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 aesthetic 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 naively 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.

The criticism may be made on these experiments that the subject has not in reality been obliged to rely entirely upon the time sense, but that he has equated the two spaces as the basis of equivalent muscle or joint sensation, which might be considered independent of the sensations which yield the notion of time. I made some experiments, however, to prove that this criticism would not be well founded. By arranging the apparatus so that the finger-tip could be held stationary, and the block with the open and filled spaces moved back and forth under it, the measurement by joint and muscle sensations was eliminated.

It will be observed that no uniform motion could be secured by simply manipulating the lever with the hand. But uniformity of motion was not necessary for the results at which I aimed here. Dresslar has laid great stress on the desirability of having uniform motion in his similar experiments. But this, it seems to me, is precisely what is not wanted. With my apparatus, I was able to give widely different rates of speed to the block as it passed under the finger-tip. By giving a slow rate for the filled space and a much more rapid rate for the open space, I found again that the subject relied hardly at all on the touch sensations that came from the finger-tip, but almost entirely on the consciousness of the amount of time consumed in passing over the spaces. The judgments were made as in the previous experiments with this apparatus. When the subject reached the point in the open space which he judged equal to the filled space, he slightly depressed his finger and stopped the moving block. In this way, the subject was deprived of any assistance from arm-movements in his judgments, and was obliged to rely on the tactual impressions received at the finger-tip, or on his time sense. That these tactual sensations played here also a very minor part in the judgment of the distance was shown by the fact that these sensations could be doubled or trebled by doubling or trebling the amount of space traversed, without perceptibly changing the judgment, provided the rate of speed was increased proportionately. Spaces that required the same amount of time in traversing were judged equal.

In all these experiments the filled space was presented first. When the open space was presented first, the results for four out of five subjects were just reversed. For short distances the filled space was underestimated, for long distances the filled space was overestimated. A very plausible explanation for these anomalous results is again to be found in the influence of the time factor. The open space seemed longer while it was being traversed, but rapidly foreshortened after it was left for the filled space. While on the other hand, if the judgment was pronounced while the subject was still in the midst of the filled space, it seemed shorter than it really was. The combination of these two illusions is plainly again responsible for the underestimation of the short filled spaces. The same double illusion may be taken to explain the opposite tendency for the longer distances.

IX.

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.[15] 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.[16] 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."[17]

[15] Wundt., W., 'Physiolog. Psych.,' 4te Aufl., Leipzig, 1893, Bd. II., S. 144.

[16] v. Helmholtz, H., 'Handbuch d. Physiol. Optik,' 2te Aufl., Hamburg u. Leipzig, 1896, S. 705.

[17] 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.

Now, the movement hypothesis does not, it seems to me, sufficiently explain all the fluctuations in the illusion. My experiments with the tactual illusion justify the belief that the movement theory is even less adequate to explain all of the variations there, unless the movement hypothesis is given a wider and richer interpretation than is ordinarily given to it. In the explanation of the tactual illusion which I have here been studying two other important factors must be taken into consideration. These I shall call, for the sake of convenience, the aesthetic factor and the time factor. These factors should not, however, be regarded as independent of the factor of movement. That term should be made wide enough to include these within its meaning. The importance of the time factor in the illusion for passive touch I have already briefly mentioned. I have also, in several places in the course of my experiments, called attention to the importance of the aesthetic element in our space judgments. I wish now to consider these two factors more in detail.

The foregoing discussion has pointed to the view that the space-perceiving and the localizing functions of the skin have a deep-lying common origin in the motor sensations. My experiments show that, even in the highly differentiated form in which we find them in their ordinary functioning, they plainly reveal their common origin. A formula, then, for expressing the judgments of distance by means of the resting skin might be put in this way. Let P and P' represent any two points on the skin, and let L and L' represent the local signs of these points, and M and M' the muscle sensations which give rise to these local signs. Then M-M' will represent the distance between P and P', whether that distance be judged directly in terms of the localizing function of the skin or in terms of its space-perceiving function. This would be the formula for a normal judgment. In an illusory judgment, the temporal and aesthetic factors enter as disturbing elements. Now, the point which I insist on here is that the judgments of the extent of the voluntary movements, represented in the formula by M and M', do not depend alone on the sensations from the moving parts or other sensations of objective origin, as Dresslar would say, nor alone on the intention or impulse or innervation as Loeb and others claim, but on the sum of all the sensory elements that enter, both those of external and those of internal origin. And, furthermore, these sensations of external origin are important in judgments of space, only in so far as they are referred to sensations of internal origin. Delabarre says, "Movements are judged equal when their sensory elements are judged equal. These sensory elements need not all have their source in the moving parts. All sensations which are added from other parts of the body and which are not recognized as coming from these distant sources, are mingled with the elements from the moving member, and influence the judgment."[18] The importance of these sensations of inner origin was shown in many of the experiments in sections VI. to VIII. In the instance where the finger-tip was drawn over an open and a filled space, in the filled half the sensations were largely of external origin, while in the open half they were of internal origin. The result was that the spaces filled with sensations of internal origin were always overestimated.

The failure to recognize the importance of these inwardly initiated sensations is the chief defect in Dresslar's reasoning. He has endeavored to make our judgments in the illusion in question depend entirely on the sensations of external origin. He insists also that the illusion varies according to the variations in quantity of these external sensations. Now my experiments have shown, I think, very clearly that it is not the numerical or quantitative extent of the objective sensations which disturbs the judgment of distance, but the sensation of inner origin which we set over against these outer sensations. The piece of plush, because of the disagreeable sensations which it gives, is judged shorter than the space filled with closely crowded tacks. Dresslar seems to have overlooked entirely the fact that the feelings and emotions can be sources of illusions in the amount of movement, and hence in our judgments of space. The importance of this element has been pointed out by Muensterberg[19] in his studies of movement.

[18] Delabarre, E.B., 'Ueber Bewegungsempfindungen,' Inaug. Dissert., Freiburg, 1891.

[19] Muensterberg, H., 'Beitraege zur Experimentellen Psychol.,' Freiburg i. B., 1892, Heft 4.

Dresslar says again, "The explanations heretofore given, wholly based on the differences in the time the eye uses in passing over the two spaces, must stop short of the real truth." My experiments, however, as I have already indicated, go to prove quite the contrary. In short, I do not think we have any means of distinguishing our tactual judgments of time from our similar judgments of space. When the subject is asked to measure off equal spaces, he certainly uses time as means, because when he is asked to measure off equal times he registers precisely the same illusion that he makes in his judgments of spatial distances. The fact that objectively equal times were used by Dresslar in his experiments is no reason for supposing that the subject also regarded these times as equal. What I have here asserted of active touch is true also of the resting skin. When a stylus is drawn over the skin, the subject's answer to the question, How long is the distance? is subject to precisely the same illusion as his answer to the question, How long is the time?

I can by a simple illustration show more plainly what I mean by the statement that the blending of the inner and outer sensations is necessary for the perception of space. I shall use the sense of sight for the illustration, although precisely the same reasoning would apply to the sense of touch. Suppose that I sat in an entirely passive position and gazed at a spot on an otherwise blank piece of paper before me. I am perfectly passive so far as motion on my part is concerned. I may be engaged in any manner of speculation or be in the midst of the so-called active attention to the spot; but I must be and for the present remain motionless. Now, while I am in this condition of passivity, suppose the spot be made to move slowly to one side by some force external to myself. I am immovable all the while, and yet am conscious of this movement of the spot from the first position, which I call A, to the new position, A', where it stops. The sensation which I now have is qualitatively different from the sensation which I had from the spot in its original position. My world of experience thus far has been a purely qualitative one. I might go on to eternity having experiences of the same kind, and never dream of space, or geometry, nor should I have the unique experience of a geometrical illusion, either optical or tactual. Now suppose I set up the bodily movements of the eyes or the head, or of the whole body, which are necessary to follow the path of that point, until I overtake it and once more restore the quality of the original sensation. This circle, completed by the two processes of external activity and restoration by internal activity, forms a group of sensations which constitutes the ultimate atom in our spatial experience. I have my first spatial experience when I have the thrill of satisfaction that comes from overtaking again, by means of my own inner activity, a sensation that has escaped me through an activity not my own. A being incapable of motion, in a world of flux, would not have the spatial experience that we have. A being incapable of motion could not make the distinction between an outer change that can be corrected by an internal change, and an outer change that cannot so be restored. Such an external change incapable of restoration by internal activity we should have if the spot on the paper changed by a chemical process from black to red.

Now such a space theory is plainly not to be confused with the theory that makes the reversibility of the spatial series its primary property. It is evident that we can have a series of sensations which may be reversed and yet not give the notion of space. But we should always have space-perception if one half of the circular process above described comes from an outer activity, and the other half from an inner activity. This way of describing the reversibility of the spatial series makes it less possible to urge against it the objections that Stumpf[20] has formulated against Bain's genetic space-theory. Stumpf's famous criticism applies not only to Bain, but also to the other English empiricists and to Wundt. Bain says: "When with the hand we grasp something moving and move with it, we have a sensation of one unchanged contact and pressure, and the sensation is imbedded in a movement. This is one experience. When we move the hand over a fixed surface, we have with the feelings of movement a succession of feelings of touch; if the surface is a variable one, the sensations are constantly changing, so that we can be under no mistake as to our passing through a series of tactual impressions. This is another experience, and differs from the first not in the sense of power, but in the tactile accompaniment. The difference, however, is of vital importance. In the one case, we have an object moving and measuring time and continuous, in the other case we have coexistence in space. The coexistence is still further made apparent by our reversing the movement, and thereby meeting the tactile series in the inverse order. Moreover, the serial order is unchanged by the rapidity of our movements."[21]

[20] Stumpf, K., 'Ueber d. psycholog. Ursprung d. Raumvorstellung,' Leipzig, 1873, S. 54.

[21] Bain, A., 'The Senses and the Intellect,' 3d ed., New York, 1886, p. 183.

Stumpf maintained in his exhaustive criticism of this theory, first, that there are cases where all of the elements which Bain requires for the perception of space are present, and yet we have no presentation of space. Secondly, there are cases where not all of these elements are present, and where we have nevertheless space presentation. It is the first objection that concerns me here. Stumpf gives as an example, under his first objection, the singing of a series of tones, C, G, E, F. We have here the muscle sensations from the larynx, and the series of the tone-sensations which are, Stumpf claims, reversed when the muscle-sensations are reversed, etc. According to Stumpf, these are all the elements that are required by Bain, and yet we have no perception of space thereby. Henri[22] has pointed out two objections to Stumpf's criticism of Bain's theory. He says that Bain assumes, what Stumpf does not recognize, that the muscle sensations must contain three elements—resistance, time, and velocity—before they can lead to space perceptions. These three elements are not to be found in the muscle sensations of the larynx as we find them in the sensations that come from the eye or arm muscles. In addition to this, Henri claims that Bain's theory demands a still further condition. If we wish to touch two objects, A and B, with the same member, we can get a spatial experience from the process only if we insert between the touching of A and the touching of B a continual series of tactual sensations. In Stumpf's instance of the singing of tones, this has been overlooked. We can go from the tone C to the tone F without inserting between the two a continuous series of musical sensations.

[22] Henri, V., 'Ueber d. Raumwahrnehmungen d. Tastsinnes,' Berlin, 1898, S. 190.

I think that all such objections to the genetic space theories are avoided by formulating a theory in the manner in which I have just stated. When one says that there must be an outer activity producing a displacement of sensation, and then an inner activity retaining that sensation, it is plain that the singing of a series of tones ascending and then descending would not be a case in point.

* * * * *



TACTUAL TIME ESTIMATION.

BY KNIGHT DUNLAP.

I. GENERAL NATURE OF THE WORK.

The experiments comprised in this investigation were made during the year 1900-1901 and the early part of the year 1901-1902. They were planned as the beginning of an attempt at the analysis of the estimation of time intervals defined by tactual stimulations. The only published work in this quarter of the field so far is that of Vierordt,[1] who investigated only the constant error of time judgment, using both auditory and tactual stimulations, and that of Meumann,[2] who in his last published contribution to the literature of the time sense gives the results of his experiments with 'filled' and 'empty' tactual intervals. The stimuli employed by Meumann were, however, not purely tactual, but electrical.

[1] Vierordt: 'Der Zeitsinn,' Tuebingen, 1868.

[2] Meumann, E.: 'Beitraege zur Psychologie des Zeitbewusstseins,' III., Phil. Studien, XII., S. 195-204.

The limitation of time intervals by tactual stimulations offers, however, a rich field of variations, which promise assistance in the analytical problem of the psychology of time. The variations may be those of locality, area, intensity, rigidity, form, consecutiveness, and so on, in addition to the old comparisons of filled and empty intervals, intervals of varying length, and intervals separated by a pause and those not so separated.

To begin with, we have selected the conditions which are mechanically the simplest, namely, the comparison of two empty time intervals, both given objectively with no pause between them. We have employed the most easily accessible dermal areas, namely, that of the fingers of one or both hands, and introduced the mechanically simplest variations, namely, in locality stimulated and intensity of stimulation.

It was known from the results of nearly all who have studied the time sense experimentally, that there is in general a constant error of over- or underestimation of time intervals of moderate length, and from the results of Meumann,[3] that variations in intensity of limiting stimulation influenced the estimation decidedly, but apparently according to no exact law. The problem first at hand was then to see if variations introduced in tactual stimulations produce any regularity of effect, and if they throw any new light on the phenomena of the constant error.

[3] Meumaun, E.: 'Beitraege zur Psychologie des Zeitsinns,' II., Phil. Studien, IX., S. 264.

The stimulations employed were light blows from the cork tip of a hammer actuated by an electric current. These instruments, of which there were two, exactly alike in construction, were similar in principle to the acoustical hammers employed by Estel and Mehner. Each consisted essentially of a lever about ten inches in length, pivoted near one extremity, and having fastened to it near the pivot an armature so acted upon by an electromagnet as to depress the lever during the passage of an electric current. The lever was returned to its original position by a spring as soon as the current through the electromagnet ceased. A clamp at the farther extremity held a small wooden rod with a cork tip, at right angles to the pivot, and the depression of the lever brought this tip into contact with the dermal surface in proximity with which it had been placed. The rod was easily removable, so that one bearing a different tip could be substituted when desired. The whole instrument was mounted on a compact base attached to a short rod, by which it could be fastened in any desired position in an ordinary laboratory clamp.

During the course of most of the experiments the current was controlled by a pendulum beating half seconds and making a mercury contact at the lowest point of its arc. A condenser in parallel with the contact obviated the spark and consequent noise of the current interruption. A key, inserted in the circuit through the mercury cup and tapping instrument, allowed it to be opened or closed as desired, so that an interval of any number of half seconds could be interposed between successive stimulations.

In the first work, a modification of the method of right and wrong cases was followed, and found satisfactory. A series of intervals, ranging from one which was on the whole distinctly perceptible as longer than the standard to one on the whole distinctly shorter, was represented by a series of cards. Two such series were shuffled together, and the intervals given in the order so determined. Thus, when the pile of cards had been gone through, two complete series had been given, but in an order which the subject was confident was perfectly irregular. As he also knew that in a given series there were more than one occurrence of each compared interval (he was not informed that there were exactly two of each), every possible influence favored the formation each time of a perfectly fresh judgment without reference to preceding judgments. The only fear was lest certain sequences of compared intervals (e.g., a long compared interval in one test followed by a short one in the next), might produce unreliable results; but careful examination of the data, in which the order of the interval was always noted, fails to show any influence of such a factor.

To be more explicit with regard to the conditions of judgment; two intervals were presented to the subject in immediate succession. That is, the second stimulation marked the end of the first interval and the beginning of the second. The first interval was always the standard, while the second, or compared interval, varied in length, as determined by the series of cards, and the subject was requested to judge whether it was equal to, or longer or shorter than the standard interval.

In all of the work under Group 1, and the first work under Group 2, the standard interval employed was 5.0 seconds. This interval was selected because the minimum variation possible with the pendulum apparatus (1/2 sec.) was too great for the satisfactory operation of a shorter standard, and it was not deemed advisable to keep the subject's attention on the strain for a longer interval, since 5.0 sec. satisfied all the requirements of the experiment.

In all work here reported, the cork tip on the tapping instrument was circular in form, and 1 mm. in diameter. In all, except one experiment of the second group, the areas stimulated were on the backs of the fingers, just above the nails. In the one exception a spot on the forearm was used in conjunction with the middle finger.

In Groups 1 and 2 the intensity of stroke used was just sufficient to give a sharp and distinct stimulation. The intensity of the stimulation was not of a high degree of constancy from day to day, on account of variations in the electric contacts, but within each test of three stimulations the intensity was constant enough.

In experiments under Group 3 two intensities of strokes were employed, one somewhat stronger than the stroke employed in the other experiments, and one somewhat weaker—just strong enough to be perceived easily. The introduction of the two into the same test was effected by the use of an auxiliary loop in the circuit, containing a rheostat, so that the depression of the first key completed the circuit as usual, or the second key completed it through the rheostat.

At each test the subject was warned to prepare for the first stimulation by a signal preceding it at an exact interval. In experiments with the pendulum apparatus the signal was the spoken word 'now,' and the preparatory interval one second. Later, experiments were undertaken with preparatory intervals of one second and 1-4/5 seconds, to find if the estimation differed perceptibly in one case from that in the other. No difference was found, and in work thereafter each subject was allowed the preparatory interval which made the conditions subjectively most satisfactory to him.

Ample time for rest was allowed the subject after each test in a series, two (sometimes three) series of twenty to twenty-four tests being all that were usually taken in the course of the hour. Attention to the interval was not especially fatiguing and was sustained without difficulty after a few trials.

Further details will be treated as they come up in the consideration of the work by groups, into which the experiment naturally falls.

II. EXPERIMENTAL RESULTS.

1. The first group of experiments was undertaken to find the direction of the constant error for the 5.0 sec. standard, the extent to which different subjects agree and the effects of practice. The tests were therefore made with three taps of equal intensity on a single dermal area. The subject sat in a comfortable position before a table upon which his arm rested. His hand lay palm down on a felt cushion and the tapping instrument was adjusted immediately over it, in position to stimulate a spot on the back of the finger, just above the nail. A few tests were given on the first finger and a few on the second alternately throughout the experiments, in order to avoid the numbing effect of continual tapping on one spot. The records for each of the two fingers were however kept separately and showed no disagreement.

The detailed results for one subject (Mr,) are given in Table I. The first column, under CT, gives the values of the different compared intervals employed. The next three columns, under S, E and L, give the number of judgments of shorter, equal and longer, respectively. The fifth column, under W, gives the number of errors for each compared interval, the judgments of equal being divided equally between the categories of longer and shorter.

In all the succeeding discussion the standard interval will be represented by ST, the compared interval by CT. ET is that CT which the subject judges equal to ST.

TABLE I.

ST=5.0 SEC. SUBJECT Mr. 60 SERIES.

CT S E L W 4. 58 1 1 1.5 4.5 45 11 4 9.5 5. 32 13 15 21.5 5.5 19 16 25 27 6. 5 4 51 7 6.5 1 2 57 2

We can calculate the value of the average ET if we assume that the distribution of wrong judgments is in general in accordance with the law of error curve. We see by inspection of the first three columns that this value lies between 5.0 and 5.5, and hence the 32 cases of S for CT 5.0 must be considered correct, or the principle of the error curve will not apply.

The method of computation may be derived in the following way: If we take the origin so that the maximum of the error curve falls on the Y axis, the equation of the curve becomes

y = ke^{-[gamma] squaredx squared}

and, assuming two points (x{1} y{1}) and (x{2} y{2}) on the curve, we deduce the formula

+-D / log k/y{1} x{1} = ————————————————- / log k/y{1} +- / log k/y{2}

where D = x{1} +- x{2}, and k = value of y when x = 0.

x{1} and x{2} must, however, not be great, since the condition that the curve with which we are dealing shall approximate the form denoted by the equation is more nearly fulfilled by those portions of the curve lying nearest to the Y axis.

Now since for any ordinates, y_{1} and y_{2} which we may select from the table, we know the value of x_{1} +- x_{2}, we can compute the value of x_{1}, which conversely gives us the amount to be added to or subtracted from a given term in the series of _CT_'s to produce the value of the average _ET_. This latter value, we find, by computing by the formula given above, using the four terms whose values lie nearest to the _Y_ axis, is 5.25 secs.

In Table II are given similar computations for each of the nine subjects employed, and from this it will be seen that in every case the standard is overestimated.

TABLE II. ST= 5.0 SECS.

Subject. Average ET. No. of Series. A. 5.75 50 B. 5.13 40 Hs. 5.26 100 P. 5.77 38 Mn. 6.19 50 Mr. 5.25 60 R. 5.63 24 Sh. 5.34 100 Sn. 5.57 50

This overestimation of the 5.0 sec. standard agrees with the results of some of the experimenters on auditory time and apparently conflicts with the results of others. Mach[4] found no constant error. Hoering[5] found that intervals over 0.5 sec. were overestimated. Vierordt,[6] Kollert,[7] Estel[8] and Glass,[9] found small intervals overestimated and long ones underestimated, the indifference point being placed at about 3.0 by Vierordt, 0.7 by Kollert and Estel and 0.8 by Glass. Mehner[10] found underestimation from 0.7 to 5.0 and overestimation above 5.0. Schumann[11] found in one set of experiments overestimation from 0.64 to 2.75 and from 3.5 to 5.0, and underestimation from 2.75 to 3.5. Stevens[12] found underestimation of small intervals and overestimation of longer ones, placing the indifference point between 0.53 and 0.87.

[4] Mach, E.: 'Untersuchungen ueber den Zeitsinn des Ohres,' Sitzungsber. d. Wiener Akad., Math.-Nat. Kl., Bd. 51, Abth. 2.

[5] Hoering: 'Versuche ueber das Unterscheidungsvermoegen des Hoersinnes fuer Zeitgroessen,' Tuebingen, 1864.

[6] Vierordt: op. cit.

[7] Kollert, J.: 'Untersuchungen ueber den Zeitsinn,' Phil. Studien, I., S. 79.

[8] Estel, V.: 'Neue Versuche ueber den Zeitsinn,' Phil. Studien, II., S. 39.

[9] Glass R.: 'Kritisches und Experimentelles ueber den Zeitsinn,' Phil. Studien, IV., S. 423.

[10] Mehner, Max: 'Zum Lehre vom Zeitsinn,' Phil. Studien, II., S. 546.

[11] Schumann, F.: 'Ueber die Schaetzung kleiner Zeitgroessen,' Zeitsch. f. Psych., IV., S. 48.

[12] Stevens, L.T.: 'On the Time Sense,' Mind, XI., p. 393.

The overestimation, however, is of no great significance, for data will be introduced a little later which show definitely that the underestimation or overestimation of a given standard is determined, among other factors, by the intensity of the stimulation employed. The apparently anomalous results obtained in the early investigations are in part probably explicable on this basis.

As regards the results of practice, the data obtained from the two subjects on whom the greatest number of tests was made (Hs and Sh) is sufficiently explicit. The errors for each successive group of 25 series for these two subjects are given in Table III.

TABLE III.

ST = 5.0 SECONDS.

SUBJECT Hs. SUBJECT Sh. CT (1) (2) (3) (4) (1) (2) (3) (4) 4. 2.5 2.5 1.5 2.5 0. .5 0. .5 4.5 6.0 3.0 3.5 7.0 5.0 3.5 2.0 .5 5. 14.0 11.0 11.0 11.0 8.5 11.5 4.0 7.0 5.5 11.5 11.5 6.0 12.5 11.0 16.0 14.0 15.0 6. 12.0 9.0 6.5 6.0 3.5 2.0 1.5 1.0 6.5 4.0 3.5 4.0 3.5 4.0 .5 0. 0.

No influence arising from practice is discoverable from this table, and we may safely conclude that this hypothetical factor may be disregarded, although among the experimenters on auditory time Mehner[13] thought results gotten without a maximum of practice are worthless, while Meumann[14] thinks that unpracticed and hence unsophisticated subjects are most apt to give unbiased results, as with more experience they tend to fall into ruts and exaggerate their mistakes. The only stipulation we feel it necessary to make in this connection is that the subject be given enough preliminary tests to make him thoroughly familiar with the conditions of the experiment.

[13] op. cit., S. 558, S. 595.

[14] op. cit. (II.), S. 284.

2. The second group of experiments introduced the factor of a difference between the stimulation marking the end of an interval and that marking the beginning, in the form of a change in locality stimulated, from one finger to the other, either on the same hand or on the other hand. Two classes of series were given, in one of which the change was introduced in the standard interval, and in the other class in the compared interval.

In the first of these experiments, which are typical of the whole group, both of the subject's hands were employed, and a tapping instrument was arranged above the middle finger of each, as above the one hand in the preceding experiment, the distance between middle fingers being fifteen inches. The taps were given either two on the right hand and the third on the left, or one on the right and the second and third on the left, the two orders being designated as RRL and RLL respectively. The subject was always informed of the order in which the stimulations were to be given, so that any element of surprise which might arise from it was eliminated. Occasionally, however, through a lapse of memory, the subject expected the wrong order, in which case the disturbance caused by surprise was usually so great as to prevent any estimation.

The two types of series were taken under as similar conditions as possible, four (or in some cases five) tests being taken from each series alternately. Other conditions were the same as in the preceding work. The results for the six subjects employed are given in Table IV.

TABLE IV.

ST= 5.0 SECS. TWO HANDS. 15 INCHES.

Subject. Average RT. No. of Series. RRL. RLL.* (Table II.) Hs. 4.92 6.55 (5.26) 50 Sh. 5.29 5.28 (5.34) 50 Mr. 5.02 6.23 (5.25) 60 Mn. 5.71 6.71 (6.19) 24 A. 5.34 5.89 (5.75) 28 Sn. 5.62 6.43 (5.47) 60

*Transcriber's Note: Original "RRL"

From Table IV. it is apparent at a glance that the new condition involved introduces a marked change in the time judgment. Comparison with Table II. shows that in the cases of all except Sh and Sn the variation RRL shortens the standard subjectively, and that RLL lengthens it; that is, a local change tends to lengthen the interval in which it occurs. In the case of Sh neither introduces any change of consequence, while in the case of Sn both values are higher than we might expect, although the difference between them is in conformity with the rest of the results shown in the table.

Another set of experiments was made on subject Mr, using taps on the middle finger of the left hand and a spot on the forearm fifteen inches from it; giving in one case two taps on the finger and the third on the arm, and in the other one tap on the finger and the second and third on the arm; designating the orders as FFA and FAA respectively. Sixty series were taken, and the values found for the average ET were 4.52 secs, for FFA and 6.24 secs, for FAA, ST being 5.0 secs. This shows 0.5 sec. more difference than the experiment with two hands.

Next, experiments were made on two subjects, with conditions the same as in the work corresponding to Table IV., except that the distance between the fingers stimulated was only five inches. The results of this work are given in Table V.

TABLE V.

ST= 5.0 SECS. TWO HANDS. 5 INCHES.

Subject RRL. RLL. No. of Series. Sh. 5.32 5.32 60 Hs. 4.40 6.80 60

It will be noticed that Hs shows a slightly wider divergence than before, while Sh pursues the even tenor of his way as usual.

Series were next obtained by employing the first and second fingers on one hand in exactly the same way as the middle fingers of the two hands were previously employed, the orders of stimulation being 1, 1, 2, and 1, 2, 2. The results of sixty series on Subject Hs give the values of average ET as 4.8 secs. for 1, 1, 2, and 6.23 sees, for 1, 2, 2, ST being 5.0 secs., showing less divergence than in the preceding work.

These experiments were all made during the first year's work. They show that in most cases a change in the locality stimulated influences the estimation of the time interval, but since the details of that influence do not appear so definitely as might be desired, the ground was gone over again in a little different way at the beginning of the present year.

A somewhat more serviceable instrument for time measurements was employed, consisting of a disc provided with four rows of sockets in which pegs were inserted at appropriate angular intervals, so that their contact with fixed levers during the revolution of the disc closed an electric circuit at predetermined time intervals. The disc was rotated at a uniform speed by an electric motor.

Experiments were made by stimulation of the following localities: (1) First and third fingers of right hand; (2) first and second fingers of right hand; (3) first fingers of both hands, close together, but just escaping contact; (4) first fingers of both hands, fifteen inches apart; (5) first fingers of both hands, thirty inches apart; (6) two positions on middle finger of right hand, on same transverse line.

A standard of two seconds was adopted as being easier for the subject and more expeditious, and since qualitative and not quantitative results were desired, only one CT was used in each case, thus permitting the investigation to cover in a number of weeks ground which would otherwise have required a much longer period. The subjects were, however, only informed that the objective variations were very small, and not that they were in most cases zero. Tests of the two types complementary to each other (e.g., RRL and RRL) were in each case taken alternately in groups of five, as in previous work.

TABLE VI.

ST= 2.0 SECS.

Subject W.

(1) CT=2.0 (3) CT=2.2 (5) CT=2.0 113 133 RRL RLL RRL RLL S 3 3 9 20 5 21 E 18 19 25 16 18 14 L 24 28 16 14 17 15

Subject P.

(1) CT=2.0 (3)CT={1.6 (5) CT={1.6 {2.4 {2.4 113 133 RRL(1.6) RLL(2.4) RRL(1.6) RLL(2.4) S 2 16 12 16 15 10 E 38 32 32 21 26 19 L 10 2 6 15 14 21

Subject B.

(1) CT=2.0 (2) CT=2.0 (6) CT=2.0 113 133 112 122 aab abb S 4 21 5 20 7 6 E 23 19 22 24 40 38 L 23 10 23 6 3 6

Subject Hy.

(1) CT=2.0 (2) CT=2.4 (1a) CT=2.0 113 133 112 122 113 133 S 12 46 17 40 17 31 E 9 2 14 8 9 7 L 29 2 19 2 14 2

In the series designated as (1a) the conditions were the same as in (1), except that the subject abstracted as much as possible from the tactual nature of the stimulations and the position of the fingers. This was undertaken upon the suggestion of the subject that it would be possible to perform the abstraction, and was not repeated on any other subject.

The results are given in Table VI., where the numerals in the headings indicate the localities and changes of stimulation, in accordance with the preceding scheme, and 'S', 'E' and 'L' designate the number of judgments of shorter, equal and longer respectively.

It will be observed that in several cases a CT was introduced in one class which was different from the CT used in the other classes with the same subject. This was not entirely arbitrary. It was found with subject W, for example, that the use of CT = 2.0 in (3) produced judgments of shorter almost entirely in both types. Therefore a CT was found, by trial, which produced a diversity of judgments. The comparison of the different classes is not so obvious under these conditions as it otherwise would be, but is still possible.

The comparison gives results which at first appear quite irregular. These are shown in Table VII. below, where the headings (1)—(3), etc., indicate the classes compared, and in the lines beneath them '+' indicates that the interval under consideration is estimated as relatively greater (more overestimated or less underestimated) in the second of the two classes than in the first,—indicating the opposite effect. Results for the first interval are given in the line denoted 'first,' and for the second interval in the line denoted 'second.' Thus, the plus sign under (1)—(3) in the first line for subject P indicates that the variation RLL caused the first interval to be overestimated to a greater extent than did the variation 133.

TABLE VII.

SUBJECT P. SUBJECT W. SUBJECT B. SUBJECT Hy. (1)—(3) (3)—(4) (1)—(3) (3)—(5) (2)—(1) (6)—(2) (2)—(1) First. + - + - - + - Sec. + + - + + + +

The comparisons of (6) and (2), and (1) and (3) confirm the provisional deduction from Table IV., that the introduction of a local change in an interval lengthens it subjectively, but the comparisons of (3) and (5), (3) and (4), and (2) and (1) show apparently that while the amount of the local change influences the lengthening of the interval, it does not vary directly with this latter in all cases, but inversely in the first interval and directly in the second. This is in itself sufficient to demonstrate that the chief factors of the influence of locality-change upon the time interval are connected with the spatial localization of the areas stimulated, but a further consideration strengthens the conclusion and disposes of the apparent anomaly. It will be noticed that in general the decrease in the comparative length of the first interval produced by increasing the spatial change is less than the increase in the comparative length of the second interval produced by a corresponding change. In other words, the disparity between the results for the two types of test is greater, the greater the spatial distance introduced.

The results seem to point to the existence of two distinct factors in the so-called 'constant error' in these cases: first, what we may call the bare constant error, or simply the constant error, which appears when the conditions of stimulation are objectively the same as regards both intervals, and which we must suppose to be present in all other cases; and second, the particular lengthening effect which a change in locality produces upon the interval in which it occurs. These two factors may work in conjunction or in opposition, according to conditions. The bare constant error does not remain exactly the same at all times for any individual and is probably less regular in tactual time than in auditory or in optical time, according to the irregularity actually found and for reasons which will be assigned later.

3. The third group of experiments introduced the factor of variation in intensity of stimulation. By the introduction of a loop in the circuit, containing a rheostat, two strengths of current and consequently of stimulus intensity were obtained, either of which could be employed as desired. One intensity, designated as W, was just strong enough to be perceived distinctly. The other intensity, designated as S, was somewhat stronger than the intensity used in the preceding work.

In the first instance, sixty series were taken from Subject B, with the conditions the same as in the experiments of Group 1, except that two types of series were taken; the first two stimulations being strong and the third one weak in the first type (SSW), and the order being reversed in the second type (WSS). The results gave values of ET of 5.27 secs. for SSW and 5.9 secs. for WSS.

In order to get comprehensive qualitative results as rapidly as possible, a three-second standard was adopted in the succeeding work and only one compared interval, also three seconds, was given, although the subject was ignorant of that fact—the method being thus similar to that adopted later for the final experiments of Group 2, described above. Six types of tests were given, the order of stimulation in the different types being SSS, WWW, SSW, WWS, SWW and WSS, the subject always knowing which order to expect. For each of the six types one hundred tests were made on one subject and one hundred and five on another, in sets of five tests of each type, the sets being taken in varied order, so that possible contrast effect should be avoided. The results were practically the same, however, in whatever order the sets were taken, no contrast effect being discernible.

The total number of judgments of CT, longer, equal, and shorter, is given in Table VIII. The experiments on each subject consumed a number of experiment hours, scattered through several weeks, but the relative proportions of judgments on different days was in both cases similar to the total proportions.

TABLE VIII.

STCT 3.0 SECS.

Subject R, 100. Subject P, 105. L E S d L E S d SSS 32 56 12 + 20 SSS 16 67 22 - 9 WWW 11 53 36 - 25 WWW 19 72 14 + 5 SSW 6 27 67 - 61 SSW 17 56 32 - 15 WWS 57 36 7 + 50 WWS 37 61 7 + 30 WSS 10 45 45 - 35 WSS 9 69 27 - 18 SWW 3 31 66 - 63 SWW 3 64 33 - 25

By the above table the absolute intensity of the stimulus is clearly shown to be an important factor in determining the constant error of judgment, since in both cases the change from SSS to WWW changed the sign of the constant error, although in opposite directions. But the effect of the relative intensity is more obscure. To discover more readily whether the introduction of a stronger or weaker stimulation promises a definite effect upon the estimation of the interval which precedes or follows it, the results are so arranged in Table IX. that reading downward in any pair shows the effect of a decrease in the intensity of (1) the first, (2) the second, (3) the third, and (4) all three stimulations.

TABLE IX.

Subject R. Subject P.

(1) SSS + 20 - 6 WSS - 35 - 55 - 18 - 12

SWW - 63 - 25 WWW - 25 - 38 + 5 + 30

(2) SSW - 61 - 15 SWW - 63 - 2 - 25 + 10

WSS - 35 - 18 WWS + 50 + 85 + 30 - 48

(3) SSS + 20 - 6 SSW - 61 - 81 - 15 - 7

WWS + 50 + 30 WWW - 25 - 75 + 5 - 25

(4) SSS + 20 - 6 WWW - 15 - 35 + 5 + 11

There seems at first sight to be no uniformity about these results. Decreasing the first stimulation in the first case increases, in the second case diminishes, the comparative length of the first interval. We get a similar result in the decreasing of the second stimulation. In the case of the third stimulation only does the decrease produce a uniform result. If, however, we neglect the first pair of (3), we observe that in the other cases the effect of a difference between the two stimulations is to lengthen the interval which they limit. The fact that both subjects make the same exception is, however, striking and suggestive of doubt. These results were obtained in the first year's work, and to test their validity the experiment was repeated at the beginning of the present year on three subjects, fifty series being taken from each, with the results given in Table X.

TABLE X.

ST = 3.0 secs. = CT.

Subject Mm. Subject A. Subject D.

S E L d S E L d S E L d SSS 24 13 13 - 11 7 30 13 + 6 10 31 9 - 1 WSS 33 9 8 - 25 20 24 6 - 14 17 27 6 - 11 SSW 19 15 16 - 3 23 16 11 - 12 10 31 9* - 1 WWW 19 12 19 0 13 26 11 - 2 1 40 9 + 8 SWW 18 30 2 - 16 23 21 6* - 17 7 38 5 - 2 WWS 13 16 21 + 8 12 30 8 - 4 15 25 10 - 5

*Transcriber's Note: Original "16" changed to "6", "19" to "9".

Analysis of this table shows that in every case a difference between the intensities of the first and second taps lengthens the first interval in comparative estimation. In the case of subject Mm a difference in the intensities of the second and third taps lengthens the second interval subjectively. But in the cases of the other two subjects the difference shortens the interval in varying degrees.

The intensity difference established for the purposes of these experiments was not great, being less than that established for the work on the first two subjects, and therefore the fact that these results are less decided than those of the first work was not unexpected. The results are, however, very clear, and show that the lengthening effect of a difference in intensity of the stimulations limiting an interval has its general application only to the first interval, being sometimes reversed in the second. From the combined results we find, further, that a uniform change in the intensity of three stimulations is capable of reversing the direction of the constant error, an intensity change in a given direction changing the error from positive to negative for some subjects, and from negative to positive for others.

III. INTERPRETATION OF RESULTS.

We may say provisionally that the change from a tactual stimulation of one kind to a tactual stimulation of another kind tends to lengthen subjectively the interval which the two limit. If we apply the same generalization to the other sensorial realms, we discover that it agrees with the general results obtained by Meumann[15] in investigating the effects of intensity changes upon auditory time, and also with the results obtained by Schumann[16] in investigations with stimulations addressed alternately to one ear and to the other. Meumann reports also that the change from stimulation of one sense to stimulation of another subjectively lengthens the corresponding interval.

[15] op. cit. (II.), S. 289-297.

[16] op. cit., S. 67.

What, then, are the factors, introduced by the change, which produce this lengthening effect? The results of introspection on the part of some of the subjects of our experiments furnish the clue which may enable us to construct a working hypothesis.

Many of the subjects visualize a time line in the form of a curve. In each case of this kind the introduction of a change, either in intensity or location, if large enough to produce an effect on the time estimation, produced a distortion on the part of the curve corresponding to the interval affected. All of the subjects employed in the experiments of Group 2 were distinctly conscious of the change in attention from one point to another, as the two were stimulated successively, and three of them, Hy, Hs and P, thought of something passing from one point to the other, the representation being described as partly muscular and partly visual. Subjects Mr and B visualized the two hands, and consciously transferred the attention from one part of the visual image to the other. Subject Mr had a constant tendency to make eye movements in the direction of the change. Subject P detected these eye movements a few times, but subject B was never conscious of anything of the kind.

All of the subjects except R were conscious of more or less of a strain, which varied during the intervals, and was by some felt to be largely a tension of the chest and other muscles, while others felt it rather indefinitely as a 'strain of attention.' The characteristics of this tension feeling were almost always different in the second interval from those in the first, the tension being usually felt to be more constant in the second interval. In experiments of the third group a higher degree of tension was felt in awaiting a light tap than in awaiting a heavy one.

Evidently, in all these cases, the effect of a difference between two stimulations was to introduce certain changes in sensation during the interval which they limited, owing to the fact that the subject expected the difference to occur. Thus in the third group of experiments there were, very likely, in all cases changes from sensations of high tension to sensations of lower, or vice versa. It is probable that, in the experiments of the second group, there were also changes in muscular sensations, partly those of eye muscles, partly of chest and arm muscles, introduced by the change of attention from one point to another. At any rate, it is certain that there were certain sensation changes produced during the intervals by changes of locality.

If, then, we assume that the introduction of additional sensation change into an interval lengthens it, we are led to the conclusion that psychological time (as distinguished from metaphysical, mathematical, or transcendental time) is perceived simply as the quantum of change in the sensation content. That this is a true conclusion is seemingly supported by the fact that when we wish to make our estimate correspond as closely as possible with external measurements, we exclude from the content, to the best of our ability, the general complex of external sensations, which vary with extreme irregularity; and confine the attention to the more uniformly varying bodily sensations. We perhaps go even further, and inhibit certain bodily sensations, corresponding to activity of the more peripherally located muscles, that the attention may be confined to certain others. But attention to a dermal stimulation is precisely the condition which would tend to some extent to prevent this inhibition. For this reason we might well expect to find the error in estimation more variable, the 'constant error' in general greater, and the specific effects of variations which would affect the peripheral muscles, more marked in 'tactual' time than in either 'auditory' or 'optical' time. Certainly all these factors appear surprisingly large in these experiments.

It is not possible to ascertain to how great an extent subject Sh inhibited the more external sensations, but certainly if he succeeded to an unusual degree in so doing, that fact would explain the absence of effect of stimulation difference in his case.

Explanation has still to be offered for the variable effect of intensity difference upon the second interval. According to all subjects except Sn, there is a radical difference in attitude in the two intervals. In the first interval the subject is merely observant, but in the second he is more or less reproductive. That is, he measures off a length which seems equal to the standard, and if the stimulation does not come at that point he is prepared to judge the interval as 'longer,' even before the third stimulation is given. In cases, then, where the judgment with equal intensities would be 'longer,' we might expect that the actual strengthening or weakening of the final tap would make no difference, and that it would make very little difference in other cases. But even here the expectation of the intensity is an important factor in determining tension changes, although naturally much less so than in the first interval. So we should still expect the lengthening of the second interval.

We must remember, however, that, as we noticed in discussing the experiments of Group 2, there is complicated with the lengthening effect of a change the bare constant error, which appears even when the three stimulations are similar in all respects except temporal location. Compare WWW with SSS, and we find that with all five subjects the constant error is decidedly changed, being even reversed in direction with three of the subjects.

Now, what determines the direction of the constant error, where there is no pause between the intervals? Three subjects reported that at times there seemed to be a slight loss of time after the second stimulation, owing to the readjustment called for by the change of attitude referred to above, so that the second interval was begun, not really at the second stimulation, but a certain period after it. This fact, if we assume it to be such, and also assume that it is present to a certain degree in all observations of this kind, explains the apparent overestimation of the first interval. Opposed to the factor of loss of time there is the factor of perspective, by which an interval, or part of an interval, seems less in quantity as it recedes into the past. The joint effect of these two factors determines the constant error in any case where no pause is introduced between ST and CT. It is then perfectly obvious that, as the perspective factor is decreased by diminishing the intervals compared, the constant error must receive positive increments, i.e., become algebraically greater; which corresponds exactly with the results obtained by Vierordt, Kollert, Estel, and Glass, that under ordinary conditions long standard intervals are comparatively underestimated, and short ones overestimated.

On the other hand, if with a given interval we vary the loss of time, we also vary the constant error. We have seen that a change in the intensity of the stimulations, although the relative intensity of the three remains constant, produces this variation of the constant error; and the individual differences of subjects with regard to sensibility, power of attention and inhibition, and preferences for certain intensities, lead us to the conclusion that for certain subjects certain intensities of stimulation make the transition from the receptive attitude to the reproductive easiest, and, therefore, most rapid.

Now finally, as regards the apparent failure of the change in SSW to lengthen the second interval, for which we are seeking to account; the comparatively great loss of time occurring where the change of attitude would naturally be most difficult (that is, where it is complicated with a change of attention from a strong stimulation to the higher key of a weak stimulation) is sufficient to explain why with most subjects the lengthening effect upon the second interval is more than neutralized. The individual differences mentioned in the preceding paragraph as affecting the relation of the two factors determining the constant error, enter here of course to modify the judgments and cause disagreement among the results for different subjects.

Briefly stated, the most important points upon which this discussion hinges are thus the following: We have shown—

1. That the introduction of either a local difference or a difference of intensity in the tactual stimulations limiting an interval has, in general, the effect of causing the interval to appear longer than it otherwise would appear.

2. That the apparent exceptions to the above rule are, (a) that the increase of the local difference in the first interval, the stimulated areas remaining unchanged, produces a slight decrease in the subjective lengthening of the interval, and (b) that in certain cases a difference in intensity of the stimulations limiting the second interval apparently causes the interval to seem shorter than it otherwise would.

3. That the 'constant error' of time judgment is dependent upon the intensity of the stimulations employed, although the three stimulations limiting the two intervals remain of equal intensity.

To harmonize these results we have found it necessary to assume:

1. That the length of a time interval is perceived as the amount of change in the sensation-complex corresponding to that interval.

2. That the so-called 'constant error' of time estimation is determined by two mutually opposing factors, of which the first is the loss of time occasioned by the change of attitude at the division between the two intervals, and the second is the diminishing effect of perspective.

It is evident, however, that this last assumption applies only to the conditions under which the results were obtained, namely, the comparison of two intervals marked off by three brief stimulations.

* * * * *



PERCEPTION OF NUMBER THROUGH TOUCH.

BY J. FRANKLIN MESSENGER.

The investigation which I am now reporting began as a study of the fusion of touch sensations when more than two contacts were possible. As the work proceeded new questions came up and the inquiry broadened so much that it seemed more appropriate to call it a study in the perception of number.

The experiments are intended to have reference chiefly to three questions: the space-threshold, fusion of touch sensations, and the perception of number. I shall deny the validity of a threshold, and deny that there is fusion, and then offer a theory which attempts to explain the phenomena connected with the determination of a threshold and the problem of fusion and diffusion of touch sensations.

The first apparatus used for the research was made as follows: Two uprights were fastened to a table. These supported a cross-bar about ten inches from the table. To this bar was fastened a row of steel springs which could be pressed down in the manner of piano keys. To each of these springs was fastened a thread which held a bullet. The bullets, which were wrapped in silk to obviate temperature sensations, were thus suspended just above the fingers, two over each finger. Each thread passed through a small ring which was held just a little above the fingers. These rings could be moved in any direction to accommodate the bullet to the position of the finger. Any number of the bullets could be let down at once. The main object at first was to learn something about the fusion of sensations when more than two contacts were given.

Special attention was given to the relation of the errors made when the fingers were near together to those made when the fingers were spread. For this purpose a series of experiments was made with the fingers close together, and then the series was repeated with the fingers spread as far as possible without the subject's feeling any strain. Each subject was experimented on one hour a week for about three months. The same kind of stimulation was given when the fingers were near together as was given when they were spread. The figures given below represent the average percentage of errors for four subjects.

Of the total number of answers given by all subjects when the fingers were close together, 70 per cent. were wrong. An answer was called wrong whenever the subject failed to judge the number correctly. In making out the figures I did not take into account the nature of the errors. Whether involving too many or too few the answer was called wrong. Counting up the number of wrong answers when the fingers were spread, I found that 28 per cent. of the total number of answers were wrong. This means simply that when the fingers were near together there were more than twice as many errors as there were when they were spread, in spite of the fact that each finger was stimulated in the same way in each case.

A similar experiment was tried using the two middle fingers only. In this case not more than four contacts could be made at once, and hence we should expect a smaller number of errors, but we should expect still to find more of them when the fingers are near together than when they are spread. I found that 49 per cent. of the answers were wrong when the fingers were near together and 20 per cent. were wrong when they were spread. It happens that this ratio is approximately the same as the former one, but I do not regard this fact as very significant. I state only that it is easier to judge in one case than in the other; how much easier may depend on various factors.

To carry the point still further I took only two bullets, one over the second phalanx of each middle finger. When the fingers were spread the two were never felt as one. When the fingers were together they were often felt as one.

The next step was to investigate the effect of bringing together the fingers of opposite hands. I asked the subject to clasp his hands in such a way that the second phalanges would be about even. I could not use the same apparatus conveniently with the hands in this position, but in order to have the contacts as similar as possible to those I had been using, I took four of the same kind of bullets and fastened them to the ends of two aesthesiometers. This enabled me to give four contacts at once. However, only two were necessary to show that contacts on fingers of opposite hands could be made to 'fuse' by putting the fingers together. If two contacts are given on contiguous fingers, they are quite as likely to be perceived as one when the fingers are fingers of opposite hands, as when they are contiguous fingers of the same hand.

These results seem to show that one of the important elements of fusion is the actual space relations of the points stimulated. The reports of the subjects also showed that generally and perhaps always they located the points in space and then remembered what finger occupied that place. It was not uncommon for a subject to report a contact on each of two adjacent fingers and one in between where he had no finger. A moment's reflection would usually tell him it must be an illusion, but the sensation of this illusory finger was as definite as that of any of his real fingers. In such cases the subject seemed to perceive the relation of the points to each other, but failed to connect them with the right fingers. For instance, if contacts were made on the first, second and third fingers, the first might be located on the first finger, the third on the second finger, and then the second would be located in between.

So far my attention had been given almost entirely to fusion, but the tendency on the part of all subjects to report more contacts than were actually given was so noticeable that I concluded that diffusion was nearly as common as fusion and about as easy to produce. It also seemed that the element of weight might play some part, but just what effect it had I was uncertain. I felt, too, that knowledge of the apparatus gained through sight was giving the subjects too much help. The subjects saw the apparatus every day and knew partly what to expect, even though the eyes were closed when the contacts were made. A more efficient apparatus seemed necessary, and, therefore, before taking up the work again in 1900, I made a new apparatus.

Not wishing the subjects to know anything about the nature of the machine or what could be done with it, I enclosed it in a box with an opening in one end large enough to allow the subject's hand to pass through, and a door in the other end through which I could operate. On the inside were movable wooden levers, adjustable to hands of different width. These were fastened by pivotal connection at the proximal end. At the outer end of each of these was an upright strip with a slot, through which was passed another strip which extended back over the hand. This latter strip could be raised or lowered by means of adjusting screws in the upright strip. On the horizontal strip were pieces of wood made so as to slide back and forth. Through holes in these pieces plungers were passed. At the bottom of each plunger was a small square piece of wood held and adjusted by screws. From this piece was suspended a small thimble filled with shot and paraffine. The thimbles were all equally weighted. Through a hole in the plunger ran a thread holding a piece of lead of exactly the weight of the thimble. By touching a pin at the top this weight could be dropped into the thimble, thus doubling its weight. A screw at the top of the piece through which the plunger passed regulated the stop of the plunger. This apparatus had three important advantages. It was entirely out of sight, it admitted of rapid and accurate adjustment, and it allowed the weights to be doubled quickly and without conspicuous effort.

For the purpose of studying the influence of weight on the judgments of number I began a series of experiments to train the subjects to judge one, two, three, or four contacts at once. For this the bare metal thimbles were used, because it was found that when they were covered with chamois skin the touch was so soft that the subjects could not perceive more than one or two with any degree of accuracy, and I thought it would take entirely too long to train them to perceive four. The metal thimbles, of course, gave some temperature sensation, but the subject needed the help and it seemed best to use the more distinct metal contacts.

In this work I had seven subjects, all of whom had had some experience in a laboratory, most of them several years. Each one took part one hour a week. The work was intended merely for training, but a few records were taken each day to see how the subjects progressed. The object was to train them to perceive one, two, three, and four correctly, and not only to distinguish four from three but to distinguish four from more than four. Hence five, six, seven, and eight at a time were often given. When the subject had learned to do this fairly well the plan was to give him one, two, three, and four in order, then to double the weight of the four and give them again to see if he would interpret the additional weight as increase in number. This was done and the results were entirely negative. The subjects either noticed no difference at all or else merely noticed that the second four were a little more distinct than the first.

The next step was to give a number of light contacts to be compared with the same number of heavy ones—the subject, not trying to tell the exact number but only which group contained the greater number. A difference was sometimes noticed, and the subject, thinking that the only variations possible were variations of number and position, often interpreted the difference as difference in number; but the light weights were as often called more as were the heavy ones.

So far as the primary object of this part of the experiment is concerned the results are negative, but incidentally the process of training brought out some facts of a more positive nature. It was early noticed that some groups of four were much more readily recognized than others, and that some of them were either judged correctly or underestimated while others were either judged correctly or overestimated. For convenience the fingers were indicated by the letters A B C D, A being the index finger. The thumb was not used. Two weights were over each finger. The one near the base was called 1, the one toward the end 2. Thus A12 B1 C2 means two contacts on the index finger, one near the base of the second finger, and one near the end of the third finger. The possible arrangements of four may be divided into three types: (1) Two weights on each of two fingers, as A12 B12, C12 D12, etc., (2) four in a line across the fingers, A1 B1 C1 D1 or A2 B2 C2 D2, (3) unsymmetrical arrangements, as A1 B2 C1 D2, etc. Arrangements of the first type were practically never overestimated. B12 C12 was overestimated once and B12 D12 was overestimated once, but these two isolated cases need hardly be taken into account. Arrangements of the second type were but rarely overestimated—A2 B2 C2 D2 practically never, A1 B1 C1 D1 a few times. Once the latter was called eight. Apparently the subject perceived the line across the hand and thought there were two weights on each finger instead of one. Arrangements of the third type were practically never underestimated, but were overestimated in 68 per cent. of the cases.

These facts in themselves are suggestive, but equally so was the behavior of the subject while making the answers. It would have hardly done to ask the person if certain combinations were hard to judge, for the question would serve as a suggestion to him; but it was easy to tell when a combination was difficult without asking questions. When a symmetrical arrangement was given, the subject was usually composed and answered without much hesitation. When an unsymmetrical arrangement was given he often hesitated and knit his brows or perhaps used an exclamation of perplexity before answering, and after giving his answer he often fidgeted in his chair, drew a long breath, or in some way indicated that he had put forth more effort than usual. It might be expected that the same attitude would be taken when six or eight contacts were made at once, but in these cases the subject was likely either to fail to recognize that a large number was given or, if he did, he seemed to feel that it was too large for him to perceive at all and would guess at it as well as he could. But when only four were given, in a zigzag arrangement, he seemed to feel that he ought to be able to judge the number but to find it hard to do so, and knowing from experience that the larger the number the harder it is to judge he seemed to reason conversely that the more effort it takes to judge the more points there are, and hence he would overestimate the number.

The comments of the subjects are of especial value. One subject (Mr. Dunlap) reports that he easily loses the sense of location of his fingers, and the spaces in between them seem to belong to him as much as do his fingers themselves. When given one touch at a time and told to raise the finger touched he can do so readily, but he says he does not know which finger it is until he moves it. He feels as if he willed to move the place touched without reference to the finger occupying it. He sometimes hesitates in telling which finger it is, and sometimes he finds out when he moves a finger that it is not the one he thought it was.

Another subject (Dr. MacDougall) says that his fingers seem to him like a continuous surface, the same as the back of his hand. He usually named the outside points first. When asked about the order in which he named them, he said he named the most distinct ones first. Once he reported that he felt six things, but that two of them were in the same places as two others, and hence he concluded there were but four. This feeling in a less careful observer might lead to overestimation of number and be called diffusion, but all cases of overestimation cannot be explained that way, for it does not explain why certain combinations are so much more likely to lead to it than others.

In one subject (Mr. Swift) there was a marked tendency to locate points on the same fingers. He made many mistakes about fingers B and C even when he reported the number correctly. When B and D were touched at the same time he would often call it C and D, and when C and D were given immediately afterward he seemed to notice no difference. With various combinations he would report C when B was given, although C had not been touched at the same time. If B and C were touched at the same time he could perceive them well enough.

The next part of the research was an attempt to discover whether a person can perceive any difference between one point and two points which feel like one. A simple little experiment was tried with the aesthesiometer. The subjects did not know what was being used, and were asked to compare the relative size of two objects placed on the back of the hand in succession. One of these objects was one knob of the aesthesiometer and the other was two knobs near enough together to lie within the threshold. The distance of the points was varied from 10 to 15 mm. Part of the time the one was given first and part of the time both were given together. The one, whether given first or second, was always given about midway between the points touched by the two. If the subject is not told to look for some specific difference he will not notice any difference between the two knobs and the one, and he will say they are alike; but if he is told to give particular attention to the size there seems to be a slight tendency to perceive a difference. The subjects seem to feel very uncertain about their answers, and it looks very much like guess-work, but something caused the guesses to go more in one direction than in the other.

Two were called less than one .... 16% of the times given. " " " equal to .... 48% " " " " " greater than .... 36% " "

Approximately half of the time two were called equal to one, and if there had been no difference in the sensations half of the remaining judgments should have been that two was smaller than one, but two were called larger than one more than twice as many times as one was called larger than two. There was such uniformity in the reports of the different subjects that no one varied much from this average ratio.

This experiment seems to indicate a very slight power of discrimination of stimulations within the threshold. In striking contrast to this is the power to perceive variations of distance between two points outside the threshold. To test this the aesthesiometer was spread enough to bring the points outside the threshold. The back of the hand was then stimulated with the two points and then the distance varied slightly, the hand touched and the subject asked to tell which time the points were farther apart. A difference of 2 mm. was usually noticed, and one of from 3 to 5 mm. was noticed always very clearly.

I wondered then what would be the result if small cards set parallel to each other were used in place of the knobs of the aesthesiometer. I made an aesthesiometer with cards 4 mm. long in place of knobs. These cards could be set at any angle to each other. I set them at first 10 mm. apart and parallel to each other and asked the subjects to compare the contact made by them with a contact by one card of the same size. The point touched by the one card was always between the points touched by the two cards, and the one card was put down so that its edge would run in the same direction as the edges of the other cards. The result of this was that:

Two were called less, 14 per cent. " " " equal, 36 " " " " " greater, 50 " "

I then increased the distance of the two cards to 15 mm., the other conditions remaining the same, and found that: