine equal parts, which number 
 from the first division over C, 10, 20, 30, and so on to 90; the segment, by 
 this means, becomes divided into 90 degrees ; each of which may again be 
 subdivided for the halves. Proceed and set one foot of the compasses in C, 
 and opening the other to the division 10, describe an arc cutting the line 
 A. C at 10 , this will then be the first division on the line of chords ; in the 
 same manner lay down all the other divisions from the segment, on to the 
 chord line, and likewise for the half divisions, as numbered 5 , 16 , &c. &c. 
 he 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 
 measures on A C, from C, and transfer them on the line I m, fig. 4, from 
 I, until the whole are put down, you will then have a regular scale o* 
 chords to work from. 
 
 s 
 
58 
 
 PRACTICAL GEOMETRY. 
 
 APPLICATION. 
 
 Suppose an angle of 30 degrees is required to be laid down; take 
 the measure 60 from 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 compasses in o, de- 
 scribe an arc intersecting the other at p, and draw n p; then will 
 p n o be an angle of 30 degrees. The number of degrees contained 
 in the side of any polygonal figure being given, the circle circumscribing 
 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 mea- 
 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 many sided 
 figure. 
 
 Line 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 au 
 equal number of parts, and is thus performed. Let a a be a line that is to 
 be divided into seven equal parts ; take the measure of this line in the com- 
 passes, and setting one foot on the sector, fig. 6, at the division marked 7, 
 open the other limb of the sector until the opposite point 7 coincides with 
 the opening in your compasses, in which situation let the sector remain ; 
 then set one foot of the compasses on the division 1 on the sector, aud close 
 them until they meet at the opposite point 1 ; this measure will then be one- 
 seventh of the line a a. If a line of the same length (b b) is required to be 
 divided into eight parts, then with such length in the compasses, set one 
 foot on the division marked 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 1, 1 will be the measure 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 limb. 
 
 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 marked 6 on the sector, and open it until the 
 compasses touch the point 6 on the opposite limb ; thus let the sector re- 
 main; next proceed and set one foot of the compasses on the division 
 marked 5, and contract or open them until they reach the opposite point 5 
 on the instrument ; this measure in the compasses 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 means. The Geometrical square may be constructed by the 
 same process, for taking the measure 4, 4 from 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 made 
 to turn or open upon a centre, moveable in a grove cut through the 
 greatest part of their length; to this centre, on each limb 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 limb 
 of the compasses, and sometimes on both. There are the line of lines, 
 the line of circles, or otherwise polygons to be inscribed in circles, 
 on one limb ; 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 limb 
 having the line of lines and of circles, as being the most 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 1 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 compasses, 
 the distance between the points of the longer legs will then be twice the 
 distance between those of the shorter ; and thus any line may be bisected 
 or divided into two equal parts. If the index be placed against 3, and the 
 compasses 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 same 
 manner for any number of parts under ten. 
 
 The numbers marked 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 from six to twenty. Thus if the index be placed at 
 6, the points of the compasses 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 compasses 
 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 measure 
 the side of an heptagon; again by placing the index at 8, and opening the 
 compasses, the longest points will contain the radius, and the shortest points 
 divide the circle in eight equal parts, and inscribe an octagon : the same 
 method must be made 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 them useless in this place, and for 
 which reason, the compasses are shown in the plate with the lines marked 
 only on one side. 
 
 The parallel ruler has been fully described with its use in Problem 16, 
 Plate 11, Figure 1. 
 
PRACTICAL 'GEOM1T1T, 
 
PERSPECTIVE. 
 
 INTRODUCTION. 
 
 Perspective is the science or art of projecting all objects on a plane 
 surface, giving them 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 may be regarded as the offspring of Geometry; 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 may be classed or comprehended under two 
 heads, namely, Theoretical and Practical ; the first of which, demonstrates 
 the nature and truth of its propositions ; the second, applying them 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 me- 
 chanic. To understand it theoretically, requires an intimate acquaintance 
 with Geometry and Mathematics ; 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 memory 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 mind fitted for such a course 
 of study : we shall therefore confine ourselves to the practical part alone, 
 
 T 
 
62 
 
 PERSPECTIVE. 
 
 and consider it more as an art than a science without omitting to mention 
 and account for, in a familiar way as occasion may require, that which other- 
 wise would belong to the theory. Neither is it intended to write a treatise 
 for those conversant in mathematical 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 information in plain and familiar 
 terms, endeavouring to reduce a science, that has hitherto been considered 
 difficult of attainment, easy in comprehension. All material objects become 
 perceptible to us by rays of light continually passing in right lines from all 
 parts of them, entering the pupil of the eye; and diverging under the same 
 angle until they are seated on the retina, a membrane or net work covering 
 the back part of it, and in a reversed position. How this impression is again 
 conveyed to the sensorium or brain, giving it its original representation, 
 has eluded the researches and reasoning faculties of the most scientific men; 
 every thing already advanced amounting only to conjecture. Those who 
 may be desirous of entering into the nature of vision, applicable to this sub- 
 ject, may 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 almost all countries; but particularly so in Italy, Germany, 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 
 thesame system pursued by us in treating on Geometry ; beginningour 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 in 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 recommended previous to entering on the prac- 
 tice ; as tending very materially to lessen the difficulties that present them- 
 selves to the student in the commencement of this study; and make 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 
 familiar to the understanding, accompanied at the same time with such dia- 
 
PERSPECTIVE. 
 
 63 
 
 grams and remarks 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 mathematician, as for the information of the untaught, 
 it would become foreign to the present purpose, and rendered in this trea- 
 tise unnecessary ; a great deal of the science being more a matter of specu- 
 lation than positive use. Those who wish to enter fully into the theory may 
 consult the works of Dr. Brook Taylor, Hamilton 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 manner by Dr. Brook Taylor; who is supposed 
 to have drawn his principles from a work written by one Guido 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 some point in the horizontal line; such point 
 being gained by imagining a plane to pass from the eye of the spectator 
 parallel to the side of an original object, until it cuts the picture. These 
 principles have since been greatly improved 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 mechanics to whom our 
 treatise is addressed. To these the knowledge of Perspective is of the 
 greatest importance, enabling them to show by a slight but spirited sketch, 
 a model of the article they design to make. In taking orders, they will 
 find in this, a real advantage over others that have not the same acquire- 
 ment. That the subject has hitherto been too mathematically 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 comprehension of humble capacities. A great advantage also arises 
 
64 
 
 PERSPECTIVE. 
 
 from a knowledge of this art, insomuch that any design can be made and 
 forwarded into distant parts, either at home or abroad, and have the same 
 effect as would be produced by a model. The master Cabinet-maker, or 
 foreman, 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 same reason the workman should not be deficient, as in this instance 
 he would he would more readily enter into the designs of his employer. If 
 therefore our explanations do not abound with technicals, but are confined 
 to plain and simple terms, it is so done to render the matter clear to the 
 student. Thus much for introduction; a considerable deal more remains 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 
 same sheet; the consequence has been a crossing or mixture 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 of Sight — Is that point imagined to pass from the eye of the 
 spectator, in a direct line, and at right angles to any transparent plane, 
 placed between him and the object; intersecting such plane in the horizon: 
 such is the point s, Plate 1, Diagram I : also s in Diagram 2, and D in 
 Diagram 3, where d ef g 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 of it. 
 
PERSPECTIVE. 
 
 65 
 
 Station Point — Is a point on the ground plane, generated by a perpen- 
 dicular line dropt from the eye of a spectator to his foot; such is S, in Dia- 
 gram 1, where the line D D may be considered as the site of the transparent 
 plane, and s the point of sight as explained above. Also G in Diagram 3, 
 where the point is shown as dropped from the spectator's eye to his foot. 
 
 Point of Distance — Is a point placed on the horizontal line right or left 
 from the point of sight, denoting the distance from the spectator to the 
 centre of the picture or transparent plane : such is S s, Diagram 1, placed 
 from s to D, right and left : s D, Diagram 2, and S D, Diagram 3, where 
 each represents the space from the spectator to the plane of the picture. 
 
 Directing Point — Is a point generated by aline passing direct from the 
 side of any original figure, and intersecting the plane of the picture on the 
 ground. DEFG, (Diagram 4,) and HKL M, (Diagram 6,) are both original 
 figures, with the line of the picture, placed above each of them ; in such case 
 a line supposed to pass from the side E F, (Diagram 4), and the angular 
 point L, (Diagram 6,) would intersect each of these lines at the points I and I; 
 such points would become directing points. A perpendicular line raised 
 from either of these points would constitute what is called the Geometrical 
 line; as D I, (Diagram 4). 
 
 Vanishing Point- — Is a point passing in a direct line from 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 ; MH and H K, of the original figure 
 H K L M. 
 
 In Diagram 5, s represents the station point, and S its distance set 
 up from the horizon. Van, Van, are the vanishing points of the sides 
 L K and L M, of the figure in Diagram 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. 
 
 r 
 
66 
 
 PERSPECTIVE. 
 
 In Parallel perspective the Point of Distance serves as a diagonal point, 
 because it passes in a line from the eye of the spectator at an angle of 45 
 degrees. This point is used for obtaining the mitre lines for all right angled 
 figures in perspective, whether parallel or inclined to the Picture; Diay, 
 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 them 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 Hue C D. 
 
 This is considered the principal line in perspective delineation ; as regu- 
 lating from its fixed and determined position, all other vanishing lines ; 
 we shall, therefore, on this account, be more particular in explaining it ; 
 the proper understanding of which will very much assist the student IB 
 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 inform 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 E F G, 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 admit: the space 
 from F to H may be considered as one meridian or twelfth part of its cir- 
 cumference, containing 30 degrees or 2085 English miles. If a spectator 
 be stationed at H, a tangent I m, drawn through this point will be his 
 horizon: if piaced at F, op will then become his horizon: a line drawn 
 
PERSPECTIVE. 
 
 67 
 
 at right angles to any one of these tangents, would pass through the 
 centre of the earth, and consequently become the centre of gravity to such 
 spectator. Suppose the spaces i H and H k, each to represent the eighth 
 part of this meridional space ; they will each measure the eighth part of 30 
 degrees, or 260 miles and 5 furlongs. Now although this space of ground 
 is literally a curved line, the angle made by the tangent or level line / m, 
 passing through H, is so small in this number of miles as to make the seg- 
 ment imperceptible, and appear to a spectator travelling over the whole, or 
 a part of it, a straight line. If therefore the earth's curvature is imperceptible 
 even in 260 miles, it must be less so in a smaller portion, so that a traveller 
 continually walking over its surface, would find himself 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 
 from thence continued to the sphere of the heavens : thus in fig. 3, if I ima- 
 gine myself placed at f, 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 aty", likewise the circle 
 M becomes the Rational Horizon of the figure at (g). The earth is so small 
 in comparison to the magnitude of the sphere of the 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 may, for the sake of 
 comparison imagine the circle H, which in this diagram represents the 
 figure of the earth, to represent the sphere of the 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 diagram, taken from an 
 eminent writer on Astronomy, explaining it nearly in his own words. Let 
 
G8 
 
 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 /* o ; the distance between these two planes is G A, 
 (equal the semidiameter of the earth) which is measured in a great circle of 
 the sphere 01 the heaven, by the angle i G e, or by the arc i e. This arc 
 in so small a circle as H i, &c. would amount 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 small 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 m, Sec; here the semidiameter of the earth G A, 
 measured in this circle, would amount to fewer degrees : for the arc K m. 
 measures a less number of degrees in the circle P K m, than does ie, in th< 
 circle H i e, 8cc. thereby making the angle K G m, less than the angle i G e. 
 But this angle may amount also to many degrees or minutes, and consequently 
 be large enough to be measured 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 o, 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 scheme, 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 measured by less angle. We may suppose the 
 sphere of the heaven so large, that the angle which should measure the 
 distance of the sensible from the rational horizon would amount only to a 
 few minutes, or perhaps not so much as one second of a minute, and conse- 
 quently too small to be measured. This in fact is the case, as mentioned 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 no sensible 
 magnitude. 
 
 The Visible 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 imperceptible. 
 
PERSPECTIVE. 
 
 69 
 
 Suppose the circle S, fig. 4, to represent the earth; if a spectator be 
 stationed at n, the line e d passing through his eye would be his Visible 
 Horizon ; a b his Sensible, and I m his Rational Horizon. The same applies 
 to the figure placed at R, as denoted by the lines e f, &c. Thus much in 
 explanation of the Horizontal line. 
 
 Vertical Line ; this is a right line drawn from 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 commonly called the central line of the 
 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 become 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 H, 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 e f ; V V, their vanishing points being there seated. 
 
 Station Line — Is a line 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 line. If the picture be placed before the spectator at S, in the 
 inclined position m b ; S e, would then become the Station line. 
 
 Planes. 
 
 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 Geometry, page 10. 
 
 x 
 
70 
 
 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 is 
 drawn may be called the plane of the picture. 
 
 A plane may 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 importance : since the boundaries of all solid bodies, 
 whether rectilineal or curvilineal, constitute planes. 
 
 There are in Perspective five elementary 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, inasmuch as all rays from 
 the object to the eye of the 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 remotest 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 rectilinear or curvilinear, parallel or inclined to the picture. 
 
 4. Directing Plane — is a plane perfectly upright ; imagined 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 (he geometrical heights of objects are supposed to be seated. 
 
 In this line, which terminates the plane of the 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 with the 
 breadth of the other, in proportion as they recede from the eye and approach this line. 
 
PERSPECTIVE. 
 
 71 
 
 5. Vertical Plane. This plane is also perfectly upright, and 
 imagined to pass from 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 may 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 er 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 parallel to the Plane of the Picture G H E F. 
 
 5. I K L M ; denotes the Vertical Plane ; called likewise direct, as 
 passing immediately 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 L M, forms an inclined 
 plane, vanishing into the vertical line V S. It may also be considered as 
 the folding flap of a writing table. 
 
 Fig. 11, represents a box, with the lid or cov r er as turning on its hinges 
 or centre N O, generating thereby a plane, taking the form of a quadrant, 
 as denoted by the letters TPRU. According as the top is more or less 
 raised, so it would generate various inclined planes ; as shown by the letters 
 P Q N O, and RS NO. 
 
 Visual Rays — are right lines drawn from the angular corners or, 
 extremities of an object, to the spectator's eye; cutting the plane of the 
 picture, and forming thereon its image or perspective representation. 
 Example : X and W, (Fig. 12), are original objects, seen through the trans- 
 parent plane abed, by the spectator stationed at S T. Lines drawn 
 from 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 abed, 
 which are denoted by^andw; A A, making 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 means 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 will appear ; 
 making the angle more or less extended in proportion to its distance. This is 
 shewn in the diagram Fig. 13 — where the line F F, by the visuals makes 
 a larger angle than the line B C, as measured on the semicircle D E. The 
 other lines marked F F, F F, &c. each show the variation of the angle, as 
 they recede more or less from the eye. 
 
 Pyramid of Rays — are visuals drawn from every extreme point of a 
 rectilineal solid to the eye; thereby forming a solid angle, composed of 
 several plane angles; making together the form of a Pyramid : such are the 
 rays drawn from the several extremities of the object y, Fig. 14, to the eve 
 at S, making a similar figure (y) on the plane Z. 
 
PRACTICAL PERSPECTIVE. 73 
 
 Cone of Rays — are visuals or right lines drawn from any globular or 
 cylindrical object ; so called from the rays passing from each extreme or 
 tangent of its surface towards the eye, and forming thereby a figure resem- 
 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 removed from it, so that the object 
 shall appear to the eye under the most agreeable and natural point 
 of view. 
 
 There is a difference between the original object and its perspective 
 representation, although the one is often mistaken for the other. If we wish 
 to see an object in its truest and most natural form, we must place ourselves 
 in a line parallel to the front of it, or in other words directly facing it ; 
 for the image formed on the retina (a net work covering the bottom or 
 back part of the eye,) from this position, will approach the nearest in 
 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 more 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 may be infinitely varied. 
 
 In reference to the shape and size of the picture no determined 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 number of objects 
 to be introduced ; the oblong rectangle is in most cases selected, as being 
 
n 
 
 PRACTICAL PERSPECTIVE. 
 
 of a 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 of the 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 from the 
 ground, as in most cases he is supposed to be standing on the Ground Plane. 
 In many instances, it is necessary to adopt or make use of a low Horizon, 
 when we would see the under side of some objects, or projecting members 
 of others more distinctly; such, for instance, as the inside of beds, the soffits 
 of cornices in low rooms, &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 in 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 become 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 resemblance 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 must 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 same to the best advantage: the question is, 
 what position and distance he should take to view it advantageously 
 under such circumstances. It is evident in this case that the picture 
 A B C D, will be seen most to advantage when the axis of the eye X 
 
PRACTICAL PERSPECTIVE. 
 
 75 
 
 is perpendicular, or at right angles to it ; because the picture in this instance 
 will be parallel to the retina or back 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 AB C D, equidistant from 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 determined ; 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 more minute parts cannot be distinguished. Let S, be the seat of 
 the eye in the picture, ABC D • if the eye be removed from 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 would 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 atS, is not two-thirds of the 
 distance S X, and will therefore be a much better boundary for its limits, 
 as seen at cl 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 ato. Again admit the extreme distance of the picture 
 from the eye not to exceed the distance K S or SL; (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 image 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 from its centre. Let AB C D, fig. 2, represent a 
 picture and S its centre; the distance S A, set on to X, is the shortest 
 to be taken. Instead therefore of making this the distance of the picture, it 
 will be more advisable to make 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 
 of the eye be directly in the 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 more advisable to place the eye at S, rather than at *. 
 It must here be remarked 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 extremity 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 b, being known, and placed parallel to the picture. 
 
 Let GG, 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 commonly called the Ground line.) Let H H, 
 represent the horizontal line ; (its height from the ground line in this diagram 
 being assumed;) S, the centre or point of sight; and D D, the points of 
 distance, taken at pleasure and set equally right and left from S. Thus far 
 being arranged, suppose a b, to measure 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 from « or b, drawn to the point 
 of distance D, will intersect the visuals, a S, and b S, in the points d and c ; 
 
PERSPECTIVE . J 
 
 Fid I. 
 
 D 
 
 & 
 
 A B C F H K 
 
 LONDON Published toy JONES feC? April e 1826- 
 
PRACTICAL PERSPECTIVE. 77 
 
 V 
 
 through these intersections draw a line d c, parallel to the base line. 
 This will complete the perspective representation of the figure abed. The 
 lines b D, or a D, are commonly called diagonal lines ; because they pass 
 through the ODposite corners of the perspective square abed. 
 
 Figure 2. 
 
 To represent a pavement of squares in perspective, two of their sides oeimj parallel 
 
 to the picture. 
 
 I et GG, represent the ground line as before ; H H, the horizontal 
 line; S the point of sight; and D, D, the points of distance. Take the 
 measure of one side of a square, and repeat it any number of times on the 
 ground line from a ; in this diagram seven are shewn : from 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 pavement will be completed ; as shewn by the black and 
 white chequers. 
 
 Figure 3. 
 
 To represent a pavement of squares, having lozenges or rhombs, with a border 
 
 between each square. 
 
 First proceed and set off the width of the border on the ground 
 line, from a, (in this diagram left white :) next set off the side of a square, 
 (here shadowed black;) and again repeat the border, and so on for as many 
 squares and borders, as you may require. In the present example there are 
 three squares, and four white spaces, making the borders; to obtain the 
 perspective representation of these, and their distance from each other, as 
 they recede from 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 b b, of the square A ; which Diagonals 
 would tend to the point of distance ; for which reason the 
 sides of the lozenge would likewise tend to the same points : 
 for all lines parallel the one to the other and amongst 
 themselves would vanish into one and the same point. 
 
 Figure 4. 
 
