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ON THE 
 
 SCIENCE OF PROPORTIONS. 
 
EDINBURGH : 
 
 JOHNSTONE, BALLANTYNE, AND CO 
 104 HIGH STREET 
 
ON THE 
 
 SCIENCE OF THOSE PROPORTIONS 
 
 BY WHICH THE 
 
 HUMAN HEAD AND COUNTENANCE 
 
 AS REPRESENTED IN WORKS OF 
 
 ANCIENT GREEK ART 
 
 ARE DISTINGUISHED FROM THOSE OF ORDINARY 
 
 NATURE. 
 
 DY 
 
 D. R. HAY, F.R.S.E. 
 
 AUTHOR OF “FIRST PRINCIPLES OF SYMMETRICAL BEAUTY,” 
 
 ETC. ETC. ETC. 
 
 WILLIAM BLACKWOOD AND SONS, 
 
 EDINBURGH AND LONDON. 
 
 M.DCCC.XLIX. 
 
Digitized by the Internet Archive 
 
 in 2016 
 
 https://archive.org/details/onscienceofthoseOOhayd 
 
TO 
 
 THE HONOURABLE 
 
 LORI) MURRAY, 
 
 ONE OF THE JUDGES OF THE COURT OF SESSION OF SCOTLAND, 
 
 F.R.S.E., ETC. ETC. ETC. 
 
 THIS WORK IS DEDICATED, AS A TESTIMONY OF THE 
 GRATITUDE, ESTEEM, AND RESPECT, 
 
 OF 
 
 THE AUTHOR. 
 
CONTENTS. 
 
 PAGt-: 
 
 PART I. DEFINITION OF .ESTHETICS, ....... 1 
 
 ... II. ON ESTHETIC CULTURE, ....... 7 
 
 ... III. ON THE HARMONY OF NUMBERS, AND THE METHOD OF APPLYING 
 
 IT TO FORM, ......... 21 
 
 ... IV. ON THE GENERAL FORM AND BEAUTY OF THE HUMAN HEAD AND 
 
 COUNTENANCE, ........ 31 
 
 ... V. THE SCIENCE OF PROPORTION IN RELATION TO REPRESENTATIONS 
 
 OF THE HUMAN HEAD AND COUNTENANCE. .... 41 
 
 NOTES, ........... 65 
 
 INDEX, 79 
 
PREFACE. 
 
 The recommendation of Sir Joshua Reynolds, that “ every 
 opportunity should be taken to discountenance the false 
 and vulgar opinion, that rules are the fetters of genius,” 
 ought never to be lost sight of by those who treat of the 
 arts of design. Such an idea is scarcely less prevalent in 
 our own day than it was when our great English painter 
 wrote, notwithstanding the practical refutation it receives 
 in the obedience yielded by genius to the rules of rhythmi- 
 cal measure, even in the highest flights of poetic inspira- 
 tion, or in the delicate creations of the musical composer, 
 in subjection to the strictly defined laws of harmony. 
 
 By an implicit obedience to the application of these 
 
 definite rules, genius has clothed the creations of fancy in 
 
 b 
 
X 
 
 PREFACE. 
 
 poetic numbers, or given form and expression to the most 
 exquisite combinations of musical sound, thereby charm- 
 ing the ear, and entrancing the soul, of the most intelligent 
 and critical student of art, through that inherent principle 
 in the human mind that responds in unison to every species 
 of harmony. 
 
 Bat while the poet and the musician are thus acknow- 
 ledged as the willing subjects of well-defined harmonic laws, 
 it has been hastily and most inconsistently assumed, that, 
 when genius seeks to give expression to its conceptions in 
 the formative arts, it is folly to imagine that any well- 
 defined laws can be demonstrated, whose bounds shall guide 
 their development, or supply safe canons for the critic’s 
 guidance. 
 
 It will be shown in the following pages, however, that 
 the laws of proportion, in their relation to the arts of design, 
 constitute the harmony of geometry as definitely as those 
 that are applicable to poetry and music produce the har- 
 mony of acoustics ; and that, consequently, the former 
 ought to hold the same relative position in those arts which 
 
PREFACE. 
 
 XI 
 
 are addressed to the eye that is accorded to the latter in 
 those which are addressed to the ear. Until so much 
 science he brought to bear upon the formative arts, the 
 student must continue to copy from individual and imper- 
 fect nature, or from the few existing remains of ancient 
 Greek art, while he remains altogether ignorant of the 
 laws by which their proportions are produced ; and, what 
 is equally detrimental to art, the accuracy of all criticism 
 must continue to rest upon the indefinite and variable basis 
 of mere opinion. 
 
 It cannot be denied that men of great genius in the 
 formative arts are generally possessed of an intuitive feel- 
 ing of appreciation for what is beautiful in form, by means 
 of which they impart to their works the most pleasing pro- 
 portions, independently of any knowledge of the definite 
 laws which govern that species of beauty ; yet even they 
 often do so at the expense of much labour, making many 
 trials before they can satisfy themselves in imparting to 
 them true proportions, along with those other qualities of 
 expression, action, &c., that belong more exclusively to the 
 
PREFACE. 
 
 xii 
 
 province of genius. To such, an application of the rules 
 which constitute the science of proportion, instead of fetter- 
 ing their genius, would doubtless promote the more free 
 exercise of its powers, and give such confidence and preci- 
 sion to their exercise as no mere mental perception of the 
 harmony and beauty of form can produce. 
 
 It is also true that the operations of the conceptive 
 faculty of the mind are uncontrolled by definite laws, and 
 that, therefore, there cannot exist any rules, by the inculca- 
 tion of which an ordinary mind can he imbued with genius 
 sufficient to produce works of high art. Nevertheless, 
 such a mind may be improved in its perceptive faculty by 
 instruction in the science of proportion, so as to he enabled 
 to exercise as correct and just an appreciation of the con- 
 ceptions of others, in works of formative art, as that mani- 
 fested by the educated portion of mankind in respect to 
 poetry and music. In short, it appears that, in those arts 
 that are addressed to the ear, men of genius communicate 
 the original conceptions of their minds under the control of 
 certain scientific laws, by means of which the educated 
 
PREFACE. 
 
 xiii 
 
 easily distinguish the true from the false, and by which the 
 works of the poet and musician may he placed above mere 
 imitations of nature, or of the works of others ; while, in 
 those arts that are addressed to the eye, such as sculpture, 
 architecture, painting, and ornamental design, no such laws 
 are as yet acknowledged. 
 
 In the following pages, the author endeavours to 
 demonstrate such definite laws of proportion. In making 
 this attempt, he has liere confined himself to their illus- 
 tration in relation to artistic representations of the human 
 head and countenance, having already, in other works, 
 shown their application in architecture, not only to general 
 proportions, but to the minutest details, and in ornamental 
 design to the production of an endless variety of beautiful 
 forms of ornamental vases, and of every species of utensil 
 pertaining to the arts of the ornamental sculptor, the silver- 
 smith, and the potter. 
 
 Some apology may appear requisite for the unartistic 
 execution of the heads which are added to the geometrical 
 illustrations of this treatise. The author is well aware that 
 
XIV 
 
 PREFACE. 
 
 they would have been greatly enhanced in effect by artistic 
 assistance in drawing them ; but he conceived that, as these 
 illustrations are added to the diagrams and skulls merely 
 to show how far the science of proportion is productive 
 of beauty in representations of the human head and coun- 
 tenance, independently of those qualities which genius only 
 can impart, this object would he sufficiently attained by 
 drawing them with his own hand, confining himself simply 
 to what in architecture would he termed geometrical eleva- 
 tions in outline. He also trusts that the anatomist will look 
 with no critical eye upon his unprofessional attempts to 
 delineate the bones of the head, in accommodating them to 
 his geometrical figures. 
 
 JORDAN BANK, EDINBURGH, 
 December, 1848. 
 
ON THE 
 
 SCIENCE OF PROPORTIONS. 
 

 
 
 
ON 
 
 THE SCIENCE OF PROPORTIONS. 
 
 PART I. 
 
 DEFINITION OF ESTHETICS. 
 
 Before entering upon the subject which it is the chief design of this 
 treatise to elucidate, it may be desirable to give some definition 
 of the science of ^Esthetics, of which proportion is the principal 
 element. Dealing, as this science does, alike with the sources and 
 the resulting principles of beauty, it does not belong exclusively 
 either to the physical or metaphysical sciences. It is scarcely 
 less dependent on the accuracy of the senses than on the power 
 of the understanding, inasmuch as the effect which it produces is 
 as essential a property of objects, as are its laws inherent in the 
 human mind. It comprehends a knowledge of those first principles in 
 the arts of design, by which certain combinations of forms and colours 
 
 B 
 
o 
 
 DEFINITION OF ^ESTHETICS. 
 
 produce an effect upon tlie mind, connected, in the first instance, with 
 sensation, and, in the second, with the reasoning faculty. It is, there- 
 fore, not only the basis of all true practice in art, but of all sound 
 judgment on questions of artistic criticism, and necessarily includes 
 those laws whereon a correct taste must be based. 
 
 Many eloquent and ingenious treatises have been written upon taste, 
 but in nearly every case, with no other effect than that of involving the 
 subject in still greater uncertainty. Even when restricted to the arts 
 of design, they have failed to exhibit any definite principles whereby 
 the true may be distinguished from the false, and some recognised 
 laws of beauty reduced to demonstration. This may be attributed, 
 in a great degree, to the neglect of a just discrimination between what 
 is merely agreeable, or capable of exciting pleasurable sensations, and 
 what is essentially beautiful; but still more to the confounding of the 
 operations of the understanding with those of the imagination. Very 
 slight reflection must suffice to show how essentially distinct these two 
 faculties of the mind are ; the former being regulated, in matters of 
 taste, by irrefragable principles existing in nature, and responded to 
 by an inherent quality of the human mind ; while the latter operates 
 in the production of ideal combinations of its own creation, in the 
 region of fancy, altogether independent of any immediate impression 
 from external nature. 
 
 The beauty of a flower, for example, or of a dew-drop, depends 
 on certain combinations of form and colour, manifestly referrible to 
 
DEFINITION OF AESTHETICS. 
 
 3 
 
 definite and systematic, though it may he as yet unrecognised, laws ; 
 but when Oberon exclaims, in “ Midsummer Night’s Dream,” — 
 
 “ And that same dew, which sometime on the buds 
 Was wont to swell, like round and orient pearls. 
 
 Stood now within the pretty flow’ret’s eyes, 
 
 Like tears that did their own disgrace bewail," — 
 
 here the poet introduces a new element of beauty, equally legitimate, 
 yet altogether distinct from that which constitutes the science of 
 AEsthetics, as here defined. It is the element of fancy, reducible to 
 no rule, yet adding fresh combinations of beauty, and a distinct source 
 of pleasure to the mind. 
 
 Our physical and mental powers may be classed under three heads, 
 in their relation to the arts of design, viz., the perceptive, the receptive, 
 and the conceptive. 
 
 The human eye, from the exquisite beauty of its structure, and the 
 intelligence displayed in its adaptation, is receptive of correct impres- 
 sions from the action of light, according to the innumerable degrees 
 and modes in which the optical phenomena operate upon it. These 
 impressions are conveyed to the sensorium by the optic nerve, and of 
 such the mind is perceptive. This perception induces an operation of 
 the understanding, or is itself an act of the mind, whereby it appre- 
 ciates the nature and quality of the impression originally made on the 
 receptive organ. The mode of this operation is intuitive, and its 
 
4 
 
 DEFINITION OF ^ESTHETICS. 
 
 degree, in regard to accuracy, is regulated by the intellectual vigour 
 of the individual. The intuitive power of the understanding thus 
 enables us to decide correctly as to proportion or deformity; but when 
 it is improved by cultivating and extending our knowledge, we can 
 investigate the causes of beauty, and assign reasons for our judgment 
 in matters of taste. These causes and effects constitute the laws of 
 ./Esthetics. 
 
 The conceptive power of the mind is that faculty by which original 
 ideas are formed with the assistance of memory, in combining what has 
 already been operated on by the intermediate powers of perception. 
 This constitutes genius. These various powers, which form the chain 
 between the material and intellectual worlds, are so beautifully inter- 
 woven, that it is difficult to assign to them their respective limits, and 
 the examination of each varied link of this chain adds to the difficulty, 
 from the closeness of their affinities and relations. 
 
 Reception thus appears to be simply the physical effect produced 
 upon the mind by direct, transmitted, or reflected light, through the 
 eye; perception, the operation of the mind by which this impression 
 is appreciated or understood, whether as to its power, in being more 
 or less strong upon the organ — its kind, in being simple or mixed — its 
 nature, in being gay or sombre — or its quality, in being harmonious 
 or discordant; but conception is the power of constructing original 
 ideas from these materials. The understanding operates, in the first 
 instance, in establishing facts, and then the judgment is formed upon 
 
DEFINITION OF AESTHETICS. 
 
 these operations by the reasoning powers, which lead, in their turn, to 
 the creations of the imagination. 
 
 When an impression is received and perceived, in the fullest sense 
 of the word, the understanding of such an impression, or the manner 
 in which the mind comprehends its nature and qualities, depends upon 
 the mental powers and education of the individual, of the modifica- 
 tions of the former of which there are as many varieties as there 
 are of countenances amongst mankind. But when we conceive an 
 impression, it is by reasoning upon others previously perceived ; for 
 we cannot conceive anything unless it resemble, or, at all events, bear 
 some analogy to an impression already perceived. Memory supplies 
 the materials for conceptions of the mind, and, probably, the only 
 materials ; but memory has received its stores from the perceptive 
 faculty, which contributes to it the result of the first impressions on 
 the organs of sense, as felt, understood, and comprehended by the 
 faculty of perception. 
 
 In the science of Aesthetics, therefore, the human mind is the sub- 
 ject, and external nature the object. Each individual mind may be 
 considered as a monad in creation — a world within itself. These two 
 separate existences — the individual mind and so much of creation as 
 lies within the scope of its powers — have a distinct relation to each 
 other : the subject is affected by the object, and the media of com- 
 munication are the sensorium and its iidets, the organs of sense — the 
 former being in direct contact with the subject, and the latter with the 
 
6 
 
 DEFINITION OF AESTHETICS. 
 
 object. The organs of sense are thus acted upon in various ways, 
 agreeably to the numerous modifications of the elements of the 
 external world, but aesthetically the mind is affected in two ways only. 
 These affections are either pleasing or displeasing, in so far as they 
 may be in harmony with, or discordant to, a mathematical principle 
 which, in various degrees, exists in the human mind, and by which 
 the truly beautiful is distinguished from the merely agreeable. 
 
 Note a. The receptive and perceptive powers may be improved by tuition and 
 practice ; and this is called AEsthetic culture. But the conce'ptive or 
 creative power is intuitive, and when developed in a high degree 
 constitutes true genius. The exercise of this power may be assisted 
 by ^Esthetic culture, but the power itself cannot be improved by any 
 mode of tuition. 
 
 Having thus briefly endeavoured to define AEsthetic science, and 
 to show that it ought to form the basis of all instruction in art, I 
 shall now proceed to inquire into the mode in which it is cultivated 
 at the present period, with a view to improve the practice of art and 
 the appreciation of its productions, as compared with what we know 
 of the mode in which it was inculcated in Greece at the period when 
 art had arrived at its highest excellence, and was most correctly 
 appreciated by the people. 
 
ON ESTHETIC CULTURE. 
 
 PART II. 
 
 ON AESTHETIC CULTURE. 
 
 Truth in the sciences has of late been sought, by tracing nature to 
 her most simple elements and first principles of action and combina- 
 tion. By this means natural philosophy has attained its present 
 advanced state ; and by the application of this knowledge, in the use- 
 ful arts, the happiest results have been produced. But in our search 
 for truth in ^Esthetic science, a course has been followed not differing 
 widely from that by which the alchymists of the middle ages con- 
 ducted their investigations ; for our ideas of visible beauty are still 
 undefined, and our attempts to produce it in the various branches of 
 art are left dependent in a great measure upon chance. Our schools 
 instituted for instruction in the arts of design, are conducted without 
 reference to any first principles, or definite laws of beauty; and, from 
 the drawing of a simple architectural moulding to the intricate com- 
 binations of form in the human figure, the pupils have to depend 
 
8 
 
 ON .ESTHETIC CULTURE. 
 
 upon their hands and eyes alone, servilely and mechanically copying 
 the works of the ancients, instead of being instructed in the principles 
 upon which the beauty of those works depends. The instruction given 
 in these schools is addressed almost exclusively to the senses, without 
 reference to the judgment or understanding of the pupils ; and they 
 are thus made to study and imitate effects without investigating causes. 
 Doubtless, men of great genius sometimes arrive at excellence in the 
 arts of design without a knowledge of the principles upon which 
 beauty of form is based ; but it should be kept in mind, that true 
 genius generally includes an intuitive perception of those principles 
 along with its creative power. It is, therefore, to the generality of 
 mankind that instruction in the definable laws of beauty will be of 
 most service, not only in improving the practice of those who follow 
 the arts professionally, but in enabling all to distinguish the true from 
 the false, and to exercise a sound and discriminating taste in judging 
 of artistical productions. .Esthetic culture should, therefore, super- 
 sede servile copying as the basis of instruction in our schools of art. 
 But it has been asserted that, by copying the great works of the 
 ancients, the mind of the pupil will become imbued with ideas similar 
 to theirs — that he will imbibe their feeling for the beautiful, and that, 
 consequently, he will become inspired with their genius, and think as 
 they thought. We, however, see very few satisfactory works of art 
 resulting from this imaginary process in the minds of the pupils; and, 
 indeed, it would be as unreasonable to suppose that the poetry of art 
 
ON AESTHETIC CULTURE. 
 
 9 
 
 is to be acquired by such means, as it would be to imagine that poetic 
 inspiration could be created by setting boys to transcribe the works 
 of the ancient poets. Sir Joshua Reynolds considers copying as a 
 delusive kind of industry, and observes that “ Nature herself is not to 
 be too closely copied. There are excellencies in the art of painting 
 beyond what is commonly called the imitation of nature. * * * A 
 
 mere copier of nature can never produce anything great.” And in 
 support of these views he quotes Proclus (Lib. II., in Timceum Platonis, 
 as cited by Junius, De Pictura Veterum), who says — “ He who takes 
 for his model such forms as nature produces, and confines himself to 
 an exact imitation of these, will never attain to what is perfectly 
 beautiful. For the works of nature are full of disproportion, and fall 
 very short of the true standard of beauty.” 
 
 It is remarked by Mr J. C. Daniel, in the Introduction to his 
 translation of M. Victor Cousin’s Pliiiosophy of the Beautiful , that 
 “ the English writers have advocated no theory which allows the beau- 
 tiful to be universal and absolute ; nor have they professedly founded 
 their views on original and ultimate principles. Thus, the doctrine 
 of the English school has for the most part been, that beauty is 
 mutable and special, and the inference that has been drawn from this 
 teaching is, that all tastes are equally just, provided that each man 
 speaks of what he feels.” He then observes, that the German and 
 some of the French writers have thought far differently ; for with 
 them the beautiful is “ simple, immutable, absolute, though its forms 
 
 c 
 
10 
 
 ON AESTHETIC CULTURE. 
 
 are manifold.” These observations are quite true as regards the 
 works of Hume, Burke, and Alison ; but these authors, although the 
 most popular, were not our only writers on taste. So far back as the 
 year 1725, the same truths advanced by the modern German and 
 French writers, and so eloquently illustrated by M. Cousin, were 
 given to the world in an anonymous publication, entitled, “ An 
 Note B. Inquiry into the Original of our Ideas of Beauty and Virtue.” This 
 author says — “ We, by absolute beauty, understand only that beauty 
 which we perceive in objects, without comparison to any thing exter- 
 nal, of which the object is supposed an imitation or picture, such as 
 the beauty perceived from the works of nature, artificial forms, 
 figures, theorems. Comparative or relative beauty is that which we 
 perceive in objects commonly considered as imitations or resemblances 
 of something else.” 
 
 Dr Reid also, in his Intellectual Powers of Man,* says, “That 
 taste which we may call rational, is that part of our constitution by 
 which we are made to receive pleasure from the contemplation of what 
 we conceive to be excellent in its kind, the pleasure being annexed to 
 this judgment, and regulated by it. This taste may be true or false, 
 according as it is founded on a true or false judgment. And if it may 
 be true or false, it must have first principles.” 
 
 M. Victor Cousin’s opinion upon this subject is, however, still more 
 
 * Chap, vi., p. 442. 
 
ON AESTHETIC CULTURE. 
 
 11 
 
 conclusive. He observes — “ If the idea of the beautiful is not abso- 
 lute, like the idea of the true — if it is nothing more than the 
 expression of individual sentiment, the rebound of a changing sen- 
 sation, or the result of each person’s fancy — then the discussions on 
 the fine arts waver without support, and will never end. For a 
 theory of the tine arts to be possible, there must be something abso- 
 lute in beauty, just as there must be something absolute in the idea 
 of goodness, to render morals a possible science.” * 
 
 That there are fixed principles which form the basis of ./Esthetic 
 science, is now very generally admitted ; and when these principles are 
 evolved with the same care which has characterized the labours of 
 investigators in natural science, and are applied in the fine arts as 
 the natural sciences have been in the useful arts, a solid foundation 
 will then be laid not only for correct practice, but also for a just 
 appreciation of productions in every branch of the arts of design. 
 
