Part IV

look to that point with delight, as we can, no doubt, improve, but should always maintain the character and form of our first model, however Duke's House, Bradford. ancient; and, if we wish to renovate or call back that same style, it must be according to the character or manner in which it was executed. Although the arts have been so ORNAMENTAL DEAWING. 205 much improved of late, it is but in altering and forming the geometrical proportion more graceful, on which we ought to trespass. I will now leave you to your perseverance, 57. Duke's House, Bradford, First Floor. in combining and accomplishing the true feature of Elizabethan, as far as the ornamental department extends ; and, should you require to proceed further towards the architectural 206 GUIDE TO portion or plans, I cannot do better than refer you to Richardson's and HakewelVs "Eliza- bethan Architecture/' both as regards external and internal fitting ; fully assured, that there you will find all you require to complete your ideas; but the portion I have treated upon is merely to found a basis, or taste, whereby the ornamental draftsman, or student, may use his or her discretion as to the simplicity, or how- ever elaborate the plan or idea may be; at the same time impress on you, it is a style peculiar to itself, and when used with judgment, and in its proper place, it is very well ; but I would not have you waste your ideas and time too much upon one style, but learn of what it is composed ; and after that, treat with it as your judgment guides you, when it is required, as it is a bad plan to make too free use of only one description of ornament, which will throw you off your principles and ideas of other kinds that you may have studied. Thus, having made yourself acquainted with all my foregoing re- marks and principles, which, if properly paid ORNAMENTAL DRAWING. 207 attention to, must inevitably repay you for the perseverance, labour, and study it may have cost you. And I again caution you, let not your mind be led away to attempt building a mansion before you can plan a cottage, but go on gradually, from step to step, and study well all portions of the art that are good, but copy little, with the exception of that which you may have retained in your memory by looking at others. After that refer again, and study to make yourself acquainted with the ideas and styles of foreign draftsmen, from whom we have derived the chief knowledge of a variety of styles in ornament, and have in many in- stances improved upon, but more often spoiled them; and why? merely for the want of that scope which foreign schools throw open to all whose minds are fixed for perfection in any particular portion of the arts ; and, before we can arrive to that, we must fully make up our minds to defy competition, by having a true school of design. It is only the want of will, and not of mind ; for I am certain, were there 208 GUIDE TO sufficient scope thrown open to the British student, with unbiassed limits of instruction given, and tutors properly selected, for a strict adherence to the same, that our country would, in a very short time, laugh at foreign artists as designers, and should only have to thank them for their original principles. Then we should have the pleasure of hearing and saying, that those whom we have for years been obliged to copy and obtain designs from, will be glad to take advantage of our superiority over them, not only in design, but novelty of invention. To remedy all this, schools of design should be formed in different manufacturing towns, and in various parts of the metropolis, so that the student may go gradually through a routine of study, and put in possession of the best exam- ples that can be placed before him ; and until this feeling operates on the public mind, (which my I hope it will shortly,) take advice, go on that principle by yourselves, and in time it will fully shew what can be done by proper practice and training. ORNAMENTAL DRAWING. 209 I now intend completing this portion of my advice, by a trifling introduction to the Gothic rules and variation of arches, and of their introduction, which will be found essentially ne- cessary in the course of design, with geometry. 15 210 GUIDE TO ON GOTHIC DETAILS, AS REGARDS CURVILINEAR PORTIONS AND PERIODS. AMONGST the various modes of architecture, there are none more suitable and open to va- riety in the study of geometry and propor- My tion, than the Gothic. intention, in this instance, is merely to give you the universal form of the various arches, and principle for striking the same, and leave you to fill them up yourself with tracery, as you please, (in those that require it;) feeling confident that it is of the utmost importance in designing or copying from any principal edifice, to know, when you perceive a Gothic window, that ofttimes the greatest difficulty arises to give the true form, solely for the want of knowing how to go geo- metrically to work ; and in another instance, it facilitates copying, in a very great measure, as regards a raving of time ; because, being tho- /'///firrr/t' Crcc&ete OF THE TTNIVERSITT CALIFORNIA- OENAMENTAL DEAWING. 