'?' JO?:-' ' ivi '1'" 3 1924 073 797 890 All books are subject to recall after two weeks Olin/Kroch Library DATE DUE fi^ffr MIOLmi n --^ aBHIMi Interltbrar f Loan : GAYLORD PRINTED IN U.S.A. Cornell University Library The original of this book is in the Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924073797890 THE BEAUTIFUL NECESSITY BY THE SAME AUTHOR EPISODES FROM AN UNWRITTEN HISTORY THE nOI.DEN PERSON IN THE HEART ARCHITECTURE AND DEMOCRACY A PRIMER OF HIGHER SPACE FOUR DIMENSIONAL VISTAS PROJECTIVE ORNAMENT ORACLE THE BEAUTIFUL NECESSITY Seven Essays on Theosophy and Architecture SECOND EDITION by CLAUDE BRAGDON, F.A.I.A. NEW YORK ALFRED • A • KNOPF mcmxxii COPYRIGHT, 1910, 1922, BY CLAUDE BKAGDON '\ C, ;'. n '^ c- <^"i \ V.--.V >«-/ 06( up, eleotrotvped, and printed ty the Vail-BaXlou Co., Binohamton, S. 7. Paper /urnia/ied by Henry Lindenmeyr d Sons, New York, Bound by H. Wolff Eetate, New York. MANUTAOTUBSD IK THB VKITBD STATES 07 AMBRIOA "Let us build altars to the Beautiful Necessity" — Emerson CONTENTS I The Art of Architecture 12 II Unity akd Polarity 29 III Changeless Change 43 IV The Bodily Temple 64 V Latent Geometry 76 VI The Arithmetic of Beauty 91 VII Frozen Music 10 i Conclusion iio PREFACE TO THE SECOND EDITION The Beautiful Necessity was first published in 1910. Save for a slim volume of privately printed verse it was my first book. I worked hard on it. Fifteen years elapsed between its begin- ning and completion; it was twice published serially — written, rewritten and tre-written — before it reached its ultimate incar- nation in book form. Confronted now with the opportunity to revise the text again, I find myself in the position of a surgeon who feels that the oper- ation he is called upon to perform may perhaps harm more than it can help. Prudence therefore prevails over my passion for dissection: warned by eminent examples, I fear that any injec- tion of my more mature and less cocksure consciousness into this book might impair its unity — that I "never could recapture the first fine careless rapture." The text stands therefore as originally published save for a few verbal changes, and whatever reservations I have about it shall be stated in this preface. These are not many nor im- portant: The Beautiful Necessity contains nothing that I need repudiate or care to contradict. Its thesis, briefly stated, is that art in all its manifestations is an expression of the cosmic life, and that its symbols constitute a language by means of which this life is published and repre- sented. Art is at all times subject to the Beautiful Necessity of proclaiming the world order. In attempting to develop this thesis it was not necessary (nor as I now think, desirable) to link it up in so definite a manner 9 10 PREFACE TO THE SECOND EDITION with theosophy. The individual consciousness is colored by the particular medium through which it receives truth, and for me that medium was theosophy. Though the book might gain a more unprejudiced hearing, and from a larger audience, by the removal of the theosophic "color-screen," it shall remain, for its removal now might seem to imply a loss of faith in the funda- mental tenets of theosophy, and such an implication would not be true. The ideas in regard to time and space are those commonly current in the world until the advent of the Theory of Rela- tivity. To a generation brought up on Einstein and Ouspen- sky they are bound to appear "lower dimensional." Merely to state this fact is to deal with it to the extent it needs to be dealt with. The integrity of my argument is not impaired by these new views. The one important influence that has operated to modify my opinions concerning the mathematical basis of the arts of space has been the discoveries of Mr. Jay Hambidge with regard to the practice of the Greeks in these matters, as exemplified in their temples and their ceramics, and named by him Dynamic Symmetry. In tracing everything back to the logarithmic spiral (which embodies the principle of extreme and mean ratios) I consider that Mr. Hambidge has made one of those generalizations which reorganizes the old knowledge and organizes the new. It would be only natural if in his immersion in his idea he overworks it, but Mr. Hambidge is a man of such intellectual integrity and thoroughness of method that he may be trusted not to warp the facts to fit his theories. The truth of the matter is that the entire field of research into the mathematics of Beauty is of such richness that wherever a man plants his meta- physical spade he is sure to come upon "pay dirt." The PREFACE TO THE SECOND EDITION II Beautiful Necessity represents the result of my own pros- pecting; Dynamic Symmetry represents the result of his. If at any point our findings appear to conflict, it is less likely that one or the other of us is mistaken than that each is right from his own point of view. Be that as it may, I should be the last man in the world to differ from Mr. Hambidge, for if he con- victed me of every conceivable error his work would still re- main the greatest justification and confirmation of my funda- mental contention — that art is an expression of the world order and is therefore orderly, organic; subject to mathematical law, and susceptible of mathematical analysis. CLAUDE BRAGDON Rochester, N. Y. April, 1922 THE ART OF ARCHITECTURE ONE of the advantages of a thorough assimilation of what may be called the theosophic idea is that it can be applied with advantage to every department of knowledge and of human activity: like the key to a cryptogram it renders clear and simple that which before seemed intricate and obscure. Let us apply this key to the subject of art, and to the art of architec- ture in particular, and see if by so doing we may not learn more of art than we knew before, and more of theosophy too. "' The theosophic idea is that everything is an expression of the Self — or whatever other name one may choose to give to that immanent unknown reality which forever hides behind all phe- nomenal life — but because, immersed as we are in materiality, our chief avenue of knowledge is sense perception, a more exact expression of the theosophic idea would be: Everything is the expression of the Self in terms of sense. Art, accordingly, is the expression of the Self in terms of sense. Now though the Self is one, sense is not one, but manifold: and therefore there are arts, each addressed to some particular faculty or group of faculties, and each expressing some particular quality or group of qualities of the Self. The white light of Truth is thus broken up into a rainbow-tinted spectrum of Beauty, in which the var- ious arts are colors^ each distinct, yet merging one into another — poetry into musig; painting into decoration; decoration becom- ing sculpture; sculpture — architecture, and so on. 12 THE ART OF ARCHITECTURE 13 In such a spectrum of the arts each one occupies a definite ^ 1 r place, and all together form a series of which music^ad^atchir tecture._are-the- -two— extremes. That such is their relative position may be demonstrated in various ways. The theosophic explanation involving the familiar idea of the "pairs of op- posites" would be something as follows. According to the Hindu-Aryan theory, Brahma, that the world niight be born, fell asunder into man and wife — became in other words name and form.* The two universal aspects of name and form are what philosophers call the two "modes of consciousness," one of time, and the other of space. These are the two gates through which ideas enter phenomenal life ; the two boxes, as it were, that contain all the toys with which we play. Everything, were we only keen enough to perceive it, bears the mark of one or the other of them, and may be classified accordingly. In such a classification music is seen to be allied to time, and architecture to space, because music is successive in its mode of manifesta- tion, and in time alone everything would occur successively, one thing following another; while architecture, on the other hand, impresses itself upon the beholder all at once, and in space alone all things would exist simultaneously. Music, which is in time \ alone, without any relation to space;, and architecture, which is in space alone, without any relation to time, are thus seen to stand at opposite ends of the art spectrum, and to be, in a sense, the only "pure" arts, because in all the others the elements of both * The quaint Oriental imagery here employed should not blind the reader to the precise scientific accuracy of the idea of which this imagery is the vehicle. Schopenhauer says: "Polarity, or the sun- dering of a force into two quantitively different and opposed activ- ities striving after re-union, ... is a fundamental type of almost all the phenomena of nature, from the magnet and the crystal to man himself." 14 THE BEAUTIFUL NECESSITY time and space enter in varying proportion, either actually or by implication. Poetry and the drama are allied to music in- asmuch as the ideas and images of which they are made up are presented successively, yet these images are for the most part forms of space. Sculpture on the other hand is clearly allied to architecture, and so to space, but the element of action, suspended though it be, affiliates it with the opposite or time pole. Painting occupies a middle position, since in it space instead of being actual has become ideal — three dimensions being expressed through the mediumship of two — and time enters into it more largely than into sculpture by reason of the greater ease with which complicated action can be indicated : a picture being nearly always time aTrested in midcourse as it were — a moment transfixed. In order to form a just conception of the relation between music and architecture it is necessary that the two should be conceived of not as standing at opposite ends of a series repre- sented by a straight line, but rather in juxtaposition, as in the ancient Egyptian symbol of a serpent holding its tail in its mouth, the head in this case corresponding to music, and the tail to architecture; in other ■^rds, though in one sense they are the most widely separated^Lthe arts, in another they are the most closely related. ^^ Music being purely in time ano^^hitecture being purely in space, each is, in a manner and tolfcdegree not possible with any of the other arts, convertible into nhe other, by reason of the correspondence subsisting between intervals of time and inter- vals of space. A perception of this may^^ve inspired the fa- mous saying that architecture is frozen rmmc, a poetical state- ment of a philosophical truth, since that which in music is ex- pressed by means of harmonious intervals of time and pitch, successively, after the manner of time, may be translated into THEARTOFARCHITECTURE 15 corresponding intervals of architectural void and solid, height and width. In another sense music and architecture are allied. They alone of all the arts are purely creative, since in them is pre- sented, not a likeness of some known idea, but a thina-in-itself brought to a distinct and complete expression of its nature. Neither a musical composition nor a work of architecture depends for its effectiveness upon resemblances to natural sounds in the one case, or to natural forms in the other. Of none of the other arts is this to such a degree true: they are not so much creative as re-creative, for in them all the artist takes his subject ready made from nature and presents it anew according to the dictates of his genius. The characteristic differences between music and architec- ture are the same as those which subsist between time and space. Now time and space are such abstract ideas that they can be dealt with best through their corresponding correlatives in the natural world, for it is a fundamental theosophic tenet that nature everywhere abounds in such correspondences; that nature, in its myriad forms, is indeed the concrete presentment of abstract unities. The energy which ever5rwhere animates form is a type of time within space; the mind working in and through the body is another expression of the same thing. Correspondingly, music is dynamic, subjective, mental, of one dimension; while architecture is static, objective, physical, of three dimensions; sustaining the same relation to music and the other arts as does the human body to the various organs which compose, and consciousnesses which animate it (it being the reservatory of these organs and the vehicle of these conscious- nesses) ; and a work of architecture in like manner may and sometimes does include all of the other arts within itself. Sculpture accentuates and enriches, painting adorns, works of l6 THE BEAUTIFUL NECESSITY literature are stored within it, poetry and the drama awake its echoes, while music thrills to its uttermost recesses, like the very spirit of life tingling through the body's fibres. Such being the relation between them, the difiference in the nature of the ideas bodied forth in music and in architecture becomes apparent. Music is interior, abstract, subjective, speaking directly to the soul in a simple and universal language whose meaning is made personal and particular in the breast of each listener: "Music alone of all the arts," says Balzac, "has power to make us live within ourselves." A work of architec- ture is the exact opposite of this: existing principally and pri- marily for the uses of {he body, it is like the body a concrete organism, attaining to esthetic expression only in the recon- ciliation and fulfilment of many conflicting practical require- ments. Music is pure beauty, the voice of the unfettered and perpetually evanishing soul of things; architecture is that soul imprisoned in a form, become subject to the law of causality, beaten upon by the elements, at war with gravity, the slave of man. One is the Ariel of the arts ; the other, Caliban. Coming now to the consideration of architecture in its his- torical rather than its philosophical aspect, it will be shown how certain theosophical concepts are applicable here. Of these none is more familiar and none more fundamental than the idea of reincarnation. By reincarnation more than mere physical re-birth is meant, for physical re-birth is but a single manifestation of that universal law of alternation of state, of animation of vehicles, and progression through related planes, in accordance with which all things move, and^as it were, make music — each cycle complete, yet part of a larger cycle, the in- carnate monad passing through correlated changes, carrying THE ART OF ARCHITECTURE 17 along and bringing into manifestation in each successive arc of the spiral the experience accumulated in all preceding states, and at the same time unfolding that power of the Self peculiar to the plane in which it is momentarily manifesting. This law finds exemplification in the history of architecture in the orderly flow of the building impulse from one nation and one country to a different nation and a different country : its new vehicle of manifestation; also in the continuity and increasing complexity of the development of that impulse in manifesta- tion ; each "incarnation" summarizing all those which have gone before, and adding some new factor peculiar to itself alone; each being a growth, a life, with periods corresponding to child- hood, youth, maturity and decadence; each also typifying in its entirety some single one of these life-periods, and revealing some special aspect or power of the Self, For the sake of clearness and brevity the consideration of only one of several architectural evolutions will be attempted : that which, arising in the north of Africa, spread to southern Europe, thence to the northwest of Europe and to England — the architecture, in short, of the so-called civilized world. This architecture, anterior to the Christian era, may be broadly divided into three great periods, during which it was successively practiced by three peoples: the Egyptians, the Greeks and the Romans. Then intervened the Dark Ages, and a new art arose, the Gothic, which was a flowering out in stone of the spirit of Christianity. This was in turn succeeded by the Renaissance, the impulse of which remains to-day unexhausted. In each of these architectures the peculiar genius of a people and of a period attained to a beautiful, complete and coherent utterance, and notwithstanding the considerable intervals of time which sometimes separated them they succeeded one another l8 THE BEAUTIFUL NECESSITY logically and inevitably, and each was related to the one which preceded and which followed it in a particular and intimate manner. The power and wisdom of ancient Egypt was vested in its priesthood, which was composed of individuals exceptionally qualified by birth and training for their high office, tried by the severest ordeals and bound by the most solemn oaths. The priests were honored and privileged above all other men, and spent their lives dwelling apart from the multitude in vast and magnificent temples, dedicating themselves to the study and practice of religion, philosophy, science and art — subjects then intimately related, not widely separated as they are now. These men were the architects of ancient Egypt: theirs the minds which directed the hands that built fhose time-defying monuments. The rites that the priests practiced centered about what are known as the Lesser and the Greater Mysteries. These con- sisted of representations by means of symbol and allegory, under conditions and amid surroundings the most awe-inspiring, of those great truths concerning man's nature, origin and destiny of which the priests — in reality a brotherhood of initiates and their pupils — were the custodians. These ceremonies were made the occasion for the initiation of neophytes into the order, and the advancement of the already initiated into its successive de- grees. For the practice of such rites, and others designed to im- press not the elect but the multitude, the great temples of Egypt were constructed. Everything about them was calculated to induce a deep seriousness of mind, and to inspire feelings of awe, dread and even terror, so as to test the candidate's fortitude of soul to the utmost. The avenue of approach to an Egyptian temple was flanked on both sides, sometimes for a mile or more, with great stone THE ART OF ARCHITECTURE 19 Sphinxes — that emblem of man's dual nature, the god emerging from the beast. The entrance was through a single high door- way between two towering pylons, presenting a vast surface sculptured and painted over with many strange and enigmatic figures, and flanked by aspiring obelisks and seated colossi with faces austere and calm. The large court thus entered was surrounded by high walls and colonnades, but was open to the sky. Opposite the first doorway was another, admitting to a somewhat smaller enclosure, a forest of enormous carved and painted columns supporting a roof through the apertures of which sunshine gleamed or dim light filtered down. Beyond this in turn were other courts and apartments culminating in some inmost sacred sanctuary. Not alone in their temples, but in their tombs and pyramids and all the sculptured monuments of the Egyptians, there is the same insistence upon the sublimity, mystery and awefulness of life, which they seem to have felt so profoundly. But more than this, the conscious thought of the masters who conceived them, the buildings of Egypt give utterance also to the toil and suffering of the thousands of slaves and captives which hewed the stones out of the heart of the rock, dragged them long distances and placed them one upon another, so that these buildings oppress while they inspire, for there is in them no freedom, no spontaneity, no individuality, but everywhere the felt presence of an iron conventionality, of a stern immutable law. In Egyptian architecture is symbolized the condition of the human soul awakened from its long sleep in nature, and become conscious at once of its divine source and of the leaden burden of its fleshy envelope. Egypt is humanity new-born, bound still with an umbilical cord to nature, and strong not so much with its own strength as with the strength of its mother. This idea is aptly symbolized in those gigantic colossi flanking the entrance 20 THE BEAUTIFUL NECESSITY to some rock-cut temple, which though entire are yet part of the living cliff out of which they were fashioned. "^ In the architecture of Greece the note of dread and mystery yields to one of pure joyousness and freedom. The terrors of childhood have been outgrown, and man revels in the indulgence of his unjaded appetites and in the exercise of his awakened reasoning faculties. In Greek art is preserved that evanescent beauty of youth which, coming but once and continuing but for a short interval in every human life, is yet that for which all ante- cedent states seem a preparation, and of which all subsequent ones are in some sort an effect. Greece typifies adolescence, the love age, and so throughout the centuries humanity has turned to the contemplation of her, just as a man all his life long secretly cherishes the memory of his first love. An impassioned sense of beauty and an enlightened reason characterize the productions of Greek architecture during its best period. The perfection then attained was possible only in a nation whereof the citizens were themselves critics and ama- teurs of art, one wherein the artist was honored -and his work appreciated in all its beauty and subtlety. The Greek architect was less bound by tradition and precedent than was the Egyptian, and he worked unhampered by any restrictions save such as, like the laws of harmony in music, helped rather than hindered his genius to express itself — ^^restrictions founded on sound reason, the value of which had been proved by experience. The Doric order was employed for all large temples, since it possessed in fullest measure the qualities of simplicity and dig- nity, the attributes appropriate to greatness. Quite properly also its formulas were more fixed than those of any other style. The Ionic order, the feminine of which the Doric may be con- sidered the corresponding masculine, was employed for smaller temples; like a woman it was more supple and adaptable than THE ART OF ARCHITECTURE 21 the Doric, its proportions were more slender and graceful, its lines more flowing, and its ornament more delicate and profuse. A freer and more elaborate style than either of these, infinitely various, seeming to obey no law save that of beauty, was used sometimes for small monuments and temples, such as the Tower of the Winds, and the monument of Lysicrates at Athens. Because the Greek architect was at liberty to improve upon the work of his predecessors if he could, no temple was just like any other, and they form an ascending scale of excellence, cul- rriinating in the Acropolis group. Every detail was considered not only with relation to its position and function, but in regard to its intrinsic beauty as well, so that the merest fragment, detached from the building of which it formed a part, is found 22 THE BEAUTIFUL NECESSITY worthy of being treasured in our museums for its own sake. Just as every detail of a Greek temple was adjusted to its posi- tion and expressed its office, so the building itself was made to fit its site and to show forth its purpose, forming with the sur- rounding buildings a unit of a larger whole. The Athenian Acropolis is an illustration of this: it is an irregular fortified hill, bearing diverse monuments in various styles, at unequal levels and at different angles with one another, yet the whole arrangement seems as organic and inevitable as the disposition of the features of a face. The Acropolis is an example of the ideal architectural republic wherein each individual contributes to the welfare of all, and at the same time enjoys the utmost personal liberty (Illustration i). Very different is the spirit bodied forth in the architecture of Imperial Rome. The iron hand of its sovereignty encased within the silken glove of its luxury finds its prototype in build- ings which were stupendous crude brute masses of brick and concrete, hidden within a covering of rich marbles and mosaics, wrought in beautiful but often meaningless forms by clever de- generate Greeks. The genius of Rome finds its most charac- teristic expression, not in temples to the high gods, but rather in those vast and complicated structures — basilicas, amphitheatres, baths — built for the amusement and purely temporal needs of the people. If Egypt typifies the childhood of the race and Greece its beautiful youth. Republican Rome represents its strong man- hood — a soldier filled with the lust of war and the love of glory — and Imperial Rome its degeneracy: that soldier become con- queror, decked out in plundered finery and sunk in sensuality, tolerant of all who minister to his pleasures but terrible to all who interfere with them. The fall of Rome marked the end of the ancient Pagan world. THE ART OF ARCHITECTURE 23 Above its ruin Christian civilization in the course of time arose. Gothic architecture is an expression of the Christian spirit; in it is manifest the reaction from licentiousness to asceticism. Man's spiritual nature, awakening in a body worn and weak- ened by debaucheries, longs ardently and tries vainly to escape. Of some such mood a Gothic cathedral is the expression: its vaulting, marvelously supported upon slender shafts by reason of a nicely adjusted equilibrium of forces ; its restless, upward- reaching pinnacles and spires; its ornament, intricate and enig- matic — all these suggest the over-strained organism of an as- cetic; while its vast shadowy interior lit by marvelously traceried and jeweled windows, which hold the eyes in a hyp- notic thrall, is like his soul : filled with world sadness, dead to the bright brief joys of sense, seeing only heavenly visions, knowing none but mystic raptures. Thus it is that the history of architecture illustrates and en- I forces the theosophical teaching that everything of man's creat- ing is made in his own image. Architecture mirrors the life of the individual and of the race, which is the life of the indi- vidual written large in time and space. The terrors of child-" hood ; the keen interests and appetites of youth ; the strong stern joy of conflict which comes with manhood ; the lust, the greed, the cruelty of a materialized old age — all these serve but as a preparation for the life of the spirit, in which the man becomes again as a little child, going over the whole round, but on a higher arc of the spiral. The final, or fourth state being only in some sort a repe- tition of the first, it would be reasonable to look for a certain correspondence between Egyptian and Gothic architecture, and such a correspondence there is, though it is more easily divined than demonstrated. In both there is the same deeply religious spirit; both convey, in some obscure yet potent manner, a sense 24 THE BEAUTIFUL NECESSITY of the soul being near the surface of life. There is the same love of mystery and of symbolism ; and in both may be observed the tendency to create strange composite figures to typify trans- cendental ideas, the sphinx seeming a blood-brother to the gar- goyle. The conditions under which each architecture flour- ished were not dissimilar, for each was formulated and con- trolled by small well-organized bodies of sincerely religious and highly enlightened men — the priesthood in the one case, the masonic guilds in the other — working together toward the consummation of great undertakings amid a populace for the most part oblivious of the profound and subtle meanings of which their work v^as full. In Mediaeval Europe, as in ancient Egypt, fragments of the Ancient Wisdom — transmitted in the symbols and secrets of the cathedral builders — determined much of Gothic architecture. The architecture of the Renaissance period, which succeeded the Gothic, corresponds again, in the spirit which animates it, to Greek architecture, which succeeded the Egyptian, for the Renaissance as the name implies was nothing other than an attempt to revive Classical antiquity. ■ Scholars writing in what they conceived to be a Classical style, sculptors modeling Pagan deities, and architects building according to their understanding of Vitruvian methods succeeded in producing works like, yet different from the originals they followed — different because, animated by a spirit unknown to the ancients, they embodied a new ideal. In all the productions of the early Renaissance, "that first transcendent springtide of the modern world," there is the evanescent grace and beauty of youth which was seen to have per- vaded Greek art, but it is a grace and beauty of a different sort. The Greek artist sought to attain to a certain abstract per- fection of type; to build a temple which should combine all the THE ART OF ARCHITECTURE 25 excellencies of every similar temple, to carve a figure, impersonal in the highest sense, v^^hich should embody every beauty. The artist of the Renaissance on the other hand delighted not so much in the type as in the variation from it. Preoccupied with the unique mystery of the individual soul — a sense of which was Christianity's gift to Christendom — he endeavored to portray that wherein a particular person is unique and singular. Acutely conscious also of his own individuality, instead of effacing it he made his work the vehicle and expression of that individuality. The history of Renaissance architecture, as Symonds has pointed out, is the history of a few eminent individuals, each one mould- ing and modifying the style in a manner peculiar to himself alone. In the hands of Brunelleschi it was stern and powerful; Bramante made it chaste, elegant and graceful; Palladio made it formal, cold, symmetrical; while with Sansovino and Sam- michele it became sumptuous and bombastic. As the Renaissance ripened to decay its architecture assumed more and more the characteristics which distinguished that of Rome during the decadence. In both there is the same lack of simplicity and sincerity, the same profusion of debased and meaningless ornament, and there is an increasing disposition to conceal and falsify the construction by surface decoration. The final part of this second or modern architectural cycle lies still in the future. It is not unreasonable to believe that the movement toward mysticism, of which modern theosophy is a phase and the spiritualization of science an episode, will flower out into an architecture which will be in some sort a reincarna- tion of and a return to the Gothic spirit, employing new materi- als, new methods, and developing new forms to show forth the spirit of the modern world, without violating ancient verities. In studying these crucial periods in the history of European architecture it is possible to trace a gradual growth or unfolding 26 THE BEAUTIFUL NECESSITY as of a plant. It is a fact fairly well established that the Greeks derived their architecture and ornament from Egypt; the Romans in turn borrowed from the Greeks; while a Gothic cathedral is a lineal descendant from a Roman basilica. The Egyptians in their constructions did little more than to place enormous stones on end, and pile one huge block upon another. They used many columns placed close together: the spaces which they spanned were inconsiderable. The upright or supporting member may be said to have been in Egyptian architecture the predominant one. A vertical line therefore may be taken as the simplest and most abstract symbol of Egyp- tian architecture (Illustration 2). It remained for the Greeks fully to develop the lintel. In their architecture the vertical member, or column, existed solely for the sake of the horizontal member, or lintel ; it rarely stood alone as in the case of an Egyp- tian obelisk. The columns of the Greek temples were reduced to those proportions most consistent with strength and beauty, and the intercolumnations were relatively greater than in Egyp- tian examples. It may truly be said that Greek architecture exhibits the perfect equality and equipoise of vertical and hori- THE ART OF ARCHITECTURE 27 zotital elements and these only, no other factor entering in. Its graphic symbol would therefore be composed of a vertical and a horizontal line (Illustration 3). The Romans, while retaining the column and lintel of the Greeks, deprived them of their structural significance and subordinated them to the semicir- cular arch and the semi-cylindrical and hemispherical vault, the truly characteristic and determining forms of Roman archi- tecture. Our symbol grows therefore by the addition of the arc of a circle (Illustration 4). In Gothic architecture column, lintel, arch and vault are all retained in changed form, but that which more than anything else differentiates Gothic architecture from any style which preceded it is the introduction of the principle of an equilibrium of forces, of a state of balance rather than a state of rest, arrived at by the opposition of one thrust with another contrary to it. This fact can be indicated graphically by two opposing inclined lines, and these united to the preceding symbol yield an accurate abstract of the elements of Gothic architecture (Illustration 5). 28 THE BEAUTIFUL NECESSITY All this is but an unusual application of a familiar theosophic teaching, namely, that it is the method of nature on every plane and in every department not to omit anything that has gone before, but to store it up and carry it along and bring it into manifestation later. Nature everywhere proceeds lilce the jingle of The House that Jack Built: she repeats each time all she has learned, and adds another line for subsequent repetition. II UNITY AND POLARITY THEOSOPHY, both as a philosophy, or system of thought, which discovers correlations between things apparently unrelated, and as a life, or system of train- ing whereby it is possible to gain the power to perceive and use these correlations for worthy ends, is of great value to the creative artist, whose success depends on the extent to which he works organically, conforming to the cosmic pattern, pro- ceeding rationally and rhythmically to some predetermined end. It is of value no less to the layman, the critic, the art amateur — to anyone in fact who would come to an accurate and intimate understanding and appreciation of every variety of esthetic endeavor. For the benefit of such I shall try to trace some of those correlations which theosophy affirms, and indicate their bearing upon art, and upon the art of architecture in particular. ^-' One of the things which theosophy teaches is that those tran- scendent glimpses of a divine order and harmony throughout the universe vouchsafed the poet and the mystic in their moments of vision are not the paradoxes — 'the paronomasia as it were — of an intoxicated state of consciousness, but glimpses of reality. We are all of us participators in a world of concrete music, geometry and number — a world of sounds, odors, forms, motions, colors, so mathematically related and coordinated that our pigmy bodies, equally with the farthest star, vibrate to the 29 30 THE BEAUTIFUL NECESSITY music of the spheres. There is a Beautiful Necessity which rules the world, which is a law of nature and equally a law of art, for art is idealized creation: nature carried to a higher power by reason of its passage through a human consciousness. Thought and emotion tend to crystallize into forms of beauty as inevitably as does the frost on a window pane. Art therefore in one of its aspects is the weaving of a pattern, the communication of an order and a method to the material or medium employed. Al- though no masterpiece was ever created by the conscious follow- ing to set rules, for the true artist works unconsciously, in- stinctively, as the bird sings or as the bee builds its honey-cell, yet an analysis of any masterpiece reveals the fact that its author (like the bird and the bee) has "followed the rules without knowing them." Helmholtz says, "No doubt is now entertained that beauty is subject to laws and rules dependent on the nature of hu'man in- telligence. The difficulty consists in the fact that these laws and rules, on whose fulfilment beauty depends, are not consciously present in the mind of the artist who creates the work, or of the observer who contemplates it." Nevertheless they are discover- able, and can be formulated, after a' fashion. We have only to read aright the lessons everywhere portrayed in the vast picture- books of nature and of art. The first truth therein published is the law of Unity — oneness ; for there is one Self, one Life, which, myriad in manifestation, is yet in essence ever one. Atom and universe, man and the world — each is a unit, an organic and coherent whole. The application of this law to art is so obvious as to be almost un- necessary of elucidati'on, for to say that a work of art must pos- sess unity, must seem to proceed from a single impulse and be the embodiment of one dominant idea, is to state a truism. In a work of architecture the coordination of its various parts with UNITY AND POLARITY 31 one another is almost the measure of its success. We remember any masterpiece — the cathedral of Paris no less than the pyra- mids of Egypt — by the singleness of its appeal ; complex it may be, but it is a coordinated complexity; variety it may possess, but bu*t it is a variety in an all-embracing unity. The second law, not contradicting but supplementing the first, is the law of Polarity, i. e., duality. All things have sex, are either masculine or feminine. This too is the reflection on a lower plane of one of those transcendental truths taught by the Ancient Wisdom, namely that the Logos, in his voluntarily circumscribing his infinite life in order that he may mani- fest, encloses himself within his limiting veil, maya, and that his life appears as spirit (male), and his maya as matter (female), the two being never disjoined during manifestation. The two terms of this polarity are endlessly repeated through- out nature: in sun and moon, day and night, fire and water, man and woman — and so on, A close inter-relation is always seen to subsist between corresponding members of such pairs of opposites: sun, day, fire, man express and embody the primal and active aspect of the manifesting deity; moon, night, water, woman, its secondary and passive aspect. Moreover, each implies or brings to mind the others of its class : man, like the sun, is lord of day; he is like fire, a devastating force; woman is subject to the lunar rhythm; like water, she is soft, sinuous, fecund. The part which this polarity plays in the arts is important, and the constant and characteristic distinction between the two terms is a thing far beyond mere contrast. In music they are the major and minor modes: the typical, or representative chords of the dominant seventh, and of the tonic (the two chords into which Schopenhauer says all music can be resolved) : a partial dissonance, and a consonance: 32 THE BEAUTIFUL NECESSITY a chord of suspense, and a chord of satisfaction. In speech the two are vowel, and consonant sounds : the type of the first being a, a sound of suspense, made with the mouth open; and of the second m, a sound of satisfaction, made by closing the mouth; their combination forms the sacred syllable Om (Aum). In painting they are warm colors, and cold : the pole of the first be- ing in red, the color of fire, which excites ; and of the second in blue, the color of water, which calms ; in the Arts of design they are lines straight (like fire), and flowing (like water) ; masses light (like the day), and dark (like night). In architecture they are the column, or vertical member, which resists the force of gravity; and the lintel, or horizontal member, which suc- cumbs to it; they are vertical lines, which are aspiring, ef- fortful; and horizontal lines, which are restful to the eye and mind. It is desirable to have an instant and keen realization of this sex quality, and to make this easier some sort of classification and analysis must be attempted. Those things which are allied to and partake of the nature of time are masculine, and those which are allied to and partake of the nature of space are fem- inine: as motion, and matter; mind, and body; etc. The English words "masculine" and "feminine" are too intimately associated with the idea of physical sex properly to designate the terms of this polarity. In Japanese philosophy and art (derived from the Chinese) the two are called In and Yo (In, feminine; Yo, masculine) ; and these little words, being free from the limi- tations of their English correlatives, will be found convenient, Yo to designate that which is simple, direct, primary, active, positive; and In, that which is complex, indirect, derivative, passive, negative. Things hard, straight, fixed, vertical, are Yo; things soft, curved, horizontal, fluctuating, are In — and so on. UNITY AND POLARITY MAPLE UAF 33 In passing it may be said that the super- iority of the line, mass, and color composition of Jap- anese prints and kak- emonos to that exhib- ited in the vastly 6 7 more pretentious easel pictures of modern Occidental artists — a superiority now generally acknowledged by connoisseurs — is largely due to the conscious following, on the part of the Japanese, of this principle of sex-complementaries. Nowhere are In and Yo more simply and adequately imaged than in the vegetable kingdom. The trunk of a tree is Yo, its foliage, In ; and in each stem and leaf the two are repeated. A calla, consisting of a single straight and rigid spadix embraced by a soft and tenderly curved spathe, affords an almost perfect expression of the characteristic differences between Yo and In and their reciprocal relation to each other. The two are not often combined in such simplicity and perfection in a single form. The straight, vertical reeds which so often grow in still, shallow water, find their complement in the curved lily-pads which lie horizontally on its surface. Trees such as pine and hemlock, which are ex-current — those in which the branches start successively (i. e., after the manner of time) from a straight and vertical central stem — are Yo; trees such as the elm and willow, which are deliquescent — those in which the trunk dis- solves as it were simultaneously (after the manner of space) into its branches — are In, All tree forms lie in or between these two extremes, and leaves are susceptible of a similar classifi- cation. It will be seen to be a classification according to time 34 THE BEAUTIFUL NECESSITY THE LAW OF POLARITY and space, for the characteristic of time is succession, and of space, simultaneousness: the first is expressed symbolically by elements arranged with relation to axial lines; the second, by elements arranged with relation to focal points (Illustrations 6,7). The student should train himself to recognize In and Yo in all their Protean presentments throughout nature — in the cloud upon the mountain, the wave against the cliflf, in the tracery of trees against the sky — that he may the more readily recognize them in his chosen art, whatever that art may be. If it happens to be painting, he will endeavor to discern this law of duality in the composition of every masterpiece, recognizing an instinctive obedience to it in that favorite device of the great Renaissance masters of making an architectural set- ting for their groups of figures, and he will delight to trace the law in all its rami- ® fications of contrast between complementaries in line, color, and mass (Illustration 8). With reference to architecture, it is true, generally speaking, that architectural forms have been developed through necessity, the function seeking and finding its -'appropriate form. For example, the buttress of a Gothic cathedral was developed by CLEOPATRA MELTING THE PEARL. £>V TIEPOLO UNITY AND POLARITY 35 the necessity of resisting the thrust of the interior vaulting without encroaching upon the nave ; the main lines of a buttress conform to the direction of the thrust, and the pinnacle with which it ter- \] \^ minates is a logical shape for the masonry neces- yv sary to hold the top in position (Illustration 9). Research along these lines is interesting and fruitful of result, but there remains a certain number of architectural forms whose origin can- not be explained in any such manner. The secret of their undying charm lies in the fact 9 that in them In and Yo stand symbolized and contrasted. They no longer obey a law of util- ity, but an abstract law of beauty, for in becoming sexually expressive as it were, the construction itself is sometimes weakened or falsified. The familiar classic console or mo- dillion is an example: although in general contour it is well adapted to its function as a supporting bracket, embedded in, and projecting from a wall, yet the scroll-like ornament with which its sides are embellished gives it the appearance of not entering the wall at all, but of being stuck against it in some miraculous manner. This defect in functional expressiveness is more than compensated for by the perfection with which feminine and masculine characteristics are expressed and contrasted in the exquisite double spiral, opposed to the straight lines of the moulding which it subtends (Illustration 10). Again, by fluting the shaft of a column its area of cross-section is diminished but the appearance of strength is enhanced because its masculine character — as a supporting member resisting the force of gravity — is emphasized. The importance of the so-called "orders" lies in the fact that they are architecture epitomized as it were. A building con- 36 THE BEAUTIFUL NECESSITY COMNTHIAN MODILUON ?^r-rp^ CLASSIC Vii,/ ■] C3RflCIAN DOE-tC CAP IONIC CAP 12 bead and reel, and other familiar ornamented mouldings (Illustrations 14, 15, 16). 38 THE BEAUTIFUL CAPrtAL FK.CM THE/TOW^aOP THE.WINDJ. xxnms. 'wMm CORINTHIAN CAP IRCMHAiaUAN BUILDINGS. ATHENE. lUDJ&TTE. FRiONt TCMPL&CP'MAW,, BOMB I CAULICULDJI OFOCKiNTHtAN CAP BALWTBE) BY SAN QAUQ 13 NECESSITY There are indications that at some time during the development of Gothic* architecture in France, this sex-dis- tinction became a recog- nized principle, mould- ing and modifying the design of a cathedral in much the same way that sex modifies bodily structure. The masonic guilds of the Middle Ages were custodians of the esoteric — which is the theosophic — side of the Christian faith, and fiOOANDTDNQUE. every student of esotericism knows how fundamental and how far-reaching is this idea of sex. I The entire cathedral symbolized the crucified body of Christ; its two towers, man and woman — that Adam and that Eve for whose redemption according to current teaching Christ suffered and was crucified. The north or right- hand tower ("the man's side") was called the sacred male pillar, Jachin; and the south, or left-hand tower ("the woman's side"), the sacred female pillar, Boaz, from the two columns flanking the gate to Solomon's Temple — itself an alle- gory to the 'bodily temple. In only a few of the French cathe- &LADANDK££X« EANDEDTOEUS UNITY AND POLARITY 39 VO IN YO IN H|HH|HHHHHHH|-l FRIEZE OF TH; EAJlJ>IEyE. EALA.CE/ >^.■^■^■^. ■.•■•■>.■>•> EOMAN C0N50Lt. VATICAN MUSBUM FRIEZE IN THE EMPIR£. $TYLB BY PBRCJBR* AND FONTAINE/. fri&2e from the temple of vesta attivoli.(roman) EOMAN DDIilC FEJEZE VlGNOLE 15 drals is this distinction clearly and consistently maintained, and of these Tours forms perhaps the most remarkable example, for in its flamboyant fagade, over and above the difference in actual breadth and apparent sturdiness of the two towers (the south being the more slender and delicate), there is a clearly marked distinction in the character of the ornamentation, that of the north tower being more salient, angular, radial — more masculine in point of fact (Illustration 17). In Notre Dame, the cathe- dral of Paris, as in the cathedral of Tours, the north tower is per- ceptibly broader than the south. The only other important dif- 40 THE BEAUTIFUL NECESSITY YD IN EGYPTIAN ORNAMENT YO.IN OaEEIC CiKNAMENT VD IN PALA220 OIEAUD. KOKE Vp IN c T a PMJZ20 FARNES£ EQNE VOIN . e^^^ QRfiEKL, HONEY3U0KUS ference appears to be in the angular label-mould above the north entrance: whatever may have been its original function or significance, it serves to de- fine the tower sexually, so to speak, as effectively as does the beard on a man's face. In Amiens the north tower is taller than the south, and more massive in its upper stages. The only traceable indication of sex in the orna- mentation occurs in the spandrels at the sides of the entrance arches: those of the north tower containing single circles, and those of the south tower containing two in one. This difference, small as it may seem, is significant, for in Europe during the Middle Ages, just as anciently in Egypt and again in Greece — in fact wher- ever and whenever the Secret Doctrine was known — sex was at- tributed to numbers, odd numbers being conceived of as mascu- line, and even, as feminine. Two, the first feminine number, thus became a symbol of femininity, accepted as such so univer- sally at the time the cathedrals were built, that two strokes of a bell announced the death of a woman, three, the death of a man. The vital, organic quality so conspic- uous in the best Gothic architecture has been attributed to the fact that neces- sity determined its characteristic forms. Professor Goodyear has demonstrated that it may be due also in part to certain subtle vertical leans and horizontal bends; and to nicely calculated variations from strict uniformity, 16 9'i ^IN 17 A ocmoo r^ CLASSIC THE ELEMBNTJ GP OOTHIC CO AND at CL&SSICCOARCHITECrOEJE; UNITY AND POLARITY 41 which find their analogue in nature, where structure is seldom rigidly geometrical. The author hazards the theory that still another reason why a Gothic ca- thedral seems so living a thing is because it abounds in contrasts be- tween what, for lack of more de- scriptive adjectives, he is forced to call masculine and feminine forms. Ruskin says, in Stones of Venice, " "All good Gothic is nothing more than the development, in various ways, and on every conceivable scale, of the group formed by the pointed arch for the bearing line below, and the gable for the protecting line above, and from the huge, gray, shaly slope of the cathedral roof, with its elastic pointed vaults beneath, to the