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Title: Visual Illusions - Their Causes, Characteristics and Applications
Author: Luckiesh, Matthew, 1883-1967
Language: English
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  VISUAL ILLUSIONS

  _THEIR CAUSES, CHARACTERISTICS AND APPLICATIONS_


  BY M. LUCKIESH

  DIRECTOR OF APPLIED SCIENCE, NELA RESEARCH LABORATORIES,
  NATIONAL LAMP WORKS OF GENERAL ELECTRIC CO.

  AUTHOR OF "COLOR AND ITS APPLICATIONS," "LIGHT AND SHADE
  AND THEIR APPLICATIONS," "THE LIGHTING ART," "THE
  LANGUAGE OF COLOR," "ARTIFICIAL LIGHT--ITS
  INFLUENCE UPON CIVILIZATION,"
  "LIGHTING THE HOME," ETC.


  100 ILLUSTRATIONS


  NEW YORK
  D. VAN NOSTRAND COMPANY
  EIGHT WARREN STREET
  1922



  COPYRIGHT, 1922, BY
  D. VAN NOSTRAND COMPANY



PREFACE


Eventually one of the results of application to the analysis and
measurement of the phenomena of light, color, lighting, and vision is a
firmly entrenched conviction of the inadequacy of physical measurements as
a means for representing what is perceived. Physical measurements have
supplied much of the foundation of knowledge and it is not a reflection
upon their great usefulness to state that often they differ from the
results of intellectual appraisal through the visual sense. In other
words, there are numberless so-called visual illusions which must be taken
into account. All are of interest; many can be utilized; and some must be
suppressed.

Scientific literature yields a great many valuable discussions from
theoretical and experimental viewpoints but much of the material is
controversial. The practical aspects of visual illusions have been quite
generally passed by and, inasmuch as there does not appear to be a volume
available which treats the subject in a condensed manner but with a broad
scope, this small volume is contributed toward filling the gap.

The extreme complexity of the subject is recognized, but an attempt toward
simplicity of treatment has been made by confining the discussion chiefly
to static visual illusions, by suppressing minor details, and by
subordinating theory. In other words, the intent has been to emphasize
experimental facts. Even these are so numerous that only the merest
glimpses of various aspects can be given in order to limit the text to a
small volume. Some theoretical aspects of the subject are still extremely
controversial, so they are introduced only occasionally and then chiefly
for the purpose of illustrating the complexities and the trends of
attempted explanations. Space does not even admit many qualifications
which may be necessary in order to escape criticism entirely.

The visual illusions discussed are chiefly of the static type, although a
few others have been introduced. Some of the latter border upon motion,
media are illusions only by extension of the term. These exceptions are
included for the purpose of providing glimpses into the borderlands.

It is hoped that this condensed discussion, which is ambitious only in
scope, will be of interest to the general reader, to painters, decorators,
and architects, to lighting experts, and to all interested in light,
color, and vision. It is an essential supplement to certain previous
works.

M. LUCKIESH

November, 1920.



CONTENTS


  CHAPTER                                       PAGE

     I. Introduction                               1

    II. The eye                                   13

   III. Vision                                    29

    IV. Some types of geometrical illusions       44

     V. Equivocal figures                         64

    VI. The influence of angles                   76

   VII. Illusions of depth and of distance       102

  VIII. Irradiation and brightness-contrast      114

    IX. Color                                    124

     X. Lighting                                 144

    XI. Nature                                   164

   XII. Painting and decoration                  179

  XIII. Architecture                             195

   XIV. Mirror Magic                             205

    XV. Camouflage                               210



LIST OF ILLUSTRATIONS


  FIGURE                                                          PAGE

  1. Principal parts of the eye                                     14

  2. Stereoscopic pictures for combining by converging or
     diverging the optical axes                                     41

  3. Stereoscopic pictures                                          41

  4. The vertical line appears longer than the equal horizontal
     line in each case                                              46

  5. The vertical dimension is equal to the horizontal one, but
     the former appears greater                                     47

  6. The divided or filled space on the left appears longer
     than the equal space on the right                              49

  7. The three lines are of equal length                            50

  8. The distance between the two circles on the left is equal
     to the distance between the outside edges of the two
     circles on the right                                           50

  9. Three squares of equal dimensions which appear different
     in area and dimension                                          51

  10. The vertical distance between the upper circle and the
      left-hand one of the group is equal to the overall length
      of the group of three circles                                 52

  11. Two equal semi-circles                                        53

  12. Arcs of the same circle                                       53

  13. Three incomplete but equal squares                            53

  14. Middle sections of the two lines are equal                    54

  15. An effect of contrasting areas (Baldwin's figure)             54

  16. An illusion of contrast                                       55

  17. Equal circles which appear unequal due to contrast
      (Ebbinghaus' figure)                                          56

  18. Equal circles appearing unequal owing to contrasting
      concentric circles                                            56

  19. Circles influenced by position within an angle                57

  20. Contrasting angles                                            57

  21. Owing to perspective the right angles appear oblique and
      vice versa                                                    58

  22. Two equal diagonals which appear unequal                      58

  23. Apparent variations in the distance between two parallel
      lines                                                         59

  24. A striking illusion of perspective                            60

  25. Distortion of a square due to superposed lines                61

  26. Distortion of a circle due to superposed lines                62

  27. Illustrating fluctuation of attention                         65

  28. The grouping of the circles fluctuates                        66

  29. Crossed lines which may be interpreted in two ways            67

  30. Reversible cubes                                              68

  31. The reversible "open book" (after Mach)                       69

  32. A reversible tetrahedron                                      69

  33. Reversible perspective of a group of rings or of a tube       70

  34. Schröder's reversible staircase                               70

  35. Thiéry's figure                                               71

  36. Illustrating certain influences upon the apparent
      direction of vision.

      By covering all but the eyes the latter appear to be
      drawn alike in both sketches                                  73

  37. Zöllner's illusion of direction                               77

  38. Parallel lines which do not appear so                         79

  39. Wundt's illusion of direction                                 79

  40. Hering's illusion of direction                                80

  41. Simple effect of angles                                       81

  42. The effect of two angles in tilting the horizontal lines      83

  43. The effect of crossed lines upon their respective
      apparent directions                                           83

  44. Another step toward the Zöllner illusion                      84

  45. The two diagonals would meet on the left vertical line        85

  46. Poggendorff's illusion. Which oblique line on the right
      is the prolongation of the oblique line on the left?          85

  47. A straight line appears to sag                                86

  48. Distortions of contour due to contact with other contours     87

  49. An illusion of direction                                      88

  50. "Twisted-cord" illusion. These are straight cords             89

  51. "Twisted-cord" illusion. These are concentric circles         89

  52. A spiral when rotated appears to expand or contract,
      depending upon direction of rotation                          90

  53. Angles affect the apparent length of lines                    91

  54. The horizontal line appears to tilt downward toward the
      ends                                                          92

  55. The horizontal line appears to sag in the middle              92

  56. The Müller-Lyer illusion                                      93

  57. Combined influence of angles and contrasting lengths          95

  58. Two equal oblique lines appear unequal because of their
      different positions                                           95

  59. An illusion of area                                           96

  60. Five equal areas showing the influence of contour upon
      judgment of area                                              97

  61. Showing the effect of directing the attention                 98

  62. Simple apparatus for demonstrating the remarkable effects
      of contrasts in brightness and color                         115

  63. Illustrating brightness-contrast                             117

  64. An effect of brightness-contrast. Note the darkening of
      the intersections of the white strips                        118

  65. The phenomenon of irradiation                                121

  66. An excellent pattern for demonstrating color-contrast        126

  67. By rotating this Mason (black and white) disk
      color-sensations are produced                                133

  68. For demonstrating retiring and advancing colors              137

  69. By combining these stereoscopically the effect of
      metallic lustre (similar to graphite in this case) is
      obtained                                                     141

  70. A bas-relief lighted from above                              146

  71. An intaglio lighted from above                               147

  72. A bas-relief lighted from the left                           148

  73. An intaglio lighted from the left                            149

  74a. A disk (above) and a sphere (below) lighted from overhead   145

    b. A disk and a sphere lighted by perfectly diffused light     145

  75. A concave hemispherical cup on the left and a convex
      hemisphere on the right lighted by a light-source of
      large angle such as a window                                 150

  76. The same as Fig. 75, but lighted by a very small
      light-source                                                 151

  77. Apparent ending of a searchlight beam                        161

  78. An accurate tracing from a photograph (continual
      exposure) of the moon rising                                 171

  79. Accurate tracings from a photograph (short exposures at
      intervals) of the sun setting                                172

  80. Explanation offered by Smith of the apparent enlargement
      of heavenly bodies near the horizon                          174

  81. Explanation of a common mirage                               176

  82. Illustrating the apparent distortion of a picture frame
      in which the grain of the wood is visible                    190

  83. Another example similar to Fig. 82                           191

  84. From actual photographs of the end-grain of a board          192

  85. Exaggerated illusions in architecture                        198

  86. Illustrating the influence of visual angle upon apparent
      vertical height                                              199

  87. Irradiation in architecture                                  200

  88. Some simple geometrical-optical illusions in architecture    201

  89. By decreasing the exposed length of shingles toward the
      top a greater apparent expanse is obtained                   202

  90. An example of a mirror "illusion"                            207

  91. Another example of "mirror magic"                            208

  92. A primary stage in the evolution of the use of
      geometrical-optical illusions on ships                       226

  93 and 94. Attempts at distortion of outline which preceded
     the adoption of geometrical-optical illusions                 228

  95 and 96. Illustrating the use of models by the Navy
     Department in developing the geometrical-optical illusion
     for ships                                                     229

  97 and 98. Examples of the geometrical-optical illusion as
     finally applied                                               231

  99. Representative earth backgrounds for an airplane
      (uncamouflaged) as viewed from above                         235

  100. Illustrating the study of pattern for airplanes. The
       photograph was taken from an altitude of 10,000 feet.
       The insert shows the relative lengths (vertical scale)
       of an airplane of 50-foot spread at various distances
       below the observer                                          239



VISUAL ILLUSIONS



I

INTRODUCTION


Seeing is deceiving. Thus a familiar epigram may be challenged in order to
indicate the trend of this book which aims to treat certain phases of
visual illusions. In general, we do not see things as they are or as they
are related to each other; that is, the intellect does not correctly
interpret the deliverances of the visual sense, although sometimes the
optical mechanism of the eyes is directly responsible for the illusion. In
other words, none of our conceptions and perceptions are quite adequate,
but fortunately most of them are satisfactory for practical purposes. Only
a part of what is perceived comes through the senses from the object; the
remainder always comes from within. In fact, it is the visual sense or the
intellect which is responsible for illusions of the various types to be
discussed in the following chapters. Our past experiences, associations,
desires, demands, imaginings, and other more or less obscure influences
create illusions.

An illusion does not generally exist physically but it is difficult in
some cases to explain the cause. Certainly there are many cases of errors
of judgment. A mistaken estimate of the distance of a mountain is due to
an error of judgment but the perception of a piece of white paper as pink
on a green background is an error of sense. It is realized that the
foregoing comparison leads directly to one of the most controversial
questions in psychology, but there is no intention on the author's part to
cling dogmatically to the opinions expressed. In fact, discussions of the
psychological judgment involved in the presentations of the visual sense
are not introduced with the hope of stating the final word but to give the
reader an idea of the inner process of perception. The final word will be
left to the psychologists but it appears possible that it may never be
formulated.

In general, a tree appears of greater length when standing than when lying
upon the ground. Lines, areas, and masses are not perceived in their
actual physical relations. The appearance of a colored object varies
considerably with its environment. The sky is not perceived as infinite
space nor as a hemispherical dome, but as a flattened vault. The moon
apparently diminishes in size as it rises toward the zenith. A bright
object appears larger than a dark object of the same physical dimensions.
Flat areas may appear to have a third dimension of depth. And so on.

Illusions are so numerous and varied that they have long challenged the
interest of the scientist. They may be so useful or even so disastrous
that they have been utilized or counteracted by the skilled artist or
artisan. The architect and painter have used or avoided them. The
stage-artist employs them to carry the audience in its imagination to
other environments or to far countries. The magician has employed them in
his entertainments and the camoufleur used them to advantage in the
practice of deception during the recent war. They are vastly entertaining,
useful, deceiving, or disastrous, depending upon the viewpoint.

Incidentally, a few so-called illusions will be discussed which are not
due strictly to errors of the visual sense or of the intellect. Examples
of these are the mirage and certain optical effects employed by the
magician. In such cases neither the visual sense nor the intellect errs.
In the case of the mirage rays of light coming from the object to the eye
are bent from their usual straight-line course and the object appears to
be where it really is not. However, with these few exceptions, which are
introduced for their specific interest and for the emphasis they give to
the "true" illusion, it will be understood that illusions in general as
hereinafter discussed will mean those due to the visual mechanism or to
errors of judgment or intellect. For the sake of brevity we might say that
they are those due to errors of visual perception. Furthermore, only those
of a "static" type will be considered; that is, the vast complexities due
to motion are not of interest from the viewpoint of the aims of this book.

There are two well-known types of misleading perceptions, namely illusions
and hallucinations. If, for example, two lines appear of equal length and
are not, the error in judgment is responsible for what is termed an
"illusion." If the perceptual consciousness of an object appears although
the object is not present, the result is termed an "hallucination." For
example, if something is seen which does not exist, the essential factors
are supplied by the imagination. Shadows are often wrought by the
imagination into animals and even human beings bent upon evil purpose.
Ghosts are created in this manner. Hallucinations depend largely upon the
recency, frequency, and vividness of past experience. A consideration of
this type of misleading perception does not advance the aims of this book
and therefore will be omitted.

The connection between the material and mental in vision is
incomprehensible and apparently must ever remain so. Objects emit or
reflect light and the optical mechanism known as the eye focuses images of
the objects upon the retina. Messages are then carried to the brain where
certain molecular vibrations take place. The physiologist records certain
physical and chemical effects in the muscles, nerves, and brain and
behold! there appears consciousness, sensations, thoughts, desires, and
volitions. How? and, Why? are questions which may never be answered.

It is dangerous to use the word _never_, but the ultimate answers to those
questions appear to be so remote that it discourages one from proceeding
far over the hazy course which leads toward them. In fact, it does not
appreciably further the aims of this book to devote much space to efforts
toward explanation. In covering this vast and complex field there are
multitudes of facts, many hypotheses, and numerous theories from which to
choose. Judgment dictates that of the limited space most of it be given
to the presentation of representative facts. This is the reasoning which
led to the formulation of the outline of chapters.

Owing to the vast complex beyond the physical phenomena, physical
measurements upon objects and space which have done so much toward
building a solid foundation for scientific knowledge fail ultimately to
provide an exact mathematical picture of that which is perceived. Much of
the author's previous work has been devoted to the physical realities but
the ever-present differences between physical and perceptive realities
have emphasized the need for considering the latter as well.

Illusions are legion. They greet the careful observer on every hand. They
play a prominent part in our appreciation of the physical world. Sometimes
they must be avoided, but often they may be put to work in various arts.
Their widespread existence and their forcefulness make visual perception
the final judge in decoration, in painting, in architecture, in
landscaping, in lighting, and in other activities. The ultimate limitation
of measurements with physical instruments leaves this responsibility to
the intellect. The mental being is impressed with things as perceived, not
with things as they are. It is believed that this intellectual or
judiciary phase which plays such a part in visual perception will be best
brought out by examples of various types of static illusions coupled with
certain facts pertaining to the eye and to the visual process as a whole.

In special simple cases it is not difficult to determine when or how
nearly a perception is true but in general, agreement among normal
persons is necessary owing to the absence of any definite measuring device
which will span the gap between the perception and the objective reality.
Illusions are sometimes called "errors of sense" and some of them are
such, but often they are errors of the intellect. The senses may deliver
correctly but error may arise from imagination, inexperience, false
assumptions, and incorrect associations, and the recency, frequency, and
vividness of past experience. The gifts of sight are augmented by the mind
with judgments based upon experience with these gifts.

The direct data delivered by the visual sense are light, intensity, color,
direction. These may be considered as simple or elemental sensations
because they cannot be further simplified or analyzed. At this point it is
hoped that no controversy with the psychologist will be provoked. In the
space available it appears unfruitful to introduce the many qualifications
necessary to satisfy the, as yet uncertain or at least conflicting,
definitions and theories underlying the science of psychology. If it is
necessary to add darkness to the foregoing group of elemental visual
sensations, this will gladly be agreed to.

The perceptions of outline-form and surface-contents perhaps rank next in
simplicity; however, they may be analyzed into directions. The perception
of these is so direct and so certain that it may be considered to be
immediate. A ring of points is apparently very simple and it might be
considered a direct sense-perception, but it consists of a number of
elemental directions.

The perception of solid-form is far more complex than outline-form and
therefore more liable to error. It is judged partially by binocular vision
or perspective and partly by the distribution of light and shade. Colors
may help to mold form and even to give depth to flat surfaces. For
example, it is well known that some colors are "advancing" and others are
"retiring."

Perhaps of still greater complexity are the judgments of size and of
distance. Many comparisons enter such judgments. The unconscious acts of
the muscles of the eye and various external conditions such as the
clearness of the atmosphere play prominent parts in influencing judgment.
Upon these are superposed the numerous psycho-physiological phenomena of
color, irradiation, etc.

In vision judgments are quickly made and the process apparently is largely
outside of consciousness. Higher and more complex visual judgments pass
into still higher and more complex intellectual judgments. All these may
appear to be primary, immediate, innate, or instinctive and therefore,
certain, but the fruits of studies of the psychology of vision have shown
that these visual judgments may be analyzed into simpler elements.
Therefore, they are liable to error.

That the ancients sensed the existence or possibility of illusions is
evidenced by the fact that they tried to draw and to paint although their
inability to observe carefully is indicated by the absence of true
shading. The architecture of ancient Greece reveals a knowledge of certain
illusions in the efforts to overcome them. However, the study of illusions
did not engage the attention of scientists until a comparatively recent
period. Notwithstanding this belated attention there is a vast scientific
literature pertaining to the multitudinous phases of the subject; however,
most of it is fragmentary and much of it is controversial. Some of it
deals with theory for a particular and often a very simple case. In life
complex illusions are met but at present it would be futile to attempt to
explain them in detail. Furthermore, there have been few attempts to
generalize and to group examples of typical phenomena in such a manner as
to enable a general reader to see the complex fabric as a whole. Finally,
the occurrence and application of illusions in various arts and the
prominence of illusions on every hand have not been especially treated. It
is the hope that this will be realized in the following chapters in so far
as brevity of treatment makes this possible.

Doubtless thoughtful observers ages ago noticed visual illusions,
especially those found in nature and in architecture. When it is
considered that geometrical figures are very commonly of an illusory
character it appears improbable that optical illusions could have escaped
the keenness of Euclid. The apparent enlargement of the moon near the
horizon and the apparent flattened vault of the sky were noticed at least
a thousand years ago and literature yields several hundred memoirs on
these subjects. One of the oldest dissertations upon the apparent form of
the sky was published by Alhazen, an Arab astronomer of the tenth century.
Kepler in 1618 wrote upon the subject.

Philosophers of the past centuries prepared the way toward an
understanding of many complexities of today. They molded thought into
correct form and established fundamental concepts and principles. Their
chief tool was philosophy, the experimental attack being left to the
scientists of the modern age. However, they established philosophically
such principles as "space and time are not realities of the phenomenal
world but the modes under which we see things apart." As science became
organized during the present experimental era, measurements were applied
and there began to appear analytical discussions of various subjects
including optical illusions. One of the earliest investigations of the
modern type was made by Oppel, an account of which appeared in 1854. Since
that time scientific literature has received thousands of worthy
contributions dealing with visual illusions.

There are many facts affecting vision regarding which no theory is
necessary. They speak for themselves. There are many equally obvious facts
which are not satisfactorily explained but the lack of explanation does
not prevent their recognition. In fact, only the scientist needs to worry
over systematic explanations and theoretical generalizations. He needs
these in order to invade and to explore the other unknowns where he will
add to his storehouse of knowledge. A long step toward understanding is
made by becoming acquainted with certain physical, physiological, and
psychological facts of light, color, and lighting. Furthermore,
acquaintance with the visual process and with the structure of the eye
aids materially. For this reason the next two chapters have been added
even at the risk of discouraging some readers.

In a broad sense, any visual perception which does not harmonize with
physical measurements may be termed an "illusion." Therefore, the term
could include those physical illusions obtained by means of prisms,
lenses, and mirrors and such illusions as the mirage. It could also
include the physiological illusions of light and color such as
after-images, irradiation, and contrast, and the psycho-physiological
illusions of space and the character of objects. In fact, the scope of the
following chapters is arbitrarily extended to include all these aspects,
but confines consideration only to "static" illusions.

In a more common sense attention is usually restricted to the last group;
that is, to the psycho-physiological illusions attending the perception of
space and the character of objects although motion is often included. It
should be obvious that no simple or even single theory can cover the vast
range of illusions considered in the broad sense because there are so many
different kinds of factors involved. For this reason explanations will be
presented wherever feasible in connection with specific illusions.
However, in closing this chapter it appears of interest to touch upon the
more generally exploited theories of illusions of the type considered in
the foregoing restricted sense. Hypotheses pertaining to illusions are
generally lacking in agreement, but for the special case of what might be
more safely termed "geometrical-optical illusions" two different theories,
by Lipps and by Wundt respectively, are conspicuous. In fact, most
theories are variants of these two systematic "explanations" of illusions
(in the restricted sense).

Lipps proposed the principle of mechanical-esthetic unity, according to
which we unconsciously give to every space-form a living personality and
unconsciously consider certain mechanical forces acting. Our judgments are
therefore modified by this anthropomorphic attitude. For example, we
regard the circle as being the result of the action of tangential and
radial forces in which the latter appear to triumph. According to Lipps'
theory the circle has a centripetal character and these radial forces
toward the center, which apparently have overcome the tangential forces
during the process of creating the circle, lead to underestimation of its
size as compared with a square of the same height and breadth. By drawing
a circle and square side by side, with the diameter of the former equal to
the length of a side of the latter, this illusion is readily demonstrated.
Of course, the square has a greater area than the circle and it is
difficult to determine the effect of this disparity in area. Figure 60
where the areas of the circle and square are equal and consequently the
height of the former is considerably greater than the latter, is of
interest in this connection. By experimenting with a series of pairs
consisting of a circle and a square, varying in dimensions from equal
heights to equal areas, an idea of the "shrinking" character of the circle
becomes quite apparent.

Wundt does not attribute the illusion to a deception or error of judgment
but to direct perception. According to his explanation, the laws of
retinal image (fixation) and eye-movement are responsible. For example,
vertical distances appear greater than horizontal ones because the effort
or expenditure of energy is greater in raising the eyes than in turning
them through an equal angle in a horizontal plane. Unconscious or
involuntary eye-movements also appear to play a part in many linear or
more accurately, angular illusions, but certainly Wundt's explanation does
not suffice for all illusions although it may explain many geometrical
illusions. It may be said to be of the "perceptive" class and Lipps'
theory to be of the "judgment" or "higher-process" class. As already
stated, most of the other proposed explanations of geometrical illusions
may be regarded as being related to one of these two theories. There is
the "indistinct vision" theory of Einthoven; the "perspective" theory of
Hering, Guye, Thiéry, and others; the "contrast" theory of Helmholtz,
Loeb, and Heyman; and the "contrast-_confluxion_" theory of Müller-Lyer.
In order not to discourage the reader at the outset, theories as such will
be passed by with this brief glimpse. However, more or less qualified
explanations are presented occasionally in some of the chapters which
follow in order to indicate or to suggest a train of thought should the
reader desire to attempt to understand some of the numerous interesting
illusions.



II

THE EYE


Helmholtz, who contributed so much toward our knowledge of the visual
process, in referring to the eye, once stated that he could make a much
better optical instrument but not a better eye. In other words, the eye is
far from an ideal optical instrument but as an eye it is wonderful. Its
range of sensitiveness and its adaptability to the extreme variety of
demands upon it are truly marvelous when compared with instruments devised
by mankind. Obviously, the eye is the connecting link between objective
reality and visual perception and, therefore, it plays an important part
in illusions. In fact, sometimes it is solely responsible for the
illusion. The process of vision may be divided into several steps such as
(1) the lighting, color, character, and disposition of objects; (2) the
mechanism by which the image is formed upon the retina; (3) various
optical defects of this mechanism; (4) the sensitiveness of the parts of
the retina to light and color; (5) the structure of the retina; (6) the
parts played by monocular and binocular vision; and (7) the various events
which follow the formation of the image upon the retina.

The mechanism of the eye makes it possible to see not only light but
objects. Elementary eyes of the lowest animals perceive light but cannot
see objects. These eyes are merely specialized nerves. In the human eye
the optic nerve spreads to form the retina and the latter is a specialized
nerve. Nature has accompanied this evolution by developing an instrument
the--eye--for intensifying and defining and the whole is the visual
sense-organ. The latter contains the most highly specialized nerve and the
most refined physiological mechanism, the result being the highest
sense-organ.

[Illustration: Fig. 1.--Principal parts of the eye.

A, Conjunctiva; B, Retina; C, Choroid; D, Sclera; E, Fovea; F, Blind Spot;
G, Optic Nerve; H, Ciliary Muscle; I, Iris; J, Cornea; K, Ligament.]

The eye is approximately a spherical shell transparent at the front
portion and opaque (or nearly so) over the remaining eighty per cent of
its surface. The optical path consists of a series of transparent liquids
and solids. The chief details of the structure of the eye are represented
in Fig. 1. Beginning with the exterior and proceeding toward the retina we
find in succession the cornea, the anterior chamber containing the aqueous
humor, the iris, the lens, the large chamber containing the vitreous
humor, and finally the retina. Certain muscles alter the position of the
eye and consequently the optical axis, and focusing (accommodation) is
accomplished by altering the thickness and shape, and consequently the
focal length, of the lens.

The iris is a shutter which automatically controls to some degree the
amount of light reaching the retina, thereby tending to protect the latter
from too much light. It also has some influence upon the definition of the
image; that is, upon what is termed "visual acuity" or the ability to
distinguish fine detail. It is interesting to compare the eye with the
camera. In the case of the camera and the photographic process, we have
(1) an inverted light-image, a facsimile of the object usually diminished
in size; (2) an invisible image in the photographic emulsion consisting of
molecular changes due to light; and (3) a visible image developed on the
plate. In the case of the eye and the visual process we have (1) an
inverted light-image, a facsimile of the object diminished in size; (2)
the invisible image in the retinal substances probably consisting of
molecular changes due to light; and (3) an _external_ visible image. It
will be noted that in the case of vision the final image is projected
outward--it is external. The more we think of this outward projection the
more interesting and marvelous vision becomes. For example, it appears
certain that if a photographic plate could see or feel, it would see or
feel the silver image upon itself but not out in space. However, this
point is discussed further in the next chapter.

In the camera and photographic process we trace mechanism, physics, and
chemistry throughout. In the eye and visual process we are able to trace
these factors only to a certain point, where we encounter the
super-physical and super-chemical. Here molecular change is replaced by
sensation, perception, thought, and emotion. Our exploration takes us from
the physical world into another, wholly different, where there reigns
another order of phenomena. We have passed from the material into the
mental world.

The eye as an optical mechanism is reducible to a single lens and
therefore the image focused upon the retina is inverted. However, there is
no way for the observer to be conscious of this and therefore the inverted
image causes no difficulty in seeing. The images of objects in the right
half of the field of view are focused upon the left half of the retina.
Similarly, the left half of the field of view corresponds to the right
half of the retina; the upper half of the former to the lower half of the
latter; and so on. When a ray of light from an object strikes the retina
the impression is referred back along the ray-line into the original place
in space. This is interestingly demonstrated in a simple manner. Punch a
pin-hole in a card and hold it about four inches from the eye and at the
same time hold a pin-head as close to the cornea as possible. The
background for the pin-hole should be the sky or other bright surface.
After a brief trial an inverted image of the pin-head is seen _in the
hole_. Punch several holes in the card and in each will be seen an
inverted image of the pin-head.

