Two were called less, 11 per cent. " " " equal, 50 " " " " " greater, 39 " "

It will be noticed that the ratio in this last series is not materially different from the ratio found when the two knobs of the aesthesiometer were compared with one knob. The ratio found when the distance was 10 mm., however, is somewhat different. At that distance two were called greater half of the time, while at 15 mm. two were called equal to one half of the time. The explanation of the difference, I think, is found in the comments of one of my subjects. I did not ask them to tell in what way one object was larger than the other—whether longer or larger all around or what—but simply to answer 'equal,' 'greater,' or 'less.' One subject, however, frequently added more to his answers. He would often say 'larger crosswise' or 'larger lengthwise' of his hand. And a good deal of the time he reported two larger than one, not in the direction in which it really was larger, but the other way. It seems to me that when the two cards were only 10 mm. apart the effect was somewhat as it would be if a solid object 4 mm. wide and 10 mm. long had been placed on the hand. Such an object would be recognized as having greater mass than a line 4 mm. long. But when the distance is 15 mm. the impression is less like that of a solid body but still not ordinarily like two objects.

In connection with the subject of diffusion the Vexirfehler is of interest. An attempt was made to develop the Vexirfehler with the aesthesiometer. Various methods were tried, but the following was most successful. I would tell the subject that I was going to use the aesthesiometer and ask him to close his eyes and answer simply 'one' or 'two.' He would naturally expect that he would be given part of the time one, and part of the time two. I carefully avoided any suggestion other than that which could be given by the aesthesiometer itself. I would begin on the back of the hand near the wrist with the points as near the threshold as they could be and still be felt as two. At each successive putting down of the instrument I would bring the points a little nearer together and a little lower down on the hand. By the time a dozen or more stimulations had been given I would be working down near the knuckles, and the points would be right together. From that on I would use only one point. It might be necessary to repeat this a few times before the illusion would persist. A great deal seems to depend on the skill of the operator. It would be noticed that the first impression was of two points, and that each stimulation was so nearly like the one immediately preceding that no difference could be noticed. The subject has been led to call a thing two which ordinarily he would call one, and apparently he loses the distinction between the sensation of one and the sensation of two. After going through the procedure just mentioned I put one knob of the aesthesiometer down one hundred times in succession, and one subject (Mr. Meakin) called it two seventy-seven times and called it one twenty-three times. Four of the times that he called it one he expressed doubt about his answer and said it might be two, but as he was not certain he called it one. Another subject (Mr. George) called it two sixty-two times and one thirty-eight times. A third subject (Dr. Hylan) called it two seventy-seven times and one twenty-three times. At the end of the series he was told what had been done and he said that most of his sensations of two were perfectly distinct and he believed that he was more likely to call what seemed somewhat like two one, than to call what seemed somewhat like one two. With the fourth subject (Mr. Dunlap) I was unable to do what I had done with the others. I could get him to call one two for four or five times, but the idea of two would not persist through a series of any length. He would call it two when two points very close together were used. I could bring the knobs within two or three millimeters of each other and he would report two, but when only one point was used he would find out after a very few stimulations were given that it was only one. After I had given up the attempt I told him what I had been trying to do and he gave what seems to me a very satisfactory explanation of his own case. He says the early sensations keep coming up in his mind, and when he feels like calling a sensation two he remembers how the first sensation felt and sees that this one is not like that, and hence he calls it one. I pass now to a brief discussion of what these experiments suggest.

It has long been known that two points near together on the skin are often perceived as one. It has been held that in order to be felt as two they must be far enough apart to have a spatial character, and hence the distance necessary for two points to be perceived has been called the 'space-threshold.' This threshold is usually determined either by the method of minimal changes or by the method of right and wrong cases.

If, in determining a threshold by the method of minimal changes—on the back of the hand, for example, we assume that we can begin the ascending series and find that two are perceived as one always until the distance of twenty millimeters is reached, and that in the descending series two are perceived as two until the distance of ten millimeters is reached, we might then say that the threshold is somewhere between ten and twenty millimeters. But if the results were always the same and always as simple as this, still we could not say that there is any probability in regard to the answer which would be received if two contacts 12, 15, or 18 millimeters apart were given by themselves. All we should know is that if they form part of an ascending series the answer will be 'one,' if part of a descending series 'two.'

The method of right and wrong cases is also subject to serious objections. There is no lower limit, for no matter how close together two points are they are often called two. If there is any upper limit at all, it is so great that it is entirely useless. It might be argued that by this method a distance could be found at which a given percentage of answers would be correct. This is quite true, but of what value is it? It enables one to obtain what one arbitrarily calls a threshold, but it can go no further than that. When the experiment changes the conditions change. The space may remain the same, but it is only one of the elements which assist in forming the judgment, and its importance is very much overestimated when it is made the basis for determining the threshold.

Different observers have found that subjects sometimes describe a sensation as 'more than one, but less than two.' I had a subject who habitually described this feeling as 'one and a half.' This does not mean that he has one and a half sensations. That is obviously impossible. It must mean that the sensation seems just as much like two as it does like one, and he therefore describes it as half way between. If we could discover any law governing this feeling of half-way-between-ness, that might well indicate the threshold. But such feelings are not common. Sensations which seem between one and two usually call forth the answer 'doubtful,' and have a negative rather than a positive character. This negative character cannot be due to the stimulus; it must be due to the fluctuating attitudes of the subject. However, if the doubtful cases could be classed with the 'more than one but less than two' cases and a law be found governing them, we might have a threshold mark. But such a law has not been formulated, and if it had been an analysis of the 'doubtful' cases would invalidate it. For, since we cannot have half of a sensation or half of a place as we might have half of an area, the subject regards each stimulation as produced by one or by two points as the case may be. Occasionally he is stimulated in such a way that he can regard the object as two or as one with equal ease. In order to describe this feeling he is likely to use one or the other of the methods just mentioned.

We might say that when the sum of conditions is such that the subject perceives two points, the points are above the threshold, and when the subject perceives one point when two are given they are below the threshold. This might answer the purpose very well if it were not for the Vexirfehler. According to this definition, when the Vexirfehler appears we should have to say that one point is above the threshold for twoness, which is a queer contradiction, to say the least. It follows that all of the elaborate and painstaking experiments to determine a threshold are useless. That is, the threshold determinations do not lead us beyond the determinations themselves.

In order to explain the fact that a person sometimes fails to distinguish between one point and two points near together, it has been suggested that the sensations fuse. This, I suppose, means either that the peripheral processes coalesce and go to the center as a single neural process, or that the process produced by each stimulus goes separately to the brain and there the two set up a single activity. Somewhat definite 'sensory circles,' even, were once believed in.

If the only fact we had to explain was that two points are often thought to be one when they are near together, 'fusion' might be a good hypothesis, but we have other facts to consider. If this one is explained by fusion, then the mistaking of one point for two must be due to diffusion of sensations. Even that might be admissible if the Vexirfehler were the only phenomenon of this class which we met. But it is also true that several contacts are often judged to be more than they actually are, and that hypothesis will not explain why certain arrangements of the stimulating objects are more likely to bring about that result than others. Still more conclusive evidence against fusion, it seems to me, is found in the fact that two points, one on each hand, may be perceived as one when the hands are brought together. Another argument against fusion is the fact that two points pressed lightly may be perceived as one, and when the pressure is increased they are perceived as two. Strong pressures should fuse better than weak ones, and therefore fusion would imply the opposite results. Brueckner[1] has found that two sensations, each too weak to be perceived by itself, may be perceived when the two are given simultaneously and sufficiently near together. This reenforcement of sensations he attributes to fusion. But we have a similar phenomenon in vision when a group of small dots is perceived, though each dot by itself is imperceptible. No one, I think, would say this is due to fusion. It does not seem to me that we need to regard reenforcement as an indication of fusion.

[1] Brueckner, A.: 'Die Raumschwelle bei Simultanreizung,' Zeitschrift fuer Psychologie, 1901, Bd. 26, S. 33.

My contention is that the effects sometimes attributed to fusion and diffusion of sensations are not two different kinds of phenomena, but are identical in character and are to be explained in the same way.

Turning now to the explanation of the special experiments, we may begin with the Vexirfehler.[2] It seems to me that the Vexirfehler is a very simple phenomenon. When a person is stimulated with two objects near together he attends first to one and then to the other and calls it two; then when he is stimulated with one object he attends to it, and expecting another one near by he hunts for it and hits upon the same one he felt before but fails to remember that it is the same one, and hence thinks it is another and says he has felt two objects. Observers agree that the expectation of two tends to bring out the Vexirfehler. This is quite natural. A person who expects two and receives one immediately looks about for the other without waiting to fixate the first, and therefore when he finds it again he is less likely to recognize it and more likely to think it another point and to call it two. Some observers[3] have found that the apparent distance of the two points when the Vexirfehler appears never much exceeds the threshold distance. Furthermore, there being no distinct line of demarcation between one and two, there must be many sensations which are just about as much like one as they are like two, and hence they must be lumped off with one or the other group. To the mathematician one and two are far apart in the series because he has fractions in between, but we perceive only in terms of whole numbers; hence all sensations which might more accurately be represented by fractions must be classed with the nearest whole number. A sensation is due to a combination of factors. In case of the Vexirfehler one of these factors, viz., the stimulating object, is such as to suggest one, but some of the other conditions—expectation, preceding sensation, perhaps blood pressure, etc.—suggest two, so that the sensation as a whole suggests one-plus, if we may describe it that way, and hence the inference that the sensation was produced by two objects.

[2] Tawney, Guy A.: 'Ueber die Wahrnehmung zweier Punkte mittelst des Tastsinnes mit Ruecksicht auf die Frage der Uebung und die Entstehung der Vexirfehler,' Philos. Stud., 1897, Bd. XIII., S. 163.

[3] See Nichols: 'Number and Space,' p. 161. Henri, V., and Tawney, G.: Philos. Stud., Bd. XI., S. 400.

This, it seems to me, may account for the appearance of the Vexirfehler, but why should not the subject discover his error by studying the sensation more carefully? He cannot attend to two things at once, nor can he attend to one thing continuously, even for a few seconds. What we may call continuous attention is only a succession of attentive impulses. If he could attend to the one object continuously and at the same time hunt for the other, I see no reason why he should not discover that there is only one. But if he can have only one sensation at a time, then all he can do is to associate that particular sensation with some idea. In the case before us he associates it with the idea of the number two. He cannot conceive of two objects unless he conceives them as located in two different places. Sometimes a person does find that the two objects of his perception are both in the same place, and when he does so he concludes at once that there is but one object. At other times he cannot locate them so accurately, and he has no way of finding out the difference, and since he has associated the sensation with the idea of two he still continues to call it two. If he is asked to locate the points on paper he fills out the figure just as he fills out the blind-spot, and he can draw them in just the same way that he can draw lines which he thinks he sees with the blind-spot, but which really he only infers.

Any sensation, whether produced by one or by many objects, is one, but there may be a difference in the quality of a sensation produced by one object and that of a sensation produced by more than one object. If this difference is clear and distinct, the person assigns to each sensation the number he has associated with it. He gives it the name two when it has the quality he has associated with that idea. But the qualities of a sensation from which the number of objects producing it is inferred are not always clear and distinct. The quality of the sensation must not be confused with any quality of the object. If we had to depend entirely on the sense of touch and always remained passive and received sensations only when we were touched by something, there is no reason why we should not associate the idea of one with the sensation produced by two objects and the idea of two with that produced by one object—assuming that we could have any idea of number under such circumstances. The quality of a sensation from which number is inferred depends on several factors. The number itself is determined by the attitude of the subject, but the attitude is determined largely by association. A number of facts show this. When a person is being experimented on, it is very easy to confuse him and make him forget how two feel and how one feels. I have often had a subject tell me that he had forgotten and ask me to give him two distinctly that he might see how it felt. In other words, he had forgotten how to associate his ideas and sensations. In developing the Vexirfehler I found it much better, after sufficient training had been given, not to give two at all, for it only helped the subject to perceive the difference between two and one by contrast. But when one was given continually he had no such means of contrast, and having associated the idea of two with a sensation he continued to do so. The one subject with whom I did not succeed in developing the Vexirfehler to any great extent perceived the difference by comparing the sensation with one he had had some time before. I could get him, for a few times, to answer two when only one was given, but he would soon discover the difference, and he said he did it by comparing it with a sensation which he had had some time before and which he knew was two. By this means he was able to make correct associations when otherwise he would not have done so. It has been discovered that when a subject is being touched part of the time with two and part of the time with one, and the time it takes him to make his judgments is being recorded, he will recognize two more quickly than he will one if there is a larger number of twos in the series than there is of ones. I do not see how this could be if the sensation of two is any more complex than that of one. But if both sensations are units and all the subject needs to do is to associate the sensation with an idea, then we should expect that the association he had made most frequently would be made the most quickly.

If the feeling of twoness or of oneness is anything but an inference, why is it that a person can perceive two objects on two fingers which are some distance apart, but perceives the same two objects as one when the fingers are brought near together and touched in the same way? It is difficult to see how bringing the fingers together could make a sensation any less complex, but it would naturally lead a person to infer one object, because of his previous associations. He has learned to call that one which seems to occupy one place. If two contacts are made in succession he will perceive them as two because they are separated for him by the time interval and he can perceive that they occupy different places.

When two exactly similar contacts are given and are perceived as one, we cannot be sure whether the subject feels only one of the contacts and does not feel the other at all, or feels both contacts and thinks they are in the same place, which is only another way of saying he feels both as one. It is true that when asked to locate the point he often locates it between the two points actually touched, but even this he might do if he felt but one of the points. To test the matter of errors of localization I have made a few experiments in the Columbia University laboratory. In order to be sure that the subject felt both contacts I took two brass rods about four inches long, sharpened one end and rounded off the other. The subject sat with the palm of his right hand on the back of his left and his fingers interlaced. I stimulated the back of his fingers on the second phalanges with the sharp end of one rod and the blunt end of the other and asked him to tell whether the sharp point was to the right or to the left of the other. I will not give the results in detail here, but only wish to mention a few things for the purpose of illustrating the point in question. Many of the answers were wrong. Frequently the subject would say both were on the same finger, when really they were on fingers of opposite hands, which, however, in this position were adjacent fingers. Sometimes when this happened I would ask him which finger they were on, and after he had answered I would leave the point on the finger on which he said both points were and move the other point over to the same finger, then move it back to its original position, then again over to the finger on which the other point was resting, and so on, several times. The subject would tell me that I was raising one point and putting it down again in the same place all of the time. Often a subject would tell me he felt both points on the same finger, but that he could not tell to which hand the finger belonged. When two or more fingers intervened between the fingers touched no subject ever had any difficulty in telling which was the sharp and which the blunt point, but when adjacent fingers were touched it was very common for the subject to say he could not tell which was which. This cannot be because there is more difference in the quality of the contacts in one case than in the other. If they were on the same finger it might be said that they were stimulating the same general area, but since one is on one hand and one on the other this is impossible. The subject does not think the two points are in the same place, because he feels two qualities and hence he infers two things, and he knows two things cannot be in the same place at the same time. If the two contacts were of the same quality probably they would be perceived as one on account of the absence of difference, for the absence of difference is precisely the quality of oneness.

These facts, together with those mentioned before, seem to me to indicate that errors of localization are largely responsible for judgments which seem to be due to fusion or diffusion of sensations. But they are responsible only in this way, they prevent the correction of the first impression. I do not mean that a person never changes his judgment after having once made it, but a change of judgment is not necessarily a correction. Often it is just the contrary. But where a wrong judgment is made and cannot be corrected inability to localize is a prominent factor. This, however, is only a secondary factor in the perception of number. The cardinal point seems to me the following:

Any touch sensation, no matter by how many objects it is produced, is one, and number is an inference based on a temporal series of sensations. It may be that we can learn by association to infer number immediately from the quality of a sensation, but that means only that we recognize the sensation as one we have had before and have found it convenient to separate into parts and regard one part after the other, and we remember into how many parts we separated it. This separating into parts is a time process. What we shall regard as one is a mere matter of convenience. Continuity sometimes affords a convenient basis for unity and sometimes it does not. There is no standard of oneness in the objective world. We separate things as far as convenience or time permits and then stop and call that one which our own attitude has determined shall be one.