crown-like points that enrich the smallest niche of its doorway, one law and one expression will be found in all. The modes of support and of decoration are infinitely various, but the real character of the building, in all good Gothic, depends on the single lines of the gable over the pointed arch endlessly rearranged and repeated." These two, an angu- lar and a curved form, like the every- where recurring column and lintel of classic architecture, are but pre- sentments'of Yo and In (Illustration 18). Every Gothic traceried win- dow, with straight and vertical mul- lions in the rectangle, losing them- selves in the intricate foliations of the arch, celebrates the marriage of this ever diverse pair. The circle and the triangle are the In and Yo of Gothic tracery, its 42 THE BEAUTIFUL NECESSITY Eve and Adam, as it were, for from their union springs that progeny of trefoil, quatrefoil, cinquefoil, of shapes fiowing like water, and shapes darting like flame, which makes such visible music to the entranced ear. By seeking to discover In and Yo in their myriad manifes- tations, by learning to discrim- inate between them, and by at- tempting to express their char- acteristic qualities in new forms of beauty — from the disposition of a facade to the shaping of a moulding — the architectural de- signer will charge his work with that esoteric significance, that excess of beauty, by which architecture rises to the dignity of a "fine" art (Illustrations 19, 20). In so doing, however, he should never forget, and the layman also should ever remember, that the supreme architectural excellence is fitness, appropriate- ness, the perfect adaptation of means to ends, and the adequate expression of both means and ends. These two aims, the one ab- stract and universal, the other concrete and individual, can al- ways be combined, just as in every human countenance are com- bined a type, which is universal, and a character, which is in- dividual. Ill CHANGELESS CHANGE TRINITY, CONSONANCE, DIVERSITY IN MONOTONY, BALANCE, RHYTHMIC CHANGE, RADIATION THE preceding essay was devoted for the most part to that "inevitable duality" which finds concrete expres- sion in countless pairs of opposites, such as day and night, fire and water, man and woman; in the art of music by two chords, one of suspense and the other of fulfilment; in speech by vowel and consonant sounds, epitomized in a and in m; in painting by warm colors and cold, epitomized in red and blue; in achitecture by the vertical column and the horizontal lintel, by void and solid — and so on. TRINITY This concept should now be modified by another, namely, that in every duality a third is latent; that two implies three, for each sex so to speak is in process of becoming the other, and this alternation engenders and is accomplished by means of a third term or neuter, which is like neither of the original two but partakes of the nature of them both, just as a child may re- semble both its parents. Twilight comes between day and night; earth is the child of fire and water; in music, besides the chord of longing and striving, and the chord of rest and satis- faction (the dominant seventh and the tonic), there is a third or resolving chord in which the two are reconciled. In the sacred 43 THE. LAW OF TRJNnTT 44 THE BEAUTIFUL NECESSITY syllable Om (Aum), which epitomizes all speech, the u sound effects a transition between the a sound and the m ; among the so- called primary colors yellow comes between red and blue ; and in architecture the arch, which is both weight and support, which is neither vertical nor horizontal, may be considered the neuter of the group of which the column and the lintel are respectively masculine and feminine. "These are the three," says Mr. Louis Sullivan, "the only three letters from which has been expanded the arch- itectural art, as a great and superb language wherewith man has ex- pressed, through the generations, the changing drift of his thoughts." It would be supererogatory to dwell at any length on this "trinity of mani- festation" as the concrete expression of that unmanifest and mystical trin- ity, that three-in-one which under various names occurs in every world- religion, where, defying definition, it was wont to find expression sym- bolically in some combination of vertical, horizontal and curved lines. The anstated cross of the Egyptians is such a symbol, the Buddhist wheel, and the fylfot or swastika inscribed within a circle, also those numerous Christian symbols combining the circle and the cross. Such ideographs have spelled profound meaning to the thinkers of past ages. We of to-day are not given to discovering anything wonderful in three strokes of a pen, but every artist in the weaving of his pattern must needs employ these mystic symbols in one form or another, and if he employs them with a full A ROMAN ICXnCAaCADE, BY VIONOLtr-THE. CQUUMN. THE> £NTABLKrUE£ AND THt AECH GOREitlPOND TO LINBJ VBRm lCAr..H0EJ20NTALAND OHtt/IO 21 CHANGLESS CHANGE 45 sense of their hidden meaning his work will be apt to gain in originality and beauty — for originality is a new and personal perception of beauty, and beauty is the name we give to truth we cannot understand. In architecture, this trinity of vertical, horizontal and curved lines finds admirable illustration in the application of columns and entablature to an arch and impost construction, so common in Roman and Renaissance work. This is a redundancy, and finds no justification in reason, because the weight is sustained by the arch, and the "order" is an appendage merely; yet the combination, illogical as it is, satisfies the sense of beauty be- cause the arch efifects a transition between the columns and the entablature, and completes the trinity of vertical, horizontal and curved lines (Illustration 21). In the entrances to many of the Gothic cathedrals and churches the same elements are better because more logically disposed. Here the horizontal lintel and its vertical supports are not decorative merely, but really per- form their proper functions, while the arch, too, has a raison d'etre in that it serves to relieve the lintel of the superincumbent weight of masonry. The same arrangement sometimes occurs in classic architecture also, as when an opening spanned by a single arch is subdivided by means of an order (Illustration 22). Three is pre-eminently the number of architecture, because it is the number of space, which for us is three-dimensional, and of all the arts architecture is most concerned with the ex- pression of spatial relations. The division of a composition into three related parts is so universal that it would seem to be the result of an instinctive action of the human mind. The twin pylons of an Egyptian temple with its entrance between, for a third division, has its correspondence in the two towers of a Gothic cathedral and the intervening screen wall of the THE LAW Of' TI^INITY ^ '^ ^ g=T CLASSIC QOTHIG 46 THE BEAUTIFUL NECESSITY nave. In the palaces ot the Renaissance a three- fold division — vertically by means of quoins or pi- lasters, and horizontally by means of cornices or string courses — ^was common, as was also the division into a principal and two subordi- nate masses (Illustration 23)- The architectural "or- ders" are divided threefold into pedestal or stylobate, column and entablature; and each of these is again divided threefold: the first into plinth, die and cornice; the second into base, shaft and capital ; the third into architrave, frieze and cornice. In many cases these again lend themselves to a threefold subdivision. A more detailed analysis of the capitals already shown to be twofold reveals a third member: in the Greek Doric this consists of the annulets immediately below the abacus ; in the other orders, the necking which divides the shaft from the cap. CONSONANCE "As is the small, so is the great" is a perpetually recurring phrase in the literature of theosophy, and naturally so, for it is a succinct statement of a fundamental and far-reaching truth. The scientist recognizes it now and then and here and there, but the occultist trusts it always and utterly. To him the microcosm THE TKENTTY Oi' HORJZONfEAlr^ <^^VEICnCAL,AND CURVED UNE$. THE* LAW OF TRINITY: A THI?f.EFOLD DIS- POSITION OF THE PARTS OF A BUIbDlNO- CHANGLESS CHANGE 47 and the macrocosm are one and the same in essence, and the forth-going impulse which calls a universe into being and the indrawing impulse which extinguishes it again, each lasting millions of years, are echoed and repeated in the inflow and outflow of the breath through the nostrils, in nutrition and excretion, in daily activity and nightly rest, in that longer day which we name a life- time, and that longer rest in Devachan — and so on until time itself is transcended. In the same way, in nature, a thing is echoed and repeated throughout its parts'. Each leaf on a tree is itself a tree in minia- ture, each blossom a modified leaf; every vertebrate animal is a complicated system of GRE.EJC-THE. ISECTHCUM. riAIiIAM K£NAI5MNCE> BMAEZO VENDRAMlN- CM£K01 At V£KICe. I FEBNCH EENAlWANCt-CH/OAU B\LA220&AU0UNLaQlt.ENa OB CEAUMEiSNIb. 28 spines; the ripple is the wave of a larger wave, and that larger wave is a part of the ebbing and flowing tide. In music this law is illustrated in the return of the tonic to itself in the octave, and its partial return in the dominant; also in a more extended sense in the repetition of a major theme in the minor, or in the treble and again in the bass, with modifications perhaps of time and key. In the art of 48 THE BEAUTIFUL NECESSITY THB LAW OF GONSONANCL: REPETITION WITH VARIATION THE.DOM&OFTHE THE SMAIA DOMES GCTHEDKADOF 1 EBEPAEtTHt BYfi-FOJL. FLOEiNCt.a THB CjKfiST IX2ME. |f<^^1'?f|Pi%. ^OQRINTHIAN CAPHALAND LJ ENTABLATUEfi. SHOWINQ COEJiE^PONDLNCE ^E.TWU,N tHBSSl VASKXJ$ PASSrS. TH& BEAD AND il£U ECHO TH&BGO AND TONQU& THBCHANNBUO TEJ- OLYPHSAtOVE ECHO THE COLUMNS BEa>V 24 painting the law is exemplified in the repetition with variation of certain colors and combinations of lines in different parts of the same picture, so disposed as to lead the eye to some focal point. Every painter knows that any important color in his picture must be echoed, as it were, in different places, for har- mony of the whole. In the drama the repetition of a speech or of an entire scene, but under circumstances which give it a different meaning, is often most effective, as when Gratiano, in the trial scene of The Merchant of Venice taunts Shylock with his own words, "A Daniel come to judgment!" or, as when in one of the later scenes of As You Like It an earlier scene is repeated, but with Rosalind speaking in her proper person and no longer as the boy Ganymede. 49 THEmWOF CONSONANCE ONE EAYCFTHE "ANQELOORSOP UNCaNQOHDRAL CHANGLESS CHANGE These recurrences, these inner consonances, these rep- ititions with variations are common in architecture also. The channeled triglyphs of a Greek Doric frieze echo the fluted columns below (Illustration 24). The bal- ustrade which crowns a col- onnade is a repetition, in some sort, of the colonnade itself. The modillions of a Corinthian cornice are but 25 elaborated and embellished dentils. Each pinnacle of a Gothic cathedral is a little tower with its spire. As Ruskin has pointed out, the great vault of the cathedral nave, together with the THE iAMfi MOTIF REPEATED WITH \5M6IATlON5' > THB LAW OF CONSONANCE,: REPETITION Ji/!!: VARIATION CHATEAU MAJNTENON.— THL CE-NTEiAL PAVILION \AnTH IT^TWO TUR)E,E/T5 ECHOES THD ENTlEli FACADE* WITH IT5 TWO TOV/LR,S 26 THE LAW OF ODNSONANCE PATTEEN FaOM Af 0DION]Al,BED$Pfi£AD 50 THE BEAUTIFUL NECESSITY pointed roof above it, is repeated in the entrance arch with its gable, and the same two elements appear in every statue-enshrin- ing niche of the doorway. In classic architecture, as has been shown, instead of the arch and gable, the column and entablature everywhere recur under different forms. The minor domes which flank the great dome of the cathe- dral of Florence enhance and reinforce the latter, and prepare the eye for a climax which would otherwise be too abrupt. The central pavilion of the Chateau Maintenon, with its two turrets, echoes the entire fagade with its two towers. Like the overture to an opera, it introduces themes which find a more extended development elsewhere (Illustration 26). This law of Consonance is operative in architecture more obscurely in the form of recurring numerical ratios, identical geometrical determining figures, parallel diagonals and the like, which will be discussed in a subsequent essay. It has also to do with style and scale, the adherence to substantially one method of construction and manner of ornament, just as in music the key, or chosen series of notes, may not be departed from except through proper modulations, or in a specific manner. Thus it is seen that in a work of art, as in a piece of tapestry, the same thread runs through the web, but goes to make up dififerent figures. The idea is deeply theosophic: one life, many manifestations; hence, inevitably, echoes, resemblances — Consonance. 27 DIVERSITY IN MONOTONY Another principle of natural beauty, closely allied to the foregoing, its complement as it were, is that of Diversity in CHANGLESS CHANGE 51 Monotony — not identity, but difference. It shows itself for the most part as a perceptible and piquant variation between indi- vidual units belonging to the same class, type, or species. No two trees put forth their branches in just the same manner, and no two leaves from the same tree exactly correspond ; no two persons look alike, though they have similiar members and features; even the markings on the skin of the thumb are different in every human hand. Browning says, "As like as a hand to another handl Whoever said that foolish thing. Could not have studied to understand — " Now every principle of natural beauty is but the presentment of some occult law, some theosophical truth; and this law of Diversity in Monotony is the presentment of the truth that identity does not exclude difference. The law is binding, yet the will is free: all men are brothers united by the ties of brotherhood, yet each is unique, a free agent, and never so free as when most bound by the Good Law. This truth nature beautifully proclaims, and art also. In architecture it is admir- ably exemplified in the metopes of the Parthenon frieze : seen at a distance these must have presented a scarcely distinguishable texture of sunlit marble and cool shadow, yet in reality each is a separate work of art. So with the capitals of the columns of the wonderful sea-arcade of the Venetian Ducal palace: alike in general contour they differ widely in detail, and unfold a Bible story. In Gothic cathedrals, in Romanesque monastery cloisters, a teeming variety of invention is hidden beneath apparent uniformity. The gargoyles of Notre Dame make similiar silhouettes against the sky, but seen near at hand what a menagerie of monsters I The same spirit of controlled indi- 52 tME BfiAtftlFUL NECESSITY THE lAW OK DIVERSITY IN MONOTONY ( ORNAMENimi ^continued) r °^*MS"T^^M-'^°^'^"^ lUDUUDUIXl ^ ORNAME:m;^^^,CONTINUED J 1 D A JDUCJUUUUOH ORNAhSlNPIpi THREE PANELS OP DASBA* DETAILS FI^MTHH TBMP1£ OFAPOUO NEAR, MILETUS'^ 28 viduality, of liberty subservient to the law of all, is exemplified in the bases of the columns of the temple of Apollo near CHANGLESS CHANGE 53 THE/ lAW C*. DIVEfcSITY.lN h/CONOIXMJY^WiMWFiM) dj Tia.iowt«.AK»D&cir.THi.mAoKrM««»i. Inrt line T Ti FECM FBOFUnSb OOOCrvXJUtIt lUB/IV Of THI. JOUTH WAU/ C« THE PISA. CATHlDBiAL. SHOWINCI VARIATION IN BtJOHT* AND WttTTHJ OT "Htt AKiOHM CT TH* AJbQAD&; AND THE) DIP OF THE. H0IU2ONTAX» STIUNO COURSE- IMMDDlATtLY AfiOVf^ 29 Miletus — each one a separate masterpiece of various ornamen- tation adorning an established architectural form (Illustration 28). The builders of the early Italian churches, instinctively obeying this law of Diversity in Monotony, varied the size of the arches in the same arcade (Illustration 29), and that this vi^as an effect of art and not of accident or carelessness Ruskin long ago discovered, and the Brooklyn Institute surveys have amply confirmed his view. Although by these means the build- ers of that day produced effects of deceptive perspective, of subtle concord and contrast, their sheer hatred of monotony and meaningless repetition may have led them to diversify their arcades in the manner described, for a rigidly equal and regular division lacks interest and vitality. BALANCE If one were to establish an axial plane vertically through the center of a tree, in most cases it would be found that the masses of foliage, however irregularly shaped on either side of such an axis, just about balanced each other. Similarly, in all our bodily movements, for every change of equilibrium there occurs an opposition and adjustment of members of such a nature that an axial plane through the center of gravity would divide the 54 THEBEAUTIFULNECESSITY body into two substantially equal masses, as in the case of the tree. This physical plane law of Balance shows itself for the most part on the human plane as the law of Compensation, whereby, to the vision of the occultist, all accounts are "squared," so to speak. It is in effect the law of Justice, aptly symbolized by the scales. The law of Balance finds abundant illustration in art: in music by the opposition, the answering, of one phrase by another of the same elements and the same length, but involving a different sequence of intervals; in painting by the disposition of masses in such a way that they about equalize one another, so that there is no sense of "strain" in the composition. In architecture the common and obvious recognition of the law of (Balance is in the symmetrical disposition of the elements, whether of plan or of elevation, on either side of axial lines. A far more subtle and vital illustration of the law occurs when the opposed elements do not exactly match, but differ from each other, as in the case of the two towers of Amiens, for example. This sort of balance may be said to be characteristic of Gothic, as symmetry is characteristic of Classic, architecture. RHYTHMIC CHANGE There is in nature a universal tendency toward refinement and compactness of form in space, or contrariwise, toward increment and diffusion; and this manifests itself in time as acceleration or retardation. It is governed, in either case, by an exact mathematical law, like the law of falling bodies. It shows itself in the widening circles which appear when one drops a stone into still water, in the convolutions of shells, in the branching of trees and the veining of leaves; the diminution in the size of the pipes of an organ illustrates it, and the spacing of the frets of a guitar. More and more science is coming to CHANGLESS CHANGE 55 recognize, what theosophy affirms, that the spiral vortex, which so beautifully illustrates this law, both in its time and its space aspects is the universal archetype, the pattern of all that is, has been, or will be, since it is the form assumed by the ultimate physical atom, and the ultimate physical atom is the physical cosmos in miniature. This Rhythmic Diminution is everywhere: it is in the eye itself, for any series of mathematically equal units, such for example as the columns and intercolumnations of a colonnade, become when seen in perspective rhythmically unequal, dimin- ishing according to the universal law. The entasis of a Classic column is determined by this law, the spirals of the Ionic volute, the annulets of the Parthenon cap, obey it (Illustration 30). In recognition of the same principle of Rhythmic Diminu- tion a building is often made to grow^ or appear to grow lighter, more intricate, finer, from the ground upward, an end attained by various devices, one of the most common being the employ- ment of the more attenuated and highly ornamented orders above the simpler and sturdier, as in the Roman Colosseum, or in the Palazzo Uguccioni, in Florence — to mention only two examples out of a great number. In the Riccardi Palace an effect of increasing refinement is obtained by diminishing the boldness of the rustication of the ashlar in successive stories; in the Farnese, by the gradual reduction of the size of the angle quoins (Illustration 30). In an Egyptian pylon it is achieved most simply by battering the wall; in a Gothic cathedral most elaborately by a kind of segregation, or breaking up, analogous to that which a tree undergoes — the strong, relatively unbroken base corresponding to the trunk, the diminishing buttresses to the tapering limbs, and the multitude of delicate pinnacles and crockets, to the outermost branches and twigs, seen against the sky. 56 THE BEAUTIFUL NECESSITY RADIATION The final principle of natural beauty to which the author would call attention is the law of Radiation, which is in a man- ner a return to the first, the law of Unity. The various parts of any organism radiate from, or otherwise refer back to common centers, or foci, and these to centers of their own. The law is represented in its simplicity in the star-fish, in its complexity in the body of man; a tree springs from a seed, the solar system centers in the sun. The idea here expressed by the term "radiation" is a famil- iar one to all students of theosophy. The Logos radiates his life and light throughout his universe, bringing into activity a host of entities which become themselves radial centers; these generate still others, and so on endlessly. This principle, like every other, patiently publishes itself to us, unheeding, every- where in nature, and in all great art as well ; it is a law of optics, for example, that all straight lines having a common direction if sufficiently prolonged appear to meet in a point, i. e., radiate from it (Illustration 31). Leonardo da Vinci employed this principle of perspective in his Last Supper to draw the specta- tor's eye to the picture's central figure, the point of sight toward which the lines of the walls and ceiling converge centering in the head of Christ. Puvis de Chavannes, in his Boston Library decoration, leads the eye by a system of triangulation to the small figure of the Genius of Enlightment above the central door (Illustration 32) ; and Ruskin, in his Elements of Drawing, has shown how artfully Turner arranged some of his compositions to attract attention to a focal point. This law of Radiation enters largely into architecture. The Colosseum, based upon the ellipse, a figure generated from two points or foci, and the Pantheon, based upon the circle, a figure CHANGLESS CHANGE 57 THL LPW OB BHYTHMIG DIMINUTION TtnRiD STORY ^ JECDNDSTOBY 1^ r ' ■ '■ ' " V FUWT STORY MSSOIM. QUDINS OP THE EAEjNEjSE* aVURCE. SHOWINO DIMmUTlOW IN EACH SUCOErEOINO STORM .i I •A' EiNLAEXAQ M£IHOD OP MTAB- LISHUIG BKX&SrS OEAOOLOMN -1 urtt)EaN£/crH ECHmuj-cp CARS OF EAEiTHENON VVZSVE-BAND ■^WFI ^. ANG1£ QtpiN5 QPTMB' 1ST STOEY OP THE. FAIBNEJB!, EAiACE AT EX3ME 30 generated from a central point, are familiar examples. The distinctive characteristic of Gothic construction, the concen- tration or focalization of the weight of the vaults and arches at 58 THE BE AUTIFUL NECESSITY certain points, is another illustration of the same principle applied to archi- tecture, beautifully exemplified in the semicircular apse of a cathedral, where the lines of the plan converge to a common center, and the ribs of the vaulting meet upon the capitals of the piers and columns, seeming to radiate thence to still other centers in the loftier vaults v^hich finally meet in a center common to all. oo, '■1MBJ. FINO&IbS er TDK. THE BODILY TEMPLE terms of such pairs are mas- culine and feminine with respect to each other, one being active and the other passive. Owing to the great size and one-sided position of the liver, the right half of the body is heavier than the left; the right arm is usually longer and more muscular than the left; the right eye is slightly higher than its fellow. In speaking and eating the lower jaw and under lip are active and mobile with relation to the upper; in winking it is the upper eyelid which is the more active. That "inevitable duality" which is exhibited in the form of the body characterizes its moti-ons also. In the act of walking for example, a forward movement is attained by means of a forward and a backward movement of the thighs on the axis of the hips ; this leg move- ment becomes twofold again below the knee, and the feet move up and down independently on the axis of the -ankle. A sim- ilar progression is followed in raising the arm and hand: motion is communicated first to the larger parts, through them to the smaller and thence to the extremities, becoming more rapid and complex as it progresses, so that all free and natural movements of the limbs describe invisible lines of beauty in the air. Coexistent with this pervasive duality there is a threefold division of the figure into trunk, head and limbs: a superior trinity of head and arms, and an inferior trinity of trunk and legs. The limbs are divided threefold into upper-arm, fore- arm and hand; thigh, leg and foot. The hand flowers out' 66 THE BEAUTIFUL NECESSITY into fingers and the foot into toes, each with a threefold articulation; and in this way is efifcctei that transition from unity to multiplicity, from simplicity to complexity, which appears to be so universal throughout nature, and of which a tree is the perfect symbol. The body is rich in veiled repetitions, echoes, consonances. The head and arms are in a sense a refinement upon the trunk and legs, there being a clearly traceable correspondence between their various parts. The hand is the body in little — "Your soft hand is a woman of itself" — the palm, the trunk; the four fingers, the four limbs ; and the thumb, the head ; -each finger is a little arm, each finger tip a little palm. The lips are the lids of the mouth, the lids are the lips of the eyes — and so on. The law of Rythmic Diminu ^ *rHE/CUE.NCHEI> HSTAND THE WAVE-BAND CDMIMED iCAIiCP JHEI/l. I @\ •THE. HAND OPEN tion is illustrated i« the tapering of the entire body and of the limbs, in the graduated sizes and lengths of the palm and the toes, and in the suc- cessively decreasing length of the palm and the joints of the fingers, so that in closing the hand the fingers describe natural spirals (Illustra- tions 37, 38). Finally, the limbs radiate as it were from the trunk, the fingers from a point in the wrist, the toes from a point in the ankle. The ribs radiate from the spinal ^-^ j ANTEFDC ^♦-THE HAND Cix3JED AOOMEAMSON BETWEEN Tttt, HAND.CLOJBD AND OPEN.ANDTHEeaEEKANTHPlX.AND SHELL* 89 A CCMEAECCN £BTWIf*J CHOTTO'S CAMEMttLE, AaXUMN lEOMTHB OR THENQN, AND THB. HUMAN JlOOEi-- THEBODILYTEMPLE 67 column like the veins of a leaf from its midrib (Illustration 39). The relation of these laws of beauty to the art of architecture has been shown already. They are reiterated here only to show that man is indeed the micro- cosm — a little world fashioned from the same elements and in accordance with the same Beauti- ful Necessity as is the greater world in which he dwells. When he builds a house or temple he builds it not literally in his own image, but according to the laws of his own being, and there are correspondences not altogether fanciful between the animate body of flesh and the inanimate body of stone. Do we not all of us,, consciously or unconsciously, recognize the fact of char- acter and physiognomy in buildings? Are they not, to our imag- ination, masculine or feminine, winning or forbidding — human, in point of fact— to a greater degree than anything else of man's creating? They are this certainly to a true lover and student of architecture. Seen from a distance the great French cathe- drals appear like crouching monsters, half beast, half human: the two towers stand like a man and a woman, mysterious and gigantic, looking out over city and plain. The campaniles of Italy rise above the churches and houses like the sentinels of a sleeping camp — nor is their strangely human aspect wholly imaginary: these giants of mountain and campagna have eyes and brazen tongues; rising four square, story above story, with a belfry or lookout, like a head, atop, their likeness to a man 68 THE BEAUTIFUL NECESSITY THE fiODYTHE ARCHETVPE OF SACJJ£D. EDIFICES ^|^ 'faqcSTHK.. " kCHUKH THEKANDARIVA TIMPLE. KHAJUEAHO •ST. OUENATBOUEN is not infrequently enhanced by a certain identity of propor- tion — of ratio, that is, of height to width: Giotto's beautiful tower is an example. The caryatid is a supporting mem- ber in the form of a woman; in the Ionic column we discern her stiffened, like Lot's wife, into a pillar, with nothing to show her feminine but the spirals of her beautiful hair. The columns which uphold the pediment of the Parthenon are unmistakably masculine: the ratio of their breadth to their height is the ratio of the breadth to the height of a man (Illustra- tion 40). At certain periods of the world's history, periods of mystical enlightenment, men have been wont to use the human figure, the soul's temple, as a sort of archetype for sa- cred edifices (Illus- tration 41). The colossi, with calm in- scrutable faces, which flank the entrance to Egyptian temples; the great bronze Buddha of Japan, with its dreaming eyes ; the little known colossal fig- THE BODILY TEMPLE 69 ures of India and China — all these belong scarcely less to the do- main of architecture than of sculpture. The relation above re- ferred to however is a matter more subtle and occult than mere obvious imitation on a large scale, being based upon some corres- pondence of parts, or similarity of proportions, or both. The correspondence between the innermost sanctuary or shrine of a JIN ivtxfCASs/ma OPTHE»TWBLFre\ CEMTurac) rLSN CF OlTHEMtALGF E£Am5MS ^^^^~ I A GCTHIC CATHB-DEAL THE- SYM5(X wmtxj^romiiulCf THL BODY OF JBSUS CHRIST—- 48 temple and the heart of a man, and between the gates of that temple and the organs of sense is sufficiently obvious, and a relation once established, the idea is susceptible of almost infinite development. That the ancients proportioned their temples from the human figure is no new idea, nor is it at all surprising. The sculpture of the Egyptians and the Greeks ALPHA NDEtTH CB[£niAL EOX SUN aisBj—EaiT CEOWNCFTHOKilS HEAD iK^ MAN') SIDE.. NCKIH-IUXNSEn KlOaTKAND CHOnOr lUCEiOFCOHS MAl£SACEEO HUjAE>"JACH1N" FEMALE SAOtfO ru.lAKj"5QA2' wmt- tEfAD 70 THE BEAUTIFUL NECESSITY reveals the fact that they studied the body abstract- ly, in its exterior present- ment. It is clear that the rules of its proportions must have been estab- lished for sculpture, and it is not unreasonable to suppose that they became canonical in architec- ture also. Vitruvius and Alberti both lay stress on the fact that all sacred buildings should be founded on the propor- tions of the human body. In France, during the Middle Ages, a Gothic cathedral became, at the *** hands of the secret ma- sonic guilds, a glorified symbol of the body of Christ. To practical-minded students of architectural history, familiar w^ith the slow and halting evolution of a Gothic cathedral from a Roman basilica, such an idea may seem to be only the maunderings of a mystical imagination, a theory evolved from the inner consciousness, entitled to no more consideration than the familiar fallacy that vaulted nave of a Gothic church was an attempt to imitate the green aisles of a forest. It should be remembered however that the habit of the thought of that time was mystical, as that of our own age is ultilitarian and scientific; and the chosen language of mysticism is always an elaborate and involved symbolism. What could be more natu- SOOTH CELESTIAL POLE > SUN SETS-WBST THE SYMBOLISM CT A GOTHIC CATHE«AL flbCM-THE. BQjICE.UaANSrHAEQE/B JENNINDS THE BODILY TEMPLE 71 ^<»^ TM; GE^METTRIGAL basis op THE/ HUMAN noVRjh o n 5TE/I6NUM' ■^ BODY 16 PUBIS -tHKiH J6 aPEtfOuUA i/EG y» THE»,5C5lA]liB>,'rHJ6' OIECLE-.AiqDTHE THE. moppErrioNj ofthe. HSUEf- AS RiSTABLI^H&D IV DOCWCRj EiIMMEJlj. ' ' 46 ral than that a building devoted to the wor- ship of a crucified Savior should be made a symbol, not of the cross only, but of the body crucified? The vesica piscis (a figure formed by the developing arcs of two equilateral triangles having a common side) which in so many cases seems to have determined the main proportion of a cathedral plan — the interior length and width across the transepts — appears as an aureole around the figure of Christ in early representations, a fact which certainly points to a relation between the two (Illustrations 42, 43). A curious little book, The Rosicrucians, by Hargrave Jennings, contains an interesting diagram which well illustrates this conception 72 THE BEAUTIFUL NECESSITY 47 of the symbolism of a cathe- dral. A copy of it is here given. The apse is seen to correspond to the head of Christ, the north transept to his right hand, the south tran- sept to the left hand, the nave to the body, and the north and south towers to the right and left feet respectively (Illus- tration 44). The cathedral builders ex- celled all others in the artfulness with which they established and maintained a relation between their architecture and the stature of a man. This is perhaps one reason why the French and English cathedrals, even those of moderate dimensions are more truly impressive than even the largest of the great Renaissance structures, such as St. Peter's in Rome. A gigantic order furnishes no true measure for the eye: its vastness is revealed only by the accident of some human pres- ence which forms a basis of comparison. That architecture is not necessarily the most awe-inspiring which gives the impres- sion of having been built by giants for the abode of pigmies; like the other arts, architecture is highest when it is most human. The mediaeval builders, true to this dictum, employed stones of a size proportionate to the strength of a man working without unusual mechanical aids; the great piers and columns, built up of many such stones, were commonly subdivided into clusters, and the circumference of each shaft of such a cluster approxi- mated the girth of a man ; by this device the moulding of the base and the foliation of the caps were easily kept in scale. Wherever a balustrade occurred it was proportioned not with THE BODILY TEMPLE the height of the wall or the 73 AOCOEDTNOIOTffi. EXSYTOAIT CANOK relation to column below, as in classic architecture, but with relation to a man's stature. It may be stated as a general rule that every work of architecture, of whatever style, should have somewhere about it something fixed and enduring to relate it to the human figure, if it be only a flight of steps in which each one is the measure of a stride. In the Farnese, the Riocardi, the Strozzi, and many another Italian palace, the stone seat about the base gives scale to the building because the beholder knows instinctively that the height of such a seat must have some relation to the length of a man's leg. In the Pitti palace the balustrade which crowns each story answers a similar purpose: it stands in no intimate relation to the gigantic arches below, but is of a height convenient for lounging elbows. The door to Giotto's cam- panile reveals the true size of the tower as nothing else could, because it is so evidently related to the human figure and not to the great windows higher up in the shaft. The geometrical plane figures which play the most important part in architectural proportion are the square, the circle and the triangle; and the human figure is intimately related to these elementary forms. If a man stand with heels together. 48 TIB :ft©Ty«THEHEIflHr •scassou THS MEDIAEVAL METHCD Of DE^fiXTNQ THE FraOEB 49 &r^.=;..i=^.r..^^^ ■SSBBBB^BBBBgC^.r^i'ViilSSiaBa'nBBBBeiB flBeBHflp3^§|i>^|^/i^ipl||BBBSBB / \ l^f tSfflF ^ '^ / \ JvfdK / s / kT I mJk ^ KjajflffM s / w KHflPnl s i-----,^-! JB|l-i>-..-^2 ^£- J*M.-_-^S- ._.^2-._-,^:Sa¥£-!^,----3-_-- _.l/\ ^>® y^'SSSiS. |lll|lll|lll|lll|<»a. "s^, ^ |lll|lll|lll{lll|lll|lll| 50 74 THE BEAUTIFUL, NECESSITY and arms outstretched horizon- tally in opposite directions, he will be inscribed, as it were, within a square; and his arms will mark, with fair accuracy, the base of an inverted equilateral triangle, the apex of which will touch the ground at his feet. If the arms be extended upward at an angle, and the legs correspond- ingly separated, the extremities will touch the circumferences of a circle having its center in the navel (Illustrations 45, 46). The figure has been variously analyzed with a view to establishing numerical ratios between its parts (Illustrations 47, 48, 49). Some of these are so simple and easily remembered that they have obtained a certain popular currency; such as that the length of the hand equals the length of the face ; that the span of the horizontally extended arms equals the height; and the well known rule that twice around the wrist is once around the neck, and twice around the nefck is once around the waist. The Roman architect Vitruvius, writing in the age of Augustus Caesar, formulated the important proportions of the statues of classical antiquity, and except that he makes the head smaller than the normal (as it should be in heroic statuary), the ratios which he gives are those to which the ideally perfect male figure should conform. Among the ancients the foot was probably the standard of all large measurements, being a more determinate length than that of the head or face, and the height was six lengths of the foot. If the head be taken as a unit, the ratio becomes i : 8, and if the face — i : 10. THE BODILY TEMPLE 75 Doctor Rimmer, in his Art Anatomy, divides the figure into four parts, three of which are equal, and correspond to the lengths of the leg, the thigh and the trunk; while the fourth part, which is two-thirds of one of these thirds, extends from the sternum to the crown of the head. One excellence of such a division aside from its simplicity, consists in the fact that it may be applied to the face as well. The lowest of the three major divisions extends from the tip of the chin to the base of the nose, the next coincides with the height of the nose (its top being level with the eyebrows), and the last with the height of the forehead, while the remaining two-thirds of one of these thirds represents the horizontal projection from the beginning of the hair on the forehead to the crown of the head. The middle of the three larger divisions locates the ears, which are the same height as the nose (Illustrations 45, 47). Such analyses of the figure, however conducted, reveals an all- pervasive harmony of parts, between which definite numerical relations are traceable, and an apprehension of these should assist the architectural designer to arrive at beauty of pro- portion by methods of his own, not perhaps in the shape of rigid formula^, but present in the consciousness as a restrain- ing influence, acting and reacting upon the mind with a con- scious intention toward rhythm and harmony. By means of such exercises, he will approach nearer to an understanding of that great mystery, the beauty and significance of numbers, of which mystery music, architecture, and the human figure are equally presentments — considered, that is, from the standpoint of the occultist. V LATENT GEOMETRY IT is a well known fact that in the microscopically minute of nature, units everywhere tend to arrange themselves with relation to certain simple geometrical solids, among which are the tetrahedron, the cube, and the sphere. This process gives rise to harmony, which may be defined as the relation between parts and unity, the simplicity latent in the infinitely complex. THE HEXAGRAM AND EQUILATERAL TR,IANQLL IN NATURE 5NOW CBXTEMS HONEY COM6 THEEACE, FLE5H FLY the potential complexity of that which is simple. Proceeding to things visible and tangible, this indwelling harmony, rhythm, proportion, which has its basis in geometry and number, is seen to exist in crystals, flower forms, leaf groups, and the like, where it is obvious; and in the more highly organized world of 76 LATENT GEOMETRY the animal kingdom also; though here the geometry is latent rather than patent, eluding though not quite defying analysis, and thus augmenting beauty, which like a woman is alluring in proportion as she eludes (Illustrations 51, 52, S3)- By the true artist, in the crystal mirror of whose mind the uni- versal harmony is focused and re- flected, this secret of the cause and source of rhythm — that it dwells in a corre- lation of parts based on an ultimate simplic- ity — is instinctively'apprehended. A knowl- edge of it formed part of the equipment of the painters who made glorious the golden noon of pictorial art in Italy during the Renaissance. The problem which preoc- cupied them was, as Symonds says of Leonardo, "to submit the freest play of form 'to simple figures lof geometry in grouping." Alberti held that the painter should above all things have mastered geometry, and it is known that the study of perspective and kindred subjects was widespread and popular. The first painter who deliberately rather than instinctively based his compositions on geometrical principles TElANqUWA/JYNOnOf CFTHff 64 78 THE BEAUTIFUL NECESSITY seems to have been THE, EAAPLOVMENT OF THS EOUILATBRAL.N, TlilANGLL IN R£-NAISSANCL PAINTINOn. THE LATTiUPPtR.. CE/hrrSL THE, MADONNA DEL. SACCO. BY OHM (K£rrOR£0) BV OWINCI ANDIUA DE>b SABSrO £5 Fra Bartolommeo, in his Last Judgment, in the church of St. Maria Nuova, in Florence. Symonds says of this pic- ture, "Simple fig- ures — the pyramid and triangle, up- right, inverted, and interwoven like the rhymes of a son- net — form the basis of the composition. This system was ad- hered to by the Fratre in all his sub- sequent vs^orks" (II- GEOMETRICAL bASlS OF THE 515TINE CEILINO PAlNTlNQy 66 LATENT GEOMETRY lustration 54). Raphael, with that power of assimilation which distin- guishes him among men of genius, learned from Fra Bartolommeo this method of disposing figures and com- bining them in masses with almost mathematical precision. It would have been indeed surprising if Leonar- do da Vinci, in whom the artist and the man of science were so wonderfully united, had not been greatly preoc- cupied with the mathematics of the art r "THE QBCMETEJCAL BASI^ CP THE PLAN IN MCHIT£CTUEAL DESIGN KfAMAKTfiSItAN TfiMrlfiofzeus' 5TBA.UtS "THE DUOKlO "MKHfiLAnnP.rn'? FUNFQK,i.I>?l£liS. WESN'-J riEjT PlANfCHLJIWUlS r\ 1 t THE CBEID£AtKeBAH :=] SAUitUEY CATHEDIUL, D INIQOJONEJ'ruCM K3tt,WHlTeWMl, j!i£m]eiM 8o THE BEAUTIFUL NECESSITY PAUADIAN VltLA NEAIO VTCENZA of painting. His Madonna of the Rocks, and Virgin on the Lap of Saint Anne, in the Louvre, exhibit the very per- fection of pyramidal com- position. It is however in his masterpiece. The Last Supper, that he combines geometrical symmetry and precision vi^ith perfect naturalness and free- dom in the grouping of in- dividually interesting and dramatic figures. Michael Angelo, Andrea del Sarto, and the great Venetians, in vi^hose work the art of painting may be said to have culmi- nated, recognized and obeyed those mathematical laws of composition known to their immediate predecessors, and the decadence of the art in the ensuing period may be traced not alone to the false sentiment and affectation of the times, but also in the abandonment by the artists of those obscurely geometrical arrangements and groupings which in the works of the greatest masters so satisfy the eye and haunt the memory of the beholder (Illustrations 55, 56). Sculpture, even more than painting, is based on geometry. The colossi of Egypt, the bas-reliefs of Assyria, the figured pedi- ments and metopes of the temples of Greece, the carved tombs of Revenna, the Delia Robbia lunettes, the sculptured tympani of arjc m nMDMPHE wr paras 69 LATENT GEOMETRY 8l EQYTTIAN GR£EP^ Gothic church por- tals, all alike lend themselves in greater or less degree to a geometrical synopsis (Illustration 57). Whenever sculpture suffered divorce from architecture the geo- metrical element became less promi- nent, doubtless be- cause of all the arts architecture is the most clearly and closely related to geometry. Indeed, it may be said that architecture is ge- ometry made visible, eo in the same sense that music is number made audible. A building is an aggregation of the commonest geometrical forms: parallelograms, prisms, pyr- amids and cones — the cylinder ap- pearing in the column, and the hemi- sphere in the dome. The plans like- wise of the world's famous buildings reduced to their simplest expression are discovered to resolve themselves into a few simple geometrical fig- ures. (Illustration's). This is the g^ "bed rock" of all excellent design. ROMAN MEDIAEVAL ^ — -^ \ \ \ / JEPF^'e^N'J" PENJ'IOJltH FDR-'THE ROTUNDA OF THE UNIVER-flTY OP VIRGINIA 82 THE BEAUTIFUL NECESSITY ! "^ APPLICATION OF THL EOUiLATERAL TRJANGLEi TO THL LR£-CHTHLUM~ AT ATHENS. WE5T 51DE« porx:h of the- caryatides LATENT GEOMETRY 83 But architecture is geometrical in another and a higher sense than this. Emerson says: "The pleasure a palace or a temple gives the eye is that an order and a method has been communicated to stones, so that they speak and geometrize, 63 become tender or sublime with expression." All truly great and beautiful works of architecture — from the Egyp- tian pyramids to the cathedrals of Ile-de-France — are harmo- niously proportioned, their prin- cipal and subsidiary masses being related, sometimes ob- viously, more often obscurely, to certain symmetrical figures of geometry, which though in- visible to the sight and not con- sciously present in the mind of the beholder, yet perform the important function of co- ordinating the entire fabric into one easily remembered whole. Upon some such principle is surely founded what Symonds THE. BQUILATE-RALTRIANOLtil RQA\AN ARCHlTECrURB A SECTION OF THi PANTHEON, RCME< 64 84 THE BEAUTIFUL NECESSITY THE E^JUILATBRAL TRIANGLE IN ITALIAN ARjGHITEX:TUR£. (R£NAI55ANCE() WINDOW IN A EQMAN PALACE, SECTION OF EiMILICA OF SAN LORENZO, FLOIttNCE, THE. HEXAGRAM IN GOTHIC ARCHITECTURE SExrriON OF windcw/ mullions in the. CteRKTOR/Y, WIN0HBSTE.R.CATHDDRAL1 (FROfAOWlUr) calls "that severe and lofty art of com- position which seeks the highest beauty of design in archi- tectural harmony supreme, above the melodies of grace- fulness of detail." There is abun- dant evidence in support of the theory that the builders of antiquity, the ma- sonic guilds of the Middle Ages, and the architects of the Italian Renaissance, knew^ and followed certain rules, but though this theory be denied or even disproved POSESWJflDOW IN, SOUTH TRANiEBT" OfiBpUE*! CATHBORAL (FROM OWJU) 66 LATENT GEOMETRY — if after all these men ob- tained their results uncon- sciously — their creations so lend themselves to a geomet- rical analysis that the claim for the existence of certain canons of proportion, based on geometry, remains unim- peached. The plane figures princi- pally employed in deter- mining architectural pro- portion are the circle, the equilateral triangle, and the square — ^which also 85 yields the right angled isosceles triangle. It will be noted that these are the two dimensional correlatives of the sphere, the tetrahe- dron and the cube, mentioned as being among the deter- mining forms in molecular structure. The question naturally arises, why the circle, the equilateral tri- angle and the square? Be- cause, aside from the fact that they are of all plane fig- ures the most elementary^ 86 THE BEAUTIFUL NECESSITY they are intimately related to the body of man, as has been shown (Illustration 45), and the body of man is as it were the architectural archetype. But this simply removes the inquiry to a dif- ferent field, it is not an an- swer. Why is the body of man so constructed and re- lated? This leads us, as does every question, to the threshold of a mystery upon which theosophy alone is able to throw light. Any 69 extended elucidation would be out of place here: it is sufficient to remind the reader that the circle is the symbol of the universe; the equilateral triangle, of the higher trinity {atma,buddhi, manas) ; and the square, of the lower quaternary of man's sevenfold nature. The square is principally used in preliminary plotting: it is the determining figure in many of the palaces of the Italian Renaissance; the LATENT GEOMETRY 87 Arc de Triomphe, in Paris is a modern example of its use (Illustrations 59, 60). The circle is often employed in con- junction with the square and the triangle. In Thomas Jefferson's Rotunda for the University of Virginia, a single great circle was the determining figure, as his original pen sketch of the building shows (Illustration 61). Some of the best Ro- man triumphal arches submit themselves to a circular synopsis, and a system of double intersecting circles has been applied, with interesting results, to fagades as widely different as those of the Parthenon and the Farnese Palace in Rome, though it would be fatuous to claim that these figures determined the propor- tions of the fagades. By far the most important figure in architectural proportion, considered from the standpoint of geometry, is the equilateral triangle. It would seem that the eye has an especial fondness for this figure, just as the ear has for certain related sounds. In- deed it might not be too fanciful to assert that the common chord of any key (the tonic with its third and fifth) is the musical equivalent of the equilateral triangle. It is scarcely necessary to dwell upon the properties and unique perfection of this figure. Of all regular polygons it is the simplest: its three equal sides subtend equal angles, each of 60 degrees; it trisects the circum- ference of a circle ; it is the graphic symbol of the number three, and hence of every threefold thing ; doubled, its generating arcs form the vesica piscis, of so frequent occurrence in early Chris- tian art; two symmetrically intersecting equilateral triangles yield the figure known as "Solomon's Seal," or the "Shield of David," to which mystic properties have always been ascribed. It may be stated as a general rule that whenever three impor- tant points in any architectural composition coincide (approxi- mately or exactly) with the three extremities of an equilateral triangle, it makes for beauty of proportion. An ancient and 88 THE BEAUTIFUL NECESSITY LIBER. PRIMVS Idea GiOMnMCAL jmcHrrecroNicAE ab ichnosiiawiia, svMnA.vTPEHAMvssiNuis rossnrr lEK OKIHOOBAPHIAM AC SCAENOOIUIFHIAM PEKOVCERE OMNTS