211 roughly acquainted with its form and character, you have only to note it down, and at your leisure you can complete it, without further trouble. There are at present more valuable works on that topic than of any other description of architecture, so that it would be folly for me to enter upon it further, than merely giving you that which is really useful to the universal draftsman, independent of its value, as regards knowledge ; for the many scattered remains of castles and cathedrals over the various parts of England, connect it with a variety of pleasing associations, that must render it a truly interesting study. I have found it so to a cer- tain extent, without attempting to give my time to those portions which are required to make an architect; and others, I hope, will do the same; although it may not be re- quired in your profession, it will, at least, give you the superior command of knowledge over many, and render you a pleasant companion, in giving an explanation of any particular cathedral, or other Gothic edifice, and in what 15 * 212 GUIDE TO period they were built. The origin of Gothic was, no doubt, from the cognate race of the Saxons, Franks, Normans, and Germans, and we can easily mark its progress of improvement from the Norman conquerors ; and in this case, whether correct or not, the word Gothic is likely to survive, and bear that title, beyond any other appellation, according to various styles that might have been given to it. And as, in an earlier portion of this work, I have informed you, that it is only by reading and studying different masters, authors, and others, that I am enabled to draw your attention to the most useful parts required; and where I have been able to facilitate any difficult points,. I have done so, and feel a pleasure' in throwing open those rules, for the benefit of all who choose to follow them. The classification of Mr. Rickman on arches, is undoubtedly the most skilful that has been suggested, and is now generally followed. He divides them into four kinds. 1st. The semi- circular, or Norman, extend- UNIVERSITY ORNAMENTAL DRAWING. 213 ing in its pure state from the time of the Conquest to the reign of Stephen, A.D. 1136, and, with the mixed or transition style, which succeeded to about the year 1190. 2nd. The early-pointed, from the reign of Eichard the First, 1189, down to the end of the reign of Edward the First, 1307. 3rd. The decorated, which prevailed during the greater part of the fourteenth century. 4th. The perpendicular, sometimes called the Florid Gothic,* which commenced about the reign of Richard the Second, and prevailed during the whole of the fifteenth century and the early part of the sixteenth, down to the period of the Reformation. The arch being the most prominent and distinguished feature in this style of archi- tecture, I shall close these remarks by a short description of the different forms of arches introduced, with the periods during which they principally prevailed. These, and many other * Henry the Seventh's Chapel, Westminster, is the finest specimen of Florid Gothic and tracery in this country. 214 GUIDE TO illustrations which may be necessary, will be treated on the most simple principles, to enable any person who can handle a lead pencil and a pair of compasses, to make himself master of their contour and method of delineation. The Norman, or Saxon arch, is the first I will commence to describe, as it was the earliest specimen we have of the circular arch. The period of its rage was between the reigns of William the First and Henry the Second. The characteristics of the style are massiveness, twisted and capped columns, sculptured figures, and corbel heads of the most grotesque forms, and sometimes ornaments of very rich design; moulding chiefly of a zig-zag form, groining and intermingling of circular headings and columns, forming a unity of style and effect ex- clusively its own. \Their intermixed columniations is supposed to have originated the pointed arch, which will be seen in the annexed plate ; the front as well as the interior of Rochester Cathedral, offers for the student an immense opening for this kind of study. The specimens ORNAMENTAL DRAWING. 