PART I

The object of this paper is to discover some of the sources of our pleasure in repeated space forms, and the laws which govern this repetition. The repetition of an object, and its regular recurrence subject to certain possible variations, is one of the basal principles of art, and of architecture in particular.

It is necessary at the outset to define our use of the word repetition more exactly, for there are obviously different meanings of the word, which may lead to confusion.

1. The term repetition may be applied to the existence of any two objects similar to each other, whether they are near together or widely sundered. Our pleasure in such a repetition would be merely that of re-seeing and recognizing the two as counterparts of each other. This kind of repetition I call conceptual, for it requires only that the memory-picture of the object be held in mind and the two recognized as similar when met again. This is not the kind of repetition which I have in mind, and I shall never use the word in this sense during the discussion.

2. In any one work of art there may be some feature repeated, some motif which is taken up and carried out in different ways throughout the whole, and these features we recognize as having an orderly relation to one another in the unity. This might be termed repetition of content, and be applied to the recurrence of some type of decoration over a window or a peculiar arch taken up in various ways throughout a cathedral. I do not use the word in this sense, but limit it still further.

3. By repetition is meant during this discussion the regular recurrence of an object, and an equally regular recurrence of intervals. The repeated object must come at uniform intervals, and this restricts us to the consideration of that repetition alone which consists of recurrence at regular intervals of some object more or less beautiful in itself, and the description of the nature of our æsthetic feeling in experiencing such a series.

Although this discussion is divided into the two divisions of experiments and analysis of architectural examples, and the experiments are described first, the investigation was not carried out separately in this order. The two went along together, the art-analysis suggesting experiments, and the experiments in turn throwing light on the analysis. The two parts of the discussion are kept separate merely for the convenience of the reader, and in the experimental discussion all allusions to the art-illustrations are excluded in order to avoid confusion. In reality the two went hand in hand, but the connection between the experiments and art-analysis will be reserved for the latter half of the paper.

The experiments were begun in the following manner: In a velvet screen about a foot high was cut a window 460 mm. by 35 mm. in size. Behind the window was a metre measure and a rod from which hung small strips of cardboard 10 mm. wide. First two, three, and four strips were hung behind the window, and the subjects were required to arrange them at the intervals where they preferred to see them repeated. The results were uniform in certain particulars and very suggestive. In their arrangements of two, three and four strips, the subjects were guided by considerations of symmetry or proportion. They insisted that although they knew that the strips were repeated, they did not feel the repetition, but the strips seemed like parts of some larger unity to be arranged with reference to the unity of the whole. With the addition of the fifth strip came a difference in their apperception. Instead of the strips seeming parts of a whole including figure they seemed like repeated units.

FAVORITE ARRANGEMENTS

2 strips3 strips4 strips5 strips
J.30 mms.4 mms. { mid. sp. = 25any symmetrical
{ ends = 10arrangement better than equality
S. 170 12 { mid. sp. = 15 { mid. sp. = 40
{ ends = 12{ ends = 30
U. 40 20 30 35
R. 30 130 { mid. sp. = 30
{ ends = 10 10
L. 23 40 70 70
W. 40 10 30 30
V. 20 10 { mid. sp. = 100
{ ends = 60 15

It will be seen, from the table, that with two exceptions they preferred five strips equally distant from one another, while with four strips, four subjects had preferred a symmetrical arrangement. These gave as their reason that with five strips the latter appeared more definitely to be repetitions of one another, while the four strips seemed more like parts of a whole which required symmetry in its arrangement. Moreover the two subjects who preferred five strips in symmetrical arrangement instead of at equal distances affirmed that a distinct feeling of repetition came with five strips that had not been felt before, only they did not enjoy this feeling of repetition as well as one of symmetry. After having seen the five strips, some subjects could feel the repetition with four strips, but none with three. The question naturally arose, what is this feeling of repetition which makes one say that four or five repeated objects deserve the name, while three or less are regarded in a different light? The analogy between the apperception of this visual repetition and auditory rhythm seemed so strong as to deserve attention.

In auditory rhythm it is necessary that there be recurrence of more than two elements; they must come at a certain rate and within a certain temporal space to seem connected with each other, and they may be subjectively grouped in different ways. The apperception of both kinds of repetition had so many analogies as to suggest that some of the factors in both experiences were identical.

To focus the problem I took a definite thesis in regard to it. Our apperception of repeated space forms is due to the rhythm of our own motor adjustments which are excited in face of repetition, harmoniously if they accord with certain rhythmic laws in us, inharmoniously if they do not. It was then necessary to find what facts would support such a thesis, to see if in reality such facts could be marshalled, and if the explanation and support they offered was conclusive enough to make it needless to look farther.

It would seem, if our pleasure in repetition depended on temporal motor responses in us, that if the amount of time normally taken to traverse a repeated series were shortened, or if the eyes were fixed and not allowed to move over the field at all, our enjoyment would cease altogether, or at least be seriously diminished. If we found it impossible to enjoy the series except when seen for a certain time, long enough for the eyes to go over it in the rhythm peculiar to each subject, we should then conclude that our enjoyment did depend, to some extent, on such temporal rhythm.

I experimented on this question with nine subjects, and the results brought out different ways of apperceiving repetition, which divided the observers into two rather well-marked types.

The apparatus was of the simplest, consisting of white silk strings hung on a wire against a black background across one side of the room. The strings were attached to the wire by little hooks, which enabled one to change their position easily, while a cloth hid the weights on the ends of the strings, so that nothing but the vertical white lines were visible.

Fifty strings (50 mm. apart) were hung before the subjects, and they were asked to survey the field and give a signal as soon as the experience became pleasant. Then having found the average length of time for each subject to enjoy these simple repetitions, a shorter period was given when they were to shut their eyes at a given signal, and see if in that shortened time they were still able to enjoy the series. Next they fixated the eyes and kept the whole body rigid, to see if pleasure was still possible when all outward motor response was checked, so far as possible.

The results of this experiment were very suggestive. Of nine subjects, all felt pleasure when allowed to move the eyes over the series at random; with eyes fixed, five felt their pleasure much altered in its quality as well as lessened, while with one it was altogether destroyed. With four, however, although there was considerable alteration in the quality of the pleasure, its amount was increased rather than lessened.

B. (1) Average time necessary to enjoy the series: 4.7 seconds.
(2) Three-second exposure. No pleasure, needs more time during the movement.
(3) Eyes fixed: 4 secs. = Av. time necessary to enjoy it. Lines bunch toward centre and fade away at sides, giving a kind of unity, but he feels constraint.

R. (1) Av. time: 4.3. Sees them in pairs.
(2) Two-sec. exposure. Very faint pleasure; feels that only a part is perceived.
(3) Eyes fixed: 4.3. One pair fixated, the others fade away, making a kind of figure. Pleasure faint and constrained.

L. (1) Av. time: 2.1.
(2) 1-sec. exposure. Pleasure faint and incomplete. He feels the pleasure comes from memory of the previous experience.
(3) Eyes fixed: 2.2. Great effort to find any pleasure. It consists mainly in seeing a few strings, and feeling there are others, even though they are not distinguished.

V. (1) Av. time: 2.2. Sees them in pairs.
(2) 1.5-sec. exposure. Enjoys the experience in memory after the eyes are shut again.
(3) Eyes fixed: 1.9. Still sees them in pairs, but cannot see enough of them, hence they are less pleasant.

W. (1) Av. time: 4.3.
(2) 2-sec. exposure. Not enough time to feel any relation between the strings, most of the pleasure supplied by the memory.
(3) Eyes fixed: 5.3. Pleasure is very faint, and consists in having the strings appear to converge to a central point, and fade at the sides.

J. (1) Av. time: 2.3. Sees them in pairs.
(2) 1.5 exposure. Less pleasant.
(3) Eyes fixed: 2.7. Series seems more like a unity and he enjoys it more, since no time is spent in exploring the field, but it is one unified experience.

U. (1) Av. time: 28. Only enjoys it by ignoring all except those in the centre—does not want so many.
(3) Eyes fixed: 18 secs. Enjoys it when eye lights on one string, so that the others can fade away equally at the sides, in one figure.

S. (1) Av. time: 5.
(2) 3-sec. exposure. Less pleasant.
(3) Eyes fixed: 8.8. Pleasure consists in converging of lines toward central point. It appears like one figure and is more intense than (1).

H. (1) Av. time: 9. Sees them in pairs.
(2) 1 sec. Just as pleasant as before.
(3) Eyes fixed: 4.6. Pleasure in unity of whole series with centre of fixation emphasized. Only felt pleasure anyhow when the eyes had stopped moving, so now it comes all the sooner.