 In reference to the application of scientific truth as the basis of 
 artistic canons in art, Sir David Brewster justly says — “ It is in the 
 fine arts principally, and in the speculations with which they are 
 associated, that the controlling power of scientific truth has not exer- 
 cised its legitimate influence. 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 
 
 * Philosophy of the Beautiful , See. London : TV. Pickering. 
 
12 
 
 ON AESTHETIC CULTURE. 
 
 lias arisen whose speculations will brook no restraint, and whose deci- 
 sions stand in opposition to the strongest convictions of our senses. 
 That the external world, in its gay colours and lovely forms, is exhi- 
 bited to the mind only as a tinted mass, neither within nor without the 
 eye, neither touching it nor distant from it — an ubiquitous chaos which 
 experience only can analyze, and touch transform into the realities 
 which compose it ; that the beautiful and sublime in nature and in art 
 derive their power over the mind from association alone — are among 
 the philosophical doctrines of the present day, which, if it be safe, it is 
 scarcely prudent to question. Nor are these opinions the emanations 
 of poetical or ill-trained minds, which ingenuity has elaborated and 
 which fashion sustains. They have been given to the world with all 
 the authority of demonstrated truth ; and in proportion to the hold 
 which they have taken of the public mind, have they operated as a 
 check upon the progress of knowledge.”* 
 
 I shall now revert to that remote period when the arts of design 
 had attained a height which succeeding ages have in vain attempted to 
 reach, and by this means endeavour to ascertain the nature of the 
 doctrines then inculcated in connection with art. That the principles 
 of art, as well as of science, were taught in the early schools of Greek 
 philosophy, is admitted by almost all writers on the subject ; and it is 
 recorded of Pythagoras, that, on his return from his travels in search 
 
 * Edinburgh Revieic , vol. lxxviii., pp. 300, 301. 
 
OF AESTHETIC CULTURE. 
 
 13 
 
 of knowledge amongst the Phoenicians, Egyptians, and Chaldeans, 
 about 520 years before the Christian era, he exhibited to his disciples 
 and pupils, amongst other discoveries and improvements, a system of 
 analogy, or key, for finding all harmonious proportions in painting, 
 sculpture, architecture, and music ; and that it was by the help of this 
 analogical principle that the Grecians excelled all other nations in the 
 arts of architecture, sculpture, and painting ; and that, after the con- 
 quest of Greece by the Romans, the Grecian artists employed at Rome 
 kept this principle a profound secret amongst themselves. 
 
 This I find quoted by Hogarth, in the Preface to his “ Analysis of 
 Beauty,” upon the authority of a writer of the period called Christo- 
 pher Le Blon ; and although I have not been able to discover so defi- 
 nite a statement of a system of harmonious proportion borne out by 
 other writers upon the Pythagorean doctrines, yet I find sufficient to 
 render it highly probable that the principles included in this analogy, 
 which the Greeks certainly employed in the arts, emanated from the 
 school of Pythagoras. 
 
 These principles, in addition to the uncertainty of their origin, 
 seem for many centuries to have been buried in oblivion. It be- 
 comes, therefore, requisite to endeavour to arrive at some knowledge 
 of their nature, in order that we may see in what respects they were 
 connected with the known doctrines of Pythagoras. 
 
 It is well known, that in the time of that great philosopher the 
 treasures of science were veiled in mystery to all but the properly 
 
14 
 
 ON AESTHETIC CULTURE. 
 
 initiated, and the results of its various branches only given to the 
 world in works of art by those who had acquired this knowledge. So 
 strictly was this secrecy maintained amongst the disciples and pupils 
 of Pythagoras, that any one divulging the sacred doctrines to the pro- 
 fane was expelled the community, and none of his former associates 
 allowed to hold further intercourse with him : it is even said, that one 
 of his pupils incurred the displeasure of the philosopher for having 
 published the solution of a problem in geometry.* The difficulty, 
 therefore, which is expressed by writers, shortly after the period 
 in which Pythagoras lived, regarding a precise knowledge of his 
 theories, is not to be wondered at, more especially when it is considered 
 that he never committed them to writing. It would appear, however, 
 that he proceeded upon the principle, that the order and beauty so 
 apparent throughout the whole universe must compel men to believe 
 in, and to refer them to, an intelligent cause. To this Supreme Intel- 
 ligence, or active principle, the name of monad, or unity, was given, 
 because it must be always the same ; to matter, or the passive prin- 
 ciple, was given that of dyad, or multiplicity, because it is subject to 
 every kind of change ; f and to the world itself was given that of triad, 
 since it was the result of intelligence and matter. Pythagoras and his 
 disciples sought for properties in the science of numbers, by the know- 
 ledge of which they might attain to that of nature ; and they conceived 
 
 * Abbe Barthelemie’s Travels of Anacharsis in Greece , vol. iv., pj>. 193, 195. 
 
 + Or, more probably, because it was subject to two states only, viz., those of chaos and order. 
 
ON AESTHETIC CULTURE. 
 
 15 
 
 those properties to be indicated in the phenomena of sonorous bodies 
 Observing that Nature herself had thus irrevocably fixed the numerical 
 value of the intervals of musical tones, they justly concluded that, as 
 she is always uniform in her works, the same laws must regulate the 
 general system of the universe.* Pythagoras, therefore, considered 
 numerical proportion as the great principle inherent in all things, and 
 traced the various forms and phenomena of the world to numbers as 
 their basis and essence. 
 
 How the principles of numbers were applied in the arts is not 
 recorded, farther than what transpires in the works of Plato, whose 
 doctrines were from the school of Pythagoras. Li explaining the 
 principle of beauty, as developed in the elements of the material 
 world, he commences in the following words : — “ But when the Artificer 
 began to adorn the universe, he first of all figured with forms and 
 numbers, fire and earth, water and air ; which possessed, indeed, cer- 
 tain traces of the true elements, but were in every respect so consti- 
 tuted, as it becomes anything to he from which Deity is absent. But 
 we should always persevere in asserting that Divinity rendered them 
 as much as possible the most beautiful and the best, when they were 
 in a state of existence opposite to such a condition.” Plato goes on 
 farther to say, that these elementary bodies must have forms ; and as 
 
 * Abbe Barthelemie (vol. ii., pp. 168, 169), who cites as his authorities, Cicer. Do Nat. Door ., 
 Lib. I., cap. ii., t. 2, p. 405; Justin Mart., Omt. ad Gent., p. 10; Aristot. Metaph., Lib. I., cap. v., 
 t. 2, p. 845. 
 
16 
 
 ON AESTHETIC CULTURE. 
 
 it is necessary that every depth should comprehend the nature of a 
 plane, and as of plane figures the triangle is the most elementary, he 
 adopts two triangles as the originals or representatives of the isosceles 
 and the scalene kinds. The first triangle of Plato is that which forms 
 the half of the square, which is regulated by the number 2 ; and the 
 second that which forms the half of the equilateral triangle, which is 
 regulated by the number 3 : from various combinations of these he 
 formed the bodies of which he considered the elements to be com- 
 posed. To these elementary figures I shall have again to refer. 
 
 Vitruvius, who studied architecture many ages after the arts of 
 Greece had been buried in the oblivion which succeeded her conquest, 
 gives the measurements of various details of monuments of Greek art 
 then existing. But he seems to have had but a vague traditionary 
 knowledge of the principle of harmony and proportion from which 
 these measurements resulted. He says — “ The several parts which 
 constitute a temple ought to be subject to the laws of symmetry; the 
 principles of which should be familiar to all who profess the science 
 of architecture. Symmetry results from proportion, which, in the 
 Greek language, is termed analogy. Proportion is the commensura- 
 tion of the various constituent parts with the whole; in the existence 
 of which symmetry is found to consist. For no building can possess 
 the attributes of composition in which symmetry and proportion are 
 disregarded; nor unless there exist that perfect conformation of parts 
 which may be observed in a Avell formed human being.” After going 
 
ON AESTHETIC CULTURE. 
 
 17 
 
 at some length into details, he adds — “Since, therefore, the human 
 figure appears to have been formed with such propriety, and that the 
 several members are commensurate with the whole, the artists of anti- 
 quity” (meaning those of Greece at the period of her highest refine- 
 ment) “ must be allowed to have followed the dictates of a judgment 
 the most rational, when, transferring to the works of art principles 
 derived from nature, every part was so regulated as to bear a just 
 proportion to the whole. Now, although these principles were univer- 
 sally acted upon , yet they were more particularly attended to in the 
 construction of temples and sacred edifices, the beauties or defects 
 of which were destined to remain as a perpetual testimony of their 
 skill or of their inability.” 
 
 Vitruvius, however, gives no explanation of this ancient principle 
 of proportion, as derived from the human form ; but plainly shows 
 his uncertainty upon the subject, by concluding this part of his essay 
 in the following words : — “ If it be true, therefore, that the decenary 
 notation was suggested by the members of man, and that the laws of 
 proportion arose from the relative measures existing between certain 
 parts of each member and the whole body, it will follow, that those 
 are entitled to our commendation who, in building temples to their 
 deities, proportioned the edifices, so that the several parts of them 
 might be commensurate with the whole.” 
 
 It thus appears certain, that the Grecians at the period of their 
 highest excellence had arrived at a knowledge of some definite 
 
 D 
 
18 
 
 ON AESTHETIC CULTURE. 
 
 mathematical law of proportion, which formed a standard of perfectly 
 symmetrical beauty, not only in the representation of the human 
 figure in sculpture and painting, but in all other works of art in 
 which beauty of form constituted an excellence. That this law was 
 not deduced from the proportions of the human figure, as supposed 
 by Vitruvius, but had its origin in mathematical science, seems 
 equally certain ; for in no other way can we satisfactorily account 
 for the beau ideal head of ancient Greek art, or the inimitable pro- 
 portions of the Parthenon at Athens, far less for the general beauty 
 of form that pervades all other works of art of the period with 
 which we are acquainted. 
 
 This system of geometrical harmony, founded upon numerical 
 relations, must, consequently, have formed part of the Greek philo- 
 sophy of the period, by means of which the arts began to progress 
 towards that great excellence which they soon after attained. A 
 little farther investigation will show, that immediately after this period 
 a theory connected with art was acknowledged and taught, and, also, 
 that there existed a Science of Proportion. 
 
 Pamphilus, the celebrated painter, who flourished about four 
 hundred years before the Christian era, from whom Apelles received 
 the rudiments of his art, and whose school was distinguished for 
 scientific cultivation, artistic knowledge, and the greatest accuracy 
 in drawing, would admit no pupil unacquainted with geometry.* The 
 
 * Miiller’s Ancient Art and its Remains. 
 
ON ^ESTHETIC CULTURE, 
 
 19 
 
 terms upon which he engaged with his students were, that each 
 should pay him one talent (£225 sterling) previous to receiving his 
 instructions : for this he engaged “ to give them, for ten years, 
 
 LESSONS FOUNDED ON AN EXCELLENT THEORY.”* 
 
 It was by the advice of Pamphilus that the magistrates of Sicyon 
 ordained that the study of drawing should constitute part of the 
 education of the citizens — “ a law,” says the Abbe Barth elemie, 
 “ which rescued the fine arts from servile hands.” 
 
 It is stated of Parrhasius, the rival of Zeuxis, who flourished 
 about the same period as Pamphilus, that he accelerated the pro- 
 gress of art by purity and correctness of design ; “ for he was 
 acquainted with the Science of Proportions. Those he gave his 
 Gods and Heroes were so happy, that artists did not hesitate to 
 adopt them.” Parrhasius, it is also stated, was the first who gave 
 “ expressive airs of heads, mouths embellished by the graces, and 
 hair pourtrayed with delicacy.” He was so admired by his contem- 
 poraries, that they decreed him the name of Legislator. f The whole 
 history of the arts in Egypt and Greece concurs to prove that they 
 were based on geometric precision, and were perfected by a continued 
 application of the same science ; while in all other countries we find 
 them originating in rude and misshapen imitations of nature. 
 
 * Annchnrsis Travels in Greece. By the Abbe Barthelemie. Yol. ii., p. 325. 
 t Ibid, vi., p. 225. The authorities the Abbe quotes are — Quintil., Lib. XII , cap. x., p. 744; 
 Plin., Lib. XXXV., cap. ix., p. 691. 
 
20 
 
 OH AESTHETIC CULTURE. 
 
 In the earliest stages of Greek art, the gods — then the only 
 statues — were represented in a tranquil and fixed posture, with the 
 features exhibiting a stiff, inflexible earnestness, their only claim to 
 excellence being symmetrical proportion ; and this attention to geo- 
 metric precision continued as art advanced towards its culminating 
 point, and was thereafter still exhibited in the neatly and regularly 
 folded drapery, and in the curiously braided and symmetrically 
 arranged hair.* 
 
 These examples, few and imperfect as they are, cannot fail to 
 exhibit the great contrast that exists between the system of elemen- 
 tary education in art practised in ancient Greece, and that adopted 
 Note c. in this country at the present period. But it would be of very little 
 service to point out this contrast, were it not followed up by some 
 attempt to develop the principles which seem to have formed the 
 excellence of the Grecian system. This attempt, therefore, consti- 
 tutes the chief object in what follows; while along with it I shall 
 also endeavour to apply those principles practically in the reconstruc- 
 tion of the artistic head of ancient Grecian art. 
 
 * Miiller’s Archceoloc/y of A rt, c^-c. 
 
cm THE HARMONY OF NUMBERS. 
 
 21 
 
 PART III. 
 
 ON THE HARMONY OF NUMBERS, AND THE METHOD 
 OF APPLYING IT TO FORM. 
 
 In several former works I have given an outline of the harmony 
 of numbers, and have shown that, by the proper application of this 
 law to various branches of the arts of design connected with the 
 practice of the architect, the painter, the sculptor, the silversmith, 
 the potter, &c., their productions might be brought to a degree 
 of perfection equalling what we find in the finest works of the 
 ancients. As, however, I am now to treat of that harmony in con- 
 nection with the highest object of art, it becomes requisite to give 
 an outline of it here, in order to make what follows more easily 
 understood. 
 
 A writer in the British and Foreign Medical Review remarks, 
 with equal comprehensiveness and truth, that “ there is harmony 
 of numbers in all nature — in the force of gravity — in the planetary 
 
99 
 
 ON THE HARMONY OF NUMBERS, AND 
 
 movements — in the laws of heat, light, electricity, and chemical 
 affinity — in the forms of animals and plants — in the perceptions of 
 the mind. The direction, indeed, of modern natural and physical 
 science is towards a generalization which shall express the funda- 
 mental laws of all by one simple numerical ratio. We think modern 
 science will soon show that the mysticism of Pythagoras was mystical 
 only to the unlettered, and that it was a system of philosophy founded 
 on the then existing mathematics ; which latter seems to have com- 
 prised more of the philosophy of numbers than our present.”* 
 
 Harmony has been philosophically defined as “ the union of con- 
 trary principles having a ratio to each other ; ” which contrary prin- 
 ciples are those of uniformity and variety, and they are produced in 
 the abstract from the various modes in which units may be combined. 
 This numerical harmony is the root of every other species of har- 
 mony, whether addressed to the ear or the eye, and arises as 
 follows : — 
 
 The first mode of combination is that of one unit with another, 
 by which the number 2 is produced, which number is a submultiple 
 of 4, b, 8, progressively, as 2, 3, 4. It is the first even number ; 
 that is, it consists of two equal and similar portions, and these are 
 its only aliquot parts. It, therefore, may be termed the first prin- 
 ciple of uniformity. The second combination of the unit is 3, which 
 is the first odd number, and is a submultiple of the numbers 6, 9, 12, 
 
 * No. xxxv, P . 171. 
 
THE METHOD OF APPLYING IT TO FORM. 
 
 these being progressive multiples of 3, by 2, 3, 4. This number being 
 also the combination of 1 and 2, may be called the first principle of 
 inequality, or variety. The third mode of union is the combination 
 of the two contrary principles of 2 and 3, in the number 5. This 
 number is the third simple multiple of the unit, because it has no 
 other aliquot parts, and combines the binary and ternary principles 
 of union amongst units. It is a submultiple of the numbers 10, 15, 
 20, progressively, as 2, 3, 4. The numbers 2, 3, and 5, are, there- 
 fore, the first three multiples of the unit that have no other aliquot 
 parts ; and it will be shown, in the sequel, that by the union, in 
 proper proportions, of the contrary principles which they exhibit, the 
 proportion and symmetrical beauty of the human head and coun- 
 tenance may be abstractedly produced. 
 
 In form, generally, these principles may be applied through the 
 medium of the circle, because by the division of its arc into parts 
 called degrees, minutes, &c., the units are adopted by which the 
 harmonic ratios of numerical quantity may be applied to that primary 
 species of plane figure upon which the beauty of form especially 
 depends, namely, the triangle. The division of the circle into 360 
 parts, seems to me to prove clearly the application of the laws of 
 harmony to form by the earliest geometers ; for no other number 
 embodies, in the same harmonious relations, the numbers to which I 
 have just alluded as the source of all harmony, namely, 2, 3, and 5. 
 
 The division of the circle by its diameter into equal parts, gives 
 
24 
 
 ON THE HARMONY OF NUMBERS, AND 
 
 the base line from which all angles are calculated, by the degrees 
 contained in the arc which stands upon it, and these are in number 
 180, divisible into minutes, &c., as just stated. The division of the 
 semicircle by two gives the perpendicular line to the base which 
 divides the arc into quadrants, each of which contains 90°, and the 
 angle thus formed with the base line is called the right angle, be- 
 cause it is the most perfect of its kind, all angles having more 
 degrees being obtuse, and those having fewer being acute. This 
 angle may, therefore, be taken as the fundamental angle, to which 
 all others, in the first instance, should relate, as to a natural key ; 
 and it is by this means that the principle of harmonic ratio may be 
 applied to every species of form. 
 
 A rectilineal triangle is the simplest component figure of any 
 other rectilineal plane figure, because it has the smallest number 
 of sides and angles. It must, therefore, be to this figure that we 
 are to look for the most simple operation of those first principles 
 which give symmetry to forms. The proportions of all triangles are 
 regulated by the relative numbers of degrees which their angles 
 contain. 
 
 The primary rectilineal plane figure is the square, which is per- 
 fectly uniform, having four angles of 90°, making in all 360°, the 
 full number contained in the circle. When a square is bisected 
 through two of its angles, it is reduced to its most elementary com- 
 ponent figure, which is an isosceles triangle, having two angles of 45° 
 
THE METHOD OF APPLYING IT TO FORM. 
 
 each, and one of 90°. This peculiar triangle, when bisected through 
 its greatest angle, always produces two triangles with angles similar 
 to itself. (Plate I., fig. 1.) The relative numbers of degrees in the Plate i. 
 angles of this triangle, therefore, exhibit the primary harmonic ratios 
 of 1 to 1, and 1 to 2, in 45° to 45°, and 45° to 90°. 
 
 The secondary rectilineal plane figure is the equilateral triangle, 
 which, like the square, is perfectly uniform, having three angles 
 of 60°, making in all 180, the number contained in the arc of the 
 semicircle. When this triangle is bisected through one of its angles, 
 it exhibits its primary component figure, which is a scalene triangle, 
 having one angle of 30°, one of 60°, and one of 90°. This peculiar 
 right-angled scalene triangle is, therefore, the elementary figure of 
 which the equilateral triangle is composed ; but it cannot, like the 
 primary isosceles triangle, be divided into two of its own kind, the 
 smallest number that this or any other right-angled scalene triangle 
 can be divided into being four. (Plate I., fig. 2.) The numbers 
 of degrees in this scalene triangle exhibit relatively to each other 
 the harmonic ratios of 1 to 2, 1 to 3, and 2 to 3, in 30° to 60°, 
 
 30° to 90°, and (10° to 90°. 
 
 The pentagon may be termed the tertiary rectilineal plane figure, 
 having five angles of 108° each, making in all 540° — the number 
 contained in three semicircles, or the amount of degrees in the 
 angles of the two preceding figures, the square and triangle. When 
 a pentagon is bisected through one of its angles and one of its sides, 
 
 E 
 
26 
 
 ON THE HARMONY OF NUMBERS, AND 
 
 the right-angled scalene triangle formed by the bisecting line and 
 the half of its side will he found to be its most elementary component 
 figure, and will contain at its three angles respectively 18°, 72°, and 
 90°. (Plate I., fig. 3.) The numbers of degrees in the three angles 
 of this triangle, therefore, exhibit in their relative quantities the har- 
 monic ratios of 1 to 4, 1 to 5, and 4 to 5, in 18° to 72°, 18° to 90°, 
 and 72° to 90°. 
 
 The degrees at the angles of those triangles, and their ratios to 
 the right angle, may be thus represented : — 
 
 II. 
 
 90° 
 
 I. I. I. 
 
 45° 45° 30' 
 
 III. 
 
 
 
 V. 
 
 
 90° 
 
 
 
 90° 
 
 
 
 II. 
 
 I. 
 
