PART II

The purpose of the latter half of this discussion of repetition is to consider a certain number of examples of its use in typical buildings of all the European styles of architecture from Greece down, and to show that the principles laid down in the earlier half have been expressed almost without exception in those of recognized merit. In other words it is to show that the laws of repetition, which have been brought out in the experiments of the first part, and which would of necessity be true if that explanation were correct, have indeed been exemplified in types of architecture universally accepted as beautiful.

The illustrations have all been drawn from architecture beginning with Greece, and not from the older Eastern styles. Egyptian architecture, although it recognized the importance of repetition to some extent, in its colonnades, avenues of sphinxes, and hieroglyphic decoration, never reduced it to any principle, nor adhered to any one scheme throughout a piece of work. Supports of the same kind and diameter have no fixed relation to each other, they may be of the same or different lengths, and may vary in diameter as well.[98] Spaces between columns of one size and design may vary considerably, and the entablatures be of different proportions. The art of Egypt was not rhythmic.

The architecture of Assyria and Chaldea had even less of repeated forms in its style. They made but little use of columns or piers, and had few arches.[99] The bare Assyrian edifice was like a great box, perpendicular to its foundations, and the long walls pierced by hardly an opening in the way of windows or doors.

Persian architecture was noted for extreme nicety of execution, but a monotony in all its forms, and conventionality about its use of the column, which makes it little more fruitful for our study of repetition as an artistic value. In its decorations of bas-relief, the pose and gesture of each figure is so exactly similar that they appear almost machine-made.[100] When a little variety is introduced, it is evidently done with misgivings, and shows none of the spontaneity or first-hand pleasure in either repetition or variation which would make it profitable for illustration.

Such a lack of feeling for repetition is, indeed, according to the peculiar genius of these styles of architecture, what might have been expected. The ruling idea, especially in Egyptian and Assyrian architecture, was ponderous strength. Everything was built with the idea of remaining immoveable through centuries to come. The enormous temples and tombs, the long palaces with their heavy walls without an opening to relieve them, the pyramids themselves like mountains of rock—all these meant strength and immutability, to which the motion and rhythm involved in repetition was totally foreign in spirit. In Persia indeed (as well as India and China, which will not be considered here) there was a change in tone. The column was used, not the massive one of Egypt, but a lighter shaft, which showed a tendency toward other effects than immensity and strength.

With this change of ideal, repetition in some kind of system made its appearance, but its variations were tentative. It had not become used to its new sense, and it was left for Greece to develop the rhythm and movement of repetition, and to combine it with proportion and symmetry into its perfection.

The method of analysis employed has been to go through a certain number of architectural photographs, picking out all the examples of repeated forms of any description, and classifying them according to the principles which they exemplified or seemed to violate. For this purpose a collection of about five thousand photographs from the library of Robinson Hall, Harvard University, was analyzed. The photographs were taken in order of styles: Greek, Roman, Romanesque, Gothic, Italian and French Renaissance, and modern. The examples of the different points in question were taken as they came in the cataloguing of the library stacks, without respect to whether they appeared to bear out the previous conclusions or not.

VARIATION OF ALTERNATING UNITS

The first principle which we shall consider is the variation allowable in the units of an alternating series. It will be remembered that the principle was as follows: (1) In any series of two alternating units, the one on which the most energy is expended is regarded as the principal unit, the less important one as an alternate. Variation of the principal unit is allowable, often desirable and even necessary; variation of the alternate never allowable, unless other circumstances change the situation. If the minor unit is changed, so that in interest it equals the major unit, the rest-phase of the rhythm is destroyed, the effect is of two rival repetitions going along together, and fatigue results. If variation in the alternates exceeded that of the principal units, the balance of the rhythm would change, the alternate become the major unit, and a new series begin.

From the very nature of the case, then, it will be impossible to look for variations in alternates, which make it exceed the principal units in interest. We must investigate alternating series, in order to see if one of the elements remains the same, while the other may or may not vary. If this were true, a rest-phase for the rhythm would be assured in the series, while the principal unit might vary, provided the same amount of attention were required in each case. (2) It will also be remembered that size and limiting shape were the factors that could not vary without doing violence to the rhythm, while content might vary almost without restriction. (3) The position of alternating units as regards each other cannot vary; the two units are so dependent on each other that the position of one must remain halfway between two of the opposite kind. In other words, if the two series of units run between each other, they form one series or rhythm. Two rhythms cannot be kept up alongside; so if one unit, however regularly placed with regard to another of its own kind, recurs at unequal distances from the other units, the feeling of the repetition is lost, the rhythm broken, unless the two units can be grouped into one, and so make a single rhythm again.

We shall, then, look for alternating series, of which the two units are at equal and invariable distances from each other; the variations of content (if such there are) occur only in the major unit; and are of the filling, not of the including shape or size.

It may be readily seen that there are difficulties in finding alternating series which exactly illustrate this particular point, or in reducing them to any system. It was necessary to look through many photographs to find one that presented the required conditions (i. e., two repeated series of units, alternating with each other), and when found, they were of so many different varieties, from windows in an apse to reliefs on a fountain, that each has had to be described by itself, and any rigid classification was impossible. Moreover, it was difficult to find a scale of judgment by which to decide whether a series was really alternating or plain repetition. From one point of view, every repetition is alternating, that is, the repeated unit always alternates with an empty space. Although such repetitions bear out the theory still further, and emphasize yet more strongly the invariability of alternates, and the possibility of variations in the principal units, I have used the term in a stricter sense, and only given illustrations of repeated objects, when one unit actually alternated with another definite unit.

Had the other sense of the term been used, examples might have been multiplied without limit, of slightly varying repeated units, and unvarying alternate blank spaces. But it was felt that such accumulation of illustration was unnecessary, and that what was true in a stricter sense of the term would be recognized as true for the larger number of cases that might be cited with a wider meaning. If the minor units had a definite enclosing outline, they were counted even though they were blank within, but without an enclosing outline, that is, if they were mere spaces, they were not considered, although the fact that there is such universal use of this type of decoration shows only more conclusively how the necessity of the invariability of alternates is taken for granted as an axiom of design.

Another type of alternate repetition was not included in the illustrations, i. e., when two sets of units alternated, without variation in either one. To this class belong all the conventionalized designs used so much in all kinds of decoration, and of which a very full account is given in Owen Jones's Grammar of Ornament.

These, to be sure, illustrate the negative points, viz., that size and shape are unalterable for rhythmic repetition; that distances must be equal and invariable; and that alternate units must not vary. But since the principal units do not vary either, it seemed needless to give them as examples of the point in question. A mention of this class of alternating repetitions, of which there is such a great number, is enough to show that they fall within the theory. But one example is as good as a thousand, and their inclusion among the illustrations for rhythmic alternates will be taken for granted without further mention.

We are left, then, to the consideration of those alternating repetitions alone, where both have a definite outline, and one or both varies to a greater or lesser extent. The effort will be to show that the unit which for some reason is of principal importance in the rhythm, is the one chosen to vary, and if not that the repetition suffers thereby.

125 EXAMPLES

The 125 illustrations of alternating repetition which were taken at random among 5000 photographs show a decided compliance with the principles already laid down. But there are many divergences as well, which it is necessary to consider, to see whether they are really contrary in principle or fall under its wider application. Eighty-two accord exactly with the principles with which we started. The distances between each set of units are equal and invariable; one unit varies in content but not in size or including shape; the alternating unit is invariable.

There is an interesting modification of this principle in the case of the metopes and triglyphs of the Greek friezes. Here the triglyphs are unquestionably the principal units structurally, and to many observers the principal beat of the rhythm when taken rhythmically. But the triglyphs never vary and the metopes do, which would seem at first to violate the rule that principal units alone, and not alternates, should vary. This difficulty is obviated in two ways. With the spatial type of observer, the triglyph is indeed the principal beat of the rhythm when the series is at such a distance that the difference in the metopes (if there is such) cannot be detected. When, however, the series is nearer at hand, there ceases to be any rhythm, but each carved relief is taken for itself without regard to the others. With the rhythmic type of observer, if the triglyph has been the principal unit before, the principal beat changes on nearer approach to the metope and the whole series shifts its accent. It is impossible for any observer to keep the triglyph as the principal unit of the rhythm, when so near that differences in the metope are easily perceived.

There are still thirty-eight cases which vary from these rules, and many of them vary in more than one respect. These exceptions fall into several classes, quite distinctly marked off from one another, and will be taken up in turn.

In five cases, the size of the principal unit varies as well as the content, but in four cases the variation of size is either at each end, or in the centre unit, to emphasize bilateral symmetry of the series as a whole. The series in this case is taken as a larger unity of which the separate units are parts; and hence they are not only repeated with respect to themselves, but are symmetrical with respect to the whole. In the other case where the size of the principal unit varies, it varies on every other one, thereby complicating but not confusing the rhythm, i. e., a stronger accent comes on every other principal unit.

There are also five cases in which the alternate spaces vary in size. Three vary regularly, thereby enriching the rhythm by introducing alternate heavy beats, and one varies at each end of the series to emphasize bilateral symmetry of the whole, with regard to the central unit. In the other case the alternates vary in both shape and size, with no regularity and from the point of view of repetition alone, disorder is all that results. This is on the Palazzo Pretoria in Pistoia, where carved shields occur at equal distances between windows. These shields are not component parts of the building, but were added with some other kind of significance; hence they express nothing so far as repetition for its own sake is concerned.

The other variations are all in the content of the alternate, minor space. Four vary symmetrically in the designs on each side of the central point, so as to accent the bilateral symmetry of the whole taken as a unity. Two vary rhythmically in design, i. e., there are two sets of designs which alternate with each other in the unaccented spaces. When they vary regularly in design, the rhythm of the whole is enriched not confused, provided there are only two sets, not three or more. The alternate spaces are passed over on the way to the principal unit, but by having an alternating design between them (varying only in detail, but of the same general character) a more complex rhythm is introduced which is good, since in both cases the alternates and principal units are so different they could not possibly be confused with each other, even though both varied. (In one case, turrets and statues vary with windows of the same shape but different decorations; in the other, arched windows and arched spaces alternate with statues.)

Eleven more cases of variation in the minor as well as major spaces fall under another head. These do not vary with regularity, but are different in each case—the detail of the design varying, while the shape, size, and distance remain unchanging. It is interesting to notice that these examples of variations of alternates were almost all taken from examples of Renaissance architecture, where a richness of effect was desired, even at the expense of regular rhythm. This could, indeed, be attained in no other way so well as this. In all these eleven cases, the conditions are alike: both of the repeated units are enclosed by limiting lines of unchanging outline. The principal units are more prominent than the others on account of greater size or interest, but the alternates, instead of retiring entirely into the background, have slight variations in decoration. This variation is always only in detail: the tracery on the pillars of the tomb of Louis XII, of the Loggia dei Novoli, in the Chiesi di Frari, Venice, etc. So unimportant in fact is the variation that it is not observed until one attends closely to it, and yet the rhythm is just enough disturbed by its presence to give a feeling of extra sensation or luxuriance which cannot be attained through variation of the major units alone. It is in the alternate spaces that the feeling of repetition lies. Any material change in them destroys the series, but a slight variation in the lines of decoration, a little rearrangement of the conventional curves in each alternate, gives, even though unattended to, in fact partly because unattended to, a vague feeling of variety, of some superfluous sensation being brought into consciousness, although the regular shape, size, and distance of the objects remains unchanged. It is this feeling of superfluity and slight disturbance which constitutes the peculiar richness of certain styles. These examples, then, far from falling outside of the laws of repetition, owe their opulence of sensations to the very principles of regular rhythm which they violate.

Another set of exceptions will involve more searching analysis. Nine of the examples described have the human form for the alternate unit, and in every case where this happens, the alternate varies. In the majority of cases where statues of the human form alternate with any other object, the statue is taken as the principal unit on account of its superior interest, but this is not always the case. In the Padua Basilica, and in the Church of St. Guistiana, cherubs alternate with conventional decorations, but the latter are so much larger and more elaborate that they would naturally be taken as the principal units. In the other seven cases, statues alternate with bas-reliefs which also have human figures in them; hence, since the bas-reliefs equal the statues in interest and exceed them in size and importance, they are taken as principal units.

It might at first be expected from the previous discussion that, in order not to shatter the repetition, the alternate statues must be alike, must be conventionalized into identity; but this is not the case. Another principle now comes into play. We demand variation in the human form whatever its place in art, even in the unimportant position of alternate in a repetition, and although they are kept as much alike in pose, size, level of head and feet, general character (i. e., cherubs do not alternate with old men, nor draped figures with undraped), yet there is some variation of pose or direction of glance, to keep them from being duplicates. We should expect this variety of repetition to be in danger of becoming fatiguing because of its lack of an unchanging rest-phase, but this difficulty was evidently felt in building them, for in every case some unchanging element has been supplied to the series to bind it together and to keep the constant changes of attention from upsetting the series. The cherubs of the Padua Basilica are in high relief against a uniform rectangular background which does not vary, and which furnishes an alternate just in character with the principal unit, the bas-relief. In the Cantoria of Donatello, although the dancing children move across the whole space, uniform double columns occur at intervals, and supply an unchanging alternate, while the children vary in position behind them. Around the pulpit of Lincoln Cathedral, although both units, reliefs, and statues vary, the pilasters behind the statues are invariable and supply a constant, unchanging factor in the series. In the alternating reliefs and statues of the Milan Cathedral or in the paintings of different sizes in All Souls Church, Oxford, an unchanging element is supplied in the frame, which is of like design in every case, so that in passing from one to the other an unvarying alternate is always present. In the Sienna font, and in the statue to Leonardo da Vinci, which are types of a vast quantity of repeated forms, there is uniformity in the minor pedestals and in the frames of the alternating bas-reliefs, which supplies the unchanging factor.

Moreover, another factor is noticeable in this kind of repeated series,—it is never long. The fatigue which would certainly result from a too long continuance of varied alternates, even with unvarying factors in the way of supports, pillars, and frames, is obviated in various ways. The series is either short and the whole has a definite bilateral symmetry, as in the Padua Basilica, and in the Oxford church; or, as in a great number of cases, the series goes around a fixed central point so that only three units are seen at a time. It is thus especially that this method is used in fonts, pulpits, and monuments, where from the circular arrangement enough can never be brought into the field at once to fatigue the attention.

This consideration of alternates which vary widely, as do human figures, even when they are alike in size, general shape, and character, and, moreover, the discovery that there is almost without exception an invariable element between the other alternating units, i. e., a third alternate; or behind them, as in the case of the pilaster behind the statue, may well bring up two questions:

(1) When the unchanging factor comes between the other two units, is not it in reality the alternate, and the two other units either variations of shape and size of one principal unit or two sets of principal units? In other words, do we not actually apperceive the two principal objects as the units of importance, and take the unvarying factor which comes between, no matter how slight it may be, as the alternate? Do we not demand the unvarying as our alternate, no matter how many variations may be in the other figures?

(2) When the unchanging factor comes behind the alternating statue, in the same plane with the bas-relief, do we not inevitably take it as the alternate in the series, and regard the statues more as episodes or attendants on the series but with real values of their own? Is not the fact that the unvarying factor and principal units are in the same plane an indication that they constitute a real series, while the statues or paintings which are in a plane by themselves make a series, harmonizing with the other, it is true, and in part coinciding with it, but felt in a different way? Therefore the actual repeated series conforms to the given conditions and is made to do so in every case by its unchanging alternate in the same plane; while human figures with values of their own never can be considered quite as alternates, but are really felt to be a series by themselves.

This introduces another question. In two more cases of varying alternates, there was variation in decoration above the level of the rest of the series. In the Borghese Casino, there is variation in the busts placed over the alternate windows. In the Venice rood-screens, there is variation in the carving of the alternating supports, which rise above the rest of the series. Is that part of the series above the level of the principal units really included in its perception? It would seem rather that when the series as a whole is being taken, those variations above the level of the main units (if they are not very marked, and they were not in either of these two cases) are ignored or only felt in a vague way as added richness. When, however, the attention is turned toward them especially, they form a series of their own, in which they become the principal units, and alternate with empty spaces. There is no limit to the changes possible in apperception, according to the level and plane of the alternating units.

There are three cases left; two where alternates vary in content with no system, and one with variation in distance. The first two are differently carved sections of railing on the side of Freiburg Cathedral, and a differently decorated frieze of squares and circles in the S. Lorenzo Cloisters, Rome. The effect is only of disconnected and fragmentary series in both cases, and especially in the latter case it is impossible to feel it as a repetition at all unless the variations are ignored, and the attention fixed on the unvarying factor of size.

The variation of distance is in the Beauvais Palais de Justice, where the first window is at an unequal distance from the others in the series. The effect is only of disorder and accident.

We have, then, surveyed all our examples of alternate repetition, and found that in the exceptions to the general principles laid down some other effect than repetition as such was sought. Either (1) symmetry for the series as a unity was required, which demanded variation of the end or central units. In so far, then, as it fulfilled the requirements of symmetry, those of repetition were disregarded.

(2) Richness of effect was accomplished by those slight variations in decoration of alternates as well as the principal units. These by their vague suggestions of different combinations of similar elements, and minor differences felt but not attended to, gave a superfluity of experience which made up its peculiar richness.

(3) When the human form (or any other form of especial meaning in itself) makes the alternate unit, some variation is demanded as in keeping with its own significance, since in proportion as a thing has meaning in itself, it must not be exactly duplicated. But an invariable alternate is always supplied in the way of a frame, or background, which is felt as the real rest-phase of the rhythm, while the varying alternate forms have a place in a series of their own. Also, since such a complex attitude would be fatiguing, such series are always short, or circular, so that few units are in the field at once.

(4) Regular variations in size or content, in either major or minor which recur at fixed intervals, give a heightened rhythmical effect by making certain beats heavier than the rest. As has been stated before, the major unit holds within it the real significance of the content of the experience; the minor unit holds the secret of the rhythmic effect.

(5) Only 4 examples of the 125 were found to repeat themselves alternately with irregular variation of alternates and violation of the other principles laid down at the start. These can only be regarded as accidents, as faulty examples of art, whose virtue lies in some other part of the work as a whole, and not by any beauty they possess in themselves as repeated series.

SUMMARY

125 Illustrations.

Several questions have been raised in this discussion of variations, but one which seems directly leading from it will be considered next.

When is variation necessary in a repeated series? We have considered the numerous cases where variation is possible, and the different ways in which a series may vary according to the idea to be expressed. Moreover, what appeared to be exceptions to the rule were shown to be guided by a desire for some other effect than repetitions as such.

But when do we demand variation in a series? Is there any case where variation of the unit is not only allowable, but positively necessary to its æsthetic value?

There were no experiments on this question, for it will be seen from what follows that they would have been impracticable. But observation of several thousand photographs has made the following clear: When the series consists of objects having an æsthetic significance of their own, not depending on something else for their value, then variation is demanded. In other words, when a thing is an end in itself, we do not tolerate an exact duplicate. It may have a place in a series of others similar to it, but its own meaning loses force if another is beside it precisely alike. When, however, an object has no great significance by itself, or when however great its value, it be regarded as means to something greater, hence not an end in itself, it may be repeated without variation.

This principle may be stated from another point of view: Any work of art, of the highest significance in itself alone, must not be repeated at all. There must not be even the suggestion of repetition. The highest values are individual, and to have a copy or a series defeats its whole reason for being. Thus, a second Sistine Madonna, or a series of Venuses, would shock our whole æsthetic feeling. Moreover, we do not want a suggestion of repetition; even a series of different Madonnas in similar frames would take away from the significance of each, in so far as they were regarded as a series, and not as a mere collection of detached units.

But grading down from these works of the highest value in art, there comes a point where an object, although possessing considerable value in itself, is not so intensely individual but that it can gain somewhat by a place in a series of others like it in some respects, but differing enough so that each still keeps its own meaning distinct from the rest.

The balance between these two artistic aims, i. e., the significance of the unit, and the rhythm of the series, must be adjusted with great nicety, and certain principles obtain wherever such series are found. It would be useless to cite the numberless cases where such series occur. Many have already been given in the examples of statues of saints, paintings on altar-pieces, and reliefs alternating with statues. One such series is a type of all. The human form represents that which has the most significance in itself, so when it is used in a rhythmic series, its individuality must be toned down and conventionalized; it must have no marked feature in one unit that does not appear in another; the head and feet must be on the same level, or vary with regularity; the general character and spirit of all must be similar, but never identical.

The reducing to a common type is the demand of the rhythmic series; the difference in attitude and arrangement of detail is the demand of the unit.

Thus, the subjects chosen for repetition of this kind are in the majority of cases apostles and saints, whose spirit and general conception are the same; typical representations of abstract qualities, such as Virtue, Courage, etc.; or conventionalized cherubs, and even animals. As has been stated before, a long series of this kind is impossible without fatigue. In proportion as the object is repeated the individual units lose their own meaning, and they must have their individuality definitely toned down and conventionalized to avoid the clash between the two artistic values. Yet their essential peculiarity must always be maintained, for we refuse to admit or allow the total identity of any expression of living values, especially as expressed in the human form.

It may be urged that statues are often arranged at regular intervals around a building, where the effect of repetition is distinct, and yet each statue is distinctly valuable for itself. But a distinction must be insisted upon. The statues form a repeated series as regards uniformity in position, height, pedestal, and color, so that the direct sensuous effect may be called rhythmic. But as the attention fastens on each for itself and takes it for its own meaning, it ceases to be part of a series at all, but becomes a unit in a world of its own.

But what of the cases where the human form is repeated in a series, and does not vary? Examples of this are rare, but they do occur, and are interesting, since they throw light on what has been already said. In the whole collection of photographs only two were found where a series of identical statues of the human form occurred,—The Porch of the Maidens in the Erectheum of Athens, and the Baths of the Forum in Pompeii. In the former case the left knee of the caryatids on the right of the centre, and the right knee of those on the left of it, are raised a little; but aside from this slight variation the six statues are exactly alike. In the latter case a row of titans all around the interior bear the ceiling on their uplifted forearms and are all alike. These two examples are very perfect of their kind, and, far from offending us, are very satisfactory. The reason is obvious. In both cases the statues are not the æsthetic end in themselves, but are there for a purpose, namely, that of a support. They are not ends but means to something else, and as soon as we feel that in regard to any work which would otherwise be of individual significance, it ceases to be individual, or to demand a peculiar expression different from all others, but may be duplicated without offence. Therefore, since the support of the superstructure obviously is dependent on the maidens in the one case and on the giants in the other, and since instead of existing simply for their own value they are there to hold up the roof, their artistic significance changes at once from ends to means, and variation is not required. Moreover, it will be found in the majority of cases that we demand this invariability in actual supports. Although we find but these two cases where caryatids are actually identical, we find also that in most cases the caryatids do not really uphold the weight, but a pillar or pier behind them supplies the real architectural support, and, that although they have a place in front of the pillar and give an apparent assistance in bearing the weight of the roof, yet the eye is not deceived. We see that the work is really done by the pillar behind them, so they that resume their place as artistic ends demanding variation, and not as means to something else. The following examples were found:

Milan. Arca di S. Pietro Martire. Pillars uphold the arch while four statues of women stand just in front. The pillars bear the weight although the statues add strength to the whole. The statues are varied.

Dijon. House of Caryatids. Piers behind the caryatids give real supports to the roof, while the figures added for decoration are all varied.

Dresden. Zwinger. Conventionalized figures ending at the waist are put on the outside of unvarying piers which bear the actual weight of the superstructure. The figures are all varied, but they cannot be conceived as really bearing the strain, since they have no foundation, but are merely added to the pier as a decoration.

Rouen. Tomb of Duc de Brezé. Four caryatids, all different, under four jutting projections of the arch. These projections are built securely into the rest of the structure and do not depend in the slightest on the figures for support. The figures are not integral parts of the whole architecturally, for the arch would stand exactly as well if they walked away, which indeed they are apparently in the act of doing.

Toulouse. Hotel de la Borde. Two caryatids under jutting projections of a window. The projections are securely built into the lintel and no weight rests on the caryatids nor even appears to. They are there solely as decorations and are different.

Paris. Hotel de Ville. Two caryatids under jutting projection of a window, again. Here is a very slight variation of the two female figures. The position of each is reversed to accent the symmetry of the whole. Very little weight is actually borne by them, but more than in the former cases, and we find proportionately less variation in the figures. They approach identity, but there is variation in detail.

These were the main instances found of the point in question, and are a type of the other minor ones found in support of pulpits, choir-stalls, and windows. It will be seen that in no case but the two classic ones given at the beginning are the human figures architecturally necessary to the structures, and in these cases they do not vary. In the other cases they are more or less playful, and the effect of the whole would be very unsteady did the superstructure actually depend upon them for support; but since piers rise invariably behind them and bear the weight, they fall into the sphere of decoration and from that point of view they must and do vary.

We have, then, considered variation of units in a repeated series, where they may vary and where they must, and we find the real value of repetition to appear in inverse proportion to the individual significance of the separate units; the more interesting or expressive the unit is in itself with individual significance, the less do we want it repeated; and so repetition of the human form must be conventionalized to the type (or to the same unvarying features), with enough individual differences still remaining to meet the demands both of the series and the individual. What apparent exceptions we have found to this rule have been shown to be meeting, in reality, another artistic demand.

ENDS OF SERIES AND ARRANGEMENT OF REPETITIONS WITHIN THE UNIT

The next question to consider is the ends necessary for a repeated series. Do they end with a heavier or with a lighter unit than the rest of the series, or with a unit of the same size? It will be remembered in the experiments touching this point that the subjects, without exception, preferred the series ending with heavier units. We should then expect, in examples of repeated groups of posts, pillars, etc., alternating with wider or more prominent ones of the same kinds, that the series would end with the heavier or more prominent one. Examples of railings or balustrades alternating with heavier supports are so common, and the supports come so invariably on the end, that repeated examples seem almost unnecessary. But another question arose in connection with this: Does not the apperception of a group of lines equidistant from each other consist in going back and forth over them from edge to edge, with no rest on one point more than on another; while in a group of lines arranged at equal distances each side of the centre but not from each other, to emphasize bilateral symmetry, does not the attention rest on the centre, and move from the centre of one group to the next?

Moreover, we found that a wider space or embankment of some sort was necessary, to finish off a series of groups in which the separate lines were equidistant from each other, than to finish the groups whose lines were symmetrically arranged. This suggests that the activity which goes back and forth in the former case, being less coördinated and not bound to a middle point, needs more at the end to stop it than is needed in the latter case, when the attention is more upon the centre of each figure. It would seem, then, that the former arrangement would be appropriate for railings and balustrades, where the effect is of continuity either running wholly around the structure and into itself again or where a continuity of parts is desired and a connected series. The other arrangement divides the series into discrete parts. If the attention is stopped at every central point, the effect is less of continuity and more of separate unities bound together externally by their equal distances. We should, then, expect such series of units much less in continuous balustrades, but if they occurred at all, that they would be in connection with separate unities that did not want continuity or place in a series emphasized at the expense of their individuality. All this we might expect from the experiments alone, although whether such a refinement would have got into architecture seems questionable. Moreover, the question whether a symmetrical group of units needs a less heavy end to finish it than a group of the equidistant type is even more difficult to illustrate. Although the two types may be given under some conditions in experiments, in actual architecture they never appear so, for the two types never appear in the same buildings allowing them to be compared. Besides, few photographs are taken exactly in front, and no two at just the same angle. Any accurate measurement of such end piers and any comparison of them is out of the question in the present methods of research.

One other question may be considered here. Does a series ever occur in which three units are repeated regularly, instead of one or two? In experiments we discovered that the subject found it impossible to feel repetitions of three in a series, and the only way that such a series was tolerable was when the three could be grouped somehow into one or two units. Therefore we should not expect to find such repetitions frequently, if at all.

To sum up: Do series always end with a heavier unit? Are units equally distant from each other more adapted to continuous or run-on railings, while units with symmetrical arrangements within themselves are found more often where separateness of objects enclosed is more aimed at than their connection? Is a less heavy end found after symmetrical series than after the other kind? Are repetitions of three units used at all, and if so in what way?

Obviously the only illustrations of these questions will be found in the arrangement of posts and pillars in balustrades of whatever description. In these cases alone do we find repeated series, with repetitions within the unit, as well as of the unit as a whole. The following examples have been taken by looking over about one thousand photographs and by recording every instance that occurred.

Having 100 illustrations of repetitions of groups, with units repeated equidistantly between them, and of elements distinctly symmetrical, several new factors came to light. In all the one thousand photographs looked over, not a single instance was found of unit-groups with the units within, arranged at other than equal distances. There were many variations in the number of units in the groups; but the number being given, the units were arranged at equal distances from each other wherever the effect desired was of detached sections or of continued series. There are obvious structural reasons for this. Any repetition of groups for a balustrade or protective railing, which is the almost exclusive use of this variety of repetition, would be weakened by wider apertures on either side of the centre. A reasonably enclosed space is necessary to make the railing of value, therefore the specifically symmetrical unit as opposed to the rhythmic unit was found always in carvings, scrolls, bas-reliefs, etc., alternating with vertical supports. We should expect, then, in general, that in railings where an aspect of continuity of progress along some border or a tendency to go around an enclosure was sought, the units would be rhythmic in character, impelling one to motion and to carrying the eye and general organism out of repose into movement. We should expect, on the contrary, that symmetrical units would be found where repose or partial distinctness of the separate elements enclosed was desired, and where the attention was not to be carried away in so marked a degree. Seventy-three of the one hundred illustrations were of balustrades where the rhythmic factor was presumably aimed at.

The Rathaus at Braunschweig had a symmetrical design alternately occurring, but with four in a section, so that the section as a whole was not symmetrical and the attention was driven on, and in the other cases some other effect than rhythm was obviously aimed at. The genius of the structures was heavy and massive and the balustrade made in keeping with them, since an effect of motion or rhythm would have clashed with the spirit of the whole.

These examples have all been of the balustrades around enclosures, balconies, etc. Since the rhythmic unit has been found more fitting for them, we should expect, conversely, that in front of separate unities, such as windows, doors, etc., the symmetrical unit would be more in evidence. At first sight, the facts do not seem to bear us out in this. Of twenty-seven examples of separate windows, doors, and gates enclosed by railings, only four had distinctly symmetrical designs. (Casa Palladio, Bergamo Chapel, Petit Trianon.) These are wrought-iron designs in the centre with repeated rods on each side, or a row of six pillars with the central two larger and more decorated. Twenty-three, however, remain to be accounted for, and the solution of the difficulty is observed at once in the distinction between odd and even numbers. As was previously suggested there are obvious difficulties in having posts in a balustrade at any but equal distances, since the gaps left by unequal distances from the centre would destroy their reason for being. This difficulty can easily be overcome in wrought iron by extra central decoration, although it is not always done by any means; but in stone balustrades, unless there is carved open-work, or solid reliefs, there is no other choice than repeated posts, either divided into sections or continuous, and no variation is possible except to have an even or odd number of them. We should then expect that there would be an odd number in separate detached enclosures, bringing a post in the centre to emphasize the balance, while in a continuous series each group would have an even number, thus giving no centre to fixate upon, but driving the attention on without repose at any one point more than another. It might seem doubtful that any such refinement should have been actually expressed in architecture, but examination of these examples shows this treatment to be very general. Of the twenty-three examples of separate enclosed details, eleven have an odd number of posts. Of the ten that remain, four are examples of windows along the side of a building, with separate detachments of balustrade in front of each. By having an even number of group-units the continuity of the row is maintained in spite of a separation of the sections. Two of the ten are sections of balustrade over the central doorway of a building. These balustrades are divided into three sections, of which the centre is widest and the ends only half as wide. Thus, although there are six posts in the central section, the balustrade as a whole is distinctly divided into a bilateral symmetrical arrangement. Three of the others have an even number of pillars, but they support an odd number of arches; and the arch, not the pillar, is taken as the unit of the repeated series. (Arches will be discussed later.) The one example unaccounted for represents a number of possible cases, where for some reason, following out a general scheme of building, or what not, the odd number is not insisted upon for separate clusters. But the fact that only one out of twenty-three is thus unexplained shows an unmistakeable tendency in the other direction.

A distinction between odd and even numbers cannot be felt above eight repetitions without actual counting, and often not even then.

The two final exceptions are of a gate and a decoration over a door (Fontainebleau, Piacenza) where there are nine or more units in the group. It is impossible to feel the system of this arrangement, and the result is proportionately confusing. A reservation must be made here concerning iron railings. There is no discrimination between odd and even in the number of iron rods in a section of railing and no tendency to symmetrical designs rather than rhythmic before detached enclosures. This is because from the nature of the case, there is no distinction possible between odd and even in the number of slender iron rods necessary to enclose a space with any security. There must of necessity be so many of them that the difference cannot be perceived, and so slight is the importance of each rod that the effect is more of a variegated surface than of actual beats of a rhythm. As soon as iron is wrought into large enough shapes, each repeated detail is of the same importance as in stone, but the slender rods commonly used in iron railings, although their repetition is rhythmic like all the others, give too slight a motor impulse to carry the attention past the heavy limits of whatever they enclose. They are found in front of many windows, but on account of the lightness of their rhythm compared with the solidity of limiting piers, no confusion results.

Having thus concluded that the odd numbers of units in groups is more adapted for separate enclosures, is the opposite true? In the continuous balustrade, previously discussed, are the units of groups made up of an even number of elements? Of the fifty-seven examples cited of continuous railings, thirty-one have an even number of posts in their groups. These conform to the rule: but what will explain the twenty-six remaining? It will be noticed that six of these have too many in a group for the eye to perceive any difference between odd and even, since they range from nine to thirteen. When so many units are in a group, the effect is always of the run-on type, whether the actual number turns out to be odd or even on subsequent count. One has a balustrade with only two sections on a side, each side of the centre door. Seven are in each section, and since the appearance of a symmetrical whole is the desired effect, an odd number is more in keeping than an even; in fact, this example, Monte Berico, might better come under the other head of separate enclosures, although it partakes of the character of both. Another balustrade with three in a section (Blois Château) is so heavy and massive in all its parts that fixity and solidity is more in keeping with it than rhythm. Eleven of them, that is, the larger proportion of all those with an odd number of pillars in a section, support arches, and the arch is taken as the unit instead of the separate pillar; and we find an even number of arch-units in each section, which is what we should have expected. It is a noticeable fact, which was previously suggested in connection with separate enclosures, that when a row of pillars supports a plain lintel, the pillar is taken as the unit of repetition. (When the row is on the front of a building, temple, etc., the opening may be the unit, if the purpose of the central door or the fact of going through is in the mind: but when the series stands for itself, the pillar is the unit.) When pillars support arches, the arch is the unit, unless it is very narrow as in the Moorish style, when the pillar is often so high and the arch so narrow in comparison that its value is weakened.

Of the thirty-one balustrades with an even number of parts in a section, four sets of pillars bear arches, and make an odd number of them. This would seem to make an exception to the rule were they not so narrow in two cases that the pillar was still the unit, and in the other two the motif of the arch was built around the intervening piers, so that they did not seem divided into sections at all, but continuous.

We have thus surveyed the whole field of repetitions of rhythmic and symmetrical units, and their difference in treatment according to the end they serve, and the results bear out our expectations. The symmetrical unit, as exemplified chiefly by an odd number of units in groups, is more used for detached enclosures; and the rhythmic type, with even numbers, is used more especially for continuous ones. In the former case the motor tendency is toward the central balance, while in the latter it is driven on out of itself through the series. When pillars support arches, the arch is the unit; when they support lintels, the pillars themselves remain the unit. Any number of units over eight loses its value of odd or even, since the difference can no longer be perceived and becomes rhythmic whether odd or even.

It must not be supposed that these rules are inevitably carried out or that the effect is necessarily poor if they are not. It shows a general æsthetic demand, however, which in individual cases may be modified by other demands, or altered in parts to make a more unified whole. When, however, the series is taken for itself, and judged entirely on its own merits, these conclusions will be found generally valid.

We have still to consider whether series always end with a heavy unit. All the series examined do end in this way; in fact we feel the necessity of this so clearly that one illustration would be as good as a hundred. But there is a difference in the use of the end unit, which is noticeable in any two series of symmetrical and rhythmic units. Of the sixteen examples of continuous series whose units were distinctly symmetrical instead of rhythmic, eight of them, although ending on supports, do not end on the principal unit of the series. This can be best shown by one or two examples. The Orvieto Cathedral has on the façade a balustrade of rectangular reliefs alternating with supports. The reliefs are undoubtedly the more interesting and important element of the series, yet the series ends with the less important element, the support or post, and we feel that it must do so. The Palazzo Contarini has a balustrade on its façade in which carved wheel-like designs alternate with supports which come at the ends. Why, in these cases, do we feel it as inevitable that the heavier and more important unit should not come at the end, as with rhythmic units we feel that they should? The answer to this is partly structural and partly æsthetic. We must feel, first of all, that the series is properly supported, that it will not fall away at the ends or down in the middle, and for this reason support of some kind must come at the end to hold it up and give a feeling of solidity and stability. But why are not these supports made the more interesting and important unit so that they might still bear up the superstructure and end the series as well? Here the æsthetic demand appears. As soon as the object is regarded as an æsthetic unity and care put upon it to make it beautiful for its own sake, it must not be thought of as the end of any series. It must be cut off from the rest of the world by supports or framed in some way, and while it still may have a place in a series, provided it is sufficiently conventionalized and not too important in itself, it must not be thought of as either ending or beginning, as depending on a series to give it importance, or lending support to anything else. It simply exists, cut off from the world, even though in the balustrade not an integral part of it, and one ought to be able to remove it without affecting the stability of the structure.

The question whether series of symmetrical units have less heavy ends to finish them than series of rhythmic units cannot be settled by these methods of analysis. While it seems certain that the rhythmic series drives the attention on by its greater motor activity, and hence would need more of an end to stop it, so many other factors enter in of more importance, such exact measurements would be necessary (quite impossible with the photographs of the scale here used), the refinement would be so great, since the stone of which most of the examples are made, by its own weight supplies a check to rhythmic activity, all these considerations make it impossible to illustrate this conclusion and it must remain an experimental result alone.

There remains one question: Is regular repetition of three units ever found? They may be in combination of some kind so that they fall into a rhythm of twos, but are they ever found repeated as three separate and distinct units? The answer to this is without exception. Of the five thousand photographs analyzed, not one instance of this kind of series was found. In many cloisters the pillars are of different design, and often one design is repeated through an otherwise varying series, but their repetition is either without scheme of any kind, or in some combination that falls into a rhythm of twos. No three-rhythm has been used in art, any more than it has been found possible in experiments.

ARCHES

It has been noticed in the preceding discussion that when a series of pillars supports arches, the arch, not the pillar, is taken as the unit. If this is so, it would seem that the arch by binding two pillars together with a curve awakens a more vigorous response than the vertical line of the pillars, and this greater expenditure of activity makes it to be taken as the element of repetition. It suggested that the arch (like the rhythmic unit) tends to drive attention on out of one unit to the next in the series. The outward thrust of the arch arouses an outward-tending activity, and for this reason a row of arches would need, to give a finished, stable effect, a wider and heavier embankment at the end than a series of lintels. The experiments on this point were inconclusive owing to the difficulty of obtaining a series of arches and of lintels which should be comparable in size. For this reason the validity of this suggestion must depend upon the actual treatment of arches in architecture. It would seem that the arch would, like the rhythmic unit, be more appropriate for continuous series than for detached short rows; or if the series were short, the ends should be treated in some way, by reduction in size, change in width of pillar, pier, or decoration, so that the outward-activity might be counteracted by some inward thrust or some accentuation of the centre. Thus the unity or balance of the series as a whole would prevent the arches from seeming to "run away" which they might appear to do without such treatment. We shall, then, look through photographs of buildings where arches are used, to find if their treatment carries out the supposition.

It may be seen at once that such a treatment of arches differs from the arrangement necessary to make plain lintels effective. The pillars on the front of Greek temples were indeed slightly farther apart at the middle entrance, and the centre was moreover further accented by the point of the pediment. But on the sides the rows of from thirteen to sixteen columns had equal interspace and no noticeably heavier columns or embankment of any kind at the ends, for none was necessary. The series appeared ended whenever it stopped, and did not carry the attention over, nor demand some finish to "hold it down," as does the arch. The pillars, to be sure, completely surrounded the temple, and so were, in name, continuous. But on a building with square corners, the other sides do not carry the series on to the eye (with variations in foreshortening of the ends) as in a circular structure, and the effect of continuity is not immediate.

Many examples might be given of buildings with pillars and lintels on the façade, which have no visible modifications of central or end columns to give balance or symmetry to the whole, and yet which are perfectly satisfactory as repeated series and do not demand either such treatment or further continuation, but are complete and finished: London, Trafalgar Square; Rome, Pantheon; Vienna, St. Karl, Barrome Kirche; Berlin, Schillerplatz, etc. These have the centre accented by the superstructure, but there is no discernible modification of the series itself.

Examples might be multiplied, but there are sufficient to illustrate the essential stability of repeated vertical units and to contract them with the outward-tending, run-on effect of arches which need various kinds of treatments to finish a series. kinds of treatments to finish a series.

Of one hundred and sixty-five examples of such series examined, only seven do not conform to the principles we have considered, and these are proportionately unsatisfactory. Forty-five illustrate buildings where the arches go completely around the outside of a structure, so that the series instead of requiring an end simply runs into itself again. It will be noticed further, that unlike series of columns around rectangular Greek temples, these are around circular structures where the series does not change its direction suddenly but by degrees. With the exception of courts and cloisters where the observer stands within and sees the whole series, these are all around domes, baptisteries, etc., where the end arches in the field at any one point of view are seen in perspective gradually fading off and yet leading attention on around the building. There may indeed be arches which go across square-cornered buildings or even around them, but in these cases some other device is necessary to make each side a finished series in itself. The mere fact of its continuance around a corner where it cannot be seen from the same point of view is not enough. (These various arrangements of arches on a flat façade will be taken up later.) Rows of arches are often used around towers square as well as round, but towers from their very shape and size allow the observer to see different sides from nearly the same point of view, so the series is not broken up into sections on different sides of the tower as it is in a larger building. Twenty more examples are of arches in interiors and are all of arches down a nave, with either a regular arch or an arch motif carried across the apse. It might be supposed that an arrangement of arches in an interior would be more difficult than on an exterior surface, since the genius of an arch is its outward thrust and its tendency to run on. Without careful treatment it would spoil the interior by trying to overstep its bounds; by making certain walls look wider than others; the arched sections utterly discrete in general character from the plain or otherwise decorated section. In point of fact, the use of the arch-series in interiors is quite conventionalized, and all the illustrations are of loggias, or of churches where the arch goes down the nave and in a more or less modified form across the apse. In the Sistine Chapel the arched windows go down the side walls and across the end in a vaulted double-arch. In some cases a series of Roman arches down the nave has a more or less pointed arch across the apse, but in every case the continuity has been kept in some way so that the series is unbroken. Moreover the columns in the cathedral naves are often so high and the arches so proportionally narrow that the pillar instead of the arch is taken as the unit. This is somewhat true in St. Mark, Venice, also in St. Sophia, Constantinople, where the large arches are divided into sections of seven smaller ones, each one of which is so narrow that the pillar is felt as the repeated unit instead of the arch; or if the arch be taken, the narrow span prevents it from too great outward thrust.

Thirty of the arch-series are on façades of buildings or in structures by themselves, as gates and triumphal arches, where the central arch is larger than the other, thereby emphasizing the middle point and drawing attention to it away from the ends. This centralizing a series or balancing it as a whole may be accomplished in various ways. Two examples make the central arch larger instead of smaller. Six make the end arches smaller while four make them larger. It will be readily seen that just which one of these variations is chosen for the series depends on the function of the series. The central arch is wider, with only one exception, when the series is of arched doors and the central door is the main entrance; while the end arches are more apt to be varied when the series is purely decorative and serves no function. The central balance may be further gained by differences of level. In the decorations of many façades, especially the early Romanesque, rows of arches go obliquely into the point of the roof and by this strong pointing toward the centre create an inward tendency. Six of the illustrations have the central arch accented by decoration; seven have heavier piers around the central and end arches; six have the end arches brought out into a nearer plane which effectually finishes the series. All these examples illustrate the necessary disposition of arches on a flat wall or façade where the series in the field of vision must end suddenly, that is, cannot gradually fade away around a corner. The variety and yet invariability of these devices shows the need felt for some finish at the end, some balance of the whole with the central accent, which need, apparently, is not felt for pillars and lintels.

When the arch-series is on a circular structure, such as apses, porches, and the like, even when it does not entirely surround it, as an arena or spire, the regular diminishing of the series on either side, owing to the curve, supplies the finish necessary, and the size and arrangement of the arches need not vary otherwise. Twelve of the examples illustrate such a use of the arch, and although in some cases, Morano Cathedral, Nomantala Church, the arches are continued into the transepts gradually tapering in size, or are modified in size growing narrower from the centre, as in the Bergamo Church, such a treatment is not necessary for finished effect. The difference in proportion resulting from a curved series, or even on arches carried around a square corner (as in porches on Goslar and Braunschweig Rathäuser), where the series is open enough to clearly see its continuity as it runs into the main building, will suffice to make a series finished without modifications of the arch-units.

There are many instances of long rows of very narrow arches on cathedral façades which are too narrow to give outward tendency, or else they have statues within them which really take the attention and form a series of vertical units in place of the arches. There is also the common device of interlacing arches, where a supporting pillar of another arch stands in the centre of every arch, thereby always driving the attention backward and restraining it. Perhaps the natural outward tendency of the arch-series and the necessity for its limitation can be seen by violations of the principle. Seven of the examples do not conform to any application of this rule and the results are not satisfactory so far as the mere series itself is concerned. Over the right and left doors of the Piacenza Cathedral are sections of nine arches which end abruptly and do not even meet each other. The Fredericksborg Schloss at Copenhagen has a row of fifteen arches enclosing a court. These run into wings on each side, to be sure, but all seen at once as they are and without central or end modification they are too sharply cut off and inclined to overstep their limits. The Loggia dei Lanzi at Florence, with its three wide arches and narrow pillars, the William Tell Chapel in Switzerland, with only two arches, illustrate forcibly the tendency of an arch to move outward, to appear too wide for the superstructure and too "active" unless bound down in some way. Four arches on the right and left of the façade of Marmonte Church, but not across the centre, have the same unfinished effect. The roman arch on one side of the St. Lo Cathedral façade with two gothic arches on the other defy every principle of repetition and symmetry as well.

From this survey of one hundred and sixty-five of arch-series we find through a variety of means a uniformity of purpose in their treatment; that all point to a common demand, however differently expressed, according to the function of the series. The series must be prevented from "running away." It must either run completely around a structure into itself, or be balanced as a whole so that the attention which naturally runs off the ends is driven towards the centre. This may be accomplished by enlarging, decreasing, decorating, or pointing toward centre of the arch by means of the obliquity of both halves of the series. It may also be brought by enlarging, decreasing, changing the plane of the end arches or altering the size of the limiting piers. The essential value of the arch may be altered by narrowing it, by filling it with something more important than itself, thereby making it only an attendant series upon its content, by interlacing it, or by any device that transforms or revises its outward tendency.

The question discussed in the experiments, as to whether narrower interspacing was required between units decorated toward the centre, and units blank, or covered entirely with non-centrally accented decoration, could not be taken up in the latter analysis. To settle such a point, illustrations would have to be found of blank and decorated units of the same shape and size, in the same structure, and their relative interspacing compared. But no such examples were found, where the spacing was not regulated by some obvious structural reason other than pure pleasure in the repetition. This must stand, therefore, solely as an experimental result.

The use made of difference in plane or end, to facilitate two series being taken along together, whereas they would be fatiguing if the same in those respects, has been touched upon in the discussion of statues and bas-reliefs, and other series of more complicated units. Where the unit and alternate are both rich and significant, and would tire the observer by following each other at the distances they are obliged to be in a series, a slight difference in plane relieves the situation, and is used largely in monuments, fountains, pulpits, and such structures.

Many other questions have come up in the investigation which might be discussed in the same manner as the preceding, but can only be hinted at in conclusion:

Just what factors make an element and its alternate congruous? What is the exact relation of lines, which makes the scroll decoration in a balustrade alternate satisfactorily with an upright support, while the alternation of the arches in the Colosseum with the Greek pillars between them is incongruous?

In what does the pleasure in repeated series differ, when the observer is not certain just what is the repeated element? May there be a bare rhythmic pleasure, when the series is too far away to distinguish what the elements are, or when they run together, so that no definite demarcation is felt between them? Do such series excite a pleasure of repetition without content as to elements, and does it differ from mere variation and contrast?

The series of unsymmetrical units was found in the experiments to have a peculiarly unstable run-on effect similar to that of rhythmic units and of arches. Are they used in the same kind of cases as the others were, when a particularly active effect is desired?

Must a space be wholly enclosed, to be taken as a unit?

In a series of projections along a wall, the projections are taken as the unit, even when they almost meet at the top of the alternate space. When they actually do meet at the top, the enclosed space becomes the unit instead.

These questions and others similar might be experimented upon, and examples of their treatment analyzed, as in the previous questions discussed.

PLATE V.