The explanation of the foregoing is not difficult. The pin-head is so
close to the eye that the image cannot be focused upon the retina;
however, it is in a very favorable position to cast a shadow upon the
retina, the light-source being the pin-hole with a bright background.
Light streaming through the pin-hole into the eye casts an erect shadow of
the pin-head upon the retina, and this erect image is projected into space
and inverted in the process by the effect of the lens. The latter is not
operative during the casting of the shadow because the pin-head is too
close to the lens, as already stated. It is further proved to be outward
projection of the retinal image (the shadow) because by multiplying the
number of pin-holes (the light-sources) there are also a corresponding
number of shadows.

The foregoing not only illustrates the inversion of the image but again
emphasizes the fact that we do not see retinal images. Even the "stars"
which we see on pressing the eye-lid or on receiving a blow on the eye are
projected into space. The "motes" which we see in the visual field while
gazing at the sky are defects in the eye-media, and these images are
projected into space. We do not see anything in the eye. The retinal image
impresses the retina in some definite manner and the impression is carried
to the brain by the optic nerve. The intellect then refers or projects
this impression outward into space as an external image. The latter would
be a facsimile of the physical object if there were no illusions but the
fact that there are illusions indicates that errors are introduced
somewhere along the path from and to the object.

It is interesting to speculate whether the first visual impression of a
new-born babe is "projected outward" or is perceived as in the eye. It is
equally futile to conjecture in this manner because there is no
indication that the time will come when the baby can answer us
immediately upon experiencing its first visual impression. The period of
infancy increases with progress up the scale of animal life and this
lengthening is doubtless responsible and perhaps necessary for the
development of highly specialized sense-organs. Incidentally, suppose a
blind person to be absolutely uneducated by transferred experience and
that he suddenly became a normal adult and able to see. What would he say
about his first visual impression? Apparently such a subject is
unobtainable. The nearest that such a case had been approached is the case
of a person born blind, whose sight has been restored. This person has
acquired much experience with the external world through other senses. It
has been recorded that such a person, after sight was restored, appeared
to think that external objects "touched" the eyes. Only through visual
experience is this error in judgment rectified.

Man studies his kind too much apart from other animals and perhaps either
underestimates or overestimates the amount of inherited, innate,
instinctive qualities. A new-born chick in a few minutes will walk
straight to an object and seize it. Apparently this implies perception of
distance and direction and a coördination of muscles for walking and
moving the eyes. It appears reasonable to conclude that a certain amount
of the wealth of capacities possessed by the individual is partly
inherited, and in man the acquired predominates. But all capacities are
acquired, for even the inherited was acquired in ancestral experience.
Even instinct (whatever that may be) must involve inherited experience.
These glimpses of the depths to which one must dig if he is to unearth the
complete explanations of visual perception--and consequently of
illusions--indicate the futility of treating the theories in the available
space without encroaching unduly upon the aims of this volume.

Certain defects of the optical system of the eye must contribute toward
causing illusions. Any perfect lens of homogeneous material has at least
two defects, known as spherical and chromatic aberration. The former
manifests itself by the bending of straight lines and is usually
demonstrated by forming an image of an object such as a wire mesh or
checkerboard; the outer lines of the image are found to be very much bent.
This defect in the eye-lens is somewhat counteracted by a variable optical
density, increasing from the outer to the central portion. This results in
an increase in refractive-index as the center of the lens is approached
and tends to diminish its spherical aberration. The eye commonly possesses
abnormalities such as astigmatism and eccentricity of the optical
elements. All these contribute toward the creation of illusions.

White light consists of rays of light of various colors and these are
separated by means of a prism because the refractive-index of the prism
differs for lights of different color or wave-length. This causes the blue
rays, for example, to be bent more than the red rays when traversing a
prism. It is in this manner that the spectrum of light may be obtained. A
lens may be considered to be a prism of revolution and it thus becomes
evident that the blue rays will be brought to a focus at a lesser
distance than the red rays; that is, the former are bent more from their
original path than the latter. This defect of lenses is known as chromatic
aberration and is quite obvious in the eye. It may be demonstrated by any
simple lens, for the image of the sun, for example, will appear to have a
colored fringe. A purple filter which transmits only the violet and red
rays is useful for this demonstration. By looking at a lamp-filament or
candle-flame some distance away the object will appear to have a violet
halo, but the color of the fringe will vary with accommodation. On looking
through a pin-hole at the edge of an object silhouetted against the bright
sky the edge will appear red if the light from the pin-hole enters the
pupil near its periphery. This optical defect of the eye makes objects
appear more sharply defined when viewed in monochromatic light. In fact,
this is quite obvious when using yellow glasses. The defect is also
demonstrated by viewing a line-spectrum focused on a ground glass. The
blue and red lines cannot be seen distinctly at the same distance. The
blue lines can be focused at a much less distance than the red lines.
Chromatic aberration can account for such an illusion as the familiar
"advancing" and "retiring" colors and doubtless it plays a part in many
illusions.

The structure of the retina plays a very important part in vision and
accounts for various illusions and many interesting visual phenomena. The
optic nerve spreads out to form the retina which constitutes the inner
portion of the spherical shell of the eye with the exception of the front
part. Referring again to Fig. 1, the outer coating of the shell is called
the sclerotic. This consists of dense fibrous tissue known as the "white
of the eye." Inside this coating is a layer of black pigment cells termed
the choroid. Next is the bacillary layer which lines about five-sixths of
the interior surface of the eye. This is formed by closely packed "rods"
and "cones," which play a dominant role in the visual process. A
light-sensitive liquid (visual purple) and cellular and fibrous layers
complete the retinal structure.

The place where the optic nerve enters the eye-ball and begins to spread
out is blind. Objects whose images fall on this spot are invisible. This
blind-spot is not particularly of interest here, but it may be of interest
to note its effect. This is easily done by closing one eye and looking
directly at one of two small black circles about two inches apart on white
paper at a distance of about a foot from the eye. By moving the objects
about until the image of the circle not directly looked at falls upon the
blind-spot, this circle will disappear. A three-foot circle at a distance
of 36 feet will completely disappear if its image falls directly upon the
blind-spot. At a distance of 42 inches the invisible area is about 12
inches from the point of sight and about 3 to 4 inches in diameter. At 300
feet the area is about 8 feet in diameter. The actual size of the retinal
blind-spot is about 0.05 inch in diameter or nearly 5 degrees. Binocular
vision overcomes any annoyance due to the blind-spots because they do not
overlap in the visual field. A one-eyed person is really totally blind for
this portion of the retina or of the visual field.

The bacillary layer consists of so-called rods and cones. Only the rods
function under very low intensities of illumination of the order of
moonlight. The cones are sensitive to color and function only at
intensities greater than what may be termed twilight intensities. These
elements are very small but the fact that they appear to be connecting
links between the retinal image and visual perception, acuity or
discrimination of fine detail is limited inasmuch as the elements are of
finite dimensions. The smallest image which will produce a visual
impression is the size of the end of a cone. The smallest distance between
two points which is visible at five inches is about 0.001 inch. Two cones
must be stimulated in such a case. Fine lines may appear crooked because
of the irregular disposition of these elemental light-sensitive points.
This apparent crookedness of lines is an illusion which is directly due to
the limitations of retinal elements of finite size.

The distribution of rods and cones over the retina is very important. In
the fovea centralis--the point of the retina on the optical axis of the
eye--is a slight depression much thinner than the remainder of the retina
and this is inhabited chiefly by cones. It is this spot which provides
visual acuteness. It is easily demonstrated that fine detail cannot be
seen well defined outside this central portion of the visual field. When
we desire to see an object distinctly we habitually turn the head so that
the image of the object falls upon the fovea of each eye. Helmholtz has
compared the foveal and lateral images with a finished drawing and a rough
sketch respectively.

The fovea also contains a yellow pigmentation which makes this area of the
retina selective as to color-vision. On viewing certain colors a
difference in color of this central portion of the field is often very
evident. In the outlying regions of the retina, rods predominate and in
the intermediate zone both rods and cones are found. Inasmuch as rods are
not sensitive to color and cones do not function at low intensities of
illumination it is obvious that visual impressions should vary, depending
upon the area of the retina stimulated. In fact, many interesting
illusions are accounted for in this manner, some of which are discussed
later.

It is well known that a faint star is seen best by averted vision. It may
be quite invisible when the eye is directed toward it, that is, when its
image falls upon the rod-free fovea. However, by averting the line of
sight slightly, the image is caused to fall on a retinal area containing
rods (sensitive to feeble light) and the star may be readily recognized.
The fovea is the point of distinct focus. It is necessary for fixed
thoughtful attention. It exists in the retina of man and of higher monkeys
but it quickly disappears as we pass down the scale of animal life. It may
be necessary for the safety of the lower animals that they see equally
well over a large field; however, it appears advantageous that man give
fixed and undivided attention to the object looked at. Man does not need
to trust solely to his senses to protect himself from dangers. He uses his
intellect to invent and to construct artificial defenses. Without the
highly specialized fovea we might see equally well over the whole retina
but could not look attentively at anything, and therefore could not
observe thoughtfully.

When an image of a bright object exists upon the retina for a time there
results a partial exhaustion or fatigue of the retinal processes with a
result that an after-image is seen. This after-image may be bright for a
time owing to the fact that it takes time for the retinal process to die
out. Then there comes a reaction which is apparent when the eye is
directed toward illuminated surfaces. The part of the retina which has
been fatigued does not respond as fully as the fresher areas, with the
result that the fatigued area contributes a darker area in the visual
field. This is known as an after-image and there are many interesting
variations.

The after-image usually undergoes a series of changes in color as well as
in brightness as the retinal process readjusts itself. An after-image of a
colored object may often appear of a color complementary to the color of
the object. This is generally accounted for by fatigue of the retinal
process. There are many conflicting theories of color-vision but they are
not as conflicting in respect to the aspect of fatigue as in some other
aspects. If the eye is directed toward a green surface for a time and then
turned toward a white surface, the fatigue to green light diminishes the
extent of response to the green rays in the light reflected by the white
surface. The result is the perception of a certain area of the white
surface (corresponding to the portion of the field fatigued by green
light) as of a color equal to white minus some green--the result of which
is pink or purple. This is easily understood by referring to the
principles of color-mixture. Red, green, and blue (or violet) mixed in
proper proportions will produce any color or tint and even white. Thus
these may be considered to be the components of white light. Hence if the
retina through fatigue is unable to respond fully to the green component,
the result may be expressed mathematically as red plus blue plus reduced
green, or synthetically a purplish white or pink. When fatigued to red
light the after-image on a white surface is blue-green. When fatigued to
blue light it is yellowish.

Further mixtures may be obtained by directing the after-image upon colored
surfaces. In this manner many of the interesting visual phenomena and
illusions associated with the viewing of colors are accounted for. The
influence of a colored environment upon a colored object is really very
great. This is known as simultaneous contrast. The influence of the
immediately previous history of the retina upon the perception of colored
surfaces is also very striking. This is called successive contrast. It is
interesting to note that an after-image produced by looking at a bright
light-source, for example, is projected into space even with the eyes
closed. It is instructive to study after-images and this may be done at
any moment. On gazing at the sun for an instant and then looking away, an
after-image is seen which passes in color from green, blue, purple, etc.,
and finally fades. For a time it is brighter than the background which may
conveniently be the sky. On closing the eyes and placing the hands over
them the background now is dark and the appearance of the after-image
changes markedly. There are many kinds, effects, and variations of
after-images, some of which are discussed in other chapters.

As the intensity of illumination of a landscape, for example, decreases
toward twilight, the retina diminishes in sensibility to the rays of
longer wave-lengths such as yellow, orange, and red. Therefore, it becomes
relatively more sensitive to the rays of shorter wave-length such as
green, blue, and violet. The effects of this Purkinje phenomenon (named
after the discoverer) may be added to the class of illusions treated in
this book. It is interesting to note in this connection that moonlight is
represented on some paintings and especially on the stage as greenish blue
in color, notwithstanding that physical measurements show it to be
approximately the color of sunlight. In fact, it is sunlight reflected by
dead, frigid, and practically colorless matter.

Some illusions may be directly traced to the structure of the eye under
unusual lighting conditions. For example, in a dark room hold a lamp
obliquely outward but near one eye (the other being closed and shielded)
and forward sufficiently for the retina to be strongly illuminated. Move
the lamp gently while gazing at a plain dark surface such as the wall.
Finally the visual field appears dark, due to the intense illumination of
the retina and there will appear, apparently projected upon the wall, an
image resembling a branching leafless tree. These are really shadows of
the blood vessels in the retina. The experiment is more successful if an
image of a bright light-source is focused on the sclerotic near the
cornea. If this image of the light-source is moved, the tree-like image
seen in the visual field will also move.

The rate of growth and decay of various color-sensations varies
considerably. By taking advantage of this fact many illusions can be
produced. In fact, the careful observer will encounter many illusions
which may be readily accounted for in this manner.

It may be said that in general the eyes are never at rest. Involuntary
eye-movements are taking place all the time, at least during
consciousness. Some have given this restlessness a major part in the
process of vision but aside from the correctness of theories involving
eye-movements, it is a fact that they are responsible for certain
illusions. On a star-lit night if one lies down and looks up at a star the
latter will be seen to appear to be swimming about more or less jerkily.
On viewing a rapidly revolving wheel of an automobile as it proceeds down
the street, occasionally it will be seen to cease revolving momentarily.
These apparently are accounted for by involuntary eye-movements which take
place regardless of the effort made to fixate vision.

If the eyelids are almost closed, streamers appear to radiate in various
directions from a light-source. Movements of the eyelids when nearly
closed sometimes cause objects to appear to move. These may be accounted
for perhaps by the distortion of the moist film which covers the cornea.

The foregoing are only a few of the many visual phenomena due largely to
the structure of the eye. The effects of these and many others enter into
visual illusions, as will be seen here and there throughout the chapters
which follow.



III

VISION


A description of the eye by no means suffices to clarify the visual
process. Even the descriptions of various phenomena in the preceding
chapter accomplish little more than to acquaint the reader with the
operation of a mechanism, although they suggest the trend of the
explanations of many illusions. At best only monocular vision has been
treated, and it does not exist normally for human beings. A person capable
only of monocular vision would be like Cyclops Polyphemus. We might have
two eyes, or even, like Argus, possess a hundred eyes and still not
experience the wonderful advantages of binocular vision, for each eye
might see independently. The phenomena of binocular vision are far less
physical than those of monocular vision. They are much more obscure,
illusory, and perplexing because they are more complexly interwoven with
or allied to psychological phenomena.

The sense of sight differs considerably from the other senses. The sense
of touch requires solid contact (usually); taste involves liquid contact;
smell, gaseous contact; and hearing depends upon a relay of vibrations
from an object through another medium (usually air), resulting finally in
contact. However, we perceive things at a distance through vibration
(electromagnetic waves called light) conveyed by a subtle, intangible,
universal medium which is unrecognizable excepting as a hypothetically
necessary bearer of light-waves or, more generally, radiant energy.

It also is interesting to compare the subjectiveness and objectiveness of
sensations. The sensation of taste is subjective; it is in us, not in the
body tasted. In smell we perceive the sensation in the nose and by
experience refer it to an object at a distance. The sensation of hearing
is objective; that is, we refer the cause to an object so completely that
there is practically no consciousness of sensation in the ear. In sight
the impression is so completely projected outward into space and there is
so little consciousness of any occurrence in the eye that it is extremely
difficult to convince ourselves that it is essentially a subjective
sensation. The foregoing order represents the sense-organs in increasing
specialization and refinement. In the two higher senses--sight and
hearing--there is no direct contact with the object and an intricate
mechanism is placed in front of the specialized nerve to define and to
intensify the impression. In the case of vision this highly developed
instrument makes it possible to see not only _light_ but _objects_.

As we go up the scale of vertebrate animals we find that there is a
gradual change of the position of the eyes from the sides to the front of
the head and a change of the inclination of the optical axes of the two
eyes from 180 degrees to parallel. There is also evident a gradual
increase in the fineness of the bacillary layer of the retina from the
margins toward the center, and, therefore, an increasing accuracy in the
perception of form. This finally results in a highly organized central
spot or fovea which is possessed only by man and the higher monkeys.
Proceeding up the scale we also find an increasing ability to converge the
optic axes on a near point so that the images of the point may coincide
with the central spots of both retinas. These changes and others are
closely associated with each other and especially with the development of
the higher faculties of the mind.

Binocular vision in man and in the higher animals is the last result of
the gradual improvement of the most refined sense-organ, adapting it to
meet the requirements of highly complex organisms. It cannot exist in some
animals, such as birds and fishes, because they cannot converge their two
optical axes upon a near point. When a chicken wishes to look intently at
an object it turns its head and looks with one eye. Such an animal sees
with two eyes independently and possibly moves them independently. The
normal position of the axes of human eyes is convergent or parallel but it
is possible to diverge the axes. In fact, with practice it is possible to
diverge the axes sufficiently to look at a point near the back of the
head, although, of course, we do not see the point.

The movement of the eyes is rather complex. When they move together to one
side or the other or up and down in a vertical plane there is no rotation
of the optical axes; that is, no torsion. When the visual plane is
elevated and the eyes move to the right they rotate to the right; when
they move to the left they rotate to the left. When the visual plane is
depressed and the eyes move to the right they rotate to the left; when
they move to the left they rotate to the right. Through experience we
unconsciously evaluate the muscular stresses, efforts, and movements
accompanying the motion of the eyes and thereby interpret much through
visual perception in regard to such aspects of the external world as size,
shape, and distance of objects. Even this brief glimpse of the principal
movements of the eyes indicates a complexity which suggests the intricacy
of the explanations of certain visual phenomena.

At this point it appears advantageous to set down the principal modes by
which we perceive the third dimension of space and of objects and other
aspects of the external world. They are as follows: (1) extent; (2)
clearness of brightness and color as affected by distance; (3)
interference of near objects with those more distant; (4) elevation of
objects; (5) variation of light and shade on objects; (6) cast shadows;
(7) perspective; (8) variation of the visor angle in proportion to
distance; (9) muscular effort attending accommodation of the eye; (10)
stereoscopic vision; (11) muscular effort attending convergence of the
axes of the eyes. It will be recognized that only the last two are
necessarily concerned with binocular vision. These varieties of
experiences may be combined in almost an infinite variety of proportions.

Wundt in his attempt to explain visual perception considered chiefly three
factors: (1) the retinal image of the eye at rest; (2) the influence of
the movements of one eye; and, (3) the additional data furnished by the
two eyes functioning together. There are three fields of vision
corresponding to the foregoing. These are the retinal field of vision, the
monocular field, and the binocular field. The retinal field of vision is
that of an eye at rest as compared with the monocular field, which is all
that can be seen with one eye in its entire range of movement and
therefore of experience. The retinal field has no clearly defined
boundaries because it finally fades at its indefinite periphery into a
region where sensation ceases.

It might be tiresome to follow detailed analyses of the many modes by
which visual perception is attained, so only a few generalizations will be
presented. For every voluntary act of sight there are two adjustments of
the eyes, namely, focal and axial. In the former case the ciliary muscle
adjusts the lens in order to produce a defined image upon the retina. In
axial adjustments the two eyes are turned by certain muscles so that their
axes meet on the object looked at and the images of the object fall on the
central-spots of the retina. These take place together without distinct
volition for each but by the single voluntary act of _looking_. Through
experience the intellect has acquired a wonderful capacity to interpret
such factors as size, form, and distance in terms of the muscular
movements in general without the observer being conscious of such
interpretations.

Binocular vision is easily recognized by holding a finger before the eyes
and looking at a point beyond it. The result is two apparently
transparent fingers. An object is seen single when the two retinal images
fall on corresponding points. Direction is a primary datum of sense. The
property of corresponding points of the two retinas (binocular vision) and
consequently of identical spatial points in the two visual fields is not
so simple. It is still a question whether corresponding points (that is,
the existence of a corresponding point in one retina for each point in the
other retina) are innate, instinctive, and are antecedent of experience or
are "paired" as the result of experience. The one view results in the
_nativistic_, the other in the _empiristic_ theory. Inasmuch as some
scientists are arrayed on one side and some on the other, it appears
futile to dwell further upon this aspect. It must suffice to state that
binocular vision, which consists of two retinas and consequently two
fields of view absolutely coördinated in some manner in the brain, yields
extensive information concerning space and its contents.

After noting after-images, motes floating in the field of view (caused by
defects in the eye-media) and various other things, it is evident that
what we call the field of view is the external projection into space of
retinal states. All the variations of the latter, such as images and
shadows which are produced in the external field of one eye, are
faithfully reproduced in the external field of the other eye. This sense
of an external visual field is ineradicable. Even when the eyes are closed
the external field is still there; the imagination or intellect projects
it outward. Objects at different distances cannot be seen distinctly at
the same time but by interpreting the eye-movements as the point of sight
is run backward and forward (varying convergence of the axes) the
intellect practically automatically appraises the size, form, and distance
of each object. Obviously, experience is a prominent factor. The
perception of the third dimension, depth or relative distance, whether in
a single object or a group of objects, is the result of the successive
combination of the different parts of two dissimilar images of the object
or group.

As already stated, the perception of distance, size, and form is based
partly upon monocular and partly upon binocular vision, and the simple
elements upon which judgments of these are based are light, shade, color,
intensity, and direction. Although the interpretation of muscular
adjustments plays a prominent part in the formation of judgments, the
influences of mathematical perspective, light, shade, color, and intensity
are more direct. Judgments based upon focal adjustment (monocular) are
fairly accurate at distances from five inches to several yards. Those
founded upon axial adjustment (convergence of the two axes in binocular
vision) are less in error than the preceding ones. They are reliable to a
distance of about 1000 feet. Judgments involving mathematical perspective
are of relatively great accuracy without limits. Those arrived at by
interpreting aerial perspective (haziness of atmosphere, reduction in
color due to atmospheric absorption, etc.) are merely estimates liable to
large errors, the accuracy depending largely upon experience with local
conditions.

The measuring power of the eye is more liable to error when the distances
or the objects compared lie in different directions. A special case is the
comparison of a vertical distance with a horizontal one. It is not
uncommon to estimate a vertical distance as much as 25 per cent greater
than an actually equal horizontal distance. In general, estimates of
direction and distance are comparatively inaccurate when only one eye is
used although a one-eyed person acquires unusual ability through a keener
experience whetted by necessity. A vertical line drawn perpendicular to a
horizontal one is likely to appear bent when viewed with one eye. Its
apparent inclination is variable but has been found to vary from one to
three degrees. Monocular vision is likely to cause straight lines to
appear crooked, although the "crookedness" may seem to be more or less
unstable.

The error in the estimate of size is in reality an error in the estimation
of distance except in those cases where the estimate is based directly
upon a comparison with an object of supposedly known size. An amusing
incident is told of an old negro who was hunting for squirrels. He shot
several times at what he supposed to be a squirrel upon a tree-trunk and
his failure to make a kill was beginning to weaken his rather ample
opinion of his skill as a marksman. A complete shattering of his faith in
his skill was only escaped by the discovery that the "squirrel" was a
louse upon his eyebrow. Similarly, a gnat in the air might appear to be an
airplane under certain favorable circumstances. It is interesting to note
that the estimated size of the disk of the sun or moon varies from the
size of a saucer to that of the end of a barrel, although a pine tree at
the horizon-line may be estimated as 25 feet across despite the fact that
it may be entirely included in the disk of the sun setting behind it.

Double images play an important part in the comparison of distances of
objects. The "doubling" of objects is only equal to the interocular
distance. Suppose two horizontal wires or clotheslines about fifty feet
away and one a few feet beyond the other. On looking at these no double
images are visible and it is difficult or even impossible to see which is
the nearer when the points of attachment of the ends are screened from
view. However, if the head is turned to one side and downward (90 degrees)
so that the interocular line is now at right angles (vertical) to the
horizontal lines, the relative distances of the latter are brought out
distinctly. Double images become visible in the latter case.

According to Brücke's theory the eyes are continuously in motion and the
observer by alternately increasing or decreasing the convergence of the
axes of the eyes, combines successively the different parts of the two
scenes as seen by the two eyes and by running the point of sight back and
forth by trial obtains a distinct perception of binocular perspective or
relief or depth of space. It may be assumed that experience has made the
observer proficient in this appraisal which he arrives at almost
unconsciously, although it may be just as easy to accept Wheatstone's
explanation. In fact, some experiences with the stereoscope appear to
support the latter theory.

Wheatstone discovered that the dissimilar pictures of an object or scene,
when united by means of optical systems, produce a visual effect similar
to that produced by the actual solid object or scene provided the
dissimilarity is the same as that between two retinal images of the solid
object or scene. This is the principle upon which the familiar stereoscope
is founded. Wheatstone formulated a theory which may be briefly stated as
follows: In viewing a solid object or a scene two slightly dissimilar
retinal images are formed in the two eyes respectively, but the mind
completely fuses them into one "mental" image. When this mental fusion of
the two really dissimilar retinal images is complete in this way, it is
obvious that there cannot exist a mathematical coincidence. The result is
a perception of depth of space, of solidity, of relief. In fact the third
dimension is perceived. A stereoscope accomplishes this in essentially the
same manner, for two pictures, taken from two different positions
respectively corresponding to the positions of the eyes, are combined by
means of optical systems into one image.

Lack of correct size and position of the individual elements of
stereoscopic pictures are easily detected on combining them. That is,
their dissimilarity must exactly correspond to that between two views of
an object or scene from the positions of the two eyes respectively (Fig.
2). This fact has been made use of in detecting counterfeit notes. If two
notes made from the same plate are viewed in a stereoscope and the
identical figures are combined, the combination is perfect and the plane
of the combined images is perfectly flat. If the notes are not made from
the same plate but one of them is counterfeit, slight variations in the
latter are unavoidable. Such variations will show themselves in a wavy
surface.

The unwillingness of the visual sense to combine the two retinal images,
if they are dissimilar to the extent of belonging to two different
objects, is emphasized by means of colors. For example, if a green glass
is placed over one eye and a red glass over the other, the colors are not
mixed by the visual sense. The addition of these two colors results
normally in yellow, with little or no suggestion of the components--red
and green. But in the foregoing case the visual field does not appear of a
uniform yellow. It appears alternately red and green, as though the colors
were rivaling each other for complete mastery. In fact, this phenomenon
has been termed "retinal rivalry."

The lenses of the stereoscope supplement eye-lenses and project on the
retina two perfect images of a near object, although the eyes are looking
at a distant object and are therefore not accommodated for the near one
(the photographs). The lenses enlarge the images similar to the action of
a perspective glass. This completes the illusion of an object or of a
scene. There is a remarkable distinctness of the perception of depth of
space and therefore a wonderful resemblance to the actual object or scene.
It is interesting to note the effect of taking the two original
photographs from distances separated by several feet. The effect is
apparently to magnify depth. It is noteworthy that two pictures taken from
an airplane at points fifty feet or so apart, when combined in the
stereoscope, so magnify the depth that certain enemy-works can be more
advantageously detected than from ordinary photographs.

Stereoscopic images such as represented in Fig. 2 may be combined without
the aid of the stereoscope if the optical axes of the eye can be
sufficiently converged or diverged. Such images or pictures are usually
upon a card and are intended to be combined beyond the plane of the card,
for it is in this position that the object or scene can be perceived in
natural perspective, of natural size, of natural form, and at natural
distance. But in combining them the eyes are looking at a distant object
and the axes are parallel or nearly so. Therefore, the eyes are focally
adjusted for a distant object but the light comes from a very near
object--the pictures on the card. Myopic eyes do not experience this
difficulty and it appears that normal vision may be trained to overcome
it. Normal eyes are aided by using slightly convex lenses. Such glasses
supplement the lenses of the eye, making possible a clear vision of a near
object while the eyes are really looking far away or, in other words,
making possible a clear image of a near object upon the retina of the
unadjusted eye. Stereoscopic pictures are usually so mounted that
"identical points" on the two pictures are farther apart than the
interocular distance and therefore the two images cannot be combined when
the optical axes of the eyes are parallel or nearly so, which is the
condition when looking at a distant object. In such a case the two
pictures must be brought closer together.

[Illustration: Fig. 2.--Stereoscopic pictures for combining by converging
or diverging the optical axes.]

[Illustration: Fig. 3.--Stereoscopic pictures.]

