Those who have made quantitative studies in the optical illusion, especially in this particular illusion for open and filled spaces, have observed and commented on the instability of the illusion.  Auerbach[11] says, in his investigation of the quantitative variations of the illusion, that concentration of attention diminishes the illusion.  In the Zoellner figure, for instance, I have been able to notice the illusion fluctuate through a wide range, without eye-movements and without definitely attending to any point, during the fluctuation of the attention.  My experiments with the tactual illusion have led me to the conclusion that it fluctuates even more than the optical illusion.  Any deliberation in the judgment causes the apparent size of the filled space to shrink.  The judgments that are given most rapidly and naively exhibit the strongest tendency to overestimation; and yet these judgments are so consistent as to exclude them from the category of guesses.

   [11] Auerbach, F., Zeitsch. f.  Psych. u.  Phys. d. 
   Sinnesorgane, 1874, Bd.  VII., S. 152.

In most of my experiments, however, I did not insist on rapid and naive judgments; but by a close observation of the subject as he was about to make a judgment I could tell quite plainly which judgments were spontaneous and which were deliberate.  By keeping track of these with a system of marks, I was able to collect them in the end into groups representing fairly well the different degrees of attention.  The illusion is always greatest for the group of spontaneous judgments, which points to the conclusion that all illusions, tactual as well as visual, are very largely a function of attention.

In Section II.  I told of my attempt to reproduce the optical illusion upon the skin in the same form in which we find it for sight, namely, by presenting the open and filled spaces simultaneously, so that they might be held in a unitary grasp of consciousness and the judgment pronounced on the relative length of these parts of a whole.  However, as I have already said, the filled space appears longer, not only when given simultaneously, but also when given successively with the open space.  In the case of the optical illusion I am not so sure that the illusion does not exist if the two spaces are not presented simultaneously and adjacent, as Muensterberg asserts.  Although, to be sure, for me the illusion is not so strong when an interval is allowed between the two spaces, I was interested to know whether this was true also in the case of a touch illusion.  My previous tables did not enable me to compare the quantitative extent of the illusion for successive and simultaneous presentation.  But I found in two series which had this point directly in view, one with the subject F and one in which G served as subject, that the illusion was emphatically stronger when the open and filled spaces were presented simultaneously and adjacent.  In this instance, the illusion was doubtless a combination of two illusions—­a shrinking of the open space, on the one hand, and a lengthening of the filled space on the other hand.  Binet says, in his studies on the well-known Mueller-Lyer illusion, that he believes the illusion, in its highest effects at any rate, to be due to a double contrast illusion.