AN ESSAY 
 
 ON 
 
 ORNAMENTAL DESIGN, &t 
 
 One of the most eminent Natural Philosophers of the present age,* 
 in a late number of the Edinburgh Review, f has observed, that the publi- 
 cation of a series of diagrams upon the princijdcs of linear harmony, with 
 the diaper designs resulting from them, might be productive of much ini- 
 proYcment in the Decorative Arts. For, as the carpets of rooms, geometrical 
 pavements, and paper hangings, are all viewed by the spectator with various 
 degi-ees of obliquity, it would be desirable to invent patterns which, though 
 they might not be the most beautiful when seen directly, have the power 
 of developing in succession a series of beautiful combinations, when viewed, 
 as they must always be, at different obliquities. 
 
 A series of such designs will form the principal illustrations of the pre- 
 sent publication, and, the Author trusts, they will be found useful in opening 
 
 * Sir David Brewster. t October 1843, Art. II. 
 
 a new field of design, not only to the decorative artist, but to damask and 
 shawl-weavers, calico-printers, stained-glass manufacturers, cabinet-makers, 
 and those engaged in other branches of the useful and ornamental arts. 
 
 Hitherto our geometric diapers, if the term may be applied to this 
 peculiar kind of ornament, have been copied from those of the ancients, with- 
 out any attempt having been made to investigate or develope the priucij)le 
 upon which they were originally formed. Perhaps the most beautiful speci- 
 mens of this class that have been handed down to us, are those of the 
 Alhambra, and they have been used, in various manufactures, for so long a 
 period, that they are now exhausted, and have become, from constant re- 
 petition, wherever they could be applied, too familiar to the eye, while, from 
 being copied by the ignorant, they are often much deteriorated and deformed. 
 Something now in this style of ornament is, therefore, required, and the 
 Author trusts, that the present series of designs will supply the desideratum. 
 
ON THE PRINCIPLES OF ORNAMENTAL DESIGN. 
 
 The total want of originality in our ornamental manufactures, seems I 
 to have been the cause of much loss to the country ; for the French, by a } 
 different mode of procedure, have attained considerable excellence in the ; 
 art of design, as applied to this branch of industry. Dr Lire, observes, 
 that “ the opinion generally entertained of the superiority of such French 
 silks as arc figured, and which depend for their beauty on tasteful arrange- 
 ments, is no more a prejudice of mankind, than the feeling in favour of the 
 works of Raphael and Titian. * * Taste is displayed both in the forms and 
 grouping of the figures, and in the disposition of the colours.”* The French 
 style of ornamental design, although it may not reach the excellence ascribed 
 to it by this author, has still originality to recommend it ; and this supe- j 
 riority has not only operated in limiting the home consumption of our own | 
 ornamental manufactures, but has been the cause of their being superseded > 
 by those of the French in almost every foreign market. 
 
 All the works hitherto published in this country on ornamental design, 
 have been, in their illustrations, merely copies from antique fragments of 
 .sculpture and from the examples given in foreign works on the same subject, 
 and. as copies, therefore, they must be inferior to the originals from which | 
 tliey are taken. It has also been clearly proved, in a legislative investigation ]j 
 into the subject, that we copy, principally from the French designs, all our || 
 
 * Philosopht/ of Manv/actures. 
 
 patterns applied to silk, cotton, and worsted manufactures. The de.signs 
 accompanying the present attempt shall therefore be original and that ori- 
 ginality will be regulated by principles founded on the unerring laws of 
 Nature. These principles the Essay itself shall gradually develope as it pro- 
 ceeds, with such explanatory examples in wood-cuts as may be required to 
 elucidate them. 
 
 Ornamental design may be classed according to its mode of application, 
 and its style may be varied agreeably to the principles about to be explained. 
 But to ai’range styles of ornament according to their origin in other nations 
 and in other ages, and set them up as models, as has almost universally been 
 the practice of those who have written upon the subject, is, to say the least 
 of it, a tacit admission of the inferiority of the conceptive powers of the 
 mind, in regard to ornamental art, in this country at the present period. 
 
 In all the arts there are first principles, and those principles are reci- 
 procated in the perceptive faculty, or power, of the human mind. W e find 
 in all Nature’s w’orks the same principle uniformly operating in the produc- 
 tion of beauty ; and while each object is reproduced after its own kind, there 
 exists an infinite variety amongst the individuals of each specific kind. 
 Amongst those we are enabled, by perception, to select that which is most 
 beautiful, and our power of doing so is regulated, in the first place, by th(* 
 degree of perfection w'e possess in the physical construction of our organs 
 of sense ; in the second, by the degree in which our intuitive faculty of 
 
ON THE PRINCIPLES OF ORNAMENTAL DESIGN. 
 
 perception reciprocates to the first principles of beauty ; and, in the third, 
 to the degree in which we have cultivated this faculty. The principles of 
 this branch of art, therefore, being grounded in nature and universal reason, 
 it must be as much under the influence of common sense as language itself; 
 and, as before observed, its laws must be fixed and natural, and have a 
 response in the mind of man. 
 
 There has been much said and written upon purity of style, and it may 
 startle some to see it asserted, that this has had only one tendency, and that 
 has been to retard the progress of the art of ornamental design in this country. 
 But many of the kinds of ornament called styles being themselves impure, 
 in so far as they are destitute of the first principles of beauty, a servile 
 adherence to them is not only a very questionable kind of purity, but calcu- 
 lated to corrupt the taste, while it retards originality of conception. 
 
 If an ornamental designer were asked to imitate another in the same 
 profession, he must either be conscious of his own inferiority, or feel his 
 reputation compromised by the request. And the same may be said of any 
 other profession where conception or originality of design is required, to 
 constitute excellence. If a poet imitates the works of another poet, he 
 thereby acknowledges his own inferiority ; and so does the artist who copies 
 the work (either ancient or modern) of another artist. But in neither case 
 can the w'orks copied constitute or supersede the laws or first principles of 
 art. The greatest merit of all works of art, either in poetry, music, painting, 
 
 or sculpture, consists in their being unlike the style of any that have preced- 
 ed them ; for there are no limits to the inventive powers of genius ; and indeed 
 it is only invention and originality that prove the possession of that divine 
 gift. But the mode of proceeding in regard to tuition in the ornamental 
 arts has, in this country, been of a very opposite character. What has 
 hitherto been understood by purity of style, is nothing more than servility 
 of copying, and if we were to inquire very closely into the origin of what are 
 termed styles of ornament, W'^e should find their claims to this distinction to 
 rest on a foundation of a very slight and unsatisfactory kind. 
 
 The most beautiful of the architectural class of ornamental designs of 
 antiquity have of course been handed dov\Ti to us from the same people an<l 
 the same era that have also supplied to us the most beautiful specimens of 
 the arts of sculpture and architecture. And, but for the perishable nature of 
 the materials, there can be little doubt but we might have owed to the same 
 period and people not only the finest specimens of pictorial art, but those of 
 that kind of design peculiar to manufactures and interior decoration. 
 
 When vve take this in connexion with wliat we know of the poetry, the 
 music, and, above all, the geometry of the same period, we can scarcely help 
 feeling convinced that some fixed principles of taste and beauty were known 
 and acknowledged amongst that extraordinary peojde at this period of their 
 general refinement. And the more so, that the progress of natural philosophy 
 in succeeding ages has proved, that there are ruling principles liy vhicli 
 
^iSbisiBLi 
 
 ON THE PRINCIPLES OF ORNAMENTAL DESIGN. 
 
 the sciences are in almost all cases identified with one another ; and by 
 which again the arts ai’e identified with the sciences, and \ipon winch they 
 are reciprocally dependant. The same eminent natural philosoidicr, already 
 quoted,* observes, “ that the disposition to this species of exchange, and to 
 introduce into the intellectual community the principles of free intercourse, 
 is by no means general ; but we are confident that art will not sufficiently 
 devclope her powers, nor science attain her most commanding position, till 
 the practical knowledge of the one is taken in return for the sound deduc- 
 tions of the other and that “ it is in the fine arts, principally, and in the 
 speculations with which tliey are associated, that the controlling power of 
 scientific truth has Jiot exercised its legitimate iiiiluence. In discussing the 
 principles of painting, sculpture, architecture, and landscape gardening, 
 philosophers have renounced science as a guide, and even as an auxiliary; 
 and a school has arisen whose speculations will brook no restraint, and 
 whose decisions stand in opposition to the strongest convictions of our 
 senses.” f 
 
 A proper comprehension of art as a whole, and as it is connected with 
 science, is therefore essential to right prax^tice, even in that humble branch i 
 of it which fonns the subject of this Essay; and upon no other foundation 
 can a standard of just criticism be established. For that criticism which 
 
 * Sir D-wJ Brewster. 
 
 t Eiliuburgli Review, Oct. 1843, .'irt. II. 
 
 judges an ornamental design by other designs of the same de.scription, with- 
 out reference to the natural and .scientific principles which ought to regulate 
 the artist in the production of such works, concludes upon false premises. 
 Were the proper mode of estimating works of decorative art adopted, those 
 contracted and prejudiced views which take precedents alone as a guide, 
 would soon give place to a correct understanding and appreciation of what 
 is truly beautiful. 
 
 The names of the kinds of ornament called xfi/les are numerous. We 
 have the Grofnif/iic, the Aj'nk'squc, the Moorish or Moresque, the Persia//, 
 the Turkish or D/fzautine, the Hindustanee, the Chinese, the Pompeian, the 
 Elizabethan, the Louis Quatorze, &c., some of which, no doubt, have what 
 may be termed national characteri.stics, and they may, so far, whether good 
 or bad, be admitted as styles, because they belong not merely to periods, 
 but to nations. Yet in general they are not worthy of being held up as 
 models of perfection, far less arc they worthy of being made to supersede 
 the necessity of studying the first principles of linear and chromatic beauty 
 in our schools of design. 
 
 A style of ornament may legitimately be named after its originator, 
 .such as the “ WateaiP style, which is probably of all comparatively modern 
 styles the most original and most graceful ; for, although it is grotesque, 
 and may not have been established upon any knowm principles, yet it is the 
 j)roduction of the intuitive good taste of an original genius. 
 

 ON THE P R I N 0 I P I. E S 
 
 Some of the styles of ornament already enumerated, are, however, only 
 characterized by the discordance of their parts, their grossness, or unmean- 
 ing profusion ; and when we apply any known principle of harmony to 
 their incongruous and absurd combinations, we are convinced of the de- 
 graded state of public taste which gave such productions even a teni})orary 
 existence, and wonder how any attempt should have been made to revive 
 them in a more enlightened era. 
 
 Strictly speaking, a mere ornament is something supplied l)y art, either 
 to conceal what utility has rendered unpleasant to the perceptive faculty, 
 or to enhance the effect of that which has been found to be otherwise tame 
 and monotonous. Wherever, therefore, we observe an ornament, we may 
 suspect a defect. Ornaments ought never to obtrude themselves upon the 
 eye, but to appear as a necessary part of that which they are meant 
 to embellish, like the graces introduced by the accomplished musician in 
 the composition of a piece of music. Ornamental design in architecture 
 ought to hold this situation, and it .should always be in harmony with the 
 subject it is intended to grace and adorn. Every ornament should have a 
 purpose and a meaning, otherwise it becomes exuberant or .superfluous ; 
 and an ornamental designer ought to be able to give a reason, based on the 
 first principles of art, for the em])loyment of every curved or .straight line in 
 his design. 
 
 There are two di.stinct classes of ornamental design. The one belongs 
 
 F ORNAMENTAL D E S I GN. 
 
 exclusively to architecture, and the other conjointly to architecture and 
 manufactures. All merely architectural ornaments are sculptured, and have 
 specific styles, agreeing with that of the architecture in which they are ap- 
 plied. The three classical styles of architecture — the Doric, the Ionic, and 
 the Corinthian — separately involve in their general proportions a certain 
 modification of the first principles of beauty ; and those principles seem to 
 have been applied under the same modification in the ornaments belonging 
 to each. The ornaments employed in architecture are in some cases em- 
 ployed to conceal defects, and in others, to soften the asperities of abrupt 
 transitions from one kind of line to another. For instance, all mouldings are 
 used to conceal necessary junctions, to soften angles, or to divide parts that 
 would otherwise be out of proportion with the requisite vacuities in the com- 
 position. The capitals of columns, and other .similar ornaments, soften the 
 meeting of two opposite lines, and graduate the pressure on the top of the 
 column. The ornaments introduced into friezes relieve the monotony of an 
 accumulation of horizontal straight lines, — hence the division of this space 
 i)y perpendicular triglyphs, sculptured figures, or foliated scroll-work. 
 
 The class of ornament that we have more particularly to treat of in this 
 Es.say, is that which may, however, in any kind of architectural subject, be 
 applied to enrich those surfaces that have been neces.sarily left plain and 
 monotonous, and used in every kind of manufacture, whether for an article 
 of dress, or to cover tlie walls, the floor, or the furniture of an apartment. 
 
Nature leaves nothing unadorned, and those of her works which are 
 apparently the least embellished, are often found, upon being carefully 
 studied, to develope, in the highest degree, the first principles of orna- 
 mental desigu, both in form and colour. For instance, the very common 
 weed called tlie Dock {Rmnex crispm), blends in its form the curved and 
 the straight line, arranged in a manner not to be surpassed by the finest 
 models of antiquity. Neither can there be pointed out in the arabesques of 
 Raphael himself, a more beautiful blending of two harmonious colours than li 
 is displayed in the mode in which the red of the stalk is blended with the 
 green of the leaves in this humble production of Nature. Thus Nature 
 affords us an inexhaustible mine of knowledge in ornamental design, and 
 no artificial attcmjft will be truly beautiful that has not its archetype in lier 
 works. Yet it appears as if this art were allowed to dwell in ancient ruins, 
 while, by the investigation of the universal principles of beauty, we might 
 lay solid foundations iq)on which to rear original and noble structures for Ij 
 her abode, l^pon these universal or first princi})les of beauty, therefore, j 
 let us base such theoretic axioms as can alone constitute the science of or- 
 namental design, seeing that it is only by such a mode of proceeding that we 
 can ever expect to establish statutes in this art, capable of checking every 
 species of fanaticism and false practice. 
 
