Harvard Psychological Studies, Volume 2

by Unknown

VISUAL IRRADIATION

BY FOSTER PARTRIDGE BOSWELL

There are various kinds of visual irradiation, of which perhaps the best-known variety is that which appears as the enlargement of a brightly illuminated surface at the expense of a contiguous one of less intensity. This has been until recently the only form recognized, and until very lately the greater part of the literature has dealt with it alone.

The whole subject was carefully investigated by Plateau in 1831, and retinal irradiation extricated from phenomena which very often accompany it. He showed that the extent of irradiation varies with the intensity of the stimulating light and the time during which it is allowed to act. He was also the first to call attention to the phenomenon of so-called negative irradiation.

Somewhat later Volkman again called attention to negative irradiation, while Aubert, in opposing the explanation advanced by Volkman, first showed the relations existing between irradiation and contrast.

Dove was the first to investigate the influence of irradiation on stereoscopic pictures, thus calling attention to the question of binocular irradiation. Experiments in this direction, however, have in general given negative results in so far as any enlargement of the binocular portion is concerned.

Helmholtz examined the manner in which the stimulation at the border-line between a light and dark field changes in intensity, and drew a curve showing these modifications of intensity due to irradiation. Hering showed that the form of the Helmholtz intensity curve would be modified by the presence of other phenomena not strictly those of irradiation.

De Roux demonstrated the difference in the extent of a real induction on the foveal and the extra-foveal parts of the retina.

Charpentier has attempted to carry forward the general explanation by saying that this spreading of neural excitation, the existence of which he proves to be beyond question, takes the form of an undulatory excitation in the free nerve-endings of the retina. Bidwell has investigated more thoroughly in some respects than Charpentier the phenomena of the after-images of moving sources of light, which have bearing upon irradiation. The same is true with regard to McDougall, von Kries, Hess, and others. Burch has instituted investigations along these lines, especially concerning the inhibition of stimuli on contiguous portions of the retina. Hess has worked carefully upon the different phases of the stimulation derived from a moving source of light, the differences in functioning of the foveal and extra-foveal parts of the retina, the respective functions of the rods and cones, and in connection with this, made investigations in the visual perception of color-blind subjects. All these observations have important bearing on irradiation, contrast, and theories of color-vision.

In connection with some work which was being done upon the after-images of moving sources of light in the Harvard laboratory in the early winter of 1903, some phenomena were observed which I believe are due to one form or other of visual irradiation. They can be seen in various ways, perhaps most advantageously by observing with fixed eyes the passage of a luminous image over the retina. What one sees as such a figure moves by is a travelling band of light, its forefront somewhat like that of the stimulating source, the rest composed of a long train of after-images which differ very decidedly from one another in intensity and color. The advantage of this well-known method of observation lies in the fact that it enables one to translate the temporal relations between the different phases of the stimulation into spatial relations between the different portions of the moving band of light. For since the figure moves across in a plane before the observer, that which appears in his consciousness first in time will likewise appear as foremost on the plane in space. Thus by observing the train of images one practically sees the different phases of the stimulation spread out in order before one. The new phenomena we observed, however, have to do with but a single phase of the stimulation, the extreme front of the stimulating image.

The intensity of light used varied considerably with the differently colored images, and was regulated so as to give as well as possible the phenomena we wished to study. With white light the intensity was less than that of an eight-candle-power electric lamp placed about ten feet distant from the observer. When colored light was employed it was necessary to use a very much stronger source of illumination, since the colored glass which was used absorbed a great deal of light and in case of colors lying toward the violet end of the spectrum greater luminosity seemed demanded.

The apparatus used consisted of a three-foot pendulum with a screen attached. This screen swung with the pendulum. In the screen was an opening about four inches wide and three inches high, into which strips of cardboard or tin backed by a piece of ground glass could be slipped. In these strips differently shaped holes were made through which the light passed. In this manner an image of any desired form might be used. Behind the screen, between it and the lamp, was a frame in which other pieces of ground or colored glass were placed. These pieces of ground glass would reduce the intensity of the light and diffuse it evenly over the image. The observer sat ten feet away. When the pendulum was set in motion, the image would appear moving back and forth in an arc. In order to shorten this arc and to aid the observer in keeping his gaze perfectly fixed, a second screen was placed before and very close to the pendulum, between it and the observer. This screen was stationary. In it was a hole six inches long and two inches wide. The top and bottom of this hole were arcs of circles parallel with the arc in which the pendulum swung. The ends were radii.

