Fig. 9.—The smaller square may be regarded as either the nearer face of a projecting figure or as the more distant face of a hollow figure.
Fig. 10.—This represents an ordinary table-glass,—the bottom of the glass and the entire rear side, except the upper portion, being seen through the transparent nearer side, and the rear apparently projecting above the front. But it fluctuates in appearance between this and a view of the glass in which the bottom is seen directly, partly from underneath, the whole of the rear side is seen through the transparent front, and the front projects above the back.
Fig. 11.—In this scroll the left half may at first seem concave and the right convex; it then seems to roll or advance like a wave, and the left seems convex and the right concave, as though the trough of the wave had become the crest, and vice versa.
A good example to begin with is Fig. 7. These outlines will probably suggest at first view a book, or better a book-cover, seen with its back toward you and its sides sloping away from you; but it may also be viewed as a book opened out towards you and presenting to you an inside view of its contents. Should the change not come readily, it may be facilitated by thinking persistently of the appearance of an open book in this position. The upper portion of Fig. 8 is practically the same as Fig. 7, and if the rest of the figure be covered up, it will change as did the book cover; when, however, the whole figure is viewed as an arrow, a new conception enters, and the apparently solid book cover becomes the flat feathered part of the arrow. Look at the next figure (Fig. 9), which represents in outline a truncated pyramid with a square base. Is the smaller square nearer to you, and are the sides of the pyramid sloping away from you toward the larger square in the rear? Or are you looking into the hollow of a truncated pyramid with the smaller square in the background? Or is it now one and now the other, according as you decide to see it? Here (Fig. 12) is a skeleton box which you may conceive as made of wires outlining the sides. Now the front, or side nearest to me, seems directed downward and to the left; again, it has shifted its position and is no longer the front, and the side which appears to be the front seems directed upward and to the right. The presence of the diagonal line makes the change more striking: in one position it runs from the left-hand rear upper corner to the right-hand front lower corner; while in the other it connects the left-hand front upper corner with the right-hand rear lower corner.
Figs. 12, 12a, 12b.—The two methods of viewing Fig. 12 are described in the text. Figs. 12a and 12b are added to make clearer the two methods of viewing Fig. 12. The heavier lines seem to represent the nearer surface. Fig. 12a more naturally suggests the nearer surface of the box in a position downward and to the left, and Fig. 12b makes the nearer side seem to be upward and to the right. But in spite of the heavier outlines of the one surface, it may be made to shift positions from foreground to background, although not so readily as in Fig. 12.
Fig. 14 will probably seem at first glimpse to be the view of a flight of steps which one is about to ascend from right to left. Imagine it, however, to be a view of the under side of a series of steps; the view representing the structure of overhanging solid masonwork seen from underneath. At first it may be difficult to see it thus, because the view of steps which we are about to mount is a more natural and frequent experience than the other; but by staring at it with the intention of seeing it differently the transition will come, and often quite unexpectedly.