 To find the representation of squares placed at different distances from each 
 other, their sides being parallel to the picture. 
 
 The horizontal line H H, and ground line G G, &c. being assumed as 
 before, let K G, be one side of the square to be represented, the depth of which, 
 K M, may 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 the 
 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, may be obtained as before directed. Another 
 method may be adopted for obtaining the side of a square, or the depth of 
 any parallelogram. Set the measure of the front side A B, upon the ground 
 line G G : if the figure is to represent a square, then the measure 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, must be drawn. If 
 the depth of the figure be equal to twice its length ; the measure B C, must 
 be repeated from C to F, and cut ofl'on the visual B S, at F; the depth in 
 this case will be represented by the length B F : If three times its length, 
 
PLrLXXXIX. 
 
 PERSPECTIVE . 2 
 
PRACTICAL PERSPECTIVE. 
 
 79 
 
 the same measure may be repeated from F to H, on the ground line, and cut 
 off on the visual B S, at the point H, as before directed. This method 
 may likewise be adopted for representing the distance of one figure from 
 another, as shewn by the tinted squares A B d e, and FG HI; likewise 
 any given depth may be obtained by this process. 
 
 Plate 2. 
 Figure 1. 
 
 The Diameter of a 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 FGH; next circumscribe this circle by the square A B C D ; 
 from the corners of which draw the diagonals A C, and B D, intersecting 
 the circle's circumference in the point abed; -these with the four central 
 points E F G H, (produced by the two diameter lines E G and F H,) will 
 make eight divisions on the circle's circumference, and become so many points 
 through which it would pass. 
 
 It is necessary in order to obtain the perspective representation of the 
 circle, to find the perspective situation of these points on the ground plane; for 
 through such points the outline of the circle (forming an elipsis) must be 
 traced. 
 
 The Ground and Horizontal lines ; the points of sight, and distance 
 being determined; 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) by the diagram, Fig. 1, Plate 1. Through the axis c, draw 
 the lines e f and g h ; intersecting the sides of the square at the points e,f g, 
 and h : these will become the four tangent points. The four other points 
 on the diagonals A C and B D, may be obtakicd by transferring the points 
 a and b, Fig. 3, upon the line A B, Fig. 1 ; as denoted by the letters a and 5; 
 from these points draw lines tending to S, which will intersect the diagonal? 
 
80 
 
 PRACTICAL PERSPECTIVE 
 
 A C and B D, in i, k, I and m. Through these eight points on the ground 
 plane, the outline of the circle must be traced. 
 
 This method of obtaining the representation of a circle by eight points 
 will answer for any circular figure of a moderate size; but for circles of larger 
 proportion, sixteen and sometimes twenty or more points are made use of. 
 
 Figure 2. 
 
 TJiis Diagram shews the same Circle in perspective, with the addition of a 
 Triangle in the centre ; which may represent Hie plan of a block for a Loo 
 Table ; the Circle representing the top. 
 
 In making the plan, first find the proportion the equilateral triangle 
 e f g, (Fig. 3), should bear to the circle, by Fig. 1, Plate 4, Geometrical 
 Figures ; and the mode of constructing it by prob. 8, Practical Geometry. 
 
 This being done, proceed and draw the circle in perspective, by the 
 method adopted in the preceding diagram. For the triangle, transfer the 
 distances F e and F 7, in the plan, upon the line A B, at m and n, as shewn 
 by the dotted curved lines ; and square these measures 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 rayy* g, at t 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 line a b, (Fig. 2,) at 
 n and n ; from 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 io 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 i p, to the horizontal line intersecting 
 it at V and V. The canted corners are found by transferring the distance 
 F h in the plan, (Fig. 3,) on to the liue A B, from F to o ; which must 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 f g at k ; a line drawn through 
 this point and terminated by the sides, i o and i p, will give the represen- 
 tation of the canted corner A, in the plan; for the corners i and k, draw 
 
PRACTICAL PERSPECTIVE. CI 
 
 lines from q and r, tending to V and V, until they intersect the side op, in 
 * 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 of a 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 comprised in every hexagon, whose sides are equal ; 
 each angle contained therein will measure 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 much, 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 determined, the following process for finding the Vanishing points 
 may be adopted. From 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 measure an angle of 60 
 degrees, and consequently measure the side of an equilateral triangle. 
 Through the divisions 1 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 a b c d ef,by problem 22, 
 Practical Geometry, commence by drawing the ground line G G, upon 
 which transfer the parallel side e rf, as at ED; from E and D, draw 
 
 2 A 
 
Si) 
 
 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 aline 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 complete the perspective repre- 
 sentation of the original figure, as shown by the tint. 
 
 Fig. 2, is a Diagram which shows how the preceding example may be 
 applied in various ways. It represents the interior of an apartment, 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. From the centre of the ceiling is sus- 
 pended a lantern of the same figure ; the Vanishing points V, V, of this 
 Diagram are laid down from the centre S, at double the distance of those in 
 fig. 1 ; the points of distance after the same ratio. The spaces e d, e d } e d, 
 refer to the original measure of the side ed, fig. I, being taken at one-fourth 
 the size. The mode of representing this floor of Hexagons will be shown 
 more at large in the following Diagram. 
 
 To represent a floor of Hexagons in parallel perspective. 
 
 Suppose G G, (Fig. 1, Plate 4,) to be the ground line ; H H, the Hori- 
 zontal line (the height of which, in this example, 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 example. Divide the Diameter, d f, of the Hexagon into two equal 
 parts, one of which will be the measure of one side. Take this measure in 
 the compasses, and repeat it along the lineG G, right and left of the centre 
 e, as often as the width or length of the floor will allow. From 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 of these 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. 
 
PL . LXXVII . 
 
 L>,«lon Published hv „W«i:C?Ncivr7 IP.'.'" 
 
PRACTICAL PERSPECTIVE. 
 
 83 
 
 Through these intersections, draw the lines I m, n o, &c. parallel to the 
 Ground line : these will receive and limit the inclined sides of each Hex- 
 agon, as at a k, c k, k n, k p, &c. by this means the whole will be completed. 
 The figure of each Hexagon must 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, 
 and the remaining 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 determined, this 
 must be set on the Horizontal line, right and left of the centre C, as at D D. 
 These then become the Vanishing points for the inclined sides, 
 
 Having proceeded thus far and constructed the figure of the octagon 
 ab c d, f g h, by problem 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 diagram, fig. 1, 
 plate 1. From 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 from 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 from 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 from the point J) by the point of distance D, will give the representation 
 of the opposite side to 6 c; also a line thrown back from e, by the opposite 
 point of distance, will give the representation of the opposite side to ah ; 
 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 measure of one side as directed in 
 problem 25, Practical Geometry, must be adopted; as shewn in the plan by 
 the divided line x x. 
 
84 
 
 PRACTICAL PERSPECTIVE. 
 
 Fig. 3, shews the method of representing one octagon within another 
 by means 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 mitre lines from each 
 corner of the octagon must be drawn. To obtain the smaller octagon, square 
 up its diameter from the plan upon the line G G, as at r s. From these points 
 draw visuals to C, which will intersect the mitres from d, c, g, and h; at I:, 
 m, p, and q; this will give the representation -if the two sides, I m and qp, in the 
 plan. The other sides are obtained by throw ing lines from the points I, m, p, 
 and q, by the points of distance terminating them on the different mitre lines, 
 as will be seen by inspection of the figure. 
 
 To represent 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 diameter of an Octagon 
 in the compasses, as a b ; and repeat it along the Ground line G G, as often 
 as occasion may require. From these divisions a, b, c, d, e,f, so placed, draw 
 visuals tending to the centre C. A line drawn from a or f, to the point of 
 distance D, will intersect these visuals in the points x rx, &c ; through these 
 points draw lines parallel to the Ground line G G, and the whole square will 
 be perspectively divided into smaller squares. Next find the centre of each 
 square on the Ground line, from 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 
 p p, pp,q q, q q, &c. which will give the measure of the sides, oo, o o, &c. on 
 all the distant squares. Lines drawn from 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 
 of the square. 
 
PRACTICAL PERSPECTIVE. 
 
 85 
 
 Plate 5. 
 
 The plan and Elevation of a Cube being given, to represent the same in parallel 
 
 Perspective. 
 
 ABCD, No. 1, Fig. 1, is the given plan of the cube : G G, the line 
 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 R 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 line) from b to c. A line 
 drawn from c to the point of distance D, will intersect the visuals a S and 
 b S, at d and e ; through these points draw the lines e g, and f d, which will 
 give the perspective plan of the cube ; and likewise its distance from the 
 directing plane. From 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 Geometrical line, and on 
 which line all original heights must be placed. On this line from 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 I. From k draw the parallel k w, intersecting the 
 perpendicular raised from f } at m. From w, draw the Visual w n ; and 
 from I draw the parallel I ?n, terminated by the former at m : this will 
 complete the representation of the Cube. 
 
 The Parallellopiped or Prism op q v t s, being under the same Visuals 
 with the Cube f d g Im w, but of greater height, its seat is obtained by set- 
 ting off its Distance from the directing Plane, upon the Ground line from b to 
 W: a line drawn from this Point will give the seat of the Prism at o p y 
 and its depth by the intersection at r. Parallels drawn from p and r, and 
 terminated by the Visuals, will complete the plan. From 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* 
 
 2b 
 
86 
 
 PRACTICAL PERSPECTIVE. 
 
 section with the Perpendiculars at t and v, will determine the height of the 
 figure, which is completed by drawing a parallel from t, to the perpen- 
 dicular line o s. 
 
 To find the Perspective representation of a Cylindrical Solid. 
 
 Let AB CD, No. 2, Fig 2, be a square inscribing the circle EFGH, 
 as making the plan of the Cylinder. 
 
 Transfer the Diameter A B of the square to the ground line, as directed 
 in the preceding figure ; and obtain the Perspective plan of the square and 
 Cylinder, by the Diagram, Plate 2. Erect Perpendiculars from the points a 
 and b, in the perspective square abed; 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 to the 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, equal to that on the Ground Plane. From i 
 draw the parallel £ k. From i, and k, draw the Visuals im and k Z, intersec- 
 ting the Diagonal lines, £ /, and k m y at l y and m; through which, draw the 
 parallel m I, which will complete the upper square. The Diagonal Points 
 may be obtained by squaring up the same points from 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. From the extremities n and p, of the Ellipsis, drop the 
 perpendiculars n e, and p g ; this will complete the Perspective represen- 
 tation of the Cylindrical Solid. Such figure is called the Frustrum of a 
 Cylinder and sometimes a truncated column. 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 t at s ; this will determine 
 the height of the column. Through s, draw a parallel, s v, terminated at v by 
 the perpendicular from t ; and complete the square with the perspective 
 circle contained in it as before described ; this being done, join the extre- 
 mities of the two Ellipses, as in the cylindrical solid placed 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 mouldings will have for their outline the 
 curve of the ellipsis 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 line, whether above or below it, will become more and more flattened, 
 until it falls into the horizon itself ; in which case it will become a straight 
 line ; as may be seen in figure 4, wherein C d, the uppermost plane, is seen 
 more fully than the plane Ce; and again C e, more plainly than.C/ 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 E F G H I K L M. Transfer the side A B of the 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) of the Octagon from the plane of the picture, from Y to p ; 
 this drawn to the distance D will intersect the Visual Y S, at a ; draw the 
 parallel a b, and complete the square a b c </, as before directed : next find 
 the perspective plan of the Octagon, by the Diagram, fig. 2, plate 4 : from 
 each angle of the Octagon so obtained, raise perpendiculars; also the 
 Geometrical line Y P, from 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 b n at o, will give the perspective height 
 of the figure. A parallel drawn from o and intersected by the perpendiculars 
 e and/, at q and p, will give the parallel 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 Prism V, being under the same Visuals, namely Y S, 
 &c. is obtained by the same process. Its seat on the ground plane is 
 
88 
 
 PRACTICAL PERSPECTIVE. 
 
 governed by that of the cylinder (before explained). Its height is deter- 
 mined by placing it on the original line Y P, as at r, in the same manner as 
 that of the preceding example. Remark, 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 mansions; all the lines that are below the Horizon 
 will answer to the concave part of the 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 same applies to the octagon ; for 
 being circumscribed by a square, it is subject to the same 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 measure of one side of the cube to be represented ; 
 and B C its distance from the directing plane. Proceed and complete the 
 Perspective plan a b c d, 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 
 b d, at the points 1, 2, 3, 4. On C erect a perpendicular C G; this will 
 become the Geometrical 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 of the top at the point 6; (the nearest to the spec- 
 tator.) From 6 draw Visuals tending to the point of sight S, and where 
 they intersect the perpendicular raised from 3, you have the projection on the 
 returning side, as at 7. From 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 Diagram 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 same 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 
 the projection in this Example, draw the Diagonals Y V and X Z, which 
 Diagonals prolong at pleasure : on the Diagonal at Y, place the projection 
 o, 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 p r. From o draw the parallel o q, 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 of the pyramidal 
 roof, from Y to V; which draw to the point of distance D, and where it 
 intersects a perpendicular raised from the centre or axis C, of the square 
 X Y Z V, will determine the perspective height at T. Lastly draw the 
 lines T p, T p, and T p, which will complete the figure. 
 
 The cornices of rooms, and the projecting members of all objects 
 seen above the Horizon may be obtained from this diagram. The square 
 figure U, may 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 same, and ob- 
 tained by the same means as that of No. 1, fig. 2 j with the addition of a 
 projecting member 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 same 
 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 figure. Next, take little more than l-7th of the line a b ; that is, run 
 the compasses along the line 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 
 from a and b to x and x ; which convey by the point of sight S, on to the 
 diagonals a c and b d, as numbered 1, 2, 3, and 4. Next draw the diameters, 
 5 6, and 7 8 : through these eight points the circle forming the projection 
 may be traced. The under curve is obtained first, by dropping perpen 
 
 2 c 
 
90 
 
 PRACTICAL PERSPECTIVE. 
 
 diculars from a and b, equal to the given thickness; through which draw 
 the parallel line o o, which line will receive the diagonal points x, x, at 10 
 and 11 ; also the central point 7, at 9: these draw to the point of sight 
 S, and where they intersect perpendiculars dropt from 1,2, 5, and 6, will 
 give so many points through which to trace the under curve. The pro- 
 jection over the cylinder No. 2, is obtained by the same 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, 
 from I to m. From I and m draw Visuals to the point of sight S, and from i 
 draw a line to the point of distance D : its intersection with the Visual 
 drawn from /, will give the seat of the front line of the block at o ; from 
 which draw a parallel line, intersecting the visual from m, at p; this will 
 give the Perspective width of the square of the block. From o and p, raise 
 perpendiculars ; next set up the thickness of the block on the Geometrical 
 line t X from itoq; this likewise draw to the point of distance D; and 
 where it intersects the perpendicular raised from o, at a, will determine 
 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 Prism, draw mitre lines from 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 line 
 a b, at 1 and 2 (in this example equal to one side of the octagonal block:) 
 this draw to the centre S, until it intersects the mitres 7, 8, 3 and 4, at 1 1, 12, 
 1 5, and 16, which will give the two sides parallel to those marked 7 8, 
 and 3 4, on the block : the remaining sides are got by throwing lines back 
 by the points of distance D, D, from 11, 12, 15, and 16, intersecting the 
 corresponding mitres at 9, 10, 13, and 14; from which intersections, the 
 two sides parallel to 1-2, and 5-6, may be drawn, completing the perspective 
 plan of the prism. From each exterior angle visible to the eye, raise per- 
 pendiculars, as in the prism V, fig. 3. Next set up the height and thickness 
 
PRACTICAL PERSPECTIVE. 
 
 91 
 
 of the top upon the Geometrical line i X, as at e ; from which draw parallels 
 at pleasure. Likewise square up the given width from k (on the Ground 
 line), intersecting the parallel drawn from e at f ; and complete the square 
 e fg h, as before directed. Lastly, set off the given measure of the canted 
 side, from e to rand from f to s ; which convey on the line above by perpen- 
 diculars. Visuals drawn from these to the centre S, will give the measure 
 of each cant on the back line hg, (of the square,) at t and v. Lines thrown 
 back by the points of Distance from these intersections (t and v,) will give the 
 four canted sides of the figure, as may be seen by inspection. By this 
 example we are taught the manner of obtaining the Perspective repre- 
 sentation of loo Tables with their pillars and bases, when of an Octagonal 
 form; it is likewise applicable in gothic designs, whether for Tables, 
 Candelabri, or any other object having octagonal supports. We shall now 
 commence with the application of these examples, by delineating the various 
 articles of Domestic Furniture in general use; giving the perspective lines 
 with each example. 
 
 Plate 6. 
 
 To represent a Library or writing 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 haif of the plan of the writing Table to be projected ; 
 abed, making the top \ffoo, the frame ; and e, e, two of the legs. 
 
 No. 3, shews the profile of part of one of the ends with its moul- 
 dings, &c. 
 
 Having drawn the Ground line 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 may 
 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 made longer, viz. 13 feet 4 inches ; the length of the table 
 
92 
 
 PRACTICAL PERSPECTIVE 
 
 being 5 feet. Proceed and square up from the plan on to the Ground line the 
 length a b, of the top, at E £; also the length f f, of the 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 marked 
 Diug, the point being off* the plate : its intersection with the visuals drawn 
 from E, F and M, will determine the perspective width of the top and frame 
 of the 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 from the nearest corner E to the 
 point of distance ; its intersection with the visual drawn from M, will 
 give the square of the leg at the corner nearest to the spectator ; which may 
 be squared to the opposite visuals drawn from F and M : this will compleat 
 the perspective plan. From E, raise a perpendicular E O at pleasure; on 
 which line square all the original heights from 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, must be drawn to the point of distance ; its intersection 
 with a perpendicular raised from the square of the frame at F, will deter- 
 mine the parallel front of the top at X , which must be continued to 
 y, on the perpendicular raised from 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 C, 
 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 from F as before ; this will be the perspective depth of 
 the frame ; which must be squared to the corresponding perpendicular 
 from F at the furthest end, intersecting it an N; this will determine the 
 length of the frame in front. From Z draw a visual to S, which by its in- 
 tersection with the perpendicular raised from the square at K, will 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 must be continued to the perpendi- 
 cular raised from E, intersecting it at A : a visual drawn from B and inter- 
 sected by the perpendicular from K, will give the return. The small 
 moulding at the bottom is found by carrying its thickness to Z, and from 
 
Fi s .4. 
 
PRACTICAL PERSPECTIVE. 
 
 93 
 
 thence conveying it by a diagonal, to the corner line of the frame; this being 
 on so small a scale, may in most instances be drawn by eye ; the bottom 
 line 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 
 from the tinted squares in the perspective plan. The diminishing of the 
 leg being determined in the profile, lines may be drawn from the under 
 part of the frame, at t t, through the diminished part at bottom at 
 v v; which two lines will unite and meet in a point on a line drawn 
 through the centre or axis, at P. Next convey the point P, by a 
 parallel, on to the original line b O, 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, 
 will 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, FM, M E, &c. (in the plan), up to the bottom line of 
 the frame, as at W, Z, R and D ; which will give the squares of the legs at 
 top : from these, draw lines to the apex points, n, O, r and s, and you have 
 the diminishing lines for the legs. From the points, 1, 2, 3, 4, 8cc. as 
 conveyed from the profile on to the original line, draw diagonals to the 
 point of distance ; their intersection with the diminishing line drawn from 
 Z, will give the heights of the respective mouldings and ornamental parts 
 of the leg Z ; which may 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. Remark that where the term diagonal is mentioned, it refers to those 
 Sines 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 lengtli 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 moulding round the lower carcase, as shewn in the profile 
 by the same 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 example is placed 17 feet and half an inch (by the scale) 
 from 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 point F on the ground line 
 G G, has been chosen as the nearest corner of the object. The next thing 
 to be performed is that of making the perspective plan (marked E) beneath 
 the ground line ; with all its parts and projections, the same as in the 
 Geometrical plan marked B. This may be placed at any distance below 
 the ground line, but in all cases the lower such plan is placed below the 
 horizon, the more distinct will 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 plan B,) from the nearest corner F ; as 
 from v to b, which will make the front line of the lower carcase. From b 
 and v, draw visuals to the point of sight : next set off the depth (W W,) 
 of the lower carcase, from b to c ; this draw to the point of distance D : 
 its intersection with the visual from b at e, will determine the perspective 
 depth of the lower carcase. A line squared from e to f, parallel to b v, will 
 complete the plan of the lower part. Next set on" the measure W Y, (in the 
 
PRACTICAL PERSPECTIVE. 
 