 Architectural ornaments, it has been observed, belong to sculpture, and 
 may therefore be fit subjects for the study of the modeller and carver ; but 
 
 to the manufacturer of carpets, damasks, calicoes, shawls, or hangings, the 
 practice of copying them servilely is worse than useless ; and their being 
 employed as almost the only models of study in some of our drawing 
 schools, has led to their misapplication in various instances. For example, 
 in many of our carpets, we find a great deal of labour bestowed in attempts 
 to give them the appearance of being composed of carved work, such as 
 highly relieved rosettes, and foliated scrolls, deeply sunk pannelling, and 
 many other attempts at a kind of deception, which, if successful, would con- 
 vey any thing but a pleasing feeling to the mind. We might walk on the 
 floor of an apartment with perfect .safety, were it strewed with bouquets of 
 flowers, although the inclination might be to step over them, instead of 
 upon them; but to walk upon a piece of boldly relieved carved work, 
 would neither be safe nor agreeable. Yet, to produce in the mind this 
 feeling of insecurity and discomfort, would appear to be the sole aim of 
 many designers of patterns for carpets. This is evidently the result of their 
 education ; for the production of a drawing in chalk which, by much labo- 
 rious stippling, is made to represent the light and shadow of sculptured 
 ornaments, is generally held up as the perfection of the art of ornamental 
 design in our schools. But all this labour is useless, inasmuch as it does not 
 a-^isist the mind in its capabilities of appreciating in nature or art what is 
 beautiful in form or colour. The outline is what constitutes the figure of 
 the ornament, and the impression of beauty or deformity is conveyed to 
 
ON THE PRINCIPLES OF ORNAMENTAL DESIGN. 
 
 the understanding as effectually by this line, when it inscribes a plane figure, j 
 as when it surrounds a solid body ; for no object in nature can depict any 
 thing upon the retina but a plane figure ; and it is only by experience that 
 
 II 
 
 we become aware of any object having other dimensions than length and j 
 breadth. Hence, as every solid form is but the fluent of a plane figure, | 
 the eye, or rather the perceptive faculty through the eye, may be so far j 
 deceived by an imitation of light and shadow within the outline of such a 
 figure, as to mistake it for a solid body, but never in regard to its configu- 
 ration. 
 
 The combination of plane figures produced by lines is, therefore, sus- 
 ceptible of every modification of the harmony of form upon the eye, inde- 
 pendently of light and shadow, and shall in this Essay be treated accordingly ; 
 neither is it necessary that an ornament should be an imitation of any 
 natural object. To the student in ornamental design, as already observed, 
 nature is no doubt an inexhaustible source of study, but it is enough for him 
 to know the principle of combination which constitutes beauty to be able 
 to produce it in his works ; and to an investigation of this principle we shall 
 now address ourselves. 
 
 The true in art is the beautifuly and the false is the deformed or nqly. 
 
 As moral truth is to the conception, the concentration of all that is elevated i 
 in the human mind, so is beauty to the perceptive faculty a combination of |' 
 the elements of the material world, upon tlie general principle of harmony, ! 
 
 whicli comprehensive quality depends upon proportionate combination. Sir 
 Isaac Newton endeavoured to show that the beauty resulting from harmoni- 
 ous combination was not confined alone to the musical scale, but that the 
 light of the sun was composed of several colours, relating to one another 
 upon a perfectly similar principle ; and farther, that the planets, in their 
 respective distances from the sun, and in their relative gravities, assimi- 
 lated to the ratios which govern music. Attempts have since been made 
 to show that the elements of beauty in the human figure may be reduced 
 to a scale of parts, having also the relative proportions of musical intervals ; 
 but for want of a proper system of applying these ratios to form in the 
 abstract, they have been reckoned fanciful and unsound. It would appear, 
 liowever, that the idea of this principle exercising a controlling influence 
 over all combinations throughout the great system of Nature is of remote 
 antiquity, for the Chaldean philosophers of the earliest ages taught that 
 the chief image of celestial truth was hannouy. 
 
 The mind of man certainly informs him that there exists, as a portion 
 of its constitution, a faculty by which he contemplates with satisfaction and 
 delight the beauty arising from order and proportion, by whatever means those 
 ideas are excited, and however much they may be concealed in the aj^parent 
 irregularity arising out of variety. The concurrence of these qualities produce 
 in every case perfect harmony, and this concurrence is attained by certain 
 modifications in the relative quantities of the elements by which any species 
 
8 
 
 ON THE IMilNOlPLES OF ORNAMENTAL DESION. 
 
 of harmony is to be produced. The well investigated laws of acoustics, have 
 shown that the modes in which sounds relate to one another in the production 
 of harmony upon the ear are purely mathematical ; and I have elsewhere 
 shown, that these harmonic ratios, as they are termed in music, are equally 
 applicable to that kind of harmony which addresses itself to the under- 
 standing through the eye, as also, that a scale of geometric figures can be 
 generated within the circle, or any of its elliptical modifications, correspond- 
 ing in every respect to the scale of musical notes.* The first principles of 
 beauty are consequently the harmonic ratios, of which a description shall 
 now be attempted. 
 
 OF THE HAILMONIC RATIOS. 
 
 It is well known that the unit has no power of multiplication or divi- 
 sion, while every other number has both those powers. The first multiple 
 of the unite is 2. It is a submultiple of the numbers 4, 6, 8, &c., progres- 
 sively, as 2, 3, 4 ; and it is the first even number. The number 3 is also 
 simply a multiple of the unit, and is the first odd number ; it is a submul- 
 tiple of C, 9, 12, &c., progressively, as 2, 3 4, and is composed of 1 and 2 
 added together. 
 
 * Tlie Natural Principles and Analogy of the llamiony of Form j" and “ Proportion, 
 or the Geometric Principles of Beauty Analyzed.” — W. Blackwood & Sons, London and 
 Edinburgh. 
 
 [ Ihe next multiple of 1, having no other aliquot parts, is 5 — a similar 
 
 ; compound of the first even and first odd numbers, 2 and 3. It is a submul- 
 |i tiple of 10, &c. These three numbers 2, 3, and 5, are, therefore, the first 
 I three multiples of 1 that are multiples of no other number — consequently 
 
 ! they are adapted to divide the elements of proportion into the primary 
 
 I harmonic ratios ; and in this capacity will be shown equally to regulate the 
 
 j effects produced by external nature upon the senses of hearing and seeing. 
 
 ' The number 5, although by it the third mode of division is performed, is of 
 
 I an intermediate character, and the middle may thus be said to be produced 
 ' by a niunber which combines the first and last. 
 
 The primary or leading liarmonic ratios produced by those inodes of 
 division, are 1 to 2, 2 to 3, 4 to 5, and the secondary ones, which complete 
 the natural scale of musical notes, being 8 to 9, 3 to 4, 3 to 5, and 8 to 15, 
 no new mode of division is required, 4, 8, 9, and 15, being multiples of 2, 3, 
 j and 5. 
 
 ; To arrange and proportion the combination of various forms by those 
 
 ! ratios, in such a manner as to produce one or unity, ought on all occasions 
 to be the aim of the artist in ornamental design ; for every composition 
 should manifest in all its parts a definite relation to a whole. This is 
 the first condition of order, and consequently the primary cause of geometric 
 1 beauty. But when the parts of a figure are perfectly homogeneous or 
 identical, there can exist in it no principle of proportion productive of this 
 
ON THE PRINCIPLES OF ORNAMENTAL DESIGN. 
 
 9 
 
 effect, because its parts are throughout as 1 to 1, producing sameness. The 
 circle, the square, and the equilateral triangle, as shall hereafter be shown, 
 are figures of this description, and consequently want within themselves 
 individually the first element of proportion — variety. 
 
 The whole scale of elementary ratios are as follow : — 
 
 ni.®sonances, which are 
 
 Consonances. 
 
 occasionally treated as 
 
 Dissonances. 
 
 
 
 (?on8onance8. 
 
 
 1 to 
 
 2 
 
 5 to 7 
 
 4 to 7 
 
 2 ... 
 
 3 
 
 7... 10 
 
 7 ... 8 
 
 3 ... 
 
 4 
 
 
 8 ... 9 
 
 3 ... 
 
 5 
 
 
 9 ... 10 
 
 4 ... 
 
 5 
 
 
 8... 15 
 
 5 ... 
 
 G 
 
 
 15 ... IG 
 
 5 ... 8 
 
 These ratios can be extended as 1 to 4, 1 to 8, &c., 2 to 6, 2 to 12, &c., 
 in combined harmony; while in the harmony of succession, melody, or out- 
 line, the dissonances 8 to 9, 9 to 10, &c. become harmonious. 
 
 The application of this mathematical principle in the production of 
 variety of musical composition is almost boundless, and a mode of applying 
 it in the production of visible beauty shall now be shown. It will, however, 
 be necessary, in the first place, to describe the elements upon which it is 
 thus to operate. 
 
 OF LINES. 
 
 Although a point and a line, mathematically considered, are individually 
 position without magnitude, and length without breadth, yet, in the arts, 
 they are understood to have a physical existence, such as may be perceived 
 through the eye, and thus convey to the mind a knowledge of where a 
 figure ends, and the space that surrounds it commences, as also of the divi- 
 sion of figures into parts. 
 
 There are only three kinds of lines used in producing forms, and they 
 are — 
 
 the straight line, the crooked line, and the curved line.* 
 
 ■* As tUe crooked line is but a combination of two or more straight lines, it might be 
 argued, that there are only two kinds of lines, the straight and the curved, and that they are 
 correlative to silence and noise in acoustics, and white and black in chromatics, especially as a 
 single straight line can enclose no figure ; while the most comprehensive and capacious of 
 figures — the circle — is produced by the homogeneous curve. Indeed, some assert that the cir- 
 cumference of a circle is but an infinite polygon, and that there is consequently none but 
 straight lines, while others assert that Nature detests a straight line, aud that every line is to 
 a certain extent curved. These speculations, liowever, are worse than ustdess, for they not 
 only misdirect the attention of the student, but bewilder him. 
 
lu 
 
 ON THE PRINCIPLES OF ORNAMENTAL DESIGN. 
 
 All varieties of form, however complex, all the similarity and dissimi- 
 larity that combine in the harmony of forms, are produced by these simple 
 elements. 
 
 The straight line has three positions ; it may be — 
 
 horizontal, vertical, or oblique. 
 
 The crooked line may be crooked in three different ways : it may pro- 
 duce — 
 
 a right angle, an acute angle, or an obtuse angle. 
 
 The curved line has also its varieties : it may be — 
 a portion of a circle. of an ellipse, or of a volute. 
 
 These are all the positive varieties of which the three kinds of lines 
 |; are susceptible. The straight line, if not horizontal or perpendicular, must 
 be oblique ; for however near it may approach one or other of its two posi- 
 tive positions, so long as it is not in either of them, it remains oblique. 
 
 I There is only one positive angle, called the right angle because it arises 
 out of the two positive positions of the straight line; for however near 
 the other two angles may approach this in either direction, they still remain 
 j simply acute or obtuse angles. The curved line, in the same way, has only 
 ! one positive curve, and that is when it forms a segment of a circle ; for the 
 ■j two diameters of an ellipse may vary to any degree, but every segment of its 
 1 circumference will form an elliptical curve ; neither will any part of a volute 
 j be found to be circular or ellijitical, and this curve may diverge in any de- 
 I gree from its centre, but its nature remains unaltered. 
 
 All oniamental designs are composed of inclosed spaces or figures, 
 arising out of those modifications of the straight and the curved line, and 
 those figures, as already observed, are reducible to an elementary series, corre- 
 j spending in every respect to the natural scales of the elements of sound and 
 j, colour. 
 
 ! OF GEOMETRICAL FIGURES. 
 
 Regular curvilinear figures must have either one or two points as a 
 centre, and have no angles ; and regular rectilinear figures must he compo.sed 
 
ON THE PRINCIPLES OF ORNAMENTAL DESIGN. 
 
 of acute angles, right angles, obtuse angles, or an equal mixture of the 
 acute and obtuse kinds. Amongst these geometrical figures there are three 
 which are perfectly simple and homogeneous in the nature of their configu- 
 ration, and are, in every other respect, quite 
 analogous to the tonic, mediant, and domi- 
 nant notes of the diatonic scale of the musi- 
 cian, and to the three primaries, blue, red, 
 and yellow, of the colourist. These figures 
 are the circle, the triangle, and the square, 
 in the relative proportions in which they 
 are given in figures 1, 2, 3. 
 
 Fig. 2. Fig. 3. 
 
 1 have endeavoured to show in other works, that these figures, in such 
 proportions, bear an analogy to the three primary parts of sound in the 
 quantity of their circumference and perimeter. I have also demonstrated. 
 
 1 1 
 
 that if two circles be produced from one centre point, having in their cir- 
 cumference the relative proportions of 1 to 2, as in figure 1, these two 
 rectilinear figures, in the proportions in which I have given them, can be 
 placed harmonically between two such circles, as shown by the dotted lines 
 in figures 2 and 3. 
 
 The homogeneous simplicity of these figures consists, first, in the circle 
 being the most perfect curve, and composed of one line drawn round one 
 point, from which every portion is equidistant ; secondly, in the equilateral 
 triangle being composed of three sides, the smallest number possessed by 
 any rectilinear figure, which sides are equal, and each of which, as w’ell as 
 each of its angles, are equidistant from one point ; and thirdly, in the square 
 being composed of four equal sides and four right angles, each side and each 
 angle being also equidistant from one point, and the right angle itself being 
 homogeneous. 
 
 Without referring to analogy, it might be shown that from their con- 
 figuration, compared to the conformation of the eye, the effects of those 
 particular forms upon that organ entitle them to hold the situation amongst 
 other forms in which I have placed them. The pupil of the eye is circular ; 
 hence the rays, or pencils of light, which pass from external objects to the 
 back of the inner chamber, or retina, are most easily transmitted when the 
 object is circular. The circle is, therefore, not only geometrically the most 
 simple of the homogeneous forms, but naturally so in reference to the 
 
12 
 
 ON THE PRINCIPLES OF ORNAMENTAL DESIGN. 
 
 organ by which it is perceived. The square is the next most consonant form 
 to the eye, as its angles, although more in number, are less acute than 
 those of the triangle, and are the exact mean between acuteness and 
 obtusity. The triangle, of the three, is the figure which, from its being com- 
 posed of acute angles and oblique lines, exercises the most powerful in- 
 fluence on that delicate organ. 
 
