Chapter XXI: Section II: showed that the shorter filled distances are (17)

To sum up the conclusions reached by this short survey of the field of primitive art, it is clear that much of the symmetry appearing in primitive art is due (1) to the conditions of construction, as in the form of dwellings, binding-patterns, weaving and textile patterns generally; (2) to convenience in use, as in the shapes of spears, arrows, knives, two-handled baskets and jars; (3) to the imitation of animal forms, as in the shapes of pottery, etc. On the other hand (1) a very great deal of symmetrical ornament maintains itself _against_ the suggestions of the shape to which it is applied, as the ornaments of baskets, pottery, and all rounded objects; and (2) all distortion, disintegration, degradation of pattern-motives, often so marked as all but to destroy their meaning, is in the direction of geometrical symmetry. In short it is impossible to account for more than a small part of the marked symmetry of primitive art by non-æsthetic influences, and we are therefore forced to conclude an original tendency to create symmetry, and to take pleasure in it. A strong negative confirmation of this is given, as noted above, by the utter lack of symmetry of the only branch of art in which the primitive man is fully preoccupied with meaning to the neglect of shape; and by the contrast of this with those branches of art in which attention to meaning is at its minimum.

The question put at the beginning of this section must thus be answered affirmatively. There is evidence of an original æsthetic pleasure in symmetry.

III. EXPERIMENTS IN SUBSTITUTIONAL SYMMETRY.

_A. Method of Experiment._

A certain degree of original æsthetic pleasure in symmetry may be considered to have been established by the preceding section, and, without considering further the problems of real or geometrical symmetry, it may now be asked whether the pleasure aroused by the form of asymmetrical objects is not at bottom also pleasure in symmetry; whether, in other words, a kind of substitution of factors does not obtain in such objects, which brings about a psychological state similar to that produced by real symmetry.

The question what these substituted factors may be can perhaps be approached by a glance at a few pictures which are accepted as beautiful in form, although not geometrically symmetrical. Let us take, for instance, several simple pictures from among the well-known altar-pieces, all representing the same subject, the _Madonna Enthroned_ with _Infant Christ_, and all of generally symmetrical outline. It seems, then, reasonable to assume that if the variations from symmetry show constantly recurring tendencies, they represent the chief factors in such a substitutional symmetry or balance, supposing it to exist. The following pictures are thus treated in detail, M. denoting Madonna; C., Child; and Cn., Central Line. The numbers refer to the collection of reproductions used exclusively in this investigation, and further described in section IV.

1. 56, Martin Schöngauer: _Madonna in Rose-arbor._ M. is seated exactly in Cn., C. on Right, turning to Right. M. turns to Left, and her long hair and draperies form one long unbroken line down to Left lower corner. All other details symmetrical.

2. 867, Titian: _Madonna_. The picture is wider than it is high. M. stands slightly to Right of Cn.; C. on Right. Both turn slightly to Left, and the drapery of M. makes a long sweep to Left. Also a deep perspective occupies the whole Left field.

3. 248, Raphael: _Madonna_ (The Bridgewater Madonna). M. sits in Cn., turning to Left; C. lies across her lap, head to Left, but his face turned up to Right, and all the lines of his body tending sharply down to Right.

In 1, all the elements of the picture are symmetrical except the position of C. on the Right, and the long flowing line to Left. In 2, there is a slightly greater variation. The mass of the figures is to Right, and the C. entirely over against the deep perspective and the flowing line on the Left, and the direction of both faces toward that side. In 3, the greater part of C.'s figure on Left is opposed by the direction of his lines and movement to Right. Thus these three pictures, whether or not they are considered as presenting a balance, at least show several well-defined factors which detach themselves from the general symmetrical scheme. (1) Interest in C. is opposed by outward-pointing line; (2) greater mass, by outward-pointing line, deep vista, and direction of attention; and (3) again interest by direction of line and suggestion of movement.

This analysis of several æsthetically pleasing but asymmetrical arrangements of space strongly suggests that the elements of large size, deep perspective, suggested movement, and intrinsic interest are in some way equivalent in their power to arouse those motor impulses which we believe to constitute the basis of æsthetic response. It is the purpose of these experiments to follow up the lines of these suggestions, reducing them to their simplest forms and studying them under exact conditions.

But before describing the instruments and methods of this experimental treatment, I wish to speak of the articles on the 'Æsthetics of Simple Form,' published as Studies from the Harvard Psychological Laboratory, by Dr. Edgar Pierce.[15] These articles, sub-entitled 'Symmetry' and 'The Functions of the Elements' seem at first sight to anticipate the discussions of this paper; but a short analysis shows that while they point in the same direction, they nevertheless deal with quite different questions and in a different manner. In the statement of his problem, indeed, Dr. Pierce is apparently treading the same path.

[15] Pierce E.: PSYCH. REV., 1894, I., p. 483; 1896, III., p.
270.

He says: "Can a feeling of symmetry, that is, of æsthetical equality of the two halves, remain where the two sides are not geometrically identical; and if so, what are the conditions under which this can result--what variations of one side seem æsthetically equal to the variations of the other side?" Some preliminary experiments resulted in the conclusion that an unsymmetrical and yet pleasing arrangement of a varied content rests on the pleasure in unity, thus shutting out the Golden Section choice, which depends on the pleasure in variety. That is, the choices made will not in general follow the golden section, but 'when the figure consists of two halves, the pleasure must be a feeling of æsthetical symmetry.'

