It is clear from Fig. 7 why a transition-band shades gradually from one pure-color band over into the other. Let us consider the transition-band 2-3 (Fig. 7). Next it on the right is a green band, on the left a red. Now at the right-hand edge of the transition-band it is seen that the deduction is mostly red and very little green, a ratio which changes toward the left to one of mostly green and very little red. Thus, next to the red band the transition-band will be mostly red, and it will shade continuously over into green on the side adjacent to the green band.
7. The next observation given ([page 175], No. 7) was that, "The bands are more strikingly visible when the two sectors differ considerably in luminosity." This is to be expected, since the greater the contrast, whether in regard to color, saturation, or intensity, between the sectors, the greater will be such contrast between the two deductions, and hence the greater will it be between the resulting bands. And, therefore, the bands will be more strikingly distinguishable from each other, that is, 'visible.'
8. "A broad but slowly-moving rod shows the bands lying over itself. Other bands can also be seen behind it on the disc."
In Fig. 9 (Plate V.) are shown the characteristic effects produced by a broad and slowly-moving rod. Suppose it to be black. It can be so broad and move so slowly that for a space the characteristic effect is largely black (Fig. 9 on both sides of x). Specially will this be true between x and y, for here, while the pendulum contributes no more photo-chemical unit-effects, it will contribute the newer one, and howsoever many unit-effects go to make up the characteristic effect, the newer units are undoubtedly the more potent elements in determining this effect. The old units have partly faded. One may say that the newest units are 'weighted.'
Black will predominate, then, on both sides of x, but specially between x and y. For a space, then, the characteristic effect will contain enough black to yield a 'perception of the rod.' The width of this region depends on the width and speed of the rod, but in Fig. 9 it will be roughly coincident with xy, though somewhat behind (to the left of) it. The characteristic will be either wholly black, as just at x, or else largely black with the yet contributory after-images (shown in the triangle aby). Some bands will thus be seen overlying the rod (1-8), and others lying back of it (9-16).
We have now reviewed all the phenomena so far enumerated of the illusion-bands, and for every case we have identified these bands with the bands which must be generated on the retina by the mere concealment of the rotating sectors by the moving rod. It has been more feasible thus far to treat these deduction-bands as if possibly they were other than the bands of the illusion; for although the former must certainly appear on the retina, yet it was not clear that the illusion-bands did not involve additional and complicated retinal or central processes. The showing that the two sets of bands have in every case identical properties, shows that they are themselves identical. The illusion-bands are thus explained to be due merely to the successive concealment of the sectors of the disc as each passes in turn behind the moving pendulum. The only physiological phenomena involved in this explanation have been the persistence as after-images of retinal stimulations, and the summation of these persisting images into characteristic effects—both familiar phenomena.
From this point on it is permissible to simplify the point of view by accounting the deduction-bands and the bands of the illusion fully identified, and by referring to them under either name indifferently. Figs. 1 to 9, then, are diagrams of the bands which we actually observe on the rotating disc. We have next briefly to consider a few special complications produced by a greater breadth or slower movement of the rod, or by both together. These conditions are called 'complicating' not arbitrarily, but because in fact they yield the bands in confusing form. If the rod is broad, the bands appear to overlap; and if the rod moves back and forth, at first rapidly but with decreasing speed, periods of mere confusion occur which defy description; but the bands of the minor color may be broader or may be narrower than those of the other color.
VII. FURTHER COMPLICATIONS OF THE ILLUSION.
9. If the rod is broad and moves slowly, the narrower bands are like colored, not with the broader, as before, but with the narrower sector.
The conditions are shown in Fig. 9. From 1 to 2 the deduction is increasingly green, and yet the remainder of the characteristic effect is also mostly green at 1, decreasingly so to the right, and at 2 is preponderantly red; and so on to 8; while a like consideration necessitates bands from x to 16. All the bands are in a sense transition-bands, but 1-2 will be mostly green, 2-3 mostly red, and so forth. Clearly the widths of the bands will be here proportional to the widths of the like-colored sectors, and not as before to the oppositely colored.