 It is well known in chromatics, that the primary colour, blue, exercises 
 a softer influence on the eye than either of the other two, red and yellow ; 
 and this no doubt occurs from its being the most allied to darkness or black 
 of the three, and hence associating more intimately with the colour of the 
 retina itself. The colour that stands next to it as a primary in the solar 
 spectrum, is red, which consequently holds the situation that the triangle 
 does in my series of forms ; and this colour is well known to affect the eye 
 more forcibly than the yellow, which, in the natural series, is furthest re- 
 moved from the blue ; so that the more acute effect of the triangle upon 
 the eye, although holding a medial situation, like that of the note E upon 
 the ear, is quite in accordance with the analogy of acoustics and chromatics. 
 
 The scales by which harmony in sound and colour is produced, have, 
 besides the three primary parts, other four of a secondary kind by which 
 these are connected. So, to complete the scale of forms, it was necessary 
 to adopt figures corresponding to these, as the 2d, 4th, 6th, and 7th notes in 
 music do to the 1st, 3d, and 5th, and as the secondary colours, orange. 
 
 green, purple, and neutral, do to the primaries, blue, red, and yellow. The 
 figures T now adopt for this purpose are the rectangle, figure 4, the rhombus, 
 figure 5, the ellipse, figure 6, and the hexagon, figure 7. 
 
 All these figures, except the ellipse, occur naturally from the intersec- 
 tions of two lines produced between two circles of the relative proportions 
 
ON THE PRINCIPLES OF ORNAMENTAL DESIGN. 
 
 13 
 
 ✓ 
 
 already stated, and form, with the three primaries, a series embracing a re- 
 presentative of every variety of geometric figures, whether right-angled, 
 acutely angled, obtusely angled, or curved. But before showing how this is 
 performed, or giving a more ample definition of these figures, it will be re- 
 quisite, in order to arrive at a proper comprehension of the subject, to show, 
 in the first place, the manner in which angles are calculated. 
 
 OF ANGLES. 
 
 Rectilinear figures are named according to the kind and number of 
 angles they contain. These angles are of three kinds, as already explain- 
 ed, and are geometrically regulated by the circle in this way : — Its cir- 
 cumference is divided into 360 equal parts, called degrees, figure 8,* which 
 
 * At what period, or by whom, the circle was thus divided, I have not been able to learn ; 
 neither have I found, in such works as I have consulted upon the subject, any reason given for 
 the choice of this particular mode of division. Being desirous to find a reason, I was led to 
 investigate whether there existed in the number 360 any peculiarities that might have led to its 
 adoption in preference to any other. This I find to be the case in the manner in which the first 
 elementary numbers in harmonic proportion, 2, 3, and 5, are combined in producing it, as shown 
 in the following analysis : — 
 
 2)360 
 
 3)360 
 
 5)360 
 
 2)72 
 
 3)45 
 
 2)180 
 
 3)120 
 
 72 
 
 2)36 
 
 3)7? 
 
 2) 90 
 
 40 
 
 
 2)18 
 
 5 
 
 45 9 
 
 2)8 3)9 
 
 2)4 3 
 
 2 
 
 5 
 
 degrees are again divided into 60th parts, called minutes ; these, again, 
 into 60 seconds, and these seconds into 60 thirds, and this subdivision 
 may be carried on to any imaginable extent. The circle is divided 
 into two equal parts by a line drawn through its centre, and cutting the 
 circumference at each end, figure 9. This line is in geometry called a 
 
 Fig. 8. Fig. 9. 
 
 diameter, and wdien horizontally placed, is the base or groundwork from 
 which all angles arise. The half of the circle is called a semicircle, and the 
 half of the semicircle a quadrant. Any line drawn from the centre of this 
 diameter to the circumference of the semicircle is a radius, and will divide 
 it into two portions called arcs. If it cut the circumference in the centre, 
 these arcs will be equal, and the angles formed with the diameter on each 
 side of the radius will be right angles ; and as these arcs contain 90 degrees, 
 
14 
 
 ON THE PRINCIPLES OF ORNAMENTAL DESIGN. 
 
 right angles are called angles of 90®, figure 
 10. But if the radius touch the circum- 
 ference at any other point than the centre, 
 two different angles are formed ; one an 
 18 U acute angle, and the other an obtuse angle, 
 because the one arc contains fewer, and 
 the other more than 90°, as shewn in 
 figures 1 1 — 12. Upon this division of the 
 
 Fig. 11. Fig. 12. 
 
 circumference of the circle depends the character of every straight line, as 
 well as every rectilinear figure, and the explanation here given wdll make 
 what follows regarding the nature of the primary figures, and the harmonic 
 progression of forms, more easily understood by those who have not studied 
 geometry. 
 
 OF CURVILINEAR FIGURES. 
 
 The circle itself, as already shown, is, in the parts that compose it, the 
 most simple aud homogeneous of all forms. Its secondary is the ellipse, 
 also a perfect curve, because it is a line in all its parts equidistant from one 
 or other of two points, and necessarily uniting its beginning and end at the 
 same point. It is heterogeneous, for these points may be placed near or 
 apart ; but the figure described by their joint radii will still be an ellipse, 
 however much it may resemble a circle from the closeness of its two centre 
 points, or, on the other hand, a straight line from their separation. These 
 points are called its/oa ; and if they remain in the same position while the 
 line which forms the circumference is increased, the ellipses thus formed will 
 continue in appearance to approach the proportions of the circle, but, al- 
 though produced to infinity, can never form that particular figure. It has 
 consequently two diameters, the longest of which is called the transverse 
 diameter, and the shortest the conjugate diameter, as shown in figure 6, 
 on which A B are the foci^ C D the transverse diameter, and E F the con- 
 jugate diameter. It will be show'n in another part, that although this 
 figure can be produced in every variety of proportion, from the straight line 
 to the circle ; yet, as it possesses the most simple kind of variety of parts 
 which constitute the first elements of proportion, there are certain rules for 
 its formation which agree mathematically with the principles of geometric 
 
 Fig. 10. 
 
ON Tin-: PR I NOT I’LES 
 
 beauty, and wliich entitle the one here given to be termed the ellipse, in 
 contradistinction to other varieties of the same figure. In this proportion 
 it is also entitled to be the key of the secondary series of geometrical 
 figures, and to produce within its circumference the rectilinear figures of that 
 class. The only other curve that can produce a form or figure useful in 
 the arts of design is the spiral : this curve, as well as that producing the 
 circle and ellipse, is a real unmixed curve ; and although it can form no 
 figure of itself, is of much importance in the arts of ornamental design in 
 producing the volute. It is a curved line, receding gradually from a focus 
 or centre, figure 13. Its centre may be 
 a point, a circular figure, or an ellipse, 
 and these may be large or small, or its 
 aberration may be in any degree ; its di- 
 rection still forms a spiral line, and tlie 
 figure it produces when closed by another 
 line, a volute. There are various other 
 curved lines, which, although inapplicable 
 in the arts of design, are of much import- 
 ance in science. They are the cycloid, the parabola, the hyperbola, and 
 others. But all these I look upon as compounds. For instance, the cycloid 
 is the mixture of a straight line and a circle ; for during the formation of 
 the circle, by the revolution of a radius arouinl its centre point circularly, 
 
 0 R N A M E N T A L L) E S I ( i N . 
 
 15 
 
 that point is traversing a straight line. If tlie revolution were stopped, and 
 the progress of the radius continued, the ends of the radius would produce 
 two parallel lines. On the other hand, if the progress were stopped, and 
 the revolution allowed to proceed, one end of the radius would describe a 
 circle. But this curve cannot of itself enclose a space or produce a figure. 
 
 The parabola, in the same way, is the mixture of an elliptic curve and 
 an angle ; or, it may be termed, an ellipse formed upon a definite and two 
 indefinite points, both acting at the same time upon the formation of the 
 curve. 
 
 The hyperbola appears to be a circular curve, having also one definite 
 and two indefinite points, which causes it to continue to approach the straight 
 line with which it is associated, as the ellipse has been shown to recede 
 from it. 
 
 OF QUADRILATERAL RECTANGULAR FIGURES. 
 
 The square is homogeneous in its parts, none of which can be altered 
 without destroying its form. The parts are, as already stated, four straight 
 lines of equal length equidistant from a centre, and uniting at their extre- 
 mities in four right angles, which are likewise equidistant from the same 
 centre, and being of 90’ each, make up the full number 3G0 contained in 
 the circumference of the circle. When a quadrilateral rectangle has tu'o ot 
 

 1C ON THE PllINCIPLKS OF 
 
 its opposite sides longer than the other two, it is called an oblong or right- 
 angled parallelogram ; and every rectangle of this kind, from a perfect square i 
 to a straight line, is so, whatever may be the proportion between its length ; 
 and breadth. In the proportion of this figure, therefore, there is the same I 
 latitude that exists in regard to the ellipse ; and as geometricians have given j 
 no rules by which to distinguish t/w parallelogram or oblong from the in- i 
 numerable series that lie between the square and the straight line, it is of : 
 importance to fix some rule for the formation of one whose proportions may 
 entitle it to that distinction. This I shall attempt in its proper place, and 
 here proceed with a definition of the other primary, and the figures that 
 are allied to it. 
 
 OF TRIANGULAR FIGURES. 
 
 The equilateral triangle is the proper triangle ; it is, like the other 
 primary figures, homogeneous in its parts, being formed of three straight 
 lines of equal length, equidistant from one point or centre, and by their 
 union producing three acute angles, also equidistant from the same point. 
 Like the square, it cannot be altered in any of its parts, without destroying 
 its form and altering its character. Each of its angles are 60°, which toge- t| 
 ther make J 80°, being half the number contained in the circumference of '■ 
 the circle. 
 
 ORNAMENTAL D E S I G N. 
 
 There are various other triangles, some of which have one right angle 
 and two acute angles ; others, one obtuse angle and two acute angles. But 
 thev cannot have less than two acute angles, or more than one right or ob- 
 tuse angle ; and, whatever their varieties in other respects may be, their 
 three angle.s make up 180°. If two straight lines of the same length meet 
 at an angle of 60°, whatever their length may be, a third .straight line join- 
 ing the other two ends will produce an equilateral triangle. 
 
 The equilateral triangle has for its secondary the rhombus, which may 
 be termed a perfect mixture of the triangle and square. The ellipse is the 
 secondary to the circle, by having two foci, while the circle has only one. 
 The secondary to the square is removed from that figure by having two ol 
 its sides shortened, while the number of its angles and the direction of its sides 
 are the same. But the rhombus is removed from the equilateral triangle 
 by being two figures of the same kind placed together, which two triangles 
 produce a quadrilateral figure. Two of its opposite angles are 60°, and the 
 other two are 120°. It has, therefore, two acute and two obtuse angles, 
 which, put together, are e(iual to four right angles. It is the only figure 
 that can occur within the circle, having an equal number of acute and obtuse 
 angles. It may be shortened until its angles be nearly right angles, or it 
 may be lengthened until it approaches the straight line so closely that its 
 figure cannot be distinguished, and it therefore possesses the peculiarities of 
 the other secondary figures. 
 
 
ON THE PRINCIPLES 
 
 OF POLYGONS. 
 
 Although this term applies to all figures having more sides than one, 
 yet those whose sides exceed four, arc generally denominated polygons ; and 
 all regular rectilinear polygons of this kind are consequently obtusely angled. 
 The hexagon has been adopted in the series as the representative of this 
 class, from its being the first regular figure of the kind that occurs from the 
 intersections of the dominant lines, as shall presently be shown. It is tlie 
 figure that approaches nearest to the configuration of the circle of any recti- 
 linear plane figure that can be joined together in any number by its sides. 
 As regular polygons increase in the number of their sides, they can scarcely 
 be distinguished from the circle. 
 
 OF THE GENESIS OF THE SERIES. 
 
 The five rectilinear figures, which, with the circle and ellipse, compose 
 the whole series, are generated in their proper relative proportions, between 
 two circles bearing to one another in circumference the ratio of 1 to 2, 
 and in area tliat of 1 to 4. The perfect square is the dominant of the series 
 of which the circle is the tonic ; and between these two figures there exists 
 a curious reciprocity in the division of the perimeter of the one, and the 
 circumference of the other, into the harmonic parts that produce the series, 
 which T sliall here explain. 
 
 0 R N A M E N 'f A L DESIGN. 
 
 17 
 
 Let the perimeter of a square inscribing a circle be divided into sixteen 
 equal parts, with lines drawn from those divisions at right angles across 
 the area of the square ; and it will be 
 found that the circumference of the circle 
 is thus divided into twelve equal parts. 
 
 Let lines be drawn from the points at 
 which the circumference of the circle is 
 cut by the traversing lines to the points 
 at which It is in contact with the peri- 
 meter of the square, and the whole series 
 of rectilinear figures will thus be pro- 
 duced, figure 14. 
 
 These lines form right angles with the sides of the exterior square, 
 angles of 30° with any radius that meets them from the centre of the circle, 
 and angles of GO" with the lines drawn to the point of contact, and they 
 inscribe the inner circle by a square having the ratio to the outer square of 
 1 to 2 in perimeter, and 1 to 4 in area. 
 
 If each of the four sides of any rectangle be divided in this manner — 
 that is, into 4 — the ellipse which it inscribes will be harmonically divided into 
 four parts by the points of contact, each of which will be subdivided by parallel 
 lines passing through the area of the oblong into three proportionate divi- 
 .sions ; and by uniting the jioints of contact with the points oT intersection, 
 

 iwmsi-^mnm 
 
 r;^vy 
 
 18 
 
 ON THE PRINCIPLES OE ORNAMENTAL DESIGN. 
 
 a series of rectilinear figures will be produced, inscribed by the ellipse, and 
 leaving an area in their centre capable of containing another ellipse of pre- 
 cisely the same proportions and half the circumference of the first. This 
 same process may be performed within any rectangle ; and the proper angles, 
 obtuse and acute, as well as the proper curve belonging to any rectangle, 
 either vertically or horizontally, thus accurately detcrinined, as shall after- 
 wards be shown. But, in the next place, it will be requisite to give some 
 account of the harmony of geometry, which may justly be termed the 
 primary cause of beauty in every ornamental design. 
 
 OF THE HARMONY OF GEOMETRY. 
 
 The circle, as already shown, is geometrically divided into 3(10 degrees, 
 See . ; and I shall endeavour to prove, that, in the division of those degrees 
 by the harmonic ratios, the principle of geometric beauty or proportion lies. 
 
