It is clear that this last principle adduced, of the multiple overlapping of bands when the rod is broad and moves slowly, can give for varying speeds of the rod the greatest variety of combinations of the bands.  Among these is to be included that of no bands at all, as will be understood from Fig. 11 (Plate VII).  And in fact, a little practice will enable the observer so to adjust the rate of the (broad) rod to that of the disc that no bands are observable.  But care must be taken here that the eye is rigidly fixated and not attracted into movement by the rod, since of course if the eye moves with the rod, no bands can be seen, whatever the rate of movement may be.

Thus, all the phenomena of these illusion-bands have been explained as the result solely of the hiding by the rod of successive sectors of the disc.  The only physiological principles involved are those (1) of the duration of after-images, and (2) of their summation into a characteristic effect.  It may have seemed to the reader tedious and unnecessary so minutely to study the bands, especially the details last mentioned; yet it was necessary to show how all the possible observable phenomena arise from the purely geometrical fact that sectors are successively hidden.  Otherwise the assertions of previous students of the illusion, that more intricate physiological processes are involved, could not have been refuted.  The present writer does not assert that no processes like contrast, induction, etc., come into play to modify somewhat the saturation, etc., of the colors in the bands.  It must be here as in every other case of vision.  But it is now demonstrated that these remoter physiological processes contribute nothing essential to the illusion.  For these could be dispensed with and the illusion would still remain.

[Illustration:  PSYCHOLOGICAL REVIEW.  MONOGRAPH SUPPLEMENT, 17.  PLATE VI. 
               Fig. 10.]

If any reader still suspects that more is involved than the persistence of after-images, and their summation into a characteristic effect, he will find it interesting to study the illusion with a camera.  The ‘physiological’ functions referred to belong as well to the dry-plate as to the retina, while the former exhibits, presumably, neither contrast nor induction.  The illusion-bands can be easily photographed in a strong light, if white and black sectors are used in place of colored ones.  It is best to arrange the other variable factors so as to make the transition-bands as narrow as possible (p. 174, No. 4).  The writer has two negatives which show the bands very well, although so delicately that it is not feasible to try to reproduce them.

VIII.  SOME CONVENIENT DEVICES FOR EXHIBITING THE ILLUSION.

The influence of the width of sector is prettily shown by a special disc like that shown in Fig. 12 (Plate VII.), where the colors are dark-red and light-green, the shaded being the darker sector.  A narrow rod passed before such a disc by hand at a moderate rate will give over the outer ring equally wide green and red bands; but on the inner rings the red bands grow narrower, the green broader.