,,visual ,,illusions ,,their ,,causes1 ,,characteristics ,,and ,,applications ,,by ,m4 ,,luckiesh ,,director ,,of ,,applied ,,science1 ,,nela ,,research ,,laboratories1 ,,national ,,lamp ,,works ,,of ,,general ,,electric ,,co4 ,,author ,,of ,,color ,,and ,,its ,,applications1 ,,light ,,and ,,shade ,,and ,,their ,,applications1 ,,the ,,lighting ,,art1 ,,the ,,language ,,of ,,color1 ,,artificial ,,light--,,its ,,influence ,,upon ,,civilization1 ,,lighting ,,the ,,home1 ,,etc4 #ajj ,,illustrations ,,new ,,york ,d4 ,,van ,,nostrand ,,company ,,eight ,,warren ,,street #aibb ,,copyright1 #aibb1 ,,by ,d4 ,,van ,,nostrand ,,company ,,preface ,eventually one of the results of application to the analysis and measurement of the phenomena of light1 color1 lighting1 and vision is a firmly entrenched conviction of the inadequacy of physical measurements as a means for representing what is perceived4 ,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 sense4 ,in other words1 there are numberless so-called visual illusions which must be taken into account4 ,all are of interest2 many can be utilized2 and some must be suppressed4 ,scientific literature yields a great many valuable discussions from theoretical and experimental viewpoints but much of the material is controversial4 ,the practical aspects of visual illusions have been quite generally passed by and1 inasmuch as there does not appear to be a volume available which treats the subject in a condensed manner but with a broad scope1 this small volume is contributed toward filling the gap4 ,the extreme complexity of the subject is recognized1 but an attempt toward simplicity of treatment has been made by confining the discussion chiefly to static visual illusions1 by suppressing minor details1 and by subordinating theory4 ,in other words1 the intent has been to emphasize experimental facts4 ,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 volume4 ,some theoretical aspects of the subject are still extremely controversial1 so they are introduced only occasionally and then chiefly for the purpose of illustrating the complexities and the trends of attempted explanations4 ,space does not even admit many qualifications which may be necessary in order to escape criticism entirely4 ,the visual illusions discussed are chiefly of the static type1 although a few others have been introduced4 ,some of the latter border upon motion1 others upon hallucinations1 and still others produced by external optical media are illusions only by extension of the term4 ,these exceptions are included for the purpose of providing glimpses into the borderlands4 ,it is hoped that this condensed discussion1 which is ambitious only in scope1 will be of interest to the general reader1 to painters1 decorators1 and architects1 to lighting experts1 and to all interested in light1 color1 and vision4 ,it is an essential supplement to certain previous works4 ,m4 ,,luckiesh ,november1 #aibj4 ,,contents ,,chapter ,,page ,i4 ,introduction #a ,,ii4 ,the eye #ac ,,iii4 ,vision #bi ,,iv4 ,some types of geometrical illusions #dd ,v4 ,equivocal figures #fd ,,vi4 ,the influence of angles #gf ,,vii4 ,illusions of depth and of distance #ajb ,,viii4 ,irradiation and brightness-contrast #aad ,,ix4 ,color #abd ,x4 ,lighting #add ,,xi4 ,nature #afd ,,xii4 ,painting and decoration #agi ,,xiii4 ,architecture #aie ,,xiv4 ,mirror ,magic #bje ,,xv4 ,camouflage #baj ,,list ,,of ,,illustrations ,,figure ,,page #a4 ,principal parts of the eye #ad #b4 ,stereoscopic pictures for combining by converging or diverging the optical axes #da #c4 ,stereoscopic pictures #da #d4 ,the vertical line appears longer than the equal horizontal line in each case #df #e4 ,the vertical dimension is equal to the horizontal one1 but the former appears greater #dg #f4 ,the divided or filled space on the left appears longer than the equal space on the right #di #g4 ,the three lines are of equal length #ej #h4 ,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 #ej #i4 ,three squares of equal dimensions which appear different in area and dimension #ea #aj4 ,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 #eb #aa4 ,two equal semi-circles #ec #ab4 ,arcs of the same circle #ec #ac4 ,three incomplete but equal squares #ec #ad4 ,middle sections of the two lines are equal #ed #ae4 ,an effect of contrasting areas 7,baldwin's figure7 #ed #af4 ,an illusion of contrast #ee #ag4 ,equal circles which appear unequal due to contrast 7,ebbinghaus' figure7 #ef #ah4 ,equal circles appearing unequal owing to contrasting concentric circles #ef #ai4 ,circles influenced by position within an angle #eg #bj4 ,contrasting angles #eg #ba4 ,owing to perspective the right angles appear oblique and vice versa #eh #bb4 ,two equal diagonals which appear unequal #eh #bc4 ,apparent variations in the distance between two parallel lines #ei #bd4 ,a striking illusion of perspective #fj #be4 ,distortion of a square due to superposed lines #fa #bf4 ,distortion of a circle due to superposed lines #fb #bg4 ,illustrating fluctuation of attention #fe #bh4 ,the grouping of the circles fluctuates #ff #bi4 ,crossed lines which may be interpreted in two ways #fg #cj4 ,reversible cubes #fh #ca4 ,the reversible open book 7after ,mach7 #fi #cb4 ,a reversible tetrahedron #fi #cc4 ,reversible perspective of a group of rings or of a tube #gj #cd4 ,schroeder's reversible staircase #gj #ce4 ,thiery's figure #ga #cf4 ,illustrating certain influences upon the apparent direction of vision4 ,by covering all but the eyes the latter appear to be drawn alike in both sketches #gc #cg4 ,zoellner's illusion of direction #gg #ch4 ,parallel lines which do not appear so #gi #ci4 ,wundt's illusion of direction #gi #dj4 ,hering's illusion of direction #hj #da4 ,simple effect of angles #ha #db4 ,the effect of two angles in tilting the horizontal lines #hc #dc4 ,the effect of crossed lines upon their respective apparent directions #hc #dd4 ,another step toward the ,zoellner illusion #hd #de4 ,the two diagonals would meet on the left vertical line #he #df4 ,poggendorff's illusion4 ,which oblique line on the right is the prolongation of the oblique line on the left8 #he #dg4 ,a straight line appears to sag #hf #dh4 ,distortions of contour due to contact with other contours #hg #di4 ,an illusion of direction #hh #ej4 ,twisted-cord illusion4 ,these are straight cords #hi #ea4 ,twisted-cord illusion4 ,these are concentric circles #hi #eb4 ,a spiral when rotated appears to expand or contract1 depending upon direction of rotation #ij #ec4 ,angles affect the apparent length of lines #ia #ed4 ,the horizontal line appears to tilt downward toward the ends #ib #ee4 ,the horizontal line appears to sag in the middle #ib #ef4 ,the ,mueller-,lyer illusion #ic #eg4 ,combined influence of angles and contrasting lengths #ie #eh4 ,two equal oblique lines appear unequal because of their different positions #ie #ei4 ,an illusion of area #if #fj4 ,five equal areas showing the influence of contour upon judgment of area #ig #fa4 ,showing the effect of directing the attention #ih #fb4 ,simple apparatus for demonstrating the remarkable effects of contrasts in brightness and color #aae #fc4 ,illustrating brightness-contrast #aag #fd4 ,an effect of brightness-contrast4 ,note the darkening of the intersections of the white strips #aah #fe4 ,the phenomenon of irradiation #aba #ff4 ,an excellent pattern for demonstrating color-contrast #abf #fg4 ,by rotating this ,mason 7black and white7 disk color-sensations are produced #acc #fh4 ,for demonstrating retiring and advancing colors #acg #fi4 ,by combining these stereoscopically the effect of metallic lustre 7similar to graphite in this case7 is obtained #ada #gj4 ,a bas-relief lighted from above #adf #ga4 ,an intaglio lighted from above #adg #gb4 ,a bas-relief lighted from the left #adh #gc4 ,an intaglio lighted from the left #adi #gd;a4 ,a disk 7above7 and a sphere 7below7 lighted from overhead #ade b4 ,a disk and a sphere lighted by perfectly diffused light #ade #ge4 ,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 #aej #gf4 ,the same as ,fig4 #ge1 but lighted by a very small light-source #aea #gg4 ,apparent ending of a searchlight beam #afa #gh4 ,an accurate tracing from a photograph 7continual exposure7 of the moon rising #aga #gi4 ,accurate tracings from a photograph 7short exposures at intervals7 of the sun setting #agb #hj4 ,explanation offered by ,smith of the apparent enlargement of heavenly bodies near the horizon #agd #ha4 ,explanation of a common mirage #agf #hb4 ,illustrating the apparent distortion of a picture frame in which the grain of the wood is visible #aij #hc4 ,another example similar to ,fig4 #hb #aia #hd4 ,from actual photographs of the end-grain of a board #aib #he4 ,exaggerated illusions in architecture #aih #hf4 ,illustrating the influence of visual angle upon apparent vertical height #aii #hg4 ,irradiation in architecture #bjj #hh4 ,some simple geometrical-optical illusions in architecture #bja #hi4 ,by decreasing the exposed length of shingles toward the top a greater apparent expanse is obtained #bjb #ij4 ,an example of a mirror illusion #bjg #ia4 ,another example of mirror magic #bjh #ib4 ,a primary stage in the evolution of the use of geometrical-optical illusions on ships #bbf #ic and #id4 ,attempts at distortion of outline which preceded the adoption of geometrical-optical illusions #bbh #ie and #if4 ,illustrating the use of models by the ,navy ,department in developing the geometrical-optical illusion for ships #bbi #ig and #ih4 ,examples of the geometrical-optical illusion as finally applied #bca #ii4 ,representative earth backgrounds for an airplane 7uncamouflaged7 as viewed from above #bce #ajj4 ,illustrating the study of pattern for airplanes4 ,the photograph was taken from an altitude of #aj1jjj feet4 ,the insert shows the relative lengths 7vertical scale7 of an airplane of #ej-;foot spread at various distances below the observer #bci ,,visual ,,illusions ,i ,,introduction ,seeing is deceiving4 ,thus a familiar epigram may be challenged in order to indicate the trend of this book which aims to treat certain phases of visual illusions4 ,in general1 we do not see things as they are or as they are related to each other2 that is1 the intellect does not correctly interpret the deliverances of the visual sense1 although sometimes the optical mechanism of the eyes is directly responsible for the illusion4 ,in other words1 none of our conceptions and perceptions are quite adequate1 but fortunately most of them are satisfactory for practical purposes4 ,only a part of what is perceived comes through the senses from the object2 the remainder always comes from within4 ,in fact1 it is the visual sense or the intellect which is responsible for illusions of the various types to be discussed in the following chapters4 ,our past experiences1 associations1 desires1 demands1 imaginings1 and other more or less obscure influences create illusions4 ,an illusion does not generally exist physically but it is difficult in some cases to explain the cause4 ,certainly there are many cases of errors of judgment4 ,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 sense4 ,it is realized that the foregoing comparison leads directly to one of the most controversial questions in psychology1 but there is no intention on the author's part to cling dogmatically to the opinions expressed4 ,in fact1 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 perception4 ,the final word will be left to the psychologists but it appears possible that it may never be formulated4 ,in general1 a tree appears of greater length when standing than when lying upon the ground4 ,lines1 areas1 and masses are not perceived in their actual physical relations4 ,the appearance of a colored object varies considerably with its environment4 ,the sky is not perceived as infinite space nor as a hemispherical dome1 but as a flattened vault4 ,the moon apparently diminishes in size as it rises toward the zenith4 ,a bright object appears larger than a dark object of the same physical dimensions4 ,flat areas may appear to have a third dimension of depth4 ,and so on4 ,illusions are so numerous and varied that they have long challenged the interest of the scientist4 ,they may be so useful or even so disastrous that they have been utilized or counteracted by the skilled artist or artisan4 ,the architect and painter have used or avoided them4 ,the stage-artist employs them to carry the audience in its imagination to other environments or to far countries4 ,the magician has employed them in his entertainments and the camoufleur used them to advantage in the practice of deception during the recent war4 ,they are vastly entertaining1 useful1 deceiving1 or disastrous1 depending upon the viewpoint4 ,incidentally1 a few so-called illusions will be discussed which are not due strictly to errors of the visual sense or of the intellect4 ,examples of these are the mirage and certain optical effects employed by the magician4 ,in such cases neither the visual sense nor the intellect errs4 ,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 not4 ,however1 with these few exceptions1 which are introduced for their specific interest and for the emphasis they give to the true illusion1 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 intellect4 ,for the sake of brevity we might say that they are those due to errors of visual perception4 ,furthermore1 only those of a static type will be considered2 that is1 the vast complexities due to motion are not of interest from the viewpoint of the aims of this book4 ,there are two well-known types of misleading perceptions1 namely illusions and hallucinations4 ,if1 for example1 two lines appear of equal length and are not1 the error in judgment is responsible for what is termed an illusion4 ,if the perceptual consciousness of an object appears although the object is not present1 the result is termed an hallucination4 ,for example1 if something is seen which does not exist1 the essential factors are supplied by the imagination4 ,shadows are often wrought by the imagination into animals and even human beings bent upon evil purpose4 ,ghosts are created in this manner4 ,hallucinations depend largely upon the recency1 frequency1 and vividness of past experience4 ,a consideration of this type of misleading perception does not advance the aims of this book and therefore will be omitted4 ,the connection between the material and mental in vision is incomprehensible and apparently must ever remain so4 ,objects emit or reflect light and the optical mechanism known as the eye focuses images of the objects upon the retina4 ,messages are then carried to the brain where certain molecular vibrations take place4 ,the physiologist records certain physical and chemical effects in the muscles1 nerves1 and brain and behold6 there appears consciousness1 sensations1 thoughts1 desires1 and volitions4 ,how8 and1 ,why8 are questions which may never be answered4 ,it is dangerous to use the word never1 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 them4 ,in fact1 it does not appreciably further the aims of this book to devote much space to efforts toward explanation4 ,in covering this vast and complex field there are multitudes of facts1 many hypotheses1 and numerous theories from which to choose4 ,judgment dictates that of the limited space most of it be given to the presentation of representative facts4 ,this is the reasoning which led to the formulation of the outline of chapters4 ,owing to the vast complex beyond the physical phenomena1 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 perceived4 ,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 well4 ,illusions are legion4 ,they greet the careful observer on every hand4 ,they play a prominent part in our appreciation of the physical world4 ,sometimes they must be avoided1 but often they may be put to work in various arts4 ,their widespread existence and their forcefulness make visual perception the final judge in decoration1 in painting1 in architecture1 in landscaping1 in lighting1 and in other activities4 ,the ultimate limitation of measurements with physical instruments leaves this responsibility to the intellect4 ,the mental being is impressed with things as perceived1 not with things as they are4 ,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 whole4 ,in special simple cases it is not difficult to determine when or how nearly a perception is true but in general1 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 reality4 ,illusions are sometimes called errors of sense and some of them are such1 but often they are errors of the intellect4 ,the senses may deliver correctly but error may arise from imagination1 inexperience1 false assumptions1 and incorrect associations1 and the recency1 frequency1 and vividness of past experience4 ,the gifts of sight are augmented by the mind with judgments based upon experience with these gifts4 ,the direct data delivered by the visual sense are light1 intensity1 color1 direction4 ,these may be considered as simple or elemental sensations because they cannot be further simplified or analyzed4 ,at this point it is hoped that no controversy with the psychologist will be provoked4 ,in the space available it appears unfruitful to introduce the many qualifications necessary to satisfy the1 as yet uncertain or at least conflicting1 definitions and theories underlying the science of psychology4 ,if it is necessary to add darkness to the foregoing group of elemental visual sensations1 this will gladly be agreed to4 ,the perceptions of outline-form and surface-contents perhaps rank next in simplicity2 however1 they may be analyzed into directions4 ,the perception of these is so direct and so certain that it may be considered to be immediate4 ,a ring of points is apparently very simple and it might be considered a direct sense-perception1 but it consists of a number of elemental directions4 ,the perception of solid-form is far more complex than outline-form and therefore more liable to error4 ,it is judged partially by binocular vision or perspective and partly by the distribution of light and shade4 ,colors may help to mold form and even to give depth to flat surfaces4 ,for example1 it is well known that some colors are advancing and others are retiring4 ,perhaps of still greater complexity are the judgments of size and of distance4 ,many comparisons enter such judgments4 ,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 judgment4 ,upon these are superposed the numerous psycho-physiological phenomena of color1 irradiation1 etc4 ,in vision judgments are quickly made and the process apparently is largely outside of consciousness4 ,higher and more complex visual judgments pass into still higher and more complex intellectual judgments4 ,all these may appear to be primary1 immediate1 innate1 or instinctive and therefore1 certain1 but the fruits of studies of the psychology of vision have shown that these visual judgments may be analyzed into simpler elements4 ,therefore1 they are liable to error4 ,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 shading4 ,the architecture of ancient ,greece reveals a knowledge of certain illusions in the efforts to overcome them4 ,however1 the study of illusions did not engage the attention of scientists until a comparatively recent period4 ,notwithstanding this belated attention there is a vast scientific literature pertaining to the multitudinous phases of the subject2 however1 most of it is fragmentary and much of it is controversial4 ,some of it deals with theory for a particular and often a very simple case4 ,in life complex illusions are met but at present it would be futile to attempt to explain them in detail4 ,furthermore1 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 whole4 ,finally1 the occurrence and application of illusions in various arts and the prominence of illusions on every hand have not been especially treated4 ,it is the hope that this will be realized in the following chapters in so far as brevity of treatment makes this possible4 ,doubtless thoughtful observers ages ago noticed visual illusions1 especially those found in nature and in architecture4 ,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 ,euclid4 ,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 subjects4 ,one of the oldest dissertations upon the apparent form of the sky was published by ,alhazen1 an ,arab astronomer of the tenth century4 ,kepler in #afah wrote upon the subject4 ,philosophers of the past centuries prepared the way toward an understanding of many complexities of today4 ,they molded thought into correct form and established fundamental concepts and principles4 ,their chief tool was philosophy1 the experimental attack being left to the scientists of the modern age4 ,however1 they established philosophically such principles as space and time are not realities of the phenomenal world but the modes under which we see things apart4 ,as science became organized during the present experimental era1 measurements were applied and there began to appear analytical discussions of various subjects including optical illusions4 ,one of the earliest investigations of the modern type was made by ,oppel1 an account of which appeared in #ahed4 ,since that time scientific literature has received thousands of worthy contributions dealing with visual illusions4 ,there are many facts affecting vision regarding which no theory is necessary4 ,they speak for themselves4 ,there are many equally obvious facts which are not satisfactorily explained but the lack of explanation does not prevent their recognition4 ,in fact1 only the scientist needs to worry over systematic explanations and theoretical generalizations4 ,he needs these in order to invade and to explore the other unknowns where he will add to his storehouse of knowledge4 ,a long step toward understanding is made by becoming acquainted with certain physical1 physiological1 and psychological facts of light1 color1 and lighting4 ,furthermore1 acquaintance with the visual process and with the structure of the eye aids materially4 ,for this reason the next two chapters have been added even at the risk of discouraging some readers4 ,in a broad sense1 any visual perception which does not harmonize with physical measurements may be termed an illusion4 ,therefore1 the term could include those physical illusions obtained by means of prisms1 lenses1 and mirrors and such illusions as the mirage4 ,it could also include the physiological illusions of light and color such as after-images1 irradiation1 and contrast1 and the psycho-physiological illusions of space and the character of objects4 ,in fact1 the scope of the following chapters is arbitrarily extended to include all these aspects1 but confines consideration only to static illusions4 ,in a more common sense attention is usually restricted to the last group2 that is1 to the psycho-physiological illusions attending the perception of space and the character of objects although motion is often included4 ,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 involved4 ,for this reason explanations will be presented wherever feasible in connection with specific illusions4 ,however1 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 sense4 ,hypotheses pertaining to illusions are generally lacking in agreement1 but for the special case of what might be more safely termed geometrical-optical illusions two different theories1 by ,lipps and by ,wundt respectively1 are conspicuous4 ,in fact1 most theories are variants of these two systematic explanations of illusions 7in the restricted sense74 ,lipps proposed the principle of mechanical-esthetic unity1 according to which we unconsciously give to every space-form a living personality and unconsciously consider certain mechanical forces acting4 ,our judgments are therefore modified by this anthropomorphic attitude4 ,for example1 we regard the circle as being the result of the action of tangential and radial forces in which the latter appear to triumph4 ,according to ,lipps' theory the circle has a centripetal character and these radial forces toward the center1 which apparently have overcome the tangential forces during the process of creating the circle1 lead to underestimation of its size as compared with a square of the same height and breadth4 ,by drawing a circle and square side by side1 with the diameter of the former equal to the length of a side of the latter1 this illusion is readily demonstrated4 ,of course1 the square has a greater area than the circle and it is difficult to determine the effect of this disparity in area4 ,figure #fj where the areas of the circle and square are equal and consequently the height of the former is considerably greater than the latter1 is of interest in this connection4 ,by experimenting with a series of pairs consisting of a circle and a square1 varying in dimensions from equal heights to equal areas1 an idea of the shrinking character of the circle becomes quite apparent4 ,wundt does not attribute the illusion to a deception or error of judgment but to direct perception4 ,according to his explanation1 the laws of retinal image 7fixation7 and eye-movement are responsible4 ,for example1 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 plane4 ,unconscious or involuntary eye-movements also appear to play a part in many linear or more accurately1 angular illusions1 but certainly ,wundt's explanation does not suffice for all illusions although it may explain many geometrical illusions4 ,it may be said to be of the perceptive class and ,lipps' theory to be of the judgment or higher-process class4 ,as already stated1 most of the other proposed explanations of geometrical illusions may be regarded as being related to one of these two theories4 ,there is the indistinct vision theory of ,einthoven2 the perspective theory of ,hering1 ,guye1 ,thiery1 and others2 the contrast theory of ,helmholtz1 ,loeb1 and ,heyman2 and the contrast-confluxion theory of ,mueller-,lyer4 ,in order not to discourage the reader at the outset1 theories as such will be passed by with this brief glimpse4 ,however1 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 illusions4 ,,ii ,,the ,,eye ,helmholtz1 who contributed so much toward our knowledge of the visual process1 in referring to the eye1 once stated that he could make a much better optical instrument but not a better eye4 ,in other words1 the eye is far from an ideal optical instrument but as an eye it is wonderful4 ,its range of sensitiveness and its adaptability to the extreme variety of demands upon it are truly marvelous when compared with instruments devised by mankind4 ,obviously1 the eye is the connecting link between objective reality and visual perception and1 therefore1 it plays an important part in illusions4 ,in fact1 sometimes it is solely responsible for the illusion4 ,the process of vision may be divided into several steps such as 7#a7 the lighting1 color1 character1 and disposition of objects2 7#b7 the mechanism by which the image is formed upon the retina2 7#c7 various optical defects of this mechanism2 7#d7 the sensitiveness of the parts of the retina to light and color2 7#e7 the structure of the retina2 7#f7 the parts played by monocular and binocular vision2 and 7#g7 the various events which follow the formation of the image upon the retina4 ,the mechanism of the eye makes it possible to see not only light but objects4 ,elementary eyes of the lowest animals perceive light but cannot see objects4 ,these eyes are merely specialized nerves4 ,in the human eye the optic nerve spreads to form the retina and the latter is a specialized nerve4 ,nature has accompanied this evolution by developing an instrument the--eye--for intensifying and defining and the whole is the visual sense-organ4 ,the latter contains the most highly specialized nerve and the most refined physiological mechanism1 the result being the highest sense-organ4 ,illustration3 ,fig4 #a4--,principal parts of the eye4 ,a1 ,conjunctiva2 ,b1 ,retina2 ,c1 ,choroid2 ,d1 ,sclera2 ,e1 ,fovea2 ,f1 ,blind ,spot2 ,g1 ,optic ,nerve2 ,h1 ,ciliary ,muscle2 ,i1 ,iris2 ,j1 ,cornea2 ,k1 ,ligament4 ,the eye is approximately a spherical shell transparent at the front portion and opaque 7or nearly so7 over the remaining eighty per cent of its surface4 ,the optical path consists of a series of transparent liquids and solids4 ,the chief details of the structure of the eye are represented in ,fig4 #a4 ,beginning with the exterior and proceeding toward the retina we find in succession the cornea1 the anterior chamber containing the aqueous humor1 the iris1 the lens1 the large chamber containing the vitreous humor1 and finally the retina4 ,certain muscles alter the position of the eye and consequently the optical axis1 and focusing 7accommodation7 is accomplished by altering the thickness and shape1 and consequently the focal length1 of the lens4 ,the iris is a shutter which automatically controls to some degree the amount of light reaching the retina1 thereby tending to protect the latter from too much light4 ,it also has some influence upon the definition of the image2 that is1 upon what is termed visual acuity or the ability to distinguish fine detail4 ,it is interesting to compare the eye with the camera4 ,in the case of the camera and the photographic process1 we have 7#a7 an inverted light-image1 a facsimile of the object usually diminished in size2 7#b7 an invisible image in the photographic emulsion consisting of molecular changes due to light2 and 7#c7 a visible image developed on the plate4 ,in the case of the eye and the visual process we have 7#a7 an inverted light-image1 a facsimile of the object diminished in size2 7#b7 the invisible image in the retinal substances probably consisting of molecular changes due to light2 and 7#c7 an external visible image4 ,it will be noted that in the case of vision the final image is projected outward--it is external4 ,the more we think of this outward projection the more interesting and marvelous vision becomes4 ,for example1 it appears certain that if a photographic plate could see or feel1 it would see or feel the silver image upon itself but not out in space4 ,however1 this point is discussed further in the next chapter4 ,in the camera and photographic process we trace mechanism1 physics1 and chemistry throughout4 ,in the eye and visual process we are able to trace these factors only to a certain point1 where we encounter the super-physical and super-chemical4 ,here molecular change is replaced by sensation1 perception1 thought1 and emotion4 ,our exploration takes us from the physical world into another1 wholly different1 where there reigns another order of phenomena4 ,we have passed from the material into the mental world4 ,the eye as an optical mechanism is reducible to a single lens and therefore the image focused upon the retina is inverted4 ,however1 there is no way for the observer to be conscious of this and therefore the inverted image causes no difficulty in seeing4 ,the images of objects in the right half of the field of view are focused upon the left half of the retina4 ,similarly1 the left half of the field of view corresponds to the right half of the retina2 the upper half of the former to the lower half of the latter2 and so on4 ,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 space4 ,this is interestingly demonstrated in a simple manner4 ,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 possible4 ,the background for the pin-hole should be the sky or other bright surface4 ,after a brief trial an inverted image of the pin-head is seen in the hole4 ,punch several holes in the card and in each will be seen an inverted image of the pin-head4 ,the explanation of the foregoing is not difficult4 ,the pin-head is so close to the eye that the image cannot be focused upon the retina2 however1 it is in a very favorable position to cast a shadow upon the retina1 the light-source being the pin-hole with a bright background4 ,light streaming through the pin-hole into the eye casts an erect shadow of the pin-head upon the retina1 and this erect image is projected into space and inverted in the process by the effect of the lens4 ,the latter is not operative during the casting of the shadow because the pin-head is too close to the lens1 as already stated4 ,it is further proved to be outward projection of the retinal image 7the shadow7 because by multiplying the number of pin-holes 7the light-sources7 there are also a corresponding number of shadows4 ,the foregoing not only illustrates the inversion of the image but again emphasizes the fact that we do not see retinal images4 ,even the stars which we see on pressing the eye-lid or on receiving a blow on the eye are projected into space4 ,the motes which we see in the visual field while gazing at the sky are defects in the eye-media1 and these images are projected into space4 ,we do not see anything in the eye4 ,the retinal image impresses the retina in some definite manner and the impression is carried to the brain by the optic nerve4 ,the intellect then refers or projects this impression outward into space as an external image4 ,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 object4 ,it is interesting to speculate whether the first visual impression of a new-born babe is projected outward or is perceived as in the eye4 ,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 impression4 ,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-organs4 ,incidentally1 suppose a blind person to be absolutely uneducated by transferred experience and that he suddenly became a normal adult and able to see4 ,what would he say about his first visual impression8 ,apparently such a subject is unobtainable4 ,the nearest that such a case had been approached is the case of a person born blind1 whose sight has been restored4 ,this person has acquired much experience with the external world through other senses4 ,it has been recorded that such a person1 after sight was restored1 appeared to think that external objects touched the eyes4 ,only through visual experience is this error in judgment rectified4 ,man studies his kind too much apart from other animals and perhaps either underestimates or overestimates the amount of inherited1 innate1 instinctive qualities4 ,a new-born chick in a few minutes will walk straight to an object and seize it4 ,apparently this implies perception of distance and direction and a cooerdination of muscles for walking and moving the eyes4 ,it appears reasonable to conclude that a certain amount of the wealth of capacities possessed by the individual is partly inherited1 and in man the acquired predominates4 ,but all capacities are acquired1 for even the inherited was acquired in ancestral experience4 ,even instinct 7whatever that may be7 must involve inherited experience4 ,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 volume4 ,certain defects of the optical system of the eye must contribute toward causing illusions4 ,any perfect lens of homogeneous material has at least two defects1 known as spherical and chromatic aberration4 ,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 checkerboard2 the outer lines of the image are found to be very much bent4 ,this defect in the eye-lens is somewhat counteracted by a variable optical density1 increasing from the outer to the central portion4 ,this results in an increase in refractive-index as the center of the lens is approached and tends to diminish its spherical aberration4 ,the eye commonly possesses abnormalities such as astigmatism and eccentricity of the optical elements4 ,all these contribute toward the creation of illusions4 ,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-length4 ,this causes the blue rays1 for example1 to be bent more than the red rays when traversing a prism4 ,it is in this manner that the spectrum of light may be obtained4 ,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 rays2 that is1 the former are bent more from their original path than the latter4 ,this defect of lenses is known as chromatic aberration and is quite obvious in the eye4 ,it may be demonstrated by any simple lens1 for the image of the sun1 for example1 will appear to have a colored fringe4 ,a purple filter which transmits only the violet and red rays is useful for this demonstration4 ,by looking at a lamp-filament or candle-flame some distance away the object will appear to have a violet halo1 but the color of the fringe will vary with accommodation4 ,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 periphery4 ,this optical defect of the eye makes objects appear more sharply defined when viewed in monochromatic light4 ,in fact1 this is quite obvious when using yellow glasses4 ,the defect is also demonstrated by viewing a line-spectrum focused on a ground glass4 ,the blue and red lines cannot be seen distinctly at the same distance4 ,the blue lines can be focused at a much less distance than the red lines4 ,chromatic aberration can account for such an illusion as the familiar advancing and retiring colors and doubtless it plays a part in many illusions4 ,the structure of the retina plays a very important part in vision and accounts for various illusions and many interesting visual phenomena4 ,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 part4 ,referring again to ,fig4 #a1 the outer coating of the shell is called the sclerotic4 ,this consists of dense fibrous tissue known as the white of the eye4 ,inside this coating is a layer of black pigment cells termed the choroid4 ,next is the bacillary layer which lines about five-sixths of the interior surface of the eye4 ,this is formed by closely packed rods and cones1 which play a dominant role in the visual process4 ,a light-sensitive liquid 7visual purple7 and cellular and fibrous layers complete the retinal structure4 ,the place where the optic nerve enters the eye-ball and begins to spread out is blind4 ,objects whose images fall on this spot are invisible4 ,this blind-spot is not particularly of interest here1 but it may be of interest to note its effect4 ,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 eye4 ,by moving the objects about until the image of the circle not directly looked at falls upon the blind-spot1 this circle will disappear4 ,a three-foot circle at a distance of #cf feet will completely disappear if its image falls directly upon the blind-spot4 ,at a distance of #db inches the invisible area is about #ab inches from the point of sight and about #c to #d inches in diameter4 ,at #cjj feet the area is about #h feet in diameter4 ,the actual size of the retinal blind-spot is about #j4je inch in diameter or nearly #e degrees4 ,binocular vision overcomes any annoyance due to the blind-spots because they do not overlap in the visual field4 ,a one-eyed person is really totally blind for this portion of the retina or of the visual field4 ,the bacillary layer consists of so-called rods and cones4 ,only the rods function under very low intensities of illumination of the