 In the first division by two, which determines the octaves in sound, the 
 diameter of the circle or horizontal line — the base of all geometrical figures 
 is produced. The second octave gives a radius perpendicular to it, pro- 
 ducing the right angle of 90° ; and the third, the angle of 45°, which is the 
 diagonal of the primary square. We have thus the first elements of figure ; 
 and this division by two gives the first harmonic ratio. Figure 15. 
 
 The next harmonic division is by three ; and when produced upon each 
 
 Fig. m. 
 
 1190 
 
 of those parts it falls upon the number 240°, 120°, and G0°, (Figure IG;) 
 and the lines produced between the first and the second, and between the 
 second and the third of these dominant divisions, arc those which, being 
 repeated from each twelfth division of the circle, will produce, by their in- 
 tersections within it, the diagram which contains the whole series of recti- 
 linear figures, and which has been already referred to. The remainder of 
 those divisions will be better understood by what follows regarding rect- 
 angles. 
 
 Rectangles only differ from one another in their proportion — that is, 
 the ratio that their length bears to their breadth. This proportion is de- 
 termined by one measurement, which is the diagonal. The difference be- 
 tween the various kinds of angles has been already explained. It has been 
 shown that the angle of 90’ is the right angle ; and that all the angles 
 
ON THE PRINCIPLES OF ORNAMENTAL DESIGN. 
 
 10 
 
 having more degrees are obtuse, and that those having less are acute. The 
 diagonal, by which the proportion of a rectangle is determined, is a line 
 drawn from the vertex of one of its angles to that which is opposite, and 
 every such diagonal must form two acute angles — the square being the only 
 figure of this kind in which these angles are the same, namely, 45°. This 
 angle is therefore to the angle of 90°, as 1 to 2, and they consequently are 
 in the harmonic ratio of octaves. As no diagonal of a rectangle can be an 
 obtuse angle, all variety of this peculiar line must be found within the 
 quadrant. 
 
 The oblong is simply a modification of the square, and this modification 
 is regulated by the number of degrees in the angle of the diagonal, which, 
 when the oblong is placed vertically, must exceed 45° ; and, when horizon- 
 tally placed, must be under that number. If, therefore, a series of these 
 diagonals be produced by a harmonic division of the degrees that occur 
 upon a quadrant — that is, by 2, by 3, and by 5 — the rectangles formed upon 
 them must bear a haimonious relation to one another. 
 
 The rectangle is the dominant figure in every series, and the diagonal 
 of the homogeneous one (45°), arises from the division of the quadrant by 
 2. The second division by 3, gives the vertical diagonal of the first ob- 
 long, 60°, and relates to the right angle as 2 to 3 ; and the third division by 
 5, gives the vertical diagonal of the second oblong, 72°, which is in the rela- 
 tive proportion to the right angle of 4 to 5. 
 
 Fiy. 17. 
 
 Fig. 19. 
 
 The square being homogeneous, has only one proper position, in which 
 its diagonal is always 45° ; the other two rectangles being heterogeneous, 
 have two, a vertical and an horizontal. Their vertical diagonals, as shown 
 above, are respectively 60° and 72°. Their horizontal diagonals are there- 
 fore 30° and 18°. The first of these latter numbers, 30°, is relatively to its 
 vertical number, 60°, as 1 to 2, and is consequently in the ratio of an octave ; 
 and being relatively to 45° as 2 to 3, it is in the harmonic ratio of a fifth, or 
 dominant to that diagonal. Its relation to the tonic, 90°, is that of a musi- 
 cal twelfth, being as 1 to 3. 
 
 The second number, 18°, is relatively to its own vertical number, 72°, 
 as a fifteenth or double octave, being as 1 to 4. It is to the tonic, 90°, as a 
 seventeenth, being relatively to it as 1 to 5 ; and is the third degree to the 
 diagonal, 22' 30', to which it relates, as 4 to 5. 
 

 
 ON THE PRINCIPLES OF ORNAMENTAL DESK.'N, 
 
 It has been shewn elsewhere,* that the three leading harmonics, agree- 
 ably to the established laws of acoustics, are produced by portions of the 
 monochord relating proportionally to one another, in the first instance, or 
 within an octave, as 1 to 2, 2 to 3, and 4 to 5, and are called the 8th, 5th, 
 and 3d degrees of the diatonic scale. But that w'hen the portions of the 
 monochord are as 1 to 2, 1 to 3, and 1 to 5, the hannonics of an 8th, a 
 12th, and a 17th, are produced. This is, therefore, precisely the case in re- 
 gard to the formation of these three rectangles. The angles of their diago- 
 nals, in the first instance, relate to the right angle as 1 to 2, 2 to 3, and 4 to 5. 
 But when the horizontal, instead of the vertical diagonal, is employed in the 
 construction of the two latter figures, the three will be found to relate to 
 the right angle as 1 to 2, 1 to 3, and 1 to 5. The harmonic ratios are 
 therefore in this instance quite analogous. 
 
 I have already shown that if each side of a square, be divided into four 
 equal parts, and lines drawn from those parts at right angles across the 
 area of the square, these lines will cut the circumference of an inscribed circle 
 into tw'elve equal parts, and by uniting those intersections, the first scries 
 of figures is produced. Now this same reciprocity exists between an oblong 
 rectangle and its inscribed ellipse, the latter being harmonically divided by 
 
 * “ Proportion, or the Geometric Principle of Beauty Analyzed," where this part of the 
 subject is treated at length. 
 
 the same process, and the intersec- 
 tions united in the same way, a 
 secondary series of figures will be 
 generated, and the process may thus 
 be continued harmonically to any 
 imaginable extent. Figures 20 and 
 21 . 
 
 When Plato endeavoured to ex- 
 plain the nature of the atomic con- 
 
 Fig. 20. 
 
 struction of the elements of the material world, he did so by saying, that 
 when the Deity began to adorn the universe, “ He first of all figui'ed with 
 forms and numbers, fire and earth, water and air,” and proceeds to show 
 that, as every body possesses profundity — as every depth comprehends the 
 nature of a plane — and as the rectitude of the base of a plane is composed 
 from triangles, those figures must constitute the first principle in the con- 
 struction of the elements. He then enumerates three triangles as being re- 
 markable for their beauty, and describes them as that which forms the half 
 of the square, and is isosceles ; a scalene triangle, such as forms the half of 
 an equilateral ; and another scalene triangle, which he describes as having 
 its longer side trebly greater in power than the shortest. Now these are 
 the identical triangles that arise out of the division of the quadrant by two, 
 by three, and by five, as .‘^hown in figures 17, 18, and 19, and that produce 
 
ON THE PRINCIPLES OF ORNAMENTAL DESIGN. 
 
 21 
 
 when joined two and two, the dominant rectangles, namely, the square, the 
 oblong, and the secondary oblong. 
 
 I now presume that I have pointed out amongst the infinite multitude 
 of geometrical figures that exist, such a series as may be truly termed the 
 elements of Form, and that these elements correspond in their number, and 
 in their relative effects upon the sense to which they are addressed, with 
 the elements of colour and of sound, inasmuch as their combinations are 
 capable of producing every variety of beauty arising from geometrical sym- 
 metry or proportion. I have likewise shown that these elements are the 
 result of a demonstrable and certain process, namely, the application of the 
 harmonic ratios of numbers to the division of a circle. Farther, I have 
 just shown that the series thus produced, proceeds from primary to second- 
 ary, and from secondary to tertiary, agreeably to the Platonic theory of the 
 atomic form of the elements. 
 
 In doing all this, however, I have only made one step in the elucida- 
 tion of my subject, and that is, the production of an alphabet for ornamental 
 design, or rather a gamut of visible harmony. 
 
 It may be requisite here to state, that this gamut has been before the 
 public for upwards of two years, and although probably not inve.stigated 
 adequately to the importance of such a step in the arts of design, yet the 
 attempt thus to establish fixed principles for geometric proportion and 
 harmony, has met in some high quarters with an approval so flattering, as to 
 
 induce me to treat it as in some measure authenticated, and now to attempt 
 its application in the art of ornamental design. 
 
 When the teacher of language exhibits to his pupil the alphabet, he en- 
 deavours to make him acquainted with the nature of the letters, and their 
 relative effect upon one another, in order that he may comprehend the 
 mode of their combination in the simple words which form the first lessons 
 in reading. In like manner the teacher of music, when he lays the gamut 
 or scale of seven musical notes before his pupil, explains to him that he 
 must not only be able to sound them upon an instrument, but also to under- 
 stand the relative effects that they have upon one another, when combined 
 in harmony, or when arranged in succession or melody. This he does like- 
 wise by the most simple passages, knowing well that the more intricate and 
 difficult can only be understood after long and assiduous study. But when 
 this apparently simple matter is accomplished, either as regards the alphabet 
 or gamut, a permanent and secure foundation is laid, for any degree of 
 knowledge in these respective branches of education, that may be consistent 
 with the talents and opportunities of the pupil. And it is perfectly under- 
 stood that the letters of the alphabet, and notes of the gamut, are capable, 
 when properly used, of producing an infinite variety of beautiful effects, 
 intellectual and sesthetical. 
 
 My object in this Essay is to carry the pupil in ornamental art as far 
 in that peculiar branch of education, as the teacher of language has carried 
 
22 
 
 0 .N THE PRINCIPLES OF ORNAMENTAL DESIGN. 
 
 his pupil when he has enabled him to spell, and probably to construct a 
 very simple sentence ; or as the teacher in music, when he has enabled the 
 tyro in that art to understand the nature of a chord. This degree of in- 
 struction may not only enable latent talent to develope itself, but, if ge- 
 nerally disseminated as a branch of polite education, would be the means of 
 enabling the public to appreciate the harmony which addresses itself to the 
 eye in forms and figures as accurately as they do that which is addressed 
 to the ear in the skilful compositions of the accomplished musician. 
 
 On this subject an elegant writer justly remarks : — “ Were every man 
 a judge and appreciator of beauty, then indeed might wo expect forms of 
 loveliness and grace to pervade the regions of domestic and every-day life, 
 to replace in our streets the expensive ugliness of our street decoration — in 
 our homes the vulgarities of ornamental deformity — and hi our churches the 
 distortion and anomalies of meretricious decoration.* 
 
 The various modes of combining the elementary series of geometrical 
 figures in the production of visible melody and harmony shall now be ex- 
 plained. Ill doing so, however, it will be requisite for me to remind the reader, 
 that I am not attempting an elucidation of any kind or style of ornament 
 in particular, but of principles which ought to regulate all compositions of 
 lines and figures, in order to make them ornamental or pleasing to the eye. 
 
 * Ailiciiic iiii, N'>. 81j. |i. ,}4J. 
 
 considering every ornament as a plane surface, because it is only as such tliat 
 it is depicted on the retina of that organ. 
 
 Every figure, viewed in this way, is supposed to be surrounded by a 
 line, technically called its outline, and when two figures arc placed in con- 
 tact with each other, or so joined as to overlap, their outlines enter into 
 combination, forming various continuous curved, angled, or mixed lines, 
 Avhich are pleasing or otherwise, according to the modes in which they 
 unite, and the forms they thus produce. 
 
 Lines, like notes in music, must, in their combinations, if contrasted at 
 all, bo so by proper intervals, or distinct differences. Wliile in their com- 
 binations in melody or succession, they may change by smaller degrees like 
 a chromatic passage in musical composition. 
 
 Geometrical figures of the same kind and size combine with each other, 
 that is, circles with circles, squares with squares, &c., and produce new 
 figures and lines. Such figures and lines have to each other a degree of 
 similarity that distinguish them as a class. So also may figures of a dissi- 
 milar kind be united in harmony, producing other figures useful in orna- 
 mental art. I shall commence the illustration of this part of my subject 
 with the circle. 
 
 OF COMBINATIONS OF THK CIRCULAR CURVE. 
 
 The circle is the j)nmarv, most comprehensive, and must perfect of 
 
ON THE PRINCIPLES 
 
 curvilinear figures ; it is remarkable for its perfect unity and symmetry, and 
 its modes of combination give rise to lines and figures of gi'eat beauty ; but 
 it wants within itself that peculicar constituent of beauty — variety. By the 
 external mode of combining circles, the most simple kind of waved or ser- 
 pentine line is formed, as also several of the figures in Gothic tracery, and 
 by the internal mode all other figures of the same kind are produced. The 
 points of union in arcs of circles forming waved lines, must be in the same 
 straight line, and they must be equal parts of circles formed by the same 
 radius. A series of those lines are given in Plate 1 * of the illustrations. 
 In figure 1, will be found that arising from the union of two semicircles, as 
 also from arcs of a fourth. In figure 2, those produced by arcs of a tliird, 
 and a sixth ; and in figure 3, those produced by arcs of a fifth, and of two- 
 fifths. This division of the circle by the harmonic numbers 2, 3, and 5, seems 
 to produce all the distinctive varieties of what may be termed the homoge- 
 neous waved line. In this plate by combining a number of circles of the 
 same radius upon this harmonic principle, various characteristic figures are 
 produced, a few of which are pointed out by being shaded. 
 
 Circles, although of the same size, will, when properly combined, give 
 rise to a great variety of figure, of which one example is given in Plate 2. 
 
 * The Plates uow commence a new series, being illustmtive of the Es^ay, ami are tliere- 
 i'ore tlifterently numbered from tlioso of tlie dia|jer derign.'i. 
 
 || In this diagram, the diaper designs numbered XXH'., XXV., and XXXII., 
 Ij will be found, besides many others of a similar character, all equally re- 
 ! markable for originality and .symmetry. 
 
 The circular curve is uniformly employed in Gothic tracery, and in 
 such works circles of various sizes are often combined, giving rise to many 
 beautiful figures and devices in this branch of ornamental design. But as 
 many excellent and elaborate works have already been, and are now publish- 
 ing, on the subject of Gothic ornaments, I do not consider it requisite to 
 give any examples here of this mode of combination, and shall therefore 
 [I proceed to the secondary curvilinear figure. 
 
 'i 
 
 I: 
 
 !i OF COMBINATIONS OF THE ELl.lPTIC CURVE. 
 