 65 
 
 plan B) from o to g, which draw to the distance as before ; its intersection 
 with the visual b e /at t, will determine the seat of the upper carcase : a 
 parallel drawn from t to i, will represent the front line. It then remains to 
 find the perspective projection of the mouldings, in the lower and upper car- 
 cases ; which may be obtained as follows : set off the projection of the 
 plinth, (marked 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 from b, by the point of distance, 
 will by its intersection with the visual drawn through o, give the projection 
 of the plinth at I; and a line squared from /, intersecting the visual drawn 
 through y, at m, will give the projection of the plinth at the furthest point 
 from the spectator. The same process must be followed for finding the pro- 
 jection of the cornice in the upper part ; observing to throw the mitre 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 
 b, perpendicularly at pleasure, as at I ; which liue consider as the Geometrical 
 line, upon which all the original heights of the figure must be placed : in 
 this Example the heights are squared from the profile C, as numbered, 
 1, 2, 3, 4, 5, 6, 7, 8. From all these heights on the original line, draw 
 visuals to the point of sight ; not the whole length, but only as far as may 
 be necessary to receive the intersections of the perpendiculars raised from 
 the perspective plan. Having proceeded thus far, commence by raising a 
 perpendicular from t, in the plan ; this will intersect the visuals drawn from 
 4, 5, 6, 7, and 8, at the points o, o, o, o, o, and thereby, determine the heights 
 of the cornice and frieze in the upper carcase. These heights squared to 
 the perpendicular raised from the point i, in the plan, will complete the 
 frieze ; and also the bottom line of the cornice in front ; giving likewise the 
 base line of the upper carcase at K. The heights of the members on the 
 lower carcase are determined on the original line itself at 1, 2, 3, and 4; 
 from which visuals alone are required to be drawn ; and these, as well 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 completed. The projecting members 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 mitre lines by the point of 
 distance, from o, t, and F, which by their intersection with perpendicular.9 
 
98 
 
 PRACTICAL PERSPECTIVE. 
 
 raised from 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 terminated by perpendiculars raised from ra 
 and r, will complete the figure. The profiling of the mouldings must be 
 regulated by the Geometrical elevation, and drawn by hand, as shewn in the 
 finished Example, fig. 2. The remainder of the finishings, viz. the pilasters, 
 pannelling, framing the upper doors for glass, &c. will depend entirely on 
 the taste of the designer. 
 
 Fig. 2, shews the same 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. 1, for the purpose of 
 keeping the latter diagram distinct and free from too great a mixture 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 from 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 <jr, at g, will give the front 
 of the writing flap. This squared to the visual from C, intersecting 
 it at f, will determine the length of the flap. To obtain the place of 
 the cheeks or sides, (X, X) of the drawer; set the measure of one of 
 them (generally about 9 inches), from D to i ; this measure thrown back 
 by the point of distance D, upon the visual D g, at h, will 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 ?n. Perpendiculars raised from h 
 and m, and cut by visuals from A and B, will determine their height. The 
 seat and height of the quadrants for supporting the fall down front, are 
 found after the same manner, as may be seen by inspection of the figure. 
 
 Remark, that the point of sight in fig. 2, is shewn at S ; and the distance 
 being the same from it as that in fig. 1, namely 17 feet and £ 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 manner the tendency of the point of sight 
 in fig. 1, is shewn by the converging lines, making the top and bottom of the 
 bookcase. 
 
i 
 
— 
 
 > 
 
PRACTICAL PERSPECTIVE. 
 
 97 
 
 Plate 8. 
 
 To represent a Chiffonier commode (Fig. i } ) 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 same manner, and by the same 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 marked a a, in the plan, denote the place of the columns 
 supporting the frieze and marble top; the squares figured I, 1, denote the 
 capitals : E F, shews the front line making the body of the commode with 
 the doors : A B C D, is the plan of the marble top. The dotted lines bb, c c 
 and d d, shew the front lines of the shelves in the upper part (making the 
 chiffonier ;) which are got by setting off the breadth of each shelf in the 
 profile, from h, (the back of the commode,) 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 
 Hue GH, from the corner B, in the plan; which consider as the Geometrical 
 line, upon which to receive all the original heights from the profile. Com- 
 mence by squaring, first, the height and thickness of the top i i, which being 
 in the plane of the picture, must be continued direct to the perpendicular 
 raised from 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. Parallels drawn from o, o, and continued 
 to the perpendicular raised from I, will complete the frieze. The columns, 
 shelves, &c. may be all obtained after the same manner; as may be seen by 
 reference to the plate, it being needless to repeat over the same process a 
 second time, as such would occasion a multitude of references which would 
 only tend to perplex the figure. It is thought proper in this example 
 to shew one door of the commode open, and at the same time to de 
 
 2 E 
 
98 
 
 PRACTICAL PERSPECTIVE. 
 
 monstrate and lay down the principles by which it is performed. It is 
 evident that every door turning on its hinges, would by its revolution, 
 generate a semicircle equal in diameter to double the width of the 
 opening. This semicircle being found perspectively, the door may be 
 shewn open on any part of its semicircumference. Suppose the d}Or 
 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 P to q ; and throw visuals by the point of sight from n, P, and q : a 
 line thrown from P by the point of distance, will by its intersection with the 
 visual thrown from n, give the breadth of the half square, containing the 
 semicircle, at r : a parallel drawn from r to t will complete the half square. 
 Draw the semidiagonal P t. Next take little more than one seventh of the 
 line q n, which convey upon the semidiagonals P r, and P t, by the point of 
 sight, at TV and v. The semicircle must then commence from the point q, and 
 be traced through the points w, *, v, terminating at n. The semicircle being 
 thus obtained, take any point on its circumference as X, for the extent you 
 mean the door to be thrown open ; a line drawn from this point to P, will 
 make the bottom 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 from X at Y, will give the upper line of the door. The point Q is 
 found by squaring a line from x until it cuts the perpendicular drawn from 
 P. The vanishing point for a door thrown open at any point upon the semi- 
 circumference of the circle may be found after the same manner; namely, by 
 joining such point with the centre where the door hinges by a line, and con- 
 tinuing it to the horizon. 
 
 Remark, 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 flight of Bedsteps, Fig. 2, in Perspective. 
 
 In this example the profile of the steps is shown parallel to the picture, 
 nd consequently would be Geometrical ; save and except the projections of 
 plinth and nosings. First set off the measure of each tread of the steps 
 
PRACTICAL PERSPECTIVE. 
 
 99 
 
 (being 9| 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 \ inches) 
 from D to E ; this conveyed by the point of distance on tLe visual drawn 
 from D, will give the perspective length of the front at F : a line squared 
 from F to G, will complete the plan of the steps The lines B H, C I, and 
 D F, will in this case be the seat of each tread. The projection of the plinth 
 and nosings being the same, both are found as follows : set off the measure 
 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 from G and D, and cut by the visuals before drawn, will 
 give the projection of the two opposite corners at a and f ; this completes the 
 plan. In raising the elevation, commence by drawing the perpendicular h i, 
 from A in the plan ; on which set up the height of each step from the ground 
 line G G, as at k, I and o : these square to the perpendiculars raised from B, 
 C, and D, intersecting them at x, n, t, m and u, which will complete the 
 profile of the steps. Visuals drawn from 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, and w s, forming 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- 
 forming 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 lid or top be thrown up perpendicularly 
 on its centre, its representation will be the dotted plane b c o y. But in 
 this instance it has been thought proper to show the top only partially open ; 
 for which purpose any point in the quadrant b x } may 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 
 
100 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 more or less vary. 
 
 Plate 9. 
 
 To represent a ohair 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 somewhere 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 ; but each equally distant 
 from 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 
 use 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 
 it; or in other words, when the Develled side of the chair is immediately 
 oefore us. 
 
 We shall give an example both ways, and commence with the side 
 view in preference ; giving a plan and elevation, with a scale, by which the 
 whole is proportioned. 
 
PRACTICAL PERSPECTIVE. 
 
 101 
 
 Tn the present example the plan of the chair seat is represented at 
 fig. 1 : the letters A A A A, 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 13 B, the back rail ; A B, and A B, are therefore the 
 inclined sides of the seat rail common to all chairs : the spray of the front 
 legs are denoted by the letters b b j those of the back by c c. The plan, fig. ] , 
 being completed, and the profile C, fig. 2, constructed, proceed and 
 transfer the depth (A A,) of the bevelled side of the chair in the plan, from 
 A to B, on the ground line, fig. 3. Next set off the measure or spray of 
 the back foot (B a,) from A to R : from R, A and B raise three perpendiculars ; 
 B I, to receive the heights for the front rail of the 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 rail and stuffing, at D D D, on the line 
 R G ; at b, b, 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, from 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 at /. From /, draw a line 
 parallel to the ground line, intersecting the visual A S at g; this will com- 
 plete the square containing the seat of the chair. 
 
 For the bevel of the sides, set off the measure B A, in the plan, from 
 B to g, and from 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 
 f o, which will give the two bevelled sides, and complete the perspective plan 
 of the seat. These lines continued will receive the spray of the back legs. 
 Next from b, b, b, on A I, draw visuals at pleasure tending to S ; and from 
 o and c, in the perspective plan raise perpendiculars until they intersect the 
 visuals drawn from b, b, 5, at o, o, o, and o, o, o ; likewise from c, c, c, on B I, 
 draw visuals to S, which terminate by a perpendicular from f at c, c, c ; draw 
 the lines co, c o, c o, and c o, c o, c o ; which will make the lines of the side 
 rails and stuffing. 
 
 To obtain the height of the back, first raise perpendiculars from x and y, 
 on the visual R S ; as x k, and y M. From K in tbe 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, at t and M, 
 will give the height of the back. The sweep of the back may be found by 
 dividing the height T (in the profile, fig. 2,) into any number of parts ; as 
 at L, L, L, L : from 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 
 h, L, L, L, to the perpendicular line R G, as at L, L, L, L; and draw 
 visuals tending to S, until 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 ; from these intersections, perpendiculars must be 
 raised until they meet, each its corresponding line, squared from 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 x 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 may then be drawn by hand ; the thickness of these 
 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 the profile : this mea- 
 sure is then tansferred from B to x, and conveyed by the point of sight on the 
 opposite side at.r. Perpendiculars raised from these points and intersected by 
 a line squared from Z Z, (in the profile) at Z Z; and by visuals drawn from Z Z 
 at z z, 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; more lines are now given than has 
 hitherto been attempted in other works of this kind , but we have chosen to be 
 thus particular in this and the following example, conviuced that those 
 who wish to learn and know the reason for that which is laid before them, 
 will 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 elbow 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 ; commence by setting the measure 
 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 
 rail 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 measure of the back rail, and set it right and left from 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 and d; the line cd will then represent the width 
 of the back rail. Set the width of the square A (in the plan) from A to a, 
 and from B to b ; these draw to the point of sight S ; a line drawn from A 
 to the point of distance, where it intersects the visual from «, will give the 
 depth of the square ; this transferred to the visuals from A, b, and B, will 
 complete the two squares containing the front legs : join b c and q d, which 
 lines will make the two bevelled sides, and these continued to the horizontal 
 line H H, will there give the vanishing points for the bevelled sides at V 1, 
 and V 2. From A, a, B, b, I and ni, 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 Geometrical line A H, at 1, 2, and 3, which continued 
 across to the perpendiculars raised from a, b, and B, will give the front Y 
 of the stuffing, with the two knees X, X, of the front legs. Lines drawn from 
 1, 2, 3, to the point of sight S, and received by the perpendicular from I, at 
 x, x, x, will make the return of the knee X, and give the plane for the scroll 
 of the arm at the nearest corner : lines drawn from x, x, x, to the vanishing 
 point V 1, and received by the perpendicular raised from c, will give the re- 
 presentation of the bevelled side of the rail and stuffing : likewise a line drawn 
 
104 
 
 PRACTICAL PERSPECTIVE. 
 
 from ;/, to the vanishing point V 2, and terminated by a parallel squared 
 from w, will complete the seat of the chair. To obtain the place of the elbows, 
 setoff the distance they recede from the front line y x, (of the profile,) from A 
 to e ; this convey on the visual A S, by the point of distance : its intersection 
 at r, will determine the place of the elbows, which must be squared across to 
 the lines I c, of, p v, and q d, intersecting them at o o, and oo; o o and o o 
 will then become the front lines for the upper scrolls. The depth w w, in 
 the profile must next be set from e to /; conveyed on the visual A S, and 
 be squared across as before mentioned ; being denoted by the tinted planes. 
 From o, o, o, and o, o, o, raise perpendiculars; next square the height y of the 
 elbow, and thickness z of the scroll, to the Geometrical line A H, at 4 and 5 : 
 lines drawn from 4 and 5, to the point of sight, received by the perpen- 
 dicular I I, and from thence conveyed by the vanishing point V, to the per- 
 pendicular o x, will give the perspective height of the elbow, and thickness 
 of the scroll at n and m; and its return at <j, g. Lines squared across from 
 n and in, 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 of the 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, might have been found; but this would 
 have occasioned much complexity of lines, and taken up much of the student's 
 time to very little purpose. The elbows being drawn in, proceed next with 
 the back of the chair ; first by finding its seat Z Z, in the perspective plan 
 below, as before directed ; the distance of which from the front line of the 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, must next be squared 
 from the profile B to the Geometrical 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 will determine its 
 perspective height; which must be squared across to X : the outline sweep 
 of the back may then be drawn by hand. The directions given in the pre- 
 ceding plate for finding points to obtain the outline of the back, will also 
 apply to this example ; 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 «, and m b B ; the diameters of which w ill regulate the 
 
PRACTICAL PERSPECTIVE. 
 
 105 
 
 projections of all the upper mouldings, whose heights must 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 of the table : to repeat the process 
 here would be needless. For the back legs set off the measure 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 I Z and q Z, as before ; which will be seen 
 by reference to the figure. 
 
 Plate 1 1. 
 
 To represent a Grecian chaise lonsjue, 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 of the 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 line H ; 
 likewise the point of sight S, and the point of distance (here out of the pic- 
 ture) on such line. Let L, (on the ground line G G,) as squared up from the 
 line D in th.e 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 N I ; 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 
 geometrical. Proceed and square up the points F and F from the plan, 
 upon the ground line at e and e ; also the squares E E, and E E, of the legs, 
 at e e and e e. On the extreme ends, e and e, raise the perpendiculars e k and 
 e i y at pleasure ; these lines limit the geometrical length of the frame, and 
 determine the place of the legs or feet. Being thus far advanced, proceed 
 and make a profile of the leg as at M ; the mouldings of which must be 
 
 2 G 
 
106 
 
 PRACTICAL PERSPECTIVE. 
 
 squared to the perpendicular e f, as shewn by the dotted lines. On N I set up 
 the heights N I and 1-2, of the under and upper parts of the rail; which square 
 across to the lines ei and e k, at the points f— -f and g — h. On the same lines 
 set up the thickness of the stuffing at i, and draw the line i k. Next set up 
 the height you intend the head scroll to be. It will 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 must also be drawn geometrical after the same manner, 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 number of 
 parts : the scroll I at 3, 4, 5, 6, and 7 ; the scroll K at 8 and 9. On I draw 
 the lines 3 — o, 4 — o, 5- — o, and 6 — o, intersecting this larger scroll at o, o, 
 
 0, o : the same is to be performed as regards the lesser scroll, by squaring 
 the points 8 and 9, to q and q. The inside outline of both scrolls must next be 
 drawn ; that at I, through the points p,p, p, p, terminating with the seat at i : 
 that of the smaller scroll at K, is to be drawn through r, finishing with the seat 
 at k: so far the geometrical figure will be completed. The next point is to 
 obtain the width E F, (of the 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, from L to Q, which convey 
 on the visual L S by the point of distance, intersecting it at R. This 
 measure must be squared to the visual N S at the point T, intersecting the 
 visuals e S and e S, at V and V. On 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 
 
 1, 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 q ; V and V to receive those marked i, o, on e, 
 and k h, on e, at s s, and x h. Lines squared from the divisions 3, 4, 5 
 and 6, on T O, until they intersect visuals drawn from p, p, p and jt>, on the 
 front scroll, will give points through which to draw the outline of the 
 back scroll from O to s : likewise lines squared from the divisions 7, 8, and 9, 
 on R P, until they intersect visuals drawn from q, q, q, on the foot scroll, 
 will giv« points through which the outline of the footscroll P, may be drawn. 
 To obtain the thickness of the two scrolls, set such thickness from L to n ; 
 which draw to the point of distance, intersecting L S at t; which must 
 
PRACTICAL PERSPECTIVE. 
 
 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 from 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 outline making the thickness must be drawn. What has been thus 
 performed for the head scroll, may be done for the foot scroll ; as shewn 
 by the planes q 8 w and q 9 w. 
 
 The thickness of the head and foot scrolls 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 from 3, 4, &c. and 8, 9, &c. will intersect these 
 two perpendiculars at a a, &c. and b b, &c. Lines squared from a, a, a, and a, 
 — b, 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 
 line; 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 from the 
 plan, the length (A A,) of the top, to the ground line at the points a and G; 
 
!08 
 
 PRACTICAL PERSPECTIVE. 
 
 likewise the seat of the blocks C C and C C, to c c and c c, on the same 
 line. 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 
 from c c, and c c. Next set off the width D D, (of the top in the plan) from G 
 to H, which convey on the visual G e, by the point of distance ; this squared to 
 the visual from a, will complete the perspective plan a b e G of the top. To 
 obtain the situation of the frame under the top, as shewn by the inside plane, 
 the learner is referred to the table, plate 6, where he will find the whole amply 
 explained. Divide G II 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 them 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 from c c and c c, will determine the seat of the 
 projections (marked 1, 2, 3, in the profile,) in the perspective plan, at o, o, 
 o } o, &c. 
 
 Commence and square from the profile, the height of the top, and depth 
 of the frame under it, to the geometrical line G G ; which draw to the point 
 of distance ; and proceed with the rest, as described in the table, plate 6. The 
 situation of the standards, with all their component 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 geometrical plan), at the points t, t &c.; these square to the 
 opposite perpendicular/? w. From all these heights on the perpendiculars 
 O v and p w, draw visuals to S, until they intersect perpendiculars raised 
 from o o, &c. in the plan; these will determine the different heights and 
 projections for both standards, by which to regulate the outline as shewn 
 in the profile. The thickness of the standards at top and bottom is regulated 
 by the planes r, r, r, &c. on both sides; which are likewise squared up from 
 the perspective plan. Figures 8 and 9, will give the situation for the stretcher 
 F, or tye of the table frame. For the rest the pupil is referred to the dire c- 
 tions given in the preceding examples ; it is needless to go through a repe- 
 
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 of the standard, as shewn in the profile, is 
 to be drawn by hand, as recommended 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 of the pattern. 
 
 Plate 13. 
 
 The plan and profile of a 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 comprised 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 method for 
 obtaining such will be found amply detailed in plate 4 Geometrical figures, 
 page 51, to which the reader is referred. 
 
