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.
[Illustration: Fig. 78.--An accurate tracing from a photograph (continual
exposure) of the moon rising.]
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.
[Illustration: Fig. 79.--Accurate tracings from a photograph (short
exposures at intervals) of the sun setting.]
Although the foregoing is conclusive evidence of the illusory character of
the enlargement there are other ways of making measurements. 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 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
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:
Altitude Relative apparent diameter
0 deg. (horizon) 100
15 " 68
30 " 50
45 " 40
60 " 34
75 " 31
90 " (zenith) 30
[Illustration: 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 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 illusions as those shown in Figs. 10
and 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 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 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 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.
In discussing the great illusions of nature, it appears appropriate to
introduce the mirage. This is not due to an error of sense of judgment.
The eye sees what is presented but the inversions and other peculiar
effects are due to variations in the refractive index of the atmosphere.
These variations account for the appearance of "lakes" in arid deserts, of
the inverted images of ships and icebergs on the sea and of "pools of
water" on pavements. The refractive index of the atmosphere is continually
changing, but the changes are chiefly of two types: (1) those due to
irregular heating and (2) those due to normal variation with altitude. The
former type are particularly responsible for mirages.
[Illustration: Fig. 81.--Explanation of a common mirage.]
A common type of mirage is illustrated in Fig. 81. This is often visible
on deserts where the hot sand causes the adjacent layer of air to expand
and therefore, the refractive index to increase. This layer of air then
may be considered to operate like an inverted prism. The rays of light
close to the earth are bent convex to the earth and the curvature of those
higher up may be reversed. The reason that an object may appear double,
or as if mirrored by the surface of a nearby pond, is clearly shown in the
illustration.
Similar atmospheric conditions are found sometimes over pavements and over
bodies of water. As one rides along in an automobile ascending an incline,
if he closely observes at the moment the line of sight is just on the
level of the pavement, he will often be rewarded by the sight of a mirage.
An approaching pedestrian may have no feet (they are replaced by a bit of
sky) and the distant pavement will appear to contain pools of water on its
surface.
Sometimes on deserts, over ice fields, or on northern seas, mirages are of
the inverted type. A horseman or ship may appear suspended in the air in
an inverted position. When the density of the air is great enough so that
only the upper rays reach the eye, the object will be seen inverted and
far above the surface upon which nothing is seen. Many modifications of
these types are possible through variations in the refractive indices of
various strata of air. Sometimes the air is stratified horizontally and
even vertically, which results in magnification as well as other peculiar
effects.
As one rides over the desert in a rapidly moving train or automobile these
vagaries of nature are sometimes very striking, because the speed of
motion will make the effects of the varying refractive indices more
marked. A distant foothill may appear to float in the air or to change its
shape very rapidly. An island surrounded by quiet air and water may appear
like a huge mushroom barely supported by a stem.
Arctic mirages are no less wonderful than those of the hot barren deserts.
While traveling along over the ice and snow distant white peaks may assume
the most fantastic shapes. At first they may appear flattened like a
table-land and then suddenly they may stretch upward like spires. They may
shrink then spread like huge mushrooms supported by the stalk-like bases
and stretching out laterally. Suddenly they may shoot upward into another
series of pinnacles as if another range had suddenly arisen. Such antics
may go on for hours as one travels along a frozen valley. Even a change of
position of the eyes accompanying a change from erect to lying down may
cause remarkable contortions of the distant mountains and one is reminded
of the psalmist's query, "Why hop ye so, ye hills?"
Although not an illusion but a physical reality, it is of interest in
passing to note the colored halo or aureole surrounding the shadows of
objects cast by the sun against a cloud, fog, or jet of steam. The most
wonderful effects are seen by the aerial traveler over a bank of clouds
when the upper sky is clear. For example, the shadow of the aircraft cast
by the sun upon a dense layer of clouds is surrounded by a halo or aureole
of the colors of the rainbow. The phenomenon is purely optical, involving
diffraction of light. A well-known example of this is the "Spectre of the
Brocken."
XII
PAINTING AND DECORATION
In the arts where colors, brightnesses, contrasts, lines, forms, and
perspectives mean so much, it is obvious that visual illusions are
important. Sometimes they are evils which must be suppressed; in some
cases they are boons to the artist if he is equal to the task of
harnessing them. Ofttimes they appear unheralded and unexpected. The
existence of visual illusions is sufficient to justify the artist's pride
in his "eye" and his dependence upon his visual judgment rather than upon
what he knows to be true. However true this may be, knowledge is as useful
to the artist as to anyone else. The artist, if he is to produce art, is
confronted with the tremendous task of perfecting an imperfect nature and
he is handicapped with tools inferior to those which nature has at her
disposal. He must deal with reflected lights from earthly materials.
Nature has these besides the great primary light-sources--the sun, the
moon, the stars, and, we might say, the sky. She also has the advantage of
overwhelming magnitudes.
These are only a few of the disadvantages under which the artist works,
but they indicate that he must grasp any advantage here and there which he
may. Knowledge cannot fail him; still, if he fears that it will take him
out of his "dream world" and taint him with earthliness, let him ponder
over da Vinci, Rembrandt, and such men. These men _knew_ many things. They
possessed much knowledge and, after all, the latter is nothing more nor
less than science when its facts are arranged in an orderly manner. If the
arts are to speak "a noble and expressive language" despite the handicaps
of the artist, knowledge cannot be drawn upon too deeply.
Perhaps in no other art are the workmen as little acquainted with their
handicaps and with the scientific facts which would aid them as in
painting. Painters, of course, may not agree as to this statement, but if
they wish to see how much of the science of light, color, lighting, and
vision they are unacquainted with, let them invade the book-shelves. If
they think they know the facts of nature let them paint a given scene and
then inquire of the scientist regarding the relative values (brightnesses)
in the actual scene. They will usually be amazed to learn that they cannot
paint the lights and shadows of nature excepting in the feeblest manner.
The range of contrast represented by their entire palette is many thousand
times less than the range of values in nature. In fact exclusive of
nature's primary light-sources, such as the sun, she sometimes exhibits a
range of brightness in a landscape a million times greater than the
painter can produce with black and white pigments. This suggests that the
artist is justified in using any available means for overcoming the
handicap and among his tools, visual illusions are perhaps the most
powerful.
A painting in the broadest sense is an illusion, for it strives to
present the three-dimensional world upon plane areas of two dimensions.
Through representation or imitation it creates an illusion. If the
artist's sensibility has been capable of adequate selection, his art will
transmit, by means of and through the truths of science, from the region
of perception to the region of emotion. Science consists of knowing; art
consists of doing. If the artist is familiar with the facts of light,
color, lighting, and vision, he will possess knowledge that can aid him in
overcoming the great obstacles which are ever-present. A glimpse of visual
illusions should strengthen him in his resolution to depend upon visual
perception, but he can utilize these very illusions. He can find a use for
facts as well as anyone. Facts as well as experience will prepare him to
do his work best.