 II 
 
 II 
 
 ij The ellipse of all geometrical figures is the most beautiful, and most 
 
 useful in the arts of design. As just observed, the circle, although remark- 
 able for unity and symmetry, wants within itself that essential constituent 
 of beauty, variety. This the ellipse possesses in an eminent degree. Its 
 j outline being formed by two radii, one of which is continually decreasing, 
 
 ' while the other is increasing, it imperceptibly varies from an oblate to an 
 : acute curve. The variety of proportion amongst individual figures of this 
 1 land is very great, extending from the circle down to the straight line ; lienee 
 
24 
 
 0'S THE PRliNCIPLES OF ORNAMENTAL DESIGN. 
 
 the necessity of fixing on two as primary and secondary of the class. (See 
 ante figs. 20 and 21). 
 
 The waved or serpentine lines produced by the combinations of this 
 figure, while they possess the most perfect mathematical uniformity, are at 
 the same time rendered truly beautiful, by partaking of the variety already 
 alluded to. These lines prevail in the contour of the most pleasing scenery, 
 composed of hill and valley — they form the characteristic figures of many 
 of the most beautiful productions of nature in the animal and vegetable 
 kingdoms, and are a leading feature in the finest specimens of the ornamental 
 designs of the ancients. 
 
 Although I have somewhat systematised the waved line of the circular 
 curve, yet, from its liomogeneous nature, equal arcs of any size, from a semi- 
 circle downwards, may be joined together in its production ; but it is not so 
 with that of the elliptic curve ; this line must be subjected to a systematic 
 division in forming continuous flowing lines, as exemplified in Plate 3. 
 
 In a former part of this Essay I promised to show that the ellipse, the 
 proportions of which arise out of the harmonic division of the circle already 
 e.xplained, is entitled to be termed the primary of its class, or in contra- 
 distinction to all other figures of the same kind, the ellipse. Perhaps I 
 cannot more clearly do this than by showing its intimate connexion with the 
 two primary rectilinear figures — the equilateral triangle and homogeneous 
 square. Plate 3, figure 1. exhibits it inscribing two equilateral triangles 
 
 united by one of their sides, and thus dividing its circumference into four 
 equal arcs. Those two triangles so joined also form the rhomb of the series. 
 When thus divided the four arcs are similar, but when divided by the angles 
 of an oblong, formed by the union of two halves of an equilateral triangle 
 united by their longest sides, the arcs are of two different kinds, oblate and 
 acute. Those two modes of dividing the circumference of the ellipse into 
 four, unite in dividing it harmonically into eight. Thus the same figure 
 which divides the circumference of the circle harmonically into three or six 
 arcs, divides the ellipse, as above shown, harmonically into four or eight. 
 Figure 2 of the same plate, exhibits the connexion of the ellipse with the 
 homogeneous square, two of which, when united by one of their angles, 
 divide the circumference of the ellipse into six arcs, at the same time 
 forming within its circumference another square, whose area is equal to 
 that of both the other two. Again, it will be observed, on examining this 
 figure, that a right-angled isosceles triangle, or half of a square, divides this 
 ellipse harmonically into three arcs, and consequently two of these divide it 
 into six arcs. These divisions occurring exactly between those already made 
 by the angles of the two smaller squares, divide the circumference harmoni- 
 cally into twelve parts. Thus we find that the harmonious division of the 
 ellipse by three and by four, reproduces the two homogeneous rectilinear 
 figures by an inverted process, the division by thi*cc producing the square, 
 and the division by four the equilateral triangle. Those who wish to in- 
 
/).R Mat/ /nv! .Vaeliirt^VacflonaldLiHi 
 
ON THE PRINCIPLES 
 
 vestigate these peculiarities farther, will find the subject treated more com- 
 prehensively ill my works on Form and Proportion.* 
 
 Figures 3, 4, 7, and 8, exhibit the only mode in which an ellipse can 
 be united to produce by arcs of a fourth part a continuous symmetrical waved 
 line. And the sixth portions that lie parallel to the transverse and conju- 
 gate diameters are the only others that, according to these divisions, will so 
 unite. 
 
 The secondary ellipse has also its peculiarities, which, independently of 
 the mode in which it is generated, arc eepially remarkable. It is divided 
 into four equal arcs by two of the triangles arising out of the division of the 
 quadrant by five, united together by their shortest sides upon the conjugate 
 diameter of the ellipse, and these divisions are each subdivided into two by 
 an oblong formed of two halves of a similar triangle, united by their longest 
 sides, — See figure 5. Figure C shows it divided into six arcs by four equila- 
 teral triangles ; the angle of 60° acting upon it in precisely the same way 
 as the angle of 90° acted upon the primary ellipse, and the angle of 36° in 
 the same way as the angle of 60° did on the same figure. 
 
 These coincidences are simply as follow : The figure arising from the 
 division of the circle by three, gives the binary division to the first ellipse. 
 
 * Piiblislied by Messrs Blackwood and Sons, Pall Mall, London, and 45 fie<»rge Street, 
 Ivlinlmrgh. 
 
 ORNAMENTAL DESIGN. 
 
 while the figure arising from the division of the circle by four, gives the ternary 
 division to the same figure. The figure arising from the division of the circle 
 by five, gives the binary division to the second ellipse, while the figure arising 
 from the division of the circle by three, produces a resolution of the whole 
 by a ternary division of the second ellipse. Therefore, I consider them the 
 second and third of the elementary curvilinear figures, and their establish- 
 ment as such is a matter of some practical importance in the arts of design, 
 as I shall now endeavour to show. 
 
 Figures 9 and 10 are waved lines, which being perfect in themselves, 
 cannot by their repetition upon the same straight line, be continued harmo- 
 niously, yet they are the most beautiful of their class, embodying, as they 
 do, all the variety of the ellipses by which they are produced. 
 
 This peculiar curve, as already observed, seems to prevail in the out- 
 line of all objects in nature that we esteem the most beautiful. In the 
 vegetable kingdom, it is particularly conspicuous in the leaves of plants, and 
 in every kind of foliage ; while its prevalence as a constituent of beauty in 
 the Animal Kingdom is equally remarkable. 
 
 Plate 4, exhibits a few of the systematic modes of combining the first 
 and second ellipses, by which figures are produced typical of wliat are gene- 
 rally acknowledged to be beautiful in the forms of leaves of plants, and petals 
 of flowers. 
 
 Figure I is composed of two of the first ellipses united at their ends 
 
ON THE PRINCIPLES 
 
 upon an angle of 45°. Figure 2 , of two of the same upon an angle of 60°, 
 and figure 3, of two of the same upon an angle of 72“. Figures 4, 5 , and 
 G, are produced by two similar ellipses, united at their centres upon angles 
 of 72 , CO , and 45“. Figures 7, 8, 9, 10, 11, 12, are similar combinations 
 of the second ellipse. Figures 13, 14, 15, IG, and 17, are harmonious com- 
 binations of other portions of these ellipses, showing, that by varying the mode 
 of union, an endless number of other figures of this kind might be produced. 
 
 Plate 5, figure 1, is an outline of the principal muscles of the human leg, 
 carefully drawn from Albinus’s work,* and on looking at this figure, it will 
 be observed that every fine in the configuration of these muscles forms an 
 aic of the second ellipse. The student who will take the trouble of a farther 
 investigation of this part of tlie subject, will find the same curve pervading 
 not only the outline of the other muscles of the human body, but that of the 
 bones themselves. The lower limb has been selected as an example, in pre- 
 ference to any other part, because it exhibits the largest and best developed 
 class of muscles. 
 
 The other examples on this plate have been selected at random from 
 bir William Jardine’s Naturalist’s Library. The horse subjected to the 
 elliptical outline in figure 2, is copied from Plate VIII., vol. xii. of that work, 
 
 * Tables of the Skoletoa and JIuscles of the Human Body. By Bernard Seigeficld Al- 
 binus. Kdinbnrijli, 1777. 
 
 OF ORNAMENTAL OESIGN. 
 
 and is called Bonaparte’s Arab ; I adopted it as apparently the most perfect 
 outline of that animal in the volume. The birds, figures 3 and 4, are the 
 i cuckoo and blackbird ; and the fishes, figures 5 and 6, a salmon and turbot, 
 
 aud are given as familiar instances, simply to show the universal prevalence 
 
 !j 
 
 |: of this cun-e in the configuration of the lower class of inhabitants of the 
 I earth, the air, and the waters. It may here be observed, however, that the 
 I more perfectly these correspond in their general outline to a harmonious 
 combination of the circumference of the ellipse, tlie more are they generally 
 ' esteemed beautiful specimens of their respective kinds. This is exemplified 
 in the striking contrast between figures 5 and G. 
 
 I These facts are of much importance to the artist, whatever branch he 
 
 i| professes, and I therefore consider this part of the subject eminently de- 
 j| serving of his attention, since it points to an apparent governing principle of 
 beauty which it would be well to study closely and assiduously, 
 jl We also find throughout Nature two opposite principles in operation in 
 the production of visible beauty, namely, uniformity and variety, and these 
 Ij mast consequently, to a certain extent, co-exist in every beautiful object. 
 
 }' In ornamental design especially, there can be no real beauty without uni- 
 foimiity amidst variety. A decorative ornamental design is seldom employed 
 I but as the part of some whole, especially the diaper, which is the most simple 
 ! of all, and only employed, as already observed, to enrich surfaces that might 
 otherwise lie tame and monotonous blanks. In this respect the diaper cor- 
 
Mem 
 
ON THE PKINCIPLES 
 
 rcsponJs to the minutia: of Nature — every moss-grown stone, the apparently 
 bare trunks of trees, the surfaces of individual leaves — are all found upon 
 examination, to be decorated and enriched with delicate and beautiful com- 
 binations, in which the variety appears infinite. When we examine the 
 higher and more apparent mathematical beauties of inanimate Nature, we 
 find a general uniformity amongst the leaves of the same species of plants, 
 as well as between the opposite sides of the same leaf ; even the trunks and 
 the branches of trees, when devoid of foliage, proclaim, by their uniform 
 similarity of configuration, the class to which they individually belong. Yet 
 there co-exists with this an endless variety amongst the individuals of every 
 species, both as to form and colour, so that the combined grandeur and 
 beauty of the forest, of the garden, and of the field, may be said to arise from 
 a compound ratio of uniformity and variety. 
 
 Principles similar to what I am endeavouring to elucidate, have been 
 insisted on by most lecturers and writers on high art, but I am not aware 
 that any attempts to systematise them have been made. Flaxman seems 
 to have felt that a ruling principle of harmony existed in forms in re- 
 gard to the curved line especially, for the only example he gives in his ex- 
 cellent lectures on Sculpture, is in reference to it. He says — “ One simple 
 instance only shall be given of opposition, and another of harmony, in lines 
 and quantities ; two equal curves set with either their convex or concave 
 faces to each other produce opposition ; but unite two curves of different 
 
 ORNAMENTAL DESIGN. 
 
 size and segment, they will produce that harmonious line termed graceful, iii 
 the human figure.” This is a facsimile of the example — 
 
 “ Opposition ) ( () 
 
 Harmony f. 
 
 Now, “ two curves of different size and segment” is not a very intelligible 
 definition. There can be no donbt of this great artist’s mind being natu- 
 rally imbued with every principle of beauty, therefore what he here meant 
 must have been such a line as may be produced by two quadrants of an 
 ellipse, as given in Plate III. figures 9 and 10. Hogarth’s “ Line of Beauty,” 
 of the application of which he has left us so many splendid e.xamples in his 
 works, is evidently the same combination of the elliptic curve ; and it was 
 probably from his “ Analysis of Beauty” that Flaxman took his example of 
 harmony. But Hogarth’s work is merely an assemblage of examples in 
 Nature and Art of the beauty of the waved line, and of the deformity arising 
 from its absence in artistical compositions, especially in reference to the human 
 figure. The only approximation he makes to the laying down of a general 
 principle, is contained in the following sentence : “ The way of composing 
 pleasing forms, is to be accomplished by making choice of variety of lines, 
 as to their shapes and dimensions ; and then again, by varying their situations 
 with each other by all the dilferent ways that can be conceived.” This is 
 but a loose principle of linear harmony, and could be tolerated only in 
 
L>8 
 
 ON THE PEINCIPLES 
 
 connexion with such excellent examples as he has collected and exhibited in 
 the two plates which accompany his “ Analysis.” 
 
 Having given examples of the prevalence of the elliptic curve, in what 
 are esteemed the most beautiful forms in Nature, and likewise shown that, 
 although apparently unacquainted with its precise geometric character, 
 Hogarth and Flaxman adopted it as the line of beauty and grace in the 
 high arts of painting and sculpture, I shall now attempt to show the mode 
 in ivhich It may elevate by its application the humble art of ornamental 
 design. 
 
 Plate C. figures 1, 2, 3, 4, and 5, are examples of the most palpable and 
 simple mode of such an application of this curve. The body of figure 1, it 
 will be observed, is simply produced by the combination of two ellipses upon 
 an angle of 45”, with other two upon a horizontal line, forming the neck. 
 Figure 2 is a similar combination upon an angle of 60”. The body of 
 figure 3 is a similar combination upon an angle of 72”, the neck being 
 formed of other two ellipses, united to these upon an angle of 18”. To these 
 are added other two ellipses, united at one of their foci upon the same ; 
 angle as the body. Figure 4 is produced by two ellipses united at one of ; 
 their ends upon an angle of 81°, the neck being formed by other two upon 
 
 an angle of 18°. Figure 5 is formed upon an angle of 45”, with a neck upon | 
 
 an angle of 16°. It may be as well here to remind the reader that, with 
 a view to simplicity, 1 calculate all angles within the quadrant, that is, I ' 
 
 ORNAMENTAL DESIGN. 
 
 imagine a vertical line raised upon a horizontal base, and from each end of 
 the horizontal line I calculate upwards. 
 
 Figure 2 of Plate 7, is the same as figure 1 of Plate 6., with this dif- 
 ference, that the curve of the neck intersects that of the body, instead of 
 touching it e.xternally. Figure 1 is two ellipses joined together at the end 
 of their conjugate diameters, which are upon angles of 36° ; their transverse 
 diameters being consequently upon angles of 54". The neck is formed of 
 two ellipses upon angles of 60”. 
 
 biguie 3, notwithstanding its small dimensions, is a composition arising 
 out of the union of four arcs of ellipses of the same size and proportions 
 used in producing the preceding seven. The faint lines upon it, as well as 
 upon all the elliptical examples, will show clearly the mode of combination. 
 