order of moonlight4 ,the cones are sensitive to color and function only at intensities greater than what may be termed twilight intensities4 ,these elements are very small but the fact that they appear to be connecting links between the retinal image and visual perception1 acuity or discrimination of fine detail is limited inasmuch as the elements are of finite dimensions4 ,the smallest image which will produce a visual impression is the size of the end of a cone4 ,the smallest distance between two points which is visible at five inches is about #j4jja inch4 ,two cones must be stimulated in such a case4 ,fine lines may appear crooked because of the irregular disposition of these elemental light-sensitive points4 ,this apparent crookedness of lines is an illusion which is directly due to the limitations of retinal elements of finite size4 ,the distribution of rods and cones over the retina is very important4 ,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 cones4 ,it is this spot which provides visual acuteness4 ,it is easily demonstrated that fine detail cannot be seen well defined outside this central portion of the visual field4 ,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 eye4 ,helmholtz has compared the foveal and lateral images with a finished drawing and a rough sketch respectively4 ,the fovea also contains a yellow pigmentation which makes this area of the retina selective as to color-vision4 ,on viewing certain colors a difference in color of this central portion of the field is often very evident4 ,in the outlying regions of the retina1 rods predominate and in the intermediate zone both rods and cones are found4 ,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 vary1 depending upon the area of the retina stimulated4 ,in fact1 many interesting illusions are accounted for in this manner1 some of which are discussed later4 ,it is well known that a faint star is seen best by averted vision4 ,it may be quite invisible when the eye is directed toward it1 that is1 when its image falls upon the rod-free fovea4 ,however1 by averting the line of sight slightly1 the image is caused to fall on a retinal area containing rods 7sensitive to feeble light7 and the star may be readily recognized4 ,the fovea is the point of distinct focus4 ,it is necessary for fixed thoughtful attention4 ,it exists in the retina of man and of higher monkeys but it quickly disappears as we pass down the scale of animal life4 ,it may be necessary for the safety of the lower animals that they see equally well over a large field2 however1 it appears advantageous that man give fixed and undivided attention to the object looked at4 ,man does not need to trust solely to his senses to protect himself from dangers4 ,he uses his intellect to invent and to construct artificial defenses4 ,without the highly specialized fovea we might see equally well over the whole retina but could not look attentively at anything1 and therefore could not observe thoughtfully4 ,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 seen4 ,this after-image may be bright for a time owing to the fact that it takes time for the retinal process to die out4 ,then there comes a reaction which is apparent when the eye is directed toward illuminated surfaces4 ,the part of the retina which has been fatigued does not respond as fully as the fresher areas1 with the result that the fatigued area contributes a darker area in the visual field4 ,this is known as an after-image and there are many interesting variations4 ,the after-image usually undergoes a series of changes in color as well as in brightness as the retinal process readjusts itself4 ,an after-image of a colored object may often appear of a color complementary to the color of the object4 ,this is generally accounted for by fatigue of the retinal process4 ,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 aspects4 ,if the eye is directed toward a green surface for a time and then turned toward a white surface1 the fatigue to green light diminishes the extent of response to the green rays in the light reflected by the white surface4 ,the result is the perception of a certain area of the white surface 7corresponding to the portion of the field fatigued by green light7 as of a color equal to white minus some green--the result of which is pink or purple4 ,this is easily understood by referring to the principles of color-mixture4 ,red1 green1 and blue 7or violet7 mixed in proper proportions will produce any color or tint and even white4 ,thus these may be considered to be the components of white light4 ,hence if the retina through fatigue is unable to respond fully to the green component1 the result may be expressed mathematically as red plus blue plus reduced green1 or synthetically a purplish white or pink4 ,when fatigued to red light the after-image on a white surface is blue-green4 ,when fatigued to blue light it is yellowish4 ,further mixtures may be obtained by directing the after-image upon colored surfaces4 ,in this manner many of the interesting visual phenomena and illusions associated with the viewing of colors are accounted for4 ,the influence of a colored environment upon a colored object is really very great4 ,this is known as simultaneous contrast4 ,the influence of the immediately previous history of the retina upon the perception of colored surfaces is also very striking4 ,this is called successive contrast4 ,it is interesting to note that an after-image produced by looking at a bright light-source1 for example1 is projected into space even with the eyes closed4 ,it is instructive to study after-images and this may be done at any moment4 ,on gazing at the sun for an instant and then looking away1 an after-image is seen which passes in color from green1 blue1 purple1 etc41 and finally fades4 ,for a time it is brighter than the background which may conveniently be the sky4 ,on closing the eyes and placing the hands over them the background now is dark and the appearance of the after-image changes markedly4 ,there are many kinds1 effects1 and variations of after-images1 some of which are discussed in other chapters4 ,as the intensity of illumination of a landscape1 for example1 decreases toward twilight1 the retina diminishes in sensibility to the rays of longer wave-lengths such as yellow1 orange1 and red4 ,therefore1 it becomes relatively more sensitive to the rays of shorter wave-length such as green1 blue1 and violet4 ,the effects of this ,purkinje phenomenon 7named after the discoverer7 may be added to the class of illusions treated in this book4 ,it is interesting to note in this connection that moonlight is represented on some paintings and especially on the stage as greenish blue in color1 notwithstanding that physical measurements show it to be approximately the color of sunlight4 ,in fact1 it is sunlight reflected by dead1 frigid1 and practically colorless matter4 ,some illusions may be directly traced to the structure of the eye under unusual lighting conditions4 ,for example1 in a dark room hold a lamp obliquely outward but near one eye 7the other being closed and shielded7 and forward sufficiently for the retina to be strongly illuminated4 ,move the lamp gently while gazing at a plain dark surface such as the wall4 ,finally the visual field appears dark1 due to the intense illumination of the retina and there will appear1 apparently projected upon the wall1 an image resembling a branching leafless tree4 ,these are really shadows of the blood vessels in the retina4 ,the experiment is more successful if an image of a bright light-source is focused on the sclerotic near the cornea4 ,if this image of the light-source is moved1 the tree-like image seen in the visual field will also move4 ,the rate of growth and decay of various color-sensations varies considerably4 ,by taking advantage of this fact many illusions can be produced4 ,in fact1 the careful observer will encounter many illusions which may be readily accounted for in this manner4 ,it may be said that in general the eyes are never at rest4 ,involuntary eye-movements are taking place all the time1 at least during consciousness4 ,some have given this restlessness a major part in the process of vision but aside from the correctness of theories involving eye-movements1 it is a fact that they are responsible for certain illusions4 ,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 jerkily4 ,on viewing a rapidly revolving wheel of an automobile as it proceeds down the street1 occasionally it will be seen to cease revolving momentarily4 ,these apparently are accounted for by involuntary eye-movements which take place regardless of the effort made to fixate vision4 ,if the eyelids are almost closed1 streamers appear to radiate in various directions from a light-source4 ,movements of the eyelids when nearly closed sometimes cause objects to appear to move4 ,these may be accounted for perhaps by the distortion of the moist film which covers the cornea4 ,the foregoing are only a few of the many visual phenomena due largely to the structure of the eye4 ,the effects of these and many others enter into visual illusions1 as will be seen here and there throughout the chapters which follow4 ,,iii ,,vision ,a description of the eye by no means suffices to clarify the visual process4 ,even the descriptions of various phenomena in the preceding chapter accomplish little more than to acquaint the reader with the operation of a mechanism1 although they suggest the trend of the explanations of many illusions4 ,at best only monocular vision has been treated1 and it does not exist normally for human beings4 ,a person capable only of monocular vision would be like ,cyclops ,polyphemus4 ,we might have two eyes1 or even1 like ,argus1 possess a hundred eyes and still not experience the wonderful advantages of binocular vision1 for each eye might see independently4 ,the phenomena of binocular vision are far less physical than those of monocular vision4 ,they are much more obscure1 illusory1 and perplexing because they are more complexly interwoven with or allied to psychological phenomena4 ,the sense of sight differs considerably from the other senses4 ,the sense of touch requires solid contact 7usually72 taste involves liquid contact2 smell1 gaseous contact2 and hearing depends upon a relay of vibrations from an object through another medium 7usually air71 resulting finally in contact4 ,however1 we perceive things at a distance through vibration 7electromagnetic waves called light7 conveyed by a subtle1 intangible1 universal medium which is unrecognizable excepting as a hypothetically necessary bearer of light-waves or1 more generally1 radiant energy4 ,it also is interesting to compare the subjectiveness and objectiveness of sensations4 ,the sensation of taste is subjective2 it is in us1 not in the body tasted4 ,in smell we perceive the sensation in the nose and by experience refer it to an object at a distance4 ,the sensation of hearing is objective2 that is1 we refer the cause to an object so completely that there is practically no consciousness of sensation in the ear4 ,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 sensation4 ,the foregoing order represents the sense-organs in increasing specialization and refinement4 ,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 impression4 ,in the case of vision this highly developed instrument makes it possible to see not only light but objects4 ,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 #ahj degrees to parallel4 ,there is also evident a gradual increase in the fineness of the bacillary layer of the retina from the margins toward the center1 and1 therefore1 an increasing accuracy in the perception of form4 ,this finally results in a highly organized central spot or fovea which is possessed only by man and the higher monkeys4 ,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 retinas4 ,these changes and others are closely associated with each other and especially with the development of the higher faculties of the mind4 ,binocular vision in man and in the higher animals is the last result of the gradual improvement of the most refined sense-organ1 adapting it to meet the requirements of highly complex organisms4 ,it cannot exist in some animals1 such as birds and fishes1 because they cannot converge their two optical axes upon a near point4 ,when a chicken wishes to look intently at an object it turns its head and looks with one eye4 ,such an animal sees with two eyes independently and possibly moves them independently4 ,the normal position of the axes of human eyes is convergent or parallel but it is possible to diverge the axes4 ,in fact1 with practice it is possible to diverge the axes sufficiently to look at a point near the back of the head1 although1 of course1 we do not see the point4 ,the movement of the eyes is rather complex4 ,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 axes2 that is1 no torsion4 ,when the visual plane is elevated and the eyes move to the right they rotate to the right2 when they move to the left they rotate to the left4 ,when the visual plane is depressed and the eyes move to the right they rotate to the left2 when they move to the left they rotate to the right4 ,through experience we unconsciously evaluate the muscular stresses1 efforts1 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 size1 shape1 and distance of objects4 ,even this brief glimpse of the principal movements of the eyes indicates a complexity which suggests the intricacy of the explanations of certain visual phenomena4 ,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 world4 ,they are as follows3 7#a7 extent2 7#b7 clearness of brightness and color as affected by distance2 7#c7 interference of near objects with those more distant2 7#d7 elevation of objects2 7#e7 variation of light and shade on objects2 7#f7 cast shadows2 7#g7 perspective2 7#h7 variation of the visor angle in proportion to distance2 7#i7 muscular effort attending accommodation of the eye2 7#aj7 stereoscopic vision2 7#aa7 muscular effort attending convergence of the axes of the eyes4 ,it will be recognized that only the last two are necessarily concerned with binocular vision4 ,these varieties of experiences may be combined in almost an infinite variety of proportions4 ,wundt in his attempt to explain visual perception considered chiefly three factors3 7#a7 the retinal image of the eye at rest2 7#b7 the influence of the movements of one eye2 and1 7#c7 the additional data furnished by the two eyes functioning together4 ,there are three fields of vision corresponding to the foregoing4 ,these are the retinal field of vision1 the monocular field1 and the binocular field4 ,the retinal field of vision is that of an eye at rest as compared with the monocular field1 which is all that can be seen with one eye in its entire range of movement and therefore of experience4 ,the retinal field has no clearly defined boundaries because it finally fades at its indefinite periphery into a region where sensation ceases4 ,it might be tiresome to follow detailed analyses of the many modes by which visual perception is attained1 so only a few generalizations will be presented4 ,for every voluntary act of sight there are two adjustments of the eyes1 namely1 focal and axial4 ,in the former case the ciliary muscle adjusts the lens in order to produce a defined image upon the retina4 ,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 retina4 ,these take place together without distinct volition for each but by the single voluntary act of looking4 ,through experience the intellect has acquired a wonderful capacity to interpret such factors as size1 form1 and distance in terms of the muscular movements in general without the observer being conscious of such interpretations4 ,binocular vision is easily recognized by holding a finger before the eyes and looking at a point beyond it4 ,the result is two apparently transparent fingers4 ,an object is seen single when the two retinal images fall on corresponding points4 ,direction is a primary datum of sense4 ,the property of corresponding points of the two retinas 7binocular vision7 and consequently of identical spatial points in the two visual fields is not so simple4 ,it is still a question whether corresponding points 7that is1 the existence of a corresponding point in one retina for each point in the other retina7 are innate1 instinctive1 and are antecedent of experience or are paired as the result of experience4 ,the one view results in the nativistic1 the other in the empiristic theory4 ,inasmuch as some scientists are arrayed on one side and some on the other1 it appears futile to dwell further upon this aspect4 ,it must suffice to state that binocular vision1 which consists of two retinas and consequently two fields of view absolutely cooerdinated in some manner in the brain1 yields extensive information concerning space and its contents4 ,after noting after-images1 motes floating in the field of view 7caused by defects in the eye-media7 and various other things1 it is evident that what we call the field of view is the external projection into space of retinal states4 ,all the variations of the latter1 such as images and shadows which are produced in the external field of one eye1 are faithfully reproduced in the external field of the other eye4 ,this sense of an external visual field is ineradicable4 ,even when the eyes are closed the external field is still there2 the imagination or intellect projects it outward4 ,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 7varying convergence of the axes7 the intellect practically automatically appraises the size1 form1 and distance of each object4 ,obviously1 experience is a prominent factor4 ,the perception of the third dimension1 depth or relative distance1 whether in a single object or a group of objects1 is the result of the successive combination of the different parts of two dissimilar images of the object or group4 ,as already stated1 the perception of distance1 size1 and form is based partly upon monocular and partly upon binocular vision1 and the simple elements upon which judgments of these are based are light1 shade1 color1 intensity1 and direction4 ,although the interpretation of muscular adjustments plays a prominent part in the formation of judgments1 the influences of mathematical perspective1 light1 shade1 color1 and intensity are more direct4 ,judgments based upon focal adjustment 7monocular7 are fairly accurate at distances from five inches to several yards4 ,those founded upon axial adjustment 7convergence of the two axes in binocular vision7 are less in error than the preceding ones4 ,they are reliable to a distance of about #ajjj feet4 ,judgments involving mathematical perspective are of relatively great accuracy without limits4 ,those arrived at by interpreting aerial perspective 7haziness of atmosphere1 reduction in color due to atmospheric absorption1 etc47 are merely estimates liable to large errors1 the accuracy depending largely upon experience with local conditions4 ,the measuring power of the eye is more liable to error when the distances or the objects compared lie in different directions4 ,a special case is the comparison of a vertical distance with a horizontal one4 ,it is not uncommon to estimate a vertical distance as much as #be per cent greater than an actually equal horizontal distance4 ,in general1 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 necessity4 ,a vertical line drawn perpendicular to a horizontal one is likely to appear bent when viewed with one eye4 ,its apparent inclination is variable but has been found to vary from one to three degrees4 ,monocular vision is likely to cause straight lines to appear crooked1 although the crookedness may seem to be more or less unstable4 ,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 size4 ,an amusing incident is told of an old negro who was hunting for squirrels4 ,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 marksman4 ,a complete shattering of his faith in his skill was only escaped by the discovery that the squirrel was a louse upon his eyebrow4 ,similarly1 a gnat in the air might appear to be an airplane under certain favorable circumstances4 ,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 barrel1 although a pine tree at the horizon-line may be estimated as #be feet across despite the fact that it may be entirely included in the disk of the sun setting behind it4 ,double images play an important part in the comparison of distances of objects4 ,the doubling of objects is only equal to the interocular distance4 ,suppose two horizontal wires or clotheslines about fifty feet away and one a few feet beyond the other4 ,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 view4 ,however1 if the head is turned to one side and downward 7#ij degrees7 so that the interocular line is now at right angles 7vertical7 to the horizontal lines1 the relative distances of the latter are brought out distinctly4 ,double images become visible in the latter case4 ,according to ,bruecke's theory the eyes are continuously in motion and the observer by alternately increasing or decreasing the convergence of the axes of the eyes1 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 space4 ,it may be assumed that experience has made the observer proficient in this appraisal which he arrives at almost unconsciously1 although it may be just as easy to accept ,wheatstone's explanation4 ,in fact1 some experiences with the stereoscope appear to support the latter theory4 ,wheatstone discovered that the dissimilar pictures of an object or scene1 when united by means of optical systems1 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 scene4 ,this is the principle upon which the familiar stereoscope is founded4 ,wheatstone formulated a theory which may be briefly stated as follows3 ,in viewing a solid object or a scene two slightly dissimilar retinal images are formed in the two eyes respectively1 but the mind completely fuses them into one mental image4 ,when this mental fusion of the two really dissimilar retinal images is complete in this way1 it is obvious that there cannot exist a mathematical coincidence4 ,the result is a perception of depth of space1 of solidity1 of relief4 ,in fact the third dimension is perceived4 ,a stereoscope accomplishes this in essentially the same manner1 for two pictures1 taken from two different positions respectively corresponding to the positions of the eyes1 are combined by means of optical systems into one image4 ,lack of correct size and position of the individual elements of stereoscopic pictures are easily detected on combining them4 ,that is1 their dissimilarity must exactly correspond to that between two views of an object or scene from the positions of the two eyes respectively 7,fig4 #b74 ,this fact has been made use of in detecting counterfeit notes4 ,if two notes made from the same plate are viewed in a stereoscope and the identical figures are combined1 the combination is perfect and the plane of the combined images is perfectly flat4 ,if the notes are not made from the same plate but one of them is counterfeit1 slight variations in the latter are unavoidable4 ,such variations will show themselves in a wavy surface4 ,the unwillingness of the visual sense to combine the two retinal images1 if they are dissimilar to the extent of belonging to two different objects1 is emphasized by means of colors4 ,for example1 if a green glass is placed over one eye and a red glass over the other1 the colors are not mixed by the visual sense4 ,the addition of these two colors results normally in yellow1 with little or no suggestion of the components--red and green4 ,but in the foregoing case the visual field does not appear of a uniform yellow4 ,it appears alternately red and green1 as though the colors were rivaling each other for complete mastery4 ,in fact1 this phenomenon has been termed retinal rivalry4 ,the lenses of the stereoscope supplement eye-lenses and project on the retina two perfect images of a near object1 although the eyes are looking at a distant object and are therefore not accommodated for the near one 7the photographs74 ,the lenses enlarge the images similar to the action of a perspective glass4 ,this completes the illusion of an object or of a scene4 ,there is a remarkable distinctness of the perception of depth of space and therefore a wonderful resemblance to the actual object or scene4 ,it is interesting to note the effect of taking the two original photographs from distances separated by several feet4 ,the effect is apparently to magnify depth4 ,it is noteworthy that two pictures taken from an airplane at points fifty feet or so apart1 when combined in the stereoscope1 so magnify the depth that certain enemy-works can be more advantageously detected than from ordinary photographs4 ,stereoscopic images such as represented in ,fig4 #b may be combined without the aid of the stereoscope if the optical axes of the eye can be sufficiently converged or diverged4 ,such images or pictures are usually upon a card and are intended to be combined beyond the plane of the card1 for it is in this position that the object or scene can be perceived in natural perspective1 of natural size1 of natural form1 and at natural distance4 ,but in combining them the eyes are looking at a distant object and the axes are parallel or nearly so4 ,therefore1 the eyes are focally adjusted for a distant object but the light comes from a very near object--the pictures on the card4 ,myopic eyes do not experience this difficulty and it appears that normal vision may be trained to overcome it4 ,normal eyes are aided by using slightly convex lenses4 ,such glasses supplement the lenses of the eye1 making possible a clear vision of a near object while the eyes are really looking far away or1 in other words1 making possible a clear image of a near object upon the retina of the unadjusted eye4 ,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 so1 which is the condition when looking at a distant object4 ,in such a case the two pictures must be brought closer together4 ,illustration3 ,fig4 #b4--,stereoscopic pictures for combining by converging or diverging the optical axes4 ,illustration3 ,fig4 #c4--,stereoscopic pictures4 ,in ,figs4 #b and #c are found dissimilar drawings of the correct dissimilarity of stereoscopic pictures4 ,it is interesting and instructive to practice combining these with the unaided eyes4 ,if ,fig4 #b is held at an arm's length and the eyes are focused upon a point several inches distant1 the axes will be sufficiently converged so that the two images are superposed4 ,it may help to focus the eyes upon the tip of a finger until the stereoscopic images are combined4 ,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 cone1 apparently possessing the third dimension and being perceived as apparently smaller than the actual pictures in the background at arm's length4 ,if the two stereoscopic pictures are combined by looking at a point far beyond the actual position of ,fig4 #b1 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 diagrams4 ,in the latter case the smaller end of the apparent solid appears to be nearer than the larger end1 but in the former case the reverse is true1 that is1 the smaller end appears to be at a greater distance4 ,the same experiments may be performed for ,fig4 #c with similar results excepting that this appears to be a shell under the same circumstances that ,fig4 #b appears to be a solid and vice versa4 ,a few patient trials should be rewarded by success1 and if so the reader can gain much more understanding from the actual experiences than from description4 ,the foregoing discussion of vision should indicate the complexity of the visual and mental activities involved in the discrimination1 association1 and interpretation of the data obtained through the eye4 ,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 doubt4 ,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 us4 ,clearness of vision is confined to a small area about the point of sight1 and it rapidly diminishes away from this point1 images becoming dim and double4 ,we sweep this point of sight backward and forward and over an extensive field of view1 gathering all the distinct impressions into one mental image4 ,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 objects4 ,certainly the acquired facility is remarkable4 ,,iv ,,some ,,types ,,of ,,geometrical ,,illusions ,no simple classification of illusions is ample or satisfactory1 for there are many factors interwoven4 ,for this reason no claims are made for the various divisions of the subject represented by and in these chapters excepting that of convenience4 ,obviously1 some divisions are necessary in order that the variegated subject may be presentable4 ,the classification used appears to be logical but very evidently it cannot be perfectly so when the logic is not wholly available1 owing to the disagreement found among the explanations offered by psychologists4 ,it may be argued that the geometrical type of illusion should include many illusions which are discussed in other chapters4 ,indeed1 this is perhaps true4 ,however1 it appears to suit the present purpose to introduce this phase of this book by a group of illusions which involve plane geometrical figures4 ,if some of the latter appear in other chapters1 it is because they seem to border upon or to include other factors beyond those apparently involved in the simple geometrical type4 ,the presentation which follows begins 7for the sake of clearness7 with a few representative geometrical illusions of various types4 ,the ,effect of the ,location in the ,visual ,field4--,one of the most common illusions is found in the letter ,s or figure #h4 ,ordinarily we are not strongly conscious of a difference in the size of the upper and lower parts of these characters2 however1 if we invert them 7#hhhh ,,ssss7 the difference is seen to be large4 ,the question arises1 ,is the difference due fundamentally to the locations of the two parts in the visual field8 ,it scarcely seems credible that visual perception innately appraises the upper part larger than the lower1 or the lower smaller than the upper part when these small characters are seen in their accustomed position4 ,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 difference4 ,that is1 for some reason through being confronted with this difference so many times1 the intellect has become adapted to it and1 therefore1 has grown to ignore it4 ,regardless of the explanation1 the illusion exists and this is the point of chief interest4 ,for the same reason the curvature of the retina does not appear to account for illusion through distortion of the image1 because the training due to experience has caused greater difficulties than this to disappear4 ,we must not overlook the tremendous corrective influence of experience upon which visual perception for the adult is founded4 ,if we have learned to correct in some cases1 why not in all cases which we have encountered quite generally8 ,illustration3 ,fig4 #d4--,the vertical line appears longer than the equal horizontal line in each case4 ,this type of illusion persists in geometrical figures and may be found on every hand4 ,a perfect square when viewed vertically appears too high1 although the illusion does not appear to exist in the circle4 ,in ,fig4 #d the vertical line appears longer than the horizontal line of the same length4 ,this may be readily demonstrated by the reader by means of a variety of figures4 ,a striking case is found in ,fig4 #e1 where the height and the width of the diagram of a silk hat are equal4 ,despite the actual equality the height appears to be much greater than the width4 ,a pole or a tree is generally appraised as of greater length when it is standing than when it lies on the ground4 ,this illusion may be demonstrated by placing a black dot an inch or so above another on a white paper4 ,now1 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 original4 ,on turning the paper through ninety degrees or by actual measurement1 the extent of the illusion will become apparent4 ,by doing this several times1 using various distances1 this type of illusion becomes convincing4 ,illustration3 ,fig4 #e4--,the vertical dimension is equal to the horizontal one1 but the former appears greater4 ,the explanation accepted by some is that more effort is required to raise the eyes1 or point of sight1 through a certain vertical distance than through an equal horizontal distance4 ,perhaps we unconsciously appraise effort of this sort in terms of distance1 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 moved8 ,we are doing this continuously1 so why do we not learn to distinguish2 furthermore1 we have overcome other great obstacles in developing our visual sense4 ,in this complex field of physiological psychology questions are not only annoying1 but often disruptive4 ,as has been pointed out in ,chapter ,,ii1 images of objects lying near the periphery of the visual field are more or less distorted1 owing to the structure and to certain defects of parts of the eye4 ,for example1 a checkerboard viewed at a proper distance with respect to its size appears quite distorted in its outer regions4 ,cheap cameras are likely to cause similar errors in the images fixed upon the photographic plate4 ,photographs are interesting in connection with visual illusions1 because of certain distortions and of the magnification of such aspects as perspective4 ,incidentally in looking for illusions1 difficulty is sometimes experienced in seeing them when the actual physical truths are known2 that is1 in distinguishing between what is actually seen and what actually exists4 ,the ability to make this separation grows with practice but where the difficulty is obstinate1 it is well for the reader to try observers who do not suspect the truth4 ,illusions of ,interrupted ,extent4--,distance and area appear to vary in extent1 depending upon whether they are filled or empty or are only partially filled4 ,for example1 a series of dots will generally appear longer overall than an equal distance between two points4 ,this may be easily demonstrated by arranging three dots in a straight line on paper1 the two intervening spaces being of equal extent1 say about one or two inches long4 ,if in one of the spaces a series of a dozen dots is placed1 this space will appear longer than the empty space4 ,however1 if only one dot is placed in the middle of one of the empty spaces1 this space now is likely to appear of less extent than the empty space4 7,see ,fig4 #g47 ,a specific example of this type of illusion is shown in ,fig4 #f4 ,the filled or divided space generally appears greater than the empty or undivided space1 but certain qualifications of this statement are necessary4 ,in a the divided space unquestionably appears greater than the empty space4 ,apparently the filled or empty space is more important than the amount of light which is received from the clear spaces1 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 line4 ,furthermore1 apparently the spacing which is the most obtrusive is most influential in causing the divided space to appear greater for a than for b4 ,the illusion still persists in c4 ,illustration3 ,fig4 #f4--,the divided or filled space on the left appears longer than the equal space on the right4 ,an idea of the magnitude may be gained from certain experiments by ,aubert4 ,he used a figure similar to a ,fig4 #f containing a total of five short lines4 ,four of them were equally spaced over a distance of #ajj mm4 corresponding to the left half of a1 ,fig4 #f4 ,the remaining line was placed at the extreme right and defined the limit of an empty space also #ajj mm4 long4 ,in all cases1 the length of the empty space appeared about ten per cent less than that of the space occupied by the four lines equally spaced4 ,various experimenters obtain different results1 and it seems reasonable that the differences may be accounted for1 partially at least1 by different degrees of unconscious correction of the illusion4 ,this emphasizes the desirability of using subjects for such experiments who have no knowledge pertaining to the illusion4 ,illustration3 ,fig4 #g4--,the three lines are of equal length4 ,illustration3 ,fig4 #h4--,the distance between the two circles on the left is equal to the distance between the outside edges of the two circles on the right4 ,as already stated there are apparent exceptions to any simple rule1 for1 as in the case of dots cited in a preceding paragraph1 the illusion depends upon the manner in which the division is made4 ,for example1 in ,fig4 #g1 a and c are as likely to appear shorter than b as equal to it4 ,it has been concluded by certain investigators that when subdivision of a line causes it to appear longer1 the parts into which it is divided or some of them are likely to appear shorter than isolated lines of the same length4 ,the reverse of this statement also appears to hold4 ,for example in ,fig4 #g1 a appears shorter than b and the central part appears lengthened1 although the total line appears shortened4 ,this illusion is intensified by leaving the central section blank4 ,a figure of this sort can be readily drawn by the reader by using short straight lines in place of the circles in ,fig4 #h4 ,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 right1 despite the fact that these distances are equal4 ,it appears that mere intensity of retinal stimulation does not account for these illusions1 but rather the figures which we see4 ,illustration3 ,fig4 #i4--,three squares of equal dimensions which appear different in area and dimension4 ,in ,fig4 #i the three squares are equal in dimensions but the different characters of the divisions cause them to appear not only unequal1 but no longer squares4 ,in ,fig4 #aj 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 group4 ,illustration3 ,fig4 #aj4--,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 circles4 ,illusions of ,contour4--,the illusions of this type1 or exhibiting this influence1 are quite numerous4 ,in ,fig4 #aa there are two semicircles1 one closed by a diameter1 the other unclosed4 ,the latter appears somewhat flatter and of slightly greater radius than the closed one4 ,similarly in ,fig4 #ab the shorter portion of the interrupted circumference of a circle appears flatter and of greater radius of curvature than the greater portions4 ,in ,fig4 #ac the length of the middle space and of the open-sided squares are equal4 ,in fact there are two uncompleted squares and an empty square between1 the three of which are of equal dimensions4 ,however the middle space appears slightly too high and narrow2 the other two appear slightly too low and broad4 ,these figures are related to the well-known ,mueller-,lyer illusion illustrated in ,fig4 #ef4 ,some of the illusions presented later will be seen to involve the influence of contour4 ,examples of these are ,figs4 #ee and #fj4 ,in the former1 the horizontal base line appears to