From these introspections it is obvious that there are two distinct ways of apperceiving repetition: One in which the rhythmic element is pronounced, so that when the time necessary for such a rhythm is shortened, or by fixating the eyes the motor response is hindered, the pleasure in the repetition is either altered or destroyed altogether. The other type takes a repeated series in the sense of a unified presentation and wants it all at once in a symmetrical whole. The rhythmic factor is present in both, as is shown by the fact that the quality of the pleasure was changed in every case when the time of exposure was shortened. But in the latter type of subject the pleasure felt in the presentation of the whole at once, and the feeling of symmetry around a middle point, are more intense than a rhythmic apperception. These two kinds of apperception remain fairly constant throughout the experiments, and for convenience' sake we shall call them spatial and temporal types. With the former, the value of the experience consists especially in having a central fixation-point from which the repeated elements fade away equally on the sides, making a symmetrical whole. With the temporal type, the pleasure is felt by means of the rhythmical passage from one element of the series to the other. In passing from point to point the rest of the field still remains in indirect vision, so to the distinctly temporal a distinctly spatial factor is also present. For this reason the temporal type of apperception is the richer of the two, and a description of it comes more nearly to the essence of repetition as such.

Up to this time, the repeated element had always been a single string. This was varied and the strings hung in pairs (50 mm. wide, 100 mm. between pairs). When the strings had hung at equal distances from each other, six out of the nine subjects had seen them in pairs while enjoying them, and had found such grouping more or less essential to enjoyment. In seven cases the pleasure was increased by this grouping. They expressed their preference in various ways: "Easier to keep track of where we are going." "Can go quicker over field, for repetitions are more well-marked." "Single line is too thin to rest on, this gives broader space for repose." All these introspections instanced the necessity of the rhythm being marked and made plain, so that there should be no confusion of point with point. The two who disliked this grouping were of the spatial type, who found no pleasure in traversing the field, hence too little content in it, in this arrangement, at any one time. Grouping of some kind would seem to faciliate the apperception to a certain class of subjects, while with others the amount and quality of the content of the field is of more consequence.

Since accents are such an important factor of auditory rhythm, the next experiment was to see if the apperception of a series of repeated elements would be facilitated by accenting every other one.

Another string was hung in every other pair thus making it more striking, but here came a difference between the feeling of accent in auditory and visual rhythms. The subjects declared the pairs in which a third line was hung were not intensified alone, as when a greater stress is put on a tone in auditory rhythm, but the pairs were changed qualitatively. The group of three became the repeated element, while the pair was only an alternating figure different from the principal unit. This unanimous testimony brought up a variety of questions. 1. Is any purely intensive accent, without involving qualitative changes, possible in visual repetition? 2. What factor makes us choose one object rather than another as the repeated element? 3. What is the value of the alternating figure in such a series? 4. What is the value of the empty space between repeated figures, and does it have as distinct a value as an alternating figure? 5. Are all the recurring objects and spaces felt as separate repetitions; if so, how many can be carried on at once?

These questions were put to the subjects in regard to the series just described with considerable uniformity of answer.

(1) No such thing as purely stress accent seemed possible. The word, signifying greater intensity without change of quality, did not apply. If one attempted to intensify the repeated object in any way, either hanging another string, thickening the strings, or any similar device, it ceased to be the old unit but became a new one, whose repetition was followed for its own sake, while the weaker one retired into the background, and was not felt as the element repeated in the series.

(2) Any regular change of the element which made it more interesting or caught the attention, fixed it as the chosen unit of the series, whose repetition was followed.

(3) Concerning the exact value of the alternating figure in the series, there was great difficulty in introspection. They all "knew the alternate figure was just as truly repeated as the principal one, but could not feel it so." The three-group formed the unit of the repeated series, and although the pair was clearly part of the experience and distinctly perceived, for some reason it was not felt as repeated in the same way as the other. It was merely an alternate, a filling, which was essential to the other, but which had no significance in itself as a repeated thing. Two subjects were able (if they tried) to carry both repetitions along together, i. e., not only feel the three-groups as coming at regular distances from each other, but the pairs as forming another interlacing series. This kind of apperception was very fatiguing, however, and they could not enjoy it. For any pleasure to be derived, the pairs must retire into the background, and attention be fastened on the three-group.

(4) If the alternating figure was to be so subordinate, was there any difference between its significance, and that of an empty space? This was everywhere answered in the same way. The alternating, or minor figure, had a very distinct value, and any irregularity in it was even more irritating than in the principal unit itself. When the space was empty they thought nothing of it, the equality of the interspacing was taken for granted; while if they felt an irregularity in it, it destroyed their pleasure in the whole series. But there was no feeling for the empty space until its regularity had been violated, while there was a distinctly pleasant factor in the minor figure, even though different in quality from the principal element.

In the foregoing experiment the differences between the spatial and temporal type of observer were still strongly marked. The former type invariably grouped the elements (usually with the three-group in the centre and a pair on each side) and they took their pleasure in the symmetry of each figure so made, moving from the centre of one to the centre of the next adjacent. In this method of apperception there was no empty space between repetitions, for the whole group of three figures was taken as the repeated unit. The empty or rest-phase was gotten in moving from the centre of one to the next, in which passage the limiting pair was ignored. One spatial subject, finding the proportions of this artificial grouping poor, got no enjoyment at all.

With the temporal type, the experience was quite different. They moved across the field with the three-group as their stopping-points. These principal elements were what they looked for, and their pleasure seemed to consist in expecting and meeting it. What part the pair played, they had difficulty in analyzing. Some said that while the three-groups occupied most of their attention, they gave a lesser degree to the pair, so that the rhythm of the passage across was marked by heavier and lighter beats. Another found the figure in the alternate space only an obstacle, and felt he was hindered in the passage from unit to unit, the only compensation being, that the "hindrance" came at regular distances. Others felt that two repetitions were actually being carried on at once. By this they meant that the two sets of elements were kept distinct, although objectively combined, but the repetition of the pair was subordinate in interest to that of the three-groups.

I tested the same thing (accents or major elements, and the value of the alternating minor elements) by simply doubling every other string of the series 50 mm. apart. In every case the effect was found poor. It was "confusing," "too much work." They all felt adjusted to the repetition of the double string and then encountered the single one, which hindered them, and by trying to keep both elements going at once they were fatigued. Most of them had a distinct feeling that they wanted to swing from one element to the next, and were baffled by the alternate. In this arrangement, even members of the spatial type who had not been able to get any rhythmic feeling before, felt the movement in the series as if they were going across, although they went (in two cases) in groups instead of single elements. They all, however, felt the single string as an obstacle which hindered their enjoyment, whether the double string or a group was taken as element. This suggested the question: What makes the difference between the minor figure being an enrichment to the experience and being a hindrance? They insisted some rest-period was necessary; some really empty space between the repeated units, and when in place of rest they had more to do, it spoilt the pleasure.

Next, two strings were hung at equal distances between the double strings, and the latter put 100 mm. instead of 50 mm. apart. This was liked better in every case, and the reasons given were much alike. The double string was still the repeated unit, while the two strings between did not feel repeated. In spite of the obvious inconsistency of the statement that they did not feel the alternates to be repeated even when they knew that they were so, just as much as the double string, several subjects made the same remark. V. felt the series as a rhythm, where the double strings were all he was interested in, although he knew he should notice if the others were changed. B. could not detect that they were of any importance, except as he imagined them absent. B. could feel either the double strings or the two strings between them as the major unit, only, whichever one he took, the other retired into obscurity. He felt the minor units in a different way as being repeated together with the majors, but very weakly, and not at all unless he previously considered that he ought to do so. L. said his attention was fastened on the double strings, but it was the "effort or ease with which he passed over the alternates which formed the pleasure." Another temporal subject felt the rhythm as the others did, with more emphasis on the double strings. But the major units seemed the rest-phase in his rhythm, i. e., he paused here in observation of the series, although his attention was most active; vice versa, the minor units required little attention, but were the active or moving parts of the rhythm. Since they all considered the strings in the alternate space merely as steps or lesser beats on the way to the major element which they sought, and as obstacles rather than otherwise, why did they prefer the space with two strings rather than one? This suggested that some factor in the alternate spaces was important other than simply the amount of resistance to overcome in getting past the two lines. In answer to this they could only say that the two strings in the alternate space formed a pleasanter unity by itself, although, as they went across, they did not think of it in terms of unity.

What, then, is the real rest-phase of the rhythm of alternating repeated objects?

In the beginning of the discussion, when the analogy between visual and auditory rhythm was felt so strongly in a certain type of subject, they had expressed themselves as if the object which they called the unit of the repeated series were the active stimulated part of the experience, while the alternate space was the rest-phase, valuable only as a period of repose or blankness before the object was again encountered. But in this case, although they felt they were putting no attention or emphasis on this space, in reality they were keenly alive to what was hung in it, even preferring more "hindrance" in the way of strings than less, which suggested that the alternate space was of more value than they were conscious of. (Some of this increase in pleasure was of course due to the increased actual distance between the double strings, but some also to the extra string.) The introspection on this question as to which part of the rhythm was actually the rest-phase (if there were any such) was difficult for them all. They felt they spent more time on the major element; that was what they looked for and found pleasure in meeting again.

