Volume 1 — STUDIES IN SYMMETRY.1

STUDIES IN SYMMETRY.1

BY ETHEL D. PUFFER.

I. THE PROBLEMS OF SYMMETRY.

The problem of æsthetic satisfaction in symmetrical forms is easily linked with the well-known theory of 'sympathetic reproduction.' If there exists an instinctive tendency to imitate visual forms by motor impulses, the impulses suggested by the symmetrical form would seem to be especially in harmony with the system of energies in our bilateral organism, and this harmony may be the basis of our pleasure. But we should then expect that all space arrangements which deviate from complete symmetry, and thus suggest motor impulses which do not correspond to the natural bilateral type would fail to give æsthetic pleasure. Such, however, is not the case. Non-symmetrical arrangements of space are often extremely pleasing.

This contradiction disappears if we are able to show that the apparently non-symmetrical arrangement contains a hidden symmetry, and that all the elements of that arrangement contribute to bring about just that bilateral type of motor impulses which is characteristic of geometrical symmetry. The question whether or not this is the fact makes the leading problem of this paper, and the answer to it must throw light on the value of the theory itself.

An exhaustive treatment of our question would thus divide itself into two parts; the first dealing with real (or geometrical) symmetry, the second with apparent asymmetry; the first seeking to show that there is a real æsthetic pleasure in geometrical symmetry, and that this pleasure is indeed based on the harmony of the motor impulses suggested by symmetry, with the natural motor impulses of the human organism; the second seeking to show in what manner æsthetically pleasing but asymmetrical arrangements conform to the same principles. Within these two groups of problems two general types of investigation are seen to be required; experiment, and the analysis of æsthetic objects.

The main question, as stated above, is of course whether the theory can explain our pleasure in arrangements which are completely or partly symmetrical. It is, however, an indispensible preliminary to this question, to decide whether the pleasure in symmetrical arrangements of space is indeed immediate and original. If it were shown to be a satisfaction of expectation, bred partly from the observation of symmetrical forms in nature, partly from the greater convenience of symmetrical objects in daily use, the whole question of a psychophysical explanation would have no point. If no original æsthetic pleasure is felt, the problem would be transformed to a demand for the explanation of the various ways in which practical satisfaction is given by symmetrical objects and arrangements. The logical order, then, for our investigation would be: First, the appearance of symmetry in the productions of primitive life, as a (debatable) æsthetic phenomenon emerging from pre-æsthetic conditions; secondly, the experimental study of real symmetry; thirdly, the analysis of geometrical symmetry in art, especially in painting and architecture, by means of which the results of the preceding studies could be checked and confirmed. Having once established a theory of the æsthetic significance of real symmetry, we should next have to examine asymmetrical, beautiful objects with reference to the relation of their parts to a middle line; to isolate the elements which suggest motor impulses; to find out how far it is possible to establish a system of substitution of these psychological factors and how far such substitution takes place in works of art—i.e., to what extent a substitutional symmetry or balance is found in pleasing arrangements. These investigations, again, would fall into the two groups of experiment and analysis. The products of civilized art are too complicated to admit of the complete analysis and isolation of elements necessary to establish such a system of substitution of psychological factors as we seek. From suggestions, however, obtained from pleasing asymmetrical arrangements, first, isolated elements may be treated experimentally, and secondly, the results checked and confirmed by works of art.

With regard to the study of objects without a natural or suggested middle line, as for instance sculpture, many types of architecture, landscapes, gardens, room-arrangements, etc., we may fitly consider it as a corollary to the study of asymmetrical objects with artificial limits which do suggest a middle. If we find, by the study of them, that a system of substitution of psychological factors does obtain, the whole field can be covered by the theory already propounded, and its application extended to the minutest details. The hypothesis, having been so far confirmed, may be then easily applied to the field of asymmetrical objects without a natural middle line.

The set of problems here suggested to the student of symmetry will not be fully followed out in this paper. The experimental treatment of geometrical symmetry, the analysis of the completely symmetrical products of civilized art, and the analysis of all forms of asymmetry except asymmetry in pictures will be omitted. If, however, the fact of an original æsthetic feeling for symmetry is established by the study of primitive art, and the theory of the balance of motor impulses through the substitution of factors is established by the experimental treatment of isolated elements, and further confirmed by the analysis of pictures, the general argument may be taken as sufficiently supported. This paper, then, will contain three sections: an introductory one on symmetry in primitive art, and two main sections, one on experiments in substitutional symmetry, and one on substitutional symmetry or balance in pictures.

II. SYMMETRY IN PRIMITIVE ART.

The question which this section will attempt to answer is this: Is there in primitive art an original and immediate æsthetic feeling for symmetry? This question depends on two others which must precede it: To what extent does symmetry actually appear in primitive art? and, How far must its presence be accounted for by other than æsthetic demands?

For the purpose of this inquiry the word primitive may be taken broadly as applying to the products of savage and half-savage peoples of to-day, as well as to those of prehistoric races. The expression primitive art, also, requires a word of explanation. The primitive man seldom makes purely ornamental objects, but, on the other hand, most of his articles of daily use have an ornamental character. We have to consider primitive art, therefore, as represented in the form and ornamentation of all these objects, constituting practically an household inventory, with the addition of certain drawings and paintings which do not appear to serve a definite practical end. These last, however, constitute only a small proportion of the material.

The method of the following outline treatment will be to deduct from the object under consideration those symmetrical elements which seem to be directly traceable to non-æsthetic influences; such elements as are not thus to be accounted for must be taken as evidence of a direct pleasure in, and desire for symmetry on the part of primitive man. These possible non-æsthetic influences may be provisionally suggested to be the technical conditions of construction, the greater convenience and hence desirability of symmetrical objects for practical use, and the symmetrical character of natural forms which were imitated.

The first great group of objects is given in primitive architecture. Here is found almost complete unanimity of design, the conical, hemispherical or beehive form being well-nigh universal. The hut of the Hottentots, a cattle-herding, half-nomadic people, is a good type of this. A circle of flexible staves is stuck into the ground, bent together and fastened at the top, and covered with skins. But this is the form of shelter constructed with the greatest ease, suitable to the demands of elastic materials, boughs, twigs, reeds, etc., and giving the greatest amount of space with the least material. There are, indeed, a few examples of the rectangular form of dwelling among various primitive races, but these seem to be more or less open to explanation by the theory advanced by Mr. V. Mendeleff, of the U.S. Bureau of Ethnology. "In his opinion the rectangular form of architecture which succeeds the type under discussion, must have resulted from the circular form by the bringing together within a limited area of many houses.... This partition would naturally be built straight as a two-fold measure of economy."2 This opinion is confirmed by Mr. Cushing's observations among the Zuñi villages, where the pueblos have circular forms on the outskirts. Thus the shape of the typical primitive dwelling is seen to be fully accounted for as the product of practical considerations alone. It may therefore be dismissed as offering no especial points of interest for this inquiry.

Next in the order of primitive development are the arts of binding and weaving. The stone axe or arrow-head, for example, was bound to a wooden staff, and had to be lashed with perfect evenness,3 and when in time the material and method of fastening changed, the geometrical forms of this careful binding continued to be engraved at the juncture of blade and handle of various implements. It should be noted, however, that these binding-patterns, in spite of their superfluous character, remained symmetrical.

On the great topic of symmetry in weaving, monographs could be written. Here it is sufficient to recall4 that the absolutely necessary technique of weaving in all its various forms of interlacing, plaiting, netting, embroidering, etc., implies order, uniformity, and symmetry. The chance introduction of a thread or withe of a different color, brings out at once an ordered pattern in the result; the crowding together or pressing apart of elements, a different alternation of the woof, a change in the order of intersection, all introduce changes by the natural necessities of construction which have the effect of purpose. So far, then, as the simple weaving is concerned, the æsthetic demand for symmetry may be discounted. While it may be operative, the forms can be explained by the necessities of construction, and we have no right to assume an æsthetic motive.

The treatment of human and animal forms in weaving is, however, indicative of a direct pleasure in symmetry. The human form appears almost exclusively (much schematized) en face. When in profile, as for instance in Mexican and South American work, it is doubled—that is, two figures are seen face to face. Animal figures, on the other hand, are much used as row-ornaments in profile.5 It would seem that only the linear conception of the row or band with its suggestions of movement in one direction, justified the use of profile (e.g., in Peruvian woven stuffs), since it is almost always seen under those conditions, indicating that a limited rectangular space is felt as satisfactorily filled only by a symmetrical figure.6 Moreover, and still more confirmatory of this theory, even these row-pattern profiles are immensely distorted toward symmetry, and every 'degradation' of form, to use Professor Haddon's term, is in the direction of symmetry. (See Fig. 1.)