In Figs. 2 and 3 are found "dissimilar" drawings of the correct
dissimilarity of stereoscopic pictures. It is interesting and instructive
to practice combining these with the unaided eyes. If Fig. 2 is held at an
arm's length and the eyes are focused upon a point several inches distant,
the axes will be sufficiently converged so that the two images are
superposed. It may help to focus the eyes upon the tip of a finger until
the stereoscopic images are combined. In this case of converging axes the
final combined result will be the appearance of a hollow tube or of a
shell of a truncated cone, apparently possessing the third dimension and
being perceived as apparently smaller than the actual pictures in the
background at arm's length. If the two stereoscopic pictures are combined
by looking at a point far beyond the actual position of Fig. 2, the
combined effect is a solid truncated cone but perceived as of about the
same size and at about the same distance from the eye as the actual
diagrams. In the latter case the smaller end of the apparent solid appears
to be nearer than the larger end, but in the former case the reverse is
true, that is, the smaller end appears to be at a greater distance. The
same experiments may be performed for Fig. 3 with similar results
excepting that this appears to be a shell under the same circumstances
that Fig. 2 appears to be a solid and vice versa. A few patient trials
should be rewarded by success, and if so the reader can gain much more
understanding from the actual experiences than from description.

The foregoing discussion of vision should indicate the complexity of the
visual and mental activities involved in the discrimination, association,
and interpretation of the data obtained through the eye. The psychology of
visual perception is still a much controverted domain but it is believed
that the glimpses of the process of vision which have been afforded are
sufficient to enable the reader to understand many illusions and at least
to appreciate more fully those whose explanations remain in doubt.
Certainly these glimpses and a knowledge of the information which visual
perception actually supplies to us at any moment should convince us that
the visual sense has acquired an incomparable facility for interpreting
the objective world for us. Clearness of vision is confined to a small
area about the point of sight, and it rapidly diminishes away from this
point, images becoming dim and double. We sweep this point of sight
backward and forward and over an extensive field of view, gathering all
the distinct impressions into one mental image. In doing this the
unconscious interpretation of the muscular activity attending
accommodation and convergence of the eyes aids in giving to this mental
picture the appearance of depth by establishing relative distances of
various objects. Certainly the acquired facility is remarkable.



IV

SOME TYPES OF GEOMETRICAL ILLUSIONS


No simple classification of illusions is ample or satisfactory, for there
are many factors interwoven. For this reason no claims are made for the
various divisions of the subject represented by and in these chapters
excepting that of convenience. Obviously, some divisions are necessary in
order that the variegated subject may be presentable. The classification
used appears to be logical but very evidently it cannot be perfectly so
when the "logic" is not wholly available, owing to the disagreement found
among the explanations offered by psychologists. It may be argued that the
"geometrical" type of illusion should include many illusions which are
discussed in other chapters. Indeed, this is perhaps true. However, it
appears to suit the present purpose to introduce this phase of this book
by a group of illusions which involve plane geometrical figures. If some
of the latter appear in other chapters, it is because they seem to border
upon or to include other factors beyond those apparently involved in the
simple geometrical type. The presentation which follows begins (for the
sake of clearness) with a few representative geometrical illusions of
various types.

_The Effect of the Location in the Visual Field._--One of the most common
illusions is found in the letter "S" or figure "8." Ordinarily we are not
strongly conscious of a difference in the size of the upper and lower
parts of these characters; however, if we invert them (8888 SSSS) the
difference is seen to be large. The question arises, Is the difference due
fundamentally to the locations of the two parts in the visual field? It
scarcely seems credible that visual perception innately appraises the
upper part larger than the lower, or the lower smaller than the upper part
when these small characters are seen in their accustomed position. It
appears to be possible that here we have examples of the effect of
learning or experience and that our adaptive visual sense has become
accustomed to overlook the actual difference. That is, for some reason
through being confronted with this difference so many times, the intellect
has become adapted to it and, therefore, has grown to ignore it.
Regardless of the explanation, the illusion exists and this is the point
of chief interest. For the same reason the curvature of the retina does
not appear to account for illusion through distortion of the image,
because the training due to experience has caused greater difficulties
than this to disappear. We must not overlook the tremendous "corrective"
influence of experience upon which visual perception for the adult is
founded. If we have learned to "correct" in some cases, why not in all
cases which we have encountered quite generally?

[Illustration: Fig. 4.--The vertical line appears longer than the equal
horizontal line in each case.]

This type of illusion persists in geometrical figures and may be found on
every hand. A perfect square when viewed vertically appears too high,
although the illusion does not appear to exist in the circle. In Fig. 4
the vertical line appears longer than the horizontal line of the same
length. This may be readily demonstrated by the reader by means of a
variety of figures. A striking case is found in Fig. 5, where the height
and the width of the diagram of a silk hat are equal. Despite the actual
equality the height appears to be much greater than the width. A pole or a
tree is generally appraised as of greater length when it is standing than
when it lies on the ground. This illusion may be demonstrated by placing a
black dot an inch or so above another on a white paper. Now, at right
angles to the original dot place another at a horizontal distance which
appears equal to the vertical distance of the first dot above the
original. On turning the paper through ninety degrees or by actual
measurement, the extent of the illusion will become apparent. By doing
this several times, using various distances, this type of illusion becomes
convincing.

[Illustration: Fig. 5.--The vertical dimension is equal to the horizontal
one, but the former appears greater.]

The explanation accepted by some is that more effort is required to raise
the eyes, or point of sight, through a certain vertical distance than
through an equal horizontal distance. Perhaps we unconsciously appraise
effort of this sort in terms of distance, but is it not logical to inquire
why we have not through experience learned to sense the difference between
the relation of effort to horizontal distance and that of effort to
vertical distance through which the point of sight is moved? We are doing
this continuously, so why do we not learn to distinguish; furthermore, we
have overcome other great obstacles in developing our visual sense. In
this complex field of physiological psychology questions are not only
annoying, but often disruptive.

As has been pointed out in Chapter II, images of objects lying near the
periphery of the visual field are more or less distorted, owing to the
structure and to certain defects of parts of the eye. For example, a
checkerboard viewed at a proper distance with respect to its size appears
quite distorted in its outer regions. Cheap cameras are likely to cause
similar errors in the images fixed upon the photographic plate.
Photographs are interesting in connection with visual illusions, because
of certain distortions and of the magnification of such aspects as
perspective. Incidentally in looking for illusions, difficulty is
sometimes experienced in seeing them when the actual physical truths are
known; that is, in distinguishing between what is actually seen and what
actually exists. The ability to make this separation grows with practice
but where the difficulty is obstinate, it is well for the reader to try
observers who do not suspect the truth.

_Illusions of Interrupted Extent._--Distance and area appear to vary in
extent, depending upon whether they are filled or empty or are only
partially filled. For example, a series of dots will generally appear
longer overall than an equal distance between two points. This may be
easily demonstrated by arranging three dots in a straight line on paper,
the two intervening spaces being of equal extent, say about one or two
inches long. If in one of the spaces a series of a dozen dots is placed,
this space will appear longer than the empty space. However, if only one
dot is placed in the middle of one of the empty spaces, this space now is
likely to appear of less extent than the empty space. (See Fig. 7.) A
specific example of this type of illusion is shown in Fig. 6. The filled
or divided space generally appears greater than the empty or undivided
space, but certain qualifications of this statement are necessary. In _a_
the divided space unquestionably appears greater than the empty space.
Apparently the filled or empty space is more important than the amount of
light which is received from the clear spaces, for a black line on white
paper appears longer than a white space between two points separated a
distance equal to the length of the black line. Furthermore, apparently
the spacing which is the most obtrusive is most influential in causing the
divided space to appear greater for _a_ than for _b_. The illusion still
persists in _c_.

[Illustration: Fig. 6.--The divided or filled space on the left appears
longer than the equal space on the right.]

An idea of the magnitude may be gained from certain experiments by Aubert.
He used a figure similar to _a_ Fig. 6 containing a total of five short
lines. Four of them were equally spaced over a distance of 100 mm.
corresponding to the left half of _a_, Fig. 6. The remaining line was
placed at the extreme right and defined the limit of an empty space also
100 mm. long. In all cases, the length of the empty space appeared about
ten per cent less than that of the space occupied by the four lines
equally spaced. Various experimenters obtain different results, and it
seems reasonable that the differences may be accounted for, partially at
least, by different degrees of unconscious correction of the illusion.
This emphasizes the desirability of using subjects for such experiments
who have no knowledge pertaining to the illusion.

[Illustration: Fig. 7.--The three lines are of equal length.]

[Illustration: Fig. 8.--The distance between the two circles on the left
is equal to the distance between the outside edges of the two circles on
the right.]

As already stated there are apparent exceptions to any simple rule, for,
as in the case of dots cited in a preceding paragraph, the illusion
depends upon the manner in which the division is made. For example, in
Fig. 7, _a_ and _c_ are as likely to appear shorter than _b_ as equal to
it. It has been concluded by certain investigators that when subdivision
of a line causes it to appear longer, the parts into which it is divided
or some of them are likely to appear shorter than isolated lines of the
same length. The reverse of this statement also appears to hold. For
example in Fig. 7, _a_ appears shorter than _b_ and the central part
appears lengthened, although the total line appears shortened. This
illusion is intensified by leaving the central section blank. A figure of
this sort can be readily drawn by the reader by using short straight lines
in place of the circles in Fig. 8. In this figure the space between the
inside edges of the two circles on the left appears larger than the
overall distance between the outside edges of the two circles on the
right, despite the fact that these distances are equal. It appears that
mere intensity of retinal stimulation does not account for these
illusions, but rather the figures which we see.

[Illustration: Fig. 9.--Three squares of equal dimensions which appear
different in area and dimension.]

In Fig. 9 the three squares are equal in dimensions but the different
characters of the divisions cause them to appear not only unequal, but no
longer squares. In Fig. 10 the distance between the outside edges of the
three circles arranged horizontally appears greater than the empty space
between the upper circle and the left-hand circle of the group.

[Illustration: Fig. 10.--The vertical distance between the upper circle
and the left-hand one of the group is equal to the overall length of the
group of three circles.]

_Illusions of Contour._--The illusions of this type, or exhibiting this
influence, are quite numerous. In Fig. 11 there are two semicircles, one
closed by a diameter, the other unclosed. The latter appears somewhat
flatter and of slightly greater radius than the closed one. Similarly in
Fig. 12 the shorter portion of the interrupted circumference of a circle
appears flatter and of greater radius of curvature than the greater
portions. In Fig. 13 the length of the middle space and of the open-sided
squares are equal. In fact there are two uncompleted squares and an empty
"square" between, the three of which are of equal dimensions. However the
middle space appears slightly too high and narrow; the other two appear
slightly too low and broad. These figures are related to the well-known
Müller-Lyer illusion illustrated in Fig. 56. Some of the illusions
presented later will be seen to involve the influence of contour. Examples
of these are Figs. 55 and 60. In the former, the horizontal base line
appears to sag; in the latter, the areas appear unequal, but they are
equal.

[Illustration: Fig. 11.--Two equal semicircles.]

[Illustration: Fig. 12.--Arcs of the same circle.]

[Illustration: Fig. 13.--Three incomplete but equal squares.]

_Illusions of Contrast._--Those illusions due to brightness contrast are
not included in this group, for "contrast" here refers to lines, angles
and areas of different sizes. In general, parts adjacent to large extents
appear smaller and those adjacent to small extents appear larger. A simple
case is shown in Fig. 14, where the middle sections of the two lines are
equal, but that of the shorter line appears longer than that of the longer
line. In Fig. 15 the two parts of the connecting line are equal, but they
do not appear so. This illusion is not as positive as the preceding one
and, in fact, the position of the short vertical dividing line may appear
to fluctuate considerably.

[Illustration: Fig. 14.--Middle sections of the two lines are equal.]

[Illustration: Fig. 15.--An effect of contrasting areas (Baldwin's
figure).]

Fig. 16 might be considered to be an illusion of contour, but the length
of the top horizontal line of the lower figure being apparently less than
that of the top line of the upper figure is due largely to contrasting the
two figures. Incidentally, it is difficult to believe that the maximum
horizontal width of the lower figure is as great as the maximum height of
the figure. At this point it is of interest to refer to other contrast
illusions such as Figs. 20, 57, and 59.

[Illustration: Fig. 16.--An illusion of contrast.]

A striking illusion of contrast is shown in Fig. 17, where the central
circles of the two figures are equal, although the one surrounded by the
large circles appears much smaller than the other. Similarly, in Fig. 18
the inner circles of _b_ and _c_ are equal but that of _b_ appears the
larger. The inner circle of _a_ appears larger than the outer circle of
_b_, despite their actual equality.

[Illustration: Fig. 17.--Equal circles which appear unequal due to
contrast (Ebbinghaus' figure).]

[Illustration: Fig. 18.--Equal circles appearing unequal owing to
contrasting concentric circles.]

In Fig. 19 the circle nearer the apex of the angle appears larger than the
other. This has been presented as one reason why the sun and moon appear
larger at the horizon than when at higher altitudes. This explanation must
be based upon the assumption that we interpret the "vault" of the sky to
meet at the horizon in a manner somewhat similar to the angle but it is
difficult to imagine such an angle made by the vault of the sky and the
earth's horizon. If there were one in reality, it would not be seen in
profile.

[Illustration: Fig. 19.--Circles influenced by position within an angle.]

[Illustration: Fig. 20.--Contrasting angles.]

If two angles of equal size are bounded by small and large angles
respectively, the apex in each case being common to the inner and two
bounding angles, the effect of contrast is very apparent, as seen in Fig.
20. In Fig. 57 are found examples of effects of lines contrasted as to
length.

[Illustration: Fig. 21.--Owing to perspective the right angles appear
oblique and vice versa.]

The reader may readily construct an extensive variety of illusions of
contrast; in fact, contrast plays a part in most geometrical-optical
illusions. The contrasts may be between existing lines, areas, etc., or
the imagination may supply some of them.

[Illustration: Fig. 22.--Two equal diagonals which appear unequal.]

_Illusions of Perspective._--As the complexity of figures is increased the
number of possible illusions is multiplied. In perspective we have the
influences of various factors such as lines, angles, and sometimes contour
and contrast. In Fig. 21 the suggestion due to the perspective of the
cube causes right angles to appear oblique and oblique angles to appear to
be right angles. This figure is particularly illusive. It is interesting
to note that even an after-image of a right-angle cross when projected
upon a wall drawn in perspective in a painting will appear oblique.

[Illustration: Fig. 23.--Apparent variations in the distance between two
parallel lines.]

A striking illusion involving perspective, or at least the influence of
angles, is shown in Fig. 22. Here the diagonals of the two parallelograms
are of equal length but the one on the right appears much smaller. That
_AX_ is equal in length to _AY_ is readily demonstrated by describing a
circle from the center _A_ and with a radius equal to _AX_. It will be
found to pass through the point _Y_. Obviously, geometry abounds in
geometrical-optical illusions.

[Illustration: Fig. 24.--A striking illusion of perspective.]

The effect of contrast is seen in _a_ in Fig. 23; that is, the short
parallel lines appear further apart than the pair of long ones. By adding
the oblique lines at the ends of the lower pair in _b_, these parallel
lines now appear further apart than the horizontal parallel lines of the
small rectangle.

The influence of perspective is particularly apparent in Fig. 24, where
natural perspective lines are drawn to suggest a scene. The square columns
are of the same size but the further one, for example, being apparently
the most distant and of the same physical dimensions, actually appears
much larger. Here is a case where experience, allowing for a diminution of
size with increasing distance, actually causes the column on the right to
appear larger than it really is. The artist will find this illusion even
more striking if he draws three human figures of the same size but
similarly disposed in respect to perspective lines. Apparently converging
lines influence these equal figures in proportion as they suggest
perspective.

[Illustration: Fig. 25.--Distortion of a square due to superposed lines.]

Although they are not necessarily illusions of perspective, Figs. 25 and
26 are presented here because they involve similar influences. In Fig. 25
the hollow square is superposed upon groups of oblique lines so arranged
as to apparently distort the square. In Fig. 26 distortions of the
circumference of a circle are obtained in a similar manner.

[Illustration: Fig. 26.--Distortion of a circle due to superposed lines.]

It is interesting to note that we are not particularly conscious of
perspective, but it is seen that it has been a factor in the development
of our visual perception. In proof of this we might recall the first time
as children we were asked to draw a railroad track trailing off in the
distance. Doubtless, most of us drew two parallel lines instead of
converging ones. A person approaching us is not sensibly perceived to
grow. He is more likely to be perceived all the time as of normal size.
The finger held at some distance may more than cover the object such as a
distant person, but the finger is not ordinarily perceived as larger than
the person. Of course, when we think of it we are conscious of perspective
and of the increase in size of an approaching object. When a locomotive or
automobile approaches very rapidly, this "growth" is likely to be so
striking as to be generally noticeable. The reader may find it of interest
at this point to turn to illustrations in other chapters.

The foregoing are a few geometrical illusions of representative types.
These are not all the types of illusions by any means and they are only a
few of an almost numberless host. These have been presented in a brief
classification in order that the reader might not be overwhelmed by the
apparent chaos. Various special and miscellaneous geometrical illusions
are presented in later chapters.



V

EQUIVOCAL FIGURES


Many figures apparently change in appearance owing to fluctuations in
attention and in associations. A human profile in intaglio (Figs. 72 and
73) may appear as a bas-relief. Crease a card in the middle to form an
angle and hold it at an arm's length. When viewed with one eye it can be
made to appear open in one way or the other; that is, the angle may be
made to appear pointing toward the observer or away from him. The more
distant part of an object may be made to appear nearer than the remaining
part. Plane diagrams may seem to be solids. Deception of this character is
quite easy if the light-source and other extraneous factors are concealed
from the observer. It is very interesting to study these fluctuating
figures and to note the various extraneous data which lead us to judge
correctly. Furthermore, it becomes obvious that often we see what we
expect to see. For example, we more commonly encounter relief than
intaglio; therefore, we are likely to think that we are looking at the
former.

Proper consideration of the position of the dominant light-source and of
the shadows will usually provide the data for a correct conclusion.
However, habit and probability are factors whose influence is difficult to
overcome. Our perception is strongly associated with accustomed ways of
seeing objects and when the object is once suggested it grasps our mind
completely in its stereotyped form. Stairs, glasses, rings, cubes, and
intaglios are among the objects commonly used to illustrate this type of
illusion. In connection with this type, it is well to realize how
tenaciously we cling to our perception of the real shapes of objects. For
example, a cube thrown into the air in such a manner that it presents many
aspects toward us is throughout its course a cube.

[Illustration: Fig. 27.--Illustrating fluctuation of attention.]

The figures which exhibit these illusions are obviously those which are
capable of two or more spatial relations. The double interpretation is
more readily accomplished by monocular than by binocular vision. Fig. 27
consists of identical patterns in black and white. By gazing upon this
steadily it will appear to fluctuate in appearance from a white pattern
upon a black background to a black pattern upon a white background.
Sometimes fluctuation of attention apparently accounts for the change and,
in fact, this can be tested by willfully altering the attention from a
white pattern to a black one. Incidentally one investigator found that the
maximum rate of fluctuation was approximately equal to the pulse rate,
although no connection between the two was claimed. It has also been found
that inversion is accompanied by a change in refraction of the eye.

[Illustration: Fig. 28.--The grouping of the circles fluctuates.]

Another example is shown in Fig. 28. This may appear to be white circles
upon a black background or a black mesh upon a white background. However,
the more striking phenomenon is the change in the grouping of the circles
as attention fluctuates. We may be conscious of hollow diamonds of
circles, one inside the other, and then suddenly the pattern may change to
groups of diamonds consisting of four circles each. Perhaps we may be
momentarily conscious of individual circles; then the pattern may change
to a hexagonal one, each "hexagon" consisting of seven circles--six
surrounding a central one. The pattern also changes into parallel strings
of circles, triangles, etc.

[Illustration: Fig. 29.--Crossed lines which may be interpreted in two
ways.]

The crossed lines in Fig. 29 can be seen as right angles in perspective
with two different spatial arrangements of one or both lines. In fact
there is quite a tendency to see such crossed lines as right angles in
perspective. The two groups on the right represent a simplified Zöllner's
illusion (Fig. 37). The reader may find it interesting to spend some time
viewing these figures and in exercising his ability to fluctuate his
attention. In fact, he must call upon his imagination in these cases.
Sometimes the changes are rapid and easy to bring about. At other moments
he will encounter an aggravating stubbornness. Occasionally there may
appear a conflict of two appearances simultaneously in the same figure.
The latter may be observed occasionally in Fig. 30. Eye-movements are
brought forward by some to aid in explaining the changes.

[Illustration: Fig. 30.--Reversible cubes.]

In Fig. 30 a reversal of the aspect of the individual cubes or of their
perspective is very apparent. At rare moments the effect of perspective
may be completely vanquished and the figure be made to appear as a plane
crossed by strings of white diamonds and zigzag black strips.

The illusion of the bent card or partially open book is seen in Fig. 31.
The tetrahedron in Fig. 32 may appear either as erect on its base or as
leaning backward with its base seen from underneath.

[Illustration: Fig. 31.--The reversible "open book" (after Mach).]

[Illustration: Fig. 32.--A reversible tetrahedron.]

The series of rings in Fig. 33 may be imagined to form a tube such as a
sheet-metal pipe with its axis lying in either of two directions.
Sometimes by closing one eye the two changes in this type of illusion are
more readily brought about. It is also interesting to close and open each
eye alternately, at the same time trying to note just where the attention
is fixed.

The familiar staircase is represented in Fig. 34. It is likely to appear
in its usual position and then suddenly to invert. It may aid in bringing
about the reversal to insist that one end of a step is first nearer than
the other and then farther away. By focusing the attention in this manner
the fluctuation becomes an easy matter to obtain.

[Illustration: Fig. 33.--Reversible perspective of a group of rings or of
a tube.]

[Illustration: Fig. 34.--Schröder's reversible staircase.]

In Fig. 35 is a similar example. First one part will appear solid and the
other an empty corner, then suddenly both are reversed. However, it is
striking to note one half changes while the other remains unchanged, thus
producing momentarily a rather peculiar figure consisting of two solids,
for example, attached by necessarily warped surfaces.

[Illustration: Fig. 35.--Thiéry's figure.]

Perhaps the reader has often witnessed the striking illusion of some
portraits which were made of subjects looking directly at the camera or
painter. Regardless of the position of the observer the eyes of the
portrait appear to be directed toward him. In fact, as the observer moves,
the eyes in the picture follow him so relentlessly as to provoke even a
feeling of uncanniness. This fact is accounted for by the absence of a
third dimension, for a sculptured model of a head does not exhibit this
feature. Perspective plays a part in some manner, but no attempt toward
explanation will be made.

In Fig. 36 are two sketches of a face. One appears to be looking at the
observer, but the other does not. If the reader will cover the lower parts
of the two figures, leaving only the two pairs of eyes showing, both pairs
will eventually appear to be looking at the observer. Perhaps the reader
will be conscious of mental effort and the lapse of a few moments before
the eyes on the left are made to appear to be looking directly at him.
Although it is not claimed that this illusion is caused by the same
conditions as those immediately preceding, it involves attention. At
least, it is fluctuating in appearance and therefore is equivocal. It is
interesting to note the influence of the other features (below the eyes).
The perspective of these is a powerful influence in "directing" the eyes
of the sketch.

In the foregoing only definite illusions have been presented which are
universally witnessed by normal persons. There are no hallucinatory phases
in the conditions or causes. It is difficult to divide these with
definiteness from certain illusions of depth as discussed in Chapter VII.
The latter undoubtedly are sometimes entwined to some extent with
hallucinatory phases; in fact, it is doubtful if they are not always
hallucinations to some degree. Hallucinations are not of interest from the
viewpoint of this book, but illusions of depth are treated because they
are of interest. They are either hallucinations or are on the border-line
between hallucinations and those illusions which are almost universally
experienced by normal persons under similar conditions. The latter
statement does not hold for illusions of depth in which objects may be
seen alternately near and far, large and small, etc., although they are
not necessarily pure hallucinations as distinguished from the types of
illusions regarding which there is general perceptual agreement.

[Illustration: Fig. 36.--Illustrating certain influences upon the apparent
direction of vision. By covering all but the eyes the latter appear to be
drawn alike in both sketches.]

In explanation of the illusory phenomena pertaining to such geometrical
figures as are discussed in the foregoing paragraphs, chiefly two
different kinds of hypotheses have been offered. They are respectively
psychological and physiological, although there is more or less of a
mixture of the two in most attempts toward explanation. The psychological
hypotheses introduce such factors as attention, imagination, judgment, and
will. Hering and also Helmholtz claim that the kind of inversion which
occurs is largely a matter of chance or of volition. The latter holds that
the perception of perspective figures is influenced by imagination or the
images of memory. That is, if one form of the figure is vividly imagined
the perception of it is imminent. Helmholtz has stated that, "Glancing at
a figure we observe spontaneously one or the other form of perspective and
usually the one that is associated in our memory with the greatest number
of images."

The physiological hypotheses depend largely upon such factors as
accommodation and eye-movement. Necker held to the former as the chief
cause. He has stated that the part of the figure whose image lies near the
fovea is estimated as nearer than those portions in the peripheral regions
of the visual field. This hypothesis is open to serious objections. Wundt
contends that the inversion is caused by changes in the points and lines
of fixation. He says, "The image of the retina ought to have a determined
position if a perspective illusion is to appear; but the form of this
illusion is entirely dependent on motion and direction." Some hypotheses
interweave the known facts of the nervous system with psychological facts
but some of these are examples of a common anomaly in theorization, for
facts plus facts do not necessarily result in a correct theory. That is,
two sets of facts interwoven do not necessarily yield an explanation which
is correct.



VI

THE INFLUENCE OF ANGLES


As previously stated, no satisfactory classification of visual illusions
exists, but in order to cover the subject, divisions are necessary. For
this reason the reader is introduced in this chapter to the effects
attending the presence of angles. By no means does it follow that this
group represents another type, for it really includes many illusions of
several types. The reason for this grouping is that angles play an
important part, directly or indirectly, in the production of illusions.
For a long time many geometrical illusions were accounted for by
"overestimation" or "underestimation" of angles, but this view has often
been found to be inadequate. However, it cannot be denied that many
illusions are due at least to the presence of angles.

Apparently Zöllner was the first to describe an illusion which is
illustrated in simple form in Fig. 29 and more elaborately in Figs. 37 to
40. The two figures at the right of Fig. 29 were drawn for another purpose
and are not designed favorably for the effect, although it may be detected
when the figure is held at a distance. Zöllner accidentally noticed the
illusion on a pattern designed for a print for dress-goods. The illusion
is but slightly noticeable in Fig. 29, but by multiplying the number of
lines (and angles) the long parallel lines appear to diverge in the
direction that the crossing lines converge. Zöllner studied the case
thoroughly and established various facts. He found that the illusion is
greatest when the long parallel lines are inclined about 45 degrees to the
horizontal. This may be accomplished for Fig. 37, by turning the page
(held in a vertical plane) through an angle of 45 degrees from normal. The
illusion vanishes when held too far from the eye to distinguish the short
crossing lines, and its strength varies with the inclination of the
oblique lines to the main parallels. The most effective angle between the
short crossing lines and the main parallels appears to be approximately 30
degrees. In Fig. 37 there are two illusions of direction. The parallel
vertical strips appear unparallel and the right and left portions of the
oblique cross-lines appear to be shifted vertically. It is interesting to
note that steady fixation diminishes and even destroys the illusion.

[Illustration: Fig. 37.--Zöllner's illusion of direction.]

The maximum effectiveness of the illusion, when the figure is held so that
the main parallel lines are at an inclination of about 45 degrees to the
horizontal was accounted for by Zöllner as the result of less visual
experience in oblique directions. He insisted that it takes less time and
is easier to infer divergence or convergence than parallelism. This
explanation appears to be disproved by a figure in which slightly
divergent lines are used instead of parallel ones. Owing to the effect of
the oblique crossing lines, the diverging lines may be made to appear
parallel. Furthermore it is difficult to attach much importance to
Zöllner's explanation because the illusion is visible under the extremely
brief illumination provided by one electric spark. Of course, the duration
of the physiological reaction is doubtless greater than that of the spark,
but at best the time is very short. Hering explained the Zöllner illusion
as due to the curvature of the retina, and the resulting difference in the
retinal images, and held that acute angles appear relatively too large and
obtuse ones too small. The latter has been found to have limitations in
the explanation of certain illusions.

