SUBJECT D.

F. V. (1) (2) (3) 40 100 47 38 60 75 60 68 80 104 78 80 100 148, -12 104 120 120 159 166 160 140 182 152, 84, 78 168 160 193 184, -75 180 180 200 - 95, 190 190

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) Subject M. 40 55 50 60 56 74 80 64 84 100 86 102 120 93 111 140 124 130 160 134 146 180 144 178

Second 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. (80x10); V. (160x10). F. V. 120 - 44, 160 -150, -105, -88 200 -94, -46, -110

(b) F. (160x10); V. (80x10). 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 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 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. 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 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.

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 classification of the 70 S.C. altarpieces can be made on a basis of these constant elements, in the order of decreasing balance. Thus: Class 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.

CLASSIFICATION 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. 927. I. = V. 517. I. = I. + D. 273. I. = V. 327. I. + Ms. = D. + V. 951. I. + L. = D. + V. 715. Unbalanced.

(5) I. + D. = D. (6) I. = (7) I. + D. = 43. I. = I. 854. I. = Ms. 725. I. + D. = I. + L. 711. I. = I. 1148. I. = I. 206. I. + D. = I. + L. 447. I. = Ms. 709. I. = D. 155. I. + D. = D. + L. 643. I. = Ms. 907. I. = D. 739. I. + D. = L. 777. I. = Ms. + I. 586. I. = Ms. + I. 331. I. + D. = V. 637. I. = Ms. + I. 137. I. = Ms. + I. 980. Unbalanced. 187. Unbalanced.

(8) I. + D. = (9) I. + (D. + D.) = (10) 0. 57. I. + D. = Ms. 835. I. + D. = Ms + I. 979. I. + D. = I. + L. 724. I. + D. = Ms + L. 134. I. + D. = D. 495. I. + D. = Ms + L. 106. I. + D. = D. + V. 182. I. + D. = Ms + V. 220. I. + D. = L. 817. I. + D. = I. 118. I. + D. = V. + L. 662. I. + D. = I. 157. Unbalanced. 806. I. + D. = I. 1136. I. + D. = I. + L. 865. I. + D. = I. + V. 1023. I. + D. = V. 531. I. + D. = L. 553. I. + D. = L.

The most used element is I., in 100 per cent. of cases; the least used, V., 13 per cent. D., in 91 per cent. of cases; Ms., 26 per cent.; L., 19 per cent. 175, 433, unbalanced.

As seen in the table, a balance of elements is kept, except in four cases which will be hereafter considered. In all cases the balance is between the interest in C., sometimes plus D., (in the attention of the figures to C.), on the one side, and other elements on the other. Very seldom are other salient points found on the C. side. When the C. side is especially 'heavy,' the number of opposing elements increases, and especially takes the form of V. and L. [cf. (7), (8), (9)], which were observed in the experimental chapter to be powerful in attracting attention. For the fairly well-balancing framework—(i), (2), (3) and (4)—Ms., I., and D. are much more often the opposing elements.

The pictures listed as unbalanced are, with one exception, among the oldest examples given; conceived in the most slavish geometrical symmetry in which, indeed, the geometrical outline almost hides the fact that the slight variations are all toward a lack of balance.

There is but one S. & S. case (1054), Titian, The Madonna of the House of Pesaro. In this, M. and C. are on a high throne on the Right, other figures lower down on the Left bearing a flag that leans back to the Left. All the lines of the figures and of the massive architecture and the general direction of attention bear down so strongly to Left that the importance of the Right figures is balanced. We should have, then, I. = I. + L. + D. The D.C. cases, seven in number, are remarkably alike. Six have a vista separating the two groups, in five remarkably deep and beautiful, as if to fix the oscillating attention there. In all, M. and C., either in position or by the direction of their lines, are nearer the Cn. than the opposing figures, which are naturally less interesting, thus giving an instance of the mechanical balance. Their general equation, then, would be I. = M. or M. + L. Having shown that the small variations from the general symmetrical type of altar-pieces are invariably, except in primitive examples, in the direction of substitutional symmetry, or balance, we may next study the Madonna pictures, using the same classifications for purposes of comparison.

MADONNA WITH INFANT CHRIST.

(1) I. + D. = D. (2) I. = D. + D. (4) I. = D. 56. I. = L. 271. I. = D. + L. 668. I. = D. + Ms. 332. I. = L. 867. I. = D. + V. + D. 14. I. = D. + I. 633. I. = D. 91. I. = D. + V. (3) I. = D. 1111. I. = D. + V. 144. I. = D. 1011. I. = D. = L. 521. I. = D. 915. I. = D. = L. 356. I. = L. + D. + D. 296. I. + Ms. = V. + L.

(5) I. + D. = D. (6) I. = 51. I. = D. 596. I. = Ms. 581. I. = D. 892. I. = Ms. 829. I. = D. + I. 224. I. = I. + D. 159. I. = I. + D. 908. I. = D. + L. 683. I. = D. + L. 1045. I. = I. + L. (7) I. + D. = 745. I. = I. + L. 344. I. + D. = Ms. 734. I. = D. + L. 949. I. + D. = Ms. + V. + L. 404. I. = D. + L. 608. I. + D. = L. 248. I. = L. 524. I. + D. = L. 37. I. = L. 97. I. = L. (8) 0. 363. I. = V. + L. 674. I. = V. + L. (9) I. + D. + D. = 62. I. = V. + L. 361. I. + D. = L. 1142. I. = V. + L. 1018. I. = V. + L. (10) 110. I. + V. = Ms. + L. 538. I. = D. 411. I. + V. = Ms. + L. 614. I. + Ms. = V. 771. I. + Ms. = V. + L. 34. D. = Ms. + L.

Most used element, I., 100 per cent.; least used, Ms., 21 per cent. D., 96 per cent.; L., 64 per cent.; V., 27 per cent.

The first thing to be noted, on comparing this table with the preceding, is the remarkable frequency of the use of the vista and the line. Among the altarpieces, the direction of attention was the element most often opposed to the interesting object; and next to that, another object of interest. These two elements, however, here sink into comparative insignificance. In general, balance is brought about through the disposition of form rather than of interests. This appears in comparing the numbers; against the use of L. in 19 per cent. of the cases among the altarpieces, we have 64 per cent. among the Madonna pictures; V. is used in the former cases 13 per cent. of the times, in the latter 27 per cent. The reason for this would appear to be that the lack of accessories in the person of saints, worshippers, etc., and the consequent increase in the size of M. and C. in the picture heightens the effect of any given outline, and so makes the variations from symmetry greater. This being the case, the compensations would be stronger—and as we have learned that V. and L. are of this character, we see why they are needed. None of the M. and C., S.C. pictures fails to give a complete balance of elements according to hypothesis. There are no well-defined cases of S. & S. or D.C.