 
 IY. 
 
 
 o 
 
 O 
 
 CD 
 
 18° 
 
 
 72° 
 
 Each of these harmonic ratios is compounded of others of a less 
 simple kind. Thus, the simple ratio of 1 to 2, between 45° and 90°, 
 is compounded of the two less simple ratios of 2 to 3, and 3 to 4, 
 in 45° to 07° 30', and 07° 30' to 90°; and these two ratios being 
 multiplied together, the lesser term of the one by the lesser term 
 of the other, and the greater term of the one by the greater term 
 of the other, produce 0 and 12, which have the same ratio to each 
 other as 1 to 2. Again, the ratio of 2 to 3, between (10° and 90°, 
 may be divided into the less simple ratios of 4 to 5, and 5 to 6, 
 
THE METHOD OF APPLYING IT TO FORM. 
 
 27 
 
 in 60° to 75°, and 75° to 90°; and these ratios being multiplied as 
 before will produce 20 and 30, which numbers have the same ratio to 
 each other as 2 to 3. Lastly, the ratio of 4 to 5, between 72° and 
 90°, is divisible into the two less simple ratios of 8 to 9, and 9 to 
 10, in 72° to 81°, and 81° to 90° ; and these ratios being multiplied 
 as before, give 72 and 90, which numbers are to each other in the 
 ratio of 4 to 5. 
 
 The following are, therefore, the numerical ratios found in the 
 angles of those three triangles : — 
 
 1 
 
 to 2 
 
 in 
 
 45° 
 
 to 
 
 OD 
 
 O 
 
 o 
 
 2 
 
 — 3 
 
 — 
 
 o 
 
 O 
 
 <D> 
 
 — 
 
 00 
 
 O 
 
 o 
 
 3 
 
 — 4 
 
 — 
 
 45° 
 
 — 
 
 CO 
 
 o 
 
 o 
 
 3 
 
 — 5 
 
 — 
 
 18° 
 
 — 
 
 o 
 
 o 
 
 CO 
 
 4 
 
 — 5 
 
 — 
 
 72° 
 
 — 
 
 oc 
 
 o 
 
 o 
 
 5 
 
 — 6 
 
 — 
 
 60° 
 
 — 
 
 72° 
 
 5 
 
 — 8 
 
 — 
 
 45° 
 
 — 
 
 72° 
 
 1 
 
 — 3 
 
 — 
 
 o 
 
 O 
 
 CO 
 
 — 
 
 o 
 
 O 
 
 CO 
 
 1 
 
 — 4 
 
 — ■ 
 
 18° 
 
 — 
 
 72° 
 
 1 
 
 — 5 
 
 
 
 18° 
 
 
 
 00 
 
 O 
 
 o 
 
 And these ratios correspond exactly to those of the rapidity in 
 the pulsations of the atmosphere, which, according to the well estab- 
 lished laws of the science of acoustics, produce the most perfect 
 consonances of sound upon the ear. This analogy, I may add, is in 
 
28 
 
 ON THE HARMONY OF NUMBERS, AND 
 
 no way forced ; but arises naturally and necessarily from these 
 simple elements of plane geometry. 
 
 The two first of these triangles have been called the two sym- 
 metrical triangles of Plato, who refers to them in the following 
 words : — “ Of the two triangles, the isosceles is allotted one nature, 
 but the oblong, or scalene, is characterized by infinity. We ought, 
 therefore, to choose the most beautiful among infinities, if we wish 
 to commence our investigations in a becoming; manner.”* These 
 three triangles are the primary elements of the five regular solids, 
 or Platonic bodies, which are, the tetrahedron — bounded by four 
 equilateral triangles ; the octahedron — bounded by eight equilateral 
 triangles ; the icosahedron — bounded by twenty equilateral triangles ; 
 the hexahedron, or cube — bounded by six squares; and the dodeca- 
 hedron — bounded by twelve pentagons. Besides these five, there can 
 be no other solids bounded by like, equal, and regular plane figures, 
 and the solid angles of which are all equal. 
 
 In describing these, Plato confines himself to the four first, and 
 merely hints at the Dodecahedron in these words : — “ There is also 
 a certain fifth composition which Divinity employed in the fabrica- 
 te D. tion of the universe.” This body may, therefore, have been dis- 
 covered by some other geometer. Be that as it may, these triangles 
 are not only the elements of the most beautiful rectilineal plane 
 figures, but of the most beautiful rectilineal solid bodies. 
 
 * The Works of Plato, translated by Taylor, vol ii., p. 526 . 
 
THE METHOD OF APPLYING IT TO FORM. 
 
 29 
 
 Every regular rectilineal plane figure has a curvilineal figure 
 which exclusively belongs to it. For instance, if we take one of the 
 equal sides of the primary isosceles triangle, which is half of the 
 square, as a radius of a curvilineal figure, of which the right angle 
 of the triangle is the centre, a circle will be described whose cir- 
 cumference will necessarily pass through both its other angles. 
 (Plate I., fig. 4.) The circle is, therefore, the curvilineal figure that 
 exclusively belongs to the primary isosceles triangle. 
 
 If, in like manner, we take the two unequal sides of the primary 
 scalene triangle, which is half of the equilateral triangle, as the semi- 
 diameters of a curvilineal figure, of which the right angle of the 
 triangle is the centre, an ellipse will be described, the circumference 
 of which will necessarily pass through each of the other two angles. 
 (Plate I., fig. 5.) This ellipse, which has many peculiar properties, 
 fully described elsewhere,* is, therefore, the curvilineal figure that 
 exclusively belongs to the primary scalene triangle. As the revo- 
 lution of the circle upon its diameter will produce a sphere, so 
 the revolution of the ellipse upon its transverse diameter null pro- 
 duce a prolate spheroid ; and these two bodies are, consequent! y, 
 the curvilineal solids arising from the elementary figures in which 
 tiie principles of geometric harmony have been found to exist. 
 It will therefore be seen, that the figures I have adopted as the 
 elements of beauty, namely, the square, the equilateral triangle, 
 
 * Essay on Ornamental Design , p. 24. 
 
30 
 
 ON the harmony of numbers. 
 
 the pentagon, the circle, and the ellipse whose proportions are derived 
 from the elementary figure of the equilateral triangle, have not been 
 chosen empirically, but are what have been in every age acknow- 
 ledged to be the most beautiful of all forms. Before applying these 
 elements in illustration of the science of those proportions which 
 distinguish the ideal head of ancient Greek art, it will be requisite 
 to say something of the general form and proportions of the 
 human head and countenance. 
 
O N THE GENERAL FORM, &c. 
 
 31 
 
 PART IV. 
 
 ON THE GENERAL FORM AND BEAUTY OF THE HUMAN 
 HEAD AND COUNTENANCE. 
 
 The most remarkable characteristics in the structure of the human 
 head are, its globular form (or rather such union of the globular 
 and spheroidal forms as results, both in the external figure and in 
 its sections, in the ovoid), and the approximation of the plane of the 
 face to a vertical line ; for in none of the lower animals does' the 
 skull present so near an approach to this form, nor the plane of the 
 face to this direction. These peculiar characteristics are variously 
 modified among the numerous races of mankind ; but one law appears 
 to influence the whole. They are invariably found most prominently 
 developed in the highly refined and most intellectual races of men, 
 while the most barbarous tribes present the greatest departure from 
 them, their heads being distinguished by compression of the anterior 
 portion of the skull, and the consequent prominence of the mouth. 
 
32 
 
 ON THE GENERAL FORM AND BEAUTY OF 
 
 generally accompanied with flatness of the nose. The highest and 
 most cultivated races, however, present only an approximation to the 
 perfect development of those distinguishing marks of humanity. 
 
 Mankind is thus characterized by the partial development of a 
 principle of beauty, in the form and position of the head and face, 
 deducible from mathematical laws. A little further investigation will 
 show, that the arrangement of the organs of sense upon the facial 
 surface approximates to the development of another modification of 
 the same principle, constituting its primary element of beauty. 
 
 In art, upon the other hand, we find that the development of this 
 principle has, at a very early period, been carried to a higher degree 
 of perfection than has been found in any single example in nature, 
 and that the works of that period present to us a degree of mathe- 
 matical beauty nowhere else discoverable. This species of beauty 
 has been called the ideal, in contradistinction to that of ordinary 
 nature, from which it differs in being free from the deformities and 
 peculiarities constituting the individuality by which men are distin- 
 guished from each other. 
 
 Some writers upon beauty have asserted that there is no original, 
 or positive beauty in the human countenance, and that our sense of 
 the beautiful, as relative to it, arises from the association of ideas 
 alone ; while others affirm that this depends entirely upon expression. 
 Sir Charles Bell, in his excellent essay upon the subject,* has shown 
 
 * The A natomy and Philosophy of Expression, S,c. Fourth Edition. London : J ohn Murray, ] 847. 
 
THE HUMAN HEAD AND COUNTENANCE. 
 
 33 
 
 most clearly that such doctrines are erroneous, and that there exists 
 in the permanent form of the human head and face an innate beauty, 
 altogether independent of the enhancement of expression, or of any 
 association of ideas in the mind of the beholder. He observes, that 
 those who have hitherto written on the sources of beauty have not 
 attained to the right principle, because they have not only lost sight 
 of nature, but of what may justly he called the philosophy of the 
 subject. In respect to the permanent form and beauty of the human 
 head and face, in contradistinction to expression, Sir Charles says — 
 “ Beauty of countenance may be defined in words, as well as demon- 
 strated in art. A face may be beautiful in sleep, and a statue with- 
 out expression may he highly beautiful.” “ But it will he said, there 
 is expression in the sleeping figure, or in the statue. Is it not rather 
 that we see in these the capacity for expression ? — that our minds are 
 active in imagining what may be the motions of those features when 
 awake or animated ? Thus, we speak of an expressive face before we 
 have seen a movement, grave or cheerful, or any indication in the 
 features of what prevails in the heart. Avoiding a mere distinction 
 in words, let us consider, first, why a certain proportion and form 
 of face is considered beautiful, and conveys the notion of capacity of 
 expression ; and, secondly, the movements, or the actual expression 
 of emotion. I believe that it is the confusion between the capacity 
 of expression and the actual indication of thought, that is the cause 
 of the extraordinary difficulty in which the subject is involved.” 
 
 F 
 
34 
 
 ON THE GENERAL FORM AND BEAUTY OF 
 
 This capacity for expression certainly enhances onr admiration of 
 the human countenance, but it is more a concomitant of the primary 
 cause of its beauty than the cause itself. This cause, I believe, will 
 be found to rest on a more simple and secure basis, namely, on geome- 
 tric harmony ; for the nearer the countenance approximates to a har- 
 monious combination of the most perfect figures in geometry, or, 
 rather, the more its general form and individual parts, with their rela- 
 tive proportions, are regulated by such figures, the higher will be its 
 degree of beauty, while unaffected by expression, and the greater will 
 be its capacity for the expression of the passions. 
 
 The Greeks were the first to impart this species of beauty to 
 representations of the human head and countenance in the statues 
 of their deities ; but the means by which they thus excelled ordinary 
 nature has been long buried in oblivion, and has, consequently, for 
 many ages, formed a subject of discussion to all who have treated 
 of the arts of design. Some of the earliest writers upon the subject, 
 in the enthusiasm of their admiration, asserted that either the gods 
 must have descended to the earth, or that the artists must have 
 ascended to heaven, in order to enable the latter to impart this qua- 
 lity to their works. Modern writers have attempted to account for 
 it more rationally, but the point is still far from being finally deter- 
 mined. Perhaps the most plausible opinion is that which attributes 
 the attainment of this excellence by the ancient Greek artists, to 
 their having long studied what the human countenance possessed in 
 
THE HUMAN HEAD AND COUNTENANCE. 
 
 35 
 
 common, and having thereby acquired the faculty of observing in 
 what individuals were deficient, they thus arrived at a perfect 
 idea of beauty. To embody this idea and refine upon nature, they 
 composed a species of collective beauty, by selecting various parts 
 from the most perfect models they could find in nature, which they 
 combined together in one figure, thus producing ideal beauty. It is, 
 therefore, the characteristic of this school, that the ideal beauty 
 of ancient Greek art can only be arrived at by means of imitation. 
 
 There have not been wanting those, however, who have affirmed, that 
 it was not by the study of natural forms that the Greeks gave ideal Note E. 
 beauty to their works, but by some creative and abstract principle. 
 
 M. Victor Cousin, in his Philosophy of the Beautiful , draws the dis- 
 tinction between what are termed real beauty and ideal beauty, more 
 clearly than any other author with whose works I am acquainted. He 
 says — “ If the object that I wish to copy after nature present some 
 beauty, the imitation is beautiful ; but, after all, I only achieve real 
 beauty. If I am not satisfied with one object, and I bring together a 
 great number of models, and, in painting a human figure, take the 
 forehead from one, the eyes from another, the smile from a third, I 
 shall obtain beauty real and collective, but not ideal ; for my work 
 wall not contain a single trait that cannot be found in one or other 
 of the originals. In the same manner that we have distinguished 
 absolute from collective ideas, we shall now separate ideal beauty 
 from real beauty. But those who advocate the real exclusively, deny 
 
36 
 
 ON THE GENERAL FORM AND BEAUTY OF 
 
 the existence of the ideal, or say that it consists only in union, or in 
 choice ; which is equivalent to the negation of the ideal. The school 
 opposed to them allows, on the contrary, only the ideal, and makes 
 a complete abstraction of the models of nature ; they are artists 
 who work de tete — this is their expression. The first school, which 
 desires to see nothing in art but an imitation of the real, forgets 
 that all it meets in nature is but imperfect beauty — that the beau- 
 tiful is concealed beneath the real. The second school, which takes 
 notice of the ideal alone, falls into the opposite error, and produces 
 works that are unapproachable by our senses. The ideal alone is 
 cold and lifeless. We need not neglect the real in the school of art, 
 any more than the collective idea in the school of metaphysics ; 
 but we ought not to pause at the merely collective, or at the merely 
 real. * * * The ideal without the real is lifeless ; but the real 
 
 without the ideal is destitute of pure beauty. Both ought to be 
 united. The two schools ought to give each other the hand, and 
 be allied: the noblest works of art are the result of such a union. 
 Thus, beauty is an absolute idea, and not a copy of finite, accidental, 
 and imperfect nature. The idea can make itself visible in the bosom 
 of nature, but it is always veiled and imperfect. It shines more 
 brightly in the works of man, because the arm guided by intelli- 
 gence approaches nearer to the model the mind has conceived ; but 
 still the idea can never be entirely unfolded.” This I conceive 
 to be a just definition of what is meant by ideal beauty. 
 
THE HUMAN HEAD AND COUNTENANCE. 
 
 37 
 
 Various attempts have been made to detine geometrically the 
 difference between the ordinary and the ideal beauty of the human 
 head and countenance, the most prominent of which is that of Cam- 
 per. He traced, upon a profile of the skull, a line in a horizontal 
 direction, passing through the foramen of the ear and the exterior 
 margin of the sockets of the front teeth of the upper jaw, upon which 
 he raised an oblique line, tangential to the margin of these sockets, 
 and to the most prominent part of the forehead. Agreeably to the 
 obliquity of this line, he determined the relative proportion of the 
 areas occupied by the brain and by the face, and hence inferred the 
 degree of intellect. When he applied this measurement to the 
 heads of the antique statues, he found the angle much greater than 
 in ordinary nature ; hut that this simple fact afforded no rule for the 
 reproduction of the ideal beauty of ancient Greek art, is very evident 
 from the heads and countenances by which his treatise is illustrated. 
 Sir Charles Bell justly remarks, that although, by Camper’s method, 
 the forehead may be thrown forward, yet, while the features of com- 
 mon nature are preserved, we refuse to acknowledge a similarity to 
 the beautiful forms of the antique marbles. 44 It is true,” he says, 
 44 that by advancing the forehead it is raised, the face is shortened, 
 and the eye brought to the centre of the head. But with all this, 
 there is much wanting — that which measurement, or a mere line, 
 will not show “us.” — 44 The truth is, that we are more moved by the 
 features than by the form of the whole head. Unless there be a 
 
38 
 
 ON THE GENERAL FORM AND BEAUTY OF 
 
 conformity in every feature to the general shape of the head, throw- 
 ing the forehead forward on the face produces deformity; and the 
 question returns with full force — How is it that we are led to con- 
 cede that the antique head of the Apollo, or of the Jupiter, is beau- 
 tiful when the facial line makes a hundred degrees with the horizontal 
 line ? In other words — How do we admit that to be beautiful which 
 is not natural? Simply for the same reason that, if we discover a 
 broken portion of an antique, a nose, or a chin of marble, we can 
 say, without deliberation, This must have belonged to a work of anti- 
 quity ; which proves that the character is distinguishable in every 
 part — in each feature, as well as in the whole head.” 
 
 Dr Oken says upon this subject:* — “ The face is beautiful whose 
 nose is parallel to the spine. No human face lias grown into this 
 estate, but every nose makes an acute angle with the spine.” “ The 
 facial angle is, as is well known, 80°. ” “ What, as yet, no man has 
 
 remarked, and what is not to be remarked, either, without our view 
 of the cranial signification, the old masters have felt through inspira- 
 tion. They have not only made the facial angle a right angle, but 
 have even stepped beyond this — the Homans going up to 96°, the 
 Greeks even to 100°. Whence comes it that this unnatural face 
 of the Grecian works of art is still more beautiful than that of the 
 Homan, when the latter comes nearer unto nature? The reason 
 
 * Phisio-philosophi/. By Dr Oken. 
 
 London : 184S. 
 
 Translated by Talk, and published by the Ray Society. 
 
THE HUMAN HEAD AND COUNTENANCE. 
 
 39 
 
 thereof resides in the fact of the Grecian artistic face representing 
 nature’s design more than that of the Roman; for in the former, the 
 nose is placed quite perpendicular, or parallel to the spinal cord, 
 and thus returns whither it has been derived.” 
 
 Other various and conflicting opinions upon this subject have been 
 given to the world ; but we find that the principle from which the 
 ideal beauty arose in the head and countenance, as represented in 
 works of ancient Greek art, is still a matter of dispute. When, how- 
 ever, we examine carefully a fine specimen, we find its beauty and 
 grandeur to depend more upon the degree of harmony amongst its 
 parts, as to their relative proportions and mode of arrangement, than 
 upon their excellence taken individually. It is, therefore, clear that 
 those who attribute the beauty of ancient Greek sculpture merely to 
 a selection of parts from various models must be in error. No assem- 
 blage of parts from ordinary nature could have produced its principal 
 characteristic, the excess in the angle of the facial line, much less 
 could it have led to that exquisite harmony of parts by which it is so 
 eminently distinguished; neither can we reasonably agree with Dr 
 Oken and others, who assert that it was produced by an exclusive 
 degree of the inspiration of genius bestowed upon the ancient Greek 
 artists. 
 
 That the inspiration of genius, combined with a careful study of 
 nature, were essential elements in the production of the great works 
 which have been handed down to us, no one will deny ; but these 
 
 Note F. 
 
40 
 
 ON THE GENERAL FORM AND BEAUTY, &c. 
 
 elements have existed in all ages, whilst the ideal head belongs 
 exclusively to the Greeks of the periods of Pythagoras and Plato. 
 Is it not, therefore, reasonable to suppose, that, besides genius and the 
 study of nature, another element was employed in the production of 
 this excellence, and that this element arose from the precise mathe- 
 matical doctrines taught in the schools of these philosophers ? 
 
 Muller has said — “ The principles which the ancients followed in 
 regard to proportions (»AA, symmetria numeris ) — and we know that 
 this was a main object of artistic study — are naturally difficult to 
 discover and determine, on account of the manifold modifications 
 introduced by the application of them to different ages, sexes, and 
 characters.” * 
 
 In what follows, I shall attempt to determine those principles of 
 Note G. proportion, and thereby to remove the difficulty referred to by so 
 many writers upon art, and to which Miiller here alludes. 
 
 * Ancient Art and its Remains. By C. O. Muller. Translated from the German, by John 
 Leitch. London : A. Fullarton & Co. 
 
THE SCIENCE OF PROPORTION. 
 
 41 
 
 PART V. 
 
 THE SCIENCE OF PROPORTION IN RELATION TO REPRE- 
 SENTATIONS OF THE HUMAN HEAD AND COUNTE- 
 NANCE. 
 
 In Part III. I have endeavoured to explain the ./Esthetic nature of 
 numerical harmonic ratio, and the method by which it may be 
 employed in applying the science of proportion to forms generally. 
 Part IY. is designed to point out the distinguishing peculiarities 
 of form in the human head and countenance, and wherein the ideal 
 representations of ancient Greek art differ from ordinary nature. 
 In the present Part it is sought to show that, by the application 
 of these principles of numerical harmonic ratio, in accordance with 
 a system of descriptive geometry, artistic representations of the 
 human head and countenance may be produced, possessing all the 
 characteristic beauties of form and proportion which distinguish 
 those of ancient Greek art ; and, at the same time, to point out 
 
 G 
 
42 
 
 THE SCIENCE OF 
 
 Plate L 
 %■ 6 . 
 
 one of the deviations from this system by which ordinary nature 
 is distinguished. 
 
