Harvard Psychological Studies, Volume 1 / Containing Sixteen Experimental Investigations from the Harvard Psychological Laboratory. - Unknown

Let Fig. 1 represent the upper portion of a color-wheel, with center at O, and with equal sectors A and B, in front of which a rod P oscillates to right and left on the same axis as that of the wheel. Let the disc rotate clockwise, and let P be observed in its rightward oscillation. Since the disc moves faster than the rod, the front of the sector A will at some point come up to and pass behind the rod P, say at p^A. P now hides a part of A and both are moving in the same direction. Since the disc still moves the faster, the front of A will presently emerge from behind P, then more and more of A will emerge, until finally no part of it is hidden by P. If, now, P were merely a line (having no width) and were not moving, the last of A would emerge just where its front edge had gone behind P, namely at p^A. But P has a certain width and a certain rate of motion, so that A will wholly emerge from behind P at some point to the right, say p^B. How far to the right this will be depends on the speed and width of A, and on the speed and width of P.

Now, similarly, at p^B the sector B has come around and begins to pass behind P. It in turn will emerge at some point to the right, say p^C. And so the process will continue. From p^A to p^B the pendulum covers some part of the sector A; from p^B to p^C some part of sector B; from p^C to P^D some part of A again, and so on.

Fig. 1.

If, now, the eye which watches this process is kept from moving, these relations will be reproduced on the retina. For the retinal area corresponding to the triangle p^AOp^B, there will be less stimulation from the sector A than there would have been if the pendulum had not partly hidden it. That is, the triangle in question will not be seen of the fused color of A and B, but will lose a part of its A-component. In the same way the triangle p^BOpC will lose a part of its B-component; and so on alternately. And by as much as either component is lost, by so much will the color of the intercepting pendulum (in this case, black) be present to make up the deficiency.

We see, then, that the purely geometrical relations of disc and pendulum necessarily involve for vision a certain banded appearance of the area which is swept by the pendulum, if the eye is held at rest. We have now to ask, Are these the bands which we set out to study? Clearly enough these geometrically inevitable bands can be exactly calculated, and their necessary changes formulated for any given change in the speed or width of A, B, or P. If it can be shown that they must always vary just as the bands we set out to study are observed to vary, it will be certain that the bands of the illusion have no other cause than the interception of retinal stimulation by the sectors of the disc, due to the purely geometrical relations between the sectors and the pendulum which hides them.

And exactly this will be found to be the case. The widths of the bands of the illusion depend on the speed and widths of the sectors and of the pendulum used; the colors and intensities of the bands depend on the colors and intensities of the sectors (and of the pendulum); while the total number of bands seen at one time depends on all these factors.

V. GEOMETRICAL DEDUCTION OF THE BANDS.

In the first place, it is to be noted that if the pendulum proceeds from left to right, for instance, before the disc, that portion of the latter which lies in front of the advancing rod will as yet not have been hidden by it, and will therefore be seen of the unmodified, fused color. Only behind the pendulum, where rotating sectors have been hidden, can the bands appear. And this accords with the first observation ([p. 167]), that "The rod appears to leave behind it on the disc a number of parallel bands." It is as if the rod, as it passes, painted them on the disc.

Clearly the bands are not formed simultaneously, but one after another as the pendulum passes through successive positions. And of course the newest bands are those which lie immediately behind the pendulum. It must now be asked, Why, if these bands are produced successively, are they seen simultaneously? To this, Jastrow and Moorehouse have given the answer, "We are dealing with the phenomena of after-images." The bands persist as after-images while new ones are being generated. The very oldest, however, disappear pari-passu with the generation of the new. We have already seen ([p. 169]) how well these authors have shown this, in proving that the number of bands seen, multiplied by the rate of rotation of the disc, is a constant bearing some relation to the duration of a retinal image of similar brightness to the bands. It is to be noted now, however, that as soon as the rod has produced a band and passed on, the after-image of that band on the retina is exposed to the same stimulation from the rotating disc as before, that is, is exposed to the fused color; and this would tend to obliterate the after-images. Thus the oldest bands would have to disappear more quickly than an unmolested after-image of the same original brightness. We ought, then, to see somewhat fewer bands than the formula of Jastrow and Moorehouse would indicate. In other words, we should find on applying the formula that the 'duration of the after-image' must be decreased by a small amount before the numerical relations would hold. Since Jastrow and Moorehouse did not determine the relation of the after-image by an independent measurement, their work neither confirms nor refutes this conjecture.