One said, "The unit is what I look for; as soon as I have it the pleasure ends and I want to move on again. The pleasure does not consist in resting on it after it is found, but in knowing I am going to meet it again, and in doing so." As to the alternate spaces, he could only say he was not consciously interested in them, he took them for granted, but knew he should feel it, if they were changed. His feeling for them was wholly negative. The other temporal subjects agreed essentially with this. The alternate figures had to be passed, but passing them was only of importance as it helped or hindered the perceiving of the major elements. All agreed that any change was noticed and felt irritating at once, although they could not understand how it should, since so little attention was paid them normally. One subject felt the alternating strings only as obstacles between the doubles, and demanded an actual, empty rest-period between any repeated units. When asked if it were really the rest-period between elements or on them, he said he felt there was a complete discharge of attention on the major units, and an attempted one on the minor or alternate units, and the attempted ones became confused.

These introspections would point to the fact that alternate minor spaces while affording rest for the attention were periods of activity of some other kind. The fact that no one could say what kind, and yet insisted on the feeling of its being important and distinctive, and moreover repudiated the idea of change in a minor space even more than in a major—this seemed to show that there was a value in the alternate spaces quite aside from attention, but fully as distinct in its own way.

As might be expected, those of my subjects to whom rhythm was not a conscious factor of the experience of repetition could not understand exactly what was meant by the distinction between rest-phase and emphasis of rhythm. In all the preceding cases where the temporal type gave the introspection I have described, the spatial subjects grouped the single lines, in Fig. 2, about the heavier pair as centre, and moved from the centre of one such group to the next. The experience then consisted of a succession of adjacent symmetrical groups, connected by movement from centre to centre. When asked if there was no pleasure in finding equal distances between their centres, i. e., any temporal element whatever, they all denied feeling any. They could not detect that they felt the distances between their centres as equal, although they knew them to be. They spent so much attention on the group that all feeling of the distance between its centre and the last was lost before going on to the next.

These two marked types of apperception of an alternating series seem varieties of emphasis, rather than of actual experience. It was evident that those in the spatial type must have some recollection of the amount of distance passed over between the various groups to feel the whole series as connected in any way; while those of the temporal type could not be wholly absorbed with the separate lines of the series as they traversed it, but were distinctly conscious of the space relations of those in the side of the field that they had just passed or were coming to.

Next, I tried to see what were the different factors which made up the value of the minor spaces. By varying both their size and filling, and doing the same to the major element, I could judge the relative value of these changes on the two, and their effect on the whole series.

The test was made in the following manner. The series as it stood consisted of a double line alternating with a single one.

With every temporal subject the double line was conceived to be the repeated thing, and the space between considered as an alternate, with a repeated line of its own, to be sure, but not felt in the same way as the other. With the spatial type, the single line was merely the limiting edge of the symmetrical figure, with a double line in the centre. One subject varied back and forth in his method of apperception, and considered the richness and variety of these different apperceptions as one of the chief sources of the pleasure therein.

Variation of alternating spaces: The minor spaces were varied by hanging two strings in one, and one in the other, and subject asked how such a change affected his feeling for them. The change was marked.

The spaces which had before been minor were so no longer. The alternate space in which two strings were hung with the boundary-line of the two double strings became the new element, and the alternate in which only one string was hung continued to be the alternate in the new series. The whole series shifted itself, and settled into a new equilibrium. Some of the subjects were able to feel all the former minor spaces still as such, but only by a definite effort, and not while taking any pleasure in it. The change in the alternates spoilt the whole scheme of the repetition as it already stood, and made a regrouping necessary. I next tried varying alternates by removing a string at intervals.

Since the strings were not removed in any regular fashion, and because the subject could not find any possible consecutive way to group them with the double strings, this variation was partially overlooked, and although confusing the series somewhat, repetition of the double strings could still be felt. Thus a mere gap where the scheme remained the same was not so disturbing as an extra feature inserted, or one noticeably changed. Something could be supplied by the subject, but not altered so easily. In these cases, however, the change was only tolerated because it was ignored. They felt it as a mistake and so overlooked it, but, accepted as a component part of the series, it was impossible to feel it as a repetition or get pleasure from it.

The next variation was in the position of alternate figures. With a three-group as the major element of the repetition and a pair of strings in the alternate space, the size of the two minor spaces was altered, thus making the distance between the three-group and adjacent pair shorter than between that and the next three-group. This immediately threw out the feeling for the old series and made a new one. The new series thus formed varied with the different subjects, although no particular difference was noticed between spatial and temporal types. They all disliked the new arrangement, in whichever of a variety of ways it was apperceived. (It will be noted the actual distance between the three-groups was not varied, but the size of the spaces each side of the minor figure, i. e., the minor figure was shifted from its central position.) One typical spatial subject took it in either of three ways: (1) He grouped the three-group and pair nearest together, into the repeated element of the new series; (2) he ignored the pair and regarded it as a repetition of three-groups; or (3) ignored the difference in the division of the alternates, and regarded them as alike. The artificiality of the latter methods of taking the series is evident. What pleasure survived after such a strain was very slight, and was moreover not of the series as given, but as imagined differently, which was not a valid judgment. Most of the subjects grouped both figures into one, and, finding the unity thus made ugly and unsymmetrical, derived no pleasure from it. One tried to keep both elements in separate series and have them go along together, equally distant from those of their own kind, although not from each other. This was, however, very fatiguing and unsatisfactory. Those who grouped the different figures said they did so because they could not help it, not because they liked it, and said it was impossible to regard the alternate figure as such, if varied from its central position. If they were all varied together, they were grouped, with the major unit, into a new one. If varied irregularly the series was spoiled—no rhythm whatever remained. It became a heap.

Next, I tried varying the size of the alternate spaces, keeping the filling in its central position.

Here also it was universally regrouped. They found it more difficult to feel the rhythm of the three-groups as separate elements than when the minor spaces had remained uniform in size, but different in the position of the filling. The alternate space, then, which had at first seemed the unimportant part of the rhythm and for which no subject could assign any conscious value whatever, was evidently a potent factor of the experience, and when varied either in size or filling (especially the former) it not only changed the feeling-tone, but shifted the entire scheme of the rhythm, or broke it up altogether.

Variation of major units: Was variation more allowable in the major than in the minor unit of a series? This was tested first in the same manner as for accents. In a series of which a double string was the major element, a third string was hung with every such double, thus changing the unit in both size and content.

The series immediately readjusted itself with the three-group as element for most of the subjects, although one was still able to feel them all as one unit, varied by the added string. Varying only the size of the major unit gave the same result.

The pairs, instead of remaining the same size, were made alternately larger and smaller, and a new repetition was made, i. e., with the larger pair as major element and the smaller one as minor. They all agreed, however, that less change was made in these cases than when the minor spaces had been changed in size. In the latter case either a regrouping was made, changing the whole character of the series, or it was spoiled altogether. With change of major units alone, however, although a new element was made, it was still possible to take it in the old way without much difficulty or change in feeling-tone.

It was then necessary to see how change of content would affect the major unit, the size remaining constant. A group of two sets of double strings 10 ccm. apart was taken as the repeated element, and these groups placed at 10 ccm. from each other.

Within one element was hung one string, and within the next two, thus varying the content while the size remained constant. In every case the answer was the same. It was not so pleasant as when the filling was the same, but the group still remained the unit of the repetition, and the series essentially the same.

Several variations were made in this element. Instead of hanging strings regularly (1 in one, and 2 in the next) they were hung irregularly, i. e., an extra one here and there at intervals in no special order. As long as the boundary-lines of each group remained at the same distance from each other, and from the next group, thus keeping the unit at uniform size, although the pleasure-tone varied, the balance of the series was not changed. No regrouping or shifting of the equilibrium resulted.

It would seem from the preceding experiments that in any series variation of the major unit was tolerated more than of the alternate; while in either case variation in content had less influence than variation in size.

Symmetry: In the previous experiment, three subjects had insisted on symmetry as a necessary attribute both of the unit and its alternate. U. (spatial type) described his experience as "a succession of symmetrical experiences or states of equilibrium; when they are not so, they must be regrouped, or pleasure is impossible." R. (temporal type) insisted especially on the necessity of the alternate figure being symmetrical as regards the major units, i. e., halfway between them; and also on symmetry as regards itself. One temporal subject said there was some pleasure in merely going from one unit to the next, even though no repose was possible on each because of its asymmetry. This suggested experiments on the importance of symmetry in repeated series. Is it necessary that the separate elements of a series be symmetrical? Must both major and minor element be symmetrical? Does this necessity vary according to the temporal or spatial type of the subject, i. e., is it more necessary to the spatial type, whose pleasure depends more on repose in the unit, than to the temporal type, whose enjoyment rests mainly in the rhythm of movement from one unit to the next? Or is it a common demand? This experiment was begun in the following simple way. The strings were hung in two group-forms; one with three and the other with four.

This was a symmetrical grouping and uniformly pleasant. The series was then changed by removing the second string in the four-group, thereby making it unsymmetrical.

This change made the repetition less pleasant in every case, but did not spoil it. Instead of the four-groups becoming more prominent they seemed less so, and the three-group on account of its "compactness" became in most cases the major element, thereby shifting the balance of the repetition, but not detracting very much from the pleasure. Next the three-group was changed by moving the middle string to the left. By this means the group which had been minor in Fig. 11, became unsymmetrical, while the four-group was regular.

This change was preferred to that in Fig. 12, although different reasons were given. One said it was because this change in arrangement made the elements more distinct, hence easier to keep apart, while in Fig. 12 they were made more alike. Moreover, one element seemed as important as the other. He did not class them as major or minor, so he could not compare the relative values of symmetry in principal and alternate units, for in this series he did not feel the distinction. The other answers to this question were rather incoherent, but the series did not seem to suffer much change, either pleasantly or otherwise. Since lack of symmetry in the element was at least tolerated in the examples already given, would it be allowable so to place the units that the two adjacent to any one unit should lie unsymmetrically on either side, that is, may the elements lie unsymmetrically with regard to one another? Suppose a four-group to be repeated at regular intervals, and a three-group likewise; if the two series were combined, must they occur halfway between each other? That is, must they be symmetrically placed as regards the intervening space, or could they be put to one side?

The subject was asked not to group them (as in previous similar arrangements), but to keep them as separate repetitions if possible, and to see if this equal distance was necessary to keep them apart. The result was the same in all cases. The subjects could not help grouping them, and found it impossible to keep them distinct unless so much effort was put into it that no pleasure was left. They said they "knew each unit was as equally distant from the next unit in its own series, as if it did not come at unequal distances from the units in the other, but they could not feel it so, and were obliged to group the two together." For this reason the experiments did not satisfactorily illustrate the point in question. It was necessary to have a series of elements whose unity was more strongly marked, and whose different parts would still remain one whole even after variations, instead of shifting into each other. It was suggested by these imperfect experiments that symmetry was not so important a factor in the different units of a series as the subjects had previously supposed; but that, on the other hand, the different units must be placed at equal distances from each other, if they are to be kept distinct either as two series or as one. Moreover, that two series could not be kept distinctly in mind as separate, anyway, without fatigue, the tendency being always to group them into one series with a new repeated element, composed of a combination of the other two. It was necessary, however, to test this more completely. By a simple device the former series was changed radically, so that the difficulties mentioned were overcome. The strings of both the three and four groups were twisted together at the bottom, thus binding them closely into separate unities. By remaining attached at the bottom, whatever variations might occur elsewhere in the figures, they could not lose their individuality and become merged in each other as before. They remained distinct groups without effort on the part of the subject.

With this I began as in the previous experiment. The subject was asked to look at the series of repetitions, enjoy them as much as possible, telling what was the pleasant factor in the experience, and how he apperceived the series. The subjects separated into types as before; the spatial type immediately grouping the elements into a larger unity and enjoying the groups more for their own sake than for their repetition, while the temporal type went from one to the next in the series, enjoying the rhythm more than the elements as such. (It may be remarked here that the subjects were perfectly naïve as to their apperception. They did not know they were separated into types, nor were they urged to be consistent. Even the experimenter did not know of the distinctness with which these types separated themselves, and consistently held to their own method of apperception, until looking over the records afterwards.)

With the temporal type the four-group was the major group. Some expressed its prominence in terms of time, i. e., they spent more time on it, and less on the three-group. One felt it as emphasized, because he moved from one four-group to the next like it, and at each step moved back and forth from left to right, to see the alternate three-groups on each side, always resting on the four-groups.

It is noticeable with these subjects, in whom the rhythmic element was more strongly developed, that although they admitted that the language of "temporal rhythm" did not adequately cover their experience (because the element did not disappear after perception as in auditory rhythm, but remained in the visual field), still they could not express themselves in other terms. L., the most extreme of this type, insisted that the experience of repetition would be exactly as pleasant if he saw the elements pass one by one behind a moving window, with never more than one in the field at once. In other words, their temporal relations were all he felt.

The others did not go so far as this, and agreed to the significance of the whole field, even while especially interested in passing from one to the next. B. partook of the characteristics of both types, and by combining the apperceptions of both bridged the chasm between them.

With the four spatial subjects, the apperception showed its usual divergence. Three grouped the elements, either with the three-group in the centre on account of its being more compact and graceful, or the four-group because it was heavier. One of them could group it either way, distinguishing between the prominence in an element due to interest and due to beauty, i. e., he found the four-group more noticeable and interesting on account of its size, while the three-group was more beautiful as a unity, on account of its proportion and grace. Therefore according as one factor or the other predominated, one or the other figure was taken as the more prominent element, and placed in the centre of the group. Sometimes they separated into two series running along together, but this was not usual.

Having got these varied introspections, with yet a certain likeness running through them, the balance of the four-group and of the three-group were varied in turns, to see how the change in symmetry of elements would affect the series; and the relative value of symmetry for the major and minor units of a series.

First, the four-group was altered, by moving the second string further to the left, while the three-group remained symmetrical.

In three cases this arrangement was preferred to the regular one previous, and each time for the same reason. The four-group was made more noticeable by being unsymmetrical, and hence more easily distinguished from the other. The two were easier kept apart, and the alternation between the two was made more clear-cut and obvious. With others the change was unpleasant for the reason that it affected them in an exactly opposite manner. The four-group lost its individuality, and, by separation into two unsymmetrical parts, could not be distinguished so well from the three-groups as formerly, hence the effect was spoiled.

A distinction was made between the relative importance and interest attached to the units, when symmetrical and when unsymmetrical. Every one agreed that making the four-group unsymmetrical gave it more prominence of a certain kind. With the first three subjects mentioned, this prominence was enough to accent the rhythm still more than before, and differentiate the two units more strongly. But with the other there was a feeling that while it gained prominence and was more noticeable, it lost coherence and interest, thence it could not be kept as the principal unit, but the attention passed over to the three-group which maintained its unity.

It would seem, then, that the mere fact of one unit in a series alternating with another, and being more noticeable, taking up a larger space, being more complicated, etc., did not insure its being the chief unit in the series. One subject voiced essentially the feeling of all, in his comment on the series: "There is a constant struggle between the prominence which the four-group gains from size and eccentricity, and the insignificance which it deserves on account of its looseness and lack of unity; it cannot hold its own as one individual thing, and because the three-group still does, it becomes in one way more prominent, while the four-group remains so in another." Another subject felt he gave more time to the four-group than before, because being separated it would not bind together again without effort. At the same time the three-group gained in interest because it was easy to find and did not vary. Another subject felt that the time spent on a unit had nothing to do with its rhythm; it was all a matter of interest and attention. Often he looked a longer time at one unit, choosing another for the chief element in his series, because it interested him more.

All this introspection brought out two things clearly:

(1) The apperception of a series of alternating units, whether of the spatial or temporal type, is not fixed, but any variation of its unit is liable to shift the emphasis. Thus, as in the present case, when a symmetrical major unit is made unsymmetrical, it may not remain the principal unit, but becomes the minor one, because the attention shifts to the other which was before relatively unimportant.

(2) Whether either element shall be the principal one or not, does not depend wholly on its objective prominence, but on the amount of beauty or interest which it holds for the observer. Neither size, complexity, nor eccentricity can force a certain unit to be taken as the major in a series, unless it thereby presents an interest which makes the observer choose it.

The next change was to vary the three-group in a similar way, by pushing the middle string to the left, thereby making it unsymmetrical.

The responses were as follows: Five said it did more violence to the series to have the alternate varied than the major unit; it was more confusing. Three preferred it, giving as their reason that it made the elements more different from each other than before, hence more easily distinguished. The preponderance of evidence was, therefore, that, although any variation from symmetry in a unit was likely to be detrimental to the repetition, it was more likely to be tolerable in the major unit than in the alternate space. In either case it was demanded that the two units be distinctly different, and it depended on the individual subject, whether in this experiment the variation of one unit or the other brought out this distinction more obviously. Aside from this consideration, however, it appeared that the alternate spaces as such required equilibrium more than the principal unit. Also, variation of symmetry in the major unit, while it made it more prominent in the way of eccentricity, also made the symmetrical minor unit more prominent in the way of interest. As one subject expressed it, "Since the others vary, the attention requires something which does not vary, and forces prominence on the minor unit, because it remains symmetrical"; and "The minor unit is too small to merit such prominence as it gets by lack of symmetry. It is distorted, and has not enough content to bear it."