 Camper’s system of comparison between the beauty of the ideal 
 head of ancient Greek art and that of ordinary nature, in its 
 various degrees of intellectual capacity, as already explained in Part 
 IV., was confined to the relative prominence upon the facial surface 
 of the frontal bone of the cranium and the lower bones of the 
 face, and was, consequently, very limited in its application. Blu- 
 
 menbach, finding this to be the case, and that, even within its 
 
 limited range, it did not accurately apply in some cases, adopted 
 what he termed the vertical rule. He drew his comparisons by 
 arranging the crania, with the cheek bones in a horizontal line, 
 so as to view them from behind the vertex, and thus he deter- 
 mined their degrees of approximation to the highest scale of intel- 
 lect by the projection of the facial bones beyond those of the 
 cranium ; while Professor Owen recommends viewing the skull 
 from its base, the lower jaw being removed. In the descriptive 
 
 geometry adopted in this treatise, all these aspects are given, with 
 
 the addition, in every case, of a front view of the skull, so that 
 the peculiarities of each aspect are derived from the same relative 
 proportions, and the harmonious or inharmonious arrangement of 
 the parts. My process is as follows: — Having determined the size 
 , of the head to be represented, construct the right-angled isosceles 
 triangle, A B C (the first of Plato, and half of the square), making 
 
PROPORTION. 
 
 43 
 
 its side, A C, one-third of the determined length ; and from the 
 point C, with a radius, C A or C B, describe the circle A B D E. 
 Construct within this circle the scalene triangle A F G (the second 
 of Plato, and half of the equilateral triangle), and taking its sides 
 as semi-diameters, describe the ellipse A F H I, of which A H is 
 the major axis, and F I the minor axis. 
 
 These two triangles are symmetrically proportioned to each other 
 in relative size, the second being formed within the curvilineal 
 figure belonging to the first, and, consequently, being in vertical 
 length to it in the ratio of 3 to 2. These curvilineal figures, as 
 explained in Part III,, are those that belong exclusively to the 
 triangles from the sides of which they have received their propor- 
 tions ; and they are, like the triangles themselves, necessarily in the 
 same symmetrical proportion to each other. 
 
 Let it now be supposed that these two curvilineal plane figures 
 represent the solid bodies which a revolution upon their vertical axes 
 would produce, namely, a sphere and a prolate spheroid, and that 
 these bodies are united and partially amalgamated, so that the cir- 
 cumference of the sphere passes through the centre of the prolate 
 spheroid, as exhibited in the next diagram. Construct the triangle Plate i., 
 A B C, describe the circle ABLE, and construct the triangle A F G, 
 as in fig. 6. Through F draw F FI, equal and parallel to G A ; pro- 
 duce G F, making F I equal to F G ; join I H, forming the triangle 
 I H F ; describe the ellipse HI R G, of which II K is the major axis, 
 
44 
 
 THE SCIENCE OF 
 
 and I G the minor axis. This diagram, therefore, represents a 
 vertical section, through A H, or side view, of fig. 6. 
 
 Fig. 8 represents a horizontal section, or vertical aspect, of these 
 Plate I., united bodies. Construct the isosceles triangle ABC, and describe 
 
 tig. S. 
 
 the circle A B D E, as in figure 6 ; make C F equal to the minor 
 axis of the ellipse A F H I, figure 6 ; bisect this line in G, and 
 with a radius, G C, describe the circle F H C I. 
 
 These two bodies, thus proportioned and united, represent the 
 typical form of the human head and face, as it arises from this 
 combination of the elements of geometrical beauty. From what 
 follows, it will he seen that the organs of sense may he proportioned 
 and arranged, agreeably to the same laws, upon the facial surface, 
 the reader bearing in view that the surfaces of these curvilineal 
 bodies, in whatever aspect they may be represented, are understood 
 to be referred to a plane — the only way in which any form can be 
 depicted on the retina of the eye. 
 
 Construct a diagram as in fig. 6, Plate I. ; bisect G H in L, 
 
 Plate II., F G in M, and G I in N ; join M L and L N ; bisect M G in 0, 
 fig. i. 
 
 and from the centre M, with the radius M 0, describe the circle 0 ; 
 make L V and N Z equal to M 0, and from the centres L and N, 
 with the radii L V and N Z, describe the circles Y and Z. Con- 
 struct the right-angled isosceles triangle L Q R, with its right angle 
 at L, and its base tangential to the circle whose centre is L, and 
 draw the line K P through L, parallel to F I ; draw A K, making 
 
PROPORTION. 
 
 45 
 
 the angle at A 18°, and complete the isosceles triangles ABE, 
 A F I, and A K P. This diagram is composed of the elements 
 of the five regular geometrical solids, and depends upon these ele- 
 ments for its proportions. 
 
 A side view of these united bodies, with a diagram of the situa- 
 tion and proportions of the organs of sense which thus present 
 themselves, is the result of the following process: — Construct a 
 diagram the same as fig. 7, Plate I. ; bisect F Iv in M ; draw the 
 line M L at right angles with II K. From L draw the line L N at 
 an angle of 60° with the line L M ; draw the line N 0 parallel to 
 H K ; draw the line L P parallel to M K, and through Iv draw 
 P K parallel to L M. From each of the points L and N describe 
 a circle with a radius equal to M O, fig. 1. Construct the right- 
 angled isosceles triangle, L Q R, with its right angle at Q ; draw 
 c d parallel to II Iv, and d S tangential to the circle around L. 
 Thus, the two triangles which determine the proportions of the 
 features are, as in fig. 1, the first and second of Plato. 
 
 To show the position of the figures represented in the two pre- 
 ceding diagrams upon a horizontal section, or vertical aspect, of the 
 two united bodies, construct a diagram the same as fig. 8, Plate I. ; 
 make a b, figs. 3 and 4, equal to a b, fig. 2 ; through a, with a 
 radius M 0, fig. 1, describe the circle of which L is the centre. 
 Construct the right-angled isosceles triangle L M N, and describe 
 circles around M, N, and C, whose radii are equal to L a. 
 
 Plate II., 
 fig. 2. 
 
 Plate II., 
 figs. 3 and 4. 
 
 o 
 
46 
 
 THE SCIENCE OF 
 
 Plate II., 
 %• 1 - 
 
 The harmonic relations of the angles of the three triangles 
 employed in the construction of these diagrams have already been 
 explained; and if we add to these triangles other two, A X D 
 and A S Y, fig. 1, we have the following series: — 
 
 First, a triangle whose angles are 
 
 45° 
 
 45° 
 
 90' 
 
 Second, 
 
 o 
 
 O 
 
 CO 
 
 o 
 
 O 
 
 CO 
 
 90' 
 
 Third, 
 
 22° 30' 
 
 67° 30' 
 
 90' 
 
 Fourth, 
 
 18° 
 
 to 
 
 o 
 
 90' 
 
 Fifth, 
 
 15° 
 
 75° 
 
 90 
 
 These exhibit the following: harmonic ratios to the right angle : — 
 
 © © © 
 
 
 Smallest Angles 
 
 i at A. 
 
 
 Middle 
 
 Angles at 
 
 B F X 
 
 K S. 
 
 
 45° 
 
 to 90° ratio 1 
 
 to 2 
 
 45° 
 
 to 90° 
 
 ratio 
 
 1 to 
 
 2 
 
 30° 
 
 — 90° - 
 
 - 1 
 
 — 3 
 
 60° 
 
 — 90° 
 
 — 
 
 2 — 
 
 3 
 
 22° 
 
 30' _ 90° - 
 
 - 1 
 
 — 4 
 
 07° 30' 
 
 — 90° 
 
 — 
 
 3 — 
 
 4 
 
 18° 
 
 — 90° - 
 
 - 1 
 
 — 5 
 
 72° 
 
 — 90° 
 
 — 
 
 4 — 
 
 5 
 
 15° 
 
 — 90° - 
 
 - 1 
 
 — 6 
 
 75° 
 
 — 90° 
 
 — 
 
 5 — 
 
 6 
 
 The consecutive relations of these angles are as follow : — 
 
 
 Smallest Angles. 
 
 
 
 
 Middle Angles. 
 
 
 30° 
 
 to 45° ratio 
 
 2 to 
 
 3 
 
 45° 
 
 to 60° ratio 3 
 
 to 4 
 
 22° 30' 
 
 — 30° — 
 
 3 — 
 
 4 
 
 o 
 
 O 
 
 CO 
 
 — 67° 30' — 8 
 
 — 9 
 
 18° 
 
 _ 22° 30' — 
 
 4 — 
 
 5 
 
 67° 30' 
 
 _ 72 0 _ 15 
 
 — 16 
 
 15° 
 
 — 18° ' — 
 
 5 — 
 
 6 
 
 72° 
 
 _ 750 _ 24 
 
 — 25 
 
PROPORTION. 
 
 47 
 
 If we now accommodate tlie anatomical structure of the bones Plate in. 
 
 figs. 1, 2, 
 
 of the head to this systematic arrangement of geometrical harmony, 3 > 4 
 we have the skull exhibited in its various aspects on Plate III., 
 figs. 1, 2, 3, 4. 
 
 In the ideal heads and countenances of ancient Greek art which 
 still exist, there is necessarily considerable variety as to general 
 forms and relative proportions of parts, and, as already observed, 
 this has led many who have treated of the subject to assume that 
 it must be difficult, if not altogether impossible, to determine any 
 definite rules for the regulation of these proportions. This difficulty 
 I shall now attempt to remove — begging of the reader, at the same 
 time, to keep in mind that I confine myself to such variety as belongs 
 to the permanent form of the anatomical structure, knowing that 
 to impart the variety which results from the action of the muscles, 
 and gives sentiment and expression to the countenance in obedience 
 to mental impulses, requires the highest efforts of genius, and, con- 
 sequently, belongs to a branch of art beyond the scope of a trea- 
 tise, the sole object of which is to point out the primary laws of 
 geometric harmony from which the countenance derives the beauty 
 of its proportions. 
 
 The principal varieties in the permanent form of the human 
 head and countenance, as represented in works of ancient Greek 
 art, are those which give, on the one hand, feminine delicacy, and, 
 on the other, masculine power ; and these are not only sometimes 
 
48 
 
 THE SCIENCE OF 
 
 blended, but exchanged, in the Greek ideal heads, as they often are 
 in those of ordinary nature. Of this, the heads of Minerva, Venus, 
 Juno, Apollo, Hercules, Bacchus, &c., afford ample evidence. But 
 in thus referring to these examples, it is scarcely necessary to 
 remark, that as the laws of harmonic proportion which I now seek 
 to illustrate leave untouched what belongs to the wider field of 
 creative genius, they can in no way interfere with the higher themes 
 Note H. of /Esthetic criticism in relation to ancient Greek art. I shall, there- 
 fore, proceed with the legitimate object of this treatise, and endea- 
 vour to show, geometrically and systematically, in what these cha- 
 racteristic varieties in form and proportion consist, without reference 
 to any existing examples. 
 
 The proportions resulting from the numerical ratios in the angles 
 of the triangles employed in constructing the diagrams in Plate II., 
 will, I believe, on referring to Plate III., be generally acknowledged 
 to have produced a purely feminine character of head in its anato- 
 mical structure, although, as compared with ordinary nature, of a 
 severely geometrical cast. The change in these ratios by which a 
 masculine character of anatomical structure may be arrived 
 at is of an equally specific kind. Instead of the series of triangles 
 employed in constructing the diagrams in Plates I. and II., the fol- 
 lowing are adopted — the first, second, and fourth being the principal, 
 and the third and fifth the two additional ones which necessarily 
 result from these : — 
 
PKOPORTIOX. 49 
 
 First, a triangle whose angles are 
 
 45° 
 
 45° 
 
 90 ! 
 
 Second, 
 
 33° 45' 
 
 56° 15' 
 
 90' 
 
 Third, 
 
 27° 
 
 63° 
 
 90' 
 
 Fourth, 
 
 22° 30' 
 
 67° 30' 
 
 90‘ 
 
 Fifth, 
 
 18° 
 
 72° 
 
 90' 
 
 Exhibiting the following ratios to the right angle : — 
 
 
 
 Smallest Angles at j 
 
 i. 
 
 
 
 Middle An 
 
 gles at 
 
 B F X 
 
 K S. 
 
 
 45° 
 
 
 to 90° ratio 
 
 1 to 
 
 2 
 
 45° 
 
 to 
 
 90° 
 
 ratio 
 
 1 to 
 
 2 
 
 33° 
 
 45' 
 
 — 90° — 
 
 3 — 
 
 8 
 
 56° 
 
 15' — 
 
 90° 
 
 — 
 
 5 — 
 
 8 
 
 27° 
 
 
 — 90° — 
 
 3 — 
 
 10 
 
 63° 
 
 — 
 
 90° 
 
 — 
 
 7 — 
 
 10 
 
 22° 
 
 30' 
 
 — 90° — 
 
 1 — 
 
 4 
 
 67° 
 
 30' — 
 
 90° 
 
 — 
 
 3 — 
 
 4 
 
 18° 
 
 
 — 90° — 
 
 1 — 
 
 5 
 
 72° 
 
 — 
 
 90° 
 
 
 
 4 — 
 
 5 
 
 The angles of these triangles have the following relations to each 
 other consecutively : — 
 
 Smallest Angles. 
 
 33° 45' to 45° ratio 3 to 4 
 
 27° — 33° 45' — 4 — 5 
 
 22° 30' — 27° —5 — 6 
 
 18° _ 22° 30' — 4 — 5 
 
 45° 
 
 Middle Angles. 
 
 to 56° 15' ratio 4 to 5 
 
 56° 15' — 63° —8—9 
 
 63° — 67° 30' — 14—15 
 
 67° 30' 
 
 72° 
 
 — 15 
 
 16 
 
 The principal change, and that which governs the other triangles, 
 it will he observed, is made upon the second triangle, which gives 
 
 Plate VI., 
 fig. 1. 
 
 H 
 
50 
 
 THE SCIENCE OE 
 
 its proportions to the prolate spheroid. Its smallest angle being 
 33° 45', is to the smallest angle of the first triangle in the ratio 
 of 3 to 4, instead of 2 to 3, which was the ratio between these 
 angles in the first diagram. The change from 30° to 33° 45' gives 
 a ratio of 8 to 9. 
 
 Between these two specific kinds of proportion there lie numerous 
 intermedia, one of which, namely, that which lies midway between 
 Plate iv., the two, I here give as a connecting link. Construct the right- 
 angled isosceles triangle ABC, and describe the circle A B E, as 
 in Plate II., fig. 1; within this construct the scalene triangle A F G, 
 making its angle at A 31° 52' 30". Taking the sides of this tri- 
 angle as semi-diameters, describe the ellipse A F H I ; within this 
 ellipse construct the scalene triangle A K L, making its angle at 
 A 21° 15' ; bisect G F in M, G I in N, and M G in O ; and with a 
 radius, M O, describe the circles of which M N and L are the centres. 
 Construct the right-angled isosceles triangle, Q L It, and the diagram 
 Plate iv., of the intermediate form of head is complete. Figs. 2, 3, and 4, 
 
 figs. 2, 3, 
 
 and 4. as in Plate II., give the various aspects of these combined figures, 
 Plate v., as referred to a plane; and Plate V., figs. 1, 2, 3, and 4, the ana- 
 
 igs. 1, 2, 
 
 .3, and 4. toiuical structure agreeably to these proportions. 
 
 A diagram of the purely masculine proportions, the triangles of 
 
 which have already been described, is formed in the following man- 
 
 Piate vi., ner : — Construct the right-angled isosceles triangle A B C, propor- 
 fig- i • 
 
 tioning the length of its sides to the full length of the intended head 
 
 O o O 
 
PROPORTION. 
 
 51 
 
 in the ratio of 4 to 11, instead of 4 to 12, as in the first diagram, 
 and describe the circle A B L E, as in fig. 1, Plate II. ; within 
 this circle construct the scalene triangle A F G, making its angle at 
 A 33° 45'. Taking the sides of this triangle as semi-diameters, 
 describe the ellipse A F FI I ; within this ellipse construct the scalene 
 triangle A K L, making its angle at A 22° 30' ; bisect G F in M, 
 G I in N, and M G in 0 ; and with a radius, M O, describe the circles 
 around M, N, and L. Construct the right-angled isosceles triangle 
 Q L R, and the two additional scalene triangles, A X Z and A S V, 
 making the first 27° at A, and the second 18° at A. Repeat all the 
 scalene triangles on the opposite side, and the diagram is complete. 
 Figs. 2, 3, and 4 receive their proportions from fig. 1, as in Plates 
 II. and IV. 
 
 In Plate VII., the anatomical structure of the bones of the head 
 is accommodated, in the four principal aspects, to this specific change 
 in the geometrical harmony. On comparing this structure of skull 
 with that given in Plate III., the characteristic difference in the 
 general form, and in the relative proportions of parts (the whole 
 being more square and massive), seems characterized by such a 
 change in form and proportion as usually distinguishes the male 
 from the female skeleton. 
 
 The effects of this process of geometrical construction of the 
 human head upon its external appearance, are exhibited in Plate 
 VIII., figs. 1 and 2 of which are a front and a side view of the 
 
 Plate VI., 
 figs. 2, 3, 
 and 4. 
 
 Plate VII., 
 figs. 1, 2, 3, 
 and 4. 
 
 Plate VIII. 
 figs. 1 and 2 
 
52 
 
 THE SCIENCE OF 
 
 head and countenance, resulting from the first species of geometrical 
 harmony. The predominating figure of this is the scalene triangle 
 of 30°, 60°, and 90°, and will, I believe, he acknowledged as decid- 
 edly feminine in character. 
 
 The head of which figs. 3 and 4 are a front and side view, is 
 Plate vm , the result of the medial combination — the predominating or ruling 
 
 figs. 3 and 4. 
 
 figure of which is the scalene triangle of 31° 52' 30", 58° 7' 30", 
 and 90°. This head is neither decidedly masculine nor decidedly 
 feminine in its general form and proportions. 
 
 The decidedly masculine character of head and countenance 
 
 which results from that species of geometrical harmony governed by 
 
 Plate vm , the triangle of 33° 45', 56° 15', and 90°, is given in front and pro- 
 figs. 5 and 6. 
 
 file, in figs. 5 and 6. 
 
 This operation of the numerical harmonic ratios in the con- 
 struction of the ideal head of ancient Greek art, proves that the 
 science of those proportions which distinguish it is identical with the 
 well-established science of acoustics, and while it is as mathematically 
 precise in its fundamental principles, it equally admits of an endless 
 variety in the production of those works which are governed by its 
 laws. It is a fact remarked by Dr Oken in his Pliysio-philosophy, 
 that “ there are only two art senses, the eye and the ear ; and thus 
 but two departments of art, the plastic and the sonant, or that of 
 form and motion.” The result of this investigation, therefore, is 
 the most satisfactory that could have been rationally looked for, 
 
PROPORTION. 
 
 namely, that these senses, in their receptive powers, and the mind, 
 in its perceptive faculty as to what these senses convey to it, are 
 governed by one law of nature. 
 
 The establishment of this law, however, induces me to differ 
 from Dr Oken and others, when they say that the ideal head of 
 ancient Greek art is unnatural, because there has not been found 
 any individual in nature with a head fully exemplifying the pro- 
 portions by which it is characterized. If I have succeeded in proving 
 that the science of these proportions is identical with the science 
 of acoustics, the ideal head of ancient Greek art is not only the most 
 beautifid, but also the most natural — its form and proportions being 
 the full development of a law which is only partially developed in 
 ordinary nature. It will be shown in the sequel that, imperfect as 
 this development is in general, it is sufficiently decided in all cases 
 to give to the human head that characteristic form which so dis- 
 tinctly marks the difference between it and those of the lower 
 animals. 
 
 It certainly has not been recorded by any who have hitherto 
 investigated the subject, that an individual has been found with a 
 head and countenance in every respect possessed of equal beauty 
 of form with those represented in ancient Greek art ; yet it remains 
 to be proved that examples of such could not have existed in nature, 
 or may not exist. No countenance can be pronounced unnatural 
 unless it be deformed ; and although such an inclination of the 
 
54 
 
 THE SCIENCE OF 
 
 major axis of the spheroid as will throw its vertex towards that of the 
 sphere, changes the relative proportions, and lowers the head and 
 countenance in the scale of humanity, this does not produce defor- 
 mity, unless carried beyond certain well-defined limits, presently to 
 be pointed out. But to give, in any degree, such a direction to the 
 major axis of the spheroid as would throw its vertex outwards 
 from that of the sphere, will produce deformity of a species too 
 often to he found in works of art, where the effect of superior intel- 
 lect is attempted to be imparted by an exaggerated imitation of the 
 peculiarities of the antique. 
 
