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.