Visual Illusions: Their Causes, Characteristics and Applications

Fig. 69.—By combining these stereoscopically the effect of metallic lustre
(similar to graphite in this case) is obtained.

One of the interesting results of retinal rivalry is found in combining two stereoscopic pictures in black and white with the black and white reversed in one of them. The apparently solid object will appear to possess lustre. The experiment may be tried with Fig. 69 by combining the two stereoscopic pictures by converging or diverging the axes of the eyes as described in connection with Figs. 2 and 3.

It will be noted that in order for two stereoscopic pictures, when combined, to produce a perfect effect of three dimensions their dissimilarity must be no more than that existing between the two views from the two eyes respectively. The dissimilarity in Fig. 69 is correct as to perspective, but the reversal of white and black in one of them produces an effect beyond that of true third dimension. When the colors are so arranged in such pictures as to be quite different in the two the effects are striking. There is, in such cases, an effect beyond that of perfect binocular combination.

By means of the stereoscope it is possible to attain binocular mixture of colors but this is usually difficult to accomplish. The difficulty decreases as the brightness and saturation of the colors decrease and is less for colors which do not differ much in hue and in brightness. These effects may be studied at any moment, for it is only necessary to throw the eyes out of focus for any object and to note the results. Many simple experiments may be arranged for a stereoscope, using black and white, and various combinations of colors. For example, Fig. 65 may be combined by means of double images (produced by converging or diverging the optical axes) so that the two inner squares are coincident. Actual observation is much more satisfactory than a detailed description.

Miscellaneous.—There are many interesting effects due to diffraction of light by edges of objects, by meshes such as a wire screen or a handkerchief, by the eye-media, etc. On looking at a very bright small light-source it may be seen to be surrounded by many colors.

Streamers of light appear to radiate from brilliant sources and all bright areas colored or colorless, when viewed amid dark surroundings, appear to be surrounded by diffuse brushes of light. These brushes are likely to be of a bluish tint.

Many of these phenomena are readily explained, but this cannot be done safely without knowing or recognizing all conditions. Many are not easily explained, especially when reported by others, who may not recognize certain important conditions. For example, authentic observers have reported that black letters on white paper appeared vivid red on a white background, under certain conditions. Of the latter, the apparently important one was “sun’s rays falling aslant the forehead.” When the eyes were shaded with the hand the letters immediately appeared black as they should.

The influence of the color of an object upon its apparent weight is relatively slight, but there is evidence of a tendency to judge a red or black object to be slightly heavier than a yellow or blue object of the same weight. It appears that hue is a minor factor in influencing the judgment and that there is no correlation between the affective quality of a color and its influence upon apparent weight. Although the scanty evidence available attributes but a slight influence to color in this respect, it is of interest in passing as a reminder of the many subtle factors which are at work modifying our judgments.

X
LIGHTING

The comparison of intaglio with low relief has been mentioned several times in preceding chapters. Examples of these as related to lighting are found in Figs. 70 to 73. Fig. 70 represents a bas-relief lighted from above and Fig. 71 would ordinarily be taken to represent a bas-relief lighted from below. However, the latter was made from a photograph of the mold (intaglio) from which the bas-relief was made and Fig. 71 really represents an intaglio lighted from above.

Similarly Fig. 72 represents the bas-relief lighted from the left and Fig. 73 ordinarily would be taken to be a bas-relief lighted from the right. However, Fig. 73 was made from a photograph of an intaglio lighted from the left. These amply demonstrate the effect of lighting as an influence upon the appearance of objects and they indicate the importance of correct assumptions in arriving at a correct judgment. In these cases the concealment of the light-source and the commonness of bas-relief as compared with intaglio are the causes for the illusion or the error in judgment. Certainly in these cases the visual sense delivers its data correctly.

Fig. 70.—A bas-relief lighted from above.

Fig. 71.—An intaglio lighted from above.

Fig. 72.—A bas-relief lighted from the left.

Fig. 73.—An intaglio lighted from the left.