215 here are of the richest description : the doorway is most elaborate, as regards sculpture ; and the scroll hinges, (which ofttimes cover the whole door,) by their several ramifications, produce an effect both sparkling and rich. ABC In reference to the plate, are plain D moulded openings ; is an enriched zig-zag, and label-headed doorway, with the scroll hinges, as I before mentioned ; E is an open- ing, with what is termed cusps introduced, and an early specimen of a semi-trefoil head ; F is an interlined opening, with an arched cornice, terminating with the angled fillet and beads. These cornices were of many forms, as mould- ing-blocks, cables, chain fillets, &c., and some- times with flowers. I will now refer to the other variations, or progress towards the pointed arch, or florid style. The semi-circular arch, fig. 1, is the only one employed in edifices erected prior to the reign of Stephen, A.D. 1136. This arch is struck from the point A. 216 GUIDE TO In the horseshoe arch, of which, fig. 2 and 3 are specimens, the centres are above the line of the springing. This arch is not very common, but is sometimes introduced along with semi-circular arches, apparently for the sake of variety. Fig. 2 is a portion of a circle; but fig. 3, after arriving at the semi-circle, you carry perpendicular lines, to elongate the figure. Fig. 4 is the segmental arch, in which the centre is below the springing line. This form is rarely combined with semi-circular arches. Its general application was to interior doors and openings, during the early and decorated periods; but even iu these it is not of frequent occurrence. This is got according to the segment required, and is termed the span or opening. Fig. 5 is the lancet arch, the height of which is greater than its width. Where this arch is used for the main outlines of doors, windows, and other openings, they may safely be attributed to the early pointed period. In OF THE ^\ IVERSITY) Of J. OENAMENTAL DKAWINQ. 217 the composition of tracery and wood carving, the lancet arch is continued through all the varieties. It is gained by dividing your base A line, B, into four equal parts, and from the two extreme points your intersection will give the figure required. Fig. 6 is the equilateral arch, of which height and width are equal, and is obtained by first getting an equilateral triangle. Fig. 7 is the drop arch, the height of which is less than its width, and is got by dividing A the base into four equal parts, as B C D, and strikiug from B C. Fig. 8 is the pointed segmented, the cen- tres of which are below the line of springing, and bisected, as at fig. 6. The three last-mentioned arches are used indifferently in the early decorated and per- pendicular styles. Fig. 9 is the pointed horseshoe. This form of arch occurs in a few buildings in the mixed or transition style, immediately succeeding the Norman. The choir of Canterbury Cathedral, 218 GUIDE TO erected A.D. 1154, offers, it is said, the finest specimens.* Divide the springing line into five parts, and after passing the semi-circle, it im- mediately collapses, as at C D. Fig. 10 is the ogee arch. This form was never used for the main arches of doors and windows of ancient buildings, as is sometimes absurdly done at the present day. Its use was confined to tracery, niches, tabernacle work, and other ornamental situations. The ogee form was also frequently applied to the canopies of doors and windows in the late decorated and early perpendicular ; it is gained from A four centres, as at B C D. Fig. 11 is the four-centred or Tudor arch. This form belongs exclusively to the reigns of Henry the Seventh and Eighth, after which time the Gothic style ceased to exist in any degree of purity. This peculiar form of arch has sometimes led to a separate classification of * The springing of an arch is the point from whence the compass, either in a semi-circle or segmental line, touches the perpendicular line ; or, more properly speaking, becomes tangent. ORNAMENTAL DEAWING. 219 this period, under the denomination of Tudor Gothic ; but the mere form of the arch hardly seems sufficient to warrant this multiplication of classes. AB CD. It is derived from the points, Fig. 12 is the three-centered or elliptic arch. This arch is sometimes, though very rarely, met with in England, in buildings of the late perpendicular : it frequently, however, occurs on the Continent, but marks the debasement and near approach of the extinction of the ABC. style ; it is obtained from the points, Fig. 13 is generally termed a lancet opening, for turrets and air openings. Fig. 14 is a canopy head, and usually placed over any recess, where a pedestal or figure is erected on the face of any Gothic structure. Fig. 15 is the spandrel. This seldom occurs except in the Tudor, or low segmental arches, and is bounded by what is termed a label moulding, and usually filled up with tracery vine, oak, or ivy leaves rudely dis- played. 