sag2 in the latter1 the areas appear unequal1 but they are equal4 ,illustration3 ,fig4 #aa4--,two equal semicircles4 ,illustration3 ,fig4 #ab4--;,arcs of the same circle4 ,illustration3 ,fig4 #ac4--,three incomplete but equal squares4 ,illusions of ,contrast4--,those illusions due to brightness contrast are not included in this group1 for contrast here refers to lines1 angles and areas of different sizes4 ,in general1 parts adjacent to large extents appear smaller and those adjacent to small extents appear larger4 ,a simple case is shown in ,fig4 #ad1 where the middle sections of the two lines are equal1 but that of the shorter line appears longer than that of the longer line4 ,in ,fig4 #ae the two parts of the connecting line are equal1 but they do not appear so4 ,this illusion is not as positive as the preceding one and1 in fact1 the position of the short vertical dividing line may appear to fluctuate considerably4 ,illustration3 ,fig4 #ad4--,middle sections of the two lines are equal4 ,illustration3 ,fig4 #ae4--;,an effect of contrasting areas 7,baldwin's figure74 ,fig4 #af might be considered to be an illusion of contour1 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 figures4 ,incidentally1 it is difficult to believe that the maximum horizontal width of the lower figure is as great as the maximum height of the figure4 ,at this point it is of interest to refer to other contrast illusions such as ,figs4 #bj1 #eg1 and #ei4 ,illustration3 ,fig4 #af4--;,an illusion of contrast4 ,a striking illusion of contrast is shown in ,fig4 #ag1 where the central circles of the two figures are equal1 although the one surrounded by the large circles appears much smaller than the other4 ,similarly1 in ,fig4 #ah the inner circles of b and c are equal but that of b appears the larger4 ,the inner circle of a appears larger than the outer circle of b1 despite their actual equality4 ,illustration3 ,fig4 #ag4--;,equal circles which appear unequal due to contrast 7,ebbinghaus' figure74 ,illustration3 ,fig4 #ah4--;,equal circles appearing unequal owing to contrasting concentric circles4 ,in ,fig4 #ai the circle nearer the apex of the angle appears larger than the other4 ,this has been presented as one reason why the sun and moon appear larger at the horizon than when at higher altitudes4 ,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 horizon4 ,if there were one in reality1 it would not be seen in profile4 ,illustration3 ,fig4 #ai4--;,circles influenced by position within an angle4 ,illustration3 ,fig4 #bj4--;,contrasting angles4 ,if two angles of equal size are bounded by small and large angles respectively1 the apex in each case being common to the inner and two bounding angles1 the effect of contrast is very apparent1 as seen in ,fig4 #bj4 ,in ,fig4 #eg are found examples of effects of lines contrasted as to length4 ,illustration3 ,fig4 #ba4--,owing to perspective the right angles appear oblique and vice versa4 ,the reader may readily construct an extensive variety of illusions of contrast2 in fact1 contrast plays a part in most geometrical-optical illusions4 ,the contrasts may be between existing lines1 areas1 etc41 or the imagination may supply some of them4 ,illustration3 ,fig4 #bb4--,two equal diagonals which appear unequal4 ,illusions of ,perspective4--,as the complexity of figures is increased the number of possible illusions is multiplied4 ,in perspective we have the influences of various factors such as lines1 angles1 and sometimes contour and contrast4 ,in ,fig4 #ba the suggestion due to the perspective of the cube causes right angles to appear oblique and oblique angles to appear to be right angles4 ,this figure is particularly illusive4 ,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 oblique4 ,illustration3 ,fig4 #bc4--;,apparent variations in the distance between two parallel lines4 ,a striking illusion involving perspective1 or at least the influence of angles1 is shown in ,fig4 #bb4 ,here the diagonals of the two parallelograms are of equal length but the one on the right appears much smaller4 ,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 ,,ax4 ,it will be found to pass through the point ,y4 ,obviously1 geometry abounds in geometrical-optical illusions4 ,illustration3 ,fig4 #bd4--;,a striking illusion of perspective4 ,the effect of contrast is seen in a in ,fig4 #bc2 that is1 the short parallel lines appear further apart than the pair of long ones4 ,by adding the oblique lines at the ends of the lower pair in b1 these parallel lines now appear further apart than the horizontal parallel lines of the small rectangle4 ,the influence of perspective is particularly apparent in ,fig4 #bd1 where natural perspective lines are drawn to suggest a scene4 ,the square columns are of the same size but the further one1 for example1 being apparently the most distant and of the same physical dimensions1 actually appears much larger4 ,here is a case where experience1 allowing for a diminution of size with increasing distance1 actually causes the column on the right to appear larger than it really is4 ,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 lines4 ,apparently converging lines influence these equal figures in proportion as they suggest perspective4 ,illustration3 ,fig4 #be4--;,distortion of a square due to superposed lines4 ,although they are not necessarily illusions of perspective1 ,figs4 #be and #bf are presented here because they involve similar influences4 ,in ,fig4 #be the hollow square is superposed upon groups of oblique lines so arranged as to apparently distort the square4 ,in ,fig4 #bf distortions of the circumference of a circle are obtained in a similar manner4 ,illustration3 ,fig4 #bf4--;,distortion of a circle due to superposed lines4 ,it is interesting to note that we are not particularly conscious of perspective1 but it is seen that it has been a factor in the development of our visual perception4 ,in proof of this we might recall the first time as children we were asked to draw a railroad track trailing off in the distance4 ,doubtless1 most of us drew two parallel lines instead of converging ones4 ,a person approaching us is not sensibly perceived to grow4 ,he is more likely to be perceived all the time as of normal size4 ,the finger held at some distance may more than cover the object such as a distant person1 but the finger is not ordinarily perceived as larger than the person4 ,of course1 when we think of it we are conscious of perspective and of the increase in size of an approaching object4 ,when a locomotive or automobile approaches very rapidly1 this growth is likely to be so striking as to be generally noticeable4 ,the reader may find it of interest at this point to turn to illustrations in other chapters4 ,the foregoing are a few geometrical illusions of representative types4 ,these are not all the types of illusions by any means and they are only a few of an almost numberless host4 ,these have been presented in a brief classification in order that the reader might not be overwhelmed by the apparent chaos4 ,various special and miscellaneous geometrical illusions are presented in later chapters4 ,v ,,equivocal ,,figures ,many figures apparently change in appearance owing to fluctuations in attention and in associations4 ,a human profile in intaglio 7,figs4 #gb and #gc7 may appear as a bas-relief4 ,crease a card in the middle to form an angle and hold it at an arm's length4 ,when viewed with one eye it can be made to appear open in one way or the other2 that is1 the angle may be made to appear pointing toward the observer or away from him4 ,the more distant part of an object may be made to appear nearer than the remaining part4 ,plane diagrams may seem to be solids4 ,deception of this character is quite easy if the light-source and other extraneous factors are concealed from the observer4 ,it is very interesting to study these fluctuating figures and to note the various extraneous data which lead us to judge correctly4 ,furthermore1 it becomes obvious that often we see what we expect to see4 ,for example1 we more commonly encounter relief than intaglio2 therefore1 we are likely to think that we are looking at the former4 ,proper consideration of the position of the dominant light-source and of the shadows will usually provide the data for a correct conclusion4 ,however1 habit and probability are factors whose influence is difficult to overcome4 ,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 form4 ,stairs1 glasses1 rings1 cubes1 and intaglios are among the objects commonly used to illustrate this type of illusion4 ,in connection with this type1 it is well to realize how tenaciously we cling to our perception of the real shapes of objects4 ,for example1 a cube thrown into the air in such a manner that it presents many aspects toward us is throughout its course a cube4 ,illustration3 ,fig4 #bg4--;,illustrating fluctuation of attention4 ,the figures which exhibit these illusions are obviously those which are capable of two or more spatial relations4 ,the double interpretation is more readily accomplished by monocular than by binocular vision4 ,fig4 #bg consists of identical patterns in black and white4 ,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 background4 ,sometimes fluctuation of attention apparently accounts for the change and1 in fact1 this can be tested by willfully altering the attention from a white pattern to a black one4 ,incidentally one investigator found that the maximum rate of fluctuation was approximately equal to the pulse rate1 although no connection between the two was claimed4 ,it has also been found that inversion is accompanied by a change in refraction of the eye4 ,illustration3 ,fig4 #bh4--,the grouping of the circles fluctuates4 ,another example is shown in ,fig4 #bh4 ,this may appear to be white circles upon a black background or a black mesh upon a white background4 ,however1 the more striking phenomenon is the change in the grouping of the circles as attention fluctuates4 ,we may be conscious of hollow diamonds of circles1 one inside the other1 and then suddenly the pattern may change to groups of diamonds consisting of four circles each4 ,perhaps we may be momentarily conscious of individual circles2 then the pattern may change to a hexagonal one1 each hexagon consisting of seven circles--six surrounding a central one4 ,the pattern also changes into parallel strings of circles1 triangles1 etc4 ,illustration3 ,fig4 #bi4--;,crossed lines which may be interpreted in two ways4 ,the crossed lines in ,fig4 #bi can be seen as right angles in perspective with two different spatial arrangements of one or both lines4 ,in fact there is quite a tendency to see such crossed lines as right angles in perspective4 ,the two groups on the right represent a simplified ,zoellner's illusion 7,fig4 #cg74 ,the reader may find it interesting to spend some time viewing these figures and in exercising his ability to fluctuate his attention4 ,in fact1 he must call upon his imagination in these cases4 ,sometimes the changes are rapid and easy to bring about4 ,at other moments he will encounter an aggravating stubbornness4 ,occasionally there may appear a conflict of two appearances simultaneously in the same figure4 ,the latter may be observed occasionally in ,fig4 #cj4 ,eye-movements are brought forward by some to aid in explaining the changes4 ,illustration3 ,fig4 #cj4--,reversible cubes4 ,in ,fig4 #cj a reversal of the aspect of the individual cubes or of their perspective is very apparent4 ,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 strips4 ,the illusion of the bent card or partially open book is seen in ,fig4 #ca4 ,the tetrahedron in ,fig4 #cb may appear either as erect on its base or as leaning backward with its base seen from underneath4 ,illustration3 ,fig4 #ca4--,the reversible open book 7after ,mach74 ,illustration3 ,fig4 #cb4--;,a reversible tetrahedron4 ,the series of rings in ,fig4 #cc may be imagined to form a tube such as a sheet-metal pipe with its axis lying in either of two directions4 ,sometimes by closing one eye the two changes in this type of illusion are more readily brought about4 ,it is also interesting to close and open each eye alternately1 at the same time trying to note just where the attention is fixed4 ,the familiar staircase is represented in ,fig4 #cd4 ,it is likely to appear in its usual position and then suddenly to invert4 ,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 away4 ,by focusing the attention in this manner the fluctuation becomes an easy matter to obtain4 ,illustration3 ,fig4 #cc4--,reversible perspective of a group of rings or of a tube4 ,illustration3 ,fig4 #cd4--,schroeder's reversible staircase4 ,in ,fig4 #ce is a similar example4 ,first one part will appear solid and the other an empty corner1 then suddenly both are reversed4 ,however1 it is striking to note one half changes while the other remains unchanged1 thus producing momentarily a rather peculiar figure consisting of two solids1 for example1 attached by necessarily warped surfaces4 ,illustration3 ,fig4 #ce4--,thiery's figure4 ,perhaps the reader has often witnessed the striking illusion of some portraits which were made of subjects looking directly at the camera or painter4 ,regardless of the position of the observer the eyes of the portrait appear to be directed toward him4 ,in fact1 as the observer moves1 the eyes in the picture follow him so relentlessly as to provoke even a feeling of uncanniness4 ,this fact is accounted for by the absence of a third dimension1 for a sculptured model of a head does not exhibit this feature4 ,perspective plays a part in some manner1 but no attempt toward explanation will be made4 ,in ,fig4 #cf are two sketches of a face4 ,one appears to be looking at the observer1 but the other does not4 ,if the reader will cover the lower parts of the two figures1 leaving only the two pairs of eyes showing1 both pairs will eventually appear to be looking at the observer4 ,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 him4 ,although it is not claimed that this illusion is caused by the same conditions as those immediately preceding1 it involves attention4 ,at least1 it is fluctuating in appearance and therefore is equivocal4 ,it is interesting to note the influence of the other features 7below the eyes74 ,the perspective of these is a powerful influence in directing the eyes of the sketch4 ,in the foregoing only definite illusions have been presented which are universally witnessed by normal persons4 ,there are no hallucinatory phases in the conditions or causes4 ,it is difficult to divide these with definiteness from certain illusions of depth as discussed in ,chapter ,,vii4 ,the latter undoubtedly are sometimes entwined to some extent with hallucinatory phases2 in fact1 it is doubtful if they are not always hallucinations to some degree4 ,hallucinations are not of interest from the viewpoint of this book1 but illusions of depth are treated because they are of interest4 ,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 conditions4 ,the latter statement does not hold for illusions of depth in which objects may be seen alternately near and far1 large and small1 etc41 although they are not necessarily pure hallucinations as distinguished from the types of illusions regarding which there is general perceptual agreement4 ,illustration3 ,fig4 #cf4--;,illustrating certain influences upon the apparent direction of vision4 ,by covering all but the eyes the latter appear to be drawn alike in both sketches4 ,in explanation of the illusory phenomena pertaining to such geometrical figures as are discussed in the foregoing paragraphs1 chiefly two different kinds of hypotheses have been offered4 ,they are respectively psychological and physiological1 although there is more or less of a mixture of the two in most attempts toward explanation4 ,the psychological hypotheses introduce such factors as attention1 imagination1 judgment1 and will4 ,hering and also ,helmholtz claim that the kind of inversion which occurs is largely a matter of chance or of volition4 ,the latter holds that the perception of perspective figures is influenced by imagination or the images of memory4 ,that is1 if one form of the figure is vividly imagined the perception of it is imminent4 ,helmholtz has stated that1 ,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 images4 ,the physiological hypotheses depend largely upon such factors as accommodation and eye-movement4 ,necker held to the former as the chief cause4 ,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 field4 ,this hypothesis is open to serious objections4 ,wundt contends that the inversion is caused by changes in the points and lines of fixation4 ,he says1 ,the image of the retina ought to have a determined position if a perspective illusion is to appear2 but the form of this illusion is entirely dependent on motion and direction4 ,some hypotheses interweave the known facts of the nervous system with psychological facts but some of these are examples of a common anomaly in theorization1 for facts plus facts do not necessarily result in a correct theory4 ,that is1 two sets of facts interwoven do not necessarily yield an explanation which is correct4 ,,vi ,,the ,,influence ,,of ,,angles ,as previously stated1 no satisfactory classification of visual illusions exists1 but in order to cover the subject1 divisions are necessary4 ,for this reason the reader is introduced in this chapter to the effects attending the presence of angles4 ,by no means does it follow that this group represents another type1 for it really includes many illusions of several types4 ,the reason for this grouping is that angles play an important part1 directly or indirectly1 in the production of illusions4 ,for a long time many geometrical illusions were accounted for by overestimation or underestimation of angles1 but this view has often been found to be inadequate4 ,however1 it cannot be denied that many illusions are due at least to the presence of angles4 ,apparently ,zoellner was the first to describe an illusion which is illustrated in simple form in ,fig4 #bi and more elaborately in ,figs4 #cg to #dj4 ,the two figures at the right of ,fig4 #bi were drawn for another purpose and are not designed favorably for the effect1 although it may be detected when the figure is held at a distance4 ,zoellner accidentally noticed the illusion on a pattern designed for a print for dress-goods4 ,the illusion is but slightly noticeable in ,fig4 #bi1 but by multiplying the number of lines 7and angles7 the long parallel lines appear to diverge in the direction that the crossing lines converge4 ,zoellner studied the case thoroughly and established various facts4 ,he found that the illusion is greatest when the long parallel lines are inclined about #de degrees to the horizontal4 ,this may be accomplished for ,fig4 #cg1 by turning the page 7held in a vertical plane7 through an angle of #de degrees from normal4 ,the illusion vanishes when held too far from the eye to distinguish the short crossing lines1 and its strength varies with the inclination of the oblique lines to the main parallels4 ,the most effective angle between the short crossing lines and the main parallels appears to be approximately #cj degrees4 ,in ,fig4 #cg there are two illusions of direction4 ,the parallel vertical strips appear unparallel and the right and left portions of the oblique cross-lines appear to be shifted vertically4 ,it is interesting to note that steady fixation diminishes and even destroys the illusion4 ,illustration3 ,fig4 #cg4--,zoellner's illusion of direction4 ,the maximum effectiveness of the illusion1 when the figure is held so that the main parallel lines are at an inclination of about #de degrees to the horizontal was accounted for by ,zoellner as the result of less visual experience in oblique directions4 ,he insisted that it takes less time and is easier to infer divergence or convergence than parallelism4 ,this explanation appears to be disproved by a figure in which slightly divergent lines are used instead of parallel ones4 ,owing to the effect of the oblique crossing lines1 the diverging lines may be made to appear parallel4 ,furthermore it is difficult to attach much importance to ,zoellner's explanation because the illusion is visible under the extremely brief illumination provided by one electric spark4 ,of course1 the duration of the physiological reaction is doubtless greater than that of the spark1 but at best the time is very short4 ,hering explained the ,zoellner illusion as due to the curvature of the retina1 and the resulting difference in the retinal images1 and held that acute angles appear relatively too large and obtuse ones too small4 ,the latter has been found to have limitations in the explanation of certain illusions4 ,this ,zoellner illusion is very striking and may be constructed in a variety of forms4 ,in ,fig4 #cg the effect is quite apparent and it is interesting to view the figure at various angles4 ,for example1 hold the figure so that the broad parallel lines are vertical4 ,the illusion is very pronounced in this position2 however1 on tilting the page backward the illusion finally disappears4 ,in ,fig4 #ch the short oblique lines do not cross the long parallel lines and to make the illusion more striking1 the obliquity of the short lines is reversed at the middle of the long parallel lines4 ,variations of this figure are presented in ,figs4 #ci and #dj4 ,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 figures4 ,illustration3 ,fig4 #ch4--,parallel lines which do not appear so4 ,illustration3 ,fig4 #ci4--,wundt's illusion of direction4 ,illustration3 ,fig4 #dj4--;,hering's illusion of direction4 ,many investigations of the ,zoellner illusion are recorded in the literature4 ,from these it is obvious that the result is due to the additive effects of many simple illusions of angle4 ,in order to give an idea of the manner in which such an illusion may be built up the reasoning of ,jastrow#a will be presented in condensed form4 ,when two straight lines such as ,a and ,b in ,fig4 #da are separated by a space it is usually possible to connect the two mentally and to determine whether or not1 if connected1 they would lie on a straight line4 ,however1 if another line is connected to one1 thus forming an angle as ,c does with ,a1 the lines which appeared to be continuous 7as ,a and ,b originally7 no longer appear so4 ,the converse is also true1 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 angle4 ,all these variations cannot be shown in a single figure1 but the reader will find it interesting to draw them4 ,furthermore1 the letters used on the diagram in order to make the description clearer may be confusing and these can be eliminated by redrawing the figure4 ,in ,fig4 #da the obtuse angle ,,ac tends to tilt ,a downward1 so apparently if ,a were prolonged it would fall below ,b4 ,similarly1 ,c appears to fall to the right of ,d4 ,illustration3 ,fig4 #da4--,simple effect of angles4 ,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 degree4 ,the illusion decreases or increases in general as the angle decreases or increases respectively4 ,although it is not safe to present simple statements in a field so complex as that of visual illusion where explanations are still controversial1 it is perhaps possible to generalize as ,jastrow did in the foregoing case as follows3 ,if the direction of an angle is that of the line bisecting it and pointing toward the apex1 the direction of the sides of an angle will apparently be deviated toward the direction of the angle4 ,the deviation apparently is greater with obtuse than with acute angles1 and when obtuse and acute angles are so placed in a figure as to give rise to opposite deviations1 the greater angle will be the dominant influence4 ,although the illusion in such simple cases as ,fig4 #da is slight1 it is quite noticeable4 ,the effect of the addition of many of these slight individual influences is obvious in accompanying figures of greater complexity4 ,these individual effects can be so multiplied and combined that many illusory figures may be devised4 ,in ,fig4 #db 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 7the letters corresponding to similar lines in ,fig4 #da74 ,in this manner they appear to be deviated considerably out of their true straight line4 ,if the reader will draw a straight line nearly parallel to ,d in ,fig4 #da and to the right1 he will find it helpful4 ,this line should be drawn to appear to be a continuation of ,c when the page is held so ,d is approximately horizontal4 ,this is a simple and effective means of testing the magnitude of the illusion1 for it is measured by the degree of apparent deviation between ,d and the line drawn adjacent to it1 which the eye will tolerate4 ,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 intervening4 ,this deviation from the true continuation may then be readily determined4 ,illustration3 ,fig4 #db4 ,the effect of two angles in tilting the horizontal lines4 ,illustration3 ,fig4 #dc4 ,the effect of crossed lines upon their respective apparent directions4 ,a more complex case is found in ,fig4 #dc 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 reverse4 ,however1 the net result is that due to the preponderance of the effect of the larger angle over that of the smaller4 ,the line ,,ec adds nothing1 for it merely introduces two angles which reinforce those above ,,ab4 ,the line ,,bc may be omitted or covered without appreciably affecting the illusion4 ,illustration3 ,fig4 #dd4--;,another step toward the ,zoellner illusion4 ,in ,fig4 #dd two obtuse angles are arranged so that their effects are additive1 with the result that the horizontal lines apparently deviate maximally for such a simple case4 ,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 discontinuous4 ,the illusion in ,fig4 #dd may be strengthened by adding more lines parallel to the oblique lines4 ,this is demonstrated in ,fig4 #ch and in other illustrations4 ,in this manner striking illusions are built up4 ,illustration3 ,fig4 #de4--,the two diagonals would meet on the left vertical line4 ,illustration3 ,fig4 #df4--,poggendorff's illusion4 ,which oblique line on the right is the prolongation of the oblique line on the left8 ,if oblique lines are extended across vertical ones1 as in ,figs4 #de and #df1 the illusion is seen to be very striking4 ,in ,fig4 #de the oblique line on the right if extended would meet the upper end of the oblique line on the left2 however1 the apparent point of intersection is somewhat lower than it is in reality4 ,in ,fig4 #df the oblique line on the left is in the same straight line with the lower oblique line on the right4 ,the line drawn parallel to the latter furnishes an idea of the extent of the illusion4 ,this is the well-known ,poggendorff illusion4 ,the upper oblique line on the right actually appears to be approximately the continuation of the upper oblique line on the right4 ,the explanation of this illusion on the simple basis of underestimation or overestimation of angles is open to criticism4 ,if ,fig4 #df is held so that the intercepted line is horizontal or vertical1 the illusion disappears or at least is greatly reduced4 ,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 angles4 ,illustration3 ,fig4 #dg4--;,a straight line appears to sag4 ,according to ,judd1#b 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 attention1 as they are in the usual positions of the ,poggendorff figure4 ,he holds further that the overestimation of this distance along the parallels 7the two vertical lines7 and the underestimation of the oblique distance across the interval are sufficient to provide a full explanation of the illusion4 ,the disappearance and appearance of the illusion1 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 turned4 ,that is1 when this ,poggendorff figure is in such a position that the intercepted line is horizontal1 the incorrect estimation of distance along the parallels has no direct bearing on the distance to which the attention is directed4 ,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 interval4 ,for a detailed account the reader is referred to the original paper4 ,some other illusions are now presented to demonstrate further the effect of the presence of angles4 ,doubtless1 in some of these1 other causes contribute more or less to the total result4 ,in ,fig4 #dg a series of concentric arcs of circles end in a straight line4 ,the result is that the straight line appears to sag perceptibly4 ,incidentally1 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 circles4 ,to the author the arcs appear distorted from those of true circles4 ,illustration3 ,fig4 #dh4--;,distortions of contour due to contact with other contours4 ,in ,fig4 #dh the bounding figure is a true circle but it appears to be distorted or dented inward where the angles of the hexagon meet it4 ,similarly1 the sides of the hexagon appear to sag inward where the corners of the rectangle meet them4 ,the influences which have been emphasized apparently are responsible for the illusions in ,figs4 #di1 #ej and #ea4 ,it is interesting to note the disappearance of the illusion1 as the plane of ,fig4 #di is varied from vertical toward the horizontal4 ,that is1 it is very apparent when viewed perpendicularly to the plane of the page1 the latter being held vertically1 but as the page is tilted backward the illusion decreases and finally disappears4 ,illustration3 ,fig4 #di4--;,an illusion of direction4 ,illustration3 ,fig4 #ej4--,twisted-cord illusion4 ,these are straight cords4 ,illustration3 ,fig4 #ea4--,twisted-cord illusion4 ,these are concentric circles4 ,the illusions in ,figs4 #ej and #ea are commonly termed twisted cord effects4 ,a cord may be made by twisting two strands which are white and black 7or any dark color7 respectively4 ,this may be superposed upon various backgrounds with striking results4 ,in ,fig4 #ej the straight cords appear bent in the middle1 owing to a reversal of the twist4 ,such a figure may be easily made by using cord and a checkered cloth4 ,in ,fig4 #ea it is difficult to convince the intellect that the cords are not arranged in the form of concentric circles1 but this becomes evident when one of them is traced out4 ,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 circumference4 ,the cord appears to form a spiral or a helix seen in perspective4 ,illustration3 ,fig4 #eb4--;,a spiral when rotated appears to expand or contract1 depending upon direction of rotation4 ,a striking illusion is obtained by revolving the spiral shown in ,fig4 #eb about its center4 ,this may be considered as an effect of angles because the curvature and consequently the angle of the spiral is continually changing4 ,there is a peculiar movement or progression toward the center when revolved in one direction4 ,when the direction of rotation is reversed the movement is toward the exterior of the figure2 that is1 there is a seeming expansion4 ,angles appear to modify our judgments of the length of lines as well as of their direction4 ,of course1 it must be admitted that some of these illusions might be classified under those of contrast and others4 ,in fact1 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 chapters4 ,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 chapters4 ,illustration3 ,fig4 #ec4--;,angles affect the apparent length of lines4 ,in ,fig4 #ec the three horizontal lines are of equal length but they appear unequal4 ,this must be due primarily to the size of the angles made by the lines at the ends4 ,within certain limits1 the greater the angle the greater is the apparent elongation of the central horizontal portion4 ,this generalization appears to apply even when the angle is less than a right angle1 although there appears to be less strength to the illusions with these smaller angles than with the larger angles4 ,other factors which contribute to the extent of the illusion are the positions of the figures1 the distance between them1 and the juxtaposition of certain lines4 ,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 case4 ,illustration3 ,fig4 #ed4--,the horizontal line appears to tilt downward toward the ends4 ,illustration3 ,fig4 #ee4--,the horizontal line appears to sag in the middle4 ,in ,fig4 #ed the horizontal straight line appears to consist of two lines tilting slightly upward toward the center4 ,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 angle4 ,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 center4 ,in ,fig4 #ee the horizontal line appears to tilt upward toward its extremities or to sag in the middle4 ,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 imagined4 ,in this case only one side of each obtuse angle is present1 the other side being formed by continuing the horizontal line both ways by means of the imagination4 ,that we do this unconsciously is attested to by many experiences4 ,for example1 we often find ourselves imagining a horizontal1 a vertical1 or a center upon which to base a pending judgment4 ,a discussion of the influence of angles must include a reference to the well-known ,mueller-,lyer illusion presented in ,fig4 #ef4 ,it is obvious in a that the horizontal part on the left appears considerably longer than that part in the right half of the diagram4 ,the influence of angles in this illusion can be easily tested by varying the direction of the lines at the ends of the two portions4 ,illustration3 ,fig4 #ef4--,the ,mueller-,lyer illusion4 ,in all these figures the influence of angles is obvious4 ,this does not mean that they are always solely or even primarily responsible for the illusion4 ,in fact1 the illusion of ,poggendorff 7,fig4 #df7 may be due to the incorrect estimation of certain linear distances1 but the angles make this erroneous judgment possible1 or at least contribute toward it4 ,many discussions of the theories or explanations of these figures are available in scientific literature of which one by ,judd#b may be taken as representative4 ,he holds that the false estimation of angles in the ,poggendorff figure is merely a secondary effect1 not always present1 and in no case the source of the illusion2 furthermore1 that the illusion may be explained as due to the incorrect linear distances1 and may be reduced to the type of illusion found in the ,mueller-,lyer figure4 ,certainly there are grave dangers in explaining an illusion on the basis of an apparently simple operation4 ,in ,fig4 #ef1 b is made up of the two parts of the ,mueller-,lyer illusion4 ,a small dot may be placed equally distant from the inside extremities of the horizontal lines4 ,it is interesting to note that overestimation of distance within the figure is accompanied with underestimation outside the figure and1 conversely1 overestimation within the figure is accompanied by underestimation in the neighboring space4 ,if the small dot is objected to as providing an additional ,mueller-,lyer figure of the empty space1 this dot may be omitted4 ,as a substitute an observer may try to locate a point midway between the inside extremities of the horizontal lines4 ,the error in locating this point will show that the illusion is present in this empty space4 ,in this connection it is interesting to note some other illusions4 ,in ,fig4 #eg the influence of several factors are evident4 ,two obviously important ones are 7#a7 the angles made by the short lines at the extremities of the exterior lines parallel to the sides of the large triangle1 and 7#b7 the influence of contrast of the pairs of adjacent parallel lines4 ,the effect shown in ,fig4 #ec is seen to be augmented by the addition of contrast of adjacent lines of unequal length4 ,an interesting variation of the effect of the presence of angles is seen in ,fig4 #eh4 ,the two lines forming angles with the horizontal are of equal length but due to their relative positions1 they do not appear so4 ,it would be quite misleading to say that this illusion is merely due to angles4 ,obviously1 it is due to the presence of the two oblique lines4 ,it is of interest to turn to ,figs4 #be1 #bf and various illusions of perspective4 ,illustration3 ,fig4 #eg4--;,combined influence of angles and contrasting lengths4 ,illustration3 ,fig4 #eh4--,two equal oblique lines appear unequal because of their different positions4 ,at this point a digression appears to be necessary and1 therefore1 ,fig4 #ei is introduced4 ,here the areas of the two figures are equal4 ,the judgment of area is likely to be influenced by juxtaposed lines and therefore1 as in this case1 the lower appears larger than the upper one4 ,similarly two trapezoids of equal dimensions and areas may be constructed4 ,if each is constructed so that it rests upon its longer parallel and one figure is above the other and only slightly separated1 the mind is tempted to be influenced by comparing the juxtaposed base of the upper with the top of the lower trapezoid4 ,the former dimension being greater than the latter1 the lower figure appears smaller than the upper one4 ,angles must necessarily play a part in these illusions1 although it is admitted that other factors may be prominent or even dominant4 ,illustration3 ,fig4 #ei4--;,an illusion of area4 ,this appears to be a convenient place to insert an illusion of area based1 doubtless1 upon form1 but angles must play a part in the illusions2 at least they are responsible for the form4 ,in ,fig4 #fj the five figures are constructed so as to be approximately equal in area4 ,however1 they appear unequal in this respect4 ,in comparing areas1 we cannot escape the influence of the length and directions of lines which bound these areas1 and also1 the effect of contrasts in lengths and directions4 ,angles play a part in all these1 although very indirectly in some cases4 ,illustration3 ,fig4 #fj4--;,five equal areas showing the influence of angles and contrasting lengths4 ,to some extent the foregoing is a digression from the main intent of this chapter1 but it appears worth while to introduce these indirect effects of the presence of angles 7real or imaginary7 in order to emphasize the complexity of influences and their subtleness4 ,direction is in the last analysis an effect of angle2 that is1 the direction of a line is measured by the angle it makes with some reference line1 the latter being real or imaginary4 ,in ,fig4 #fa1 the effect of diverting or directing attention by some subtle force1 such as suggestion1 is demonstrated4 ,this force appears to contract or expand an area4 ,the circle on the left appears smaller than the other4 ,of course there is the effect of empty space compared with partially filled space1 but this cannot be avoided in this case4 ,however1 it can be shown that the suggestions produced by the arrows tend to produce apparent reduction or expansion of areas4 ,note the use of arrows in advertisements4 ,illustration3 ,fig4 #fa4--,showing the effect of directing the attention4 ,although theory is subordinated to facts in this book1 a glimpse here and there should be interesting and helpful4 ,after having been introduced to various types and influences1 perhaps the reader may better grasp the trend of theories4 ,the perspective theory assumes1 and correctly so1 that simple diagrams often suggest objects in three dimensions1 and that the introduction of an imaginary third dimension effects changes in the appearance of lines and angles4 ,that is1 lengths and directions of lines are apparently altered by the influence of lines and angles1 which do not actually exist4 ,that this is true may be proved in various cases4 ,in fact the reader has doubtless been convinced of this in connection with some of the illusions already discussed4 ,vertical lines often represent lines extending away from the observer1 who sees them foreshortened and therefore they may seem longer than horizontal lines of equal length1 which are not subject to foreshortening4 ,this could explain such illusions as seen in ,figs4 #d and #e4 ,however this theory is not as easily applied to many illusions4 ,according to ,thiery's perspective theory a line that appears nearer is seen as smaller and a line that seems to be further away is perceived as longer4 ,if the left portion of b1 ,fig4 #ef1 be reproduced with longer oblique lines at the ends but with the same length of horizontal lines1 it will appear closer and the horizontal lines will be judged as shorter4 ,the reader will find it interesting to draw a number of these portions of the ,mueller-,lyer figure with the horizontal line in each case of the same length but with longer and longer obliques at the ends4 ,the dynamic theory of ,lipps gives an important role to the inner activity of the observer1 which is not necessarily separated from the objects viewed1 but may be felt as being in the objects4 ,that is1 in viewing a figure the observer unconsciously separates it from surrounding space and therefore creates something definite in the latter1 as a limiting activity4 ,these two things1 one real 7the object7 and one imaginary1 are balanced against each other4 ,a vertical line may suggest a necessary resistance against gravitational force1 with the result that the line appears longer than a horizontal one resting in peace4 ,the difficulty with this theory is that it allows too much opportunity for purely philosophical explanations1 which are likely to run to the fanciful4 ,it has the doubtful advantage of being able to explain illusions equally well if they are actually reversed from what they are4 ,for example1 gravity could either contract or elongate the vertical line1 depending upon the choice of viewpoint4 ,the confusion theory depends upon attention and begins with the difficulty of isolating from illusory figures the portions to be judged4 ,amid the complexity of the figure the attention cannot easily be fixed on the portions to be judged4 ,this results in confusion4 ,for example1 if areas of different shapes such as those in ,fig4 #fj are to be compared1 it is difficult to become oblivious of form or of compactness4 ,in trying to see the two chief parallel lines in ,fig4 #ch1 in their true parallelism the attention is being subjected to diversion1 by the short oblique parallels with a compromising result4 ,surely this theory explains some illusions successfully1 but it is not so successful with some of the illusions of contrast4 ,the fact that practice in making judgments in such cases as ,figs4 #de and #ef reduces the illusion even to ultimate disappearance1 argues in favor of the confusion theory4 ,perhaps the observer devotes himself more or less consciously to isolating the particular feature to be judged and finally attains the ability to do so4 ,according to ,auerbach's indirect-vision theory the eyes in judging the two halves of the horizontal line in a1 ,fig4 #ef1 involuntarily draw imaginary lines parallel to this line but above or below it4 ,obviously the two parts of such lines are unequal in the same manner as the horizontal line in the ,mueller-,lyer figure appears divided into two unequal parts4 ,somewhat analogous to this in some cases is ,brunot's mean-distance theory4 ,according to this we establish centers of gravity in figures and these influence our judgments4 ,these are glimpses of certain trends of theories4 ,none is a complete success or failure4 ,each explains some illusions satisfactorily1 but not necessarily exclusively4 ,for the present1 we will be content with these glimpses of the purely theoretical aspects of visual illusions4 ,,vii ,,illusions ,,of ,,depth ,,and ,,of ,,distance ,besides the so-called geometrical illusions discussed in the preceding chapters1 there is an interesting group in which the perception of the third dimension is in error4 ,when any of the ordinary criteria of relief or of distance are apparently modified1 illusions of this kind are possible4 ,there are many illusions of this sort1 such as the looming of objects in a fog2 the apparent enlargement of the sun and moon near the horizon2 the flattening of the vault of the sky2 the intaglio seen as relief2 the alteration of relief with lighting2 and various changes in the landscape when regarded with the head inverted4 ,although some of the criteria for the perception of depth or of distance have already been pointed out1 especially in ,chapter ,,iii1 these will be mentioned again4 ,distance or depth is indicated by the distribution of light and shade1 and an unusual object like an intaglio is likely to be mistaken for relief which is more common4 ,an analysis of the lighting will usually reveal the real form of the object4 7,see ,figs4 #gj1 #ga1 #gb1 #gc1 #gf and #gg47 ,in this connection it is interesting to compare photographic negatives with their corresponding positive prints4 ,distance is often estimated by the definition and color of objects seen through great depths of air 7aerial perspective74 ,these distant objects are blurred by the irregular refraction of the light-rays through non-homogeneous atmosphere4 ,they are obscured to some degree by the veil of brightness due to the illuminated dust1 smoke1 etc41 in the atmosphere4 ,they are also tinted 7apparently7 by the superposition of a tinted atmosphere4 ,thus we have dim distance1 blue peaks1 azure depths of sky1 etc41 represented in photographs1 paintings1 and writings4 ,incidentally1 the sky above is blue for the same general reasons that the atmosphere1 intervening between the observer and a distant horizon1 is bluish4 ,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 atmosphere4 ,however1 is the latter a full explanation8 ,to some extent we judge unknown size by estimated distance1 and unknown distance by estimated size4 ,when a person is viewing a great mountain peak for the first time1 is he not likely to assume it to be comparable in size to the hills with which he has been familiar8 ,even by allowing considerable1 is he not likely to greatly underestimate the size of the mountain and1 as a direct consequence1 to underestimate the distance proportionately8 ,this incorrect judgment would naturally be facilitated by the absence of dimness and blueness due to the atmospheric haze4 ,angular perspective1 which apparently varies the forms of angles and produces the divergence of lines1 contributes much information in regard to relative and absolute distances from the eye of the various objects or the parts of an object4 ,for example1 a rectangle may appear as a rhomboid4 ,it is obvious that certain data pertaining to the objects viewed must be assumed1 and if the assumptions are incorrect1 illusions will result4 ,these judgments also involve1 as most judgments do1 other data external to the objects viewed4 ,perhaps these incorrect judgments are delusions rather than illusions1 because visual perception has been deluded by misinformation supplied by the intellect4 ,size or linear perspective is a factor in the perception of depth or of distance4 ,as has been stated1 if we know the size experience determines the distance2 and conversely1 if we know the distance we may estimate the size4 ,obviously estimates are involved and these when incorrect lead to false perception or interpretation4 ,as an object approaches1 the axes of the eyes converge more and more and the eye-lens must be thickened more and more to keep the object in focus4 ,as stated in ,chapter ,,iii1 we have learned to interpret these accompanying sensations of muscular adjustment4 ,this may be demonstrated by holding an object at an arm's length and then bringing it rapidly toward the eyes1 keeping it in focus all the time4 ,the sensations of convergence and accommodation are quite intense4 ,the two eyes look at a scene from two different points of view respectively and their images do not perfectly agree1 as has been shown in ,figs4 #b and #c4 ,this binocular disparity is responsible to some degree for the perception of depth1 as the stereoscope has demonstrated4 ,if two spheres of the same size are suspended on invisible strings1 one at six feet1 the other at seven feet away1 one eye sees the two balls in the same plane1 but one appears larger than the other4 ,with binocular vision the balls appear at different distances1 but judgment appraises them as of approximately equal size4 ,at that distance the focal adjustment is not much different for both balls1 so that the muscular movement1 due to focusing the eye1 plays a small part in the estimation of the relative distance4 ,binocular disparity and convergence are the primary factors4 ,some have held that the perception of depth1 that is1 of a relative distance1 arises from the process of unconsciously running the point of sight back and forth4 ,however1 this view1 unmodified1 appears untenable when it is considered that a scene illuminated by a lightning flash 7of the order of magnitude of a thousandth of a second7 is seen even in this brief moment to have depth4 ,objects are seen in relief1 in actual relation as to distance and in normal perspective1 even under the extremely brief illumination of an electric spark 7of the order of magnitude of one twenty-thousandth of a second74 ,this can also be demonstrated by viewing stereoscopic pictures with a stereoscope1 the illumination being furnished by an electric spark4 ,under these circumstances relief and perspective are quite satisfactory4 ,surely in these brief intervals the point of sight cannot do much surveying of a scene4 ,parallax aids in the perception of depth or distance4 ,if the head be moved laterally the view or scene changes slightly4 ,objects or portions of objects previously hidden by others may now become visible4 ,objects at various distances appear to move nearer or further apart4 ,we have come to interpret these apparent movements of objects in a scene in terms of relative distances2 that is1 the relative amount of parallactic displacement is a measure of the relative distances of the objects4 ,the relative distances or depth locations of different parts of an object can be perceived as fluctuating or even reversing4 ,this is due to fluctuations in attention1 and illusions of reversible perspective are of this class4 ,it is quite impossible for one to fix his attention in perfect continuity upon any object4 ,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 successively4 ,this applies equally well to the auditory sense and perhaps to the other senses4 ,emotional coloring has much to do with the fixation of attention2 that which we admire1 desire1 love1 hate1 etc41 is likely to dwell more in the focus of attention than that which stirs our emotions less4 ,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 object4 ,it has been suggested that the illusion is due to the consequent variations in the tension of convergence4 ,third dimensional movements may be produced for binocular or monocular vision during eye-closure4 ,they are also produced by opening the eyes as widely as possible1 by pressure on the eye-balls1 and by stressing the eyelids4 ,however1 these are not important and are merely mentioned in passing4 ,an increase in the brightness of an object is accompanied by an apparent movement toward the observer1 and conversely a decrease in brightness produces an apparent movement in the opposite direction4 ,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 darkness4 ,rapidly moving thin clouds may produce such an effect by varying the brightness of the moon4 ,some peculiar impressions of this nature may be felt while watching the flashing light of some light-houses or of other signaling stations4 ,it has been suggested that we naturally appraise brighter objects as nearer than objects less bright4 ,however1 is it not interesting to attribute the apparent movement to irradiation8 7,see ,chapter ,,viii47 ,a bright object appears larger than a dark object of the same size and at the same distance4 ,when the same object varies in brightness it remains in consciousness the same object and therefore of constant size2 however1 the apparent increase in size as it becomes brighter must be accounted for in some manner and there is only one way open4 ,it must be attributed a lesser distance than formerly and therefore the sudden increase in brightness mediates a consciousness of a movement forward1 that is1 toward the observer4 ,if two similar objects1 such as the points of a compass1 are viewed binocularly and their lateral distance apart is altered1 the observer is conscious of a third dimensional movement4 ,inasmuch as the accommodation is unaltered but convergence must be varied as the lateral distance between the two1 the explanation of the illusion must consider the latter4 ,the pair of compass-points are very convenient for making a demonstration of this pronounced illusion4 ,the relation of size and distance easily accounts for the illusion4 ,obviously this type of illusion cannot be illustrated effectively by means of diagrams1 so the reader must be content to watch for them himself4 ,some persons are able voluntarily to produce illusory movements in the third dimension1 but such persons are rare4 ,many persons have experienced involuntary illusions of depth4 ,carr found1 in a series of classes comprising #cej students1 #eh persons who had experienced involuntary depth illusions at some time in their lives4 ,five of these also possessed complete voluntary control over the phenomenon4 ,the circumstances attending visual illusions of depth are not the same for various cases1 and the illusions vary widely in their features4 ,like other phases of the subject1 this has been treated in many papers1 but of these only one will be specifically mentioned1 for it will suffice4 ,carr#c has studied this type of illusion comparatively recently and apparently quite generally1 and his work will be drawn upon for examples of this type4 ,apparently they may be divided into four classes3 7#a7 ,those of pure distance2 that is1 an object may appear to be located at varying distances from the observer1 but no movement is perceived4 ,for example1 a person might be seen first at the true distance2 he might be seen next very close in front of the eyes2 then he might suddenly appear to be quite remote2 7#b7 illusions of pure motion2 that is1 objects are perceived as moving in a certain direction without any apparent change in location4 ,in other words1 they appear to move1 but they do not appear to traverse space2 7#c7 illusions of movement which include a change in location4 ,this appears to be the most common illusion of depth2 7#d7 those including a combination of the first and third classes4 ,for example1 the object might first appear to move away from its true location and is perceived at some remote place4 ,shortly it may appear in its true original position1 but this change in location does not involve any sense of motion4 ,these peculiar illusions of depth are not as generally experienced as those described in preceding chapters4 ,a geometrical illusion1 especially if it is pronounced1 is likely to be perceived quite universally1 but these illusions of depth are either more difficult to notice or more dependent upon psychological peculiarities far from universal among people4 ,it is interesting to note the percentages computed from ,carr's statistics obtained upon interrogating #cej students4 ,of these1 #ag per cent had experienced depth-illusions and between one and two per cent had voluntary control of the phenomenon4 ,of the #dh who had experienced illusions of this type and were able to submit detailed descriptions1 #be per cent belonged to class 7#a7 of those described in the preceding paragraph2 #d per cent to class 7#b72 #eb per cent to class 7#c72 and #ag per cent to class 7#d74 ,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 unaffected4 ,for most persons these illusions involve normal perceptual objects1 although it appears that they are phases of hallucinatory origin4 ,inasmuch as these illusions cannot be illustrated diagrammatically we can do no better than to condense some of the descriptions obtained and reported by ,carr4#c ,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 follows3 ,the observer on a clear day was gazing down a street which ended a block away1 a row of houses forming the background at the end of the street4 ,the observer was talking to and looking directly at a companion only a short distance away4 ,soon this person 7apparently7 began to move down the street1 until she reached the background of houses at the end1 and then slowly came back to her original position4 ,the movement in both directions was distinctly perceived4 ,during the illusory movement there was no vagueness of outline or contour1 no blurring or confusion of features2 the person observed1 seemed distinct and substantial in character during the illusion4 ,the perceived object moved in relation to surrounding objects2 there was no movement of the visual field as a whole4 ,the person decreased in size during the backward movement and increased in size during the forward return movement4 ,with many persons who experience illusions of depth1 the objects appear to move to1 or appear at1 some definite position and remain there until the illusion is voluntarily overcome1 or until it disappears without voluntary action4 ,a condensation of a typical description of this general type presented by ,carr is as follows3 ,all visual objects suddenly recede to the apparent distance of the horizon and remain in that position several minutes1 returning at the end of this period to their original positions4 ,this return movement is very slow at the beginning1 but the latter phase of the movement is quite rapid4 ,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 position4 ,in all cases 7encountered by ,carr7 the motion in both directions is an actual experience reality and the subject was helpless as to initiating1 stopping1 or modifying the course of the illusion in any way4 ,objects and even visual images 7which are subject to the same illusions7 decrease in size in proportion to the amount of backward movement and grow larger again on their return movement4 ,the objects are always clearly defined as if in good focus4 ,in this particular case the illusion occurred about twice a year1 under a variety of conditions of illumination1 at various times of the day1 but apparently under conditions of a rather pronounced fatigue4 ,in regard to the variation in the size of objects1 many who have experienced these illusions of depth testify that the size seems to change in proportion to the apparent distance1 according to the law of perspective4 ,some persons appear in doubt as to this change and a few have experienced the peculiar anomaly of decreasing size as the objects apparently approached4 ,many persons who have experienced these peculiar illusions report no change in the distinctness of objects2 almost as many are uncertain regarding this point2 and as many report a change in distinctness4 ,apparently there are phases of hallucinatory origin so that there is a wide variety of experiences among those subject to this type of illusion4 ,according to ,carr's investigation internal conditions alone are responsible for the illusion with more persons than those due to external conditions alone4 ,with some persons a combination of internal and external conditions seem to be a necessity4 ,fixation of vision appears to be an essential objective condition for many observers4 ,that is1 the illusion appeared while fixating a speaker or singer in a church or a theater4 ,with others the illusion occurs while reading4 ,some reported that fixation upon checkered or other regularly patterned objects was an essential condition4 ,among the subjective conditions reported as essential are steady fixation1 concentration of attention1 complete mental absorption1 dreamy mental abstraction1 and fatigue4 ,ocular defects do not appear to be essential1 for the illusions have been experienced by many whose eyes were known to be free from any abnormalities4 ,period of life does not appear to have any primary influence1 for those who are subject to these peculiar illusions often have experienced them throughout many years4 ,in some cases it is evident that the illusions occur during a constrained eye position1 while lying down1 immediately upon arising from bed in the morning1 and upon opening the eyes after having had them closed for some time4 ,however1 the necessity for these conditions are exceptional4 ,the control of these illusions of depth1 that is1 the ability to create or to destroy them1 appears to be totally lacking for most of those who have experienced them4 ,some can influence them1 a few can destroy them1 a few can indirectly initiate them1 but those who can both create and destroy them appear to be rare4 ,it may seem to the reader that the latter part of this chapter departs from the main trend of this book1 for most of these illusions of depth are to a degree of hallucinatory origin4 ,furthermore it has been the intention to discuss only those types of illusions which are experienced quite uniformly and universally4 ,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 experienced4 ,many other phases of depth illusions have been recorded in scientific literature4 ,the excellent records presented by ,carr could be drawn upon for further glimpses1 but it appears that no more space should be given to this exceptional type4 ,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 manner4 ,however1 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 chapters4 ,,viii ,,irradiation ,,and ,,brightness-,,contrast ,many interesting and striking illusions owe their existence to contrasts in brightness4 ,the visual phenomenon of irradiation does not strictly belong to this group1 but it is so closely related to it and so dependent upon brightness-contrast that it is included4 ,a dark line or spot will appear darker in general as the brightness of its environment is increased2 or conversely1 a white spot surrounded by a dark environment will appear brighter as the latter is darkened4 ,in other words1 black and white1 when juxtaposed1 mutually reinforce each other4 ,black print on a white page appears much darker than it really is4 ,this may be proved by punching a hole in a black velvet cloth and laying this hole over a black portion of a large letter4 ,the ink which appeared so black in the print1 when the latter was surrounded by the white paper1 now appears only a dark gray4 ,incidentally a hole in a box lined with black velvet is much darker than a piece of the black velvet surrounding the hole4 ,the effects of brightness-contrast are particularly striking when demonstrated by means of lighting1 a simple apparatus being illustrated diagrammatically in ,fig4 #fb4 ,for example1 if a hole ,h is cut in an opaque white blotting paper and a large piece of the white blotting paper is placed at ,c1 the eye when placed before the opening at the right will see the opening at ,h filled with the background ,c4 ,the hole ,h may be cut in thin metal1 painted a dull white1 and may be of the shape of a star4 ,this shape provides an intimacy between the hole and its environment which tends to augment the effects of contrasts4 ,r and ,f are respectively the rear and front lamps4 ,that is1 the lamps ,r illuminate ,c1 which fills the hole and apparently is the hole2 and the lamps ,f illuminate the diffusing white environment ,e4 ,the two sets of lamps may be controlled by separate rheostats1 but if the latter are unavailable the lamps 7several in each set7 may be arranged so that by turning each one off or on1 a range of contrasts in brightness between ,e and ,h 7in reality ,c7 may be obtained4 7,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-contrast47 ,illustration3 ,fig4 #fb4--,simple apparatus for demonstrating the remarkable effects of contrasts in brightness and color4 ,if1 for example1 ,c is very feebly illuminated and ,e is very bright1 ,c will be pronounced black2 but when the lamps ,f are extinguished and no light is permitted to reach ,e1 the contrast is reversed1 and ,c may actually appear white4 ,of course1 it is obvious that white and black are relative terms as encountered in such a case4 ,in fact in brightness-contrasts relative and not absolute values of brightness are usually the more important4 ,in order to minimize the stray light which emerges from ,h1 it is well to paint the inside of both compartments black with the exception of sufficiently large areas of ,c and ,e4 ,the use of black velvet instead of black paint is sometimes advisable4 ,it is also well to screen the lamps as suggested in the diagram4 ,this simple apparatus will demonstrate some very striking effects of contrasts in brightness and will serve1 also1 to demonstrate even more interesting effects of contrasts in color4 ,two opposite contrasts obtainable by means of a simple apparatus illustrated in ,fig4 #fb may be shown simultaneously by means of white1 black1 and gray papers arranged as in ,fig4 #fc4 ,in this figure the gray is represented by the partially black ,vs1 each of which contains equal amounts of black and of white4 ,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 ,vs4 ,an excellent demonstration may be made by the reader by using two ,vs1 cut from the same sheet of gray paper1 and pasted respectively upon white and black backgrounds1 as in ,fig4 #fc4 ,it will be apparent that the one amid the black environment appears much brighter than the one 7same gray7 amid the white environment4 ,this can be demonstrated easily to an audience by means of a figure two feet long4 ,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 background4 ,the persistency of the illusion is found to be remarkable1 for it will exist even when the one ,v is actually a much darker gray than the other4 ,to become convinced that the two grays are of the same brightness in ,fig4 #fc1 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 ,vs when the card is laid upon ,fig4 #fc4 ,the grays in the holes should now appear alike because their environments are similar4 ,illustration3 ,fig4 #fc4--;,illustrating brightness-contrast4 ,the importance of contrasts in brightness and in color cannot be overemphasized1 and it appears certain that no one can fully realize their effectiveness without witnessing it in a manner similar to that suggested in ,fig4 #fb4 ,illustration3 ,fig4 #fd4--;,an effect of brightness-contrast4 ,note the darkening of the intersections of the white strips4 ,many illusions of brightness-contrast are visible on every hand4 ,for example1 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 sky4 ,conversely1 in ,fig4 #fd1 dark spots appear where the white bars cross4 ,this is purely an illusion and the same type may be witnessed by the observant many times a day4 ,in ,fig4 #fd it is of interest to note that the illusion is weak for the crossing upon which the point of sight rests1 but by averted vision the illusion is prominent for the other crossings4 ,this is one of the effects which depends upon the location in the visual field4 ,no brightness-contrasts are seen correctly and often the illusions are very striking4 ,if a series of gray papers is arranged from black to white1 with the successive pieces overlapped or otherwise juxtaposed1 a series of steps of uniform brightness is not seen4 ,an instrument would determine the brightness of each as uniform1 but to the eye the series would appear somewhat fluted4 ,that is1 where a light gray joined a darker gray the edge of the former would appear lighter than its actual brightness1 and the edge of the darker gray would appear darker than it should4 ,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 #a1 #b1 #c1 #d1 etc41 thickness would be produced4 ,on viewing this by transmitted light a series of grays is seen1 and the effect of contrast is quite apparent4 ,such a pattern can be made photographically by rotating before a photographic plate a disk with openings arranged properly in steps4 ,many demonstrations of the chief illusion of brightness-contrast are visible at night under glaring lighting conditions4 ,it is difficult or impossible to see objects beyond automobile headlights1 and adjacent to them1 in the visual field4 ,objects similarly located in respect to any surface sufficiently bright are more or less obscured4 ,characters written upon a blackboard1 placed between two windows1 may be invisible if the surfaces seen through the window are quite bright1 unless a sufficient quantity of light reaches the blackboard from other sources4 ,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-opening4 ,the term blinding light owes its origin to this effect of brightness-contrast4 ,the line of juncture between a bright and a dark surface may not be seen as a sharp line1 but as a narrow band of gray4 ,when this is true it is possible that an undue amount of area is credited to the white4 ,in preceding paragraphs we have seen the peculiar effect at the border-lines of a series of grays4 ,this may have something to do with the estimate2 however1 irradiation may be due to excitation of retinal rods and cones adjacent to1 but not actually within the bright image4 ,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 line4 ,at the actual crossings the black appears to run up the narrow angle somewhat like ink would under the influence of surface tension4 ,this is particularly striking when two gratings or even two ordinary fly-screens are superposed4 ,the effect is visible when passing two picket-fences1 one beyond the other4 ,if a dark object is held so that a straight edge appears to cross a candle-flame or other light-source1 at this portion the straight edge will appear to have a notch in it4 ,irradiation in general has been defined as the lateral diffusion of nervous stimuli beyond the actual stimulus4 ,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 surfaces4 ,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 surface4 ,a filament of a lamp appears to grow in size as the current through it is slowly increased from a zero value2 that is1 as it increases in brightness4 ,in ,fig4 #fe the small inner squares are of the same size but the white square appears larger than the black one4 ,it seems that this apparent increase is made at the expense of the adjacent dark area4 ,this phenomenon or illusion is strongest when the brightness is most intense1 and is said to be greatest when the accommodation is imperfect4 ,a very intense light-source may appear many times larger than its actual physical size4 ,illustration3 ,fig4 #fe4--,the phenomenon of irradiation4 ,doubtless a number of factors may play a part in this phenomenon4 ,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 region1 but this must be practically instantaneous in order to satisfy results of experiments4 ,eye-movements may play some part for1 despite the most serious efforts to fixate the point of sight1 a fringe will appear on the borders of images which is certainly due to involuntary eye-movements4 ,irradiation has also been ascribed to spherical aberration in the eye-lens and to diffraction of light at the pupil4 ,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 pupil4 ,it has been suggested that chromatic aberration in the eye-lens is a contributory cause1 but this cannot be very important1 for the illusion is visible with monochromatic light which eliminates chromatic aberration4 ,the experimental evidence appears to indicate that the phenomenon is of a physical nature4 ,there are variations in the effects attributable to radiation1 and it is difficult to reduce them to simple terms4 ,perhaps it may aid the reader to have before him the classification presented by ,boswell4#d ,he describes the varieties of irradiation as follows3 #a4 ,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 light4 #b4 ,irradiation within the stimulated portion of the retina after the form of a figure becomes distinctly perceptible4 #c4 ,emanations of decreasing intensity extend themselves outward and backward from a moving image until lost in the darkness of the background4 #d4 ,a well known form of irradiation which occurs when a surface of greater intensity enlarges itself at the expense of one of less intensity4 #e4 ,a form having many of the characteristics of the first type1 but occurring only after long periods of stimulation1 of the magnitude of #cj to #fj seconds or more4 ,,ix ,,color ,in order to simplify the presentation of the general subject1 discussions of color have been omitted in so far as possible from the preceding chapters4 ,there are almost numberless phenomena involving color1 many of which are illusions1 or seemingly so4 ,it will be obvious that many are errors of sense2 some are errors of judgment2 others are errors due to defects of the optical system of the eye2 and many may be ascribed to certain characteristics of the visual process4 ,it is not the intention to cover the entire field in detail2 indeed1 this could not be done within the confines of a large volume4 ,however1 substantial glimpses of the more important phases of color as related to illusions are presented in this chapter4 ,in the early chapters pertaining to the eye and to vision some of the following points were necessarily touched upon1 but the repetition in the paragraphs which follow is avoided as much as possible4 ,simultaneous ,contrast4--,that the life of color is due to contrast is demonstrable in many ways4 ,if a room is illuminated by deep red light1 at first this color is very vivid in consciousness2 however1 gradually it becomes less saturated4 ,after a half hour the color is apparently a much faded red but upon emerging from the room into one normally lighted1 the latter appears very markedly greenish in tint4 ,the reason that the pure red light does not appear as strongly colored as it really is1 is due to the lack of contrast4 ,in a similar manner at night we see white objects as white even under the yellowish artificial light4 ,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 appearance4 ,an apparatus constructed after the plan of ,fig4 #fb is very effective for demonstrating the remarkable effects of color-contrast but some additions will add considerably to its convenience4 ,if the lamps ,f are divided into three circuits1 each emitting1 respectively1 red1 green1 and blue primary colors1 it is possible by means of controlling rheostats to illuminate ,e1 the environment1 with light of any hue 7including purple71 of any saturation1 and of a wide range of intensities or resulting brightnesses4 ,thus we have a very simple apparatus for quickly providing almost numberless environments for ,h4 ,the same scheme can be applied to lamps ,r1 with the result that a vast array of colors may be seen through the hole ,h4 ,if the hole is the shape of the star in ,fig4 #ff it will be found very effective4 ,the observer will actually see a star of any desired color amid an environment of any desired color4 ,care should be taken to have the star cut in very thin material in order to eliminate conspicuous boundary lines4 ,it is quite satisfactory to use a series of colored papers on a slide at ,c and ordinary clear lamps at ,r4 ,by means of this apparatus both contrasts--hue and brightness--may be demonstrated4 ,of course1 for black and white only brightness-contrast is present2 but in general where there is color-contrast there is also brightness-contrast4 ,the latter may be reduced or even eliminated if the brightness of the star and of its surroundings are made equal1 but it is difficult to make a satisfactory balance in this respect4 ,assuming1 however1 that brightness-contrast is eliminated1 we have left only hue and saturation contrast1 or what will be termed 7rather loosely1 it is admitted7 color-contrast4 ,illustration3 ,fig4 #ff4--;,an excellent pattern for demonstrating color-contrast4 ,if the surroundings are dark and1 for example1 an orange star is seen alone1 it does not appear very colorful4 ,however1 if the surroundings are now made bright with white light1 the star appears quite saturated4 ,with blue or green light the orange star appears even more intensely orange1 but when the color-contrast is reduced1 as in the case of yellow or red surroundings1 the vividness of the orange star again decreases4 ,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 hue4 ,if their hues are close together spectrally this effect is not as apparent4 ,for example1 if orange and green are contrasted1 the orange will appear reddish in hue and the green will appear bluish4 ,let us now assume the star to be white1 and that the surroundings are of any color of approximately the same brightness4 ,the star which is really white will now appear decidedly tinted and of a hue approximately complementary to that of the surroundings4 ,when the latter are of a green color the white star will assume a purplish tinge2 when red the white star will appear of a blue-green tint2 when yellow the white star will appear bluish4 ,this is an illusion in any sense of the term4 ,the strength of this illusion caused by simultaneous contrast is very remarkable4 ,for example1 if a grayish purple star is viewed amid intense green surroundings it will appear richly purple1 but when the surroundings are changed to a rich purple the grayish purple star will even appear greenish4 ,the apparent change of a color to its complementary by merely altering its environment is really a remarkable illusion4 ,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 card4 ,for example1 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 white1 black1 or gray cardboard4 ,by means of colored papers the same color may be placed in many different environments and the various contrasts may be viewed simultaneously4 ,the extent of the illusion is very evident when revealed in this simple manner4 ,however1 too much emphasis cannot be given to ,figs4 #fb and #ff as a powerful means for realizing the greatest effects4 ,after-images4--,after looking at bright objects we see after-images of the same size and form which vary more or less in color4 ,these after-images are due to persistence or fatigue of the visual process1 depending upon