 These eight outlines are not copied &om ancient vases, but are simply 
 the result of a systematic combination of the elliptic curve. I mention this, 
 because they thus produce figures typical of all that we know of those much 
 admired productions of the ancient Grecians. 
 
 The almost infinite variety that might be produced by this means in 
 the form of every kind of domestic utensil, as well as ornamental vases, may 
 give some interest to this portion of my Essay ; the more especially, as we 
 sometimes find in periodical works dedicated to art, the most shapeless, 
 grotesque, and absurd productions of this kind exhibited in woodcuts, and 
 accompanied with eulogiums upon their beauty, evidently written by persons 
 
U J/./hj Im 
 
‘ 7 ^ 
 
ON THE PRINCIPLES OF 0 I! N A M E iN T A L D E S I C N. 
 
 as ignorant of what is truly beautiful, as the potter who produced the speci- I 
 men, and consequently calculated to mislead the public taste. 
 
 Plate 7. figure 4, is an outline of a Grecian vase of Parian marble, * 
 and of the finest workmanship, in the collection at the Villa Albani near 
 Rome. This I carefully traced from Tatham’s Etchings,* and applied my j 
 elliptical rule to it, and the result, as shown upon the figure, is a proof that 
 the Grecians at the period of their highest refinement, applied the elliptical 
 curve in a manner similar to that which I am attempting to elucidate. But, 
 indeed, I have scarcely ever met with any specimens of such works that did 
 not exhibit an intimate knowledge and systematic application of the geo- 
 metric principle of beauty, as well as of the elliptic curve. That this curve 
 is a principal constituent of beauty in outline, there can be no doubt, and 
 from investigations which I may at some future time submit to the public, | 
 I am led to believe that the curve which has been found to pervade every I 
 part of the outline of the Parthenon at Athens, even to the entasis of the I 
 column, is of this nature. ] 
 
 Plate 8. is a general combination of this figure, and in the diagram , 
 thus formed, will be found the outlines of the diapers XIX., XX., XXI., 
 XXII., XXVI., XXVIL, and XXXIII., as well as many others, which I 
 leave to the student to find out by his own ingenuity. 
 
 * Etcliings representing tlic best examples of Grecian ami Homan Arcliilcctural Orna- 
 ment, &:c. By C. Tiitliam. Lonflon, 1S26. 
 
 OF COMBINATIONS OF THE STRAIGHT LINE. 
 
 Figures composed of straight outlines are of comparatively rare occur- 
 rence in Nature, except in the crystallization of salts, acids, some minerals, 
 in the stems of some plants, and occasionally in the trunks of trees. The 
 whole .system of geometry, however, depends upon the straight line ; and 
 there can be no perfect composition of artistical' configuration without a 
 straight line entering into it, either in an understood or apparent manner. 
 For instance, the bend of every joint in the human frame, notwithstanding 
 the curvature of its outline, must be upon an axis of straight lines, which 
 form an angle at a point between the ends of the bones; a regularly 
 waved line must be concave and convex in the same straight line ; and 
 the ellipse itself owes its beauty to the circumstance of having a straight 
 line for its centre, which, when of the proper relative proportions, imparts 
 to it that perfect ratio of uniformity and variety already explained. 
 
 Figures composed of straight lines may be so formed as to possess in 
 their configuration that uniformity amidst variety that constitutes geometric 
 beauty, even when confined to rectangles ; and thus may a monotonous form 
 be converted into an ornamental design. This I shall attempt to illustrate 
 by a series of examples, commencing by exhibiting some errors which, 
 though not uncommon in practice, are sufficiently palpable when pointed out. 
 
30 
 
 {)y T H E P in NCI P 1. E6 
 
 O F O li N A M ]i N i' A L D E 6 1 G X. 
 
 Let us take, for example, tlie front of an edifice forming a horizontally 
 placed rectangle, and suppose it to be put down in a situation where the 
 upper or sky-line appeared tame aud monotonous from its not entering 
 into harmonious combination with any other set of objects. Suppose that 
 an attempt was therefore made to render it less so, but that this attempt 
 was restricted to the projection of other three rectangles. Now, let per- 
 fect uniformity be applied to this mode of improving the outline, and 
 we have figure 1. Plate 9. This is probably the first idea that would 
 occur to an untutored mind, but that inherent mathematical principle 
 by which external objects operate msthetically upon the understanding, 
 detects the want of the constituent of beauty, variety, while the dis- 
 proportion of the height of the additional rectangles is palpable and 
 offensive. They are therefore, as in figure 2, reduced to a proportionate 
 height, while the uniformity remains in every line but that which gave the 
 disproportion just alluded to. The next attempt would naturally be to impart 
 variety to these rectangles, and to the spaces between them, and supposing 
 that with this view they were divided harmonically with different lengths, 
 while in order to combine uniformity with this variety, they were loft all of 
 the same height, as in figure 3. This variety has, however, produced relative 
 disproportion amongst these projections, for the centre one, from its increased 
 length, appears too low. It would at first sight appear, that to make it 
 higher than the other two would destroy the requisite uniformitv, and so it 
 
 would were the height not increased by the infusion of another kind of 
 uniformity in place of that which is destroyed. The uniformity thus im- 
 parted must be in the diagonal of these projected rectangles, as shewn in 
 Ij figure 4, where these diagonals will each bo found to be upon an angle 
 of 10 . Here we have at last in this simple example proportionate variety 
 j in the lengths of the various parts, combined with perfect mathematical 
 uniformity in the diagonals of the projections, which uniformity adds the 
 proportionate variety to their height ; the former thus lying concealed as in 
 many beautiful objects in nature, while the variety is apparent to the most 
 casual observer. In this last figure the division of the lengths is changed 
 from that of figure 3, being now in the ratios of 1, 3, 6. and 8, instead of 1, 
 2, and 4. 
 
 The combined harmony of rectangles differs from that of their union in 
 outline, in so far as they are then supposed to be inscribed in a general out- 
 line with which they must harmonise, and w'ithin which they must be 
 in harmony amongst themselves. Such combinations are the rectangular 
 openings in the fa9ade of a building ; the pannelliiig of the ceiling, walls, 
 doors, or window-shutters of an apartment. These may all be made to form 
 ornamental designs, by attention to the harmony of their diagonals relative- 
 ly to one another, as well as to the spaces that surround them ; or they may 
 turn out, as they often do, heterogeneous and discordant mixtures of this par- 
 ticular figure. In plate 10, I have given a harmonious combination of ho- 
 

HZ HlV.i'l 
 
PI.ATi: XII 
 

PIATE 15. 
 
 /} H Jfnu Junf ^i hnt.fJhnlonaUZd^. 
 
ON THE PIU NCI PEES OF ORNAMENTAL DESION. 
 
 mogeneous squares. The largest has a perimeter of fourteen inches, within 
 which are placed other two with areas in the ratio to it of 1 to 2. Within 
 these again are placed other two, having each a ratio to the first of 1 to 4 in 
 area, and 1 to 2 in perimeter. From the intermediate squares being joined at 
 their angles, instead of the outer ones, a species of variety is given, arising 
 from the excess in the ratio of their perimeter relatively to that of their 
 area. The arrangement of rectangles of various proportions is, however, a 
 more complex kind of ornamental design, as shall afterwards be shown. 
 
 The combinations of straight lines forming acute and obtuse angles fol- 
 low the same principle in their arrangement, as just explained in regard to 
 the rectangle. Whatever may be the variety of size amongst angular projec- 
 tions, arising from the same straight line in a composition, there ought to be 
 uniformity in the degrees of the angle, as shown in Plate 11. fig. 1. This 
 is more apparent when combined with the proportionate rectangles, fig. 2. 
 It is the same with acute as with obtuse angular projections in this respect. 
 They must be of the same angle when arranged upon the same straight line, 
 for the harmony depends as much upon the imaginary figure generated be- 
 tween two forms placed together, as upon the forms themselves ; thus two 
 projecting triangular figures of different degrees of angle, when placed upon 
 the same straight line, generate the discordant figure of an irregular trape- 
 zium, by an imaginary line between them parallel to the base. 
 
 In Plate 12, I have given a combination of the equilateral triangle upon 
 
 the principle already explained in regard to that of the homogcjieous rect- 
 angle. 
 
 Plato 13 exhibits a much more difficult combination than any yet 
 given. It is that of the two primary rectilinear figures — the square and the 
 equilateral triangle, the same lines producing arrangements of those very 
 dissimilar forms, as exemplified in those that surround the dodecagon upon 
 this diagram. The various figures that arise out of this combination will 
 afford some scope for the ingenuity of the student. 
 
 There yet remains one figure to be noticed, namely, the pentagon. It 
 results from the division of the circle by five, and probably ought to hold in 
 the general series the situation in wliich I have placed the hexagon ; but I 
 preferred the latter figure for tlie reasons already given. Tliis figure is pro- 
 ductive of much beauty when properly arranged, of which the diagrams. Plates 
 14 and 15 are examples; the former showing its rectilinear mode, and the 
 latter its circular mode of combination. It has, like all other geometrical 
 plane figures, peculiarities connected with solids ; but these are apart from 
 the subject of this essay. 
 
 My object being to elicit and explain the true principle of beauty in 
 forms and figures, though but with reference to what has been considered 
 a humble department of art, I must continue to appeal to the highest autho- 
 rities ; for the same principle that guides the hand of the professor of high 
 art in his attempts to produce beauty, ought also to guide tliat of the humble 
 
mechanic, who would impart a similar quality to his works, as the same moral 
 principle governs alike the actions of the prince and the peasant. I shall 
 therefore first attempt to ascertain to what principle we may attribute the 
 symmetrical beauty universally admitted to exist in some objects, commencing 
 witli the highest authority in nature, the human figure. 
 
 OF THE GEOMETRIC PRINCIPLE OF BEAUTY AS EXEMPLIFIED IN THE i 
 HUMAN FIGURE. ,j 
 
 Vitruvius, amongst otlier vague ideas regarding the practice of the ancient , 
 Grecians in architecture, supposes the proportion of their temples to have 
 been deduced from those of the human body. This supposition is very na- ! 
 tui-al, inasmuch as the human figure is the most truly beautiful work of crea- : 
 tion, and the Grecian temple the most scientific specimen of art. But a ^ 
 little investigation will show us that this quality was more likely to have ; 
 been imparted to the works of the ancient Grecians, through the know- i 
 ledge of a universal mathematical principle of harmony inherent in the hu- 
 man mind, producing a response to every developement of its laws presented 
 to the senses, whether in sound, form, or colour. Of the developement of this 
 principle, in geometric proportion, the human figure is the highest example ! 
 in nature, and the Grecian temple the most perfect in art. The variety ,| 
 that pervades all nature is apparent to every one, but the extent of the 
 uniformity that constitutes the beauty of this variety is only ascertained 
 
 ORNAMENTAL DESIGN. 
 
 by close observation of its general laws, and by a careftd investigation 
 of particular productions. By such means the natural philosopher has been 
 enabled to classify and arrange the objects of his study. By such means 
 also, the relations of the various parts of the universe, and the constituent 
 parts of the chemical combinations throughout nature, have been ascertain- 
 ed. It is precisely so in msthetical science with regard to configuration. 
 When any object is presented to the eye, its variety is at once apparent, 
 and to a perfect organ and quick perception, its beauty also, if it possess 
 any. But the manner in which the uniformity that constitutes beauty 
 is imparted to this variety, can be perceived only through a knowledge 
 of that governing mathematical law of harmony and proportion, already 
 noticed. The human figure owes much of its beauty to variety, but when 
 we examine carefully the relative proportions of its parts, it will be found 
 that in the most perfect specimens the uniformity is in the ratio of the 
 variety ; and farther, that this uniformity amidst variety is produced by the 
 same harmonic ratios that regulate the laws of acoustics and chromatics ; 
 but to proceed to the proof. 
 
 Let the whole length of a perfect skeleton be divided into 90 parts, 
 the first grand division is from the sole of the foot to the os pubis, and 
 it contains 45 of those parts {the ratio to the whole of 1 to 2). The 
 Second from the same to the fifth or last rcHchra of the loins, GO parts 
 (ratio 2 to 8). The third from the same to the upper bone of the ste\'~ 
 
ON THE PRINCIPLES 
 
 mini or breast bone, 72 parts (ratio 4 to 5). From the same to the bottom 
 of the lower mandible or jaw-bone 78f parts (ratio 7 to 8). From the same 
 to the top of the same bone, 80 parts (ratio 8 to 9). From the same to the 
 top of the os ileum or flank bone, 54 parts (ratio 3 to 5). From the same 
 to the bottom of the os sacrum or great bone of the spine, 48 parts (ratio 8 
 to 15). From the crown of the head to the bottom of the patella or knee 
 bone, 67^ parts (ratio 3 to 4). From the crown of the head to the bottom 
 of the first vertebra of the back, and from the top of the os sacrum or great 
 bone, of the spine, to the atlas or uppermost vertebra of the neck, are each 30 
 parts (ratio 1 to 3). From the bottom of the os pubis to that of the patella, 
 and from the bottom of the patella to the sole of the foot, each 22^ parts 
 (ratio 1 to 4). From the crown of the head to the bottom of the first bone 
 of the sternum, from the os pubis to the first vertebra of the back, from the 
 clavicle to the lowest rib, and from the top of the humerus or large bone of 
 the arm to its junction with the ulna and radius, each 18 parts (ratio 1 to 5). 
 From the o? pubis to the top of the fifth or last vertebra of the loins, and 
 from the crown of the head to the twelftli or last vertebra of the back, are 
 each 15 parts (ratio 1 to C). The fore-arm, from where the ulna and radius 
 join the humerus to their union with the lunar bones of the wrist, is about 
 13 parts (ratio 1 to 7). The length of the facial surface from the crown of 
 the head to the point of the chin, the length of the sternura or breast bone, 
 and the vertical length of the pelvis are each 11:|: parts (ratio 1 to 8). The 
 
 0 R N A M E N T A L D E S I U N. 
 
 cranium from its highest point to where it joins the atlas, is 7^ parts (ratio 
 1 to 12). 
 