These introspections from temporal and spatial subject alike, all point to the fact of a certain value attached to the alternating units in a series. (1) The units must not be too much alike in interest, or they rival each other. (2) They must not have more prominence given them as regards the whole than they have interest to sustain. (3) There must be a congruity between the two elements so that one shall not be noticeable in one way, and one in another, thus carrying the attention in two different directions.

One more thing was suggested by this experiment: (4) The subjects who had invariably grouped their different elements in other series found it very difficult to do so in this, or wholly impossible. None of them did so when taking the series naturally, but moved on from one to the next just as the rhythmic type did. They felt "forced to move on," "no place to rest," while one in whom the rhythmic feeling was weakest was much fatigued by this movement, and insisted on having something stable to rest upon if he was to gain any pleasure at all.

Next the series was varied by making both units unsymmetrical; first with the balance tipping the same, and second in opposite ways.

Those who preferred this gave essentially the same reason. They agreed that the unity of both elements was broken up by this change, and they did not stand out distinctly from each other; but all felt a certain congruity in having both major and minor units follow the same scheme in composition. They were not distinctly an alternating series, but harmonized better as lines. The two spatial subjects, who disliked this arrangement more than the other, gave the same reason: the unity of the elements was spoiled, they did not "hang together." Their dislike was similar in kind to that of the others, only the congruity which made up for it with the former failed to satisfy these. With the symmetry broken and the balance tipping in different ways, the feeling was not strong in either direction. They still criticised it in the same terms of congruity and distinctness, with no especial change on account of this modification.

These experiments all pointed to the fact that (1) a certain amount of congruity and equality was necessary between elements of a series (although it did not establish what were the essential features of such a harmony). (2) It is more pleasant, as a rule, to have the elements symmetrical, although symmetry was not a necessity for an agreeable series. (3) Provided the change in the symmetry of the units was not enough to shift the whole order of the series, changing the major to minor units (and vice versa), any varying of the symmetry of a minor unit was more disturbing to the repetition than of the major, while varying their symmetrical position, as regards the unit on either side, was absolutely destructive to the order.

The next experiment dealt with a different side of the question. Since the unit of a repeated series may be a group with repetitions inside itself, does the repetition of lines or figures inside the group differ from the repetition of the groups as a whole? If so, how? That is, in the enjoyment of a series of groups with repeated lines in the group, in what respect does our apperception of the repetition differ in the two cases? Or does it in reality differ at all?

To test this, the strings were arranged in the following way. 10 groups of five strings were hung 100 mm. wide and 100 mm. apart. Each unit had, then, five repetitions within it.

The arrangement was pleasant to all the subjects, and they described the effect of the experience, falling at once into the spatial and temporal types as before (this was wholly naïve, for the same questions were asked of each, and they had no idea of being grouped in types). The introspection of both types must be taken in some detail, to fully analyze the experience.

Spatial: J. felt he took in all groups at once. Each unit seemed like a rich experience in itself, but he could not detect any rhythm in it, nor in the whole series. The pleasure consisted in getting a number of similar objects in the field at once, and enjoying the combination of them all, feeling that they stretched away in each direction. H. and U. grouped several unit-groups into a larger unity and enjoyed the cluster as a whole. They did not group them in any particular system, nor could they detect the slightest pleasure in moving from one such group to the next. One found his enjoyment solely in the contrast effects in each, while the other laid it to the space relations of each independently. The pleasure only came when each group of groups was spread before him. Those outside the immediate field meant nothing to him, and the movement between them had absolutely no conscious interest for him. S. said that enjoyment stopped altogether during motion of any kind, and the experience was pleasant only during total repose, on whatever happened to be in his field at once.

With the temporal type came a marked difference in apperception.

B. affirmed the pleasure to consist in going from one cluster to another, and to begin just at the point where he meets the next stimulation and feels it is going to be the same as the one previous. It is the expectation, rather than the verification recurring at intervals, which makes up the pleasure; not the actual movement, or subsequent contemplation of a group. The pleasure came in pulses; in knowing by seeing from the side of the eyes that the experience is to be repeated, and on reaching the edge of a new group, in the feeling that the experience is just about to begin.

R. felt that she "wriggled around" in each group of lines, and that a certain feeling came from "wriggling" among the lines in a particular fashion.

The pleasure consisted in having this feeling recur at regular intervals. The repetitions inside the group and of the group as a whole differed in this respect: For the separate unit-group, it apparently consisted in repeated short irregular movements, back and forth, enough to bring about a certain feeling which seemed pleasant and sufficient unto itself. Repetition of the groups as a whole meant movement across the field in one direction, for the purpose of meeting another group, and getting the required feeling from it again. The pleasure was not in the movement or in any repose (she could detect no repose at all), but in experiencing the group again, feeling that it had been so before, and would be again.

L. (the most extreme of the temporal type) agreed with R. that the lines inside the group were perceived and enjoyed temporally, as well as the groups as a whole. There was no experiencing the groups at once. He felt that he moved regularly across the field encountering five lines, one after the other, then an empty space, then five lines more. The only meaning which the group as such had for him was the five accents which came near one another in time. He could feel no unity whatever apart from this. He was even certain that his pleasure would be identical if in some mechanical way the same figure could be pushed forward, so that the same amount of time and movement would be necessary to reach it that was required to move from one figure to the next on the field. The experience was in every way analogous to auditory rhythm with him, and he was unable to express himself in other than temporal terms. Immediate perception, repose on the object, or groupings, had no significance for him.

The other two subjects were links between the extremes already described. They could feel each group, and sometimes even the whole series at once apparently, and yet were all the time conscious of a certain rhythm in going from one to the next. The whole experience seemed immediate at first, but on reflection a certain alternate rhythm was felt to be present, which was too rapid to take any considerable time, but yet had to be included as a factor in the experience. These introspections I believe to throw light on the nature of the whole experience of repetition. Since there are two methods of apperception so extreme, but moreover certain subjects partake of the characteristics of both, it might seem that both types represent but one side of the experience. Since both are enjoying the same objective series, but in their description of their feeling in face of it emphasize such different sides (leaving at the same time the other side unaccounted for), and since certain subjects share the experience of both, it might be that the sum of both methods of apperception was necessary to the fullest appreciation of the repetition in question, only in certain subjects one aspect of it was so much stronger that the other possible factors in the experience were overlooked.

It would tend to bear out this view, that when it was suggested to those of the temporal type (always excepting L.) that according to their description the other groups remaining in the field, after having performed their part in a temporal series, ought to have no further influence in the repetition, whereas they did in reality, they admitted the fact, but could not account for it. Moreover, those of the spatial type admitted that their enjoyment in having spaces equal, and in having repeated objects exactly like one another, had a certain character which no other experience possessed. This did not seem accounted for by any description they could give of its effect on them, although they could not detect what this other elusive factor might be.

These introspections, therefore, and the confessions on the part of both that there was a feeling of something more which they could not hold long enough to describe, suggested that both types were but opposite ends of a series of possible apperceptive types, and that in both cases certain essential features were emphasized at the expense of the others.

After these experiments, the next step was to find how a series of groups was apperceived when the lines in each group were arranged symmetrically about a centre, as distinguished from their arrangement at invariable distances apart. The same number and size of groups were taken, but the arrangement of lines in each varied as stated above.

Spatial subjects: J. felt a different kind of pleasure from that felt with Fig. 19. Here the enjoyment was in each unit for itself, a certain repose in its symmetry. Although he fixated on the centre of the groups, and in going across the field moved from centre to centre, there was no feeling of rhythm whatever, merely enjoyment of the unit itself. Moreover, although he had detected no rhythm in the previous experience, this one seemed distinctly different in having lost a feature that the other had. He felt by comparison that the other had had a temporal character, some movement in the groups, which was wholly lacking in this. This was more beautiful and restful, the other more exciting and rich.

H. and S. both enjoyed this series better on account of possibility of greater repose in the unit-groups. The pleasure was solely in each unit for itself, not in their repetition, so the group which offered most balance and equilibrium in itself was pleasantest. S. also found enjoyment in slight variations in the groups (trifling difference in distance, different light effect, etc.). It is noticeable that when repetition alone was the main feature of the series, any variation was either ignored or found unpleasant. But when the unit for itself is the object of enjoyment, variation if slight is another element of pleasure.

There is also pleasure in the mere repeating of symmetrical groups, although, when the attention is turned to this feature, the feeling of symmetry is less felt. Even when attending chiefly to the repetition of the groups, the symmetry of each is felt somewhat, which makes the whole experience better than Fig. 19, but the two attitudes seem to hinder, rather than help each other.

This introspection was suggestive, giving rise to two more questions: (1) When is variation allowable, and when not? Is it adapted only to objects when taken, as ends-in-themselves, and not when considered as means to something else, i. e., as means to make a series or border, or anything which takes attention from themselves as unities with individual meaning? (2) Is a distinctly symmetrical group as adapted to repetition, as such, as one with merely equal divisions? Does it not tend more to repose in itself, instead of to the motion necessary for the apperception of a repeated series? These questions will be considered later.

Temporal type: R. felt a difference in the movement across, in that in Fig. 20 it was from the centre of one unit to the next, while in Fig. 19 there was no regularity in the movement.

L. felt the difference between the two apperceptions very strongly. In Fig. 20 the movements seemed organized. He felt as if his attention (if not his eyes) went back and forth from edge to edge of the unit, finally settling in the centre; while in Fig. 19 the very essence of the apperception was that every line was compared with every other, meaning a great number of movements in both directions, not stopping in the centre. If he did rest finally in the centre, in the unit of Fig. 19, instead of seeming evenly repeated, it too became symmetrically perceived, but the usual way to get from one such unit to the next was to move from and to any point in the next adjacent, other than the central one. In either case the pleasure came in identification of the second figure with the first, and the feeling, "I have seen it before." The pleasure lay in the process of recurrence of sameness.

V. also, who had not felt much motion in Fig. 19 at first, felt it strongly now in comparison with Fig. 20. He said in the former, although he did not make actual movements across (in fact his eyes were plainly at rest), he was sure he felt "dispositions to do so" which were lacking in Fig. 20. The pleasure came in the first moment of repose after finding the new unit was the same as the old.

After we had investigated the different methods of apperceiving groups of repeated lines, and compared the effects of different groupings, and studied the feeling of one unit alternating with another, another question arose.

These questions had all referred to the alternation of two units; either a unit with an empty space, or with a space of different filling. How did the apperception differ when three repeated units alternated with each other? To test this, three spaces were taken equally wide (110 mm.) and equally distant from each other (150 mm.), but with three different designs within them. These designs were of the same general character and importance although different, and repeated themselves regularly.

The subjects were asked as before to describe their reaction on the series. Not one of all the number was able to feel the repetition of the three units; what pleasure they got from the series (if indeed they got any) was from other sources. The general type of answer was formulated more fully by L. He saw 1, then looked for 2 and found it different, but could have included it in the series if it were not for 3. That being still different sent 1 and 2 out of mind, so that he could not feel any repetition of 1 when he met it again. He felt a certain sense of repetition in that the spacing and general motifs were the same, but there was no pleasure in that. What pleasure he got was wholly intellectual, not immediate, except for a slight pleasure in their uniformity of position. In him the rhythmic feeling had always been of the strongest, but he found in this experience none whatever. It was simply impossible to keep the three units going at once. Another temporal subject tried to group 2 and 3 as one element, with one as an alternate, thus reducing it to a rhythm of twos. This process was labored, but otherwise no enjoyment was possible. The spatial subjects derived what pleasure they could, either from the units separately, with no regard to their repetition, or from some method of grouping, by which their difference could be overlooked. One expressed his pleasure solely in terms of contrast of the white strings against a black ground. Any immediate feeling for the repetition was impossible for either type. It will be noticed that the feeling of the repetition is quite different from the knowing it is there. They were all perfectly conscious that 1 was repeated again after 3, but could not feel it, while repeated simply after 2, they could feel it.

Next, the series was varied again. The size of the blocks, instead of being alike, was varied three ways, while the designs remained similar.

The interspaces were 150 mm. in every case, but 1 was 150 mm. wide; 2 = 110 mm.; 3 = 70 mm. All the spatial subjects found Fig. 22 worse than Fig. 21. The irregularity and general disorder was more pronounced. Although the rhythm had never consciously given them pleasure, and, when not violated, was never noticed, still the threefold difference in size violates some feeling which they can only express in rhythmic terms. Some tried to group the three units into a larger group, but this being unsymmetrical displeased them. Others picked out the most satisfactorily proportioned unit and ignored the others, but any possible apperception was irritating. The temporal subjects found it equally poor. They felt the continual dissatisfaction of having their expectation, that the adjacent unit should be the same, disappointed. They all said that they could carry the feeling of repetition over one dissimilar unit (i. e., in an alternating series of two different units), but that the third difference completely upset the scheme. When only the filling varied as in Fig. 21, it could be partially ignored, but difference in size could not be ignored, and only the equal distances apart kept them from being a heap. They could not feel the evenness of the empty interspaces, however. They were not consciously present in the experience at all, they merely knew they must be even. There was no feeling-tone whatever to the empty alternates.

Only one subject preferred Fig. 22 to Fig. 21, and the reason was obvious. 1, 2, and 3 appeared as the same unit where variation in size was apperceived as due to perspective. Thus, instead of appearing as three units repeated, they were one set which progressed by means of "pulsations" or regular intervals of perspective. This gave an added richness to the rhythm, and was very pleasant. As three separate units of different size, there was no meaning in the series whatever.

It is evident from these introspections that, although the likes and dislikes may vary, the principles on which they are based have much in common.

The points on which they agreed unanimously were the following:

(1) There is no feeling of repetition for three separate units. The series may be enjoyed by means of subjective grouping of one kind or another, but as separate elements, the feeling of repetition is broken by adding the third.

(2) There is a distinction between perceiving or knowing a repetition, and feeling it. Even though a subject is equally conscious that elements are repeated according to some scheme in two different cases, he may feel it in one case and not in the other.

(3) The empty spaces between the elements have no conscious part to play in the experience. Even when there is a figure in the alternate space, it comes very little into consciousness as part of the repetition, yet it is alterations in these alternates which make or mar the feeling of repetition. A series may not be beautiful in itself, but if the alternates are regular, it feels repeated. Vice versa, the units may be enjoyable in themselves, but they do not feel repeated unless the alternates are regular and conform to certain requirements. In the units lies the meaning of the repetition, in the regular alternates the possibility of its expression.

(4) The rhythmic character of repetition is not felt by a certain type of subject, when it goes smoothly. When a variation is made which would destroy any possible rhythm, its lack is felt, and its violation finds expression only in rhythmic terms.

(5) More violation is done to a series to have the size of units varied than the filling. (This corroborates previous experiments.)

(6) A certain amount of ignoring and regrouping can be done by the subject. The series is not taken exactly as given, but with selective attention.

(7) In a series of different elements alternating, the most prominent one is chosen for the major unit, and the others for alternates. This prominence is more influenced by size than any other factor, but may be due to intrinsic interest of any kind.

(8) The major and minor elements must have a certain difference from each other, both in appearance and interest, and they must be different enough for the difference to be easily perceived, but not enough to be incongruous. They must differ in interest enough, so that one is easily more prominent than the other, or may be made subservient to the other, in the apperception.

(9) Variations are pleasant in the principal unit repeated, but not in the alternating figure unless very slight indeed, or affecting only secondary parts of the figure, not the main lines.

(10) Not the time actually spent on a unit makes it more or less prominent, but the feeling of more or less "energy" expended on it.

Ends: In an alternating repetition, must the series end on a light or heavy beat? That is, must the major or minor unit be on the end?

To test this a series of strings was hung in which a group of three alternated with a single string.

The subjects were asked to look at it with the three-groups on the end, and with the single string. In every case the three-group ending was emphatically declared the best. What reasons were given were much the same, although most of them could give no explanation at all. S. said the minor space on the end left him "hanging in mid-air, it needs the heavy beat to land me again." Others said it was "ragged" unless the three-group ended the series. R. said anything interesting would do on the end, as well as the larger-sized unit, it simply needed something of sufficient interest to stop the rhythmic process and keep one from going on.

It was impossible to describe the experience except in rhythmic terms, and those in whom this sense was not strong could give no account whatever for the difference in their feeling for end.

It will be remembered that some experiments were previously described relating to the difference in apperception of a group of lines equally distant from one another, and a group averaged at equal distances each side of a middle point, but unequally from each, to emphasize the bilateral symmetry. Two such series were now taken to find if there were any difference necessary in appropriate endings. Since the two types of groups differed so much in apperception, did that difference so extend to the whole series that a different space was needed at the end to finish them off?

The method of experiment was the following: Two series of repeated groups were hung (100 mm. wide and 100 mm. between) with the design of the groups varied as described. At the end of each a strip of cardboard was hung, which the subject was asked to move so that it bounded the amount of space at the end, necessary to finish the series adequately.

Thus b is the cardboard strip, and a the space which was to be varied according to his taste. The same experiment was tried with each series, with the following results:

I II
U.a = 96mm. a = 90
J.33 50
S.97 90
H.109 104
R.160 150
V.170 135
T.145 125
W.80 68

In the case of every one but J. the subjects preferred a longer end space with I than with II. J. was, however, of the extreme spatial type who gave as his explanation that with II, when the central line was prominent, the end (a) must equal just the distance to another middle line, while with I it must harmonize with the shorter distances in the group, but not exactly equal them, for that would make it too narrow.