In Fig. 74 the upper object is a disk and the lower is a sphere. In a Fig. 74 the lighting is due to a source of light of rather small physical dimensions directly above the objects. The same objects illuminated by means of highly diffused light (that is, light from many directions and of uniform intensity) appear as in b. Both objects now appear as disks. It is obvious that under appropriate lighting a disk might be taken for a sphere and vice versa, depending upon which dominates the judgment or upon the formulation of the attendant assumptions. Incidentally an appearance quite similar to that of a, Fig. 74 is obtained when the light-source is near the observer; that is, when it lies near the line of sight.

Somewhat similar to the confusion of intaglio with bas-relief is the confusion of the two hemispherical objects illustrated in Fig. 75. The one on the left is concave toward the observer. In other words, both could be hemispherical shells—one a mold for the other. Under the lighting which existed when the original photographs were made they could both be taken for hemispheres. The lighting was due to a large light-source at the left, but if the object on the left is assumed (incorrectly) to be a hemisphere convex toward the observer or a sphere, it must be considered to be lighted from the right, which is also an incorrect assumption. Obviously, if the direction of the dominant light is clear to the observer, he is not likely to make the error in judgment. Incidentally the object on the right might be assumed to be a sphere because a sphere is more commonly encountered than a hemisphere.

Fig. 76.—The same as Fig. 75, but lighted by a very small light-source.

The same objects are represented in Fig. 76 lighted from the left by means of a light-source of relatively small dimensions; that is, a source subtending a relatively small solid-angle at the objects. In this case the sharp shadow due to the edge of the hemispherical cup (on the left) is likely to cause the observer to inquire further before submitting his judgment. The more gradual modulation of light and shade as in the case of a sphere or a hemisphere convex toward the observer is not present in the case of the cup. This should be sufficient information for the careful observer to guide him, or at least to prevent him from arriving at the definite conclusion that the left-hand object is a hemisphere with its convex side toward him. Furthermore it should be noted that we often jump at the conclusion that an object is a sphere even though we see with one eye practically only a hemisphere and with two eyes hardly enough more to justify such a conclusion. However, spheres are more commonly encountered than hemispheres, so we take a chance without really admitting or even recognizing that we do.

The foregoing figures illustrate several phases which influence our judgments and the wonder is that we do not make more errors than we do. Of course, experience plays a large part and fortunately experience can be depended upon in most cases; however, in the other cases it leads us astray to a greater extent than if we had less of it.

The photographer, perhaps, recognizes more than anyone else the pitfalls of lighting but it is unfortunate that he is not better acquainted with the fundamentals underlying the control of light. Improper lighting does produce apparent incongruous effects but adequately controlled it is a powerful medium whose potentiality has not been fully realized. The photographer aims to illuminate and to pose the subject with respect to the source or sources of light so that undesirable features are suppressed and desirable results are obtained.

Finally his work must be accepted by others and the latter, being human, possess (unadmittedly of course) a desire to be “good looking.” Lighting may be a powerful flatterer when well controlled and may be a base revealer or even a creator of ugliness.

Incidentally, the photographer is always under the handicap of supplying a “likeness” to an individual who perhaps never sees this same “likeness” in a mirror. In other words, the image which a person sees of himself in a mirror is not the same in general that the photographer supplies him in the photographic portrait. The portrait can be a true likeness but the mirrored image in general cannot be. In the mirror there is a reversal of the parts from right to left. For example, a scar on the right cheek of the actual face appears on the left cheek in the mirror. Faces are not usually symmetrical and this reversal causes an individual to be familiar with his own facial characteristics in this reversed form. This influence is very marked in some cases. For example, suppose the left side of a companion’s face to be somewhat paralyzed on one side due to illness. We have become more or less oblivious to the altered expression of the left side by seeing it so often. However, if we catch a glimpse of this companion’s face in the mirror and the altered expression of the left side now appears upon the right side of the face, the contrast makes the fact very conspicuous. Perhaps this accounts for the difference which exists between the opinions of the photographer (or friends) and of the subject of the portrait.