220 GUIDE TO It will be perceived, by the foregoing remarks, that the form of the arch is not, in most cases, sufficient of itself to determine the period or class to which an edifice belongs ; but we may arrive pretty nearly, by examining nar- rowly the tracery, buttresses, pinnacles, and openings, (which openings were composed of various foils), and the variety necessary to be known by the general draftsman, is given in the annexed plate. fell Cinque Scif - OF THE >* :VERSITT; OF ,/ 7r in ?>ewfen the Tarty Watts. ORNAMENTAL DRAWING. 221 GEOMETRY SIMPLIFIED. AN abridged history of the origin of Geo- metry will, I dare say, not be unacceptable to many of my subscribers, although the subject has been treated on many times before ; I shall dwell no longer than I consider necessary either for the youth or student, that they may be able to answer and solve any early or useful question. The word GEOMETRY is of Greek origin, and signifies measuring the earth, or any distances thereon; it, no doubt, had its rise in Egypt, where the inundations of the Nile render it necessary to distinguish lands by considering their figures, that they might be enabled to lay them out in just dimensions and situations. Some authors assert that it was the invention of the Babylonians ; others, the Egyptians ; and that they borrowed it from the Babylonians. Thales } a celebrated Phoenician philosopher, who died five hundred and forty- 222 GUIDE TO eight years before Christ, calculated eclipses, and gave general notions of the universe ; Pythagoras, of Samos, who flourished five hundred and twenty years before Christ, introduced it from Egypt into Greece; and discovered the five regular Geometrical bodies, viz. the Cube, Tetrahedron, Octahedron, Icosahedron, and Dodecahedron. Euclid, of Alexandria, was particularly distinguished in elementary Geometry ; about a hundred years after him, Archimedes extended the limits of Geometry, by his measure of the sphere and the circle ; at a later period, Apollonius, of Perga, who flourished two hundred and sixty, or two hundred and thirty years before Christ, did much for the practice of higher Geometry. In Italy, about the sixteenth century, the sciences first revived after the dark ages, and several mathematicians were distinguished for their studies ; the French, and particularly the Germans followed. Justus Byrge laid the foundation of logarithms, and was the inventor of the proportional circle, although ORNAMENTAL DRAWING. 223 others ascribe the invention to Galileo. Rei- nerus Gemina Frisius, who died in 1555, in- vented the instrument used in surveying, called the plain table. Simon Stevin, of Bruges, applied the decimal measure to Geometry ; and, in 1684, Leibnitz advanced the science by the in- vention of the differential calculus ; arid Newton, by the theory of the fluxions. Robert Hook, who died in 1703, was the first who considered the influence of the refraction of light in mea- suring heights. Ludolph, of Ceulon, or Co- logne, who died at Leyden, in 1610, discovered the proportion between the diameter and the circumference of the circle. In recent times, the French have been most distinguished in this art, and have produced the best elementary works on the subject, some of which are excel- lent. Among the most approved modern works of this kind, are those of Euclid, translated by Simpson Ingram and Playfair : and the treatises of Professor Leslie and M. Legendre. From a Perusal of the above history of the progress of Geometrical science, it must be 224 GUIDE TO evident that any attempt at a complete conscientious treatise on the subject, would swell the present article to a most inconvenient length, and indeed would be completely incompatible with the general arrangement of the work : I purpose, therefore, confining myself to a series of useful definitions, which may be said to form the alphabet of the science. Problems, illustrative of the application of geometry to the useful arts, will be found in the annexed illustrations. In attempting to exemplify or illustrate the following definitions, I am perfectly aware that many of my expressions and illustrations will be objected to by the rigid mathematician, but as I have before stated, that my object is simplicity, and to convey the first rudiments of this science to those who may be entirely unacquainted with it. DEFINITIONS TO THE PLATE. A point is that which has position, but not magnitude, as fig. 1. ORNAMENTAL DRAWING. 