Chapter V: Section II: showed that the shorter filled distances are (1)

underestimated, while the longer distances are overestimated, and that between the two there is somewhat of an 'indifferent zone.' In those experiments the judgments were made directly on the cutaneous distances themselves. In the experiments the results of which are plotted in these curves, the judgment of distances is indirectly reached through the function of localization. But it will be observed that the results are substantially the same. The longer distances are overestimated and the shorter distances underestimated. The curves in Figs. 4, 5 and 6 were plotted on the combined results for two subjects. But before the combination was made the two main tendencies which I have just mentioned were observed to be the same for both subjects.

It will be remembered also that in these experiments, where the judgment of distance was based directly on the cutaneous impression, the underestimation of the short, filled distance was lessened and even turned into an overestimation, by giving greater distinctness to the end points, in allowing them to come in contact with the skin just before or just after the filling. The results here are again the same as before. The tendency to underestimate is lessened by this device. Whenever, then, a filled space is made up of points which are distinctly perceived as discrete--and this is shown in the longer curves by the comparative accuracy with which the points are located--these spaces are overestimated.

In all of these experiments on localization, the judgments were given with open eyes, by naming the visual points under which the tactual points seemed to lie. I have already spoken of the other method which I also employed. This consisted in marking points on paper which seemed to correspond in number and position to the points on the skin. During this process the eyes were kept closed. This may appear to be a very crude way of getting at the illusion, but from a large number of judgments which show a surprising consistency I received the emphatic confirmation of my previous conclusion, that filled spaces were overestimated. These experiments were valuable also from the fact that here the cutaneous space was estimated by the muscle sense, or active touch, as it is called.

In the experiments so far described the filling in of the closed space was always made by means of stationary points. I shall now give a brief account of some experiments which I regard as very important for the theory that I shall advance later. Here the filling was made by means of a point drawn over the skin from one end of a two-point distance to the other.

These experiments were made on four different parts of the skin--the forehead, the back of the hand, the abdomen, and the leg between the knee and the thigh. I here forsook the plan which I had followed almost exclusively hitherto, that of comparing the cutaneous distances with each other directly. The judgments now were secured indirectly through the medium of visual distances. There was placed before the subject a gray card, upon which were put a series of two-point distances ranging from 2 to 20 cm. The two-point distances were given on the skin, and the subject then selected from the optical distances the one that appeared equal to the cutaneous distance. This process furnished the judgments on open spaces. For the filled spaces, immediately after the two-point distance was given a blunt stylus was drawn from one point to the other, and the subject then again selected the optical distance which seemed equal to this distance filled by the moving point.

The results from these experiments point very plainly in one direction. I have therefore thought it unnecessary to go into any further detail with them than to state that for all subjects and for all regions of the skin the filled spaces were overestimated. This overestimation varied also with the rate of speed at which the stylus was moved. The overestimation is greatest where the motion is slowest.

Vierordt[7] found the same result in his studies on the time sense, that is, that the more rapid the movement, the shorter the distance seems. But lines drawn on the skin are, according to him, underestimated in comparison with open two-point distances. Fechner[8] also reported that a line drawn on the skin is judged shorter than the distance between two points which are merely touched. It will be noticed, however, that my experiments differed from those of Vierordt and Fechner in one essential respect. This difference, I think, is sufficient to explain the different results. In my experiments the two-point distance was held on the skin, while the stylus was moved from one point to the other. In their experiments the line was drawn without the points. This of course changes the objective conditions. In simply drawing a line on the skin the subject rapidly loses sight of the starting point of the movement. It follows, as it were, the moving point, and hence the entire distance is underestimated. I made a small number of tests of this kind, and found that the line seemed shorter than the point distance as Fechner and Vierordt declared. But when the point distance is kept on the skin while the stylus is being drawn, the filling is allowed its full effect in the judgment, inasmuch as the end points are perceived as stationary landmarks. The subjects at first found some difficulty in withholding their judgments until the movement was completed. Some subjects declared that they frequently made a preliminary judgment before the filling was inserted, but that when the moving point approached the end point, they had distinctly the experience that the distance was widening. In these experiments I used five sorts of motion, quick and heavy, quick and light, slow and heavy, slow and light, and interrupted. I made no attempt to determine either the exact amount of pressure or the exact rate. I aimed simply at securing pronounced extremes. The slow rate was approximately 3, and the fast approximately 15 cm. per second.