The screen was so placed with reference to the observer that the moving image would pass directly across the middle of the opening, appearing from behind one side and disappearing behind the other. In the centre of the opening, directly in front of the place occupied by the moving image when the pendulum was at rest, were two luminous fixation-points, one above the other, below the path of the moving light. In order to measure apparent spatial differences between the phases of the stimulation, two wires were stretched vertically across the opening in the stationary screen. These wires could be moved nearer together or farther apart. Thus by measuring the apparent distances in space between the different parts of the moving figure a measure could be had of their temporal differences in coming into consciousness. The luminous image moved, during the time it was visible, at a velocity of about one and a quarter feet per second. Since the observer sat about ten feet from the instrument, this would be at an angular velocity of about seven degrees per second. In one experiment a higher and a lower velocity were also employed.

It was of course very easy to change the figures and vary them widely in form, color, and intensity. Most of those employed, however, were rather small, subtending an angular distance of not more than one degree. Since the whole opening did not subtend an angle of more than three degrees or so, nearly all the phases of the stimulation occurred at the fovea.

We noticed that the form of the stimulating images themselves seemed to suffer modification as the light swung by, not only because of the train of after-images which dragged behind them over the retina, but in other ways as well. For instance, a circular image (Plate III, Fig. 1) appeared crescent-shaped, and its forward edge possessed greater curvature than the segment of the circle which produced it. It was longer also from horn to horn than the diameter of the generating circle, and a faint haze surrounded the points extending outward and backward until lost in the blackness of the background. Von Kries remarks that a circular moving image appears cylindrical in form with a concave edge behind. By using a little higher speed we observed this phenomenon. At first we thought the crescent-shaped image to be due merely to an intensely black after-process, which Bidwell describes as following the positive image of a bright white light. This, taking place before the circular disc of light had gone forward a distance equal to its own diameter, would overlap the bright image from behind and a crescent-shaped figure would result, but the increase in width and convexity of the stimulating image as well as the laterally trailing clouds of light remained to be explained, and as this could not be done in terms of anything which might happen to the back of the image, another explanation had to be sought. In order to determine the effect of the form of the figure used as a source of light on the form of the apparent image, several differently shaped figures were employed. In place of the original circle, an oblong pointed at both ends was tried (Plate III, Fig. 2). The front of this figure appeared very convex indeed, while the ends, which, owing to the shape of the figure, were very much less effective as a stimulating source, trailed far behind the centre.

A crescent-shaped figure (Plate III, Fig. 4) gave rise to a very pretty phenomenon. When it moved toward its concave side, it appeared very much less concave on that side than the real figure, but when it moved the other way, toward its convex side, it seemed very much more curved than it was in reality.[23]

PLATE III.

No. 3, a simple oblong figure, appeared curved like the others, almost as perfect a crescent as any of them.

The idea occurred to me that perhaps all these modifications in the curvature of the figures could be explained if we assumed two things: First: that there is a spreading of excitation from one portion of the retina to another. Each point will therefore be stimulated not only by the light falling directly upon it, but it will also derive a certain reënforcement of its stimulation from the points surrounding it. Thus a point lying toward the centre of one of these figures would be more favorably situated for receiving reënforcement than one located toward the periphery, where there are few neighboring points, and those lying mostly in one direction, namely, toward the centre.

