It was of course very easy to change the figures and vary them widely in form, color, and intensity. Most of those employed, however, were rather small, subtending an angular distance of not more than one degree. Since the whole opening did not subtend an angle of more than three degrees or so, nearly all the phases of the stimulation occurred at the fovea.

We noticed that the form of the stimulating images themselves seemed to suffer modification as the light swung by, not only because of the train of after-images which dragged behind them over the retina, but in other ways as well. For instance, a circular image (Plate III, Fig. 1) appeared crescent-shaped, and its forward edge possessed greater curvature than the segment of the circle which produced it. It was longer also from horn to horn than the diameter of the generating circle, and a faint haze surrounded the points extending outward and backward until lost in the blackness of the background. Von Kries remarks that a circular moving image appears cylindrical in form with a concave edge behind. By using a little higher speed we observed this phenomenon. At first we thought the crescent-shaped image to be due merely to an intensely black after-process, which Bidwell describes as following the positive image of a bright white light. This, taking place before the circular disc of light had gone forward a distance equal to its own diameter, would overlap the bright image from behind and a crescent-shaped figure would result, but the increase in width and convexity of the stimulating image as well as the laterally trailing clouds of light remained to be explained, and as this could not be done in terms of anything which might happen to the back of the image, another explanation had to be sought. In order to determine the effect of the form of the figure used as a source of light on the form of the apparent image, several differently shaped figures were employed. In place of the original circle, an oblong pointed at both ends was tried (Plate III, Fig. 2). The front of this figure appeared very convex indeed, while the ends, which, owing to the shape of the figure, were very much less effective as a stimulating source, trailed far behind the centre.

A crescent-shaped figure (Plate III, Fig. 4) gave rise to a very pretty phenomenon. When it moved toward its concave side, it appeared very much less concave on that side than the real figure, but when it moved the other way, toward its convex side, it seemed very much more curved than it was in reality.[23]

PLATE III.

No. 3, a simple oblong figure, appeared curved like the others, almost as perfect a crescent as any of them.

The idea occurred to me that perhaps all these modifications in the curvature of the figures could be explained if we assumed two things: First: that there is a spreading of excitation from one portion of the retina to another. Each point will therefore be stimulated not only by the light falling directly upon it, but it will also derive a certain reënforcement of its stimulation from the points surrounding it. Thus a point lying toward the centre of one of these figures would be more favorably situated for receiving reënforcement than one located toward the periphery, where there are few neighboring points, and those lying mostly in one direction, namely, toward the centre.

This may be represented diagramatically, as in the illustration (Plate IV, Fig. 10), where the horizontal coördinates represent the spatial dimensions of an oblong image and the vertical coördinates the intensity of the excitation due to direct stimulation and its reënforcement by surrounding points at various portions of the figure.[24] Secondly I assumed that the stimulation at one part of the figure being thus rendered more intense, that part would appear in consciousness more quickly than the others and cause a modification in the form of the figure.[25] For example, in the case of the oblong figure, the light would be rendered most intense at the centre and less and less intense toward the ends, for the points in the centre of the figure will have their intensity increased by nervous excitation spreading to them from points lying toward the ends. Those toward the ends will be reënforced by light coming only from toward the centre. Thus the intensity of the centre of the figure will be increased, and as the figure moves across before the observer, the centre, appearing first in consciousness, would likewise appear foremost in space, the points near the centre a little later and so on, until finally, the ends being the last to appear, the whole front of the figure would take the form of a convex curve, after the manner in which it was observed. The back of the figure also appears curved, probably because of the fact that the front of the negative after-image, which closely follows it, is of the same shape as the front of the positive image, as was shown in the case of the circular figure.[26]

It is of course a well-known psychological fact that a light of greater intensity will take less time in coming into consciousness than one of less intensity. In this case, however, it was necessary to find some way of showing such differences between lights which were very little different in intensity. For one is practically unable to see any difference in intensity between the parts of a stationary image. So unless it could be shown that a difference in intensity between two sources of illumination, so small as to be imperceptible to the observer, will nevertheless make its presence known by the appearance of the brighter light in consciousness before the other, the explanation which I have suggested for the curvature of the images would have to be abandoned.