conditions4 ,after looking at the sun for a moment a very bright after-image is seen4 ,undoubtedly this at first is due to a persistence of the visual process1 but as it decays it continuously changes color and finally its presence is due to fatigue4 ,after-images may be seen after looking intently at any object and then directing the eyes toward a blank surface such as a wall4 ,a picture-frame will be seen as a rectangular after-image2 a checkered pattern will be seen as a checkered after-image4 ,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-image4 ,the effects are seen in paintings and many peculiar phenomena in the various arts are directly traceable to after-images4 ,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 case4 ,let us assume that vision is fixed upon a green square upon a gray or white background4 ,despite the utmost effort on the part of the observer to gaze fixedly upon this green square1 the latter will begin to appear fringed with a pinkish border4 ,this is due to the after-image of the green square and it is displaced slightly due to involuntary eye-movements4 ,after gazing as steadily as possible for a half minute1 or even less1 if the point of sight is turned to the white paper a pink square is seen upon it4 ,furthermore1 this pink square moves over the field with the point of sight4 ,this is the type most generally noticed4 ,after-images have been classified as positive and negative4 ,the former are those in which the distribution of light and shade is the same as in the original object4 ,those in which this distribution is reversed1 as in the photographic negative1 are termed negative4 ,after-images undergo a variety of changes in color but in general there are two important states4 ,in one the color is the same as in the original object and in the other it is approximately complementary to the original color4 ,in general the negative after-image is approximately complementary in color to the color of the original object4 ,after-images are best observed when the eyes are well rested1 as in the morning upon awakening4 ,with a little practice in giving attention to them1 they can be seen floating in the air1 in the indefinite field of the closed eyes1 upon a wall1 or elsewhere1 and the changes in the brightness and color can be readily followed4 ,negative after-images are sometimes very persistent and therefore are more commonly noticed than positive ones4 ,the positive after-image is due to retinal inertia1 that is1 to the persistency of the visual process after the actual stimulus has been removed4 ,it is of relatively brief duration4 ,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 background1 and as a positive upon a dark background1 such as is readily provided by closing the eyes4 ,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 closed4 ,upon repeating the experiment the progression of colors will be found to be always the same for the same conditions4 ,the duration of the after-image will be found to vary with the brightness and period of fixation of the object4 ,it is interesting to note that an after-image is seen with difficulty when the eyes are in motion1 but it becomes quite conspicuous when the eyes are brought to rest4 ,an after-image due to the stimulation of only one eye sometimes seems to be seen by the other eye4 ,naturally this has given rise to the suggestion that the seat of after-images is central rather than peripheral2 that is1 in the brain rather than at the retina4 ,however1 this is not generally the case and the experimental evidence weighs heavily against this conclusion4 ,if ,fig4 #eb is revolved about its center and fixated for some time striking effects are obtained upon looking away suddenly upon any object4 ,the latter will appear to shrink if the spiral has seemed to run outward1 or to expand if the spiral has seemed to run inward4 ,these are clearly after-images of motion4 ,as stated elsewhere1 we may have illusions of after-images as well as of the original images4 ,for example1 if a clearly defined plane geometrical figure such as a cross or square is bright enough to produce a strong after-image1 the latter when projected upon a perspective drawing will appear distorted2 that is1 it is likely to appear in perspective4 ,a simple way of demonstrating after-images and their duration is to move the object producing them4 ,for example1 extinguish a match and move the glowing end4 ,if observed carefully without moving the eye a bluish after-image will be seen to follow the glowing end of the match4 ,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 vision4 ,growth and ,decay of ,sensation4--,although many after-images may not be considered to be illusions in the sense in which the term is used here1 there are many illusions in which they at least play a part4 ,furthermore1 it is the intention throughout these chapters to adhere to a discussion of static illusions1 it is difficult to avoid touching occasionally upon motion4 ,the eyes are in motion most of the time1 hence1 certain effects of an illusory nature may be superposed upon stationary objects4 ,the persistence of vision has been demonstrated by every small boy as he waved a glowing stick seized from a bonfire4 ,fireworks owe much of their beauty to this phenomenon4 ,a rapidly revolving spoked wheel may appear to be a more or less transparent disk1 but occasionally when a rapid eye-movement moves the point of sight with sufficient speed in the direction of motion1 the spokes reappear momentarily4 ,motion-pictures owe their success to this visual property--the persistence of vision4 ,if a lantern-slide picture be focused upon black velvet or upon a dark doorway1 the projected image will not be seen4 ,however1 if a white rod be moved rapidly enough in the plane of the image1 the latter may be seen in its entirety4 ,the mixture of colors1 by rotating them on disks1 owes its possibility to the persistence of the color-sensations beyond the period of actual stimulation4 ,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 growth1 and also of decay1 vary for different colors4 ,in general1 the growth and the decay are not of similar or uniform rates4 ,furthermore1 the sensation often initially overshoots its final steady value1 the amount of overshooting depending upon the intensity and color of the stimulus4 ,these effects may be witnessed in their extensive variety by rotating disks so constructed that black and various colors stimulate the retina in definite orders4 ,an interesting case of this kind may be demonstrated by rotating the disk shown in ,fig4 #fg4 ,notwithstanding the fact that these are only black and white stimuli1 a series of colored rings is seen varying from a reddish chocolate to a blue-green4 ,experiment will determine the best speed1 which is rather slow under a moderate intensity of illumination4 ,the reddish rings will be outermost and the blue-green rings innermost when the disk is rotated in one direction4 ,upon reversing the direction of rotation the positions of these colored rings will be reversed4 ,by using various colors1 such as red and green for the white and black respectively1 other colors will be produced1 some of which are very striking4 ,the complete explanation of the phenomenon is not clear1 owing to the doubt which exists concerning many of the phenomena of color-vision1 but it appears certain that the difference in the rates of growth and decay of the various color-sensations 7the white stimulus includes all the spectral hues of the illuminant7 is at least partially1 if not wholly1 responsible4 ,illustration3 ,fig4 #fg4--;,by rotating this ,mason 7black and white7 disk color-sensations are produced4 ,an interesting effect1 perhaps due wholly or in part to the differences in the rates of growth and decay of color-sensations1 may be observed when a colored pattern is moved under a low intensity of illumination1 the eyes remaining focused upon a point in space at about the same distance as the object4 ,a square of red paper pasted in the center of a larger piece of blue-green paper is a satisfactory object4 ,on moving this object gently1 keeping the point of sight fixed in its plane of movement1 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 square4 ,perhaps chromatic aberration plays some part in making this effect so conspicuous4 ,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 clock4 ,when the latter is moved in the plane of the dial1 the greenish luminous figures appear separated from the red dial and seem to lag behind during the movement4 ,for such demonstrations it is well to experiment somewhat by varying the intensity of the illumination and the speed of movement4 ,relatively low values of each appear to be best4 ,although the various color-sensations grow and decay at different rates1 the latter depend upon conditions4 ,it appears that blue-sensation rises very rapidly and greatly overshoots its final steady value for a given stimulus4 ,red ranks next and green third in this respect4 ,the overshooting appears to be greater for the greater intensity of the stimulus4 ,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 second4 ,chromatic ,aberration4--,it is well known that the eye focuses different spectral colors at different points4 ,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 index4 ,if a white object is viewed by the eye1 it should appear with a purplish fringe2 however1 the effect is observed more readily by viewing a light-source through a purple filter which transmits only violet and red light4 ,the light-source will have a red or a violet fringe1 depending upon the accommodation or focus of the eye4 ,this effect is perhaps best witnessed on viewing a line spectrum such as that of the mercury arc1 focused upon a ground glass4 ,the violet and blue lines are not seen in good focus when the eyes are focused upon the green and yellow lines4 ,furthermore1 the former can be seen in excellent focus at a distance too short for accommodating the eyes to the green and the yellow lines4 ,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 7violet1 blue7 than for those of longer wave-length 7such as yellow74 ,narrow slits covered with diffusing glass and illuminated respectively by fairly pure blue1 green1 yellow1 and red lights may be substituted4 ,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 respectively4 ,it is also observed when fine detail such as black lines are held close to the eye for colored fringes are seen4 ,this optical defect is responsible for certain visual illusions4 ,an excellent demonstration of chromatic aberration in the eye is found by viewing fine detail through a purple filter4 ,now if a red filter be superposed on the purple one only the red light is transmitted4 ,notwithstanding the decrease in illumination or rather of light reaching the eye1 measurement shows that finer detail can be discriminated than in the first case4 ,a similar result is found on superposing a blue filter upon the purple one4 ,retiring and ,advancing ,colors4--,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 former4 ,the author#e obtained actual measurements of this phenomenon1 but the evidence also indicated that the effects were not the same for all persons4 ,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 colors4 ,in the case of red and green letters1 for example1 the former appear 7to most persons7 to be considerably nearer the observer than the green letters4 ,it has appeared to the writer that the illusion is apparent even for white letters upon a dark background4 ,in general1 the colors whose dominant hues are of the shorter wave-lengths 7violet1 blue1 blue-green1 green7 are retiring and those whose dominant hues are of the longer wave-lengths 7yellow1 orange1 red7 are advancing4 ,illustration3 ,fig4 #fh4--;,for demonstrating retiring and advancing colors4 ,in order to obtain experimental measurements two light-tight boxes1 each containing a light-source1 were arranged to run independently upon tracks4 ,over the front end of each a diaphragm was placed so that the observer saw two characters as in ,fig4 #fh4 ,a saturated red filter was placed over one and a saturated blue filter over the other4 ,in a dark room the observer saw a blue ,e and a red ,h standing out in the darkness4 ,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 him4 ,this was done for a series of distances of the stationary box from the observer's eye4 ,nearly all the observers 7without being acquainted with the positions7 were obliged to set the red ,h further behind the blue ,e in order that both appeared at the same distance4 ,this added distance for the red ,h was as much as #b4d feet when the blue ,e was at a distance of #bd feet4 ,in other words the difference in the positions of the two was as much as #aj per cent of the total distance in this case4 ,many other interesting data were obtained but most of these are not particularly of interest here4 ,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 curvatures1 etc41 of certain eye-media for the observers4 ,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 eye4 ,this may not be the true explanation1 or it may be only partially correct4 ,perhaps some of the illusion is purely psychological in origin4 ,certainly the illusion is very apparent to most careful observers4 ,color-sensibility of the ,retina4--,this aspect was touched upon in ,chapter ,,iii1 but the differences in the sensibility of various areas of the retina to various colors are of sufficient importance to be discussed further4 ,the ability to distinguish light and color gradually fades or decreases at the periphery of the visual field1 but the actual areas of the fields of perception vary considerably1 depending upon the hue or spectral character of the light reaching the retina4 ,the extreme peripheral region of the visual field is color-blind2 that is1 color ceases to be perceived before brightness-perception vanishes in the outskirts of the visual field4 ,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 stimuli4 ,there is some disagreement as to the relative sizes of these fields but it appears that they increase in size in the following order3 green1 red1 blue1 white 7colorless74 ,the performances of after-images1 and the rates of growth and decay of sensation vary for different colors and for different areas of the retina1 but it would be tedious to peruse the many details of these aspects of vision4 ,they are mentioned in order that the reader may take them into account in any specific case4 ,as already stated1 the central part of the visual field--the fovea upon which we depend for acute vision--contains a yellowish pigmentation1 which is responsible for the term yellow spot4 ,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 vision4 ,the effect of the selectivity of the yellow spot is noticeable in viewing certain colors4 ,purkinje ,effect4--,the relative sensibility of the retina varies for different colors with a change in brightness2 or it may be better to state that the relative sensations for various colors alters as the brightness values are reduced to a low intensity4 ,for example1 if a reddish purple 7consisting of red and blue or violet rays7 be illuminated in such a manner that the intensity of illumination1 and consequently its brightness1 may be reduced from normal to a low value 7approximating moonlight conditions71 it will be seen to vary from reddish purple to violet4 ,in doing this its appearance changes through the range of purples from reddish to violet4 ,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 screens4 ,in general the ,purkinje effect may be described as an increasing sensibility of the retina for light of shorter wave-lengths 7violet1 blue1 green7 as the brightness decreases1 or a corresponding decreasing sensibility for light of longer wave-lengths 7yellow1 orange1 red74 ,the effect may be seen on any colored surfaces at twilight illumination4 ,a blue and a red flower1 which appear of the same brightness before sunset will begin to appear unequal in this respect as twilight deepens4 ,the red will become darker more rapidly than the blue if there are no appreciable changes in the color of the daylight4 ,finally all color disappears4 ,it is better to perform this experiment under artificial light1 in order that the spectral character of the illuminant may be certain to remain constant4 ,in this case rheostats must not be used for dimming the light because of the attendant changes in color or quality of the light4 ,the ,purkinje effect may be noticed by the careful observer and it is responsible for certain illusions4 ,apparently it cannot operate over one portion of the retina1 while the remainder is stimulated by normal intensities of light4 ,retinal ,rivalry4--,many curious effects may be obtained by stimulating the two retinas with lights1 respectively different in color4 ,for example1 it is interesting to place a blue glass before one eye and a yellow or red one before the other4 ,the two independent monocular fields strive for supremacy and this rivalry is quite impressive4 ,for a moment the whole field may appear of one color and then suddenly it will appear of the other color4 ,apparently the fluctuation of attention is a factor4 ,usually it does not seem to be possible to reach a quiescent state or a perfect mixture of the two colors in this manner4 ,the dependence of one monocular field upon the other1 and also their independence1 are emphasized by this experiment4 ,it is of interest to consider the illusions of reversible perspective and others in ,chapter ,v in this connection4 ,illustration3 ,fig4 #fi4--;,by combining these stereoscopically the effect of metallic lustre 7similar to graphite in this case7 is obtained4 ,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 them4 ,the apparently solid object will appear to possess lustre4 ,the experiment may be tried with ,fig4 #fi by combining the two stereoscopic pictures by converging or diverging the axes of the eyes as described in connection with ,figs4 #b and #c4 ,it will be noted that in order for two stereoscopic pictures1 when combined1 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 respectively4 ,the dissimilarity in ,fig4 #fi is correct as to perspective1 but the reversal of white and black in one of them produces an effect beyond that of true third dimension4 ,when the colors are so arranged in such pictures as to be quite different in the two the effects are striking4 ,there is1 in such cases1 an effect beyond that of perfect binocular combination4 ,by means of the stereoscope it is possible to attain binocular mixture of colors but this is usually difficult to accomplish4 ,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 brightness4 ,these effects may be studied at any moment1 for it is only necessary to throw the eyes out of focus for any object and to note the results4 ,many simple experiments may be arranged for a stereoscope1 using black and white1 and various combinations of colors4 ,for example1 ,fig4 #fe may be combined by means of double images 7produced by converging or diverging the optical axes7 so that the two inner squares are coincident4 ,actual observation is much more satisfactory than a detailed description4 ,miscellaneous4--,there are many interesting effects due to diffraction of light by edges of objects1 by meshes such as a wire screen or a handkerchief1 by the eye-media1 etc4 ,on looking at a very bright small light-source it may be seen to be surrounded by many colors4 ,streamers of light appear to radiate from brilliant sources and all bright areas colored or colorless1 when viewed amid dark surroundings1 appear to be surrounded by diffuse brushes of light4 ,these brushes are likely to be of a bluish tint4 ,many of these phenomena are readily explained1 but this cannot be done safely without knowing or recognizing all conditions4 ,many are not easily explained1 especially when reported by others1 who may not recognize certain important conditions4 ,for example1 authentic observers have reported that black letters on white paper appeared vivid red on a white background1 under certain conditions4 ,of the latter1 the apparently important one was sun's rays falling aslant the forehead4 ,when the eyes were shaded with the hand the letters immediately appeared black as they should4 ,the influence of the color of an object upon its apparent weight is relatively slight1 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 weight4 ,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 weight4 ,although the scanty evidence available attributes but a slight influence to color in this respect1 it is of interest in passing as a reminder of the many subtle factors which are at work modifying our judgments4 ,x ,,lighting ,it should be obvious by this time that the lighting of objects or of a scene can alone produce an illusion1 and that it can in still more cases contribute toward an illusion4 ,furthermore1 there are many cases of illusions in lighting due to brightness and color4 ,many effects of lighting have been described elsewhere with detailed analyses of the underlying principles1 but a condensed survey applying particularly to illusions will be presented here4 ,the comparison of intaglio with low relief has been mentioned several times in preceding chapters4 ,examples of these as related to lighting are found in ,figs4 #gj to #gc4 ,fig4 #gj represents a bas-relief lighted from above and ,fig4 #ga would ordinarily be taken to represent a bas-relief lighted from below4 ,however1 the latter was made from a photograph of the mold 7intaglio7 from which the bas-relief was made and ,fig4 #ga really represents an intaglio lighted from above4 ,similarly ,fig4 #gb represents the bas-relief lighted from the left and ,fig4 #gc ordinarily would be taken to be a bas-relief lighted from the right4 ,however1 ,fig4 #gc was made from a photograph of an intaglio lighted from the left4 ,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 judgment4 ,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 judgment4 ,certainly in these cases the visual sense delivers its data correctly4 ,illustration3 ,fig4 #gj4--;,a bas-relief lighted from above4 ,illustration3 ,fig4 #ga4--;,an intaglio lighted from above4 ,illustration3 ,fig4 #gb4--;,a bas-relief lighted from the left4 ,illustration3 ,fig4 #gc4--;,an intaglio lighted from the left4 ,illustration3 ,fig4 #gd4--;a4 ,a disk 7above7 and a sphere 7below7 lighted from overhead4 b4 ,a disk and a sphere lighted by perfectly diffused light4 ,in ,fig4 #gd the upper object is a disk and the lower is a sphere4 ,in a ,fig4 #gd the lighting is due to a source of light of rather small physical dimensions directly above the objects4 ,the same objects illuminated by means of highly diffused light 7that is1 light from many directions and of uniform intensity7 appear as in b4 ,both objects now appear as disks4 ,it is obvious that under appropriate lighting a disk might be taken for a sphere and vice versa1 depending upon which dominates the judgment or upon the formulation of the attendant assumptions4 ,incidentally an appearance quite similar to that of a1 ,fig4 #gd is obtained when the light-source is near the observer2 that is1 when it lies near the line of sight4 ,illustration3 ,fig4 #ge4--;,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 window4 ,somewhat similar to the confusion of intaglio with bas-relief is the confusion of the two hemispherical objects illustrated in ,fig4 #ge4 ,the one on the left is concave toward the observer4 ,in other words1 both could be hemispherical shells--one a mold for the other4 ,under the lighting which existed when the original photographs were made they could both be taken for hemispheres4 ,the lighting was due to a large light-source at the left1 but if the object on the left is assumed 7incorrectly7 to be a hemisphere convex toward the observer or a sphere1 it must be considered to be lighted from the right1 which is also an incorrect assumption4 ,obviously1 if the direction of the dominant light is clear to the observer1 he is not likely to make the error in judgment4 ,incidentally the object on the right might be assumed to be a sphere because a sphere is more commonly encountered than a hemisphere4 ,illustration3 ,fig4 #gf4--,the same as ,fig4 #ge1 but lighted by a very small light-source4 ,the same objects are represented in ,fig4 #gf lighted from the left by means of a light-source of relatively small dimensions2 that is1 a source subtending a relatively small solid-angle at the objects4 ,in this case the sharp shadow due to the edge of the hemispherical cup 7on the left7 is likely to cause the observer to inquire further before submitting his judgment4 ,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 cup4 ,this should be sufficient information for the careful observer to guide him1 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 him4 ,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 conclusion4 ,however1 spheres are more commonly encountered than hemispheres1 so we take a chance without really admitting or even recognizing that we do4 ,the foregoing figures illustrate several phases which influence our judgments and the wonder is that we do not make more errors than we do4 ,of course1 experience plays a large part and fortunately experience can be depended upon in most cases2 however1 in the other cases it leads us astray to a greater extent than if we had less of it4 ,the photographer1 perhaps1 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 light4 ,improper lighting does produce apparent incongruous effects but adequately controlled it is a powerful medium whose potentiality has not been fully realized4 ,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 obtained4 ,finally his work must be accepted by others and the latter1 being human1 possess 7unadmittedly of course7 a desire to be good looking4 ,lighting may be a powerful flatterer when well controlled and may be a base revealer or even a creator of ugliness4 ,incidentally1 the photographer is always under the handicap of supplying a likeness to an individual who perhaps never sees this same likeness in a mirror4 ,in other words1 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 portrait4 ,the portrait can be a true likeness but the mirrored image in general cannot be4 ,in the mirror there is a reversal of the parts from right to left4 ,for example1 a scar on the right cheek of the actual face appears on the left cheek in the mirror4 ,faces are not usually symmetrical and this reversal causes an individual to be familiar with his own facial characteristics in this reversed form4 ,this influence is very marked in some cases4 ,for example1 suppose the left side of a companion's face to be somewhat paralyzed on one side due to illness4 ,we have become more or less oblivious to the altered expression of the left side by seeing it so often4 ,however1 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 face1 the contrast makes the fact very conspicuous4 ,perhaps this accounts for the difference which exists between the opinions of the photographer 7or friends7 and of the subject of the portrait4 ,all the illusions of brightness-contrast may be produced by lighting4 ,surfaces and details may appear larger or smaller1 harsh or almost obliterated1 heavy or light2 in fact1 lighting plays an important part in influencing the mood or expression of a room4 ,a ceiling may be lifted by light or it may hang low and threatening when dark1 due to relatively little light reaching it4 ,columns may appear dark on a light background or vice versa1 and these illustrate the effects of irradiation4 ,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 altered1 the various moods may be considered to be illusions4 ,it should be obvious that lighting is a potent factor4 ,in connection with lighting it should be noted that contrasts play a prominent role as they always do4 ,these have been discussed in other chapters1 but it appears advantageous to recall some of the chief features4 ,the effect of contrast is always in the direction of still greater contrast4 ,that is1 black tends to make its surroundings white2 red tends to make its surroundings blue-green 7complementary71 etc4 ,the contrast-effect is greatest when the two surfaces are juxtaposed and the elimination of boundary lines of other colors 7including black or white7 increases its magnitude4 ,the contrast-effect of colors is most conspicuous when there is no brightness-contrast1 that is1 when the two surfaces are of equal brightness and therefore differ chiefly in hue4 ,this effect is also greatest for saturated colors4 ,it has been stated that cold colors produce stronger contrast-effects than warm colors1 but experimental evidence is not sufficiently plentiful and dependable to verify this statement4 ,as the intensity of illumination increases1 colors appear to become less saturated4 ,for example1 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 illumination4 ,in general1 black and white are the final appearances of colors for respectively very low and very high brightness4 ,as the intensity of illumination decreases1 hue finally disappears and with continued decrease the color approaches black4 ,conversely1 as the intensity of illumination increases1 a color becomes apparently less and less saturated and tends toward white4 ,for example1 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 sunlight4 ,visual adaptation also plays a prominent part1 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 hue4 ,the tendency of sensations of light toward a middle gray is not as easily recognized as changes in color but various facts support this conclusion4 ,in lighting it is important to recognize the tendency of color toward neutrality4 ,for example1 a warm yellow light soon disappears as a hue and only its subtle influence is left2 however1 a yellow vase still appears yellow because it is contrasted with objects of other colors4 ,in the case of colored light the light falls upon everything visible1 and if there is no other light-source of another color with which to contrast it1 its color appears gradually to fade4 ,this is an excellent example of the tremendous power and importance of contrast4 ,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 be4 ,physical measurements are as essential in lighting as in other phases of human endeavor for forming a solid foundation1 but in all these activities where visual perception plays an important part judgment is finally the means for appraisal4 ,wherever the psychological aspect is prominent physical measurements are likely to be misleading if they do not agree with mental appraisals4 ,of course the physical measurements should be made and accumulated but they should be considered not alone but in connection with psychological effects4 ,the photometer may show a very adequate intensity of illumination2 nevertheless seeing may be unsatisfactory or even impossible4 ,an illumination of a few foot-candles under proper conditions at a given surface is quite adequate for reading2 however1 this surface may appear quite dark if the surroundings are bright enough4 ,in such a case the photometer yielded results quite likely to be misinterpreted as satisfactory4 ,it should be obvious that many illusions discussed in preceding chapters are of interest in this connection4 ,an interesting example of the illusion of color may be easily demonstrated by means of a yellow filter4 ,for this purpose a canary glass is quite satisfactory4 ,when such a filter is placed before the eyes a daytime scene outdoors1 for example1 is likely to appear to be illuminated to a greater intensity than when the eyes are not looking through the filter4 ,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 glass4 ,in other words1 the brightnesses of objects in the scene are reduced on the average about fifty per cent1 still the subject is impressed with an apparent increase in the intensity of illumination 7and in brightness7 when the filter is placed before the eyes4 ,of course1 the actual reduction in brightness depends upon the color of the object4 ,in such a case as the foregoing1 true explanations are likely to involve many factors4 ,for this reason explanations are usually tedious if they are to be sufficiently qualified to be reasonably near completeness4 ,in this case it appears that the yellow filter may cause one to appraise the intensity of illumination as having increased1 by associating such an influence as the sun coming out from behind a cloud4 ,if we look into the depths where light and color accumulated their psychological powers1 we are confronted on every hand by associations many of which are more or less obscure1 and therefore are subtly influential4 ,the psychological powers of colors could have been discussed more generally in the preceding chapter1 but inasmuch as they can be demonstrated more effectively by lighting 7and after all the effect is one of light in any case7 they will be discussed briefly here4 ,they have been presented more at length elsewhere4 ,it is well known that the artist1 decorator1 and others speak of warm and cold colors1 and these effects have a firm psychological foundation4 ,for example1 if a certain room be illuminated by means of blue light1 it does seem colder4 ,a theater illuminated by means of bluish light seems considerably cooler to the audience than is indicated by the thermometer4 ,if this lighting is resorted to in the summer time the theater will be more inviting and1 after all1 in such a case it makes little difference what the thermometer indicates4 ,the cold light has produced an illusion of coolness4 ,similarly warm light1 such as yellow or orange1 is responsible for the opposite feeling and it is easily demonstrated that an illusion of higher temperature may be produced by its use4 ,as already stated1 color-schemes in the decorations and furnishings produce similar effects but in general they are more powerful when the primary light is colored4 ,in the latter case no object is overlooked for even the hands and faces of the beings in the room are colored by the light4 ,in the case of color-schemes not all objects are tinged with the desired warm or cold color4 ,in the foregoing1 associations play a prominent role4 ,the sky has been blue throughout the numberless centuries during which the human organism evolved4 ,the blue-sky during all these centuries has tinged the shadows outdoors a bluish color4 ,that shade is relatively cool we know by experience and perhaps we associate coolness or cold with the aerial realm4 ,these are glimpses of influences which have cooeperated toward creating the psychological effect of coldness in the case of bluish light4 ,by contrast with skylight1 sunlight is yellowish1 and a place in the sun is relatively warm4 ,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 influences4 ,we could go further into the psychology of light and color and conjecture regarding effects directly attributable to color1 such as excitement1 depression1 and tranquillity4 ,in so doing we would be led far astray from illusions in the sense of the term as used here4 ,although this term as used here is still somewhat restricted1 it is broader in scope than in its usual applications4 ,however1 it is not broad enough to lead far into the many devious highways and byways of light and color4 ,if we did make these excursions we would find associations almost universally answering the questions4 ,the question would arise as to innate powers of colors and we would find ourselves wondering if all these powers were acquired 7through associations7 and whether or not some were innate4 ,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 unanswered4 ,as an example let us take the case of the restfulness or depression due to blue4 ,we note that the blue sky is quite serene or tranquil and we find that the delicate sensibilities of poets verify this impression4 ,this association could account for the impression or feeling of tranquillity associated with blue4 ,on proceeding further1 we would find nature's solitudes often tinged with the blue skylight1 for these solitudes are usually in the shade4 ,thus their restfulness or even depressiveness may be accounted for--partially at least4 ,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 analysis4 ,besides these our individual experiences which have molded our likes and dislikes must be taken into account4 ,this phase of light and color has been treated elsewhere4#f ,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 7,fig4 #gg74 ,for years the apparent ending has more or less carelessly been attributed to the diminution of the density of atmospheric fog or haze1 but recently ,karrer#ac has suggested what appears to be the correct explanation4 ,when the beam of light from a powerful searchlight is directed into space1 its path is visible owing to the scattering of some of the light by dust and moisture particles and the molecules of the air itself4 ,while obviously the beam itself must go on indefinitely1 its luminous path appears to end abruptly at no very great distance from the source4 ,this is true whether the beam is photographed or viewed with the naked eye4 ,illustration3 ,fig4 #gg4--;,apparent ending of a searchlight beam4 ,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 untenable4 ,furthermore1 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 origin4 ,again1 the apparent length of the beam varies with the position of the observer1 and bears a direct ratio to his distance from the searchlight4 ,the fact is1 that the luminous path of the beam has no definite ending1 and extends to a very great distance--practically to infinity4 ,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 line4 ,just as the horizon recedes when the landscape is viewed from an elevation1 so the beam appears longer when one's distance from it is increased4 ,the outer portion appears brighter1 because here the line of sight pierces it to great depth4 ,that the ending of the beam appears close at hand is no doubt partly due to the brightness distribution1 but is also a matter of perspective arising from the manner in which the beam is adjusted4 ,searchlight operators in the army were instructed to adjust the light to throw a parallel beam4 ,accordingly1 the adjustments were so made that the beam appeared the same width at its outer extremity as at its base4 ,the result seems to be a short parallel shaft of light1 but is really a divergent cone of infinite extent1 its angle of divergence being such as exactly to offset the effects of perspective4 ,if the beam were a truly parallel one it would seem to come to a point1 just as the edges of a long straight stretch of country road seem to meet at the horizon4 ,if the sides of the road were not parallel1 but diverged from the observer's eye at exactly the rate at which they ordinarily would appear to converge1 then the road would seem to be as wide where it passed out at the horizon as at the observer's feet4 ,if there were no other means in the landscape of judging the distance of the horizon than by the perspective afforded by the road1 it would likely be inferred that the road only extended a short distance on the level1 and then went down a hill1 that is1 passed abruptly from the observer's view4 ,these conditions obtain ideally in the case of the searchlight beam4 ,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 itself1 and the operator in adjusting it to appear parallel eliminates the perspective4 ,the angle at which the beam must diverge to appear parallel to an observer depends upon the distance of the observer from the searchlight4 ,a beam which seems parallel to a person close to it will not appear so at a distance4 ,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 parallelity4 ,to summarize1 the apparent abrupt ending of a searchlight beam is purely an optical illusion4 ,it really has no ending2 it extends to infinity4 ,,xi ,,nature ,visual illusions abound everywhere1 and there are a number of special interest in nature4 ,inasmuch as these are representative of a wide range of conditions and are usually within the possible experience of nearly everyone daily1 they appear worthy of special consideration4 ,some of these have been casually mentioned in other chapters but further data may be of interest4 ,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 paragraphs4 ,many illusions which may be seen in nature will be passed by because their existence should be obvious after reading the preceding chapters4 ,for example1 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 ones4 ,the apparent movement of the sun1 moon1 and stars1 when clouds are floating past1 is a powerful1 though commonplace1 illusion but we are more specifically interested in static illusions4 ,however1 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 illusions4 ,it is demonstrated by lying face upward on a starlit night and fixing the gaze upon a star4 ,the latter appears to move more or less jerkily over its dark background4 ,the magnitude and involuntary nature of these eye-movements is demonstrated in this manner very effectively4 ,the effect sometimes known as aerial perspective has been mentioned heretofore4 ,the atmosphere is not perfectly transparent or colorless and is not homogeneous from an optical standpoint4 ,it scatters rays of the shorter wave-lengths more than those of the longer wave-lengths4 ,hence it appears of a bluish tint and anything seen through great distances of it tends toward a reddish color4 ,the blue sky and the redness of the setting sun are results of this cause4 ,distant signal-lights are reddened1 due to the decrease in the rays of shorter wave-length by scattering4 ,apparently we have come to estimate distance to some extent through the amount of blurring and tinting superposed upon the distant scene4 ,in the high ,rockies where the atmosphere is unusually clear1 stretches of fifty miles of atmosphere lying between the observer and the distant peaks will show very little haze4 ,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 ,rockies4 ,after misjudging distance so often to his own discomfiture a tourist is said to have been found disrobing preparatory to swimming across an irrigation ditch4 ,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 river4 ,of course1 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 territory4 ,it is a common experience that things loom in a fog1 that is1 that they appear larger than they really are4 ,an explanation which has been offered is that of an excess of aerial perspective which causes us to overestimate distance and therefore to overestimate size4 ,if this explanation is correct1 it is quite in the same manner that in clear atmosphere in the mountains we underestimate distance and1 consequently1 size4 ,however1 another factor may enter in the latter case1 for the illusion is confined chiefly to newcomers2 that is1 in time one learns to judge correctly4 ,on entering a region of real mountains the first time1 the newcomer's previous experience with these formations is confined to hills relatively much smaller4 ,even allowing considerably for a greater size when viewing the majestic peaks for the first time1 he cannot be expected to think in terms of peaks many times larger than his familiar hills4 ,thus underestimating the size of the great peaks1 he underestimates the distance4 ,the rarity of the atmospheric haze aids him in making this mistake4 ,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 account4 ,the apparent form of the sky has attracted the attention of many scientific investigators for centuries4 ,there are many conflicting opinions as to the causes of this appearance of form1 but there is general agreement that the sky appears usually as a flattened vault4 ,the sky is bright1 due to scattering of light by actual particles of solid matter and moisture and possibly by molecules of gas4 ,lack of optical homogeneity due to varying refractive index is likely to be partially responsible4 ,usually a prominent layer of haze about a mile in thickness 7although this varies considerably7 lies next to the earth's surface4 ,the top of this haze is fairly well defined as aerial travelers know1 but the sky above is still far from black1 indicating scattered light and illuminated particles still higher4 ,as one continues to ascend1 thereby leaving more and more of the luminous haze behind1 the sky becomes darker and darker4 ,often at altitudes of four or five miles the sky is very dark and the sun is piercingly bright4 ,usually there is little or no bright haze adjacent to the sun at these high altitudes as is commonly seen from the earth's surface4 ,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 persists4 ,there is some agreement that the dome of the sky appears less depressed at the zenith by night than by day4 ,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 surface4 ,dember and ,uibe assumed the apparent shape as a part of a sphere 7justifying this assumption to their satisfaction7 and obtained estimates of the apparent depression at the zenith4 ,they estimated the middle point of the arc from the zenith to the horizon and then measured the angular altitude of that point4 ,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 ,germany4 ,on very clear moonless nights they found that the shape of the sky-dome differs little from that of a hemisphere4 ,they concluded that the phenomenon is apparently due to optical conditions of the atmosphere which have not been determined4 ,it is of interest to note the appearance of the sky when cumulus clouds are present4 ,the bases of these vary in height1 but are found at altitudes from three to five thousand feet4 ,they appear to form a flat roof of clouds bending downward at the horizon1 thus giving the appearance of a vaulted but flattened dome4 ,this apparent shape does not differ much in clear weather1 perhaps due largely to the accustomedness of the eye and to the degradation of color from blue to gray toward the horizon4 ,furthermore the lower sky is usually much brighter than the zenith and the latter being darker appears to hang lower4 ,it is of interest to note how persistent is the illusion of a flattened dome1 for when one rises rapidly in the air and1 within a few minutes1 is on the level with the clouds or the dense low-lying haze1 he is mildly surprised to find these are levels and not vaulted roofs4 ,despite the fact that by many previous experiences he has learned what to expect1 the feeling of mild surprise is born each time on ascending rapidly4 ,the appearance of the flattened vault of the sky is held by some to account for the apparent enlargement of the sun1 moon1 and the constellations at the horizon4 ,that is1 they appear more distant at the horizon and we instinctively appraise them as being larger than when they are at higher altitudes4 ,it is certain that these heavenly bodies do appear much larger when they are rising or setting than when they are nearer the zenith4 ,in fact1 this is one of the most remarkable and surprising illusions which exist4 ,furthermore this apparent enlargement has been noted universally1 still many persons have attributed it to an actual optical magnification4 ,although we are more familiar with this enlargement in connection with the sun and moon1 it still persists with the constellations4 ,for example1 ,orion is apparently very large2 in fact1 this is the origin of the name4 ,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 doubted4 ,certainly the moon appears greatly enlarged while near the horizon1 even when there is doubt as to an appreciable appearance of flattening of the sky-dome4 ,many peculiar conditions and prejudices must be taken into account4 ,for example1 if various persons are asked to give an idea of how large is the disk of the sun or moon1 their answers would vary usually with the head of a barrel as the maximum4 ,however1 the size of a tree at a distant sky-line might unhesitatingly be given as thirty feet4 ,at the horizon we instinctively compare the size of the sun1 moon1 and constellations with hills1 trees1 houses1 and other objects1 but when the former are high toward the zenith in the empty sky we may judge them in their isolated position to be nearer1 hence smaller4 ,normally the retinal image grows larger as the object approaches1 but this same sensation also arises when an object grows in size without altering its distance4 ,if the moon be viewed through field-glasses the image is larger than in the case of the unaided eyes1 but it is quite common for observers to state that it appears smaller4 ,the enlargement may be interpreted as approach and inasmuch as we1 through habit1 allow for enlargement as an object approaches1 we also must reduce it in our imagination to its natural size4 ,perhaps in this case we overdo this reduction4 ,james states that the increased apparent size of the moon near the horizon is a result of association and probability4 ,it is seen through vaporous air and looks dimmer and duskier than when it rides on high2 and it is seen over fields1 trees1 hedges1 streams1 and the like1 which break up the intervening space and makes us the better realize the latter's extent4 ,both these causes may make the moon seem more distant when it is at low altitudes and as its visual angle grows less1 we may think that it must be a larger body and we so perceive it4 ,certainly it looks particularly large when a well-known object is silhouetted against its disk4 ,before proceeding further with explanations1 it may be of interest to turn to ,fig4 #gh which is an accurate tracing of the path of the moon's image across a photographic plate4 ,the camera was placed in a fixed position and the image of the moon's disk on rising was accurately focused on a panchromatic plate4 ,a dense red filter was maintained over the lens throughout in order to eliminate the effect of selective absorption of the atmosphere4 ,but the slightest enlargement was detected in the width of the path near the horizon as compared with that at the highest altitude4 ,this copy was made because it was thought better for reproduction than the photograph which would require a half-tone4 ,this is positive evidence that the phenomenon is an illusion4 ,illustration3 ,fig4 #gh4--;,an accurate tracing from a photograph 7continual exposure7 of the moon rising4 ,similarly ,fig4 #gi is a copy of a negative of several exposures of the sun4 ,owing to the greater brightness1 continuous exposure was not considered feasible4 ,a panchromatic plate and red filter was used as in the case of the moon4 ,the various exposures were made without otherwise adjusting the camera4 ,again no enlargement at the horizon was found4 ,illustration3 ,fig4 #gi4--;,accurate tracings from a photograph 7short exposures at intervals7 of the sun setting4 ,although the foregoing is conclusive evidence of the illusory character of the enlargement there are other ways of making measurements4 ,on viewing the sun at the horizon a bright after-image is obtained4 ,this may now be projected upon the sky as a background at any desired altitude4 ,it will appear much smaller at the zenith than the sun appears at the horizon4 ,certainly this is a simple and conclusive demonstration of the illusion4 ,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 zenith4 ,if the variation in the position of the eyes is held to account for the illusion1 this explanation may be supported by using a horizontal telescope with adjustable cross-hairs1 and a mirror4 ,by varying the position of the latter the disk of the sun may be measured at any altitude without varying the position of the eye4 ,when everything is eliminated from the field but the moon's disk1 it is found to be constant in size4 ,however1 this is not conclusive evidence that the variation in the position of the line of sight accounts for the illusion4 ,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 phenomena4 ,these are said to be unaffected by the altitude of the moon except for refraction4 ,but even this does not change the horizontal diameter and actually diminishes the vertical one4 ,the moon is further away when near the horizon than when at the zenith1 the maximum increase in distance being one-half the diameter of the earth4 ,this would make the moon appear about one-sixtieth1 or one-half minute of arc smaller at the horizon than at the zenith4 ,this is not only in the wrong direction to aid in accounting for the apparent enlargement1 but it is so slight as to be imperceptible to the unaided eye4 ,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 zenith4 ,they found that the relative apparent diameters of the sun and of the moon varied with altitude as follows3 ,altitude ,relative apparent diameter #j deg4 7horizon7 #ajj #ae #fh #cj #ej #de #dj #fj #cd #ge #ca #ij 7zenith7 #cj ,illustration3 ,fig4 #hj4--;,explanation offered by ,smith of the apparent enlargement of heavenly bodies near the horizon4 ,they also found a similar relation between the altitude and the apparent size of constellations4 ,fig4 #hj is a reproduction of a diagram which ,smith submitted as illustrating the cause of the illusion of apparent enlargement of heavenly bodies near the horizon4 ,if the sky seems to be a flattened vault1 the reason for the apparent decrease in the size of the sun1 the moon1 or the constellations1 as they approach the zenith1 is suggested by the diagram4 ,it has also been suggested that such illusions as those shown in ,figs4 #aj and #ai are associated with that of apparent enlargement of heavenly bodies near the horizon4 ,it will be left to the reader to decide whether or not there is any similarity or relation4 ,zoth appears to have proved1 to his own satisfaction at least1 that the chief factors are not aerial perspective1 the apparent curvature or form of the sky1 and the comparison of the sun or moon with objects of known size4 ,he maintained that the illusion of apparent decrease in size as these bodies increase in altitude is due to the necessary elevation of the eye4 ,no available experimental evidence seems to refute his statement4 ,in fact1 ,guttman's experiments seem to confirm it to some extent4 ,the latter found that there was an apparent diminution in the size of objects of several per cent1 in objects slightly more than a foot distant from the eyes1 as they were raised so that the line of vision changed from horizontal to an angle of forty degrees4 ,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 bodies4 ,notwithstanding arguments to the contrary1 it is difficult to eliminate aerial perspective and the apparent form of the sky as important factors4 ,that no explanation of this illusion has been generally accepted indicates the complexity of the causes4 ,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 mystery4 ,variations in the transparency and brightness of the air must play some part4 ,in discussing the great illusions of nature1 it appears appropriate to introduce the mirage4 ,this is not due to an error of sense of judgment4 ,the eye sees what is presented but the inversions and other peculiar effects are due to variations in the refractive index of the atmosphere4 ,these variations account for the appearance of lakes in arid deserts1 of the inverted images of ships and icebergs on the sea and of pools of water on pavements4 ,the refractive index of the atmosphere is continually changing1 but the changes are chiefly of two types3 7#a7 those due to irregular heating and 7#b7 those due to normal variation with altitude4 ,the former type are particularly responsible for mirages4 ,illustration3 ,fig4 #ha4--;,explanation of a common mirage4 ,a common type of mirage is illustrated in ,fig4 #ha4 ,this is often visible on deserts where the hot sand causes the adjacent layer of air to expand and therefore1 the refractive index to increase4 ,this layer of air then may be considered to operate like an inverted prism4 ,the rays of light close to the earth are bent convex to the earth and the curvature of those higher up may be reversed4 ,the reason that an object may appear double1 or as if mirrored by the surface of a nearby pond1 is clearly shown in the illustration4 ,similar atmospheric conditions are found sometimes over pavements and over bodies of water4 ,as one rides along in an automobile ascending an incline1 if he closely observes at the moment the line of sight is just on the level of the pavement1 he will often be rewarded by the sight of a mirage4 ,an approaching pedestrian may have no feet 7they are replaced by a bit of sky7 and the distant pavement will appear to contain pools of water on its surface4 ,sometimes on deserts1 over ice fields1 or on northern seas1 mirages are of the inverted type4 ,a horseman or ship may appear suspended in the air in an inverted position4 ,when the density of the air is great enough so that only the upper rays reach the eye1 the object will be seen inverted and far above the surface upon which nothing is seen4 ,many modifications of these types are possible through variations in the refractive indices of various strata of air4 ,sometimes the air is stratified horizontally and even vertically1 which results in magnification as well as other peculiar effects4 ,as one rides over the desert in a rapidly moving train or automobile these vagaries of nature are sometimes very striking1 because the speed of motion will make the effects of the varying refractive indices more marked4 ,a distant foothill may appear to float in the air or to change its shape very rapidly4 ,an island surrounded by quiet air and water may appear like a huge mushroom barely supported by a stem4 ,arctic mirages are no less wonderful than those of the hot barren deserts4 ,while traveling along over the ice and snow distant white peaks may assume the most fantastic shapes4 ,at first they may appear flattened like a table-land and then suddenly they may stretch upward like spires4 ,they may shrink then spread like huge mushrooms supported by the stalk-like bases and stretching out laterally4 ,suddenly they may shoot upward into another series of pinnacles as if another range had suddenly arisen4 ,such antics may go on for hours as one travels along a frozen valley4 ,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 query1 ,why hop ye so1 ye hills8 ,although not an illusion but a physical reality1 it is of interest in passing to note the colored halo or aureole surrounding the shadows of objects cast by the sun against a cloud1 fog1 or jet of steam4 ,the most wonderful effects are seen by the aerial traveler over a bank of clouds when the upper sky is clear4 ,for example1 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 rainbow4 ,the phenomenon is purely optical1 involving diffraction of light4 ,a well-known example of this is the ,spectre of the ,brocken4 ,,xii ,,painting ,,and ,,decoration ,in the arts where colors1 brightnesses1 contrasts1 lines1 forms1 and perspectives mean so much1 it is obvious that visual illusions are important4 ,sometimes they are evils which must be suppressed2 in some cases they are boons to the artist if he is equal to the task of harnessing them4 ,ofttimes they appear unheralded and unexpected4 ,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 true4 ,however true this may be1 knowledge is as useful to the artist as to anyone else4 ,the artist1 if he is to produce art1 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 disposal4 ,he must deal with reflected lights from earthly materials4 ,nature has these besides the great primary light-sources--the sun1 the moon1 the stars1 and1 we might say1 the sky4 ,she also has the advantage of overwhelming magnitudes4 ,these are only a few of the disadvantages under which the artist works1 but they indicate that he must grasp any advantage here and there which he may4 ,knowledge cannot fail him2 still1 if he fears that it will take him out of his dream world and taint him with earthliness1 let him ponder over da ,vinci1 ,rembrandt1 and such men4 ,these men knew many things4 ,they possessed much knowledge and1 after all1 the latter is nothing more nor less than science when its facts are arranged in an orderly manner4 ,if the arts are to speak a noble and expressive language despite the handicaps of the artist1 knowledge cannot be drawn upon too deeply4 ,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 painting4 ,painters1 of course1 may not agree as to this statement1 but if they wish to see how much of the science of light1 color1 lighting1 and vision they are unacquainted with1 let them invade the book-shelves4 ,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 7brightnesses7 in the actual scene4 ,they will usually be amazed to learn that they cannot paint the lights and shadows of nature excepting in the feeblest manner4 ,the range of contrast represented by their entire palette is many thousand times less than the range of values in nature4 ,in fact exclusive of nature's primary light-sources1 such as the sun1 she sometimes exhibits a range of brightness in a landscape a million times greater than the painter can produce with black and white pigments4 ,this suggests that the artist is justified in using any available means for overcoming the handicap and among his tools1 visual illusions are perhaps the most powerful4 ,a painting in the broadest sense is an illusion1 for it strives to present the three-dimensional world upon plane areas of two dimensions4 ,through representation or imitation it creates an illusion4 ,if the artist's sensibility has been capable of adequate selection1 his art will transmit1 by means of and through the truths of science1 from the region of perception to the region of emotion4 ,science consists of knowing2 art consists of doing4 ,if the artist is familiar with the facts of light1 color1 lighting1 and vision1 he will possess knowledge that can aid him in overcoming the great obstacles which are ever-present4 ,a glimpse of visual illusions should strengthen him in his resolution to depend upon visual perception1 but he can utilize these very illusions4 ,he can find a use for facts as well as anyone4 ,facts as well as experience will prepare him to do his work best4 ,the artist may suggest brilliant sunlight by means of deep shadow4 ,the old painters gained color at the expense of light and therefore lowered the scale of color in their representations of nature4 ,it is interesting to see how increasing knowledge1 as centuries passed1 directed painters as it did others onward toward the truth4 ,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 nature4 ,by doing this he was able to put color in shadows as well as in lights4 ,gradually paintings became more brilliant4 ,monet1 ,claude1 and others worked toward this goal until the brightnesses of paintings reached the limits of pigments4 ,the impressionists1 in their desire to paint nature's light1 introduced something which was nothing more nor less than science4 ,all this time the true creative artist was introducing science--in fact1 illusions--to produce the perfect illusion which was his goal4 ,a survey of any representative paintings' gallery shows the result of the application of more and more knowledge1 as the art of painting progressed through the centuries4 ,surely we cannot go back to the brown shadows and sombre landscapes of the past4 ,in the earliest art1 in the efforts of children1 in the wall-paintings of the ,egyptians1 and in ,japanese representation of nature1 the process is selective and not imitative4 ,certain things are chosen and everything else is discarded4 ,in such art selection is carried to the extreme4 ,much of this simplicity was due to a lack of knowledge4 ,light and shade1 or shading1 was not introduced until science discovered and organized its facts4 ,quite in the same manner linear and aerial perspective made their appearances until in our present art the process of selection is complex4 ,in our paintings of today objects are modeled by light and shade2 they are related by perspective2 backgrounds and surroundings are carefully considered2 the proper emphasis of light1 shade and color are given to certain details4 ,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 things4 ,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 kind4 ,mystery in art as in other activities is merely lack of understanding due to inadequate knowledge4 ,mysteries of today become facts tomorrow4 ,science moves with certainty into the unknown1 reaping and binding the facts and dropping them behind where they may be utilized by those who will4 ,the painter can imitate aerial perspective although many centuries elapsed before mankind was keen enough to note its presence in nature4 ,the atmospheric haze diminishes the brightness of very bright objects and increases that of dark objects4 ,it blurs the distant details and adds a tinge of blue or violet to the distance4 ,in painting it is a powerful illusion which the painter has learned to employ4 ,the painter can accurately imitate mathematical or linear perspective but the art of early centuries does not exhibit this feature4 ,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 distance4 ,converging lines and the other manifold details of perspective are aiding the artist in his efforts toward the production of the great illusion of painting4 ,the painter cannot imitate focal perspective or binocular perspective4 ,he can try to imitate the definition in the central portion of the visual field and the increased blurring toward the periphery4 ,focal perspective is not of much importance in painting1 because it is scarcely perceptible at the distances at which paintings are usually viewed4 ,however the absence of binocular perspective in painting does decrease the effectiveness of the illusion very markedly4 ,for this reason a painting is a more successful illusion when viewed with one eye than with two eyes4 ,of course1 in one of nature's scenes the converse is true because when viewing it with both eyes all the forms of perspective cooeperate to the final end--the true impression of three dimensions4 ,the painter may imitate the light and shade of solid forms and thereby apparently model them4 ,in this respect a remarkable illusion of solid form or of depth may be obtained4 ,for example1 a painted column may be made to appear circular in cross-section or a circle when properly shaded will appear to be a sphere4 ,both of these1 of course1 are pure illusions4 ,some stage paintings are remarkable illusions of depth1 and their success depends chiefly upon linear perspective and shadows4 ,however1 the illusion which was so complete at a distance quite disappears at close range4 ,the inadequate range of brightnesses or values obtainable by means of pigments has already been discussed4 ,the sky in a landscape may be thousands of times brighter than a deep shadow or a hole in the ground4 ,a cumulus cloud in the sky may be a hundred thousand times brighter than the deepest shadow4 ,however1 the artist must represent a landscape by means of a palette whose white is only about thirty times brighter than its black4 ,if the sun is considered we may have in a landscape a range of brightness represented by millions4 ,this illustrates the pitiable weakness of pigments alone as representative media4 ,will not light transmitted through media some day be utilized to overcome this inherent handicap of reflecting media8 ,to what extent is the success of stained glass windows due to a lessening of this handicap8 ,the range of brightness in this case may be represented by a black 7non-transmitting7 portion to the brightness of the background 7artificial or sky7 as seen through an area of clear glass4 ,transparencies have an inherent advantage over ordinary paintings in this respect and many effective results may be obtained with them even in photography4 ,it is interesting to study the effect of greatly increasing the range of values or brightnesses in paintings by utilizing non-uniform distributions of light4 ,let us take a given landscape painting4 ,if a light-source be so placed that it is close to the brighter areas 7perhaps clouds and sky near the sun7 it will illuminate this brighter portion several times more intensely than the more distant darker portions of the picture 7foreground of trees1 underbrush1 deep shadows1 etc474 ,the addition to the effectiveness of the illusion is quite perceptible4 ,this effect of non-uniform lighting may be carried to the extreme for a painting by making a positive lantern-slide 7rather contrasty7 of the painting and projecting this slide upon the painting in accurate superposition4 ,now if the painting is illuminated solely by the lantern-slide the range of contrast or brightness will be enormously increased4 ,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 slide4 ,the original range of contrast in the painting1 perhaps twenty to one1 is now increased perhaps to more than a thousand to one4 ,this demonstration will be surprising to anyone and will emphasize a very important point to the painter4 ,the painter has at his disposal all the scientific facts of light1 color1 and vision4 ,many of these have been presented elsewhere1#i and those pertaining to illusions have been discussed in preceding chapters4 ,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 decorator4 ,many tricks may be interjected into the foreground for their effect upon the background and vice versa4 ,for example1 a branch of a tree drooping in the foreground apparently close to the observer1 if done well1 will give a remarkable depth to a painting4 ,modeling of form may be effected to some extent by a judicious use of the retiring and advancing colors4 ,this is one way to obtain the illusion of depth4 ,after-images play many subtle parts in painting4 ,for example1 in a painting where a gray-blue sky meets the horizon of a blue-green body of water1 the involuntary eye-movements may produce a pinkish line just above the horizon4 ,this is the after-image of the blue-green water creeping upward by eye-movements4 ,many vivid illusions of this character may be deliberately obtained by the artist4 ,some of the peculiar restless effects obtained in impressionistic painting 7stippling of small areas with relatively pure hues7 are due to contrasts and after-images4 ,a painting came to the author's notice in which several after-images of the sun1 besides the image of the sun itself1 were disposed in various positions4 ,their colors varied in the same manner as the after-image of the sun4 ,doubtless the painter strove to give the impression which one has on gazing at the sun4 ,whether or not this attempt was successful does not matter but it was gratifying to see the attempt made4 ,there are many interesting effects obtainable by judicious experimentation4 ,for example1 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 produced4 ,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 remarkable4 ,by separating the etched glass from the painting a slight distance1 a very good imitation porcelain was produced4 ,the optical properties of varnishes vary and their effect varies considerably1 depending upon the mode of application4 ,these and many other details are available to the painter and decorator4 ,an interesting example among many is a cellulose lacquer dyed with an ordinary yellow dye4 ,the solution appears yellow by transmitted light or it will color a surface yellow4 ,by spraying this solution on a metallic object such as a nickel-plated piece1 in a manner that leaves the medium rough or diffusing1 the effect is no longer merely a yellow but a remarkable lustre resembling gilt4 ,quite in the same manner many effects of richness1 depth of color1 haziness1 etc41 are obtainable by the artist who is striving to produce a great illusion4 ,all the means for success which the painter possesses are also available to the decorator2 however1 the latter may utilize some of the illusions of line1 form1 irradiation1 etc41 which the architect encounters4 ,the decorator's field may be considered to include almost all of the painter's and much of the architect's4 ,this being the case1 little space will be given to this phase of the subject because painting and architecture are separately treated4 ,the decorator should begin to realize more fully the great potentiality of lighting in creating moods or in giving expression to an interior4 ,the psychology of light and the use of lighting as a mode of expression have barely been drawn upon by the decorator4 ,lighting has already been discussed so it will be passed by at this point4 ,the practice of hanging pictures on walls which are brilliantly colored is open to criticism4 ,there are galleries in existence where paintings are hung on brilliant green or rose walls4 ,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 wall4 ,on the green wall1 the white paper appears pinkish2 on the rose wall1 it appears bluish or greenish4 ,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 colors4 ,similarly1 if a woman must have a colored background1 it is well to choose one which will induce the more desirable tints in her appearance4 ,the designer of gowns certainly must recognize these illusions of color which may be desirable or undesirable4 ,the lighting of a picture has already been mentioned1 but the discussion was confined solely to distribution of light4 ,the quality of the light 7its spectral character7 may have an enormous influence upon the painting4 ,in fact with the same painting many illusions may be produced by lighting4 ,in general1 paintings are painted in daylight and they are not the same in appearance under ordinary artificial light4 ,for this reason the artist is usually entitled to the preservation of the illusion as he completed it4 ,by using artificial daylight which has been available for some years1 the painting appears as the artist gave it his last touch4 ,of course1 it is quite legitimate to vary the quality of light in case the owner desires to do so1 but the purpose here is to emphasize the fact that the quality of light is a powerful influence upon the appearance of the painting4 ,the influence is not generally enough recognized and its magnitude is appreciated by relatively few persons4 ,all other considerations aside1 a painting is best hung upon a colorless background and black velvet for this purpose yields remarkable results4 ,gray velvet is better1 when the appearance of the room is taken into consideration1 as it must be4 ,however1 the influence of dark surroundings toward enhancing the illusion is well worth recognizing4 ,in the case of a special picture or a special occasion1 a painting may be exhibited in a booth--a huge shadow-box not unlike a show-window in which the light-sources are concealed4 ,such experiments yield many interesting data pertaining to the illusions which the painter strives to obtain4 ,illustration3 ,fig4 #hb4--;,illustrating the apparent distortion of a picture frame in which the grain of the wood is visible4 ,incidentally on viewing some picture frames in which the grain of the wood was noticeable1 the frames did not appear to be strictly rectangular4 ,the illusions were so strong that only by measuring the frames could one be convinced that they were truly rectangular and possessed straight sides4 ,two of these are represented in ,figs4 #hb and #hc4 ,in the former1 the horizontal sides appear bent upward in the middle and the two vertical sides appear bowed toward the right4 ,in ,fig4 #hc1 the frame appears considerably narrower at the left end than at the right4 ,both these frames were represented in the original drawings by true rectangles4 ,many illusions are to be seen in furniture and in other woodwork in which the grain is conspicuous4 ,this appears to the author to be an objection in general to this kind of finish4 ,in ,fig4 #hd there is reproduced a photograph of the end of a board which was plane or straight notwithstanding its warped1 or bowed1 appearance4 ,the original photographs were placed so as to be related as shown in the figure4 ,various degrees of the illusion are evident4 ,the reader will perhaps find it necessary to convince himself of the straightness of the horizontal edges by applying a straight edge4 ,these are examples of the same illusion as shown in ,figs4 #cg to #dj4 ,illustration3 ,fig4 #hc4--;,another example similar to ,fig4 #hb4 ,illustration3 ,fig4 #hd4--;,from actual photographs of the end-grain of a board4 ,perhaps a brief statement regarding the modern isms in art may be of interest4 ,in considering some of the extreme examples1 we must revise our idea that art is or should be always beautiful4 ,the many definitions of art would lead us too far afield to discuss them here but in its most extended and popular sense1 art may be considered to mean everything which we distinguish from nature4 ,certainly art need not be beautiful1 although it does seem that the world would welcome the beautiful and would get along contentedly without art that is ugly or repulsive4 ,the modern isms must be viewed with consideration1 for there are many impostors concealing their inabilities by flocking to these less understood fields4 ,however1 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 light1 shade1 and color4 ,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 color4 ,some of them admit that they strive to paint through child's eyes and mind--free from experience1 prejudice1 and imitation4 ,these need all the scientific knowledge which is available--and maybe more4 ,in closing this chapter1 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 tools4 ,art cannot be manufactured by means of formulae4 ,this would not be true if we knew a great deal more than we do pertaining to the science of light1 color1 and vision4 ,the artist's fine sensibility will always be the dominating necessity in the production of art4 ,he must possess the ability to compose exquisitely2 he must be able to look at nature through a special temperament2 he must be gifted in eye and