That we do associate a sensation with whatever idea we have previously connected it with, even though that idea be that of the number of objects producing it, is clearly shown by some experiments which I performed in the laboratory of Columbia University. I took three little round pieces of wood and set them in the form of a triangle. I asked the subject to pass his right hand through a screen and told him I wanted to train him to perceive one, two, three and four contacts at a time on the back of his hand, and that I would tell him always how many I gave him until he learned to do it. When it came to three I gave him two points near the knuckles and one toward the wrist and told him that was three. Then I turned the instrument around and gave him one point near the knuckles and two toward the wrist and told him that was four. As soon as he was sure he distinguished all of the points I stopped telling him and asked him to answer the number. I had four subjects, and each one learned very soon to recognize the four contacts when three were given in the manner mentioned above. I then repeated the same thing on the left hand, except that I did not tell him anything, but merely asked him to answer the number of contacts he felt. In every case the idea of four was so firmly associated with that particular kind of a sensation that it was still called four when given on the hand which had not been trained. I gave each subject a diagram of his hand and asked him to indicate the position of the points when three were given and when four were given. This was done without difficulty. Two subjects said they perceived the four contacts more distinctly than the three, and two said they perceived the three more distinctly than the four.

It seems very evident that the sensation produced by three contacts is no more complex when interpreted as four than when interpreted as three. If that is true, then it must also be evident that the sensation produced by one contact is no more complex when interpreted as two than when interpreted as one. The converse should also be true, that the sensation produced by two contacts is no less complex when interpreted as one than when interpreted as two. Difference in number does not indicate difference in complexity. The sensation of four is not made up of four sensations of one. It is a unit as much as the sensation of one is.

There remains but one point to be elaborated. If number is not a quality of objects, but is merely a matter of attitude of the subject, we should not expect to find a very clear-cut line of demarcation between the different numbers except with regard to those things which we constantly consider in terms of number. Some of our associations are so firmly established and so uniform that we are likely to regard them as necessary. It is not so with our associations of number and touch sensations. We have there only a vague, general notion of what the sensation of one or two is, because usually it does not make much difference to us, yet some sensations are so well established in our minds that we call them one, two or four as the case may be without hesitation. Other sensations are not so, and it is difficult to tell to which class they belong. Just so it is easy to tell a pure yellow color from a pure orange, yet they shade into each other, so that it is impossible to tell where one leaves off and the other begins. If we could speak of a one-two sensation as we speak of a yellow-orange color we might be better able to describe our sensations. It would, indeed, be convenient if we could call a sensation which seems like one with a suggestion of two about it a two-one sensation, and one that seems nearly like two but yet suggests one a one-two sensation. Since we cannot do this, we must do the best we can and describe a sensation in terms of the number it most strongly suggests. Subjects very often, as has been mentioned before, describe a sensation as 'more than one but less than two,' but when pressed for an answer will say whichever number it most resembles. A person would do the same thing if he were shown spectral colors from orange to yellow and told to name each one either orange or yellow. At one end he would be sure to say orange and at the other yellow, but in the middle of the series his answers would likely depend upon the order in which the colors were shown, just as in determining the threshold for the perception of two points by the method of minimal changes the answers in the ascending series are not the same as those in the descending series. The experiments have shown that the sensation produced by two points, even when they are called one, is not the same as that produced by only one point, but the difference is not great enough to suggest a different number.

If the difference between one and two were determined by the distance, then the substitution of lines for knobs of the aesthesiometer ought to make no difference. And if the sensations produced by two objects fuse when near together, then the sensations produced by lines ought to fuse as easily as those produced by knobs.

In regard to the higher numbers difficulties will arise unless we take the same point of view and say that number is an inference from a sensation which is in itself a unit. It has been shown that four points across the ends of the fingers will be called four or less, and that four points, one on the end of each alternate finger and one at the base of each of the others, will be called four or more—usually more. In either case each contact is on a separate finger, and it is hardly reasonable to suppose there is no diffusion when they are in a straight row, but that when they are in irregular shape there is diffusion. It is more probable that the subject regards the sensation produced by the irregular arrangement as a novelty, and tries to separate it into parts. He finds both proximal and distal ends of his fingers concerned. He may discover that the area covered extends from his index to his little finger. He naturally infers, judging from past experience, that it would take a good many points to do that, and hence he overestimates the number. When a novel arrangement was given, such as moving some of the weights back on the wrist and scattering others over the fingers, very little idea of number could be gotten, yet they were certainly far enough apart to be felt one by one if a person could ever feel them that way, and the number was not so great as to be entirely unrecognizable.

* * * * *



THE SUBJECTIVE HORIZON.

BY ROBERT MACDOUGALL.

I.

The general nature of the factors which enter into the orientation of the main axes of our bodies, under normal and abnormal conditions, has been of much interest to the psychologist in connection with the problem of the development of space and movement perception. The special points of attack in this general investigation have comprised, firstly, the separation of resident, or organic, from transient, or objective, factors; secondly, the determination of the special organic factors which enter into the mechanism of judgment and their several values; and thirdly, within this latter field, the resolution of the problem of a special mechanism of spatial orientation, the organ of the static sense.

The special problem with which we are here concerned relates to the group of factors upon which depends one's judgment that any specified object within the visual field lies within the horizontal plane of the eyes, or above or below that plane, and the several functions and values of these components. The method of procedure has been suggested by the results of preceding investigations in this general field.

The first aim of the experiments was to separate the factors of resident and transient sensation, and to determine the part played by the presence of a diversified visual field. To do so it was necessary to ascertain, for each member of the experimental group, the location of the subjective visual horizon, and the range of uncertainty in the observer's location of points within that plane. Twelve observers in all took part in the investigation. In the first set of experiments no attempt was made to change the ordinary surroundings of the observer, except in a single point, namely, the provision that there should be no extended object within range of the subject's vision having horizontal lines on a level with his eyes.

The arrangements for experimentation were as follows: A black wooden screen, six inches wide and seven feet high, was mounted between two vertical standards at right angles to the axis of vision of the observer. Vertically along the center of this screen and over pulleys at its top and bottom passed a silk cord carrying a disc of white cardboard, 1 cm. in diameter, which rested against the black surface of the screen. From the double pulley at the bottom of the frame the two ends of the cord passed outward to the observer, who, by pulling one or the other, could adjust the disc to any desired position. On the opposite side of the screen from the observer was mounted a vertical scale graduated in millimeters, over which passed a light index-point attached to the silk cord, by means of which the position of the cardboard disc in front was read off. The observer was seated in an adjustable chair with chin and head rests, and a lateral sighting-tube by which the position of the eyeball could be vertically and horizontally aligned. The distance from the center of the eyeball to the surface of the screen opposite was so arranged that, neglecting the radial deflection, a displacement of 1 mm. in either direction was equal to a departure of one minute of arc from the plane of the eyes' horizon.

The observer sat with the light at his back, and by manipulation of the cords adjusted the position of the white disc freely up and down the screen until its center was judged to be on a level with the eye. Its position was then read off the vertical scale by the conductor (who sat hidden by an interposed screen), and the error of judgment was recorded in degrees and fractions as a positive (upward) or negative (downward) displacement. The disc was then displaced alternately upward and downward, and the judgment repeated. From the time of signalling that the point had been located until this displacement the observer sat with closed eyes. These determinations were made in series of ten, and the individual averages are in general based upon five such series, which included regularly the results of sittings on different days. In some cases twice this number of judgments were taken, and on a few occasions less. The number of judgments is attached to each series of figures in the tables. In that which follows the individual values and their general averages are given as minutes of arc for (a) the constant error or position of the subjective horizon, (b) the average deviation from the objective horizon, and (c) the mean variation of the series of judgments.

TABLE I.

Observer. Constant Error. Average Deviation. Mean Variation. A (100) -19.74 38.78 10.67 C (90) -18.18 23.89 10.82 D (100) -19.84 33.98 7.95 E (50) - 4.28 72.84 6.90 F (100) +46.29 46.29 2.05 G (50) +14.96 35.40 8.40 H (50) -27.22 27.46 5.78 I (50) + 6.62 53.34 7.45 K (50) + 1.08 30.26 6.59 L (20) -56.70 56.70 10.39

Average: -7.70 41.89 7.69

The average subjective horizon shows a negative displacement, the exceptional minority being large. No special facts could be connected with this characteristic, either in method of judgment or in the past habits of the reactor. The average constant error is less than an eighth of a degree, and in neither direction does the extreme reach the magnitude of a single degree of arc. Since the mean variation is likewise relatively small, there is indicated in one's ordinary judgments of this kind a highly refined sense of bodily orientation in space.