 The human head, like every other object in nature, must have 
 uniformity, combined with variety, to render it symmetrically beau- 
 tiful ; but these qualities must be confined within certain bounds 
 in their relations to each other. The uniformity consists in the 
 correspondence between the lateral halves, and the variety in the 
 relative proportions and situations of the features. There are, con- 
 sequently, even in the ideal head, various modes in which the fea- 
 tures may be arranged, without departing from ideal beauty, but 
 only producing a change in its character. One of these changes is 
 
 Plate ix., exemplified in Plate IX. Figs. 1 and 2 of this Plate are a front 
 
 tigs. 1 and 2. 
 
 and side view of the head, resulting from the first process, with the 
 triangles G M L, and G N L, Plate II., fig. 1, altered from 30°, (10°, 
 and 90° each, to 31° 52' 30", 58° 7' 30", and 90°, being the propor- 
 tions of tl ie triangle upon which the ellipse of the intermediate head 
 
PROPORTION. 
 
 oo 
 
 is described. Figs. 3 and 4 are a front and side aspect of the same Plate ix , 
 
 figs. 3 and 4. 
 
 bead, with these triangles altered to 33° 45', 56° 15', and 90° — the 
 same proportions as the triangle upon which the ellipse of the mas- 
 culine head is described. Figs. 5 and 6 are a front and side view of Plate ix., 
 
 figs. 5 and 6. 
 
 the intermediate head, with this change, that the point L, fig. 1, Plate 
 IV., is placed upon the circumference of the circle, by which the centre 
 triangles have angles of 37° 30', 52° 30', and 90°. These changes 
 give a more sensual cast to the features, without, however, reducing 
 their intellectual capacity, because they do not affect the form of the 
 cranium, or its relative proportion to the bones of the face, but 
 simply the relative proportions between the length of the upper and 
 of the under jaw. But the variety of ordinary nature is of a different 
 description, and most frequently manifests itself in the development 
 of these laws in an infinity of degrees of imperfection. 
 
 In regard to this original perfection in the form and proportions 
 of the human head and countenance — for such I conceive it to be — 
 innumerable causes have operated, and do still continue to operate, 
 on the one hand, in degrading it, and, on the other, in counteracting 
 this degradation ; and to these operations may be attributed that 
 endless variety of countenance by which nations, classes, and indi- 
 viduals, are distinguished. Amongst such causes the effect of climate, 
 and, still more, the degree of civilization under which a people is 
 trained, seem to be the most effective. There can be no doubt that 
 all the features are affected, to a great extent, by continual exposure 
 
• 5(3 
 
 THE SCIENCE OF 
 
 to excesses of heat or cold ; but their character is more permanently 
 formed by the degrees of moral restraint, as well as by the priva- 
 tions and toil induced by the state of society. In savage life, on the 
 one hand, the want of mental cultivation, and the consequent dor- 
 mancy of the reasoning powers, must ultimately rob the countenance 
 of its inherent capacity for intellectual expression. The modes, also, 
 by which the means of existence are procured, along with continual 
 exposure to the inclemency of the seasons, must produce a permanent 
 expression of mere animal desire, and even, in some cases, of brutal 
 ferocity. In civilized life, on the other hand, the employment of the 
 higher faculties of the mind, agreeable occupations and amusements, 
 refined modes of supplying the wants of nature, and the protection 
 afforded from the inclemency of the weather, must all conduce towards 
 regularity of the features, and impart to the countenance a permanent 
 composure and serenity. 
 
 As the passions by which the mind is thus moved, and the modes 
 in which the wants of nature are supplied, act upon the muscles of 
 the face, in giving them an enduring character, so must these 
 muscles, in course of time, act upon the hones to which they are 
 attached, producing a permanent effect upon the structure of the 
 skull, which ultimately becomes hereditary in nations and classes. 
 Hence the protruding jaws and high cheek-bones of savage tribes, as 
 compared with those of the more civilized races of mankind. 
 
 I shall now endeavour to illustrate the process by which the 
 
PROPORTION. 
 
 57 
 
 anatomical structure of the head geometrically changes from the most 
 perfect development of the science of proportion, as exemplified in 
 works of ancient Greek art, down to the most imperfect of ordinary 
 nature. 
 
 It has been observed in Part IV., that the structural characteristic 
 of the human head was such a mixture of the globular, or spherical, 
 and spheroidal forms, as resulted in an ovoidal figure, either in a 
 front or vertical aspect, and that the natural position of the profile 
 tended towards a vertical direction ; also, that the nearer to the per- 
 fectly vertical, the more intellectual and beautiful is the cast of the 
 countenance, and consequently, the more it inclines towards the hori- 
 zontal, it becomes the less marked by these characteristics of humanity. 
 In the combination of the sphere with the prolate spheroid, which 
 forms the basis of the geometrical process by which the ideal heads 
 explained in this part, and shown in Plates VIII. and IX., are pro- 
 duced, the axis of the spheroid is made parallel to a vertical line 
 passing through the centre of the sphere; to which parallelism, agree- 
 ably to the principles adopted in this treatise, the principal distinc- 
 tion between the artistic head of ancient Greek art and that of 
 ordinary nature is to be attributed. According to the same principles, 
 I shall now proceed to show how a departure from this parallelism 
 affects the general structure of the head, and relative position of the 
 features upon the facial surface, and that it does so without any 
 change being made on the proportions farther than what the degree 
 
 i 
 
58 
 
 THE SCIENCE OF 
 
 of this inclination produces. The farthest limit to which I shall carry 
 this inclination of the axis is 27°, which gives the general form and 
 characteristic proportions of the head of the African negro, or those 
 of a European of the lowest grade. According to many writers on the 
 natural history of man, there have existed abnormal races of a lower 
 class than this change in the geometrical structure indicates ; but the 
 discussion of such questions does not influence my subject, as the 
 existence or non-existence of such races leaves the principles I am 
 attempting to demonstrate unaffected. 
 
 Between the vertical position of the axis and an inclination of 27°, 
 there are an ample number of gradations to embrace every species 
 of characteristic form ; but in order to give a sufficiently marked dis- 
 tinction, I shall take, as a connecting link, an inclination of 18°. The 
 parallelism of the axis of the spheroid to the vertical axis of the 
 sphere, in the examples already given, enabled me to commence with 
 the diagram of a front view of the head and countenance ; but, as in 
 such an aspect the inclination about to be given could not be per- 
 ceived, unless in its effects, I shall now commence with the diagram 
 of a profile, which, accordingly, is fig. 1, in the following examples, 
 instead of fig. 2, as in those already given. The change from the 
 ideal, exhibited in this connecting link, may be described as follows : — 
 Construct a diagram of the circle and first ellipse, with their prin- 
 cipal divisions, as in fig. 2, Plate II., but, instead of making the 
 major axis of the ellipse II K parallel to the vertical diameter A I) 
 
 Plate X., 
 
 % 1- 
 
PROPORTION. 
 
 59 
 
 of the circle A E D B, give its vertex, H, an inclination of 18°, 
 keeping its centre, F, on the circumference of the circle A E D B, 
 and its own circumference tangential to a line, Y Z, drawn through 
 A, at right angles with A D. Upon this diagram draw the line a b 
 through F, parallel to A D. At right angles with a b, draw the lines 
 E t, through C ; c d, through X ; e S, through L ; and g h, through f. Plate X., 
 
 figs. 2, 3, 
 
 The other three diagrams, figs. 2, 3, and 4, of this example, take their and 4. 
 proportions from the vertical and horizontal lines of fig. 1. 
 
 Plate XI. exhibits the change upon the anatomical structure of Plate XI., 
 
 figs. 1, 2, 3, 
 
 the bones of the head and face, produced by this inclination of the aiul 4 - 
 axis of the first ellipse, and, consequently, of the axis of the pro- 
 late spheroid which it represents. 
 
 Plate XII. exhibits the change upon the anatomical structure, Plate xii., 
 
 figs. I, 2, 3, 
 
 agreeably to the second, or intermediate, proportions. and 4 - 
 
 Plate XIII. exhibits the change upon the anatomical structure, Plate xm., 
 
 figs. 1, 2, 3, 
 
 agreeably to the third, or most masculine, proportions. and 4 - 
 
 Figs, 1, 2, 3, 4, 5, and 6, of Plate XIV., exemplify the external Plate xiv., 
 
 figs. ], 2, 3, 
 
 appearance of the heads and countenances formed upon the anato- 4 - aml <>• 
 
 mical structure, agreeably to the three kinds of proportions, as 
 
 modified by the inclination of 18° of the prolate spheroid. 
 
 The diagram in Plate XV., except in one point, being the same Plate xv., 
 
 % 4 - 
 
 as that given in Plate X., farther description is unnecessary, than 
 merely to state that the inclination of the axis of the spheroid is 
 here carried to 27°, which I conceive to be its natural limit. This 
 
60 
 
 THE SCIENCE OF 
 
 Figs. 2, 3, 4. 
 Plates XVI., 
 XVII., and 
 XVIII. 
 
 Plate XIX. 
 
 Plate XX., 
 figs. 1. 2, 3, 
 4, 5, and 6. 
 
 Plate XXI. 
 
 farther inclination, it will he observed, materially affects the other 
 figures, and gives to the three anatomical structures which follow, in 
 Plates XVI., XVII, and XVIII., the peculiar characteristics of form 
 which belong to the skull of the negro. These, like the three fore- 
 going skulls, are drawn upon diagrams of the first, second, and third 
 class, or of the feminine, medial, and masculine proportions ; and 
 the following example gives the heads and countenances formed 
 upon them, with the characteristic thick lips and woolly hair of the 
 African negro. 
 
 Although thick lips and woolly hair (unless in rare and apparently 
 accidental exceptions) compose part of the clothing of this structure 
 of skull in the African negro, they do not seem to assist in lower- 
 ing the intellectual character of the countenance resulting from it. 
 These peculiarities in the clothing of the structure appear rather to 
 modify the effects of its departure from the mathematical beauty with 
 which the Creator originally endowed it. This I have endeavoured 
 to make apparent, by clothing the same skulls with such European 
 features as are suitable to their structure. A species of countenance 
 is thus produced not unfrequently to he met with amongst ourselves, 
 and evidently the result of a degraded state of society. 
 
 When we compare the heads on Plate XIV. with the antique or 
 ideal heads on Plate VIII., there seems a very considerable hiatus. 
 In order, therefore, to give a connecting link, I have exemplified 
 the effects of an inclination of 9°, the exact intermediate between 
 
PROPORTION. 
 
 61 
 
 a vertical position and an inclination of 18°. The head and features 
 resulting from this diagram, and given in Plate XXII., although Plate xxii. 
 
 figs. 3 and 4- 
 
 exhibiting such an approximation to a full development of the 
 science of proportion as we seldom meet with in ordinary nature, 
 is still evidently devoid of the peculiar grandeur produced by the 
 perfect parallelism of the axis of the prolate spheroid to the vertical 
 axis of the sphere. 
 
 To the Plates given in illustration of the nature of the science 
 of proportion, and the mode of its application, I have added other 
 three, in order to show the effect of some of those geometric heads 
 when freed from the lines of the diagrams, and decorated in the 
 Greek style. 
 
 Figs. 1 and 2, of Plate XXIII., are a front view and profile of a Plate xxm. 
 female head, drawn agreeably to the geometric diagram and anato- 
 mical structure in Plates II. and III. Figs. 3 and 4, are a front and 
 side aspect of a male head, drawn agreeably to the diagram and ana- 
 tomical structure in Plates VI. and VII. These heads are given, with 
 the lines upon them, in Plate VIII., figs. 1 and 2, 5 and 6. 
 
 Figs. 1, 2, 3, and 4, of Plate XXIV., are front views and profiles Plate xxiv. 
 of two female heads, drawn agreeably to the geometric diagram and 
 anatomical structure in Plates II. and IIP, and modified, as shown 
 
 in Plate IX., figs 1, 2, 3, and 4. 
 
 Figs. 1 and 2, of Plate XXV., are a front view and profile of a Plate xxv 
 female head, drawn agreeably to the geometric diagram and ana- 
 
(32 
 
 THE SCIENCE OF PROPORTION. 
 
 tomical structure in Plates IV. and V. This head is given, with the 
 geometrical lines upon it, in Plate VIII., figs. 3 and 4. Figs. 3 and 4, 
 are a front view and profile of the same head, with the geometrical 
 construction modified, as shown by the male head, figs. 5 and 6, 
 Plate IX. 
 
 Thus have I endeavoured to trace to its primary elements the 
 beauty of proportion which distinguishes the artistic head of ancient 
 Greek art from that of ordinary nature. I have shown that these 
 elements are of the most simple kind, and that the peculiarity of 
 their nature consists in an embodiment of the fundamental principles 
 of numerical ratio ; which, thus applied, are as much the cause of that 
 harmony of form by which all the parts unite in one pleasing whole, 
 as they are, by a well understood law of nature, the source of harmony 
 amongst various sounds when simultaneously addressed to the ear. 
 These ratios are, therefore, the first principles of formative beauty, 
 and constitute a science of proportion sufficiently definite to admit of 
 universal application in the arts of design. 
 
NOTES. 
 

 
NOTES. 
 
 NOTE A, (P. 6.) 
 
 The distinction between the truly beautiful and the merely agreeable is clearly defined 
 by Cousin. He observes — “ When we cast our eyes over existing nature, whether it 
 be over the life that is called human, or that more extensive organic life, or even over 
 inanimate nature, subject only to mechanical laws, we meet with objects that make us 
 feel pleasing or painful sensations. A form is present to your eyes, and at the moment 
 that you know it is, you feel an agreeable or a disagreeable sensation. If you are asked 
 why it pleases you, you cannot give a reason ; if you ai’e told that it displeases others, 
 you are not surprised, because you know that sensibility is not constant, and that it is 
 not necessary to dispute about sensations. Up to this point we have not slipped into 
 the domain of art ; its object is beauty, and we are but at the agreeable. Now, does 
 it not sometimes happen that a form is not only agreeable to us, but, beyond this, that 
 it appears beautiful to us ? When we were asked why it was agreeable to us, we could 
 only have answered, according to our individual right, ‘ I am the sole judge of what 
 pleases or displeases me; 1 but when we are asked why we call this form beautiful, we 
 appeal to an authority which is not our own, which is imposed on all men — the authority 
 of reason. ...... 
 
 “To the question, AVhat are the characteristics of the agreeable and of the beautiful l 
 we reply, that it will be shown presently that unity, proportion, simplicity, regularity, 
 
 K 
 
66 
 
 NOTES. 
 
 grandeur, and generality, appear more or less in objects that we call beautiful ; and that 
 variety, motion, pliantness, energy, and individuality, are marks of the agreeable.”* 
 
 The want of a more extensive dissemination of such correct and comprehensive views 
 upon this subject, has led to the erroneous notion that every one has a right to hold his 
 own opinions as to the beauty of proportion in works of formative art. The author, 
 therefore, feels that he cannot recommend too strongly to his readers the study of Cousin’s 
 excellent work, from which the above extract is taken. 
 
 NOTE B, (P. 10.) 
 
 The full title of the work here referred to is — An Inquiry into the Original of our Ideas 
 of Beauty and Virtue : in two Treatises , in which the Principles of the late Earl of Sha/ts- 
 bury are Explained and Defended against the Author of the Fable of the Bees ; and the 
 Ideas of Moral Good and Evil are established , according to the Sentiments of the Ancient 
 Moralists. With an Attempt to introduce a Mathematical Calculation in subjects of Morality. 
 London: 1725. 
 
 The author of this work makes many excellent observations upon the nature of 
 beauty with reference to art, from which I shall select the following. He observes (p. 6) 
 — “ The only pleasure of sense that our philosophers seem to consider, is that which 
 accompanies the simple ideas of sensation ; but there are vastly greater pleasures in 
 those complex ideas of objects, which obtain the names of beautiful, regular, harmo- 
 nious.” 
 
 At p. 7 he says, “It is of no consequence whether we call these ideas of beauty and 
 harmony, perceptions of the external senses of seeing and hearing, or not. I should 
 rather choose to call our power of perceiving these ideas an internal sense , were it only for 
 the convenience of distinguishing them from other sensations of seeing and hearing which 
 men may have without perception of beauty and harmony.” 
 
 ' The Philosophy of the Beautiful. From the French of Victor Cousin. Translated, with Notes and an 
 Introduction, by Jesse Cato Daniel, Cheshunt College. London : William Pickering. 1848. 
 
NOTES. 
 
 67 
 
 This is exactly the difference between what we are enabled to pronounce as beautiful, 
 or, simply, as pleasing to our senses. 
 
 At p. 33 are the following observations : — “ As to the works of art, were we to run 
 through the various artificial contrivances or structures, we should find the foundation 
 of the beauty which appears in them to be constantly some kind of uniformity , or unity 
 of proportion among the parts, and of each part to the whole. As there is a vast diver- 
 sity of proportions possible, and different kinds of uniformity , so there is room enough for 
 that diversity of fancies observable in architecture , gardening , and such like arts, in dif- 
 ferent nations: they all may have uniformity , though the parts in one may differ from 
 those in another. The Chinese or Persian buildings are not like the Grecian and Roman , 
 and yet the former has its uniformity of the various parts to each other, and to the whole, 
 as well as the latter. In that kind of architecture which the Europeans call regular , 
 the uniformity of parts is very obvious, the several parts are regular figures , and either 
 equal or similar at least in the same range ; the pedestals are parallelopipedons , or square 
 prisms ; the pillars, cylinders nearly ; the arches circular, and all those of the same row 
 equal ; there is the same proportion everywhere observed in the same range between the 
 diameters of pillars, and their heights — their capitals, and the diameters of arches— the 
 heights of the pedestals, the projections of the cornice, and all ornaments in each of our five 
 orders. And though other countries do not follow the Grecian or Roman proportions, yet 
 there is even among them a proportion retained, a uniformity , and resemblance of cor- 
 responding figures ; and every deviation in one part from that proportion which is 
 observed in the rest of the building, is displeasing to every eye, and destroys or diminishes 
 at least the beauty of the whole. 
 
 “ The same might be observed through all other works of art , even to the meanest 
 utensil, the beauty of every one of which we shall always find to have the same foundation 
 of uniformity amidst variety, without which they shall appear mean, irregular, and 
 deformed.” 
 
 The soundness of these doctrines is not surpassed, and has been seldom equalled, by 
 writers upon art of the present day. 
 
68 
 
 NOTES. 
 
 NOTE C, (P. 20.) 
 
 I think it requisite to lay the following facts before the reader, connected as they are 
 with the mode of aesthetic culture adopted in this country. 
 
 So far back as March 1836, a select committee of the House of Commons was 
 appointed “ to inquire into the best means of extending a knowledge of the Arts and 
 of the Principles of Design among the people (especially the manufacturing popula- 
 tion) of the country ; also, to inquire into the constitution, management, and effects 
 of institutions connected with the arts. 1,1 
 
 Amongst many others, I had the honour to be examined before this committee, and 
 on that occasion stated my firm conviction that the best mode of extending a knowledge 
 of art and of the principles of design among the people (especially the manufacturing 
 population) of the country, would be to disseminate such printed instructions as would 
 enable the rising generation to commence a system of self-tuition, by first practising the 
 drawing of geometrical figures by the free hand, and then to study from the large well- 
 developed leaves of such plants as were to be found on the road-sides and hedge-rows 
 throughout the country ; observing, that as great elegance of form is to be found in the 
 common dock, the thistle, the fern, and even in a stalk of oats or barley, those who thus 
 formed their taste, when they came to study the ornamental remains of Athens and 
 Rome, would find themselves familiar with the source from which the beauty of those 
 works was in a great measure derived ; for the ancients adopted the most common pro- 
 ductions of nature for the leading features of their ornamental designs. I also observed, 
 that this kind of study could not be commenced too early, or made too general, as, 
 independently of its usefulness, it would prove a continual source of pleasure to all who 
 might adopt it — and being a means of drawing out the latent talent of the country, 
 would thereby form a test by which teachers could select their pupils ; concluding, 
 that schools established upon such a basis would conduce more to originality of orna- 
 mental design amongst our manufacturing population than any other means that could 
 be employed. 
 
NOTES. 
 
 69 
 
 When asked by the chairman, if I did not consider that free access to a collection of 
 casts from the antique would be of service, I replied, “Undoubtedly it would; but 
 such examples would be of tenfold benefit to those who had brought themselves to a 
 degree of proficiency by the mode I have already recommended. It is at this stage that 
 the works of the ancients ought to be studied, in order to derive benefit from their beau- 
 tiful combinations, but not servilely copied : I consider servile copying of the works of 
 others very injurious to the ornamental designer, as it retards originality of conception.” 
 — {Report, 568 — Arts and Manufactures — 1 6th August 1836. Pp. 37 to 43.) 
 
 Such was the general tenor of the suggestions I made on that occasion ; but they do 
 not seem to have had any weight with the committee, as the result of its labours was the 
 establishment, early in the following year (1837), of a Government School of Design at 
 Somerset House, in which the means employed for “ extending a knowledge of the Arts 
 and of the Principles of Design amongst the manufacturing population of the country” 
 have been lately brought to light, in the following manner : — 
 
 In 1847, ten years after the establishment of this school, a committee of the Board 
 of Trade was appointed to investigate the mode in which it forwarded the objects for 
 which it was instituted. One of the leading witnesses examined before this committee 
 says — “ At present, copying is the plan laid down, and thus the pupil is led to no higher 
 exertion of his faculties than the desire to imitate.” Another witness says — “ Instead 
 of any attempt being made to teach the principles of any style of ornament, the only 
 principle acted upon is that of continual copying. And this system is not merely suf- 
 fered, but encouraged ; indeed, I may say that it is the only system taught.” 
 
 The result of this investigation has necessarily been an alteration in the constitution 
 of the school, by which it is hoped better means may be used for extending a knowledge 
 of art amongst the people. 
 
 One of the resolutions, in the Report of the second special committee, augurs well, 
 being a step towards a system of self-tuition, namely — “ That the Committee of Instruc- 
 tion should take into immediate consideration the question of establishing elementary 
 schools, and the practicability of relieving the head school of a large number of young 
 students who have not attained a certain degree of knowledge of the principles and prac- 
 tice of drawing.” 
 
70 
 
 NOTES. 
 
 The facts to which I have alluded, however, fully warrant the statements I have made 
 in the text regarding our mode of aesthetic culture. 
 
 NOTE D, (P. 28.) 
 
 In order that the reader may judge for himself as to the accuracy of what I have stated 
 in the text regarding the Platonic theory, as translations of the works of that phi- 
 losopher are not very widely circulated, I shall here (as in a former work) give the whole 
 passage referring to these triangles : — 
 
 “ But when the Artificer began to adorn the universe, he first of all figured with forms 
 and numbers fire and earth, water and air, which possessed, indeed, certain traces of the 
 true elements, but were in every respect so constituted as it becomes anything to be from 
 which Deity is absent. But we should always persevere in asserting that Divinity ren- 
 dered them as much as possible the most beautiful and the best, when they were in a 
 state of existence opposite to such a condition. I shall now, therefore, endeavour to 
 unfold to you the distribution and generation of these by a discourse, unusual indeed, 
 but to you who have trod in all the paths of erudition through which demonstration is 
 necessarily obtained, perspicuous and plain. In the first place, then, that fire and earth, 
 water and air, are bodies, is perspicuous to every one. But every species of body pos- 
 sesses profundity ; and it is necessary that every depth should comprehend the nature 
 of a plane. Again, the rectitude of the base of a plane is composed from triangles. But 
 all triangles originate from two species, one of which possesses one right angle, and the 
 other two acute angles, and one of these contains one right angle distributed with equal 
 sides ; but, in the other, unequal angles are distributed with unequal sides. Hence, pro- 
 ceeding according to assimilative reasons, conjoined with necessity, we shall establish a 
 principle of this kind as the origin of fire and all other bodies. The supernal principles 
 of these, indeed, are known to Divinity, and to the man who is in friendship with 
 I )i vinity. 
 
 “ But it is necessary to relate by what means four most beautiful bodies were pro- 
 duced, dissimilar, indeed, to each other, but which are able, from certain dissolutions 
 
NOTES. 
 
 71 
 
 into each other, to become the sources of each other’s generation ; for if we are able to 
 accomplish this, we shall obtain the truth concerning the generation of earth and fire, 
 and of those elements which are situated according to analogy between these ; and then 
 we shall not assent to any one who should assert that there are visible bodies more beau- 
 tiful than these, each of which subsists according to one kind. W e must endeavour, 
 therefore, to harmonize the four sorts of bodies excelling in beauty, and to evince by this 
 means that we sufficiently comprehend the nature of these. Of the two triangles, indeed, 
 the isosceles is allotted one nature, but the oblong or scalene is characterized by infinity. 
 We ought, therefore, to choose the most beautiful among infinities, if we wish to com- 
 mence our investigation in a becoming manner. And if any one shall assert that he has 
 chosen something more beautiful for the composition of these, we shall suffer his opinion 
 to prevail, considering him not as an enemy, but as a friend. Of many triangles, there- 
 fore, we shall establish one as most beautiful (neglecting the rest) — I mean the equila- 
 teral, which is composed from three parts of a scalene triangle. To assign the reason 
 of this would, indeed, require a prolix dissertation ; but a pleasant reward will remain 
 for him who, by a diligent investigation, finds this to be the case. We have, therefore, 
 selected two triangles out of many, from which the body of fire and of the other elements 
 is fabricated, one of which is isosceles, but the other is that which always has its longer 
 side triply greater in power than the shorter. 
 
 “ But that which we formerly asserted without sufficient security, it is now necessary 
 more accurately to define ; for it appeared to us, though improperly, that all these four 
 natures were mutually generated from each other ; but they are in reality generated from 
 the triangles which we have just described — three of them, indeed, from one triangle con- 
 taining unequal sides ; but the fourth alone is aptly composed from the isosceles triangle. 
 All of them, therefore, are not able, by a dissolution into each other, to produce from 
 many small things a mighty few, or the contrary. This, indeed, can be effected by three 
 of them ; for, as all the three are naturally generated from one triangle, when the greater 
 parts are dissolved, many small parts are composed from them, receiving figures accom- 
 modated to their natures. And, again, when the many small parts, being scattered 
 according to triangles, produce a number of one bulk, they complete one mighty species 
 of a different kind. And thus much may suffice concerning their mutual generation. 
 
NOTES. 
 
 72 
 
 “ It now remains that we should speak concerning the quality of each of their kinds, 
 and relate from what concurring numbers they were collected together. The first species, 
 indeed, is that which was composed from the fewest triangles, and is the element of that 
 which has its longer side twice the length of the shorter side, which it subtends. But 
 two of these being mutually placed according to the diameter, and this happening thrice, 
 the diameters and the shorter sides passing into the same as into a centre, hence one 
 equilateral triangle is produced from six triangles ; but four equilateral triangles, being 
 composed according to three plane angles, fonn one solid angle, and this the most obtuse 
 of all the plane angles from which it is composed. Hence, from four triangles of this 
 kind receiving their completion, the first solid species was constituted, distributive of the 
 whole circumference into equal and similar parts. But the second was formed from the 
 same triangles, but at the same time constituted according to eight equilateral triangles, 
 which produced one solid angle from four planes, so that the second body received its 
 completion from the composition of six triangles of this kind. And the third arose from 
 the conjunction of twice sixty elements, and twelve solid angles, each of which having 
 twenty equilateral bases, is contained by five plane equilateral triangles. In this manner, 
 then, the other elements generated these. But the isosceles triangle, being constituted 
 according to four triangles, and collecting the right angles at the centre, and forming one 
 equilateral quadrangle, generated the nature of the fourth element. But six such as 
 these being conjoined, produced eight solid angles, eacli of which is harmonized together, 
 according to three plane right angles. Hence the figure of the body thus composed is 
 cubical, obtaining six plane quadrangular equilateral bases. There is also a certain fifth 
 composition, which Divinity employed in the fabrication of the universe, and when he 
 delineated those forms, the contemplation of which may justly lead some one to doubt 
 whether it is proper to assert that the number of worlds is infinite or finite.” — 
 The Works of Plato, translated by Taylor, Vol. II., p. 52G. 
 
NOTES. 
 
 73 
 
 NOTE E, (P. 35.) 
 
 In the year 1807, the Academie des Inscriptions et Belles Li tires offered a prize on the 
 following question : “ What were the chief causes which produced the great schools of 
 sculpture and painting among the Greeks; and by what means can they be reproduced?” 
 On the competition for this prize, M. Victor Cousin makes the following remarks : — 
 
 “ The successful writer, M. Emerie David, maintained that it was by the contempla- 
 tion and constant study of real forms, by the exact reproduction of natural objects, that 
 the ancients had raised the arts to the highest degree of perfection ; and that, therefore, 
 imitation alone could help us to reach the Grecian beauty, the true expression of life. 
 M. Quatremere de Quincy contested this opinion, and affirmed that it was not by the 
 study of natural forms, but by realizing ideal beauty, that the Greeks brought those 
 works to light which are not found in nature. He showed that there are two great prin- 
 ciples in the arts, the one individual and imitative — the other general, abstract, absolute, 
 and creative. The first can produce nothing but portraits — the second arrives at the 
 purely beautiful. M. Emerie David maintained that ideal beauty is the model, and the 
 model is in nature. M. Quatremere proved that the model, however beautiful it may be, 
 is always nothing but one of the less imperfect of the human species. Art, according to 
 M. de Quincy, expresses the general and the absolute ; according to M. Emerie David, it- 
 expresses the individual. These two theories can be reconciled, if, in the arts, we are not 
 ruled entirely by the individual, or entirely by the absolute. Shall we resign ourselves to 
 the exclusive contemplation of the individual, or shall we view the model as a perfect 
 ideal, of which there is not a vestige in living nature? The question again returns to 
 that of the mathematical circle. My opinion is, that we begin at once, at the same 
 moment, with the individual and the absolute. At the sight of a natural figure which 
 possesses some rude proportion, the mind gifted with power to conceive of the absolute 
 and general, when this figure is presented to it, constructs it into a perfect circle. But 
 man can never realize in matter a geometrical circle : he can only produce a natural one, 
 and therefore an imperfect one. It is thus that, in the idea of the true, the beautiful, 
 and the good, there are always two elements blended — the one concrete and particular, 
 
 L 
 
74 
 
 NOTES. 
 
 the other abstract and absolute. As we have already said, there are two kinds of abstrac- 
 tion : First , We examine several individuals; we overlook their differences, that we may 
 attend to their resemblances ; thence we form a kind of collective unity : this operation 
 of the mind may be called comparative abstraction ; Secondly, By an abstraction of another 
 kind, one object being given, without having recourse to any comparison, we disengage 
 from that one object a general and absolute view-point. I call this operation of the 
 mind, immediate abstraction. This is true not only of pure geometry, but of the concep- 
 tion of the beautiful in the fine arts, and of the good in morals Ideal beauty, 
 
 then, is evolved from real beauty, by an immediate abstraction which perceives the one in 
 the other. The operation is twofold ; if it were not, we should obtain the individual by 
 itself, or the absolute by itself — that is to say, life without the ideal, or the ideal without 
 life. Art must devote itself to the production of the ideal and of nature equally. 11 — 
 Philosophy of the Beautiful , p. 32. 
 
 NOTE F, (P. 39.) 
 
 In the article on the Fine Arts, in the seventh edition of the Encyclopaedia Britannica, 
 the author (Hazlitt) attributes the ideal beauty of the Greek statues to the immediate 
 imitation of nature, and remarks — “ What has given rise to the common notion of the 
 •ideal as something quite distinct from actucd nature , is probably the perfection of the 
 Greek statues. Not seeing among ourselves anything to correspond in beauty and gran- 
 deur, either with the features or form of the limbs in these exquisite remains of antiquity, 
 it was an obvious, but a superficial conclusion, that they must have been created from the 
 idea existing in the artist’s mind, and could not have been copied from anything existing 
 in nature;” and continues to argue that “the general form both of the face and figure 
 which we observe in the old statues is not an ideal abstraction — is not a fanciful inven- 
 tion of the sculptor, but is as completely local and national (though it happens to bo more 
 beautiful) as the figures on a Chinese screen, or the copperplate engraving of a negro 
 chieftain in a book of travels. 11 He farther remarks, that “ the Greek form appears to 
 
1n t 0TES. 
 
 < o 
 
 have been naturally beautiful, and had, besides, every advantage of climate, of dress, of 
 exercise, and inodes of life to improve it and supposes from these causes, operating in 
 conjunction with that of the artist having every opportunity afforded him for studying the 
 human form, ideal beauty was produced. 
 
 In the article on Painting, in the same publication, the author (Hayden) attributes 
 the perfection of Greek art to a very different cause, and observes — “ The whole history 
 of ancient art shows the estimation in which the unsophisticated judgment of the 
 public was held. Aristotle says — ‘ The multitude is the surest judge of the productions 
 of art.’ ‘ If you do not get the applause of the public,’ says some one else, ‘ what cele- 
 brity can you attain ?’ and Cicero makes the public the supreme judge. Thus, then, no 
 one ought to wonder at the perfection of Greek genius in everything, stimulated as it was 
 by these secondary causes, and the one acting upon the other in a climate adapted in 
 every way for comfort, health, and for convenience. The Greeks were men like ourselves; 
 not larger, as their arms prove, and not handsomer, for there exist as fine forms, in either 
 sex, in Great Britain, as ever graced the atelier of Zeuxis ; indeed, Cicero complains of 
 the plainness of the Athenians. When genius and secondary causes unite, as they some- 
 times do, then such men as Pericles and Alexander, and Polygnotus, Zeuxis, and Apelles, 
 are the result.” 
 
 These very opposite opinions, advanced in the same publication by two such popular 
 writers on the fine arts, prove how very unsettled the question still remains. 
 
 As to the particular proportions of the human countenance, generally given in those 
 lectures upon the principles and practice of the arts, upon which the public has so much 
 reliance, Haydon’s directions are a fair specimen. He says — “The head is four noses 
 from top to chin, and from ending of hair in front, three to chin ; make the forehead 
 broad, not ‘ villanous low,’ as Shakspeare says ; the eyes, an eye separate ; the face, from 
 the root of the hair to the chin, three noses ; the upper lip, a fourth of the nose ; the 
 ear, two noses sideways from the nostrils,” &c . — Lectures on Fainting , p. 7 1 . 
 
7 6 
 
 NOTES. 
 
 NOTE G, (P. 40.) 
 
 Jn farther illustration of this part of my subject, I shall here give some quotations from 
 Mengs, Winckelmann, Leonardo da Vinci, and J3ossi, which I have selected (along 
 with some accompanying observations of the author) from one of the best works upon the 
 beauty of the human form with which I am acquainted.* 
 
 Mengs, in treating of the remains of ancient Etruscan and Greek statues, says — “ In 
 these figures we find a proportion, impossible to be known and practised without an art 
 which furnishes sure rides. These rules could not be founded otherwise than in propor- 
 tion, which was invented and practised by the Greeks.” 
 
 That the Greeks,” says Bossi, “ wrote much on this subject (their doctrine respect- 
 ing symmetry) we have ample evidence in Pliny, Vitruvius himself, Philostratus the 
 younger, and others. 
 
 “ Polycletus did not confine himself to giving a commentary upon this fundamental 
 point, but, in illustration of his treatise, according to Galen, made an admirable statue, 
 that confirmed the precepts laid down in the work; and The Rule of Polycletus, the name 
 given to this statue, became so famous for its beauty, that it passed into a proverb to 
 express a perfect body, as we may find in Lucian. But of so many treatises not a frag- 
 ment remains (except the few lines of Vitruvius), nor is there now any hope that a ves- 
 tige will be found, unless something may remain for posterity amongst the papyri of 
 Heroul aneum.” 
 
 Upon this Mr Walker justly remarks — “ Now, to approach to the ancients in excel- 
 lence is quite impossible, until some one shall explain the great principles upon which 
 they acted, Assuredly they are, in some of the most important respects, unknown at 
 present. Servile imitation will never answer the purpose ; and to learn as the ancients 
 did, and reach perfection, perhaps in as many ages, is not very rational, when we can 
 avail ourselves of their practice to discover their principles.” “ It is probable,” says 
 Winckelmann, “ that the Grecian artists, in imitation of the Egyptians, had fixed, by 
 well-determined rules, not only the largest, but even the very smallest proportions, and 
 
 Beauty, illustrated chiefly by an Analysis and Classification <f Beauty in Woman. By Alexander Walker. 
 London : Ilenry G. Bohn. 184(5. 
 
NOTES. 
 
 77 
 
 the measure of the length proper to every age and to every kind of contour; and pro- 
 bably all these rules were learnt by young persons from books that treated of symmetry.” 
 
 Mr Walker then proceeds to show that these rules were of three kinds, namely, nume- 
 rical, geometrical, and harmonic — that the first is evidently that of which Vitruvius has 
 preserved some notions-— that the second has been treated of by Leonardo da Vinci, and 
 more lately by Camper. But as to the harmonic method, he observes that it has always 
 been the chief difficulty, and evidently formed a stumblingblock even to Leonardo da 
 Vinci, in regard to whom he quotes the following from Bossi : “ He (Leonardo da Vinci) 
 thought but little of any general measure of the species ; and that the true proportion 
 admitted by him, and acknowledged to be of difficult investigation, is solely the propor- 
 tion of an individual in regard to himself which, according to the true imitation, should 
 be different in all the individuals of a species , as is the case in nature. ‘ Thus , 1 says he 
 (Leonardo da Vinci), ‘ all the parts of any animal should correspond with the whole ; that 
 which is short and thick, should have every member short and thick ; that which is long 
 and thin, every member long and thin ; and that which is between the two, members of 
 a proportionate size. From this and other precepts, it follows, that, when he speaks of 
 proportion, he is to be understood as referring to the harmony of parts of an individual , 
 and not to the general rule of imitation in reference to dimensions. It would seem he 
 felt within himself that he did not reach the perfection of those wonderful ancients of 
 whom he professed himself the admirer and disciple. 
 
 “ It became, therefore, Leonardo’s particular care and study to approach as nearly as 
 he could to the ancients in the true imitation of beautiful nature under the guidance of 
 philosophy. But, whether from want of great examples, or from not sufficiently penetrat- 
 ing, as he himself thought, into these artifices, or from comprehending them too late, he 
 
 modestly laments that he did not possess the ancient art of proportions But 
 
 how difficult it is to combine the beautiful and elegant with easy and harmonic mea- 
 sures, maybe judged from the vain attempts of many otherwise ingenious men 
 
 The difficulty will be still more evident, if we reflect how arduous a task it is to make the 
 proportions that the Greeks denominated numerical, harmonic, and geometrical, agree 
 together, and to apply them, thus agreeing, to the formation of rules and measures of a 
 visible object so various in its component parts as the human body.” 
 
78 
 
 NOTES. 
 
 NOTE H, (P. 48.) 
 
 The reader who wishes to become acquainted with the merits of those remains of ancient 
 Greek art, to which I have referred in the text, freed from all dry technicalities, and 
 resulting from careful observation and study of the originals, is referred to a recent work, 
 entitled, Ancient and Modern Art , Historical and Critical , by George Cleghorn, Esq., 
 published by Messrs W. llhickwood and Sons, in which he will find that elegant and 
 correct style of ^Esthetic criticism which can only emanate from a highly cultivated mind 
 and sound judgment. 
 
INDEX TO PLATES. 
 
 PLATE 
 
 I. The geometrical figures and forms which arise from an application of the first principles of 
 symmetrical beauty. 
 
 II. These elements of harmonic proportion combined in four diagrams. 
 
 III. The anatomical structure of the human head accommodated to the foregoing diagrams. 
 
 IV. Four diagrams of an intermediate kind of proportion between those of the feminine and mas- 
 
 culine characters. 
 
 V. The anatomical structure of the human head accommodated to these diagrams. 
 
 VI. Four diagrams of the masculine character of proportions. 
 
 VII. The anatomical structure of the human head accommodated to these diagrams. 
 
 VIII. Front views and profiles of the ideal heads and countenances produced by an application 
 of the above three kinds of proportions. 
 
 IX. Front views and profiles of the first and second of the foregoing ideal heads, with the pro- 
 portions of the features modified. 
 
 X. The diagrams in Plate II. modified in their general character. 
 
 XI. The anatomical structure of the human head accommodated to these modified diagrams. 
 
 XII. The anatomical structure of the human head accommodated to the diagrams in Plate IV., 
 similarly modified. 
 
 XIII. The anatomical structure of the human head accommodated to the diagrams in Plate VI., 
 
 similarly modified. 
 
 XIV. Profiles and front views of heads and countenances of a low class of ordinary nature, pro- 
 
 duced by this modification of the diagrams. 
 
 XV. The diagrams in Plate II. still farther modified in their general character. 
 
80 
 
 INDEX TO PLATES. 
 
 PLATE 
 
 XVI. The anatomical structure of the human head accommodated to these modified diagrams. 
 
 X\ II. The anatomical structure of the human head accommodated to the diagrams in Plate IV , 
 similarly modified. 
 
 V^III. The anatomical structure of the human head accommodated to the diagrams in Plate VI.. 
 similarly modified. 
 
 XIX. Profiles and front views of heads and countenances of negroes, produced by this modifica- 
 tion of the diagrams. 
 
 XX. Profiles and front views of heads and countenances of the lowest class of Europeans, pro- 
 duced by this modification of the diagrams. 
 
 XXI. The diagrams in Plate II. modified in a less degree than either of the foregoing. 
 
 XXII. A profile and front view of the anatomical structure of the head and countenance of a high 
 class of ordinary nature, produced by this modification. 
 
 XX III. Figs. 1 and 2, a front view and profile of an ideal head proportioned agreeably to the 
 diagrams in Plate II. Figs. 3 and 4, the same proportioned agreeably to the diagrams 
 in Plate VI. 
 
 XXIV. Front views and profiles of ideal heads proportioned agreeably to the diagrams in Plate II., 
 with the features modified as in figs. 1, 2, 3, and 4, of Plate IX. 
 
 XXV. Figs. 1 and 2, a front view and profile of an ideal head proportioned agreeably to the 
 diagrams in Plate IV. Figs. 3 and 4 the same, with the features modified as in figs. 
 5 and 6 of Plate IX. 
 
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WORKS BY D. R. HAY, F.R.S.E. 
 
 i. 
 
 FIRST PRINCIPLES OF SYMMETRICAL BEAUTY. 
 
 Octavo. 100 Plates. Price 6s. 
 
 THE PRINCIPLES OF BEAUTY IN COLOURING SYSTEMATIZED. 
 
 Octavo, with 14 Coloured Diagrams. Second Edition. Price 15s. 
 
 III. 
 
 A NOMENCLATURE OE COLOURS, HUES, TINTS, AND SHADES, 
 APPLICABLE TO THE ARTS AND NATURAL SCIENCES , 
 
 TO MANUFACTURES, Ac. 
 
 With 228 Examples. Price 35s. 
 
 IV. 
 
 AN ESSAY ON ORNAMENTAL DESIGN, IN WHICH ITS TRUE 
 PRINCIPLES ARE DEVELOPED AND ELUCIDATED, Ac. 
 
