The one generalization that I have thus far drawn from the investigation—namely, that the optical illusions are not reversed in passing from the field of touch, and that we therefore have a safe warrant for the conclusion that sight and touch do function alike—has contained no implicit or expressed assertion as to the origin of our notion of space. I have now reached the point where I must venture an explanation of the illusion itself.
The favorite hypothesis for the explanation of the geometrical optical illusions is the movement theory. The most generally accepted explanation of the illusion with whose tactual counterpart this paper is concerned, is that given by Wundt. Wundt’s explanation rests on variation in eye movements. When the eye passes over broken distances, the movement is made more difficult by reason of the frequent stoppages. The fact that the space which is filled with only one point in the middle is underestimated, is explained by Wundt on the theory that the eye has here the tendency to fix on the middle point and to estimate the distance by taking in the whole space at once without moving from this middle point. A different explanation for this illusion is offered by Helmholtz. He makes use of the aesthetic factor of contrasts. Wundt insists that the fact that this illusion is still present when there are no actual eye movements does not demonstrate that the illusion is not to be referred to a motor origin. He says, “If a phenomenon is perceived with the moving eye only, the influence of movement on it is undoubtedly true. But an inference cannot be drawn in the opposite direction, that movement is without influence on the phenomenon that persists when there is no movement."
 Wundt., W., ‘Physiolog.
Psych.,’ 4te Aufl., Leipzig, 1893,
Bd. II., S. 144.
 v. Helmholtz, H., ‘Handbuch
d. Physiol. Optik,’ 2te Aufl.,
Hamburg u. Leipzig, 1896, S. 705.
 Wundt, W., op. citat., S. 139.
Satisfactorily as the movement hypothesis explains this and other optical illusions, it yet falls short of furnishing an entirely adequate explanation. It seems to me certain that several causes exist to produce this illusion, and also the illusion that is often associated with it, the well-known Mueller-Lyer illusion. But in what degree each is present has not yet been determined by any of the quantitative studies in this particular illusion. I made a number of tests of the optical illusion, with these results: that the illusion is strongest when the attention is fixed at about the middle of the open space, that there is scarcely any illusion left when the attention is fixed on the middle of the filled space. It is stronger when the outer end-point of the open space is fixated than when the outer end of the filled space is fixated. For the moving eye, I find the illusion to be much stronger when the eye passes over the filled space first, and then over the open space, than when the process is reversed.