All the illusions of brightness-contrast may be produced by lighting. Surfaces and details may appear larger or smaller, harsh or almost obliterated, heavy or light; in fact, lighting plays an important part in influencing the mood or expression of a room. A ceiling may be “lifted” by light or it may hang low and threatening when dark, due to relatively little light reaching it. Columns may appear dark on a light background or vice versa, and these illustrate the effects of irradiation. A given room may be given a variety of moods or expressions by varying the lighting and inasmuch as the room and its physical characteristics have not been altered, the various moods may be considered to be illusions. It should be obvious that lighting is a potent factor.

In connection with lighting it should be noted that contrasts play a prominent rôle as they always do. These have been discussed in other chapters, but it appears advantageous to recall some of the chief features. The effect of contrast is always in the direction of still greater contrast. That is, black tends to make its surroundings white; red tends to make its surroundings blue-green (complementary), etc. The contrast-effect is greatest when the two surfaces are juxtaposed and the elimination of boundary lines of other colors (including black or white) increases its magnitude. The contrast-effect of colors is most conspicuous when there is no brightness-contrast, that is, when the two surfaces are of equal brightness and therefore differ chiefly in hue. This effect is also greatest for saturated colors. It has been stated that cold colors produce stronger contrast-effects than warm colors, but experimental evidence is not sufficiently plentiful and dependable to verify this statement.

As the intensity of illumination increases, colors appear to become less saturated. For example, a pure red object under the noonday sun is likely to be painted an orange red by the artist because it does not appear as saturated as it would under a much lower intensity of illumination. In general, black and white are the final appearances of colors for respectively very low and very high brightness. As the intensity of illumination decreases, hue finally disappears and with continued decrease the color approaches black. Conversely, as the intensity of illumination increases, a color becomes apparently less and less saturated and tends toward white. For example, on viewing the sun through a colored glass the sun appears of a much less saturated color than the haze near the sun or a white object illuminated by sunlight.

Visual adaptation also plays a prominent part, and it may be stated that all sensations of light tend toward a middle gray and all sensations of color tend toward neutrality or a complete disappearance of hue. The tendency of sensations of light toward a middle gray is not as easily recognized as changes in color but various facts support this conclusion. In lighting it is important to recognize the tendency of color toward neutrality. For example, a warm yellow light soon disappears as a hue and only its subtle influence is left; however, a yellow vase still appears yellow because it is contrasted with objects of other colors. In the case of colored light the light falls upon everything visible, and if there is no other light-source of another color with which to contrast it, its color appears gradually to fade. This is an excellent example of the tremendous power and importance of contrast. It is the life of color and it must be fully appreciated if the potentiality of lighting is to be drawn upon as it should be.

Physical measurements are as essential in lighting as in other phases of human endeavor for forming a solid foundation, but in all these activities where visual perception plays an important part judgment is finally the means for appraisal. Wherever the psychological aspect is prominent physical measurements are likely to be misleading if they do not agree with mental appraisals. Of course the physical measurements should be made and accumulated but they should be considered not alone but in connection with psychological effects.

The photometer may show a very adequate intensity of illumination; nevertheless seeing may be unsatisfactory or even impossible. An illumination of a few foot-candles under proper conditions at a given surface is quite adequate for reading; however, this surface may appear quite dark if the surroundings are bright enough. In such a case the photometer yielded results quite likely to be misinterpreted as satisfactory. It should be obvious that many illusions discussed in preceding chapters are of interest in this connection.

An interesting example of the illusion of color may be easily demonstrated by means of a yellow filter. For this purpose a canary glass is quite satisfactory. When such a filter is placed before the eyes a daytime scene outdoors, for example, is likely to appear to be illuminated to a greater intensity than when the eyes are not looking through the filter. This is true for a glass used by the author notwithstanding the fact that the filter transmits only about one-half as much light as a perfectly clear colorless glass. In other words, the brightnesses of objects in the scene are reduced on the average about fifty per cent, still the subject is impressed with an apparent increase in the intensity of illumination (and in brightness) when the filter is placed before the eyes. Of course, the actual reduction in brightness depends upon the color of the object.

In such a case as the foregoing, true explanations are likely to involve many factors. For this reason explanations are usually tedious if they are to be sufficiently qualified to be reasonably near completeness. In this case it appears that the yellow filter may cause one to appraise the intensity of illumination as having increased, by associating such an influence as the sun coming out from behind a cloud. If we look into the depths where light and color accumulated their psychological powers, we are confronted on every hand by associations many of which are more or less obscure, and therefore are subtly influential.

