VII.

I have already spoken of the defects of the apparatus with which the experiments of the previous chapter were made. I shall now give an account of some experiments that were made with an apparatus designed to overcome these difficulties. This is shown in Fig. 10. The block _C_ was clamped to a table, while the block _A_ could be moved back and forth by the lever _B_, in order to bring up different lengths of filled space for judgment. For each judgment the subject brought his finger back to the strip _D_, and by moving his finger up along the edge of this strip he always came into contact with the first point of the new distance. The lever was not used in the present experiment; but in later experiments, where the points were moved under the finger tip, which was held stationary, this lever was very useful in producing different rates of speed. In one series of experiments with this apparatus the filled spaces were presented first, and in another series the open spaces were presented first. In the previous experiments, so far as I have reported them, the filled spaces were always presented first.

[Illustration: FIG. 10.]

In order to enable the subject to make proper connections with the first point in the filled space, when the open space was presented first, a slight depression was put in the smooth surface. This depression amounted merely to the suggestion of a groove, but it sufficed to guide the finger.

The general results of the first series of experiments with this apparatus were similar to those already given, but were based on a very much larger number of judgments. They show at once that the short filled spaces are overestimated, while the longer spaces are underestimated. The uniformity of this law has seemed to me one of the most significant results of this entire investigation. In the results already reported from the experiments with the former apparatus, I have mentioned the fact that the judgments upon the distances fluctuate more widely when one is filled and the other open, than when both are open. This fluctuation appeared again in a pronounced way in the present experiments. I now set about to discover the cause of this variation, which was so evidently outside of the limits of Weber's law.

TABLE XI.

I. II. Subjects. R. B. A. R. B. A. 2= 3.1 3.2 3.7 2.7 2.5 3.1 3= 4.5 4.4 4.1 4.1 4.0 3.6 4= 5.3 5.0 4.3 4.2 4.6 4.6 5= 6.0 5.1 5.8 5.9 5.2 4.3 6= 6.8 5.6 6.2 6.9 5.3 6.0 7= 7.4 7.2 6.9 7.6 7.3 6.8 8= 8.1 8.4 7.3 8.3 9.7 7.8 9= 9.3 9.0 8.5 9.5 8.9 8.7 Filled 10= 10.1 10.0 8.1 10.3 10.0 9.2 Spaces. 11= 10.5 9.3 9.7 10.6 8.7 9.6 12= 11.7 10.6 10.6 11.8 9.7 10.2 13= 12.3 10.9 10.9 11.1 10.2 9.6 14= 12.2 11.5 12.2 10.4 9.6 11.3 15= 13.6 12.3 11.9 13.1 10.1 9.6 16= 14.1 13.5 14.1 12.3 13.2 13.3 17= 14.9 12.9 14.6 14.1 12.6 13.7 18= 15.0 15.3 14.9 15.0 15.3 13.8 19= 15.2 14.6 15.2 14.1 13.9 14.2 20= 17.1 16.5 15.7 16.1 16.4 14.7

The first line of group I. reads: 'When the finger-tip was passed over a filled space of 2 cm., the subject _R_ measured off 3.1 cm. on the open space, the subject _B_ 3.2 cm., and the subject _A_ 3.7.' In group II., the numbers represent the distance measured off when both spaces were unfilled.

In my search for the cause of the variations reported previously I first tried the plan of obliging the subject to attend more closely to the filled space as his finger was drawn over it. In order to do this, I held a piece of fine wire across the line of the filled space, and after the subject had measured off the equal open space he was asked to tell whether or not he had crossed the wire. The wire was so fine that considerable attention was necessary to detect it. In some of the experiments the wire was inserted early in the filled space, and in some near the end. When it was put in near the beginning, it was interesting to notice, as illustrating the amount of attention that was being given to the effort of finding the wire, that the subject, as soon as he had discovered it, would increase his speed, relax the attention, and continue the rest of the journey more easily.

The general effect of this forcing of the attention was to increase the apparent length of the filled space. This conclusion was reached by comparing these results with those in which there was no compelled attention. When the obstacle was inserted early, the space was judged shorter than when it came at the end of the filled space. This shows very plainly the effect of continued concentration of attention, when that attention is directed intensely to the spot immediately under the finger-tip. When the attention was focalized in this way, the subject lost sight of the space as a whole. It rapidly faded out of memory behind the moving finger-tip. But when this concentration of attention was not required, the subject was able to hold together in consciousness the entire collection of discrete points, and he overestimated the space occupied by them. It must be remembered here that I mean that the filled space with the focalized attention was judged shorter than the filled space without such concentration of attention, but both of these spaces were judged shorter than the adjacent open space. This latter fact I shall attempt to explain later. Many other simple devices were employed to oblige the subject to fix his attention on the space as it was traversed by the finger. The results were always the same: the greater the amount of attention, the longer the distance seemed.

In another experiment, I tried the plan of tapping a bell as the subject was passing over the filled space and asking him, after he had measured off the equivalent open space, whether the sound had occurred in the first half or in the second half of the filled space.

When the finger-tip was drawn over two adjacent open spaces, and during the first a bell was tapped continuously, this kind of filled space was underestimated if the distance was long and overestimated if the distance was short. So, too, if a disagreeable odor was held to the nostrils while the finger-tip was being drawn over one of the two adjacent open spaces, the space thus filled by the sensations of smell followed the law already stated. But if an agreeable perfume was used, the distance always seemed shorter than when an unpleasant odor was given.

In all of these experiments with spaces filled by means of other than tactual sensations, I always compared the judgment on the filled and open spaces with judgments on two open spaces, in order to guard against any error due to unsymmetrical, subjective conditions for the two spaces. It is difficult to have the subject so seat himself before the apparatus as to avoid the errors arising from tension and flexion. In one experiment, a piece of plush was used for the filled space and the finger drawn over it against the nap. This filled space was judged longer than a piece of silk of equal length. The sensations from the plush were very unpleasant. One subject said, even, that they made him shudder. This was of course precisely what was wanted for the experiment. It showed that the affective tone of the sensation within the filled space was a most important factor in producing an illusory judgment of distance.

The overestimation of these filled spaces is evidently due in a large measure to æsthetic motives. The space that is filled with agreeable sensations is judged shorter than one which is filled with disagreeable sensations. In other words, the illusions in judgments on cutaneous space are not so much dependent on the quality of sensations that we get from the outer world through these channels, as from the amount of inner activity that we set over against these bare sense-perceptions.

I have already spoken of the defects of this method of measuring off equivalent distances as a means of getting at the quantitative amount of the illusion. The results that have come to light thus far have, however, amply justified the method. I had no difficulty, however, in adapting my apparatus to the other way of getting the judgments. I had a short curved piece of wire inserted in the handle, which could be held across the line traversed, and thus the end of the open space could be marked out. Different lengths were presented to the subject as before, but now the subject passed his finger in a uniform motion over the spaces, after which he pronounced the judgment 'greater,' 'equal,' or 'less.' The general result of these experiments was not different from those already given. The short, filled spaces were overestimated, while the longer ones were underestimated. The only difference was found to be that now the transition from one direction to the other was at a more distant point. It was, of course, more difficult to convert these qualitative results into a quantitative determination of the illusion.

Before passing to the experiments in which the open spaces were presented first, I wish to offer an explanation for the divergent tendencies that were exhibited through all the experiments of the last two sections, namely, that the short filled spaces are overestimated and the long spaces underestimated. Let us take two typical judgments, one in which a filled space of 3 cm. is judged equal to an open space of 4.2 cm., and then one in which the filled space is 9 cm., and is judged equal to an open space of 7.4 cm. In the case of the shorter distance, because of its shortness, after the finger leaves it, it is held in a present state of consciousness for some moments, and does not suffer the foreshortening that comes from pastness. This is, however, only a part of the reason for its overestimation. After the finger-tip has left the filled space, and while it is traversing the first part of the open space, there is a dearth of sensations. The tactual sensations are meager and faint, and muscular tensions have not yet had time to arise. It is not until the finger has passed over several centimeters of the distance, that the surprise of its barrenness sets up the organic sensations of muscular strain. One subject remarked naïvely at the end of some experiments of this kind, that the process of judging was an easy and comfortable affair so long as he was passing over the filled space, but when he set out upon the open space he had to pay far more strict attention to the experiment.

By a careful introspection of the processes in my own case, I came to the conclusion that it is certainly a combination of these two illusions that causes the overestimation of the short filled distances. In the case of the long distances, the underestimation of the filled space is, I think, again due to a combination of two illusions. When the finger-tip leaves the filled space, part of it, because of its length, has already, as it were, left the specious present, and has suffered the foreshortening effect of being relegated to the past. And, on the other hand, after the short distance of the open space has been traversed the sensations of muscular strain become very pronounced, and cause a premature judgment of equality.

One subject, who was very accurate in his judgments, and for whom the illusion hardly existed, said, when asked to explain his method of judging, that after leaving the filled space he exerted a little more pressure with his finger as he passed over the open space, so as to get the same quantity of tactual sensations in both instances. The muscular tension that was set up when the subject had passed out over the open space a short way was very plainly noticeable in some subjects, who were seen at this time to hold their breath.

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.