The final experiments were arrangements of lines and simple figures on a square, black background in which the center was marked by a white vertical line with a blue or a red line on each side. On one side of these central lines a line was fixed; and the subject had to place on the other side lines and simple figures of different sizes and different colors, so as to balance the fixed line. The results showed that lines of greater length, or figures of greater area must be put nearer the center than shorter or smaller ones--'A short line must be farther than a long one, a narrow farther than a wide, a line farther than a square; an empty interval must be larger than one filled, and so on.' And for colors, "blue, maroon and green, the dark colors, are the farthest out; white, red and orange, the bright colors, are nearest the center. This means that a dark color must be farther out than a bright one to compensate for a form on the other side. The brightness of an object is then a constant substitute for its distance in satisfying our feeling of symmetry."

Now from these conclusions two things are clear. By his extremely emphasized central line, and his explicit question to the subjects, 'Does this balance?' the author has excluded any other point of view than that of mechanical balance. His central fulcrum is quite overpowering. Secondly, his inquiry has dealt only with size and color, leaving the questions of interest, movement, and perspective untouched. But just the purpose of this experimental study is to seek for the different and possibly conflicting tendencies in composition, and to approximate to the conditions given in pictorial art. It is evident, I think, that the two studies on symmetry will not trespass on each other's territory. The second paper of Dr. Pierce, on 'The Functions of the Elements,' deals entirely with the relation of horizontal and vertical positions of the æsthetic object and of the subject to æsthetic judgments, and has therefore no bearing on this paper.

For his apparatus Dr. Pierce used a surface of black cloth stretched over black rubber, 1 m. square. Now an investigation which is to deal with complicated and varied relations, resembling those of pictures, demands an instrument resembling them also in the shape of the background. A rectangle 600 mm. broad by 400 mm. high seemed to meet this requirement better than the square of Dr. Pierce. Other parts, also, of his instrument seemed unfitted for our purpose. The tin, 5 cm. broad and confined to the slits across the center of the square, gave not enough opportunity for movement in a vertical direction, while the scale at the back was very inconvenient for reading. To supply these lacks, a scale graduated in millimeters was attached on the lower edge of the board, between a double track in which ran slides, the positions of which could be read on the scale. To the slides were attached long strips of tin covered with black cloth. On these strips figures glued to small clamps or clasps could be slipped up or down; this arrangement of coördinates made it possible to place a figure in any spot of the whole surface without bringing the hands into the field of view. The experiments were made in a dark room, in which the apparatus was lighted by an electric globe veiled by white paper and hung above and behind the head of the subject, so as not to be seen by him and to cast no shadow: in this soft light of course the black movable strips disappeared against the black background. A gray paper frame an inch and a half wide was fitted to the black rectangle to throw it up against the black depths of the dark room--thus giving in all details the background of a picture to be composed.

The differences in method between the two sets of experiments were fundamental. In Dr. Pierce's experiments the figures were pulled from one side to the other of the half-square in question, and the subject was asked to stop them where he liked; in those of the writer the subject himself moved the slides back and forth until a position was found æsthetically satisfactory. The subject was never asked, Does this balance? He was indeed requested to abstract from the idea of balance, but to choose that position which was the most immediately pleasing for its own sake, and so far as possible detached from associations.

I have said that Dr. Pierce intentionally accentuated the center. The conditions of pictorial composition suggest in general the center only by the rectangular frame. Most of my experiments were, therefore, made without any middle line; some were repeated with a middle line of fine white silk thread, for the purpose of ascertaining the effect of the enhanced suggestion of the middle line.

But the chief difference came in the different treatment of results. Dr. Pierce took averages, whereas the present writer has interpreted individual results. Now, suppose that one tendency led the subject to place the slide at 50 and another to place it at 130 mm. from the center. The average of a large number of such choices would be 90--a position very probably disagreeable in every way. For such an investigation it was evident that interpretation of individual results was the only method possible, except where it could be conclusively shown that the subjects took one and only one point of view. They were always encouraged to make a second choice if they wished to do so, as it often happened that one would say: 'I like both of these ways very much.' Of course, individual testimony would be of the highest importance, and a general grouping into classes and indication of the majority tendency would be the only way to treat the results statistically. And indeed in carrying out the experiments this caution was found absolutely necessary. In all but one or two of the sections, the taking of averages would have made the numerical results absolutely unintelligible. Only the careful study of the individual case, comparison of various experiments on the same person to find personal tendencies, and comparison of the different tendencies, could give valuable results for the theory of symmetry.

The first question to be taken up was the influence of right and left positions on choice. A long series of experiments was undertaken with a line 80×10 mm. on one side and a line 160×10 mm. on the other, in which the positions of these were reversed, and each in turn taken as fixed and variable, with a view to determining the effect of right and left positions. No definite conclusions emerged; and in the following experiments, most of which have been made for both right and left positions, the results will be treated as if made for one side alone, and, where averages are taken, will be considered as indifferently left or right.

The experiments of Dr. Pierce were made for only one position of the fixed line--at 12 cm. distance from the center. The characteristic of the following experiments is their reference to all positions of the fixed line. For instance a fixed line, 10 cm. in length at 12 cm. distance from the center, might be balanced by a line 5 cm. in length at 20 cm. distance. But would the distance be in the same proportion for a given distance of the fixed line of say 20 or 25 cm.? It is clear that only a progressive series of positions of the fixed line would suggest the changes in points of view or tendencies of choice of the subject. Accordingly, for all the experiments the fixed line or other object was placed successively at distances of 20, 40, 60 mm., etc., from the center; or at 40, 80 mm., etc., according to the character of the object, and for each of these fixed points the subject made one or two choices. Only an understanding of the direction in which the variable series moved gave in many cases an explanation for the choice.