The psychological powers of colors could have been discussed more generally in the preceding chapter, but inasmuch as they can be demonstrated more effectively by lighting (and after all the effect is one of light in any case) they will be discussed briefly here. They have been presented more at length elsewhere.

It is well known that the artist, decorator, and others speak of warm and cold colors, and these effects have a firm psychological foundation. For example, if a certain room be illuminated by means of blue light, it does seem colder. A theater illuminated by means of bluish light seems considerably cooler to the audience than is indicated by the thermometer. If this lighting is resorted to in the summer time the theater will be more inviting and, after all, in such a case it makes little difference what the thermometer indicates. The “cold” light has produced an illusion of coolness. Similarly “warm” light, such as yellow or orange, is responsible for the opposite feeling and it is easily demonstrated that an illusion of higher temperature may be produced by its use. As already stated, color-schemes in the decorations and furnishings produce similar effects but in general they are more powerful when the primary light is colored. In the latter case no object is overlooked for even the hands and faces of the beings in the room are colored by the light. In the case of color-schemes not all objects are tinged with the desired “warm” or “cold” color.

In the foregoing, associations play a prominent rôle. The sky has been blue throughout the numberless centuries during which the human organism evolved. The blue-sky during all these centuries has tinged the shadows outdoors a bluish color. That shade is relatively cool we know by experience and perhaps we associate coolness or cold with the aerial realm. These are glimpses of influences which have coöperated toward creating the psychological effect of coldness in the case of bluish light. By contrast with skylight, sunlight is yellowish, and a place in the sun is relatively warm. South rooms are usually warmer than north rooms in this hemisphere when artificial heat is absent and the psychological effect of warmth has naturally grown out of these and similar influences.

We could go further into the psychology of light and color and conjecture regarding effects directly attributable to color, such as excitement, depression, and tranquillity. In so doing we would be led far astray from illusions in the sense of the term as used here. Although this term as used here is still somewhat restricted, it is broader in scope than in its usual applications. However, it is not broad enough to lead far into the many devious highways and byways of light and color. If we did make these excursions we would find associations almost universally answering the questions. The question would arise as to innate powers of colors and we would find ourselves wondering if all these powers were acquired (through associations) and whether or not some were innate. And after many interesting views of the intricate subject we would likely conclude that the question of the innateness of some of the powers of color must be left unanswered.

As an example let us take the case of the restfulness or depression due to blue. We note that the blue sky is quite serene or tranquil and we find that the delicate sensibilities of poets verify this impression. This association could account for the impression or feeling of tranquillity associated with blue. On proceeding further, we would find nature’s solitudes often tinged with the blue skylight, for these solitudes are usually in the shade. Thus their restfulness or even depressiveness may be accounted for—partially at least. These brief glimpses are presented in order that they may suggest to the reader another trend of thought when certain illusions of light and color are held up for analysis. Besides these our individual experiences which have molded our likes and dislikes must be taken into account. This phase of light and color has been treated elsewhere.[6]

A very unusual kind of optical illusion is illustrated by the phenomenon of the apparent ending of a searchlight beam which has attracted much attention in connection with the powerful searchlights used for locating aeroplanes (Fig. 77). For years the apparent ending has more or less carelessly been attributed to the diminution of the density of atmospheric fog or haze, but recently Karrer[13] has suggested what appears to be the correct explanation.

When the beam of light from a powerful searchlight is directed into space, its path is visible owing to the scattering of some of the light by dust and moisture particles and the molecules of the air itself. While obviously the beam itself must go on indefinitely, its luminous path appears to end abruptly at no very great distance from the source. This is true whether the beam is photographed or viewed with the naked eye.

Fig. 77.—Apparent ending of a searchlight beam.

The fact that the appearance of the beam is no different when it is directed horizontally than when directed vertically proved that the common assumption pertaining to the ending of the haze or fog is untenable. Furthermore, photometric measurements on the different portions of the beam as seen from a position near the searchlight show that the beam is actually brighter at its outer termination than near its origin. Again, the apparent length of the beam varies with the position of the observer, and bears a direct ratio to his distance from the searchlight.

