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