Portraits.

A study of the Madonna pictures of all types, then, results in an overwhelming confirmation of the hypothesis of substitutional symmetry. It may be objected that the generally symmetrical framework of these pictures suggests a complete balance, and the next step in our analysis would, therefore, be a type of picture which is less bound by tradition to the same form. The portrait would seem to combine this desideratum with generally large and simple outlines, so that the whole surface can be statistically reported with comparative ease. A detailed analysis of a couple of portraits may justify the classification adopted.

900. Anton Raphael Mengs, Self-Portrait. The head of the painter is exactly in Cn., but is turned sharply to Right, while his shoulders turn Left. His arm and hand are stretched out down to Right, while his other hand, holding pencil, rests on his portfolio to Left. Hence, the D. of attention plus that of L. on Right, balances I. in implements, plus D. of body on Left, or D. + L. = D. + I.

438. B. van der Helst, Portrait of Paul Potter. The head of the subject is entirely to Left of Cn., his easel on Right. His body is turned sharply to Right, and both hands, one holding palette and brushes, are stretched down to Right. His full face and frontward glance are on Left. Hence, Ms. + I. in person balances I. in implements + D. of L., or Ms. + I. = I. + L.

It is seen that the larger elements in these pictures are the directions of the head and body, and the position of the head, with reference to Cn. The following classification is based on this framework.

CLASSIFICATION OF PORTRAITS.

A. Head in Cn. I. Body front, head front, 6 II. Body turned, head turned other way, 7 D. = D. III. Body turned, head front, 31 D. = IV. Body front, head turned, 1 D. = V. Body turned, head turned same way, 106 D. + D. =

B. Head not in Cn. I. Body turned to empty side, head to same, 18 Ms.=D. II. Body turned to empty side, head front, 23 Ms. = D. III. Body turned to empty side, head to other, 3 Ms. + D. = D. IV. Body front, head front, 2 Ms. = V. Body turned from empty side, head same way, 10 Ms. + D. =

This is also in order of less complete balancing of the original elements. The principal characteristics of the different divisions are as follows:—

A. I. (Symmetrical.) Most used element, L.; least used, V.

II. (Balanced, D. = D.) Most used element, L.; least used, V.

III. (D. = .) Most used element, Ms., in 74 per cent, of cases opposed to D.; in 30 per cent, of cases, D. of glance opposed to D. of body; least used, V. (1 per cent.).

IV. One case only.

V. (D. = .) Most used element, Ms., in 73 per cent. of cases opposed to D.; in 40 per cent. of cases, D. of glance opposed to D.; in 28 per cent. Ms. + D. of glance opposed to D.; least used element, V. (15 per cent.). I. 39 per cent.; L. 38 per cent.

B. I. (Balanced, Ms. + I. = D.) Most used element (not counting those already included in equation), I., 55 per cent.; least used, V., 2 per cent.; L., 50 per cent. In 44 per cent., D. of glance opposed to D.

II. (Ms. + I. = D.) Most used element (not in equation), I., 52 per cent. Least used, V., 26 per cent. L., 43 per cent. In 21 per cent., D. of glance opposed to D.

III. (Ms. + I. + D. = D.) Three cases. Two cases V. on empty side.

IV. (Ms. + I. = .) Two cases. One case V. on empty side.

V. (Ms. + I. + D. = .) Most used element, L., 60 per cent.; least used, V., 10 per cent.; 33-1/3 per cent., D. of glance to empty side.

The portrait class is an especially interesting object for study, inasmuch as while its general type is very simple and constant, for this very reason the slightest variations are sharply felt, and have their very strongest characteristic effect. We shall, therefore, find that the five principal factors in composition express themselves very clearly. The general type of the portrait composition is, of course, the triangle with the head at the apex, and this point is also generally in the central line—in 73 per cent. of the whole number of cases, as is seen from the table. All cases but one are longer than they are wide, most are half-length or more. Nevertheless, great richness of effect is brought about by emphasizing variations. For instance, the body and head are, in the great majority of cases, turned in the same way, giving the strongest possible emphasis to the direction of attention—especially powerful, of course, where all the interest is in the personality. But it is to be observed that the very strongest suggestion of direction is given by the direction of the glance; and in no case, when most of the other elements are directed in one way, does the glance fail to come backward. (Cf. A. II., V., and B. I., II., V.)

A. It is of especial value for our conclusions that that division in which the constant elements are least balanced (V.) is far the most numerous. Comparison of this with III. shows that the principal element, direction of movement of head or body, is balanced by the larger mass of the body or accessories. Very significant, also, is the great increase in the use of V. in this most irregular class (15 per cent. as against 1 per cent. in III.). Three cases (214, 1087, 154, all A.V.,) fail to show substitutional symmetry.

B. With the head on one side of Cn., of course the greatest interest is removed to one side, and the element of direction is brought in to balance. Again, with this decrease in symmetry, we see the significant increase in the use of the especially effective elements, V. and L. (Cf. B. I., II., III., IV., and especially V.) In fact, the use of the small deep vista is almost confined to the class with heads not in the middle. The direction of the glance also plays an important part. It is to be noted that in B. I. and II., I. appears as the most frequently used element, exclusive of the general equation, which is, of course, between the mass of the body and interest of the face, on one side, and the direction of suggested movement on the other. This means that very often the direction of movement alone is not sufficient to balance the powerful Ms. + I. of the other side, and that the eye has to be attracted by a definite object of interest. This is usually the hand, with or without an implement—like the palette, etc., of our first examples—or a jewel, vase, or bit of embroidery. This is very characteristic of the portraits of Rembrandt and Van Dyck.

In general, it may be said that (1) portraits with the head in the center of the frame show a balance between the direction of suggested movement on one side, and mass or direction of attention, or both together, on the other; while (2) portraits with the head not in the center show a balance between mass and interest on one side, and direction of attention, or of line, or vista, or combinations of these, on the other. The hypothesis of substitutional symmetry is thus completely confirmed.

Genre.

Still more unsymmetrical in their framework than portraits, in fact the most unfettered type of all, are the genre pictures. Being so irregular, they admit of no complete classification based on constant elements in the framework, such as was possible for the types already dealt with. A grouping, based on types of composition, is indeed possible, as of triangles, diagonals, etc., but as this begs the question of the relative importance of line and direction of attention, and assumes that the shape is all-important, it will not be made use of here. The broad divisions and the relative use of the elements are given as follows:

S.C. 63. Most frequent form (I. = or I. + D. =). Most used element, I., 89 per cent.; least used, L., 44 per cent.; D., 57 per cent.; Ms., 57 per cent.; V., 46 per cent.