225 A line is the trace of a point, or that which would be described by the progressive motion of a point, and consequently has length only, as fig. 2. Superfices have length and breadth, but not thickness, as that might be unbounded ; for instance, the top is the surface, as fig. 3. A solid is a figure of three dimensions, having length, breadth, and thickness. Hence, surfaces are extremities of solids, and lines the extremities of surfaces, and points the extrem- ities of lines, as fig. 4. If two lines will always coincide, however applied, when any two points in the one coincide with the two points in the other, the two lines are called straight lines, or otherwise right lines. A curve continually changes its direction between its extreme points, and has no part straight, as fig. 5. Parallel lines are always at the same distance, and will never meet, though ever so far produced, as fig. 6. 16 226 GUIDE TO Oblique right lines change their distance, and would meet if produced, as an acute angle. Angles are known and measured by the number of degrees they contain at the extreme opening. One line is perpendicular to another, when it inclines no more to one side than the other, as fig. 7. A straight line is a tangent to a circle, when it touches the circle without cutting, when both are produced, as fig. 8. An angle is the inclination of two lines to- wards one another in the same plane, meeting in a point, as fig. 9. Angles are either right, acute, or obtuse. A right angle is that which is made by one line perpendicular to another, or when the angles on each side are equal. All angles meet at a point; when this is the case, each is denoted by three letters. The right angle is the criterion of judging of every other angle ; d b c is a right angle, a b c an obtuse angle, e b c an acute angle, as fig. 10. OF THE UNIVERSITY ORNAMENTAL DRAWING. 227 An acute angle is less than a right angle, as fig. 11. An obtuse angle is greater than a right angle, as fig. 12. A plane is a surface with which a straight line will every where coincide, and is otherwise called a straight surface ; for instance, if I cut through a piece of timber, or a tree, the end surface is the plane, as fig. 13. All angles are known from their extreme openings, and are divided into degrees, as fig. 16. Here is a diagram for explanation. From a to b will be an angle of 15 degrees ; from a to c, 35 ; and from a to d, 60. These are all acute angles, being within the right line. From a to e is an obtuse angle, of 120 degrees. This diagram is on the principle of using the sextant. An equilateral triangle has all its three sides equal, as fig. 17. An isosceles triangle has only two sides equal, as a b, b c, as fig. 18 : this is the figure of one of the principal powers in the laws of 16 * 228 GUIDE TO mechanics, viz., a wedge, being made according to the power required ; for instance, a wedge of so many degrees, is measured as an acute angle of so many degrees. A scalene triangle has all its sides unequal, as fig, 19, and is to be found in the following portion of a building, or angled bay window, whose ends are not equal to its front, as fig. 20 ; a being an equilateral triangle, and the two ends, b b, scalene triangles, forming the front elevation, as the annexed illustration. Trapezium is a quadrilateral figure; that is to say, a figure with four sides. In this instance every side is unequal, as fig. 21. An octagon is a polygon of eight sides. This figure is placed here, merely to shew the prin- OF THE TTNIVERSITTJ ORNAMENTAL DRAWING. 229 ciple of gaining it. First form a square, and from each angle or corner you strike a segment, whose arc shall touch the centre, and at the termination of each curve angular lines, drawn from end to end, the dotted line is a perfect octagon, as fig. 22. This principle is laid down for perspective. A rhombus is a parallelogram, whose sides are equal, but not at right angles, as fig. 23. A rhomboid, whose horizontal lines are equal, and oblique lines unequal, with the ho- rizontal, as fig. 24. Eadius lines. Those lines starting from a centre, and all acute angles, as fig. 25. Solids and bodies, when either are bounded A by surfaces, sides, and ends. book is solid. Hence a square, with six equal sides, is a solid, or cube; that is to say, in measurement. Twelve inches each way is a foot cube. When solids or superfices have more sides than one, then they become polygons ; if all equal sides, they are regular, if otherwise, irre- gular, of which they are named up to twelve ; 230 GUIDE TO beyond that they are termed polygons of thn> teen or fourteen sides, and so on; but I will name the figures, as it is of the greatest utility to know them : 1, a line; 2, a parallelogram; 3, a triangle ; 4, a quadrilateral ; 5, a pentagon, five sides; 6, a hexagon, six sides; 7, a hepta- gon, seven sides ; 8, an octagon, eight sides ; 9, a nonagon, nine sides ; 10, a decagon, ten sides; 1.1, an undecagon, eleven sides; 12, a duodecagon, twelve sides. Base is the part on which any figure stands. A Altitude is the height of any body erect. circle is a figure bounded by a line, termed the circumference, or periphery, and equi- distant from the centre, or point, from whence it is obtained. The interior of a circle is divided into component parts, each of which has its classification. On reference to the plate, fig. 26, a & is the diamefcer ; c d is the cord of an arch ; and d b is the segment of a circle. Cones may be brought under one head, without entering into the number of terms usually given. Any solid figure rising to an ORNAMENTAL DEAWING. 231 apex, or point, is called a cone ; if angled, it is called a poly gon-cone, or cone of so many sides ; if the cone be circular, it may be divided into four parts, viz , a fru strum of a cone, that is to say, when it is cut parallel with the base, it is then a circle, as fig. 27 shews. If cut parallel to its axis, it then forms a hyperbolic curve, as a b c, fig. 28 ; and if cut parallel to the sides of the cone, it is called a parabolic curve, as a b c, fig. 29 ; and if cut through in the angle, it then becomes an ellipsis, as a, fig. 30. 27. 28. 29. 30. Frustrum. Hyperbolic. i\ r3 Parabolic. A cr 3\ Ellipsis. Among the various geometrical figures that become useful to the ornamental draftsman, beside mouldings and archways, are the variety of ovals, ellipses, and foils ; the description of which terminates this volume. There are many who with the compasses can strike an ellipsis, 232 GUIDE TO no doubt, but we will suppose you have no instruments ; it then becomes necessary to be able to do without them, yet work with cer- tainty, and which, with a few useful diagrams, will be found not only essential, but pleasant to study. The first I shall commence with will be the ellipsis, using instruments. Fig. 31 is the elongated ellipsis, and is obtained by two circles, from the centres, c d : you gain by the intersecting segments the points, e f, from which you pass your diagonal lines, g h i k. By placing the compasses on the points c d, you strike from h to &, and from g to i ; and from / and e you obtain a curve g h and i k, and you have an ellipsis complete; but let me remind you, in striking any of these geometrical figures, you cannot be too parti- cular as regards your division ; for the least deviation will throw every other portion en- tirely wrong, and you will have the same work to do over again, for the want of a little care at first ; and where you should have but one point- hole, by carelessness you perforate the paper like X ** OF THE (UNIVERSITY^ ^c OENAMENTAL DKAWING. 233 a sieve, winch always spoils a drawing ; to avoid this, you should get a pair of what are termed spring dividers, to enumerate your divisions, as by that means you can do without pricking the paper so much, by merely laying the points on, and having a screw to work the compasses, you can divide to the greatest nicety, and keep your divisions more true than with the other compasses, the least pressure of the hand will close them a trifle, which, if imperceptible in one or two divisions, when you come to a hundred, it is then you find it out : this is advice which, perhaps, in the ardour of your studies, you might not think of Fig. 32 is a short ellipsis, got on the same principle as the first, but instead of forming two tangent circles, you intersect them and work on the former principle. Fig. 33 is a rule by which the oval is obtained, whatever is to be the width, the length, to be proportionate, must be three times its width, as for instance, the perpendicular line a b, is divided from the point c; strike the 234 GUIDE TO semi-circle, from which you form a parallelo- gram, d e f g, which is to be divided into twelve parts on each side, and the base to be twentyfour parts ; by merely intersecting these divisions it will form an oval of itself, viz. by passing lines from 1 to 1, 2 to 2, 3 to 3, and so on regularly; now, I always found too much trouble in this principle, and could not rest easy until I had found out a much better figure, and on a more simple plan ; which, after trying a great many without success, I at last hit upon one, and every person I have shown it to is satisfied of its superiority. Fig. 34 is an oval, the exterior form of which is gained by two circles, the sizes being governed by the diameter; strike the circle, a, then the smaller one, 6, tangent to it; next strike your intersecting arcs, c, which are to be divided into nine equal parts; draw your diagonal lines, c a b d, which gives you the stopping points for your segments, d d d d, then place the point of the compasses on /, and it will give you the segmental curve, d d d d; UNIVERSITY ORNAMENTAL DRAWING. 235 you will find this oval a complete egg shape. Now, we want to obtain a segmental arch and a semi-elliptic, without having sufficient room for striking the same with the compasses ; in the connected plate, fig. 35 and 36, I have given two very excellent principles, which I think have not appeared before. The elliptic one is the principle laid down by Kennie, in planning the elliptic arches of New London Bridge. In obtaining or striking this arch, whatever may be the height from your springing line, &, the same width you take from that line to carry your radius lines, as at c ; divide your springing line into eighteen parts, or more, remembering to keep even numbers. The greater the number of divisions, the more certain you are to obtain a segmental line; then carry your radius from the point, c, through each of the divisions to the boundary line, a e, a e ; next divide the end, a e, in nine equal parts, and from the point, b, you carry your lines to the end division, which intersection gives you the arc, a b c. 236 GUIDE TO The verse sine arch, fig. 37, is on the same principle, but requires no radius points. Get the height of your arch, and form two acute angles from the base line, a a to &, and on those angles, from the extreme points, a, obtain a right angle, a c, a c, and another at a d, a d, which will form one of your divisions of eighteen at the top; and next divide your springing line a a, into eighteen equal parts, and your end in nine parts, carry your lines out to e b, and your intersecting lines, b a, to b d, will be the segmental arch. There is another system by which you may obtain a segment, and which you will find in the plate. The more obtuse the angle, on the sides of which you make a number of divisions, the better the curve appears by the intersection of the numerous divisions; as, from a b c is divided into fourteen parts, cross from 1 to 1, 2 to 2, 3 to 3, 4 to 4, and so on, and the segment is given. This is a very useful diagram, especially when the angle is more acute in its OENAMENTAL DEAWING. 237 altitude; you will find ifc the only way of describing an hyperbolic curve with facility. The difficulty of obtaining a quantity of division in a small space, as I before mentioned, with the compasses, I will now draw your attention to. To prevent your perforating the paper like a sieve, divide, for instance, one inch in length into twenty parts; you would, no doubt, go a great many times over that line before you would get the right division, but, on reference to the plate, you will find an unerring principle to work upon. Let a c be the base, at a right angle, with that carry up a perpendicular line, a 6, of any height, and at ran- dom run up your divisions, no matter how many, if you go to work accurately ; after this is done, carry a converging line from c to b, and from your base draw parallel lines, touching from side to side, until you have sufficient for your number of divisions, as d e; from that, at each intersecting on the angle, carry parallel lines from the perpendicular, e to /; so, by carrying 238 GUIDE TO these lines to the base, the number of divisions are obtained. This is exceedingly valuable in dividing modules into minutes, in drawing ar- chitecture; in fact, in every instance when small divisions are required. m on ORNAMENTAL DRAWING. 239 ON MOULDINGS. MANY of my readers may attribute blame to me for inserting the above-mentioned por- tions of architecture, and perhaps say, that it has nothing to do with ornament. No: that I will allow. There certainly is no occasion for moulding in a running scroll, but there is in the boundary of it, and that according to the cha- racter or style, of course. As a matter of fact, the moulding surrounding it should and ought to be in accordance with it, but it is not always the case; and to prove to you the necessity of such information, is the reason I trespass thus far. This portion of decoration is an indispen- sable accompaniment to all my former remarks, and co-practice of geometry. As an instance 240 GUIDE TO of the utility of your being acquainted with mouldings, how would an ornamented frieze appear, without the upper mouldings formed a cornice, and protection to all the bas-relief and ornamental risings, and which, in their origin, were of a rude and massive form, brought into a subordinate one by the Greeks, to protect, strengthen, and unite the whole of their buildings ? The number of mouldings generally used are eight, and each and every one of utility. The first and most simple form is the fillet, fig. 1, which is the smallest in proportion to the whole of the others, and its chief use is to divide the superior mouldings, and prevent the heavy inharmonious effect that would be produced by two or more geometrical mouldings being placed together. Fig. 2 is the astragal, or round fillet, which may be, if required, ornamented as fig. 3. Its chief use is to divide the capital from the shaft of any column or pilaster, and may be either entirely round, or semi-circular. LI OF THE UNIVERSITT ORNAMENTAL DRAWING. 