Chapter II: Part 2

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 resemble 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 satisfaction (the dominant seventh and the tonic), there is a third or resolving chord in which the two are reconciled. In the sacred 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 architectural art, as a great and superb language wherewith man has expressed, through the generations, the changing drift of his thoughts."

It would be supererogatory to dwell at any length on this "trinity of manifestation" as the concrete expression of that unmanifest and mystical trinity, that _three-in-one_ which under various names occurs in every world-religion, where, defying definition, it was wont to find expression symbolically 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 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 because the arch effects 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 perform their proper functions, while the arch, too, has a raison d'être 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 expression 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 nave. In the palaces of the Renaissance a threefold division--vertically by means of quoins or pilasters, and horizontally by means of cornices or string courses--was common, as was also the division into a principal and two subordinate masses (Illustration 23).

The architectural "orders" 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 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 lifetime, 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 miniature, each blossom a modified leaf; every vertebrate animal is a complicated system of 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 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 harmony 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.

These recurrences, these inner consonances, these repetitions with variations are common in architecture also. The channeled triglyphs of a Greek Doric frieze echo the fluted columns below (Illustration 24). The balustrade which crowns a colonnade is a repetition, in some sort, of the colonnade itself. The modillions of a Corinthian cornice are but 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 pointed roof above it, is repeated in the entrance arch with its gable, and the same two elements appear in every statue-enshrining 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 cathedral 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 Château Maintenon, with its two turrets, echoes the entire façade 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 different figures. The idea is deeply theosophic: one life, many manifestations; hence, inevitably, echoes, resemblances--_Consonance_.

DIVERSITY IN MONOTONY

Another principle of natural beauty, closely allied to the foregoing, its complement as it were, is that of _Diversity in Monotony_--not identity, but difference. It shows itself for the most part as a perceptible and piquant variation between individual 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 hand!
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 admirably 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! The same spirit of controlled individuality, of liberty subservient to the law of all, is exemplified in the bases of the columns of the temple of Apollo near Miletus--each one a separate masterpiece of various ornamentation 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 was 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 builders 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 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 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, diminishing 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 Diminution 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 employment 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.

RADIATION

The final principle of natural beauty to which the author would call attention is the law of _Radiation_, which is in a manner 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 familiar 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, everywhere 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 spectator'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 Enlightenment 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 generated from a central point, are familiar examples. The distinctive characteristic of Gothic construction, the concentration or focalization of the weight of the vaults and arches at certain points, is another illustration of the same principle applied to architecture, 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 which finally meet in a center common to all.

The tracery of the great roses, high up in the façades of the cathedrals of Paris and of Amiens, illustrate Radiation, in the one case masculine: straight, angular, direct; in the feminine: curved, flowing, sinuous. The same _Beautiful Necessity_ determined the characteristics of much of the ornament of widely separated styles and periods: the Egyptian lotus, the Greek honeysuckle, the Roman acanthus, Gothic leaf work--to snatch at random four blossoms from the sheaf of time. The radial principle still inherent in the debased ornament of the late Renaissance gives that ornament a unity, a coherence, and a kind of beauty all its own (Illustration 35).

Such are a few of the more obvious laws of natural beauty and their application to the art of architecture. The list is by no means exhausted, but it is not the multiplicity and diversity of these laws which is important to keep in mind, so much as their relatedness and coördination, for they are but different aspects of the One Law, that whereby the Logos manifests in time and space. A brief recapitulation will serve to make this correlation plain, and at the same time fix what has been written more firmly in the reader's mind.

First comes the law of _Unity_; then, since every unit is in its essence twofold, there is the law of _Polarity_; but this duality is not static but dynamic, the two parts acting and reacting upon one another to produce a third--hence the law of _Trinity_. Given this third term, and the innumerable combinations made possible by its relations to and reactions upon the original pair, the law of _Multiplicity in Unity_ naturally follows, as does the law of _Consonance_, or repetition, since the primal process of differentiation tends to repeat itself, and the original combinations to reappear--but to reappear in changed form, hence the law of _Diversity in Monotony_. The law of _Balance_ is seen to be but a modification of the law of Polarity, and since all things are waxing and waning, there is the law whereby they wax and wane, that of _Rhythmic Change_. _Radiation_ rediscovers and reaffirms, even in the utmost complexity, that essential and fundamental unity from which complexity was wrought.

Everything, beautiful or ugly, obeys and illustrates one or another of these laws, so universal are they, so inseparably attendant upon every kind of manifestation in time and space. It is the number of them which finds illustration within small compass, and the aptness and completeness of such illustration, which makes for beauty, because beauty is the fine flower of a sort of sublime ingenuity. A work of art is nothing if not _artful_: like an acrostic, the more different ways it can be read--up, down, across, from right to left and from left to right--the better it is, other things being equal. This statement, of course, may be construed in such a way as to appear absurd; what is meant is simply that the more a work of art is freighted and fraught with meaning beyond meaning, the more secure its immortality, the more powerful its appeal. For enjoyment, it is not necessary that all these meanings should be fathomed, it is only necessary that they should be felt.

Consider for a moment the manner in which Leonardo da Vinci's Last Supper, an acknowledged masterpiece, conforms to everyone of the laws of beauty enumerated above (Illustration 32). It illustrates the law of Unity in that it movingly portrays a single significant episode in the life of Christ. The eye is led to dwell upon the central personage of this drama by many artful expedients: the visible part of the figure of Christ conforms to the lines of an equilateral triangle placed exactly in the center of the picture; the figure is separated by a considerable space from the groups of the disciples on either hand, and stands relieved against the largest parallelogram of light, and the vanishing point of the perspective is in the head of Christ, at the apex, therefore, of the triangle. The law of Polarity finds fulfilment in the complex and flowing lines of the draped figures contrasted with the simple parallelogram of the cloth-covered table, and the severe architecture of the room. The law of Trinity is exemplified in the three windows, and in the subdivision of the twelve figures of the disciples into four groups of three figures each. The law of Consonance appears in the repetition of the horizontal lines of the table in the ceiling above; and in the central triangle before referred to, continued and echoed, as it were, in the triangular supports of the table visible underneath the cloth. The law of Diversity in Monotony is illustrated in the varying disposition of the heads of the figures in the four groups of three; the law of Balance in the essential symmetry of the entire composition; the law of Rhythmic Change in the diminishing of the wall and ceiling spaces; and the law of Radiation in the convergence of all the perspective lines to a single significant point.

To illustrate further the universality of these laws, consider now their application to a single work of architecture: the Taj Mahal, one of the most beautiful buildings of the world (Illustration 36). It is a unit, but twofold, for it consists of a curved part and an angular part, roughly figured as an inverted cup upon a cube; each of these (seen in parallel perspective, at the end of the principal vista) is threefold, for there are two sides and a central parallelogram, and two lesser domes flank the great dome. The composition is rich in consonances, for the side arches echo the central one, the subordinate domes the great dome, and the lanterns of the outstanding minarets repeat the principal motif. Diversity in Monotony appears abundantly in the ornament, which is intricate and infinitely various; the law of Balance is everywhere operative in the symmetry of the entire design. Rhythmic Change appears in the tapering of the minarets, the outlines of the domes and their mass relations to one another; and finally, the whole effect is of radiation from a central point, of elements disposed on radial lines.

It would be fatuous to contend that the prime object of a work of architecture is to obey and illustrate these laws. The prime object of a work of architecture is to fulfill certain definite conditions in a practical, economical, and admirable way, and in fulfilling to express as far as possible these conditions, making the form express the function. The architect who is also an artist however will do this and something beyond: working for the most part unconsciously, harmoniously, joyously, his building will obey and illustrate natural laws--these laws of beauty--and to the extent it does so it will be a work of art; for art is the method of nature carried into those higher regions of thought and feeling which man alone inhabits: regions which it is one of the purposes of theosophy to explore.

IV

THE BODILY TEMPLE

Carlyle says: "There is but one temple in the world, and that is the body of man." If the body is, as he declares, a temple, it is not less true that a temple or any work of architectural art is a larger body which man has created for his uses, just as the individual self is housed within its stronghold of flesh and bones. Architectural beauty like human beauty depends upon the proper subordination of parts to the whole, the harmonious interrelation between these parts, the expressiveness of each of its function or functions, and when these are many and diverse, their reconcilement one with another. This being so, a study of the human figure with a view to analyzing the sources of its beauty cannot fail to be profitable. Pursued intelligently, such a study will stimulate the mind to a perception of those simple yet subtle laws according to which nature everywhere works, and it will educate the eye in the finest known school of proportion, training it to distinguish minute differences, in the same way that the hearing of good music cultivates the ear.

Those principles of natural beauty which formed the subject of the two preceding essays are all exemplified in the ideally perfect human figure. Though essentially a unit, there is a well marked division into right and left--"Hands to hands, and feet to feet, in one body grooms and brides." There are two arms, two legs, two ears, two eyes, and two lids to each eye; the nose has two nostrils, the mouth has two lips. Moreover, the terms of such pairs are masculine 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 motions 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 movement becomes twofold again below the knee, and the feet move up and down independently on the axis of the ankle. A similar 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, forearm and hand; thigh, leg and foot. The hand flowers out into fingers and the foot into toes, each with a threefold articulation; and in this way is effected 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 _Rhythmic Diminution_ is illustrated in 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 successively decreasing length of the palm and the joints of the fingers, so that in closing the hand the fingers describe natural spirals (Illustrations 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 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 microcosm--a little world fashioned from the same elements and in accordance with the same _Beautiful 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 character and physiognomy in buildings? Are they not, to our imagination, 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 cathedrals 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 is not infrequently enhanced by a certain identity of proportion--of ratio, that is, of height to width: Giotto's beautiful tower is an example. The caryatid is a supporting member 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 (Illustration 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 sacred edifices (Illustration 41). The colossi, with calm inscrutable faces, which flank the entrance to Egyptian temples; the great bronze Buddha of Japan, with its dreaming eyes; the little known colossal figures of India and China--all these belong scarcely less to the domain of architecture than of sculpture. The relation above referred to however is a matter more subtle and occult than mere obvious imitation on a large scale, being based upon some correspondence of parts, or similarity of proportions, or both. The correspondence between the innermost sanctuary or shrine of a 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 reveals the fact that they studied the body abstractly, in its exterior presentment. It is clear that the rules of its proportions must have been established for sculpture, and it is not unreasonable to suppose that they became canonical in architecture also. Vitruvius and Alberti both lay stress on the fact that all sacred buildings should be founded on the proportions of the human body.

In France, during the Middle Ages, a Gothic cathedral became, at the hands of the secret masonic guilds, a glorified symbol of the body of Christ. To practical-minded students of architectural history, familiar with 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 utilitarian and scientific; and the chosen language of mysticism is always an elaborate and involved symbolism. What could be more natural than that a building devoted to the worship 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 of the symbolism of a cathedral. 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 transept to the left hand, the nave to the body, and the north and south towers to the right and left feet respectively (Illustration 44).

The cathedral builders excelled 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 presence which forms a basis of comparison. That architecture is not necessarily the most awe-inspiring which gives the impression of having been built by giants for the abode of pigmies; like the other arts, architecture is highest when it is most human. The mediæval 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 approximated 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 relation to the height of the wall or the 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 Riccardi, 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 campanile 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, and arms outstretched horizontally 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 correspondingly 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 neck is once around the waist. The Roman architect Vitruvius, writing in the age of Augustus Cæsar, 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 1:8, and if the face--1:10.

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 proportion by methods of his own, not perhaps in the shape of rigid formulæ, but present in the consciousness as a restraining influence, acting and reacting upon the mind with a conscious 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 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 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, 53).

By the true artist, in the crystal mirror of whose mind the universal harmony is focused and reflected, this secret of the cause and source of rhythm--that it dwells in a correlation of parts based on an ultimate simplicity--is instinctively apprehended. A knowledge 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 preoccupied them was, as Symonds says of Leonardo, "to submit the freest play of form to simple figures of 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 seems to have been Fra Bartolommeo, in his Last Judgment, in the church of St. Maria Nuova, in Florence. Symonds says of this picture, "Simple figures--the pyramid and triangle, upright, inverted, and interwoven like the rhymes of a sonnet--form the basis of the composition. This system was adhered to by the Fratre in all his subsequent works" (Illustration 54). Raphael, with that power of assimilation which distinguishes him among men of genius, learned from Fra Bartolommeo this method of disposing figures and combining them in masses with almost mathematical precision. It would have been indeed surprising if Leonardo da Vinci, in whom the artist and the man of science were so wonderfully united, had not been greatly preoccupied with the mathematics of the art of painting. His Madonna of the Rocks, and Virgin on the Lap of Saint Anne, in the Louvre, exhibit the very perfection of pyramidal composition. It is however in his masterpiece, The Last Supper, that he combines geometrical symmetry and precision with perfect naturalness and freedom in the grouping of individually interesting and dramatic figures. Michael Angelo, Andrea del Sarto, and the great Venetians, in whose work the art of painting may be said to have culminated, 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 pediments and metopes of the temples of Greece, the carved tombs of Revenna, the Della Robbia lunettes, the sculptured tympani of Gothic church portals, all alike lend themselves in greater or less degree to a geometrical synopsis (Illustration 57). Whenever sculpture suffered divorce from architecture the geometrical element became less prominent, doubtless because of all the arts architecture is the most clearly and closely related to geometry. Indeed, it may be said that architecture is geometry made visible, in the same sense that music is number made audible. A building is an aggregation of the commonest geometrical forms: parallelograms, prisms, pyramids and cones--the cylinder appearing in the column, and the hemisphere in the dome. The plans likewise of the world's famous buildings reduced to their simplest expression are discovered to resolve themselves into a few simple geometrical figures. (Illustration 58). This is the "bed rock" of all excellent design.

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, become tender or sublime with expression." All truly great and beautiful works of architecture from the Egyptian pyramids to the cathedrals of Ile-de-France--are harmoniously proportioned, their principal and subsidiary masses being related, sometimes obviously, more often obscurely, to certain symmetrical figures of geometry, which though invisible to the sight and not consciously present in the mind of the beholder, yet perform the important function of coördinating the entire fabric into one easily remembered whole. Upon some such principle is surely founded what Symonds calls "that severe and lofty art of composition which seeks the highest beauty of design in architectural harmony supreme, above the melodies of gracefulness of detail."

There is abundant evidence in support of the theory that the builders of antiquity, the masonic 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--if after all these men obtained their results unconsciously--their creations so lend themselves to a geometrical analysis that the claim for the existence of certain canons of proportion, based on geometry, remains unimpeached.

The plane figures principally employed in determining architectural proportion are the circle, the equilateral triangle, and the square--which also yields the right angled isosceles triangle. It will be noted that these are the two dimensional correlatives of the sphere, the tetrahedron and the cube, mentioned as being among the determining forms in molecular structure. The question naturally arises, why the circle, the equilateral triangle and the square? Because, aside from the fact that they are of all plane figures the most elementary, 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 different field, it is not an answer. Why is the body of man so constructed and related? This leads us, as does every question, to the threshold of a mystery upon which theosophy alone is able to throw light. Any 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 Arc de Triomphe, in Paris is a modern example of its use (Illustrations 59, 60). The circle is often employed in conjunction 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 Roman triumphal arches submit themselves to a circular synopsis, and a system of double intersecting circles has been applied, with interesting results, to façades 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 proportions of the façades.

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. Indeed 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 circumference 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 Christian 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 important points in any architectural composition coincide (approximately or exactly) with the three extremities of an equilateral triangle, it makes for beauty of proportion. An ancient and notable example occurs in the pyramids of Egypt, the sides of which, in their original condition, are believed to have been equilateral triangles. It is a demonstrable fact that certain geometrical intersections yield the important proportions of Greek architecture. The perfect little Erechtheum would seem to have been proportioned by means of the equilateral triangle and the angle of 60 degrees, both in general and in detail (Illustration 62). The same angle, erected from the central axis of a column at the point where it intersects the architrave, determines both the projection of the cornice and the height of the architrave in many of the finest Greek and Roman temples (Illustrations 67-70). The equilateral triangle used in conjunction with the circle and the square was employed by the Romans in determining the proportions of triumphal arches, basilicas and baths. That the same figure was a factor in the designing of Gothic cathedrals is sufficiently indicated in the accompanying facsimile reproductions of an illustration from the Como Vitruvius, published in Milan in 1521, which shows a vertical section of the Milan cathedral and the system of equilateral triangles which determined its various parts (Illustration 71). The _vesica piscis_ was often used to establish the two main internal dimensions of the cathedral plan: the greatest diameter of the figure corresponding with the width across the transepts, the upper apex marking the limit of the apse, and the lower, the termination of the nave. Such a proportion is seen to be both subtle and simple, and possesses the advantage of being easily laid out. The architects of the Italian Renaissance doubtless inherited certain of the Roman canons of architectural proportion, for they seem very generally to have recognized them as an essential principle of design.

Nevertheless, when all is said, it is easy to exaggerate the importance of this matter of geometrical proportion. The designer who seeks the ultimate secret of architectural harmony in mathematics rather than in the trained eye, is following the wrong road to success. A happy inspiration is worth all the formulæ in the world--if it be really happy, the artist will probably find that he has "followed the rules without knowing them." Even while formulating concepts of art, the author must reiterate Schopenhauer's dictum that the _concept_ is unfruitful in art. The mathematical analysis of spatial beauty is an interesting study, and a useful one to the artist; but it can never take the place of the creative faculty, it can only supplement, restrain, direct it. The study of proportion is to the architect what the study of harmony is to a musician--it helps his genius adequately to express itself.

VI

THE ARITHMETIC OF BEAUTY