This may be represented diagramatically, as in the illustration (Plate IV, Fig. 10), where the horizontal coördinates represent the spatial dimensions of an oblong image and the vertical coördinates the intensity of the excitation due to direct stimulation and its reënforcement by surrounding points at various portions of the figure.[24] Secondly I assumed that the stimulation at one part of the figure being thus rendered more intense, that part would appear in consciousness more quickly than the others and cause a modification in the form of the figure.[25] For example, in the case of the oblong figure, the light would be rendered most intense at the centre and less and less intense toward the ends, for the points in the centre of the figure will have their intensity increased by nervous excitation spreading to them from points lying toward the ends. Those toward the ends will be reënforced by light coming only from toward the centre. Thus the intensity of the centre of the figure will be increased, and as the figure moves across before the observer, the centre, appearing first in consciousness, would likewise appear foremost in space, the points near the centre a little later and so on, until finally, the ends being the last to appear, the whole front of the figure would take the form of a convex curve, after the manner in which it was observed. The back of the figure also appears curved, probably because of the fact that the front of the negative after-image, which closely follows it, is of the same shape as the front of the positive image, as was shown in the case of the circular figure.[26]

It is of course a well-known psychological fact that a light of greater intensity will take less time in coming into consciousness than one of less intensity. In this case, however, it was necessary to find some way of showing such differences between lights which were very little different in intensity. For one is practically unable to see any difference in intensity between the parts of a stationary image. So unless it could be shown that a difference in intensity between two sources of illumination, so small as to be imperceptible to the observer, will nevertheless make its presence known by the appearance of the brighter light in consciousness before the other, the explanation which I have suggested for the curvature of the images would have to be abandoned.

The following experiments do show, as I believe, that of two sources of light not perceptibly different in intensity, the brighter will appear in consciousness before the other, and that in the case of these figures the curvature of the image is due to a heightened intensity of the light in the centre through reënforcement of the excitation there present by stimulation spreading from the ends.

EXPERIMENT I

In the first of these experiments three dots of about three sixteenths of an inch were placed in a vertical row about three eighths of an inch apart (Plate IV, Fig. 1). No change was then observed in the form of the figure. The row of dots swung across the opening in a perfectly vertical line one directly above the other (Plate IV, Fig. 2). They were presumably too far apart for irradiation to take place between them. When, however, another dot was interposed between each end dot and the centre dot (Plate IV, Fig. 3), so that the excitement could extend from one dot to the next, the front of the line of dots no longer appeared vertical, but decidedly convex, the centre dot being perhaps three eighths of an inch before the dots on the ends (Plate IV, Fig. 4).

PLATE IV.

Absolutely the only difference between the two cases was that in the one, irradiation presumably could not occur, while in the other it conceivably could.

EXPERIMENT II

In the second of these experiments the curvature of a line of dots was observed and measured. Then the centre dots were slightly darkened (Plate IV, Fig. 5) by shading lightly with a lead pencil the ground glass which travelled with the pendulum and held in place the card from which the dots were cut, until the front of the image lost its curvature and appeared vertical (Plate IV, Fig. 6). The pendulum was then stopped and the row of dots observed closely, in order to see whether the dots in the centre were perceptibly of less intensity than those on the ends. No perceptible difference was found.

EXPERIMENT III

All the dots were covered, except the shaded central and the two unshaded end dots, in order that no irradiation might take place between them (Plate IV, Fig. 7). The pendulum was again set in motion, and the centre dot, instead of remaining co-linear with the dots on the ends, appeared considerably behind them (Plate IV, Fig. 3). This would show that irradiation must heighten the intensity of the excitation in the centre of the figure—for the two cases just mentioned are alike in every respect except that in the first (Fig. 6), where the dots were near enough together so that irradiation might occur between them, the intensity of the centre dot, which was objectively fainter than the end dots, was heightened enough by this induced excitation to appear in consciousness as soon as the two end dots, which were objectively of greater intensity; whereas in the second case (Fig. 7), where the dots were too far apart for irradiation to take place between them, the centre dot, being objectively of less intensity than the end dots, appeared behind them.

These experiments show that of two sources of light very little different in intensity the brighter will appear in consciousness before the other. Other things being equal, the difference in intensity may even be so small as to be imperceptible by direct comparison; it is able nevertheless to make its presence known by the order in which the lights appear. Exner made some experiments in 1868 to determine the time necessary for the perception of lights of different intensity. He used, however, stationary images of brief duration and tried to eliminate the effects of the after-image by flooding the visual field with light. This method has its disadvantages. It is incapable of measuring the minute temporal differences in latent perception of sources of light very slightly different in intensity.