241 Fig. 4 is of the same character, but of a much bolder form, and chiefly used in the base moulding of a column, and termed alorus. The exterior end is got from the point a, and projects no further than the vertical line in face of the plinth, as fig. 5. Fig. 6 is the ovolo, or quarter round, and is now chiefly used in an admixture of Roman mouldings; but there is so massive an appearance with it, that, at the present day, the inventive genius of architects has greatly improved upon it and adhered more strictly to what is termed the Grecian ovolo, as fig. 7, which is much lighter and more graceful in appearance. Fig. 6 is the quarter of a circle, and gained from the point, a; but the Grecian is got from any acute angle. You may allow for the projection and depth of your moulding, from any angle you please, keeping the circular end in proportion, as fig. 7. Fig. 8 is termed the cavetto, or hollow. This moulding was chiefly used by the Egyptians, surrounding their temples, as I have 17 242 GUIDE TO before described; it is chiefly employed in covering the other members; and, being strong at the extreme points, supports others. This is obtained from the point, a. Fig. 9 is the cyma-recta, or cymatium. When you have ascertained the projection of your moulding, draw the angular line, a h, which you will divide into two equal parts, as at c; which divisions will form the bases for two equi- lateral triangles, as a e d, and c b e, From the point e, you strike c b, and from d, a c; which when joined, is the cymatreum of the moulding. Fig. 10 is the ogee, and drawn in the same manner as fig. 9, but reversed. It is a moulding well adapted to support other members, A from the strength of its extreme points. very rich effect is produced in this moulding by turning the top end, and leaving a small opening, as fig. 11 shews, and is termed a quirked moulding, by having the appearance of a black line, by the indentation of the hollow under the fillet. Fig. 12 is the cyma-reversa, and the same tf"'-f"f i%yxxx//^i^g^^%^%%^a W//////Wff/M'WfW/>/) Those above the line are sections of Gothic mouldings ; those below are termed mtillions, or sections of the upright bars and tracey in varioiw Gothic windows. OF THE UNIVERSITY ORNAMENTAL DRAWING. 248 as the above, in an inverted position and used for base mouldings only. Fig. 13 is a very peculiar moulding, and used to give power to the surrounding members, and to effect a good profile : it is termed a scotia mouth. After you have determined the projection of your top and bottom extremity, as a b, the perpendicular line, a c, is divided into three equal parts, and from the point, d, describe the quarter circle, a e ; then divide the horizontal line, e f, into five equal parts. From the point, f, draw e g, and by striking an arc from the point, /, from the two inner divisions, will give you the point to intersect your angle, c h, and from that angle you raise your perpen- dicular, b li y the extremity of which you divide into three equal parts ; then strike the arc, g k ; from that you strike the remainder of the arc, to complete the mouldings, from h, which is from k to 6. This moulding is an excellent study, and I would advise you not to be conquered by the seeming difficulty of its appearance. 244 GUIDE TO There is another more simple way of obtaining this moulding, by merely dividing the height into three parts, two for which will form the width, by intersecting six parts, as diagram. The point, a, will give you the arc from b c, and from the point, d, will form the other arc, c e. I think I have treated on every thing necessary for your instruction, ac- cording to my promise; and as my last advice (al- though it has been repeated before) is, study well and assiduously that which is good, and feel not daunted at trifling obstacles that may occur ; for, rest assured, after surmounting one, you will not rest, until you have surmounted others, and overtopped the apex of difficulties ; then all must run smooth, and your labours be repaid : and whilst you are performing these energetic feats of perseverance to reach perfection in the arts, you will be viewed with a jealous eye by your fellow-students, until they exert them- ORNAMENTAL DRAWING. 245 selves in the same manner. Then, by those means, the art of design ere long must become . extended, and hold the crayon of superiority over all other countries. FINIS.