[7] 'Zeitsinn,' Tübingen, 1858.

[8] Fechner, G. Th., 'Elem. d. Psychophysik,' Leipzig, 1889; 2.
Theil, S. 328.

I have already said that these filled spaces were invariably overestimated and that the slower the movement, the greater, in general, is the overestimation. In addition to the facts just stated I found also, what Hall and Donaldson[9] discovered, that an increase in the pressure of a moving point diminishes the apparent distance.

[9] Hall, G. St., and Donaldson, H.H., 'Motor Sensations on the
Skin,' _Mind_, 1885, X., p. 557.

Nichols,[10] however, says that heavy movements seem longer and light ones shorter.

[10] _Op. citat.,_ p. 98.

V.

There are several important matters which might properly have been mentioned in an earlier part of this paper, in connection with the experiments to which they relate, but which I have designedly omitted, in order not to disturb the continuity in the development of the central object of the research. The first of these is the question of the influence of visualization on the judgments of cutaneous distances. This is in many ways a most important question, and confronts one who is making studies in tactual space everywhere. The reader may have already noticed that I have said but little about the factor of visualization in any of my experiments, and may have regarded it as a serious omission. It might be offered as a criticism of my work that the fact that I found the tactual illusions to exist in the same sense as the optical illusions was perhaps due to the failure to exclude visualization. All of the subjects declare that they were unable to shut out the influence of visualizing entirely. Some of the subjects who were very good visualizers found the habit especially insistent. I think, however, that not even in these latter cases does this factor at all vitiate my conclusions.

It will be remembered that the experiments up to this time fall into two groups, first, those in which the judgments on the cutaneous distances were reached by direct comparisons of the sensations themselves; and secondly, those in which the sensations were first localized and then the judgment of the distance read from these localizations. Visualizing, therefore, entered very differently into the two groups. In the first instance all of the judgments were made with the eyes closed, while all of the localizations were made with the eyes open. I was uncertain through the whole of the first group of experiments as to just how much disturbance was being caused in the estimation of the distance by visualizing. I therefore made a series of experiments to determine what effect was produced upon the illusion if in the one set of judgments one purposely visualized and in the other excluded visualizing as far as possible. In my own case I found that after some practice I could give very consistent judgments, in which I felt that I had abstracted from the visualized image of the arm almost entirely. I did not examine these results until the close of the series, and then found that the illusion was greater for those judgments in which visualization was excluded; that is, the filled space seemed much larger when the judgment was made without the help of visualization. It is evident, therefore, that the tactual illusion is influenced rather in a negative direction by visualization.

In the second group of experiments, where the judgments were obtained through the localization of the points, it would seem, at first sight, that the judgments must have been very largely influenced by the direct vision used in localizing the points. The subject, as will be remembered, looked down at a card of numbered points and named those which were directly over the contacts beneath. Here it should seem that the optical illusion of the overestimation of filled spaces, filled with points on the card, would be directly transmitted to the sensation on the skin underneath. Such criticism on this method of getting at the illusion has already been made orally to me. But this is obviously a mistaken objection. The points on the card make a filled space, which of course appears larger, but as the points expand, the numbers which are attached to them expand likewise, and the optical illusion has plainly no influence whatever upon the tactual illusion.

A really serious objection to this indirect method of approaching the illusion is, that the character of the cutaneous sensation is never so distinctly perceived when the eyes are open as when they are closed. Several subjects often found it necessary to close their eyes first, in order to get a clear perception of the locality of the points; they then opened their eyes, to name the visual points directly above. Some subjects even complained that when they opened their eyes they lost track of the exact location of the touch points, which they seemed to have when their eyes were closed. The tactual impression seems to be lost in the presence of active vision.

On the whole, then, I feel quite sure in concluding that the overestimation of the filled cutaneous spaces is not traceable to the influence of visualization. Parrish has explained all sporadic cases of overestimation as due to the optical illusion carried over in visualization. I have already shown that in my experiments visualization has really the opposite effect. In Parrish's experiments the overestimation occurred in the case of those collections of points which were so arranged as to allow the greatest differentiation among the points, and especially where the end-points were more or less distinct from the rest. This, according to my theory, is precisely what one would expect.

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 Zöllner 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 naïvely 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 naïve 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 Münsterberg 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 Müller-Lyer illusion, that he believes the illusion, in its highest effects at any rate, to be due to a double contrast illusion.