This Zöllner illusion is very striking and may be constructed in a variety
of forms. In Fig. 37 the effect is quite apparent and it is interesting to
view the figure at various angles. For example, hold the figure so that
the broad parallel lines are vertical. The illusion is very pronounced in
this position; however, on tilting the page backward the illusion finally
disappears. In Fig. 38 the short oblique lines do not cross the long
parallel lines and to make the illusion more striking, the obliquity of
the short lines is reversed at the middle of the long parallel lines.
Variations of this figure are presented in Figs. 39 and 40. In this case
by steady fixation the perspective effect is increased but there is a
tendency for the parallel lines to appear more nearly truly parallel than
when the point of sight is permitted to roam over the figures.

[Illustration: Fig. 38.--Parallel lines which do not appear so.]

[Illustration: Fig. 39.--Wundt's illusion of direction.]

[Illustration: Fig. 40.--Hering's illusion of direction.]

Many investigations of the Zöllner illusion are recorded in the
literature. From these it is obvious that the result is due to the
additive effects of many simple illusions of angle. In order to give an
idea of the manner in which such an illusion may be built up the reasoning
of Jastrow[1] will be presented in condensed form. When two straight lines
such as _A_ and _B_ in Fig. 41 are separated by a space it is usually
possible to connect the two mentally and to determine whether or not, if
connected, they would lie on a straight line. However, if another line is
connected to one, thus forming an angle as _C_ does with _A_, the lines
which appeared to be continuous (as _A_ and _B_ originally) no longer
appear so. The converse is also true, for lines which are not in the same
straight line may be made to appear to be by the addition of another line
forming a proper angle. All these variations cannot be shown in a single
figure, but the reader will find it interesting to draw them. Furthermore,
the letters used on the diagram in order to make the description clearer
may be confusing and these can be eliminated by redrawing the figure. In
Fig. 41 the obtuse angle _AC_ tends to tilt _A_ downward, so apparently if
_A_ were prolonged it would fall below _B_. Similarly, _C_ appears to fall
to the right of _D_.

[Illustration: Fig. 41.--Simple effect of angles.]

This illusion apparently is due to the presence of the angle and the
effect is produced by the presence of right and acute angles to a less
degree. The illusion decreases or increases in general as the angle
decreases or increases respectively.

Although it is not safe to present simple statements in a field so complex
as that of visual illusion where explanations are still controversial, it
is perhaps possible to generalize as Jastrow did in the foregoing case as
follows: If the direction of an angle is that of the line bisecting it and
pointing toward the apex, the direction of the sides of an angle will
apparently be deviated toward the direction of the angle. The deviation
apparently is greater with obtuse than with acute angles, and when obtuse
and acute angles are so placed in a figure as to give rise to opposite
deviations, the greater angle will be the dominant influence.

Although the illusion in such simple cases as Fig. 41 is slight, it is
quite noticeable. The effect of the addition of many of these slight
individual influences is obvious in accompanying figures of greater
complexity. These individual effects can be so multiplied and combined
that many illusory figures may be devised.

In Fig. 42 the oblique lines are added to both horizontal lines in such a
manner that _A_ is tilted downward at the angle and _B_ is tilted upward
at the angle (the letters corresponding to similar lines in Fig. 41). In
this manner they appear to be deviated considerably out of their true
straight line. If the reader will draw a straight line nearly parallel to
_D_ in Fig. 41 and to the right, he will find it helpful. This line
should be drawn to appear to be a continuation of _C_ when the page is
held so _D_ is approximately horizontal. This is a simple and effective
means of testing the magnitude of the illusion, for it is measured by the
degree of apparent deviation between _D_ and the line drawn adjacent to
it, which the eye will tolerate. Another method of obtaining such a
measurement is to begin with only the angle and to draw the apparent
continuation of one of its lines with a space intervening. This deviation
from the true continuation may then be readily determined.

[Illustration: Fig. 42. The effect of two angles in tilting the horizontal
lines.]

[Illustration: Fig. 43. The effect of crossed lines upon their respective
apparent directions.]

A more complex case is found in Fig. 43 where the effect of an obtuse
angle _ACD_ is to make the continuation of _AB_ apparently fall below
_FG_ and the effect of the acute angle is the reverse. However, the net
result is that due to the preponderance of the effect of the larger angle
over that of the smaller. The line _EC_ adds nothing, for it merely
introduces two angles which reinforce those above _AB_. The line _BC_ may
be omitted or covered without appreciably affecting the illusion.

[Illustration: Fig. 44.--Another step toward the Zöllner illusion.]

In Fig. 44 two obtuse angles are arranged so that their effects are
additive, with the result that the horizontal lines apparently deviate
maximally for such a simple case. Thus it is seen that the tendency of the
sides of an angle to be apparently deviated toward the direction of the
angle may result in an apparent divergence from parallelism as well as in
making continuous lines appear discontinuous. The illusion in Fig. 44 may
be strengthened by adding more lines parallel to the oblique lines. This
is demonstrated in Fig. 38 and in other illustrations. In this manner
striking illusions are built up.

[Illustration: Fig. 45.--The two diagonals would meet on the left vertical
line.]

[Illustration: Fig. 46.--Poggendorff's illusion. Which oblique line on the
right is the prolongation of the oblique line on the left?]

If oblique lines are extended across vertical ones, as in Figs. 45 and 46,
the illusion is seen to be very striking. In Fig. 45 the oblique line on
the right if extended would meet the upper end of the oblique line on the
left; however, the apparent point of intersection is somewhat lower than
it is in reality. In Fig. 46 the oblique line on the left is in the same
straight line with the lower oblique line on the right. The line drawn
parallel to the latter furnishes an idea of the extent of the illusion.
This is the well-known Poggendorff illusion. The upper oblique line on the
right actually appears to be approximately the continuation of the upper
oblique line on the right. The explanation of this illusion on the simple
basis of underestimation or overestimation of angles is open to criticism.
If Fig. 46 is held so that the intercepted line is horizontal or vertical,
the illusion disappears or at least is greatly reduced. It is difficult to
reconcile this disappearance of the illusion for certain positions of the
figure with the theory that the illusion is due to an incorrect appraisal
of the angles.

[Illustration: Fig. 47.--A straight line appears to sag.]

According to Judd,[2] those portions of the parallels lying on the
obtuse-angle side of the intercepted line will be overestimated when
horizontal or vertical distances along the parallel lines are the subjects
of attention, as they are in the usual positions of the Poggendorff
figure. He holds further that the overestimation of this distance along
the parallels (the two vertical lines) and the underestimation of the
oblique distance across the interval are sufficient to provide a full
explanation of the illusion. The disappearance and appearance of the
illusion, as the position of the figure is varied appears to demonstrate
the fact that lines produce illusions only when they have a direct
influence on the direction in which the attention is turned. That is, when
this Poggendorff figure is in such a position that the intercepted line is
horizontal, the incorrect estimation of distance along the parallels has
no direct bearing on the distance to which the attention is directed. In
this case Judd holds that the entire influence of the parallels is
absorbed in aiding the intercepted line in carrying the eye across the
interval. For a detailed account the reader is referred to the original
paper.

Some other illusions are now presented to demonstrate further the effect
of the presence of angles. Doubtless, in some of these, other causes
contribute more or less to the total result. In Fig. 47 a series of
concentric arcs of circles end in a straight line. The result is that the
straight line appears to sag perceptibly. Incidentally, it may be
interesting for the reader to ascertain whether or not there is any doubt
in his mind as to the arcs appearing to belong to circles. To the author
the arcs appear distorted from those of true circles.

[Illustration: Fig. 48.--Distortions of contour due to contact with other
contours.]

In Fig. 48 the bounding figure is a true circle but it appears to be
distorted or dented inward where the angles of the hexagon meet it.
Similarly, the sides of the hexagon appear to sag inward where the corners
of the rectangle meet them.

The influences which have been emphasized apparently are responsible for
the illusions in Figs. 49, 50 and 51. It is interesting to note the
disappearance of the illusion, as the plane of Fig. 49 is varied from
vertical toward the horizontal. That is, it is very apparent when viewed
perpendicularly to the plane of the page, the latter being held
vertically, but as the page is tilted backward the illusion decreases and
finally disappears.

[Illustration: Fig. 49.--An illusion of direction.]

[Illustration: Fig. 50.--"Twisted-cord" illusion. These are straight
cords.]

[Illustration: Fig. 51.--"Twisted-cord" illusion. These are concentric
circles.]

The illusions in Figs. 50 and 51 are commonly termed "twisted cord"
effects. A cord may be made by twisting two strands which are white and
black (or any dark color) respectively. This may be superposed upon
various backgrounds with striking results. In Fig. 50 the straight "cords"
appear bent in the middle, owing to a reversal of the "twist." Such a
figure may be easily made by using cord and a checkered cloth. In Fig. 51
it is difficult to convince the intellect that the "cords" are not
arranged in the form of concentric circles, but this becomes evident when
one of them is traced out. The influence of the illusion is so powerful
that it is even difficult to follow one of the circles with the point of a
pencil around its entire circumference. The cord appears to form a spiral
or a helix seen in perspective.

[Illustration: Fig. 52.--A spiral when rotated appears to expand or
contract, depending upon direction of rotation.]

A striking illusion is obtained by revolving the spiral shown in Fig. 52
about its center. This may be considered as an effect of angles because
the curvature and consequently the angle of the spiral is continually
changing. There is a peculiar movement or progression toward the center
when revolved in one direction. When the direction of rotation is reversed
the movement is toward the exterior of the figure; that is, there is a
seeming expansion.

Angles appear to modify our judgments of the length of lines as well as of
their direction. Of course, it must be admitted that some of these
illusions might be classified under those of "contrast" and others. In
fact, it has been stated that classification is difficult but it appears
logical to discuss the effect of angles in this chapter apart from the
divisions presented in the preceding chapters. This decision was reached
because the effect of angles could be seen in many of the illusions which
would more logically be grouped under the classification presented in the
preceding chapters.

[Illustration: Fig. 53.--Angles affect the apparent length of lines.]

In Fig. 53 the three horizontal lines are of equal length but they appear
unequal. This must be due primarily to the size of the angles made by the
lines at the ends. Within certain limits, the greater the angle the
greater is the apparent elongation of the central horizontal portion. This
generalization appears to apply even when the angle is less than a right
angle, although there appears to be less strength to the illusions with
these smaller angles than with the larger angles. Other factors which
contribute to the extent of the illusion are the positions of the figures,
the distance between them, and the juxtaposition of certain lines. The
illusion still exists if the horizontal lines are removed and also if the
figures are cut out of paper after joining the lower ends of the short
lines in each case.

[Illustration: Fig. 54.--The horizontal line appears to tilt downward
toward the ends.]

[Illustration: Fig. 55.--The horizontal line appears to sag in the
middle.]

In Fig. 54 the horizontal straight line appears to consist of two lines
tilting slightly upward toward the center. This will be seen to be in
agreement with the general proposition that the sides of an angle are
deviated in the direction of the angle. In this case it should be noted
that one of the obtuse angles to be considered is _ABC_ and that the
effect of this is to tilt the line _BD_ downward from the center. In Fig.
55 the horizontal line appears to tilt upward toward its extremities or to
sag in the middle. The explanation in order to harmonize with the
foregoing must be based upon the assumption that our judgments may be
influenced by things not present but imagined. In this case only one side
of each obtuse angle is present, the other side being formed by continuing
the horizontal line both ways by means of the imagination. That we do this
unconsciously is attested to by many experiences. For example, we often
find ourselves imagining a horizontal, a vertical, or a center upon which
to base a pending judgment.

A discussion of the influence of angles must include a reference to the
well-known Müller-Lyer illusion presented in Fig. 56. It is obvious in _a_
that the horizontal part on the left appears considerably longer than that
part in the right half of the diagram. The influence of angles in this
illusion can be easily tested by varying the direction of the lines at the
ends of the two portions.

[Illustration: Fig. 56.--The Müller-Lyer illusion.]

In all these figures the influence of angles is obvious. This does not
mean that they are always solely or even primarily responsible for the
illusion. In fact, the illusion of Poggendorff (Fig. 46) may be due to the
incorrect estimation of certain linear distances, but the angles make this
erroneous judgment possible, or at least contribute toward it. Many
discussions of the theories or explanations of these figures are available
in scientific literature of which one by Judd[2] may be taken as
representative. He holds that the false estimation of angles in the
Poggendorff figure is merely a secondary effect, not always present, and
in no case the source of the illusion; furthermore, that the illusion may
be explained as due to the incorrect linear distances, and may be reduced
to the type of illusion found in the Müller-Lyer figure. Certainly there
are grave dangers in explaining an illusion on the basis of an apparently
simple operation.

In Fig. 56, _b_ is made up of the two parts of the Müller-Lyer illusion. A
small dot may be placed equally distant from the inside extremities of the
horizontal lines. It is interesting to note that overestimation of
distance within the figure is accompanied with underestimation outside the
figure and, conversely, overestimation within the figure is accompanied by
underestimation in the neighboring space. If the small dot is objected to
as providing an additional Müller-Lyer figure of the empty space, this dot
may be omitted. As a substitute an observer may try to locate a point
midway between the inside extremities of the horizontal lines. The error
in locating this point will show that the illusion is present in this
empty space.

In this connection it is interesting to note some other illusions. In Fig.
57 the influence of several factors are evident. Two obviously important
ones are (1) the angles made by the short lines at the extremities of the
exterior lines parallel to the sides of the large triangle, and (2) the
influence of contrast of the pairs of adjacent parallel lines. The effect
shown in Fig. 53 is seen to be augmented by the addition of contrast of
adjacent lines of unequal length.

An interesting variation of the effect of the presence of angles is seen
in Fig. 58. The two lines forming angles with the horizontal are of equal
length but due to their relative positions, they do not appear so. It
would be quite misleading to say that this illusion is merely due to
angles. Obviously, it is due to the presence of the two oblique lines. It
is of interest to turn to Figs. 25, 26 and various illusions of
perspective.

[Illustration: Fig. 57.--Combined influence of angles and contrasting
lengths.]

[Illustration: Fig. 58.--Two equal oblique lines appear unequal because of
their different positions.]

At this point a digression appears to be necessary and, therefore, Fig. 59
is introduced. Here the areas of the two figures are equal. The judgment
of area is likely to be influenced by juxtaposed lines and therefore, as
in this case, the lower appears larger than the upper one. Similarly two
trapezoids of equal dimensions and areas may be constructed. If each is
constructed so that it rests upon its longer parallel and one figure is
above the other and only slightly separated, the mind is tempted to be
influenced by comparing the juxtaposed base of the upper with the top of
the lower trapezoid. The former dimension being greater than the latter,
the lower figure appears smaller than the upper one. Angles must
necessarily play a part in these illusions, although it is admitted that
other factors may be prominent or even dominant.

[Illustration: Fig. 59.--An illusion of area.]

This appears to be a convenient place to insert an illusion of area based,
doubtless, upon form, but angles must play a part in the illusions; at
least they are responsible for the form. In Fig. 60 the five figures are
constructed so as to be approximately equal in area. However, they appear
unequal in this respect. In comparing areas, we cannot escape the
influence of the length and directions of lines which bound these areas,
and also, the effect of contrasts in lengths and directions. Angles play a
part in all these, although very indirectly in some cases.

[Illustration: Fig. 60.--Five equal areas showing the influence of angles
and contrasting lengths.]

To some extent the foregoing is a digression from the main intent of this
chapter, but it appears worth while to introduce these indirect effects of
the presence of angles (real or imaginary) in order to emphasize the
complexity of influences and their subtleness. Direction is in the last
analysis an effect of angle; that is, the direction of a line is measured
by the angle it makes with some reference line, the latter being real or
imaginary. In Fig. 61, the effect of diverting or directing attention by
some subtle force, such as suggestion, is demonstrated. This "force"
appears to contract or expand an area. The circle on the left appears
smaller than the other. Of course there is the effect of empty space
compared with partially filled space, but this cannot be avoided in this
case. However, it can be shown that the suggestions produced by the arrows
tend to produce apparent reduction or expansion of areas. Note the use of
arrows in advertisements.

[Illustration: Fig. 61.--Showing the effect of directing the attention.]

Although theory is subordinated to facts in this book, a glimpse here and
there should be interesting and helpful. After having been introduced to
various types and influences, perhaps the reader may better grasp the
trend of theories. The perspective theory assumes, and correctly so, that
simple diagrams often suggest objects in three dimensions, and that the
introduction of an imaginary third dimension effects changes in the
appearance of lines and angles. That is, lengths and directions of lines
are apparently altered by the influence of lines and angles, which do not
actually exist. That this is true may be proved in various cases. In fact
the reader has doubtless been convinced of this in connection with some
of the illusions already discussed. Vertical lines often represent lines
extending away from the observer, who sees them foreshortened and
therefore they may seem longer than horizontal lines of equal length,
which are not subject to foreshortening. This could explain such illusions
as seen in Figs. 4 and 5. However this theory is not as easily applied to
many illusions.

According to Thiéry's perspective theory a line that appears nearer is
seen as smaller and a line that seems to be further away is perceived as
longer. If the left portion of _b_, Fig. 56, be reproduced with longer
oblique lines at the ends but with the same length of horizontal lines, it
will appear closer and the horizontal lines will be judged as shorter. The
reader will find it interesting to draw a number of these portions of the
Müller-Lyer figure with the horizontal line in each case of the same
length but with longer and longer obliques at the ends.

The dynamic theory of Lipps gives an important role to the inner activity
of the observer, which is not necessarily separated from the objects
viewed, but may be felt as being in the objects. That is, in viewing a
figure the observer unconsciously separates it from surrounding space and
therefore creates something definite in the latter, as a limiting
activity. These two things, one real (the object) and one imaginary, are
balanced against each other. A vertical line may suggest a necessary
resistance against gravitational force, with the result that the line
appears longer than a horizontal one resting in peace. The difficulty
with this theory is that it allows too much opportunity for purely
philosophical explanations, which are likely to run to the fanciful. It
has the doubtful advantage of being able to explain illusions equally well
if they are actually reversed from what they are. For example, gravity
could either contract or elongate the vertical line, depending upon the
choice of viewpoint.

The confusion theory depends upon attention and begins with the difficulty
of isolating from illusory figures the portions to be judged. Amid the
complexity of the figure the attention cannot easily be fixed on the
portions to be judged. This results in confusion. For example, if areas of
different shapes such as those in Fig. 60 are to be compared, it is
difficult to become oblivious of form or of compactness. In trying to see
the two chief parallel lines in Fig. 38, in their true parallelism the
attention is being subjected to diversion, by the short oblique parallels
with a compromising result. Surely this theory explains some illusions
successfully, but it is not so successful with some of the illusions of
contrast. The fact that practice in making judgments in such cases as
Figs. 45 and 56 reduces the illusion even to ultimate disappearance,
argues in favor of the confusion theory. Perhaps the observer devotes
himself more or less consciously to isolating the particular feature to be
judged and finally attains the ability to do so. According to Auerbach's
indirect-vision theory the eyes in judging the two halves of the
horizontal line in _a_, Fig. 56, involuntarily draw imaginary lines
parallel to this line but above or below it. Obviously the two parts of
such lines are unequal in the same manner as the horizontal line in the
Müller-Lyer figure appears divided into two unequal parts.

Somewhat analogous to this in some cases is Brunot's mean-distance theory.
According to this we establish "centers of gravity" in figures and these
influence our judgments.

These are glimpses of certain trends of theories. None is a complete
success or failure. Each explains some illusions satisfactorily, but not
necessarily exclusively. For the present, we will be content with these
glimpses of the purely theoretical aspects of visual illusions.



VII

ILLUSIONS OF DEPTH AND OF DISTANCE


Besides the so-called geometrical illusions discussed in the preceding
chapters, there is an interesting group in which the perception of the
third dimension is in error. When any of the ordinary criteria of relief
or of distance are apparently modified, illusions of this kind are
possible. There are many illusions of this sort, such as the looming of
objects in a fog; the apparent enlargement of the sun and moon near the
horizon; the flattening of the "vault" of the sky; the intaglio seen as
relief; the alteration of relief with lighting; and various changes in the
landscape when regarded with the head inverted.

Although some of the criteria for the perception of depth or of distance
have already been pointed out, especially in Chapter III, these will be
mentioned again. Distance or depth is indicated by the distribution of
light and shade, and an unusual object like an intaglio is likely to be
mistaken for relief which is more common. An analysis of the lighting will
usually reveal the real form of the object. (See Figs. 70, 71, 72, 73, 76
and 77.) In this connection it is interesting to compare photographic
negatives with their corresponding positive prints.

Distance is often estimated by the definition and color of objects seen
through great depths of air (aerial perspective). These distant objects
are "blurred" by the irregular refraction of the light-rays through
non-homogeneous atmosphere. They are obscured to some degree by the veil
of brightness due to the illuminated dust, smoke, etc., in the atmosphere.
They are also tinted (apparently) by the superposition of a tinted
atmosphere. Thus we have "dim distance," "blue peaks," "azure depths of
sky," etc., represented in photographs, paintings, and writings.
Incidentally, the sky above is blue for the same general reasons that the
atmosphere, intervening between the observer and a distant horizon, is
bluish. The ludicrous errors made in estimating distances in such regions
as the Rockies is usually accounted for by the rare clearness and
homogeneity of the atmosphere. However, is the latter a full explanation?
To some extent we judge unknown size by estimated distance, and unknown
distance by estimated size. When a person is viewing a great mountain peak
for the first time, is he not likely to assume it to be comparable in size
to the hills with which he has been familiar? Even by allowing
considerable, is he not likely to greatly underestimate the size of the
mountain and, as a direct consequence, to underestimate the distance
proportionately? This incorrect judgment would naturally be facilitated by
the absence of "dimness" and "blueness" due to the atmospheric haze.

Angular perspective, which apparently varies the forms of angles and
produces the divergence of lines, contributes much information in regard
to relative and absolute distances from the eye of the various objects or
the parts of an object. For example, a rectangle may appear as a rhomboid.
It is obvious that certain data pertaining to the objects viewed must be
assumed, and if the assumptions are incorrect, illusions will result.
These judgments also involve, as most judgments do, other data external to
the objects viewed. Perhaps these incorrect judgments are delusions rather
than illusions, because visual perception has been deluded by
misinformation supplied by the intellect.

Size or linear perspective is a factor in the perception of depth or of
distance. As has been stated, if we know the size experience determines
the distance; and conversely, if we know the distance we may estimate the
size. Obviously estimates are involved and these when incorrect lead to
false perception or interpretation.

As an object approaches, the axes of the eyes converge more and more and
the eye-lens must be thickened more and more to keep the object in focus.
As stated in Chapter III, we have learned to interpret these accompanying
sensations of muscular adjustment. This may be demonstrated by holding an
object at an arm's length and then bringing it rapidly toward the eyes,
keeping it in focus all the time. The sensations of convergence and
accommodation are quite intense.

The two eyes look at a scene from two different points of view
respectively and their images do not perfectly agree, as has been shown in
Figs. 2 and 3. This binocular disparity is responsible to some degree for
the perception of depth, as the stereoscope has demonstrated. If two
spheres of the same size are suspended on invisible strings, one at six
feet, the other at seven feet away, one eye sees the two balls in the same
plane, but one appears larger than the other. With binocular vision the
balls appear at different distances, but judgment appraises them as of
approximately equal size. At that distance the focal adjustment is not
much different for both balls, so that the muscular movement, due to
focusing the eye, plays a small part in the estimation of the relative
distance. Binocular disparity and convergence are the primary factors.

Some have held that the perception of depth, that is, of a relative
distance, arises from the process of unconsciously running the point of
sight back and forth. However, this view, unmodified, appears untenable
when it is considered that a scene illuminated by a lightning flash (of
the order of magnitude of a thousandth of a second) is seen even in this
brief moment to have depth. Objects are seen in relief, in actual relation
as to distance and in normal perspective, even under the extremely brief
illumination of an electric spark (of the order of magnitude of one
twenty-thousandth of a second). This can also be demonstrated by viewing
stereoscopic pictures with a stereoscope, the illumination being furnished
by an electric spark. Under these circumstances relief and perspective are
quite satisfactory. Surely in these brief intervals the point of sight
cannot do much surveying of a scene.

Parallax aids in the perception of depth or distance. If the head be moved
laterally the view or scene changes slightly. Objects or portions of
objects previously hidden by others may now become visible. Objects at
various distances appear to move nearer or further apart. We have come to
interpret these apparent movements of objects in a scene in terms of
relative distances; that is, the relative amount of parallactic
displacement is a measure of the relative distances of the objects.

The relative distances or depth locations of different parts of an object
can be perceived as fluctuating or even reversing. This is due to
fluctuations in attention, and illusions of reversible perspective are of
this class. It is quite impossible for one to fix his attention in perfect
continuity upon any object. There are many involuntary eye-movements which
cannot be overcome and under normal conditions certain details are likely
to occupy the focus of attention alternately or successively. This applies
equally well to the auditory sense and perhaps to the other senses.
Emotional coloring has much to do with the fixation of attention; that
which we admire, desire, love, hate, etc., is likely to dwell more in the
focus of attention than that which stirs our emotions less.

A slight suggestion of forward and backward movements can be produced by
successively intercepting the vision of one eye by an opaque card or other
convenient object. It has been suggested that the illusion is due to the
consequent variations in the tension of convergence. Third dimensional
movements may be produced for binocular or monocular vision during
eye-closure. They are also produced by opening the eyes as widely as
possible, by pressure on the eye-balls, and by stressing the eyelids.
However, these are not important and are merely mentioned in passing.

An increase in the brightness of an object is accompanied by an apparent
movement toward the observer, and conversely a decrease in brightness
produces an apparent movement in the opposite direction. These effects may
be witnessed upon viewing the glowing end of a cigar which is being smoked
by some one a few yards away in the darkness. Rapidly moving thin clouds
may produce such an effect by varying the brightness of the moon. Some
peculiar impressions of this nature may be felt while watching the
flashing light of some light-houses or of other signaling stations. It has
been suggested that we naturally appraise brighter objects as nearer than
objects less bright. However, is it not interesting to attribute the
apparent movement to irradiation? (See Chapter VIII.) A bright object
appears larger than a dark object of the same size and at the same
distance. When the same object varies in brightness it remains in
consciousness the same object and therefore of constant size; however, the
apparent increase in size as it becomes brighter must be accounted for in
some manner and there is only one way open. It must be attributed a lesser
distance than formerly and therefore the sudden increase in brightness
mediates a consciousness of a movement forward, that is, toward the
observer.

If two similar objects, such as the points of a compass, are viewed
binocularly and their lateral distance apart is altered, the observer is
conscious of a third dimensional movement. Inasmuch as the accommodation
is unaltered but convergence must be varied as the lateral distance
between the two, the explanation of the illusion must consider the latter.
The pair of compass-points are very convenient for making a demonstration
of this pronounced illusion. The relation of size and distance easily
accounts for the illusion.

Obviously this type of illusion cannot be illustrated effectively by means
of diagrams, so the reader must be content to watch for them himself. Some
persons are able voluntarily to produce illusory movements in the third
dimension, but such persons are rare. Many persons have experienced
involuntary illusions of depth. Carr found, in a series of classes
comprising 350 students, 58 persons who had experienced involuntary depth
illusions at some time in their lives. Five of these also possessed
complete voluntary control over the phenomenon. The circumstances
attending visual illusions of depth are not the same for various cases,
and the illusions vary widely in their features.

Like other phases of the subject, this has been treated in many papers,
but of these only one will be specifically mentioned, for it will suffice.
Carr[3] has studied this type of illusion comparatively recently and
apparently quite generally, and his work will be drawn upon for examples
of this type. Apparently they may be divided into four classes: (1) Those
of pure distance; that is, an object may appear to be located at varying
distances from the observer, but no movement is perceived. For example, a
person might be seen first at the true distance; he might be seen next
very close in front of the eyes; then he might suddenly appear to be quite
remote; (2) illusions of pure motion; that is, objects are perceived as
moving in a certain direction without any apparent change in location. In
other words, they appear to move, but they do not appear to traverse
space; (3) illusions of movement which include a change in location. This
appears to be the most common illusion of depth; (4) those including a
combination of the first and third classes. For example, the object might
first appear to move away from its true location and is perceived at some
remote place. Shortly it may appear in its true original position, but
this change in location does not involve any sense of motion.

