Chapter XXII: Section II: showed that the shorter filled distances are (18)

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

The subjects were directed to try to _feel_ the third dimension as vividly as possible--to project themselves down the vistas, as it were--and then to arrange the squares in the most pleasing manner. The experiments were made by _A_, _M_, _S_, _H_ and _D_. Not all made the same number of repetitions, but as their notes were unusually suggestive, I have made use of all the results, and shall quote the notes for the most part _verbatim_:

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

F. V.
Subject _H_. 40 90
60 57
80 13
100 12
120 39
140 - 1
160 -32
180 -71, +50

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

F. V.
Subject _S_. 40 85 95
60 170 195
80 160 180
100 185 200
120 185 - 35, 200
140 85 20
160 115 115
180 100

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

SUBJECT G.

F. V.
(1) (2) (3) (4)¹ (5)¹
40 48 31 36 30 23
60 105 31 40 51 39
80 111 71 60 64 54
100 104 63 78 60 86
120 123 75 91 62 115
140 136 82 111 56 137
160 162 93 148 72 156
180 107 115 181 83 176

¹Second pair (Court).

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

SUBJECT A.

F. V.
(1) (2) (3) (4)² (5)²
40 70 66 140 59 130
60 80 73 159 62 138
80 103 71 120 77 134
100 113 94 108 93 100
120 119 88 96 96 63
140 108 92 60,164 82 43
160 92 118 70 109 50
180 130 154 78 101 50

²Second pair (Court).

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

SUBJECT D.

F. V.
(1) (2) (3)
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)¹
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

¹Second pair (Court).

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

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

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

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

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

EXP. I. (_a_) F. (80×10); V. (160×10).
F. V.
120 - 44,
160 -150, -105, -88
200 -94, -46, -110

(_b_) F. (160×10); V. (80×10).
F. V.
120 -70, -80
160 -114
200 -155, -146, -148

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

* * * * *

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

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

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

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

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

IV. SYMMETRY IN PICTURES.

_A. The Balancing Factors._

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

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

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

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

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

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

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