II.

In order to separate the resident organic factors from those presented by the fixed relations of the external world, an adaptation of the mechanism was made for the purpose of carrying on the observations in a darkened room. For the cardboard disc was substituted a light carriage, riding upon rigid parallel vertical wires and bearing a miniature ground-glass bulb enclosing an incandescent electric light of 0.5 c.p. This was encased in a chamber with blackened surfaces, having at its center an aperture one centimeter in diameter, which was covered with white tissue paper. The subdued illumination of this disc presented as nearly as possible the appearance of that used in the preceding series of experiments. No other object than this spot of moving light was visible to the observer. Adjustment and record were made as before. The results for the same set of observers as in the preceding case are given in the following table:

TABLE II.

Subject. Constant Error. Average Deviation. Mean Variation. A (50) - 52.76 55.16 30.08 C (30) - 7.40 42.00 35.31 D (50) - 14.24 38.60 30.98 E (50) - 43.12 86.44 30.19 F (100) - 2.01 72.33 20.27 G (100) - 21.89 47.47 32.83 H (50) - 1.62 59.10 29.95 I (50) - 32.76 41.60 24.40 K (50) - 61.70 100.02 52.44 L (40) -128.70 128.90 27.83

Average: - 36.62 67.16 31.43

Changes in two directions may be looked for in the results as the experimental conditions are thus varied. The first is a decrease in the certainty of judgment due to the simple elimination of certain factors upon which the judgment depends. The second is the appearance of definite types of error due to the withdrawal of certain correctives of organic tendencies which distort the judgment in specific directions. The loss in accuracy is great; the mean variation increases from 7.69 to 31.43, or more than 400 per cent. This large increase must not, however, be understood as indicating a simple reduction in the observer's capacity to locate points in the horizontal plane of the eyes. The two series are not directly comparable; for in the case of the lighted room, since the whole visual background remained unchanged, each determination must be conceived to influence the succeeding judgment, which becomes really a correction of the preceding. To make the two series strictly parallel the scenery should have been completely changed after each act of judgment. Nevertheless, a very large increase of uncertainty may fairly be granted in passing from a field of visual objects to a single illuminated point in an otherwise dark field. It is probable that this change is largely due to the elimination of those elements of sensation depending upon the relation of the sagittal axis to the plane against which the object is viewed.

The change presented by the constant error can here be interpreted only speculatively. I believe it is a frequently noted fact that the lights in a distant house or other familiar illuminated object on land, and especially the signal lights on a vessel at sea appear higher than their respective positions by day, to the degree at times of creating the illusion that they hang suspended above the earth or water. This falls in with the experimental results set forth in the preceding table. It cannot be attributed to an uncomplicated tendency of the eyes of a person seated in such a position to seek a lower direction than the objective horizon, when freed from the corrective restraint of a visual field, as will be seen when the results of judgments made in complete darkness are cited, in which case the direction of displacement is reversed. The single illuminated spot which appears in the surrounding region of darkness, and upon which the eye of the observer is directed as he makes his judgment, in the former case restricts unconscious wanderings of the eye, and sets up a process of continuous and effortful fixation which accompanies each act of determination. I attribute the depression of the eyes to this process of binocular adjustment. The experience of strain in the act of fixation increases and decreases with the distance of the object regarded. In a condition of rest the axes of vision of the eyes tend to become parallel; and from this point onward the intensity of the effort accompanying the process of fixation increases until, when the object has passed the near-point of vision, binocular adjustment is no longer possible. In the general distribution of objects in the visual field the nearer, for the human being, is characteristically the lower, the more distant the higher, as one looks in succession from the things at his feet to the horizon and vice versa. We should, therefore, expect to find, when the eyes are free to move in independence of a determinate visual field, that increased convergence is accompanied by a depression of the line of sight, decreased convergence by an elevation of it. Here such freedom was permitted, and though the fixed distance of the point of regard eliminated all large fluctuations in convergence, yet all the secondary characteristics of intense convergence were present. Those concerned in the experiment report that the whole process of visual adjustment had increased in difficulty, and that the sense of effort was distinctly greater. To this sharp rise in the general sense of strain, in cooeperation with the absence of a corrective field of objects, I attribute the large negative displacement of the subjective horizon in this series of experiments.

III.

In the next set of experiments the room was made completely dark. The method of experimentation was adapted to these new conditions by substituting for the wooden screen one of black-surfaced cardboard, which was perforated at vertical distances of five millimeters by narrow horizontal slits and circular holes alternately, making a scale which was distinctly readable at the distance of the observer. Opposite the end of one of these slits an additional hole was punched, constituting a fixed point from which distances were reckoned on the scale. As the whole screen was movable vertically and the observer knew that displacements were made from time to time, the succession of judgments afforded no objective criterion of the range of variation in the series of determinations, nor of the relation of any individual reaction to the preceding. The method of experimentation was as follows: The observer sat as before facing the screen, the direction of which was given at the beginning of each series by a momentary illumination of the scale. In the darkness which followed the observer brought the direction of sight, with open eyes, as satisfactorily as might be into the plane of the horizontal, when, upon a simple signal, the perforated scale was instantly and noiselessly illuminated by the pressure of an electrical button, and the location of the point of regard was read off the vertical scale by the observer himself, in terms of its distance from the fixed point of origin described above. The individual and general averages for this set of experiments are given in the following table:

TABLE III.

Observer. Constant Error. Average Deviation. Mean Variation. A (50) + 7.75 20.07 19.45 C " + 14.41 25.05 2.94 D " + 14.42 34.54 29.16 E " +108.97 108.97 23.13 F " - 5.12 23.00 2.02 G " + 20.72 34.80 10.23 H " + 35.07 53.60 33.95 I " + 25.52 30.68 22.49 K " - 8.50 40.65 21.07

Average: + 23.69 41.26 17.16

The point at which the eyes rest when seeking the plane of the horizon in total darkness is above its actual position, the positive displacement involved being of relatively large amount.

In addition to the removal of the whole diversified visual field there has now been eliminated the final point of regard toward which, in the preceding set of experiments, the sight was strained; and the factor of refined visual adjustment ceases longer to play a part in the phenomenon. The result of this release is manifested in a tendency of the eyes to turn unconsciously upward. This is their natural position when closed in sleep. But this upward roll is not an uncomplicated movement. There takes place at the same time a relaxation of binocular convergence, which in sleep may be replaced by a slight divergence. This tendency of the axes of vision to diverge as the eyes are raised is undoubtedly connected biologically with the distribution of distances in the higher and lower parts of the field of vision, of which mention has already been made. Its persistence is taken advantage of in the artificial device of assisting the process of stereoscopic vision without instruments by holding the figures to be viewed slightly above the primary position, so that the eyes must be raised in order to look at them and their convergence thereby decreased. It is by the concomitance of these two variables that the phenomena of both this and the preceding series of experiments are to be explained. In the present case the elimination of a fixed point of regard is followed by a release of the mechanism of convergence, with a consequent approximation to parallelism in the axes of vision and its concomitant elevation of the line of sight.

The second fact to be noted is the reduction in amount of the mean variation. The series of values under the three sets of experimental conditions hitherto described is as follows: I. 7'.69; II. 31'.42; III. 17'.16. This increase of regularity I take to be due, as in the case of the lighted room, to the presence of a factor of constancy which is not strictly an element in the judgment of horizontality. This is a system of sensory data, which in the former case were transient—the vision of familiar objects; and in the latter resident—the recognition of specific experiences of strain in the mechanism of the eye. The latter sensations exist under all three sets of conditions, but they are of secondary importance in those cases which include the presence of an objective point of regard, while in the case of judgments made in total darkness the observer depends solely upon resident experiences. Attention is thus directed specifically toward these immediate sensational elements of judgment, and there arises a tendency to reproduce the preceding set of eye-strains, instead of determining the horizon plane afresh at each act of judgment upon more general data of body position.

If the act of judgment be based chiefly upon sensory data connected with the reinstatement of the preceding set of strains, progressions should appear in these series of judgments, provided a constant factor of error be incorporated in the process. This deflection should be most marked under conditions of complete darkness, least in the midst of full illumination. Such a progression would be shown at once by the distribution of positive and negative values of the individual judgments about the indifference point of constant error. As instances of its occurrence all cases have been counted in which the first half of the series of ten judgments was uniformly of one sign (four to six being counted as half) and the second half of the opposite sign. The percentages of cases in which the series presented such a progression are as follows: In diffused light, 7.6%; in darkness, point of regard illuminated, 18.3%; in complete darkness, 26.1%. The element of constant error upon which such progressions depend is the tendency of the eye to come to rest under determinate mechanical conditions of equilibrium of muscular strain.

The relation of the successive judgments of a series to the reinstatement of specific eye-strains and to the presence of an error of constant tendency becomes clearer when the distribution of those series which show progression is analyzed simultaneously with reference to conditions of light and darkness and to binocular and monocular vision respectively. Their quantitative relations are presented in the following table:

TABLE IV.

Illumination. Per Cent. Showing Progress. Binocular. Monocular.

In light. 7.6 % 50 % 50 % In darkness. 18.3 34.2 65.8

Among judgments made in daylight those series which present progression are equally distributed between binocular and monocular vision. When, however, the determinations are of a luminous point in an otherwise dark field, the preponderance in monocular vision of the tendency to a progression becomes pronounced. That this is not a progressive rectification of the judgment, is made evident by the distribution of the directions of change in the several experimental conditions shown in the following table:

TABLE V. Light. Darkness. Direction of Change. Binocular. Monocular. Binocular. Monocular. Upward. 50 % 100 % 38.4 % 65.0 % Downward. 50 00.0 61.6 35.0 Const. Err. -7.70 +11.66 -36.62 -3.38

When the visual field is illuminated the occurrence of progression in binocular vision is accidental, the percentages being equally distributed between upward and downward directions. In monocular vision, on the contrary, the movement is uniformly upward and involves a progressive increase in error. When the illuminated point is exposed in an otherwise dark field the progression is preponderatingly downward in binocular vision and upward in vision with the single eye. The relation of these changes to phenomena of convergence, and the tendency to upward rotation in the eyeball has already been stated. There is indicated, then, in these figures the complication of the process of relocating the ideal horizon by reference to the sense of general body position with tendencies to reinstate simply the set of eye-muscle strains which accompanied the preceding judgment, and the progressive distortion of the latter by a factor of constant error due to the mechanical conditions of muscular equilibrium in the resting eye.

IV.

The influence of this factor is also exhibited when judgments made with both eyes are compared with those made under conditions of monocular vision. The latter experiments were carried on in alternate series with those already described. The figures are given in the following tables:

TABLE VI.

JUDGMENTS MADE IN DIFFUSED LIGHT.

Observer. Constant Error. Average Deviation. Mean Variation. A (50) - 28.46 29.04 8.87 C " + 7.54 14.86 8.01 D " + 39.32 43.28 13.83 E " + 50.46 65.26 9.86 F " + 62.30 62.30 1.60 G " 0.00 45.28 9.66 H " + 22.92 79.12 5.07 I " + 14.36 51.96 8.02 K " + 9.26 38.10 9.55 L " - 61.10 61.10 6.36 Average: + 11.66 49.03 8.18

TABLE VII.

JUDGMENTS IN ILLUMINATED POINT.

Observer. Constant Error. Average Deviation. Mean Variation. A (50) - 38.42 51.96 32.64 C (30) - 29.03 41.23 35.75 D (20) - 30.87 34.07 17.24 E (50) + 65.30 75.86 29.98 F " + 50.74 50.74 5.89 G " + 66.38 88.10 44.98 H " + 65.40 80.76 42.93 I " - 0.02 80.22 47.53 K " - 44.60 52.56 32.93 L " - 71.06 73.30 31.86 Average: - 3.38 62.88 32.17

The plane of vision in judgments made with the right eye alone is deflected upward from the true horizon to a greater degree than it is depressed below it in those made with binocular vision, the respective values of the constant errors being -7'.70 and +11'.66, a difference of 19'.36. When the field of vision is darkened except for the single illuminated disc, a similar reversion of sign takes place in the constant error. With binocular vision the plane of the subjective horizon is deflected downward through 36'.62 of arc; with monocular vision it is elevated 3'.38, a difference of 40'.00, or greater than in the case of judgments made in the lighted room by 20'.64. This increase is to be expected in consequence of the elimination of those corrective criteria which the figured visual field presents. The two eyes do not, of course, function separately in such a case, and the difference in the two sets of results is undoubtedly due to the influence of movements in the closed eye upon that which is open; or rather, to the difference in binocular functioning caused by shutting off the visual field from one eye. The former expression is justified in so far as we conceive that the tendency of the closed eye to turn slightly upward in its socket affects also the direction of regard in the open eye by attracting toward itself its plane of vision. But if, as has been pointed out, this elevation of the line of sight in the closed eye is accompanied by a characteristic change in the process of binocular convergence, the result cannot be interpreted as a simple sympathetic response in the open eye to changes taking place in that which is closed, but is the consequence of a release of convergence strain secondarily due to this act of closing the eye.

Several points of comparison between judgments made with binocular and with monocular vision remain to be stated. In general, the process of location is more uncertain when one eye only is used than when both are employed, but this loss in accuracy is very slight and in many cases disappears. The loss in accuracy is perhaps also indicated by the range of variation in the two cases, its limits being for binocular vision +46'.29 to -56'.70, and for monocular +62'.30 to -61'.10, an increase of 20'.41. In the darkened room similar relations are presented. The mean variations are as follows: binocular vision, 31'.42; monocular, 32'.17. Its limits in individual judgments are: binocular, -1'.62 to -128'.70, monocular, +66'.38 to -71'.06, an increase of 10'.36. In all ways, then, the difference in accuracy between the two forms of judgment is extremely small, and the conclusion may be drawn that those significant factors of judgment which are independent of the figuration of the visual field are not connected with the stereoscopic functioning of the two eyes, but such as are afforded by adjustment in the single eye and its results.

VI.

The experimental conditions were next complicated by the introduction of abnormal positions of the eyes, head and whole body. The results of tipping the chin sharply upward or downward and keeping it so fixed during the process of location are given in the following table, which is complete for only three observers:

TABLE VIII.

Observer. Upward Rotation. Downward Rotation. C.E. A.D. M.V. C.E. A.D. M.V. L (50) +43.98 43.98 5.62 +28.32 28.32 5.02 K (50) -33.72 33.72 71.33 +19.49 19.49 55.22 L (20) -39.10 45.90 33.60 -68.65 69.25 25.20 Average: - 9.61 41.20 36.85 -19.94 39.02 28.48 Normal: -64.14 67.08 33.51

The results of rotating the whole body backward through forty-five and ninety degrees are given in the following table:

TABLE IX.

Observer. Rotation of 45 deg.. Rotation of 90 deg.. C.E. A.D. M.V. C.E. A.D. M.V. B (30) + 4.10 24.57 18.56 D (30) +291.03 291.03 61.86 G (50) +266.78 266.78 22.83 +200.16 200.16 11.00 F (60) +116.45 116.45 17.14 - 36.06 36.30 6.29 J (20) +174.30 174.63 30.94 Average: +170.53 174.69 30.66

The errors which appear in these tables are not consistently of the type presented in the well-known rotation of visual planes subjectively determined under conditions of abnormal relations of the head or body in space. When the head is rotated upward on its lateral horizontal axis the average location of the subjective horizon, though still depressed below the true objective, is higher than when rotation takes place in the opposite direction. When the whole body is rotated backward through 45 deg. a positive displacement of large amount takes place in the case of all observers. When the rotation extends to 90 deg., the body now reclining horizontally but with the head supported in a raised position to allow of free vision, an upward displacement occurs in the case of one of the two observers, and in that of the other a displacement in the opposite direction. When change of position takes place in the head only, the mean variation is decidedly greater if the rotation be upward than if it be downward, its value in the former case being above, in the latter below that of the normal. When the whole body is rotated backward through 45 deg. the mean variation is but slightly greater than under normal conditions; when the rotation is through 90 deg. it is much less. A part of this reduction is probably due to training. In general, it may be said that the disturbance of the normal body relations affects the location of the subjective horizon, but the specific nature and extent of this influence is left obscure by these experiments. The ordinary movements of eyes and head are largely independent of one another, and even when closed the movements of the eyes do not always symmetrically follow those of the head. The variations in the two processes have been measured by Muensterberg and Campbell[1] in reference to a single condition, namely, the relation of attention to and interest in the objects observed to the direction of sight in the closed eyes after movement of the head. But apart from the influence of such secondary elements of ideational origin, there is reason to believe that the mere movement of the head from its normal position on the shoulders up or down, to one side or the other, is accompanied by compensatory motion of the eyes in an opposite direction, which tends to keep the axis of vision nearer to the primary position. When the chin is elevated or depressed, this negative reflex adjustment is more pronounced and constant than when the movement is from side to side. In the majority of cases the retrograde movement of the eyes does not equal the head movement in extent, especially if the latter be extreme.

[1] Muensterberg, H., and Campbell, W.W.: PSYCHOLOGICAL REVIEW, I., 1894, p. 441.

The origin of such compensatory reactions is connected with the permanent relations of the whole bodily organism to the important objects which surround it. The relations of the body to the landscape are fairly fixed. The objects which it is important to watch lie in a belt which is roughly on a horizontal plane with the observing eye. They move or are moved about over the surface of the ground and do not undergo any large vertical displacement. It is of high importance, therefore, that the eye should be capable of continuous observation of such objects through facile response to the stimulus of their visual appearance and movements, in independence of the orientation of the head. There are no such determinate spatial relations between body position and the world of important visual objects in the case of those animals which are immersed in a free medium; and in the organization of the fish and the bird, therefore, one should not expect the development of such free sensory reflexes of the eye in independence of head movements as we know to be characteristic of the higher land vertebrates. In both of the former types the eye is fixed in its socket, movements of the whole head or body becoming the mechanism of adjustment to new objects of observation. In the adjustment of the human eye the reflex determination through sensory stimuli is so facile as to counteract all ordinary movements of the head, the gaze remaining fixed upon the object through a series of minute and rapidly repeated sensory reflexes. When the eyes are closed and no such visual stimuli are presented, similar reflexes take place in response to the movements of the head, mediated possibly by sensations connected with changes in position of the planes of the semicircular canals.

VII.

If eye-strain be a significant element in the process of determining the subjective horizon, the induction of a new center of muscular equilibrium by training the eyes to become accustomed to unusual positions should result in the appearance of characteristic errors of displacement. In the case of two observers, A and H, the eyes were sharply raised or lowered for eight seconds before giving judgment as to the position of the illuminated spot, which was exposed at the moment when the eyes were brought back to the primary position. The effect of any such vertical rotation is to stretch the antagonistic set of muscles. It follows that when the eye is rotated in the contrary direction the condition of equilibrium appears sooner than in normal vision. In the case of both observers the subjective horizon was located higher when judgment was made after keeping the eyes raised, and lower when the line of sight had been depressed. In the case of only one observer was a quantitative estimation of the error made, as follows: With preliminary raising of the eyes the location was +36'.4; with preliminary lowering, -11'.4.

When the illuminated button is exposed in a darkened room and is fixated by the observer, it undergoes a variety of changes in apparent position due to unconscious shifting of the point of regard, the change in local relations of the retinal stimulation being erroneously attributed to movements in the object. These movements were not of frequent enough occurrence to form the basis of conclusions as to the position at which the eyes tended to come to a state of rest. The number reported was forty-two, and the movement observed was rather a wandering than an approximation toward a definite position of equilibrium. The spot very rarely presented the appearance of sidewise floating, but this may have been the result of a preconception on the part of the observer rather than an indication of a lessened liability to movements in a horizontal plane. Objective movements in the latter direction the observer knew to be impossible, while vertical displacements were expected. Any violent movement of the head or eyes dispelled the impression of floating at once. The phenomenon appeared only when the illuminated spot had been fixated for an appreciable period of time. Its occurrence appears to be due to a fatigue process in consequence of which the mechanism becomes insensible to slight changes resulting from releases among the tensions upon which constant fixation depends. When the insensitiveness of fatigue is avoided by a slow continuous change in the position of the illuminated spot, no such wandering of the eye from its original point of regard occurs, and the spot does not float. The rate at which such objective movements may take place without awareness on the part of the observer is surprisingly great. Here the fatigue due to sustained fixation is obviated by the series of rapid and slight sensory reflexes which take place; these have the effect of keeping unchanged the retinal relations of the image cast by the illuminated spot, and being undiscriminated in the consciousness of the observer the position of the point of regard is apprehended by him as stationary. The biological importance of such facile and unconscious adjustment of the mechanism of vision to the moving object needs no emphasis; but the relation of these obscure movements of the eyes to the process of determining the plane of the subjective horizon should be pointed out. The sense of horizontality in the axes of vision is a transient experience, inner conviction being at its highest in the first moments of perception and declining so characteristically from this maximum that in almost every case the individual judgment long dwelt upon is unsatisfactory to the observer. This change I conceive to be a secondary phenomenon due to the appearance of the visual wanderings already described.

VIII.

The influence of sensory reflexes in the eye upon the process of visual orientation was next taken up in connection with two specific types of stimulation. At top and bottom of the vertical screen were arranged dark lanterns consisting of electric bulbs enclosed in blackened boxes, the fronts of which were covered with a series of sheets of white tissue-paper, by which the light was decentralized and reduced in intensity, and of blue glass, by which the yellow quality of the light was neutralized. Either of these lanterns could be illuminated at will by the pressure of a button. All other experimental conditions remained unchanged. The observers were directed to pay no special regard to these lights, and the reports show that in almost every case they had no conscious relation to the judgment. The results are presented in the following table:

TABLE X.

Light Below. Light Above. Observer. Const.Err. Av.Dev. M.Var. Const.Err. Av.Dev. M.Var. C (40) +156.37 156.37 19.67 +169.85 169.85 19.22 D (20) + 39.30 43.30 17.95 + 46.65 47.35 15.41 F (30) + 19.47 19.47 8.83 + 58.37 58.37 7.83 G (50) + 66.11 112.76 14.65 +117.86 117.86 13.10 H (30) -147.63 147.63 21.07 -105.30 105.30 30.31 J (20) + 1.90 31.95 22.33 + 44.40 44.40 20.55 Average: + 22.59 85.28 17.42 + 55.30 90.52 17.74

The eye is uniformly attracted toward the light and the location of the disk correspondingly elevated or depressed. The amount of displacement which appears is relatively large. It will be found to vary with the intensity, extent and distance of the illuminated surfaces introduced. There can be little doubt that the practical judgments of life are likewise affected by the distribution of light intensities, and possibly also of significant objects, above and below the horizon belt. Every brilliant object attracts the eye toward itself; and the horizon beneath a low sun or moon will be found to be located higher than in a clouded sky. The upper half of the ordinary field of view—the clear sky—is undiversified and unimportant; the lower half is full of objects and has significance. We should probably be right in attributing to these characteristic differences a share in the production of the negative error of judgment which appears in judgments made in daylight. The introduction of such supplementary stimuli appears to have little effect upon the regularity of the series of judgments, the values of the mean variations being relatively low: 17'.42 with light below, 17'.74 with it above.

IX.

In the final series of experiments the influence of limiting visual planes upon the determination of the subjective horizon was taken up. It had been noticed by Dr. Muensterberg in the course of travel in hill country that a curious negative displacement of the subjective horizon took place when one looked across a downward slope to a distant cliff, the altitude (in relation to the observer's own standpoint) of specific points on the wall of rock being largely overestimated. Attributing the illusion to a reconstruction of the sensory data upon an erroneous interpretation of the objective relations of the temporary plane of the landscape, Dr. Muensterberg later made a series of rough experiments by stretching an inclined cord from the eye downward to a lower point on an opposite wall and estimating the height above its termination of that point which appeared to be on a level with the observing eye. He found an illusion present similar to the case of an extended slope of country.

The first experiments of this group repeated those just described. The previous mechanical conditions were varied only by the introduction of a slender cord which was stretched from just below the eyes to the bottom of the vertical screen. Full results were obtained from only two observers, which are given in the following table:

TABLE XI.

Observer. Const. Err. Av. Dev. Mean Var. Exp. Conds.

C (30) +123.92 123.92 11.94 Cord present and G (30) +66.47 66.47 15.56 consciously referred to. C (30) +126.90 126.90 6.31 Cord not present. G (30) +83.20 83.20 6.31 C (30) +126.93 126.93 6.39 Cord present but not G (30) +86.63 86.63 9.40 consciously referred to.

Averages. I +95.19 95.19 13.75 " II +105.05 105.05 6.31 " III +106.78 106.78 7.89

The effect of introducing such an objective plane of reference is twofold: the mean variation is increased, and the plane of the subjective horizon is displaced downwards. First, then, it acts as a simple factor of disturbance; it distracts from those habitual adjustments upon which the accuracy of the judgment depends. Secondly, it enters as a source of constant error into the determination of the subjective horizon, which is attracted toward this new objective plane. In the third section of the table are given the results of judgments made in the presence of such a plane but without conscious reference to it.[2] The figures here are of intermediate value in the case of the mean variation and of slightly greater value than the first in that of the constant error. In other words, the introduction of such a plane cannot be wholly overlooked, though it may be greatly abstracted from.

[2] In the preceding experiments the cord was definitely to be taken into account in making the judgment. The method of so doing was by running the eye back and forth over the cord preliminary to determining the location of the point.

The single cord was next replaced by a plane of blackened wood six inches wide and extending from the observer to the vertical screen. This strip was arranged in two ways: first, from the observer's chin to the bottom of the screen, and secondly, from the feet of the observer to a point on the screen a short distance below the plane of the objective horizon. The individual and average results are given in the following table:

TABLE XII.

Observer. Descending Plane. Ascending Plane.

A. (10) +18.80 18.80 5.24 +35.10 35.10 8.27 E. (20) +79.30 79.30 11.56 +131.67 131.67 12.07 H. (10) -37.50 37.50 16.80 -46.90 46.90 7.90 K. (30) +71.40 71.40 12.85 +48.05 48.05 5.11 Average: +33.00 51.75 11.61 +41.95 65.43 8.34

The introduction of a descending plane lowers the apparent horizon; that of an ascending plane elevates it. The general disturbance of judgment appears distinctly greater in the case of a downward than in that of an upward incline.

The results of a third variation of the experimental conditions may be presented at once. In it the location of the subjective horizon under normal conditions was compared with the results of adjustments made when the screen bearing the white disc was rotated backward from the observer through an angle of varying magnitude. The averages for each of the two subjects are as follows:

TABLE XIII.

Observer Const. Err. Av. Dev. Mean Var. Rotation. F (20) +130.50 130.50 3.20 20 deg. " " +115.50 115.50 1.10 50 deg. J (20) +443.10 443.10 9.47 45 deg.

These experiments were carried on in the presence of the definitely figured visual field of the lighted room, and the observers were conscious of taking these permanent features into account as correctives in making their judgments. Before proceeding, this defect was remedied as far as possible by enclosing the apparatus of experimentation, including the observer, between two walls of black fabric. Nothing was to be seen but these two walls, and the inclined plane which terminated the observer's view. The position of the screen remained constant at an inclination of 45 deg.. The upper bounding lines of the enclosing walls, on the contrary, were adjusted in three different relations to the plane of the gravity horizon. In the first arrangement these lines were horizontal; in the second the ends next to the observer were depressed five degrees; while in the final arrangement these ends were elevated through a like angular distance.

The inclined position of the screen was of course observed by every reactor, but of the changes in the enclosing walls no subject was informed, and none discerned them on any occasion. Each observer was questioned as to alterations in the experimental conditions after the use of each arrangement, and at the close of the whole series inquiry was made of each as to the planes of the upper boundaries of the walls. On various occasions, but not customarily, the observer was aware of a change of some kind in the whole set of conditions, but the particular feature altered was not suspected. The results for all three arrangements are given in the following table; of the sections of this table the third is incomplete, full results having been reached in the cases of only three observers:

TABLE XV.

Ascending Planes. Descending Planes. Observer Const. Err. Av. Dev. M. Var. Const. Err. Av. Dev. M. V. C (50) - 8.02 11.82 9.47 - 48.14 48.14 9.52 F (50) + 78.88 78.88 2.89 + 25.54 25.54 1.98 G (50) - 22.56 24.64 6.58 -101.20 101.20 7.39 H (50) - 83.84 83.84 11.78 -230.20 230.20 11.88 J (50) +315.64 315.64 18.16 +120.12 120.12 9.01 Average: + 55.96 102.96 9.78 -44.98 104.84 7.96

Horizontal Planes. Observer. Const. Err. Av. Dev. Mean Var. C (50) - 27.86 27.86 9.58 G (50) - 73.84 73.84 7.59 J (50) +243.72 243.72 18.52

For every individual observer, the position of the disc on the screen has been affected by each change in the direction of these visible lines. In every case, also, its location when these boundaries lay in a horizontal plane was intermediate between the other two. The importance of such relations in the objects of the visual field as factors in our ordinary determination of the subjective horizon is made evident by these experimental results. They become construction lines having assumed permanence in the world of visual-motor experience. The conception of unchanging spatial relations in the fundamental lines of perspective vision receives constant reinforcement from the facts of daily experience. The influence of the above-described changes in experimental conditions is mediated through their effect upon the location of the focus of the limiting and perspective lines of vision. As the plane of the upper boundaries of the enclosing walls was elevated and depressed the intersection of the two systems of lines was correspondingly raised and lowered, and in dependence upon the location of this imaginary point the determination of the position of the white disc was made, and the plane of perspective positively or negatively rotated.

Why such perspective lines should enter into the process of judgment it is not difficult to infer. The plane of perspective for human beings is characteristically horizontal, in consequence of the distribution of important objects within the field of visual perception. Roughly, the belt of the earth's horizon contains the loci of all human perspective planes. Both natural and artificial arrangements of lines converge there. The systems of visual objects on the earth and in the sky are there broken sharply off in virtue of their practically vast differences in quality and significance for the observer. The latter perspective probably never extends downward illusorily to points on the earth's surface; and the former system of objects is carried continuously upward to skyey points only on relatively rare occasions, as when one mistakes clouds for mountains or the upper edge of a fog-belt on the horizon for the rim of sea and sky. The point of convergence of the fundamental lines of perspective thus becomes assimilated with the idea of the visual horizon, as that concept has fused with the notion of a subjective horizon. There can be little doubt that the disposition of such lines enters constantly into our bodily orientation in space along with sensations arising from the general body position and from those organs more specially concerned with the static sense.

Upon the misinterpretation of such objective planes depends the illusion of underestimation of the height or incline of a hill one is breasting, and of the converse overestimation of one seen across a descending slope or intervening valley. The latter illusion is especially striking, and in driving over forest roads (in which case the correction of a wider range of view is excluded) the stretch of level ground at the foot of a hill one is descending is constantly mistaken for an opposing rise. This illusion is put into picturesque words by Stevenson when he describes the world, seen from the summit of a mountain upon which one stands, as rising about him on every side as toward the rim of a great cup. The fitness of the image may be proved by climbing the nearest hill. In all such cases a reconstruction of the sensory data of judgment takes place, in which the most significant factor is the plane determined by the positions of the observing eye and the perspective focus. In these judgments of spatial relationship, as they follow one another from moment to moment, this plane becomes a temporary subjective horizon, and according as it is positively or negatively rotated do corresponding illusions of perception appear.

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THE ILLUSION OF RESOLUTION-STRIPES ON THE COLOR-WHEEL.

BY EDWIN B. HOLT.

If a small rod is passed slowly before a rotating disc composed of two differently colored sectors, the rod appears to leave behind it on the disc a number of parallel bands of about the width of the rod and of about the colors, alternately arranged, of the two sectors. These appear not to move, but gradually to fade away.

This phenomenon was first observed by Muensterberg, and by him shown to Jastrow,[1] who, with Moorehouse, has printed a study, without, however, offering an adequate explanation of it.

[1] Jastrow, J., and Moorehouse, G.W.: 'A Novel Optical Illusion,' Amer. Jour. of Psychology, 1891, IV., p. 201.

I. APPARATUS FOR PRODUCING THE ILLUSION.

Any form of color-wheel may be used, but preferably one which is driven by electricity or clock-work, so that a fairly constant speed is assured. Several pairs of paper discs are needed, of the ordinary interpenetrating kind which permit a ready readjustment of the ratios between the two sectors, as follows: one pair consisting of a white and a black disc, one of a light-and a dark-colored disc (light green and dark red have been found admirably suited to the purpose), and a pair of discs distinctly different in color, but equal in luminosity.

The rod should be black and not more than a quarter of an inch broad. It may be passed before the rotating disc by hand. For the sake of more careful study, however, the rod should be moved at a constant rate by some mechanical device, such as the pendulum and works of a Maelzel metronome removed from their case. The pendulum is fixed just in front of the color-disc. A further commendable simplification of the conditions consists in arranging the pendulum and disc to move concentrically, and attaching to the pendulum an isosceles-triangular shield, so cut that it forms a true radial sector of the disc behind it. All the colored bands of the illusion then appear as radial sectors. The radial shields should be made in several sizes (from 3 to 50 degrees of arc) in black, but the smallest size should also be prepared in colors matching the several discs. Such a disposition, then, presents a disc of fused color, rotating at a uniform rate, and in front of this a radial sector oscillating from side to side concentrically with the disc, and likewise at a uniform rate. Several variations of this apparatus will be described as the need and purpose of them become clear.

II. PREVIOUS DISCUSSION OF THE ILLUSION.

Although Jastrow and Moorehouse (op. cit.) have published a somewhat detailed study of these illusion-bands, and cleared up certain points, they have not explained them. Indeed, no explanation of the bands has as yet been given. The authors mentioned (ibid., p. 204) write of producing the illusion by another method. "This consists in sliding two half discs of the same color over one another leaving an open sector of any desired size up to 180 degrees and rotating this against a background of a markedly different color, in other words we substitute for the disc composed of a large amount of one color, which for brevity we may call the 'majority color,' and a small amount of another, the 'minority color,' one in which the second color is in the background and is viewed through an opening in the first. With such an arrangement we find that we get the series of bands both when the wire is passed in front of the disc and when passed in back between disc and background; and further experimentation shows that the time relations of the two are the same. (There is, of course, no essential difference between the two methods when the wire is passed in front of the disc.)" That is true, but it is to be borne in mind that there is a difference when the wire is passed behind the disc, as these authors themselves state (loc. cit., note):—"The time-relations in the two cases are the same, but the color-phenomena considerably different." However, "these facts enable us to formulate our first generalization, viz., that for all purposes here relevant [i.e., to a study of the time-relations] the seeing of a wire now against one background and then immediately against another is the same as its now appearing and then disappearing; a rapid succession of changed appearances is equivalent to a rapid alternation of appearance and disappearance. Why this is so we are unable to say," etc. These authors now take the first step toward explaining the illusion. In their words (op. cit., p. 205), "the suggestion is natural that we are dealing with the phenomena of after-images.... If this is the true explanation of the fact that several rods are seen, then we should, with different rotation rates of disc and rod, see as many rods as multiplied by the time of one rotation of the disc would yield a constant, i.e., the time of an after image of the kind under consideration." For two subjects, J.J. and G.M., the following tabulation was made.

J.J. G.M. Av. time of rot. of disc when 2 images of rod were seen .0812 sec. .0750 sec. " " " " 3 " " " " .0571 " .0505 " " " " " 4 " " " " .0450 " .0357 " " " " " 5 " " " " .0350 " .0293 " " " " " 6 " " " " .0302 " .0262 "

"Multiplying the number of rods by the rotation rate we get for J.J. an average time of after image of .1740 sec. (a little over 1/6 sec.) with an average deviation of .0057 (3.2%); for G.M. .1492 (a little over 1/7 sec.) with an average deviation of .0036 (2.6%). An independent test of the time of after-image of J.J. and G.M. by observing when a black dot on a rotating white disc just failed to form a ring resulted in showing in every instance a longer time for the former than for the latter." That this constant product of the number of 'rods' seen by the time of one rotation of the disc equals the duration of after-image of the rod is established, then, only by inference. More indubitable, since directly measured on two subjects, is the statement that that person will see more 'rods' whose after-image persists longer. This result the present writer fully confirms. What relation the 'constant product' bears to the duration of after-image will be spoken of later. But aside from all measurement, a little consideration of the conditions obtaining when the rod is passed behind the disc will convince any observer that the bands are indeed after-images somehow dependent on the rod. We may account it established that the bands are after-images.

From this beginning one might have expected to find in the paper of Jastrow and Moorehouse a complete explanation of the illusion. On other points, however, these authors are less explicit. The changes in width of the bands corresponding to different sizes of the sectors and different rates of movement for the rod and disc, are not explained, nor yet, what is more important, the color-phenomena. In particular the fact needs to be explained, that the moving rod analyzes the apparently homogeneous color of the disc; or, as Jastrow and Moorehouse state it (op. cit., p. 202): "If two rotating discs were presented to us, the one pure white in color, and the other of ideally perfect spectral colors in proper proportion, so as to give a precisely similar white, we could not distinguish between the two; but by simply passing a rod in front of them and observing in the one case but not in the other the parallel rows of colored bands, we could at once pronounce the former to be composite, and the latter simple. In the indefinitely brief moment during which the rod interrupts the vision of the disc, the eye obtains an impression sufficient to analyze to some extent into its elements this rapid mixture of stimuli." The very question is as to how the eye obtains the 'impression sufficient to analyze' the mixture.

It may be shown at this point that the mistake of these authors lies in their recognition of but one set of bands, namely (ibid., p. 201), 'bands of a color similar to that present in greater proportion' on the disc. But, on the other hand, it is to be emphasized that those bands are separated from one another, not by the fused color of the disc, as one should infer from the article, but by other bands, which are, for their part, of a color similar to that present in lesser proportion. Thus, bands of the two colors alternate; and either color of band is with equal ease to be distinguished from the fused color of the main portion of the disc.

Why our authors make this mistake is also clear. They first studied the illusion with the smaller sector of the disc open, and the rod moving behind it; and since in this case the bands are separated by strips not of the minority but of the fused color, and are of about the width of the rod itself, these authors came to recognize bands of but one sort, and to call these 'images of the rod.' But now, with the rod moving in front of the disc, there appear bands of two colors alternately disposed, and neither of these colors is the fused color of the disc. Rather are these two colors approximately the majority and minority colors of the disc as seen at rest. Thus, the recognition of but one set of bands and the conclusion (ibid., p. 208) that 'the bands originate during the vision of the minority color,' are wholly erroneous. The bands originate as well during the vision of the majority color, and, as will later be shown, the process is continuous.

Again, it is incorrect, even in the case of those bands seen behind the open sector, to call the bands 'images of the rod,' for images of the rod would be of the color of the rod, whereas, as our authors themselves say (ibid., p. 201), the bands 'are of a color similar to that present in greater proportion' on the disc. Moreover the 'images of the rod' are of the most diverse widths. In fact, we shall find that the width of the rod is but one of several factors which determine the width of its 'images,' the bands.

Prejudiced by the same error is the following statement (ibid., p. 208): "With the majority color darker than the minority color the bands are darker than the resulting mixture, and lighter when the majority color is the lighter." If this is to be true, one must read for 'the bands,' 'the narrower bands.'

Another observation found in this article must be criticised. It is asserted that difference of shade between the two sectors of the disc, as well as difference of color, is essential to the illusion. To support this, four cases are given: two in which the sectors were so similar in luminosity as to bring out the illusion but faintly; two in which like luminosities yielded no illusion at all. The present writer agrees that if the two sectors are closely similar in luminosity, the illusion is fainter. He also selected a red and a green so near each other in brightness that when a rod 4 mm. broad (which is the largest rod that Jastrow and Moorehouse mention having used) was passed by hand before the disc, no trace of a band could be seen. The pendulum, however, bearing a shield considerably wider than 4 mm. (say of 15 degrees) and moving before the very same red and green shades, mixed in the same proportions, yielded the illusion with the utmost clearness. Colors of like luminosities yield the illusion less strikingly, nevertheless they yield it.