D.C. 19. Most frequent form (I. + D. = I. + D.) Most used element, I. (all cases); least used, L., 31 per cent.; V., 47 per cent.; Ms., 63 per cent.; D., 42 per cent.

S.&S. 11. Most frequent form (I. or I. + Ms. = V. or V. +). Most used element, I., 100 per cent.; least used, L., 20 per cent.; V., 82 per cent.; Ms., 72 per cent.; D., 27 per cent.

As these are pictures with a human interest, and, therefore full of action and particular points of interest, it was to be expected that I. would be in all forms the element most frequently appearing. In compositions showing great variations from geometrical symmetry, it was also to be expected that V. and L., elements which have been little used up to this point, should suddenly appear in very high percentages; for, as being the most strikingly 'heavy' of the elements, they serve to compensate for other variations combined. In general, however, the balance is between the interesting side, which is also often the most occupied (I. + Ms.), and the direction of suggestion to the other side.

For the first time in this investigation the S. & S. and D.C. types appear in appreciable numbers. It is of some significance that the most irregular type of all, S. & S., in which the weight of interest and of mass is overwhelmingly on one side, should be invariably balanced by the third dimension (V.). As these somewhat infrequent cases are especially enlightening for the theory of substitutional symmetry, it is worth while to analyze one in detail.

286. Pieter de Hooch, The Card-players, in Buckingham Palace, portrays a group completely on the Right of Cn., all facing in to the table between them. Directly behind them is a high light window, screened, and high on the wall to the extreme Right are a picture and hanging cloaks. All goes to emphasize the height, mass and interest of the Right side. On the Left, which is otherwise empty, is a door half the height of the window, giving on a brightly lighted courtyard, from which is entering a woman, also in light clothing. The light streams in diagonally across the floor. Thus, with all the 'weight' on the Right, the effect of this deep vista on the Left and of its brightness is to give a complete balance, while the suggestion of line from doorway and light makes, together with the central figure, a roughly outlined V, which serves to bind together all the elements. This matter of binding together of elements is reserved for further discussion—the purpose of this detailed description is only to show the extraordinary power of a single element, vista, to balance a whole composition of others, and its significance in the tables as an increasing accompaniment of increasing variations from symmetry.

The D.C. cases, inasmuch as they always present a balance of interest at least, are less valuable for our theory; among the variations the larger side, Ms., is often balanced by a vista, or, combining with the usual equation for genre pictures, Ms. + I. + D. = V. + I. + D. There is only one picture which cannot be schematized (263).

Landscape.

The landscape is another type of unfettered composition. As it represents no action or single object or group of objects, its parts are naturally more or less unconnected. It should, therefore, be said that no picture was taken as D.C. unless there was a distinct separation of the two sides. The typical examples are analyzed in detail.

S.C. 912. J. van Ruysdael, Forest Landscape, in the London National Gallery. In the Cn. is a stagnant pool, backed on the Right by thick woods. A dead tree, white, very prominent in the Right foreground, another at its foot sloping down to Cn. On the Left a bank sloping down to Cn., a tree at its foot; behind both, and seen also between the two central trees, bright sky and clouds. Thus, there is on the Right, Mass and Direction to Cn.; on the Left, Vista and Direction to Cn.; Ms. + D. = V. + D.

D.C. 642. Hobbema, The Watermill, in Buckingham Palace. On the Right, a bank sloping upward, a large cluster of trees, a path leading down to Right lower corner. On the Left, somewhat lower, the mill, and water in front of it, flowing down to Left; clearest sky between mill and trees. Thus Mass and Direction out are placed over against Interest (in mill) and Direction out, plus possibly a hint of Vista, or Ms. + D. = I. + D + V.

S.C. 65. Most frequent form, Ms. + I. = V. + L. Most used element, V., 98 per cent.; least used, D., 22 per cent. I. 73 per cent.; Ms. 66 per cent.; L. 31 per cent.

S. & S. One case. Ms. + I. + V. = V.

D.C. 22. Most frequent form, Ms. + I. or Ms. = V. or V. + (almost invariable). Most used element, V., 100 per cent.; least used, D., per cent. Ms. 82 per cent.; I. 73 per cent.; L. 23 per cent.

It was, of course, to be expected that in pictures without action there should be little suggestion of attention or of direction of movement. What is less evident is the reason for the high percentage of I. Of course, figures do appear in many examples, and in most pictures some inanimate object is emphasized—as, for instance, the mill in our second example. But the most remarkable point of difference in these tables from the preceding is the presence of V. in practically every example. It is, of course, natural that somewhere in almost every picture there should be a break to show the horizon line, for the sake of variety, if for nothing else—but what is significant is the part played by this break in the balancing of the picture. In about two thirds of the examples the vista is enclosed by lines, or masses, and when near the center, as being at the same time the 'heaviest' part of the picture, serves as a fulcrum or center to bind the parts—always harder to bring together than in the other types of pictures—into a close unity. The most frequent form of this arrangement, as seen by the table, is a diagonal, which just saves itself by turning up at its far end. Thus the mass, and hence usually the special interest of the picture, is on the one side, on the other the vista and the sloping line of the diagonal. In very few cases is the vista behind an attractive or noticeable part of the picture, the fact showing that it acts in opposition to the latter, leading the eye away from it, and thus serving at once the variety and richness of the picture, and its unity. A pure diagonal would have line and vista both working at the extreme outer edge of the picture, and thus too strongly—unless, indeed, balanced by very striking elements near the other edge.

This function of the vista as a unifying element is of interest in connection with the theory of Hildebrand,[16] that the landscape should have a narrow foreground and wide background, since that is most in conformity with our experience. He adduces Titian's Sacred and Profane Love as an example. But of the general principle it may be said that not the reproduction of nature, but the production of a unified complex of motor impulses, is the aim of composition, and that this aim is best reached by focusing the eye by a narrow background—i.e., vista. No matter how much it wanders, it returns to that central spot and is held there, keeping hold on all the other elements. Of Hildebrand's example it may be said that the pyramidal composition with the dark and tall tree in the center effectually accomplishes the binding together of the two figures, so that a vista is not needed. A wide background without that tree would leave them rather disjointed.

[16] A. Hildebrand, 'Das Problem der Form in der Bildenden Kunst,' Strassburg, 1897.

Another interesting observation concerns the use of water in landscapes. In nearly all appears an expanse of water, and in four fifths of the cases it is either on the same side as the vista, or in the same line with it. This is no doubt partly due to the light-effects which can be got on the water, but it also greatly reinforces the peculiar effect of the vista. That effect, as has been repeatedly said, is to concentrate, to hold, to fixate vision. The same thing is true of the horizontal line, as was shown by some preliminary experiments not here reported. The contrast to the ordinary trend of lines—particularly in a landscape—together with the strong suggestion of quiet and repose, serve to give the same concentrating effect to the horizontal lines as to the vista.

In general, it may be said that balance in landscape is effected between Mass and Interest on one side and Vista and Line on the other; and that unity is given especially by the use of Vista and the horizontal lines of water.

A survey of the subject-types remaining on the list of page 514 shows that they may quite well be grouped together with those already examined; that is, the Holy Families, Adorations, Crucifixions, and Annunciations are very symmetrical in type, and present the same characteristics as the Altarpieces. The Miscellaneous (mostly religious) pictures, the Descents, and the Allegorical are, for the most part, freely composed, irregular, full of action, and resemble the genre pictures. The Single Figure pictures, Religious, Allegorical and Genre, and the Portrait Groups, resemble the portraits. Therefore, it may be considered that the existence of a perfect substitutional symmetry has been established, inasmuch as it has been shown to be almost invariably present in the types examined.

The experimental treatment of the isolated elements determined the particular function of each in distributing attention in the field of view. The object of large size claims attention, but does not rivet it nor draw it out powerfully; the intrinsically interesting object does excite it, but limits it to a comparatively small field; the suggestion of movement or of attention on the part of pictured objects carries the attention through the field of its operation; the vista rivets the attention without powerfully exciting it, and the line extending in a certain direction carries the attention in the same way as does the suggestion of movement. But the preceding statistical analysis has shown that while all are possibly operative in a given picture, some are given much more importance than others, and that in pictures of different types different elements predominate.

The following table gives the distribution of the elements in the single-center pictures already examined. The numbers represent the per cent. of the whole number of balanced pictures in which the given element appears once or more.

S.C. Ms. I. D. V. L.

Alt. p. 26 100 91 13 31 Mad. 21 100 96 27 64 Port. 80 63 98 17 61 Genre 57 89 57 46 44 Lands. 66 73 22 98 31

It is seen that in those classes with a general symmetrical framework, the altar and Madonna pictures, the elements of interest and direction of attention are overwhelmingly predominant—which is the more to be expected as they appear, of course, as variations in a symmetry which has already, so to speak, disposed of mass and line. They give what action there is, and when they are very strongly operative, we see by page 516, (8) and (9) and note, that they are opposed by salient lines and deep vistas, which act more strongly on the attention than mass; compare further Mad., V. 27 per cent., L. 64 per cent., as against Alt., V. 13 per cent., L. 19 per cent., as confirming the view that they are used in the more irregular and active pictures. But I. keeps its predominance throughout the types, except in the portraits, where, indeed, we should not expect it to be so powerful, since the principal object of interest must always be the portrait head, and that is in most cases in the Cn., and therefore not counted. Yet I. has a respectable representation even in the portrait table, showing that such objects as jewels, embroideries, beautiful hands, etc., count largely too in composition. Its greatest is in the genre table, where, of course, human interests constitute the subject matter.

It is among the portraits that the direction of suggestion is most operative. Since these pictures represent no action, it must be given by those elements which move and distribute the attention; in accordance with which we see that line also is unusually influential. As remarked above, the altarpieces and Madonna pictures, also largely without action, depend largely for it on D., in the form of direction of attention (D. 91 per cent.).

The vista, as said above, rivets and confines the attention. We can, therefore, understand how it is that in the genre table it suddenly appears very numerous. The active character of these pictures naturally requires to be modified, and the vista introduces a powerful balancing element, which is yet quiet; or, it might be said, inasmuch as energy is certainly expended in plunging down the third dimension, the vista introduces an element of action of counterbalancing character. In the landscape it introduces the principal element of variety. It is always to be found in those parts of the picture which are opposed to other powerful elements, and the 'heavier' the other side, the deeper the vista. This is especially to be noted in all pictures of the S. & S. type, where the one side is very 'heavy' and the deep vista practically invariable on the other. Also in D.C. pictures it serves as a kind of fulcrum, or unifying element, inasmuch as it rivets the attention between the two detached sides. (Cf. D.C. among Alt. and Mad.)

The direction of suggestion by means of the indication of a line (L.), quite naturally is more frequent in the Madonna-picture and Portrait classes. Both these types are of large simple outline, so that L. would be expected to tell, but more or less irregular, so that it would not appear on both sides, thus neutralizing its action, as often in the symmetrical altarpieces. This neutralizing explains why it has a comparatively small per cent. in the landscape table, it having appeared in minor form all over the field, but less often in large salient outline. It is worth noticing that for the D.C. of both genre and landscape, the per cent. drops appreciably. As it is, in a decided majority of cases, combined with V.—the shape being more or less a diagonal slope—it is clear that it acts as a kind of bond between the two sides, carrying the attention without a break from one to the other.

The element of mass requires less comment. It appears in greatest number in those pictures which have little action, portraits and landscapes, and which are yet not symmetrical—in which last case mass is, of course, already balanced. In fact, it must of necessity exert a certain influence in every unsymmetrical picture, and so its percentage, even for genre pictures, is large.

Thus we may regard the elements as both attracting attention to a certain spot and dispersing it over a field. Those types which are of a static character abound in elements which disperse the attention; those which are of a dynamic character, in those which make it stable. The ideal composition seems to combine the dynamic and static elements—to animate, in short, the whole field of view, but in a generally bilateral fashion. The elements, in substitutional symmetry, are then simply means of introducing variety and action. As a dance in which there are complicated steps gives the actor and beholder a varied and thus vivified 'balance,' and is thus more beautiful than the simple walk, so a picture composed in substitutional symmetry is more rich in its suggestions of motor impulse, and thus more beautiful, than an example of geometrical symmetry.

B. Principles of Composition.

The particular function of the elements which are substituted for geometrical symmetry has been made clear; their presence lends variety and richness to the balance of motor impulses. But the natural motor response to stimulation has another characteristic which belongs to us as individuals. The motor response must be balanced, but also unified. In a picture, therefore, there must be a large outline in which all the elements are held together, corresponding to this requirement of unity. Now this way of holding together, this manner of combination, may vary; and I hope to show that it not only varies with the subject and purpose of the picture, but bears a very close relation thereto—that, in short, it is what determines the whole character of the picture. Just what this relation is will appear in the study of our material.

Examples of these types of composition may best be found by analyzing a few very well-known pictures. We may begin with the class first studied, the Altarpiece, choosing a picture by Botticelli, in the Florence Academy (746). Under an arch is draped a canopy held up by angels; under this, again, sits the M. with the C. on her lap, on a throne, at the foot of which, on each side, stand three saints. The outline of the whole is markedly pyramidal—in fact, there are, broadly speaking, three pyramids; of the arch, the canopy, and the grouping. A second, much less symmetrical example of this type, is given by another Botticelli in the Academy—Spring (140). Here the central female figure, topped by the floating Cupid, is slightly raised above the others, which, however, bend slightly inward, so that a triangle, or pyramid with very obtuse angle at the apex, is suggested; and the whole, which at first glance seems a little scattered, is at once felt, when this is grasped, as closely bound together.

Closely allied to this is the type of the Madonna of Burgomaster Meyer, Holbein (725), in the Grand-Ducal Castle, Darmstadt. It is true that the same pyramid is given by the head of the M. against the shell-like background, and her spreading cloak which envelops the kneeling donors. But still more salient is the diamond form given by the descending rows of these worshipping figures, especially against the dark background of the M.'s dress. A second example, without the pyramid backing, is found in Rubens' Rape of the Daughters of Leucippus (88), in the Alte Pinakothek at Munich. Here the diamond shape formed by the horses and struggling figures is most remarkable—an effect of lightness which will be discussed later in interpreting the types.

The famous Bull of Paul Potter (149), in the Royal Museum at the Hague, furnishes a third type, the diagonal. High on one side are grouped the herdsman, leaning on a tree which fills up the sky on that side, and his three sheep and cow. The head of the bull is turned toward this side, and his back and hind leg slope down to the other side, as the ground slopes away to a low distant meadow. The picture is thus divided by an irregular diagonal. Somewhat more regular is the diagonal of the Evening Landscape, by Cuyp (348), in the Buckingham Palace, London. High trees and cliffs, horsemen and others, occupy one side, and the mountains in the background, the ground and the clouds, all slope gradually down to the other side.

It is a natural transition from this type to the V-shape of the landscapes by Aart van der Neer, Dutch Villages, 245 and 420, in the London National Gallery and in the Rudolphinum at Prague, respectively. Here are trees and houses on each side, gradually sloping to the center to show an open sky and deep vista. Other examples, of course, show the opening not exactly in the center.

In the Concert by Giorgione (758), in the Pitti Gallery, Florence, is seen the less frequent type of the square. The three figures turned toward each other with heads on the same level make almost a square space-shape, although it might be said that the central player gives a pyramidal foundation. This last may also be said of Verrocchio's Tobias and the Archangels in the Florence Academy, for the square, or rather rectangle, is again lengthened by the pyramidal shape of the two central figures. The unrelieved square, it may here be interpolated, is not often found except in somewhat primitive examples. Still less often observed is the oval type of Samson's Wedding feast, Rembrandt (295), in the Royal Gallery, Dresden. Here one might, by pressing the interpretation, see an obtuse-angled double-pyramid with the figure of Delilah for an apex, but a few very irregular pictures seem to fall best under the given classification.

Last of all it must be remarked that the great majority of pictures show a combination of two or even three types; but these are usually subordinated to one dominant type. Such, for instance, is the case with many portraits, which are markedly pyramidal, with the double-pyramid suggested by the position of the arms, and the inverted pyramid, or V, in the landscape background. The diagonal sometimes just passes over into the V, or into the pyramid; or the square is combined with both.

It is, of course, not necessary at this point to show how it is that such an apparently unsymmetrical shape as the diagonal, alone or in combination with other forms, nevertheless produces an effect of balance. In all these cases of the diagonal type the mass or interest of the one side, or the direction of subordinate lines backward to it, balances the impulse of the line descending to the other side. The presence of balance or substitutional symmetry is taken for granted in this treatment, having been previously established, and only the modifications of this symmetry are under consideration.

Now, in order to deal properly with the question of the relation of the type of composition to the subject of the picture, complete statistical information will be necessary. A table of the pictures, classified by subjects and distributed under the heads of the six major types, is accordingly subjoined.

Pyramid. Double-Pyr. Diagonal. S.C. D.C. S.S. S.C. D.C. S.S. S.C. D.C. S.S. Altarpieces, 49 0 1 10 4 0 1 0 0 Mad. w. C., 40 0 0 7 0 0 0 0 0 Holy Family, 25 0 4 0 0 1 2 2 2 Adorations, 19 0 0 0 0 0 0 0 0 Crucifixions, 11 0 0 7 0 1 0 0 1 Desc. fr. Cross, 12 0 0 3 0 0 1 0 0 Annunciations, 0 8 0 0 4 0 0 0 0 Misc. Religious, 55 16 3 4 4 0 10 7 5 Allegorical, 20 2 1 4 0 0 4 0 2 Genre, 25 4 4 5 0 0 18 2 1 Landscape, 8 2 1 3 0 0 25 6 0 Port. Group, 20 4 2 9 0 0 3 3 2 Rel. Single Fig., 20 0 0 2 0 0 2 0 0 Alleg. S.F., 7 0 0 2 0 0 3 0 0 Portrait S.F., 179 0 0 28 0 0 0 0 0 Genre S.F., 15 0 0 1 0 0 1 0 0

V-shaped. Square. Oval. S.C. D.C. S.S. S.C. D.C. S.S. S.C. D.C. S.S. Altarpieces, 6 1 0 4 1 0 0 1 0 Mad. w. C., 0 0 0 0 0 0 0 0 0 Holy Family, 13 3 6 0 0 0 0 0 0 Adorations, 0 0 0 0 0 0 0 0 0 Crucifixions, 0 0 0 3 0 0 0 0 0 Desc. fr. Cross, 5 0 1 3 0 0 2 0 0 Annunciations, 0 1 0 0 8 0 0 0 0 Misc. Religious, 20 14 2 9 12 1 2 2 3 Allegorical, 3 2 1 3 1 0 3 1 0 Genre, 10 7 6 4 4 0 1 3 0 Landscape, 20 12 0 4 0 0 5 2 0 Port. Group, 10 7 1 0 3 0 0 0 0 Rel. Single Fig., 3 0 0 1 0 0 0 0 0 Alleg. S.F., 0 0 0 0 0 0 0 0 0 Portrait S.F., 0 0 0 0 0 0 0 0 0 Genre S.F., 1 0 0 0 0 0 0 0 0

What types are characteristic of the different kinds of pictures? In order to answer this question we must ask first, What are the different kinds of pictures? One answer, at least, is at once suggested to the student on a comparison of the pictures with their groupings according to subjects. All those which represent the Madonna enthroned, with all variations, with or without saints, shepherds or Holy Family, are very quiet in their action; that is, it is not really an action at all which they represent, but an attitude—the attitude of contemplation. This is no less true of the pictures I have called 'Adorations,' in which, indeed, the contemplative attitude is still more marked. On the other hand, such pictures as the 'Descents,' the 'Annunciations,' and very many of the 'miscellaneous religious,' allegorical and genre pictures, portray a definite action or event. Taking together, for instance, in two groups of five each, the first ten classes in the table, we find that they fall to the six types in the following proportion:

P. D.P. Dg. V. Sq. Ov. I. 66 13 05 13 03 0 II. 43 07 14 20 12 04

Inasmuch as II. contains also many 'contemplative' pictures, while I. contains no 'active' ones, the contrast between the proportions of the groups would really be sharper than the figures indicate. But as it is, we see that the pyramid type is characteristic of the 'contemplative' pictures in a much higher degree. If the closely allied double-pyramid type is taken with it, we have 79 per cent of the 'contemplative' to 50 per cent, of the 'active' ones. This view is confirmed by contrasting the 'Adoration,' the most complete example of one group, with the genre pictures, the most complete example of the other—and here we see that in the first all are pyramidal, and in the second only 26 per cent. A class which might be supposed to suggest the same treatment in composition is that of the portraits—absolute lack of action being the rule. And we find, indeed, that no single type is represented within it except the pyramid and double-pyramid, with 86 per cent. of the former. Thus it is evident that for the type of picture which expresses the highest degree of quietude, contemplation, concentration, the pyramid is the characteristic type of composition.

But is it not also characteristic of the 'active' pictures, since, as we see, it has the largest representation in that class too? Perhaps it might be said that, inasmuch as all pictures are really more 'quiet' than they are 'active,' so the type par excellence is the pyramidal—a suggestion which is certainly borne out by the table as a whole. But setting aside for the moment the pyramid and its sub-variety, we see that the diagonal V-shaped and square types are much more numerous in the roughly outlined 'active' class. Taking, again, the genre class as especially representative, we find 23 per cent. of the diagonal type, and 25 per cent. of the V-shaped. We have seen how closely allied are these two types, and how gradually one passes over into the other, so that we may for the nonce take them together as making up 47 per cent. of the whole. The type of picture which expresses the highest degree of activity, which aims to tell a story, has, then, for its characteristic type the V and its varieties.

The landscape picture presents a somewhat different problem. It cannot be described as either 'active' or 'passive,' inasmuch as it does not express either an attitude or an event. There is no definite idea to be set forth, no point of concentration, as with the altarpieces and the portraits, for instance; and yet a unity is demanded. An examination of the proportions of the types shows at once the characteristic type.

P. D.P. Dg. V. Sq. Or. Landscapes, 13 03 35 36 05 08

It is now necessary to ask what must be the interpretation of the use of these types of composition. Must we consider the pyramid the expression of passivity, the diagonal or V, of activity? But the greatly predominating use of the second for landscapes would remain unexplained, for at least nothing can be more reposeful than the latter. It may aid the solution of the problem to remember that the composition taken as a whole has to meet the demand for unity, at the same time that it allows free play to the natural expression of the subject. The altarpiece has to bring about a concentration of attention to express or induce a feeling of reverence. This is evidently brought about by the suggestion of the converging lines to the fixation of the high point in the picture—the small area occupied by the Madonna and Child—and by the subordination of the free play of other elements. The contrast between the broad base and the apex gives a feeling of solidity, of repose; and it seems not unreasonable to suppose that the tendency to rest the eyes above the center of the picture directly induces the associated mood of reverence or worship. Thus the pyramidal form serves two ends; primarily that of giving unity; and secondarily, by the peculiarity of its mass, that of inducing the feeling-tone appropriate to the subject of the picture.

Applying this principle to the so-called 'active' pictures, we see that the natural movement of attention between the different 'actors' in the picture must be allowed for, while yet unity is secured. And it is clear that the diagonal type is just fitted for this. The attention sweeps down from the high side to the low, from which it returns through some backward suggestion of lines or interest in the objects of the high side. Action and reaction—movement and return of attention—is inevitable under the conditions of this type; and this it is which allows the free play—which, indeed, constitutes and expresses the activity belonging to the subject, just as the fixation of the pyramid constitutes the quietude of the religious picture. Thus it is that the diagonal composition is particularly suited to portray scenes of grandeur, and to induce a feeling of awe in the spectator, because only here can the eye rove in one large sweep from side to side of the picture, recalled by the mass and interest of the side from which it moves. The swing of the pendulum is here widest, so to speak, and all the feeling-tones which belong to wide, free movement are called into play. If, at the same time, the element of the deep vista is introduced, we have the extreme of concentration combined with the extreme of movement; and the result is a picture in the 'grand style'—comparable to high tragedy—in which all the feeling-tones which wait on motor impulses are, as it were, while yet in the same reciprocal relation, tuned to the highest pitch. Such a picture is the Finding of the Ring, Paris Bordone (1048), in the Venice Academy. All the mass and the interest and the suggestion of attention is toward the right—the sweep of the downward lines and of the magnificent perspective toward the left—and the effect of the whole space-composition is of superb largeness of life and feeling. With it may be compared Titian's Presentation of the Virgin (107), also in the Academy, Venice. The composition, from the figure moving upward to one high on the right, to the downward lines, waiting groups and deep vista on the left, is almost identical with that of the Bordone. Neither is pure diagonal—that is, it saves itself at last by an upward movement. Compare also the two great compositions by Veronese, Martyrdom of St. Mark, etc. (1091), in the Doge's Palace, Venice, and Esther before Ahasuerus (566), in the Uffizi, Florence. In both, the mass, direction of interest, movement and attention are toward the left, while all the lines tend diagonally to the right, where a vista is also suggested—the diagonal making a V just at the end. Here, too, the effect is of magnificence and vigor.

If, then, the pyramid belongs to contemplation, the diagonal to action, what can be said of the type of landscape? It is without action, it is true, and yet does not express that positive quality, that will not to act, of the rapt contemplation. The landscape uncomposed is negative; and it demands unity. Its type of composition, then, must give it something positive besides unity. It lacks both concentration and action; but it can gain them both from a space composition which shall combine unity with a tendency to movement. And this is given by the diagonal and V-shaped type. This type merely allows free play to the natural tendency of the 'active' picture; but it constrains the neutral, inanimate landscape. The shape itself imparts motion to the picture: the sweep of line, the concentration of the vista, the unifying power of the inverted triangle between two masses, act, as it were, externally to the suggestion of the object itself. There is always enough quiet in a landscape—the overwhelming suggestion of the horizontal suffices for that; it is movement that is needed for richness of effect; and, as I have shown, no type imparts the feeling of movement so strongly as the diagonal and V-shaped type of composition. It is worth remarking that the perfect V, which is of course more regular, concentrated, quiet, than the diagonal, is more frequent than the diagonal among the 'Miscellaneous Religious' pictures (that is, it is more needed), since after all, as has been said, the final aim of all space composition is just the attainment of repose. But the landscapes need energy, not repression; and so the diagonal type is proportionately more numerous.

The square and oval types, as is seen from the table, are far less often used. The oval, most infrequent of all, appears only among the 'active' pictures, with the exception of landscape. It usually serves to unite a group of people among whom there is no one especially striking—or the object of whose attention is in the center of the picture, as in the case of the Descent from the Cross. It imparts a certain amount of movement, but an equable and regular one, as the eye returns in an even sweep from one side to the other.

The square type, although only three per cent. of the whole number of pictures, suggests a point of view which has already been touched on in the section on Primitive Art. The examples fall into two classes: in the first, the straight lines across the picture are unrelieved by the suggestion of any other type; in the second, the pyramid or V is suggested in the background with more or less clearness by means of architecture or landscape. In the first class are found, almost exclusively, early examples of Italian, Dutch and German art; in the second, pictures of a later period. The rigid square, in short, is found only at an early stage in the development of composition. Moreover, all the examples are 'story' pictures, for the most part scenes from the lives of the saints, etc. Many of them are double-center—square, that is, with a slight break in the middle, the grouping purely logical, to bring out the relations of the characters. Thus, in the Dream of Saint Martin, Simone Martini (325), a fresco at Assisi, the saint lies straight across the picture with his head in one corner. Behind him on one side, stand the Christ and angels, grouped closely together, their heads on the same level. Compare also the Finding of the Cross, Piero della Francesca (1088), a serial picture in two parts, with their respective backgrounds all on the same level; and most of the frescoes by Giotto at Assisi—in particular St. Francis before the Sultan (1057), in which the actors are divided into parties, so to speak.

These are all, of course, in one sense symmetrical—in the weight of interest, at least—but they are completely amorphous from an aesthetic point of view. The forms, that is, do not count at all—only the meanings. The story is told by a clear separation of the parts, and as, in most stories, there are two principal actors, it merely happens that they fall into the two sides of the picture. Interesting in connection with this is the observation that, although the more anecdotal the picture the more likely it is to be 'double-centered,' the later the picture the less likely it is to be double-centered. Thus the square and the double-center composition seem often to be found in the same picture and to be, both, characteristic of early composition. On the other hand, a rigid geometrical symmetry is also characteristic, and these two facts seem to contradict each other. But it is to be noted, first, that the rigid geometrical symmetry belongs only to the Madonna Enthroned, and general Adoration pieces; and secondly, that this very rigidity of symmetry in details can coexist with variations which destroy balance. Thus, in the Madonna Enthroned, Giotto (715), where absolute symmetry in detail is kept, the Child sits far out on the right knee of the Madonna. Compare also Madonna, Vitale di Bologna (157), in which the C. is almost falling off M.'s arms to the right, her head is bent to the right, and a monk is kneeling at the right lower corner; also Madonna, Ottaviano Nelli (175)—all very early pictures. Hence, it would seem that the symmetry of these early pictures was not dictated by a conscious demand for symmetrical arrangement, or rather for real balance, else such failures would hardly occur. The presence of geometrical symmetry is more easily explained as the product, in large part, of technical conditions: of the fact that these pictures were painted as altarpieces to fill a space definitely symmetrical in character—often, indeed, with architectural elements intruding into it. We may even venture to connect the Madonna pictures with the temple images of the classic period, to explain why it was natural to paint the object of worship seated exactly facing the worshipper. Thus we may separate the two classes of pictures, the one giving an object of worship, and thus taking naturally, as has been said, the pyramidal, symmetrical shape, and being moulded to symmetry by all other suggestions of technique; the other aiming at nothing except logical clearness. This antithesis of the symbol and the story has a most interesting parallel in the two great classes of primitive art—the one symbolic, merely suggestive, shaped by the space it had to fill, and so degenerating into the slavishly symmetrical, the other descriptive, 'story-telling' and without a trace of space composition. On neither side is there evidence of direct aesthetic feeling. Only in the course of artistic development do we find the rigid, yet often unbalanced, symmetry relaxing into a free substitutional symmetry, and the formless narrative crystallizing into a really unified and balanced space form. The two antitheses approach each other in the 'balance' of the masterpieces of civilized art—in which, for the first time, a real feeling for space composition makes itself felt.

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THE AESTHETICS OF UNEQUAL DIVISION.

BY ROSWELL PARKER ANGIER.

PART I.

The present paper reports the beginnings of an investigation designed to throw light on the psychological basis of our aesthetic pleasure in unequal division. It is confined to horizontal division. Owing to the prestige of the golden section, that is, of that division of the simple line which gives a short part bearing the same ratio to the long part that the latter bears to the whole line, experimentation of this sort has been fettered. Investigators have confined their efforts to statistical records of approximations to, or deviations from, the golden section. This exalts it into a possible aesthetic norm. But such a gratuitous supposition, by limiting the inquiry to the verification of this norm, distorts the results, tempting one to forget the provisional nature of the assumption, and to consider divergence from the golden section as an error, instead of another example, merely, of unequal division. We have, as a matter of fact, on one hand, investigations that do not verify the golden section, and, on the other hand, a series of attempts to account for our pleasure in it, as if it were, beyond dispute, the norm. In this way the statistical inquiries have been narrowed in scope, and interpretation retarded and misdirected. Statistically our aim should be to ascertain within how wide limits aesthetically pleasing unequal divisions fall; and an interpretative principle must be flexible enough to include persistent variations from any hypothetical norm, unless they can be otherwise accounted for. If it is not forced on us, we have, in either case, nothing to do with the golden section.

Since Fechner, the chief investigation in the aesthetics of simple forms is that of Witmer, in 1893.[1] Only a small part of his work relates to horizontal division, but enough to show what seems to me a radical defect in statistical method, namely, that of accepting a general average of the average judgments of the several subjects, as 'the most pleasing relation' or 'the most pleasing proportion.'[2] Such a total average may fall wholly without the range of judgments of every subject concerned, and tells us nothing certain about the specific judgments of any one. Even in the case of the individual subject, if he shows in the course of long experimentation that he has two distinct sets of judgments, it is not valid to say that his real norm lies between the two; much less when several subjects are concerned. If averages are data to be psychophysically explained, they must fall well within actual individual ranges of judgment, else they correspond to no empirically determinable psychophysical processes. Each individual is a locus of possible aesthetic satisfactions. Since such a locus is our ultimate basis for interpretation, it is inept to choose, as 'the most pleasing proportion,' one that may have no correspondent empirical reference. The normal or ideal individual, which such a norm implies, is not a psychophysical entity which may serve as a basis of explanation, but a mathematical construction.

[1] Witmer, Lightner: 'Zur experimentellen Aesthetik einfacher raeumlicher Formverhaeltnisse,' Phil. Studien, 1893, IX., S. 96-144, 209-263.

