I have thus far continually spoken of the space containing the tacks as being the filled space, and the smooth surface as the open space.  But now we see that in reality the name should be reversed, especially for the longer distances.  The smooth surface is, after the first few centimeters, very emphatically filled with sensations arising from the organism which, as I have already intimated, are of the most vital importance in our spatial judgments.  Now, according to the most generally accepted psychological theories, it is these organic sensations which are the means whereby we measure time, and our spatial judgments are, in the last analysis, I will not for the present say dependent on, but at any rate fundamentally related to our time judgments.

VIII.

In the last section I attempted to explain the overestimation of short filled spaces, and the underestimation of long filled spaces by active touch, as the result of a double illusion arising from the differences in the manner and amount of attention given to the two kinds of spaces when they are held in immediate contrast.  This explanation was of course purely theoretical.  I have thus far offered no experiments to show that this double illusion of lengthening, on the one hand, and shortening, on the other, does actually exist.  I next made some simple experiments which seemed to prove conclusively that the phenomenon does not exist, or at least not in so important a way, when the time factor is not permitted to enter.

In these new experiments the filled and the open spaces were compared separately with optical distances.  After the finger-tip was drawn over the filled path, judgment was given on it at once by comparing it directly with an optical distance.  In this way the foreshortening effect of time was excluded.  In all these experiments it was seen that the filled space was judged longer when the judgment was pronounced on it at once than when an interval of time was allowed, either by drawing the finger-tip out over the open space, as in the previous experiment, or by requiring the subject to withhold his judgment until a certain signal was given.  Any postponement of the judgment resulted in the disappearance of a certain amount of the illusion.  The judgments that were made rapidly and without deliberation were subject to the strongest illusion.  I have already spoken of the unanimous testimony which all who have made quantitative studies in the corresponding optical illusions have given in this matter of the diminution of the illusion with the lapse of time.  The judgments that were made without deliberation always exhibited the strongest tendency to illusion.