Each choice, it should be added, was itself the outcome of a long series of trials to find the most pleasing position. Thus, each subject made only about ten choices in an hour, each of which, as it appears in the tables, represents a large number of approximations.

_B. Experiments on Size._

I have said that different tendencies or types of choice in arrangement appeared. It will be convenient in the course of explaining in detail the method of experiment, to discuss at the same time the meaning of these types of choice.

From analysis of the pictures, the simplest suggestion of balance appeared in the setting off against each other of objects of different sizes;--an apparent equivalence of a large object near the center with a small object far from the center; thus inevitably suggesting the relations of the mechanical balance, or lever, in which the heavy short arm balances the light long arm. This was also the result of Dr. Pierce's experiments for one position of his fixed line. The experiments which follow, however, differ in some significant points from this result. The instrument used was the one described in the preceding section. On one side, in the middle of the vertical strip, was placed the 'fixed' line, denoted by F., and the subject moved the 'variable' line, denoted by V., until he found the arrangement æsthetically pleasing. The experimenter alone placed F. at the given reading, and read off the position of V. After the choice F. was placed at the next interval, V. was again tried in different positions, and so on. In the following tables the successive positions of F. are given in the left column, reading downward, and the corresponding positions of V. in the right column. The different choices are placed together, but in case of any preference the second choice is indicated. The measurements are always in millimeters. Thus, F. 40, V. 60, means that F. is 40 mm. to one side of the center, and V. 60 mm. to the opposite side. F. 80×10, V. 160×10, means that the white cardboard strips 80 mm.×10 mm., etc., are used. The minus sign prefixed to a reading means that the variable was placed on the side of the fixed line. An X indicates æsthetic dislike--refusal to choose. An asterisk (*) indicates a second choice.

The following tables are specimen sets made by the subjects _C, O_, and _D_.

I. (a) F. 80×10, V. 160×10.

F. V.
C. O. D.

40 62, 120 166, 130 28, 24
80 70, 110 104, 102 80, 126
120 46, X 70, 46 68,--44, 128*
160 26, 96 50, 25 85, 196,--88*
200 20, X 55, X --46, 230,* 220,--110*

I. (b) F. 160×10, V. 80×10.

F. V.
C. O. D.

40 74, 64 60, 96 27, 34
80 76, 65 72, 87 55, 138
120 60, 56 48, 82 70, 174
160 29, 74 16, 77 --114, 140, 138, 200
200 96, 36 25, 36 177,--146,--148, 230

Now, on Dr. Pierce's theory, the variable in the first set should be nearer the center, since it is twice the size of the fixed line;--but the choices V. 120, 166, 130 for F. 40; V. 110, 104, 102, 126 for F. 80; V. 128 for F. 120; V. 196 for F. 160; V. 230, 220 for F. 200, show that other forces are at work. If these variations from the expected were slight, or if the presence of second choices did not show a certain opposition or contrast between the two positions, they might disappear in an average. But the position of F. 40, over against V. 120, 166, 130, is evidently not a chance variation. Still more striking are the variations for I. (_b_). Here we should expect the variable, being smaller, to be farther from the center. But for F. 40, we have V. 27, 34; for F. 80, all nearer but two; for F. 120, V. 60, 56, 48, 82, 70; for F. 160, V. 29, 74, 16, 77, 138, and for F. 200, V. 96, 36, 25, 36, 177--while several positions on the same side of the center as the constant show a point of view quite irreconcilable with mechanical balance.

II. (a) F. 2 LINES 80×10. V. SINGLE LINK 80×10.

F. V.
C. O. P.

40- 60 58, 114* 138, 20 96, 84 166
60- 80 48 40, 138* 100, 56 150
80-100 64 70, 162* 47, 87 128
100-120 70 to 80 60 53, 53 X
120-140 58 82 50, 48 35
140-160 74 95 to 100 22, 32 37
160-180 72 102 X, X 42
180-200 90 X X, X 50

Here the variable should supposedly be the farther out; but we have V. 58, 20 for F. 40-60; V. 48, 40, 56 for F. 60; V. 64, 70, 87 for F. 80; no larger choice for F. 100-120; indeed, from this point on everything nearer, and very much nearer. We can trace in these cases, more clearly perhaps than in the preceding, the presence of definite tendencies. _O_ and _P_, from positions in accord with the mechanical theory, approach the center rapidly; while _C_ is seldom 'mechanical,' but very slowly recedes from the center. The large number of refusals to choose assures us that the subjects demand a definitely pleasant arrangement--in other words, that every choice is the expression of a deliberate judgment.

Taking again the experiments 1. (a) and 1. (b), and grouping the results for nine subjects, _C_, _O_, _A_, _S_, _H_, _G_, _D_, and _P_, we obtain the following general types of choice. The experiments were repeated by each subject, so that we have eighteen records for each position. I should note here that preliminary experiments showed that near the frame the threshold of difference of position was 10 mm., or more, while near the center it was 4 or 5 mm.; that is, arrangements were often judged symmetrically equal which really differed by from 4 to 10 mm., according as they were near to or far from the center. In grouping types of choice, therefore, choices lying within these limits will be taken as belonging to the same type.

EXP. 1. (a) F.(80 X 10). V.(160 X 10).

1. F. 40. V. 40.¹

Types of Choice for V.
(1) 24 24 25 28
(2) 40 42 45 45 40 40 40
(3) 62 65
(4) 100 105 1O9 120 130 136 120
(5) 166 180 200 200 200 200 160 160

¹This table is obtained by taking from the full list, not given
here, of 1. (b) F. (l60 X 10), V. (80 X 10), those positions of
160 X 10 where the variable 80 X 10 has been placed at or near
40, thus giving the same arrangement as for 1. (a).

It might be objected that a group 40-65 (2-3) would not be larger than one of 100-136 (4), but the break between 45 and 62 shows the zones not continuous. Moreover, as said above, the positions far from the center have a very large difference threshold.

I. (a) 2. F. 80:--(1) 24, (2) 50, (3) 68 70, (4) 80 85 94 95
85, (5) 102 104 110 120 124 126 125* 132, (6) 187; also V.
80:--(2) 40 40, (4) 80, (5) 120 120, (6) 160 160.

I. (a) 3. F. 120:--(1) 44 46, (2) 64 48 70 70, (3) 85 95 97
91, (4) 113 113 118, (5) 168 169 178;--44, X; also V.
120:--(1) 40 40, (3) 80 80 80, (4) 120 120, (5) 160 160.

I. (a) 4. F. 160:--(1) 25 26, (2) 40 50 57, (3) 82 85 95 100*,
(4) 114 115 130, (5) 145 145 156 162, (6) 196,
(7)--88*--150*--105.

I. (a) 5. F. 200:--(1) 20 23 28 36, (2) 55, (3) 108 124 130*,
(4) 171 189 199 195, (5) 220 230*, (6)--46--90--110*.

On comparing the different groups, we find that in 1 and 2 there is a decided preference for a position somewhat less than half way between center and frame--more sharply marked for 1 than for 2. From 3 onward there is a decided preference for the mechanical arrangement, which would bring the larger strip nearer. Besides this, however, there are groups of variations, some very near the center, others approaching to symmetry. The maintenance of geometrical symmetry at a pretty constant ratio is to be noted; as also the presence of positions on the same side of the center as the fixed line. Before discussing the significance of these groups we may consider the results of Experiment II. (F. double line 80×10, V. single line 80×10) without giving complete lists.

We notice therein, first of all, the practical disappearance of the symmetrical choice; for F. 40-60, 60-80, 80-100, a tendency, decreasing, however, with distance from the center, to the mechanical arrangement; for F. 100-120, and all the rest, not one mechanical choice, and the positions confined almost entirely to the region 35-75. In some cases, however, the mechanical choice for (1) 40-80, (2) 60-80, was one of two, _e.g._, we have for (1) 20 and 138, for (3) 70 and 162; in the last two cases the mechanical being the second choice.

Now the reversals of the mechanical choice occur for Exp. I. in 1 and 2 (F. 40 and F. 80); that is, when the small fixed line is near the center, the larger variable is distant. For Exp. II. the reversals, which are much more marked, occur in all cases _beyond_ F. 40, F. 60 and F. 80; that is, when the double constant line is far from the center, the single variable approaches. If the mechanical theory prevailed, we should have in Exp. I. the lines together in the center, and in Exp. II. both near the fringe.

From the individual testimony, based both on I. (_a_) and I. (_b_), it appears that subject _M_ is perfectly uniform in mechanical choice when the fixed line is the small line--_i.e._ when it moves out, the larger is placed near the center; but when the conditions of mechanical choice would demand that, as the larger fixed line moves out, the small variable one should move out farther, he regularly chooses the reverse. Nevertheless, he insists that in just these cases he has a feeling of equilibrium.

_A_ also takes the mechanical choice as the small fixed line goes farther from the center; but when the fixed line is large and leaves the center, he reverses the mechanical choice--evidently because it would take the small line too far out. As he says, 'he is always disturbed by too large a black space in the center.'

_G_ almost always takes the mechanical choice;--in one whole set of experiments, in which the fixed line is the large line, he reverses regularly.

_H_ takes for F. (80×10) the mechanical choice only for the positions F. 160 and F. 200--_i.e._, only when F. is very far from the center and he wishes V. (160×10) nearer. For F. (160×10) he makes six such choices out of ten, but for positions F. 160 and F. 200 he has V. 44, 65 and 20.

_S_ takes for F. (160×10) at F. 120, V. 185 and-70; says of V. 185, which is also his choice for F. (160×10) at F. 80, 'I cannot go out further, because it is so hard to take in the whole field.' For F. (160×10) at F. 200, he has V. 130 and 60; says of V. 60, 'Very agreeable elements in connection with the relation of the two lines.'

_C_ takes for F. (80×10) only one mechanical choice until it is at F. 120. Then always mechanical, _i.e._, nearer center; for F. (160×10) makes after the position F. 40 no mechanical choice, _i.e._, V. is nearer center.

It is evident from the above tables and individual cases that the reversals from the mechanical choice occur only when the mechanical choice would bring both lines in the center, or both near the edges, and the subjective testimony shows from what point of view this appears desirable. The subjects wish 'to take in the whole field,' they wish 'not to be disturbed by too large a black space in the center'; and when, in order to cover in some way the whole space, the small line is drawn in or the large one pushed out, they have, nevertheless, a feeling of equilibrium in spite of the reversal of mechanical balance.

Accepting for the present, without seeking a further psychological explanation, the type of 'mechanical balance,' in which amount of space is a substitute for weight, as the one most often observed, we have to seek some point of view from which this entire reversal is intelligible. For even the feeling that 'the whole field must be covered' would hardly account for an exact interchanging of positions. If size gives 'weight,' why does it not always do so? A simple answer would seem to be given by the consideration that we tend to give most attention to the center of a circumscribed space, and that any object in that center will get proportionately more attention than on the outskirts. The small line near the center, therefore, would attract attention by virtue of its centrality, and thus balance the large line, intrinsically more noticeable but farther away. Moreover, all the other moments of æsthetic pleasure, derived from the even filling of the space, would work in favor of this arrangement and against the mechanical arrangement, which would leave a large black space in the middle.

The hypothesis, then, that the demand for the filling of the whole space without large gaps anywhere enters into competition with the tendency to mechanical balance, and that this tendency is, nevertheless, reconciled with that demand through the power of a central position to confer importance, would seem to fit the facts. It is, of course, clear that neither 'mechanical balance' nor the balance of 'central' with 'intrinsic' importance have been yet accounted for on psychological grounds; it is sufficient at this point to have established the fact of some kind of balance between elements of different qualities, and to have demonstrated that this balance is at least not always to be translated into the 'mechanical' metaphor.

_C. Experiments on Movement._

In the preceding experiments the element of size was isolated, and it was sought to discover, in pleasing combinations of objects of different sizes, the presence of some kind of balance and the meaning of different tendencies of arrangement. The relative value of the two objects was taken as determined on the assumption, supported by common sense, that under like conditions a large object is given more attention than a small one. If the unequal objects seem to balance each other, then the only other condition in which they differ, their distance from the center, must be the cause of their balancing. Thus the influence of relative position, being the only unknown quantity in this balance-equation, is easily made out.

The following experiments will deal with the as yet quite undetermined elements of suggested movement, perspective and intrinsic interest. By combining objects expressing them, each with another simple object of the same size, another equation will be obtained in which there is only one unknown quantity, the sizes of the objects being equal and the influence of relative position being at least clearly indicated.

1. Movement.

The experiments on suggestion of movement were made by _C_, _O_ and _P_. Suggestions of movement in pictures are of two kinds--given by lines pointing in a direction which the eye of the spectator tends to follow, and by movement represented as about to take place and therefore interpreted as the product of internal energy. Thus, the tapering of a pyramid would give the first kind of suggestion, the picture of a runner the second kind. Translated into terms of experiment, this distinction would give two classes dealing with (A) the direction of a straight line as a whole, and (B) the expression of internal energy by a curve or part of a line. In order to be able to change the direction of a straight line at a given point, a strip of tin two inches long was fastened by a pivot to the usual clasp which slipped up and down on the vertical black strip. The tin strip could be moved about the pivot by black threads fastened to its perforated ends. A strip of cardboard glued upon it would then take its direction. The first experiments, made with the usual 80×10 strip, proved very disagreeable. The subject was much disturbed by the blunt ends of the strip. The variable (pivoted) line was then slightly pointed at the upper end, and in the final experiments, in which both are oblique, both strips were pointed at each end. In Exp. III. a line pointing at an angle from the perpendicular was set over against a line of the same dimensions in the ordinary position.

Exp. III. (_a_) F. (80×10) pointed up toward center at 145°,
V. (80×10).

F. 40:--(1) 39 48 48, (2) 60 66 68, (3) 97 97, (4) 156* 168*.

F. 60:--(1) 45, (2) 60 62 65 68 90, (3) 90 94, (4) 117 128 152
155.

F. 80:--(1) 50 44*, (2) 74 76 77, (3) 94 100 106 113 115 116,
(4) 123 124* 140 165* 169*.

F. 100:--(1) 36 58 60 65* 65 74 77 80 87, (2) 98 108 118, (3)
114* 168 186* 170 136*.

F. 120:--(1) 40 46 54 60 63 76 96 97 111, (2) 115 120 126*
137*, (3) 170 170*.

F. 140:--(1) 45 52 65 65 76 76 86 90, (2) 109 111, (3) 125
140*, (4) 168*.

F. 160:--(1) 38 50 50 60, (2) 80 90 96 98 98, (3) 176*.

F. 180:--(1) 21 23, (2) 54 70 84 90, (3) 100 100 108 114 120,
(4) 130 145*.

F. 200:--(1) -2, (2) 33 37 50, (3) 106 110 to 120 115 120 130
132 138 142.

The most striking point about these groups is the frequency of positions far from the center when F. also is far out. At F. 120, a position at which the mechanical choice usually prevails if F. is smaller, a very marked preference indeed appears for positions of V. nearer the center--in fact, there is only one opposing (first) choice. Now, if it is not the wide space otherwise left which pulls the variable in,--and we see from a note that the subjects have no feeling of a large empty space in the center,--it must be that F. has the same effect as if it were really smaller than V., that is, mechanically 'light.' We see, in fact, that the moment F. has passed the point, between 80 and 100, at which both lines close together in the center would be disagreeable, the preference is marked for inner positions of V., and I repeat that this cannot be for space-filling reasons, from the testimony of F. 200 (3).

And this 'lightness' of the line pointed in at 45° is indeed what we should have expected _a priori_ since we found that objective heaviness is balanced by a movement out from the center on the mechanical principle. If movement out and objective heaviness are in general alike in effect, then movement in and objective lightness should be alike in effect, as we have found to be the case from the preceding experiments. The inward-pointed line does not actually move in, it is true, but it strongly suggests the completion of the movement. It enters into the 'mechanical' equation--it appears to balance--as if it had moved.

The point, however, in which this 'lightness' of the inward-pointed line differs from that of the small or short line is its space-filling quality. It suggests movement in a certain direction, and, while giving the mechanical effect of that movement as completed, seems also in a sense to cover that space. We see from F. 180 (3), (4), and 200 (3), that the subject does not shrink from large spaces between the lines, and does not, as in Exp. I. (_a_), 4 and 5, bring the variable, which in both cases is evidently 'heavier,' to the center. This must be from the fact that the empty space does not in this experiment feel empty--it is filled with energy of the suggested movement. This view is confirmed by the dislike which the subjects show to the position F. 40; F., being 'lighter,' but the object of attention as close to the center, might well balance V. far out. But as if the whole variable field would be in that case 'overfilled,' the records show 50 per cent. of refusals to choose for this position.

In brief, then, a straight line suggesting movements in a certain direction has the effect, in the general scheme of mechanical balance, of a static position in which this movement has been carried out, with the added suggestion of the filling of the space over which such movement is suggested.

A few additional experiments were made with a point on the upper end of V. The groups of III. (_a_) are maintained almost exactly: F. 120 is again strikingly 'mechanical'; after F. 120 there are only two mechanical choices out of nineteen; while for F. 40, as in Exp. III. (_a_), out of six choices, four are either refusals or question-marked.

Exp. IV. Both lines took oblique directions, and, to get a pleasing effect, were pointed at both ends. They were of the usual size, 80×10 mm., but 1 mm. broader to allow for the effect of length given by the points. F. was fixed at 45°, as in III. (_a_), on the points 40, 80, 120 and 160; V. moved also on fixed points, 60, 100, 140, 180, for each position of F., but on each point was adjusted at a pleasing angle. Thus, there were four positions of V. to each of F., each with one or two angular positions; V. was always in the first quadrant.

The numbers of the table give the angular degrees of V.

F. 40, V. 60:--(1) 10 12 38 44, (2) 50 57* 60, (3) 70.
V. 100:--(1) 15 15 30 30, (2) 50 55 50, (3) 69 70*.
V. 140:--(1) 12* 14 18 18, (2) 60 60 49, (3) 72.
V. 180:--(1) 12 10 38, (2) 60 50, (3) 75.
[Many refusals at 140 and 180.]

F. 80, V. 60:--(1) 11, (2) 25 35 36*, (3) 45 48 55 58 60, (4) 69.
V. 100:--(1) 16 15, (2) 24 27 35 40, (3) 52, (4) 62 74*.
V. 140:--(1) 10 15 16, (2) 22 28, (3) 40 40 59 59, (4) 70.
V. 180:--(1) 14 8, (2) 28, (3) 41 46, (4) 68 79.

F. 120, V. 60: (1) 28, (2) 42 44 35, (3) 52 58 62 65 65.
V. 100:--(1) 9, (2) 23 25, (3) 38 40 40 42 58, (4) 68 70.
V. 140:--(1) 10, (2) 20 26 21* 24 29, (3) 34 42 42 44 55*, (4) 75.
V. 180:--(1) 17 26, (2) 40 42 46, (3) 62 64 70 70*.

F. 160, V. 60:--(1) 20 39, (2) 18, (3) 58 60 64 68 70.
V. 100:--(1) 23 25 30 38, (2) 44 44 49, (3) 55 58 65.
V. 140:--(1) 5, (2) 31 35 40 40 32, (3) 54 55 68.
V. 180:--(1) 50 50 58 60, (2) 75.

The tendency to mechanical balance would, according to our previous analysis, lead the variable to take a direction which, in its suggestion of motion inward, should be more or less strong according as it were farther from or nearer to the center than the fixed line. Such motion inward would, of course, be more strongly suggested by an angle less than 45° than by an angle greater than 45°, and it seems that the angles chosen are in general in harmony with this expectation. For the positions where F. is nearer the center than V. there is a preponderance of the angles less than 45° (cf. F. 40 and F. 80, V. 100 and 140; F. 120, V. 140, 180). When V. passes over to a position farther from the center than F. (_e.g._, from F. 80, V. 60, to F. 80, V. 100 and from F. 120, V. 60, to F. 120, V. 140) the change is marked. In every case where F. is farther from the center than V. (_i.e._, F. 80, V. 60; F. 120, V. 60 and V. 100; F. 160, V. 60, V. 100 and V. 140), there are to be noticed a lack of the very small angles and a preponderance of the middle and larger angles. F. 160, V. 140 and 180 seem to be the only exceptions, which are easily explainable by a dislike of the extremely small angle near the edge; for it appears from the remarks of the subjects that there is always a subconsciousness of the direction suggested by the lower pointed end of the line. For the outer positions of both lines, a large angle would leave the center empty, and a small one would be disagreeable for the reason just given; and so we find, indeed, for F. 160, V. 100, 140, 160, the middle position the favorite one.

The representation of action may be translated into experimental terms by expressing it as a line which changes its direction, thus seeming to be animated by some internal energy. The forms chosen were three curves 'bulging' from a straight line in differing degrees, and two straight lines with projections. _C_ and _O_ were the subjects. The results are given in outline.

Exp. V. Curve I. See Fig. 12, I

(1) Curve out (turned away from center).

(_a_) F. (80×10), V. Curve.

About half the positions of V. are farther from the center
than F. _O_ at first refuses to choose, then up to F. 120 puts
V. farther from the center than F. _C_ has a set of positions
of V. nearer the center and several second choices farther
than F.

(_b_) F. Curve, V. (80×10).

No position of V. nearer center than F. _O_ puts line farther
out up to F. 160, then nearer than F. _C_ has a set of nearly
symmetrical choices and another where V. is much farther out
than F.

(2) Curve in (turned toward center).

(_a_) F. (80×10), V. Curve.

_C_ is absolutely constant in putting V. farther from center
than F. _O_, after F. 100, brings it slightly nearer.

(_b_) F. Curve, V. (80×10).

_C_, except for F. 40, invariably puts V. nearer center than
F. _O_ moves between 90 and 135, putting V. farther to F.
100, nearly symmetrical at F. 100 and 120, and after F. 120,
from 100 to 135.

Exp. V. Curve II. See Fig. 12, II.

(1) Curve out.

(_a_) F. (80×10), V. Curve.

In every case but one V. is nearer center than F.

(_b_) F. Curve, V. (80×10).

_C_ puts V. farther from center than F. _O_ puts V. farther or
symmetrical up to F. 120, then nearer than F.

(2) Curve in.

(_a_) F. 80×10, V. Curve.

_C_ has V. always farther from center than F., but a second
parallel set, omitting F. 40 (all second choices), of
symmetrical positions. _O_ begins with V. farther from center,
but from F. 120 has V. always nearer, though gradually
receding from the center.

(_b_) F. Curve. V. (80×10).

_C_, refusing for F. 40, continues his parallel sets, one with
V. always nearer than F., another with symmetrical positions.
_O_ begins with V. nearer, changes at F. 120, and continues
with V. farther.

Recapitulating these results, grouping together the outward and inward positions of the curves, and indicating the distance of the line from the center by C.-L., and of the curve from the center by C.-Cv., we have:

_Out_.

Cv. I. (_a_) Indeterminate.
(_b_) C.-Cv. < C.-L. (except where large gap would be left).

Cv. II. (_a_) C.-Cv. < C.-L. (all cases but one).
(_b_) C.-Cv. < C.-L. (except where large gap would be left).

_In._

Cv. I. (_a_) C.-Cv. > C.-L. (except a few cases to avoid gap).
(_b_) C.-Cv. > C.-L. (more than half of cases).

Cv. II. (_a_) C.-Cv. > C.-L. (except a few cases to avoid gap).
(_b_) C.-Cv. > C.-L. (except a few cases to avoid gap).

It is evident that in the great majority of cases when the curve turns out it is placed nearer the center, when it turns in, farther from the center, than the straight line. The numerical differences for choices of the same type for the two curves are slight, but regular, and the general tendencies are more sharply marked for the line of greater curvature. When Curve II. is 'out,' it is usually nearer the center than Curve I. for the corresponding positions of the straight line; when 'in' it is always farther from the center than Curve I. The greater curvature of II. has clearly produced this difference, and the effect of the curvature in general is evidently to make its side 'lighter' when turned toward the center, and 'heavier' when turned away. Thus, all but the exceptions already noted seem to belong to the mechanically balanced arrangement, in which the suggestion of force working in the direction of the curve has the same effect as, in Exp. IV., the direction of the line. The exceptions noted, especially numerous choices of _O_, seem governed by some fixed law. The evidence would seem to be overwhelming that the reversals of the mechanical balance occur only where the lines would be crowded together in the center or would leave an empty gap there. The remaining exceptions--the symmetrical choices mentioned, made by _C_--are explained by him as follows. He says there are two ways of regarding the curve, (1) as a striving in the direction of the 'bulge,' and (2) as the expression of a power that presses together; and that the usual choices are the result of the first point of view, the symmetrical choices of the second. Naturally, a pressure bending down the line would be conceived as working in a vertical direction, and the line would be treated as another (80×10)--giving, as is the case, symmetrical positions. Thus, we may consider the principle of the suggestion of movement by a curve, as giving the same effect as if the movement suggested had actually taken place, to have been established, the positive evidence being strong, and the exceptions accounted for. It is worth noting that the curve-out series are always more irregular--the subject repeating that it is always harder to choose for that position. Probably the demands of space-filling come into sharper conflict with the tendency to mechanical balance, which for the outward curve would always widely separate the two lines.

Exp. V. Curve III. See Fig. 12, III.

A series with the upper end turned out from the center was unanimously pronounced as ugly. The inward position only appears in the results, which are given in full.

(_a_) F. (80×10), V. CURVE.

F. V.
O. C.

40 106 126 68 73
80 106 128 109 102
120 140 88 156 110* 154 72*
160 104 66 182 80 136* 130*
200 X 52 178 220* 162

(_b_) F. CURVE, V. (80×10)

F. V.
O. C.

40 126 122 73 80
80 122 128 66 112* 40
120 90 116 97 156* 55 105
160 65 43 120 182* 87 134
200 70 50 148 66

This curve exemplifies the same principles as the preceding. _O_ takes the natural mechanical choice from (_a_) F. 40 to F. 120, and from (_b_) F. 120 to F. 200. A mechanical choice, however, for (_a_) F. 120 ff., and for (_b_) F. 40 to F. 120, would have brought the lines too far apart in (_a_), and too near together in (_b_), hence the reversal. _C_ inclines always to the mechanical choice, but recognizes the other point of view in his second choices.

Exp. V. Curve IV. See Fig. 12, IV.

Curve in.

(_a_) F. (80×10), V. Curve.

_C_ puts V. always further than F. and, even for F. 200, has
V. 230, X. _O_ puts V. farther up to F. 120, then puts it
nearer than F., and always refuses to choose for F. 200.

(_b_) F. Curve, V. (80×10).

_C_ always puts V. nearer than F. _O_ puts V. farther for F.
40 and F. 80, beyond that, nearer than F.; but refuses to
choose once each for F. 40, and F. 200.

The same principles of choice appear. _C_ maintains the
mechanical choice, and _O_ reverses it only beyond (_a_) F.
120, and up to (_b_) F. 120, to fill space well, showing his
preference for the mechanical choice by changing into it at an
unusually early point.

Exp. V. Curve V. See Fig. 12, V.

Curve in.

(_a_) F. (80×10), V. Curve.

_C_ puts V. farther than F., except for F. 200, V. 125 and X.
_O_ also, changing as usual at F. 120 to V. nearer than F.

(_b_) F. Curve, V. (80×10).

_O_ puts V. always farther than F. _O_ has V. farther for F.
40 and F. 80, then nearer than F. Refuses to choose for F.
200. Results exactly parallel with those of Curve IV.

Comparing all the results of this whole series of experiments on the suggestion of movement, we may conclude that movement, whether suggested by a whole line or part of a line, produces in terms of mechanical balance the same effect that the balanced object would produce after the completion of the suggested motion. This tendency to balance, it appears, lies at the basis of our preference; it often gives way, however, before considerations of space-filling, when the figure which on the scheme of mechanical balance is weaker, gains interest and so 'heaviness' by being brought nearer the center.

_D. Experiments on Interest._

By intrinsic interest is meant the interest which would attach to an object quite apart from its place in the space composition. In a picture it would be represented by the interest in an important person, in an unusual object, or in an especially beautiful object, if that beauty were independent of the other forms in the picture--as, for instance, a lovely face, or a jeweled goblet, etc. When the question of the influence of interest on composition came to be discussed, it was found very difficult to abstract the form of the object from the content presented; still more difficult to obtain an effect of interest at all without the entrance of an element of form into the space arrangement. Disembodied intellectual interest was the problem, and the device finally adopted seemed to present, in as indifferent a form as possible, a content whose low degree of absolute interest was compensated for by constant change. Stamps of various countries in black and white reproductions and very small outline pictures on squares of the same size as the stamps were taken as material. The figures were so small in relation to the board that any influence on composition of the lines composing them was impossible; the outline pictures, indeed, gave to the eye which abstracted from their content an impression scarcely stronger than the neighboring blank square.

The first set of experiments (VI.) had a small outline picture on the side, and on the other a white paper square of the same size. The necessary interest was given in the form of novelty by changing the picture for every choice. The subjects were _M_, _G_ and _D_. The results were of the same type for each subject and could therefore be averaged.

Exp. VI. (1).

_(a)_ F. Picture, V. Blank. Eight choices for each. _M_,
Average: V. 17 mm. farther from center. _G_, Average: V. 10
mm. farther from center. (Symmetrical position beyond F. 120.)
_D_, Average: V. 25.8 mm. farther from center.

_(b)_ F. Blank, V. Picture. _M_, Average: V. 33 mm. nearer
center. _G_, Average: V. 4 mm. nearer center. (Symmetrical
beyond F. 120.) _D_, Average: V. 30 mm. nearer center. (But V.
farther at F. 40.)

These results are practically unanimous. They show that an object which possesses intrinsic interest acts like a mechanically heavy object, being placed nearer the center than a blank. Two marked deviations from the mechanical choice occur--although they have not affected the average sufficiently to destroy the general harmony of results. _G_, in both _(a)_ and _(b)_, chooses symmetrical positions from F. 120 on. His notes ['_(a)_ F. 140, V. 136, picture unimportant'; '_(b)_ F. 120 and ff., loses relation as they separate'; '_(b)_ F. 160, picture makes no impression'] show clearly that for positions wide apart the picture, already a faint outline, becomes only a white square like the other and is put into geometrical symmetry.

Exp. VI. (2), by _G_ and _D_. A stamp on one side unchanged, took the place of the blank; on the other side the stamp was changed for each choice.

_(a)_ F. unchanged stamp; V. changed stamp.

_D_. Two series, (1) V. always nearer center. (2) Same, except
F. 20, V. 52; F. 80, V. 94; F. 140, V. 152; F. 160, V. 175.

_G_. Two series. (1) V. much farther from center up to F. 140,
then nearer. (2) V. farther throughout, except F. 160, V. 121.

_(b)_ F. changed stamp; V. unchanged stamp.

_D_. Two series. (1) V. farther up to F. 100, then
symmetrical. (2) V. farther up to F. 100, then symmetrical or
nearer center.

_G_. Two series. (1) V. farther up to F. 120, then
symmetrical, and beyond F. 140, nearer center. F. 140, V. 63.
(2) V. much farther up to F. 120, then nearer center, but more
nearly symmetrical than (1). A complete series of second
choices beginning at F. 40, V. slightly nearer center than F.

Analyzing results, we find the changed stamp, which has the interest of novelty, nearly always nearer the center than the unchanged. This would indicate a balance of the mechanical type, in which the interest makes an object 'heavier.' The exceptions are in _(a)_ four choices of _D_, _G_ to F. 140, and in _(b)_, _D_'s choice beyond F. 200, and _G_'s beyond F. 120. The deviations are thus seen to be all of the same type: for positions of F. near the center, when a mechanical choice would have brought V. still nearer [(_a_)], it is instead put farther away; for positions of F. far from the center, when a mechanical choice would have put V. still farther away [(_b_)], it is instead brought near. The exceptions are thus fully accounted for by the demand for space-filling.

_E. Experiments on Depth._