While my method does not give the absolute time taken by any one light to enter consciousness, it is a very much more delicate method than Exner's for measuring differences in time of latent perception of sources of light very close to one another in intensity. It would be a very easy matter, having found the time of latent perception for a light of standard intensity, to determine by this method the time of lights of greater or less intensity.

These experiments also show that when irradiation is absent, the curvature of the images is absent; when irradiation is presumably present, curvature is present. For I find, not only in these, but also in a number of other experiments, that under all conditions in which the presence of irradiation is to be expected, the form of the images tends to be modified in precisely the manner that the assumption of its presence would lead one to anticipate. In all cases where irradiation is presumably absent, the contour of the front of the moving figure depends entirely on the amount of light proceeding from its different parts.

It is next in order to say something of the physiological causes of the phenomena we have been considering.

It is probable from what has been observed that in the case of the curved figures we are dealing with a form of visual irradiation which is due to the spreading of neural excitation over or through the layers of the retina. It is also evident from the close connection between irradiation and intensity that it must be of such a kind that the excitation produced in one part of the retina may communicate itself readily to another part. We have also seen in the case of the moving line of dots that the several dots could remain distinct from one another and yet could reënforce each other by means of communicated excitation. It must also be a very rapid form of irradiation, for the curvature of the figures does not increase very much during the time they are visible.

I think that the demands made by these different facts are best met by assuming that the spread of the nervous excitation which gives the reënforcement takes place in one of the interconnecting layers of nerve cells and fibres underlying the rods and cones. The line of dots which appeared curved and yet perfectly distinct from one another could very well communicate excitation to one another along these fibrils, and the intensity of one part be raised by the excitation of the near-lying parts. The fact that the dots remain distinct would not be contradictory. For in that case very near-lying parts might communicate excitation to one another without arousing to any very great activity the nerves that lead to the brain from the small unstimulated portions which lie between them. In this manner the intensity of the centre dots could be heightened enough to make the row appear convex, without any merging into one another on the part of the several dots. The fact that the dots do not fuse shows that the curvature is not due merely to a forward-spreading of the excitation in the retina. However, there is always a certain amount of light visible between the dots, with all the colors. This is especially noticeable with green light.

The fact that the elements of the retina form a kind of concatenated series from without inwards, a number of rods and cones corresponding to but one ganglion cell, furnishes a further bit of evidence in support of the explanation just advocated, since the irradiated excitation would tend to be "drained off" through the group of ganglion cells corresponding to the most highly stimulated portions and leave the intervening spaces comparatively free from centrally proceeding excitation. Thus also the individual dots in the five-dot figures may appear entirely distinct from one another and yet the centre ones be reënforced enough by irradiation to appear in consciousness in advance of the others.

SUBSIDIARY EXPERIMENTS

A number of other observations were made which present various exemplifications of the principles we have considered.

EXPERIMENT IV

An oblong figure, all its parts objectively of the same intensity, had its ends slightly darkened. When this was done the curvature had increased from twelve sixteenths to fourteen sixteenths of an inch.

The pendulum was stopped, and a very slight difference was perceived between the ends and the centre of the figure. This difference in intensity was greater than in the dot experiment, when the image had been darkened enough in the centre to make it appear vertical, because in this case, when the ends were darkened the centre would still be reënforced by irradiation from a considerable space which intervened between the shading and the centre.

EXPERIMENT V

The centre of the oblong figure was considerably darkened so as to counteract the effect of induction. By properly varying the amount of shading, one may make the front of the figure appear less convex, vertical, or even concave. This shows perfectly the effect of differences in intensity upon the curvature of the figure, but does not show so neatly as the similar experiments performed with the dots, the influence of the presence or absence of irradiation upon the intensity of the centre of the figure and so upon the curvature.

The illustration shows a case where the centre was too much darkened.

