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 WILLIAM MACZEKLIS _ GLASGOW 
 
 

DESCRIPTION OF PLATE, 
 
 HINTS FOR YOUNG TRADESMEN, No. I. 
 
 Fig. 1, on this Plate, represents a sideboard front, with a diagram explanatory of the method 
 of delineating it. For the benefit of apprentices, we may here explain the system of working out 
 the figure with the compasses, the practice of which will initiate the young artist into several 
 processes of a like character. 
 
 The oval may be drawn in a variety of ways, but the diagram before us will show both the 
 method of delineation and the rule for finding it. The circle, 1 to 7 , is divided into equal parts, 
 as the regulator of the figure. By placing the 1 higher and the 7 lower, or the reverse, the oval 
 will be made long or flat at pleasure. The point of the compasses is first placed at 1 on the 
 circle, the leg being extended to 1 on the large sweep, thus drawing a portion of a circle to the 
 first dotted line on the right. Then sweep from 2, and extend the compasses as before, up to 7 . 
 The upper portion is done in the same way—extending from the lower 4 to the upper 4 all round 
 to 1, where the circle intersects the dotted line. The dotted line from 4, up through the sweep, 
 gives the list on the top. 
 
 Mouldings of this character are termed Roman, although, strictly speaking, a Roman mould¬ 
 ing is produced by parts of circles, whilst Greek mouldings are formed of ovals. Now this figure 
 is formed of parts of ovals, and, owing to its roundness, has been claimed by the Romans as 
 altered by them from the Greek ; like the Composite order of architecture, which is a compound 
 of Corinthian and Ionic. 
 
 The small ogee below is divided into four equal parts, with the points on one line. 
 
 Fig. 2 is a perspective elevation of a portion of a chair. In delineating this, it is to be 
 remembered that 18 inches is the ordinary height of a chair seat from the floor. First we must 
 determine the size of the front, which is usually equal to the height. The front is then to be 
 divided into four equal parts—that is, one part blank, one part the front of the chair, and the 
 other two the side. At the upper corner, to the left, the dotted line, running three parts, cuts 
 the depth of the back leg ; the dotted line coming from the right to the centre, on the ground 
 line, cuts the leg a second time. Generally, the point of sight is put 5 feet 6 inches high by the 
 scale beneath the figure ; but if this were done, it would appear to be suspended. In the figure 
 before us, this point is only 2 feet 6 inches from the floor to the eye. 
 
THE CABINET-MAKERS’ SKETCH BOOK. 
 
 Tig. 3 is drawn on the same principle, adapted for cubes, such as wardrobes, sideboards, and 
 cheffoniers. In the case of a wardrobe, the point of sight may be about five feet from the floor. 
 To lay it down, first draw the four fronts; then, from the right corner on the upper line, draw 
 the dotted lines. This done, the line from C to B is to be drawn, cutting the square of the 
 blocks. Then raise the perpendicular, and, with the T-square, draw the horizontal line, showing 
 the top. Afterwards draw a line from corner to corner on the shaded side, giving the centre of 
 the blocks, and, raising the square, draw the top line. 
 
description of plate.-counices. 
 
 Fitf. 1, 011 Plate, is well adapted for a bookcase of large dimensions. Oil a smaller scale it 
 will answer well for a large wardrobe. It is, however, more suitable for the former ; and as in a 
 large library the cornices usually go up to the ceiling, it would, on this account, show to fine 
 effect. The extent between g and the dotted lino near the centre of the screw-nail, represents a 
 
 piece of fir_the upper part being held on by the screw. On this is planted the top moulding 
 
 of solid mahogany or oak. Beneath, the double line represents the portion which is veneered, 
 down to the bead. Round, under this again, is another veneer, continued through the under 
 curve as far as b, which is solid. The oval moulding is solid, and is planted on the fir, as also is 
 the short length between the large moulding and bead. 1 he bead itself is solid, and the succeed¬ 
 ing longer, or frieze portion again is veneered. The under bead and portion at g is solid, to 
 allow of working out the under hollow. The upper piece of fir, where the top moulding is 
 planted on, is glued on before it is veneered.—See the dotted line cutting the veneer. 
 
 To delineate this, place the compass leg at A, and extend to A, sweeping round, to give the 
 requisite size of wood for a blocking, which, as it is not seen, may be square. Next place the 
 compass point at e, and extend it to c, aud perform the same operation, and afterwards the like 
 from B to b. Then, for the large mouldings, place the compasses at n, and extend to n, then 
 from e to E, on the sweep. We are thus explicit, in order that the young apprentice may see 
 his way perfectly clear. 
 
 In commencing to delineate this cornice, the perpendicular and horizontal pieces of fir must 
 first be framed ; then plant on b first, afterwards the large moulding, then the two beads and c 
 below. The top moulding and three beads may be gilt. 
 
 Fig. 2 exhibits the groundwork of an S, and forms the plan of an oval. After laying down 
 the perpendicular and horizontal lines, describe the three circles. The intersecting lines cut the 
 outer circle, for the start of the oval. The compass point is to be placed at the top of the circle, 
 i the perpendicular line—extending the leg to the top of the small circle, sweeping round for 
 the start of the oval. 
 
 To form the oval, the compass point is to bo placed at the upper edge of the top of the small 
 circle, extending to the under edge of the under small circle; the point is then to be placed on 
 the cross line, sweeping round on the horizontal line, which gives the extent of the flat sides of 
 the oval, and the same on the side. 
 
IV THE CABINET-MAKERS’ SKETCH BOOK. 
 
 Fig. 3 very nearly resembles fig. 1, and requires little description. The compass point is to 
 be placed at a, and extended to a, outside, for the sweep. The same must be done from b to b, 
 and o to d. This cornice will answer well for a rich bed in mahogany. Either of the two, 
 reversed, will give the base for a fire-screen, stand, or other article of a similar class. 
 
 Fig. 4 is a diagram to give the height above a cornice in a room, whether for a wardrobe or 
 bed. It affords its own explanation, 
 
DESCRIPTION OF PLATE, 
 
 HINTS FOR YOUNG TRADESMEN, No. 2. 
 
 This sheet will afford very good practice for beginners. Figs. 1, 2, and 3, are very similar to 
 each other; they each exhibit ample scope for design and proportion. In fig. 1, the fines of one 
 moulding are carried round to form another totally different. In the numeral and literal refer¬ 
 ences, 1 is the start, a adjoining it being twice its width, whilst 2 is half the width of 1. b. Is 
 half of a, and 3 half of 2. Particular attention is necessary for 1, 2, 3, and 4, which are all fists. 
 Referring to the height of 1 above the horizontal fine of a, b, c, 2 must be carried half way up, 
 and 3 and 4 the same. The dotted fines indicate the centre for describing the circle. The 
 sections at the ends are formed into squares by the dotted fines, for the purpose of measuring the 
 distance back to each member. 
 
 Fig. 2 is the corner of a panel, usually considered a difficult piece of work. The cutting of 
 the inside circle is the part to be carefully looked after. If a panel corner is drawn from the 
 outside without just attention to the breadth of moulding, great risk of spoiling the work is 
 incurred. Frequently a marble slab is formed to a fine outline, the section of the moulding only 
 being given ; then, on commencing to form the margin, it will not work, and great alteration is 
 necessary to bring it in. The dotted fines give a clear explanation of how this is done. 
 
 Fig. 3 differs little from the last. The three figures formed by the dotted lines give the 
 proportions. 
 
 Fig. 4 is an example of hand-sketching—a sideboard being chosen for the purpose. Having- 
 fixed on the scale of the figure, the elevation must first be drawn, dividing it into four equal parts. 
 The dotted line must then be drawn from a, on the left corner, to d, cutting c, giving the breadth 
 of gable. The perpendicular is then to be raised from c to f ; then draw from e on the right 
 to f and c, for the height of the end of back, and from f to c for the breadth of top. 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
DESCRIPTION OF PLATE.-SIDEBOARD DETAILS. 
 
 In fig. 1 arc shown the dotted lines for working the compasses round the sweeps of the large 
 moulding, a. Is the top above the drawer, b, Is first worked to fit the moulding, and is after¬ 
 wards shaped as shown, and glued on the moulding. This detail is I inch thick when finished. 
 
 Fig. 2 is treated in a similar manner. The ogee moulding is veneered lengthways, and the 
 drop is planted on after the veneer is polished. The two vertical dotted lines in the outline, or 
 profile, show tko drawer front, and the cross line from a to the lower part of d is the drawer front. 
 
 Fig. 3 very closely resembles fig. 1. The three points are clearly shown by the dotted lines; 
 so also is the drawer front. 
 
 In fig. i, the only difference is the carved ornaments on the front at B, which is first fitted on 
 the large moulding, and then carved. The outline, b c, is the section. 
 
 Fig. 5 is a truss in the same style, intended to suit fig. 3. It may either bo pierced or sunk, 
 but is shown sunk. Of course, in this view, only a single pendant is shown, but there are 
 four in reality, turned from beneath the first bead and list. The flowers may be planted on, and 
 about half the breadth of the front of the truss at the top, and a quarter of the breadth at the 
 under side, yet as free and graceful as possible. 
 
BED AND DETAILS. 
 
 DESCRIPTION OF PLATE.— 
 
 The end of this bed is the only important feature. The cornice is not so high at the sides 
 and the end next the wall. The curtain at the end is higher than at the sides, as shown. The 
 part of the curtain at the edge of the post is fixed, the other portion, working out on rings, going 
 into the hollow on a straight rod, which is concealed under the cornice. For the covering of the 
 cornice below, there is a piece of flat wood which carries the hollow right through. On the 
 sides, the curtain works on a rod to the centre, or even to the head of the bed. The pillar is 
 veneered, and goes up through the cornice by means of a round tenon. The mouldings are all 
 sunk in after the pillar is cleaned off, and then the ornaments are fitted on. Bay wood is the best 
 for the pillar, veneered with very rich Boa Constrictor mahogany, or myrtle. The moulding and 
 ornaments to be of the same colour of wood, but plain, as they are well opened up. The footboard 
 demands our attention only in details. Its section is exhibited at g, h, j, k, and l. The cornice 
 again is shown on a large'scale at a, b, c, d. and e. 
 
ADVERTISEMENT. 
 
 The Publisher, desirous to do everything in his power to render the Sketch-Book, if 
 possible, still more worthy the extensive patronage already bestowed upon it, has induced 
 Mr. Thomson to visit Paris, for the purpose of inspecting the various Manufactories and 
 Collections of F urniture in that capital, so celebrated for its taste in the Decorative Art. 
 Mr. Thomson is now in London, where there is at present a rich field presented to the 
 designer, in the collection of furniture from all parts of the world, to be found in the 
 Great Exhibition ; amongst which we see every variety of taste in designing, com¬ 
 bined with the utmost skill in execution. Subjoined is copy of a letter received from 
 Mr. T. during his stay in Paris :— 
 
 Drake’s English Hotel, Hue St. ILonore, 
 Paris, 18 th September, 1851. 
 
 Mr. Mackenzie, 
 
 Dear Sir, 
 
 Since my arrival in Paris I have visited Versailles, 
 and most of the public places here, and have occupied my leisure moments in making 
 rough outlines of some of the most striking articles I have seen. The grandeur of the 
 palaces and churches, especially the Magdalene, far exceeds anything I had ever con¬ 
 ceived ; and I am certain my visit to this place will be suggestive of many ideas that 
 will be of benefit to my new work. 
 
 I intend to return to London in a few days, and shall remain there till the close of 
 the Great Exhibition. You therefore may expect me in Glasgow about the middle of 
 October. 
 
 I am, Dear Sir, yours truly, 
 
 P. THOMSON. 
 

 .TS/ 12 A 03 STSI 3 VGA 
 
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THE 
 
 CABINET-MAKERS’ SKETCH BOOK. 
 
 LINEAR PERSPECTIVE. 
 
 CHAPTER I. 
 
 1. Linear Perspective may be defined to be tlie drawing of objects in tlicir exact proportions, 
 with respect to height, length, and breadth, as they appear to the eye when placed in any 
 position. This may be illustrated by placing a pane of glass, or other transparent substance, 
 betwixt the eye and an object, and by keeping the eye steady, and tracing the different lines 
 upon the object; if these lines be distinctly marked on the transparent plane, there would be a 
 linear 'perspective view of the object. 
 
 2. It is necessary for the person commencing to learn perspective—if he has not got a pre¬ 
 vious knowledge of mechanical drawing—to understand the use of the instruments commonly 
 used. We will here, in the first place, explain some of these, and show the manner of using them. 
 
 The drawing-board is generally made of deal, of a size according to the intended use. W e 
 would here recommend one for drawing perspective of about two feet nine inches, or three feet 
 long, by two feet or two feet four inches broad, made of 1 inch or If inch stuff, neatly planed 
 and clamped at the edges to keep it from warping. The paper might be fastened upon it, either 
 by drawing-board pins, which is a very good and the most expeditions method, or by sealing 
 wax, or by paste, which is done in the following manner:—Having cut the paper to the size 
 required, wet the back of it with a sponge dipped in clean water, passing it over several times, 
 and leaving it a short time till the water is absorbed, and the paper lies flat; run a rim of paste 
 round the edge, about three quarters of an inch wide; then turn the wetted side of the paper 
 downward on the drawing-board, and press the pasted rim close to the board with a paper knife, 
 or some hard substance, pressing as much of the paste out as possible, that the paper may adhere 
 firmly to the board. The face of the paper should be then w r etted in the centre with a sponge, 
 taking care not to pass it on the pasted rim :• without this precaution, the centre would be dry 
 before the edges, and the paste would not hold. 
 
 The best sort of drawing-boards are those made in a panel form: m these, there is an out¬ 
 side frame rebated on the inside, into which there is a moveable panel fitted, also rebated, to 
 allow of the panel coming nearly flush with the upper surface of the frame. The paper is 
 placed upon this panel, and then put into its place, where it is fastened by two pieces of wood 
 in the back. This is undoubtedly the best sort of drawing-board, as it keeps the paper stretched, 
 and answers well for drawings which have a deal of minute work about them, and also for 
 
 colouring. . 
 
 The next instrument is the T square, which is so well known that we would just recommend 
 it to he made straight and strong, not to bend when drawing near its end; those made with a 
 
THE CABINET-MAKERS’ SKETCH BOOK. 
 
 screw, for drawing lines at any inclination, are most preferred. There are also small pieces of 
 mahogany of a right-angled triangular form, called set squares, which by moving along the edge 
 of the T square, lines can be drawn at angles for which the squares are made—those with 45° 
 and 60° are very useful. 
 
 Compasses are very useful instruments in mechanical drawing. They should be fine pointed, 
 and move freely at the joint, which should not, however, be too slack, for then a little compression 
 might move them from their position. Those with fixed legs are called dividers. When the 
 moveable leg is taken out, there is a leg which can be put into its place, having a piece of lead 
 pencil fastened into it, for drawing circular lines in lead, and also another for circular ink lines. 
 
 Drawing-pens are very useful instruments for drawing lines in ink, after being marked out 
 with lead. The handle is made mostly of brass or ivory, having two steel prongs on the one 
 end, which can be brought close, or widened (betwixt which the ink is placed), by means of a 
 screw, for drawing the lines fine or broad. There are also bow-pens, for drawing small circles in 
 ink, which are very useful, and similar ones for drawing lead lines. 
 
 Parallel rulers are for drawing parallel lines: they are generally made of two pieces of wood, 
 connected by two pieces of brass, fastened to them near the ends, allowing the wood to move 
 freely: by holding on or pressing upon it, the other can be moved, and it is still held in its 
 parallel position by the pieces of brass. Parallel rules moving on rollers are to be preferred. 
 
 These instruments, with scales, and a few others occasionally used, are those employed in 
 mechanical drawing ; those used in perspective will be described farther on. It may be remarked 
 that there are cases or boxes of instruments, containing compasses, drawing-pens, scales, &c., of 
 different prices, from a few shillings to a number of guineas, to be got in almost every town of 
 note in the three kingdoms—the student, by seeing them applied, will learn their use far better 
 than by a written description. 
 
 3. It is presumed that the student is acquainted with practical geometry—raising perpen¬ 
 diculars, describing squares, triangles, circles, ellipses, pentagons, hexagons, &c.; if not, we would 
 recommend him to learr that in Bonnycastle’s Mensuration, or some other work, as there are 
 many, and it would therefore be useless to enter upon the subject here. 
 
 4. There are five ways in which mechanical drawings are generally done:—1st, The iclmo- 
 graphic or ground plan of an object is the seat of the different parts, showing their correspondence, 
 situation, and magnitude, without any reference to the height. 2d, The orthography or elevation, 
 which is the appearance any object would present if an eye could view every part perpendicu¬ 
 larly. 3d, Sections —these are cuts made through the object, showing its internal arrangements. 
 If the section be parallel to the front, it is called a longitudinal section, and if from front to rear 
 
 a transverse or lateral section; any other is called an oblique section. 4th, The scenographic _ 
 
 that is, the representation of objects as they appear to the eye when in any position_or the per¬ 
 
 spective view. The scenographic is better applied to the perspectives of objects, as houses, for 
 instance, when scenery is introduced. 5th, The development —this is the representation of any 
 circular, elliptical, or polygonal figure, &c., when taken and spread out upon a plane, thereby 
 giving the appearance of an orthographic projection or elevation. Having gone thus far, we will 
 begin now and explain some of the fundamental parts of the science. 
 
 5. If a person stand at the middle of one end of 
 a long road, which is supposed horizontal, straight, 
 and of a uniform breadth, the sides will seem to 
 approach nearer and nearer to each other as they 
 arc farther from his eye; and if the road be very 
 long, the sides of it at the farthest end will seem to 
 meet, and there an object that would cover the 
 whole breadth of the road, and be of a height equal 
 to that breadth, would appear to be a mere point. 
 
 If a b and c d, fig. 1, be two parallel sides of a road, and o the place of the observer — suppose 
 
LINEAR PERSPECTIVE. 
 
 3 
 
 the road to be divided into squares, a c i e, e i k f &c., the person standing at o will see these 
 two sides as if they were gradually approaching towards one another, as in fig. 2 ; and the squares 
 will seem to diminish in size as they are farther from the eye—so that the first square, a c i e, 
 fig. 1, will appear as a c i e, fig. 2; the second square, e ikf fig. 1, will appear as eikf fig. 2; 
 and so on till the last square, which would vanish into a point, as s in fig. 2, where a s and c s 
 meet. 
 
 6. The point, s, where the parallel sides of the road seem to meet, is called the point of sight, 
 and is still opposite to the observer, and at the height of the eye. The place where the obser¬ 
 ver’s eye is placed is called the place of the observer, or the point of view. The line, p s, passing 
 through the point of sight, is called the horizon. 
 
 CHAPTER II. 
 
 1. In the annexed figure it is intended to show more particularly the principles upon which 
 this kind of perspective depends, g i k l is called the ground plane, upon which there is a square, 
 p r s q, to be drawn in perspective; f a b c is the plane of the picture, upon which the repre¬ 
 sentation is to be made; e is t\\e point of view, sometimes called the point of sight; it is the place 
 of the observer’s eye, and hereafter 
 shall be called the point of view, and 
 the point of sight shall be applied 
 to the point opposite the eye in the 
 horizon, to which lines and planes 
 perpendicular to the plane of the 
 picture converge, m n is the hori¬ 
 zon of the picture, or the represen¬ 
 tation of the meeting of the sky and 
 water, if an observer were looking 
 at the ocean ; and it may, be re¬ 
 marked that the horizon, m n, is still 
 on a level with the eye. If a sketch 
 were made on the top of a mountain, the horizon would then be high up; and if made from a 
 valley or some low place, the horizon would then be low down: and in every linear perspective 
 drawing, there must be a horizon or horizontal line. We might suppose m n was the representa¬ 
 tion of the line or visible connection of sky and land; and this apparent meeting or line, though 
 below the level of the eye, is still put at the eye’s height, as the distance from the eye to the 
 picture is so small, that there can be no sensible difference in taking the horizontal line, m n, at 
 the height of the eye. 
 
 e d is perpendicular to the horizon, m n; the point, d, is called the point of sight ; the line, a b, 
 in which the plane of the picture and the ground plane intersect, is called the section line: now, 
 if lines be drawn from p q it s to e, the points, pqrs , where these lines intersect the plane of the 
 picture, being joined, will form the perspective representation of the square. The operation just 
 mentioned may be said to be of no very great use in drawing perspective, as a transparent plane 
 cannot always be held before an object, for perspectives are made of houses, bridges, machinery, 
 &c., before any of them are built or constructed ; indeed, if perspective consisted only in this, it 
 were very contracted, and therefore of no great importance. We see, therefore, recourse must 
 be had to other means. The point, h, in the ground plane, directly under the eye, is the point 
 to which the lines are drawn from the object; we have drawn two in the diagram, as more would 
 only have caused confusion: and from the points, a b, where they meet the section line, we raise 
 
4 
 
 THE CABINET-MAKERS’ SKETCH BOOK. 
 
 perpendiculars until they meet lines drawn to the point of sight in q s, from the points where 
 p q and n s meet the section line produced. If two other lines had been drawn from p r 
 to h, and perpendiculars raised as before, they would have marked out p r; if then, p r, q s, &c., 
 be joined, there would be formed p qr s, the perspective representation. This will be better 
 understood by the following, with respect to the square. 
 
 2. To put a square in perspective. Let a b c d be the square which is to he drawn, and e the 
 point of view. We will suppose, in the first case, that the plane of the picture, or the section 
 
 line,/ g, coincides with the side, a b, of the square, and that the point of view is exactly opposite 
 the side, a b, of the square, the visual rays, e d, e c, are drawn, making the side, d c. 
 Fig. 5. appear equal to h k. The side of the square is eight feet, and is laid down 
 
 -1 at the scale of an eighth of an inch to the foot. In fig. 3, a b is made equal 
 
 to a b, fig. 2, because it touches the section line or plane of the picture, and 
 therefore it is the real size. Draw the horizontal line, y z, at the height of 
 
 _i __ the eye, about five feet four inches, and as the observer stands opposite the 
 
 tt1 ll k m 0 middle of the side, a b, the point of sight, p, will be also opposite the middle; 
 join p a , p b , make h k equal to h k, and put half on each side of the central line, and draw the 
 Fig. a perpendicular h d, k c, and join c d —then abed will be the per- 
 
 D 0 spective representation. 
 
 3. In the second case we, will suppose that the plane of the 
 picture does not touch the side of the square, hut the observer 
 is still standing opposite the middle of the side, as in fio-. 4. 
 
 Draw the visual rays, e a, e d, e c, e b ; then the apparent 
 sizes of d c and a b will be h k, l m ; then, in fig. 5, draw the base 
 line n o, and at the proper height the horizontal line y z ; leave 
 ofi h k, Im, no, respectively equal to h k, l m, a b, one half on 
 each side of the central line; join n p, o p, and draw the perpen¬ 
 diculars, la, h d, k c, m b, and join ab, c d; then abed will be 
 the square. 
 
 4. In the third case, we will suppose the observer stands to one side, and that the plane of the 
 Fi R- 7 - picture does not coincide with the side of the square, the plane 
 
 -1---£—; of the picture being still parallel to the side of the square, as in 
 
 * 1 fig. 6. 
 
 Let the visual rays be drawn as before, and let e o he the 
 principal one, or the one directed to the point of sight. In 
 1 r h m k 0 fi§- ( ^ 110 to the base, and y z the horizontal line, p the 
 
 point of sight, o p the principal visual ray ; leave off o n, ol.or, &c„ equal to o s, o l, o r, &c.; join 
 n r, raise the perpendiculars, la,hd, &c, and join ab, cd; then abed is the square. Now, the 
 attentive reader will easily see the connection of this method with that mentioned in description 
 
LINEAR PERSPECTIVE. 
 
 Fig. a. 
 
 of fig. 1. The point, e, in figs. 2, 4, and 6, is the same as n, fig. 1, which is the point perpen¬ 
 dicularly under the eye on the ground plane. The lines, though drawn from the object to it, 
 mark out on the section line the apparent length and breadth virtually the same as if they were 
 drawn to the point of view. Again, in fig. 1, from the points where the visual rays cut the 
 section line, perpendiculars were raised, meeting lines passing to the point of sight; the same 
 is adopted in figs 3, 5, and 7, where the perpendiculars are also raised, meeting lines passing 
 to the same point. 
 
 In the three examples which we have given with respect to the square, and in other subsequent 
 examples, we might have done with one figure, but we would like 
 to impress these first principles upon the mind of the reader in as 
 easy a manner as possible; we have therefore adopted two figures, 
 that it may be the better understood. It is evident, that if a b c d, 
 in figs. 2, 4, and 6, had been a right-angled parallelogram or rec¬ 
 tangle, its perspective could have been as easily made ; and if a b, 
 in fig. 6, had touched the section line, it would have been easier. 
 
 We might also mention, that if a bcd had been a pavement 
 divided into squares, or of it were a square garden, or a rectangular 
 one with straight walks and flower 'plots, it could be very easily 
 drawn by going upon the same principle which we have adopted. 
 
 5. There is still another case with respect to the square, viz.:— 
 when the section line is oblique to all of the sides, as in fig. 8. 
 
 Draw f g parallel to the section line, as also k h, and draw the 
 perpendiculars, kf, n g ; draw the visual rays, ef,ed, &c., and e o, the principal one. 
 
 Now, let the base line and also the horizontal one be drawn, 
 fig. 9, as before, and also f g K k' } the perspective representation of 
 fghk, and let op correspond with e o the principal visual ray; leave 
 o li, o k', &c., equal to o h, o k, &c., and let the perpendiculars be raised 
 till they meet the lines passing to the point of sight, &c., marking out 
 the points,/, k, &c., corresponding with those in fig. 8, as also abed, 
 which points being joined, mark out the perspective representation. 
 
 We have drawn all the lines necessary on the figures, so that the student will clearly see 
 the method of proceeding. 
 
 CHAPTER III. 
 
 1. It will be seen, by reference to the preceding chapter, that in the three cases of the 
 square which were taken into consideration, in which the plane of the picture was parallel to 
 two of its sides, these sides were parallel to one another in the representation, and the other 
 two sides converged to the point of sight; but (in 5) where the sides were oblique to the plane 
 of the picture, it was seen, that in the representation, the two sides, which in the former cases 
 were parallel, are no longer so, but converge to a point on the horizontal line, whilst the other 
 two converge to another point also on the horizontal line. This will take place if they be 
 accurately constructed; whereas, those lines which circumscribe the square,, converge to the 
 point of sight, or are parallel to one another, as the case may be. These points to which the 
 lines converge are called vanishing points, and are in general on the horizon. 
 
 2. Linear perspective is of two kinds. The first is called direct or parallel; it is the same as 
 described in Chap. II. This is the easier sort: it is so called, because, in the face of the object 
 (which is parallel to the plane of the picture) in the representation, the horizontal lines are parallel, 
 
TIIE CABINET-MAKERS' SKETCH BOOK. 
 
 whilst on the end or flank these lines converge to the point of sight. The second kind is called 
 indirect, because those lines which, in the former case, were parallel to one another and to the 
 
 Fig. I. 
 
 
 
 
 \b 
 
 d \« <• 
 
 V jbf 
 
 \ 
 
 
 horizon, in this are not, hut converge to the vanish¬ 
 ing point; and also those on the end or flank, which in 
 the former case converged to the point of sight, in this 
 they converge to a vanishing point. 
 
 As the two kinds are differently managed, and the 
 direct being the easier, we shall consider it first:— 
 
 3. By proceeding nearly in the same manner as that 
 adopted (in 5), we could, by direct perspective, put the 
 plan of any object into this sort of it when the figure is 
 bounded by right lines; and, as will subsequently be seen, 
 the plan of any figure, no matter by what sort of lines 
 bounded. Now, that we may be perfectly understood in 
 this, we will put first a triangle, and then any rectilineal 
 figure, by this method in o perspective. 
 
 4. To put a triangle into perspective by the direct method. 
 
 Let abc, fig. 1, be the triangle, df the section line, e the point of view. 
 
 Draw the visual 
 
 Fig. 2 
 
 A 
 
 / C 
 
 
 da ec 
 
 \g b f 
 
 rays, ea,ec,eb, cutting the section line in a c b ; draw 
 z also the perpendiculars, a d, b f, c e, and the principal 
 visual ray, e g. 
 
 In fig. 2, draw the base line, df at the proper height, 
 also the horizontal line, y z. Let g p represent the prin¬ 
 cipal visual ray, proceeding to the point of sight, p ; leave 
 off g d, g a, Sec., equal to g d, g a, Se c. Draw lines to the 
 point of sight, r, from d, e, f, and raise perpendiculars 
 from a, b, c, to meet these lines respectively, and they will mark out the points, a, b, c, which 
 being joined, give the required representation. 
 
 Fig. 3. 5. To put any rectilineal figure into perspective 
 
 by the direct method. 
 
 Since any rectilineal figure is composed of tri¬ 
 angles connected with one another, it follows that 
 the figure can be easily put into perspective when 
 the method of putting the triangle is known. 
 
 Let a b c d f, fig. 3, be the rectilineal figure, e n 
 the section line, e the point of view; draw the visual 
 rays, e a, e f, &c., and the perpendiculars, a e, f g, 
 See. 
 
 Then, in fig. 4, draw the base line, e n, the hori¬ 
 zontal line, y z, and take the point of sight, p, and 
 let p h be the principal visual ray. Leave off h e, h a, 
 See., respectively, equal to h e, h a, in fig. 3, and draw 
 the lines e p, g p, k p, m p, n p, to the point of sight, 
 an d from the points a,f Sec., draw perpendiculars 
 until they respectively meet the other lines in the points a, f, & c.; these points being joined will 
 give the representation. 
 
 6. Having now shown the method of putting the plan of any object, when bounded by right 
 lines, into this perspective, before proceeding to the consideration of objects with regard to height, 
 we would recommend the reader who may read this, and who would wish to become acquainted 
 with this useful branch of science, to make all the figures two or three times the size here shown, 
 and afterwards progressively introduce others which the fancy may dictate—such as quadrila- 
 
LINEAR PERSPECTIVE. 
 
 7 
 
 terals, pentagons, hexagons, &c.—as a short practice will sooner and more efficiently bring it 
 home to the mind than any descriptions, no matter how well and how easily written. 
 
 We are well aware, from a very particular examination of the principles of direct per¬ 
 spective contained in various works, such as Ferguson’s, Hayter’s, and a voluminous work by a 
 French Jesuit, translated by Chambers, &c., &c., that the way we treat it is different from theirs 
 a little; yet ours is conducted in the same manner as that adopted in indirect perspective—with 
 this difference, that in the latter there are vanishing points to which the lines converge, whereas it 
 is to the point of sight they converge in the former, as described by writers on this branch; and it 
 is our opinion, that it is founded upon rational principles, and deduciblc from mathematical prece¬ 
 dents, and easy in its application. 
 
 7. With respect to the distance the observer should stand from the object, some lay it down 
 as a rule to stand off the distance of the two visible 
 sides taken together—as, if the object were a house, 
 to stand off a distance equal to the length of the 
 two sides which are seen; whilst others consider 
 this too little, and we think it answers better to stand 
 farther off than this—say about as much, and one- 
 fourth or one-third as much more. It greatly de¬ 
 pends on taste; but there are some positions which 
 give better perspectives than others, as is very soon 
 learned from practice. Others stand off such a dis¬ 
 tance as the angle comprehended between the ex¬ 
 treme visual rays which proceed to the object, may be about 60 as the angle, aeb, in fig. 2 
 of Chapter II. 
 
 Fig- 4. 
 
 
 
 
 
 / 
 
 /! % 
 
 / 
 
 
 •fI V\\ 
 
 
 1 
 
 | j\ V \ 
 
 
 i rk \ 
 
 e a 
 
 9 
 
 f :A id k c b n 
 
 CHAPTER IV. 
 
 To put a cube, parallelopiped, or a box in perspective .—Let the dimensions of it be i feet 
 
 long, 4 broad, and 3 high. Make the plan, abcd, d F ‘ g ' 1 '_c 
 
 fig. 1; draw the section line, eg; take e, the point \ 
 
 of view at a distance, equal to a b and b c together, \ \ 
 
 from the object, and draw the visual rays, e a, e b, 
 
 &c., and produce d a, c b, to e and/ - . \ \ 
 
 In fig. 2, draw the base line, and at the proper A _\_ 
 
 height, say about five feet four inches, the horizontal ; N v _ \ --^ 
 
 line, t p; take the point of sight, p, leave off g e,g a, \ \ \ \ 
 
 &c., equal to ge,ga, &c.; in fig. 1, draw ep,/p, _ \ \ 
 
 to the point of sight, p, and raise the perpendiculars, a a, b b, c c, d d; join ^ 
 abcd, then a b c d is the perspective representation of the rectangular base. \ \ 
 
 Here we would remark more fully what has been stated before, that when- \ 
 ever any part of an object touches the plane of the picture, it is made the real size ; \ \ 
 
 that is, with respect to the scale by which the object is represented, and the \\ 
 
 smaller, the greater the distance from the observer. Now, a person at e, fig. 1, \\_ 
 
 would see an object at d, smaller than at b; but at b it would be the real size, X 
 
 because it touches the plane of the picture. In fig. 2, <?e is on the plane of the 
 picture, and perpendicular to the base line, eg; if then the height of the box, three . L 
 
 feet, be left off on e e, and a fine drawn to the point of sight, p, the point, f, vlieie it cuts ie 
 perpendicular, a f, will give a f the perspective height required, the parallel, f g, and a so t ie 
 

 line, g p, intersecting the perpendicular from c in h, and then draw the parallel, n l ; this then 
 will give the required representation. 
 
 A perpendicular from/would have answered equally as well for the height line. If the 
 
 Fig. 2. Fig. 3. 
 
 
 >1 \« c \0 \g ;b f 
 
 I i 
 
 object were a cube, its perspective would be found in the same way ; and if 
 the object touched the section line, its perspective would be still more easily 
 found. 
 
 2. To put a pyramid in perspective .—Let it be a triangular one, each side 
 of which is six feet, and the perpendicular height seven. 
 
 Let abc, fig. 3, be the plan of the pyramid, o the centre, take f. the point 
 of view, and let the section line be parallel to side, a b, and touch the angle, 
 c; draw the visual rays, and the principal one, e g, and the perpendiculars, 
 a e, o c, b /. 
 
 In fig. 4, let p be the point of sight, y z the horizontal line, and e g the 
 base line; leave off g e, g a, See., equal to g e, g a, &c., in fig. 3 ; and because the lines, a e, o c, 
 b f are perpendicular to the section line in fig. 4, they will converge to the point of sight. Raise 
 
 Fig. 4. Fig. 5. 
 
 the perpendiculars, a a, o o, b b, 
 and they will give the points, 
 o, a, b, the latter two of which 
 being joined with c, gives the 
 perspective of the base. Draw the perpendicular, c g, and leave off the 
 height on it, seven feet, and draw the line, g p, to the point of sight, p : 
 the point n, where it cuts the perpendicular from the centre o, is the vertex 
 of the pyramid, which being joined with a, b, and c, gives the required re¬ 
 presentation. Only one side of it is seen when the point of view is opposite 
 the middle of that side. 
 
 If abc, fig. 3, were the plane of the base of a frustrum of a pyramid, and the dotted lines 
 a b c its top, its perspective would be found by putting the small triangle in perspective, as in 
 fig. 4, and raising perpendiculars until they would meet the lines from a b and c to h, and then 
 joining these points for the top, the base being previously formed as before. 
 
 It is .evident from this, that any pyramid, whether triangular, rectangular, octagonal, 
 
LINEAR PERSPECTIVE. 
 
 9 
 
 &c., or any frustrums of these, might in this manner be put in perspective, and also any 
 prism. 
 
 3. To put the block of a house in this perspective .—In fig. 5, let the dotted lines indicate 
 the outline of the walls, and the drawn lines the roof; the section line touches one side of 
 the roof. 
 
 In fig. 6, p is the point of sight, y z the horizontal line, a c the height line, which touches one 
 corner of the roof, a b the base line. The roof 
 being the most difficult part, is done in the follow¬ 
 ing manner:—The height, ag, to the spouting, is 
 left off on a c, and its depth (five or six inches), 
 and then two lines are drawn horizontal to the 
 other side, and then from its extreme projection, 
 which is found by plan lines, two lines are drawn to 
 the point of sight. Now the height to the under 
 side of the projection of the roof must be perspec- 
 tively laid off, and it, together with the line of projection, and two short lines (one at g to the 
 point of sight, the other at the remote corner horizontal), will show the soffit or under side of the 
 projection of roof. For the height, leave off a c equal to the whole height, and run a line to the 
 point of sight, cutting a perpendicular in d, which corresponds with d in fig. 5, and then a hori¬ 
 zontal line, cutting the perpendiculars in c and f which points again with e and f, fig. 5, and 
 then draw lines to the extremities of the roof. The plinth may be easily put round the two 
 sides, and the rest of it is easy. 
 
 Fig. (i. 
 
 CHAPTER V. 
 
 The drawing of curves in perspective, or curvilinear perspective, is more complex, and there¬ 
 fore more difficult, than that of right-lined or rectilinear perspective. The ellipse, hyperbola, 
 parabola, &c., are seldom drawn Fi-. i. 
 
 in perspective ; if so, the method 
 of points, which are here pointed 
 out for the circle, are equally ap¬ 
 plicable with respect to them. It 
 is evident, that if the eye be 
 directly over the centre of a 
 circle, or in a line drawn perpen¬ 
 dicular to its plane from the cen¬ 
 tre, its perspective representation 
 will also be a circle; for, if the 
 plane of the picture be put be¬ 
 twixt the eye and the original 
 circle, and of course parallel to 
 it, and lines drawn from the eye 
 to the circumference of the original, these lines would evidently trace out a circle on the plane of 
 the picture. 
 
 Let d e e be a plane on which there is the circle, bgc, and o its centre, and o a the principal 
 visual ray, passing through the eye, a ; now, if rays be supposed to pass from every point of the 
 circumference to a, these rays will form a cone, and every plane, parallel to the original d e f, 
 
 c 
 

 
 , 
 
 >; 
 
 1 
 
 will be cut by these rays in a circle. If the plane, d ef be parallel to d e f, and which might 
 represent the plane of the picture, it will be cut also in a circle, as b (j c ; it will bo greater or 
 less than the original, according as it is farther oft*, or nearer to the eye, than it. In 
 mathematical language, the diameter of this circle is to the original in the ratio of their 
 distances. 
 
 Fig. 2 . Now, suppose another plane, as d e f , intersects the cone of rays, 
 
 but is not parallel to the original, it can be proved mathematically that 
 b <j c, the perspective representation, will be an ellipse : it may be said 
 the perspective of a circle is generally an ellipse. 
 
 If the eye of the observer be in the same plane with that of the 
 circle, it will then appear as a straight line. A familiar example of 
 this may be seen in a tea-cup, which, if a person hold in his hand, with 
 the eye over the middle of it, will then appear as a circle; and if it be 
 gradually turned round, it will assume the forms of ellipses, becoming 
 more and more elongated, until finally it appears as a straight line, or it will assume appear¬ 
 ances of ellipses ot every possible eccentricity, from 
 zero, or the circle, to one of the diameters, or the 
 straight line. 
 
 2. To put a circle in perspective .— Let e f g ii be a 
 circle ; draw two perpendicular diameters, ef, c h, 
 and tangents at their extremities; then abcd is a 
 square. 
 
 If this square be put in perspective by the method 
 previously pointed out, and the points, f, g, ii, e, found, 
 there would then be four points given, through which 
 the circle must pass. This way will do where great 
 accuracy is not required, but the number of points may 
 be increased. The point, k, may be taken in the curve, 
 and through it parallels to the sides ; the perspective 
 ol k may then be found, and also in the same way any 
 number of points as may be thought necessary, and then 
 the circle traced out with the hand. 
 
 The following way finds eight points which perhaps 
 might be accurate enough for general use. 
 
 Let a c b d be a circle, say four feet in diameter, and 
 m the point from which it is viewed; draw the two 
 diameters, a b, c d, perpendicular to one another, and 
 such that c u is perpendicular to the section line, o e, 
 Draw any two lines, ef, g n, parallel to c d, and cutting 
 the circle; and draw lines from the various points to the 
 point of view. In fig. 4, draw the line o e, and parallel to 
 it y z, the horizontal line, and take into it p, the point of 
 sight; leave off* of, o c, &c., o e , o d , & c., equal to oe, 
 o c, &c., and o e, o d , &c., in fig. 3. 
 
 Because ef,c d, are perpendicular to the section line 
 in fig. 3, in fig. 4 they will run to the point of sight, p, and 
 then perpendiculars from e d, &c., will meet these fines in 
 points e, d, &c., which mark out points in the circum¬ 
 ference of the circle ; and with a steady hand the perspec¬ 
 tive of the circle may be traced out after the rest of the 
 points have been found in the same manner. 
 
 which in this case touches the circle. 
 
 Fig. 4. 
 

 LINEAR PERSPECTIVE. 
 
 11 
 
 \ 
 
 B 
 
 A 
 
 y \ 
 
 3. In a former chapter, the method of putting any rectilineal figure into perspective was shown, 
 and by the method of points, as applied to the circle, any curvilineal figure may also be put into 
 it; and as all figures on the same plane, no matter how irregular they may be, are bounded by 
 straight lines or curves, (or the figure may be called mixtilincal,') it is evident that the methods 
 for these two conjoined will be the mode of proceeding in general cases. 
 
 4. To put a cone in perspective. —Let a b c, fig. 5, be the plane of a cone three feet in diame- 
 
 Fi g . s. ter at base, and four feet high. Fig. 6. 
 
 __ Let f o be the section line, and 
 
 e the point of view, eight feet 
 from the cone; let d be the seat 
 of the vertex ; draw d f perpen¬ 
 dicular, and draw the visual ray, 
 
 E I>. 
 
 In fig. 6, let y z be the hori¬ 
 zontal line, p the point of sight, 
 and o f the base line ; the base of 
 the cone being a circle, it must 
 therefore be first put into per- 
 \ \ spective. Make o f, o a, equal to o f, o a, in fig. 5, draw the 
 
 \ \ ; perpendiculars f g, a d, and leave off the height of the cone on f g, 
 
 \ \ i ! four feet, aud from this point draw a line to p ; then where it cuts 
 
 \ \ ■ j perpendicular from a in d, d will be the vertex ; then draw tangents 
 
 \\\ from d to the curve—they will form slant sides of the cone. Or if 
 
 \1 oe, o b, be made equal to o e, o 6, in fig. 5, and perpendiculars 
 
 drawn, they will touch the curve in two points, to which, if lines be 
 drawn from n, they will form the slant sides of the cone. In fig. 5, eb is the representation of 
 the apparent size of the diameter of the circle, found by drawing lines to represent visual rays 
 to touch the circle. 
 
 5. To put a cylinder in perspective.— The top and bottom are equal circles; the bottom circle 
 
 can first be put into perspective, and then the top one directly 
 over it. The plane of the picture touches the cylinder ; f g 
 is the line on which the height is laid off; y z is the horizontal 
 line, and p the point of sight, as before. The two lines, a b 
 
 and c d, may be made to touch the circles in a b, and c d; or these points may be found by 
 the method shown in the last example. 
 
 6. To put a globe in perspective .—If the plane of the picture be perpendicular to \ 
 ray, passing to the centi c of the sphere, the representation will be a circle; but if 
 
 i 
 
12 THE CABINET-MAKERS' SKETCH BOOK. 
 
 perpendicular, the representation will be an ellipse. Let a b c be the plane of the sphere, e the 
 point of view, and d f the section line. Now, if lines he drawn from e to touch the sphere in 
 a and b, a b will be the apparent size of the diameter, and a b its representation. A section of 
 the sphere through a b will be a small circle of the sphere, of which a b is the diameter; and all 
 the visual rays from e to touch the sphere, will touch the circumference of this circle. The 
 perspective of the globe will then be found by putting this circle into perspective by the method 
 previously shown. 
 
Let not the practical student be repelled from the study of this treatise, as if there were 
 something unintelligible in the word Geometry. A geometrical form is simply a regular form, 
 or a form of which the development is founded on some definite rule—a geometrical rule or law. 
 A piece of lump-sugar, casually broken from a larger mass of the same substance, or a clod of 
 earth turned over by the plough, or the outline of the sea-coast, cannot be said to possess a geo¬ 
 metrical form, in the ordinary sense of the phrase; because we followed no law of form in giving 
 a separate existence to the former objects, nor can we recognise any regularity in the form of any 
 one of the three. In each case, the form is rather a compound of a multitude of other forms 
 equally irregular, thrown together in an irregular manner. In a more comprehensive sense, 
 indeed, it may be affirmed, without contradiction, that the form of the clod, such as it is, has 
 resulted from the recognised laws of gravity and cohesion, and must of course possess some 
 definite relation of parts ; but without being hypercritical, and raising any argument on this 
 point, which is really beside the question, every intelligent artisan will understand the nature ot 
 the distinction, as regards form or outliue, between shapeless masses of wood, iron, earth, or loaf- 
 sugar, and the erect, square, and rounded mass of a steam cylinder, or the precise exactitude of 
 a spur-wheel. 
 
 Again, to approach still nearer, by comparison, to the distinctive idea of geometrical forms, 
 there are many forms which, while they are not geometrical, are nevertheless characterised by a 
 simplicity, harmony, and grace, which set them at a wide distance from such rude forms as those 
 we have been contemplating. We need only allude to the human form, as a pre-eminent example 
 of the distinct class of forms now alluded to. The simplicity of the human form is greatly owing 
 to its being composed solely of curve lines; now, not only are straight lines excluded from the 
 figure, but circular lines also, at least so far as that they never constitute any feature in the out¬ 
 line. In tracing the contour of the body in any given attitude, or from any given point of view, 
 we no sooner arrive at an elevation or a depression which begins to assume a circular outline, 
 than it sweeps into another curve, either rounder or flatter than the one which precedes it, or of 
 which the convergency may be reversed, so as to form an undulation. If we may be permitted 
 to apply the language of geometry at all, we would say that the radius of curvature perpetually 
 varies, and is frequently reversed; and that the utmost approximation to a geometrical analysis of 
 the figure would be the remote generality, that it is composed of very short segments of circles, 
 directly and reversely running into one another. That this definition is of no practical utility, 
 however, is very evident from the fact, that no one ever yet could delineate the human form on 
 geometrical principles, as we daresay no one ever attempted it. He who could seriously set him¬ 
 self to accomplish such an impossibility would be scouted, pitied, or laughed to scorn. 
 
 In the meantime, to cut short these preliminary remarks, we hope we have succeeded in 
 assisting the student to understand what geometrical forms are not. It behoves us now to explain to 
 him what geometry is, and to initiate him into such of the problems of geometry as arc necessary for 
 
 
 HU 
 
14 
 
 THE CABINET-MAKERS’ SKETCH BOOK. 
 
 his aid iii tlie practical delineation of his compositions. In approaching this introductory expo¬ 
 sition, vve mean to state and illustrate only such propositions as are of directly practical use in 
 the delineation of all ordinary matters of design, to the exclusion of such as may safely be left to 
 remain within the pasteboard walls of Euclid. We utter this apparently irreverent sentence— 
 irreverent towards the memory of the immortal Euclid—with the proviso, that we speak of what 
 is wanted only for the immediate necessities of the draughtsman—of what he cannot do without. 
 We know from experience that many an artisan will consent to devote his attention to the 
 acquisition of a few plain methods of doing a few plain things, when he would be effectually 
 scared from the regular study of a system embracing the development of the principles of geo¬ 
 metry. We heartily recommend the study of Euclid’s Elements of Geometry to such as are able 
 and willing to bestow upon it the leisure and application necessary for its prosecution, as they 
 will thereby not only acquire a complete conception of the nature of the science, but will also 
 provide themselves with a fund of general ideas on the relations of figure, which will, in many 
 cases, be of very great advantage to them. 
 
 Geometry, then, is the science which treats of the properties and relations of magnitudes ; that 
 is, of things which have length, or length and breadth, or length, breadth, and thickness. The 
 word is derived from two Greek words, signifying the earth and measure, obviously embodying the 
 idea of measuring the earth. Some more specific explanations, however, are required; and we 
 shall now explain what are the things referred to in the definition. 
 
 A solid is that which extends in three directions ; that is, which has length, breadth, and thick¬ 
 ness. The application of these distinctive terms to the three dimensions of a body, is simply a 
 matter of convenience. In applying the reasonings of geometry to a solid, it does not matter 
 though the solid were turned upside down, or round about; whether its thickness or height should 
 exchange its name for its length, or its length under one aspect should be called its breadth under 
 another aspect. 
 
 A surface or superficies is that which has only length and breadth. It may be called the 
 boundary of a solid, as it has no thickness. 
 
 A line has only length, without cither breadth or thickness; and it may properly be distin¬ 
 guished as the boundary of a surface, the simple termination of it. 
 
 A point has neither length, breadth, nor thickness ; .it has simply position. For example, the 
 intersection or crossing of two lines which pass through each other, is a point; it obviously has 
 a position or locality, but cannot be said to have either length, breadth, or thickness. In like 
 manner, the extremity of a line is a point; it terminates the line. 
 
 In attempting to represent lines and points on the surface of paper by means of drawing in¬ 
 struments, the representations can never more than approximate to the things intended to be 
 shown. For the finest line that can be drawn will have some breadth; and, indeed, if it had no 
 breadth, it could not be visible. In the same way, a point may be represented by a very minute 
 dot or puncture on the surface; still, as it covers some surface, it is not a geometrical point; it 
 is only an approximation, or something very near what is intended. Since, then, all material 
 representations of objects on paper, by means of lines, arc really only approximations in propor¬ 
 tion to the fineness of the lines employed, those drawings will be the most correct in which the 
 finest lines are employed, other circumstances being the same. It should be understood, then, 
 that the foregoing definitions are not without their practical value, as they set before the student 
 the standard of perfection to which, if not really attainable, he should strive to approach as nearly 
 as possible. 
 
 In studying the following definitions, the reader is requested to refer, where necessary, to the 
 accompanying 1 able of Geometrical Figures for illustrations of the objects of the definitions. 
 
 A straight line is the shortest way between the points constituting its extremities. Straightness 
 is exemplified in the strings ot a violin when screwed up into a state of tension. If a straight line 
 were bent at particular points in its length, it would become a series of straight lines, termed in 
 familiar language a zig-zag. 
 
PRACTICAL GEOMETRY. 
 
 15 
 
 A curve line is one which continually changes its direction between its extremities. It is 
 evidently not the shortest way between its extremities ; neither is it a zig-zag, as this is composed 
 of straight lines. 
 
 A plane surface, or plane simply, is a surface which contains the smallest extent of surface 
 that can be enclosed by its boundaries. This is exemplified in the end of a drum, which, when 
 screwed up or stretched into musical trim, is perfectly flat, as we would say in ordinary language. 
 And it is clear that the shortest distance between any two points on the surface of the drum-end, 
 must lie in that surface; that is, in general, if any two points be taken in a plane, the straight 
 line which joins them will lie wholly in that plane. For illustration of this, if we apply a “ straight 
 edge” to the stretched surface of the drum, we shall find that it coincides with that surface, into 
 whatever direction it may be turned. 
 
 A curve surface is one which is continually deflected, no part of it being a plane. The 
 shell of an egg presents a curve surface, whether it be viewed externally or internally. The 
 exterior surface of the superficies is denominated a convex surface, and the interior a concave 
 
 surface. 
 
 Parallel lines arc straight lines in the same plane, which are equally distant from each other 
 at every part. They, consequently, never can meet, though produced or extended ever so far 
 either way. 
 
 A rectilineal angle is the quantity of divergence of two straight lines, which cither meet or 
 cut each other at a point, without regard to the lengths of the lines. As there are numberless 
 positions in which the lines meeting or intersecting may be placed in relation to each other, so 
 there may be numberless angles at which they may stand. These may be arranged into three 
 classes—right angles, obtuse angles, and acute angles. 
 
 A right angle is formed by one line standing on another, so that the ad- Fi s- L 
 
 jacent angles may be equal, each of these angles being a right angle. Thus the » 
 
 line, d b (fig. 1), standing on the line, ab c, forms with it the two angles 
 at b ; and if these angles be equal, then each is a right angle. Further, the 
 line, n b, is called a perpendicular to the line, a c, in virtue of its right-angular 
 position. A B c 
 
 Here we may shortly explain, that, in designating an angle, we employ the 
 letters used to denote its sides. Thus, the angle contained by the lines, a b and d b, is called 
 the angle, aed; and that contained by d b and b c is the angle, d b c. 
 
 An obtuse angle is one which is greater than a right angle. Thus, if the dot line, f i (fig. 2), 
 be at right angles to the line, efg, the line, f ii, inclining to one side of the 
 perpendicular, f i, will form the obtuse angle, e f h. 
 
 An acute angle is one which is less than a right angle. Thus, the line, f h 
 (fig. 2), inclining toward f g, off the perpendicular, forms the acute angle, 
 
 II F G. 
 
 A plane triangle is a surface bounded by three straight lines. When three 
 sides are all equal, it is termed equilateral; when two of them are equal, it 
 is called isosceles; all other plane triangles arc classed as scalene triangles. Any side may be 
 called the base. Triangles are denominated also according to the magnitudes of their angles. 
 When the three angles are acute, a triangle is called acute-angled; when one angle is obtuse, 
 it is obtuse-angled; when one is a right angle, the triangle is named a right-angled triangle. 
 
 In a right-angled triangle, the side opposite the right angle is called the hypothenuse ; the other 
 sides are called, indiscriminately, one of them the base, and the other the perpendicular. 
 
 A quadrilateral figure is that which is bounded by four straight lines. When the opposite 
 sides are parallel, it is called a parallelogram. When a parallelogram has right angles, it is called 
 a rectangle ; when a rectangle has all its sides equal, it is termed a square ; when a parallelogram 
 has no right angles, it is termed a rhomboid; when the four sides of a Hiomboid are equal, it is 
 termed a rhombus or lozenge. 
 
THE CABINET-MAKERS’ SKETCH BOOK. 
 
 A quadrilateral figure is termed a trapezium, when neither pair of its opposite sides are parallel. 
 A trapezium with two sides parallel is called a trapezoid. 
 
 A diagonal is a straight line joining two angles of a figure, not ad jacent. 
 
 Plane figures of more than four sides are called polygons. When the sides of a polygon are 
 equal, it is a regular polygon ; when they are unequal, it is irregular. The distinctive appella¬ 
 tions of polygons, derived from the number of their sieves, may be learned from the Table, under 
 the head of Regular Polygons. 
 
 The circle is a plane figure, bounded by one curve line, called the circumference, and is such 
 that the circumference is at all points equally distant from a point within it, 
 called the centre. Thus the curve line, a e f, in the annexed figure (fig. 3), 
 is the circumference; the area enclosed is the circle ; the point o, from which 
 lines, o a, o b, o e, drawn to the circumference, are all equal, is the centre. 
 Any line, as o a, drawn to the circumference from the centre, is termed a 
 radius; and a line, b o e, passing through the centre, and terminated both 
 ways by the circumference, is called a diameter. The radius is, then, half the 
 diameter. 
 
 An arc of a circle is any part of the circumference, as cfd. 
 
 A chord of a circle is a straight line joining any two points of the circumference, as c d, join¬ 
 ing the points c and d. 
 
 A sector of a circle is the space cut off by two radii, as a o b, or a o e. When the radii are at 
 right angles, the sector is called a quadrant. 
 
 A segment of a circle is the space cut off by a chord, as the space, cfd, cut off by the chord, 
 
 C D. 
 
 A semicircle is a portion of a circle cut off by a diameter, as the space, bfe, cut off by the 
 diameter, b e. This space amounts to half the circle. 
 
 A tangent to a circle is a straight line which touches it, meeting it only at one point, 
 called the point of contact. 
 
 Of solids there are a great variety. As planes are bounded by lines, and derive their names 
 from the character and dispositions of these lines; so solids are bounded by surfaces, either plane or 
 curve, and derive their titles therefrom. Regular solids, bounded exclusively by planes, cannot 
 have fewer than four sides. A four-sided solid is termed a tetrahedron. A solid having more 
 than four sides is a polyhedron. The specific titles of polyhedrons will be learned from the Table, 
 which see also for the definitions of prism, pyramid, &c. 
 
 If the student has taken the pains to understand the foregoing definitions, lie will proceed 
 with pleasure to the study of the following problems and their practical solution. 
 
 Peoblem I. To bisect (or divide into two equal parts) a given straight line by a perpendicular 
 drawn to it. 1 
 
 F ' s ' 4 ' 1. To bisect the given line, a b (fig. 4), set one foot of the compasses 
 
 on the extremity, a, as a centre; and with any convenient radius that is 
 e\ idently greater than half the line, describe the arc, c r>; similarly, from 
 the point, b, as a centre, describe another arc with the same radius, cutting 
 the first one at the points, c and d. 
 
 2. Through the points of intersection, c and d, draw a straight line, 
 ceb. This line will divide the given line, A b, into two equal parts, a e, 
 e b, at the point, e ; and will also be a perpendicular to the line. 
 
 It is not necessary, in practice, to draw the complete arcs, c i>. An 
 ... experienced eye can readily anticipate the points of intersection of the 
 
 arcs, within small hunts. Neither is it necessary to do more than apply a straight edge to these 
 
 points of intersection, and tick the point, e : unless, indeed, the perpendicular itself be wanted 
 which is nrlon nuca 3 
 
PRACTICAL GEOMETRY. 
 
 1 
 
 The same process serves for the bisection of a circular arc ; for, supposing a b to be the chord 
 of the arc, the perpendicular which bisects the chord will also bisect the arc. 
 
 Problem II. To draw a perpendicular to a given straight line, from a given point in that line. 
 
 First .— When the point is near the middle of the line. 
 
 1. Let ab (fig. 5) be the line, and c the point near the middle, from Fig. 5. 
 
 which the perpendicular is to be drawn. On c, as a centre, with any 
 convenient radius, set off equal parts, c d and c e, on the line, a b. 
 
 2. On d and e, as centres, and with a longer radius, describe arcs 
 intersecting at f, and, if wanted, on the other side of the line also. 
 
 3. Draw the line, f c. It will be a perpendicular to the line, a b, at 
 
 the given point, c. I c E B 
 
 Second. —When the point is at or near one extremity of the line. 
 
 1. Take any convenient point, c (fig. 6), obviously within the perpendicular to be drawn from 
 the given point, b ; place one foot on c, and extending the other to b, describe a circle, abd. 
 cutting the line a b at a. 
 
 2. Set a straight edge to the points, a and c, and draw a line, cutting the 
 
 circle at d. . d 
 
 3. Draw b d, which will be the perpendicular required. 
 
 Another Method. —1. From the given point, b, set off, on the given line, 0 y 
 
 a distance such as b a, equal to three of any units of measure, as three inches, 
 or three feet. \_1_ 
 
 2. From b, as a centre, with a radius of four of the same parts, describe ' 1 .- 
 
 an arc, supposed to pass through d. 
 
 3. From a, as a centre, with a radius of five parts, describe an arc, cutting the other arc at i>. 
 
 4. Draw d b for the perpendicular required. 
 
 This last method of solving the problem can be easily applied on a large scale for laying down 
 perpendiculars on the ground. Timbers also may be set at right angles by the same method. 
 The numbers three, four, and five, are, it is to be observed, taken to measure respectively the 
 base, the perpendicular, and the liypothenuse, of the right-angled triangle, abd. Any multiples 
 of these numbers may be used with equal propriety, when convenient; as six, eight, and ten, or 
 nine, twelve, and fifteen, whether inches, feet, or any other unit of length. 
 
 When a series of perpendiculars to the same straight line are required, they may, if not above 
 six inches long or so, be drawn with ease by means of a straight edge and a triangle, after one of 
 the perpendiculars has been found, by the foregoing method. Thus, one edge of the triangle, 
 a b (fig. 7), being set to the perpendicular found, and the edge of the rule, c d, applied to the 
 base, if the triangle be slid along the edge of the rule, its side, a b, will run parallel to the line 
 to which it was set, and will consequently yield perpendiculars as far as the rule may extend. 
 
 A similar application of the triangle and straight edge enables us to draw parallels to any 
 given line. 
 
 / 
 
 
 / 
 
 / ° 
 
 A 
 
 -V- 
 
 1 -! 
 
 V 
 
 Problem III. To draw a perpendicular to a given line from a given point without the line. 
 First .— When the point is conveniently near the middle of the line. 
 
IS 
 
 THE CABINET-MAKERS’ SKETCH BOOK. 
 
 1. Let A b (fig. S) be the line, and c the point without it. On c, as a centre, with a 
 conveniently long radins, describe an arc, cutting the line, a b, at the points, d e. 
 
 2. On the points, d e, as centres, and with a longer radius (the longer the more accurate 
 the work is likely to be), describe the arcs intersecting at f. 
 
 3. Set a straight edge to the points, c and f, and draw a straight line from c to the line, a b. 
 This wall be the perpendicular required. 
 
 If there bC no room below the line, a b, the intersections, f, may be taken above, that is, between 
 the point, c, and the line. This mode is not, however, so good as the one already described 
 because it is not likely to be so exact. 
 
 Second .—When the point is near the end of the line. 
 
 1. In the figure annexed to the second case of Prob. II. (fig. 6), let d bo the given point, 
 and a b the straight line. From d draw any straight line, d a, meeting a b at a. 
 
 2. Bisect a d at c, and on c, as a centre, with c a as a radius, describe an arc, cuttino- a b at b. 
 
 3. Draw d b for the perpendicular required. 
 
 Problem IV. To describe a square on a given straight line. 
 
 i'ig. o. 1. Let a b (fig. 9) be the straight line, or the base of the proposed square. 
 
 c n Draw a c and b d perpendicular to the base, from its extremities, and make 
 
 each of them equal to a b. 
 
 2. Draw the line, c d ; this will complete the square, abcd, on the line, a b. 
 A rectangle may be constructed in the same manner. Having determined 
 
 -- l one of the sides, perpendiculars are drawn from each end of it, of the proper 
 
 equal lengths, and their extremities joined. 
 
 W hen the centre line of a rectangle is given, the figure may ’be very accurately described in 
 the following manner:— 
 
 Tig. io. 1. Let a b (fig. 10) be the centre line, and c the middle of the 
 
 D length of the figure. Draw the perpendicular, d e, through the 
 
 o - ; q point, c. 
 
 K P V "T M 2. Set off c f and c g on each side, equal to half the length of 
 
 the rectangle. 
 
 A ; p- - ~j - B **• ^ et c H ail d c 1 on the line, d e, each equal to half the 
 
 breadth of the rectangle ; with the same radius, and from the centres, 
 L p.. v . : . 7 i F g, describe arcs, k, l, m, n. 
 
 *■ \ n 4- From the intersections at h i, and with the half-length as 
 
 radius, describe arcs, o, p, q, b, cutting the others. The four fines 
 joining the extreme points of intersection will constitute the rectangle. 
 
 Problem \ . To draw a line parallel to a given line. 
 hirst. To draw the parallel at a given distance. 
 
 1. Let a b (fig. 11) be the given line. Open the legs of the compasses to the required dis- 
 
 B P 
 
 tanee, and from any two points, c and d, (the farther apart the better,) describe two circular 
 arcs on the side towards which the parallel is to he drawn. 
 
 . 2 ‘ A PP ] y a straight edge tangentially to the arcs at e and r, and draw the straight line, o n ; 
 this will be a parallel to the given line. 
 
 Second. To draw the parallel through a given point. 
 
 1. Let c (fig. 12) be the point; from c draw any oblique line, c d to a b. 
 
PRACTICAL GEOMETRY. 
 
 19 
 
 2. From c and d, as centres, describe arcs, d e and c f. 
 
 3. Make d e equal to c f, and through the points, c, e, draw the parallel, g ii. This is the 
 line required. 
 
 The methods of describing squares and rectangles, already given, are also available for draw¬ 
 ing parallels, though they are not so generally ready of application as the foregoing. 
 
 Problem VI. To divide a straight line into any number of equal parts. 
 
 1. Let a b (fig. 13) be the straight line, to be divided into, say, five equal parts. Through 
 
 the points, a and b, draw two parallels, a c, bd, p lg< 13< 
 
 forming any convenient angle with ab. ' ° 
 
 2. Take any convenient distance, and lay it off / 
 
 four times (one less than the number of parts required) / 
 
 along the lines, a c and b d, from the points, A and b / / / _ 
 
 respectively; and join the first on a c to the fourth j J-- 
 
 on b d, the second on a c to the third on b d, and d ^ 
 
 so on. The lines so drawn will divide a b into the required number of equal parts. 
 
 With the assistance of the straight edge and the triangle, or a Fig. u. 
 
 couple of triangles, this process may be considerably expedited. 
 
 Thus, having drawn an oblique line, a c, from the point, a, lay off \ 
 
 five equal parts on it; set the edge of the triangle to the point, b, 
 
 and the fifth graduation on a c (fig. 14), slide the triangle parallel 
 
 to itself in the direction, b a, and draw parallels from the points of \ 
 
 division on a c to the line a b ; the latter will thus be divided into * 
 
 five equal parts. 
 
 Fig. 15. 
 
 Problem VII. To construct an equilateral triangle. 
 
 1. Let ab (fig. 15) be the length of the side of the triangle. On a and 
 
 b, as centres, describe arcs, cutting each other at c. 
 
 2. Join a c and b c ; the triangle, abc, thus formed, is equilateral. 
 
 Problem VIII. To construct a triangle, having its three sides of given lengths. 
 
 1. Let a b (fig. 16) equal the base of the triangle. On a, as a centre, with a radius equal to 
 one of the sides, describe an arc. 
 
 2. On b, as a centre, with a radius equal to the third side, describe an arc, cutting the former at c. 
 
 3. Join a- c and b c. The triangle is thus completed as required. 
 
 This problem is useful in enabling us to locate a point, the distance of which from two other 
 
 points is known. Thus, the position of the point, c, is readily ascertained by the foregoing process, 
 when its distances from the points a and b are given. 
 
 Problem IX. To draw a straight line so as to form any required angle with another straight 
 line. 
 
20 
 
 THE CABINET-MAKERS’ SKETCH BOOK. 
 
 1. Let b a c (fig. 17) be the given angle, and d e the line upon which an equal angle is to 
 be drawn at the point, d. From the points a and d, with any convenient radius, describe arcs f g 
 and ii i. 
 
 2. Set off the length of the arc f g, contained between the lines a b and a c, upon the arc ii i; 
 and draw d i. The angle, edi, will be equal to the given angle, bac, 
 
 Proble tfX. To bisect a given ,an gle. 
 
 1. Let bac (fig. 18) be the given angle. On a, as a centre, describe an arc, cutting the sides 
 of the angle at d and e. 
 
 2, On d and e, as centres, describe arcs, cutting each other at f. The line a f will bisect the 
 angle, as required. 
 
 X 
 
 Problem XI.—To find the centre of a circle, or of a segment of a circle. 
 
 Fig. 19. First. — For the centre of a circle. 
 
 1. Let abcd (fig. 19) be a circle, of which the centre is to be found. 
 Draw and chord a c. 
 
 2. Bisect the chord at e, and draw b d perpendicular to it, bounded both 
 ways by the circumference. Then b d is a diameter. 
 
 3. Bisect b d at f ; this point will be the centre of the circle. 
 
 Or the following method may be adopted; and it is the more expeditious 
 
 „ of the two. 
 
 1. From any point, b, in the circumference, with a radius not greater than that of the circle, 
 describe a circular arc. 
 
 Fi - 20 * 2. From two other points, a and c (fig. 20), beyond this arc, one on each 
 
 side, describe other arcs with the same radius, each cutting the first arc in 
 two points. 
 
 3. Through the two points of intersection thus found, draw straight lines 
 meeting at the point o. This will be the centre of the circle. 
 
 Second .—For the centre of a circular segment or arc. The second pro¬ 
 cess for finding the centre of a circle may also be applied to find the centre 
 of a segment. In the diagram annexed to the description of that process, if 
 the segment, a b c, be given, its extremities, a and c, and any intermediate point, b, may be taken 
 for the centres on which the curves are described, and the centre, o, will be found, as already 
 explained. If the curve be greater than a semicircle, as a d c, the same process is applicable; 
 or if it be much greater, the first method may be resorted to. It is obviously of importance that 
 the points, a, b, and c, be well apart, and about equally distant too, and also that the arcs em¬ 
 ployed be of as large a radius as convenient, as the process is then likely to be more accurate. 
 
 V 
 
 / 
 
 Problem XII.— To draw a tangent to a circle through a given point. 
 
 There are several varieties of this problem, depending upon the position of the given point, 
 and the accessibility of the centre. 
 
 First .—When the point is outside the circumference, and the centre 
 given. 
 
 1. Let p (fig. 21) be the point, and o the centre of the circle, a. With 
 the radius, p o, on the centre, p, describe the arc, oab, 
 
 2. W ith the diameter of the given circle, as radius, on the centre, o, cut 
 the arc at b ; join o b, and bisect it at c. The line, pca, will be a tangent 
 to the circle, touching it at a. Here it may be observed, that as the line, 
 p c a, is perpendicular to o b, it is identical with the line employed in the pro¬ 
 cess for bisecting the line, o b ; thus there may be but one operation in per¬ 
 forming this bisection, and drawing the line, p a. 
 
PRACTICAL GEOMETRY. 
 
 21 
 
 Fig. 23. 
 
 The tangent may be drawn in the following manner also. Draw bo to the centre ; upon p 
 o as a diameter describe a semicircle, cutting the circle in a ; the line p a is the tangent. 
 
 Second. When the given point is in the circumference, and the centre given. 
 
 1. Let a (fig. 22) be the given point. Draw o a d, making a d equal to o a ; and draw bac 
 perpendicular to it, and b a is the tangent required. 
 
 Third. When the centre is inaccessible, as the given 
 point is in the circumference. 
 
 1. Let abc (fig. 23) be the given arc, and a the 
 given point. Set off from a two equal arcs, ab,bc, and 
 draw the straight lines, a b and a c. 
 
 2. Make the angle bad equal to the angle bac. 
 
 Then a d is the tangent. 
 
 This is a very simple operation, and it may be employed 
 with advantage even though the centre be given. 
 
 Another mode is to set off on each side of the point a, equal arcs a b and a e ; to join e b, 
 and to draw a perpendicular, a f, to it, and finally to draw a b perpendicular to a f. 
 
 Problem XIII.—To describe a circle that shall pass through three given points. 
 
 The second process for finding the centre of a circle (Prob. XI.) is exactly applicable for 
 this purpose. Referring to the accompanying figure, suppose a, b, and c, to be the three given 
 points; the point o being found by the method there delineated, it is the centre of the circle 
 required, and by taking the distance to any of the points a, b, c, as a radius, the circle may be 
 described passing through all the three points. 
 
 Also this problem is obviously identical with that which requires to circumscribe a triangle, as 
 in this case a circle is to be described passing through the three points terminating its angles; 
 the problem which proposes to describe an arc of a circle passing through the extremities of a 
 straight line with a given rise , is but another form of the one now discussed. For example, in 
 the figure accompanying the first process under Problem XI., if a b be the straight line, and e b 
 the given rise, being a perpendicular to it at the middle point e, it is clearly a case of the 12th 
 problem; as we have the three points, a, b, c, and we wish to describe an arc passing through 
 these three points. This problem will be useful for finding the diameter of any large object, 
 when only a part of the circumference is accessible. 
 
 Fig. 24. 
 
 Problem XIV. To draw a number of radial lines upon tlio circumference of a circle, the 
 centre being inaccessible. 
 
 1. If the radii are at equal distances, divide the circumference, or a part of it, into the required 
 number of equal parts, at the points A, b, c, &c. 
 
 2. On the points A, B, c, &c., as centres, with radii larger than 
 a division, describe arcs cutting each other at b, c, &c.; thus, from 
 a and c, as centres, describe arcs intersecting at b ; and from b and 
 D, as centres, describe arcs cutting a,c; and so on. The lines, 
 
 ABi,cc, &c., will be radial lines, as desired. 
 
 In presenting the foregoing methods of performing geometrical operations, no account is taken 
 of the use that might be made of the common T square, and the triangles, or of the parallel ruler. 
 These instruments will, however, where applicable, assist considerably on many occasions, in 
 simplifying the solution of the problems, and with an accuracy generally quite sufficient for prac¬ 
 tical purposes. When, for example, a tangent is to be drawn to a circle through a given point 
 in the circumference, one edge of the triangle might be set to the radius at that point, and the 
 parallel ruler set to the perpendicular edge of the triangle, and then shifted to the circumference, 
 where the tangent could he drawn, or, if the tangent be parallel to an edge of the board, the T 
 square will suffice to draw it. 
 
TIIE CABINET-MAKERS’ SKETCH BOOK. 
 
 Problem XY. On a given line to describe a regular pentagon. 
 
 «Lct a b (fig. 25) be the given line, bisect a b at c, and draw c f perpendicular to a b. Set 
 off on this line, a length, c d, equal to a b, the given side of the required pentagon. Draw a d, 
 and produce it indefinitely, make d e equal to half a b. From a, as a 
 centre, with the length a e, as a radius, describe the arc e f, cutting 
 c f in f. 
 
 2. From af and b as centres, with ab as a radius, describe arcs 
 cutting each other in a and h. 
 
 3. Draw the lines a f and n b, when agfhb will be the pentagon 
 required. 
 
 Problem XVI. To describe a pentagon in a given circle. Let 
 agfhb (fig. 25) be the given circle. 
 
 1. Draw the diameters, i k and l f, perpendicular to each other; bisect m k in a. Upon a , 
 as a centre, with the distance a f, describe the arc f b. Upon f, as a centre, with the distance 
 f b y describe the arc b g, cutting the circle at g. Join g a, and carry it round the circle five 
 times, and it will produce the required pentagon. The arcs contained between the extremities 
 of any side of the pentagon, as n k, being bisected as at n k, will give the sido of a decagon, or 
 ten-sided figure, inscribed in the same circle. 
 
 Fig. 25. 
 
 S E 
 
 Fig. 26. 
 
 Problem XVII. To construct a hexagon on a given line. 
 
 1. Let a b (fig. 26) be the given line. On the extremities of this 
 line, with the extent of the line as a radius, describe arcs intersecting 
 each other at c. 
 
 2. On c, as a centre, with the same radius, describe a circle. From 
 the intersections at d and e, with the arcs before described, set off df 
 and e g on the circle. 
 
 3. Join a d, d f, f g, and e b, which will form the hexagon required. 
 When the circumscribing circle is given, the following method may 
 
 be adopted. 
 
 Take the radius of the given circle in the compasses, and apply it to the circumference, which 
 will divide it into six equal parts. Draw a chord to each arc, and the six chords will form the 
 hexagon required. 
 
 Problem XVIII. To inscribe a regular octagon in a given square. 
 
 Let a b c d (fig. 27) be the given square. Draw the diagonals, a d 
 and b c, intersecting at e. 
 
 Upon a b c d as centres, with a radius e c, describe the arcs, h e l, 
 k e n, m e g, and f e i. Join k g, h i, m n, and f l, and the required octagon 
 is produced. 
 
 If a circle is given, in which to inscribe a regular octagon, it may be 
 done in the following simple manner. 
 
 1. Draw two diameters at right angles to each other. 
 
 2. Bisect the four arcs thus obtained, and draw chords to each; 
 which chords shall form the octagon required. 
 
 Problem XIX. To describe any regular polygon upon a given line. 
 
 Let a b (fig 28) be the given line. Produce a b any length in either direction, as a c. From 
 a as a centre, with a d as a radius, describe a semicircle, divide it into as many equal parts as the 
 polygon is to have sides ; in the present instance we have chosen five, as a d b c, the number of 
 points required to produce a pentagon. 
 
 Fig. 27. 
 
PRACTICAL GEOMETRY. 
 
 23 
 
 2. Draw lines through all the divisions (minus one), as a d, a b e, a c f. 
 
 3. From d and b as centres, with a b as a radius, describe arcs, cutting a e in e, and a f in 
 f. Draw the lines de,ef, and f b ; when 
 a d e f b shall be the polygon required. 
 
 Problem XX. To describe any regu¬ 
 lar polygon in a given circle. 
 
 1. Let afbd (fig. 29) be the given 
 circle. Draw the diameter, a b. From 
 e, as a centre, erect the perpendicular, 
 e f c, cutting the circle at f. Divide e f 
 into four equal parts, and set off three 
 similar divisions from f to c. 
 
 2. Divide the diameter, a b, into as many equal parts as the polygon is required to have 
 sides. 
 
 3. From c, through the second division in the diameter, draw the line c d, and a d shall be 
 the side of the polygon required. 
 
 In each of these examples we have shown a pentagon, on account of its simplicity, but the 
 same rule is applicable to polygons of any number of sides. 
 
 THE ELLIPSE. 
 
 The fact of circular surfaces changing their appearance with the different positions of the ob¬ 
 server’s eye, is so well known as to render any observations on that head needless; but in order to 
 delineate them under all circumstances, it is essentially requisite that the student should under¬ 
 stand that the elliptical curve thus assumed by the circular one is strictly regular, and is to be 
 produced by rules as fixed and certain, as that by which we describe the circle itself. With the 
 assistance of the annexed figure (30), which we have 
 selected as a familiar explanation of the principles of 
 the ellipse, the student will have ro difficulty in under¬ 
 standing the plain definition of it. The line a b, passing 
 through the length of the figure, is called its transverse 
 axis. 
 
 The point g, which bisects the transverse axis, is the 
 centre of the ellipse. The line c d, crossing this centre 
 at right angles to the transverse axis, is termed the con¬ 
 jugate axis. 
 
 The point f in the transverse axis, and corresponding point h at the same distance from the 
 centre on the other side, are called the foci of the ellipse. 
 
 A right line// or ee passing through a focus of the figure at right angles to the transverse 
 axis, and terminated at either end hv a curve, is called tlie latus rectum, or sometimes the para- 
 meter. 
 
 A straight line passing in any direction through the centre of the figure, and terminated at 
 either end by the curve, as gg or h h, is called a diameter. 
 
 A line drawn through any diameter parallel to a tangent at the extremity of that diameter 
 terminated by a curve, is called a double ordinate. 
 
 The ellipse is constructed by the motion of a point about the centre of the figure g, begin¬ 
 ning its course at the extremity of a diameter, as at a, and taking such a path as that its distance 
 from one of the foci, together with its distance from the other, shall be, in every point through- 
 
 Fig. 30. 
 
 Fig. 28. Fig. 29. 
 
24 
 
 THE CABINET-MAKERS’ SKETCH BOOK. 
 
 out its course, exactly equal to tlie whole length of the transverse axis, a b. A practical ap¬ 
 plication of this principle is to he found in the following method, which is often resorted to in the 
 workshop for producing an ellipse. In the preceding figure, if the transverse and conjugate axes 
 are given, the foci are determined by taking half the tranverse axis, as a g, and with that extent in 
 the compasses, and on the extremity c of the conjugate as a -centre, describing an arc, which cuts 
 a b in the points f and h, which are the foci. 
 
 If pins are fixed in these points, and a thread equal in length to the transverse axis is fastened 
 to them by its extremities, a pencil so applied to the thread as to keep it continually stretched, or 
 forming two straight lines, will, if progressively moved about the centre, describe the ellipse. 
 Thus, in the figure before us, h c f may be supposed to be thread, which, if gradually moved 
 round the centre, will, at different points of its travel, take the position of the inclined lines n and 
 e f, describing by the entire revolution of the pencil the ellipse, acbd. 
 
 Problem XXI. The transverse and conjugate diameters of an ellipse being given, as a b and 
 
 c d, to describe the curve itself through a number of 
 points, to be determined at the extremities of any 
 number of diameters at pleasure. 
 
 1. Through the extremity, d (fig. 31), of the con¬ 
 jugate axis, draw e f parallel to the transverse axis ; 
 extend the line c d to g, and make it equal to a s or s b, 
 half the transverse axis. 
 
 2. Upon g, with the radius g d, describe the circle, 
 h d k ; through the centre, s, draw the lines, s, l, e, s, 
 m, &c. at pleasure, respectively cutting the line e f 
 at e r, &c. Join the points thus determined on the line 
 e f with the centre g, and mark the points of intersec¬ 
 tion produced on the arc, h d k, at l, m , n, o, &c.; draw 
 lines from h, /, m, &c., parallel to g d, until they respec¬ 
 tively intersect the extremities of the diameter at a, l, m, n, &c.; these points will be in the 
 periphery of the ellipse, and a curve traced through them will describe the figure. 
 
 A figure which is often substituted for the ellipse for practical purposes, but is decidedly 
 inferior to it in point of regularity and beauty of contour, may be 
 drawn by means of circles in the following manner:— 
 
 1. Let ab (fig. 32) he a given transverse diameter; divide a b 
 into three equal parts, by the points o v. From o and v as centres, 
 with o a or v b as a radius, describe equal circles, dvf and ego, 
 cutting each other in the points i and k. 
 
 2. Draw the lines kod,ivg,iof, and k v e, cutting the circles in 
 the points def and g. 
 
 3. From i and k as centres, with k d or i g as a radius, describe the curvilincal tangents, 
 n e and f g, when the figure, a d, e b, g f, will be the ellipse required. 
 
 There are various methods of describing ellipses mechanically at present in use, probably the 
 best of which is that invented by Mr. Ridley. By this instrument every species of ellipse, from 
 a circle down to a right line, may be correctly formed. 
 
 1 he instrument consists mainly of a beam, a, carrying three sliding sockets, b c cl (fig. 33), 
 which may be set at any distance from each other. On the sockets, b and d, small sheaves are 
 fitted to revolve on pins, and the centre one, c, is fitted to receive a pencil or tracer. 
 
 To explain the action of this apparatus, wo shall suppose a b to be the transverse, and c d the 
 conjugate axis of the required ellipse, intersecting each other at e. The inner edge of a square, f, 
 is now to he applied to the lines, c, £, b, at such a parallel distance therefrom as to allow tho 
 
 Fig. 31. 
 
 H O K 
 
centres of the sheaves on the sliding bar to move exactly over the centre of the lines constituting 
 the axes of the ellipse. To adjust the position of the 
 sockets to produce the given ellipse, the distance between 
 the pencil and the sheave, b, is made equal to half the 
 length of the transverse axis, and c d equal to half the 
 conjugate. If now the bar is moved along the edge of 
 the square, as shown by the dotted lines, the tracing point 
 will describe one quarter of the ellipse, each of the re¬ 
 maining portions being described in a similar manner. 
 
 This simple apparatus has since been considerably 
 improved; instead of the plain square of wood, two 
 grooved pieces of metal crossing each other at right angles, 
 so as to form four squares, are substituted. The pins in 
 the pencil beam are fitted to slide in the grooves which 
 are made along the upper side of the squares. In this 
 manner, the whole of the ellipse may be described at once, 
 
 with the exception of the slight portion which the thickness of the square covers; these are easily 
 filled in by hand. 
 
 We now come to the consideration of the two curvilincal figures, the parabola and 
 hyperbola, which, together with the ellipse, are generally treated under the head of Conic Sec¬ 
 tions, that is, as curves produced by the intersection of a flat surface with the curve surface of 
 a cone. 
 
 Let abc (fig. 34) represent a vertical section through the centre of a cone, the figure which 
 is produced is a triangle. 
 
 If the entire cone is cut by a plane passing through it in the direction of d e, parallel to the 
 base, the figure produced will be similar to the base, 
 
 that is, a circle. F,g - 34, 
 
 If the section is made in the direction f k, parallel 
 with the opposite sloping side of the cone, as a b, the 
 curve described on the surface will be a parabola. If 
 the intersecting plane pass through the cone in the 
 direction f i, perpendicular to the base and parallel to 
 the axis, the curve produced on the surface of the cone 
 by the section is an hyperbola. 
 
 If the intersecting plane pass through the cone in 
 any oblique direction, as k l, the curve described on its 
 surface will be an ellipse. As we have already explained the construction of the ellipse, we shall 
 now proceed to examine that of the parabola. 
 
 THE PARABOLA. 
 
 In order to enter fully upon the geometrical construction of this figure, we shall, in the first 
 place, exhibit its mechanical formation, so as to enable us to set before the student the most 
 explicit rules for application in practice. 
 
 In the annexed figure (35), let a b c be a straight-edged ruler, and a b d a common joiner's 
 square ; and let a thread of a length equal to b d be fixed by one extremity to the end of the 
 square n, and the other to any point e, between the two rulers. If now the side as of the 
 square be moved along the edge of the ruler, abc, and a pencil is applied to the edge b d, so as 
 always to keep the thread stretched, at the same time that it allows it to slip round its point F, 
 the pencil will describe a curve, f l n which is a parabola. 
 
 
26 
 
 THE CABINET-MAKERS’ SKETCH BOOK. 
 
 The point e, about which the thread moves, is called the directrix, 
 
 A line h k, drawn through the focus e, and perpendicular to the directrix, is called the axis 
 of the figure. 
 
 The point h, in which the axis cuts the curve, is called the vertex of the figure. 
 
 A line g n, passing through the focus e, at right angles to the axis, and terminated by the 
 curve, is the parameter. 
 
 Any line which can be drawn within the limits of the curve, parallel to the axis, as j k, is 
 called a diameter. 
 
 If a tangent were drawn to j k at j, the extremity of the diameter, a line l o, drawn parallel 
 to it, is called a double ordinate. 
 
 That part of any diameter which is contained within any part of the curve itself and its ordi¬ 
 nate, as j k, is termed an abscissa. 
 
 Fig. 35. 
 
 Fig. 36. 
 
 Problem XXII. Let a b (fig. 36) be the given axis of a parabola, and c d a double ordinate. 
 It is required to delineate the curve by a process which shall determine a number of points in its 
 course. * 
 
 1. Through a draw e f, parallel to the double ordinate, c d. Through c and d draw the 
 perpendiculars, c e and e f, parallel to a b. 
 
 2. Divide b c and b d into any number of equal parts, as five. Likewise divide c e and d f in 
 a similar manner. 
 
 3. Through the points ab c and d in c d, on each side of the point b, draw the perpendiculars 
 a ebfeg dli, & c., and through the points ab c and d, in c e and d f, draw lines to the upper 
 extremity a, of the transverse axis a b, respectively, cutting the perpendiculars drawn from the 
 line c d, in the points ef g h, then will the points of intersection to the right and left of the trans¬ 
 verse axis be situated in the curve of the required parabola, and which will be completed by tracing 
 a line steadily through them. 
 
 THE HYPERBOLA. 
 
 In giving a familiar explanation of the properties of this curve, we shall again have recourse 
 to the mechanical process of its formation, to the end that we may the more easily define its 
 leading characteristics. 
 
 Referring to the accompanying woodcut (fig. 37), we shall suppose the points b and c to be 
 determined, and a straight ruler, a b, to be made moveable on one of its extremities, about the 
 point b, as a centre. To the end a of this ruler, one end of a thread is attached, the other being 
 fixed at the determined point c. Now, let a pencil be applied to the thread, so as to press a 
 portion of it against the edge of the ruler, as a d, and keep the other portion, d c, tightly 
 stretched. The ruler being made to traverse on the given point e, at the same time that 
 
PRACTICAL GEOMETRY. 
 
 the pencil d moves along its edge, always preserving the tension of the threads ; and the motion 
 of the pencil or point n, will be in the curve dfg, which is that of an hyperbola. 
 
 If the extremity of the ruler, which now moves on the point b as a centre, was removed to 
 c, and there made to traverse in a similar manner, the 
 
 end of the thread now set at c, being now placed at b, Fi s- 37. 
 
 the curve described would be an opposite hyperbola. 
 
 The points b and c, on which the ruler traverses, 
 are called the foci. 
 
 A line terminated by the curves of the hyperbola and 
 its opposite, and which, if continued at either extreme, 
 would pass through either of the foci, as i h in the figure, 
 is called the transverse axis. A line passing through 
 the centre m of the figure to the right and left of it, and 
 terminated by the intersection of the arc of a circle, which is described on the point h as a 
 centre, with the distance c m as a radius, is called the conjugate axis. Any line, as v w, drawn 
 through the centre m, is called a diameter. If a tangent, with either of the curves, be drawn to 
 the extremity of v w, another line, as f f, drawn parallel to that tangent, and through the centre 
 m, is called a conjugate diameter to that at the extremity of which the tangent was drawn. A 
 line drawn through any diameter parallel to its conjugate diameter, and terminated by the curve, 
 is called a double ordinate. If any diameter be continued within the curve, and is terminated 
 by the curve and a double ordinate, the part within is termed an abscissa. A line drawn through 
 the focus of the figure, and at right angles to the transverse axis, is called the parameter. 
 
 If through the extremity of the transverse axis, i h, a line, r s, is drawn parallel to the conju¬ 
 gate axis, n o, and equal to n o, having h r and h l respectively equal to m n and m o, their right 
 lines drawn through the centre m, and the points r and s, as are the lines m x and m y, are called 
 asymptotes. 
 
 When the transverse and conjugate diameters are equal, the hyperbola is termed equilateral 
 or right-angled. 
 
 The recapitulation of these dry and uninteresting terms may appear formidable to the student, 
 but he must bear in mind that a complete knowledge of these is essentially necessary to enable 
 him to comprehend and construct any hyperbolic curves with which he may meet in practice. 
 For curves of a large size, the foregoing mechanical system of construction is very useful and accu¬ 
 rate ; but, as before adverted to, in order to attain a complete 
 knowledge of the subject, as well as to be able to cope with 
 the different forms which occur, it is necessary to under¬ 
 stand correctly their geometrical construction. 
 
 Problem XXIII. The diameter of an hyperbola, a b (fig. 
 
 38), its abscissa, b c, and double ordinate, d e, being given, 
 it is required to delineate the curve by determining a certain 
 number of points which shall be in its course. 
 
 1. Through b draw g f parallel to d e, and from the ex¬ 
 tremities, d and e, of the ordinates, draw d g and e f parallel 
 to the abscissa, b c, cutting g f in the points f and g. 
 
 2. Divide c d and c e, each into any number of equal 
 parts, as four ; and through the points of division, a b c, on 
 each side of the point c, draw lines to a. 
 
 3. Divide d g and e f into the same number of equal 
 parts, and from the points of division on d g and e f, draw 
 
 lines to b. A curve drawn through the intersections at a be, on each side the diameter, ’ 
 that of the hyperbola required. 
 
28 
 
 THE CABINET-MAKERS’ SKETCH BOOK. 
 
 
 Problem XXIV. The transverse and conjugate diameters, a b and c d (fig. 39), being given, 
 it is required to determine a certain number of points in the curve with a view to its delineation. 
 Through the extremity b, of the diameter a b, draw f g parallel to c d, the other diameter; 
 
 and make b f and b g equal to the semi-diameters 
 e c or e d. Through the points f and g thus deter¬ 
 mined, draw e h and e j, which will be the symptotes 
 of the figure. 
 
 From a, as before, draw lines at pleasure towards 
 the curve to be described, as a g, a h, a j, a k, cutting 
 the asymptotes at the points abed, and efg, and h, 
 &c. Set off the distances a h, h g, a f a ^respectively, 
 from the points a b c and d on the lines from a ; and 
 the points g h, j k, will be in the curve required. 
 
 If the student has gone over this course of prac¬ 
 tice in the construction of geometrical curves, by per¬ 
 forming the examples themselves on a large scale, he will be enabled, in his future operations, 
 to make use of them in any drawings which come before him in his every-day practice. There 
 arc numerous other useful curve lines which admit of regular definitions, as the Cycloid, Epicy¬ 
 cloid, &c. The first of these curves, the Cycloid (fig. 40), may be defined in a familiar man¬ 
 ner, by supposing it to be the periphery of a cart-wheel 
 Fis ' 40, rolling along a level road. Thus the circle a b, in the annexed 
 
 woodcut, may be supposed to represent the cart-wheel rolling 
 in the direction aba, and a to be the given point in its peri¬ 
 phery. Under these conditions, the track of the point a during 
 one revolution will be indicated by the curve line, a c a, g a, 
 which is termed the cycloidal curve. The properties of the 
 cycloid may be briefly defined as follows:—If the generating circle is placed in the centre of the 
 curve, its diameter coinciding with the axis, a b, and if from any point there be drawn a tangent, 
 c e, the ordinate, c n e, perpendicular to the axis, and the chord of the circle, then 
 The right line, cd,= the circular arc, ad. 
 
 The cycloidal arc, a c, = double the chord, a d. 
 
 The semi-cycloid, a c a, = double the diameter, a b, and 
 The tangent, c f, is parallel to the chord, a d. 
 
 If the ball of a pendulum is caused to move in a cycloidal curve, its vibrations will be isochro¬ 
 nous ; that is, they will all be performed in precisely the same amount of time. 
 
 The epicycloid (fig. 41) differs from the cycloid in this, that 
 it is generated by a point in one circle rolling upon the circum¬ 
 ference of another, instead of a level surface. The cycloid may, 
 however, be brought under the same definition, by regarding 
 the straight line as the circumference of a circle whose diameter 
 is infinitely great. 
 
 This definition of the curve will be understood by reference to 
 the accompanying figure, in which a is the generating or rolling 
 circle, and b the fundamental one, or that upon which it rolls in 
 describing the exterior epicycloidal curve, c d. If the generat¬ 
 ing circle, instead of rolling on the outside, were to roll within 
 he interior circle, a point in the former would describe an in* 
 tcrior epicycloid, or, as it is more recently termed, the hypocycloid. 
 
CHAPTER I. 
 
 The moderns have applied the term “order” to those architectural forms with which the 
 ancient Greeks and Romans composed the exteriors of their temples. There are generally 
 understood to be five orders of Architecture, namely—the Tuscan, the Doric, the Ionic, the 
 Corinthian, and the Composite. The Doric, the Ionic, and the Corinthian orders were origi¬ 
 nally designed by the Greeks, who knew nothing of the Tuscan and the Composite orders. 
 The Romans borrowed the three Grecian orders, and modified them to suit their own purposes ; 
 and to these they added the Tuscan and Composite orders. The latter orders, however, have 
 little claim to be separately classed, as they have much in common with the former three. The 
 Tuscan order, by its title, enables us to assign its origin to Tuscany, which is indeed the more 
 certain by the fact, that the Tuscans were originally a colony of Dorians. The Composite order, 
 as the name implies, is compounded from the other orders, and may be called in truth a corrupted 
 Corinthian. The characteristics of an order are determined not so much by the ornaments with 
 which it is embellished, as by the essential proportions of its parts. 
 
 It appears then from this, that there are three Grecian and five Roman orders ; and the 
 Doric, Ionic, and Corinthian being common to both, they are distinguished as Grecian Doric, 
 Roman Doric, and similarly for the Ionic and Corinthian. 
 
 The leading members of an order are—1. a platform ; 2. perpendicular supports ; and 3. a 
 lintelling or covering connecting the tops of the supports, and covering the edifice. 1 he pro¬ 
 portioning of these parts to the edifice and to each other, with the addition of suitable decorations, 
 constitutes an order or rule. The principal member is the upright support or column, the 
 accompanying members being subservient to this leading feature ; the bottom of the column 
 rests either on a general platform, or upon a particular square plinth. The lower part of the 
 column resting upon the square plinth is usually encompassed with a selection of mouldings, 
 which, from their position, are, in conjunction with the plinth, termed the Base of the column. 
 The upper end is likewise covered with a plinth, which, in conjunction with the accompanying 
 mouldings on the upper end of the column, is termed the Capital of the column. The body of 
 the column, or that part situated between the base and the capital, is called the Shaft. The lin¬ 
 telling or covering which lies upon the columns is denominated the Entablature, and is subdivided 
 into three parts—the Architrave, Frieze, and Cornice. The architrave represents a mere lintel, 
 embracing the tops of the columns; the frieze is intended to signify generally the ends of the 
 cross-beams resting upon the lintels, having the spaces between them filled up, and having also 
 a plain moulding to separate it from the a chitravc, and to conceal the horizontal joint formed 
 by the two members ; the upper member or cornice represents the projecting eaves of a Greek 
 roof, showing the ends of the rafters. The whole is distinctly exemplified in the Grecian Doric 
 order. 
 
 Mouldings .—Before going into the details of the orders, it will be necessary to give an account 
 of the various mouldings employed in Greek and Roman architecture. And, in the first place, 
 
30 
 
 THE CABINET-MAKERS' SKETCH BOOK. 
 
 mouldings may be defined to be prismatic or annular solids, formed by plane and curved sur¬ 
 faces, which are employed as ornaments, and are considered as forming constituent parts of an 
 order. It we conceive a straight moulding to be cut through at right angles to its length, the 
 section thus formed is termed its profile, and exhibits exactly its characteristic outline, from 
 which its name is derived. Annular mouldings, again, or such as are formed upon a round sur¬ 
 face, as the surface of a column, must bo cut by a plane passing through the centre line or axis 
 of the column, in order to exhibit their characteristic sections or profiles.* * 
 
 A prevailing gracefulness of outline characterises the mouldings of the Grecian orders, which 
 at once distinguishes them from the more unpretending and simpler mouldings of the Romans. 
 Various modes are employed for describing the Roman, and more especially the Greek mould¬ 
 ings, so various are their applications and the modifications of form to which they are subject. 
 The Roman mouldings, however, are usually composed of circular arcs. The Grecian mould¬ 
 ings exhibit every variety of conic section—elliptical, parabolical, and hyperbolical—the circle 
 being seldom employed but in small cavettos and mouldings of contrary flexure. 
 
 The regular mouldings are eight in number, and are thus named:—The Fillet or Band, the 
 Torus, the Astragal or Bead, the Ovolo, the Cavetto, the Cyma recta, the Cyma reversa or 
 Talon, and the Scotia. 
 
 The fillet, a, fig. 1, is the smallest rectangular member in any composition of mouldino-s. 
 
 When it stands upon a flat surface, its projection from the surface is generally 
 made equal to its height. In general it is employed to separate other mem¬ 
 bers. 
 
 In the following descriptions, the extreme points of the curves are always 
 - —assumed to be given. 
 
 The torus and astragal, shaped like ropes, arc intended to bind and 
 strengthen the parts to which they are applied. In form the torus is a semi- 
 
 * circle, which projects from a vertical diameter. Thus, in fig. 2, let a b be the 
 vertical diameter, from which the torus projects ; bisect, or divide in two equal 
 parts, the line, a b, at the point, c ; from c as a centre, describe the semicircle, a db ; this will be 
 the profile of the torus, which, it will be noticed, is surmounted by a fillet, b e. The astragal is 
 described in the same way as the torus, the only distinction between them being that, when 
 employed in the same order, the astragal is smaller than the torus. The torus is generally em¬ 
 ployed in the bases of 
 columns; the astragal, 
 both in bases and capitals. 
 
 The ovolo is a member 
 strong at the extremity, 
 and obviously intended 
 for support; it is usually 
 employed above the eye, as a supporter to the essential members of the composition. The 
 Roman ovolo consists of a quadrant or a less portion of a circle, and is described as in fig. 3, the 
 height and projection being given. And first, let the height be equal to the projection. Draw 
 a b equal to the height, and b c at right angles with, and equal to, a b, for the projection. The 
 quadrant, a c, described from the centre, b, with a radius, b a, or b c, is the contour of the ovolo. 
 But, when the projection is less than the height, as in fig. 4, draw a b and b c, as before, at right 
 angles, a b being the height, and b c the projection. From the point, a, draw an arc of a circle. 
 
 b d, with the radius, a b, and from the point, c, with the same radius, describe another arc, cutting 
 the former arc at d; the point, a, is the centre from which the ovolo is to be described, with the 
 radius, da, or dc ', this being done, the curve, a c, is the contour of the ovolo. 
 
 * It is by some considered preposterous to lay down rules for the construction of contours, which are said to he subjected to no law of 
 form, except what is furnished by the individual’s own taste. Seeing, however, that beautiful outlines may doubtless he traced by means 
 of regular geometiical constructions, we think the insertion of the more common of these methods will be useful to those who cannot readily 
 sketch for themselves. 
 
The Greek ovolo, fig. 5, unlike the Roman ovolo, cannot be described by means of circular arcs ; 
 it must be described by finding a number of points in it. For this purpose draw the tangent, a c, 
 from the lower extremity, a, indicating the inclination of the curve at that point; draw also the 
 vertical line, cl b c, through the extreme point, b, or projection of the curve. Draw b e parallel 
 to c a, and a cf parallel to c b ; make e f equal to a e ; divide the lines e b and b c into the same 
 convenient number of equal parts ; draw straight lines from the 
 point, a, to the points of division in b c, and similarly draw 
 straight lines from the point, f through the points of division in 
 b e, meeting successively the lines drawn from a to be, the 
 points of intersection of the pairs of lines thus drawn will be as 
 many points in the contour of the moulding, and a curve line 
 traced so as to embrace these points will be the greater part of 
 the contour. The remaining part, b g, if required to be deter¬ 
 mined in the same manner, may be found by drawing lines from 
 a instead of f through the points in b e, and from f to b d, 
 instead of from a to b c. Of course this will give a good deal 
 
 more of the curve than is necessary. The curve drawn in this manner is a portion of an ellipse, 
 somewhat greater than a fourth of the whole circumference. The recess of the moulding, b g d, 
 at its projecting point, is denominated a quirck. Fig. 5 is, from its great projection relatively to 
 its height, adapted for capitals of Doric columns. With less projection, it would be suitable for 
 entablature. 
 
 To describe the hyperbolical mob— fig. 6—as employed in Doric capitals ; having given the 
 projection, b, of the curve, and the lower extremity, a, draw the lino, a c, in the direction 
 of the lower end of the curve, and b c vertically 
 through the point, b ; draw a g vertically from 
 a, and b e and c d perpendicular to a g ; set off 
 ef equal to a d, and e g equal to a e ; join bf and 
 divide bf and b cinto the same convenient number 
 of equal parts ; draw straight lines from a to the 
 points of division in b c, and also straight lines from 
 g through the points in fb ; the successive inter¬ 
 sections of these lines, as in the foregoing case, 
 are the positions of as many points in the con¬ 
 tour. This is the general form of the ovolos in 
 the capitals of the Grecian Doric. It will be 
 seen that the lower part towards ci is nearly 
 straight, and is succeeded by four fillets, shown 
 in section on a large scale, and rounded away on 
 the under sides into the fundamental line, n o. 
 
 The cavetto —figs. 7, 8, and 9—which is the 
 reverse of the ovolo, both in regard to form and 
 to the weakness of the extreme parts, is well 
 adapted for purposes of shelter for the other 
 members. It is always employed as a finishing, 
 and is here applied where strength is required. 
 
 It is never used in bases or capitals, but fre¬ 
 quently in entablatures ; thus in the Roman 
 
 Doric order, it forms the crowning member of the cornice, and is evidently employed to over¬ 
 hang and shield the under members. The cavetto is described in the same way as the Roman 
 ovolo; by arcs of circles, which may be either full quadrants or of less extent, 
 cavetto—fig. 9— 
 
 The Greek 
 
 somewhat elliptical, and may be described by a combination of two circular 
 
arcs, thus : Let a b be the projection of the moulding, and a c the vertical line ; from the point, a , 
 draw b d vertically from b, and make it equal to b e, which is two-tliirds of b a ; from the centre, 
 d, describe the arc, b i; draw i n perpendicular to e d, make n o equal to n i, draw o p perpen¬ 
 dicular to a c, and meeting e d produced in p, and from the centre, p, thus found, describe the 
 arc, i o. The contour, b i o c, will represent the Greek cavetto. 
 
 The conge or scape —figs. 10 and 11—is a species of cavetto, and is not recognised as a distinct 
 moulding. In section it is partly concave and partly straight, the latter part being vertical. It 
 
 Fl > ^ is employed in the columns of 
 
 some of the orders, for joining 
 the capitals and bases to the 
 shafts. Let a b be the projec¬ 
 tion of the moulding from the 
 vertical line, a e, which it is re¬ 
 quired to touch ; and first, if 
 the projection, a b, is equal to 
 the height of the curve, make 
 a c —fig. 10—equal to a b ; and 
 from the points, b and c, as centres, with a b or cic as a radius, describe the arcs intersecting at d; 
 from d, with the same radius, describe the arc, b c; this completes the contour of the conge. 
 The centre, d, may likewise be found by drawing b d vertically, and making it equal to a b. 
 
 If the conge contains less than a quarter of a circle, as in fig. 11, let be be the tangent to the 
 curve at the point, b ; on the vertical, a f, set off the distance, c d, equal to c b ; draw b e at right 
 
 angles to b c, and d e at right angles to c d; from 
 the point, e, as a centre, describe the arc, b d; 
 this completes the contour of the moulding, b df 
 These are the simple Roman forms of the 
 conge. It is obvious that the curve may be varied 
 into a combination of arcs of different radii, in the 
 same way as the cavetto—fig. 9—which would 
 render it more appropriate for Grecian profiles. 
 
 The cymatium, or ogee, is the term applied to 
 a moulding of which the section is compounded 
 of a concave and convex surface. There are two species of cymatium : the cyma recta, or 
 simply, the cyma, and the cyma reversa or talon. The Roman cymatium is usually composed 
 of circular arcs, which may either be equal to or less than a fourth of a circumference. 
 
 Thus, in the accompanying figures, 12 and 13, 
 the former of which represents the cyma recta, 
 and the latter the talon, let a and b be the ex¬ 
 tremities of the curve, join a b and bisect, or di¬ 
 vide it equally at the point, c; from the points a 
 and c as centres, with the same radius, describe 
 arcs cutting at the point, e d; likewise, from the 
 points, b and c, as centres, with the same radius, 
 describe arcs cutting at the point, e; from the 
 points, d and e, thus found, as centres, describe 
 the arcs, a c and c b ; then the curve of double flexure, a c b, fig. 12, is the cyma recta, and the 
 curve, acb, fig. 13, is the cyma reversa or talon. In the former, it will be observed, the concave 
 portion of the surface is uppermost, whereas in the latter it is undermost. If the curve is 
 required to be made quicker, a shorter radius than a c or cb must be used in describing the two 
 parts of the contour. The projection of the upper end of the curve over the under, as n b, fig. 
 12, is generally equal to the height, a n, of the moulding. 
 
ORDERS OF ARCHITECTURE. 
 
 33 
 
 =7;-^ 
 
 The Greek cyma-recta differs little from the Roman, except in that its projection over the 
 under fillet is less than that of the latter, and that its curvature is also less. It may be described 
 similarly to the Roman cyma (fig. 12) by means of circular arcs, described with radii of greater 
 length than a c or c b. The nature of the Greek cyma-reversa, or talon, is represented in fig. 14 ; 
 the curvature of the moulding is much more deeply marked than that of 
 the Roman talon. The concave portion, a e, is deeply indented, and the con- Fig. h. 
 
 vex portion, hue, projects considerably, and is quirked or turned inwards at b. 
 
 The following is a simple mode of constructing the moulding, first intro¬ 
 duced by Mr. A. M. Nicholson:—Join the points, a b, the extremities of 
 the curve; bisect a & at the point c ; upon b c, as a diameter, describe the 
 semicircle cdb, and on a e describe the semicircle aec; draw perpendicu¬ 
 lars, do and c, from any number of points in b c and c a, meeting the circum¬ 
 ferences of the semicircles; from the same points draw a series of horizontal 
 lines, as represented in the figure, equal in length to the corresponding per¬ 
 pendiculars, o n equal to o d, for example. The curve line, b n c a, traced through the extremities 
 of the lines, will be the contour of the moulding. 
 
 The curve might be rendered flatter by using arcs of circles of a diameter greater than a c or 
 c b, as, of course, the height, o d, of the arcs would not be so great as it is in the figure ; this will 
 be exemplified in describing fig. 17, which follows; also, if the upper part, bnc, be required to 
 be larger than the under part, c a, of the contour, this may be effected by shifting the point, c, 
 nearer to a, before drawing the circular arcs. 
 
 The cyma, like the cavctto, is always used as a finishing, and never applied when strength is 
 required, as it is weak in the extreme parts, though it is applicable as a means of shelter to crown¬ 
 ing members. The talon, on the contrary, strong towards its extremity, is, like the ovolo, well 
 adapted for supporting weight. 
 
 The scotia , fig. 15, like the fillet, is employed in bases to separate, contrast, and increase the 
 effect of other mouldings, and conveys a graceful turn to the profile. To 
 describe the scotia, the extremities, a and b, of the moulding being given: 
 
 —Draw the perpendicular, ac, then be is the projection of the moulding; 
 draw the perpendicular, b e; add onc-lialf of a c and two-thirds of be into 
 one length, which set off from b to d ; from the centre, d, with the radius, 
 b d, describe the semicircle, bf e ; join e a, and produce it to J ; then join df 1 K 
 cutting ac in g\ from g, as a centre, describe the arc af; this arc, in con¬ 
 junction with bf completes the contour, afb, of the scotia. 
 
 Another mode of describing the scotia is represented in fig. 16. Join 
 the extremities, a and b, and bisect a b in c ; draw e c d horizontally, and 
 make c d equal to the required recess of the curve, and c e equal to c d ; 
 draw f d g parallel to a b ; divide a /and a c into the same convenient number of equal parts, and 
 to the points of division in af draw straight lines from d ; draw also straight lines from e, through 
 the points in a c, till they meet successively 
 the lines drawn to a f. Having performed 
 the same operation on the upper side, the 
 series of intersections thus found are points 
 in the curve, and by tracing a line through 
 them the contour will be completed. 
 
 In fig. 17, a method is given in some 
 respects similar to the preceding. Having 
 joined a b, describe upon it the semicircle, 
 
 a db; from the centre, c, draw a series of lines perpendicularly from a b. meeting the circum¬ 
 ference, adb; draw also a series of horizontal lines from the same points in a b, as shown in the 
 figure, making these lines equal to the corresDonding lines in the semicircle, c e equal to c d, foi 
 
34 
 
 THE CABINET-MAKERS' SKETCH BOOK. 
 
 example ; the extremities of these lines will be as many points in the curve. If the recess of the 
 curve is required to be less than e c, as, for instance, c n, then set oIF c o equal to c n, and describe 
 an arc, u o h, from the centre, i, which will be found after one or two trials ; performing the same 
 operation as in the other case, we find the contour, anb. 
 
 In comparing these three modes of describing scotias, it is to be remarked that the second is 
 the most generally applicable, whether the recess and the projection be great or small compared 
 with the height. In the third mode, when the projection is small, the form of the curve approxi¬ 
 mates to that of the circular arc employed in describing it. Both of these modes of description 
 are applicable to mouldings of any recess and projection. The mode first described, to produce 
 graceful contours, should be confined to those of medium proportions, when, for example, the pro¬ 
 jection is two-fifths of the height, as in fig. 15. 
 
 The shaft of a column, like the mouldings which constitute the other portions of the column, 
 may be described with various contours. The shaft is never cylindrical, that is, of equal diameter 
 throughout,; it is always tapered to a certain extent towards the upper end. The degree of taper 
 is termed the diminution of the shaft; the diminution usually applied to columns ranoes between 
 one-fourth and one-sixth of the diameter at the bottom of the shaft. The following simple modes 
 of diminishing the shaft of a column may be applied, when the diameter at the top and bottom are 
 determined:— 
 
 Let the vertical lino, A b, Plate A, fig. 1, bo the altitude of the column, and b c the half dimi¬ 
 nution at the upper end of the shaft; divide A b into any number of equal parts, A a, a b ,. . . and 
 also b c into the same number of equal parts, B 1, 1 2, ... draw the horizontal lines, (if b g, . . . 
 and draw other lines from the points 1, 2, ... slanting towards A, to meet the horizontal lines 
 respectively at the points/ g, h , ... that is, the line drawn from 1 towards a, to meet the line 
 af at the point / the line from 2, towards a, to meet b g at g, and so on ; the points, b, c, d, e, 
 and / thus found, will be points in the contour of the shaft, and by joining them into one 
 bent lino, A fghile c, this line will bo the contour, or entasis, as it has been termed, of the 
 column. 
 
 But suppose that less swell or bulging is to he given to the shaft; then, in fig. 2, divide A b, 
 as before, into a number of equal parts, and b c into two equal parts at D; divide d c into as 
 many equal parts as a b ; then proceed, exactly as in fig. 1, to find the points, / g, h, i, k, in the 
 contour. This will obviously bring the outline nearer to a straight lino from a to b. In this 
 figure, e f is supposed to ho the axis or centre line of the column, e g and E A being the semi¬ 
 diameters at the bottom, and n,fc, the semi-diameters or radii at the top. To explain a third 
 mode of determining the entasis of the shaft : On a g as a chord, describe the circular arc, a o g, 
 proportionally less than a semicircle, as the swell is intended to be less; from the point n draw 
 the vertical line, » p, parallel, of course, to e f ; divide the arc, g p, into any number of equal 
 parts, G 1, 1 2, 2 3, ...; divide the altitude, e f, into the same number of equal parts ; through 
 the points of division draw the horizontal lines, ft. sm,h n, ... and draw the vertical parallel 
 linos, 11, 2 m, 3 n,... meeting the others respectively at the points l, m, n, o, p ; the curve line 
 drawn through these points will be the entasis of the column. 
 
 In many instances the shafts of columns are not finished with plain round surfaces; their 
 surfaces are frequently fluted, that is, indented by longitudinal flutes or grooves, throughout the 
 whole extent of the shaft. The flutes, when cut, are applied entirely round the shaft, and their 
 profile, which is shown by the section of the column, taken horizontally, is generally an arc of a 
 circle, equal to, or less, than the semi-circuinference. 
 
 There arc two varieties of fluting represented in profile in figs. 3 and 6, Plate A, and shown 
 also in elevation by figs. 4, 5, and 7, 10. In figs. 0 and 7, it will be observed that the flutes are 
 regularly separated by fillets; while in figs. 3 and 4, no such intervention exists, the flutes meet 
 each other edge to edge, and form a sharp anglo or arris at their junction; the intervention of 
 the fillets, as they strengthen the projecting angles, permits of the flutes being cut much deeper 
 than when they follow each other consecutively. The circumference of fluted columns are 
 
ORDERS OF ARCHITECTURE. 
 
 35 
 
 always measured, in the one case, over the exterior surfaces of the fillets, and, in the other over 
 the angles formed by the flutes. 
 
 To describe the flutes of a column without fillets: Let a b, fig. 3, be the diameter of the 
 shaft at the lower end ; bisect a b at c, and describe the semicircle aefb; draw a d and b c 
 perpendicular to a b, and d c parallel to a b, touching the “circle; draw also deg and cfg to 
 the centre; divide the semi-circumference into half as many equal parts as there are flutes in 
 the whole circumference; more particularly, let there be twenty flutes in the circumference 
 then ten of these are due to the semicircle, aefb, and they ought to be so disposed as to have 
 nine of them whole, and the tenth divided between the two extremities, a and b, in order that 
 a flute may stand directly in front, as seen in the figure, where the line, d c, touches the circle. 
 To this end, then, divide the arc, ef. into five equal parts, and continue the division towards 
 a and b, making two whole divisions and a half, as f d and d c, and c b. These points of division 
 determine the arrises of the flutes. To strike the form of the flute, describe arcs from the centres, 
 c and d, with the radius, c d, intersecting at e ; from e, with the same radius, describe the con¬ 
 cave surface, cd; this forms the flute—the same process is applied to find the others. Having 
 drawn the concentric semicircle, a b, for the diameter of the shaft at the upper end, if radial lines 
 be drawn from the arrises of the flutes in the circle, aefb, towards the centre, g, the points at 
 which they meet the circle, a b, will be the arrises of the fluting at the upper end of the shaft, 
 which is described similarly to that at the bottom. The figure, as now completed, becomes a half¬ 
 plan of the shaft of the column. Fig. 4 is a bottom elevation of the column, derived from the plan, 
 as indicated by the dot lines ; and fig. 5 is a top elevation 
 
 To describe flutes with fillets in the shaft of a column : Let a b, fig. G, Plate A, be the diameter 
 of the column ; bisect it at g, and describe a semicircle, as before, upon the diameter, a b ; draw 
 a d and b c perpendicular, and d c parallel to ab, touching the circle; join d g and c g. Let 
 there be twenty-four flutes in the circumference; there will then be eleven whole and two half¬ 
 flutes in the semi-circumference, and five wholes and two halves in the quarter circumference. 
 If, therefore, this space be divided into six equal parts, the points of division will be the centres 
 from which the flutes are described, and by running on the divisions to the points a and b, the 
 centres for the whole semi-circumference will be ascertained, and will divide it into twelve equal 
 arcs. Take any one of these arcs, f d, and divide it into five equal parts ; then, with two of these 
 parts as a radius, from each of the aforesaid centres, describe a semicircle; this will be the sec¬ 
 tion of the flute; the flutes of the interior circle, representing the upper diameter of the shaft, 
 are found by drawing radial lines, which appears sufficiently obvious from the figure. Figs. 7, 
 8, and 9, arc elevations of the bottom of the column, as found from the plan by means of the 
 dot lines ; fig. 9 represents the most usual mode of finishing the flutes at the bottom of the shaft; 
 fig. 10 is the corresponding elevation of the upper end. 
 
 In describing by relative dimensions the proportions of each particular order of architecture, 
 it is desirable, for the sake of perspicuity and facility of reference, tliat in all the orders one com¬ 
 mon standard of measurement should be adopted, to which the proportional dimensions of all the 
 parts of each order should be referred, being expressed in parts of that standard. For this pur¬ 
 pose the diameter of the shaft of the column at the base, in each order, is taken as the standard 
 of reference for all the parts or members of the particular order. The advantage of this is 
 twofold; for, first, the proportions of an order arc seen by a few glances; and, secondly, the 
 relative proportions of corresponding parts in different orders are likewise readily ascertained. 
 On this principle we shall proceed in defining the orders separately. The diameter at the base, 
 in each order, is divided into 60 equal parts, denominated seconds, and constituting the scale of 
 parts for the particular order; this affords a ready means of accurately noting the proportions, 
 which are expressed in seconds and fractions of seconds, when these occur. 
 
36 
 
 THE CABINET-MAKERS’ SKETCH BOOK. 
 
 OF THE GRECIAN DORIC ORDER. 
 
 This order, illustrated by Plate A, is tlic most ancient of the orders, and, while employed by 
 the Greeks, was without a base. The surface of the shaft is usually worked into twenty very 
 flat flutes, meeting each other at an edge—this will be explained by the half-plan given in the 
 plate. The edge is sometimes a little rounded; the upper member of the capital is a square 
 abacus or thin plinth, under which there is a large and elegant ovolo of great projection ; on the 
 base or lower part of the ovolo there are three fillets, or annulets, which project from the surface 
 of the evolo, and have, of course, equally recessed spaces betwixt them; the flutings of the 
 column terminate on the under sides of the lowest of these fillets, being finished by a cavctto or 
 a conge. The general outline formed by the junction of the conge with the ovolo, constitutes a 
 cyma-reversa, the effect of which is most graceful. 
 
 The architrave consists of one vertical face, with a continuous band or fillet at its upper 
 edge; to the under side of this band are suspended a series of smaller fillets, with drops or 
 guttm; these fillets are of the same length as the breadth of the triglyphs in the frieze, and arc 
 placed exactly below them. 
 
 The frieze consists of rectangular projections and recesses, placed alternately. The projec¬ 
 tions or tablets are diversified on the face by two vertical channels, and two half ones cut on the 
 right and left edges, constituting three whole channels, and hence called triglyphs. The square 
 spaces alternating with the triglyplis are named metopes, and arc frequently decorated with 
 sculptures. 
 
 The cornice is distinguished by a conspicuous coronet, a term applied to a vertical or inclined 
 plane surface which considerably overhangs the members underneath. To the corona, immediately 
 over the triglyphs, blocks named mutules are suspended, of which the soffit or under side is 
 inclined downwards from the roof; the mutules are also furnished with guttm or drops depend¬ 
 ing from their soffits. 
 
 The proportions of the different members of the Doric order, as practised by the Greeks, 
 range within considerably wide limits. The following arc the average proportions for the 
 members of the order. Taking the diameter at the bottom of the shaft as the standard of 
 measurement, the column is six diameters in height. The diameter at the upper end of the 
 shaft is tliree-fourths of a diameter; that is, the shaft diminishes one-fourth of the diameter. 
 The height of the capital is half a diameter; that of the ovolo, including the annulets, and that 
 of the abacus, are each one-quarter of the upper diameter, the annulets together being one-fifth 
 of one of the parts. The horizontal dimension of the abacus is six times its height. 
 
 The height of the entablature is one-third of that of the column, or two diameters. If it be 
 
 divided into eight equal parts, these are distributed 
 r~— --- — -between the architrave, the frieze, and the cor¬ 
 
 nice, ifi the proportion of 3, 3, 2: thus, the height 
 of the architrave is equal to that of the frieze, and 
 that of the cornice is two-thirds of either. The 
 inner edge of the triglyph at the angle of the 
 building is in a vertical line with the axis of the 
 column ; the breadth of the triglypli is three-fifths 
 of its height, which is also that of the frieze, and 
 the breadth being divided into nine equal parts, 
 two are occupied by each glyph or channel, one by 
 each semiglyph, and one by each of the three inter- 
 glyphs, or flat surfaces between the glyphs. 
 
 All this is shown in the annexed figure, which is a horizontal section of a portion of the 
 entablature, viewed from below, and taken through the frieze. It exhibits the section of the 
 
ORDERS OF ARCHITECTURE. 
 
 37 
 
 triglyphs, as well as the arrangement of the inutules in the cornice, with their drops. The 
 metopes are square; the height of the capital of the triglyph is one-seventli of its whole height, 
 and that of the metope one-ninth. The height of the cornice being divided into five equal parts, 
 the lowest is given to the fillet, the mutule, and the drops; the next two to the corona, and the 
 remaining two parts arc subdivided and disposed of as shown in the detail figure, Plate A. T he 
 projection of the cornice over the capital of the triglyph is equal to its height; and being divided 
 into four equal parts, three arc given to the projection of the corona, and they are further sub¬ 
 divided as shown in the plate. 
 
 The number of annulets in the capital vary from three to five; and the number of horizontal 
 grooves separating the shaft from the capital, vary from one to three. 
 
 In the scales which we have attached to the outline drawing of the order, three sets of dimen¬ 
 sions are given, the nature of which are indicated by the initial letters at the bottom of the scales. 
 The first scale contains the “particular heights” of all the members of the order, expressed in 
 seconds, each figure standing opposite the member to which it refers. The second scale contains 
 the “ general heights ” of the members, each division of the order being specified. The third 
 scale contains the “projections” of all the particular members, beyond the centre line of the 
 column, expressed in seconds. 
 
 OF THE GRECIAN IONIC ORDER. 
 
 The Ionic order, like the Doric, may be primarily divided into column and entablature; in 
 its secondary divisions, however, a new element is introduced, as, besides the shaft, capital, archi¬ 
 trave, frieze, and cornice, it is provided with a base to the column. 
 
 The origin of the Ionic order is problematical; its capital, which is its principal characteristic, 
 has been compared to the curls in the head-dress of females, to the spiral horns of rams, the bark 
 of some trees when dried in the sun, the form of various sea-shells, and so on. The order is a 
 medium between the grave solidity of the Doric, and the elegance and delicacy of the Corinthian. 
 
 In the architrave and frieze, all appearances of triglyphs and guttse are omitted; in the cor¬ 
 nice, instead of the bold mutules of the Doric, the ends of several pieces of wood are substituted, 
 which are by way of support to the covering tiles, and are represented by dentils or teeth. The 
 other portions of the cornice are analogous to those in the Doric, and consist principally of a 
 cyma, ovolo, and cornice. The great recess of the mouldings under the cornice gives it a 
 striking prominence; this relieves its apparent heaviness, though both the dentil band and the 
 cymatium of the frieze are introduced under it. 
 
 The base of the column consists of two tori, separated by a scotia, with fillets, and a square 
 plinth, on which the column rests; though in some cases the plinth is dispensed with, and the 
 column stands immediately upon the general platform which supports the whole. 
 
 In the volute of the capital, the lower edge of the channel which runs between the upper and 
 under spirals, is formed into a curve bending downwards in the middle, and revolving about the 
 spirals on both sides. The volute rests upon the ovolo, astragal, and fillet, which terminate the 
 shaft. The ovolo is always cut into eggs, surrounded by borders, with tongues between them. 
 The shaft is, in general, cut into twenty-four flutes, with fillets between them, and the flutes are 
 sometimes made with an elliptical section, which makes them flatter than when.they are circular. 
 The taper of the shaft is also less than that of the Doric. 
 
 Besides the special dimensions, given in Plate B, of the Ionic order, the following may be 
 noted as the general proportions of the order. The column is eight and a half diameters in 
 height; the diameter of the upper end of the shaft is five-sixths of a diameter; the taper of the 
 shaft is one-sixth. The height of the base, including the plinth, is half a diameter; the heights 
 of the tori and the scotia are nearly equal; the upper fillet of the scotia projects as much as the 
 
38 
 
 THE CABINET-MAKERS’ SKETCH BOOK. 
 
 upper torus. The projection of the lower torus beyond the lower radius of the shaft, is one-fifth 
 of a diameter. The height of the capital is half a diameter; the height of the volute is seven- 
 twelfths of a diameter; dividing the height of the volute into three equal parts, the top of the 
 lower one reaches to the bottom of the ovolo, and the second division to the top of the festoon, 
 on the axis of the column. 1 he curvature of the outer spiral springs immediately from the ovolo 
 with which the volute is crowned. 
 
 Dividing the whole height of the order into twenty-one parts, four of these go to the entabla- 
 tm e, which is, therefore, two diameters in height; the height is equally distributed between the 
 aichitrave, the frieze, and the cornice. Dividing the height of the architrave into four parts, 
 one part is due to the mouldings of the upper portion or capita!; subdividing the capital into 
 nine equal parts, give one to the upper fillet, three to the cavetto, four to the ovolo, and one to 
 the bead. Divide the height of the frieze into six equal parts, and give the upper part to the 
 talon, which forms the capital. Divide the cornice into three equal parts; subdivide the upper 
 and lower thirds, each into six parts; in the upper third, give one part to the upper fillet, four 
 to the cyma-recta, and one to the lower fillet, and turn one down into the middle third, for the 
 ovolo under: dispose of the parts in the lower third as appears by the scale. 
 
 The projection of the cornice over the cymatium of the frieze is equal to its height; the 
 projections of the subordinate members will be obvious at once from the scales attached. 
 
 The volutes of the Ionic capitals are composed of two or more spirals of the same kind, which, 
 after making a number of revolutions, terminate at the centre upon a central point resembling a 
 button, denominated the eye of the volute. The spirals, which project from the surface to give 
 them relief, are termed the Items of the volute; the interspaces being called the channels. 
 
 These definitions will be understood on referring to the detail drawings of the Ionic order, 
 in Plate B. There the front elevation of the capital is represented, showing the central eye, and 
 the spirals terminating in it. The back elevation of the capital is the same as the front. The 
 flanks, shown as side elevations in fig. 1, Plate B, have somewhat the appearance of a balustre. 
 In the plan, %. 2, this portion of the capital, supposed to be viewed from the under side, appears 
 square in its general outline. Fig. 3 is a vertical section of the capital, exhibiting the profile in 
 flank; fig. i is a vertical section, drawn to the same centre line, and in a plane at right angles to 
 that of the preceding section, exhibiting the contour of the front and back elevations of the capi¬ 
 tal. From these figures it will be observed, that the volutes fit like a cap upon the circular 
 tablet formed by the ovolo. There are no precise rules for the form of the capital in flank, 
 except, perhaps, that the parallel beads which decorate the scroll should run directly into the 
 interspaces of the carvings upon the ovolo; otherwise, the configuration of the parts is left to the 
 taste of the designer. The shaft of the column has been represented fluted in these details, 
 that the correspondence of the flutes with the carvings upon the ovolo may be shown. 
 
 1 o describe the Ionic volute: the number of revolutions or quarters of which the spirals are 
 to consist being given, the vertical height, also, of the spiral, and the diameter of the eyeLet 
 A b, Plate B, fig. 5, bo the height of the volute, and let the spiral make three revolutions, con¬ 
 sisting, therefore, of twelve quarters; bisect a b at the point c, and from a b cut off a d, equal 
 to the given radius of the eye ; divide D c into as many given parts as there are quarter revolu¬ 
 tions in the spiral to be drawn (which in this case are twelve in number), at the points 1, 2, 3, 
 ... 11, 1-. To prevent confusion, we have indicated this division upon a parallel line, n' c'; 
 draw c e at any angle with c d, and make it equal to two of these parts; join d e, and from the 
 points 1, 2, 3 .... draw straight lines, 1 r, 2 o, 3 H, . .. parallel toes; taking c d equal to one 
 part, draw df perpendicular to A b, and equal to 12 e ; draw fg perpendicular to df and equal 
 to 11 q ; draw again g h perpendicular to/p, and equal to 10 p. Proceed in this manner until 
 all the sides of this winding fretwork are drawn; then, the points d,f g, ... p, q, r, so found, 
 are the centres from which the quadrants which compose the spiral must be successively described 
 For this purpose, produce df to 1, fg to 2, g h to 3, and so on; the quadrants, as they are de¬ 
 scribed, will be limited by these lines; from the centre, d, with the radius, d B , describe the 
 
ORDERS OF AECHITECTURE. 
 
 39 
 
 quadrant, b 1; from the centre, f with the radius,/, describe the quadrant, 1, 2; from g, with 
 the radius, g 2, describe in like manner the quadrant, 2, 3 ; proceed in this way till the last arc, 11, 
 12, is described from the centre, q, with the radius, q 11; then, finally, describe the circle at the 
 centre, from the point, r, and with the radius, r 12. If the operation he accurately performed, 
 this radius, r 12, will be equal to a d, as required, and the spiral line will be completed. 
 
 But as the process, as it is now described, is very liable to inaccuracy, the method of finding 
 the centres shown on a larger scale at fig. A, is at once more expeditious and more certain. 
 Having drawn df perpendicular to the vertical line, bisect it at e ; draw e r perpendicular to df 
 equal to d e or ef and join d r and / r ; divide e r into three equal parts, es,st,tr, and draw 
 isk and n t o parallel to df] draw /g perpendicular to df, and equal to 11 Q; draw g h and i h 
 respectively parallel and perpendicular to df meeting at the point h ; draw the diagonals g p 
 and h q parallel to dr and / r, and draw the perpendiculars k l, o p, r q, n m. In this way all 
 the centres are determined, namely, d,fg,li,. . . . o,p, q, r. 
 
 To describe the second spiral line, which, with the first one, comprehends the thickness of the 
 hem, a similar process is applicable. Set off b k for the thickness of the hem at that part, and, 
 supposing the hem to diminish in thickness by equal amounts for each half revolution, divide b e 
 into six equal parts; as the spiral describes six half revolutions, it will diminish in thickness one- 
 sixth of b e for each half revolution ; set off, therefore, a s equal to 5-Gths of b n, then e s is the 
 height of the second spiral. Bisect r s at t, and set off s v equal to the radius of the eye ; then, 
 dividing t v into 12 equal parts, the method already described for finding the centres may bo 
 applied. 
 
 The method already described, though it is well adapted to the description of the single 
 spiral, is not applicable where there are many spirals. In this case, the principle of the loga¬ 
 rithmic spiral may be employed. The nature of this spiral is such, that being divided into equal 
 angular segments, as quadrants or half quadrants, its distances from the centre, at the ends of 
 the segments successively, decrease in a geometrical ratio. 
 
 To describe the Ionic volute, on the principle of the logarithmic spiral: the centre, the ver¬ 
 tical height, and the distance between the first and second revolutions of the outer spiral being 
 given. 
 
 Definition. — The vertical line o a, fig. 6, drawn from the centre o of the spiral, and expressing 
 also the height of it above the centre, is termed the cathetus. 
 
 If then o A he the cathetus, o the centre, and a i the distance between the first and second 
 revolutions, produce a o to E, and draw s o c .it right angles to A E; bisect the angles at the 
 centre by the straight lines b o f and non; find a mean geometrical proportional between o A 
 and o i, and make o e equal to it; find also a mean proportional between o a and o e, and make 
 o c equal to this mean. Having thus found the consecutive points A, b, and c, the distances of 
 which from the centre are in geometrical progression, the others in succession will be found by 
 the aid of proportional compasses. Having set the compasses, so that the ratio of the lengths of 
 the legs on the opposite sides of the centre pin may be that of o a to o b, it is obvious that if the 
 distance a o, be taken between the longer ends, the shorter ends will measure the distance b o; 
 and, in like manner, that if the longer ends be set to b o, the shorter ends will measure c o. 
 Farther, by taking o o in the one end, we have d o in the other; and proceeding in this way, we 
 may find successively the distances E o, F o, g o, &c., which furnish as many points in the spiral; 
 and, by tracing a curve lino through the points thus found, the spiral will be. completed. The 
 divisions marked off upon the line a g indicate the commencements of the other spirals, of which 
 the volute consists, which, it will he observed, are disposed in three sets. 
 
 Another method of setting off the spiral by means of proportional compasses, without prick¬ 
 ing the paper, is to construct a scale of parts a b o, fig. 7. This method also expedites the pro¬ 
 cess considerably. Having found o A and o b, as before, and set the compasses in the manner 
 already described, make o a, fig. 7, equal to o A, fig. G, by the longer ends of the compasses, and 
 mark off o h , the distance between the shorter ends. Take again o b, between the longer ends, 
 
40 
 
 THE CABINET-MAKERS’ SKETCH BOOK. 
 
 and mark o c, between the short ends; similarly, from o c find o d, and so on, till the distance 
 o i, is found. And here the accuracy of the process may be tested, as o i, fig. 7, should be equal 
 to o i, fig. 6. Join the points of division in a i to the point b ; draw the horizontal line i e, and 
 from e draw the vertical e f, cutting i b at the point g ; draw again the horizontal and vertical 
 lines g h and h k i. Then the three scales a o, e f and h i, will afford eight points in each of 
 the three revolutions of the first spiral acegi: o 6 is equal to o b, o c equal to o c, o d equal 
 to o d, and so on; and lastly, o i or f e is equal to o i. Following the same process, the eight 
 divisions on the scale f e give eight points in the second revolution i k l, and the scale i h gives 
 eight points to the third revolution l m n. 
 
 1 he points thus determined for the spiral may be transferred to the edge of a slip of paper, 
 and thence marked by a pencil point upon the drawing, fig. 6. 
 
 1 he same scale, fig. 7, may be employed for the other spiral lines in the volute, the com¬ 
 mencements of which are marked on the line a i, fig. G, for, by dividing the parallel lino a i, 
 which is equal to a i, in the same manner as a i, and drawing horizontal lines from these several 
 points of division, as indicated in the figure by dot lines, the perpendiculars drawn from the 
 points at which these lines meet a b, furnish scales for the first revolutions respectively. For 
 example, if we draw a horizontal line l m from the point l, meeting a b at the point m, the per¬ 
 pendicular mon becomes a scale of parts for setting off the first revolution of the spiral which 
 starts at the same point l, fig. G. The scales p it q and s u t, formed in the same manner as 
 before, serve to define the second and third revolutions of the same spiral. In this way, then, 
 it is clear we can readily construct a set of scales for each individual spiral. Another mode of 
 finding a series of points in a spiral is represented by the scale, fig. 8. 
 
 Referring for convenience to fig. 6, divide the whole height a e into 16 equal parts, making 
 the portion a o above the centre equal to 9 parts, and leaving of course 7 for the portion o e. 
 In fig. 8, make o e equal to o e, fig. 6, and draw a perpendicular o a equal to o a, fig. G ; join 
 a e, and on e as a centre describe the arc a p ; divide that arc into 28 equal parts, and join'the 
 points of division to the centre e. The straight line a o intersected by these radii at the points, 
 b, c, d, &c., forms the scale for the first spiral: thus o a is the distance o a, fig. 6; o b gives the 
 distance o b, o c gives the distance o c ; o d gives the distance o d, and so on; till lastly o n gives 
 the radius o n of the eye, which is described by a circle on the centre o. Having thus marked 
 off a seiies of points in the curve, it may be completed either by describing arcs of circles con¬ 
 necting the points which have been set off, or by tracing by hand a curve line through them. 
 
 1 he other spiral lines of the volute may be described in like manner by making a new scale for 
 each. 
 
 In this example, the radius of the eye has been made equal to the first four divisions of the 
 line a, the remaining 24 divisions being distributed along the spiral. We may, of course, secure 
 any number of divisions for the radius of the eye; if we are to secure 8 divisions, for example, 
 then as 24 are due to the spiral, the arc must be divided into 24 + 8 or 32 parts. 
 
 OF THE GRECIAN CORINTHIAN ORDER. 
 
 The Corinthian is the third and last of the Grecian orders. Upon this order the ancients 
 lavished the utmost efforts of their creative genius; it is the most magnificent and elegant of 
 the orders. 
 
 The great distinguishing feature of this order is its capital. The capital consists of a solid 
 body or nucleus in the shape of a bell, and hence commonly called the bell of the capital; the 
 bell is surrounded with two tiers of foliage, consisting of acanthus leaves, of which there are 8 in 
 each tier; the upper end of the shaft finishes with an astragal, which appears to bind together 
 the leaves at the roots; surmounting these are 8 caulicoli, or twisted and fluted stalks, springing 
 
ORDERS OF ARCHITECTURE. 
 
 41 
 
 from between the leaves of the upper tier, and spreading each into two open volutes, which sup¬ 
 port the abacus: the abacus consists of a 
 
 square tablet, concave on the four sides Fi s- 
 
 or edges, and having the acute angles thus 
 formed cut away ; the edge of the abacus 
 is wrought into an ovolo and a cavetto, 
 separated by a fillet—one of the upper 
 tier of leaves fronts each side of the 
 abacus; the space beneath the abacus, 
 unoccupied by the leaves, is taken up with 
 slender caulicoli or stalks, which spring 
 from between every two leaves, and pro¬ 
 ceed to the corners, and to the centres of 
 the sides of the abacus, where they are 
 formed into delicate volutes. The centre 
 of each side of the abacus is adorned with 
 a rosette, or small flower. 
 
 The base of the column, as represented 
 in Plate E, is the same as the Iouic base, 
 consisting of two tori, separated by a 
 scotia, the whole resting on a square 
 plinth. The shaft of the column should 
 be fluted when the entablature is enriched. 
 
 In the cornice of the entablature the 
 dentil band is preserved, as in the Ionic 
 order, and is overhung by a fascia, from 
 which enriched medallions project. The 
 entablature bears a close resemblance to 
 that of the Ionic order. 
 
 The following are the general propor¬ 
 tions of the Corinthian order:—In its 
 general arrangement, it is similar to the 
 Ionic: the column is ten diameters in 
 height; the diameter at the upper end is 
 five-sixths of that at the under end, the 
 taper being therefore one-sixth. The 
 height of the base is half a diameter; the 
 projection of its upper torus is equal to 
 that of the upper fillet of the scotia. The 
 height of the capital is 1 ^ diameters, of 
 which one diameter is occupied by the 
 leaves and volutes, the remaining sixth 
 being given to the depth of the abacus; 
 the height occupied by the leaves and 
 volutes being divided into three equal parts, the lower part is due to the lower tier of leaves, the 
 second part to the second tier, and the third part to the caulicoli and volutes. The height of 
 the principal volutes is three-fourths of one of these parts. The droop or descent of the tips of 
 the leaves is one-third of the height assigned to them; their form is seen more explicitly in the 
 engravings, which give the general form of the foliage before it is cut, in which fig. 1 is the ele¬ 
 vation, and fig. 2 the semi-plan of the capital. It will be seen that the circumference of the 
 bell is divided between eight leaves in each tier. The abacus, which is seen in both these figures, 
 
42 
 
 THE CABINET-MAKERS’ SKETCH BOOK. 
 
 Fig. 4. 
 
 is supposed to be cut from a square plinth, shown in dot lines in the plan, the diagonals of which 
 
 measure two diameters 
 of the column; the 
 curvature of each side 
 is an arc of a circle, of 
 which the centre is 
 formed by constructing 
 an equilateral triangle 
 upon the side of the 
 square, the vertex of 
 the triangle being the 
 centre. Figs. 3 and 4 
 
 show the general form and manner of raffling the leaves. 
 
 Dividing the whole height of the order into five parts, one of these is due to the entablature, 
 which is therefore one-fourth of the height of the column, or 
 two and a half diameters high. The architrave is three- 
 fourths of a diameter high, the frieze is two-thirds, and the 
 cornice one and a twelfth. Dividing the height of the archi¬ 
 trave into five parts, one of these is due to the fillet, the quirked 
 cyma-reversa, and the bead; the other four parts are divided 
 equally among the three fascia which compose the remainder of 
 the architrave. The frieze is commonly ornamented, though 
 frequently left quite flat and plain. The height of the cornice 
 being divided into three parts, they are disposed among the 
 members in the manner exhibited by Plate C. The projection 
 of the cornice over the frieze is equal to its height; the pro¬ 
 jections of the members of which it is composed are given on 
 the plate. The modillions which overhang the dentil band are represented in fig. 5. 
 
 OF THE ROMAN DORIC ORDEP. 
 
 In the progress of their conquests, the Romans extended their dominions over the colonies of 
 Greece, over Greece itself, and over some parts of Asia. It was not till they had acquired the 
 mastery of these, their more polished neighbours, that they possessed any opportunity of becom¬ 
 ing acquainted with the architecture of Greece, as well as with its sculptures and paintings. 
 The columnar architecture of the Romans, imitating that of the Grecians, is evidently of the 
 same family, though greatly inferior in simplicity and harmony. The Doric order of the 
 Romans, which we are now to describe, affords an illustration of this remark; it strikingly con¬ 
 trasts with the simple and energetic Doric of the Grecians, and is by no means an improvement 
 on this beautiful order of architecture. 
 
 The column of the.Roman Doric had originally no base, but the addition of a base is certainly 
 an improvement, and renders the parts of the order consistent with one another. The capital 
 has a greater number of members than that of the Grecian, and are of a light and round char¬ 
 acter, while those ot the other are broad and $at. The shaft is more slender than the other, 
 and is very seldom fluted; when it is fluted, the flutes are separated by fillets, as in fig. 6, Plate 
 A, and are twenty in number ; the shaft is finished at the upper end with an astragal and a fillet, 
 which support the capital, instead of one or more channels, as in the Grecian. In the capital, 
 three fillets, with a quarter-round and a semi-torus, are intended to represent the ovolo and 
 
ORDERS OF ARCHITECTURE. 
 
 43 
 
 annulets of the Greek capital; and the height of the abacus, instead of being plain, is divided 
 into a projecting fillet, a cyma, and a fascia. 
 
 The architrave is, like the other, furnished with a band along its upper edge, from which the 
 fillets and guttse depend. The guttse, also, are six in number, but are coniform instead of cylin¬ 
 drical, and project from the surface of the architrave fully more than half their diameter. The 
 face of the architrave is vertical, and stands in a line with the superior diameter of the column, 
 though it is sometimes set a trifle within the point. In the frieze, the triglyphs project from, 
 instead of being coincident with, the architrave; and those next the angle of the building are, as 
 represented in Plate C, placed directly over the centre of the column, instead of being on the 
 angle; the glyphs, of which there are two wholes and two halves, are finished square at the upper 
 edge, and the tops slope downwards towards the back at the samo angle with the sides. 
 
 In the cornice, the members are all lighter than those of the Grecian (there is, in fact, a 
 greater subdivision), with the exception of the mutules, which are boldly developed, and have 
 no guttse. 
 
 Besides the special dimensions which we have given in Plate C, we may state the following 
 general proportions of the order:—Dividing the whole height of the order into five equal parts, 
 one of these is given to the entablature, the height of which is therefore one-fourth of that of the 
 column. The column tapers one-sixth throughout the shaft, and is eight diameters high, of 
 which one diameter is distributed equally between the capital and the base. The plinth in the 
 base is one-third of the height. The height of the capital is nearly equally divided between the 
 abacus with its mouldings, the ovolo with its fillets, and the neck. 
 
 The entablature is two diameters in height, and being divided into eight equal parts, these are 
 distributed among the cornice, the frieze, and the architrave, in the proportions of 3, 3, and 2. 
 This distribution contrasts strongly with that of the entablature of the Doric. The height of 
 the architrave, which is half a diameter, being divided into three, one of the parts is due to the 
 band, fillet, and guttse, of which the height of the band is equal to that of the fillet and guttae 
 together. The frieze is three-fourths of a diameter in height: it is divided horizontally into 
 triglyphs and metopes, of which the former are each half a diameter in breadth, and on the whole 
 depth of the frieze—dividing the breadth of the triglyph into twelve parts, the extreme twelfths 
 arc due to the semiglyphs, and the remaining ten parts are distributed equally between the two 
 whole glyphs and the three vertical plane surfaces, or shanks, which separate them, two parts being 
 given to each member. The plat-band or fascia, which crowns the triglyph, is one-eighteenth 
 of its height. The cornice is three-fourths of a diameter high. The breadth of the dentils is the 
 same as that of the triglyphs, and their projection is equal to their breadth. 
 
 THE ROMAN IONIC ORDER. 
 
 The Roman Ionic is the modification of the original Grecian, practised by the Romans after 
 their conquest over the Greeks. The general proportions of the Roman and Grecian Ionics are 
 nearly alike ; the minutise and detail, however, are considerably different. This will be perceived 
 at once on referring to the plates of these orders—Plates B and D. 
 
 In the column of the Roman Ionic, the attic base is always employed. The capital is consi¬ 
 derably distinguished from that of the Grecian by the straightness of the under edge of the 
 channel of the volutes over the quarter round, and the absence of the hem which bordered the 
 under side of this channel in the Grecian. The shaft may be either plain or fluted, with twenty 
 or twenty-four flutes, in plan a trifle more than semicircular. The fillets between the flutes 
 should have between one-third and one-fourth of their width. The egg and dart ornament of 
 the quarter round in the capital should correspond with the flutes of the column, there being an 
 
44 
 
 THE CABINET-MAKERS’ SKETCH BOOK. 
 
 egg exactly over each flute, and a dart, of course, over each fillet. The volutes may he described 
 according to the methods already given for those of the Grecian order. 
 
 Dividing the whole height of the order into five parts, one of these pertains to the entabla¬ 
 ture, the others to the column: the height of the entablature is, therefore, one-fourth of that of 
 the column. The shaft of the column tapers one-sixth; the whole height of the column is nine 
 diameters, half a diameter is given to the base, and seven-twentieths, or twenty-one minutes, to 
 the capital. 
 
 The entablature is two and a quarter diameters high. Dividing its height into five equal 
 parts of twenty-seven minutes, two of these parts go to the depth of the cornice, and the 
 remaining three are divided equally between the architrave and the frieze. The faces of the 
 frieze, and the lowest member of the architrave, are directly on the outline of the upper end of 
 the shaft; this gives them a less heavy aspect than the corresponding members of the Grecian, 
 which project considerably. The projection of the cornice from the face of the frieze is equal 
 to its height. 
 
 The Ionic entablature is occasionally reduced to two-ninths of the height of the column; this 
 may readily be accomplished without altering its internal proportions, by making its module or 
 scale of parts less, by one-ninth, than the diameter of the column, and setting off its parts from 
 this scale in the proportions exhibited in the plate. In the decoration of the interior of apart¬ 
 ments, when much delicacy is required, the height of the entablature may, according to Nichol¬ 
 son, be reduced to even onc-fiftli of the column, by observing the same method, and making the 
 module only four-fifths of the diameter. 
 
 OF THE ROMAN CORINTHIAN ORDER. 
 
 This order, Plate D, is the only one in which the Romans have truthfully represented the 
 original from which it is derived. In detail, this order is but slightly different from its prototype. 
 
 Dividing the whole height of the order into five parts, one part is due to the entablature, 
 which is therefore one-fourth of the column, as in the Grecian. The height of the column is ten 
 diameters, and the entablature, consequently, two and a half diameters. The cornice is one 
 diameter, or two-fifths of the entablature, high; the remaining three-fifths are divided equally 
 between the frieze and the architrave, three-fourths of a diameter to each. These general pro¬ 
 portions, it will be observed, arc the same as those of the Roman Ionic order. The entablature 
 of the latter is frequently substituted in the Corinthian order. 
 
 THE COMPOSITE ORDER. 
 
 The Composite order is derived from the three original orders, or, more strictly perhaps, 
 from the Roman Ionic and Corinthian, being a compound of the two orders. There are a great 
 variety of designs recognised as the Composite order; we have given the design in Plate D from 
 Chambers, who,.in composing it, endeavoured to avoid the faults and unite the perfections of 
 those with which he was acquainted. The entablature has one-fourth of the height of the column ; 
 the column is ten diameters high, consequently the entablature is two and a half diameters, of 
 which the cornice has one diameter, and the frieze and the architrave each three-fourths of a 
 diameter. The base is precisely the same as in the other orders: the shaft is fluted similarly to 
 the Ionic; the capital retains the two tiers of acanthus leaves in the Corinthian, and also the 
 abacus in the same order ; the Ionic scroll, however, is introduced between these members. The 
 cornice differs from the Corinthian only in having the medallion square, and composed of two fascias. 
 
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