 The semicircle 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 semicircle K L M, bounds the triangle, in which is formed the block. : 
 the semicircle N U O W P, inscribes the ornamental moulding 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 complete, of which arc half is only given in the plate before 
 us, for want of room. As all the other references relate to the operative part 
 of the circle, to say any thing farther as regards them in the plan would be 
 needless : we shall therefore proceed to the operation. Having as before, 
 
 2h 
 
110 
 
 PRACTICAL PERSPECTIVE. 
 
 determined the Ground line and the height of the Horizontal line, with the 1 
 
 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 something as to the choice of the point of view. It will 
 in all cases be most 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 means its figure will be better made 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 diameter 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 complete the perspective square A B C D, as shewn 
 in the diagram, 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 ellipsis 
 or perspective plan of the table top. Take the distance D x, from the plan 
 in the compasses, and set it on the line A B, from A to x, and from B to x ; 
 visuals drawn from #and x, intersecting the diagonals A D and B C, at 
 X, X, X, and X, will 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 
 from i and i, to S, will intersect the diagonals A D and B C at r, r, r, and r, 
 and thereby produce a square circumscribing the ellipsis, making the frame 
 under the top of the table. The measure 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 from y 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 Doints 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 g R h h 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 
 
PRACTICAL PERSPECTIVE. 
 
 Ill 
 
 transfer the measure f g, from F to 5 and F to 6. Next take the measures 
 F f, B h, and h o, and set them from B to c, from B to d, and from d to f; 
 these convey on the visual B D by the point of distance, intersecting it at 
 m, I and b. Lines squared from m and / and intersected by the visuals 
 drawn from 1, 2, and 3, 4, will give the two canted sides h h and h h ; also 
 a line squared from b, intersecting the visuals drawn from 5 and 6, will 
 produce the canted corner eg. 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 QRS T, 
 and the one within marked E are found by setting the corresponding 
 measures E O. &c. in the plan, from F to 9, from 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 
 of the 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 
 Hnes of the 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 moulding 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 will 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 from the 
 profile, and is here marked G G. Commence and transfer the heights 6, 7 
 and 8 from the profile, to 6, 7 and 8, on the geometrical line G G. From 8 
 on the geometrical line, square the line 8-8, which make equal to A B in the 
 plan below : from 8 and 8 draw visuals tending to S ; lines drawn from 8 
 and 8 to the points of distance, will intersect these visuals at 9 and 9, and 
 
112 
 
 PRACTICAL PERSPECTIVE. 
 
 complete the perspective square of the top. The eight points through which 
 to draw the ellipsis, are squared up from the corresponding points in the per- 
 spective plan. For obtaining the thickness of the top, a line must be squared 
 from 7 to 7 ; and for the depth of the rail, a line must be drawn from 6 to 
 the point of distance, intersecting a perpendicular squared from r in the 
 plan ; from thence squared across, and terminated by a perpendicular squared 
 up from r on the opposite corner, intersecting it at a. The planes producing 
 the points, through which to describe the two ellipses making the thickness 
 of the top and depth of the rail, are squared up from the points X, X and y, y 
 in the plan ; for further instruction, the student is referred to plate 5, fig. 6, 
 No. 1 and 2, page 89. To obtain the representation of the block, proceed 
 and raise a perpendicular from b, in the plan up to the ground line at x, 
 upon which to receive all the perspective heights forming the thickness of 
 the block, and place for the front foot. Square from the profile to the 
 line G G, the heights 1 and 2; these convey on the perpendicular from 
 x by the point of sight S, at b, b and b ; lines squared from these points 
 determine the perspective height of the front foot, likewise the thickness of the 
 block at the canted corner eg. Lines squared up from e g, in the plan, 
 will intersect these lines so squared, at o o, o o, and produce the canted 
 corner as seen in front, and give the situation of the front foot at e g. From 
 eg, o o, and o o, draw lines tending to the vanishing points V and V; and 
 square up the points h h and h h from the plan, until they intersect these 
 vanishing lines at the points p p, p p; this will determine the extremities of 
 the block at the furthest corners ; lines drawn from o and o, to the two 
 vanishing points, and intersecting lines drawn from p and p. to the same 
 points, will give the two canted corners of the block at q and q. It now 
 remains to find the seat of the square Q R S T (in the plan below,) on the top 
 of the block above ; to obtain which, draw a line from 2 to the point of 
 distance, which line intersected by a perpendicular squared up from R in 
 the ground plan, will give the front of the square at r. A line squared from 
 r and intersected by a perpendicular squared up from Q, will give the point 
 q above, and determine one side of the square; visuals drawn from q and r and 
 terminated by the diagonals at t and s, will give the two returning sides of 
 the same square ; which is completed by drawing a parallel from t to s. 
 Within this square, the circle regulating the base moulding of the pillar 
 
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 from 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 «, answering to those marked 3 and 4 in the profile. 
 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 q to o; 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 from 1 to the point of distance at w, 
 which must 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. 
 
 All circular objects, and particularly tables, are best represented perspec- 
 tively with the eye placed in the centre, or equally betwixt its two extremes ; 
 answering to what is termed a central view : this has been adopted in the 
 present example. In all cases where a circular object, as the one before us, 
 comes under practice, the central point of view is recommended 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 will become very much elongated 
 at the furthest extremity from him ; and vice versa, the nearest end will 
 become very much foreshortened : thus, although the block be placed exactly 
 in the centre, the top of the table will appear to hang over more on one side 
 than the other, producing thereby a distorted appearance. These obser- 
 vations have been deemed necessary in order that the learner may avoid 
 adopting that point of view ever found to produce a bad effect. 
 
 2 i 
 
114 PRACTICAL PERSPECTIVE. 
 
 Plate 14. 
 
 The perspective representation of a chevol dressing glass, the front being placed 
 parallel to the picture ; shewing the mode and manner of finding per- 
 spective by the inclination of the swing frame, thrown back in any iin lined 
 position. 
 
 Fig. A, shews one half the elevation of the cheval frame and glass, as 
 seen in front. Fig. B, shews the profile of one of the standards, with the 
 inclined position of the swing frame, as marked by the letters X X. 
 
 The ground line is denoted by the letters G G ; the horizontal line 
 by the letters H H, and in this example is placed 4 feet 9 inches from the 
 ground. The points of sight and distance are both placed out of the picture; 
 the point of sight being 7 feet 2£ inches by the scale from D on the right 
 hand ; the point of distance being the same measure from 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 from the nearest side of the 
 object, and the further the point of distance is removed back from the front 
 of it, the greater similarity will 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 same elevation, is set from C to b, right and 
 left, on the same 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, will intersect the visual a d at d; a line squared from d, and 
 intersecting the visuals drawn from 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 marked 
 ffffmnd gg g g, denote the front and depth of the two blocks which receive 
 the claws, and answer to the measure marked pp in the profile : this measure 
 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. 
 
PRACTICAL PERSPECTIVE. 
 
 115 
 
 The tinted plane marked k k shews the situation and perspective width 
 of the glass frame : this is found by taking from the front elevation the mea- 
 sure C c, and setting it right and left of the centre C, as at c c, from which 
 visuals must be drawn as before, intersecting a line squared from q, at k 
 and k. For the remainder, the student is referred to the example itself, where 
 he will find in the perspective plan, all the lines laid down, necessary for work- 
 ing his draught. So much 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 example are all transferred as usual from the profile and 
 front elevation upon the two original lines marked F and G ; as denoted by 
 the figures 1, 2, 3, &c. and 1, 2, 3, &c. and carried from thence by visuals 
 to the point of sight, intersecting perpendiculars raised from the corres- 
 ponding places in the perspective plan, as will 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 obtaining, perspectively, the inclined position of the 
 glass frame, its swing being thrown back at any supposed inclination. 
 Let X X, in the profile B, be the supposed inclination of the swing- 
 frame : from X and X drop perpendiculars, intersecting the ground line 
 at x and x. Take half the measure 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 
 on the visual a d at m and m; lines squared from m and m, intersecting 
 the visuals drawn from c and c will give the seat of the top line 
 y x, of the glass frame at I and / ; the seat of the bottom line y x, at n and n. 
 From c and c on the ground line raise the perpendiculars E and E, upon 
 which lines transfer from 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 determine 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 w, intersecting them at y and x, y and x: lines drawn from x 
 through z to x, and from y through z to y, will represent the inclined position 
 
PRACTICAL PERSPECTIVE. 
 
 of the glass frame, which is completed by squaring lines from x ana x, top 
 and bottom. The banding forming the face of the frame, is placed on the 
 perpendicular E, as at V, and conveyed from thence by the point of sight on 
 the inclined line xxj the same measure will answer for the three other 
 sides. The divisions comprising the ornamental parts of the stretcher, are 
 taken from the front elevation, and placed on the ground line, right and 
 left of the centre C, at r r and s s ; from thence conveyed on the line k k, by 
 visuals drawn to the point of sight, and then carried by perpendiculars upon 
 the line of the stretcher, as may 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 from the point of distance parallel to the inclined 
 position of the glass frame, and continued until it intersects such perpen- 
 dicular : in this instance the vanishing point for the inclined 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 
 much trouble and inconvenience to the learner. 
 
 The inclined line from 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 from 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 all 
 doors and box-lids thrown open ; dressing-glass frames, wheel-spokes, See. 
 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 rinding the 
 position of an inclined surface perspectively, as observed above. 
 
PRACTICAL PERSPECTIVE. 
 
 117 
 
 Fig. 2 
 
 The learner may suppose A B, Fig. 1, to represent the edge of a glass 
 frame, or any other object, as moveable on its pivot or axis C, round which it 
 revolves. It is therefore evident, that if the frame be turned on its centre, it 
 will by its evolution describe the dotted circle A E B F. If the same frame 
 be removed from its perpendicular position A, to the point A, 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 frame would rest at g, and make the angle g C B, 
 equal the angle A C h ; therefore let the frame be moved into any position ; 
 whether perpendicular, inclined, or horizontal, it would still describe a circle : 
 consequently its top and bottom edges would be limited by the periphery of 
 a circle. 
 
 Fig. 2. Shews the circle A E B F, fig. 1, as represented perspec- 
 tively, the same forming the ellipsis abed: parallel with it, is shewn another 
 ellipsis efgh,as produced from the same circle. In both these ellipses the 
 lines k k and I / 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 frame converge from 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. 
 
llg 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 Preliminary 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 time instructions for laying down the lines, 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 < 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, accompanied with a 
 scale of feet and inches, enabling the workman to ascertain correctly, every 
 geometrical measure, 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 more 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 generally 
 useful, given one example 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 illustrated in the annexed diagram. 
 
 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 6 c 
 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 of the 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 d c would make with the plane P P; as shewn by the arcs efandgh; 
 e f being equal to a b, and g h equal to cC. 
 
 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 i, 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 b, 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 measured by scale. 
 
 This branch of perspective may be generally applied to all objects, 
 approaching in their dimension and form to that of a square ; that is, in any 
 figure wherein one side does not materially exceed the other ; as in chairs, 
 bedsteads, pedestals for sideboards, &c: it may also be successfully applieO 
 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 most 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 dimen- 
 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 illustrate the foregoing observations by the following example ; 
 (representing a four-post bedstead, as such would appear to the eye when 
 inclined to the picture). 
 
PRACTICAL PERSPECTIVE. 
 
 121 
 
 Plate 15. 
 
 To represent a four post bedstead and furniture in inclined perspective, the sane 
 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, from 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 example 
 of the bedstead, could not be shewn in the plate for want of room, the 
 method for laying them 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 same being one sixth of the original distance of 
 the station point for the bedstead, as set up from C on the horizontal line 
 below. Let a b c d, be the plan of an original figure, as inclined to the parallel 
 line GG; its inclination being shewn by the angles ecb and f c d. From 
 the station point S, lay down the angle g S h, equal to the angle ecb in the 
 original figure A ; also from S, lay down the angle i S h, equal to the angle 
 f c d, in the same figure. From S, through h and k, draw the lines S V 
 and S V : V and V, will then become the vanishing points for the sides a b, 
 d c, and a d, b c. Bisect the angle k S h at I ; a line drawn from S through 
 /, will produce the diagonal point at m. The distance 1 — S, laid down on the 
 horizontal line from V, will produce the right hand point of distance at the 
 distance 2 S, laid down from V, will produce the point of distance %■ on the 
 left hand. The picture is then prepared for practice ; having the two 
 vanishing points, * and -J for the sides of the object, with the two points of 
 distance - and ~, for the purpose of cutting off on the vanishing lines 
 
 2 L 
 
122 
 
 PRACTICAL PERSPECTIVE. 
 
 c — 1 and c — 2, any original measure of length or breadth. The diagonal 
 point m, serves as a vanishing point for any diagonal or mitre line in the 
 plan A, and by means of which, all mitres are projected. Transfer from c 
 on the line G G, the side c b of the fig. A, at e ; likewise the side c d at f 9 
 on the same line ; these measures conveyed on the vanishing lines c — 1 
 and c — 2 by the points of distance, will give the perspective length and 
 breadth of the figure, at o and p : lines drawn from o and p to the points 
 V and 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 
 c, set up the intended height of the object, as at y ; which draw to the 
 vanishing points as before, intersecting the perpendiculars from o and p, 
 at s and t : the figure is then completed. We shall now commence 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, from 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 frame, at 5 and 6; and that of the risers 
 on the laths at 7. From O, 5 and 6, draw lines to the respective vanishing 
 points : next take six feet from the scale, which set off from O to 6, on the 
 right hand of the geometrical line ; and set off 7 feet from O to 7, on the 
 left hand of the same line : these measures being conveyed on to the 
 vanishing lines O V and O V by the points of distance, will determine the 
 length and width of the bedstead at a and b. From a and b, draw lines to the 
 vanishing points, intersecting each other ate; and from a and 6, raise up 
 perpendiculars until they meet the vanishing lines 6 V and 6 V at e and f; 
 ae and b f will then represent the two extreme corners of the bedstead. The 
 situation of each post on the ground is thus found : take Ah inches from the 
 scale for the diameter, which set off on the ground line from O to /), right and left 
 from () to p, and from 7 to p : these measures convey on the vanishing lines 
 O V and O V by the points of distance, at y, y, y, and y. Lines drawn from 
 y, y, &c. to the vanishing points, intersecting each other at z } z, &c. will 
 produce the perspective squares ay z, yOyz. z y b, and dz y c. Thus much 
 
PRACTICAL PERSPECTIVE. 
 
 123 
 
 being done, proceed next with the teaster; first by drawing the line T T 
 through the point 6, upon which line, set off' the breadth of the teaster lath, 
 viz. 31 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. Lines drawn from u, u, &c. as also from e, s ; s, s ; and s,f, to 
 the respective vanishing points, intersecting each other at t and w, will 
 complete the teaster frame of the bedstead ; and perpendiculars squared up 
 from the planes a y z, y o y z, &c. terminating with the plane of the teaster, 
 will give the representation of each post, considered as a square body. For 
 the side and foot rails of the bedstead, the ornamental 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 at <j, 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 must be joined bylines drawn to the right hand vanishing- 
 point. The bedstead being thus completed, *he 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, | 
 the size of the perspective example. The distance of each vanishing point, 
 and point of distance in this example, as set off on the horizontal line from 
 the centre C, is as follows. 
 
 Ft. In. 
 
 Station point 20 2 upwards from C. 
 
 Right hand vanishing point . 19 S\ 
 
 Left hand Ditto ... 20 7 ( the horizontal line 
 
 Right hand point of distance . 8 4^ from the centre C. 
 
 Left hand Ditto ... 8 7 J 
 In concluding this portion of the drawing book, it may be proper to 
 furnish such hints and observations as will assist the learner, not only in his 
 studies, but at the same time point out to him the course he may persue with 
 
324 
 
 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 the result of many 
 years study and practice in as small a compass as the subject would possibly 
 admit of; to 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, must be left to the ;, idg- 
 ment of the reader. The science of Geometry is made the corner stone 
 Oi my structure : the principles of this science the student is strongly 
 advised to make himself acquainted with ; and first with the definitions ; not 
 contenting himself with a mere reading, but to use every endeavour and all 
 possible means to imprint them on his memory; so as to have them present 
 at all times, as occasion may call them into use. 
 
 Although this may appear dry, and be attended with some 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 comprehension, and at the 
 same 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 ! He wno would reap 
 the fruits of an harvest, must sow ! and he who would seek to gain diamonds, 
 must be content to search and dig for them ! The same reasoning applies 
 to all those who wish to acquire knowledge ; they must 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 
 recommended 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 iu 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 memory: 
 in addition to which, the written instructions being thus before the student, 
 will render a reference to the work less irksome, and where the references 
 are many, less perplexing. 
 
 This practice is recommended by the Author, from 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 must be pursued as is here 
 recommended with regard to the Geometry ; the pupil 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 make 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 well 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 true 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 inclined perspective, 
 answer to the diagonal lines of a square in Geometry : This is quite 
 
 2m. 
 
126 
 
 PRACTICAL PERSPECTIVE. 
 
 sufficient to shew the accordance and relation, existing between the two 
 sciences. 
 
 In framing the perspective examples, as applicable to objects of furniture, 
 attention has been paid to give such only as would be really useful, and at 
 the same time pleasing and interesting ; being fully 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 mathematical 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 compasses with 
 shifting limbs, the one for a pencil, the other for ink; a drawing pen with 
 steel point, and a pair of bow compasses for the purpose of striking smaller 
 circles ; and these also adapted to receive a shifting limb for pencil or ink, as 
 occasion may require : In addition to these, may be added a plain scale, 
 as described in Geometry, page 55. These instruments are all that are 
 necessary for the student in this department of drawing ; the sector, pro- 
 portional compasses, &c. being more in use amongst 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 light, in which case, the water-mark with the maker's name, must 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 frame; 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 
 
 willbeeasie- understood, by reference to the annexed wood-cut, (fig. 1,) 
 which represents it with its front face upwards ; shewing a framing 
 all round, equal to two inches. 
 Figure % shows a section of 
 the same board ; the upper 
 face A, Fig. 1, being denoted 
 atB; by which maybe seen, 
 the manner in which the loose 
 pannel is made to fit into the 
 frame. The size of the 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 made 
 of a length proportionable to 
 that of the board in use. In 
 many of these squares, the stock is made to consist of two parts ; 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 
 moveable part of the stock is placed at the edge of the drawing board, the 
 other half with the blade attached to it, becomes 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 utility 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 geometry.) 
 
 Ft. In. 
 2 0 
 
128 
 
 ORNAMENTAL DRAWING. 
 
 ELEMENTS OF ORNAMENT, 
 
 AND 
 
 DRAWING IN GENERAL. 
 
 Preliminary Observations. 
 
 Ornamental drawing constitutes a very essential part in the qualification 
 of those artisans for whose use this work has been composed ; vjz. that 
 of the Upholsterer and Cabinet-maker : 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 many years prac- 
 tice and experience. 
 
 This part of our work opens a wide field for great and continued grati- 
 fication ; for without ornamental embellishment, 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- 
 ment of drawing. It remains now to point out the direct road in which the 
 student may 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 Mathematics 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 pupil is to gain a freedom of hand for sketching, 
 and to attain a thorough acquaintance with every line in all its circumvo- 
 lutions and bearings; and this can only be achieved by continual practice. 
 This mode has all along been considered as the most conducive in the end 
 towards producing perfection of outline in drawing; added to which, a double 
 advantage is obtained ; namely, that of designing ornament 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 
 will 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 familiar 
 manner, 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 most cases a very imperfect copy of the original. 
 
 As Ornamental Drawing therefore forms an essential qualification 
 both to the upholsterer and the cabinet-maker, it should be practised and 
 be well understood previous to the study of Perspective. 
 
 Perspective as applicable to furniture drawing, differs in some measure 
 from the practice of it in Architecture ; the one being almost wholly confined 
 to straight lines ; whereas the other is in a great measure coupled with lines 
 that are curved, or on the sweep. By the rules of perspective, the planes 
 which inscribe all elliptical curve lines are produced; and by the 
 same 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 
 recommended; and which may be practised jointly with the study of 
 geometry : our system therefore commences with a series of simple and 
 compound outlines, as comprised in plates CX. and CXI. the same having 
 been carefully studied and wholly adapted to ornamental 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 all 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 of his 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 freedom to his hand ; and of this he can only 
 be convinced by the trial. We shall now commence with the series of exam- 
 ples given in this treatise. 
 
ORNAMENTAL DRAWING. 
 
 13! 
 
 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 themselves, the foundation of every species of orna- 
 mental composition. These outlines, varied in their form, must be practised 
 by the learner, until he finds his hand capable of drawing them fluently and 
 with freedom. This will be greatly facilitated by copying them 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 himself. The outlines 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, common 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 lines of all continued scrolls ; 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 of the tulip flower ; and Fig. 9, 
 is the two halves put together. This species of ornament is much used for 
 the ends of cornice poles. 
 
 Fig. 10, shows the outline for a scroll which is commonly adapted to the 
 same use. 
 
 Fig. 11, exhibits the outline of the Archer's bow ; is often used as an 
 ornamental finish in its simple form, but more frequently adorned with foliage. 
 
13'i 
 
 ORNAMENTAL DRAWING. 
 
 This outline has been much used for the 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 commonly called in architecture the Vitruvian scroll : 
 this ornament 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 outline of a portion of the circle, when drawn per- 
 spectively. The external face of all circular objects, such as columns, &c. 
 when seen below the eye, partake of this outline. 
 
 Fig. 15, shows the outline of a portion of the perspective circle, when 
 viewed sideways, or removed to the right or left hand of the spectator. 
 
 Fig. 16, pourtrays that portion of the perspective circle, as being the 
 most distant from the spectator. 
 
 Fig. 17, exhibits the outline of the upper part of the perspective circle, 
 when drawn in a perpendicular position. 
 
 Fig 18, is the outline of the perspective circle when complete : the flat 
 surfaces of all circular objects partake of this outline w hen seen below the eye. 
 These various outlines of the circle are here given, as being considered 
 most essential for the pupil's practice ; so that in exercising his hand, he may 
 draw such outlines with more truth and facility, as they occur in the practice 
 of perspective drawing. These five simple forms being well studied and 
 practised by the hand, will save the student much 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 
 marked 8 aud 9 in the preceding plate. It is chiefly 
 used in ornamental w ork to fill up the vacant space 
 betwixt two scrolls as rising one out of the other: thus, as in the wood cut. 
 
EILKME1TTS OF © 1NAME N TAIL .D KA^G » 
 
 N°2. 
 
 I f 
 
ORNAMENTAL DRAWING. 
 
 133 
 
 Fig. 19: — the same ornament reversed. 
 
 Fig. 20 : is compounded of the outlines numbered I, 5, and 6 in phto 
 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 of the leaf, as bearing a similitude to the palm of the 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 compounded 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 outline when cloathed with foliage, is applicable to the pur- 
 poses of decoration in various ways ; it is sometimes made use of as the 
 outline of a 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, &c; 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 of which must be regulated 
 accordingly. In copying these figures, the pupil should commence from the 
 top, as in Fig. 1, and complete the uppermost 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 little 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 outline only, 
 in regard to its width and height. The leaf adjoining, being produced from 
 the preceding outline, is divided into nineteen parts, forming so many 
 smaller divisions of the leaf ; and these are pointed at their extremities. 
 The third leaf partakes of the same 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, with 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 of the 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 ; the leaf adjoining has the same number 
 
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 remaining leaf offers the same outline, but is varied in its detail ; 
 having eleven divisions, inwardly scrolling at their several terminations. 
 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, of the simple outline 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 all ornamental composition, and are here purposely intro- 
 duced, as being essential to the student's practice. 
 
 The ornamental specimens given in this plate are variously used in de- 
 corating the 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 of a 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 making the turn over. 
 
 In the two first examples, each division of the leaf consists of five smaller 
 divisions, and being divided after this manner it is then called a hand or palm of 
 the leaf. The third example in this plate consists also of seven principal divi- 
 sions, each of which are again subdivided variously ; the two lowermost 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 
 
ORNAMENTAL DRAWING. 
 
 examples are divided, each alike into nine parts. It now remains to furnish 
 the practitioner with some instruction as to the manner in which he must 
 proceed, in copying the examples given in the two foregoing plates, with 
 correctness and ease to himself. 
 
 Commencing 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 
 must be raised, and which may answer for the centre or stem of the leaf. 
 Let him 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 will 
 then serve as a g uide 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 many 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 manner ; the variation consists in the terminations 
 being more rounded, with the addition of a hollow or flute within each 
 division : it is drawn after the same 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 from the third. 
 These leaves are all subject to one and the same outline as to their outside 
 form ; being varied in their detail at the pleasure of the artist. 
 
ORNAMENTAL DRAWING. 
 
 137 
 
 The third range in this plate shows the manner 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 line for as many leaves as are required. 
 
 In the fourth range, the two first leaves are both under one outline, the 
 second being a slight deviation from the first; the same is to be observed of the 
 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, will soon find himself 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 drawing 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 lead pencil 
 should always be used, and that with great lightness when sketching in the 
 rough outline, so that any mistake 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 oi 
 rendering directions less necessary in what is to follow. 
 
 In Fig. 1, Plate CXX1, which represents in simple outline, fig. 2 ; the 
 base line should first be drawn ; afterwards the centre or perpendicular line : 
 the base line will receive all the widths, the perpendicular the heights. 
 The outside sweep line, with the turn over of the leaf must then be drawn ; 
 afterwards, the distance of each pipe from the centre line in Fig. 2, must bt 
 set off right and left from the centre in 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 palm or hand of leaves being thus denoted, the outline corn- 
 
 2 p 
 
138 
 
 ORNAMENTAL DRAWING. 
 
 prising' them may be 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 him ; inscribing 
 such object, first in simple outline; dividing such outline 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 pupil in reference to the first figure, must commence and draw a 
 line across his board or paper, which may be considered as the central line 
 of the Patera. Upon any part of this line as a centre, he will then with his 
 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 line may then be divided into eight equal parts : lines drawn from these 
 points to the apex, will determine the centre or stem of each leaf. Another 
 semicircle must 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 within 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 of the ornament 
 called the eve of the Patera. It will bo seen that one half the rancje of leaves 
 in this Patera are drawn quite plain, forming a mere outline. The 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 
 Hien that of the smaller circles within it; but instead of eight parts, this 
 
4- 
 
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 to follow the curve of the other, from the centre or 
 apex. The whole circumference 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 frequently 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 
 outline 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 the 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 him, making use of his own judgment, 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 CXX11. 
 
 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 ; from whence a continuation if 
 
140 
 
 ORNAMENTAL DRAWING. 
 
 supposed to be made, both from the right and the left hand. The fourti 
 example is a composition from various ornamental fragments discovered at 
 Pompeii ; intended likewise as the central part of a frieze ornament. 
 
 All these examples are here given solely for the purpose of practice 
 in copying, and should be drawn on an enlarged scale ; observing the same 
 rules as to dividing them into parts for their simple outline, as is detailed in 
 the preceding plates. 
 
 With these examples we shall conclude all we have to offer on the 
 score of outline in Ornamental Drawing, convinced that enough has already 
 been given for the practice of the learner ; at least as much as is sufficient 
 for the present purpose. If the student can so far perfect himself in drawing, 
 as to copy correctly all the examples here given in this treatise, there is 
 every promise of his succeeding, when those of a more difficult nature are 
 placed before him. 
 
SHADOWING. 
 
 141 
 
 SHADOWING. 
 
 Previous to entering' upon the practical part of this section of the work, 
 it will become 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 will 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 mediums ; the materiality 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 of light, and the effect of it as pro- 
 ducing shade from solid bodies, is all that is needful or can be any way 
 useful in this work. 
 
 The rays of light as proceeding from 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 from their regular course, by the rarity and density 
 of the different mediums, or atmospheres through which they have to pass : 
 this in mathematics is what is termed refraction of light ; the theory and 
 demonstration of which belongs exclusively to optics. 
 
 It may however be necessary to state, that this refraction of rays pro- 
 duces what is commonly termed daylight ; that is, the light we experience 
 when the Sun is concealed from our view by the density of the atmosphere. 
 In this case the shadows from solid objects, are mellowed and much 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 medium ; and thus falling with their full brilliancy on such objects a? 
 are intended for shade, or from which shadows are to be cast. 
 
 2 Q 
 
I42 SHADOWING. 
 
 It must likewise be observed, that as the diameter of the Sun's body 
 greatly exceeds that of the earth, and his distance from us being so 
 immense; the shadows of all solid bodies will be found to flow in a parallel 
 direction : this may be seen by any observer under a clear sunshine, when 
 the shadows, as cast from the iron railings before a dwelling house, will be 
 projected from each bar, the one perfectly parallel to the other. 
 
 The rays of light falling on solid objects, such as are opaque, or whose 
 surfaces are not penetrable by light j such rays are diverted from 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 in shadow, 
 come more especially under our notice. 
 
 This will 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 
 from 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 oft' in the 
 direction, E. Now we say, the angle 
 of reflection (E C G,) is equal to the angle 
 is, the angle made by the falling ray B, 
 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 
 from 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 collection of rays, would illuminate the ceiling at H ; 
 it would again be reflected from H at an equal angle (as shewn by the line 
 H a) until interrupted again by the floor or some 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 well conceived and understood, has been 
 sometimes ably and beautifully managed by painters both in oil and water 
 
 of incidence (B C F) ; that 
 with a perpendicular dropt 
 
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 
 illuminated side of some 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, from 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 
 from S would impinge, or strike on the block B at the point C, from 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 of the 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 illuminated 
 at its extremities by means 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 published, entitled " Sciography, or Examples foi 
 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 CXXIII. 
 
 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 from 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 month 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 
 our earth will appear to rise and set in different points of the horizon at 
 different periods of the 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 
 tirst Example in Plate CXXIII. will serve to elucidate what we have to say 
 by way of explanation on this subject. In the example now before us, we 
 have here supposed the time of the Sun's rising to take place at a little before 
 five o'clock in the morning ; 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 the figure to be stationary 
 
SHAB OW§ o 
 
PROJECTION OF SHADOWS. 
 
 145 
 
 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 of the shadows, as they would be 
 projected by the sun in the opposite direction, at the corresponding hours 
 after mid-day. It will be necessary to observe that the lines from the foot 
 of the figure, as denoting the length of his shadow at the different hours of the 
 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 to which it may be useful to say something as to the 
 material to be made use of in tinting, generally termed China or Indian ink, 
 which is of various qualities. The best is that which is found to rub smoothly 
 without 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 of a mixture of sepia, (an article to be procured at 
 any of the colour shops) which partakes of a rich brown tint, and will give a 
 decided tone, retaining the same force when dry as when wet ; this will 
 tend to remove the defect experienced in the use of Indian ink alone, and 
 give at the same time a soft and mellow effect to the drawing. 
 
 2 R 
 
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 
 generally of a black colour; the other is termed the sable pencil, as being 
 manufactured from 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 of a 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 will 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 w ithin the 
 duck or goose quill, will be found to be quite as large as will 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 receptacles for tint, besides 
 a shelving groove, in which the ink is generally rubbed. The three hollow 
 receptacles serve for mixing up three different degrees of tint from the same 
 colour, before the process of tinting is commenced upon. To elucidate 
 what we now recommend, the student is referred to the Example marked A, 
 in Plate CXXIII. 
 
 No. 1, Exhibits a tint composed of Indian ink and a small portion of 
 sepia, which being mixed 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 denominated the second 
 tint. 
 
 No. 3, Exhibits the second tint as strengthened still further by a larger 
 addition of the two colours before mentioned, and is then termed the third 
 
PROJECTION OF SHADOWS. 
 
 147 
 
 gradation of tint. These three gradations of tint are almost all 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 shall have occasion to notice in 
 the fourth Example. Having thus given ample instruction as to the mixing 
 of tint in all its variety of tones, we now proceed to practice , 
 referring our student to the second Example, which represents a cubical 
 block a b c d e f g. In this Example the luminary is supposed to be 
 inclined to the front face (ad 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 f i, as measured 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 determine the sun's inclination as f k, which 
 being done, lines may be drawn parallel to this from g and h, at pleasure 
 The sun's declination being next determined by the angle m c w, lines parallel 
 to such must be drawn from the points d and c, where the rays of the luminary 
 would strike the object; their intersection with the inclined lines fk and 
 g /, at the points k and Z,wiil determine the utmost projection of the shadow at 
 hi. A line drawn from I parallel to e f, until it cuts the inclined line from 
 h, at o, will give the shadow of the side opposite to a d e f. All the inclined 
 lines, denoting the sun's inclination and declination, may be drawn as to 
 their parallelism by means of the T square with its moveable haunch or 
 shoulder. The outline of the 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, Example 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 ad e /and 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 of the shadowed 
 side of his object, commencing upwards from d c, and soften it into the 
 original tint by passing his brush slightly 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 penumbration of shadow ; that is, allowing some 
 reflection of light, either directly or indirectly, to fall on your object in shade, 
 by which the uniformity and flatness is counteracted. It will be sufficient 
 to say that the shadow on the ground is to be managed after the same 
 manner, observing to keep the darkest part of the shadow close to the bottom 
 edge of the object ; by which means a brilliancy and force will be given to 
 the object which it would not attain without. 
 
 Example 3. This object has a capping or projection A C D; the 
 same 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 
 more or less, according to the time of day in which it is projected. The 
 sun's elevation (or declination) is denoted by the dotted line A B, and 
 determines the depth of the shadow as projected from the capping A C, at B ; 
 which must then be squared across to E. The whole of the figure may 
 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 
 of the projecting cap A C D ; 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 C D. Again with the same 
 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 manner 
 in which shadowing is managed and effected; and enable him to 
 comprehend more clearly what will be offered to him in the next plate. A 
 complete and comprehensive dissertation on the laws of shadow might 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 pillars, 
 bedposts, pedestals, &c. as partaking more or less of a cylindrical form, will 
 require to be shadowed after the manner here laid down. 
 
 Having prepared a tint equal to the tone of No. 1, (Example A,) com- 
 mence with the column No 1, and with this tint in your brush pass it down 
 the shaft, in width equal to x x ; 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 
 moulding 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 
 moulding ; only not so broad : this must again be softened off at both 
 
 edges ; observing not to cover the tint first laid on entirely, but to leave a 
 portion remaining : your column 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 
 column direct from 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 column will then be brought up to the effect 
 of No. 3. 
 
 This will be found sufficient for most subjects of a cylindrical form ; but 
 where a greater strength of effect is required, the tint No. 3, a little 
 strengthened, may again be passed down from the right hand edge of the 
 shaft to the breadth of c f 3 and softened off as before ; which will 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 of the column where the sun's rays are supposed 
 to strike direct : by this means 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 
 mode and manner 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 of a 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 perspective! y, 
 and Fig. C the geometrical 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 from it on the wall and ground ; and likewise 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 number 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 Examples, will be enabled to project the 
 cast shadows for almost 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 must be laid 
 down in the plan, as shewn by the parallel line A- m, i I and eg. From the 
 intersection of these lines at m, I and g, on the wall line W W, perpen- 
 diculars are raised to the base or ground line G G, on which the sideboard 
 or original object is placed; asats, v, and u. From these points, radial lines 
 are drawn to the station or point of sight S ; which give the same points 
 perspectively on the wall line at w, and n\ 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 of the artist. It would argue want of taste to 
 
PROJECTION OF SHADOWS. 
 
 151 
 
 represent the shadows of too great a length, as supposing the sun to 
 be elevated very little above the horizon ; as well as to make them 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 determined by the line 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 of the sideboard top and rail : this 
 must be squared across to the geometrical line X at o. From this point a 
 radial must be drawn to S, intersecting the back line of the sideboard at p, 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 
 from b to z, will give the sun's declination perspectively ; to which all the 
 lines projecting the shadows from the pedestals on the wall must be drawn 
 parallel; viz. those drawn from the several projections of the top and rail; 
 these are intersected by a perpendicular raised from /?;, 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 meet in the point V, 
 which then becomes 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 from 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 of the truss at w, will give the depth of the shadow perspectively; 
 which must again be squared across on the pedestals, until intersected by per- 
 pendiculars raised from o and q in the plan. The outline of the shadows as pro- 
 duced by the truss supports, may then be drawn by hand from the points already 
 obtained. Sometimes 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 much 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 from the plan and profile, 
 proceed and transfer them 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 lines as laid down in the same, which, 
 with the instruction already given in the previous Example, will be quite 
 sufficient for him 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 of the 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 in 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 from 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. Commence by squaring these dif- 
 ferent points (I, 2, 3, 4,) across to the geometrical line G. The shadow 
 cast on the bookcase from the overhauging of the desk in the perspective 
 figure, would be equal to its geometrical depth, inasmuch as it falls on the 
 front face of the bookcase, which in itself is geometrical. This shadow is 
 intersected at d by a line 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 from the shelves, would be conveyed per- 
 spectively from the geometrical line, to the back line of the figure by the 
 point of sight, and from thence squared across, until intersected by lines 
 drawn parallel to e d, from f and g. A line squared across from 3, until 
 intersected by the inclined line drawn from h, will give the shadow as cast 
 from the side of the secretaire drawer on the frame containing the pidgeon 
 holes and small drawers. 
 
■S !lADirWES T G , 
 
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, until they impinge on the back ; as will be seen by 
 inspection of the figure. What has been already discussed in the previous 
 Examples, will 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 will be sufficient in Examples either of chairs or tables, to 
 represent the shadow as cast from the legs, by a mere touch of the brush as 
 shewn in this Example. 
 
 Plate CXXV. 
 
 It will now be requisite to draw the pupil's attention to the nature of 
 drapery in its outline, which consists of a composition of folds, either broken 
 or forming 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 made use of for producing 
 gracefulness of folding drapery, and which is mostly 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 linen 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 the same 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 still stronger degree of tint, leaving a portion uncovered of both 
 first and second tints : but should the pupil wish to give a more determined 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 of the 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 from the stem. 
 
 Fig. 2, which represents the same leaf under its first tint, will 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 Example 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 full brush, washing in the broad 
 shade from the turnover, together with the shadow cast from 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 all 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 
 
3JHLABOWWG. 
 
 cu i c d> 
 
 Icmdon.Tublishea Jcnesfc C°. Sef:2 2.1827. 
 
PROJECTION OF SHADOWS. 
 
 155 
 
 process we are taugnt to detach or make 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 
 penumbrate it towards the edge of the first shade. The same is to be 
 observed as regards the shadow cast from the outside of the leaf, which 
 must 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 must 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 brilliancy may be 
 given to the drawing by a judicious use of dark and spirited touches, placed in 
 such situation where we know that light 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 Example 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 measured from the perpendicular dotted line. 
 What has already been said in the previous Example as regards light and 
 shade in the shadowing of foliage, will likewise apply to this ; namely that 
 of laying on the shades with the first tint generally, as shewn in the second 
 Example in this plate, observing that the pen lines in the outline Example 
 be left out in all parts excepting in the outline form of the leaves ; and the 
 larger turn overs. 
 
156 
 
 PROJECTION OF SHADOWS. 
 
 Plate CVI. 
 
 The first subject in this plate exhibits the same ornament under its 
 second gradation of tint, to effect which, the pupil is referred to the 
 directions given with Plate CXXVI. With respect to the finished Example 
 in this plate, the pupil is required to make use of his own abilities, as he 
 must by this time 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 piate shew in some measure, how far, by a 
 judicious combination of forms, a tasteful design in ornament may be produced: 
 this is what is termed 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 i? 
 commonly termed Colouring. 
 
KI..E.M]E^rTS OF OfflAlIE If To 
 
V ! I ( XXV II 
 
 A. B. C. Are //><• three Primitive Gflourj, 
 
 D r.t. tied mix-'d with Yellow, 
 
 E. Ay. fifue , riii.r tf H-if/i }', //<■!!: 
 
 F. Is. Mile, mix'd. )r///i fir,/ , 
 
 v f ) [. o I' [ I I v r, , 
 
 A 
 
 making /t/i Orange-. 
 
 tna/wrta a. ti/ern . 
 
 making a frtrplr 
 
 YMoivs ,_, Slues 
 
 a , . «v f 
 
 -Z2 
 
 .'■'I IT I V K '!' ITN'TS , y\ IXKI). 
 
 .V s , 
 
 mien' 
 
 wit/i Med. 
 
 J3\ 
 
 16\ 
 
 A/ 1 
 
 y<rj wit/i Btu* 
 
 7B 
 
 .v 
 
 Blur 
 >vlf* Asa 
 
 21 
 
 Burnt Vm&er 
 felle>n» with Jfu/vil 
 
 with Vermiffioji- . Terra de, Sieitna. 
 
 Car/nine 
 witli tt'vme 
 
 27% 
 
 YeUo w Cker 
 with 
 
 Burnt Si&ii/lt; 
 
 ROXED COIOI'BS 
 
 luttiti/t JnA- 
 with (iu rnuie . 
 
 33 
 
 lii/rimir Jti/rnt ' . 
 t HttW .Sifimrl 
 
 isPrussian Blue. 
 
 /iirmiiw .(nimlit'Ot' 
 
 Jf/nr Sienna . 
 
 Bui itt miller 
 
 35 
 
 J. iaht Jted 
 
 tohtJirti M itA 
 
 ZivAt tie J. 
 Burnt fj?iAe/: 
 .Burnt Sien/ia . 
 
 Jiitt'. 
 nwreRat i-Blii< 
 
 IrUt* 
 Amr MM 
 
 *6 
 
 Dtt* 
 . -r A 
 
 JitM'wm 
 
 - 
 
 Zeitow Oker. 
 Burnt Sienna. . 
 Burnt I 'in tier. 
 
 -/.>- 3.5. fiat 
 more Burnt rmtier. 
 
 Venetian Bed. 
 trr'inr A'; 
 
 tiirmuie .(• 
 Burnt f'niAe/ 
 
 /nrvv Btur 
 
COLOURING. 
 
 157 
 
 COLOURING. 
 
 There are, properly speaking-, but three primitive colours ; viz. blue, 
 yellow, and red. These colours by a mixture one with the 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 : that is, partaking of many 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 yellow and Roman ochres ; vermillion, 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 recommended. Those already enumerated are all that are 
 likely to be brought into use in colouring either drapery, or cabinet furniture , 
 or any other subje'ct confined to the two branches of Upholsterer and 
 
 2 u 
 
158 COLOURING. 
 
 Cabinet-maker. It remains therefore to give some instructions loour pupil 
 as to the art or manner 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 light. 
 
 No. 10 and 11, 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 small 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 same, mixed up with a greater proportion of the blue ; 
 and then becomes a full grass green 
 
 The management of these tints in colouring must be after the same man- 
 ner as those preceding. 
 
 No. 21, Is Prussian blue, with a small portion of carmine, and makes 
 when thus mixed, 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 vermillion. 
 
 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 composed of a light mixture of burnt umber, and burnt 
 terra de sienna, producing a warm drab colour. 
 
 No. 30, Is produced by a stronger mixture of the same colours; 
 making 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. 
 
COLOURING. 
 
 No. 34, Is carmine mixed up with raw sienna, burnt sienna, and a small 
 portion of blue; this mixture produces a mellow warm 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 all 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 yellow drapery. 
 
 No. 37, Is produced by a slight wash of light 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 of the 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, £cc. whose 
 trimmings are intended to be either blue or gold. 
 
 No. 42, Is Venetian red with Prussian blue, producing a grey tint; 
 curtains, &tc. 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 gold or blue. 
 
 No. 44, Is compounded of Venetian red and 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 termed a neutral tint. The neutral tint is much used 
 amongst artists, in painting landscape scenery or subjects of architecture. 
 In the former, this tint is varied in its mixture or tone according to that 
 portion of the landscape over which any positive colour is to be placed. Thus, 
 this tint should partake more of the blue or grey tone, for some portions of 
 the clouds and distant objects in the landscape • it should be mixed up with 
 more of the red where rocks and warm fore ground occupy a place in the 
 picture, and again this tint should partake more 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 same tint lightly mixed, the blue holding the pre- 
 ference. 
 
 No. 49, Is a mixture of Venetian red, crome and flake white. 
 
 No. 50, Is what may be termed a lavender tint, and is compounded of 
 flake white, carmine and Indian ink. 
 
 There are many other tints to be produced in water coloar painting by 
 the mixture 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 salmon colours, as No. 49 ; the lavender tint, No. 50, and 
 many 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 
 much 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 ample directions for the mixing of transparent 
 colours, and producing all their variety of tint, it only remains to offer 
 instructions as to the manner of disposing them in any drawing that is 
 intended for colour. 
 
 It' must 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 example, 
 
 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 of a 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 more 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 master more effective, which at all 
 times cannot but be of service, inasmuch as explanation by word of mouth 
 is often better understood than much reasoning on paper. With an earnest 
 desire that his limited knowledge may prove of service to his friends and 
 students, the author here consigns them to their own studies, trusting the 
 helps he has afforded them 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 terras to 
 elicit what he wished others to comprehend as well as himself. Having said 
 thus much, the remaining portion will henceforth consist in explanatory 
 descriptions of the different designs of furniture introduced throughout the 
 work, together with their uses, mode of manufacture, &c. We shall first 
 commence with those of decoration, as they are exhibited in the platen 
 offering such remarks as the change of fashion and times have occasioned. 
 
INTERIOR DECORATION. 
 
 163 
 
 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 embellishment. 
 Not to go further back than the period in which architecture flourished 
 amongst the Egyptians, we find in the ruins of their temples, their 
 catacombs and obelisks now existing, many examples of ornamental deco- 
 ration, evidently the work of hands, superior in talent to the common 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 from the Egyptians, or the Egyptians from the Hindoos, 
 can be but of little moment at this period : it is sufficient that we observe in 
 the works of both nations an accordance and similarity as to the disposal of 
 their parts into imposing 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 temples, their vases and other works of art. To these succeeded the 
 decoration of the Etruscans, a Grecian colony, visible in the remains 
 of their public and private buildings, baths, &c. lately discovered at 
 Pompeii and Herculaneum. From the era of this people, we pass on to the 
 time in which the arts of design flourished amongst the Romans, when decora- 
 tion may 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 men of genius flourished, whose works may be seen in the Vatican 
 and palaces of modern Rome ; and likewise in many of those in the neigh- 
 bouring states of Italy, as also in various parts of France. However much 
 we may admire and become prejudiced in favour of the light and airy stvle 
 reigning throughout, and almost 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 manly 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 may not be paying an exaggerated encomium 
 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 whom 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 oruamental 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 many proficients in this 
 department of art we must not omit to mention Mr. R. Nelson, whose 
 abilities entitle him to great praise, and to whom the Author feels himself 
 indebted for many valuable practical hints. Several others might be here 
 enumerated, but we shall close this article bv merely intimating that the 
 present work will contain specimens 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, Roman and Saracenic or Gothic styles. Specimens will likewise 
 be given of that of the Franks in the age of Louis XIV, together with the 
 present prevailing taste now in vogue in our own island Great Britain ; all 
 of which will be noticed in the descriptive account accompanying each 
 design. 
 
INTERIOR DECORATION. 
 
 165 
 
 Plate XXVIII. 
 
 In this plate are given four different designs for corner ornaments 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 
 ornaments are worked in various ways ; sometimes carved and finished in 
 gold ; on other occasions painted in oil or distemper, as representing the 
 effect of basso relievo ; and frequently executed by the French in a style 
 which they term Rehaussee 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 manner on a brown ground, and which is commonly called the golden 
 print; it is now extremely 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 blossom, a stone colour, &c. ; the stone 
 colour decreasing in force to almost a white, and approaching nearly to a 
 cream colour. In all these cases the style of the panel may be of a similar 
 colour as the ground, but worked darker for the purpose of giving the 
 appearance of projection to the panel itself. A gold moulding 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 apartment, will in this case 
 make the finish. Where the corner ornaments are carved and gilt, the straight 
 mouldings betwixt them forming the panels must be of gold also. In cases 
 where the ornaments are painted, the mouldings apparently parting from them 
 should be painted also ; which may then be relieved from the ground by a dark 
 line underneath, and a light one above : the same 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 rooms and boudoirs. 
 The ornament in the middle of the plate will answer as a central ornament 
 in decoration ; whether upright or horizontal, in carving or painting in relief. 
 
 2 Y 
 
166 
 
 INTERIOR DECORATION. 
 
 Plate CXXXIII. 
 
 The four designs given in this plate, and numbered 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 and 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 ornamental Pilasters, intended 
 to be painted in distemper 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 arrangement of 
 ornament, will always present a pleasing and imposing effect; particularly 
 when executed with taste by the artist, as regards light and shade. 
 
 Plate LXXXVI. 
 
 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 ornamented frame above, which should be finished entirely in Or, Matt 
 and burnished gold. On the external Angles, marked A A of the chimnej 
 
ANTERIOR DECOKATIOS, I 
 
 t [ 
 
 4 
 
CHYM^EX GILA § § -9s DECOHATIOH, 
 
 London. Published W Jones & C? Or 
 
INTERIOR DECORATION. 
 
 167 
 
 breast, are to be fixed gilt mouldings. In handsome apartments, the base, 
 and sarbase mouldings of the dado, marked A A, are frequently finished 
 in gold. A gold moulding to suit, should be carried round the room 
 under the lower member of the cornice at top ; and over the upper 
 member of the dado at bottom. The internal angles should have a 
 double moulding, the reverse of those that are on the external angles of the 
 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 frame. 
 
 Plate XXXIX. 
 
 Four designs for mouldings fully enriched are given in this plate, 
 which may be used for various purposes : viz. for the cornices of windows, 
 in which case they are intended to form the upper mouldings, and should be 
 carved and finished in gold ; or, where the expence becomes an object, the 
 ornaments may be procured in composition. These mouldings on a smaller 
 scale may be accommodated for cabinet furniture, and may be either cast in 
 metal or carved in wood. The Greek frett, and Italian guilloche, of which 
 we have given examples in plate XL. may be as variously applied in 
 Decoration : for example, the frett may be adopted to ornament 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 guilloche is peculiarly adapted for soffit decoration, and may 
 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. 
 
INTERIOR DECORATION. 
 
 Plate CXLVII. 
 
 EGYPTIAN DECORATION. 
 
 This plate and the three that follow it, offer in themselves specimens 
 of the different styles of decoration in use amongst the antients, but adapted 
 to our modern English apartments. We shall commence 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 time a vestige 
 of any of their private buildings or Palaces, yet we have sufficient specimens 
 still existing in their temples, grottos, &c. from whence a style after their man- 
 mer may be drawn : this has been successfully attempted by the elder 
 Piranese in his design for a coffee-room at Rome, as shewn in his works ; 
 but it is too close a copy of a style and manner which in all its parts is 
 massive 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 forms the entrance 
 side. The casing for the doors is copied from the doorway or entrance as seen 
 in most of the 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 ornamental decoration 
 on which should be of raised gold : the frieze also should be worked after 
 the same manner. The four angles of the room may receive a moulding in 
 the form of a 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 may represent the portraits of Cleopatra and Antony. The 
 bookcase will be seen to partake of the general form and character of the 
 Egyptian temple, before the pilasters of which are placed bronzed figures 
 
INTERIOR DECORATION. 
 
 169 
 
 of Osiris and Isis and other Egyptian Deities : all the other embellishments 
 in this apartment should partake of a similar 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 from 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 time made themselves masters 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 
 magnificent structures, their temples. 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 numerous 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 may 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 may be termed an apartment 
 decorated after the Grecian taste ; compiled from the materials already 
 
 2 z 
 
170 
 
 INTERIOR DECORATION 
 
 alluded to, and suited to the general proportion of our modern houses. 
 This apartment may be considered as a withdrawing Room, being connected 
 with that considered as the principal or state drawing room. 
 
 As very few even of our best modern houses can boast of much 
 profusion of architectural embellishment, we shall presume that the whole 
 of the decoration in the piate before us to be entirely the effect of painting 
 either in oil or distemper ; the sofa and tripods forming an exception : the 
 first an article of indulgence, the two other menbles forming receptacles for 
 flowers or perfiimes ; being appropriated to thesame use as the larger Chinese 
 vases, and which when filled with the leaves of dried flowers and other 
 aromatics, is termed by the French, une Pot Pourri. It is needless to enlarge 
 further on this plate, as we shall have occasion to make some observations on 
 the design in the next, which may be applied to this likewise. 
 
 Plate CXLIX. 
 
 ETRUSCAN DECORATION. 
 
 The design in this plate is after the taste which prevailed amongst the 
 Etruscans at Pompeii, a part of Magna Grseca, where many of the 
 Roman nobility erected their villas. The subject of the present plate 
 forms a design for decorating the walls of a morning room ; and is com- 
 posed from the paintings in Fresco recently found on the walls of an apart- 
 ment in the Villa of Marcus Arius Diomede at Pompeii. The execution 
 is evidently by the hands of Greek Artists ; as are also those paintings 
 found in the villas of — Acteon, and C. V r ibins Pansa* in the same town. 
 There is a great degree of taste preserved in the arrangement of the 
 colouring ; for we find the panel forming the body of the wall, kept of a 
 light colour, and producing the effect of projection when opposed to the 
 
 * Pansa was one of the two last Consuls who enjoyed the dignity of chief Magistrate before 
 the decline of the Roman Empire ; he pursued the assassinators of Julias Caesar, and was killed in 
 a battle near Malina ; some suppose he was put to death by Octavius by the means of poison. 
 
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, whi?h 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 lightness 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, marble vases, statues, consoles, pilasters and panels found 
 amongst their ruins that we are alone enabled to form any idea of the 
 magnificent arrangement and decoration 01 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 made 
 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 of 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 became 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 Roman 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 became eliptical and much flattened ; this 
 species of arch was the earliest in general use in England, and both the one 
 and the other, viz. the lancet and eliptic forms were called Gothic, however 
 improperly; which have nevertheless been brought to very great per- 
 fection, the proof of which may be 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 building 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 
 massive and heavy, consisting chiefly of bold and highly relieved mouldings, 
 with other members partaking of the 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 specimen of the taste that prevailed 
 in the age of Louis XIV. and displays the style of decoration used during 
 that period, in the best houses of the nobility and gentry in France. 
 We generally find the walls of most of their apartments divided into 
 compartments and ornamented with pilasters, painted frequently in imita- 
 tion of the finest marble ; and sometimes panelled out, and decorated with 
 richly carved ornament. The mouldings around the panelling on the walls 
 were usually of a very bold prefecture, and wholly enriched. Most of this 
 species of decoration was executed in Norman oak, and would frequently 
 be partially gilt ; and the interior panelling, if not left in the plain oak, 
 was generally filled up with the finest Coblentz tapestry. 
 
 If we refer to the Meubles or Garniture of these apartments, we shall 
 find them to partake of the same boldness of form and enrichment of 
 detail, as displayed in the architectural embellishment of the rooms. In 
 most of their tables, the tops were of the finest and variegated marbles, 
 around the edges of which would be fixed a bold projecting moulding of 
 brass, chased and gilt ; and the frieze or rail under the moulding was fre- 
 quently enriched with finely executed ornaments in Or Molu. The pillars or 
 supports to these tables were sometimes of a turned form, and richly decorated j 
 at other times the supports would be composed of grotesque chimera figures 
 and foliage ornament associated together : a plinth, either of fine marble, 
 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-frames, &e. each, and 
 all partook of the same splendid style of enrichment ; and although there 
 might and did exist, a bad taste in the design and arrangement of many of 
 the parts composing 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 mansion of the nobleman ; 
 but is no ways answerable to the dwellings of persons of small fortune. This 
 
 3 A 
 
174 
 
 INTERIOR DECORATION. 
 
 style of decoration has lately been introduced by Messrs. Philip 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. James Wyatt, his late Majesty's surveyor-general. As this mansion 
 is solely appropriated to nightly purposes of pleasure, perhaps such a taste 
 may be in unison with the wasteful transfer made of property in such esta- 
 blishments. From the extravagant expence attending it, such a style of 
 decoration cannot be recommended, except in instances wherein property 
 would justify its adoption. 
 
 Plate CLIII. 
 
 The style of decoration exhibited in this plate may properly be termed 
 French, inasmuch as it was first introduced into this country by certain 
 French artists, brought over from France by Messrs. G. and F. Echardts ; 
 who not only engaged in their service the most eminent decorative painters, 
 but also those excelling in the flower and landscape departments. These 
 efforts, although aided at the time 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, improving upon the lessons 
 of their neighbours, have succeeded in producing a similar effect at a much 
 less expence ; for what before was only effected by the hand, has now 
 been accomplished by the art of printing. 
 
 A different style of decoration has lately been introduced from France 
 by the manufacture of a composition of paper into every species of ornament, 
 whether for the walls of an apartment or interior decoration in general. This 
 species of manufacture has been called Papier Mache, which in fact is nothing 
 more than paper reduced to paste, and then forced into moulds of the form re- 
 quired. In this instance we now excel our inventive neighbours in the execu- 
 tion of the same article; the English manufacture being more durable as well 
 as more imitative of real carved work, from 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 from the great inventive faculties of some of their first rate 
 artists, being men wno l, aV e acquired and possess a taste for the beautiful, and 
 
HOUSEHOLD FURNITURE. 
 
 175 
 
 have been foremost in furnishing materials for all the inventive and orna- 
 mental decorations necessary to the embellishment of the houses of their 
 principal nobility and gentry. These observations will render it unnecessary 
 to go into a lengthened explanation of the plate before us ; it will 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 distemper 
 color, aided only by mouldings in gold where the panne! would require it. 
 It will be easily seen by comparison, 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 ornaments (putting expence out of the question), will 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-rooms : 
 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 damask, 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 may 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 makes 
 up very beautifully, not requiring a lining. Drapery will ever give 
 consequence to an apartment, and although it may for a time be in disuse 
 from the caprice of fashion, it will always be adopted wherever a good 
 
17G 
 
 HOUSEHOLD FURNITURE. 
 
 taste prevails ; economy may render the plain vallance 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 almost every design as applicable to domestic furniture, there arises 
 a necessity for using a variety of colours, inasmuch as a gay and more lively 
 effect is produced by the contrast ; but if we refer to a more chaste style 
 of colouring, and particularly so as regards curtains, it will be found in the 
 use of one colour alone, such tint predominating throughout the whole : two 
 other tints may be used, but the three must be of one stock, each varying from 
 the other only by a darker or lighter gradation of the same tint. Where 
 drabs are entirely used, a modest or quaker-like appearance will ensue, 
 but nevertheless the general effect will be pleasing and in true taste. 
 
 Plate XXXIII. No. 4. 
 
 The observations made on the designs in the preceding plate 2, will 
 applyjikewise to the two designs exhibited in this ; which being likewise 
 intended for drawing room decoration, what becomes necessary in the one 
 will be found equally so in the other. 
 
 Plate XXXVII. No. 6. 1 
 
 We have in this plate given a design for the decoration of a single win- 
 dow, wherein drapery has been dispensed with; the same being intended for a 
 drawing room : as such, the materials should be of the same quality as before 
 recommended for such rooms. The cornice is carved and gilt, and in design 
 after the style and manner used in France during the lifetime of Louis XIV. 
 The vallance or mantle is gathered into flutes, from each of which ruav be 
 suspended a tassel. This style of curtain has something handsome and rich 
 in its appearance ; it is sometimes termed petticoat, and at other times 
 hammercloth 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 room, in which 
 case we would recommend the material to be either of fine cloth, Merino 
 damask, or of moreen. 
 
 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 form 
 a handsome arrangement. 
 
 Plate XCV. 
 
 The style of window decoration exhibited in this plate is similar in taste 
 to that which prevailed in England about the period when Queen Elizabeth 
 was on the throne ; the same continuing in use afterwards until superseded 
 by a taste for drapery, first introduced into this country from France. It 
 is a style certainly well adapted for rooms that have but little blank 
 space or dead light above the windows, and may 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 same 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 bullion 
 fringe is suspended from the lath. 
 
 Plate XCVI 
 
 ... design, shewing the style and manner of fitting up the curtains and 
 drapery to a circular headed window : its enrichments will entirely depend 
 on the apartment it is appropriated to, for this window is equallv 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 
 cantonier tails can be admitted, as in this design, a finish is then made to the 
 window, which makes any other addition unnecessary. The taste or system 
 of using bronzed metal or its imitation 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, composition may be 
 used. To this cornice is attached what is properly termed a stone drapery, 
 from its existing in most of the antique female statues at Rome, and forming 
 that portion of the vestment attached to each shoulder by a button, and which 
 falls down on the breast into folds similar to those in the present design. This 
 design is intended for a drawing room, from the enrichment of the cornice and 
 great depth of the drapery : but with a plain japanned or painted cornice, 
 and less depth of drapery, the same 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, will apply equally to this, and render further ob- 
 servation needless. 
 
HOUSEHOLD FURNITURE. 
 
 179 
 
 Plate XIX. No. 5. 
 
 In this design the two windows arp 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, will equally answer for 
 this. 
 
 Plate CXt. 
 
 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, 
 &c, 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. 
 
180 
 
 HOUSEHOLD FURNITURE. 
 
 Plate CXLI. 
 
 This plate presents a design for a suit of curtains and drapery adapted for 
 three windows. The drapery is arranged in continuation over the windows 
 and two piers, the same being suspended from a pole cornice with ornamental 
 ends richly carved and gilt, and having ornaments in the piers to suit. 
 The drapery in this design is of an opposite colour to that of the curtains, 
 which is frequently done for the purpose of giving a better effect in the 
 drawing. In execution there can be but one choice, viz. that the cur- 
 tains and draperies be of one colour, whatever the material may be of which 
 they are made ; nevertheless, where the quantity of silk or other material 
 may fall short of what is requisite for the whole suit, we are not so restricted 
 by rule as to be precluded the advantage of using two colours, whenever the 
 same may be done with taste and judgment. This arrangement of curtains 
 and drapery has already been executed in a light blue tabaret, with gold 
 coloured trimmings, and a cornice similar to that of the present design ; pro- 
 ducing, in the whole, an effect that gave universal satisfaction. 
 
 Plate LXXIII. 
 
 As there have been many houses of Gothic structure erected, particu- 
 larly in different parts of the country, it has been thought necessary in the 
 present work to introduce a few specimens in that style. The design in 
 this plate is adapted for an apartment of three windows, such being placed 
 in a circular wall. The cornice is supposed to be of oak, in which case it 
 will require to be wholly carved ; but where expence is an objection, it 
 may be manufactured of deal, and the ornamental parts made of composi- 
 tion; the whole of which may afterwards be japanned closely in imitation 
 of oak by a skillful painter or japanner. The valance is well suited for 
 such a style of design, where festoon drapery would become improper; and 
 the arrangement would answer equally well for the drawing room, dining 
 room, or library. 
 
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, commonly 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 climate 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 many cases admitting 
 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. The principal bedrooms in cottages, small villas, 
 &c. may 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 the 
 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, which 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 manufactured either of silk, of chintz, or 
 Merino damask, and the whole will then form a bedstead and hangings 
 suitable for a state apartment. 
 
 Plate CXVIX. 
 
 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 trimmed 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 of the 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 FURNITURE. 
 
 Plate CXXX. 
 
 In this design, the expence of cornice with its ornaments, &c. has been 
 dispensed with; the whole embellishment consisting in the wreaths and shells 
 necessary for supporting the festoons. These ornaments 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 
 &c. 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 \ inches square, the other two requiring a 
 scantling of only 5 \ 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 XCVIL 
 
 The field, or as they are sometimes termed tent bedsteads, are so much 
 in common use as to render a description of them almost 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, may be 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 orne. 
 
 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 composition, so far as relates to a bed somewhat above that 
 in common 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 domestic comfort s 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 humble 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 Doles placed over 
 
 3 D 
 
186 
 
 HOUSEHOLD FURNITURE. 
 
 each end of the couch, so as to keep the curtains a sufficient distance from 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. 
 
 C II A 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 tombs 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 specimen of chair after this taste was one, designed some 
 years back for furnishing of the drawing rooms of Henry Baring, Esq., and 
 manufactured for him by the Author. A similar style of chair may likewise 
 
HOUSEHOLD FURNITURE. 
 
 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 of the 
 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 of the chairs, 
 contained in the present collection of designs, beginning with 
 
 Plate III. 
 
 The two designs contained in this Plate are wholly fanciful ; the one on 
 the left hand being after that of the French school, and the other partly 
 Grecian. They are both intended for furnishing the drawing room, the 
 frames being manufactured in rosewood, with 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 either 
 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. Both 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 frame 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 frame to be 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 
 
190 
 
 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 made 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 the 
 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 CXXXV1. 
 
 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 wrought 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 of a 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 must be regulated by the rest of 
 the furniture in the apartment. 
 
HOUSEHOLD FURNITURE. 
 
 193 
 
 CABINET FURNITURE. 
 
 There are no people of any country whatever tnat excel the English 
 in the manufacture, the construction, or taste in design as regards the article 
 of cabinet furniture in general ; all of which is distinguished by a lightness, 
 and a fitness for the purpose intended ; accompanied by a delicacy and 
 neatness of finish, peculiar to the British artizan, that no where has its 
 equal. We do not by this encomium on our own countrymen, mean to 
 debar our neighbours or competitors of their share of merit. The artizans 
 of France are ingenious in their invention, but are rarely to be distinguished 
 for their care in construction : — no people are more ready at contrivance, but 
 withal they have not patience to avoid clumsiness in their finishing. In almost 
 all their designs for furniture there reigns throughout a heaviness, arising in 
 a great measure from their aiming too much at architectural character ; 
 than which, as it is applied to furniture, nothing can be in worse taste or 
 keeping : — It gives to their wardrobes, escrutoires, bookcases, &c. more 
 the appearance of ponderous masses of wood ; and in many instances 
 renders them unsightly as articles of taste. If however, they are deficient 
 in point of taste in design as regards their larger articles of domestic 
 furniture, they amply excel in those of the smaller kind ; for in whatever 
 relates to articles for feminine use, such as their work-tables, writing-tables, 
 chiffoniers, dejune-tables, trick-track tables, dressing-tables, and many other 
 meubles of the same kind, — all these possess an elegance and taste in their 
 design, as well as a great degree of beauty in the ornamental decoration of 
 their parts, to which they as pieces of furniture are chiefly indebted for that 
 pleasing effect prevailing in them ; such ornaments being the production and 
 design of perhaps a first rate artist : and the execution as to the modelling, 
 casting and finishing in metal, being equally excellent. 
 
 In this place we must not omit to mention another race of artizans ; 
 viz. the Germans, as being ingenious in almost every branch of mecha- 
 nical art placed under their hands : — they possess the grand essential 
 
 3 p 
 
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 them 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 
 known 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. Boileau, who was 
 formerly employed 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 he 
 has never been surpassed by any modern 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. 
 
 195 
 
 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 ; 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 have mirrors placed over them. The lower design in Plate 
 XXVII. is represented as having its sides inclosed, the panels of which on 
 
196 
 
 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 or 
 rosewood, fine mahogany, or of any other fancy woods. The table in the 
 second design is furnished with a backgammon board, and a sliding cover, 
 divided either for draughts or chess. A profile and plan is given with 
 each table. 
 
HOUSEHOLD FURNITURE 
 
 197 
 
 Plato 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 ornamental 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 almost 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, &c, as shewn in the plan : — one of these 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 
 class 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 necessary 
 for the toilette : this table, like the one preceding, has its dressing 
 glass fixed to the back, and may be manufactured of woods of the same 
 description. 
 
 3 G 
 
198 
 
 HOUSEHOLD FURNITURE. 
 
 Plate LIX. 
 
 This design is intended as a double wash-hand table, and is wholly 
 after the French taste. The top containing the basons, &c. is intended to be 
 of marble, and the frame under it to be made of the finest figured mahogany, 
 which in the inside is lined throughout with lead. This table is supported 
 by four truss shaped legs, resting on a plinth ; the ornamental parts of which 
 maybe of metal, 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, accompanied 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 rosewood ; if of 
 the latter, the whole of the ornamental 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 shelf, and the rings 
 attached to the swans heads. The same 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, See. 
 
HOUSEHOLD FURNTTURE. 
 
 199 
 
 Plate CXXX1X. 
 
 Two designs for tripod stands for flower baskets. These stands being- 
 intended for the drawing room, should be of the finest mahogany or rose- 
 wood, with their ornamental parts in metal gilt, or in wood carved and gilt. 
 In economical cases they may be manufactured in common wood, and 
 japanned. A plan is given with each scale, by which the parts may be 
 measured. 
 
 Plate XXXV. 
 
 Two designs for card tables with pillar and claw supports ; which when 
 much enriched as in those before us, should be made of rosewood, having 
 some parts finished in gilding : — the tops are best when lined with velvet 
 instead of cloth. The advantage in the construction of these tables consists 
 chiefly in the top turning round upon the frame, in which case it then 
 answers as a kind of loo table. 
 
 Plate CIX. 
 
 A design for a hall table. This description of table in general is very 
 plain in its design, when adapted for the common hall or entrance to most 
 houses ; but we here give a design for a table, answerable for the hall of the 
 nobleman's mansion: it will be sufficient to say that the material used in its 
 construction should be mahogany, and whatever constitutes ornament about 
 it, should be carved out of the same wood. In some cases a drawer may 
 be added for containing cards of address, the Court Guide and other books, 
 which the hall porter may have occasion for. 
 
HOUSEHOLD FURNITURE. 
 
 Plate XCIX. 
 
 A design for a sideboard table : this description of sideboard is adapted 
 for a dining room in a moderate sized house, where room would be 
 wanted for separate pedestals and the space necessary between them and the 
 side table. This sideboard may likewise be used on an enlarged scale where 
 pedestals are not required ; the use of which is substituted by a sarcophagus 
 cellaret being placed under the centre. The whole design is made plain to 
 the workman by the addition of the plan, profile, and scale of feet. 
 
 Plate IV. 
 
 In this plate is given a design for a sideboard and cellaret, with circular 
 pedestals at each end detached ; their use being explained by the plan below , 
 in which will be found letters of reference to each part. It is to be observed 
 that such a sideboard with its pedestals will require a space of at least 
 14 feet, and therefore no way adapted for small houses. 
 
 Plate LXXV. 
 
 Exhibits a design for a pedestal sideboard ; the one side adapted for 
 a cellaret or store for wine; the other being fitted up with racks and a heater, 
 and lined throughout with tin, for the purpose of keeping the plates warm 
 during the time of dining. Under the centre is placed an oval open cistern 
 lined with lead inside, intended for holding the ale and beer jugs, as well as 
 to contain I he ice for cooling the wine in hot weather. 
 
 Plate LXVI. 
 
 Two designs for pedestals to stand detached from the sideboard : — they 
 are here given geometrically, and therefore may be measured by the scale. 
 These pedestals may be fitted up for the same purposes as those described 
 in Plate LXXV. 
 
HOUSEHOLD FURNITURE. 
 
 201 
 
 Plate LX1II. 
 
 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 form 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 el 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 of the solid. 
 The insides are lined with lead to receive the beer and ale jugs ; or at other 
 
 3 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 CVIT. 
 
 Contains two designs for cellarets or stores for wine, 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 of the mouldings, kc. 
 
 Plate VI. 
 
 This elegant piece of drawing room furniture is intended for the 
 end of an apartment, to be placed opposite the chimney piece; or in 
 
HOUSEHOLD FURNITURE 
 
 203 
 
 some cases it may be placed between two doors. The inclosed ends are 
 generally appropriated for the reception of music books, &c. : — sometimes 
 the tops are made of valuable marbles, or otherwise of their imitation 
 called scagliola. 
 
 Plate CIL 
 
 This Plate shews two designs for drawing room commodes, intended 
 for filling up the piers between the windows of a drawing room ; the doors 
 of each commode have an ornamental brass guard fixed before the silk. 
 A profile is given with each design as a guide to the workman in measuring 
 the parts. 
 
 Plate LXIX. 
 
 Contains a design for a commode in the Gothic style, to be manufac- 
 tured of rosewood when intended for the drawing room; in which case the 
 open space in the centre may be appropriated for the reception of ornamental 
 China jars, and be filled up with plate glass at the back. When appro- 
 priated for the library, this piece of furniture may be made of mahogany, 
 and the centre space in that case, be destined for receiving the terrestial and 
 celestial globes. 
 
 Plate LXXII. 
 
 In this plate are given eight various patterns for the supporting feet of 
 cabinets or commodes the design marked A, A, being shewn in profile 
 as well as in front. The last three designs are intended as supports for 
 foot-stools. 
 
 Plate LXI 
 
 Exhibits two designs for dressing room commodes after the French taste. 
 The drawer over the truss supports in the first design is sometimes 
 
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 effect 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 outside 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 aud 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 habiliiraents de mat. The proportions may be obtained 
 from the elevation and scale as before mentioned 
 
HOUSEHOLD FURNITURE. 
 
 205 
 
 Plate CVIII. 
 
 This design for a lady's dwarf wardrobe is of similar dimensions to that 
 in the preceding Plate, but is different as to the arrangement of tht 
 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 CI. 
 
 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 
 projections. 
 
 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 Je 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 r 
 
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 LXL 
 
 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 CXXXVIII. 
 
 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 the 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 
 shut out from a view of the 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, &e., 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 XLI. 
 
 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 of 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 for the 
 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 
 
208 
 
 HOUSEHOLD FURNITURE. 
 
 bookcase has now been brought into general use ; — it affords au opportunity 
 for placing antique vases, or pieces of curious ornamental china on its top, 
 leaving an ample space on the wall above for the placing of pictures. All 
 the dimensions in regard to height may be obtained from the elevation, 
 the front being nearly geometrical ; and the plan will give all the required 
 projections. 
 
 Plate CXLII. 
 
 A design for a dwarf bookcase, intended to occupy the entire blank 
 space which the walls of a library may offer ; whether between two doors 
 or any other side of the apartment. The style of this bookcase may pro- 
 perly be termed Roman ; and those who are best acquainted with the anti- 
 quities of Italy, will at once see from whence the composition has been 
 drawn. The central part with the wings, is represented as having the 
 doors filled with silk, the intention of which is to afford more variety, 
 and in some measure give repose to the eye, which is oftentimes little studied 
 in the arrangement of extensive libraries ; for nothing can distress the eye 
 more than the sight of a countless number of volumes occupying one entire 
 space. What we have before observed in the preceding article as to the 
 placing of vases, &c. on its top, will also apply to this, and render it unne- 
 cessary to add any thing further. 
 
 Plate XCIII. 
 
 This Plate contains six various designs for fitting up the panels of 
 bookcase doors. The three designs in the upper portion of the plate 
 represent only one half the height of each door : — the parts may be mea- 
 sured by the scale given. 
 
HOUSEHOLD FURNITURE. 
 
 209 
 
 Plate XVIII. 
 
 The candelabra in this Plate are intended for drawing rooms 01 first 
 rate dimensions, and may be executed after two manners : — the one wholly 
 in carving; the other by the use of composition. They may be finished 
 either wholly in gilding, or otherwise with a mixture of bronze. 
 
 Plate CXV. 
 
 Contains two additional designs for candelabra, on a scale of greater 
 magnificence than the preceding, and adapted only for state apartments. In 
 other respects, the manufacture of these ornamental articles of furniture, as 
 regards their finishing, will be the same as those last described. 
 
 Plate CXXXIV. 
 
 In this Plate are given four different designs for candelabra of smaller 
 dimensions, intended to be placed on dwarf bookcases, commodes, or pier 
 tables ; and sometimes on encoignures or angular commodes, meubles which 
 are very much used by the French in the angular corners of their apartments. 
 They may be finished after the same manner as the preceding. 
 
 Plate XXII. 
 
 In the larger dwellings of our nobility and gentry, and likewise in the 
 apartments of individuals of smaller fortune, the Jardiniere has always been 
 considered an essential article of furniture, as containing, whether in 
 summer or winter, all the varieties and endless beauties of Flora. In France, 
 this species of interior furnishing is carried to a very extravagant extent as 
 far as materials and decoration will allow. We have contented ourselves 
 
 3 K 
 
210 
 
 HOUSEHOLD FURNITURE. 
 
 with supposing the body, the supporting columns and plinths in the present 
 design, to be executed wholly of mahogany, with no other embellishment 
 than merely the fineness of the wood and the beauty of its polish, the caps 
 and bases of the columns being cast in metal and gilt. The upper basket 
 may be of wire work painted. The body of the Jardiniere is lined inside with 
 lead, having a socket and plug to let off the water which may accumulate 
 from refreshing the plants. The aviary may have its ornamental supports 
 and its cornice of bronzed metal, the spaces between which and the dome 
 above being filled with wire work, the whole standing upon a marble plinth, 
 on which is placed a marble vase containing water for the warbling inha- 
 bitants in their wiery castle. 
 
 Plate LXVII. 
 
 On the left of the plate are three designs for cornice centres, from 
 which the drapery would be suspended and pass off right and left, and again 
 be suspended by ornamental ends, such as those shewn on the right hand 
 of the plate. These ornamental embellishments to the window curtains are 
 mostly carved and finished in gilding; sometimes brass or composition is 
 substituted, for the sake of economy. 
 
 Plate XCI1 
 
 The first design in this plate exhibits a cornice, adapted for the 
 window of a house furnished after the Gothic style, the manner in which it 
 is cabled, fluted and ornamented with beads, being of Saxon invention ; 
 this cornice with its ends, &c. will appear best when executed in oak. 
 
 The two last designs should be wholly carved and gilt, to produce a 
 good effect, although in some cases composition may be resorted to, where 
 the expence of carving would otherwise prevent the adoption of the design. 
 
HOUSEHOLD FURNITURE 
 
 Plate CXXXV. 
 
 Three designs with their profiles are here given for ornamental 
 brackets, intended as supports from the wall for glass lustres or girandoles ; 
 they are likewise used for carrying ornamental china, antique vases, for nieta! 
 or plaister figures holdinglights, and lastly for supporting ornamental French 
 clocks. Their material and manufacture will be varied according to their 
 use ; some being executed in mahogany or rosewood, some carved and gilt 
 and some executed in plaister and finished as bronze. 
 
 Plate CXLV. 
 
 The annexed plate represents the interior of a boudoir fitted up after 
 the manner of a tent. In the dwellings of persons of rank and fortune, 
 where there is a range of several rooms on a floor, one of these rooms is 
 generally fitted up as a boudoir; an apartment specially belonging to the lady 
 of the mansion, and fitted up accordingly. It answers as a morning room 
 for the receiving of visitors, and in the evening makes a portion of the 
 whole suite of apartments, when thrown open for the reception of a nume- 
 rous assembly. There have been many modes adopted with regard to the 
 fitting up and decorating the boudoir : — in the present design the repre- 
 sentation offers the interior of a state tent, whose plan is octangular. The 
 face of each side is covered with calico gathered into plaits, which may 
 be either of one plain colour, or these plaits may vary alternately in colour; 
 viz. green and white, white and pink, lilac and yellow, or otherwise, 
 as choice and taste may dictate. The perpendicular height for the line of 
 plaits may be nine feet six inches or ten feet, if the height of the principal 
 story will admit ; from whence the calico or furniture, covering each face of 
 the wall will be gathered up into one common centre in the ceiling, after the 
 manner of a tent. Along the top of the plinth or skirting of the room, a 
 finish is made with a gold coloured rope, either of silk or worsted, and the 
 same finishing is continued along the top of the walls from whence the tent- 
 
212 
 
 HOUSEHOLD FURNITURE 
 
 !ike 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 from 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 alight cast : — the chairs may 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 
 octangnlar form : — dejune tables, amd light chiffoniers are admissible; and, 
 where a recess is formed, it may be occupied by an escritoire with an orna- 
 mental 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, agreeablv 
 to the Latin motto, to associate in our choice the Utile cum Duke. 
 
I 
 
BIWING lOOM WfflBOW CURTAIN. 
 
DRAPERY AMD GUM TAW FOR CIRCULAR. HEADER WfflBOWo 
 
 London. Published, by Jones %c C'Apnl28.1327. 
 
London.. Published "by Jones Sc C? July 28.1827. 
 
VENETIAN WINDOW, and CURTA I N 
 
 III 
 
 London. Published by Jones 2_C? April. 29. 1826 
 
LONDON Publ by JONES &. C° April 15.1826. 
 
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CHAISE . LONGUES 
 
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CHAT R LEGS & MAILS, 
 
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23 
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London. Published by Jones «• f\"j u , lP 10.1826. 
 
WINE . COOLERS. AFTER. THE. ANTIQUE 
 
1 
 
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Prodis 
 
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DRAWING. ROOM. CHIMNEY. CLASSES. 
 
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C1NDELAB1A FOB COMMOMS, PK1 TABLES k c , 
 
JAIUDIi^IEXE ASD AVIARY. 
 
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XV n. 
 
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214 
 
 INDEX. 
 
 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 parallel 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 parallel 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 given, 24. 
 To describe the arc of a circle which shall pass through three given points, 24. To divide 
 the circle into three parts 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. 
 
 Circumference of the 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. 
 Co?npasses, 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. 
 
 Cyma'reversa, rule for describing it by means of ordinates, 41. 
 
 Decoration, interior, observations on its origin, rise and progress amongst the ancients, and its 
 •radual improvement to the present time, 164. Observations on decorative painting, 165. 
 
 The different 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. 
 
INDEX. 
 
 215 
 
 Of rectangles, 9. Of polygons, 10. Of arcs, 10. Of planes and superfices, 10, 11. Of 
 the ellipsis, 11. 
 
 Definitions, perspective — of points, 64, 65. Of lines, 66 — 69. Of planes, 70,71. 
 Diagonal line in geometry, defined, 4. 
 Diagonal line in perspective, defined, 78. 
 
 Diagonal point in perspective, defined, 65. Its use explained, 66. 
 
 Diagrams, for elucidating and explaining the diagonal line in perspective, 78. For elucidating 
 the doctrine of inclined planes, 117. For elucidating the principles of angular and parallel 
 perspective, pointing out the distinction between the two branches, 119. For elucidating and 
 explaining the laws of reflected light, and the means by which it is conveyed to adjacent 
 objects, 142. 
 
 Diameter, of an ellipsis, transverse and conjugate, defined, 11. 
 Directing point in perspective, defined, 65. 
 
 plane in perspective, defined, 70. 
 
 Distance, point of ', in perspective, defined, 65. 
 
 , points of, in angular perspective, process for laying them down, detailed, 121. 
 
 , of the picture, explained and illustrated, 73 — 76. 
 
 Dividing point in perspective, defined, 65. 
 
 Division of the circle, process laid down, 6. 
 
 Dome, elliptical, to find the outline or curve for the ribs of, 49. 
 
 Drapery, principles laid down for shadowing the folds of, 153. 
 
 Draught, ichnographic, or plan, defined, 11. Orthographic draught or elevation, 12. Sceno- 
 
 graphic draught or perspective representation, 12. 
 Drawing hoard, its construction described and explained, 127. Directions for laying down the 
 
 paper, 126. 
 
 Drawing, ornamental, preliminary observations on, 128. The principles laid down and illustrated 
 by various examples, 131 — 140. 
 
 Echinus molding parabolic, method for describing it, 39. Method for describing it of the elliptic 
 form, 40. 
 
 Egyptian decoration, observations on, and the style described, 168. 
 Elbow chair, to represent the same perspectively, 103 — 105. 
 
 Ellipsis, definitions of, 11. Problems for describing it, 32. Problem for finding the foci, 32. 
 English decoration, observations on the present style, 174. 
 Equilateral triangle, definition of, 8. Problem for constructing it, 17. 
 
 Etruscan decoration, observations on the specimens lately discovered in the excavations at Pompeii, 
 170. 
 
 Extent, point of, defined, 2. 
 
 External angle, in geometry, defined, 5. 
 
 Face molding, of a raking pediment, rule laid down for finding the mitre, 50. Rule for finding 
 
 the mitre for the face mold of a circular pediment, 51. 
 Feet, scale of, described, 55. Its construction laid down, 56. 
 Figures, definitions of the various kinds in geometry, 9, 10. 
 
216 
 
 INDEX. 
 
 Figures, polygonal, problems for contracting the various kinds, 28 — 31. 
 
 , geometrical, rules laid down for forming the outlines of moldings ; vases of various 
 
 shapes ; fretts, guilloche borders, &c. 37 — 54. 
 Flight of bed-steps, to represent the same in parallel perspective, 103 — 105. 
 Foci of an ellipsis, rule for finding them, 32. 
 
 Foliage ornament, instructions for drawing of, 131 — 140. Rules laid down for the shadowing 
 of, 154—156. 
 
 Four post bedstead, to represent the same in inclined perspective, 121. 
 Frett, Greek, manner of forming it, 42. 
 
 Furniture, observations on its origin, progress, &c. i. — viii. Rules laid down for the casting of 
 
 shadows, with examples, 150 — 153. 
 , upholstery, observations on, with descriptions of the various designs introduced, 175 — 
 
 190. Observations on the cabinet branch, &c. 190. 
 
 Geometry, definitions in, 1 — 12. Problems illustrating the practical part, 12 — 36. Its use in 
 
 facilitating the knowledge of perspective pointed out, 125. 
 Geometrical figures, rules laid down for the formation of various kinds, 37 — 54. 
 Globe, manner of forming the shape of the gores for its covering, 48. 
 Gothic arch, rule for finding the centres for describing it, 36. 
 
 decoration, preliminary remarks on the style, 171. 
 
 Greek decoration, the style described, 169. 
 Ground or base line in perspective, defined, 66. 
 plane in perspective, defined, 70. 
 
 Guilloche, Italian, different modes laid down for forming it, 43. 
 
 Hexagon, to inscribe the same in a circle, 29. To represent the same in parallel perspective, 81. 
 
 Method of finding the vanishing points for the inclined sides, 8 1 . 
 Hexagons in perspective, to represent a floor of, 82. 
 
 Horizon; the rational, sensible and visible, defined, explained and illustrated, 67 — 68. 
 Horizontal points, defined and their use explained, 2. 
 line in geometry explained, 4. 
 
 line in perspective defined, and its use explained, 69. 
 
 line, observations for determining the height of, 74. 
 
 plane, defined, 70. 
 
 Hyperbola, manner of describing it from the cone, 35. 
 Hypothenuse, of a right-angled triangle defined, 8. 
 
 Ichnography, of an object defined, 11. 
 Incidence, point of, defined, 2. 
 Inclined line in geometry defined, 3. 
 
 Inclined planes, definitions of, 71. Further explained and illustrated. 1 16 — 1 18. 
 
 Inclined perspective, preliminary observations on, 118 — 120. Its principles laid down and 
 
 demonstrated, 121—123. 
 Interior decoratian, preliminary observations on, 165. The various styles described. 168 -174. 
 Internal angle, defined, 6. 
 
INDEX. 
 
 217 
 
 Intersection, point of, defined, 2. 
 
 Introduction and prefatory address to the work, I — VIII. 
 
 to perspective, 61 — 64. 
 
 Isoceles triangle, defined, 9. 
 
 Leaves, instructions for drawing the outline of various kinds, 134 — 137. Instructions for sha- 
 dowing the same, 154 — 155. 
 Level line, in geometry, defined, 4. 
 
 Library or writing table, to represent the same in perspective, 91 — 93. 
 
 Library chairs, described, 188. 
 
 Light and shade, laws of, considered, 141. 
 
 Light, reflected on other bodies, accounted for and explained, 142 — 143. 
 Lines in geometry, definitions of, 2 — 4. 
 
 Line of lines, and line of polygons, on the sector, their use explained, 58, 59. 
 
 Lines, proportional, nature and theory of, 26. Their use explained and illustrated, 27. 
 
 Line, given, problem for bisecting it, 19. Problem for trisecting a given line, 19. The applica- 
 tion and use of these problems explained, 19. 
 
 Loo table, to find the proportion of a triangular block for the same, 51. To represent a circular 
 loo table with its pillar and triangular block, in perspective, 109 — 113. 
 
 Mathematical point and line, defined, 1 — 2. 
 
 instruments for drawing, described, 54. 
 
 Mixed triangle, defined, 8. 
 Mixtilineal angle, defined, 5. 
 
 Mouldings, rules for describing various kinds, 38 — 43. 
 Obtuse angle, defined, 8. 
 
 Occasional table, to represent the same in perspective, 107. 
 
 Octagon, problems for constructing it, 30. To represent an octagon perspectively, 83. To 
 
 represent an octangular solid in perspective, 87 — 90. 
 Ordinate lines, defined, 4 — 11. To describe the ellipsis by means of ordinates, 31. To describe 
 
 the cima recta, and cima reversa by the same means, 41 . 
 Ornamental drawing, preliminary observations on, 128. Instructions for drawing various kinds 
 
 of simple outlines, 131. For drawing various compound forms, 132 — 134. Principles of 
 
 ornamental composition, 139. 
 Orthographic projection, defined, 12. 
 Ovolo molding, to find a centre for describing it, 38. 
 
 Parallel lines, defined, 4. To draw one line parallel to another.. 21. The application and use of 
 
 the problem, 22. 
 Parallel ruler, description and use of, 22. 
 Parallelogram, defined, 9. 
 
 Parobola, to describe the same from the cone, 34. 
 
 Pateras, ornamental, instructions for drawing various kinds of, 138. 
 
 Pavement o r squares in perspective, mode of representing the same, 77, 
 
 3 M 
 
218 
 
 INDEX. 
 
 Pediment, to find the outline of the face mold for the raking and circular, 50, 51. 
 Pentagon, to inscribe the same in a circle, 28. 
 Periphery of an ellipsis, defined, 1 1 . 
 
 Perpendicular line, defined, 3. To let fall a line from a given point that shall be perpend: 
 to another line, 12. The application and use of the problem explained, 12. To erect 
 perpendicular on a givei? line, 13. To raise a perpendicular at the end of a line, 13. To 
 raise a perpendicular by means of a scale, 14. 
 
 Perspective, general introduction, 61 — 64, Applied to furniture drawing, 73. The difference 
 between parallel and inclined perspective explained, 119. 
 
 Picture, observations on the position and distance of, 73. 
 
 Physical line, defined, 3. 
 
 Pilasters, their application in interior decoration, 166, 
 Plan, in drawing or design explained, 11. 
 Planes and superfices in geometry, defined, 10, 11. 
 Planes in perspective, definitions of, 70. 
 
 Points in geometry, definitions of the various, 1, 2. Definitions of the various points made 
 
 in perspective, 64 — 66. 
 Polygons, line of, on the sector, its use explained, 59. 
 Polygonal figures, defined, 10. 
 
 Prism, octagonal, to represent the same perspectively, 90. 
 
 Projection of shadows applied to furniture, observations on, and rules laid down, 144 — 153 
 Proportional compasses, description and use of, 59. 
 Protractor, description and use of, 55. 
 Pyramid of rays, defined, 72. 
 
 Rational horizon, defined, 67. 
 
 Rays visual in perspective, defined, 72. 
 
 Rectangle in geometry, defined, 9, 
 
 Reflection and refraction of light, explained and illustrated, 141 — 143. 
 Rhombus and rhomboid, defined, 9 
 Right angle, defined, 5 — 7, 
 Right angled triangle, defined, 8. 
 
 Ribs of an elliptical dome, to find the curve or outline, 49. 
 Roman decoration, the style described, 171. 
 
 Scale of feet and inches described, 55. Its construction and use, 56. The construction and 
 use of the scale of tenths, 56. The construction and use of the scale of chords on (he 
 
 sector, 57. 
 Scalene triangle, defined, 8. 
 Scenographic draught, defined, 12. 
 
 Scotia Greek, rule for describing it, 39. Rule for describing the Roman, 39. 
 
 Secretaire desk and bookcase, to represeut the same in perspective, 94. 
 
 Sensible and rational horizons, coincidence between the two, shown and illustrated, 67. 
 
INDEX. 
 
 219 
 
 Shadoics, rules for projecting them, 145. Instructions for shadowing of drapery, 153. Shadowing 
 
 of leaves, 154. Shadowing of foliage ornament, 155. 
 Sideboard, rules for proportioning, the top, the moulding, and under rail, 54. 
 Sight, point of, in perspective, defined, 64. 
 Sofa, to represent the same perspectively, 105. 
 
 Solids, cylindrical, and octagonal, to represent the same perspectively, 86 — 89. 
 Square in geometry, defined, 9. 
 
 Square in geometry, problems for constructing it, 18. Their application, 18, 19. 
 Square, bevelled, its construction and use, 22, 127. 
 
 Square of octagons, to represent the same in perspective, 84. To find the perspective repre- 
 sentation of squares, placed at different distances from each other, 78. To represent a 
 geometrical square perspectively, 76. 
 
 Station point, defined, 2. 
 
 Station line in perspective, defined, 69. 
 
 Table top, to find the proportion of the width, the length being given, 27. 
 
 Table, for a library, to represent the same perspectively, 91 — 93. To represent an occasional 
 table in perspective, 107 — 109. To represent a circular loo table in perspective, 109 — 113. 
 Tenths, scale of, its construction, and use, 56. 
 Transverse diameter of an ellipsis, defined, 11. 
 Trapezium, defined, 10. 
 
 Triangle, equilateral, problem for constructing it, 17. To make one triangle equal to another, 17. 
 
 To inscribe a triangle in a circle, 27. To represent a triangle perspectively, 72. 
 Triangular block for a loo table, to find the proportion of the same, 51. 
 Triangles, definitions of, 8. 
 
 Truss support, mode of finding the outline by numbers, 52 — 54. 
 
 Vanishing points in perspective, defined, 65. 
 Vanishing lines, defined, 69. 
 
 Vanishing point for an inclined plane, rule for finding the same, 117. To find the vanishing 
 
 points for an object inclined to the picture, 121. 
 Vase, geometrical rules for finding the outline of the Greek or the Etruscan, 44—46. Rule for 
 
 finding the outline of the Roman vase according to Serlio, 46. 
 Vertical line, defined, 69. 
 Vertical plane, nature of, defined, 71. 
 Visible horizon, explained, 67. 
 
 Visual rays in perspective, defined and their nature explained, 72. 
 View, central, of an object, best adapted for some cases, 113. 
 
DIRECTIONS TO THE BINDER FOR PLACING THE PLATES. 
 
 GEOMETRY. 
 
 Plate 1, co face page 2 
 
 2, VII 4 
 
 3, XLIV 5 
 
 4, XLV 6 
 
 5, XLVi 8 
 
 6, XLVII 10 
 
 7, XLVIII 11 
 
 8, 49 13 
 
 9, 50 15 
 
 10, 51 18 
 
 11, 52 22 
 
 12, 53 26 
 
 13, 54 32 
 
 GEOMETRICAL FIGURES. 
 
 Plate 1, XXV 37 
 
 2, XL 42 
 
 2, LXV 44 
 
 3, LVII 48 
 
 4, LVI 51 
 
 LV1II..„„ 55 
 
 PERSPECTIVE. 
 
 Plate A, LXXXVII 65 
 
 B, LXXXV1II 66 
 
 C, LXXVIII 71 
 
 D, LXXIX 75 
 
 Plate 1, XXX 76 
 
 2, LXXXIX 79 
 
 3, LXXV1 81 
 
 4, LXXV11 83 
 
 5, LXXXII 85 
 
 6, LXXI 92 
 
 7, LXXXIV 94 
 
 8, XCI 97 
 
 9, XVI 100 
 
 10, CXX , 103 
 
 11, CXIV 105 
 
 12, CIII 108 
 
 13, CX11 110 
 
 14, CV 114 
 
 15, CXV1 121 
 
 ORNAMENTAL DRAWING. 
 
 Plate CX 131 
 
 CXI 133 
 
 XX 134 
 
 CXX1 136 
 
 XXI 138 
 
 CXX11 140 
 
 SHADOWING. 
 
 Plate CXXIII 144 
 
 CXX1V 150 
 
 CXXV 153 
 
 CXX VI 154 
 
 C 156 
 
 CVI 156 
 
 XIV 156 
 
 COLOURING. 
 Plate CXXVII 158 
 
 INTERIOR DECORATION. 
 
 Plates XXVIII. C XXXIII. LXXXV. , to follow 
 LXXXVI. XXXIX 1 p. 166. 
 
 Plates CXLVII. CXLVIII. CXLIX. , to follow 
 CL. CLI. CLII. CLIII S p 174. 
 
 WINDOW CURTAINS. 
 Piatesll. XXXI11. XXXVII. CXLIV. 
 XCV. XCVI. CXXIX. XII. 
 XIX. CXI. XI. CXLI. LXXIII. 
 
 BEDS. 
 
 Plates V. LXX. CXV1I. CXXX. 
 XLIII. XCVJI. CXIII. XIII. 
 LX. 
 
 CHAIRS AND SOFAS. 
 Plates III. CXLVI. CXLIII. LXVIII. 
 XXXII. CIX. XXXVIII. 
 CXXXVII. LXXXI. XCIV. X. 
 CXXVI. IX. CIV. LXXIV. 
 CXXXI. 
 
 TABLES. 
 Plates XXIV. CXVIH. XL1I XXVII. 
 LXIV. LXXXI1I.VIIIXXVI. 
 XXXVI. L1X. CXXVI. 
 CXXXII. CXXXIX. XXXV. 
 CIX. 
 
 SIDEBOARDS. 
 Plates XC1X. IV. LXXV. LXVI. 
 LXTILXVn. XXIX. LV.CVII. 
 
 COMMODES. 
 Plates LXXX. VI. CII. LXIX 
 LXX1I. LXII. 
 
 WARDROBES. 
 Plates XC. CVIII. XXXI. 
 
 DRESSING GLASSES. 
 Plate CI . 
 
 CHIMNEY GLASSES. 
 Plate XV. 
 
 FIRE SCREENS. 
 Plate LXI. 
 
 SCREEN LIBRAI RE. 
 Plate CXXXVIII. 
 
 BOOKCASES. 
 Plates XXIII. XLI XCVIII. 
 CXLII. XCIII. 
 
 CANDELABRA,^. 
 Plates X VII I. C X \ . C X X X IV. X X 1 1 
 
 LXVII. XCII. CXX XV. J 
 
 Blatc CXLV. To be placed opposite the engraved 
 Title, at the begiiiniii"- of the book.