The fact is, that the luminous path of the beam has no definite ending, and extends to a very great distance—practically to infinity. It appears to be sharply cut off for the same reason that the boundary between earth and sky in a flat landscape is a sharp line. Just as the horizon recedes when the landscape is viewed from an elevation, so the beam appears longer when one’s distance from it is increased. The outer portion appears brighter, because here the line of sight pierces it to great depth.

That the ending of the beam appears close at hand is no doubt partly due to the brightness distribution, but is also a matter of perspective arising from the manner in which the beam is adjusted. Searchlight operators in the army were instructed to adjust the light to throw a parallel beam. Accordingly, the adjustments were so made that the beam appeared the same width at its outer extremity as at its base. The result seems to be a short parallel shaft of light, but is really a divergent cone of infinite extent, its angle of divergence being such as exactly to offset the effects of perspective.

If the beam were a truly parallel one it would seem to come to a point, just as the edges of a long straight stretch of country road seem to meet at the horizon. If the sides of the road were not parallel, but diverged from the observer’s eye at exactly the rate at which they ordinarily would appear to converge, then the road would seem to be as wide where it passed out at the horizon as at the observer’s feet. If there were no other means in the landscape of judging the distance of the horizon than by the perspective afforded by the road, it would likely be inferred that the road only extended a short distance on the level, and then went down a hill, that is, passed abruptly from the observer’s view.

These conditions obtain ideally in the case of the searchlight beam. There is no other means of judging the position in space of the “end” of an unobstructed searchlight beam than by the perspective of the beam itself, and the operator in adjusting it to appear parallel eliminates the perspective.

The angle at which the beam must diverge to appear parallel to an observer depends upon the distance of the observer from the searchlight. A beam which seems parallel to a person close to it will not appear so at a distance. This fact probably accounts for the difficulties encountered during “searchlight drill” in the army in getting a beam which satisfied both the private operating the lamp and the officer down the field as to its parallelity.

To summarize, the apparent abrupt ending of a searchlight beam is purely an optical illusion. It really has no ending; it extends to infinity.

XI
NATURE

Visual illusions abound everywhere, and there are a number of special interest in nature. Inasmuch as these are representative of a wide range of conditions and are usually within the possible experience of nearly everyone daily, they appear worthy of special consideration. Some of these have been casually mentioned in other chapters but further data may be of interest. No agreement has been reached in some cases in the many suggested explanations and little or no attempt of this character will be made in the following paragraphs. Many illusions which may be seen in nature will be passed by because their existence should be obvious after reading the preceding chapters. For example, a tree appears longer when standing than after it has been felled for the same reason that we overestimate vertical lines in comparison with horizontal ones. The apparent movement of the sun, moon, and stars, when clouds are floating past, is a powerful, though commonplace, illusion but we are more specifically interested in static illusions. However, it is of interest to recall the effect of involuntary eye-movements or of fluctuation in fixation because this factor in vision is important in many illusions. It is demonstrated by lying face upward on a starlit night and fixing the gaze upon a star. The latter appears to move more or less jerkily over its dark background. The magnitude and involuntary nature of these eye-movements is demonstrated in this manner very effectively.

The effect sometimes known as aerial perspective has been mentioned heretofore. The atmosphere is not perfectly transparent or colorless and is not homogeneous from an optical standpoint. It scatters rays of the shorter wave-lengths more than those of the longer wave-lengths. Hence it appears of a bluish tint and anything seen through great distances of it tends toward a reddish color. The blue sky and the redness of the setting sun are results of this cause. Distant signal-lights are reddened, due to the decrease in the rays of shorter wave-length by scattering. Apparently we have come to estimate distance to some extent through the amount of blurring and tinting superposed upon the distant scene.

In the high Rockies where the atmosphere is unusually clear, stretches of fifty miles of atmosphere lying between the observer and the distant peaks will show very little haze. A person inexperienced in the region is likely to construe this absence of haze as a shorter distance than the reality and many amusing incidents and ludicrous mistakes are charged against the tenderfoot in the Rockies. After misjudging distance so often to his own discomfiture a tourist is said to have been found disrobing preparatory to swimming across an irrigation ditch. He had lost confidence in his judgment of distance and was going to assume the risk of jumping across what appeared to be a ditch but what might be a broad river. Of course, this story might not be true but it serves as well as any to emphasize the illusion which arises when the familiar haze is not present in strange territory.

It is a common experience that things “loom in a fog,” that is, that they appear larger than they really are. An explanation which has been offered is that of an “excess of aerial perspective” which causes us to overestimate distance and therefore to overestimate size. If this explanation is correct, it is quite in the same manner that in clear atmosphere in the mountains we underestimate distance and, consequently, size. However, another factor may enter in the latter case, for the illusion is confined chiefly to newcomers; that is, in time one learns to judge correctly. On entering a region of real mountains the first time, the newcomer’s previous experience with these formations is confined to hills relatively much smaller. Even allowing considerably for a greater size when viewing the majestic peaks for the first time, he cannot be expected to think in terms of peaks many times larger than his familiar hills. Thus underestimating the size of the great peaks, he underestimates the distance. The rarity of the atmospheric haze aids him in making this mistake. This is not offered as a substitute for aerial perspective as the primary cause of the illusion but it appears to the author that it is a cause which must be taken into account.

The apparent form of the sky has attracted the attention of many scientific investigators for centuries. There are many conflicting opinions as to the causes of this appearance of form, but there is general agreement that the sky appears usually as a flattened vault. The sky is bright, due to scattering of light by actual particles of solid matter and moisture and possibly by molecules of gas. Lack of optical homogeneity due to varying refractive index is likely to be partially responsible. Usually a prominent layer of haze about a mile in thickness (although this varies considerably) lies next to the earth’s surface. The top of this haze is fairly well defined as aerial travelers know, but the sky above is still far from black, indicating scattered light and illuminated particles still higher. As one continues to ascend, thereby leaving more and more of the luminous haze behind, the sky becomes darker and darker. Often at altitudes of four or five miles the sky is very dark and the sun is piercingly bright. Usually there is little or no bright haze adjacent to the sun at these high altitudes as is commonly seen from the earth’s surface. At these high altitudes the author is not conscious of a flattened vault as at the earth’s surface but the illusion of a hemispherical dome still persists.

There is some agreement that the dome of the sky appears less depressed at the zenith by night than by day. This is in accord with the author’s observation at very high altitudes on occasions when the sky was much darker than when viewed from the earth’s surface. Dember and Uibe assumed the apparent shape as a part of a sphere (justifying this assumption to their satisfaction) and obtained estimates of the apparent depression at the zenith. They estimated the middle point of the arc from the zenith to the horizon and then measured the angular altitude of that point. They found that the degree of clearness of the sky has considerable influence upon the apparent height and they state that the sky appears higher in the sub-tropics than in Germany. On very clear moonless nights they found that the shape of the sky-dome differs little from that of a hemisphere. They concluded that the phenomenon is apparently due to optical conditions of the atmosphere which have not been determined.

It is of interest to note the appearance of the sky when cumulus clouds are present. The bases of these vary in height, but are found at altitudes from three to five thousand feet. They appear to form a flat roof of clouds bending downward at the horizon, thus giving the appearance of a vaulted but flattened dome. This apparent shape does not differ much in clear weather, perhaps due largely to the accustomedness of the eye and to the degradation of color from blue to gray toward the horizon. Furthermore the lower sky is usually much brighter than the zenith and the latter being darker appears to hang lower. It is of interest to note how persistent is the illusion of a flattened dome, for when one rises rapidly in the air and, within a few minutes, is on the level with the clouds or the dense low-lying haze, he is mildly surprised to find these are levels and not vaulted roofs. Despite the fact that by many previous experiences he has learned what to expect, the feeling of mild surprise is born each time on ascending rapidly.

The appearance of the flattened vault of the sky is held by some to account for the apparent enlargement of the sun, moon, and the constellations at the horizon. That is, they appear more distant at the horizon and we instinctively appraise them as being larger than when they are at higher altitudes. It is certain that these heavenly bodies do appear much larger when they are rising or setting than when they are nearer the zenith. In fact, this is one of the most remarkable and surprising illusions which exist. Furthermore this apparent enlargement has been noted universally, still many persons have attributed it to an actual optical magnification. Although we are more familiar with this enlargement in connection with the sun and moon, it still persists with the constellations. For example, Orion is apparently very large; in fact, this is the origin of the name. That this enlargement is an illusion can be shown in several ways but that it is solely due to the influence of the apparent flattened form of the sky may be doubted. Certainly the moon appears greatly enlarged while near the horizon, even when there is doubt as to an appreciable appearance of flattening of the sky-dome.

Many peculiar conditions and prejudices must be taken into account. For example, if various persons are asked to give an idea of how large is the disk of the sun or moon, their answers would vary usually with the head of a barrel as the maximum. However, the size of a tree at a distant sky-line might unhesitatingly be given as thirty feet. At the horizon we instinctively compare the size of the sun, moon, and constellations with hills, trees, houses, and other objects, but when the former are high toward the zenith in the empty sky we may judge them in their isolated position to be nearer, hence smaller.

Normally the retinal image grows larger as the object approaches, but this same sensation also arises when an object grows in size without altering its distance. If the moon be viewed through field-glasses the image is larger than in the case of the unaided eyes, but it is quite common for observers to state that it appears smaller. The enlargement may be interpreted as approach and inasmuch as we, through habit, allow for enlargement as an object approaches, we also must reduce it in our imagination to its natural size. Perhaps in this case we overdo this reduction.

James states that the increased apparent size of the moon near the horizon “is a result of association and probability. It is seen through vaporous air and looks dimmer and duskier than when it rides on high; and it is seen over fields, trees, hedges, streams, and the like, which break up the intervening space and makes us the better realize the latter’s extent.” Both these causes may make the moon seem more distant when it is at low altitudes and as its visual angle grows less, we may think that it must be a larger body and we so perceive it. Certainly it looks particularly large when a well-known object is silhouetted against its disk.

Before proceeding further with explanations, it may be of interest to turn to Fig. 78 which is an accurate tracing of the path of the moon’s image across a photographic plate. The camera was placed in a fixed position and the image of the moon’s disk on rising was accurately focused on a panchromatic plate. A dense red filter was maintained over the lens throughout in order to eliminate the effect of selective absorption of the atmosphere. But the slightest enlargement was detected in the width of the path near the horizon as compared with that at the highest altitude. This copy was made because it was thought better for reproduction than the photograph which would require a half-tone. This is positive evidence that the phenomenon is an illusion.

Similarly Fig. 79 is a copy of a negative of several exposures of the sun. Owing to the greater brightness, continuous exposure was not considered feasible. A panchromatic plate and red filter was used as in the case of the moon. The various exposures were made without otherwise adjusting the camera. Again no enlargement at the horizon was found.

If the variation in the position of the eyes is held to account for the illusion, this explanation may be supported by using a horizontal telescope with adjustable cross-hairs, and a mirror. By varying the position of the latter the disk of the sun may be measured at any altitude without varying the position of the eye. When everything is eliminated from the field but the moon’s disk, it is found to be constant in size. However, this is not conclusive evidence that the variation in the position of the line of sight accounts for the illusion.

As a demonstration of the absence of enlargement of the size of the moon near the horizon some have brought forward measurements of the lunar circles and similar phenomena. These are said to be unaffected by the altitude of the moon except for refraction. But even this does not change the horizontal diameter and actually diminishes the vertical one. The moon is further away when near the horizon than when at the zenith, the maximum increase in distance being one-half the diameter of the earth. This would make the moon appear about one-sixtieth, or one-half minute of arc smaller at the horizon than at the zenith. This is not only in the wrong direction to aid in accounting for the apparent enlargement, but it is so slight as to be imperceptible to the unaided eye.

Nearly two centuries ago Robert Smith and his colleagues concluded that the sky appears about three times as far away at the horizon as at the zenith. They found that the relative apparent diameters of the sun and of the moon varied with altitude as follows: