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), t.i.tian, _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 ma.s.sive 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 subst.i.tutional symmetry, or balance, we may next study the Madonna pictures, using the same cla.s.sifications 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 subst.i.tutional symmetry. It may be objected that the generally symmetrical framework of these pictures suggests a complete balance, and the next step in our a.n.a.lysis 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 a.n.a.lysis of a couple of portraits may justify the cla.s.sification 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 cla.s.sification is based on this framework.

CLa.s.sIFICATION 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. =