It would mean, then, that the apperception of the repeated group in I (if it accords with the subject's own introspection) consists in repeated fluctuations of attention over the five strings, with no repose on any one more than another. The movement is back and forth from edge to edge, and hence needs more of an end to finish it than in a series of symmetrical units where the movement is not back and forth, but balanced and resting on the central point. In other words, in Group I there is a rhythm of movement within the group itself, as well as of the whole, while in II it is balanced and coördinated from the centre of each group, out and back, so that a longer, or at least more important end of some description is necessary to break the rhythm, and stop the series in I than in II.

It is noticeable also that H. and S. thought in both cases they were making the end spaces equal to the interspaces; but after Series I, a was made 102 and 109; and after Series II 95 and 104 respectively. This naturally raised another question: Does a series of groups, with repetitions within each, tend to make one overestimate distances between or at the end, or at least does one overestimate these distances in comparison with a series of symmetrical units?

The subjects were so unanimous in preferring a larger "embankment" after Series I than II, that it was useless to test them further on that point, and the experiment was changed to the other question according to the suggestion above.

A series of eight cards was prepared (125 mm. wide) on four of which five heavy black strips were drawn equally distant from each other, and on the others a much wider strip in the centre with another on each side near the edges. Of the two series just made, one was composed of what we have called "rhythmic units" and the other of "symmetrical units."

The subjects were asked to arrange the two separate series so that the interspaces should be exactly equal to the units. It will be observed that the rhythmic unit had a black strip on each edge, thereby apparently decreasing its size, while the edge of the symmetrical unit was white. In this respect the comparison was hardly fair, but the result was the following. The figures represent an average of two trials, and stand for the size estimate of the interspaces for each subjects respectively, in the two series.

I II
J.132.5 130
S.125122
U.133129
H.128124
R.126122
W.136133
V.129131

Average difference of estimate of both series = 2.64. Mean variation = 1.37.

It might be contended, however, that Series I is an example of optical illusion, that the card was overestimated for that reason, and the interspaces necessarily made wider. To avoid this difficulty another series was made. Two sets of cards (125 mm. wide) were prepared; one with five black strips at equal distances apart as before (excepting that the strips were made heavier), the other with six strips. The card with an odd number of strips had thereby a strip in the middle upon which the attention could centre,—possessed a kind of balance. The card with an even number of strips had, moreover, no such central line but only a space, thus preventing repose of attention, and making the unit more pronouncedly rhythmic. (It will be noticed in the foregoing table that one subject, V, made narrower interspaces in I than in II. He said he felt the units as centring around the group of three lines in the centre, not as proceeding equally to the edge. The unit became thus for him symmetrical instead of rhythmic, which could easily account for the difference in estimation.)

The results in the present case are an average of three trials:

I, 5 strips II, 6 strips
J.129137
S.125129
U.132133
H.125131
R.127138
W.126133
V.123129

Average difference in estimate of both series = 6.1. Mean variation = 2.1.

Since both these figures represent an effect usually explained by optical illusion, that factor may be counted out, and the difference in the estimate be accounted for by the difference in the rhythm of the units. The difference in estimation between the two rhythmic units, differing only in odd and even number of strips, is greater than between the rhythmic and more strictly symmetrical, and yet the two were more comparable in construction. It would seem, then, that the greater overestimation of II is due to the rhythmic movement which is not limited or driven back to a central line as in I, but, by continuing over the limits, produces a greater feeling of breadth.

The same question was experimented on in another way. Smaller strips of cardboard all 50 mm. wide, but with different designs, were hung behind the narrow window previously used. Four of each set were hung at a time behind the window, and subjects arranged them so that the interspaces appeared to equal the strips. These designs were to illustrate different points in question. The difference in estimation for an empty card, and a filled one; the difference according to the strongly centred, or rhythmic, or slant lines of the filling. These experiments were not so complete as the former ones, since the subjects were scattered; hence they represent only one trial or an average of two. But the results conform with what we have been led to expect.

I II III IV V
J.495752.55253
S.5156504951
U.5354495048
H.53524951
R.525251.54851
W.5055505052
V.5153494851
Average =51 54 50.649.4 51
Mean Variation = 1.5 1.41.2 1.06 .9

These results point to the fact that there is a tendency to overestimate the strips unless there is a strong central accent, which draws the attention back to the middle of the strip, in which case it is slightly underestimated. This would seem to be contradicted in I, where the centre is strongly marked by slant lines coming toward it. But the subjects, instead of taking the lines as pointing towards the centre, in almost every case felt them as leading away from it, and the oblique lines gave an appearance of greater breadth, which result was carried out by the greater overestimation of II. In this case, in addition to slant lines, there was no central accent, and the overestimation was proportionately large. III and IV were intended to illustrate the difference in estimate of rhythmic and symmetrical units, but although a slight difference is apparent, the subjects did not feel III as strongly rhythmic, because the black lines on the ends of the strip were ignored against the black background, and only the two central lines were taken. This made it more a balanced than a rhythmic unit, so it is not a fair type of the point in question.

We may say, in conclusion, that oblique lines (which involve a more complex muscular adjustment to perceive them) give an impression of greater distance traversed, hence are overestimated; of two rhythmic groups, the one containing an even number is more overestimated than the odd, since the movement across is unchecked, and not balanced around a central line; a series of strongly centred groups is more correctly estimated as to its interspacing, and even slightly underestimated, because of the check imposed by the centre of fixation in each group. Although these results are very uniform, a more complete series of experiments should be done on this subject, to make the conclusions thoroughly valid.

Another question was suggested by these results: Is it more agreeable to have a series of repeated space forms nearer or farther apart when a design is within? Does the design, by drawing attention to itself (especially if it be markedly central), make the objects demand narrower or wider interspacing? To test this question, four blank strips of cardboard were hung behind the narrow window, and the subjects arranged them at the distance apart which suited them best. Then two other sets of cards, of the same size, but of different designs, were hung successively the same way, and these arranged also at the most agreeable distances. One decorated card had a circle within a rectangle, the other a triangle of gilt stars. The judgments were made in pairs, i. e. the blank cards and the one with the circular design were arranged twice in succession; then the blank cards and the star design. This gives three judgments for the blank cards, two for the circular, and one for the star design, and the judgments are given in full, since an average would disguise the point in question.

I II III
J.5050
55 52
55 50
S.3570
45 20
55 35
H. 8575
90 65
U.5045
50 48
57 50
R.4525
15 10
45 23
L.9035
65 65
W.2010
25 10
25 0
V.4560
30 35
30 25

Although the favorite arrangements varied somewhat on the different days, the filled cards were with only four exceptions preferred nearer together than the empty ones at any one trial, and two of these put them equal. (The choice of V. was affected by the fact that the circular designs produced such strong after-images that he was obliged to put them farther apart, to avoid confusion with the real design.) The reason suggested by the subjects for a narrower interspacing with decorated cards was that, when they attended to the design, they paid no attention to the actual edge of the card, but the card ended so far as its interest was concerned with the design. Therefore they had to be nearer together to bring the designs, not the whole field of the cards, into a series. If, then, the design extended over all the card, and its interest was no more in the centre than the ends, would this difference in interspacing cease to be demanded?

Another series of cards was hung with a design of oblique lines over the whole field, and these arranged as the others were, at the most agreeable distances.

I IV
J.53 mm. J.53 mm.
S.45S.47
U.52U.50
R.35R.37
W.23W.43
V.35V.34

If, for the sake of comparison, the average be taken of the favorite arrangements of the four blank cards, and they compared with the interspacing of the oblique line design, it will be seen they approach each other closely, except in the case of W.

These experiments would seem to show that an empty space, or one completely covered with decoration, is taken in its entirety when repeated in the series. But when decorated, especially toward the centre, the design, instead of the whole including space, is taken as the repeated unit, and for this reason the different units must approach each other to make a satisfactory series.

To what extent does change in level and plane affect the units of a series? To test this, a series of diamond shapes was hung on the same level and at equal distances, and the subjects enjoyed them as a repeated series.

Then another row was hung above them, and halfway between.

The subjects grouped them either in twos or threes, thus transforming them into one series of similar group-units of triplets and pairs. They were asked if they could take them up and down, one after the other without grouping, as they would have done when on the same level. With a little practice two of them succeeded, but they found the series tiresome when taken in this way, and deprived of much of its pleasure.

The series was then changed by hanging a smaller diamond between the others, at the same level.

This was enjoyed even more than the other, as an alternating series, but when the smaller diamond was hung between but on a higher level although it could still be included if grouped in some way with one or two of the larger diamonds, it baffled all attempts to include it as an alternate minor unit in the other series. The two series separated, and one ran along above the other, or else a definite grouping took place, so that the large and small diamonds made one group-unit which was repeated. But to combine two different elements as major and minor units of one series, when the two were on different levels, was generally declared impossible.

Provided units stay on the same level, however, a difference in plane does not prevent their being in one series, provided the plane varies regularly, and the variation is not too great. The variation in plane of a few inches, used with these shapes, did not prevent their being taken as one series, although it much facilitated their being taken as two, if desired.

These experiments have all pointed to the fact that our pleasure in repeated space forms is an immediate experience. We do not look over the series and merely recognize that regular repetitions occur, but there is an immediate feeling of repetition, analogous to our feeling of auditory rhythm. This feeling does not always accompany a recognition that certain repetitions occur, but is a distinct experience in itself dependent upon certain conditions in the series. The series excites a certain response in the observer, which, if it corresponds with his rhythmic organization, is pleasant, and if not, is otherwise.

With a certain class of subjects this rhythmic response is very noticeable, and they feel it as a conscious part of the experience. With others, the symmetrical properties of the series are the more prominent, and they detect no rhythmic response until the necessary objective conditions for such a rhythm are violated. Then they feel it as keenly as the other type.

In a series of units, there is a rhythmic discharge of energy on each, the fixed temporal intervals being regulated by the alternating space. When the units are too near together, or when the alternating spaces vary irregularly in size, this rhythm is disturbed. If the alternating spaces vary regularly in size, a richer rhythm is introduced, which increases the pleasure up to a certain point when more variation makes it too complicated, and confusion results. When one element alternates with another, the one on which more energy is expended for any reason becomes the principal unit. The other has less significance as to its content than as to its size, for on this depends the regularity of the rhythm. Variations in the content of alternating figures must be cautious not to disturb, by the extra attention necessary to take them in, the rhythm of the whole. Variation in the principal unit may take place almost without limit, provided there is an equal amount of interest in each, thus making a rhythm of equal discharges. There must be an alternation of two, i. e. of discharge of attention and rest. However rich the rhythm is made by greater and lesser accents or groupings, the rhythm must fall eventually into a discharge of attention, and a rest-period. In the temporal type of subject, to whom the actual motion across the series is a necessary factor of the pleasure, this discharge and rest-period of attention is exactly inverse to the motion across the alternate and rest upon the unit. That is, on the principal unit is the discharge of the attention, but the rest-period of the motion across; while the alternate unit supplies the field which is travelled over, but requires but little attention.

The rhythm of the series may be not only of the units, but inside the units as well, in groups of elements. The rhythm inside such a group may be of two kinds: (1) a rhythm, which is at the same time restrained and coördinated about a central point or line, and (2) a rhythm which goes back and forth from edge to edge, and has a tendency to overstep its limits, thereby carrying on the series with more activity. The former is more connected with odd-number groups, and the latter with even, although modifications in their arrangement may reverse the effect. Since the eye moves more slowly and intricately over a curve than over a straight line,[86] it may be that that is the reason why an arched series is taken as the unit of a series, rather than the vertical supports (as it invariably is in some unfinished experiments not recorded here), whereas in a series of lintels the horizontal line of the lintels requires less muscular adjustment to perceive it than the vertical support, therefore the latter are taken as the units.

In any case, the unit of the series which attracts the most attention and interest, for whatever reason, is taken as the principal unit, and may vary in details, while the alternate must be invariable, except in certain cases where it meets other demands. There may be rhythm in a series, and at the same time symmetry with respect to a middle point. In such a case a balance must be obtained between the two different motor responses.

A series of analogies between the rhythm of sounds and of visual objects, will illustrate more forcibly the similar demands of both.

(1) Auditory Rhythm: Periodicity is necessary. Accentuation may be supplied by the subject, but there must be fixed temporal intervals, and if the temporal conditions are not fulfilled, no impression of rhythm is possible.[87]

Visual Repetition: Alternate spaces must be of invariable size, or the series is broken up. Different degrees of interest may attach to the principal unit, or the subject may group them in different ways, but the alternate spaces must be uniform, or there is no feeling of rhythmic repetition.

(2) Auditory Rhythm: Sounds must recur within a certain rate. When succession falls below, or rises above a certain rate, no impression of rhythm results.[88] A certain voluminousness is necessary for very slow measures, to make the separate elements connect themselves in a series.[89]

Visual Repetition: Objects must recur at certain proportionate distances from each other, to connect themselves into a series. Larger objects may be at a greater distance from each other than smaller ones, and still form a series.

(3) Auditory Rhythm: "Perception of rhythm is an impression, an immediate affection of consciousness, depending on a particular kind of sensory experience. It is never a construction or reflective perception that certain relations of intensity, duration, etc., do obtain."[90]

Visual Repetition: The feeling of rhythm in a visual series is immediate, and wholly distinct from the knowledge that certain objects do recur. This is especially illustrated in repetitions of three distinct units, when subjects saw and understood the scheme of repetition, but could not feel it.

(4) The number of units in an auditory group depends on the rate of succession, but any higher number of elements in a group than six or eight falls back into smaller groups.[91] Eight is about the highest number that can be held in a rhythmic group.[92]

Visual Repetition: Eight is the highest number that can be held in a rhythmic group, and some subjects can only hold seven. Many more units can be felt in a group, when the size of the including space is taken as the measure and compared; but no more than eight can be felt and recognized as the number of units it is. (There may be exceptions to this rule in either auditory or visual rhythm, but this is the norm in both cases.)

(5) Auditory Rhythm: In all long series, there is a subordination of the higher rhythmic quantities, so that opposition of simple alternate phases tends more and more to predominate over triplicated structures.[93]

Visual Repetition: However complicated the repetition becomes, with regular variations of the size of major or alternate units, the units tend to re-group themselves, and so resolve ultimately into a simple alternate repetition of two group-elements.

(6) Auditory Rhythm: "The introduction of variations in the figure of a group does not in any way affect the sense of equivalence between the unlike units."[94]

Visual Repetition: Changes in the content of the major unit do not affect the repetition provided the alternate space remains invariable.

(7) "Feeling of rhythm is more definite as we proceed in a verse, or in a series of simple sound sensations. At first the cycle is not perfectly adjusted, and complete automatism established."[95]

Visual Repetition: Observers often had to look over a series several times "to learn it" as they said, before the rhythm was felt.

To these may be added several other analogies, which, owing to the fact that visually repeated objects remain in the field, while auditory rhythm is purely successive, have other features which somewhat confuse the resemblance. The principle, however, is the same in both.

(8) Auditory Rhythm: "At the close of a period, we have a pause, during which the tension between the two opposing muscle-sets dies out, and we have a feeling of finality."[96]

Visual Repetition: An alternating series must end on the heavy unit, but since one does not look at series from left to right any more than from right to left, a heavy unit must be at both ends, not on one alone. In auditory rhythm, this final pause is not a function of any of the intervals of the period, for it comes at the end, when the sounds are no more present. But in visual repetition, after feeling the series rhythmically, it is still in the field, either as an unending series, or as a whole, in which each part is equally related to all the others. The final pause of a series that ends must be at each end, and the series perfect from either point of view. It therefore fulfils the demands of symmetry as well as rhythm, but since symmetry in its strict sense has no meaning for sound-series, this double finality of visual repetition cannot be analogued in auditory rhythm.

(9) I have found no recorded experiments of rhythms of sounds of different timbre and pitch, i. e., a regular rhythm of a bell with a violin, a piano with a whistle, etc. It would seem, however, that such a succession would produce the same irritation as a visual repetition of incongruous elements; as a circle introduced into the Greek fret, or a series of Renaissance columns and Egyptian monoliths. In both cases, the whole set of adjustments for each element would be thrown into confusion by encountering the next one, which would require a different attitude. Such a readjustment would be impossible in the space necessary for the perception of any rhythm, hence there must be congruity in elements, either auditory or visual, to be in a series at all.

(10) Auditory Rhythm: "If every alternate element of a temporally uniform sound-series receive increased stress, the interval which succeeds the unaccented sound will appear of greater duration."[97]

Visual Repetition: The distance between unit groups with a strongly accented centre appeared shorter than between rhythmic groups where the movement was not restrained at the centre, but went from edge to edge. The principles which explain these similarities are, however, different.

In the auditory rhythm, the stronger accented beat excites a greater response than the unaccented. This lasts over longer in consciousness, and for that reason the interval after the accent seems shorter.

In visual rhythm, however, the symmetrically rhythmic group drives the attention in toward the centre, and whatever excursion it makes to either side, it returns finally to the centre. In the even-number rhythmic group, there is no such central line to restrain it, and as one goes across it one has less check at the edge, the rhythm does not wholly finish, and the space is thereby overestimated. The overestimation is due to the rhythmic activity in the group which oversteps its limit.

The essentially rhythmic character of the experience is, however, the same in both. The experience of visual repetition is only one-sided when the symmetry or proportion of a finished series is regarded as the explanation of its essential character, and when the temporal rhythmic factor is neglected.