This distortion of contrasted distances I have found in more than one case in this investigation--not only in the case of distances in which there is a qualitative difference, but also in the case of two open distances. In one experiment, in which open distances on the skin were compared with optical point distances, a distance of 10 cm. was given fifty times in connection with a distance of 15 cm., and fifty times in connection with a distance of 5 cm. In the former instance the distance of 10 cm. was underestimated, and in the other it was overestimated.

The general conclusion of the entire investigation thus far may be summed up in the statement: _Wherever the objective conditions are the same in the two senses, the illusion exists in the same direction for both sight and touch._

VI.

Thus far all of my experiments were made with _passive_ touch. I intend now to pursue this problem of the relation between the illusions of sight and touch into the region of _active_ touch. I have yielded somewhat to the current fashion in thus separating the passive from the active touch in this discussion. I have already said that I believe it would be better not to make this distinction so pronounced. Here again I have concerned myself primarily with only one illusion, the illusion which deals with open and filled spaces. This is the illusion to which Dresslar[12] devoted a considerable portion of his essay on the 'Psychology of Touch,' and which he erroneously thought to be the counterpart of the optical illusion for open and filled spaces. One of the earliest notices of this illusion is that given by James,[13] who says, "Divide a line on paper into two equal halves, puncture the extremities, and make punctures all along one of the halves; then, with the finger-tip on the opposite side of the paper, follow the line of punctures; the empty half will seem much longer than the punctured half."

[12] Dresslar, F.B., _Am. Journ. of Psy._, 1894, VI., p. 313.

[13] James, W., 'Principles of Psychology,' New York, 1893,
II., p. 250.

James has given no detailed account of his experiments. He does not tell us how many tests were made, nor how long the lines were, nor whether the illusion was the same when the open half was presented first. Dresslar took these important questions into consideration, and arrived at a conclusion directly opposite to that of James, namely, that the filled half of the line appears larger than the open half. Dresslar's conclusion is, therefore, that sight and touch function alike. I have already said that I think that Parrish was entirely right in saying that this is not the analogue of the familiar optical illusion. Nevertheless, I felt sure that it would be quite worth the while to make a more extensive study than that which Dresslar has reported. Others besides James and Dresslar have experimented with this illusion. As in the case of the illusion for passive touch, there are not wanting champions of both opinions as to the direction in which this illusion lies.

I may say in advance of the account of my experiments, that I have here also found a ground of reconciliation for these two divergent opinions. Just as in the case of the illusion for passive touch, there are here also certain conditions under which the filled space seems longer, and other conditions under which it appears shorter than the open space. I feel warranted, therefore, in giving in some detail my research on this illusion, which again has been an extended one. I think that the results of this study are equally important with those for passive touch, because of the further light which they throw on the way in which our touch sense functions in the perception of the geometrical illusions. Dresslar's experiments, like those of James, were made with cards in which one half was filled with punctures. The number of punctures in each centimeter varied with the different cards. Dresslar's conclusion was not only that the filled space is overestimated, but also that the overestimation varies, in a general way, with the number of punctures in the filling. Up to a certain point, the more holes there are in the card, the longer the space appears.

I had at the onset of the present experiment the same feeling about Dresslar's work that I had about Parrish's work, which I have already criticised, namely, that a large number of experiments, in which many variations were introduced, would bring to light facts that would explain the variety of opinion that had hitherto been expressed. I was confident, however, that what was most needed was a quantitative determination of the illusion. Then, too, inasmuch as the illusion, whatever direction it takes, is certainly due to some sort of qualitative differences in the two kinds of touch sensations, those from the punctured, and those from the smooth half, it seemed especially desirable to introduce as many changes into the nature of the filling as possible. The punctured cards I found very unsatisfactory, because they rapidly wear off, and thus change the quality of the sensations, even from judgment to judgment.

The first piece of apparatus that I used in the investigation of the illusion for open and filled space with active touch is shown in Fig. 7. A thimble _A_, in which the finger was carried, moved freely along the rod _B_. The filled spaces were produced by rows of tacks on the roller _C_. By turning the roller, different kinds of fillings were brought into contact with the finger-tip. The paper _D_, on which the judgments were recorded by the subject, could be slowly advanced under the roller _E_. Underneath the thimble carrier there was a pin so arranged that, by a slight depression of the finger, a mark was made on the record paper beneath. A typical judgment was made as follows; the subject inserted his finger in the thimble, slightly depressed the carrier to record the starting points, then brought his finger-tip into contact with the first point in the filled space. The subject was, of course, all the while ignorant of the length or character of the filling over which he was about to pass. The finger-tip was then drawn along the points, and out over the smooth surface of the roller, until the open space passed over was judged equal to the filled space. Another slight depression of the finger registered the judgment on the paper below. The paper was then moved forward by turning the roller _E_, and, if desired, a different row of pins was put in place for judgment by revolving the roller _C_. The dividing line between the open and filled spaces was continuously recorded on the paper from below by a pin not shown in the illustration.

The rollers, of which I had three, were easily removed or turned about, so that the open space was presented first. In one of the distances on each roller both spaces were unfilled. This was used at frequent intervals in each series and served somewhat the same purpose as reversing the order in which the open and filled spaces were presented. With some subjects this was the only safe way of securing accurate results. The absolute distances measured off were not always a sure criterion as to whether the filled space was under-or overestimated. For example, one rather erratic subject, who was, however, very constant in his erratic judgments, as an average of fifty judgments declared a filled space of 4 cm. to be equal to an open space of 3.7 cm. This would seem, on the surface, to mean that the filled space had been underestimated. But with these fifty judgments there were alternated judgments on two open spaces, in which the first open space was judged equal to the second open space of 3.2 cm. From this it is obvious that the effect of the filling was to cause an overestimation--not underestimation as seemed at first sight to be the case.

In another instance, this same subject judged a filled space of 12.0 cm. to be equal to an open space of 12.9 cm., which would seem to indicate an overestimation of the filled space. But an average of the judgments on two open spaces that were given in alternation shows that an equivalence was set up between the two at 13.7 cm. for the second open space. This would show that the filling of a space really produced an underestimation.

The same results were obtained from other subjects. In my experiments on the illusion for passive touch, I pointed out that it is unsafe to draw any conclusion from a judgment of comparison between open and filled cutaneous spaces, unless we had previously determined what might be called a standard judgment of comparison between two open spaces. The parts of our muscular space are quite as unsymmetrical as the parts of our skin space. The difficulties arising from this lack of symmetry can best be eliminated by introducing at frequent intervals judgments on two open spaces. As I shall try to show later, the psychological character of the judgment is entirely changed by reversing the order in which the spaces are presented, and we cannot in this way eliminate the errors due to fluctuations of the attention.

The apparatus which I used in these first experiments possesses several manifest advantages. Chief among these was the rapidity with which large numbers of judgments could be gathered and automatically recorded. Then, in long distances, when the open space was presented first, the subject found no difficulty in striking the first point of the filled space. Dresslar mentioned this as one reason why in his experiments he could not safely use long distances. His subjects complained of an anxious straining of the attention in their efforts to meet the first point of the filled space.

There are two defects manifest in this apparatus. In the first place, the other tactual sensations that arise from contact with the thimble and from the friction with the carrier moving along the sliding rod cannot be disregarded as unimportant factors in the judgments. Secondly, there is obviously a difference between a judgment that is made by the subject's stopping when he reaches a point which seems to him to measure off equal spaces, and a judgment that is made by sweeping the finger over a card, as in Dresslar's experiments, with a uniform motion, and then, after the movement has ceased, pronouncing judgment upon the relative lengths of the two spaces. In the former case the subject moves his finger uniformly until he approaches the region of equality, and then slackens his speed and slowly comes to a standstill. This of course changes the character of the judgments. Both of these defects I remedied in another apparatus which will be described later. For my present purpose I may disregard these objections, as they affect alike all the judgments.

In making the tests for the first series, the subject removed his finger after each judgment, so that the position of the apparatus could be changed and the subject made to enter upon the new judgment without knowing either the approximate length or the nature of the filling of this new test. With this apparatus no attempt was made to discover the effects of introducing changes in the rate of speed. The only requirement was that the motion should be uniform. This does not mean that I disregarded the factor of speed. On the contrary, this _time_ element I consider as of the highest consequence in the whole of the present investigation. But I soon discovered, in these experiments, that the subjects themselves varied the rate of speed from judgment to judgment over a wide range of rates. There was no difficulty in keeping track of these variations, by recording the judgments under three groups, fast, slow and medium. But I found that I could do this more conveniently with another apparatus, and will tell at a later place of the results of introducing a time element. In these first experiments the subject was allowed to use any rate of speed which was convenient to him.

TABLE IX.

Subjects P R F Rr
2= 3.8 3.6 2.9 2.8
3= 4.1 4.1 4.2 3.9
4= 4.7 5.1 4.3 4.3
Filled 5= 5.2 5.6 5.8 6.0
Spaces. 6= 6.0 6.3 6.4 5.2
7= 6.8 6.5 6.6 7.0
8= 7.5 7.6 7.2 7.4
9= 8.3 8.1 8.2 8.6
10= 8.9 9.1 8.7 8.5

TABLE X.

Subjects P R F Rr
2= 4.0 3.8 3.2 2.6
3= 4.3 4.2 4.4 3.6
4= 4.6 5.6 4.6 4.8
Filled 5= 5.4 6.1 5.6 5.7
Spaces. 6= 6.2 6.4 6.8 6.9
7= 7.3 6.8 7.9 7.2
8= 7.8 7.4 7.3 7.8
9= 8.6 8.0 7.9 8.9
10= 9.3 9.1 8.9 8.5

TABLES IX. AND X.

First line reads: 'When the finger-tip was drawn over a filled
distance of 2 cm., the subject _P_ measured off 3.8 on the
open surface, the subject _R_ 3.6, etc.' Each number is the
average of five judgments. In Table IX. the points were set at
regular intervals. In Table X. the filling was made irregular
by having some points rougher than the others and set at
different intervals.

I can give here only a very brief summary of the results with this apparatus. In Tables IX. and X. I give a few of the figures which will show the tendency of the experiments. In these tests a different length and a different filling were given for each judgment. The result of the experiments of this group is, first, that the _shorter filled spaces are judged longer and the longer spaces shorter_ than they really were. Second, that an increase in the number of points in the filled space causes no perceptible change in the apparent length. Third, that when the filling is so arranged as to produce a tactual rhythm by changing the position or size of every third point, the apparent length of the space is increased. It will be noticed, also, that this is just the reverse of the result that was obtained for passive touch. These facts, which were completely borne out by several other experiments with different apparatus which I shall describe later, furnish again a reason why different investigators have hitherto reported the illusion to exist, now in one direction, now in the other. Dresslar drew the conclusion from his experiments that the filled spaces are always overestimated, but at the same time his figures show an increasing tendency towards an underestimation of the filled spaces as the distances increased in length. I shall later, in connection with similar results from other experiments on this illusion, endeavor to explain these anomalous facts.

In section IV. I mentioned the fact that I found the illusion for passive touch to be subject to large fluctuations. This is true also of the illusion for active touch. When the finger-tip is drawn over the filled, and then out over the open space, the limits between which the stopping point varies is a much wider range than when the finger-tip is drawn over two open spaces. In the latter case I found the variation to follow Weber's Law in a general way. At first I thought these erratic judgments were mere guesses on the part of the subject; but I soon discovered a certain consistency in the midst of these extreme fluctuations. To show what I mean, I have plotted some diagrams based on a few of the results for three subjects. These diagrams are found in Fig. 8. It will be observed that the curve which represents the collection of stopping points is shorter and higher where the judgments were on two open spaces. This shows plainly a greater accuracy in the judgments than when the judgments were on a filled and an open space, where the curves are seen to be longer and flatter. This fluctuation in the illusion becomes important in the theoretical part of my discussion, and, at the risk of apparently emphasizing unduly an insignificant matter, I have given in Fig. 9 an exact copy of a sheet of judgments as it came from the apparatus. This shows plainly how the illusion wears away with practice, when one distance is given several times in succession. The subject was allowed to give his judgment on the same distance ten times before passing to another. A glance at the diagram will show how pronounced the illusion is at first, and how it then disappears, and the judgment settles down to a uniform degree of accuracy. It will be seen that the short filled space is at first overestimated, and then, with the succeeding judgments, this overestimation is gradually reduced. In the case of the longer filled distances (which could not be conveniently reproduced here) the spaces were at first underestimated, and then this underestimation slowly decreased.

None of the qualitative studies that have hitherto been made on this illusion have brought to light this significant wearing away of the illusion.

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.

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.

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.

I have already said that the illusion for passive touch was greatest when the two spaces were presented simultaneously and adjacent. Dresslar has mentioned in his studies on the 'Psychology of Touch,' that the time factor cannot enter into an explanation of this illusion; but the experiments of which I have just spoken seem to point plainly to a very intimate relation between this illusion and the illusions in our judgments of time. We have here presented on a diminutive scale the illusions which we see in our daily experience in comparing past with present stretches of time. It is a well-known psychological experience that a filled time appears short in passing, but long in retrospect, while an empty time appears long in passing, but short in retrospect. Now this illusion of the open and filled space, for the finger-tip, is at every point similar to the illusion to which our time judgment is subject. If we pronounce judgment on a filled space or filled time while we are still actually living in it, it seems shorter than it really is, because, while we pay attention to the discrete sensations of external origin, we lose sight of the sensations of internal origin, which are the sole means whereby we measure lapse of time, and we consequently underestimate such stretches of time or space. But when the sensations from the outer world which enter into such filled spaces or times exist only in memory, the time-measuring sensations of internal origin are allowed their full effect; and such spaces and times seem much longer than when we are actually passing through them.

I dwell on this illusion at a length which may seem out of proportion to its importance. My object has been to show how widely different are the objective conditions here from what they are in the optical illusion which has so often been called the analogue of this. James[14] has said of this tactual illusion: 'This seems to bring things back to the unanalyzable laws, by reason of which our feeling of size is determined differently in the skin and in the retina even when the objective conditions are the same.' I think that my experiments have shown that the objective conditions are not the same; that they differ in that most essential of all factors, namely, the time element. Something very nearly the analogue of the optical illusion is secured when we take very short open and filled tactual spaces, and move over them very rapidly. Here the illusion exists in the same direction as it does for sight, as has already been stated. On the other hand, a phenomenon more nearly parallel to the tactual illusion, as reported in the experiments of James and Dresslar, is found if we take long optical distances, and traverse the open and filled spaces continuously, without having both parts of the line entirely in the field of view at any one moment. I made a few experiments with the optical illusion in this form. The filled and open spaces were viewed by the subject through a slot which was passed over them. These experiments all pointed in the direction of an underestimation of a filled space. Everywhere in this illusion, then, where the objective conditions were at all similar for sight and touch, the resulting illusion exists in the same direction for both senses.

[14] James, William, 'Principles of Psychology,' New York, II.,
p. 250.

Throughout the previous experiments with the illusion for active touch we saw the direct influence of the factor of time. I have yet one set of experiments to report, which seems to me to prove beyond the possibility of a doubt the correctness of my position. These experiments were made with the apparatus shown in Fig. 10. The subjects proceeded precisely as before. The finger-tip was passed over the filled space, and then out over the open space, until an equivalent distance was measured off. But while the subject was drawing his fingers over the spaces, the block _A_ was moved in either direction by means of the lever _B_. The subjects were all the while kept ignorant of the fact that the block was being moved. They all expressed great surprise on being told, after the experiments were over, that the block had been moved under the finger-tip through such long distances without their being able to detect it. The block always remained stationary as the finger passed over one space, but was moved either with or against the finger as it passed over the other space.

TABLE XII.

A B C D E
4 7.1 2.6 2.4 6.5
5 8.3 3.1 3.3 8.7
6 8.2 3.3 4.1 9.2
7 9.7 3.6 3.7 10.1
8 10.5 3.7 4.5 10.6
9 12.4 4.8 5.1 11.5
10 13.1 4.7 5.3 13.2
11 13.3 5.3 6.1 14.6
12 13.7 6.9 7.2 12.7
13 14.6 7.5 8.1 13.2
14 15.3 8.2 9.4 15.6
15 15.7 8.7 10.3 14.9

Column _A_ contains the filled spaces, columns _B_, _C_, _D_,
_E_ the open spaces that were judged equal. In _B_ the block
was moved with the finger, and in _C_ against the finger as it
traversed the filled space, and in _D_ and _E_ the block was
moved with and against the finger respectively as it passed
over the open space. The block was always moved approximately
one-half the distance of the filled space.

I have given some of the results for one subject in Table XII. These results show at a glance how potent a factor the time element is. The quantity of tactual sensations received by the finger-tip enters into the judgment of space to no appreciable extent. With one subject, after he had passed his finger over a filled space of 10 cm. the block was moved so as almost to keep pace with the finger as it passed over the open space. In this way the subject was forced to judge a filled space of 10 cm. equal to only 2 cm. of the open space. And when the block was moved in the opposite direction he was made to judge a distance of 10 cm. equal to an open distance of 16 cm.