This criticism would apply to judgments of unequal division on either side the center of a horizontal line. It would apply all the more to any general average of judgments including both sides, for, as we shall soon see, the judgments of individuals differ materially on the two sides, and this difference itself may demand its explanation. And if we should include within this average, judgments above and below the center of a vertical line, we should have under one heading four distinct sets of averages, each of which, in the individual cases, might show important variations from the others, and therefore require some variation of explanation. And yet that great leveller, the general average, has obliterated these vital differences, and is recorded as indicating the 'most pleasing proportion.'[3] That such an average falls near the golden section is immaterial. Witmer himself, as we shall see,[4] does not set much store by this coincidence as a starting point for explanation, since he is averse to any mathematical interpretation, but he does consider the average in question representative of the most pleasing division.

[2] op. cit., 212-215.

[3] Witmer: op. cit., S. 212-215.

[4] op. cit., S. 262.

I shall now, before proceeding to the details of the experiment to be recorded, review, very briefly, former interpretative tendencies. Zeising found that the golden section satisfied his demand for unity and infinity in the same beautiful object.[5] In the golden section, says Wundt,[6] there is a unity involving the whole; it is therefore more beautiful than symmetry, according to the aesthetic principle that that unification of spatial forms which occurs without marked effort, which, however, embraces the greater manifold, is the more pleasing. But to me this manifold, to be aesthetic, must be a sensible manifold, and it is still a question whether the golden section set of relations has an actual correlate in sensations. Witmer,[7] however, wrote, at the conclusion of his careful researches, that scientific aesthetics allows no more exact statement, in interpretation of the golden section, than that it forms 'die rechte Mitte' between a too great and a too small variety. Nine years later, in 1902, he says[8] that the preference for proportion over symmetry is not a demand for an equality of ratios, but merely for greater variety, and that 'the amount of unlikeness or variety that is pleasing will depend upon the general character of the object, and upon the individual's grade of intelligence and aesthetic taste.' Kuelpe[9] sees in the golden section 'a special case of the constancy of the relative sensible discrimination, or of Weber's law.' The division of a line at the golden section produces 'apparently equal differences' between minor and major, and major and whole. It is 'the pleasingness of apparently equal differences.'

[5] Zelsing, A.: 'Aesthetische Forschungen,' 1855, S. 172; 'Neue Lehre von den Proportionen des menschlichen Koerpera,' 1854, S. 133-174.

[6] Wundt, W.: 'Physiologische Psychologie,' 4te Aufl., Leipzig, 1893, Bd. II., S. 240 ff.

[7] op. cit., S. 262.

[8] Witmer, L.: 'Analytical Psychology,' Boston, 1902, p. 74.

[9] Kuelpe, O.: 'Outlines of Psychology,' Eng. Trans., London, 1895, pp. 253-255.

These citations show, in brief form, the history of the interpretation of our pleasure in unequal division. Zeising and Wundt were alike in error in taking the golden section as the norm. Zeising used it to support a philosophical theory of the beautiful. Wundt and others too hastily conclude that the mathematical ratios, intellectually discriminated, are also sensibly discriminated, and form thus the basis of our aesthetic pleasure. An extension of this principle would make our pleasure in any arrangement of forms depend on the mathematical relations of their parts. We should, of course, have no special reason for choosing one set of relationships rather than another, nor for halting at any intricacy of formulae. But we cannot make experimental aesthetics a branch of applied mathematics. A theory, if we are to have psychological explanation at all, must be pertinent to actual psychic experience. Witmer, while avoiding and condemning mathematical explanation, does not attempt to push interpretation beyond the honored category of unity in variety, which is applicable to anything, and, in principle, is akin to Zeising's unity and infinity. We wish to know what actual psychophysical functionings correspond to this unity in variety. Kuelpe's interpretation is such an attempt, but it seems clear that Weber's law cannot be applied to the division at the golden section. It would require of us to estimate the difference between the long side and the short side to be equal to that of the long side and the whole. A glance at the division shows that such complex estimation would compare incomparable facts, since the short and the long parts are separated, while the long part is inclosed in the whole. Besides, such an interpretation could not apply to divisions widely variant from the golden section.

This paper, as I said, reports but the beginnings of an investigation into unequal division, confined as it is to results obtained from the division of a simple horizontal line, and to variations introduced as hints towards interpretation. The tests were made in a partially darkened room. The apparatus rested on a table of ordinary height, the part exposed to the subject consisting of an upright screen, 45 cm. high by 61 cm. broad, covered with black cardboard, approximately in the center of which was a horizontal opening of considerable size, backed by opal glass. Between the glass and the cardboard, flush with the edges of the opening so that no stray light could get through, a cardboard slide was inserted from behind, into which was cut the exposed figure. A covered electric light illuminated the figure with a yellowish-white light, so that all the subject saw, besides a dim outline of the apparatus and the walls of the room, was the illuminated figure. An upright strip of steel, 11/2 mm. wide, movable in either direction horizontally by means of strings, and controlled by the subject, who sat about four feet in front of the table, divided the horizontal line at any point. On the line, of course, this appeared as a movable dot. The line itself was arbitrarily made 160 mm. long, and 11/2 mm. wide. The subject was asked to divide the line unequally at the most pleasing place, moving the divider from one end slowly to the other, far enough to pass outside any pleasing range, or, perhaps, quite off the line; then, having seen the divider at all points of the line, he moved it back to that position which appealed to him as most pleasing. Record having been made of this, by means of a millimeter scale, the subject, without again going off the line, moved to the pleasing position on the other side of the center. He then moved the divider wholly off the line, and made two more judgments, beginning his movement from the other end of the line. These four judgments usually sufficed for the simple line for one experiment. In the course of the experimentation each of nine subjects gave thirty-six such judgments on either side the center, or seventy-two in all.

In Fig. 1, I have represented graphically the results of these judgments. The letters at the left, with the exception of X, mark the subjects. Beginning with the most extreme judgments on either side the center, I have erected modes to represent the number of judgments made within each ensuing five millimeters, the number in each case being denoted by the figure at the top of the mode. The two vertical dot-and-dash lines represent the means of the several averages of all the subjects, or the total averages. The short lines, dropped from each of the horizontals, mark the individual averages of the divisions either side the center, and at X these have been concentrated into one line. Subject E obviously shows two pretty distinct fields of choice, so that it would have been inaccurate to condense them all into one average. I have therefore given two on each side the center, in each case subsuming the judgments represented by the four end modes under one average. In all, sixty judgments were made by E on each half the line. Letter E represents the first thirty-six; E squared the full number. A comparison of the two shows how easily averages shift; how suddenly judgments may concentrate in one region after having been for months fairly uniformly distributed. The introduction of one more subject might have varied the total averages by several points. Table I. shows the various averages and mean variations in tabular form.