The shape of primitive pottery is conditioned by the following influences: The shapes of utensils preceding clay, such as skins, gourds, shells, etc., which have been imitated, the forms of basket models, and the conditions of construction (formation by the hands). For all these reasons, most of these shapes are circular. The only (in the strict sense) symmetrical shapes found are of unmistakably animal origin, and it is interesting to notice the gradual return of these to the eurhythmic form; puma, bird, frog, etc., gradually changing into head, tail and leg excrescences, and then handles and nodes (rectangular panels), upon a round bowl or jar L, as shown in the figures. In fact, in ancient American pottery,7 at least, all the symmetrical ornamentations can be traced to the opposition of head and tail, and the sides between them, of these animal forms. But beyond this there is no degradation of the broad outline of the design. The head and tail, and sides, become respectively handles and nodes—but the symmetry becomes only more and more emphasized. And as in the case of textiles, the ornaments of the rectangular spaces given by the nodes are strikingly symmetrical. Many of these are from animal motives, and nearly always heads are turned back over the body, tails exaggerated, or either or both doubled, to get a symmetrical effect. Although much of the symmetrical ornament, again, is manifestly from textile models, its symmetrical character is so carefully preserved against the suggestions of the circular form that a direct pleasure in its symmetry may be inferred. (See Figs. 2-7.)

Fig. 2.

Figs. 3. AND 4.

The subject of drawing can be here only touched upon, but the results of study go to show, in general, two main directions of primitive expression: pictorial representation, aiming at truth of life, and symbolic ornament. The drawings of Australians, Hottentots and Bushmen, and the carvings of the Esquimaux and of the prehistoric men of the reindeer period show remarkable vigor and naturalness; while the ornamentation of such tribes as the South Sea Islanders has a richness and formal beauty that compare favorably with the decoration of civilized contemporaries. But these two types of art do not always keep pace with each other. The petroglyphs of the North American Indians8 exhibit the greatest irregularity, while their tattooing is extremely regular and symmetrical. The Brazilian savage 9 draws freehand in a very lively and grotesque manner, but his patterns are regular and carefully developed. Again, not all have artistic talents in the same direction. Dr. Schurtz, in his 'Ornamentik der Aino,'10 says: "There are people who show a decided impulse for the direct imitation of nature, and especially for the representation of events of daily life, as dancing, hunting, fishing, etc. It is, however, remarkable that a real system of ornamentation is scarcely ever developed from pictorial representations of this kind; that, in fact, the people who carry out these copies of everyday scenes with especial preference, are in general less given to covering their utensils with a rich ornamentive decoration."11 Drawing and ornament, as the products of different tendencies, may therefore be considered separately.

The reason for the divergence of drawing and ornament is doubtless the original motive of ornamentation, which is found in the clan or totem ideas. Either to invoke protection or to mark ownership, the totem symbol appears on all instruments and utensils; it has been shown, indeed, that practically all primitive ornament is based on totemic motives.12 Now, since a very slight suggestion of the totem given by its recognized symbol is sufficient for the initiated, the extreme of conventionalization and degradation of patterns is allowable, and is observed to take place. The important point to be noted in this connection is, however, that all these changes are toward symmetry. The most striking examples might be indefinitely multiplied, and are to be found in the appended references (see Figs. 8 and 9).

Fig. 5.

Fig. 6.

Fig. 7.

We may distinguish here, also, between the gradual disintegration and degradation of pattern toward symmetry, as seen in the examples just given, and the deliberate distortion of figures for a special purpose. This is strikingly shown in the decorative art of the Indians of the North Pacific coast. They systematically represent their totem animals—their only decorative motives—as split in symmetrical sections, and opened out flat on the surface which is to be covered13 (see Fig. 11). Dr. Boas argues that their purpose is to get in all the received symbols, or to show the whole animal, but, however this may be, every variation introduces symmetry even where it is difficult to do so, as in the case, for instance, of bracelets, hat-brims, etc. (Fig. 10). This may in some cases be due to the symmetrical suggestions of the human body in tattooing,14 but it must be so in comparatively few.

Fig. 8.

Fig. 9.

Fig. 10.

The primitive picture has for its object not only to impart information, but to excite the very definite pleasure of recognition of a known object. All explorers agree in their accounts of the savage's delight in his own naïve efforts at picture making. All such drawings show in varying degrees the same characteristics; first of all, an entire lack of symmetry. In a really great number of examples, including drawings and picture-writing from all over the world, I have not found one which showed an attempt at symmetrical arrangement. Secondly, great life and movement, particularly in the drawings of animals. Thirdly, an emphasis of the typical characteristics, the logical marks, amounting sometimes to caricature. The primitive man draws to tell a story, as children do. He gives with real power what interests him, and puts in what he knows ought to be there, even if it is not seen, but he is so engrossed by his interest in the imitated object as to neglect entirely its relation to a background.

Fig. 11.

Now, this very antithesis of ornament and picture is enlightening as to the dawn of æsthetic feeling, and the strongest confirmation of our hypothesis of an original impulse to symmetry in art. In the ornamentation of objects the content or meaning of the design is already supplied by the merest hint of the symbol which is the practical motive of all ornamentation. The savage artist need, therefore, concern himself no more about it, and the form of his design is free to take whatever shape is demanded either by the conditions of technique and the surface to be ornamented, or by the natural æsthetic impulse. We have found that technical conditions account for only a small part of the observed symmetry in pattern, and the inference to a natural tendency to symmetry is clear. Pictorial representation, on the other hand, is enjoyed by the primitive man merely as an imitation, of which he can say, 'This is that animal'—to paraphrase Aristotle's Poetics. He is thus constrained to reproduce the form as it shows meaning, and to ignore it as form, or as his natural motor impulses would make it.

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.

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.

4062, 120166, 13028, 24

8070, 110104, 10280, 126

12046, X70, 4668,—44, 128*

16026, 9650, 2585, 196, —88*

20020, X55, X—46, 230,* 220, —110*

I. (b) F. 160×10, V. 80×10.

F.V.

C.O.D.

4074, 6460, 9627, 34

8076, 6572, 8755, 138

12060, 5648, 8270, 174

16029, 7416, 77—114, 140, 138, 200

20096, 3625, 36177, —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- 6058, 114*138, 2096, 84166

60- 804840, 138*100, 56150

80-1006470, 162*47, 87128

100-12070 to 806053, 53X

120-140588250, 4835

140-1607495 to 10022, 3237

160-18072102X, X42

180-20090XX, X50

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)24242528

(2)40424545404040

(3)6265

(4)100105109120130136120

(5)166180200200200200160160

¹This table is obtained by taking from the full list, not given here, of 1. (b) F. (160 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.

Fig. 12.

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 106126 6873

80106128109102

12014088156110*15472*

1601046618280136*130*

200X52178220*162

(b) F. CURVE, V. (80×10)

F.V.

O.C.

401261227380

8012212866112*40

1209011697156*55105

1606543120182*87134

200705014866

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.

The experiments on suggestion of depth in the third dimension were as follows. It was desired to contrast two objects differing only with respect to the degree to which they expressed the third dimension. Those objects that do express the third dimension are, in general, views down streets, colonnades, corridors, gates, etc., or, in landscape, deep valleys, vistas between trees, distant mountains, etc. It is evident that representations of products of human handiwork would be less unnatural when isolated for experiment, and two pairs of pictures were accordingly prepared as follows: There was drawn on a square of 80 mm. the picture of the mouth of a railway tunnel, closed tightly by an apparently massive door; and another picture of identical form and surroundings, but showing the rails entering at a slight curve, the deep blackness within, and the small circle of light at the farther end. The second pair consisted of the gateway of a baronial castle, with heraldic bearings and closed iron-wrought doors; and the same gateway open, showing a flagged pavement and an open court with fountain beyond. The perspective effect was heightened by all possible means for both pictures, and care was taken to have the contrast of black and white the same for each pair, so that to the half-shut eye, opened and closed forms seemed to have the same tone.

The subjects were directed to try to feel the third dimension as vividly as possible—to project themselves down the vistas, as it were—and then to arrange the squares in the most pleasing manner. The experiments were made by A, M, S, H and D. Not all made the same number of repetitions, but as their notes were unusually suggestive, I have made use of all the results, and shall quote the notes for the most part verbatim:

Exp. VIII. F. Closed Tunnel. V. Open Tunnel.

F.V.

Subject H.4090

6057

8013

10012

12039

140- 1

160-32

180-71, +50

Notes.—H finds that he neglects the closed tunnel almost entirely, eye is constantly attracted to open tunnel, F. 180, choice of evils. Position of closed tunnel makes the pictures disagreeable. F. 80, V. 13, closed tunnel grows more uninteresting as it goes out, while the open tunnel seems heavier than ever. F. 140, V.-1, closed tunnel loses force and doesn't gain weight. Open tunnel hangs together with the black field beyond it.

F.V.

Subject S.408595

80170195

60160180

100185200

120185 —35, 200

1408520

160115115

180100

Notes.—F. 120, V. 185. After this there is too large a black space between squares, and so a more central position is taken, but there is the necessity of avoiding symmetry, which is displeasing. F. 160, V. 115 is not symmetrical and so is more pleasing. F. 60, V. 195:—the open tunnel holds the eyes, while the other allows them to wander, and so it needs a bigger field on each side. F. 80, V. 180:—a position close together is possible, but it is hard to take them so except as one picture, and that is also difficult. F. 100, V. 200:—there is the same objection to any position which seems to be an acknowledgment of similarity; that is, symmetrical position seems to imply that they are alike, and so is disagreeable. F. 120, V.-35, 200:—now they can be close together because the black tunnel harmonizes with the black to the right, and seems to correspond in distance and depth, while the tunnel 'hangs together' with the black to the left. (Cf. H, F. 160, V.—32.) F. 140, V. 20:—when they are together it is difficult to apperceive the frame as a whole; but this position is not far apart, and not disagreeable because the larger stretch of black to the right again hangs together with the tunnel. F. 160, V. 115:—when the open tunnel was in the middle, the closed one seemed to have no business at all, therefore the open tunnel had to be moved over. The only position which was not disagreeable.

SUBJECT G.

F.V.

(1)(2)(3)(4)¹(5)¹

404831363023

6010531405139

8011171606454

10010463786086

120123759162115

1401368211156137

1601629314872156

18010711518183176

¹Second pair (Court).

Notes.—(1) All quite unsatisfactory. The arrangement difficult to apperceive as a whole. Each picture taken by itself. (2) The tunnel closed doesn't amount to much. (3) The significance of the tunnel gives it weight. For F. 160, V. 148, and F. 180, V. 180, relation difficult. (4) Court closed gets weaker as gets farther from center. (5) At F. 100, begins to lose relation between pictures, as if one were in one room, one in another.

SUBJECT A.

F.V.

(1)(2)(3)(4)²(5)²

40706614059130

60807315962138

801037112077134

1001139410893100

12011988969663

1401089260, 1648243

160921187010950

1801301547810150

²Second pair (Court).

Notes.—(1) Difficult to apperceive together. From F. 140, V. 108, depth is more strongly imagined. (3) Tunnel closed has not much value. (5) F. 80, V. 134, taken with reference both to frame and to the other picture—must not be symmetrical nor too far out.

SUBJECT D.

F.V.

(1)(2)(3)

401004738

60756068

801047880

100148, -12104120

120159166160

140182152, 84, 78168

160193184, -75180

180200-95, 190190

Note.—F. 100, V.-12; F. 140, V.-52; F. 160, V. -75: they must be close together when on the same side.

F.V.

(1)(2)¹

Subject M.405550

605674

806484

10086102

12093111

140124130

160134146

180144178

¹Second pair (Court).

Note.—(1) Quite impossible to take both together; necessary to keep turning from one to the other to get perception of depth together with both.

The subjects agree in remarking on the lack of interest of the closed tunnel, and the attractive power of the open tunnel, and notes which emphasize this accompany choices where the open tunnel is put uniformly nearer. (Cf. H, F. 180, V. 50; F. 80, V. 13; G, (2), (3), (4), (5); A, (3), and F. 140.) As a glance at the results shows that the open tunnel is placed on the whole nearer the center, we may conclude that these choices represent a mechanical balance, in which the open tunnel, or depth in the third dimension, is 'heavier.'

But another point of view asserts itself constantly in the results of S, and scatteringly in those of the others. Analyzing at first only the results of S, we find that up to F. 140, with one exception, he places the open tunnel much farther out than the other; and from F. 140 on, nearer. He says, F. 120, V. 185, 'After this there is too large a black space'; that is, in bringing the open tunnel in, he is evidently filling space. But why does he put the open tunnel so far out? It seems that he is governed by the desire for ease in the apperception of the two objects. In his note for F. 80, V. 180, this point of view comes out clearly. He thinks of the objects as being apperceived side by side with the space about each (which apparently takes on the character of its object), and then he seems to balance these two fields. Cf. F. 60, V. 195: 'The closed tunnel allows the eyes to wander, and so it needs a bigger field on each side.' Evidently there is an implication here of the idea of balance. Cf. also F. 120: 'The black tunnel harmonizes with the black to the right, and seems to correspond in distance and depth,' while the closed tunnel 'hangs together with the black on the left.' In brief, the view of F. seems to be that the closed tunnel is less interesting, and partly because it 'allows the eyes to wander,' partly as compensation for the greater heaviness of the open tunnel, it takes with it a larger space than the open tunnel. It is on the whole better to put them apart, because it is more difficult to apperceive them when close together, and so the open tunnel in the earlier choices must, of course, go farther from the center. When these points conflict with the necessity of filling space, the open tunnel comes nearer the center. In general, the notes which emphasize the difficulty of apperceiving the two pictures as flat and deep together accompany choices where the tunnel is put uniformly farther out, or symmetrically. Cf. G, (1), (5); A, (1); M, F. 40, etc.

Thus we may continue to separate the two points of view, that of mechanical balance and that of another kind of balance, which we have known heretofore as 'space-filling,' made possible by the power of the center to give 'weight,' but which seems to be now more explicitly recognized as a balancing of 'fields.' At this point we need repeat only, however, that the suggestion of depth in the third dimension seems to confer 'weight,' 'heaviness,' 'balancing power' on its object.

Before making a general survey of the results of this chapter, it is necessary to consider a type of choice which has been up to this point consistently neglected—that in which the variable has been placed on the same side of the center as the fixed object. On the theory of balance, either in its simple mechanical form or in its various disguises, this choice would at first seem to be inexplicable. And yet the subjects usually took special pleasure in this choice, when they made it at all. These minus choices are confined to three or four subjects and to two or three experiments. Exp. I. (a) and (b) show the largest number. We have:

EXP. I. (a) F. (80×10); V. (160×10).

F.V.

120- 44,

160-150,-105,-88

200-94,-46,-110

(b) F. (160×10); V. (80×10).

F.V.

120-70,-80

160-114

200-155,-146,-148

It will be noticed that, with two exceptions, none of the positions chosen are nearer than 70 mm. to the center, and that most of them are much farther away. The two lines seem to be more pleasing when they are pretty close together on the same side. S, in I. (b) F. 120, V.-70, notes: 'If V. is nearer O, there is a tendency to imagine a figure by the connection of the ends of the two lines, which is disagreeable. 'The only other minus choices were in Exp. VII., by S,, H, and D. S, F. 120, V.-35, says: 'Now they can be close together,' and H, F. 140, 160 and 180, V. -1, -32, -71, notes the same. So also D, F. 100, V. -12; F. 140, V. -52; F. 160, V. -75; F. 180, V. -95. It is evident from this insistence on the closeness together of the objects, and this desire to form no figure, that the two are taken as one, and set off against the blackness on the other side. It seems as if this were not taken as empty space, but acquired a meaning of its own. The association with pictures in which the empty space is occupied by a deep vista or an expanse of sky is almost irresistible. The case of Exp. VII. seems a little different. S, at least, separates the two fields as usual, but for him also the black space is living, 'corresponds in distance and depth.' It is at least certain that there is no subjective feeling of emptiness or of unoccupied energies on the empty side. And it would seem that some influence from the objects sweeps across the central field and vitalizes it. The most natural view would seem to be that the ease of apperception of the two objects together, and the tendency of the eye movement to begin on the occupied side, and to sweep across to the unoccupied, which we think of as deep, combine to give a feeling of pleasure and of balance.

We have now reached a point from which a backward glance can be cast upon the territory traversed. Experiment with the isolated elements in pictorial composition has shown that pleasing arrangements of these elements can be interpreted by the formula of mechanical balance. This principle was obtained by opposing two lines whose relative value (corresponding to 'weight' in balance) was known; and it was found that their relative positions corresponded to the relation of the arms of a balance. Further opposition of lines, of which one was already determined in 'weight,' showed the same variations and suggested certain valuations of the undetermined lines on the basis of this common term of weight. Thus, the line suggesting movement out from the center fitted the formula if taken as 'heavy' and vice versa, the line suggesting movement in, if taken as 'light.' Similarly, objects of interest and objects suggesting movement in the third dimension were 'heavy' in the same interpretation. But this interpretation, in its baldest form, fitted only a majority of the pleasing arrangements; the minority, in which the consistent carrying out of the lever principle would have left a large unoccupied space in the center, exactly reversed it, bringing the 'light' element to the center and the 'heavy' to the outer edge. Later experiments showed that this choice implied a power in the 'lighter' objects, owing to their central position, to cover or infuse with vitality the empty space about them, so that the principle of balance seemed to maintain itself in one form or another.

All this does not go beyond the proof that all pleasing space arrangements can be described in terms of mechanical balance. But what is this mechanical balance? A metaphor, no matter how consistently carried out, explains nothing. The fact that a small object far from the center is usually opposed by a large object near the center tells us nothing of the real forces involved. Physical balance can be explained by principles of mechanics, but no one will maintain that the visual representation of a long line weighs more than that of a short one. Moreover, the elements in the balance seem utterly heterogeneous. The movement suggested by an idea—the picture of a man running—has been treated as if equivalent to the movement actually made by the eye in following a long line; the intrinsic interest—that is, the ideal interest—of an object insignificant in form has been equated to the attractive power of a perspective which has, presumably, a merely physiological effect on the visual mechanism. What justification can be given either of this heterogeneous collection of elements or of the more or less arbitrary and external metaphor by which they have been interpreted?

I believe that the required justification of both points of view is given in the reduction of all elements to their lowest term—as objects for the expenditure of attention. A large object and an interesting object are 'heavy' for the same reason, because they call out the attention; a deep perspective, because the eye rests in it;—why, is another question. And expenditure of effort is expenditure of attention; thus, if an object on the outskirts of the field of vision requires a wide sweep of the eye to take it in, it demands the expenditure of attention, and so is felt as 'heavy.' It may be said that involuntary attention is given to the object of intrinsic interest, while the uninteresting object far on the outskirts needs a voluntary effort to perceive it, and that the two attitudes cannot be treated as identical. To this it may be answered that an object on the outskirts of a field of view so definitely limited calls out of itself a reflex movement of the eye toward it, as truly spontaneous as the impulse toward the object of intrinsic interest. But what is 'the expenditure of attention' in physiological terms? It is nothing more than the measure of the motor impulses directed to the object of attention. And whether the motor impulse appears as the tendency to fixate an object or as the tendency to follow out the suggestions of motion in the object, they reduce to the same physiological basis. It may here be objected that our motor impulses are, nevertheless, still heterogeneous, inasmuch as some are toward the object of interest, and some along the line of movement. But it must be said, first, that these are not felt in the body, but transferred as values of weight to points in the picture—it is the amount and not the direction of excitement that is counted; and secondly, that even if it were not so, the suggested movement along a line is felt as 'weight' at a particular point.

From this point of view the justification of the metaphor of mechanical balance is quite clear. Given two lines, the most pleasing arrangement makes the larger near the center, and the smaller far from it. This is balanced because the spontaneous impulse of attention to the near, large line, equals in amount the involuntary expenditure of attention to apprehend the small farther one. And this expenditure of motor impulses is pleasing, because it is the type of motor impulses most in harmony with our own physical organism.

We may thus think of a space to be composed as a kind of target, in which certain spots or territories count more or less, both according to their distance from the center and according to what fills them. Every element of a picture, in whatever way it gains power to excite motor impulses, is felt as expressing that power in the flat pattern. A noble vista is understood and enjoyed as a vista, but it is counted in the motor equation, our 'balance,' as a spot of so much intrinsic value at such and such a distance from the center. The skilful artist will fill his target in the way to give the maximum of motor impulses with the perfection of balance between them.

IV. SYMMETRY IN PICTURES.

A. The Balancing Factors.

The experimental treatment of suggestions as to the elements in pictorial composition has furnished an hypothesis for the basis of our pleasure in a well-composed picture, and for the particular function of each of the several elements. This hypothesis may be expressed as follows: (1) The basis of æsthetic pleasure in composition is a balance of motor impulses on the part of the spectator; (2) this balance of motor impulses is brought about by means of the elements, through the power which they possess of drawing the attention with more or less strength towards a certain field. But to the experimental working out of an hypothesis must succeed a verification, in its application to the masterpieces of civilized art. We have, then, to ask whether there is in all great pictures a balance, i.e., an equal distribution of attention on the two sides of the central line suggested by the frame of the picture. It might be, for instance, that a picture of pleasing composition would show, when analyzed, all the attractions for attention on one side; which would go far to impugn either our hypothesis of balance as the basis of pleasure, or our attribution of particular functions to the elements. But as this second matter may be considered to have been sufficiently determined by the results of the preceding section, the first question only remains: Is there a balance of attention in a good picture—or rather, in the particular good pictures known to the student of art?

This question could only be answered by the examination of a large number of pictures of accepted merit, and it was also desirable that they should be studied in a form which lent itself to the easy comparison of one picture with another. These conditions seemed to be best fulfilled by the collection of reproductions in black and white known as the Classischer Bilderschatz, published by F. Bruckmann, at Munich, which contains over a thousand pictures arranged in schools. Of these a thousand were taken—substantially the first thousand issued, after the frescoes, triptych doors, panels, etc., which are evidently parts of a larger whole, had been laid aside. In the following discussion the pictures will be designated, when they are not further described, by the numbers which they bear in this collection.

The equations in the following discussion are based on a system of exact measurement, corresponding to that followed in the experimental section. This numerical treatment is pre-supposed in all the general attributions of balance in the analysis of single pictures. The method of measurement was given by the conditions of viewing pictures, which are framed and thus isolated from surrounding influences, and referred, as compositions, to the middle line suggested by this emphasized frame. An adjustable frame of millimeter paper, divided in half vertically by a white silk thread, was fitted over the picture to be measured, and measurements were made to left and to right of this thread-line and, as required, vertically, by reference to the millimeter frame divisions.

The main question, of course, to be answered by a statistical examination of these thousand pictures refers to the existence of balance, but many other problems of symmetry are also seen to be closely involved; the relative frequency of the elements in pictures of different types, and the result of their employment in producing certain emotional effects, also the general types of space arrangement as a whole, the feeling-tone belonging to them, and the relation between content and shape. The first question will not be treated in this paper in the statistical fulness which was necessary to establish my conclusions in the investigation itself, inasmuch as the tables were very extensive. But examples of the tables, together with the full results, will be given, and a sufficient amount of detailed discussion to show my methods. The two other subjects, the use of the elements and the types of composition, will be briefly treated. I expect in other publications to go more closely into statistical detail on these matters than is possible in a merely experimental thesis.

In the beginning of the proposed statistical analysis a natural objection must first be forestalled: it will be said, and truly, that color also has its effect in bringing about balance, and that a set of black and white reproductions, therefore, ignores an important element. To this it may be answered, first, that as a matter of fact the color scheme is, as it were, superimposed upon the space-shape, and with a balance of its own, all the elements being interdependent; and secondly, that the black and white does render the intensity contrasts of the colors very well, giving as light and dark, and thus as interesting (= attractive) and the reverse, those factors in the scheme which are most closely related to the complex of motor impulses. After having compared, in European galleries, the originals of very many of these reproductions with the equation of balance worked out from the black and white, the writer has seldom found an essential correction needed.

The pictures were first classified by subjects. This may seem less logical than a division by types of arrangement. But it really, for a majority, amounted to the same thing, as the historical masterpieces of art mostly follow conventional arrangements; thus the altarpieces, portraits, genre pictures, etc., were mostly after two or three models, and this classification was of great convenience from every other point of view. The preliminary classification was as follows: (1) Religious, Allegorical and Mythical Pictures; (2) Portraits; (3) Genre; (4) Landscape. The historical pictures were so extremely few that they were included in the religious, as were also all the allegorical pictures containing Biblical persons. Some pictures, of which Watteau's are representative, which hovered between genre and landscape, were finally classified according as they seemed to owe their interest to the figures or to the scenery. A preliminary classification of space arrangements, still with reference to content, showed three large general types: (1) A single subject or group in the middle; (2) the same somewhat on one side, with subordinate elements occupying the rest of the space; (3) two objects or groups each occupying a well-defined center. These were designated as Single Center, Single and Subordinate Center, and Double Center pictures, or S.C., S. & S., and D.C. They are in proportions of S.C. 79 per cent., S. & S. 5 percent., D.C. 16 per cent. The D.C. type is evidently already explicitly balanced as regards shape and intrinsic interest, and is hence of comparative unimportance to our problem. The S.C. will show a balance, if at all, in more or less accessory factors; S. & S., broadly, between interest and other factors. As logically more important, this last group will be treated more fully. The full classification of the thousand pictures by subjects is as follows:

S.C.D.C.S.S.

Altarpieces787071

Madonna & Child474700

Holy Family67401413

Adorations191900

Crucifixions232102

Descents f. Cross272601

Annunciations210210

Misc. Religious162935514

Allegorical463664

Genre93631911

Landscape8865221

Portrait Groups6442175

Relig. Single Fig.282800

Alleg. Single Fig.121200

Portrait Single Fig.20720700

Genre Single Fig.181800

Altarpieces.

The pictures of the first group, consisting of the Madonna and Infant Christ surrounded by worshippers, and briefly designated as Altarpieces, are good for detailed study because they present a simple type, and it will be easy to show whether the variations from symmetry are in the direction of balance or not. A few examples will make this clear. The Madonna in the S.C. pictures is invariably seated holding the Christ.

In the following descriptions M. will denote Madonna, C. Child, Cn. central line. The elements, Size or Mass, Direction of Motion or Attention, Direction of Line, Vista, and Interest, will be set down as Ms., D., L., V., and I. A couple of examples will show the method of describing and of drawing a conclusion as to balance.

1. 969. Lorenzo Lotto, Madonna with St. Bernard and St. Onofrius. C. is on one side turning to the same; M. leans far to the other; hence interest in C., and direction of C.'s attention are over against Mass of M. and direction of M.'s attention; i.e., I. + D. = Ms. + D., and so far, balance. The surrounding saints are insignificant, and we may make the equation I. = Ms.