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Chapter 11 - Nature:
The Sky, A Flattened Vault
1   2   3   4   Chapter 11 - Nature:

Chapter 11 - Nature:
Apparent Enlargement of Heavenly Bodies at the Horizon

The flattened vault appearance of the sky is thought by some to explain the apparent enlargement of the sun, moon, and constellations when viewed 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 optical 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 optical 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.

Related Image
Fig. 78. - An accurate tracing from a
photograph (continual exposure) of
the moon rising.

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 optical 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.

Although the foregoing is conclusive evidence of the illusory character of the enlargement there are other ways of making measurements.

Related Image
Fig. 79. - Accurate tracings from a photograph
(short exposures at intervals)
of the sun setting.

On viewing the sun at the horizon a bright after-image is obtained. This may now be projected upon the sky as a background at any desired altitude. It will appear much smaller at the zenith than the sun appears at the horizon. Certainly this is a simple and conclusive demonstration of the optical illusion. In this case the after-image of the sun or the sun itself will usually appear at least twice as large as the after-image at the zenith.

If the variation in the position of the eyes is held to account for the optical 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 optical 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:

Altitude   Relative Apparent Diameter
0 degrees Horizon 100
15 degrees   68
30 degrees   50
45 degrees   40
60 degrees   34
75 degrees   31
90 degrees Zenith 30
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Fig. 80. - Explanation offered by Smith of the apparent enlargement
of heavenly bodies near the horizon.

They also found a similar relation between the altitude and the apparent size of constellations. Fig. 80 is a reproduction of a diagram which Smith submitted as illustrating the cause of the optical illusion of apparent enlargement of heavenly bodies near the horizon. If the sky seems to be a flattened vault, the reason for the apparent decrease in the size of the sun, the moon, or the constellations, as they approach the zenith, is suggested by the diagram.

It has also been suggested that such optical illusions as those shown in Fig. 10 and Fig. 19 are associated with that of apparent enlargement of heavenly bodies near the horizon. It will be left to the reader to decide whether or not there is any similarity or relation.

Zoth appears to have proved, to his own satisfaction at least, that the chief factors are not aerial perspective, the apparent curvature or form of the sky, and the comparison of the sun or moon with objects of known size. He maintained that the optical illusion of apparent decrease in size as these bodies increase in altitude is due to the necessary elevation of the eye. No available experimental evidence seems to refute his statement. In fact, Guttman's experiments seem to confirm it to some extent. The latter found that there was an apparent diminution in the size of objects of several per cent, in objects slightly more than a foot distant from the eyes, as they were raised so that the line of vision changed from horizontal to an angle of forty degrees. The magnitude of this diminution is not sufficient to promote the acceptance of elevation of the eyes as a primary cause of the optical illusion in respect to the heavenly bodies.

Notwithstanding arguments to the contrary, it is difficult to eliminate aerial perspective and the apparent form of the sky as important factors. That no explanation of this optical illusion has been generally accepted indicates the complexity of the causes. Certainly the reddish coloration of the sun and moon near the horizon and the contrast with the misty atmosphere combined with the general vague aspect of the atmosphere contribute something if no more than a deepening of the mystery. Variations in the transparency and brightness of the air must play some part.

Chapter 11 - Nature:
The Sky, A Flattened Vault
1   2   3   4   Chapter 11 - Nature:

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About This Book Preface Chap 1, Introduction Chap 2, The Eye Chap 3, Vision Chap 4, Geometrical Chap 5, Figures Chap 6, Angles Chap 7, Depth/Distance Chap 8 Brightness/Contrast Chap 9, Color Chap 10, Lighting Chap 11, Nature Chap 12, Painting/Decorating Chap 13, Architecture Chap 14, Magic Mirror Chap 15, Camouflage

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