APPENDIX.

In pages34,35, and58, I have reiterated an opinion advanced in several of my former works, viz., that, besides genius, and the study of nature, an additional cause must be assigned for the general excellence which characterises such works of Grecian art as were executed during a period commencing about 500B.C., and ending about 200B.C.And that this cause most probably was, that the artists of that period were instructed in a system of fixed principles, based upon the doctrines of Pythagoras and Plato. This opinion has not been objected to by the generality of those critics who have reviewed my works; but has, however, met with an opponent, whose recondite researches and learned observations are worthy of particular attention. These are given in an essay by Mr C. Knight Watson, “On the Classical Authorities for Ancient Art,” which appeared in theCambridge Journal of Classical and Sacred Philologyin June 1854. As this essay is not otherwise likely to meet the eyes of the generality of my readers, and as the objections he raises to my opinion only occupy two out of the sixteen ample paragraphs which constitute the first part of the essay, I shall quote them fully:—

“The next name on our list is that of the famous Euphranor (B.C.362). For the fact that to the practice of sculpture and of painting he added an exposition of the theory, we are indebted to Pliny, who says (xxxv. 11, 40), ‘Volumina quoque composuit de symmetria et coloribus.’ When we reflect on thecriticalposition occupied by Euphranor in the history of Greek art, as a connecting link between the idealism of Pheidias and the naturalism of Lysippus, we can scarcely overestimate the value of a treatise on art proceeding from such a quarter. This is especially the case with the first of the two works here assigned to Euphranor. The inquiries which of late years have been instituted by Mr D. R. Hay of Edinburgh, on the proportions of the human figure, and on the natural principles of beauty as illustratedby works of Greek art, constitute an epoch in the study of æsthetics and the philosophy of form. Now, in the presence of these inquiries, or of such less solid results as Mr Hay’s predecessors in the same field have elicited, it naturally becomes an object of considerable interest to ascertain how far these laws of form and principles of beauty were consciously developed in the mind, and by the chisel, of the sculptor: how far any such system of curves and proportions as Mr Hay’s was used by the Greek as a practical manual of his craft. Without in the least wishing to impugn the accuracy of that gentleman’s results—a piece of presumption I should do well to avoid—I must be permitted to doubt whether the ‘Symmetria’ of Euphranor contained anything analogous to them in kind, or indeed equal in value. It must not be forgotten that the truth of Mr Hay’s theory is perfectly compatible with the fact, that of such theory the Greek may have been utterly ignorant. It is on this fact I insist: it is here that I join issue with Mr Hay, and with his reviewer in a recent number ofBlackwood’s Magazine. Or, to speak more accurately,—while I am quite prepared to find that the Elgin marbles will best of all stand the test which Mr Hay has hitherto applied, I believe, to works of a later age, I am none the less convinced that it is precisely that golden age of Hellenic art to which they belong, precisely that first and chief of Hellenic artists by whom they were executed, to which and to whom any such line of research on the laws of form would have been pre-eminently alien. Pheidias, remember, by the right of primogeniture, is the ruling spirit of idealism in art. Of spontaneity was that idealism begotten and nurtured: by any such system as Mr Hay’s, that spontaneity would be smothered and paralysed. Pheidias copied an idea in his own mind—‘Ipsius in mente insidebat species pulchritudinis eximia quædam’ (Cic.);—later ages copiedhim. He created: they criticised. He was the author of Iliads: they the authors of Poetics. Doubtless, if you unsphere thespiritof Mr Hay’s theories, you will find nothing discordant with what I have here said. That is a sound view of Beauty which makes it consist in that due subordination of the parts to the whole, that due relation of the parts to each other, which Mendelssohn had in his mind when he said that the essence of beauty was ‘unity in variety’—variety beguiling the imagination, the perception of unity exercising the thewes and sinews of the intellect. On such a view of beauty, Mr Hay’s theory may,in spirit, be said to rest. But here, as in higher things, it is the letter that killeth, while the spirit giveth life. And accordingly I must enter a protest against any endeavour to foist upon the palmy days of Hellenic art systems of geometrical proportions incompatible, as I believe, with those higher and broader principles by which the progress of ancient sculpture was ordered and governed—systems which will bear nothing of that ‘felicity and chance by which’—and not by rule—‘Lord Bacon believed that a painter may make a better face than ever was:’ systems which take no account of that fundamental distinction between the schools ofAthens and of Argos, and their respective disciples and descendants, without which you will make nonsense of the pages of Pliny, and—what is worse—sense of the pages of his commentators;—systems, in short, which may have their value as instruments for the education of the eye, and for instructions in the arts of design, but must be cast aside as matters of learned trifling and curious disputation, where they profess to be royal roads to art, and to map the mighty maze of a creative mind. And even as regards the application of such a system of proportions to those works of sculpture which are posterior to the Pheidian age, only partial can have been the prevalence which it or any otheronesystem can have obtained. The discrepancies of different artists in the treatment of what was called, technically called,Symmetria(as in the title of Euphranor’s work) were, by the concurrent testimony of all ancient writers, far too salient and important to warrant the supposition of any uniform scale of proportions, as advocated by Mr Hay. Even in Egypt, where one might surely have expected that such uniformity would have been observed with far greater rigour than in Greece, the discoveries of Dr Lepsius (Vorläufige Nachricht, Berlin, 1849) have elicited three totally different κανόνες, one of which is identical with the system of proportions of the human figure detailed in Diodorus. While we thus venture to differ from Mr Hay on the historical data he has mixed up with his inquiries, we feel bound to pay him a large and glad tribute of praise for having devised a system of proportions which rises superior to the idiosyncracies of different artists, which brings back to one common type the sensations of eye and ear, and so makes a giant stride towards thatcodification, if I may so speak, of the laws of the universe which it is the business of the science to effect. I have no hesitation in saying, that, for scientific precision of method and importance of results, Albert Durer, Da Vinci, and Hogarth, not to mention less noteworthy writers, must all yield the palm to Mr Hay.“I am quite aware that in the digression I have here allowed myself, on systems of proportions prevalent among ancient artists, and on the probable contents of such treatises as that of Euphranor,De Symmetria, I have laid myself open to the charge of treating an intricate question in a very perfunctory way. At present the exigencies of the subject more immediately in hand allow me only to urge in reply, that, as regards the point at issue—I mean the ‘solidarité’ between theories such as Mr Hay’s and the practice of Pheidias—theonus probandirests with my adversaries.”

“I am quite aware that in the digression I have here allowed myself, on systems of proportions prevalent among ancient artists, and on the probable contents of such treatises as that of Euphranor,De Symmetria, I have laid myself open to the charge of treating an intricate question in a very perfunctory way. At present the exigencies of the subject more immediately in hand allow me only to urge in reply, that, as regards the point at issue—I mean the ‘solidarité’ between theories such as Mr Hay’s and the practice of Pheidias—theonus probandirests with my adversaries.”

I am bound, in the first place, gratefully to acknowledge the kind and complimentary notice which, notwithstanding our difference of opinion, this author has been pleased to take of my works; and, in the second, to assure him that if any of them profess to be “royal roads to art,” or to “map the mighty maze of a creative mind,” they certainly profess to do more than I ever meant they should; for I never entertained the idea that asystem of æsthetic culture, even when based upon a law of nature, was capable of effecting any such object. But I doubt not that this too common misapprehension of the scope and tendency of my works must arise from a want of perspicuity in my style.

I have certainly, on one occasion,[27]gone the length of stating that as poetic genius must yield obedience to the rules of rhythmical measure, even in the highest flights of her inspirations; and musical genius must, in like manner, be subject to the strictly defined laws of harmony in the most delicate, as well as in the most powerfully grand of her compositions; so must genius, in the formative arts, either consciously or unconsciously have clothed her creations of ideal beauty with proportions strictly in accordance with the laws which nature has set up as inflexible standards. If, therefore, 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; the former ought, certainly, to hold the same relative position in those arts which are addressed to the eye, that is accorded to the latter in those which are addressed to the ear. Until so much science be brought to bear upon the arts of design, the student must continue to copy from individual and imperfect objects in nature, or from the few existing remains of ancient Greek art, in total ignorance 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 artistic genius are possessed of an intuitive feeling of appreciation for what is beautiful, by means of which they impart to their works the most perfect proportions, independently of any knowledge of the definite laws which govern that species of beauty. But they often do so at the expense of much labour, making many trials before they can satisfy themselves in imparting to them the true proportions which their minds can conceive, and which, along with those other qualities of expression, action, or attitude, which belong more exclusively to the province of genius. In such cases, an acquaintance with the rules which constitute the science of proportion, instead of proving fetters to genius, would doubtless afford her such a vantage ground as would promote the more free exercise of her powers, and give confidence and precision in the embodiment of her inspirations; qualities which, although quite compatible with genius, are not always intuitively developed along with that gift.

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 be 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 be enabled to exercise as correct and just an appreciation ofthe conceptions of others, in works of plastic art, as that manifested by the educated portion of mankind in respect to poetry and music. In short, it appears that, in those arts which 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 easily distinguish the true from the false, and by which the works of the poet and musical composer may be placed above mere imitations of nature, or of the works of others; while, in those arts that are addressed to the eye in their own peculiar language, such as sculpture, architecture, painting, and ornamental design, no such laws are as yet acknowledged.

Although I am, and ever have been, far from endeavouring “to foist upon the palmy days of Hellenic art” any system incompatible with those higher and more intellectual qualities which genius alone can impart; yet, from what has been handed down to us by writers on the subject, meagre as it is, I cannot help continuing to believe that, along with the physical and metaphysical sciences, æsthetic science was taught in the early schools of Greece.

I shall here take the liberty to repeat the proofs I advanced in a former work as the ground of this belief, and to which the author, from whose essay I have quoted, undoubtedly refers. It is well known that, in the time of Pythagoras, the treasures of science were veiled in mystery to all but the properly initiated, and the results of its various branches only given to the world in the works of those who had acquired this knowledge. So strictly was this secresy 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.[28]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 refer them to, an intelligible cause. 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 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.[29]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. In 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 be 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 further to say, that these elementary bodies must have forms; and as 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, and 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 have already referred.

Vitruvius, who studied architecture 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 well-formed human being.” After going at some length into details, he adds—“Since, therefore, the human figure appears to have been formed with such propriety, that the several members are commensurate with the whole, the artists of antiquity (meaning those of Greece at the period of her highest refinement) must be allowed to have followed the dictates of a judgment the most rational, when, transferring to works of art principles derived from nature, every part was so regulated as to bear a just proportion to the whole. Now, although the principles were universallyacted 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 shews 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 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 architectural design, and indeed in all works where beauty of form and harmony of proportion constituted 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 proportions of the beau ideal forms of the ancient Greek deities, or of those of their architectural structures, such as the Parthenon, the temple of Theseus, &c., or for the beauty that pervades all the other formative art of the period.

This system of geometrical harmony, founded, as I have shewn it to be, upon numerical relations, must consequently have formed part of the Greek philosophy of the period, by means of which the arts began to progress towards that great excellence which they soon after attained. A little further investigation will shew, 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.[30]The 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.”[31]

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 thecitizens—“a law,” says the Abbé Barthélémie, “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 progress 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 so admired by his contemporaries, that they decreed him the name of Legislator.[32]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.

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 geometric 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.[33]

These researches, imperfect as they are, cannot fail to exhibit the great contrast that exists between the system of elementary education in art practised in ancient Greece, and that adopted in this country at the present period. But it would be of very little service to point out this contrast, were it not accompanied by some attempt to develop the principles which seem to have formed the basis of this excellence amongst the Greeks.

But in making such an attempt, I cannot accuse myself of assuming anything incompatible with the free exercise of that spontaneity of genius which the learned essayist says is the parent and nurse of idealism. For it is in no way more incompatible with the free exercise of artistic genius, that those who are so gifted should have the advantage of an elementary education in the science of æsthetics, than it is incompatible with the free exercise of literary or poetic genius, that those who possess it should have the advantage of such an elementary education in the science of philology as our literary schools and colleges so amply afford.

The letter from which I have made a quotation at page42, arose out of the following circumstance:—In order that my theory, as applied to the orthographic beauty of the Parthenon, might be brought before the highest tribunal which this country afforded, I sent a paper upon the subject, accompanied by ample illustrations, to the Royal Institute of British Architects, and it was read at a meeting of that learned body on the 7th of February 1853; at the conclusion of which, Mr Penrose kindly undertook to examine my theoretical views, in connexion with the measurements he had taken of that beautiful structure by order of the Dilettanti Society, and report upon the subject to the Royal Institute. This report was published by Mr Penrose, vol. xi., No. 539 ofThe Builder, and the letter from which I have quoted appeared in No. 542 of the same journal. It was as follows:—

“GEOMETRICAL RELATIONS IN ARCHITECTURE.“Will you allow me, through the medium of your columns, to thank Mr Penrose for his testimony to the truth of Mr Hay’s revival of Pythagoras? The dimensions which he gives are to me the surest verification of the theory that I could have desired. The minute discrepancies form that very element of practical incertitude, both as to execution and direct measurement, which always prevails in materialising a mathematical calculation under such conditions.“It is time that the scattered computations by which architecture has been analysed—more than enough—be synthetised into those formulæ which, as Mrs Somerville tells us, ‘are emblematic of omniscience.’ The young architects of our day feel trembling beneath their feet the ground whence men are about to evoke the great and slumbering corpse of art. Sir, it is food of this kind a reviving poetry demands.——‘Give us truths,For we are weary of the surfaces,And die of inanition.’“I, for one, as I listen to such demonstrations, whose scope extends with every research into them, feel as if listening to those words of Pythagoras, which sowed in the mind of Greece the poetry whose manifestation in beauty has enchained the world in worship ever since its birth. And I am sure that in such a quarter, and in such thoughts,wemust look for the first shining of that lamp of art, which even now is prepared to burn.“I know that this all sounds rhapsodical; but I know also that until the architect becomes a poet, and not a tradesman, we may look in vain forarchitecture: and I know that valuable as isolated and detailed investigations are in their proper bearings, yet that such purposes and bearings are to be found in the enunciation of principles sublime as the generalities of ‘mathematical beauty.’“Autocthon.”

“GEOMETRICAL RELATIONS IN ARCHITECTURE.

“Will you allow me, through the medium of your columns, to thank Mr Penrose for his testimony to the truth of Mr Hay’s revival of Pythagoras? The dimensions which he gives are to me the surest verification of the theory that I could have desired. The minute discrepancies form that very element of practical incertitude, both as to execution and direct measurement, which always prevails in materialising a mathematical calculation under such conditions.

“It is time that the scattered computations by which architecture has been analysed—more than enough—be synthetised into those formulæ which, as Mrs Somerville tells us, ‘are emblematic of omniscience.’ The young architects of our day feel trembling beneath their feet the ground whence men are about to evoke the great and slumbering corpse of art. Sir, it is food of this kind a reviving poetry demands.

——‘Give us truths,For we are weary of the surfaces,And die of inanition.’

——‘Give us truths,

For we are weary of the surfaces,

And die of inanition.’

“I, for one, as I listen to such demonstrations, whose scope extends with every research into them, feel as if listening to those words of Pythagoras, which sowed in the mind of Greece the poetry whose manifestation in beauty has enchained the world in worship ever since its birth. And I am sure that in such a quarter, and in such thoughts,wemust look for the first shining of that lamp of art, which even now is prepared to burn.

“I know that this all sounds rhapsodical; but I know also that until the architect becomes a poet, and not a tradesman, we may look in vain forarchitecture: and I know that valuable as isolated and detailed investigations are in their proper bearings, yet that such purposes and bearings are to be found in the enunciation of principles sublime as the generalities of ‘mathematical beauty.’

“Autocthon.”

Of the work alluded to at page58I was favoured with two opinions—the one referring to the theory it propounds, and the other to its anatomical accuracy—both of which I have been kindly permitted to publish.

The first is from SirWilliam Hamilton, Bart., professor of logic and metaphysics in the University of Edinburgh, and is as follows:—

“Your very elegant volume is to me extremely interesting, as affording an able contribution to what is the ancient, and, I conceive, the true theory of the Beautiful. But though your doctrine coincides with the one prevalent through all antiquity, it appears to me quite independent and original in you; and I esteem it the more, that it stands opposed to the hundred one-sided and exclusive views prevalent in modern times.—16 Great King Street, March 5, 1849.”

The second is fromJohn Goodsir, Esq., professor of anatomy in the University of Edinburgh, and is as follows:—

“I have examined the plates in your work on the proportions of the human head and countenance, and find the head you have given as typical of human beauty to be anatomically correct in its structure, only differing from ordinary nature in its proportions being more mathematically precise, and consequently more symmetrically beautiful.—College, Edinburgh, 17th April 1849.”

I shall here shew, as I have done in a former work, how the curvilinear outline of the figure is traced upon the rectilinear diagrams by portions of the ellipse of (¹⁄₃), (¹⁄₄), (¹⁄₅), and (¹⁄₆).

Plate XIX.

The outline of the head and face, from points (1) to (3) (fig. 1,Plate XIX.), takes the direction of the two first curves of the diagram. From point (3),the outline of the sterno-mastoid muscle continues to (4), where, joining the outline of the trapezius muscle, at first concave, it becomes convex after passing through (5), reaches the point (6), where the convex outline of the deltoid muscle commences, and, passing through (7), takes the outline of the arm as far as (8). The outline of the muscles on the side, the latissimus dorsi and serratus magnus, commences under the arm at the point (9), and joins the outline of the oblique muscle of the abdomen by a concave curve at (10), which, rising into convexity as it passes through the points (11) and (12), ends at (13), where it joins the outline of the gluteus medius muscle. The outline of this latter muscle passes convexly through the point (14), and ends at (15), where the outline of the tensor vaginæ femoris and vastus externus muscle of the thigh commences. This convex outline joins the concave outline of the biceps of the thigh at (16), which ends in that of the slight convexity of the condyles of the thigh-bone at (17). From this point, the outline of the outer surface of the leg, which includes the biceps, peroneus longus, and soleus muscles, after passing through the point (18), continues convexly to (19), where the concave outline of the tendons of the peroneus longus continues to (20), whence the outline of the outer ankle and foot commences.

The outline of the mamma and fold of the arm-pit commences at (21), and passes through the points (22) and (23). The circle at (24) is the outline of the areola, in the centre of which the nipple is placed.

The outline of the pubes commences at (25), and ends at the point (26), from which the outline of the inner surface of the thigh proceeds over the gracilis, the sartorius, and vastus internus muscles, until it meets the internal face of the knee-joint at (27), the outline of which ends at (28). The outline of the inside of the leg commences by proceeding over the gastrocnemius muscle as far as (29), where it meets that of the soleus muscle, and continues over the tendons of the heel until it meets the outline of the inner ankle and foot at (30).

The outline of the outer surface of the arm, as viewed in front, proceeds from (8) over the remainder of the deltoid, in which there is here a slight concavity, and, next, from (31) over the biceps muscle till (32), where it takes the line of the long supinator, and passing concavely, and almost imperceptibly, into the long and short radial extensor muscles, reaches the wrist at (33). The outline of the inner surface of the arm from opposite (9) commences by passing over the triceps extensor, which ends at (34), then over the gentle convexity of the condyles of the bone of the arm at (35), and, lastly, over the flexor sublimis which ends at the wrist-joint (36).

The outline of the front of the figure commences at the point (1), (fig. 2,Plate II.), and, passing almost vertically over the platzsma-myoidis muscles, reaches the point (2), where the neck ends by a concave curve. From (2) the outline rises convexly over the ends of the clavicles, and continues so over the pectoral muscle till it reaches (3), where the mamma swells outconvexly to (4), and returns convexly towards (5), where the curve becomes concave. From (5) the outline follows the undulations of the rectus muscle of the abdomen, concave at the points (6) and (7), and having its greatest convexity at (8). This series of curves ends with a slight concavity at the point (9), where the horizontal branch of the pubes is situated, over which the outline is convex and ends at (10).

The outline of the thigh commences at the point (11) with a slight concave curve, and then swells out convexly over the extensors of the leg, and, reaching (12), becomes gently concave, and, passing over the patella at (13), becomes again convex until it reaches the ligament of that bone, where it becomes gently concave towards the point (14), whence it follows the slightly convex curve of the shin-bone, and then, becoming as slightly concave, ends with the muscles in front of the leg at (15).

The outline of the back commences at the point (16), and, following with a concave curve the muscles of the neck as far as (17), swells into a convex curve over the trapezius muscle towards the point (18); passing through which point, it continues to swell outward until it reaches (19), half way between (18) and (20); whence the convexity, becoming less and less, falls into the concave curve of the muscles of the loins at (21), and passing through the point (22), it rises into convexity. It then passes through the point (23), follows the outline of the gluteus maximus, the convex curve of which rises to the point (24), and then returns inwards to that of (25), where it ends in the fold of the hip. From this point the outline follows the curve of the hamstring muscles by a slight concavity as far as (26), and then, becoming gently convex, it reaches (27); whence it becomes again gently concave, with a slight indication of the condyle of the thigh-bone at (28), and, reaching (29), follows the convex curve of the gastrocnemius muscle through the point (30), and falling into the convex curve of the tendo Achilles at (31), ends in the concavity over the heel at (32).

The outline of the front of the arm commences at the point (33), by a gentle concavity at the arm-pit, and then swells out in a convex curve over the biceps, reaching (34), where it becomes concave, and passing through (35), again becomes convex in passing over the long supinator, and, becoming gently concave as it passes the radial extensors, rises slightly at (36), and ends at (37), where the outline of the wrist commences. The outline of the back of the arm commences with a concave curve at (38), which becomes convex as it passes from the deltoid to the long extensor and ends at the elbow (39), from below which the outline follows the convex curve of the extensor ulnaris, reaching the wrist at the point (40).

It will be seen that the various undulations of the outline are regulated by points which are determined generally by the intersections and sometimes by directions and extensions of the lines of the diagram, in the same manner in which I shewed proportion to be imparted, in a late work, to the osseous structure. The mode in which the curves of (¹⁄₂), (¹⁄₃), (¹⁄₄), (¹⁄₅), and(¹⁄₆) are thus so harmoniously blended in the outline of the female figure, only remains to be explained.

The curves which compose the outline of the female form are therefore simply those of (¹⁄₂), (¹⁄₃), (¹⁄₄), (¹⁄₅), and (¹⁄₆).

Manner in which these curves are disposed in the lateral outline (figure 1,Plate XIX.):—

Manner in which they are disposed in the outline (figure 2,Plate XIX.):—

Plate XX.

In order to exemplify more clearly the manner in which these various curves appear in the outline of the figure, I give inPlate XX.the whole curvilinear figures, complete, to which these portions belong that form the outline of the sides of the head, neck, and trunk, and of the outer surface of the thighs and legs.

The various angles which the axes of these ellipses form with the vertical, will be found amongst other details in the works I have just referred to.

At page85I have remarked upon the variety that may be introduced into any particular form of vase; and, in order to give the reader an idea of the ease with which this may be done without violating the harmonic law, I shall here give three examples:—

Plate XXI.

The first of these (Plate XXI.) differs from the Portland vase, in the concave curve of the neck flowing more gradually into the convex curve of the body.

Plate XXII.

The second (Plate XXII.) differs from the same vase in the same change of contour, as also in being of a smaller diameter at the top and at the bottom.

Plate XXIII.

The third (Plate XXIII.) is the most simple arrangement of the elliptic curve by which this kind of form may be produced; and it differs from the Portland vase in the relative proportions of height and diameter, and in having a fuller curve of contour.

The following comparison of the angles employed in these examples, with the angles employed in the original, will shew that the changes of contour in these forms, arise more from the mode in which the angles are arranged than in a change of the angles themselves:—

The harmonic elements of each are therefore simply the following parts of the right angle:—

So far as I know, there has been only one attempt in modern times, besides my own, to establish a universal system of proportion, based on a law of nature, and applicable to art. This attempt consists of a work of 457 pages, with 166 engraved illustrations, by Dr Zeising, a professor in Leipzic, where it was published in 1854.

One of the most learned and talented professors in our Edinburgh University has reviewed that work as follows:—

“It has been rather cleverly said that the intellectual distinction between an Englishman and a Scotchman is this—‘Give an Englishman two facts, and he looks out for a third; give a Scotchman two facts, and he looks out for a theory.’ Neither of these tests distinguishes the German; he is as likely to seek for a third fact as for a theory, and as likely to build a theory on two facts as to look abroad for further information. But once let him have a theory in his mind, and he will ransack heaven and earth until he almost buries it under the weight of accumulated facts. This remark applies with more than common force to a treatise published last year by Dr Zeising, a professor in Leipsic, ‘On a law of proportion which rules all nature.’ The ingenious author, after proving from the writings of ancient and modern philosophers that there always existed the belief (whence derived it is difficult to say), that some law does bind into one formula all the visible works of God, proceeds to criticise the opinions of individual writers respecting that connecting law. It is not our purpose to follow him through his lengthy examination. Suffice it to say that he believes he has found the lost treasure in theTimæusof Plato, c. 31. The passage is confessedly an obscure one, and will not bear a literal translation. The interpretation which Dr Zeising puts on it is certainly a little strained, but we are disposed to admit that he does it with considerable reason. Agreeably to him, the passage runs thus:—‘That bond is the most beautiful which binds the things as much as possible into one; and proportion effects this most perfectly when three things areso united that the greater bears to the middle the same ratio that the middle bears to the less.’

“We must do Dr Zeising the justice to say that he has not made more than a legitimate use of the materials which were presented to him in the writings of the ancients, in his endeavour to establish the fact of the existence of this law amongst them. The canon of Polycletes, the tradition of Varro mentioned by Pliny relative to that canon, the writings of Galen and others, are all brought to bear on the same point with more or less force. The sum of this portion of the argument is fairly this,—that the ancient sculptors hadsomelaw of proportion—some authorised examplar to which they referred as their work proceeded. That it was the law here attributed to Plato is by no means made out; but, considering the incidental manner in which that law is referred to, and the obscurity of the passages as they exist, it is, perhaps, too much to expect more than this broad feature of coincidence—the fact that some law was known and appealed to. Dr Zeising now proceeds to examine modern theories, and it is fair to state that he appears generally to take a very just view of them.

“Let us now turn to Dr Zeising’s own theory. It is this—that in every beautiful form lines are divided in extreme and mean ratio; or, that any line considered as a whole, bears to its larger part the same proportion that the larger bears to the smaller—thus, a line of 5 inches will be divided into parts which are very nearly 2 and 3 inches respectively (1·9 and 3·1 inches). This is a well-known division of a line, and has been called thegoldenrule, but when or why, it is not easy to ascertain. With this rule in his hand, Dr Zeising proceeds to examine all nature and art; nay, he even ventures beyond the threshold of nature to scan Deity. We will not follow him so far. Let us turn over the pages of his carefully illustrated work, and see how he applies his line. We meet first with the Apollo Belvidere—the golden line divides him happily. We cannot say the same of the division of a handsome face which occurs a little further on. Our preconceived notions have made the face terminate with the chin, and not with the centre of the throat. It is evident that, with such a rule as this, a little latitude as to the extreme point of the object to be measured, relieves its inventor from a world of perplexities. This remark is equally applicable to thearmwhich follows, to which the rule appears to apply admirably, yet we have tried it on sundry plates of arms, both fleshy and bony, without a shadow of success. Whether the rule was made for the arm or the arm for the rule, we do not pretend to decide. But let us pass hastily on to page 284, where the Venus de Medicis and Raphael’s Eve are presented to us. They bear the application of the line right well. It might, perhaps, be objected that it is remarkable that the same rule applies so exactly to the existing position of the figures, such as the Apollo and the Venus, the one of which is upright, and the other crouching. But let that pass. We find Dr Zeising next endeavouring to square his theory with the distances of theplanets, with wofully scanty success. Descending from his lofty position, he spans the earth from corner to corner, at which occupation we will leave him for a moment, whilst we offer a suggestion which is equally applicable to poets, painters, novelists, and theorisers. Never err in excess—defect is the safe side—it is seldom a fault, often a real merit. Leave something for the student of your works to do—don’t chew the cud for him. Be assured he will not omit to pay you for every little thing which you have enabled him to discover. Poor Professor Zeising! he is far too German to leave any field of discovery open for his readers. But let us return to him; we left him on his back, lost for a time in a hopeless attempt to double Cape Horn. We will be kind to him, as the child is to his man in the Noah’s ark, and set him on his legs amongst his toys again. He is now in the vegetable kingdom, amidst oak leaves and sections of the stems of divers plants. He is in his element once more, and it were ungenerous not to admit the merit of his endeavours, and the success which now and then attends it. We will pass over his horses and their riders, together with that portly personage, the Durham ox, for we have caught a glimpse of a form familiar to our eyes, the ever-to-be-admired Parthenon. This is the true test of a theory. Unlike the Durham ox just passed before us, the Parthenon will stand still to be measured. It has so stood for twenty centuries, and every one that has scanned its proportions has pronounced them exquisite. Beauty is not an adaptation to the acquired taste of a single nation, or the conventionality of a single generation. It emanates from a deep-rooted principle in nature, and appeals to the verdict of our whole humanity. We don’t find fault with the Durham ox—his proportions are probably good, though they be the result of breeding and cross-breeding; still we are not sure whether, in the march of agriculture, our grandchildren may not think him a very wretched beast. But there is no mistake about the Parthenon; as a type of proportion it stands, has stood, and shall stand. Well, then, let us see how Dr Zeising succeeds with his rule here. Alas! not a single point comes right. The Parthenon is condemned, or its condemnation condemns the theory. Choose your part. We choose the latter alternative; and now, our choice being made, we need proceed no further. But a question or two have presented themselves as we went along, which demand an answer. It may be asked—How do you account for the esteem in which this law of the section in extreme and mean ratio was held? We reply—That it was esteemed just in the same way that a tree is esteemed for its fruit. To divide a right angle into two or three, four or six, equal parts was easy enough. But to divide it into five or ten such parts was a real difficulty. And how was the difficulty got over? It was effected by means of this golden rule. This is its great, its ruling application; and if we adopt the notion that the ancients were possessed with the idea of the existence of angular symmetry, we shall have no difficulty in accounting for their appreciation of this problem. Nay, we may even go further, andadmit, with Dr Zeising, the interpretation of the passage of Plato,—only with this limitation, that Plato, as a geometer, was carried away by the geometry of æsthetics from the thing itself. It may be asked again—Is it not probable thatsomeproportionality does exist amongst the parts of natural objects? We reply—That,à priori, we expect some such system to exist, but that it is inconsistent with the scheme ofleast effort, which pervades and characterises all natural succession in space or in time, that that system should be a complicated one. Whatever it is, its essence must be simplicity. And no system of simple linear proportion is found in nature; quite the contrary. We are, therefore, driven to another hypothesis, viz.—that the simplicity is one of angles, not of lines; that the eye estimates by search round a point, not by ascending and descending, going to the right and to the left,—a theory which we conceive all nature conspires to prove. Beauty was not created for the eye of man, but the eye of man and his mental eye were created for the appreciation of beauty. Examine the forms of animals and plants so minute that nothing short of the most recent improvements in the microscope can succeed in detecting their symmetry; or examine the forms of those little silicious creations which grew thousands of years before Man was placed on the earth, and, with forms of marvellous and varied beauty, they all point to its source in angular symmetry. This is the keystone of formal beauty, alike in the minutest animalcule, and in the noblest of God’s works, his own image—Man.”

THE END.

BALLANTYNE AND COMPANY, PRINTERS, EDINBURGH.

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