 The parts of the human body are no less remaihable for the harmony 
 of their subdivisions. In the arm the radius and ulna are to the humerus in 
 the ratio of 2 to 3, The hand, from the wrist bone to the point of the 
 longest finger, is to the whole length of the arm (hand included) in the ratio 
 of 1 to 4. The length of the foot is to the length of the leg, taken from the 
 sole of the foot to the head of the thigh bone, in the ratio of 1 to 4. The 
 division of the human countenance into the harmonic ratios is equally worthy 
 of notice in this place. On the transverse diameter, from the crown of the 
 head to the centre of the eye, is in the ratio of 1 to 2 of the whole length. 
 From the same to the point of the nose, 3 to 4 ; and to the mouth, 5 to 6. 
 From the point of the chin to the mouth, 1 to 6 ; to the nose, 1 to 4 ; to the 
 centre of the eye, 1 to 2 ; and to the setting on of the hair, 5 to 6. Upon 
 the conjugate diameter, the eye, the width of the nose and the mouth are as 
 1 to 5. But these ratios of the countenance I have given in detail, and with 
 illustrations in another work.* Every minutiae of the human figure is full 
 of this species of harmony. The eye itself in its division into the parts by 
 which its extraordinary functions are performed, displays It in an eminent 
 degree, as I have already endeavoured to show.f 
 
 * “ Laws of Harmonic Colouring," 5tli edit. "W. Orr & Co. Loinlon. 
 
 I “ Proj'ortion or tlic Geometric Priiicijile of Beauty Analysed." Blackwoods, Lend. & Ed. 
 
Tlie ratios in tlie liumati l)oJy 
 are in tlie order of their sim- 
 
 Theae Ratios iu the pulsations of 
 the atmosphere, produced by 
 [ilifity as follow : — similar divisions of the mono- 
 
 chord, are called, 
 
 Ratios. 
 
 I to 2 An octave. 
 
 t... 3 A twelfth, 
 
 1 ••• 4 ... fifteenth or second octave. 
 
 2.. . 3 fifth. 
 
 I ... 5 ... seventeenth. 
 
 1 ... 6 ... nineteenth. 
 
 3 ... 4 ... fourth. 
 
 1 ... 7 
 
 3.. . 5 sixth. 
 
 I 8 ... twenty-second or third octave. 
 
 4 ... 5 ... third. 
 
 5 ••• 6 ... third minor. 
 
 1.. .12 ... twenty-si.xth. 
 
 0... 7 
 
 8 ... 9 ... major tone or second. 
 
 8 ... 15 ... seventh. 
 
 To some this may appear a rather unnecessary digression, but believing 
 that in investigations of this kind, wliere first principles are traced to the 
 
 OF ORNAMENTAL DESIGN. 
 
 highest works of the Deity, the student in ornamental design will take a 
 deep and profitable interest, I shall follow it up with a few farther remarks. 
 
 At first sight it may appear strange, that there should be fixed rules 
 I for the beauty of what nature produces in such infinite variety. But it is well 
 known in art that there is a standard of perfection for the proportions of the 
 :! human figure, rarely if ever found in any individual, and that the statues of 
 I ancient Greece display an approximation to this standard hitherto unattained 
 in any other similar works of art. This, I believe, is what is understood by the 
 I of the ancients. Sir Joshua Reynolds and many other writers on 
 
 ! art, suppose that it was attained by selecting parts from various models in na- 
 ture, and combining them in one individual ; and this has been almost uni- 
 formly recommended to the student iu art, as the best mode of arriving at 
 ' tlie same degree of perfection. Such a mode of combination is, however, 
 
 . not only very difficult and uncertain in its results, but unnatural. Beauty 
 ! is the truth of art, and, like moral truth, it is embodied in one universal 
 j governing principle. This principle ought to be familiar to the artist, and 
 I according to the amount of intuitive genius he may possess, will it appear 
 in his works, as the moral principle of integrity produces the greatest effects 
 when combined with high talent, and a wide .sphere of action. 
 
 'i Now, it is well known, that in the operation of the moral principle of 
 
 tnith in producing rectitude of conduct in mankind, there exists as much 
 variety as there does in the human countenance ; but no one would assume 
 
0 N T HE P U I N C 1 F 1. K S OF ORNAMENTAL D E S I G N. 
 
 35 
 
 from this, that there existed no standard of excellence, even although that 
 standard may never have been attained by any individual. Copying parts 
 from various figures, in order to produce a perfect whole, is in art what 
 imitating the good actions of other individuals, without any governing prin- 
 ciple, would be in morals. I shall now proceed to inquire into the operation 
 of this geometric principle of beauty in what may be justly considered the 
 highest authority in art. 
 
 OF THE GEOMETRIC PRINCIPLE OF BEAUTY, AS EXEMPLIFIED IN THE 
 PORTICO OF THE PARTHENON. 
 
 The proportions of this portico have for many ages excited the admira- 
 tion of mankind, and are still referred to as the most perfect example of this 
 kind of beauty known in architecture. It is therefore a subject of some in- 
 terest to inquire into the nature of those proportions, and especially to ascer- 
 tain how far they are governed by the same principle of ratio just exemplified in 
 the human figure. The two subjects are quite dissimilar in their general con- 
 tour, there being no conceivable likeness between a Grecian portico and a 
 human figure. But the beauty of their proportions are traceable to a similar 
 principle differently applied. In the human figure it has been shown that the 
 proportions consist in the division of an imaginary or mathematical straight 
 line passing through the centre of the leading bones in the skeleton ; and 
 
 ill the portico the operation of the same principle of harmonic ratio, will bo 
 seen upon the imaginary lino called the diagonal in each of those rectangles 
 which, combined together, form what may be fairly termed its skeleton, as 
 shown on Plate 16. But it is not in the various lengths of these diagonal 
 lines that we are to look for the developement of the harmonic ratios, but to 
 the degrees of the angle they form with the longest side of each rectangle, 
 which of course, when vertically placed, must be above, and when horizon- 
 tally placed, below 45'’ ; and the following is the result. 
 
 The entire portico, from the extreme of the base of the outer columns 
 to the upper point or apex of the pediment is inscribed in a rectangle, the 
 diagonal of which is 30°, bearing to tlie angle of 45'’, the ratio of 2 to 3, and 
 to the angle of 90“, that of 1 to 3. 
 
 The angle of the pediment itself is 15°, bearing to the diagonal of the 
 inscribing rectangle the ratio of 1 to 2 ; to the angle of 45°, that of 1 to 3 ; 
 and to the angle of 90°, that of 1 to 6. 
 
 The diagonal of the rectangle under the pediment inscribing the co- 
 lumns with their architrave and frieze is 22° 30', bearing to the diagonal of 
 the inscribing rectangle, the ratio of 3 to 4 ; to the angle 45°, that of 1 to 2 ; 
 and to the angle 90°, that of 1 to 4. 
 
 The diagonal of the rectangle inscribing the columns is 18°, bearing to 
 the diagonal of the inscribing rectangle, the ratio of 3 to 5 ; to the angle of 
 45°, that of 2 to 5 ; and to the angle of 90°, that of 1 to 5. 
 
3n 
 
 ON THE PUlNOlPEES OF OHSAMENTAL DESIGN. 
 
 The diagonal of the rectangle inscribing the architrave and frieze is ,, 
 5' 37' 30", bearing to the diagonal of the inscribing rectangle, the ratio of ;; 
 3 to le ; to the angle of 45°, that of 1 to 8 ; and to the angle of 90", that of |j 
 
 1 to le. l| 
 
 The rectangles of the six centre columns, which I have taken at their i 
 mean diameter, have each a diagonal of 80°, bearing to the angle of 90°, the 
 ratio of 8 to 9 ; and the five intercolumniations between these have each a ' 
 diagonal of 75°, bearing to those of the columns, the ratio of 15 to 16, and i 
 to the angle of 90°, that of 5 to 6. 
 
 The rectangles of the two outer columns and their intercolumniations I 
 have diagonals of 78° 45', being to the right angle in the ratio of 7 to 8. 
 
 The two outer columns, with their intercolumniations, are necessarily out 
 of harmony with those that lie between them, for the ratio of 78° 45' is to 80° 
 as 23 to 24, and that of 78° 45' to 75° as 63 to 62, ratios too far removed 
 from the primary elements to have a harmonious relation. But the circum- 
 stance of these outer columns being of greater diameter than the other six, 
 is well known to have arisen from a knowledge of the fact, that any up- 
 right object placed between us and the sky will appear more slender than ] 
 when placed against a background in shade. As these outer columns of the 
 portico were so situated, while the other six could only be viewed against 
 the inner portion of the building, it became requisite to increase their 
 diameter, the discord being neutralised by this optical illusiou. I 
 
 From the same cause that a solid body appears more slender than it 
 really is when viewed against the light, an open space seen between two solid 
 bodies appears wider ; and this assists in harmonising the two outer inter- 
 columniations. 
 
 The harmonic ratios of the Par- 
 thenon are in the order of 
 their simplicity as follow : — 
 
 Ratios of 
 1 to 2 
 
 1 ... 3 
 1 ... 4 
 2... 3 
 1 ... 5 
 1 ... G 
 
 2.. . 5 
 
 3.. . 4 
 
 3.. . 5 
 1 ... 8 
 
 5.. . 6 
 1 ... 16 
 6 ... 9 
 3 ... 16 
 
 15 ... IG 
 
 Names of those ratios wl.en applied to the 
 vibrations produced by the division of tho 
 munochord. 
 
 An octave. 
 
 A twelfth. 
 
 ... fifteenth or second octave. 
 
 ... fifth. 
 
 ... seventeenth, 
 
 ... nineteenth. 
 
 ... tenth. 
 
 ... fourth. 
 
 ... sixth. 
 
 ... twenty-second or third octave. 
 ... minor third. 
 
 ... twenty-ninth or fourth octave. 
 ... major second or tone. 
 
 An eighteenth. 
 
 A semitone or minor second. 
 
ON THE PRINCIPLES 
 
 It may here be interesting to see what etfect the harmonic ratios thus 
 found to exis't in the Parthenon, will have when applied to a vertical com- 
 position. Plate 17. exhibits such an arrangement, w'hich might probably 
 act as the geometric skeleton of a Gothic structure, thus affording in the 
 requisite subdivisions of these elementary parts into doors, windows, but- 
 tresses, &c. ample latitude for the introduction of harmonious accompaniments 
 to this general outline. The following are the angles of these diagonals 
 with their relation to those of the Parthenon. 
 
 P.artlicnon, Plate 16. 
 
 
 Plate 17 with its ratios to 90° 
 
 15° horizontal 
 
 18° 
 
 corresponds to 
 
 75° vertical 
 
 72° 
 
 5 to G 
 
 4 
 
 22” 30' 
 
 
 67° 30' 
 
 .'I 4 
 
 30° 
 
 
 60° 
 
 9 . 3 
 
 
 
 80° 
 
 8 ... 9 
 
 5 R 
 
 76” 
 
 
 
 78" 45' 
 
 
 78” 45' 
 
 7 ... 8 
 
 The ratios in the portico of the Parthenon are agreeable to the dimen- 
 sions of the elevation in Stewart’s Athens, as given in Plate VI. of that 
 work. But as the angle of the pediment in Plates VL, VII„ and X^^ all 
 
 ORNAMENTAL DESIGN. 
 
 o7 
 
 differ, I adopted that of the latter, as being the most likely to be correct, 
 because the pediment is there given by itself. 
 
 OF COMBINATIONS OF THE CURVED AND THE STRAIGHT JANE. 
 
 Hitherto the combinations of figures and lines treated of in this E.ssay, 
 have been confined to those of a similar kind, that is, curvilinear with 
 curvilinear, and rectilinear with rectilinear figures. It now remains to be 
 shown how those two kinds of lines, and the figures resulting froiti them, 
 may be harmoniously united in ornamental design. 
 
 The rules by which each of those classes of lines and figures have been 
 shown to combine amongst themselves individually, must be observed in their 
 union with one another. It has been showm that two curved lines can only 
 meet each other harmoniously in the same straight line ; so, to unite a straight 
 line with a curved line in successive harmony, they ought also to be made 
 to meet each other in the same manner. This mode of combination ought 
 to be observed in the forms of all apertures in solid surfaces, which are 
 intended to be rendered ornamental by means of the combination of those 
 two kinds of lines. No doubt an ornamental appearance is often attempted 
 to be given in such cases by placing horizontally upon vertical lines, a smaller 
 arc of a circle than its half, but the effect is discordant, and such a mode 
 of combination need never be resorted to, while the elliptic curve upon its 
 
38 
 
 ON THE PRINCIPLES OF ORNAMENTAL DESIGN. 
 
 transverse diameter, whateva* its proportion may be, will, when placed hori- 
 zontally upon vertical lines, meet them harmoniously. 
 
 In like manner, curvilinear figures, when projected from a straight line, 
 in order to produce perfect harmony of opposition or contrast in the out- 
 line of any object, ought to meet the straight line at right-angles, and here 
 likewise all projections under a semicircle ought to be elliptic. When, on 
 the other hand, the curvilinear figure exceeds a semicircle in height, it must 
 be formed of two smaller arcs, either of the circle or ellipse, and conse- 
 (iuently have an angle, its summit being pointed. This necessity seems to 
 arise from the nature of the elliptic curve preventing its being used vertically 
 in the formation of any such figures. The principal cause of this is evidently 
 its exuberance of curvature towards the extremity of the transverse diame- 
 ter ; but it would exceed the limits, and be apart from the object of this 
 Essay, to enter upon the discussion of this point here, and I therefore beg 
 the student in the meantime to take it for granted. 
 
 On Plate 11. figure 3, is placed three semicircles of harmonic rela- 
 tive proportions, and at harmonic intervals, upon a straight line ; yet the 
 curves are not proportionate in comparative quantity to the straight line. 
 This defect is at once removed by adding to the composition those three harmo- 
 nic rectangles, given in Plate 10. figure 4, the nature of which has been already 
 explained. Figure 4, Plato 11, exhibits this proportionate combination of the 
 straight and the curved line with the right angle ; and this figure is worthy 
 
 of some attention from the student. He will in it observe that the pro- 
 jected semicircles necessarily follow a law which always proportions their 
 height to their length ; for tlieir radii are to them what the diagonals are to 
 the rectangles upon which these semicircles are placed. These are propor- 
 tions arising from necessity, because the figure is formed by the motion of 
 the line which gives them ; and the proportions of the rectangle may be 
 naturally deduced from these, because the diagonal is the only single line 
 within that figure that can regulate its proportions. 
 
