This is also in order of less complete balancing of the original elements. The princ.i.p.al 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 cla.s.s 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 princ.i.p.al 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 princ.i.p.al element, direction of movement of head or body, is balanced by the larger ma.s.s of the body or accessories. Very significant, also, is the great increase in the use of V. in this most irregular cla.s.s (15 per cent. as against 1 per cent. in III.). Three cases (214, 1087, 154, all A.V.,) fail to show subst.i.tutional 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 cla.s.s 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 ma.s.s 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 ma.s.s or direction of attention, or both together, on the other; while (2) portraits with the head not in the center show a balance between ma.s.s and interest on one side, and direction of attention, or of line, or vista, or combinations of these, on the other. The hypothesis of subst.i.tutional 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 cla.s.sification 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 a.s.sumes 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 ma.s.s 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 subst.i.tutional symmetry, it is worth while to a.n.a.lyze 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, ma.s.s 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 a.n.a.lyzed 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, Ma.s.s 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 cl.u.s.ter 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 Ma.s.s 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 ma.s.ses, 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 ma.s.s, 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 t.i.tian'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,' Stra.s.sburg, 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 Ma.s.s 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 subst.i.tutional 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 a.n.a.lysis 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 cla.s.ses 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 ma.s.s 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 ma.s.s; 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 princ.i.p.al 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 const.i.tute 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 princ.i.p.al 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.