 Oblong Folio. 57 Plates and numerous Woodcuts. Price £2, 2s. 
 
 PROPORTION, OR THE GEOMETRIC PRINCIPLE OF BEAUTY 
 ANALYZED. 
 
 Quarto. 17 Plates and 38 Woodcuts. Price 25s. 
 
 THE NATURAL PRINCIPLES AND ANALOGY OF THE HARMONY 
 OF FORM. 
 
 Quarto. 18 Plates and numerous Woodcuts. Price 15s. 
 
 VII. 
 
 THE LAWS OF HARMONIOUS COLOURING ADAPTED TO 
 INTERIOR DECORATIONS, Ac. 
 
 Sixth Edition. With Coloured Diagram. Price 7s. 6d. 
 
 W. BLACKWOOD & SONS, EDINBURGH AND LONDON. 
 
OPINIONS OF THE PRESS. 
 
 I 
 
 NOTICES OF THE THREE WORKS ON “PROPORTION,” “ FORM,” AND “ COLOUR,” IN 
 
 The Edinburgh Review, Oct. 184 3. 
 
 “ These works are highly honourable to Mr 
 Hay as a practical man. He has been long known 
 | as an extensively employed and elegant artist 
 in the department of decorative painting; and 
 he has found leisure, notwithstanding the pres- 
 sure of his professional avocations, to appear 
 before the public as an author, with strong 
 claims to its attention and respect. He is one of 
 the few artists who have drawn the resources of 
 their profession from the recognised fountains 
 of knowledge; and who, in offering the lessons 
 of their experience at the shrine of science, have 
 been anxious to listen, in return, to her infallible 
 counsels. The disposition to this species of ex- 
 change, 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 develop her powers, nor 
 science attain her most commanding position, 
 till the practical knowledge of the one is taken 
 in return for the sound deductions of the other. 
 
 “ Many causes have concurred to place art and 
 science at variance: but these causes have been 
 gradually diminishing, and in the present ad- 
 vanced state of the mechanical and useful arts, 
 they have almost wholly disappeared. It is in 
 the fine arts, principally, and in the speculations 
 with which they are associated, that the con- 
 trolling power of scientific truth has not exer- 
 cised its legitimate influence. In discussing the 
 principles of painting, sculpture, architecture, 
 and landscape gardening, philosophers have re- 
 nounced science as a guide, and even as an auxi- 
 liary; and a school has arisen whose speculations 
 will brook no restraint, and whose decisions 
 stand in opposition to the strongest convictions 
 of our senses. That the external world, in its 
 gay colours and lovely forms, is exhibited to the 
 mind only as a tinted mass, neither within nor 
 without the eye, neither touching it nor distant 
 from it — an ubiquitous chaos which experience 
 only can analyze, and touch transform into the 
 realities which compose it — that the beautiful 
 and sublime in nature and in art derive their 
 power over the mind from association alone — are 
 among the philosophical doctrines of the present 
 day, which, if it be safe, it is scarcely prudent to 
 question. Nor are these opinions the emanations 
 of poetical or ill-trained minds, which ingenuity 
 has elaborated, and which fashion sustains. They 
 are conclusions at which most of our most dis- 
 tinguished philosophers have arrived. They 
 have been given to the world with all the au- 
 thority of demonstrated truth; and in propor- 
 tion to the hold which they have taken of the 
 public mind, have they operated as a check upon 
 the progress of knowledge. 
 
 “ While opinions like these were con- 
 sidered as sound and well established, philoso- 
 phers never thought of studying the laws of 
 visible direction in single and double vision, by 
 which all the difficulties of the subject have 
 been subsequently removed; and, in like man- 
 ner, while the present theories of taste prevail, 
 there can be no inducement to discover the rules 
 of harmonious colouring, or to investigate the 
 origin of beautiful forms, or to develop the 
 laws of regular and irregular symmetry. When 
 speculation, however, is thus in the ascendant, 
 ; and theorists least apprehensive of danger, truth 
 
 is often securing auxiliaries from localities the 
 least likely to supply them. The sovereignty 
 of association in matters of taste had never been 
 recognised by practical men, who study nature 
 principally through the eye; and the painter, 
 the sculptor, the architect, and the landscape 
 gardener, had been striving in their respective 
 spheres to discover those ‘ laws of harmony,’ 
 both in colour and form, which ought to regu- 
 late the taste, and direct the hand of the artist. 
 In so far as we know, Mr Hay is the first and 
 the only modern artist who has entered upon 
 the study of these subjects without the tram- 
 mels of prejudice and authority. Setting aside 
 the ordinances of fashion, as well as the dicta of 
 speculation, he has sought the foundation of his 
 profession in the properties of light, and in the 
 laws of visual sensation, by which these proper- 
 ties are recognised and modified. The truths 
 to which he has appealed are fundamental and 
 irrefragable; and the conclusions which he has 
 deduced from them will admit of no modifica- 
 tion either from taste or fashion. In the adap- 
 tation of his principles, indeed, to the various 
 circumstances in which they are to be applied, 
 taste and judgment are undoubtedly required; 
 and even in the decoration of the boudoir and 
 the drawing-room harmony of colour and sym- 
 metry of form may be made to co-exist with, 
 and even to control, the caprices of fashion, and 
 the glitter of meretricious ornament. 
 
 “ Notwithstanding some trivial points of dif- 
 ference between Mr Hay’s views and our own, 
 we have derived the greatest pleasure from the 
 perusal of these works. They are all composed 
 with accuracy, and even elegance. His opinions 
 and views are distinctly brought before the 
 reader, and stated with that modesty which 
 characterizes genius, and that firmness which 
 indicates truth.” 
 
 — 0 — 
 
 The British and Foreign Medical 
 Review. No. XXXV. P.171. 
 
 “ There is harmony of numbers in all nature 
 — in the force of gravity — in the planetary move- 
 ments— in the laws of heat, light, electricity, and 
 chemical affinity — in the forms of animals and 
 plants — in the perceptions of the mind. The 
 direction, indeed, of modern natural and phy- 
 sical science is towards a generalization, which 
 shall express the fundamental laws of all by one 
 simple numerical ratio. We would refer to 
 Professor Whewell's ‘ Philosophy of the Induc- 
 tive Sciences,’ but more particularly to Mr Hay’s 
 ‘Researches into the Laws of Harmonious Co- 
 louring and Form.’ From these it appears that 
 the number seven is distinguished in the laws 
 regulating the harmonious perception of forms, 
 colours, and sounds, and probably of taste also, 
 if we could analyze our sensations of this kind 
 with mathematical accuracy. We think modern 
 science will soon show that the mysticism of 
 Pythagoras was mystical only to the unlettered, 
 and that it was a system of philosophy founded 
 on the then existing mathematics, which latter 
 seem to have comprised more of the philosophy 
 of numbers than our present.” 
 
 Fraser’s Magazine. 
 
 “ We have now gone over all Mr Hay's works, 
 but, we confess, not in a manner calculated to 
 
OPINIONS OF THE PRESS. 
 
 3 
 
 do them the justice they deserve. This, indeed, 
 could be done only in the pages of a work de- 
 voted to scientific pursuits, and whose particular 
 class of readers may be supposed to possess that 
 peculiar turn of mind which delights in philoso- 
 phical inquiry, and in the abstruse investigations 
 of science. In a periodical like ours, such in- 
 quiries would be out of place. 
 
 “Yet, enough has been said, it is presumed, to 
 show that the author of the works we have just 
 been noticing is a remarkable man. He un- 
 
 doubtedly is. He is a leader in his vocation; one 
 of those men who stand prominently out in the 
 front of his fellows, and who, by the force of 
 original genius, have acquired a certain ascen • 
 deney over the public mind. 
 
 “ Looking to the philosophical spirit and cha- 
 racter of Mr Hay's treatises, we cannot but con- 
 sider them valuable acquisitions, their purpose 
 being to improve the general taste, and by con- 
 sequence — for it is a consequence thereof — to 
 contribute to the advancement of civilization. 
 
 
 NOTICES OF THE “FIRST PRINCIPLES OF SYMMETRICAL BEAUTY,” IN 
 
 The Spectator, Oct. 31, 1846. 
 
 “ This is a grammar of pure form, in which the 
 elements of symmetrical, as distinguished from 
 picturesque beauty, are demonstrated, by reduc- 
 ing the outlines or planes of curvilinear and 
 rectilinear forms to their origin in the principles 
 of geometrical proportion. In thus analyzing 
 symmetry of outline in natural and artificial ob- 
 jects, Mr Hay determines the fixed principles of 
 beauty in positive shape, and shows how beau- 
 tiful forms may be reproduced and infinitely 
 varied with mathematical precision. Hitherto 
 the originating and copying of beautiful colours 
 have been alike empirical; the production of a 
 new design for a vase or a jug has been a matter 
 of chance between the eye and the hand ; and the 
 copying of a Greek moulding or ornament, a 
 merely mechanical process. By a series of pro- 
 blems, Mr Hay places both the invention and 
 imitation of beautiful forms on a sure basis of 
 science, giving to the fancy of original minds a 
 clue to the evolving of new and elegant shapes, 
 in which the infinite resources of nature are 
 made subservient to the uses of art. 
 
 “ The volume is illustrated by one hundred 
 diagrams, beautifully executed, that serve to ex- 
 plain the text, and suggest new ideas of beauty 
 of contour in common objects. To designers of 
 pottery, hardware, and architectural ornaments, 
 this work is particularly valuable : but artists of 
 every kind, and workmen of intelligence, will 
 find it of great utility.” 
 
 — o — 
 
 The Athenaeum, Jan. 2, 134 7. 
 
 “ The volume before us is the seventh of Mr 
 Hay’s works. It is the most practical and sys- 
 tematic, and likely to be one of the most useful. 
 It is, in short, a grammar of form, or a spelling- 
 book of beauty. This is beginning at the right 
 end of the matter; and the necessity for this 
 kind of knowledge will inevitably, though 
 gradually, be felt. The work will, therefore, be 
 
 ultimately appreciated and adopted as an intro- 
 duction to the study of beautiful forms. 
 
 “ The third part of the work treats of the 
 Greek oval or composite ellipse, as Mr Hay calls 
 it. It is an ellipsis of three foci, and gives 
 practical forms or vases and architectural 
 mouldings, which are curious to the architect, 
 and will be very useful both to the potter, the 
 moulder, and the pattern-drawer. A fourth 
 part contains applications of this to practice. Of 
 the details worked out with so much judgment 
 and ingenuity by Mr Hay, we should in vain at- 
 tempt to communicate just notions without the 
 engravings of which his book is full. We must, 
 therefore, refer to the work itself. The forms 
 there given are full of beauty, and so far tend 
 to prove the system.” 
 
 — o — 
 
 The Glasgow Courier, Nov. lO, 
 1846 . 
 
 “ This is a work which could not fail, under any 
 circumstances, to be highly appreciated by those 
 professionally engaged in the pursuits of art, as 
 well as by that numerous class amongst general 
 society who are now happily accustomed to feel 
 an intelligent interest in connection with the 
 productions of artistic genius; whilst it seems 
 to possess at the present time more particularly, 
 a very high degree of value in relation to the 
 efforts now made under legislative encourage- 
 ment for advancing amongst the producing 
 classes a knowledge of the principles of sym- 
 metrical beauty by the instrumentality of schools 
 of design. In conclusion, we may state that, 
 valuable as all Mr Hay’s preceding works on 
 painting and design are acknowledged to be, we 
 question whether there is any one of them which 
 can claim to rank superior, if even equal, to the 
 present, in point of practical value. And we feel 
 much pleasure in recommending it to general 
 notice as a work fitted to convey both instruc- 
 tion and pleasure to the artist as well as the 
 general reader.” 
 
 NOTICES OF “THE PRINCIPLES OF BEAUTY IN COLOURING” IN 
 
 The Spectator. 
 
 “ In this new analysis of the harmonies of 
 colour, Mr Hay has performed the useful ser- 
 vice of tracing to the operation of certain fixed 
 principles the sources of beauty in particular 
 combinations of hues and tints; so that artists 
 may, by the aid of this book, produce with 
 mathematical certainty the richest effects, hither- 
 to attainable by genius alone. Mr Hay has re- 
 duced this branch of art to a perfect system, 
 and proved that an offence against good taste 
 in respect to combinations of colour is in effect 
 a violation of natural laws. 
 
 “ The volume is of beautiful exterior, fit for 
 the drawing-room table; and the diagrams of 
 colours are bound up in a separate volume con- 
 nected with the text, yet distinct from it, like 
 two books under one cover, so that the reader 
 can refer to the illustrations without inter- 
 ruption.” 
 
 — o — 
 
 The Britannia. 
 
 “ From Mr Hay’s theory, scientifically stated 
 and ably reasoned, it results that the mind has in 
 its very constitution certain instincts directing 
 it to the perception of beauty in colour as in 
 
4 
 
 OPINIONS OF THE PRESS 
 
 sound, and that the greatest artist in colour, at 
 least, is he who follows those instincts most un- 
 erringly. Mr Hay is well skilled in the practice 
 of colour, and in its harmonious combinations ; 
 and more confidence, therefore, will be felt in his 
 conclusions when it is known that his own suc- 
 cess sprung from the application of his own prin- 
 ciples. 
 
 “ Mr Hay has illustrated his theory by ex- 
 amples in colour, disposed, not on the artistic, 
 but on the mathematical principles, and has 
 spared no labour to render his Essay acceptable 
 to the scientific inquirer.” 
 
 — o — 
 
 The Athenaeum. 
 
 “ Mr Hay is already well known to our readers 
 by a long series of books on beauty. We had 
 first, ‘The Natural Principles and Analogy of 
 the Harmony of Form’ developed; then, not 
 long after, his Treatise on ‘ Proportion, or the 
 Geometric Principle of Beauty ; ’ and next, his 
 ‘ Essay on Ornamental Design,’ with its fifty- 
 seven plates. Thus much on beauty of form ; 
 but we have also had a similar series on beauty of 
 colour — first, in ‘ The Laws of Harmonious Co- 
 louring;’ then in ‘ The Nomenclature of Colours, 
 Hues, and Tints ; ’ and, finally, the conclusion of 
 
 this matter, in ‘ The Principles of Beauty in Co- 
 louring,’ now before us. We have enumerated 
 these six steps of this series, because we have re- 
 garded, and do still continue to regard, the pro- 
 duction of Mr Hay’s works as a remarkable 
 psychological phenomenon — one which it is in- 
 structive both for the philosopher and the critic 
 to study with care and interest, not unmingled 
 with respect. In these books we behold a strong, 
 manly, honest mind, endowed with considerable 
 sensibility, and working its way slowly, labori- 
 ously, almost even groping it, among the chaotic 
 masses of beautiful and unbeautiful things in the 
 material world, in the endeavour to extricate 
 from this heterogeneous mass a few of those 
 beautiful, deep-seated, elusive truths, in virtue 
 of which inert matter becomes endowed with that 
 living soul which we love, which we call beauty, 
 and which Plato denominated ro xa.Xov x,ai 
 ayccdov, the soul of the world. In this long 
 series of Mr Hay’s works, we are enabled to trace 
 his progress from year to year in this arduous 
 pursuit of the beautiful and true. We see how 
 his mind has been gradually guided by Nature 
 herself out of one track, and into another, and 
 ever and anon leading him to some vein of the 
 beautiful and true, hitherto unworked.” 
 
 NOTICES OF “THE NOMENCLATURE OF COLOURS,” &c. IN 
 
 The Daily Mews. 
 
 “ A nomenclature of colours, in which their 
 enumerable hues and tints should be divided 
 from their primary elements, has long been a 
 desideratum It is so, however, no longer, thanks 
 to the talent and industry of Mr D. R Hay. 
 
 “In this work Mr Hay has brought a larger 
 amount of practical knowledge to bear on the 
 subject of colour than any other writer with 
 whom we are acquainted, and in proportion to 
 this practical knowledge, is, as might be ex- 
 pected, the excellence of his treatise. There is 
 much in this volume which we would most ear- 
 nestly recommend to the notice of artists, house 
 decorators, and, indeed, to all whose business or 
 profession requires a knowledge of the manage- 
 ment of colour. The work is replete with hints 
 which they might turn to profitable account, and 
 which they will find nowhere else.” 
 
 “ An anxiety to be useful, to render his know- 
 ledge and acquirements subservient to practical 
 purposes, is evident in every page of Mr Hay’s 
 work, a quality which cannot fail to be duly 
 appreciated by all who take an interest in the 
 advancement of art.” 
 
 — o — 
 
 The Athenaeum. 
 
 “ We have formerly stated the high opinion 
 we entertain of Mr Hay’s previous exertions 
 for the improvement of decorative art in this 
 country. We have already awarded him the 
 merit of invention and creation of the new and 
 beautiful in form. In his former treatises he 
 furnished a theory of definite proportions for 
 the creation of the beautiful in form. In the 
 present work he proposes to supply a scale of 
 definite proportions, for chromatic beauty. For 
 this purpose he sets out very properly with a 
 precise nomenclature of colour. In this he has 
 constructed a vocabulary for the artist — an 
 alphabet for the artisan. He has gone farther 
 — he constructs words of three syllables. From 
 this time it will be possible to write a letter in 
 
 Edinburgh about a coloured composition, which 
 shall be read off in London, Paris, Petersburgh, or 
 Pekin, and shall so express its nature that it can 
 be reproduced in perfect identity. This Mr Hay 
 has done, or at least so nearly, as to deserve our 
 thanks on behalf of art, and artists of all grades, 
 even to the decorative artisan — not one of whom, 
 be he house painter, china pattern drawer, or 
 calico printer, should be without this simple 
 manual of ‘ words for colours.’ ” 
 
 The Scotsman. 
 
 “ Here is another professional work by Mr 
 Hay, and one distinguished by all the charac- 
 teristics by which his other works recommend 
 themselves to public notice and favour — vigour, 
 originality, and an entire and thorough mastery 
 of his subject, 
 
 “ Taking the work altogether, there can be no 
 doubt of its being one of the very best of its kind 
 that has yet been presented to the public. The 
 amount of practical knowledge it contains, and 
 the masterly way in which that knowledge is 
 placed before the reader, cannot fail to impress 
 him with sentiments of the highest respect for 
 the talents and acquirements of the author. Nor 
 will these sentiments be weakened by noting the 
 philosophical spirit in which, when opportunity 
 offers, he treats his subject — affording in this, 
 evidence of an order of intellect equal to much 
 greater things than the demands of his pro- 
 fession.” 
 
 — o — 
 
 The Courant, 
 
 “ The whole tenor of the work evinces, on the 
 part of the author, a sincere desire to advance 
 art, a spirit of genuine philosophy, and a lively 
 appreciation of the beautiful. Never before has 
 been exhibited so systematic, so complete, so 
 satisfactory an arrangement of colours. The 
 whole of the chromatic scale, through all its 
 gradations and modulations, is shown. Its melo- 
 dies, harmonies, and contrasts, are all clearly 
 
ON MR D. R. HAYS WORKS. 
 
 O 
 
 defined. All the individual colours, tints, and 
 hues, are placed in their proper position, ex- 
 tending- through a series of two hundred and 
 forty. The arrangement is so skilful, that the 
 eye wanders delighted over them all, from the 
 fiery and exciting colour of red, down to the most 
 gentle and retiring of the neutral tones.” 
 
 — o — 
 
 The Glasgow Constitutional. 
 
 “This, perhaps, will be found to be the most 
 generally useful of the many valuable and very 
 ingenious works with which its indefatigable 
 author has, within these few years, enriched our 
 literature. It so far surpasses all previous at- 
 tempts of the kind as to preclude any comparison 
 with them. 
 
 “ The book addresses itself more immediately 
 to those engaged in the study of the arts, sci- 
 ences, and manufactures; and of its value and 
 importance to this class of persons we need say 
 nothing. But w r e would strongly recommend 
 it also to the attention of all who take an interest 
 in objects of taste, as containing an amount of in- 
 formation which they will find nowhere else, and 
 from which even those whose eye has been most 
 carefully cultivated in the perception aud dis- 
 crimination of colour, will find that they have 
 much to learn.” 
 
 Edinburgh Weekly Journal. 
 
 “ Mr Hay may in his works, both as an artist 
 and an author, be almost considered as the 
 founder of a new department of design. That 
 he was thoroughly master of his subject, the 
 
 warm approbation which has greeted his works 
 on Harmonious Colouring, Form, Proportion, 
 &c., sufficiently evinces ; and the present work 
 may be considered as the practical application ot 
 some of the theories jjropounded, as, after 
 teaching his disciples how to use their tools to 
 produce the best effects, he here gives the tools 
 themselves, viz., colours, mapped out, arranged, 
 classified, and described, not only as to the es- 
 sential composition, qualities, and effects of each, 
 but also its relations to its neighbour and its 
 antagonist tints, and the exact influences over 
 all by the interference, more or less, of the two 
 great opposites, black and white, darkness and 
 light.” 
 
 — o — 
 
 The Glasgow Argus. 
 
 “ Mr Hay is not alone a patron of the arts, but, 
 as an instructor of the followers of art, he is a 
 benefactor to the public. All his works, whether 
 he writes upon ornamental design, or the har- 
 mony of form, the laws of harmonious colour- 
 ing, or brings his comprehensive mind to bear 
 analytically upon the geometric principles of 
 beauty, while they improve and delight the 
 reader, render him the more capable of being of 
 use, by extending his sphere of action, and 
 placing him nearer that perfection it must be 
 the constant aim of every artist to arrive at. 
 
 “ The primary colours are taken by Mr Hay in 
 their natural order ; and not only will the artist 
 and the connoisseur find ample material for 
 thought, but the naturalist, the mineralogist, 
 and the botanist, will discover new lights opened 
 out to them of the most valuable tendency. 
 
 NOTICES OF THE ESSAY ON 
 
 The A then scum, April 12, 1845. 
 
 “ In conclusion, Mr Hay’s book goes forth with 
 our best wishes. It must do good. It must be 
 prolific of thought — stimulant of invention. It 
 is to be acknowledged as a benefit of an unusual 
 character conferred on the arts of ornamental 
 design.” 
 
 — o — 
 
 The Spectator, January 4, 1845. 
 
 “ Mr Hay has studied the subject deeply and 
 scientifically. In this treatise on ornamental de- 
 sign, the student will find a clue to the discovery 
 of the source of an endless variety of beautiful 
 forms and combinations of lines, in the applica- 
 tion of certain fixed laws of harmonious propor- 
 tion to the purposes of art. Mr Hay also ex- 
 emplifies the application of his theory of linear 
 harmony to the production of beautiful forms 
 generally, testing its soundness by applying it 
 to the human figure, and the purest creations of 
 Greek art.” 
 
 Fraser’s Magazine, Jan. 1845. 
 
 “ We come now to Mr Hay’s last, and, 
 
 we are almost tempted to say, his best work, be- 
 cause of the more popular nature of its interest. 
 Each part is enriched by diagrams of great 
 
 “ORNAMENTAL DESIGN” IN 
 beauty, direct emanations of principle, and, con- 
 sequently, presenting entirely new combinations 
 of form. Had our space permitted, we should 
 have made some extracts from this ‘ Essay on 
 Ornamental Design;’ and we would have done 
 so, because of the discriminating taste by which 
 it is pervaded, and the forcible observations 
 which it contains ; but we cannot venture on the 
 indulgence.” 
 
 — o — 
 
 Civil Engineer and Architect’s 
 Journal, May, 184 5 
 
 “ Mr Hay has paid particular attention to this 
 branch of design, which is of extensive applica- 
 tion, and as to which few accessible examples 
 exist. It will, from its intrinsic interest, prove 
 an attractive work for the study and the draw- 
 ing-room.” 
 
 — o — 
 
 Renfrewshire Advertiser, Feb. 1845. 
 
 “ So broad are the principles, and so pervad- 
 ing the illustrations, which Mr Hay has laid 
 down in this work, that it cannot be said to in- 
 clude no other students than those connected 
 with the industrial arts, to whom he has ad- 
 dressed his able and important Essay. It in- 
 volves the whole range of ornamental design.” 
 
 NOTICES OF THE WORK ON “FORM” IN 
 
 The Athenaeum. 
 
 “ The study of the true , the goods and the beau- 
 tifuls has formed an important occupation of life 
 in all highly civilized nations, and has been in- 
 
 culcated by the truest patriots and the highest 
 philanthropists. Science, virtue, and beauty, 
 form the noblest elements of creation, and of 
 the human soul — they form the first objects of 
 
6 
 
 OPINIONS OF THE PRESS 
 
 uur national institutions, the highest elements 
 of a national character, and the best themes of a 
 i national literature. 
 
 44 It would be a great step in the advancement 
 of our national civilization, were the love of the 
 beautiful, and the power of appreciating the 
 value of its manifestations, more intimately 
 | mixed up with the associations and habits of our 
 j countrymen. That we have artists of high 
 powers — architects of consummate skill — that 
 we have, or have had, Barrys and Cockerells, 
 Wilkies and Etty^, Landseers and Mulreadys, 
 Flaxmans and Chantreys and Westmacotts, is 
 matter of national congratulation, but does little 
 j to prove the existence of a high standard of 
 | national taste. The habit of enjoying the beau- 
 ! tiful, and the power of appreciating it, should 
 pervade the national character, should determine 
 its national institutions, and be diffused among 
 the peasantry of our streets and hamlets. 4 The 
 farmer and the mechanic (we quote Clianning) 
 should cultivate the perception of beauty .'' — 
 
 4 Every man should aim to impart this perfec- 
 tion to his labours.’ Were every man a judge 
 and appreciator of beauty, then, indeed, might 
 we expect forms of loveliness and grace to per- 
 vade the regions of domestic and every-day life 
 — to replace, in our streets, the expensive ugli- 
 ness of our street decoration — in our homes, the 
 | vulgarities of ornamental deformity — and in our 
 churches, the distortions and anomalies of mere- 
 tricious decoration. 
 
 “We hail, therefore, with delight, the appear- 
 ance among us of any evidence of progress to- 
 wards the diffusion of correct principles in taste, 
 of accurate knowledge in art — and we receive 
 the work before us as a harbinger of better 
 times — as an index of the wider diffusion of 
 knowledge in art. 
 
 “ Hay on 4 Harmonious Colouring ’ formed the 
 precursor to Hay on the 4 Harmony of Form.’ 
 The former work was chiefly designed to correct 
 and direct the public taste in the decorations of 
 domestic life : the present has a higher aim — 
 the determination of the forms and proportions 
 which give to objects and structures a maximum 
 of beauty. 
 
 “ The fact that Mr Hay, by an independent 
 process of his own mind, versant about propor- 
 tion and beauty, has arrived exactly at some of 
 the identical proportions of the Platonic theory, 
 as we understand and apply it, is to be reckoned 
 as an important psychological phenomenon, de- 
 monstrating the inherence of certain fixed and 
 essential principles of proportion and beauty in 
 the human soul. 
 
 “All Mr Hay’s proportions are, therefore, 
 good. They exist in the best specimens of per- 
 fect architecture; they are necessary elements 
 in judicious decoration. They give rise to sym- 
 metry and simple numerical proportions in an- 
 gular compositions They pervade the works 
 of the Greek artists, and were the identical prin- 
 ciples taught by the philosophers who gave wis- 
 dom to the times of Pericles and Phidias.” 
 
 — o — 
 
 The Court Gazette. 
 
 “ This is a work of great talent and value. It 
 has the peculiar merit of being new and original, 
 in the midst of the sickly spirit of repetition, 
 which seems to shed its drowsy influence over 
 the largest department of modern publication. 
 
 It is devoted to Form. The author is one of 
 the individuals peculiarly endowed with that rich 
 gift which constitutes the sculptor, the archi-l 
 
 tect, and the painter ; and hence the ingenious 
 theory developed in this work, which logically 
 associates sight with sound, geometry with 
 acoustics. It is the developed theory of Plato, 
 who eloquently commented on the music of 
 beautiful forms— a theory which Darwin, the 
 Platonic poet, in a note to his 4 Temple of Na- 
 ture,’ practically carries out, by suggesting the 
 construction of a machine which, while pro- 
 ducing the varied notes of the gamut to the 
 ear, should, at the same time, present to the eye 
 the 4 various modulations ’ of the prismatic co- 
 lours. Mr Hay’s theory is somewhat like this, 
 but practically developed for the painter, the 
 sculptor, and the architect. The illustrated 
 architectural examples deserve especial notice. 
 The geometrical production of the fa§ade of a 
 Doric temple, from the projected combination 
 of the vescica piscis, or double circle — (the free- 
 masons’ secret of Ancient Egypt, and the monas- 
 tic architects’ of the middle ages) — is most curi- 
 ous. We cordially recommend to our readers 
 this ingenious work, which is profoundly philo- 
 sophical in its geometrical analysis of abstract 
 form, and replete with the exciting spirit of 
 poetry and music in its tasteful associations.” 
 
 — o — 
 
 The Sun. 
 
 44 The object of this treatise is to show that the 
 impressions made upon the eye by forms are 
 really founded on natural principles; and that 
 the proportions and peculiarities of form which 
 produce the most pleasing impressions, are in 
 reality, as well as appearance, dictated by nature, 
 being a response to those principles in the hu- 
 man mind. The treatise is singularly well writ- 
 ten, both as respects manner and matter, exhibit- 
 ing a force and closeness of reasoning which lead 
 to the inference that the author has a decided 
 penchant for mathematical pursuits, and is ex- 
 tensively acquainted with that difficult and com- 
 plicated science. He gives several curious and 
 interesting plates, illustrative of certain theories 
 advanced in the course of his treatise. These 
 plates are finished off 1 with the utmost nicety, 
 and artists and men of science will derive many 
 a useful suggestion from them.” 
 
 — o — 
 
 The Glasgow Herald. 
 
 “It is, of course, impossible, in a cursory 
 notice like this, to do more than indicate the 
 general character of the very profound, as well 
 as extremely interesting theory which Mr Hay 
 
 has propounded The volume, we may 
 
 remark in conclusion, contains numerous most 
 beautiful diagrams, illustrative of the author’s 
 theory ; and the reader may feel himself amused, 
 as well as instructed, by studying 4 the melody 
 of the portico of the Parthenon,’ expressed in 
 musical notes, as well as by the intervals of Mr 
 Hay’s scale of harmony of form.” 
 
 — 0—— 
 
 The Glasgow Citizen* 
 
 44 This is decidedly an able, as well as original, 
 publication, in some degree in the subject, but 
 more so in the author’s manner of treating it. 
 
 44 To persons of taste and knowledge in art, 
 Mr Hay’s work will be peculiarly acceptable, and 
 we are confident that such will consider it as no 
 slight contribution to the cause of art and sci- 
 ence.” 
 
 The Caledonian Mercury, 
 
 44 This treatise on the principles of linear liar- 
 
ON MR D. R. HAY'S WORKS. 
 
 i 
 
 mony, will eminently conduce, we think, to one 
 main object, which its ingenious author seems to 
 have had in view, namely, the improvement and 
 guidance of the public taste in judging of works 
 of art that owe their excellence to beauty of 
 form. Mr Hay has here undertaken to demon- 
 strate, and, so far as we are able to judge, he has 
 done so clearly and convincingly, that the im- 
 pressions made upon the eye by forms are really 
 
 founded on natural principles — that the propor- 
 tions and peculiarities of form which produce 
 the most pleasing impressions are dictated by 
 nature, being a response to these principles in 
 the human mind — and that forms are, in all 
 respects, analogous to sounds ; so that a system 
 of linear harmony may be established similar to i 
 that which regulates the arrangement of musical 
 notes.” 
 
 NOTICES OF THE WORK ON “HARMONIOUS COLOURING ADAPTED TO 
 DECORATION,” IN 
 
 The Critic, May 1, 184 3. 
 
 “ The volume before us is an evidence of the 
 great progress which has been made of late years 
 
 in the taste for decorative .art To Mr 
 
 Hay belongs the merit of having been among 
 the first to invite the attention of his country- 
 men to decoration as an art. He first reduced 
 to rule and reason the paints and papers to be 
 used in the various rooms of a dwelling. The 
 choice of colours was little more than a freak of 
 fancy, until he showed why one should be pre- 
 ferred to another.” 
 
 — o — 
 
 Fraser’s Magazine. 
 
 “ In the absence, in the general case, of all in- 
 dications of taste in the internal decorations of 
 our dwellings, or which is, perhaps, yet more to 
 be lamented, in the presence of the evidences of 
 a bad one, our understandings have been hither- 
 to wrapped in a kind of Cimmerian darkness, as 
 regards the employment of decorative painting 
 for domestic purposes, for the embellishment of 
 our dwellings. A ray of light, however, and a 
 brilliant one, has been let into this dark pro- 
 found by Mr Hay, who not only points to a bet- 
 ter state of things, but leads the way. Urged 
 by the irrepressible energies of an active, vigor- 
 ous, and original mind, Mr Hay has stepped from 
 the ranks of a profession, hitherto of the hum- 
 blest pretension — a profession whose practice 
 was thought to require little judgment, and still 
 less taste — and has rendered himself remarkable 
 by the ability with which he exposes this fallacy. 
 Mr Hay has, in truth, elevated house-painting to 
 the dignity of an art — an achievement which he 
 has accomplished simply by recognising princi- 
 ples, the power of which in producing the most 
 beautiful , in both form and colour, his own 
 practice has long illustrated. In his ‘Laws of 
 Harmonious Colouring,’ Mr Hay blends the sci- 
 entific with the practical, which, in popular lan- 
 guage, means two things: first, that he begins 
 at the beginning of his subjects; and, second, 
 that he gives reasons for all he advances. 
 
 “ The art of house-painting has hitherto been 
 considered a very humble one ; but it would be 
 no difficult task to show, that it is far from being 
 so inherently, and that its degradation was wholly 
 the result of combined negligence and incapacity. 
 The proof of this may be found in the elevation 
 to which it has been raised by the genius and 
 talent of Mr Hay.” 
 
 The Spectator. 
 
 ‘ Mr D R. Hay of Edinburgh affords another 
 and a striking proof of the advantage, as well as 
 the pleasure, derivable by a craftsman in intel- 
 lectualizing his labour by scientific study. He 
 thoroughly understands his subject — a merit 
 
 that does not belong to all writers — and he lays 
 down the principles of Harmony in Colour, as 
 applicable to decorative purposes, explicitly and 
 fully and in a practical manner.” 
 
 — o — 
 
 The Morning Chronicle. 
 
 “ In the early part of his work, Mr Hay throws 
 a most important light on the theory of colours, 
 by the agency of which he has been enabled to 
 go much further towards the elucidation of this 
 subject than any previous writer. He then, in 
 a lucid manner, explains the relations which 
 colours, in their various tints, hues, and shades, 
 should have to each other to produce an har- 
 monious result. 
 
 “ After the extracts we have made, it is hardly 
 necessary to observe, that this is a work of great 
 originality; and we have not the least hesitation 
 in adding, that we believe that a diffusion of the 
 knowledge of the principles laid down in it 
 would prove of material use to our manufac- 
 turers. In addition also to the utility of the 
 study of those laws which regulate harmonious 
 colouring to those engaged in productive in- 
 dustry, there can be little doubt that a know- 
 ledge of them would greatly enhance the plea- 
 sure derived from pictorial art.” 
 
 — o — 
 
 The Atlas. 
 
 “ This is a new and improved edition of Mr 
 Hay’s work on the ‘ Laws of Harmonious Colour- 
 ing, and is adapted to every art and science in 
 which colours form an accessory. Every line of 
 this useful book shows that the author under- 
 stands his business ; and he has contrived to in- 
 tellectualize his subject in a very interesting 
 manner. The principles of harmony in colour, 
 as applied to decorative purposes, are explained 
 and enforced in a lucid and practical style, and 
 the relations of the various tints and shades to 
 each other, so as to produce an harmonious re- 
 sult, are descanted upon most satisfactorily and 
 originally. The applications of the laws of colour- 
 ing to house-painting is an era in science; and 
 the precepts given cannot fail to dignify the 
 calling, by converting it into an imaginative as 
 well as an agreeable and useful pursuit.” 
 
 — o — 
 
 The Ulster Times, 
 
 “We are happy to see that the good taste of 
 the public has called for a third edition of Mr 
 Hay’s ingenious treatise on this interesting sub- 
 ject. While we hail Mr Hay’s work as likely to 
 popularize the delightful study of which it 
 treats, we can assure the scientific and the re- 
 fined, that they will find in it many observations 
 worth their attention.” 
 
8 
 
 OPINIONS OF THE PRESS. 
 
 The Architectural Magazine. 
 
 “ It is impossible to peruse the work before us 
 without being convinced that the author is tho- 
 roughly acquainted with the science of his art. 
 We have given as distinct an idea as we can of 
 Mr Hay’s treatise without the aid of his coloured 
 plates; and we have done so with a view of 
 showing every young architect, or other person 
 connected with houses or furniture, how much 
 they may gain from Mr Hay’s book In short, 
 there is no other such work on the subject of 
 which it treats, and none of which it may be so 
 truly said, that it ought to be in the hands of 
 every one at all connected, however remotely, 
 with building or furnishing. We repeat, that 
 we cannot too strongly recommend Mr Hay’s 
 work to our readers.” 
 
 The Edinburgh Chronicle. 
 
 “ This work, written by an eminent citizen of 
 Edinburgh, has been long before the public, and 
 has been so highly appreciated, that it has now 
 undergone three impressions. It is well worthy 
 of this great success, for it is a production of 
 uncommon originality and genius ; and, while it 
 is honourable to the taste and talents of its 
 author, it cannot fail to prove extremely useful, 
 not merely to the young aspirant, but to the 
 most experienced and eminent artist, particu- 
 larly to the house-painter. House-painting has 
 hitherto been considered as scarcely connected 
 with art at all, and has consequently, in practice, 
 been characterized by no exhibition of taste or 
 ‘ harmonious colouring but Mr Hay has struck 
 out new lights as to his profession, and has 
 shown in this publication that the business of a 
 house-painter should be founded on science, and 
 regulated by laws, as well as the higher depart- 
 ments of art. And, what is more, he is the great 
 sublime he draws. In his own extensive busi- 
 ness, he has carried most successfully into effect 
 those great principles which he has so well de- 
 veloped in the work before us ; indeed, his own 
 bright example has done for the art of ‘ harmo- 
 nious colouring,’ in this city and neighbourhood, 
 more than has been effected by his predecessors 
 in the same profession for centuries. 
 
 — o — 
 
 Chambers 7 Journal. 
 
 “ An exceedingly instructive little volume has 
 fallen under the notice of the editor, entitled, 
 
 * The Laws of Harmonious Colouring, adapted 
 to House-Painting,” by D. R. Hay, house painter 
 in Edinburgh, and a perusal of which would be | 
 
 sure to refine the taste of the artisan engaged 
 in this ingenious profession, and be particularly 
 serviceable to gentlemen in the embellishment 
 of their residences. It will have been often re- 
 marked, that the colouring of the walls in our 
 houses is in many cases unpleasing to the eye, 
 and quite out of character with the furniture, 
 the carpets, the degree of light, or the nature of 
 the chambers. One room is painted green, be- 
 cause green is a pretty bright colour; while 
 another, for some reason equally frivolous, is 
 daubed over with a pink salmon tint. To cor- 
 rect these, and many other absurdities in house- 
 painting, Mr Hay has presented us with a variety 
 of comprehensive rules.” 
 
 — o — 
 
 The Literary Journal. 
 
 “We are glad that Mr Hay’s book has gone to 
 a second edition; and we doubt not that the, 
 ability and excellent knowledge of his profession 
 which it displays, will meet with the reward to 
 which they are well entitled.” 
 
 — o — 
 
 The Patriot. 
 
 “ It is impossible to read Mr Hay’s clear, lucid 
 remarks, without being at once convinced that 
 he is completely master of his subject. Indeed, 
 we have never perused a work which, in a less 
 obtrusive manner, contained more useful and 
 well arranged information.” 
 
 — o — 
 
 The Civil Engineer and Architect’s 
 Journal. 
 
 “ Mr Hay’s book is the fourth edition of a 
 work decidedly esteemed for its practicability, 
 cheapness, and the soundness of its principles; 
 and to it is added, in this edition, an excellent 
 treatise on house-painting. It is, indeed, the 
 cheapest and best book on the subject, and one 
 to which our readers, of aH classes, may refer 
 with advantage and delight.” 
 
 — o — 
 
 Loudon’s Encyclopaedia of Archi- 
 tecture. 
 
 “ After consulting all the works that are con- 
 sidered the most valuable on the subject of house 
 and ornamental painting, we think that by far 
 the best, and indeed the only one that embraces 
 principles, is a work entitled, ‘ The Laws of Har- 
 monious Colouring,* &c., by Mr D. R. Hay, house- 
 painter, Edinburgh. We strongly recommend 
 Mr Hay’s work to every painter who aims at ex- 
 cellence in his profession, and to every amateur 
 who wishes to judge for himself.” 
 
 Ancient and Modern Art, Historical and Critical. 
 
 By George Cleghorn, Esq. 
 
 “ But of all the treatises on the harmonic theory, those of Mr Hay of Edinburgh — already well 
 known to the public for his excellent work on the ‘ Laws of Harmonious Colouring’— are the most J 
 satisfactory. He has illustrated his subject by a series of publications, embracing ‘ The Harmony 
 of Form;’ ‘Proportion, or the Geometrical Principle of Beauty Analysed;’ ‘ The True Principles 
 of Ornamental Design as applied to Decorative Arts,’ &c. In the opinion of the best judges, he has j 
 all but arrived at the solution of the Platonic theory — a discovery which involves an important 
 psychological phenomenon, demonstrating the existence of certain fixed principles of proportion 
 and beauty in the human mind. The development of such principles may be of essential service in 
 their application to architecture, and that description of decorative art connected with geometrical 
 figures. It is impossible to read these treatises without being convinced that the author is well 
 versed in geometry, music, and acoustics. His style is clear, graceful, and philosophical. His 
 works are not only highly interesting, but quite original, and well worth the attention both of the 
 artist and the philosopher. 
 
 EDINBURGH: JOHNSTONE, PALLANTYNE, AND CO. 
 
GETTY CENTER LIBRARY 
 
 
 3 3125 00113 4366 
 
 
 , _