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 a.s.serts itself constantly in the results of _S_, and scatteringly in those of the others. a.n.a.lyzing 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 s.p.a.ce'; that is, in bringing the open tunnel in, he is evidently filling s.p.a.ce. 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 s.p.a.ce 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 s.p.a.ce 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 s.p.a.ce, 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 's.p.a.ce-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. (8010); V. (16010).

F. V.

120 - 44, 160 -150, -105, -88 200 -94, -46, -110

(_b_) F. (16010); V. (8010).

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 s.p.a.ce, but acquired a meaning of its own. The a.s.sociation with pictures in which the empty s.p.a.ce 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 s.p.a.ce 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 s.p.a.ce 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 s.p.a.ce 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 s.p.a.ce 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 att.i.tudes 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 s.p.a.ce 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 n.o.ble 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 aesthetic 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 a.n.a.lyzed, 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 _Cla.s.sischer 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 a.n.a.lysis 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 s.p.a.ce 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 a.n.a.lysis 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 s.p.a.ce-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 cla.s.sified 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 cla.s.sification was of great convenience from every other point of view. The preliminary cla.s.sification 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 cla.s.sified according as they seemed to owe their interest to the figures or to the scenery. A preliminary cla.s.sification of s.p.a.ce 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 s.p.a.ce; (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 cla.s.sification of the thousand pictures by subjects is as follows:

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

Altarpieces 78 70 7 1 Madonna & Child 47 47 0 0 Holy Family 67 40 14 13 Adorations 19 19 0 0 Crucifixions 23 21 0 2 Descents f. Cross 27 26 0 1 Annunciations 21 0 21 0 Misc. Religious 162 93 55 14 Allegorical 46 36 6 4 Genre 93 63 19 11 Landscape 88 65 22 1 Portrait Groups 64 42 17 5 Relig. Single Fig. 28 28 0 0 Alleg. Single Fig. 12 12 0 0 Portrait Single Fig. 207 207 0 0 Genre Single Fig. 18 18 0 0

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 Ma.s.s, 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 Ma.s.s 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.

2. 368. Raffaelino di Francesco, _Madonna Enthroned._ The C. is on Right facing front, M. turns away Left, hence interest in C. is over against direction of M.'s attention. Moreover, all the saints but one turn Left, and of two small vistas behind the throne, the one on the Left is deeper. The superior interest we feel in C. is thus balanced by the tendency of attention to the opposite side, and we have I. = D.

+ V.

It is clear that the broad characteristics of the composition can be symmetrically expressed, so that a cla.s.sification of the 70 S.C.

altarpieces can be made on a basis of these constant elements, in the order of decreasing balance. Thus: Cla.s.s 1, below, in which the C. is one side of the central line, turned away from the center, the M.

turned to the other, balances in these broad lines, or I. + D. = D.; while in (9), I. + D. + D. = (x), the constant elements work all on one side.

CLa.s.sIFICATION OF ALTARPIECES.

1 C. one side turned to same, M. to other 11 2 " " " other, " " 8 3 " " " front, " " 2 4 " " " other, M. front. 9 5 " " " facing M. 6 6 " " " front, M. front. 7 7 " " " " M. turned to same. 6 8 " " " to same M. turned front. 7 9 " " " " M. " to same, 14 10 " in middle, turned front. 0

Thus the constant elements, understanding always that C. has more interest than M., are as follows: For (1) I. + D. = D.; (2) I. = D. + D.; (3) I. = D.; (4) I. = D.; (5) I. + D. = D.; etc. These are in order of complete balance, but it will be seen that from (7) on, while the factors are constant, the framework is not balanced; _e.g._ in (9) both I. and D. work on the same side. For these groups, therefore, the variations, if there is balance, will be more striking. Eliminating the balancing elements in the framework, the tables for the ten groups are:

(1) I. + D. = D. (2) I. = D. + D(M). (3) I. = D.

969. I. = Ms. 680. I. = D. 1094. Ms. + I. = I. + D.

601. I. = Ms. 735. I. = D. 33. I. = I. + D 49. I. = Ms. + I. 1121. I. = D.

634. I. = Ms. + I. 1035. I. = D. (4) I. = D.

584. I. = I. 333. I. = I. + D. 775. I. = D.

686. I. = I. 80. I. = I. + D. 746. I. = D.

794. I. = D. 753. I. = I. + D. 1106. I. = Ms. + D.

164. I. = D. 1114. I. = D. + L. 781. I. = Ms. + D.

368. I. = D. + V. 1131. I. = I. + D.