 Triangular figures, when arranged upon the same base with curvilinear 
 figures, ought to be in exact proportion to these in their configuration, 
 whatever their relative sizes may be. The mode of doing this is exhibited 
 in Plate 18. figures 1, 2, and 3. When the angle of an isosceles triangle 
 exceeds 45°, the curvilinear figures to be associated with it as a projection 
 from the same line, or even in the same composition, must also be angled, 
 for the reasons just stated in regard to the exuberance in the curve of the 
 semi-ellipse produced upon the conjugate diameter. Arcs of a circle have 
 been hitherto employed in such cases, of which those of a sixth of the whole 
 circumference produce the most beautiful figure. Such an angled curvilinear 
 figure has exactly the proportions of the semi-ellipse already referred to’ 
 without the exuberance towards its apex, and it consequently associates 
 with the equilateral triangle. 
 
 Figures of this kind, however, would be improved in the ratio of the 
 


 
 
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ON TIIK 1‘RINCII'LKS OK 0 K N A iM E N T A L DESIGN. 
 
 increased variety imparted to them by a diminution of their curvature as 
 they approach their apex. Figure 4 is excelled in beauty by figure C, be- 
 cause its curve being elliptic, it has that variety amidst uniformity that con- 
 stitutes the true principle of beauty already explained. This figure will, 
 therefore, whether vertical or horizontal, be always more beautiful >\’hen 
 formed by arcs of the ellipse united upon its transverse diameter, tlian by 
 arcs of circles, as exemplified in figures 5 to 12. To produce similar figures 
 in architecture, it is not unusual, I am aware, to unite in one line arcs of 
 circles of different radii ; but combinations of this kind are unnatural and in- 
 harmonious. There may be in the constructive portion of the science of 
 that art, substantial reasons for using In all pointed arches arcs of the cir- 
 cular curve in preference to those of the elliptic curve, and if there really 
 be such reasons, the true principle of beauty must, in this particular in- 
 stance, continue to be sacrificed to utility. 
 
 In Plates 19, 20, and 21, are given diagrams of various combinations 
 of the straight and the circularly curved line. In Plate 19, will be found 
 the outlines of the diapers numbered XXIX. and XXX; in Plate 20, 
 the outlines of I., III., IV., VI., VIL VIII., IX., XII., and XIII; and 
 in Plate 21, the outlines of II., V., X.. XL, XIV., XV., XVI., XVII., 
 XVIII., XXIII., XXVIII., and XXXI. Many other designs of this kind 
 can be taken from these diagrams, and they may thus afford profitable 
 amusement to the student. Plate 22, is another combination of the straight 
 
 and curved line, upon which three geometric diapers are marked, in order 
 to show the mode of producing this peculiar kind of ornament. 
 
 In Nature we often find the straight and the curved line beautifully 
 associated, especially in the manner in which the branches of some plants 
 leave their parent stems. But it is not consistent with the infinite variety 
 tliat pervades all her works that there should be mathematical exactness 
 in every case, or that there should be an equality of beauty amongst indi- 
 vidual objects of any class of combinations ; it is enough that the general or 
 governing principle appears to operate, while the extent of its influence is con- 
 tinually varying. A knowledge of the modes in which this princiide operates 
 upon the perceptive faculty, forms the true science of aesthetics. The results 
 of a proper study of this science, are a just appreciation of what is most 
 beautiful amidst the variety of Nature, and a correct judgment as to works 
 of art, while it assists the artist not only in selecting objects of study, but in 
 imjearting beauty to his works. At the same time, it must be acknowledged, 
 that no absolute perfection can be attained in productions of art, because, 
 as before observed, although the mathematical principle that governs esthe- 
 tics, like the principle of truth that governs morals, be perfect in itself, as 
 emanating from the Deity, yet its operation in art is applied through an 
 imperfect medium. So that our attempts in this way, as in moral recti- 
 tude, will be after all but humble approximations to perfection. It will 
 therefore be in the ratio of the general diffusion of a knowdedge of their first 
 
lo 
 
 ON THE PRINCIPLES OF ORNAMENTAL DESIGN. 
 
 principles that we will be able properly to appreciate and practise the arts 
 of design. 
 
 ON THE DECORATIVE ORNAMENTS OF ANCIENT GREECE. 
 
 We find in the decorative ornaments of ancient Greece, the same chaste 
 beauty that pervades its statuary and architecture, and this is evidently 
 not imparted to those works by any servile copying, even of any of Nature’s 
 ])roductions, but by the application of a mathematical principle, which enabled 
 its artists in every case to treat form in the abstract ; or, if I may use the 
 term in this humble Essay, in a philosophical manner. Indeed, I believe 
 it probable, that the learned have found the philosophy, as well as the 
 poetry of the same period, displaying an equal adherence to high governing 
 principles, uncontrolled by dogmas and precedents, and thereby forming the 
 closest approximations to perfection, combined with the greatest simplicity, 
 ever exhibited in the intellectual efforts of the human mind. 
 
 Many remnants of the decorative ornaments of ancient Greece have 
 survived the ravages of time, the dilapidations of hostile invasion, and no 
 less destructive effects of ages of barbarous possession of the country. These 
 remnants are now carefully preserved in many pnblic and private collections 
 throughont Europe, and have been carefully copied by travellers, the accuracy 
 of whose artistical labours maybe fairly depended npon. Amongst the most 
 prominent of these enterprising artists are Tatham, Kinnard, and Donaldson, 
 
 from whose works I have cojiied the examples in Plate 23. Figures 1 and 
 2, are from Tatham’s work. The fii-st is from an antique fragment of 
 a Grecian frieze in the Villa Albani near Rome, and represents one of the 
 most beautiful specimens of this peculiar style of decorative ornament that I 
 have met with. The second is half of the side of a seat of Parian marble 
 in a chapel near Rome. 
 
 Figure 3, is from the Supplement to Stewart’s Athens, by Mr Kin- 
 nard. It is the top of a sepulchral marble, inscribed to the memory of an 
 Attic citizen, of a town at a defile of Mount Pames, of great importance 
 during the Peloponnesian war. It is remarkable from its contonr being 
 formed of two arcs of an ellipse, and for the characteristic elegance of the 
 ornament which it inscribes. 
 
 Figures 4 and 5 are the only two curvilinear ornaments of the Parthe- 
 non. The first being one of the oniamental apices termed antefixic, an- 
 ciently placed over the horizontal cornices, and the second is upon the soffit 
 of the cornice. 
 
 Figure 6 is from Mr T. L. Donaldson’s supplement to Stewart’s 
 Athens, and appears to be the production of a later period than any of the 
 other specimens given. In it there appears less accuracy of style, with more 
 exuberance of fancy, and it may be taken as an example of one of the first 
 steps from that severity that distinguishes the more classical specimens of 
 attic ornament, to the more florid style that succeeded it. 
 
PLATt: f3. 
 

ON THE PRINCIPLES OF ORNAMENTAL DESIGN. 
 
 41 
 
 These examples are selected as giving fair specimens of the general 
 characteristics of this classical style of decorative ornamental design. And 
 it will be observed, that amongst them the peculiar figure generally call- 
 ed a “ Honeysuckle ornament,” holds a prominent place; upon the beauty 
 of which figure it would be a waste of words to expatiate. I agree 
 with Mr Kinnard in believing that it was no direct imitation of that 
 plant, neither do I conceive that it has any particular prototype in nature, 
 but- is simply the result of the application of the same general principle at- 
 tempted to be developed in this Essay, upon which form may be treated 
 abstractly in the production of beauty. To those who wish to gain a learned, 
 historical, and critical knowledge of this peculiar style of ornament, apart 
 from the application of this lesthetical principle, I would recommend the 
 perusal of the two excellent Essays of Kinnard and Donaldson, my object here 
 being simply to develope the existence of such a principle in its construction. 
 
 In Plate 24, ocular demonstration is given of the fact, that the beauty 
 of this figure arises from its being the combination of the elliptic curve with 
 a straiglit line. Figure 1 is the centre part of one of those ornaments, 
 figure 2 one of the side parts, and figure 3, one of the parts of the antefixae 
 of the Parthenon. 
 
 From these figures it M’ill be seen, that a complete ornament of this 
 kind has as its centre a straight line, from which diverges on each side 
 elliptic curves, becoming gradually more acute, until they reach on either side 
 
 the outer line of the spiral curve that proceeds from a circular point. We 
 have, therefore, in this single ornament, the two most beautifully varying 
 curves, proceeding from the two primary mathematical figures, the point 
 and the straight line, so associated that they proceed from the one until they 
 are resolved into the other. 
 
 In geometry there are many varieties of the spiral curve, with rules for 
 their formation. But the most beautiful, and that which is most useful in 
 ornamental design, is what is called the spiral of Archimedes. It is so called 
 from his demonstration of its nature, by which it is proved that if the arc 
 of a circle be divided into any number of ecpial parts, and radii drawn from 
 the centre to these points, the spiral line commencing at the end of one of 
 those radii, where it proceeds from the centre point of the circle, and ending 
 at its other extremity, will divide all the intermediate radii in arithmetical 
 progression of 1, 2, 3, &c. of similar parts, as it recedes from the centre. But 
 the simple mode of producing this line is, by unwinding a thread from a 
 cylinder with a pencil at its end, by which the curve will be accurately de- 
 scribed. Its beauty is somewhat like that of the ellipse, depending upon 
 the uniformity of its variety, which property it receives from a continual and 
 imiform increase of its radii. 
 
 This curve, associated with the waved line, is a leading feature in all foli- 
 ated ornaments, many beautiful examples of which, taken from fragments of 
 ancient sculjiture, will be found in the works just alluded to. But theso 
 
42 
 
 ON THE PRINCIPLES OE ORNAMENTAL DESIGN. 
 
 seem generally to belong to the Italian style of ornamental design, in 
 which it would appear the elliptic curve fell into disuse even in the contour 
 of mouldings, and other architectural adornments. 
 
 The decorative ornament of ancient Greece may therefore, with perfect |; 
 propriety be termed “ a style,” as it embodies a principle of pure geometric 
 beauty, for which there existed in art no jn-ecedent, and which mifortunately 
 has been lost to succeeding ages. To copy the fragments that still exist of 
 this pure style, without inquiring into the principle upon which its beauty 
 depends, has been too long the practice in our schools of design, and the 
 futility of such a practice is exemplified in the total want of originality, 
 combined with classic beauty, that still prevails in this as well as in other 
 countries. 
 
 (L\ THE DECORATIVE WORKS OF RAPHAEL. 
 
 What are erroneously termed the “ arabesques” of Raphael, are perhaps 
 the most beautiful series of painted decorative ornaments now in existence. 
 But “ arabesques” they are not. The “ arabesque,” or moresque,” species of 
 ornament, is that particular kind of diajjcr design, whether painted or carved, 
 applied to the enrichment of flat surfaces, and is composed of combinations 
 either of geometrical figures, or of the representation of objects in inani- 
 mate nature. 
 
 But the decorative works of Raphael in the Loggie of the Vatican 
 take a much wdder range of art. They embrace allegorical subjects of the 
 highest class, expressed by exquisite delineations of the human figure, varied 
 by every age, and every grade, all equally expressive of the sentiment they 
 are intended to inspire, despite the fanciful and even grotesque situations 
 in which they are generally placed. These works embody also the most beau- 
 tifully ornamental combinations of the lower grades of animate nature, and 
 arc no less remarkable for their graceful embodiment of her foliated produc- 
 tions. In these latter, the scientific combinations of the straight with the 
 spirally curved line are most conspicuous, while the geometric division of 
 the various parts are generally harmonious and accurate. These are the 
 natural results of such a genius as that of Raphael ; but whether from his 
 having allowed his fancy at times to run riot, or from his assistants having 
 been allowed in some cases to exercise their own peculiar fancies, there are 
 ij chimeras and absurdities introduced, which cause these great works to boar 
 I an analogy to the more correct works of the ancient Grecians, similar to that 
 ; which some of the poems of Byron bear to those of Homer, 
 j The student in ornamental design should therefore be cautious in his 
 
 j selection of objects of study from the works even of this great artist. And 
 I consider this caution the more requisite, from having repeatedly seen those 
 objectionable parts selected for imitation in what is usually misnamed an 
 ornamental design.” 
 
ox THE PRINCIPLES OF ORNAMENTAL DESIGN. 
 
 43 
 
 (IN' 'I'lIE MOST SIMPLE MODE OF ATTAINING THE POWER OF GRAPHIC 
 DEFINITION. 
 
 An experience of thirty years in such matters has convinced me that a 
 much more accurate idea can be given of the configuration of an object, by a 
 few tolerably correct lines, in five minutes, than it would take in ordinary 
 cases half an hour to describe. I would therefore recommend to the em- 
 ployer who wishes to express his ideas of form distinctly, as well as to the 
 artist who is to put such ideas into execution, that, in addition to the attain- 
 ment of a knowledge of principles, they should each aciiuire the power of 
 thus expressing themselves. Such a facility is as useful to the nobleman as 
 to the artizan, for it often happens that the style of language in which they 
 individually attempt to explain their ideas of such matters to each other, is 
 to a certain extent, reciprocally unintelligible, while the import of a few 
 geometric lines could at once be comprehended, and an understanding brought 
 about which words might fail to establish. 
 
 The mode by which this facility may be attained is more simple than is 
 
 generally supposed ; indeed, so much so, tiiat it might be taught to children 
 along with the alphabet. It is as follows : 
 
 Let a large black painted board bo provided, upon which the drawing 
 with white chalk of circles, equilateral triangles, squares, ovals, rhombs, 
 oblongs, and hexagons should be separately practised on as large a scale as 
 the length of the arm will allow, and with no more separate motions than 
 there are angles in the figure. This must be performed with as little mo- 
 tion of the body as possible, and without any guide to the hand but the eye. 
 Let this practice be continued till each of the above figures can be so pro- 
 duced with a tolerable degree of accuracy, when the practice may be changed 
 to the production of the various waved lines of the circle and ellipse, their 
 combinations with the straight line, and lastly the spiral. A degree of ac- 
 curacy of hand and eye will thus be secured, which will not only infuse it- 
 self in a striking manner into every more minute production, but tnust be a 
 surer means of developing latent talent, than that generally employed in our 
 schools of design, namely, of setting boys to copy, on a small scale, what they 
 do not understand, like so many humble transcribers of ancient manuscripts. 
 
 EDINDURGU : MACPHERSON St STME, TRINTERS. 
 
 RO.SE LANE. 
 

 
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