CONTENTS

CHAPTER PAGE
[I.]Introduction[1]
[II.]The eye[13]
[III.]Vision[29]
[IV.]Some types of geometrical illusions[44]
[V.]Equivocal figures[64]
[VI.]The influence of angles[76]
[VII.]Illusions of depth and of distance[102]
[VIII.]Irradiation and brightness-contrast[114]
[IX.]Color[124]
[X.]Lighting[144]
[XI.]Nature[164]
[XII.]Painting and decoration[179]
[XIII.]Architecture[195]
[XIV.]Mirror Magic[205]
[XV.]Camouflage[210]


LIST OF ILLUSTRATIONS

FIGURE PAGE
[1.]Principal parts of the eye[14]
[2.]Stereoscopic pictures for combining by converging or diverging the optical axes[41]
[3.]Stereoscopic pictures[41]
[4.]The vertical line appears longer than the equal horizontal line in each case[46]
[5.]The vertical dimension is equal to the horizontal one, but the former appears greater[47]
[6.]The divided or filled space on the left appears longer than the equal space on the right[49]
[7.]The three lines are of equal length[50]
[8.]The distance between the two circles on the left is equal to the distance between the outside edges of the two circles on the right[50]
[9.]Three squares of equal dimensions which appear different in area and dimension[51]
[10.]The vertical distance between the upper circle and the left-hand one of the group is equal to the overall length of the group of three circles[52]
[11.]Two equal semi-circles[53]
[12.]Arcs of the same circle[53]
[13.]Three incomplete but equal squares[53]
[14.]Middle sections of the two lines are equal[54]
[15.]An effect of contrasting areas (Baldwin’s figure)[54]
[16.]An illusion of contrast[55]
[17.]Equal circles which appear unequal due to contrast (Ebbinghaus’ figure)[56]
[18.]Equal circles appearing unequal owing to contrasting concentric circles[56]
[19.]Circles influenced by position within an angle[57]
[20.]Contrasting angles[57]
[21.]Owing to perspective the right angles appear oblique and vice versa[58]
[22.]Two equal diagonals which appear unequal[58]
[23.]Apparent variations in the distance between two parallel lines[59]
[24.]A striking illusion of perspective[60]
[25.]Distortion of a square due to superposed lines[61]
[26.]Distortion of a circle due to superposed lines[62]
[27.]Illustrating fluctuation of attention[65]
[28.]The grouping of the circles fluctuates[66]
[29.]Crossed lines which may be interpreted in two ways[67]
[30.]Reversible cubes[68]
[31.]The reversible “open book” (after Mach)[69]
[32.]A reversible tetrahedron[69]
[33.]Reversible perspective of a group of rings or of a tube[70]
[34.]Schröder’s reversible staircase[70]
[35.]Thiéry’s figure[71]
[36.]Illustrating certain influences upon the apparent direction of vision.
By covering all but the eyes the latter appear to be drawn alike in both sketches[73]
[37.]Zöllner’s illusion of direction[77]
[38.]Parallel lines which do not appear so[79]
[39.]Wundt’s illusion of direction[79]
[40.]Hering’s illusion of direction[80]
[41.]Simple effect of angles[81]
[42.]The effect of two angles in tilting the horizontal lines[83]
[43.]The effect of crossed lines upon their respective apparent directions[83]
[44.]Another step toward the Zöllner illusion[84]
[45.]The two diagonals would meet on the left vertical line[85]
[46.]Poggendorff’s illusion. Which oblique line on the right is the prolongation of the oblique line on the left?[85]
[47.]A straight line appears to sag[86]
[48.]Distortions of contour due to contact with other contours[87]
[49.]An illusion of direction[88]
[50.]“Twisted-cord” illusion. These are straight cords[89]
[51.]“Twisted-cord” illusion. These are concentric circles[89]
[52.]A spiral when rotated appears to expand or contract, depending upon direction of rotation[90]
[53.]Angles affect the apparent length of lines[91]
[54.]The horizontal line appears to tilt downward toward the ends[92]
[55.]The horizontal line appears to sag in the middle[92]
[56.]The Müller-Lyer illusion[93]
[57.]Combined influence of angles and contrasting lengths[95]
[58.]Two equal oblique lines appear unequal because of their different positions[95]
[59.]An illusion of area[96]
[60.]Five equal areas showing the influence of contour upon judgment of area[97]
[61.]Showing the effect of directing the attention[98]
[62.]Simple apparatus for demonstrating the remarkable effects of contrasts in brightness and color[115]
[63.]Illustrating brightness-contrast[117]
[64.]An effect of brightness-contrast. Note the darkening of the intersections of the white strips[118]
[65.]The phenomenon of irradiation[121]
[66.]An excellent pattern for demonstrating color-contrast[126]
[67.]By rotating this Mason (black and white) disk color-sensations are produced[133]
[68.]For demonstrating retiring and advancing colors[137]
[69.]By combining these stereoscopically the effect of metallic lustre (similar to graphite in this case) is obtained[141]
[70.]A bas-relief lighted from above[146]
[71.]An intaglio lighted from above[147]
[72.]A bas-relief lighted from the left[148]
[73.]An intaglio lighted from the left[149]
[74a.]A disk (above) and a sphere (below) lighted from overhead[145]
[b.]A disk and a sphere lighted by perfectly diffused light[145]
[75.]A concave hemispherical cup on the left and a convex hemisphere on the right lighted by a light-source of large angle such as a window[150]
[76.]The same as Fig. 75, but lighted by a very small light-source[151]
[77.]Apparent ending of a searchlight beam[161]
[78.]An accurate tracing from a photograph (continual exposure) of the moon rising[171]
[79.]Accurate tracings from a photograph (short exposures at intervals) of the sun setting[172]
[80.]Explanation offered by Smith of the apparent enlargement of heavenly bodies near the horizon[174]
[81.]Explanation of a common mirage[176]
[82.]Illustrating the apparent distortion of a picture frame in which the grain of the wood is visible[190]
[83.]Another example similar to Fig. 82[191]
[84.]From actual photographs of the end-grain of a board[192]
[85.]Exaggerated illusions in architecture[198]
[86.]Illustrating the influence of visual angle upon apparent vertical height[199]
[87.]Irradiation in architecture[200]
[88.]Some simple geometrical-optical illusions in architecture[201]
[89.]By decreasing the exposed length of shingles toward the top a greater apparent expanse is obtained[202]
[90.]An example of a mirror “illusion”[207]
[91.]Another example of “mirror magic”[208]
[92.]A primary stage in the evolution of the use of geometrical-optical illusions on ships[226]
[93] and [94.]Attempts at distortion of outline which preceded the adoption of geometrical-optical illusions[228]
[95] and [96.]Illustrating the use of models by the Navy Department in developing the geometrical-optical illusion for ships[229]
[97] and [98.]Examples of the geometrical-optical illusion as finally applied[231]
[99.]Representative earth backgrounds for an airplane (uncamouflaged) as viewed from above[235]
[100.]Illustrating the study of pattern for airplanes. The photograph was taken from an altitude of 10,000 feet. The insert shows the relative lengths (vertical scale) of an airplane of 50-foot spread at various distances below the observer[239]

VISUAL ILLUSIONS