in hand2 he must be master of unusual visual and intellectual processes4 ,but knowledge will aid him as well as those in other activities4 ,a superior acquaintance with scientific facts lifted past masters above their fellows and what helped ,leonardo da ,vinci1 ,rembrandt1 ,velasquez1 ,turner1 ,claude1 ,monet1 and other masters will help artists of today4 ,what would not those past masters have accomplished if they had available in their time the greater knowledge of the present6 ,,xiii ,,architecture ,many illusions are found in architecture and1 strangely enough1 many of these were recognized long before painting developed beyond its primitive stages4 ,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 them4 ,drawings reveal many illusions to the architect1 but many are not predicted by them4 ,the ever-changing relations of lines and forms in architecture as we vary our viewpoint introduce many illusions which may appear and disappear4 ,no view of a group of buildings or of the components of a single structure can be free from optical illusions4 ,we never see in the reality the same relations of lines1 forms1 colors1 and brightnesses as indicated by the drawings or blue-prints4 ,perhaps this is one of the best reasons for justifying the construction of expensive models of our more pretentious structures4 ,no detailed account of the many architectural illusions will be attempted1 for it is easy for the reader to see many of the possibilities suggested by preceding chapters4 ,however1 a few will be touched upon to reveal the magnitude of the illusory effect and to aid the observer in looking for or recognizing them1 or purely for historical interest4 ,in architecture the eye cannot be wholly satisfied by such tools as the level1 the square1 and the plumb-line4 ,the eye is satisfied only when the appearance is satisfactory4 ,for the purpose of showing the extent of certain architectural illusions1 the compensatory measures applied by the ,greeks are excellent examples4 ,these also reveal the remarkable application of science to architecture as compared with the scanty application in painting of the same period4 ,during the best period of ,grecian art many refinements were applied in order to correct optical illusions4 ,it would be interesting to know to what extent the magnitude of the illusions as they appeared to many persons were actually studied4 ,the ,parthenon of ,athens affords an excellent example of the magnitude of the corrections which the designer thought necessary in order to satisfy the eye4 ,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 straight4 ,this is also true of the stylobate1 or substructure of a colonnade1 and of pediments and other features4 ,these lines were often convex instead of being straight as the eye desires to see them4 ,in the ,parthenon1 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 fronts4 ,vertical features were made to incline inward in order to correct the common appearance of leaning outward at the top4 ,in the ,parthenon1 the axes of the columns are not vertical1 but they are inclined inward nearly three inches4 ,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 ground4 ,the eleven-foot frieze and architrave is inclined inward about one and one-half inches4 ,in ,fig4 #he1 a represents the front of a temple as it should appear2 b represents its appearance 7exaggerated7 if it were actually built like a without compensations for optical illusions2 c represents it as built and showing the physical corrections 7exaggerated7 in order that it may appear to the eye as a does4 ,tall columns if they are actually straight are likely to appear somewhat shrunken in the middle2 therefore they are sometimes made slightly swollen in order to appear straight4 ,this outward curvature of the profile is termed an entasis and in the ,parthenon column1 which is thirty-four feet in height1 amounted to about three-fourths of an inch4 ,in some early ,grecian works1 it is said that this correction was overdone but that its omission entirely is quite unsatisfactory4 ,some authorities appear to believe that an excellent compromise is found in the ,parthenon columns4 ,illustration3 ,fig4 #he4--;,exaggerated illusions in architecture4 ,one of the conditions which is responsible for certain illusions and has been compensated for on occasions is represented in ,fig4 #hf4 ,on the left are a series of squares of equal size placed in a vertical row4 ,if these are large so that they might represent stories in a building they will appear to decrease in size from the bottom upward1 because of the decreasing projection at the eye4 ,this is obvious if the eye is considered to be at the point where the inclined lines meet4 ,in order to compensate for the variation in visual angle1 there must be a series of rectangles increasing considerably in height toward the top4 ,the correction is shown in the illustration4 ,it is stated that an inscription on an ancient temple was written in letters arranged vertically1 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 ,fig4 #hf4 ,obviously a given correction would be correct only for one distance in a given plane4 ,illustration3 ,fig4 #hf4--;,illustrating the influence of visual angle upon apparent vertical height4 ,in ,chapter ,,viii the phenomenon of irradiation was discussed and various examples were presented4 ,it exerts its influence in the arts as elsewhere4 ,columns viewed against a background of white sky appear of smaller diameter than when they are viewed against a dark background4 ,this is illustrated in ,fig4 #hg where the white and the black columns are supposed to be equal in diameter4 ,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 advantage4 ,in ,fig4 #hh some commonplace illusions are presented1 not for what they are worth1 but to suggest how prevalent they may be4 ,where the pole or column intersects the arches or circle1 there is an apparent change in the direction of the curved lines4 ,the different types of arches show different degrees of the illusion4 ,it may be of interest for the reader to refer to preceding chapters and to ascertain what types of illusions are involved4 ,illustration3 ,fig4 #hg4--;,irradiation in architecture4 ,if a high wall ends in a series of long horizontal steps at a slightly inclined sidewalk1 the steps are not likely to appear horizontal4 ,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 shading4 ,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 alone4 ,the same principal can be applied in many ways4 ,for example1 in ,fig4 #hi the roof appears quite extensive when viewed so that the end-walls of the structure are not seen4 ,such illusions find applications in the moving-picture studio where extensive interiors1 great fortresses1 and even villages must be erected within small areas4 ,incidentally the camera aids to create the illusion of magnitude in photographs because it usually magnifies perspective1 thereby causing scenes to appear more extensive in the photographs than in the reality4 ,illustration3 ,fig4 #hh4--,some simple geometrical-optical illusions in architecture4 ,balance in architecture is subject to illusions and might be considered an illusion itself4 ,for example1 our judgment of balance is based largely upon mechanical laws4 ,a composition must appear to be stable2 that is1 a large component such as a tower must not be situated too far from what we take as a center of gravity1 to appear capable of tipping the remainder of the structure4 ,in physics we would apply the term moment4 ,each mass may be multiplied by its distance from the center of gravity1 thus determining its moment4 ,for a building or other composition to appear stable the sum of these moments must be zero2 that is1 those tending to turn the figure in one direction must be counterbalanced by those tending to turn it in another direction4 ,in appraising a composition1 our intellect summates the effects of different parts somewhat in this manner and if satisfactory1 balance is considered to have been attained4 ,the colors of the various components exert an influence in this respect1 so it is seen that illusions may have much to do with the satisfactoriness of architectural compositions4 ,illustration3 ,fig4 #hi4--;,by decreasing the exposed length of shingles toward the top a greater apparent expanse is obtained4 ,various illusions of height1 of ceiling1 composedness1 etc41 may be obtained by the color of the ceiling4 ,a dark cornice in an interior may appear to be unsupported if the walls below are light in color1 without any apparent vertical supports for the cornice4 ,we are then subjected to the illusion of instability or incongruity4 ,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 themselves4 ,color and brightness in such cases are very important4 ,the architectural details on exteriors evolved under daylighting outdoors so that their form has been determined by the shadows desired4 ,the architect leads his lights and shadows around the building modeling it as he desires4 ,an offset here and a depression there models the exterior in light and shade4 ,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 lighting4 ,indoors the architect has a powerful controllable medium in artificial light which he may draw upon for producing various expressions or moods in rooms4 ,the effect of shadows is interesting when viewing some structures flood-lighted at night4 ,in those cases where the light is directed upward there is a reversal of shadows which is sometimes very unsatisfactory4 ,it is interesting to experiment with various ornamental objects lighted from various directions4 ,for example1 a ,corinthian capital lighted from below may produce an unpleasant impression upon the observer4 ,we do not like to have the dominant light from below1 perhaps because it is annoying to the eyes4 ,possibly this is an instinct acquired by experience in snow-fields or on the desert1 or it may be a heritage of ancestral experience gained under these glaring conditions4 ,this dislike manifests itself when we appraise shadow-effects and therefore our final impression is tempered by it4 ,all sculptured objects depend for their appearance upon the lighting1 and they are greatly influenced by it4 ,in sculpture1 in a strict sense1 illusions play a lesser part than in other arts4 ,perhaps in those of very large proportions various corrections have been applied4 ,a minor detail of interest is the small cavity in the eye1 corresponding to a reversed cornea4 ,this depression catches a shadow which gives considerable expression to the eye4 ,,xiv ,,mirror ,,magic ,strictly speaking there are fewer illusions found in the practice of the magician than is generally supposed2 that is1 the eye usually delivers correctly to the intellect1 but the judgment errs for various reasons4 ,the illusion is due to false assumptions1 to the distracting words1 to unduly accented superfluous movements of the magician2 or in general to downright trickery4 ,much of the magician's success is due to glibness of tongue and deftness of fingers1 but many of the more notable tricks were those involving the use of mirrors and the control of light4 ,black curtains1 blackened assistants1 and controlled light have played prominent parts in the older magic1 but the principles of these are easily understood4 ,however1 the mirror perhaps has done more to astound the audience than any other device employed by the magician4 ,for this reason1 and because its effects are commonly termed illusions1 some representative examples will be presented4 ,in a previous chapter attention was called to the simple but usually overlooked fact that1 for example1 the image of a face in a mirror is reversed as to right and left4 ,when this fact is overlooked we may be astonished at the changed expression of an intimate friend as we view the face 7reversed7 in the mirror4 ,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 is4 ,inasmuch as faces are not accurately symmetrical and many are quite unsymmetrical the effects of the mirror are sometimes startling4 ,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 sees4 ,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 mirror4 ,if he desires to see himself as others see him1 he can arrange two mirrors vertically almost at a right-angle4 ,by a little research he will find an image of his own face1 which is not reversed2 that is1 an image whose right ear is really his right ear4 ,a famous illusion which astounded audiences was the sphinx illustrated in ,fig4 #ij4 ,the box was placed upon a table and when opened there was revealed a ,sphinxian head1 but why it was called a ,sphinx is clothed in mystery because upon some occasions it talked4 ,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 diagram4 ,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 leg4 ,the walls1 floor1 and ceiling of the box-like recess in which the table was placed were covered with the same material4 ,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 ,w4 ,thus the table appeared to be open underneath and the possibilities of the apparatus are evident4 ,illustration3 ,fig4 #ij4--;,an example of a mirror illusion4 ,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 hand4 ,walking to the table he could place the box over a trap-door and by the time he had unlatched the door of the box1 the assistant kneeling under the table could have his head thrust upward through the trap-door of the table-top into the box4 ,after a few impressive words1 supposed to be ,hindoo but in reality were ,hoodoo1 presto6 and the ,sphinx was revealed4 ,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 statue4 ,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 mirror4 ,doubtless a careless accomplice lost his job1 but the damage had been done1 for the trick was revealed4 ,this illusion is so effective that it1 or variations of it1 are still in use4 ,illustration3 ,fig4 #ia4--;,another example of mirror magic4 ,another simple case is illustrated in ,fig4 #ia4 ,a large plate-glass mirror ,m was placed at an angle of approximately #de degrees from the floor4 ,through a hole in it an assistant's head and shoulders projected and the edge of the opening was covered with a draped cloth4 ,the audience saw the image of the ceiling ,c of the alcove reflected by the mirror but being ignorant of the presence of the mirror1 assumed this image to be the rear wall4 ,this trick was effective for many years4 ,obviously the mirrors must be spotlessly clean and the illuminations of the walls1 ceiling1 and in some cases1 the floor must be very uniform4 ,furthermore1 no large conspicuous pattern could be used for lining the box-like recess4 ,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 being4 ,the possibilities of mirrors in such fields are endless and they can be studied on a small scale by anyone interested4 ,the pseudoscope which produces effects opposite to those of the stereoscope is an interesting device4 ,the foregoing is the faintest glimpse of the use of the mirror1 but it does not appear advisable to dwell further upon its use1 for after all the results are not visual illusions in the sense of the term as usually employed throughout this book4 ,,xv ,,camouflage ,illusions played many roles in the science and art of deception during the ,world ,war1 but they served most prominently in the later stages of the war upon the sea4 ,inasmuch as the story of the science of camouflage is not generally available1 it appears worth while to present it briefly4 ,besides being of interest1 it will reveal to the reader the part that the science of light1 color1 lighting1 and vision played in deception4 ,furthermore1 the reader will sense the numberless illusions which are woven into camouflage as developed in nature1 and in human activities4 ,the word camouflage by origin does not include all kinds of deception2 however1 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 ,war4 ,terrestrial ,camouflage4--,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 enemy4 ,it is an art older than the human race1 for its beginnings may be traced back to the obscurity of the early ages of the evolution of animal life4 ,the name was coined by the ,french to apply to a definite art which developed during the ,great ,war to a high state1 as many other arts developed by drawing deeply upon the resources of scientific knowledge4 ,with the introduction of this specific word to cover a vast field of activity in scientifically concealing and deceiving1 many are led to believe that this is a new art1 but such is not the case4 ,however1 like many other arts1 such as that of flying1 the exigencies of modern warfare have provided an impetus which has resulted in a highly developed art4 ,scientists have recognized for many years1 and perhaps more or less vaguely for centuries1 that ,nature exhibits wonderful examples of concealment and deception4 ,the survival of the fittest1 as ,darwin expressed his doctrine1 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 lived4 ,naturally1 markings1 habits1 and environment became more and more adapted to each other until the species became in equilibrium with ,nature sufficiently to insure its perpetuity4 ,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 enemy4 ,the rabbit is mottled because ,nature's infinite variety of highlights1 shadows1 and hues demand variety in the markings of an animal if the latter is to be securely hidden4 ,solid color does not exist in ,nature's landscapes in large areas4 ,the rabbit is lighter underneath to compensate for the lower intensity of illumination received on these portions4 ,as winter approaches1 animals in rigorous climates need warmer coats1 and the hairs grow longer4 ,in many cases the color of the hairs changes to gray or white1 providing a better coating for the winter environment4 ,animals are known to mimic inanimate objects for the sake of safety4 ,for example1 the bittern will stand rigid with its bill pointed skyward for many minutes if it suspects an enemy4 ,non-poisonous snakes resemble poisonous ones in general characteristics and get along in the world on the reputation of their harmful relatives4 ,the drone-bee has no sting1 but to the casual observer it is a bee and bees generally sting4 ,some animals have very contrasting patterns which are conspicuous in shape1 yet these very features disguise the fact that they are animals4 ,close observation of fishes in their natural environment provides striking examples of concealing coloration4 ,vast works have been written on this subject by scientists1 so it will only be touched upon here4 ,there are many examples of mobile camouflage to be found in ,nature4 ,seasonal changes have been cited in a foregoing paragraph4 ,the chameleon changes its color from moment to moment4 ,the flounder changes its color and pattern to suit its environment4 ,it will even strive to imitate a black and white checkerboard4 ,in looking at a bird1 animal1 insect1 or other living thing it is necessary to place it in its natural environment at least in the imagination1 before analyzing its coloration4 ,for example1 a male mallard duck hanging in the market is a very gaudy object1 but place it in the pond among the weeds1 the green leaves1 the highlights1 and the shadows1 and it is surprisingly inconspicuous4 ,the zebra in the zoo appears to be marked for the purpose of heralding its presence anywhere in the range of vision1 but in its reedy1 bushy1 grassy environment it is sufficiently inconspicuous for the species to survive in ,nature's continuous warfare4 ,thus studies of ,nature reveal the importance of general hue1 the necessity for broken color or pattern1 the fact that black spots simulate shadows or voids1 the compensation for lower illumination by counter-shading1 and many other facts4 ,the artist has aided in the development of camouflage1 but the definite and working basis of all branches of camouflage are the laws and facts of light1 color1 and vision as the scientist knows them4 ,just as lower animal life has unconsciously survived or evolved by being fitted to do so1 mankind has consciously1 or at least instinctively1 applied camouflage of various kinds to fool his prey or his enemy4 ,many of us in hunting ducks have concealed the bow of our sneak-boat with mud and weeds1 or in the season of floating ice1 with a white cloth4 ,in our quest of water fowl we use decoys and grass suits4 ,the ,esquimau stalks his game behind a piece of ice4 ,in fact1 on every hand we find evidences of this natural instinct4 ,the ,indian painted his face and body in a variety of colors and patterns4 ,did he do this merely to be hideous8 ,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 body4 ,in past wars there is plenty of evidence that concealment and deception were practiced to the full extent justifiable by the advantages or necessity4 ,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 deception4 ,with the advent of the airplane1 aerial photography became a more important factor than visual observation in much of the reconnaissance4 ,this necessitated that camouflage in order to be successful had to meet the requirements of the photographic eye1 as well as that of the human eye4 ,in other words1 the special characteristics of the colors used had to be similar to those of ,nature's colors4 ,for example1 chlorophyl1 the green coloring matter of vegetation1 is a peculiar green as compared with green pigments4 ,when examined with a spectroscope it is seen to reflect a band of deep red light not reflected by ordinary pigments4 ,in considering this aspect it is well to bear in mind that the eye is a synthetic apparatus2 that is does not analyze color in a spectral sense4 ,an artist who views color subjectively and is rarely familiar with the spectral basis may match a green leaf perfectly with a mixture of pigments4 ,a photographic plate1 a visual filter1 or a spectroscope will reveal a difference which the unaided eye does not4 ,some time before the ,great ,war began1 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 surroundings4#i ,studies were made of various filters1 made with the object of the experiment in mind1 in viewing the uniforms of various armies4 ,further developments were made by applying the same principles to colored lights and painted pictures4 ,many of these have been described elsewhere4 ,with the development of the science of camouflage1 filters came into use for the detection of camouflage4 ,as a result of the demand for avoiding detection by photographic plates and by various colored filters1 some paints provided for the camoufleur were developed according to the spectral requirements4 ,many other applications of science were developed so that camouflage can now be called an art based upon sound scientific principles4 ,natural lighting is so variable that it is often impossible to provide camouflage which will remain satisfactory from day to day2 therefore1 a broad knowledge of ,nature's lighting is necessary in order to provide the best compromise4 ,there are two sources of light in the daytime1 namely1 the sun and the sky4 ,the relative amounts of light contributed by these two sources is continually changing4 ,the sky on cloudless days contributes from one-tenth to one-third of the total light received by a horizontal surface at noon4 ,light from the sky and light reflected from the surroundings illuminate the shadows4 ,these shadows are different in color than highlights1 although these finer distinctions may be ignored in most camouflage because color becomes less conspicuous as the distance of observation increases4 ,in general1 the distribution of brightness or light and shade is the most important aspect to be considered4 ,the camoufleur worries over shadows more than any other aspect generally4 ,on overcast days camouflage is generally much more successful than on sunny days4 ,obviously1 counter-shading is resorted to in order to eliminate shadows1 and where this is unsuccessful confusion is resorted to by making more shadows4 ,the shape and orientation of a building is very important to those charged with the problem of rendering it inconspicuous to the enemy1 but little attention has been paid to these aspects4 ,for example1 a hangar painted a very satisfactory dull green will be distinguishable by its shape as indicated by its shadow and shaded sides4 ,in this zone a hangar1 for example1 would be more readily concealed if its length lay north and south4 ,its sides could be brought with a gradual curve to the ground and its rear1 which is during most of the day in shadow1 could be effectively treated to conceal the shadow4 ,a little thought will convince the reader of the importance of shape and orientation4 ,broken color or pattern is another fundamental of camouflage which1 of course1 must be adapted to its environment4 ,for our trucks1 cannon1 and many other implements of war1 dark green1 yellow1 dark blue1 light gray1 and other colors have been used in a jumble of large patterns4 ,a final refinement is that of the blending of these colors at a distance1 where the eye no longer resolves the individual patches1 to a color which simulates the general hue of the surroundings4 ,for example1 red and green patches at a distance blend to yellow2 yellow and blue patches blend to a neutral gray if suitably balanced1 but if not1 to a yellow-gray or a blue-gray2 red1 green1 and blue if properly balanced will blend to a gray2 black1 white and green patches will blend to a green shade1 and so on4 ,these facts are simple to those who are familiar with the science of light and color1 but the artist1 whose knowledge is based upon the mixture of pigments1 sometimes errs in considering this aspect of color-blending by distance4 ,for example1 it is not uncommon for him to state that at a distance yellow and blue patches blend to make green1 but the addition of lights or of juxtaposed colors is quite different in result from the addition of pigments by intimately mixing them4 ,in constructing such a pattern of various colors it is also desirable to have the final mean brightness approximate that of the general surroundings4 ,this problem can be solved by means of the photometer and a formula provided1 which states1 for example1 that a certain percentage of the total area be painted in gray1 another percentage in green1 and so on4 ,the photometer has played an important role in establishing the scientific basis of camouflage4 ,the size of the pattern must be governed by the distance at which it is to be viewed1 for obviously if too small the effect is that of solid color1 and if too large it will render the object conspicuous1 which is a disadvantage ranking next to recognizable4 ,where the artist is concerned with a background which does not include the sky1 that is1 where he deals only with illuminated objects on the earth1 his trained eye is valuable provided the colors used meet the demands made by photographic plates and visual color-filters4 ,in other words1 the sky as a background gives trouble to all who are unfamiliar with scientific measurements4 ,the brightnesses of sky and clouds are outside the scale of brightnesses ordinarily encountered in a landscape4 ,many interesting instances of the artist's mistakes in dealing with these backgrounds could be presented2 however1 the artist's trained eye has been a great aid in constructing patterns and various other types of camouflage4 ,one of the most conspicuous aspects of the earth's surface is its texture4 ,from great heights it appears flat1 that is1 rolling land is ironed out and the general contour of the ground is flattened4 ,however1 the element of texture always remains4 ,this is the chief reason for the extensive use of netting on which dyed raffia1 foliage1 pieces of colored cloth1 etc41 are tied4 ,such network has concealed many guns1 headquarters1 ammunition dumps1 communication trenches1 roadways1 etc4 ,when this has been well done the concealment is perfect4 ,one of the greatest annoyances to the camoufleur is the lack of dullness or flatness of the paints1 fabrics1 and some of the other media used4 ,when viewed at some angles the glint of highlights due to specular reflection renders the work very conspicuous4 ,for this reason natural foliage or such material as dyed raffia has been very successful4 ,systems of network and vertical screens have been extensively employed on roadways near the front1 not for the purpose of concealing from the enemy the fact that the roadways exist1 but to make it necessary to shell the entire roadway continually if it is hoped to prevent its use4 ,although the camoufleur is provided with a vast amount of material for his work1 many of his requirements are met by the material at hand4 ,obviously1 the most convenient method of providing concealment for a given environment is to use the materials of the environment4 ,hence1 rubbish from ruined buildings or villages supplies camouflage for guns1 huts1 etc41 in that environment4 ,in woods the material to simulate the woods is at hand4 ,many of these aspects are so obvious to the reader that space will not be given to their consideration4 ,the color of the soil is important1 for if it is conspicuous the camoufleur must provide screens of natural turf4 ,in this great game of hocus-pocus many deceptions are resorted to4 ,replicas of large guns and trenches are made2 dummy soldiers are used to foil the sniper and to make him reveal his location1 and papier-mache horses1 trees1 and other objects conceal snipers and observers and afford listening posts4 ,gunners have been dressed in summer in green flowing robes4 ,in winter white robes have been utilized4 ,how far away from modern warriors are all the usual glitter and glamour of military impedimenta in the past parades of peace time6 ,the armies now dig in for concealment4 ,the artillery is no longer invisible behind yonder hill1 for the eyes of the aerial observer of the camera reveal its position unless camouflaged for the third dimension4 ,in the foregoing only the highlights of a vast art have been viewed1 but the art is still vaster1 for it extends into other fields4 ,sound must sometimes be camouflaged and this can only be done by using the same medium--sound4 ,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 past4 ,a notable method is the use of velocity of sound4 ,records are made at various stations of the firing of a gun and the explosion of the shell4 ,by trigonometric laws the position of the gun is ascertained4 ,it is said that the ,germans fired a number of guns simultaneously with the #ge-mile gun in order to camouflage its location4 ,the airplane and submarine would gladly employ sound camouflage in order to foil the sound detector if practicable solutions were proposed4 ,the foregoing is a brief statement of some of the fundamental principles of land camouflage4 ,let us now briefly consider the eyes of the enemy4 ,of course1 much concealment and deception is devised to foil the observer who is on the ground and fairly close4 ,the procedure is obvious to the average imagination2 however1 the reader may not be acquainted with the aerial eyes from which concealment is very important4 ,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 them4 ,field glasses cannot be used as satisfactorily in an airplane as on solid ground1 owing to vibration and other movements4 ,the difference is not as great in the huge flying boats as it is in the ordinary airplane4 ,the camera can record many details with higher accuracy than the eye4 ,at an altitude of one mile the lens can be used at full aperture and thus very short exposures are possible4 ,this tends to avoid the difficulty due to vibration4 ,when the plates are developed for detail and enlargements are made1 many minute details are distinguishable4 ,furthermore1 owing to the fact that the spectral sensibilities of photographic emulsions differ from that of the eye1 contrasts are brought out which the eye would not see4 ,this applies also to camouflage which is devised merely to suit the eye4 ,individual footprints have been distinguished on prints made from negatives exposed at an altitude of #fjjj feet4 ,by means of photography1 daily records can be made if desired and these can be compared4 ,a slight change is readily noted by such comparison by skilled interpreters of aerial photographs4 ,the disappearance of a tree from a clump of trees may arouse suspicion4 ,sometimes a wilted tree has been noted on a photograph which naturally attracts attention to this position4 ,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 guns4 ,by paths converging toward a certain point1 it may be concluded from the photographs that an ammunition dump or headquarters is located there even though the position itself was well camouflaged4 ,continuous photographic records may reveal disturbances of turf and lead to a more careful inspection of the region for sapping operations1 etc4 ,by these few details it is obvious that the airplane is responsible for much of the development of camouflage on land1 owing to the necessity which it created for a much more extensive concealment4 ,the entire story of land camouflage would overflow the confines of a volume1 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 founded4 ,marine ,camouflage4--,at the time of the ,spanish-,american war1 our battleships were painted white1 apparently with little thought of attaining low visibility4 ,later the so-called battleship gray was adopted1 but it has been apparent to close observers that this gray is in general too dark4 ,apparently it is a mixture of black and white4 ,the ships of the ,british navy were at one time painted black1 but preceding the ,great ,war their coats were of a warm dark gray4 ,germany adopted dark gray before the close of the last century and ,austria adopted the ,german gray at the outbreak of the war4 ,the ,french and ,italian fleets were also painted a warm gray4 ,this development toward gray was the result of an aim toward attaining low visibility4 ,other changes were necessitated by submarine warfare which will be discussed later4 ,in the early days of unrestricted submarine warfare many schemes for modifying the appearance of vessels were submitted4 ,many of these were merely wild fancies with no established reasoning behind them4 ,here again science came to the rescue and through research and consultation1 finally straightened out matters4 ,the question of low visibility for vessels could be thoroughly studied on a laboratory scale1 because the seascape and natural lighting conditions could be reproduced very closely4 ,even the general weather conditions could be simulated1 although1 of course1 the experiments could be prosecuted outdoors with small models1 as indeed they were4 ,mr4 ,l4 ,a4 ,jones#aj carried out an investigation on the shore of ,lake ,ontario1 and laboratory experiments were conducted by others with the result that much light was shed on the questions of marine camouflage4 ,this work confirmed the conclusion of the author and others that our battleship gray was too dark4 ,of course1 the color best adapted is that which is the best compromise for the extreme variety in lighting and weather conditions4 ,these vary in different parts of the world1 so naturally those in the war zone were of primary importance4 ,all camouflage generally must aim to be a compromise best suited for average or dominating conditions4 ,for example1 in foggy weather a certain paint may render a ship of low visibility1 but on a sunny day the ship might be plainly visible4 ,however1 if ships are rendered of low visibility for even a portion of the time it is obvious that an advantage has been gained4 ,cloudiness increases generally from the equator northward1 as indicated by meteorological annals4 ,in order to study low visibility a scale of visibility must be established1 and it is essential to begin with the fundamentals of vision4 ,we distinguish objects by contrasts in brightness and in color and we recognize objects by these contrasts which mold their forms4 ,in researches in vision it is customary to devise methods by which these contrasts can be varied4 ,this is done by increasing or decreasing a veil of luminosity over the object and its surroundings and by other means4 ,much work has been done in past years in studying the minimum perceptible contrast1 and it has been found to vary with hue1 with the magnitude of brightness1 and with the size of the image1 that is1 with the distance of an object of given size4 ,in such problems as this one much scientific work can be drawn upon4 ,a simple1 though rough1 scale of visibility may be made by using a series of photographic screens of different densities4 ,a photographic screen is slightly diffusing1 still the object can be viewed through it very well4 ,such methods have been employed by various investigators in the study of visibility4 ,owing to the curvature of the earth1 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 superstructure4 ,for an observer in a certain position the visibility range varies as the square root of the distance of the object from him4 ,such data are easily available1 so they will not be given here4 ,so far we have considered the ship itself when1 as a matter of fact1 on clear days the smoke cloud emitted by the ship is usually visible long before a ship's superstructure appears on the horizon4 ,this led to the prevention of smoke by better combustion1 by using smokeless fuels1 etc4 ,the irregular skyline of a ship is perhaps one of the most influential factors which tend to increase its visibility4 ,many suggestions pertaining to the modification of the superstructure have been made1 but these are generally impracticable4 ,false work suffers in heavy seas and high winds4 ,after adopting a suitable gray as1 a low-visibility paint for ships1 perhaps the next refinement was counter shading2 that is1 shadows were painted a lighter color1 or even white4 ,the superstructure was painted in some cases a light blue1 with the hope that it would fade into the distant horizon4 ,however1 the effectiveness of the submarine demanded new expedients because within its range of effectiveness no ingenuity could render its intended prey invisible4 ,the effective gun-fire from submarines is several miles and torpedoes can be effective at these distances4 ,however1 the submarine prefers to discharge the torpedo at ranges within a mile4 ,it is obvious that1 in average weather1 low visibility ceases to be very effective against the submarine4 ,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 velocity4 ,the submarine gunner must have the range1 speed1 and course of the target in order to fire a torpedo with any hope of a hit4 ,therefore1 any uncertainties that could be introduced pertaining to these factors would be to the advantage of the submarine's prey4 ,for example1 low visibility gave way to confusibility in the discussions of defence against the submarine and the slogan1 ,a miss is as good as a mile was adopted4 ,the foregoing factors cannot be determined ordinarily with high accuracy1 so that it appeared possible to add somewhat to the difficulties of the submarine commander4 ,many optical illusions have been devised and studied by scientists4 ,in fact1 some of these tricks are well known to the general reader4 ,straight lines may appear broken1 convergent1 or divergent by providing certain patterns or lines intermingled with them4 ,many of these were applied to models in laboratory experiments and it has been shown that confusion results as to the course of the vessel4 ,the application of these on vessels has resulted in the grotesque patterns to be seen on ships during the latter stage of the war4 ,it is well known that these illusions are most effective when the greatest contrasts are used1 hence black and white patterns are common4 ,color has not been utilized as definitely as pattern in confusibility1 although there is a secondary aim of obtaining low visibility at a great distance by properly balancing the black1 white1 and other colors so that a blue-gray results at distances too great for the individual patterns to be resolved by the eye4 ,color could be used for the purpose of increasing the conclusion by apparently altering the perspective4 ,for example1 blue and red patterns on the same surface do not usually appear at the same distance1 the red appearing closer than the blue4 ,illustration3 ,fig4 #ib4--;,a primary stage in the evolution of the use of geometrical-optical illusions on ships4 ,such apparently grotesque patterns aimed to distort the lines of the ship and to warp the perspective by which the course is estimated4 ,this was the final type of marine camouflage at the close of the war4 ,besides relying upon these illusions1 ships zigzagged on being attacked and aimed in other ways to confuse the enemy4 ,no general attempt was made to disguise the bow1 because the bow-wave was generally visible4 ,however1 attempts have been made to increase it apparently and even to provide one at the stern4 ,in fact1 ingenuity was heavily drawn upon and many expedients were tried4 ,after low-visibility was abandoned in favor of the optical illusion for frustrating the torpedo-attack by the submarine1 there was a period during which merely a mottled pattern was used for vessels4 ,gradually this evolved toward such patterns as shown in ,fig4 #ib4 ,in this illustration it is seen that the optical-illusion idea has taken definite form4 ,during the period of uncertainty as to the course the pattern should take1 a regularity of pattern was tried1 such as illustrated in ,figs4 #ic and #id4 ,finally1 when it dawned more or less simultaneously upon various scientific men1 who were studying the problems of protecting vessels upon the seas1 that the geometrical-optical illusion in its well-known forms was directly adaptable1 renewed impetus was given to investigation4 ,the scientific literature yielded many facts but the problems were also studied directly by means of models4 ,the latter study is illustrated by ,figs4 #ie and #if1 the originals having been furnished by ,mr4 ,e4 ,l4 ,warner1#aa who among others prosecuted a study of the application of illusions to vessels4 ,the final results were gratifying1 as shown to some extent in ,figs4 #ig and #ih1 also kindly furnished by ,mr4 ,warner4 ,it is seen that these patterns are really deceiving as to the course of the vessel4 ,illustration3 ,figs4 #ic and #id4--;,attempts at distortion of outline which preceded the adoption of geometrical-optical illusions for ships4 ,illustration3 ,figs4 #ie and #if4--;,illustrating the use of models by the ,navy ,department in developing the geometrical-illusion for ships4 ,the convoy system is well known to the reader4 ,this saved many vessels from destruction4 ,vessels of the same speed were grouped together and steamed in flocks across the ,atlantic4 ,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 adage1 ,in unity there is strength4 ,before the war began1 a ,brazilian battleship launched in this country was provided with a system of blue lights for use when near the enemy at night4 ,blue was adopted doubtless for its low range compared with light of other colors4 ,we know that the setting sun is red because the atmospheric dust1 smoke1 and moisture have scattered and absorbed the blue and green rays more than the red and yellow rays4 ,in other words the penetrating power of the red and yellow is greater than that of the blue rays4 ,this country made use of this expedient to some extent4 ,of course1 all other lights were extinguished and portholes were closed in ocean travel during the submarine menace4 ,illustration3 ,figs4 #ig and #ih4--;,examples of the geometrical-optical illusion as finally applied4 ,naturally smoke-screens were adopted as a defensive measure on sea as well as on land4 ,destroyers belch dense smoke from their stacks in order to screen battleships4 ,many types of smoke-boxes have been devised or suggested4 ,the smoke from these is produced chemically and the apparatus must be simple and safe4 ,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 course4 ,these expedients were likely to render shell-fire and observations inaccurate4 ,this mode of defense is obviously best suited to unarmed vessels4 ,in the use of smoke-boxes the direction and velocity of the wind must be considered4 ,the writer is unacquainted with any attempts made to camouflage submarines under water1 but that this can be done is evident from aerial observations4 ,when looking over the water from a point not far above it1 as on a pier1 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 water4 ,the brightness of the surface of water is due to mirrored sky and clouds ordinarily4 ,for a perfectly smooth surface of water1 the reflection factor is #b per cent for perpendicular incidence4 ,this increases only slightly as the obliquity increases to an angle of about #fj degrees4 ,from this point the reflection-factor of the surface rapidly increases1 becoming #ajj per cent at #ij degrees incidence4 ,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 submarines4 ,the depth at which an object can be seen in water depends1 of course1 upon its clarity4 ,it may be surprising to many to learn that the brightness of water1 such as rivers1 bays1 and oceans1 as viewed perpendicularly to its surface1 is largely due to light diffused within it4 ,this point became strikingly evident during the progress of work in aerial photometry4 ,a submerged submarine may be invisible for two reasons3 7#a7 ,it may be deep enough to be effectively veiled by the luminosity of the mass of water above it 7including the surface brightness7 or1 7#b7 ,it may be of the proper brightness and color to simulate the brightness and color of the water4 ,it is obvious that if it were white it would have to attain concealment by submerging deeply4 ,if it were a fairly dark greenish-blue it would be invisible at very small depths4 ,in fact1 it would be of very low visibility just below the surface of the water4 ,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 overhead4 ,the visibility of submarines is well exemplified by viewing large fish such as sharks from airships at low altitudes4 ,they appear as miniature submarines dark gray or almost black amid greenish-blue surroundings4 ,incidentally1 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 waters4 ,the latter as viewed vertically are about one-half the brightness of the former under the same conditions and are decidedly bluer4 ,the ,visibility of ,airplanes4--,in the ,great ,war the airplane made its debut in warfare and in a short time made a wonderful record1 yet when hostilities ceased aerial camouflage had not been put on a scientific basis4 ,no nation had developed this general aspect of camouflage systematically or to an extent comparable with the developments on land and sea4 ,one of the chief difficulties was that scientific data which were applicable were lacking4 ,during the author's activities as ,chairman of the ,committee on ,camouflage of the ,national ,research ,council he completed an extensive investigation#ab of the fundamentals upon which the attainment of low visibility for airplanes must be based4 ,solutions of the problems encountered in rendering airplanes of low visibility resulted and various recommendations were made1 but the experiences and data will be drawn upon here only in a general way4 ,in this general review details would consume too much space1 for the intention has been to present a broad view of the subject of camouflage4 ,the visibility of airplanes presents some of the most interesting problems to be found in the development of the scientific basis for camouflage4 ,the general problem may be subdivided according to the type of airplane1 its field of operation1 and its activity4 ,for example1 patrol craft which fly low over our own lines would primarily be camouflaged for low visibility as viewed by enemies above4 7,see ,fig4 #ii47 ,high-flying craft would be rendered of low visibility as viewed primarily by the enemy below4 ,airplanes for night use present other problems and the visibility of seaplanes is a distinct problem1 owing to the fact that the important background is the water1 because seaplanes are not ordinarily high-flying craft4 ,in all these considerations it will be noted that the activity of the airplanes is of primary importance1 because it determines the lines of procedure in rendering the craft of low visibility4 ,this aspect is too complicated to discuss thoroughly in a brief resume4 ,illustration3 ,fig4 #ii4--,representative earth backgrounds for an airplane 7uncamouflaged7 as viewed from above4 ,the same fundamentals of light1 color1 and vision apply in this field as in other fields of camouflage1 but different data are required4 ,when viewing aircraft from above1 the earth is the background of most importance4 ,cumulus clouds on sunny days are generally at altitudes of #djjj to #gjjj feet4 ,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 above4 ,in other words1 the compromise in this case is to accept the earth as a background and to work on this basis4 ,we are confronted with seasonal changes of landscape1 but inasmuch as the summer landscape was of greatest importance generally1 it was the dominating factor in considering low visibility from above4 ,on looking down upon the earth one is impressed with the definite types of areas such as cultivated fields1 woods1 barren ground and water4 ,different landscapes contain these areas in various proportions1 which fact must be considered4 ,many thousand determinations of reflection-factor and of approximate hue were made for these types of areas1 and upon the mean values camouflage for low visibility as viewed from above was developed4 ,a few values are given in the accompanying table1 but a more comprehensive presentation will be found elsewhere4#ab ,mean ,reflection-,factors 7,from thousands of measurements made by viewing vertically downward during summer and fall from various altitudes47 ,per ,cent ,woods #d4c ,barren ground #ac4j ,fields 7grazing land and growing crops7 #f4h ,inland water 7rivers and bays7 #f4h ,deep ocean water #c4e ,dense clouds #gh4j ,wooded areas are the darkest general areas in a landscape and possess a very low reflection-factor4 ,from above one sees the deep shadows interspersed among the highlights4 ,these shadows and the trapping of light are largely responsible for the low brightness or apparent reflection-factor4 ,this is best illustrated by means of black velvet4 ,if a piece of cardboard is dyed with the same black dye as that used to dye the velvet1 it will diffusely reflect #b or #c per cent of the incident light1 but the black velvet will reflect no more than #j4e per cent4 ,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 cardboard4 ,cultivated fields on which there are growing crops are nearly twice as bright as wooded areas1 depending1 of course1 upon the denseness of the vegetation4 ,barren sunbaked lands are generally the brightest large areas in a landscape1 the brightness depending upon the character of the soil4 ,wet soil is darker than dry soil1 owing to the fact that the pores are filled with water1 thus reducing the reflection-factor of the small particles of soil4 ,a dry white blotting paper which reflects #ge per cent of the incident light will reflect only about #ee per cent when wet4 ,inland waters which contain much suspended matter are about as bright as grazing land and cultivated fields4 ,shallow water partakes somewhat of the color and brightness of the bed1 and deep ocean water is somewhat darker than wooded areas4 ,quiet stagnant pools or small lakes are sometimes exceedingly dark2 in fact1 they appear like pools of ink1 owing to the fact that their brightness as viewed vertically is almost entirely due to surface reflection4 ,if it is due entirely to reflection at the surface1 the brightness will be about #b per cent of the brightness of the zenith sky4 ,that is1 when viewing such a body of water vertically one sees an image of the zenith sky reduced in brightness to about #b per cent4 ,the earth patterns were extensively studied with the result that definite conclusions were formulated pertaining to the best patterns to be used4 ,although it is out of the question to present a detailed discussion of this important phase in this resume1 attention will be called to the manner in which the earth patterns diminish with increasing altitude4 ,the insert in ,fig4 #ajj shows the actual size of an image of a #ej-;foot airplane from #j to #af1jjj feet below the observer as compared with corresponding images 7to the same scale7 of objects and areas on the earth's surface #aj1jjj feet below the observer4 ,for simplicity assume a camera lens to have a focal length equal to #aj inches1 then the length x of the image of an object #ajj feet long will be related to the altitude h in this manner3 x #ajj ----- ----- or xh #ajjj #aj h ,by substituting the values of altitude h in the equation the values of the length x of the image are found4 ,the following values illustrate the change in size of the image with altitude3 ,altitude h in feet ,size of image x in inches #a1jjj #a4jj #b1jjj #j4ej #c1jjj #j4cc #d1jjj #j4be #aj1jjj #j4aj #bj1jjj #j4je ,it is seen that the image diminishes less rapidly in size as the altitude increases4 ,for example1 going from #ajjj feet to #bjjj feet the image is reduced to one-half4 ,the same reduction takes place in ascending from #aj1jjj to #bj1jjj feet4 ,by taking a series of photographs and knowing the reduction-factor of the lens it is a simple matter to study pattern4 ,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 evident4 ,illustration3 ,fig4 #ajj4--;,illustrating the study of pattern for airplanes4 ,the photograph was taken from an altitude of #aj1jjj feet4 ,the insert shows the relative lengths 7vertical scale7 of an airplane of #ej-;foot spread at various distances below the observer4 ,it is impracticable to present colored illustrations in this resume and values expressed in numbers are meaningless to most persons1 so a few general remarks will be made in closing the discussion of low visibility as viewed from above in spring1 summer and fall4 ,a black craft is of much lower visibility than a white one4 ,white should not be used4 ,the paints should be very dark shades4 ,the hues are approximately the same for the earth areas as seen at the earth's surface4 ,inland waters are a dirty blue-green or bluish-green1 and deep ocean water is a greenish-blue when viewed vertically1 or nearly so4 ,mean hues of these were determined approximately4 ,before considering other aspects of camouflage it is well to consider such features as haze1 clouds and sky4 ,there appear to be two kinds of haze which the writer will arbitrarily call earth and high haze1 respectively4 ,the former consists chiefly of dust and smoke and usually extends to an altitude of about one mile1 although it occasionally extends much higher4 ,its upper limit is very distinct1 as seen by the false horizon4 ,this horizon is used more by the pilot when flying at certain altitudes than the true horizon4 ,at the top of this haze cumulus clouds are commonly seen to be poking out like nearly submerged icebergs4 ,the upper haze appears somewhat whiter in color and appears to extend sometimes to altitudes of several or even many miles4 ,the fact that the earth haze may be seen to end usually at about #ejjj to #fjjj feet and the upper haze to persist even beyond #bj1jjj feet has led the author to apply different names for convenience4 ,the upper limit of the earth haze is determined by the height of diurnal atmospheric convection4 ,haze aids in lowering the visibility of airplanes by providing a luminous veil1 but it also operates at some altitudes to increase the brightness of the sky1 which is the background in this case4 ,the sky generally decreases considerably in brightness as the observer ascends4 ,the brightness of the sky is due to scattered light1 that is1 to light being reflected by particles of dust1 smoke1 thinly diffused clouds1 etc4 ,by making a series of measurements of the brightness of the zenith sky for various altitudes1 the altitude where the earth haze ends is usually plainly distinguishable4 ,many observations of this character were accumulated4 ,in some extreme cases the sky was found to be only one-tenth as bright when observed at high altitudes of #ae1jjj to #bj1jjj feet as seen from the earth's surface4 ,this accounts partly for the decrease in the visibility of an airplane as it ascends4 ,at #bj1jjj feet the sky was found to contribute as little as #d 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 clear4 ,doubtless1 it has been commonly noted that airplanes are generally very dark objects as viewed from below against the sky4 ,even when painted white they are usually much darker than the sky4 ,as they ascend the sky above them becomes darker1 although to the observer on the ground the sky remains constant in brightness4 ,however1 in ascending1 the airplane is leaving below it more and more luminous haze which acts as a veil in aiding to screen it until1 when it reaches a high altitude1 the combination of dark sky behind it and luminous haze between it and the observer on the ground1 it becomes of much lower visibility4 ,another factor which contributes somewhat is its diminishing size as viewed from a fixed position at the earth4 ,the minimum perceptible contrast becomes larger as the size of the contrasting patch diminishes4 ,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 ordinarily1 excepting at very high altitudes for very clear skies1 it is necessary1 in order to attain low visibility for airplanes as viewed from below1 to supply some additional illumination to the lower surfaces4 ,computations have shown that artificial lighting is impracticable1 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 sky4 ,on overcast days an airplane will nearly always appear very much darker than the sky4 ,that is1 the brightness of the lower sides can in no other manner be made equal to that of the sky4 ,however1 low visibility can be obtained on sunny days which is an advantage over high visibility at all times1 as is the case with airplanes now in use4 ,many observations and computations of these and other factors have been made1 so that it is possible to predict results4 ,transparent media have obvious advantages1 but no satisfactory ones are available at present4 ,having considered low visibility of aircraft as viewed from above and from below1 respectively1 it is of interest to discuss briefly the possibility of attaining both of these simultaneously with a given airplane4 ,frankly1 it is not practicable to do this4 ,an airplane to be of low visibility against the earth background must be painted or dyed very dark shades of appropriate color and pattern4 ,this renders it almost opaque and it will be a very dark object when viewed against the sky4 ,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 sky1 except at high altitudes4 ,in the latter cases the contrast is not as great as already explained4 ,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 days4 ,on overcast days clouds and haze must be depended upon to screen the craft4 ,in considering these aspects it is well to recall that the two sources of light are the sun and the sky4 ,assuming the sun to contribute #hj 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 brightness1 then the brightness of the horizontal upper surface will equal #e ,,rb1 where ,r is the reflection-factor of the surface and ,b is the brightness 7different in the two cases7 of the sky4 ,on a uniformly overcast day the brightness of the surface would be equal to ,,rb4 ,now assuming ,re to be the mean reflection-factor of the earth1 then the lower side of a horizontal opaque surface suspended in the air would receive light in proportion to ,re,b4 ,if this lower surface were a perfect mirror or a perfectly reflecting and diffusing surface its brightness would equal #e ,re,b on the sunny day and ,re,b on the overcast day where ,b is the value 7different in the two cases7 of the brightness of the uniform sky4 ,the surface can never be a perfect reflector1 so on an overcast day its brightness will be a fraction 7,,rre7 of the brightness ,b of the uniform sky4 ,inasmuch as ,re is a very small value it is seen that low visibility of airplanes as viewed from below generally cannot be attained on an overcast day4 ,it can be approached on a sunny day and even realized by adopting the expedient already mentioned4 ,further computations are to be found elsewhere4#ab ,seasonable changes present no difficulties1 for from a practical standpoint only summer and winter need be generally considered4 ,if the earth is covered with snow an airplane covered completely with white or gray paint would be fairly satisfactory as viewed from above1 and if a certain shade of a blue tint be applied to the lower surfaces1 low visibility as viewed from below would result4 ,the white paint would possess a reflection-factor about equal to that of snow1 thus providing low visibility from above4 ,inasmuch as the reflection-factor of snow is very high1 the white lower sides of an airplane would receive a great deal more light in winter than they would in summer4 ,obviously1 a blue tint is necessary for low visibility against the sky1 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 magnitude4 ,in winter the barren ground would be approximately of the same color and reflection-factor as in summer1 so it would not be difficult to take this into consideration4 ,seaplanes whose backgrounds generally consist of water would be painted of the color and brightness of water with perhaps a slight mottling4 ,the color would generally be a very dark shade1 approximating blue-green in hue4 ,aircraft for night use would be treated in the same manner as aircraft for day use1 if the moonlight is to be considered a dominant factor4 ,this is one of the cases where the judgment must be based on actual experience4 ,it appears that the great enemy of night raiders is the searchlight4 ,if this is true the obvious expedient is to paint the craft a dull jet black4 ,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 searchlight4 ,this can be readily proved by the use of black1 gray1 and white cards in the beam of an automobile head-light4 ,the white card can be seen in the outskirts of the beam where the gray or black cannot be seen1 and the gray can be picked up where the black one is invisible4 ,the science of vision accounts for this as it does for many other questions which arise in the consideration of camouflage or low visibility4 ,some attempts have been made to apply the principle of confusibility to airplanes as finally developed for vessels to circumvent the submarine1 but the folly of this appears to be evident4 ,air battles are conducted at terrific speeds and with skillful maneuvering4 ,triggers are pulled without computations and the whole activity is almost lightning-like4 ,to expect to confuse an opponent as to the course and position of the airplane is folly4 ,the camouflage of observation balloons has not been developed1 though experiments were being considered in this direction as the war closed4 ,inasmuch as they are low-altitude crafts it appears that they would be best camouflaged for the earth as a background4 ,their enemies pounce down upon them from the sky so that low visibility from above seems to be the better choice4 ,in the foregoing it has been aimed to give the reader the general underlying principles of camouflage and low visibility1 but at best this is only a resume4 ,in the following references will be found more extensive discussions of various phases of the subject4 ,,references #a4 ,a ,study of ,zoellner's ,figures and ,other ,related ,figures1 ,j4 ,jastrow1 ,amer4 ,jour4 of ,psych4 #ahia1 #d1 p4 #cha4 #b4 ,a ,study of ,geometrical ,illusions1 ,c4 ,h4 ,judd1 ,psych4 ,rev4 #ahii1 #f1 p4 #bda4 #c4 ,visual ,illusions of ,depth1 ,h4 ,a4 ,carr1 ,psych4 ,rev4 #aiji1 #af1 p4 #bai4 #d4 ,irradiation of ,light1 ,f4 ,p4 ,boswell1 ,psych4 ,bul4 #aije1 #b1 p4 #bjj4 #e4 ,retiring and ,advancing ,colors1 ,m4 ,luckiesh1 ,amer4 ,jour4 ,psych4 #aiah1 #bi1 p4 #ahb4 #f4 ,the ,language of ,color1 #aiah1 ,m4 ,luckiesh4 #g4 ,apparent ,form of the ,dome of the ,sky1 ,ann4 d4 ,physik1 #aiah1 #ee1 p4 #chg2 ,sci4 ,abs4 #aiah1 ,no4 #aadg4 #h4 ,course on ,optics1 #agch1 ,robert ,smith4 #i4 ,color and ,its ,applications1 #aiae and #aiba2 ,light and ,shade and ,their ,applications1 #aiaf1 ,m4 ,luckiesh4 #aj4 ,report of ,the ,submarine ,defense ,association1 ,l4 ,t4 ,bates and ,l4 ,a4 ,jones4 #aa4 ,marine ,camouflage ,design1 ,e4 ,l4 ,warner1 ,trans4 ,i4 ,e4 ,s4 #aiai1 #ad1 p4 #bae4 #ab4 ,the ,visibility of ,airplanes1 ,m4 ,luckiesh1 ,jour4 ,frank4 ,inst4 ,march and ,april1 #aiai2 also ,aerial ,photometry1 ,astrophys4 ,jour4 #aiai1 #di1 p4 #ajh4 #ac4 ,jour4 ,amer4 ,opt4 ,soc41 ,e4 ,karrer1 #aiba4 ,the foregoing are only a few references indicated in the text4 ,hundreds of references are available and obviously it is impracticable to include such a list4 ,the most fruitful sources of references are the general works on psychology4 ,e4 ,b4 ,titchener's ,experimental ,psychology 7vol4 #a7 contains an excellent list4 ,a chapter on ,space in ,william ,james' ,principles of ,psychology 7vol4 ,,ii7 will be found of interest to those who wish to delve deeper into visual perception4 ,other general references are ,elements of ,physiological ,psychology by ,ladd and ,woodworth2 the works of ,helmholtz2 a contribution by ,hering in ,hermann's ,handb4 d4 ,phys4 ,bk4 ,,iii1 part #a2 ,physiological ,psychology by ,wundt2 ,e4 ,b4 ,delabarre1 ,amer4 ,jour4 ,psych4 #ahih1 #i1 p4 #egc2 ,w4 ,wundt1 ,taeuschungen1 p4 #aeg and ,philos4 ,stud4 #ahih1 #ad1 p4 #a2 ,t4 ,lipps1 ,raumaesthetik and ,zeit4 f4 ,psych4 #ahif1 #ab1 #ci4 ,,index ,aberration1 #ai spherical1 #abb chromatic1 #ace ,aerial perspective1 #afe1 #ahc ,after-images1 #bd1 #be1 #ei1 #abh1 #ahf positive and negative1 #abi ,airplanes1 visibility of1 #bcc camouflage for different types1 #bcd size of image at various altitudes1 #bch camouflage for various conditions1 #bdj ,alhazen1 #h ,angles1 influence of1 #gf various effects of1 #ha contours and1 #hg apparent effect on length1 #ia theories1 #ih ,animals1 protective coloration1 #baa ,architecture1 #aie balance in1 #bja ,arcs1 circular1 illusions due to1 #hf ,areas1 juxtaposed1 illusions of1 #if ,artist1 #agi ,attention1 fluctuation of1 #fe1 #ajf1 #ada1 #afd ,aubert1 #di ,auerbach's indirect vision theory1 #ajj ,aureole1 #agh ,balance in architecture1 #bja ,bas-relief1 #adc ,battleships1 #bbb ,binocular disparity1 #aje ,binocular vision1 #bi1 #ca ,blending of colors in camouflage1 #baf ,blind spot1 #ba ,blue light on war-vessels1 #bcj ,boswell1 varieties of irradiation1 #abb ,brightness1 illusions due to variations in1 #ajg and color contrasts1 #aad apparatus1 #aae and hue1 #abe sky1 #bda ,brucke's theory1 #cg ,brunot's mean distance theory1 #aja ,camouflage1 #baj terrestrial1 #baj detection of1 #bae marine1 #bbb airplane1 #bcd ,carr1 observations on distance illusions1 #ajh ,chromatic aberration1 #ai1 #ace ,chlorophyl1 #bad ,circle1 #aa arcs of1 illusion1 #hf contracting and expanding illusion1 #ih ,clouds1 #bce ,color1 #abd after-images1 #abh blending in camouflage1 #baf contrasts and brightness1 #aad growth and decay of sensation1 #aca illusions of1 #aef retiring and advancing1 #ach saturation1 #aed sensibility of retina1 #ach warm and cold1 #aeh ,confusability1 #bbf ,confusion theory of angular illusions1 #ajj ,contour1 illusions of1 #eb and angles1 illusions1 #hg ,contracting and expanding circles1 illusion of1 #ih ,contrasts1 illusions of1 #ec simultaneous1 #abd1 #aed apparatus for1 #aae1 #abe color1 #aad1 #aed1 #ahh brightness1 #aad ,convergence1 illusions of1 #ajh1 #aia ,cord1 twisted1 illusion1 #hh ,daylight1 artificial1 #ahi ,decoration1 painting and1 #agi ,decorator1 #ahh ,dember1 #afg ,depth and distance1 illusions1 #ajb ,direction1 illusions of ,zoellner's1 #gf ,wundt's1 #gi ,hering's1 #hj ,disk1 ,mason1 #acb ,distance and depth1 illusions1 #ajb and size1 #ce1 #ajd1 #aff ,distance illusions1 ,carr's observations1 #ajh ,double images1 #cg ,dynamic theory of angular illusions1 #ii ,enlargement of sun and moon at horizon1 apparent1 #afi ,equivocal figures1 #fd ,euclid1 #h ,extent1 interrupted1 illusions of1 #dh ,external image1 #ae1 #ag1 #cd ,eye1 physiology1 #ac position1 #cj adjustments1 #cc defects1 #ai ,fatigue1 #abh ,field1 visual1 effect of location in1 #dd ,figures1 equivocal1 #fd ,filters1 color1 #bad ,fluctuation of attention1 #fe1 #ajf1 #ada1 #afd ,focusing1 #ad ,form of sky1 apparent1 #aff ,fovea centralis1 #bb1 #bc1 #aci ,frames1 picture1 effect of wood grain1 #aij ,geometrical illusions1 #dd ,glare1 #aai ,grain of wood1 apparent distortions due to1 #aij ,grecian art1 #aif ,growth and decay of color sensation1 #aca ,guttman1 #age ,hallucination1 #d1 #gb ,halo1 #agh ,haze1 illusions1 etc41 #ajc1 #aff1 #ahc earth and high1 #bdj ,helmholtz1 #ac1 #gd ,hering1 #gd illusion of direction1 #hj ,hue and brightness1 #abe ,illusions1 geometrical1 #dd equivocal figures1 #fd influence of angles1 #gf of depth and distance1 #ajb irradiation and brightness contrast1 #aad color1 #abd light and shadows1 #add in nature1 #afd in painting and decoration1 #agi mirror1 #bje camouflage1 #baj ,image after-1 #bd1 #be1 #ei1 #abh1 #abi1 #ahf double1 #cg external1 #ae1 #ag1 #cd retinal1 inversion of1 #af of airplane1 size at various altitudes1 #bch ,indirect vision theory1 ,auerbach's1 #ajj ,intaglio1 #adc ,interrupted extent1 illusions of1 #dh ,iris1 #ae ,irradiation1 #abj and brightness contrast1 #aad varieties of 7,boswell71 #abb in architecture1 #aii ,james1 #agj ,jastrow1 #hj ,jones1 ,l4 ,a41 #bbc ,judd1 #hf1 #ic ,judgment1 #a ,karrer1 #afj ,kepler1 #h ,light1 effect of spectral character1 #ahi ,lighting1 illusions of depth and distance due to1 #ajb contrasts1 #aed diffusion1 effect of1 #ade direction1 effect of1 #add1 #aea ending of searchlight beam1 #afj warm and cold colors1 #aeh ,lipps1 #aj1 #aa dynamic theory of1 #ii ,location in visual field1 effect1 #dd ,mean distance theory1 ,brunot's1 #aja ,mechanical1 esthetic unity1 #aa ,magician1 #c ,magic1 mirror1 #bje ,marine camouflage1 #bbb ,mason disk1 #acb ,mirage1 #c1 #agf ,mirror magic1 #bje ,miscellaneous color effects1 #adj ,moon1 apparent size at horizon1 #h1 #cf1 #afi theories of1 #agc apparent radius of crescent1 #aba ,mueller-,lyer illusion1 #ec1 #ic ,national ,research ,council1 ,committee on ,camouflage1 #bcd ,nature1 #afd ,necker1 #gd ,oppel1 #i ,painting and decoration1 #agi ,painter1 #b1 #agi1 #ahf ,parallax1 #aje ,parthenon of ,athens1 #aif ,persistence of vision1 #aca ,perspective1 #eh in architecture1 #aih aerial #afe1 #ahc theory1 #ih ,photographer1 #aeb ,photography1 use in detection of camouflage1 #bbj ,photometer1 #aef1 #bag ,pigments1 #ahd ,poggendorff illusion1 #he ,protective coloration1 animals1 #baa ,psychology1 #b1 #f1 #aeg of light1 #aic ,purkinje phenomenon1 #bf1 #aci ,reflection-factors1 #bcf ,retina1 #ad1 #bj inertia1 #acj color sensibility1 #ach ,retinal rivalry1 #adj ,retiring and advancing colors1 #acf ,reversal of mirror image1 #bje ,rods and cones1 #ba ,schroeder's staircase1 #gj ,sculpture1 #bjd ,searchlight beam1 ending of1 #afj ,sensation1 color1 growth and decay1 #aca ,sense1 #a ,shading1 counter1 for vessels1 #bbd ,shadows1 importance in camouflage1 #bae ,size and distance1 #ce1 #cf illusions of1 #ajd1 #aff ,sky apparent form of1 #aff brightness1 #bda ,skylight and sunlight1 relative proportions of1 #bae1 #bdc ,smith1 ,robert1 #agc ,smoke-screens1 #bcj ,spectral character of light1 #ahi ,sphere1 illusions1 #ade1 #aej1 #aea ,spherical aberration1 #ai ,sphinx illusion1 #bjf ,spiral illusions1 #ij ,spraying1 paint1 #ahg ,stereoscope1 #ci1 #adb ,stereoscopic vision1 #ch1 #da1 #ada ,submarines1 #bbe camouflage for1 #bcb ,sun1 apparent enlargement at horizon1 #afi ,sunlight and skylight1 relative proportions in nature1 #bae1 #bdc ,terrestrial camouflage1 #baj ,theory of influence of angles1 #ih perspective1 #ih dynamic1 #ii confusion1 #ajj indirect vision1 #ajj mean distance1 #aja ,thiery's figure1 #ga ,thiery's perspective theory1 #ii ,transparencies1 #ahe ,twisted cord illusions1 #hh ,uibe1 #afg ,vertical vs4 horizontal distances1 #aa1 #cf1 #df ,visibility1 low1 for vessels1 #bbb of airplanes1 #bcc ,vision1 #bi persistence of1 #aca stereoscopic1 #ch ,visual perception1 #cb1 #cc ,warm and cold colors1 #aeh ,warner1 ,e4 ,l41 #bbg ,wheatstone1 #cg ,wood grain1 illusions caused by1 #aia ,world ,war1 #bac ,wundt1 #aj1 #aa1 #cb1 #gd illusion of direction1 #gi ,yellow spot1 #aci ,zoellner's illusion1 #fg1 #gf ,zoth1 #age ,,other ,,books ,,by ,m4 ,,luckiesh ,,color ,,and ,,its ,,applications ,second ,edition1 ,revised and ,enlarged4 #f x #i1 #aej illustrations1 #d color plates1 #dca pages4 #d4ej ,the object of this treatise is not only to discuss the many applications of color1 but to establish a sound scientific basis for these applications4 ,the book is authoritative1 well illustrated1 and contains many references and a wealth of new material4 ,it was written by an investigator in the general field of color and is therefore not narrowly limited in scope4 ,it fills a distinct gap that has existed on the book shelves4 ,,light ,,and ,,shade ,,and ,,their ,,applications #f x #i1 #ace illustrations1 #bgg pages #c4jj ,the book is a condensed record of several years' research by the author in the science of light and shade4 ,it is the first published work which deals with the science of light and shade in a complete and analytical manner4 ,the author has the faculty of bringing forth scientific facts in such a manner as to be helpful to those interested in the various arts4 ,the book is of extremely wide interest because it deals with the appearances of objects and hence with vision and with lighting4 ,it is well illustrated and represents the first elaborate attempt to formulate the science of light and shade and to correlate it with various arts4 ,,ultraviolet ,,radiation1 ,its ,properties1 ,production1 ,measurement and ,applications4 #f x #i1 #ab plates1 #bgj pages #c4ej ,it is the primary aim of this book to present authentic data of such scope as to be useful to the chemist1 physicist1 engineer1 biologist1 ophthalmologist and physician and others interested in ultraviolet radiation4 ,theory has been subordinated to experimental facts because the latter are not affected by the inevitable changes in theory4 ,much of the literature on this subject is confusing because of the lack of care in the choice of definitions and of limited value resulting from carelessness in specifying important factors4 ,from this mass of isolated material the author has cooerdinated much valuable data4 ,the many references which are included increase the usefulness of the book4 ,,lighting ,,the ,,home #e x #g-a_/b1 illustrated1 #bhi pages #b4jj ,this is a pioneer book4 ,it ranks with books on interior decoration and furniture as a help toward transforming a house into a home4 ,it is practical in that it offers advice on all sorts of lighting problems and it is fascinating reading as well4 ,,artificial ,,light1 ,,its ,,influence ,,on ,,civilization #f x #i1 illustrated1 #cff pages #c4jj ,this story of the achievements of artificial light is written especially for the man in the street who is not interested in technical scientific terms and formulae1 but who looks with admiration upon the huge signs which flash and sparkle above the crowds on the ,great ,white ,way1 who marvels at the colors and brilliance of a spectacular theatrical production and desires to know how it is accomplished1 and who takes a natural delight in hearing about scientific discoveries when they are explained in the simple1 vivid language he understands best4 ,,the ,,lighting ,,art1 ,,its ,,practice ,,and ,,possibilities #f x #i1 illustrated1 #bbi pages #b4ej ,this book discusses lighting as engineering plus art1 and treats the subject as a branch of interior and exterior decoration4 ,the technical aspect of the subject is not neglected1 but the main emphasis is upon the why and not merely the how of lighting4 ,,the ,,language ,,of ,,color #f x #i1 illustrated1 #bhb pages #b4jj ,a practical volume on color1 the various fields in which it is used and its importance in portraying the ideas that make for progress4 ,a book of special interest to all those who deal in color schemes and values4 ,,the ,,book ,,of ,,the ,,sky #f x #i1 illustrated1 #bcf pages #c4ej ,the beauties1 wonders1 awesome spectacles1 inspiring panoramas1 and extensive ranges of vision which await the aerial traveler1 make of cloudland a veritable fairyland if he will open his consciousness to them4 ,aircraft have brought this new world of experiences within easy reach of mankind and it is one of the aims of this volume to awaken those who fly1 or would fly1 to the variety of interest which air travel affords4 ,the ,literature of ,engineering and the ,industries ,on our shelves is the most complete stock of engineering1 scientific1 technical and industrial books in the ,united ,states4 ,a large number of these we publish and for an ever increasing number we are the sole agents4 ,all inquiries are cheerfully and carefully answered and complete catalogs as well as special lists are sent free on request4 ,d4 ,van ,nostrand ,company ,,publishers ,,and ,,booksellers #h ,,warren ,,street ,,new ,,york ,transcriber's ,notes3 ,passages in italics are indicated by italics4 ,subscripted characters are indicated by subscript4 ,the following misprints have been corrected3 imgaes corrected to images 7page #abh7 bove corrected to above 7page #agg7 verticle corrected to vertical 7page #bci7 colo corrected to color 7,index7 ,other than the corrections listed above1 inconsistencies in spelling and hyphenation have been retained from the original4 ,the inverted #h and ,s characters at the top of page #de cannot be properly represented in this text version4