Chapter VI: Section II: showed that the shorter filled distances are (2)

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 æsthetic 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 Müller-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 æsthetic 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 æsthetic 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 æsthetic 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 Münsterberg[19] in his studies of movement.

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

[19] Münsterberg, H., 'Beiträge 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 coëxistence in space. The coëxistence 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,' Tübingen, 1868.

[2] Meumann, E.: 'Beiträge 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.: 'Beiträge 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 (½ 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]²x²}

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. Höring[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 über den Zeitsinn des Ohres,'
_Sitzungsber. d. Wiener Akad._, Math.-Nat. Kl., Bd. 51, Abth.
2.

[5] Höring: 'Versuche über das Unterscheidungsvermögen des
Hörsinnes für Zeitgrössen,' Tübingen, 1864.

[6] Vierordt: _op. cit._

[7] Kollert, J.: 'Untersuchungen über den Zeitsinn,' _Phil.
Studien_, I., S. 79.

[8] Estel, V.: 'Neue Versuche über den Zeitsinn,' _Phil.
Studien_, II., S. 39.

[9] Glass R.: 'Kritisches und Experimentelles über den
Zeitsinn,' _Phil. Studien_, IV., S. 423.

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

[11] Schumann, F.: 'Ueber die Schätzung kleiner Zeitgrössen,'
_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.

_ST=CT=_ 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.