These peculiar illusions of depth are not as generally experienced as
those described in preceding chapters. A geometrical illusion, especially
if it is pronounced, is likely to be perceived quite universally, but
these illusions of depth are either more difficult to notice or more
dependent upon psychological peculiarities far from universal among
people. It is interesting to note the percentages computed from Carr's
statistics obtained upon interrogating 350 students. Of these, 17 per cent
had experienced depth-illusions and between one and two per cent had
voluntary control of the phenomenon. Of the 48 who had experienced
illusions of this type and were able to submit detailed descriptions, 25
per cent belonged to class (1) of those described in the preceding
paragraph; 4 per cent to class (2); 52 per cent to class (3); and 17 per
cent to class (4).

Usually the illusion involves all objects in the visual field but with
some subjects the field is contracted or the objects in the periphery of
the field are unaffected. For most persons these illusions involve normal
perceptual objects, although it appears that they are phases of
hallucinatory origin.

Inasmuch as these illusions cannot be illustrated diagrammatically we can
do no better than to condense some of the descriptions obtained and
reported by Carr.[3]

A case in which the peripheral objects remain visible and stationary at
their true positions while the central portion of the field participates
in the illusion is as follows:

    The observer on a clear day was gazing down a street which ended a
    block away, a row of houses forming the background at the end of the
    street. The observer was talking to and looking directly at a
    companion only a short distance away. Soon this person (apparently)
    began to move down the street, until she reached the background of
    houses at the end, and then slowly came back to her original position.
    The movement in both directions was distinctly perceived. During the
    illusory movement there was no vagueness of outline or contour, no
    blurring or confusion of features; the person observed, seemed
    distinct and substantial in character during the illusion. The
    perceived object moved in relation to surrounding objects; there was
    no movement of the visual field as a whole. The person decreased in
    size during the backward movement and increased in size during the
    forward return movement.

With many persons who experience illusions of depth, the objects appear to
move to, or appear at, some definite position and remain there until the
illusion is voluntarily overcome, or until it disappears without voluntary
action. A condensation of a typical description of this general type
presented by Carr is as follows:

    All visual objects suddenly recede to the apparent distance of the
    horizon and remain in that position several minutes, returning at the
    end of this period to their original positions. This return movement
    is very slow at the beginning, but the latter phase of the movement is
    quite rapid. If the subject closes her eyes while the objects appear
    at their distant position she cannot even _imagine_ those objects
    located anywhere except at their apparent distant position.

    In all cases (encountered by Carr) the motion in both directions is an
    actual experience reality and the subject was helpless as to
    initiating, stopping, or modifying the course of the illusion in any
    way. Objects and even visual images (which are subject to the same
    illusions) decrease in size in proportion to the amount of backward
    movement and grow larger again on their return movement. The objects
    are always clearly defined as if in good focus. In this particular
    case the illusion occurred about twice a year, under a variety of
    conditions of illumination, at various times of the day, but
    apparently under conditions of a rather pronounced fatigue.

In regard to the variation in the size of objects, many who have
experienced these illusions of depth testify that the size seems to change
in proportion to the apparent distance, according to the law of
perspective. Some persons appear in doubt as to this change and a few have
experienced the peculiar anomaly of decreasing size as the objects
apparently approached.

Many persons who have experienced these peculiar illusions report no
change in the distinctness of objects; almost as many are uncertain
regarding this point; and as many report a change in distinctness.
Apparently there are phases of hallucinatory origin so that there is a
wide variety of experiences among those subject to this type of illusion.

According to Carr's investigation internal conditions alone are
responsible for the illusion with more persons than those due to external
conditions alone. With some persons a combination of internal and external
conditions seem to be a necessity. Fixation of vision appears to be an
essential objective condition for many observers. That is, the illusion
appeared while fixating a speaker or singer in a church or a theater. With
others the illusion occurs while reading. Some reported that fixation upon
checkered or other regularly patterned objects was an essential condition.
Among the subjective conditions reported as essential are steady fixation,
concentration of attention, complete mental absorption, dreamy mental
abstraction, and fatigue.

Ocular defects do not appear to be essential, for the illusions have been
experienced by many whose eyes were known to be free from any
abnormalities.

Period of life does not appear to have any primary influence, for those
who are subject to these peculiar illusions often have experienced them
throughout many years. In some cases it is evident that the illusions
occur during a constrained eye position, while lying down, immediately
upon arising from bed in the morning, and upon opening the eyes after
having had them closed for some time. However, the necessity for these
conditions are exceptional.

The control of these illusions of depth, that is, the ability to create or
to destroy them, appears to be totally lacking for most of those who have
experienced them. Some can influence them, a few can destroy them, a few
can indirectly initiate them, but those who can both create and destroy
them appear to be rare.

It may seem to the reader that the latter part of this chapter departs
from the main trend of this book, for most of these illusions of depth are
to a degree of hallucinatory origin. Furthermore it has been the intention
to discuss only those types of illusions which are experienced quite
uniformly and universally. The digression of this chapter is excused on
the basis of affording a glimpse along the borderland of those groups of
illusions which are nearly universally experienced. Many other phases of
depth illusions have been recorded in scientific literature. The excellent
records presented by Carr could be drawn upon for further glimpses, but it
appears that no more space should be given to this exceptional type. The
reader should be sufficiently forewarned of this type and should be able
to take it into account if peculiarities in other types appear to be
explainable in this manner. However, in closing it is well to emphasize
the fact that the hallucinatory aspect of depth illusions is practically
absent in types of illusions to which attention is confined in other
chapters.



VIII

IRRADIATION AND BRIGHTNESS-CONTRAST


Many interesting and striking illusions owe their existence to contrasts
in brightness. The visual phenomenon of irradiation does not strictly
belong to this group, but it is so closely related to it and so dependent
upon brightness-contrast that it is included. A dark line or spot will
appear darker in general as the brightness of its environment is
increased; or conversely, a white spot surrounded by a dark environment
will appear brighter as the latter is darkened. In other words, black and
white, when juxtaposed, mutually reinforce each other. Black print on a
white page appears much darker than it really is. This may be proved by
punching a hole in a black velvet cloth and laying this hole over a
"black" portion of a large letter. The ink which appeared so black in the
print, when the latter was surrounded by the white paper, now appears only
a dark gray. Incidentally a hole in a box lined with black velvet is much
darker than a piece of the black velvet surrounding the hole.

The effects of brightness-contrast are particularly striking when
demonstrated by means of lighting, a simple apparatus being illustrated
diagrammatically in Fig. 62. For example, if a hole _H_ is cut in an
opaque white blotting paper and a large piece of the white blotting paper
is placed at _C_, the eye when placed before the opening at the right will
see the opening at _H_ filled with the background _C_. The hole _H_ may be
cut in thin metal, painted a dull white, and may be of the shape of a
star. This shape provides an intimacy between the hole and its environment
which tends to augment the effects of contrasts. _R_ and _F_ are
respectively the rear and front lamps. That is, the lamps _R_ illuminate
_C_, which "fills" the hole and apparently is the hole; and the lamps _F_
illuminate the diffusing white environment _E_. The two sets of lamps may
be controlled by separate rheostats, but if the latter are unavailable the
lamps (several in each set) may be arranged so that by turning each one
off or on, a range of contrasts in brightness between _E_ and _H_ (in
reality _C_) may be obtained. (By using colored lamps and colored papers
as discussed in Chapter IX the marvelous effects of color-contrast may be
superposed upon those of brightness-contrast.)

[Illustration: Fig. 62.--Simple apparatus for demonstrating the remarkable
effects of contrasts in brightness and color.]

If, for example, _C_ is very feebly illuminated and _E_ is very bright,
_C_ will be pronounced black; but when the lamps _F_ are extinguished and
no light is permitted to reach _E_, the contrast is reversed, and _C_ may
actually appear "white." Of course, it is obvious that white and black are
relative terms as encountered in such a case. In fact in
brightness-contrasts relative and not absolute values of brightness are
usually the more important. In order to minimize the stray light which
emerges from _H_, it is well to paint the inside of both compartments
black with the exception of sufficiently large areas of _C_ and _E_. The
use of black velvet instead of black paint is sometimes advisable. It is
also well to screen the lamps as suggested in the diagram. This simple
apparatus will demonstrate some very striking effects of contrasts in
brightness and will serve, also, to demonstrate even more interesting
effects of contrasts in color.

Two opposite contrasts obtainable by means of a simple apparatus
illustrated in Fig. 62 may be shown simultaneously by means of white,
black, and gray papers arranged as in Fig. 63. In this figure the gray is
represented by the partially black _V_s, each of which contains equal
amounts of black and of white. When held at some distance this serves as a
gray and the same effect is apparent as is described for the case of
actually gray _V_s. An excellent demonstration may be made by the reader
by using two _V_s, cut from the same sheet of gray paper, and pasted
respectively upon white and black backgrounds, as in Fig. 63. It will be
apparent that the one amid the black environment appears much brighter
than the one (same gray) amid the white environment. This can be
demonstrated easily to an audience by means of a figure two feet long. It
is interesting to carry the experiment further and place a _V_ of much
darker gray on the black background than the _V_ on the white background.
The persistency of the illusion is found to be remarkable, for it will
exist even when the one _V_ is actually a much darker gray than the other.
To become convinced that the two grays are of the same brightness in Fig.
63, it is only necessary to punch two holes in a white or gray card at
such a distance apart that they will lie respectively over portions of the
two _V_s when the card is laid upon Fig. 63. The grays in the holes should
now appear alike because their environments are similar.

[Illustration: Fig. 63.--Illustrating brightness-contrast.]

The importance of contrasts in brightness and in color cannot be
overemphasized, and it appears certain that no one can fully realize
their effectiveness without witnessing it in a manner similar to that
suggested in Fig. 62.

[Illustration: Fig. 64.--An effect of brightness-contrast. Note the
darkening of the intersections of the white strips.]

Many illusions of brightness-contrast are visible on every hand. For
example, the point at which the mullions of a window cross will be seen to
appear brighter than the remaining portions of them when viewed against a
bright sky. Conversely, in Fig. 64, dark spots appear where the white bars
cross. This is purely an illusion and the same type may be witnessed by
the observant many times a day. In Fig. 64 it is of interest to note that
the illusion is weak for the crossing upon which the point of sight rests,
but by averted vision the illusion is prominent for the other crossings.
This is one of the effects which depends upon the location in the visual
field.

No brightness-contrasts are seen correctly and often the illusions are
very striking. If a series of gray papers is arranged from black to white,
with the successive pieces overlapped or otherwise juxtaposed, a series of
steps of uniform brightness is not seen. An instrument would determine the
brightness of each as uniform, but to the eye the series would appear
somewhat "fluted." That is, where a light gray joined a darker gray the
edge of the former would appear lighter than its actual brightness, and
the edge of the darker gray would appear darker than it should. This may
also be demonstrated by laying a dozen pieces of white tissue paper in a
pile in such a manner that a series of 1, 2, 3, 4, etc., thickness would
be produced. On viewing this by transmitted light a series of grays is
seen, and the effect of contrast is quite apparent. Such a pattern can be
made photographically by rotating before a photographic plate a disk with
openings arranged properly in steps.

Many demonstrations of the chief illusion of brightness-contrast are
visible at night under glaring lighting conditions. It is difficult or
impossible to see objects beyond automobile headlights, and adjacent to
them, in the visual field. Objects similarly located in respect to any
surface sufficiently bright are more or less obscured. Characters written
upon a blackboard, placed between two windows, may be invisible if the
surfaces seen through the window are quite bright, unless a sufficient
quantity of light reaches the blackboard from other sources.
Stage-settings have been changed in perfect obscurity before an audience
by turning on a row of bright lights at the edge of the stage-opening. The
term "blinding light" owes its origin to this effect of
brightness-contrast.

The line of juncture between a bright and a dark surface may not be seen
as a sharp line, but as a narrow band of gray. When this is true it is
possible that an undue amount of area is credited to the white. In
preceding paragraphs we have seen the peculiar effect at the border-lines
of a series of grays. This may have something to do with the estimate;
however, irradiation may be due to excitation of retinal rods and cones
adjacent to, but not actually within the bright image.

A remarkable effect which may be partially attributable to irradiation can
be produced by crossing a grating of parallel black lines with an oblique
black line. At the actual crossings the black appears to run up the narrow
angle somewhat like ink would under the influence of surface tension. This
is particularly striking when two gratings or even two ordinary
fly-screens are superposed. The effect is visible when passing two
picket-fences, one beyond the other. If a dark object is held so that a
straight edge appears to cross a candle-flame or other light-source, at
this portion the straight edge will appear to have a notch in it.

Irradiation in general has been defined as the lateral diffusion of
nervous stimuli beyond the actual stimulus. It is not confined to the
visual sense but irradiation for this sense is a term applied to the
apparent enlargement of bright surfaces at the expense of adjacent darker
surfaces. The crescent of the new moon appears larger in radius than the
faint outline of the darker portion which is feebly illuminated chiefly by
light reflected from the earth's surface. A filament of a lamp appears to
grow in size as the current through it is slowly increased from a zero
value; that is, as it increases in brightness. In Fig. 65 the small inner
squares are of the same size but the white square appears larger than the
black one. It seems that this apparent increase is made at the expense of
the adjacent dark area. This phenomenon or illusion is strongest when the
brightness is most intense, and is said to be greatest when the
accommodation is imperfect. A very intense light-source may appear many
times larger than its actual physical size.

[Illustration: Fig. 65.--The phenomenon of irradiation.]

Doubtless a number of factors may play a part in this phenomenon. It
appears possible that there is a rapid spreading of the excitation over
the retina extending quite beyond the border of the more intensely
stimulated region, but this must be practically instantaneous in order to
satisfy results of experiments. Eye-movements may play some part for,
despite the most serious efforts to fixate the point of sight, a fringe
will appear on the borders of images which is certainly due to involuntary
eye-movements.

Irradiation has also been ascribed to spherical aberration in the eye-lens
and to diffraction of light at the pupil. Printed type appears
considerably reduced in size when the pupil is dilated with atropin and is
restored to normal appearance when a small artificial pupil is placed
before the dilated pupil. It has been suggested that chromatic aberration
in the eye-lens is a contributory cause, but this cannot be very
important, for the illusion is visible with monochromatic light which
eliminates chromatic aberration. The experimental evidence appears to
indicate that the phenomenon is of a physical nature.

There are variations in the effects attributable to radiation, and it is
difficult to reduce them to simple terms. Perhaps it may aid the reader to
have before him the classification presented by Boswell.[4] He describes
the varieties of irradiation as follows:

    1. Very rapid spreading of the excitation over the retina extending
    far beyond the border of the stimulated region and occurring
    immediately upon impact of the stimulating light.

    2. Irradiation within the stimulated portion of the retina after the
    form of a figure becomes distinctly perceptible.

    3. Emanations of decreasing intensity extend themselves outward and
    backward from a moving image until lost in the darkness of the
    background.

    4. A well known form of irradiation which occurs when a surface of
    greater intensity enlarges itself at the expense of one of less
    intensity.

    5. A form having many of the characteristics of the first type, but
    occurring only after long periods of stimulation, of the magnitude of
    30 to 60 seconds or more.



IX

COLOR


In order to simplify the presentation of the general subject, discussions
of color have been omitted in so far as possible from the preceding
chapters. There are almost numberless phenomena involving color, many of
which are illusions, or seemingly so. It will be obvious that many are
errors of sense; some are errors of judgment; others are errors due to
defects of the optical system of the eye; and many may be ascribed to
certain characteristics of the visual process. It is not the intention to
cover the entire field in detail; indeed, this could not be done within
the confines of a large volume. However, substantial glimpses of the more
important phases of color as related to illusions are presented in this
chapter. In the early chapters pertaining to the eye and to vision some of
the following points were necessarily touched upon, but the repetition in
the paragraphs which follow is avoided as much as possible.

_Simultaneous Contrast._--That the life of color is due to contrast is
demonstrable in many ways. If a room is illuminated by deep red light, at
first this color is very vivid in consciousness; however, gradually it
becomes less saturated. After a half hour the color is apparently a much
faded red but upon emerging from the room into one normally lighted, the
latter appears very markedly greenish in tint. The reason that the pure
red light does not appear as strongly colored as it really is, is due to
the lack of contrast. In a similar manner at night we see white objects as
white even under the yellowish artificial light. The latter appears very
yellow in color when it is first turned on as daylight wanes but as
darkness falls and time elapses it gradually assumes a colorless
appearance.

An apparatus constructed after the plan of Fig. 62 is very effective for
demonstrating the remarkable effects of color-contrast but some additions
will add considerably to its convenience. If the lamps _F_ are divided
into three circuits, each emitting, respectively, red, green, and blue
primary colors, it is possible by means of controlling rheostats to
illuminate _E_, the environment, with light of any hue (including purple),
of any saturation, and of a wide range of intensities or resulting
brightnesses. Thus we have a very simple apparatus for quickly providing
almost numberless environments for _H_. The same scheme can be applied to
lamps _R_, with the result that a vast array of colors may be seen through
the hole _H_. If the hole is the shape of the star in Fig. 66 it will be
found very effective. The observer will actually see a star of any desired
color amid an environment of any desired color. Care should be taken to
have the star cut in very thin material in order to eliminate conspicuous
boundary lines. It is quite satisfactory to use a series of colored papers
on a slide at _C_ and ordinary clear lamps at _R_. By means of this
apparatus both contrasts--hue and brightness--may be demonstrated. Of
course, for black and white only brightness-contrast is present; but in
general where there is color-contrast there is also brightness-contrast.
The latter may be reduced or even eliminated if the brightness of the star
and of its surroundings are made equal, but it is difficult to make a
satisfactory balance in this respect. Assuming, however, that
brightness-contrast is eliminated, we have left only hue and saturation
contrast, or what will be termed (rather loosely, it is admitted)
color-contrast.

[Illustration: Fig. 66.--An excellent pattern for demonstrating
color-contrast.]

If the surroundings are dark and, for example, an orange star is seen
alone, it does not appear very colorful. However, if the surroundings are
now made bright with white light, the star appears quite saturated. With
blue or green light the orange star appears even more intensely orange,
but when the color-contrast is reduced, as in the case of yellow or red
surroundings, the vividness of the orange star again decreases. This may
be summarized by stating that two widely different colors viewed in this
manner will mutually affect each other so that they appear still more
different in hue. If their hues are close together spectrally this effect
is not as apparent. For example, if orange and green are contrasted, the
orange will appear reddish in hue and the green will appear bluish.

Let us now assume the star to be white, and that the surroundings are of
any color of approximately the same brightness. The star which is really
white will now appear decidedly tinted and of a hue approximately
complementary to that of the surroundings. When the latter are of a green
color the white star will assume a purplish tinge; when red the white star
will appear of a blue-green tint; when yellow the white star will appear
bluish. This is an illusion in any sense of the term.

The strength of this illusion caused by simultaneous contrast is very
remarkable. For example, if a grayish purple star is viewed amid intense
green surroundings it will appear richly purple, but when the surroundings
are changed to a rich purple the grayish purple star will even appear
greenish. The apparent change of a color to its complementary by merely
altering its environment is really a remarkable illusion.

The importance of simultaneous contrast is easily demonstrated upon a
painting by isolating any colored object from its surroundings by means of
a hole in a gray card. For example, an orange flower-pot amid the green
foliage of its surroundings will appear decidedly different in color and
brightness than when viewed through a hole in a white, black, or gray
cardboard. By means of colored papers the same color may be placed in many
different environments and the various contrasts may be viewed
simultaneously. The extent of the illusion is very evident when revealed
in this simple manner. However, too much emphasis cannot be given to Figs.
62 and 66 as a powerful means for realizing the greatest effects.

_After-images._--After looking at bright objects we see after-images of
the same size and form which vary more or less in color. These
after-images are due to persistence or fatigue of the visual process,
depending upon conditions. After looking at the sun for a moment a very
bright after-image is seen. Undoubtedly this at first is due to a
persistence of the visual process, but as it decays it continuously
changes color and finally its presence is due to fatigue.

After-images may be seen after looking intently at any object and then
directing the eyes toward a blank surface such as a wall. A picture-frame
will be seen as a rectangular after-image; a checkered pattern will be
seen as a checkered after-image. When these after-images are projected
upon other objects it is obvious that the appearance of the latter is
apparently altered especially when the observer is not conscious of the
after-image. The effects are seen in paintings and many peculiar phenomena
in the various arts are directly traceable to after-images.

It appears unnecessary to detail the many effects for the explanations or
at least the general principles of after-images are so simple that the
reader should easily render an analysis of any given case.

Let us assume that vision is fixed upon a green square upon a gray or
white background. Despite the utmost effort on the part of the observer to
gaze fixedly upon this green square, the latter will begin to appear
fringed with a pinkish border. This is due to the after-image of the green
square and it is displaced slightly due to involuntary eye-movements.
After gazing as steadily as possible for a half minute, or even less, if
the point of sight is turned to the white paper a pink square is seen upon
it. Furthermore, this pink square moves over the field with the point of
sight. This is the type most generally noticed.

After-images have been classified as positive and negative. The former are
those in which the distribution of light and shade is the same as in the
original object. Those in which this distribution is reversed, as in the
photographic negative, are termed "negative." After-images undergo a
variety of changes in color but in general there are two important states.
In one the color is the same as in the original object and in the other it
is approximately complementary to the original color. In general the
negative after-image is approximately complementary in color to the color
of the original object.

After-images are best observed when the eyes are well rested, as in the
morning upon awakening. With a little practice in giving attention to
them, they can be seen floating in the air, in the indefinite field of the
closed eyes, upon a wall, or elsewhere, and the changes in the brightness
and color can be readily followed. Negative after-images are sometimes
very persistent and therefore are more commonly noticed than positive
ones. The positive after-image is due to retinal inertia, that is, to the
persistency of the visual process after the actual stimulus has been
removed. It is of relatively brief duration. If an after-image of a window
is projected on a white area it is likely to appear as a "negative" when
projected upon a white background, and as a "positive" upon a dark
background, such as is readily provided by closing the eyes. It may be of
interest for the reader to obtain an after-image of a bright surface of a
light-source and study its color changes with the eye closed. Upon
repeating the experiment the progression of colors will be found to be
always the same for the same conditions. The duration of the after-image
will be found to vary with the brightness and period of fixation of the
object.

It is interesting to note that an after-image is seen with difficulty when
the eyes are in motion, but it becomes quite conspicuous when the eyes are
brought to rest.

An after-image due to the stimulation of only one eye sometimes seems to
be seen by the other eye. Naturally this has given rise to the suggestion
that the seat of after-images is central rather than peripheral; that is,
in the brain rather than at the retina. However, this is not generally the
case and the experimental evidence weighs heavily against this conclusion.

If Fig. 52 is revolved about its center and fixated for some time striking
effects are obtained upon looking away suddenly upon any object. The
latter will appear to shrink if the spiral has seemed to run outward, or
to expand if the spiral has seemed to run inward. These are clearly
after-images of motion.

As stated elsewhere, we may have illusions of after-images as well as of
the original images. For example, if a clearly defined plane geometrical
figure such as a cross or square is bright enough to produce a strong
after-image, the latter when projected upon a perspective drawing will
appear distorted; that is, it is likely to appear in perspective.

A simple way of demonstrating after-images and their duration is to move
the object producing them. For example, extinguish a match and move the
glowing end. If observed carefully without moving the eye a bluish
after-image will be seen to follow the glowing end of the match. In this
case the eyes should be directed straight ahead while the stimulus is
moving and the observation must be made by averted or indirect vision.

_Growth and Decay of Sensation._--Although many after-images may not be
considered to be illusions in the sense in which the term is used here,
there are many illusions in which they at least play a part. Furthermore,
it is the intention throughout these chapters to adhere to a discussion of
"static" illusions, it is difficult to avoid touching occasionally upon
motion. The eyes are in motion most of the time, hence, certain effects of
an illusory nature may be superposed upon stationary objects.

The persistence of vision has been demonstrated by every small boy as he
waved a glowing stick seized from a bonfire. Fireworks owe much of their
beauty to this phenomenon. A rapidly revolving spoked wheel may appear to
be a more or less transparent disk, but occasionally when a rapid
eye-movement moves the point of sight with sufficient speed in the
direction of motion, the spokes reappear momentarily. Motion-pictures owe
their success to this visual property--the persistence of vision. If a
lantern-slide picture be focused upon black velvet or upon a dark doorway,
the projected image will not be seen. However, if a white rod be moved
rapidly enough in the plane of the image, the latter may be seen in its
entirety. The mixture of colors, by rotating them on disks, owes its
possibility to the persistence of the color-sensations beyond the period
of actual stimulation. The fact that it takes time for sensations of light
to grow and decay is not as important here as the fact that the rates of
growth, and also of decay, vary for different colors. In general, the
growth and the decay are not of similar or uniform rates. Furthermore, the
sensation often initially "overshoots" its final steady value, the amount
of "overshooting" depending upon the intensity and color of the stimulus.
These effects may be witnessed in their extensive variety by rotating
disks so constructed that black and various colors stimulate the retina in
definite orders.

An interesting case of this kind may be demonstrated by rotating the disk
shown in Fig. 67. Notwithstanding the fact that these are only black and
white stimuli, a series of colored rings is seen varying from a reddish
chocolate to a blue-green. Experiment will determine the best speed,
which is rather slow under a moderate intensity of illumination. The
reddish rings will be outermost and the blue-green rings innermost when
the disk is rotated in one direction. Upon reversing the direction of
rotation the positions of these colored rings will be reversed. By using
various colors, such as red and green for the white and black
respectively, other colors will be produced, some of which are very
striking. The complete explanation of the phenomenon is not clear, owing
to the doubt which exists concerning many of the phenomena of
color-vision, but it appears certain that the difference in the rates of
growth and decay of the various color-sensations (the white stimulus
includes all the spectral hues of the illuminant) is at least partially,
if not wholly, responsible.

[Illustration: Fig. 67.--By rotating this Mason (black and white) disk
color-sensations are produced.]

An interesting effect, perhaps due wholly or in part to the differences in
the rates of growth and decay of color-sensations, may be observed when a
colored pattern is moved under a low intensity of illumination, the eyes
remaining focused upon a point in space at about the same distance as the
object. A square of red paper pasted in the center of a larger piece of
blue-green paper is a satisfactory object. On moving this object gently,
keeping the point of sight fixed in its plane of movement, the central red
square will appear to shake like jelly and a decided trail of color will
appear to cling to the lagging edge of the central square. Perhaps
chromatic aberration plays some part in making this effect so conspicuous.

A similar case will be noted in a photographic dark-room illuminated by
red light upon observing the self-luminous dial of a watch or clock. When
the latter is moved in the plane of the dial, the greenish luminous
figures appear separated from the red dial and seem to lag behind during
the movement. For such demonstrations it is well to experiment somewhat by
varying the intensity of the illumination and the speed of movement.
Relatively low values of each appear to be best.

Although the various color-sensations grow and decay at different rates,
the latter depend upon conditions. It appears that blue-sensation rises
very rapidly and greatly overshoots its final steady value for a given
stimulus. Red ranks next and green third in this respect. The overshooting
appears to be greater for the greater intensity of the stimulus. The time
required for the sensation to reach a steady value depends both upon the
spectral character and the brightness of the color but is usually less
than a second.

_Chromatic Aberration._--It is well known that the eye focuses different
spectral colors at different points. This is true of any simple lens and
the defect is overcome in the manufacture of optical instruments by
combining two lenses consisting respectively of glasses differing
considerably in refractive index. If a white object is viewed by the eye,
it should appear with a purplish fringe; however, the effect is observed
more readily by viewing a light-source through a purple filter which
transmits only violet and red light. The light-source will have a red or a
violet fringe, depending upon the accommodation or focus of the eye.

This effect is perhaps best witnessed on viewing a line spectrum such as
that of the mercury arc, focused upon a ground glass. The violet and blue
lines are not seen in good focus when the eyes are focused upon the green
and yellow lines. Furthermore, the former can be seen in excellent focus
at a distance too short for accommodating the eyes to the green and the
yellow lines. This experiment shows that the focal length of the optical
system of the eye is considerably shorter for the spectral hues of shorter
wave-length (violet, blue) than for those of longer wave-length (such as
yellow). Narrow slits covered with diffusing glass and illuminated
respectively by fairly pure blue, green, yellow, and red lights may be
substituted.

The effect may be demonstrated by trying to focus fine detail such as
print when two adjacent areas are illuminated by blue and red lights
respectively. It is also observed when fine detail such as black lines are
held close to the eye for colored fringes are seen. This optical defect is
responsible for certain visual illusions.

An excellent demonstration of chromatic aberration in the eye is found by
viewing fine detail through a purple filter. Now if a red filter be
superposed on the purple one only the red light is transmitted.
Notwithstanding the decrease in illumination or rather of light reaching
the eye, measurement shows that finer detail can be discriminated than in
the first case. A similar result is found on superposing a blue filter
upon the purple one.

_Retiring and Advancing Colors._--For years the artist and the decorator
have felt that certain colors seem to advance nearer than others or that
the latter seem to retire more than the former. The author[5] obtained
actual measurements of this phenomenon, but the evidence also indicated
that the effects were not the same for all persons. The phenomenon is very
noticeable in the case of the image of a colored lantern-slide projected
upon a screen and is readily observed when the image consists of letters
of various colors. In the case of red and green letters, for example, the
former appear (to most persons) to be considerably nearer the observer
than the green letters. It has appeared to the writer that the illusion is
apparent even for white letters upon a dark background. In general, the
colors whose dominant hues are of the shorter wave-lengths (violet, blue,
blue-green, green) are retiring and those whose dominant hues are of the
longer wave-lengths (yellow, orange, red) are advancing.

[Illustration: Fig. 68.--For demonstrating retiring and advancing colors.]

In order to obtain experimental measurements two light-tight boxes, each
containing a light-source, were arranged to run independently upon tracks.
Over the front end of each a diaphragm was placed so that the observer saw
two characters as in Fig. 68. A saturated red filter was placed over one
and a saturated blue filter over the other. In a dark room the observer
saw a blue _E_ and a red _H_ standing out in the darkness. One of these
boxes was fastened so as to be immovable and the observer moved the other
to and fro by means of a cord over pulleys until the two characters
appeared equi-distant from him. This was done for a series of distances of
the stationary box from the observer's eye. Nearly all the observers
(without being acquainted with the positions) were obliged to set the red
_H_ further behind the blue _E_ in order that both appeared at the same
distance. This added distance for the red _H_ was as much as 2.4 feet when
the blue _E_ was at a distance of 24 feet. In other words the difference
in the positions of the two was as much as 10 per cent of the total
distance in this case.

Many other interesting data were obtained but most of these are not
particularly of interest here. Some of the experiments tended to show the
effect of certain optical defects in the eye and the variations and even
reversal of the effect for some persons were accounted for by differences
in the curvatures, etc., of certain eye-media for the observers. These
details are not of interest here but it may be of interest to know that
the phenomenon may be accounted for by the chromatic aberration in the
eye. This may not be the true explanation, or it may be only partially
correct. Perhaps some of the illusion is purely psychological in origin.
Certainly the illusion is very apparent to most careful observers.

_Color-sensibility of the Retina._--This aspect was touched upon in
Chapter III, but the differences in the sensibility of various areas of
the retina to various colors are of sufficient importance to be discussed
further. The ability to distinguish light and color gradually fades or
decreases at the periphery of the visual field, but the actual areas of
the fields of perception vary considerably, depending upon the hue or
spectral character of the light reaching the retina. The extreme
peripheral region of the visual field is "color-blind"; that is, color
ceases to be perceived before brightness-perception vanishes in the
outskirts of the visual field. These fields for various colors depend in
size and contour not only upon the hue or spectral character of the
light-stimuli but also upon the intensity and perhaps upon the size of
the stimuli. There is some disagreement as to the relative sizes of these
fields but it appears that they increase in size in the following order:
green, red, blue, white (colorless). The performances of after-images, and
the rates of growth and decay of sensation vary for different colors and
for different areas of the retina, but it would be tedious to peruse the
many details of these aspects of vision. They are mentioned in order that
the reader may take them into account in any specific case.

As already stated, the central part of the visual field--the fovea upon
which we depend for acute vision--contains a yellowish pigmentation, which
is responsible for the term "yellow spot." This operates as a yellow
filter for this central area and modifies the appearance of visual fields
quite the same as if a similar yellow filter was placed in the central
position of the field of vision. The effect of the selectivity of the
"yellow spot" is noticeable in viewing certain colors.

_Purkinje Effect._--The relative sensibility of the retina varies for
different colors with a change in brightness; or it may be better to state
that the relative sensations for various colors alters as the brightness
values are reduced to a low intensity. For example, if a reddish purple
(consisting of red and blue or violet rays) be illuminated in such a
manner that the intensity of illumination, and consequently its
brightness, may be reduced from normal to a low value (approximating
moonlight conditions), it will be seen to vary from reddish purple to
violet. In doing this its appearance changes through the range of purples
from reddish to violet. This can be accomplished by orientation of the
purple surface throughout various angles with respect to the direction of
light or by reducing the illumination by means of screens.

In general the Purkinje effect may be described as an increasing
sensibility of the retina for light of shorter wave-lengths (violet, blue,
green) as the brightness decreases, or a corresponding decreasing
sensibility for light of longer wave-lengths (yellow, orange, red). The
effect may be seen on any colored surfaces at twilight illumination. A
blue and a red flower, which appear of the same brightness before sunset
will begin to appear unequal in this respect as twilight deepens. The red
will become darker more rapidly than the blue if there are no appreciable
changes in the color of the daylight. Finally all color disappears. It is
better to perform this experiment under artificial light, in order that
the spectral character of the illuminant may be certain to remain
constant. In this case rheostats must not be used for dimming the light
because of the attendant changes in color or quality of the light.

The Purkinje effect may be noticed by the careful observer and it is
responsible for certain illusions. Apparently it cannot operate over one
portion of the retina, while the remainder is stimulated by normal
intensities of light.

_Retinal Rivalry._--Many curious effects may be obtained by stimulating
the two retinas with lights, respectively different in color. For example,
it is interesting to place a blue glass before one eye and a yellow or
red one before the other. The two independent monocular fields strive for
supremacy and this rivalry is quite impressive. For a moment the whole
field may appear of one color and then suddenly it will appear of the
other color. Apparently the fluctuation of attention is a factor. Usually
it does not seem to be possible to reach a quiescent state or a perfect
mixture of the two colors in this manner. The dependence of one monocular
field upon the other, and also their independence, are emphasized by this
experiment. It is of interest to consider the illusions of reversible
perspective and others in Chapter V in this connection.

[Illustration: 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


It should be obvious by this time that the lighting of objects or of a
scene can alone produce an illusion, and that it can in still more cases
contribute toward an illusion. Furthermore, there are many cases of
illusions in lighting due to brightness and color. Many effects of
lighting have been described elsewhere with detailed analyses of the
underlying principles, but a condensed survey applying particularly to
illusions will be presented here.

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.

[Illustration: Fig. 70.--A bas-relief lighted from above.]

[Illustration: Fig. 71.--An intaglio lighted from above.]

[Illustration: Fig. 72.--A bas-relief lighted from the left.]

[Illustration: Fig. 73.--An intaglio lighted from the left.]

[Illustration: Fig. 74.--_a._ A disk (above) and a sphere (below) lighted
from overhead. _b._ A disk and a sphere lighted by perfectly diffused
light.]

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.

[Illustration: Fig. 75.--A concave hemispherical cup on the left and a
convex hemisphere on the right lighted by a light-source of large angle
such as a window.]

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.

[Illustration: 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.

[Illustration: 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.

[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.

The artist may suggest brilliant sunlight by means of deep shadow. The old
painters gained color at the expense of light and therefore lowered the
scale of color in their representations of nature. It is interesting to
see how increasing knowledge, as centuries passed, directed painters as it
did others onward toward the truth. Turner was one of the first to abandon
the older methods in an attempt to raise the scale of his paintings toward
a brilliance more resembling nature. By doing this he was able to put
color in shadows as well as in lights. Gradually paintings became more
brilliant. Monet, Claude, and others worked toward this goal until the
brightnesses of paintings reached the limits of pigments. The
impressionists, in their desire to paint nature's light, introduced
something which was nothing more nor less than science. All this time the
true creative artist was introducing science--in fact, illusions--to
produce the perfect illusion which was his goal. A survey of any
representative paintings' gallery shows the result of the application of
more and more knowledge, as the art of painting progressed through the
centuries. Surely we cannot go back to the brown shadows and sombre
landscapes of the past.

In the earliest art, in the efforts of children, in the wall-paintings of
the Egyptians, and in Japanese representation of nature, the process is
selective and not imitative. Certain things are chosen and everything else
is discarded. In such art selection is carried to the extreme. Much of
this simplicity was due to a lack of knowledge. Light and shade, or
shading, was not introduced until science discovered and organized its
facts. Quite in the same manner linear and aerial perspective made their
appearances until in our present art the process of selection is complex.
In our paintings of today objects are modeled by light and shade; they are
related by perspective; backgrounds and surroundings are carefully
considered; the proper emphasis of light, shade and color are given to
certain details. The present complexity provides unprecedented
opportunities for the application of knowledge pertaining to illusions but
it should be understood that this application tends only toward realism of
external things. Idealism in art and realism of character and expression
are accomplished by the same tools--pigments and brushes--as realism of
objective details is attained and there is nothing mysterious in the
masterpieces of this kind. Mystery in art as in other activities is merely
lack of understanding due to inadequate knowledge. Mysteries of today
become facts tomorrow. Science moves with certainty into the unknown,
reaping and binding the facts and dropping them behind where they may be
utilized by those who will.

The painter can imitate aerial perspective although many centuries elapsed
before mankind was keen enough to note its presence in nature. The
atmospheric haze diminishes the brightness of very bright objects and
increases that of dark objects. It blurs the distant details and adds a
tinge of blue or violet to the distance. In painting it is a powerful
illusion which the painter has learned to employ.

The painter can accurately imitate mathematical or linear perspective but
the art of early centuries does not exhibit this feature. In a painting a
tremendously powerful illusion of the third dimension is obtained by
diminishing the size of objects as they are represented in the distance.
Converging lines and the other manifold details of perspective are aiding
the artist in his efforts toward the production of the great illusion of
painting.

The painter cannot imitate focal perspective or binocular perspective. He
can try to imitate the definition in the central portion of the visual
field and the increased blurring toward the periphery. Focal perspective
is not of much importance in painting, because it is scarcely perceptible
at the distances at which paintings are usually viewed. However the
absence of binocular perspective in painting does decrease the
effectiveness of the illusion very markedly. For this reason a painting is
a more successful illusion when viewed with one eye than with two eyes. Of
course, in one of nature's scenes the converse is true because when
viewing it with both eyes all the forms of perspective coöperate to the
final end--the true impression of three dimensions.

The painter may imitate the light and shade of solid forms and thereby
apparently model them. In this respect a remarkable illusion of solid form
or of depth may be obtained. For example, a painted column may be made to
appear circular in cross-section or a circle when properly shaded will
appear to be a sphere. Both of these, of course, are pure illusions. Some
stage paintings are remarkable illusions of depth, and their success
depends chiefly upon linear perspective and shadows. However, the illusion
which was so complete at a distance quite disappears at close range.

The inadequate range of brightnesses or values obtainable by means of
pigments has already been discussed. The sky in a landscape may be
thousands of times brighter than a deep shadow or a hole in the ground. A
cumulus cloud in the sky may be a hundred thousand times brighter than the
deepest shadow. However, the artist must represent a landscape by means of
a palette whose white is only about thirty times brighter than its black.
If the sun is considered we may have in a landscape a range of brightness
represented by millions.

This illustrates the pitiable weakness of pigments alone as
representative media. Will not light _transmitted_ through media some day
be utilized to overcome this inherent handicap of reflecting media? To
what extent is the success of stained glass windows due to a lessening of
this handicap? The range of brightness in this case may be represented by
a black (non-transmitting) portion to the brightness of the background
(artificial or sky) as seen through an area of clear glass. Transparencies
have an inherent advantage over ordinary paintings in this respect and
many effective results may be obtained with them even in photography.

It is interesting to study the effect of greatly increasing the range of
values or brightnesses in paintings by utilizing non-uniform distributions
of light. Let us take a given landscape painting. If a light-source be so
placed that it is close to the brighter areas (perhaps clouds and sky near
the sun) it will illuminate this brighter portion several times more
intensely than the more distant darker portions of the picture (foreground
of trees, underbrush, deep shadows, etc.). The addition to the
effectiveness of the illusion is quite perceptible. This effect of
non-uniform lighting may be carried to the extreme for a painting by
making a positive lantern-slide (rather contrasty) of the painting and
projecting this slide upon the painting in accurate superposition. Now if
the painting is illuminated solely by the "lantern-slide" the range of
contrast or brightness will be enormously increased. The lightest portions
of the picture will now be illuminated by light passing through the almost
totally transparent portions of the slide and the darkest portions by
light greatly reduced by passing through the nearly opaque portions of the
slide. The original range of contrast in the painting, perhaps twenty to
one, is now increased perhaps to more than a thousand to one. This
demonstration will be surprising to anyone and will emphasize a very
important point to the painter.

The painter has at his disposal all the scientific facts of light, color,
and vision. Many of these have been presented elsewhere,[9] and those
pertaining to illusions have been discussed in preceding chapters. These
need not be repeated here excepting a few for the purpose of reminding the
reader of the wealth of material available to the painter and decorator.
Many tricks may be interjected into the foreground for their effect upon
the background and vice versa. For example, a branch of a tree drooping in
the foreground apparently close to the observer, if done well, will give a
remarkable depth to a painting. Modeling of form may be effected to some
extent by a judicious use of the "retiring" and "advancing" colors. This
is one way to obtain the illusion of depth.

After-images play many subtle parts in painting. For example, in a
painting where a gray-blue sky meets the horizon of a blue-green body of
water, the involuntary eye-movements may produce a pinkish line just above
the horizon. This is the after-image of the blue-green water creeping
upward by eye-movements. Many vivid illusions of this character may be
deliberately obtained by the artist. Some of the peculiar restless effects
obtained in impressionistic painting (stippling of small areas with
relatively pure hues) are due to contrasts and after-images.

A painting came to the author's notice in which several after-images of
the sun, besides the image of the sun itself, were disposed in various
positions. Their colors varied in the same manner as the after-image of
the sun. Doubtless the painter strove to give the impression which one has
on gazing at the sun. Whether or not this attempt was successful does not
matter but it was gratifying to see the attempt made.

There are many interesting effects obtainable by judicious
experimentation. For example, if a gray medium be sprayed upon a landscape
in such a manner that the material dries in a very rough or diffusing
surface some remarkable effects of fog and haze may be produced. While
experimenting in this manner a very finely etched clear glass was placed
over a landscape and the combined effect of diffusely reflected light and
of the slight blurring was remarkable. By separating the etched glass from
the painting a slight distance, a very good imitation "porcelain" was
produced. The optical properties of varnishes vary and their effect varies
considerably, depending upon the mode of application. These and many other
details are available to the painter and decorator. An interesting example
among many is a cellulose lacquer dyed with an ordinary yellow dye. The
solution appears yellow by transmitted light or it will color a surface
yellow. By spraying this solution on a metallic object such as a
nickel-plated piece, in a manner that leaves the medium rough or
diffusing, the effect is no longer merely a yellow but a remarkable lustre
resembling gilt. Quite in the same manner many effects of richness, depth
of color, haziness, etc., are obtainable by the artist who is striving to
produce a great illusion.

All the means for success which the painter possesses are also available
to the decorator; however, the latter may utilize some of the illusions of
line, form, irradiation, etc., which the architect encounters. The
decorator's field may be considered to include almost all of the painter's
and much of the architect's. This being the case, little space will be
given to this phase of the subject because painting and architecture are
separately treated. The decorator should begin to realize more fully the
great potentiality of lighting in creating moods or in giving expression
to an interior. The psychology of light and the use of lighting as a mode
of expression have barely been drawn upon by the decorator. Lighting has
already been discussed so it will be passed by at this point.

The practice of hanging pictures on walls which are brilliantly colored is
open to criticism. There are galleries in existence where paintings are
hung on brilliant green or rose walls. The changes in the appearance of
the object due to these highly colored environments are easily
demonstrated by viewing a piece of white paper pinned upon the wall. On
the green wall, the white paper appears pinkish; on the rose wall, it
appears bluish or greenish. A portrait or a picture in which there are
areas of white or delicate tints is subject to considerable distortions in
the appearance of its colors. Similarly, if a woman must have a colored
background, it is well to choose one which will induce the more desirable
tints in her appearance. The designer of gowns certainly must recognize
these illusions of color which may be desirable or undesirable.

The lighting of a picture has already been mentioned, but the discussion
was confined solely to distribution of light. The quality of the light
(its spectral character) may have an enormous influence upon the painting.
In fact with the same painting many illusions may be produced by lighting.
In general, paintings are painted in daylight and they are not the same in
appearance under ordinary artificial light. For this reason the artist is
usually entitled to the preservation of the illusion as he completed it.
By using artificial daylight which has been available for some years, the
painting appears as the artist gave it his last touch. Of course, it is
quite legitimate to vary the quality of light in case the owner desires to
do so, but the purpose here is to emphasize the fact that the quality of
light is a powerful influence upon the appearance of the painting. The
influence is not generally enough recognized and its magnitude is
appreciated by relatively few persons.

All other considerations aside, a painting is best hung upon a colorless
background and black velvet for this purpose yields remarkable results.
Gray velvet is better, when the appearance of the room is taken into
consideration, as it must be. However, the influence of dark surroundings
toward enhancing the illusion is well worth recognizing. In the case of a
special picture or a special occasion, a painting may be exhibited in a
booth--a huge shadow-box not unlike a show-window in which the
light-sources are concealed. Such experiments yield many interesting data
pertaining to the illusions which the painter strives to obtain.

[Illustration: Fig. 82.--Illustrating the apparent distortion of a picture
frame in which the grain of the wood is visible.]

Incidentally on viewing some picture frames in which the grain of the wood
was noticeable, the frames did not appear to be strictly rectangular. The
illusions were so strong that only by measuring the frames could one be
convinced that they were truly rectangular and possessed straight sides.
Two of these are represented in Figs. 82 and 83. In the former, the
horizontal sides appear bent upward in the middle and the two vertical
sides appear bowed toward the right. In Fig. 83, the frame appears
considerably narrower at the left end than at the right. Both these frames
were represented in the original drawings by true rectangles.

Many illusions are to be seen in furniture and in other woodwork in which
the grain is conspicuous. This appears to the author to be an objection in
general to this kind of finish. In Fig. 84 there is reproduced a
photograph of the end of a board which was plane or straight
notwithstanding its warped, or bowed, appearance. The original photographs
were placed so as to be related as shown in the figure. Various degrees of
the illusion are evident. The reader will perhaps find it necessary to
convince himself of the straightness of the horizontal edges by applying a
straight edge. These are examples of the same illusion as shown in Figs.
37 to 40.

[Illustration: Fig. 83.--Another example similar to Fig. 82.]

[Illustration: Fig. 84.--From actual photographs of the end-grain of a
board.]

Perhaps a brief statement regarding the modern _isms_ in art may be of
interest. In considering some of the extreme examples, we must revise our
idea that art is or should be always beautiful. The many definitions of
art would lead us too far afield to discuss them here but in its most
extended and popular sense, art may be considered to mean everything
which we distinguish from nature. Certainly art need not be beautiful,
although it does seem that the world would welcome the beautiful and would
get along contentedly without art that is ugly or repulsive. The modern
_isms_ must be viewed with consideration, for there are many impostors
concealing their inabilities by flocking to these less understood fields.
However, there are many sincere workers--research artists--in the modern
_isms_ and their works may best be described at present as experiments in
the psychology of light, shade, and color. They have cast aside or reduced
in importance some of the more familiar components such as realism and are
striving more deeply to utilize the psychology of light and color. Some of
them admit that they strive to paint through child's eyes and mind--free
from experience, prejudice, and imitation. These need all the scientific
knowledge which is available--and maybe more.

In closing this chapter, it appears necessary to remind the artist and
others that it is far from the author's intention to subordinate the
artist's sensibility to the scientific facts or tools. Art cannot be
manufactured by means of formulae. This would not be true if we knew a
great deal more than we do pertaining to the science of light, color, and
vision. The artist's fine sensibility will always be the dominating
necessity in the production of art. He must possess the ability to compose
exquisitely; he must be able to look at nature through a special
temperament; he must be gifted in eye and in hand; he must be master of
unusual visual and intellectual processes. But knowledge will aid him as
well as those in other activities. A superior acquaintance with scientific
facts lifted past masters above their fellows and what helped Leonardo da
Vinci, Rembrandt, Velasquez, Turner, Claude, Monet, and other masters will
help artists of today. What would not those past masters have accomplished
if they had available in their time the greater knowledge of the present!



XIII

ARCHITECTURE


Many illusions are found in architecture and, strangely enough, many of
these were recognized long before painting developed beyond its primitive
stages. The architecture of classic Greece displays a highly developed
knowledge of many geometrical illusions and the architects of those
far-off centuries carefully worked out details for counteracting them.
Drawings reveal many illusions to the architect, but many are not
predicted by them. The ever-changing relations of lines and forms in
architecture as we vary our viewpoint introduce many illusions which may
appear and disappear. No view of a group of buildings or of the components
of a single structure can be free from optical illusions. We never see in
the reality the same relations of lines, forms, colors, and brightnesses
as indicated by the drawings or blue-prints. Perhaps this is one of the
best reasons for justifying the construction of expensive models of our
more pretentious structures.

No detailed account of the many architectural illusions will be attempted,
for it is easy for the reader to see many of the possibilities suggested
by preceding chapters. However, a few will be touched upon to reveal the
magnitude of the illusory effect and to aid the observer in looking for
or recognizing them, or purely for historical interest. In architecture
the eye cannot be wholly satisfied by such tools as the level, the square,
and the plumb-line. The eye is satisfied only when the _appearance_ is
satisfactory. For the purpose of showing the extent of certain
architectural illusions, the compensatory measures applied by the Greeks
are excellent examples. These also reveal the remarkable application of
science to architecture as compared with the scanty application in
painting of the same period.

During the best period of Grecian art many refinements were applied in
order to correct optical illusions. It would be interesting to know to
what extent the magnitude of the illusions as they appeared to many
persons were actually studied. The Parthenon of Athens affords an
excellent example of the magnitude of the corrections which the designer
thought necessary in order to satisfy the eye. The long lines of the
architrave--the beam which surmounts the columns or extends from column to
column--would appear to sag if it were actually straight. This is also
true of the stylobate, or substructure of a colonnade, and of pediments
and other features. These lines were often convex instead of being
straight as the eye desires to see them.

In the Parthenon, the stylobate has an upward curvature of more than four
inches on the sides of the edifice and of more than two and a half inches
on the east and west fronts. Vertical features were made to incline inward
in order to correct the common appearance of leaning outward at the top.
In the Parthenon, the axes of the columns are not vertical, but they are
inclined inward nearly three inches. They are said also to be inclined
toward each other to such a degree that they would meet at an altitude of
one mile above the ground. The eleven-foot frieze and architrave is
inclined inward about one and one-half inches.

In Fig. 85, _a_ represents the front of a temple as it should appear; _b_
represents its appearance (exaggerated) if it were actually built like _a_
without compensations for optical illusions; _c_ represents it as built
and showing the physical corrections (exaggerated) in order that it may
appear to the eye as _a_ does.

Tall columns if they are actually straight are likely to appear somewhat
shrunken in the middle; therefore they are sometimes made slightly swollen
in order to appear straight. This outward curvature of the profile is
termed an entasis and in the Parthenon column, which is thirty-four feet
in height, amounted to about three-fourths of an inch. In some early
Grecian works, it is said that this correction was overdone but that its
omission entirely is quite unsatisfactory. Some authorities appear to
believe that an excellent compromise is found in the Parthenon columns.

[Illustration: Fig. 85.--Exaggerated illusions in architecture.]

One of the conditions which is responsible for certain illusions and has
been compensated for on occasions is represented in Fig. 86. On the left
are a series of squares of equal size placed in a vertical row. If these
are large so that they might represent stories in a building they will
appear to decrease in size from the bottom upward, because of the
decreasing projection at the eye. This is obvious if the eye is
considered to be at the point where the inclined lines meet. In order to
compensate for the variation in visual angle, there must be a series of
rectangles increasing considerably in height toward the top. The
correction is shown in the illustration. It is stated that an inscription
on an ancient temple was written in letters arranged vertically, and in
order to make them appear of equal size they were actually increased in
size toward the top according to the law represented in Fig. 86. Obviously
a given correction would be correct only for one distance in a given
plane.

[Illustration: Fig. 86.--Illustrating the influence of visual angle upon
apparent vertical height.]

In Chapter VIII the phenomenon of irradiation was discussed and various
examples were presented. It exerts its influence in the arts as elsewhere.
Columns viewed against a background of white sky appear of smaller
diameter than when they are viewed against a dark background. This is
illustrated in Fig. 87 where the white and the black columns are supposed
to be equal in diameter.

The careful observer will find numberless optical illusions and
occasionally he will recognize an attempt on the part of the architect to
apply an illusory effect to his advantage. In Fig. 88 some commonplace
illusions are presented, not for what they are worth, but to suggest how
prevalent they may be. Where the pole or column intersects the arches or
circle, there is an apparent change in the direction of the curved lines.
The different types of arches show different degrees of the illusion. It
may be of interest for the reader to refer to preceding chapters and to
ascertain what types of illusions are involved.

[Illustration: Fig. 87.--Irradiation in architecture.]

If a high wall ends in a series of long horizontal steps at a slightly
inclined sidewalk, the steps are not likely to appear horizontal.

Some remarkable illusions of depth or of solid form are given to flat
surfaces when snow is driven against them so as to adhere in decreasing
amounts similar to shading.

A suggestion of augmented height may be given to a low tower by
decreasing the size of its successive portions more rapidly than demanded
by perspective alone. The same principal can be applied in many ways. For
example, in Fig. 89 the roof appears quite extensive when viewed so that
the end-walls of the structure are not seen. Such illusions find
applications in the moving-picture studio where extensive interiors, great
fortresses, and even villages must be erected within small areas.
Incidentally the camera aids to create the illusion of magnitude in
photographs because it usually magnifies perspective, thereby causing
scenes to appear more extensive in the photographs than in the reality.

[Illustration: Fig. 88.--Some simple geometrical-optical illusions in
architecture.]

Balance in architecture is subject to illusions and might be considered an
illusion itself. For example, our judgment of balance is based largely
upon mechanical laws. A composition must appear to be stable; that is, a
large component such as a tower must not be situated too far from what we
take as a center of gravity, to appear capable of tipping the remainder
of the structure. In physics we would apply the term "moment." Each mass
may be multiplied by its distance from the center of gravity, thus
determining its moment. For a building or other composition to appear
stable the sum of these moments must be zero; that is, those tending to
turn the figure in one direction must be counterbalanced by those tending
to turn it in another direction. In appraising a composition, our
intellect summates the effects of different parts somewhat in this manner
and if satisfactory, balance is considered to have been attained. The
colors of the various components exert an influence in this respect, so it
is seen that illusions may have much to do with the satisfactoriness of
architectural compositions.

[Illustration: Fig. 89.--By decreasing the exposed length of shingles
toward the top a greater apparent expanse is obtained.]

Various illusions of height, of ceiling, composedness, etc., may be
obtained by the color of the ceiling. A dark cornice in an interior may
appear to be unsupported if the walls below are light in color, without
any apparent vertical supports for the cornice. We are then subjected to
the illusion of instability or incongruity. Dark beams of ceilings are not
so obtrusive because our intellect tells us that they are supports passing
over the top of the walls and are therefore able to support themselves.
Color and brightness in such cases are very important.

The architectural details on exteriors evolved under daylighting outdoors
so that their form has been determined by the shadows desired. The
architect leads his lights and shadows around the building modeling it as
he desires. An offset here and a depression there models the exterior in
light and shade. The forms must be powerful enough to resist the
obliterating effect of overcast skies but notwithstanding all precautions
the expression of an exterior varies considerably with nature's lighting.
Indoors the architect has a powerful controllable medium in artificial
light which he may draw upon for producing various expressions or moods in
rooms. The effect of shadows is interesting when viewing some structures
flood-lighted at night. In those cases where the light is directed upward
there is a reversal of shadows which is sometimes very unsatisfactory.

It is interesting to experiment with various ornamental objects lighted
from various directions. For example, a Corinthian capital lighted from
below may produce an unpleasant impression upon the observer. We do not
like to have the dominant light from below, perhaps because it is annoying
to the eyes. Possibly this is an instinct acquired by experience in
snow-fields or on the desert, or it may be a heritage of ancestral
experience gained under these glaring conditions. This dislike manifests
itself when we appraise shadow-effects and therefore our final impression
is tempered by it.

All sculptured objects depend for their appearance upon the lighting, and
they are greatly influenced by it. In sculpture, in a strict sense,
illusions play a lesser part than in other arts. Perhaps in those of very
large proportions various corrections have been applied. A minor detail of
interest is the small cavity in the eye, corresponding to a reversed
cornea. This depression catches a shadow which gives considerable
expression to the eye.



XIV

MIRROR MAGIC


Strictly speaking there are fewer illusions found in the practice of the
magician than is generally supposed; that is, the eye usually delivers
correctly to the intellect, but the judgment errs for various reasons. The
"illusion" is due to false assumptions, to the distracting words, to
unduly accented superfluous movements of the magician; or in general to
downright trickery. Much of the magician's success is due to glibness of
tongue and deftness of fingers, but many of the more notable "tricks" were
those involving the use of mirrors and the control of light. Black
curtains, blackened assistants, and controlled light have played prominent
parts in the older magic, but the principles of these are easily
understood. However, the mirror perhaps has done more to astound the
audience than any other device employed by the magician. For this reason,
and because its effects are commonly termed illusions, some representative
examples will be presented.

In a previous chapter attention was called to the simple but usually
overlooked fact that, for example, the image of a face in a mirror is
reversed as to right and left. When this fact is overlooked we may be
astonished at the changed expression of an intimate friend as we view the
face (reversed) in the mirror. Similarly our own features are reversed as
to right and left and we are acquainted with this reversed image rather
than the appearance of our face as it is. Inasmuch as faces are not
accurately symmetrical and many are quite unsymmetrical the effects of the
mirror are sometimes startling. It might be of interest for the reader to
study his face in the mirror and note that the right ear is the left ear
of the image which he sees. He will also find it of interest to compare
the face of a friend as viewed directly with the appearance of its image
in the mirror. If he desires to see himself as others see him, he can
arrange two mirrors vertically almost at a right-angle. By a little
research he will find an image of his own face, which is not reversed;
that is, an image whose right ear is really his right ear.

A famous "illusion" which astounded audiences was the sphinx illustrated
in Fig. 90. The box was placed upon a table and when opened there was
revealed a Sphinxian head, but why it was called a Sphinx is clothed in
mystery because upon some occasions it talked. As a matter of fact it
belonged to a body which extended downward from the table-top and this
kneeling human being was concealed from the audience by two very clean
plate-glass mirrors _M_ shown in the accompanying diagram. The table
actually appeared to have three legs but the audience if it noticed this
at all assumed the fourth leg was obscured by the foremost leg. The walls,
floor, and ceiling of the box-like recess in which the table was placed
were covered with the same material. It is seen by the diagram that the
mirrors _M_ reflected images of the side walls _W_ and these images were
taken by the audience to be portions of the rear wall _W_. Thus the table
appeared to be open underneath and the possibilities of the apparatus are
evident.

[Illustration: Fig. 90.--An example of a "mirror" illusion.]

The magician with a fine flow of language could dwell at length upon the
coming to life of the head of an ancient statue which he had in the box in
his hand. Walking to the table he could place the box over a trap-door and
by the time he had unlatched the door of the box, the assistant kneeling
under the table could have his head thrust upward through the trap-door of
the table-top into the box. After a few impressive words, supposed to be
Hindoo but in reality were Hoodoo, presto! and the Sphinx was revealed.
It conversed after a period of silence extending back to the days of
Rameses when a wrathful god condemned an unfortunate king to imprisonment
in the stone statue. The original trick awed audiences for many nights and
defied explanation until one night a keen observer noted finger-prints on
what proved to be a mirror. Doubtless a careless accomplice lost his job,
but the damage had been done, for the trick was revealed. This "illusion"
is so effective that it, or variations of it, are still in use.

[Illustration: Fig. 91.--Another example of "mirror magic."]

Another simple case is illustrated in Fig. 91. A large plate-glass mirror
_M_ was placed at an angle of approximately 45 degrees from the floor.
Through a hole in it an assistant's head and shoulders projected and the
edge of the opening was covered with a draped cloth. The audience saw the
image of the ceiling _C_ of the alcove reflected by the mirror but being
ignorant of the presence of the mirror, assumed this image to be the rear
wall. This trick was effective for many years. Obviously the mirrors must
be spotlessly clean and the illuminations of the walls, ceiling, and in
some cases, the floor must be very uniform. Furthermore, no large
conspicuous pattern could be used for lining the box-like recess.

The foregoing examples illustrate the principles involved in the
appearance of ghosts on the stage and of a skeleton or other gruesome
object in place of a human being. The possibilities of mirrors in such
fields are endless and they can be studied on a small scale by anyone
interested. The pseudoscope which produces effects opposite to those of
the stereoscope is an interesting device.

The foregoing is the faintest glimpse of the use of the mirror, but it
does not appear advisable to dwell further upon its use, for after all the
results are not visual illusions in the sense of the term as usually
employed throughout this book.



XV

CAMOUFLAGE


Illusions played many roles in the science and art of deception during the
World War, but they served most prominently in the later stages of the war
upon the sea. Inasmuch as the story of the science of camouflage is not
generally available, it appears worth while to present it briefly. Besides
being of interest, it will reveal to the reader the part that the science
of light, color, lighting, and vision played in deception. Furthermore,
the reader will sense the numberless illusions which are woven into
camouflage as developed in nature, and in human activities. The word
_camouflage_ by origin does not include all kinds of deception; however,
by extension it may and will here signify almost the entire art and
science of deception as found in nature and as practiced in the World War.

_Terrestrial Camouflage._--Camouflage is an art which is the natural
outgrowth of our instinct for concealment and deception when pitting our
wits against those of a crafty prey or enemy. It is an art older than the
human race, for its beginnings may be traced back to the obscurity of the
early ages of the evolution of animal life. The name was coined by the
French to apply to a definite art which developed during the Great War to
a high state, as many other arts developed by drawing deeply upon the
resources of scientific knowledge. With the introduction of this specific
word to cover a vast field of activity in scientifically concealing and
deceiving, many are led to believe that this is a new art, but such is not
the case. However, like many other arts, such as that of flying, the
exigencies of modern warfare have provided an impetus which has resulted
in a highly developed art.

Scientists have recognized for many years, and perhaps more or less
vaguely for centuries, that Nature exhibits wonderful examples of
concealment and deception. The survival of the fittest, as Darwin
expressed his doctrine, included those individuals of a species who were
best fitted by their markings and perhaps by peculiar habits to survive in
the environment in which they lived. Naturally, markings, habits, and
environment became more and more adapted to each other until the species
became in equilibrium with Nature sufficiently to insure its perpetuity.
If we look about us upon animal life we see on every hand examples of
concealing coloration and attitudes designed to deceive the prey or enemy.
The rabbit is mottled because Nature's infinite variety of highlights,
shadows, and hues demand variety in the markings of an animal if the
latter is to be securely hidden. Solid color does not exist in Nature's
landscapes in large areas. The rabbit is lighter underneath to compensate
for the lower intensity of illumination received on these portions. As
winter approaches, animals in rigorous climates need warmer coats, and the
hairs grow longer. In many cases the color of the hairs changes to gray or
white, providing a better coating for the winter environment.

Animals are known to mimic inanimate objects for the sake of safety. For
example, the bittern will stand rigid with its bill pointed skyward for
many minutes if it suspects an enemy. Non-poisonous snakes resemble
poisonous ones in general characteristics and get along in the world on
the reputation of their harmful relatives. The drone-bee has no sting, but
to the casual observer it is a bee and bees generally sting. Some animals
have very contrasting patterns which are conspicuous in shape, yet these
very features disguise the fact that they are animals. Close observation
of fishes in their natural environment provides striking examples of
concealing coloration. Vast works have been written on this subject by
scientists, so it will only be touched upon here.

There are many examples of "mobile" camouflage to be found in Nature.
Seasonal changes have been cited in a foregoing paragraph. The chameleon
changes its color from moment to moment. The flounder changes its color
and _pattern_ to suit its environment. It will even strive to imitate a
black and white checkerboard.

In looking at a bird, animal, insect, or other living thing it is
necessary to place it in its natural environment at least in the
imagination, before analyzing its coloration. For example, a male mallard
duck hanging in the market is a very gaudy object, but place it in the
pond among the weeds, the green leaves, the highlights, and the shadows,
and it is surprisingly inconspicuous. The zebra in the zoo appears to be
marked for the purpose of heralding its presence anywhere in the range of
vision, but in its reedy, bushy, grassy environment it is sufficiently
inconspicuous for the species to survive in Nature's continuous warfare.

Thus studies of Nature reveal the importance of general hue, the necessity
for broken color or pattern, the fact that black spots simulate shadows or
voids, the compensation for lower illumination by counter-shading, and
many other facts. The artist has aided in the development of camouflage,
but the definite and working basis of all branches of camouflage are the
laws and facts of light, color, and vision as the scientist knows them.

Just as lower animal life has unconsciously survived or evolved by being
fitted to do so, mankind has consciously, or at least instinctively,
applied camouflage of various kinds to fool his prey or his enemy. Many of
us in hunting ducks have concealed the bow of our sneak-boat with mud and
weeds, or in the season of floating ice, with a white cloth. In our quest
of water fowl we use decoys and grass suits. The Esquimau stalks his game
behind a piece of ice. In fact, on every hand we find evidences of this
natural instinct. The Indian painted his face and body in a variety of
colors and patterns. Did he do this merely to be hideous? It seems very
possible that the same instinct which made him the supreme master of
wood-craft caused him to reap some of the advantages of concealment due to
the painting of his face and body.

In past wars there is plenty of evidence that concealment and deception
were practiced to the full extent justifiable by the advantages or
necessity. In the World War the advent of the airplane placed the third
dimension in reconnaissance and called for the application of science in
the greatly extended necessity for concealment and deception. With the
advent of the airplane, aerial photography became a more important factor
than visual observation in much of the reconnaissance. This necessitated
that camouflage in order to be successful had to meet the requirements of
the photographic eye, as well as that of the human eye. In other words,
the special characteristics of the colors used had to be similar to those
of Nature's colors. For example, chlorophyl, the green coloring matter of
vegetation, is a peculiar green as compared with green pigments. When
examined with a spectroscope it is seen to reflect a band of deep red
light not reflected by ordinary pigments. In considering this aspect it is
well to bear in mind that the eye is a synthetic apparatus; that is does
not analyze color in a spectral sense. An artist who views color
subjectively and is rarely familiar with the spectral basis may match a
green leaf perfectly with a mixture of pigments. A photographic plate, a
visual filter, or a spectroscope will reveal a difference which the
unaided eye does not.

Some time before the Great War began, it occurred to the writer that
colored filters could be utilized in aiding vision by increasing the
contrast of the object to be viewed against its surroundings.[9] Studies
were made of various filters, made with the object of the experiment in
mind, in viewing the uniforms of various armies. Further developments were
made by applying the same principles to colored lights and painted
pictures. Many of these have been described elsewhere. With the
development of the science of camouflage, filters came into use for the
detection of camouflage. As a result of the demand for avoiding detection
by photographic plates and by various colored filters, some paints
provided for the camoufleur were developed according to the spectral
requirements. Many other applications of science were developed so that
camouflage can now be called an art based upon sound scientific
principles.

Natural lighting is so variable that it is often impossible to provide
camouflage which will remain satisfactory from day to day; therefore, a
broad knowledge of Nature's lighting is necessary in order to provide the
best compromise. There are two sources of light in the daytime, namely,
the sun and the sky. The relative amounts of light contributed by these
two sources is continually changing. The sky on cloudless days contributes
from one-tenth to one-third of the total light received by a horizontal
surface at noon. Light from the sky and light reflected from the
surroundings illuminate the shadows. These shadows are different in color
than highlights, although these finer distinctions may be ignored in most
camouflage because color becomes less conspicuous as the distance of
observation increases. In general, the distribution of brightness or light
and shade is the most important aspect to be considered.

The camoufleur worries over shadows more than any other aspect generally.
On overcast days camouflage is generally much more successful than on
sunny days. Obviously, counter-shading is resorted to in order to
eliminate shadows, and where this is unsuccessful confusion is resorted to
by making more shadows. The shape and orientation of a building is very
important to those charged with the problem of rendering it inconspicuous
to the enemy, but little attention has been paid to these aspects. For
example, a hangar painted a very satisfactory dull green will be
distinguishable by its shape as indicated by its shadow and shaded sides.
In this zone a hangar, for example, would be more readily concealed if its
length lay north and south. Its sides could be brought with a gradual
curve to the ground and its rear, which is during most of the day in
shadow, could be effectively treated to conceal the shadow. A little
thought will convince the reader of the importance of shape and
orientation.

Broken color or pattern is another fundamental of camouflage which, of
course, must be adapted to its environment. For our trucks, cannon, and
many other implements of war, dark green, yellow, dark blue, light gray,
and other colors have been used in a jumble of large patterns. A final
refinement is that of the blending of these colors at a distance, where
the eye no longer resolves the individual patches, to a color which
simulates the general hue of the surroundings. For example, red and green
patches at a distance blend to yellow; yellow and blue patches blend to a
neutral gray if suitably balanced, but if not, to a yellow-gray or a
blue-gray; red, green, and blue if properly balanced will blend to a gray;
black, white and green patches will blend to a green shade, and so on.
These facts are simple to those who are familiar with the science of
light and color, but the artist, whose knowledge is based upon the mixture
of pigments, sometimes errs in considering this aspect of color-blending
by distance. For example, it is not uncommon for him to state that at a
distance yellow and blue patches blend to make green, but the addition of
lights or of juxtaposed colors is quite different in result from the
addition of pigments by intimately mixing them.

In constructing such a pattern of various colors it is also desirable to
have the final mean brightness approximate that of the general
surroundings. This problem can be solved by means of the photometer and a
formula provided, which states, for example, that a certain percentage of
the total area be painted in gray, another percentage in green, and so on.
The photometer has played an important rôle in establishing the scientific
basis of camouflage. The size of the pattern must be governed by the
distance at which it is to be viewed, for obviously if too small the
effect is that of solid color, and if too large it will render the object
conspicuous, which is a disadvantage ranking next to recognizable.

Where the artist is concerned with a background which does not include the
sky, that is, where he deals only with _illuminated_ objects on the earth,
his trained eye is valuable provided the colors used meet the demands made
by photographic plates and visual color-filters. In other words, the sky
as a background gives trouble to all who are unfamiliar with scientific
measurements. The brightnesses of sky and clouds are outside the scale of
brightnesses ordinarily encountered in a landscape. Many interesting
instances of the artist's mistakes in dealing with these backgrounds could
be presented; however, the artist's trained eye has been a great aid in
constructing patterns and various other types of camouflage. One of the
most conspicuous aspects of the earth's surface is its texture. From great
heights it appears flat, that is, rolling land is ironed out and the
general contour of the ground is flattened. However, the element of
texture always remains. This is the chief reason for the extensive use of
netting on which dyed raffia, foliage, pieces of colored cloth, etc., are
tied. Such network has concealed many guns, headquarters, ammunition
dumps, communication trenches, roadways, etc. When this has been well done
the concealment is perfect.

One of the greatest annoyances to the camoufleur is the lack of dullness
or "flatness" of the paints, fabrics, and some of the other media used.
When viewed at some angles the glint of highlights due to specular
reflection renders the work very conspicuous. For this reason natural
foliage or such material as dyed raffia has been very successful.

Systems of network and vertical screens have been extensively employed on
roadways near the front, not for the purpose of concealing from the enemy
the fact that the roadways exist, but to make it necessary to shell the
entire roadway continually if it is hoped to prevent its use.

Although the camoufleur is provided with a vast amount of material for his
work, many of his requirements are met by the material at hand.
Obviously, the most convenient method of providing concealment for a
given environment is to use the materials of the environment. Hence,
rubbish from ruined buildings or villages supplies camouflage for guns,
huts, etc., in that environment. In woods the material to simulate the
woods is at hand. Many of these aspects are so obvious to the reader that
space will not be given to their consideration. The color of the soil is
important, for if it is conspicuous the camoufleur must provide screens of
natural turf.

In this great game of hocus-pocus many deceptions are resorted to.
Replicas of large guns and trenches are made; dummy soldiers are used to
foil the sniper and to make him reveal his location, and papier-maché
horses, trees, and other objects conceal snipers and observers and afford
listening posts. Gunners have been dressed in summer in green flowing
robes. In winter white robes have been utilized. How far away from modern
warriors are all the usual glitter and glamour of military impedimenta in
the past parades of peace time! The armies now dig in for concealment. The
artillery is no longer invisible behind yonder hill, for the eyes of the
aerial observer of the camera reveal its position unless camouflaged for
the third dimension.

In the foregoing only the highlights of a vast art have been viewed, but
the art is still vaster, for it extends into other fields. Sound must
sometimes be camouflaged and this can only be done by using the same
medium--sound. In these days of scientific warfare it is to be expected
that the positions of enemy guns would be detected by other means than
employed in the past. A notable method is the use of velocity of sound.
Records are made at various stations of the firing of a gun and the
explosion of the shell. By trigonometric laws the position of the gun is
ascertained. It is said that the Germans fired a number of guns
simultaneously with the "75-mile" gun in order to camouflage its location.
The airplane and submarine would gladly employ sound camouflage in order
to foil the sound detector if practicable solutions were proposed.

The foregoing is a brief statement of some of the fundamental principles
of land camouflage. Let us now briefly consider the eyes of the enemy. Of
course, much concealment and deception is devised to foil the observer who
is on the ground and fairly close. The procedure is obvious to the average
imagination; however, the reader may not be acquainted with the aerial
eyes from which concealment is very important. As one ascends in an
airplane to view a landscape he is impressed with the inadequacy of the
eyes to observe the vast number of details and of the mind to retain them.
Field glasses cannot be used as satisfactorily in an airplane as on solid
ground, owing to vibration and other movements. The difference is not as
great in the huge flying boats as it is in the ordinary airplane. The
camera can record many details with higher accuracy than the eye. At an
altitude of one mile the lens can be used at full aperture and thus very
short exposures are possible. This tends to avoid the difficulty due to
vibration. When the plates are developed for detail and enlargements are
made, many minute details are distinguishable. Furthermore, owing to the
fact that the spectral sensibilities of photographic emulsions differ from
that of the eye, contrasts are brought out which the eye would not see.
This applies also to camouflage which is devised merely to suit the eye.
Individual footprints have been distinguished on prints made from
negatives exposed at an altitude of 6000 feet. By means of photography,
daily records can be made if desired and these can be compared. A slight
change is readily noted by such comparison by skilled interpreters of
aerial photographs. The disappearance of a tree from a clump of trees may
arouse suspicion. Sometimes a wilted tree has been noted on a photograph
which naturally attracts attention to this position. It has been said that
the belligerents resorted to transplanting trees a short distance at a
time from day to day in order to provide clearance for newly placed guns.
By paths converging toward a certain point, it may be concluded from the
photographs that an ammunition dump or headquarters is located there even
though the position itself was well camouflaged. Continuous photographic
records may reveal disturbances of turf and lead to a more careful
inspection of the region for sapping operations, etc. By these few details
it is obvious that the airplane is responsible for much of the development
of camouflage on land, owing to the necessity which it created for a much
more extensive concealment. The entire story of land camouflage would
overflow the confines of a volume, but it is hoped that the foregoing will
aid the reader in visualizing the magnitude of the art and the scientific
basis upon which terrestial camouflage is founded.

_Marine Camouflage._--At the time of the Spanish-American war, our
battleships were painted white, apparently with little thought of
attaining low visibility. Later the so-called "battleship gray" was
adopted, but it has been apparent to close observers that this gray is in
general too dark. Apparently it is a mixture of black and white. The ships
of the British navy were at one time painted black, but preceding the
Great War their coats were of a warm dark gray. Germany adopted dark gray
before the close of the last century and Austria adopted the German gray
at the outbreak of the war. The French and Italian fleets were also
painted a warm gray. This development toward gray was the result of an aim
toward attaining low visibility. Other changes were necessitated by
submarine warfare which will be discussed later.

In the early days of unrestricted submarine warfare many schemes for
modifying the appearance of vessels were submitted. Many of these were
merely wild fancies with no established reasoning behind them. Here again
science came to the rescue and through research and consultation, finally
straightened out matters. The question of low visibility for vessels could
be thoroughly studied on a laboratory scale, because the seascape and
natural lighting conditions could be reproduced very closely. Even the
general weather conditions could be simulated, although, of course, the
experiments could be prosecuted outdoors with small models, as indeed
they were. Mr. L. A. Jones[10] carried out an investigation on the shore
of Lake Ontario, and laboratory experiments were conducted by others with
the result that much light was shed on the questions of marine camouflage.
This work confirmed the conclusion of the author and others that our
battleship gray was too dark. Of course, the color best adapted is that
which is the best compromise for the extreme variety in lighting and
weather conditions. These vary in different parts of the world, so
naturally those in the war zone were of primary importance. All camouflage
generally must aim to be a compromise best suited for average or
dominating conditions. For example, in foggy weather a certain paint may
render a ship of low visibility, but on a sunny day the ship might be
plainly visible. However, if ships are rendered of low visibility for even
a portion of the time it is obvious that an advantage has been gained.
Cloudiness increases generally from the equator northward, as indicated by
meteorological annals.

In order to study low visibility a scale of visibility must be
established, and it is essential to begin with the fundamentals of vision.
We distinguish objects by contrasts in brightness and in color and we
recognize objects by these contrasts which mold their forms. In researches
in vision it is customary to devise methods by which these contrasts can
be varied. This is done by increasing or decreasing a veil of luminosity
over the object and its surroundings and by other means. Much work has
been done in past years in studying the minimum perceptible contrast, and
it has been found to vary with hue, with the magnitude of brightness, and
with the size of the image, that is, with the distance of an object of
given size. In such problems as this one much scientific work can be drawn
upon. A simple, though rough, scale of visibility may be made by using a
series of photographic screens of different densities. A photographic
screen is slightly diffusing, still the object can be viewed through it
very well. Such methods have been employed by various investigators in the
study of visibility.

Owing to the curvature of the earth, the distance at which a vessel can be
seen on a clear day is limited by the height of the observer and of the
ship's superstructure. For an observer in a certain position the
visibility range varies as the square root of the distance of the object
from him. Such data are easily available, so they will not be given here.
So far we have considered the ship itself when, as a matter of fact, on
clear days the smoke cloud emitted by the ship is usually visible long
before a ship's superstructure appears on the horizon. This led to the
prevention of smoke by better combustion, by using smokeless fuels, etc.

The irregular skyline of a ship is perhaps one of the most influential
factors which tend to increase its visibility. Many suggestions pertaining
to the modification of the superstructure have been made, but these are
generally impracticable. False work suffers in heavy seas and high winds.

After adopting a suitable gray as, a "low-visibility" paint for ships,
perhaps the next refinement was counter shading; that is, shadows were
painted a lighter color, or even white. The superstructure was painted in
some cases a light blue, with the hope that it would fade into the distant
horizon. However, the effectiveness of the submarine demanded new
expedients because within its range of effectiveness no ingenuity could
render its intended prey invisible. The effective gun-fire from submarines
is several miles and torpedoes can be effective at these distances.
However, the submarine prefers to discharge the torpedo at ranges within a
mile. It is obvious that, in average weather, low visibility ceases to be
very effective against the submarine. The movement of a target is of much
less importance in the case of gun-fire than in the case of the torpedo
with its relatively low velocity. The submarine gunner must have the
range, speed, and course of the target in order to fire a torpedo with any
hope of a hit. Therefore, any uncertainties that could be introduced
pertaining to these factors would be to the advantage of the submarine's
prey. For example, low visibility gave way to confusibility in the
discussions of defence against the submarine and the slogan, "A miss is as
good as a mile" was adopted. The foregoing factors cannot be determined
ordinarily with high accuracy, so that it appeared possible to add
somewhat to the difficulties of the submarine commander.

Many optical illusions have been devised and studied by scientists. In
fact, some of these tricks are well known to the general reader. Straight
lines may appear broken, convergent, or divergent by providing certain
patterns or lines intermingled with them. Many of these were applied to
models in laboratory experiments and it has been shown that confusion
results as to the course of the vessel. The application of these on
vessels has resulted in the grotesque patterns to be seen on ships during
the latter stage of the war. It is well known that these illusions are
most effective when the greatest contrasts are used, hence black and white
patterns are common. Color has not been utilized as definitely as pattern
in confusibility, although there is a secondary aim of obtaining low
visibility at a great distance by properly balancing the black, white, and
other colors so that a blue-gray results at distances too great for the
individual patterns to be resolved by the eye. Color could be used for the
purpose of increasing the conclusion by apparently altering the
perspective. For example, blue and red patterns on the same surface do not
usually appear at the same distance, the red appearing closer than the
blue.

[Illustration: Fig. 92.--A primary stage in the evolution of the use of
geometrical-optical illusions on ships.]

Such apparently grotesque patterns aimed to distort the lines of the ship
and to warp the perspective by which the course is estimated. This was
the final type of marine camouflage at the close of the war. Besides
relying upon these illusions, ships zigzagged on being attacked and aimed
in other ways to confuse the enemy. No general attempt was made to
disguise the bow, because the bow-wave was generally visible. However,
attempts have been made to increase it apparently and even to provide one
at the stern. In fact, ingenuity was heavily drawn upon and many
expedients were tried.

After low-visibility was abandoned in favor of the optical illusion for
frustrating the torpedo-attack by the submarine, there was a period during
which merely a mottled pattern was used for vessels. Gradually this
evolved toward such patterns as shown in Fig. 92. In this illustration it
is seen that the optical-illusion idea has taken definite form. During the
period of uncertainty as to the course the pattern should take, a
regularity of pattern was tried, such as illustrated in Figs. 93 and 94.
Finally, when it dawned more or less simultaneously upon various
scientific men, who were studying the problems of protecting vessels upon
the seas, that the geometrical-optical illusion in its well-known forms
was directly adaptable, renewed impetus was given to investigation. The
scientific literature yielded many facts but the problems were also
studied directly by means of models. The latter study is illustrated by
Figs. 95 and 96, the originals having been furnished by Mr. E. L.
Warner,[11] who among others prosecuted a study of the application of
illusions to vessels. The final results were gratifying, as shown to some
extent in Figs. 97 and 98, also kindly furnished by Mr. Warner. It is
seen that these patterns are really deceiving as to the course of the
vessel.

[Illustration: Figs. 93 and 94.--Attempts at distortion of outline which
preceded the adoption of geometrical-optical illusions for ships.]

[Illustration: Figs. 95 and 96.--Illustrating the use of models by the
Navy Department in developing the geometrical-illusion for ships.]

The convoy system is well known to the reader. This saved many vessels
from destruction. Vessels of the same speed were grouped together and
steamed in flocks across the Atlantic. Anyone who has had the extreme
pleasure of looking down from an airplane upon these convoys led by
destroyers and attended by chasers is strongly impressed with the old
adage, "In unity there is strength."

Before the war began, a Brazilian battleship launched in this country was
provided with a system of blue lights for use when near the enemy at
night. Blue was adopted doubtless for its low range compared with light of
other colors. We know that the setting sun is red because the atmospheric
dust, smoke, and moisture have scattered and absorbed the blue and green
rays more than the red and yellow rays. In other words the penetrating
power of the red and yellow is greater than that of the blue rays. This
country made use of this expedient to some extent. Of course, all other
lights were extinguished and portholes were closed in ocean travel during
the submarine menace.

[Illustration: Figs. 97 and 98.--Examples of the geometrical-optical
illusion as finally applied.]

Naturally smoke-screens were adopted as a defensive measure on sea as well
as on land. Destroyers belch dense smoke from their stacks in order to
screen battleships. Many types of smoke-boxes have been devised or
suggested. The smoke from these is produced chemically and the apparatus
must be simple and safe. If a merchantman were attacked by a submarine
immediately smoke-boxes would be dumped overboard or some which were
installed on deck would be put into operation and the ship would be
steered in a zigzag course. These expedients were likely to render
shell-fire and observations inaccurate. This mode of defense is obviously
best suited to unarmed vessels. In the use of smoke-boxes the direction
and velocity of the wind must be considered. The writer is unacquainted
with any attempts made to camouflage submarines under water, but that this
can be done is evident from aerial observations. When looking over the
water from a point not far above it, as on a pier, we are unable to see
into the water except at points near us where our direction of vision is
not very oblique to the surface of the water. The brightness of the
surface of water is due to mirrored sky and clouds ordinarily. For a
perfectly smooth surface of water, the reflection factor is 2 per cent for
perpendicular incidence. This increases only slightly as the obliquity
increases to an angle of about 60 degrees. From this point the
reflection-factor of the surface rapidly increases, becoming 100 per cent
at 90 degrees incidence. This accounts for the ease with which we can see
into the water from a position directly overhead and hence the airplane
has been an effective hunter of submerged submarines. The depth at which
an object can be seen in water depends, of course, upon its clarity. It
may be surprising to many to learn that the brightness of water, such as
rivers, bays, and oceans, as viewed perpendicularly to its surface, is
largely due to light diffused within it. This point became strikingly
evident during the progress of work in aerial photometry.

A submerged submarine may be invisible for two reasons: (1) It may be deep
enough to be effectively veiled by the luminosity of the mass of water
above it (including the surface brightness) or, (2) It may be of the
proper brightness and color to simulate the brightness and color of the
water. It is obvious that if it were white it would have to attain
concealment by submerging deeply. If it were a fairly dark greenish-blue
it would be invisible at very small depths. In fact, it would be of very
low visibility just below the surface of the water. By the use of the
writer's data on hues and reflection-factors of earth and water areas it
would be easy to camouflage submarines effectively from enemies overhead.
The visibility of submarines is well exemplified by viewing large fish
such as sharks from airships at low altitudes. They appear as miniature
submarines dark gray or almost black amid greenish-blue surroundings.
Incidentally, the color of water varies considerably from the dirty
yellowish-green of shallow inland waters containing much suspended matter
to the greenish-blue of deep clear ocean waters. The latter as viewed
vertically are about one-half the brightness of the former under the same
conditions and are decidedly bluer.

_The Visibility of Airplanes._--In the Great War the airplane made its
début in warfare and in a short time made a wonderful record, yet when
hostilities ceased aerial camouflage had not been put on a scientific
basis. No nation had developed this general aspect of camouflage
systematically or to an extent comparable with the developments on land
and sea. One of the chief difficulties was that scientific data which were
applicable were lacking. During the author's activities as Chairman of the
Committee on Camouflage of the National Research Council he completed an
extensive investigation[12] of the fundamentals upon which the attainment
of low visibility for airplanes must be based. Solutions of the problems
encountered in rendering airplanes of low visibility resulted and various
recommendations were made, but the experiences and data will be drawn upon
here only in a general way. In this general review details would consume
too much space, for the intention has been to present a broad view of the
subject of camouflage.

The visibility of airplanes presents some of the most interesting problems
to be found in the development of the scientific basis for camouflage. The
general problem may be subdivided according to the type of airplane, its
field of operation, and its activity. For example, patrol craft which fly
low over our own lines would primarily be camouflaged for low visibility
as viewed by enemies above. (See Fig. 99.) High-flying craft would be
rendered of low visibility as viewed primarily by the enemy below.
Airplanes for night use present other problems and the visibility of
seaplanes is a distinct problem, owing to the fact that the important
background is the water, because seaplanes are not ordinarily high-flying
craft. In all these considerations it will be noted that the activity of
the airplanes is of primary importance, because it determines the lines
of procedure in rendering the craft of low visibility. This aspect is too
complicated to discuss thoroughly in a brief résumé.

[Illustration: Fig. 99.--Representative earth backgrounds for an airplane
(uncamouflaged) as viewed from above.]

The same fundamentals of light, color, and vision apply in this field as
in other fields of camouflage, but different data are required. When
viewing aircraft from above, the earth is the background of most
importance. Cumulus clouds on sunny days are generally at altitudes of
4000 to 7000 feet. Clouds are not always present and besides they are of
such a different order of brightness from that of the earth that they
cannot be considered in camouflage designed for low visibility from
above. In other words, the compromise in this case is to accept the earth
as a background and to work on this basis. We are confronted with seasonal
changes of landscape, but inasmuch as the summer landscape was of greatest
importance generally, it was the dominating factor in considering low
visibility from above.

On looking down upon the earth one is impressed with the definite types of
areas such as cultivated fields, woods, barren ground and water. Different
landscapes contain these areas in various proportions, which fact must be
considered. Many thousand determinations of reflection-factor and of
approximate hue were made for these types of areas, and upon the mean
values camouflage for low visibility as viewed from above was developed. A
few values are given in the accompanying table, but a more comprehensive
presentation will be found elsewhere.[12]


_Mean Reflection-Factors_

(From thousands of measurements made by viewing vertically downward during
summer and fall from various altitudes.)

                                            Per Cent

  Woods                                        4.3
  Barren ground                               13.0
  Fields (grazing land and growing crops)      6.8
  Inland water (rivers and bays)               6.8
  Deep ocean water                             3.5
  Dense clouds                                78.0

Wooded areas are the darkest general areas in a landscape and possess a
very low reflection-factor. From above one sees the deep shadows
interspersed among the highlights. These shadows and the trapping of
light are largely responsible for the low brightness or apparent
reflection-factor. This is best illustrated by means of black velvet. If a
piece of cardboard is dyed with the same black dye as that used to dye the
velvet, it will diffusely reflect 2 or 3 per cent of the incident light,
but the black velvet will reflect no more than 0.5 per cent. The velvet
fibers provide many light traps and cast many shadows which reduce the
relative brightness or reflection-factor far below that of the flat
cardboard. Cultivated fields on which there are growing crops are nearly
twice as bright as wooded areas, depending, of course, upon the denseness
of the vegetation. Barren sunbaked lands are generally the brightest large
areas in a landscape, the brightness depending upon the character of the
soil. Wet soil is darker than dry soil, owing to the fact that the pores
are filled with water, thus reducing the reflection-factor of the small
particles of soil. A dry white blotting paper which reflects 75 per cent
of the incident light will reflect only about 55 per cent when wet.

Inland waters which contain much suspended matter are about as bright as
grazing land and cultivated fields. Shallow water partakes somewhat of the
color and brightness of the bed, and deep ocean water is somewhat darker
than wooded areas. Quiet stagnant pools or small lakes are sometimes
exceedingly dark; in fact, they appear like pools of ink, owing to the
fact that their brightness as viewed vertically is almost entirely due to
surface reflection. If it is due entirely to reflection at the surface,
the brightness will be about 2 per cent of the brightness of the zenith
sky. That is, when viewing such a body of water vertically one sees an
image of the zenith sky reduced in brightness to about 2 per cent.

The earth patterns were extensively studied with the result that definite
conclusions were formulated pertaining to the best patterns to be used.
Although it is out of the question to present a detailed discussion of
this important phase in this résumé, attention will be called to the
manner in which the earth patterns diminish with increasing altitude. The
insert in Fig. 100 shows the actual size of an image of a 50-foot airplane
from 0 to 16,000 feet below the observer as compared with corresponding
images (to the same scale) of objects and areas on the earth's surface
10,000 feet below the observer.

For simplicity assume a camera lens to have a focal length equal to 10
inches, then the length _x_ of the image of an object 100 feet long will
be related to the altitude _h_ in this manner:

   _x_      100
  ----- =  -----  or _xh_ = 1000
    10      _h_

By substituting the values of altitude _h_ in the equation the values of
the length _x_ of the image are found. The following values illustrate the
change in size of the image with altitude:

  Altitude _h_ in feet            Size of image _x_ in inches

         1,000                                1.00
         2,000                                0.50
         3,000                                0.33
         4,000                                0.25
        10,000                                0.10
        20,000                                0.05

It is seen that the image diminishes less rapidly in size as the altitude
increases. For example, going from 1000 feet to 2000 feet the image is
reduced to one-half. The same reduction takes place in ascending from
10,000 to 20,000 feet. By taking a series of photographs and knowing the
reduction-factor of the lens it is a simple matter to study pattern. An
airplane of known dimensions can be placed in the imagination at any
altitude on a photograph taken at a known altitude and the futility of
certain patterns and the advantages of others are at once evident.

[Illustration: Fig. 100.--Illustrating the study of pattern for airplanes.
The photograph was taken from an altitude of 10,000 feet. The insert shows
the relative lengths (vertical scale) of an airplane of 50-foot spread at
various distances below the observer.]

It is impracticable to present colored illustrations in this résumé and
values expressed in numbers are meaningless to most persons, so a few
general remarks will be made in closing the discussion of low visibility
as viewed from above in spring, summer and fall. A black craft is of much
lower visibility than a white one. White should not be used. The paints
should be very dark shades. The hues are approximately the same for the
earth areas as seen at the earth's surface. Inland waters are a dirty
blue-green or bluish-green, and deep ocean water is a greenish-blue when
viewed vertically, or nearly so. Mean hues of these were determined
approximately.

Before considering other aspects of camouflage it is well to consider such
features as haze, clouds and sky. There appear to be two kinds of haze
which the writer will arbitrarily call earth and high haze, respectively.
The former consists chiefly of dust and smoke and usually extends to an
altitude of about one mile, although it occasionally extends much higher.
Its upper limit is very distinct, as seen by the "false" horizon. This
horizon is used more by the pilot when flying at certain altitudes than
the true horizon. At the top of this haze cumulus clouds are commonly seen
to be poking out like nearly submerged icebergs. The upper haze appears
somewhat whiter in color and appears to extend sometimes to altitudes of
several or even many miles. The fact that the "earth" haze may be seen to
end usually at about 5000 to 6000 feet and the upper haze to persist even
beyond 20,000 feet has led the author to apply different names for
convenience. The upper limit of the "earth" haze is determined by the
height of diurnal atmospheric convection. Haze aids in lowering the
visibility of airplanes by providing a luminous veil, but it also operates
at some altitudes to increase the brightness of the sky, which is the
background in this case.

The sky generally decreases considerably in brightness as the observer
ascends. The brightness of the sky is due to scattered light, that is, to
light being reflected by particles of dust, smoke, thinly diffused clouds,
etc. By making a series of measurements of the brightness of the zenith
sky for various altitudes, the altitude where the earth haze ends is
usually plainly distinguishable. Many observations of this character were
accumulated. In some extreme cases the sky was found to be only one-tenth
as bright when observed at high altitudes of 15,000 to 20,000 feet as seen
from the earth's surface. This accounts partly for the decrease in the
visibility of an airplane as it ascends. At 20,000 feet the sky was found
to contribute as little as 4 per cent of the total light on a horizontal
plane and the extreme harshness of the lighting is very noticeable when
the upper sky is cloudless and clear.

Doubtless, it has been commonly noted that airplanes are generally very
dark objects as viewed from below against the sky. Even when painted white
they are usually much darker than the sky. As they ascend the sky above
them becomes darker, although to the observer on the ground the sky
remains constant in brightness. However, in ascending, the airplane is
leaving below it more and more luminous haze which acts as a veil in
aiding to screen it until, when it reaches a high altitude, the
combination of dark sky behind it and luminous haze between it and the
observer on the ground, it becomes of much lower visibility. Another
factor which contributes somewhat is its diminishing size as viewed from a
fixed position at the earth. The minimum perceptible contrast becomes
larger as the size of the contrasting patch diminishes.

Inasmuch as there is not enough light reflected upward from the earth to
illuminate the lower side of an opaque surface sufficiently to make it as
bright as the sky ordinarily, excepting at very high altitudes for very
clear skies, it is necessary, in order to attain low visibility for
airplanes as viewed from below, to supply some additional illumination to
the lower surfaces. Computations have shown that artificial lighting is
impracticable, but measurements on undoped airplane fabrics indicate that
on sunny days a sufficient brightness can be obtained from direct sunlight
diffused by the fabric to increase the brightness to the order of
magnitude of the brightness of the sky. On overcast days an airplane will
nearly always appear very much darker than the sky. That is, the
brightness of the lower sides can in no other manner be made equal to that
of the sky. However, low visibility can be obtained on sunny days which is
an advantage over high visibility at all times, as is the case with
airplanes now in use. Many observations and computations of these and
other factors have been made, so that it is possible to predict results.
Transparent media have obvious advantages, but no satisfactory ones are
available at present.

Having considered low visibility of aircraft as viewed from above and from
below, respectively, it is of interest to discuss briefly the possibility
of attaining both of these simultaneously with a given airplane. Frankly,
it is not practicable to do this. An airplane to be of low visibility
against the earth background must be painted or dyed very dark shades of
appropriate color and pattern. This renders it almost opaque and it will
be a very dark object when viewed against the sky. If the lower surfaces
of the airplane are painted as white as possible the airplane still
remains a dark object against the blue sky and a very dark object against
an overcast sky, except at high altitudes. In the latter cases the
contrast is not as great as already explained. A practicable method of
decreasing the visibility of airplanes at present as viewed from below is
to increase the brightness by the diffuse transmission of direct sun-light
on clear days. On overcast days clouds and haze must be depended upon to
screen the craft.

In considering these aspects it is well to recall that the two sources of
light are the sun and the sky. Assuming the sun to contribute 80 per cent
of the total light which reaches the upper side of an opaque horizontal
diffusing surface at midday at the earth and assuming the sky to be
cloudless and uniform in brightness, then the brightness of the horizontal
upper surface will equal 5 _RB_, where _R_ is the reflection-factor of the
surface and _B_ is the brightness (different in the two cases) of the sky.
On a uniformly overcast day the brightness of the surface would be equal
to _RB_. Now assuming _R{e}_ to be the mean reflection-factor of the
earth, then the lower side of a horizontal opaque surface suspended in the
air would receive light in proportion to _R{e}B_. If this lower surface
were a perfect mirror or a perfectly reflecting and diffusing surface its
brightness would equal 5 _R{e}B_ on the sunny day and _R{e}B_ on the
overcast day where _B_ is the value (different in the two cases) of the
brightness of the uniform sky. The surface can never be a perfect
reflector, so on an overcast day its brightness will be a fraction
(_RR{e}_) of the brightness _B_ of the uniform sky. Inasmuch as _R{e}_
is a very small value it is seen that low visibility of airplanes as
viewed from below generally cannot be attained on an overcast day. It can
be approached on a sunny day and even realized by adopting the expedient
already mentioned. Further computations are to be found elsewhere.[12]

Seasonable changes present no difficulties, for from a practical
standpoint only summer and winter need be generally considered. If the
earth is covered with snow an airplane covered completely with white or
gray paint would be fairly satisfactory as viewed from above, and if a
certain shade of a blue tint be applied to the lower surfaces, low
visibility as viewed from below would result. The white paint would
possess a reflection-factor about equal to that of snow, thus providing
low visibility from above. Inasmuch as the reflection-factor of snow is
very high, the white lower sides of an airplane would receive a great deal
more light in winter than they would in summer. Obviously, a blue tint is
necessary for low visibility against the sky, but color has not been
primarily considered in the preceding paragraphs because the chief
difficulty in achieving low visibility from below lies in obtaining
brightness of the proper order of magnitude. In winter the barren ground
would be approximately of the same color and reflection-factor as in
summer, so it would not be difficult to take this into consideration.

Seaplanes whose backgrounds generally consist of water would be painted of
the color and brightness of water with perhaps a slight mottling. The
color would generally be a very dark shade, approximating blue-green in
hue.

Aircraft for night use would be treated in the same manner as aircraft for
day use, if the moonlight is to be considered a dominant factor. This is
one of the cases where the judgment must be based on actual experience. It
appears that the great enemy of night raiders is the searchlight. If this
is true the obvious expedient is to paint the craft a dull jet black.
Experiments indicate that it is more difficult to pick up a black craft
than a gray or white one and also it is more difficult to hold it in the
beam of the searchlight. This can be readily proved by the use of black,
gray, and white cards in the beam of an automobile head-light. The white
card can be seen in the outskirts of the beam where the gray or black
cannot be seen, and the gray can be picked up where the black one is
invisible. The science of vision accounts for this as it does for many
other questions which arise in the consideration of camouflage or low
visibility.

Some attempts have been made to apply the principle of confusibility to
airplanes as finally developed for vessels to circumvent the submarine,
but the folly of this appears to be evident. Air battles are conducted at
terrific speeds and with skillful maneuvering. Triggers are pulled without
computations and the whole activity is almost lightning-like. To expect to
confuse an opponent as to the course and position of the airplane is
folly.

The camouflage of observation balloons has not been developed, though
experiments were being considered in this direction as the war closed.
Inasmuch as they are low-altitude crafts it appears that they would be
best camouflaged for the earth as a background. Their enemies pounce down
upon them from the sky so that low visibility from above seems to be the
better choice.

In the foregoing it has been aimed to give the reader the general
underlying principles of camouflage and low visibility, but at best this
is only a résumé. In the following references will be found more extensive
discussions of various phases of the subject.



REFERENCES

1. A Study of Zöllner's Figures and Other Related Figures, J. Jastrow,
Amer. Jour. of Psych. 1891, 4, p. 381.

2. A Study of Geometrical Illusions, C. H. Judd, Psych. Rev. 1899, 6, p.
241.

3. Visual Illusions of Depth, H. A. Carr, Psych. Rev. 1909, 16, p. 219.

4. Irradiation of Light, F. P. Boswell, Psych. Bul. 1905, 2, p. 200.

5. Retiring and Advancing Colors, M. Luckiesh, Amer. Jour. Psych. 1918,
29, p. 182.

6. The Language of Color, 1918, M. Luckiesh.

7. Apparent Form of the Dome of the Sky, Ann. d. Physik, 1918, 55, p. 387;
Sci. Abs. 1918, No. 1147.

8. Course on Optics, 1738, Robert Smith.

9. Color and Its Applications, 1915 and 1921; Light and Shade and Their
Applications, 1916, M. Luckiesh.

10. Report of The Submarine Defense Association, L. T. Bates and L. A.
Jones.

11. Marine Camouflage Design, E. L. Warner, Trans. I. E. S. 1919, 14, p.
215.

12. The Visibility of Airplanes, M. Luckiesh, Jour. Frank. Inst. March and
April, 1919; also Aerial Photometry, Astrophys. Jour. 1919, 49, p. 108.

13. Jour. Amer. Opt. Soc., E. Karrer, 1921.

The foregoing are only a few references indicated in the text. Hundreds of
references are available and obviously it is impracticable to include such
a list. The most fruitful sources of references are the general works on
psychology. E. B. Titchener's Experimental Psychology (vol. 1) contains an
excellent list. A chapter on Space in William James' Principles of
Psychology (vol. II) will be found of interest to those who wish to delve
deeper into visual perception. Other general references are Elements of
Physiological Psychology by Ladd and Woodworth; the works of Helmholtz; a
contribution by Hering in Hermann's Handb. d. Phys. Bk. III, part 1;
Physiological Psychology by Wundt; E. B. Delabarre, Amer. Jour. Psych.
1898, 9, p. 573; W. Wundt, Täuschungen, p. 157 and Philos. Stud. 1898, 14,
p. 1; T. Lipps, Raumaesthetik and Zeit. f. Psych. 1896, 12, 39.



INDEX


  Aberration, 19
    spherical, 122
    chromatic, 135

  Aerial perspective, 165, 183

  After-images, 24, 25, 59, 128, 186
    positive and negative, 129

  Airplanes, visibility of, 233
    camouflage for different types, 234
    size of image at various altitudes, 238
    camouflage for various conditions, 240

  Alhazen, 8

  Angles, influence of, 76
    various effects of, 81
    contours and, 87
    apparent effect on length, 91
    theories, 98

  Animals, protective coloration, 211

  Architecture, 195
    balance in, 201

  Arcs, circular, illusions due to, 86

  Areas, juxtaposed, illusions of, 96

  Artist, 179

  Attention, fluctuation of, 65, 106, 141, 164

  Aubert, 49

  Auerbach's indirect vision theory, 100

  Aureole, 178


  Balance in architecture, 201

  Bas-relief, 143

  Battleships, 222

  Binocular disparity, 105

  Binocular vision, 29, 31

  Blending of colors in camouflage, 216

  Blind spot, 21

  Blue light on war-vessels, 230

  Boswell, varieties of irradiation, 122

  Brightness,
    illusions due to
      variations in, 107
      and color contrasts, 114
      apparatus, 115
      and hue, 125
      sky, 241

  Brucke's theory, 37

  Brunot's mean distance theory, 101


  Camouflage, 210
    terrestrial, 210
    detection of, 215
    marine, 222
    airplane, 234

  Carr, observations on distance illusions, 108

  Chromatic aberration, 19, 135

  Chlorophyl, 214

  Circle, 11
    arcs of, illusion, 86
    contracting and expanding illusion, 98

  Clouds, 235

  Color, 124
    after-images, 128
    blending in camouflage, 216
    contrasts and brightness, 114
    growth and decay of sensation, 131
    illusions of, 156
    retiring and advancing, 138
    saturation, 154
    sensibility of retina, 138
    warm and cold, 158

  Confusability, 226

  Confusion theory of angular illusions, 100

  Contour, illusions of, 52
    and angles, illusions, 87

  Contracting and expanding circles, illusion of, 98

  Contrasts, illusions of, 53
    simultaneous, 124, 154
    apparatus for, 115, 125
    color, 114, 154, 188
    brightness, 114

  Convergence, illusions of, 108, 191

  Cord, twisted, illusion, 88


  Daylight, artificial, 189

  Decoration, painting and, 179

  Decorator, 188

  Dember, 167

  Depth and distance, illusions, 102

  Direction, illusions of
    Zöllner's, 76
    Wundt's, 79
    Hering's, 80

  Disk, Mason, 132

  Distance and depth, illusions, 102
    and size, 35, 104, 166

  Distance illusions, Carr's observations, 108

  Double images, 37

  Dynamic theory of angular illusions, 99


  Enlargement of sun and moon at horizon, apparent, 169

  Equivocal figures, 64

  Euclid, 8

  Extent, interrupted, illusions of, 48

  External image, 15, 17, 34

  Eye, physiology, 13
    position, 30
    adjustments, 33
    defects, 19


  Fatigue, 128

  Field, visual, effect of location in, 44

  Figures, equivocal, 64

  Filters, color, 214

  Fluctuation of attention, 65, 106, 141, 164

  Focusing, 14

  Form of sky, apparent, 166

  Fovea centralis, 22, 23, 139

  Frames, picture, effect of wood grain, 190


  Geometrical illusions, 44

  Glare, 119

  Grain of wood, apparent distortions due to, 190

  Grecian art, 196

  Growth and decay of color sensation, 131

  Guttman, 175


  Hallucination, 4, 72

  Halo, 178

  Haze, illusions, etc., 103, 166, 183
    earth and high, 240

  Helmholtz, 13, 74

  Hering, 74
    illusion of direction, 80

  Hue and brightness, 125


  Illusions, geometrical, 44
    equivocal figures, 64
    influence of angles, 76
    of depth and distance, 102
    irradiation and brightness contrast, 114
    color, 124
    light and shadows, 144
    in nature, 164
    in painting and decoration, 179
    mirror, 205
    camouflage, 210

  Image
    after-, 24, 25, 59, 128, 129, 186
    double, 37
    external, 15, 17, 34
    retinal, inversion of, 16
    of airplane, size at various altitudes, 238

  Indirect vision theory, Auerbach's, 100

  Intaglio, 143

  Interrupted extent, illusions of, 48

  Iris, 15

  Irradiation, 120
    and brightness contrast, 114
    varieties of (Boswell), 122
    in architecture, 199


  James, 170

  Jastrow, 80

  Jones, L. A., 223

  Judd, 86, 93

  Judgment, 1


  Karrer, 160

  Kepler, 8


  Light, effect of spectral character, 189

  Lighting, illusions of depth and distance due to, 102
    contrasts, 154
    diffusion, effect of, 145
    direction, effect of, 144, 151
    ending of searchlight beam, 160
    warm and cold colors, 158

  Lipps, 10, 11
    dynamic theory of, 99

  Location in visual field, effect, 44


  Mean distance theory, Brunot's, 101

  Mechanical, esthetic unity, 11

  Magician, 3

  Magic, mirror, 205

  Marine camouflage, 222

  Mason disk, 132

  Mirage, 3, 176

  Mirror magic, 205

  Miscellaneous color effects, 140

  Moon, apparent size at horizon, 8, 36, 169
    theories of, 173
    apparent radius of crescent, 121

  Müller-Lyer illusion, 53, 93


  National Research Council, Committee on Camouflage, 234

  Nature, 164

  Necker, 74


  Oppel, 9


  Painting and decoration, 179

  Painter, 2, 179, 186

  Parallax, 105

  Parthenon of Athens, 196

  Persistence of vision, 131

  Perspective, 58
    in architecture, 198
    aerial 165, 183
    theory, 98

  Photographer, 152

  Photography, use in detection of camouflage, 220

  Photometer, 156, 217

  Pigments, 184

  Poggendorff illusion, 85

  Protective coloration, animals, 211

  Psychology, 2, 6, 157
    of light, 193

  Purkinje phenomenon, 26, 139


  Reflection-factors, 236

  Retina, 14, 20
    inertia, 130
    color sensibility, 138

  Retinal rivalry, 140

  Retiring and advancing colors, 136

  Reversal of mirror image, 205

  Rods and cones, 21


  Schröder's staircase, 70

  Sculpture, 204

  Searchlight beam, ending of, 160

  Sensation, color, growth and decay, 131

  Sense, 1

  Shading, counter, for vessels, 224

  Shadows, importance in camouflage, 215

  Size and distance, 35, 36
    illusions of, 104, 166

  Sky
    apparent form of, 166
    brightness, 241

  Skylight and sunlight, relative proportions of, 215, 243

  Smith, Robert, 173

  Smoke-screens, 230

  Spectral character of light, 189

  Sphere, illusions, 145, 150, 151

  Spherical aberration, 19

  Sphinx illusion, 206

  Spiral illusions, 90

  Spraying, paint, 187

  Stereoscope, 39, 142

  Stereoscopic vision, 38, 41, 141

  Submarines, 225
    camouflage for, 232

  Sun, apparent enlargement at horizon, 169

  Sunlight and skylight, relative proportions in nature, 215, 243


  Terrestrial camouflage, 210

  Theory of influence of angles, 98
    perspective, 98
    dynamic, 99
    confusion, 100
    indirect vision, 100
    mean distance, 101

  Thiéry's figure, 71

  Thiéry's perspective theory, 99

  Transparencies, 185

  Twisted cord illusions, 88


  Uibe, 167


  Vertical vs. horizontal distances, 11, 36, 46

  Visibility, low, for vessels, 222
    of airplanes, 233

  Vision, 29
    persistence of, 131
    stereoscopic, 38

  Visual perception, 32, 33


  Warm and cold colors, 158

  Warner, E. L., 227

  Wheatstone, 37

  Wood grain, illusions caused by, 191

  World War, 213

  Wundt, 10, 11, 32, 74
    illusion of direction, 79


  Yellow spot, 139


  Zöllner's illusion, 67, 76

  Zoth, 175



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Transcriber's Notes:

Passages in italics are indicated by _italics_.

Subscripted characters are indicated by {subscript}.

The following misprints have been corrected:
  "imgaes" corrected to "images" (page 128)
  "bove" corrected to "above" (page 177)
  "verticle" corrected to "vertical" (page 239)
  "colo" corrected to "color" (Index)

Other than the corrections listed above, inconsistencies in spelling and
hyphenation have been retained from the original.

The inverted "8" and "S" characters at the top of page 45 cannot be
properly represented in this text version.





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