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

Front matter

*

QtA.

*

Part I. Definition Of .esthetics, ....... 1

... II. ON ESTHETIC CULTURE, ....... 7

... III. ON THE HARMONY OF NUMBERS, AND THE METHOD OF APPLYING

... 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

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 rhythmical measure, even in the highest flights of poetic inspiration, 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 charming 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 acknowledged 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 harmony 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 imperfect 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 feeling of appreciation for what is beautiful in form, by means of which they impart to their works the most pleasing proportions, 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 fettering their genius, would doubtless promote the more free exercise of its powers, and give such confidence and precision 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 inculcation 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 conceptions of others, in works of formative art, as that manifested 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 illustration 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 silversmith, 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 countenance, 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 elevations 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.

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, therefore, 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.

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 impressions 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 appreciates the nature and quality of the impression originally made on the receptive organ. The mode of this operation is intuitive, and its

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 interwoven, 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 modifications 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 subject, 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 communication are the sensorium and its iidets, the organs of sense — the former being in direct contact with the subject, and the latter with the

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 combination. By this means natural philosophy has attained its present advanced state ; and by the application of this knowledge, in the useful 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 conducted 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 combinations of form in the human figure, the pupils have to depend

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, supersede 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.

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 beautiful 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

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 external, 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

ON AESTHETIC CULTURE.

conclusive. He observes — “ If the idea of the beautiful is not absolute, like the idea of the true — if it is nothing more than the expression of individual sentiment, the rebound of a changing sensation, 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 absolute 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 exercised 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.

ON AESTHETIC CULTURE.

lias 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 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.

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 conquest 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 Christopher Le Blon ; and although I have not been able to discover so definite 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 becomes, 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

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 profane 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 Intelligence, or active principle, the name of monad, or unity, was given, because it must be always the same ; to matter, or the passive principle, 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 knowledge 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.

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, certain traces of the true elements, but were in every respect so constituted, 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.

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 composed. 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 commensuration 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