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