The two ends were comparatively free from shading. In each end-part irradiation took place. The points lying toward the centres of these ends received reënforcement, both from points lying toward the centre of the figure and from the extreme ends, and so the centres of the ends of the image were considerably brighter than either the extreme ends of the figure itself, or the sides of the end-parts toward the heavily shaded centre of the figure. Accordingly each end appeared convex for a short distance. The whole figure, however, being considerably brighter at the two ends than at the centre, on account of the heavy shading, the ends appeared in consciousness first and the centre afterwards, so that the figure as a whole seemed concave.

EXPERIMENT VI

An oblong figure was shaded rather heavily at one end, gradually becoming lighter toward the other, while about a third of the figure was free from shading. The shaded end always seemed to lag behind. The extreme front of the figure was at a point a little distance from the other end, before the shaded portion began. So that the front of the whole figure appeared, not like a segment of a circle, but like part of an oval with the bulge toward the brighter end.

Beyond the ends of all these images faint clouds of light were seen, as has been mentioned before, extending outward and backward, gradually decreasing in intensity, until lost in the surrounding blackness of the background.

Charpentier's bands, sometimes more and sometimes less in number, were observable in all of my figures and with all colors. Very often they appeared to be parallel to the forefront of the image, or even of a slightly greater degree of curvature.

EXPERIMENT VII

It is a well-known fact that a rotating color-disc, having colors which just fuse at a certain intensity, will show flicker at a slightly less intensity.

A color-disc was set in motion and the speed found where the colors were on the point of fusing. A piece of black cardboard, with a hole about an inch in diameter, was held close to the screen.

Around the periphery of the hole flickering appeared, while at the centre there was fusion. (The cardboard was held very close to the disc, so that there would be no shadows on the disc near its edges.) This fusion at the centre of the disc is probably due to the fact that the centre of the field is of slightly greater intensity than the edges, owing to irradiation. This difference in intensity makes the difference between the fusion at the centre and the slight flicker seen at the periphery.

Karl Marbe in a recent article mentions the difference in fusion between a point in the centre of the disc and a point near its border, and he thinks the increase of flickering in the latter is due to some influence on the part of the moving edge which separates the different parts of the disc. It would seem more probable from this last experiment that the fusion at the centre of the field of view was due to reënforcement of intensity by irradiation, and that the flicker about the periphery of the field was due to the lack of such reënforcement.

EXPERIMENT VIII

Three large dots were used and the centre one covered with tissue paper. The two end dots then appeared ahead of the centre dots. They were larger than the centre dot, due to irradiation over their borders. But this increase in size did not account for their position ahead in space. The centres of all the dots were not co-linear, but the middle dot was behind the others, thus, of course, showing the greater time necessary for the perception of the less luminous object.

EXPERIMENT IX

Figure observed with centre curved backward
at the fovea, and ends curved forward
owing to irradiation.

This was exactly similar to the preceding, except that the intensities of the various dots were reversed. The end dots were covered with tissue paper, instead of the centre one. Then the centre dot appeared first and the end dots after it.

EXPERIMENT X

Professor Hess finds that an image which, compared to those we used, was very long, subtending an angular distance of about thirty degrees, and which extends entirely across the fovea and overlaps the surrounding parts of the retina will appear curved backwards at the fovea, owing to the longer time of latent perception of the fovea and the macula. The accompanying illustration shows a modification of one of Hess's figures, in which the presence of this phenomenon and that of the convex image are both shown. The two phenomena were observed when a two-inch image was observed at a distance of about fourteen inches. The intensity of the light was that of an eight-candle-power lamp with three pieces of ground glass in front of it. (Very many of Hess's intensities are too great to give convex images.) Thus the image would be about 12° in height. About 5/12 of the figure would then fall on the macula and fovea and appear curved backwards in relation to the ends. The ends where they fell on the extra foveal parts of the retina appeared convex in front and concave at the rear as any small image of the right intensity does which falls on a homogeneous part of the retina.

EXPERIMENT XI

Charpentier, Bidwell, and others have made the observation that if a small source of light be exposed for a brief interval, excitation will proceed out in all directions over the retina, but if the light be exposed for a slightly longer period, the excitation will contract again and the light appear nearly its proper size and in its proper location at the stimulated portion of the retina. Using variously shaped figures we obtained analogous results, and the additional fact appeared that the outgoing excitation proceeds from the borders of the figures and that its form is somewhat determined by the form of the figure. An oblong image appeared vaguely elliptical, a diamond-shaped figure in the form of a more pointed ellipse, etc. These images were exposed for only a small fraction of a second, by means of a shutter. As the exposure grew longer the true form of the figures came out more and more clearly. There thus seems to be a general spreading of the stimulation in all directions over the retina from the borders of the images. Then, upon a slightly longer duration of the stimulus, this very rapid irradiation of excitation contracts and the irradiation becomes confined within the borders of the stimulated portion and affects the intensity of the different portions of the image. With strong intensities and certain colors it is, however, never wholly confined to the stimulated portion even of moving images. Charpentier speaks of "clouds of light accompanying his figures." With green light these clouds are especially noticeable. His "palm branch" phenomenon is a good instance of the irradiation of stimulation.

Besides these experiments which I have just described, several phenomena of a like sort were observed in connection with other experiments which were being performed in the laboratory at the same time. Dr. Holt was experimenting with a bright circular spot of light about one half inch in diameter, surrounded by a very faint ring about one half inch wide. When the whole image was moved about, the spot would seem to go back and forth across the less intense part so that the whole image looked like a jelly-fish swimming about in the water.

When the figure was allowed to remain stationary for a few moments it would resume its natural shape. Otherwise the bright part would seem to advance faster than the rest, sometimes even overlapping the border. This phenomenon was due to the fact that a bright light requires less time in coming into consciousness than a less intense one, and is, of course, the same in principle as those which were performed with dots when the bright dot moved ahead of the rest.

Another one of these phenomena occurred when an isosceles triangle was moved in a direction parallel to its base. The side toward which it moved appeared curved forward, with the apex bent backward. Toward the bottom, where there was the best chance for irradiation to have its effect, appeared the most advanced portion of the figure, while the bottom corner, although objectively the most advanced part of the figure, appeared rounded off and somewhat behind the part just above.

A narrow, vertical image with a large bulge behind the central part appeared with a large portion of this bulge in advance of the centre of the figure.

All these experiments show that a more intense object is, other things being equal, always located ahead of other objects co-linear with it. And I assume irradiation to account for the priority in localization of parts of the figure which are not objectively of greater intensity than others, but whose position makes them subject to reënforcement. The localization itself may be a function of more central organs, and not directly a question of the coming into consciousness more quickly of a more intense stimulation, although that seems to be the simplest explanation, but in any case priority of localization varies directly with the degree of intensity.

If the light is not bright enough to produce much irradiation the image will lose its curvature. If the light is too bright, although there may be a maximum of irradiation aroused and the absolute difference in intensity between the ends and centre of the image be at its greatest, yet this difference may not be great enough in proportion to the absolute intensity of the light to make the centre of the image appear in advance of the rest.

The curvature also varies with the angle subtended by the image and the portion of the retina upon which the image falls. If the image were too long, although all the processes which produce curvature be present, yet the front of the image would still appear vertical, because of the fact that each point in this long line would not derive reënforcement sensibly greater than that of the neighboring points. The best one could expect would be that these long figures should have their ends rounded off, which is usually the case. Most of the images which Professor Hess used in his experiments were too long to appear curved. All the images whose curvature we measured did not subtend an angle greater than 1° 10´, and were all seen on the fovea.

An image which subtends an angle of more than about 2° will hardly appear curved when it passes over the fovea.

We were sometimes able to see the curvature reversed. This happened in my own case about once in a hundred times, usually when my eyes were fatigued by the repeated passing of the moving light back and forth over the same portion of the retina. With other observers it occurred more often.

Slight vertical differences in fixation would cause the central part of the path taken by the moving light to become more fatigued than the edges and so to respond more slowly to the stimulation and reverse the curvature. It may be that some brain process which has to do with the apperception of the form and movement of visual objects becomes fatigued or does not always function properly, and so the curvature of the image may sometimes appear reversed. At any rate the more usual cases are those in which the convexity is present. The others, owing to the number of factors involved, and the vast majority of the opposite cases, may be regarded as due to temporary defects in the psycho-physical mechanism, which when properly working would give the more usual result.

QUANTITATIVE EXPERIMENTS

The object of the following experiments was to measure the amount of curvature produced by differing degrees of intensity of light at different speeds. An oblong figure was employed one fourth inch wide and two inches long. As has been mentioned, two vertical wires were stretched across the path in which the light moved. As the light swung by, it was attempted to get the wires at such a distance from one another that when one appeared tangent to the curve at the front of the figure the other would seem to cross the image at the point of intersection of the curve with the rest of the figure, as indicated in the diagram. ([Plate IV, Fig. 9.])

The distance between the wires was then read off on a scale. Thus one was able to obtain a measure of the curvature of the figure when it was moving at different speeds and illuminated by different intensities of light, and to compare the observations of different subjects. The mean error in this work is surprisingly little, considering the difficulties in making the judgment as the light passed rapidly by the wires. Usually the moving light had to be observed several times before the curvature of the front of the moving image could be measured exactly. It would be perfectly obvious that the front was considerably curved, but it would often be wholly impossible to tell just how much it was curved, until the pendulum had swung back and forth four or five times. Fatigue and darkness adaptation modify the judgments considerably. If one's eyes were partially adapted to darkness some little difficulty was experienced in seeing clearly the curvature of the image. Fatigue comes on very rapidly indeed. Usually it was impossible to get more than four judgments without resting, and often only two could be made. It was sometimes impossible to measure the curvature at the exact point when the light passed under the cross-wires, so the curvature had to be observed carefully and compared with the distance between the wires, and a judgment made when the wires were not superimposed upon the image. With each intensity of light two judgments were taken, one when the cross-wires had to be brought nearer together, the other when they had to be moved farther apart. Several series of measurements were made by different observers, and the results averaged up and compared.

The following curves and tables give the different observations for the nine different intensities of white light,[27] and the three speeds which were used. In the case of the high speed the light moved across the opening in the screen placed before the pendulum at a velocity of about 1.5 ft. per sec. The middle speed was about 1.27 ft. per sec. and the low speed about .917 feet per sec. In all cases an oblong image was used, ¼ inch wide and 2 inches long. The numerals on the left of the plotted curves give the apparent curvature of the image in sixteenths of an inch, and were obtained by measuring the distance between the cross-wires when this distance measured the apparent curvature of the image in the way described above. The figures at the bottom designate the different intensities of light which were used. Number one is the greatest intensity, number nine the least; the others those in between.

High Speed. This curve shows very well indeed what seems to be typical of the relations between the intensity of the moving light and the apparent curvature of the front edge of the image. With the lowest degrees of intensity the amount of the curvature is very little. Sometimes it was difficult to measure it at all. The light was so faint and the speed so rapid that probably very little reënforcement or irradiation took place, although what did occur would show its presence most prominently, since, on account of the high speed at which the pendulum moved, any part of the image which should come into consciousness ahead of the rest, even by a very little time, would appear considerably in advance of the rest of the image in space. Of course a certain amount of time would be required for the stimulus to spread itself over the retina, since it has to overcome a certain amount of resistance in the nerve-layers, and if this time were not given, the curvature of the resulting image would be of course decreased. As the light brightened, however, the curvature increased rapidly, until finally, when the intensity of the light neared its highest point, the curvature ceased becoming greater, and finally decreased. The mean error in eight judgments taken by two people for each intensity of light was about .099 in.

The measurements with the middle speed were very similar. The curvature with the lowest intensity of light was somewhat greater than when this same light moved with the highest speed. The maximum point of curvature was reached with a light of less intensity, and the curvature was less. When yet higher intensities were used, the curve decreased rapidly. The amount of curvature was also much less with the brightest light than with the higher speed. The following table shows the judgments of three observers for this speed: