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+
+The Project Gutenberg EBook of Visual Illusions, by Matthew Luckiesh
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: Visual Illusions
+       Their Causes, Characteristics and Applications
+
+Author: Matthew Luckiesh
+
+Release Date: June 1, 2011 [EBook #36297]
+
+Language: English
+
+Character set encoding: ISO-8859-1
+
+*** START OF THIS PROJECT GUTENBERG EBOOK VISUAL ILLUSIONS ***
+
+
+
+
+Produced by Bryan Ness and the Online Distributed
+Proofreading Team at http://www.pgdp.net (This file was
+produced from images generously made available by The
+Internet Archive.)
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+</pre>
+
+
+
+
+<p class="center"><span class="giant">VISUAL ILLUSIONS</span></p>
+<p class="center"><span class="large"><i>THEIR CAUSES, CHARACTERISTICS</i></span><br />
+<span class="large"><i>AND APPLICATIONS</i></span></p>
+<p>&nbsp;</p>
+<p class="center"><small>BY</small><br />
+<span class="large">M. LUCKIESH</span></p>
+<p class="center"><small>DIRECTOR OF APPLIED SCIENCE, NELA RESEARCH LABORATORIES,<br />
+NATIONAL LAMP WORKS OF GENERAL ELECTRIC CO.</small></p>
+<p class="center"><small>AUTHOR OF &#8220;COLOR AND ITS APPLICATIONS,&#8221; &#8220;LIGHT AND SHADE<br />
+AND THEIR APPLICATIONS,&#8221; &#8220;THE LIGHTING ART,&#8221; &#8220;THE<br />
+LANGUAGE OF COLOR,&#8221; &#8220;ARTIFICIAL LIGHT&mdash;ITS<br />
+INFLUENCE UPON CIVILIZATION,&#8221;<br />
+&#8220;LIGHTING THE HOME,&#8221; ETC.</small></p>
+<p>&nbsp;</p>
+<p class="center"><strong>100 ILLUSTRATIONS</strong></p>
+<p>&nbsp;</p>
+<div class="figcenter"><img src="images/printer.jpg" alt="" /></div>
+<p>&nbsp;</p>
+<p class="center">NEW YORK<br />
+D. VAN NOSTRAND COMPANY<br />
+EIGHT WARREN STREET<br />
+1922</p>
+
+<p>&nbsp;</p><p>&nbsp;</p>
+<p class="center"><span class="smcap">Copyright, 1922, by</span><br />
+D. VAN NOSTRAND COMPANY</p>
+
+
+<p>&nbsp;</p><p>&nbsp;</p>
+<hr style="width: 50%;" />
+<p><span class="pagenum"><a name="Page_iii" id="Page_iii">[Pg iii]</a></span></p>
+<h2>PREFACE</h2>
+
+<p class="dropcap"><span class="caps">Eventually</span> one of the results of application to the analysis and
+measurement of the phenomena of light, color, lighting, and vision is a
+firmly entrenched conviction of the inadequacy of physical measurements as
+a means for representing what is perceived. Physical measurements have
+supplied much of the foundation of knowledge and it is not a reflection
+upon their great usefulness to state that often they differ from the
+results of intellectual appraisal through the visual sense. In other
+words, there are numberless so-called visual illusions which must be taken
+into account. All are of interest; many can be utilized; and some must be
+suppressed.</p>
+
+<p>Scientific literature yields a great many valuable discussions from
+theoretical and experimental viewpoints but much of the material is
+controversial. The practical aspects of visual illusions have been quite
+generally passed by and, inasmuch as there does not appear to be a volume
+available which treats the subject in a condensed manner but with a broad
+scope, this small volume is contributed toward filling the gap.</p>
+
+<p>The extreme complexity of the subject is recognized, but an attempt toward
+simplicity of treatment has been made by confining the discussion chiefly
+to static visual illusions, by suppressing minor details, and by<span class="pagenum"><a name="Page_iv" id="Page_iv">[Pg iv]</a></span>
+subordinating theory. In other words, the intent has been to emphasize
+experimental facts. Even these are so numerous that only the merest
+glimpses of various aspects can be given in order to limit the text to a
+small volume. Some theoretical aspects of the subject are still extremely
+controversial, so they are introduced only occasionally and then chiefly
+for the purpose of illustrating the complexities and the trends of
+attempted explanations. Space does not even admit many qualifications
+which may be necessary in order to escape criticism entirely.</p>
+
+<p>The visual illusions discussed are chiefly of the static type, although a
+few others have been introduced. Some of the latter border upon motion,
+others upon hallucinations, and still others produced by external optical
+media are illusions only by extension of the term. These exceptions are
+included for the purpose of providing glimpses into the borderlands.</p>
+
+<p>It is hoped that this condensed discussion, which is ambitious only in
+scope, will be of interest to the general reader, to painters, decorators,
+and architects, to lighting experts, and to all interested in light,
+color, and vision. It is an essential supplement to certain previous
+works.</p>
+
+<p><span style="margin-left: 2em;">M. LUCKIESH</span><br />
+<span style="margin-left: 4em;">November, 1920.</span></p>
+
+
+<p>&nbsp;</p><p>&nbsp;</p>
+<hr style="width: 50%;" />
+<p><span class="pagenum"><a name="Page_v" id="Page_v">[Pg v]</a></span></p>
+<h2>CONTENTS</h2>
+
+<table border="0" cellpadding="0" cellspacing="5" summary="table">
+<tr><td><small>CHAPTER</small></td><td>&nbsp;</td><td align="right"><small>PAGE</small></td></tr>
+<tr><td align="right"><a href="#I">I.</a></td><td>Introduction</td><td align="right"><a href="#Page_1">1</a></td></tr>
+<tr><td align="right"><a href="#II">II.</a></td><td>The eye</td><td align="right"><a href="#Page_13">13</a></td></tr>
+<tr><td align="right"><a href="#III">III.</a></td><td>Vision</td><td align="right"><a href="#Page_29">29</a></td></tr>
+<tr><td align="right"><a href="#IV">IV.</a></td><td>Some types of geometrical illusions</td><td align="right"><a href="#Page_44">44</a></td></tr>
+<tr><td align="right"><a href="#V">V.</a></td><td>Equivocal figures</td><td align="right"><a href="#Page_64">64</a></td></tr>
+<tr><td align="right"><a href="#VI">VI.</a></td><td>The influence of angles</td><td align="right"><a href="#Page_76">76</a></td></tr>
+<tr><td align="right"><a href="#VII">VII.</a></td><td>Illusions of depth and of distance</td><td align="right"><a href="#Page_102">102</a></td></tr>
+<tr><td align="right"><a href="#VIII">VIII.</a></td><td>Irradiation and brightness-contrast</td><td align="right"><a href="#Page_114">114</a></td></tr>
+<tr><td align="right"><a href="#IX">IX.</a></td><td>Color</td><td align="right"><a href="#Page_124">124</a></td></tr>
+<tr><td align="right"><a href="#X">X.</a></td><td>Lighting</td><td align="right"><a href="#Page_144">144</a></td></tr>
+<tr><td align="right"><a href="#XI">XI.</a></td><td>Nature</td><td align="right"><a href="#Page_164">164</a></td></tr>
+<tr><td align="right"><a href="#XII">XII.</a></td><td>Painting and decoration</td><td align="right"><a href="#Page_179">179</a></td></tr>
+<tr><td align="right"><a href="#XIII">XIII.</a></td><td>Architecture</td><td align="right"><a href="#Page_195">195</a></td></tr>
+<tr><td align="right"><a href="#XIV">XIV.</a></td><td>Mirror Magic</td><td align="right"><a href="#Page_205">205</a></td></tr>
+<tr><td align="right"><a href="#XV">XV.</a></td><td>Camouflage</td><td align="right"><a href="#Page_210">210</a></td></tr></table>
+<p><span class="pagenum"><a name="Page_vi" id="Page_vi">[Pg vi]</a></span></p>
+
+
+<p>&nbsp;</p><p>&nbsp;</p>
+<hr style="width: 50%;" />
+<p><span class="pagenum"><a name="Page_vii" id="Page_vii">[Pg vii]</a></span></p>
+<h2>LIST OF ILLUSTRATIONS</h2>
+
+<table width="65%" border="0" cellpadding="0" cellspacing="5" summary="table">
+<tr><td><small>FIGURE</small></td><td>&nbsp;</td><td align="right"><small>PAGE</small></td></tr>
+<tr><td align="right" valign="top"><a href="#fig1">1.</a></td>
+    <td>Principal parts of the eye</td>
+    <td align="right" valign="bottom"><a href="#Page_14">14</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig2">2.</a></td>
+    <td>Stereoscopic pictures for combining by converging or diverging the optical axes</td>
+    <td align="right" valign="bottom"><a href="#Page_41">41</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig3">3.</a></td>
+    <td>Stereoscopic pictures</td>
+    <td align="right" valign="bottom"><a href="#Page_41">41</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig4">4.</a></td>
+    <td>The vertical line appears longer than the equal horizontal line in each case</td>
+    <td align="right" valign="bottom"><a href="#Page_46">46</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig5">5.</a></td>
+    <td>The vertical dimension is equal to the horizontal one, but the former appears greater</td>
+    <td align="right" valign="bottom"><a href="#Page_47">47</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig6">6.</a></td>
+    <td>The divided or filled space on the left appears longer than the equal space on the right</td>
+    <td align="right" valign="bottom"><a href="#Page_49">49</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig7">7.</a></td>
+    <td>The three lines are of equal length</td>
+    <td align="right" valign="bottom"><a href="#Page_50">50</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig8">8.</a></td>
+    <td>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</td>
+    <td align="right" valign="bottom"><a href="#Page_50">50</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig9">9.</a></td>
+    <td>Three squares of equal dimensions which appear different in area and dimension</td>
+    <td align="right" valign="bottom"><a href="#Page_51">51</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig10">10.</a></td>
+    <td>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</td>
+    <td align="right" valign="bottom"><a href="#Page_52">52</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig11">11.</a></td>
+    <td>Two equal semi-circles</td>
+    <td align="right" valign="bottom"><a href="#Page_53">53</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig12">12.</a></td>
+    <td>Arcs of the same circle</td>
+    <td align="right" valign="bottom"><a href="#Page_53">53</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig13">13.</a></td>
+    <td>Three incomplete but equal squares</td>
+    <td align="right" valign="bottom"><a href="#Page_53">53</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig14">14.</a></td>
+    <td>Middle sections of the two lines are equal</td>
+    <td align="right" valign="bottom"><a href="#Page_54">54</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig15">15.</a></td>
+    <td>An effect of contrasting areas (Baldwin&#8217;s figure)</td>
+    <td align="right" valign="bottom"><a href="#Page_54">54</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig16">16.</a></td>
+    <td>An illusion of contrast</td>
+    <td align="right" valign="bottom"><a href="#Page_55">55</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig17">17.</a></td>
+    <td>Equal circles which appear unequal due to contrast (Ebbinghaus&#8217; figure)</td>
+    <td align="right" valign="bottom"><a href="#Page_56">56</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig18">18.</a></td>
+    <td>Equal circles appearing unequal owing to contrasting concentric circles</td>
+    <td align="right" valign="bottom"><a href="#Page_56">56</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig19">19.</a></td>
+    <td>Circles influenced by position within an angle</td>
+    <td align="right" valign="bottom"><a href="#Page_57">57</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig20">20.</a></td>
+    <td>Contrasting angles</td>
+    <td align="right" valign="bottom"><a href="#Page_57">57</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig21">21.</a></td>
+    <td>Owing to perspective the right angles appear oblique and vice versa</td>
+    <td align="right" valign="bottom"><a href="#Page_58">58</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig22">22.</a></td>
+    <td>Two equal diagonals which appear unequal</td>
+    <td align="right" valign="bottom"><a href="#Page_58">58</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig23">23.</a></td>
+    <td>Apparent variations in the distance between two parallel lines</td>
+    <td align="right" valign="bottom"><a href="#Page_59">59</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig24">24.</a></td>
+    <td>A striking illusion of perspective</td>
+    <td align="right" valign="bottom"><a href="#Page_60">60</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig25">25.</a></td>
+    <td>Distortion of a square due to superposed lines</td>
+    <td align="right" valign="bottom"><a href="#Page_61">61</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig26">26.</a></td>
+    <td>Distortion of a circle due to superposed lines</td>
+    <td align="right" valign="bottom"><a href="#Page_62">62</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig27">27.</a></td>
+    <td>Illustrating fluctuation of attention</td>
+    <td align="right" valign="bottom"><a href="#Page_65">65</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig28">28.</a></td>
+    <td>The grouping of the circles fluctuates</td>
+    <td align="right" valign="bottom"><a href="#Page_66">66</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig29">29.</a></td>
+    <td>Crossed lines which may be interpreted in two ways</td>
+    <td align="right" valign="bottom"><a href="#Page_67">67</a></td></tr>
+<tr><td align="right" valign="top"><span class="pagenum"><a name="Page_viii" id="Page_viii">[Pg viii]</a></span><a href="#fig30">30.</a></td>
+    <td>Reversible cubes</td>
+    <td align="right" valign="bottom"><a href="#Page_68">68</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig31">31.</a></td>
+    <td>The reversible &#8220;open book&#8221; (after Mach)</td>
+    <td align="right" valign="bottom"><a href="#Page_69">69</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig32">32.</a></td>
+    <td>A reversible tetrahedron</td>
+    <td align="right" valign="bottom"><a href="#Page_69">69</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig33">33.</a></td>
+    <td>Reversible perspective of a group of rings or of a tube</td>
+    <td align="right" valign="bottom"><a href="#Page_70">70</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig34">34.</a></td>
+    <td>Schr&ouml;der&#8217;s reversible staircase</td>
+    <td align="right" valign="bottom"><a href="#Page_70">70</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig35">35.</a></td>
+    <td>Thi&eacute;ry&#8217;s figure</td>
+    <td align="right" valign="bottom"><a href="#Page_71">71</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig36">36.</a></td>
+    <td>Illustrating certain influences upon the apparent direction of vision.</td></tr>
+<tr><td>&nbsp;</td><td>By covering all but the eyes the latter appear to be drawn alike in both sketches</td>
+    <td align="right" valign="bottom"><a href="#Page_73">73</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig37">37.</a></td>
+    <td>Z&ouml;llner&#8217;s illusion of direction</td>
+    <td align="right" valign="bottom"><a href="#Page_77">77</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig38">38.</a></td>
+    <td>Parallel lines which do not appear so</td>
+    <td align="right" valign="bottom"><a href="#Page_79">79</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig39">39.</a></td>
+    <td>Wundt&#8217;s illusion of direction</td>
+    <td align="right" valign="bottom"><a href="#Page_79">79</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig40">40.</a></td>
+    <td>Hering&#8217;s illusion of direction</td>
+    <td align="right" valign="bottom"><a href="#Page_80">80</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig41">41.</a></td>
+    <td>Simple effect of angles</td>
+    <td align="right" valign="bottom"><a href="#Page_81">81</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig42">42.</a></td>
+    <td>The effect of two angles in tilting the horizontal lines</td>
+    <td align="right" valign="bottom"><a href="#Page_83">83</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig43">43.</a></td>
+    <td>The effect of crossed lines upon their respective apparent directions</td>
+    <td align="right" valign="bottom"><a href="#Page_83">83</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig44">44.</a></td>
+    <td>Another step toward the Z&ouml;llner illusion</td>
+    <td align="right" valign="bottom"><a href="#Page_84">84</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig45">45.</a></td>
+    <td>The two diagonals would meet on the left vertical line</td>
+    <td align="right" valign="bottom"><a href="#Page_85">85</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig46">46.</a></td>
+    <td>Poggendorff&#8217;s illusion. Which oblique line on the right is the prolongation of the oblique line on the left?</td>
+    <td align="right" valign="bottom"><a href="#Page_85">85</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig47">47.</a></td>
+    <td>A straight line appears to sag</td>
+    <td align="right" valign="bottom"><a href="#Page_86">86</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig48">48.</a></td>
+    <td>Distortions of contour due to contact with other contours</td>
+    <td align="right" valign="bottom"><a href="#Page_87">87</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig49">49.</a></td>
+    <td>An illusion of direction</td>
+    <td align="right" valign="bottom"><a href="#Page_88">88</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig50">50.</a></td>
+    <td>&#8220;Twisted-cord&#8221; illusion. These are straight cords</td>
+    <td align="right" valign="bottom"><a href="#Page_89">89</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig51">51.</a></td>
+    <td>&#8220;Twisted-cord&#8221; illusion. These are concentric circles</td>
+    <td align="right" valign="bottom"><a href="#Page_89">89</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig52">52.</a></td>
+    <td>A spiral when rotated appears to expand or contract, depending upon direction of rotation</td>
+    <td align="right" valign="bottom"><a href="#Page_90">90</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig53">53.</a></td>
+    <td>Angles affect the apparent length of lines</td>
+    <td align="right" valign="bottom"><a href="#Page_91">91</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig54">54.</a></td>
+    <td>The horizontal line appears to tilt downward toward the ends</td>
+    <td align="right" valign="bottom"><a href="#Page_92">92</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig55">55.</a></td>
+    <td>The horizontal line appears to sag in the middle</td>
+    <td align="right" valign="bottom"><a href="#Page_92">92</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig56">56.</a></td>
+    <td>The M&uuml;ller-Lyer illusion</td>
+    <td align="right" valign="bottom"><a href="#Page_93">93</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig57">57.</a></td>
+    <td>Combined influence of angles and contrasting lengths</td>
+    <td align="right" valign="bottom"><a href="#Page_95">95</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig58">58.</a></td>
+    <td>Two equal oblique lines appear unequal because of their different positions</td>
+    <td align="right" valign="bottom"><a href="#Page_95">95</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig59">59.</a></td>
+    <td>An illusion of area</td>
+    <td align="right" valign="bottom"><a href="#Page_96">96</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig60">60.</a></td>
+    <td>Five equal areas showing the influence of contour upon judgment of area</td>
+    <td align="right" valign="bottom"><a href="#Page_97">97</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig61">61.</a></td>
+    <td>Showing the effect of directing the attention</td>
+    <td align="right" valign="bottom"><a href="#Page_98">98</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig62">62.</a></td>
+    <td>Simple apparatus for demonstrating the remarkable effects of contrasts in brightness and color</td>
+    <td align="right" valign="bottom"><a href="#Page_115">115</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig63">63.</a></td>
+    <td>Illustrating brightness-contrast</td>
+    <td align="right" valign="bottom"><a href="#Page_117">117</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig64">64.</a></td>
+    <td>An effect of brightness-contrast. Note the darkening of the intersections of the white strips</td>
+    <td align="right" valign="bottom"><a href="#Page_118">118</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig65">65.</a></td>
+    <td>The phenomenon of irradiation</td>
+    <td align="right" valign="bottom"><a href="#Page_121">121</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig66">66.</a></td>
+    <td>An excellent pattern for demonstrating color-contrast</td>
+    <td align="right" valign="bottom"><a href="#Page_126">126</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig67">67.</a></td>
+    <td>By rotating this Mason (black and white) disk color-sensations are produced</td>
+    <td align="right" valign="bottom"><a href="#Page_133">133</a></td></tr>
+<tr><td align="right" valign="top"><span class="pagenum"><a name="Page_ix" id="Page_ix">[Pg ix]</a></span><a href="#fig68">68.</a></td>
+    <td>For demonstrating retiring and advancing colors</td>
+    <td align="right" valign="bottom"><a href="#Page_137">137</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig69">69.</a></td>
+    <td>By combining these stereoscopically the effect of metallic lustre (similar to graphite in this case) is obtained</td>
+    <td align="right" valign="bottom"><a href="#Page_141">141</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig70">70.</a></td>
+    <td>A bas-relief lighted from above</td>
+    <td align="right" valign="bottom"><a href="#Page_146">146</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig71">71.</a></td>
+    <td>An intaglio lighted from above</td>
+    <td align="right" valign="bottom"><a href="#Page_147">147</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig72">72.</a></td>
+    <td>A bas-relief lighted from the left</td>
+    <td align="right" valign="bottom"><a href="#Page_148">148</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig73">73.</a></td>
+    <td>An intaglio lighted from the left</td>
+    <td align="right" valign="bottom"><a href="#Page_149">149</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig74">74a.</a></td>
+    <td>A disk (above) and a sphere (below) lighted from overhead</td>
+    <td align="right" valign="bottom"><a href="#Page_145">145</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig74">b.</a></td>
+    <td>A disk and a sphere lighted by perfectly diffused light</td>
+    <td align="right" valign="bottom"><a href="#Page_145">145</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig75">75.</a></td>
+    <td>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</td>
+    <td align="right" valign="bottom"><a href="#Page_150">150</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig76">76.</a></td>
+    <td>The same as Fig. 75, but lighted by a very small light-source</td>
+    <td align="right" valign="bottom"><a href="#Page_151">151</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig77">77.</a></td>
+    <td>Apparent ending of a searchlight beam</td>
+    <td align="right" valign="bottom"><a href="#Page_161">161</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig78">78.</a></td>
+    <td>An accurate tracing from a photograph (continual exposure) of the moon rising</td>
+    <td align="right" valign="bottom"><a href="#Page_171">171</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig79">79.</a></td>
+    <td>Accurate tracings from a photograph (short exposures at intervals) of the sun setting</td>
+    <td align="right" valign="bottom"><a href="#Page_172">172</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig80">80.</a></td>
+    <td>Explanation offered by Smith of the apparent enlargement of heavenly bodies near the horizon</td>
+    <td align="right" valign="bottom"><a href="#Page_174">174</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig81">81.</a></td>
+    <td>Explanation of a common mirage</td>
+    <td align="right" valign="bottom"><a href="#Page_176">176</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig82">82.</a></td>
+    <td>Illustrating the apparent distortion of a picture frame in which the grain of the wood is visible</td>
+    <td align="right" valign="bottom"><a href="#Page_190">190</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig83">83.</a></td>
+    <td>Another example similar to Fig. 82</td>
+    <td align="right" valign="bottom"><a href="#Page_191">191</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig84">84.</a></td>
+    <td>From actual photographs of the end-grain of a board</td>
+    <td align="right" valign="bottom"><a href="#Page_192">192</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig85">85.</a></td>
+    <td>Exaggerated illusions in architecture</td>
+    <td align="right" valign="bottom"><a href="#Page_198">198</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig86">86.</a></td>
+    <td>Illustrating the influence of visual angle upon apparent vertical height</td>
+    <td align="right" valign="bottom"><a href="#Page_199">199</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig87">87.</a></td>
+    <td>Irradiation in architecture</td>
+    <td align="right" valign="bottom"><a href="#Page_200">200</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig88">88.</a></td>
+    <td>Some simple geometrical-optical illusions in architecture</td>
+    <td align="right" valign="bottom"><a href="#Page_201">201</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig89">89.</a></td>
+    <td>By decreasing the exposed length of shingles toward the top a greater apparent expanse is obtained</td>
+    <td align="right" valign="bottom"><a href="#Page_202">202</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig90">90.</a></td>
+    <td>An example of a mirror &#8220;illusion&#8221;</td>
+    <td align="right" valign="bottom"><a href="#Page_207">207</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig91">91.</a></td>
+    <td>Another example of &#8220;mirror magic&#8221;</td>
+    <td align="right" valign="bottom"><a href="#Page_208">208</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig92">92.</a></td>
+    <td>A primary stage in the evolution of the use of geometrical-optical illusions on ships</td>
+    <td align="right" valign="bottom"><a href="#Page_226">226</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig93">93</a>&nbsp;and&nbsp;<a href="#fig94">94.</a></td>
+    <td>Attempts at distortion of outline which preceded the adoption of geometrical-optical illusions</td>
+    <td align="right" valign="bottom"><a href="#Page_228">228</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig95">95</a>&nbsp;and&nbsp;<a href="#fig96">96.</a></td>
+    <td>Illustrating the use of models by the Navy Department in developing the geometrical-optical illusion for ships</td>
+    <td align="right" valign="bottom"><a href="#Page_229">229</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig97">97</a>&nbsp;and&nbsp;<a href="#fig98">98.</a></td>
+    <td>Examples of the geometrical-optical illusion as finally applied</td>
+    <td align="right" valign="bottom"><a href="#Page_231">231</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig99">99.</a></td>
+    <td>Representative earth backgrounds for an airplane (uncamouflaged) as viewed from above</td>
+    <td align="right" valign="bottom"><a href="#Page_235">235</a></td></tr>
+<tr><td align="right" valign="top"><a href="#fig100">100.</a></td>
+    <td>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</td>
+    <td align="right" valign="bottom"><a href="#Page_239">239</a></td></tr></table>
+
+
+
+<p>&nbsp;</p><p>&nbsp;</p>
+<hr style="width: 50%;" />
+<p><span class="pagenum"><a name="Page_1" id="Page_1">[Pg 1]</a></span></p>
+<p class="center"><span class="giant">VISUAL ILLUSIONS</span></p>
+<h2><a name="I" id="I"></a>I<br />INTRODUCTION</h2>
+
+<p class="dropcap"><span class="caps">Seeing</span> is deceiving. Thus a familiar epigram may be challenged in order to
+indicate the trend of this book which aims to treat certain phases of
+visual illusions. In general, we do not see things as they are or as they
+are related to each other; that is, the intellect does not correctly
+interpret the deliverances of the visual sense, although sometimes the
+optical mechanism of the eyes is directly responsible for the illusion. In
+other words, none of our conceptions and perceptions are quite adequate,
+but fortunately most of them are satisfactory for practical purposes. Only
+a part of what is perceived comes through the senses from the object; the
+remainder always comes from within. In fact, it is the visual sense or the
+intellect which is responsible for illusions of the various types to be
+discussed in the following chapters. Our past experiences, associations,
+desires, demands, imaginings, and other more or less obscure influences
+create illusions.</p>
+
+<p>An illusion does not generally exist physically but it is difficult in
+some cases to explain the cause. Certainly there are many cases of errors
+of judgment. A mistaken estimate of the distance of a mountain<span class="pagenum"><a name="Page_2" id="Page_2">[Pg 2]</a></span> is due to
+an error of judgment but the perception of a piece of white paper as pink
+on a green background is an error of sense. It is realized that the
+foregoing comparison leads directly to one of the most controversial
+questions in psychology, but there is no intention on the author&#8217;s part to
+cling dogmatically to the opinions expressed. In fact, discussions of the
+psychological judgment involved in the presentations of the visual sense
+are not introduced with the hope of stating the final word but to give the
+reader an idea of the inner process of perception. The final word will be
+left to the psychologists but it appears possible that it may never be
+formulated.</p>
+
+<p>In general, a tree appears of greater length when standing than when lying
+upon the ground. Lines, areas, and masses are not perceived in their
+actual physical relations. The appearance of a colored object varies
+considerably with its environment. The sky is not perceived as infinite
+space nor as a hemispherical dome, but as a flattened vault. The moon
+apparently diminishes in size as it rises toward the zenith. A bright
+object appears larger than a dark object of the same physical dimensions.
+Flat areas may appear to have a third dimension of depth. And so on.</p>
+
+<p>Illusions are so numerous and varied that they have long challenged the
+interest of the scientist. They may be so useful or even so disastrous
+that they have been utilized or counteracted by the skilled artist or
+artisan. The architect and painter have used or avoided them. The
+stage-artist employs them to carry the audience in its imagination to
+other<span class="pagenum"><a name="Page_3" id="Page_3">[Pg 3]</a></span> environments or to far countries. The magician has employed them in
+his entertainments and the camoufleur used them to advantage in the
+practice of deception during the recent war. They are vastly entertaining,
+useful, deceiving, or disastrous, depending upon the viewpoint.</p>
+
+<p>Incidentally, a few so-called illusions will be discussed which are not
+due strictly to errors of the visual sense or of the intellect. Examples
+of these are the mirage and certain optical effects employed by the
+magician. In such cases neither the visual sense nor the intellect errs.
+In the case of the mirage rays of light coming from the object to the eye
+are bent from their usual straight-line course and the object appears to
+be where it really is not. However, with these few exceptions, which are
+introduced for their specific interest and for the emphasis they give to
+the &#8220;true&#8221; illusion, it will be understood that illusions in general as
+hereinafter discussed will mean those due to the visual mechanism or to
+errors of judgment or intellect. For the sake of brevity we might say that
+they are those due to errors of visual perception. Furthermore, only those
+of a &#8220;static&#8221; type will be considered; that is, the vast complexities due
+to motion are not of interest from the viewpoint of the aims of this book.</p>
+
+<p>There are two well-known types of misleading perceptions, namely illusions
+and hallucinations. If, for example, two lines appear of equal length and
+are not, the error in judgment is responsible for what is termed an
+&#8220;illusion.&#8221; If the perceptual consciousness of an object appears although
+the object is not present, the<span class="pagenum"><a name="Page_4" id="Page_4">[Pg 4]</a></span> result is termed an &#8220;hallucination.&#8221; For
+example, if something is seen which does not exist, the essential factors
+are supplied by the imagination. Shadows are often wrought by the
+imagination into animals and even human beings bent upon evil purpose.
+Ghosts are created in this manner. Hallucinations depend largely upon the
+recency, frequency, and vividness of past experience. A consideration of
+this type of misleading perception does not advance the aims of this book
+and therefore will be omitted.</p>
+
+<p>The connection between the material and mental in vision is
+incomprehensible and apparently must ever remain so. Objects emit or
+reflect light and the optical mechanism known as the eye focuses images of
+the objects upon the retina. Messages are then carried to the brain where
+certain molecular vibrations take place. The physiologist records certain
+physical and chemical effects in the muscles, nerves, and brain and
+behold! there appears consciousness, sensations, thoughts, desires, and
+volitions. How? and, Why? are questions which may never be answered.</p>
+
+<p>It is dangerous to use the word <i>never</i>, but the ultimate answers to those
+questions appear to be so remote that it discourages one from proceeding
+far over the hazy course which leads toward them. In fact, it does not
+appreciably further the aims of this book to devote much space to efforts
+toward explanation. In covering this vast and complex field there are
+multitudes of facts, many hypotheses, and numerous theories from which to
+choose. Judgment dictates that of the limited space most of it be given
+to<span class="pagenum"><a name="Page_5" id="Page_5">[Pg 5]</a></span> the presentation of representative facts. This is the reasoning which
+led to the formulation of the outline of chapters.</p>
+
+<p>Owing to the vast complex beyond the physical phenomena, physical
+measurements upon objects and space which have done so much toward
+building a solid foundation for scientific knowledge fail ultimately to
+provide an exact mathematical picture of that which is perceived. Much of
+the author&#8217;s previous work has been devoted to the physical realities but
+the ever-present differences between physical and perceptive realities
+have emphasized the need for considering the latter as well.</p>
+
+<p>Illusions are legion. They greet the careful observer on every hand. They
+play a prominent part in our appreciation of the physical world. Sometimes
+they must be avoided, but often they may be put to work in various arts.
+Their widespread existence and their forcefulness make visual perception
+the final judge in decoration, in painting, in architecture, in
+landscaping, in lighting, and in other activities. The ultimate limitation
+of measurements with physical instruments leaves this responsibility to
+the intellect. The mental being is impressed with things as perceived, not
+with things as they are. It is believed that this intellectual or
+judiciary phase which plays such a part in visual perception will be best
+brought out by examples of various types of static illusions coupled with
+certain facts pertaining to the eye and to the visual process as a whole.</p>
+
+<p>In special simple cases it is not difficult to determine when or how
+nearly a perception is true but in<span class="pagenum"><a name="Page_6" id="Page_6">[Pg 6]</a></span> general, agreement among normal
+persons is necessary owing to the absence of any definite measuring device
+which will span the gap between the perception and the objective reality.
+Illusions are sometimes called &#8220;errors of sense&#8221; and some of them are
+such, but often they are errors of the intellect. The senses may deliver
+correctly but error may arise from imagination, inexperience, false
+assumptions, and incorrect associations, and the recency, frequency, and
+vividness of past experience. The gifts of sight are augmented by the mind
+with judgments based upon experience with these gifts.</p>
+
+<p>The direct data delivered by the visual sense are light, intensity, color,
+direction. These may be considered as simple or elemental sensations
+because they cannot be further simplified or analyzed. At this point it is
+hoped that no controversy with the psychologist will be provoked. In the
+space available it appears unfruitful to introduce the many qualifications
+necessary to satisfy the, as yet uncertain or at least conflicting,
+definitions and theories underlying the science of psychology. If it is
+necessary to add darkness to the foregoing group of elemental visual
+sensations, this will gladly be agreed to.</p>
+
+<p>The perceptions of outline-form and surface-contents perhaps rank next in
+simplicity; however, they may be analyzed into directions. The perception
+of these is so direct and so certain that it may be considered to be
+immediate. A ring of points is apparently very simple and it might be
+considered a direct sense-perception, but it consists of a number of
+elemental directions.</p>
+
+<p><span class="pagenum"><a name="Page_7" id="Page_7">[Pg 7]</a></span>The perception of solid-form is far more complex than outline-form and
+therefore more liable to error. It is judged partially by binocular vision
+or perspective and partly by the distribution of light and shade. Colors
+may help to mold form and even to give depth to flat surfaces. For
+example, it is well known that some colors are &#8220;advancing&#8221; and others are
+&#8220;retiring.&#8221;</p>
+
+<p>Perhaps of still greater complexity are the judgments of size and of
+distance. Many comparisons enter such judgments. The unconscious acts of
+the muscles of the eye and various external conditions such as the
+clearness of the atmosphere play prominent parts in influencing judgment.
+Upon these are superposed the numerous psycho-physiological phenomena of
+color, irradiation, etc.</p>
+
+<p>In vision judgments are quickly made and the process apparently is largely
+outside of consciousness. Higher and more complex visual judgments pass
+into still higher and more complex intellectual judgments. All these may
+appear to be primary, immediate, innate, or instinctive and therefore,
+certain, but the fruits of studies of the psychology of vision have shown
+that these visual judgments may be analyzed into simpler elements.
+Therefore, they are liable to error.</p>
+
+<p>That the ancients sensed the existence or possibility of illusions is
+evidenced by the fact that they tried to draw and to paint although their
+inability to observe carefully is indicated by the absence of true
+shading. The architecture of ancient Greece reveals a knowledge of certain
+illusions in the efforts to overcome them. However, the study of illusions
+did not<span class="pagenum"><a name="Page_8" id="Page_8">[Pg 8]</a></span> engage the attention of scientists until a comparatively recent
+period. Notwithstanding this belated attention there is a vast scientific
+literature pertaining to the multitudinous phases of the subject; however,
+most of it is fragmentary and much of it is controversial. Some of it
+deals with theory for a particular and often a very simple case. In life
+complex illusions are met but at present it would be futile to attempt to
+explain them in detail. Furthermore, there have been few attempts to
+generalize and to group examples of typical phenomena in such a manner as
+to enable a general reader to see the complex fabric as a whole. Finally,
+the occurrence and application of illusions in various arts and the
+prominence of illusions on every hand have not been especially treated. It
+is the hope that this will be realized in the following chapters in so far
+as brevity of treatment makes this possible.</p>
+
+<p>Doubtless thoughtful observers ages ago noticed visual illusions,
+especially those found in nature and in architecture. When it is
+considered that geometrical figures are very commonly of an illusory
+character it appears improbable that optical illusions could have escaped
+the keenness of Euclid. The apparent enlargement of the moon near the
+horizon and the apparent flattened vault of the sky were noticed at least
+a thousand years ago and literature yields several hundred memoirs on
+these subjects. One of the oldest dissertations upon the apparent form of
+the sky was published by Alhazen, an Arab astronomer of the tenth century.
+Kepler in 1618 wrote upon the subject.</p>
+
+<p>Philosophers of the past centuries prepared the<span class="pagenum"><a name="Page_9" id="Page_9">[Pg 9]</a></span> way toward an
+understanding of many complexities of today. They molded thought into
+correct form and established fundamental concepts and principles. Their
+chief tool was philosophy, the experimental attack being left to the
+scientists of the modern age. However, they established philosophically
+such principles as &#8220;space and time are not realities of the phenomenal
+world but the modes under which we see things apart.&#8221; As science became
+organized during the present experimental era, measurements were applied
+and there began to appear analytical discussions of various subjects
+including optical illusions. One of the earliest investigations of the
+modern type was made by Oppel, an account of which appeared in 1854. Since
+that time scientific literature has received thousands of worthy
+contributions dealing with visual illusions.</p>
+
+<p>There are many facts affecting vision regarding which no theory is
+necessary. They speak for themselves. There are many equally obvious facts
+which are not satisfactorily explained but the lack of explanation does
+not prevent their recognition. In fact, only the scientist needs to worry
+over systematic explanations and theoretical generalizations. He needs
+these in order to invade and to explore the other unknowns where he will
+add to his storehouse of knowledge. A long step toward understanding is
+made by becoming acquainted with certain physical, physiological, and
+psychological facts of light, color, and lighting. Furthermore,
+acquaintance with the visual process and with the structure of the eye
+aids materially. For this reason the next two chapters have been added
+even at the risk of discouraging some readers.</p>
+
+<p><span class="pagenum"><a name="Page_10" id="Page_10">[Pg 10]</a></span>In a broad sense, any visual perception which does not harmonize with
+physical measurements may be termed an &#8220;illusion.&#8221; Therefore, the term
+could include those physical illusions obtained by means of prisms,
+lenses, and mirrors and such illusions as the mirage. It could also
+include the physiological illusions of light and color such as
+after-images, irradiation, and contrast, and the psycho-physiological
+illusions of space and the character of objects. In fact, the scope of the
+following chapters is arbitrarily extended to include all these aspects,
+but confines consideration only to &#8220;static&#8221; illusions.</p>
+
+<p>In a more common sense attention is usually restricted to the last group;
+that is, to the psycho-physiological illusions attending the perception of
+space and the character of objects although motion is often included. It
+should be obvious that no simple or even single theory can cover the vast
+range of illusions considered in the broad sense because there are so many
+different kinds of factors involved. For this reason explanations will be
+presented wherever feasible in connection with specific illusions.
+However, in closing this chapter it appears of interest to touch upon the
+more generally exploited theories of illusions of the type considered in
+the foregoing restricted sense. Hypotheses pertaining to illusions are
+generally lacking in agreement, but for the special case of what might be
+more safely termed &#8220;geometrical-optical illusions&#8221; two different theories,
+by Lipps and by Wundt respectively, are conspicuous. In fact, most
+theories are variants of these two systematic &#8220;explanations&#8221; of illusions
+(in the restricted sense).</p>
+
+<p><span class="pagenum"><a name="Page_11" id="Page_11">[Pg 11]</a></span>Lipps proposed the principle of mechanical-esthetic unity, according to
+which we unconsciously give to every space-form a living personality and
+unconsciously consider certain mechanical forces acting. Our judgments are
+therefore modified by this anthropomorphic attitude. For example, we
+regard the circle as being the result of the action of tangential and
+radial forces in which the latter appear to triumph. According to Lipps&#8217;
+theory the circle has a centripetal character and these radial forces
+toward the center, which apparently have overcome the tangential forces
+during the process of creating the circle, lead to underestimation of its
+size as compared with a square of the same height and breadth. By drawing
+a circle and square side by side, with the diameter of the former equal to
+the length of a side of the latter, this illusion is readily demonstrated.
+Of course, the square has a greater area than the circle and it is
+difficult to determine the effect of this disparity in area. <a href="#fig60">Figure 60</a>
+where the areas of the circle and square are equal and consequently the
+height of the former is considerably greater than the latter, is of
+interest in this connection. By experimenting with a series of pairs
+consisting of a circle and a square, varying in dimensions from equal
+heights to equal areas, an idea of the &#8220;shrinking&#8221; character of the circle
+becomes quite apparent.</p>
+
+<p>Wundt does not attribute the illusion to a deception or error of judgment
+but to direct perception. According to his explanation, the laws of
+retinal image (fixation) and eye-movement are responsible. For example,
+vertical distances appear greater than <span class="pagenum"><a name="Page_12" id="Page_12">[Pg 12]</a></span>horizontal ones because the effort
+or expenditure of energy is greater in raising the eyes than in turning
+them through an equal angle in a horizontal plane. Unconscious or
+involuntary eye-movements also appear to play a part in many linear or
+more accurately, angular illusions, but certainly Wundt&#8217;s explanation does
+not suffice for all illusions although it may explain many geometrical
+illusions. It may be said to be of the &#8220;perceptive&#8221; class and Lipps&#8217;
+theory to be of the &#8220;judgment&#8221; or &#8220;higher-process&#8221; class. As already
+stated, most of the other proposed explanations of geometrical illusions
+may be regarded as being related to one of these two theories. There is
+the &#8220;indistinct vision&#8221; theory of Einthoven; the &#8220;perspective&#8221; theory of
+Hering, Guye, Thi&eacute;ry, and others; the &#8220;contrast&#8221; theory of Helmholtz,
+Loeb, and Heyman; and the &#8220;contrast-<i>confluxion</i>&#8221; theory of M&uuml;ller-Lyer.
+In order not to discourage the reader at the outset, theories as such will
+be passed by with this brief glimpse. However, more or less qualified
+explanations are presented occasionally in some of the chapters which
+follow in order to indicate or to suggest a train of thought should the
+reader desire to attempt to understand some of the numerous interesting
+illusions.</p>
+
+
+<p>&nbsp;</p><p>&nbsp;</p>
+<hr style="width: 50%;" />
+<p><span class="pagenum"><a name="Page_13" id="Page_13">[Pg 13]</a></span></p>
+<h2><a name="II" id="II"></a>II<br />THE EYE</h2>
+
+<p class="dropcap"><span class="caps">Helmholtz,</span> who contributed so much toward our knowledge of the visual
+process, in referring to the eye, once stated that he could make a much
+better optical instrument but not a better eye. In other words, the eye is
+far from an ideal optical instrument but as an eye it is wonderful. Its
+range of sensitiveness and its adaptability to the extreme variety of
+demands upon it are truly marvelous when compared with instruments devised
+by mankind. Obviously, the eye is the connecting link between objective
+reality and visual perception and, therefore, it plays an important part
+in illusions. In fact, sometimes it is solely responsible for the
+illusion. The process of vision may be divided into several steps such as
+(1) the lighting, color, character, and disposition of objects; (2) the
+mechanism by which the image is formed upon the retina; (3) various
+optical defects of this mechanism; (4) the sensitiveness of the parts of
+the retina to light and color; (5) the structure of the retina; (6) the
+parts played by monocular and binocular vision; and (7) the various events
+which follow the formation of the image upon the retina.</p>
+
+<p>The mechanism of the eye makes it possible to see not only light but
+objects. Elementary eyes of the<span class="pagenum"><a name="Page_14" id="Page_14">[Pg 14]</a></span> lowest animals perceive light but cannot
+see objects. These eyes are merely specialized nerves. In the human eye
+the optic nerve spreads to form the retina and the latter is a specialized
+nerve. Nature has accompanied this evolution by developing an instrument
+the&mdash;eye&mdash;for intensifying and defining and the whole is the visual
+sense-organ. The latter contains the most highly specialized nerve and the
+most refined physiological mechanism, the result being the highest
+sense-organ.</p>
+
+<p><a name="fig1" id="fig1"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig1.jpg" alt="" /></div>
+<p class="center">Fig. 1.&mdash;Principal parts of the eye.</p>
+<p class="center">A, Conjunctiva; B, Retina; C, Choroid; D, Sclera;<br />E, Fovea; F, Blind Spot;
+G, Optic Nerve;<br />H, Ciliary Muscle; I, Iris; J, Cornea; K, Ligament.</p>
+<p>&nbsp;</p>
+
+<p>The eye is approximately a spherical shell transparent at the front
+portion and opaque (or nearly so) over the remaining eighty per cent of
+its surface. The optical path consists of a series of transparent liquids
+and solids. The chief details of the structure of the eye are represented
+in <a href="#fig1">Fig. 1</a>. Beginning with the exterior and proceeding toward the retina we
+find in succession the cornea, the anterior chamber containing the aqueous
+humor, the iris, the lens, the large chamber containing the vitreous
+humor, and finally the retina. Certain muscles alter the position of the
+eye and consequently the optical axis, and focusing (accommodation) is
+accomplished by altering<span class="pagenum"><a name="Page_15" id="Page_15">[Pg 15]</a></span> the thickness and shape, and consequently the
+focal length, of the lens.</p>
+
+<p>The iris is a shutter which automatically controls to some degree the
+amount of light reaching the retina, thereby tending to protect the latter
+from too much light. It also has some influence upon the definition of the
+image; that is, upon what is termed &#8220;visual acuity&#8221; or the ability to
+distinguish fine detail. It is interesting to compare the eye with the
+camera. In the case of the camera and the photographic process, we have
+(1) an inverted light-image, a facsimile of the object usually diminished
+in size; (2) an invisible image in the photographic emulsion consisting of
+molecular changes due to light; and (3) a visible image developed on the
+plate. In the case of the eye and the visual process we have (1) an
+inverted light-image, a facsimile of the object diminished in size; (2)
+the invisible image in the retinal substances probably consisting of
+molecular changes due to light; and (3) an <i>external</i> visible image. It
+will be noted that in the case of vision the final image is projected
+outward&mdash;it is external. The more we think of this outward projection the
+more interesting and marvelous vision becomes. For example, it appears
+certain that if a photographic plate could see or feel, it would see or
+feel the silver image upon itself but not out in space. However, this
+point is discussed further in the next chapter.</p>
+
+<p>In the camera and photographic process we trace mechanism, physics, and
+chemistry throughout. In the eye and visual process we are able to trace
+these factors only to a certain point, where we encounter<span class="pagenum"><a name="Page_16" id="Page_16">[Pg 16]</a></span> the
+super-physical and super-chemical. Here molecular change is replaced by
+sensation, perception, thought, and emotion. Our exploration takes us from
+the physical world into another, wholly different, where there reigns
+another order of phenomena. We have passed from the material into the
+mental world.</p>
+
+<p>The eye as an optical mechanism is reducible to a single lens and
+therefore the image focused upon the retina is inverted. However, there is
+no way for the observer to be conscious of this and therefore the inverted
+image causes no difficulty in seeing. The images of objects in the right
+half of the field of view are focused upon the left half of the retina.
+Similarly, the left half of the field of view corresponds to the right
+half of the retina; the upper half of the former to the lower half of the
+latter; and so on. When a ray of light from an object strikes the retina
+the impression is referred back along the ray-line into the original place
+in space. This is interestingly demonstrated in a simple manner. Punch a
+pin-hole in a card and hold it about four inches from the eye and at the
+same time hold a pin-head as close to the cornea as possible. The
+background for the pin-hole should be the sky or other bright surface.
+After a brief trial an inverted image of the pin-head is seen <i>in the
+hole</i>. Punch several holes in the card and in each will be seen an
+inverted image of the pin-head.</p>
+
+<p>The explanation of the foregoing is not difficult. The pin-head is so
+close to the eye that the image cannot be focused upon the retina;
+however, it is in a very favorable position to cast a shadow upon the
+retina, the light-source being the pin-hole with a bright<span class="pagenum"><a name="Page_17" id="Page_17">[Pg 17]</a></span> background.
+Light streaming through the pin-hole into the eye casts an erect shadow of
+the pin-head upon the retina, and this erect image is projected into space
+and inverted in the process by the effect of the lens. The latter is not
+operative during the casting of the shadow because the pin-head is too
+close to the lens, as already stated. It is further proved to be outward
+projection of the retinal image (the shadow) because by multiplying the
+number of pin-holes (the light-sources) there are also a corresponding
+number of shadows.</p>
+
+<p>The foregoing not only illustrates the inversion of the image but again
+emphasizes the fact that we do not see retinal images. Even the &#8220;stars&#8221;
+which we see on pressing the eye-lid or on receiving a blow on the eye are
+projected into space. The &#8220;motes&#8221; which we see in the visual field while
+gazing at the sky are defects in the eye-media, and these images are
+projected into space. We do not see anything in the eye. The retinal image
+impresses the retina in some definite manner and the impression is carried
+to the brain by the optic nerve. The intellect then refers or projects
+this impression outward into space as an external image. The latter would
+be a facsimile of the physical object if there were no illusions but the
+fact that there are illusions indicates that errors are introduced
+somewhere along the path from and to the object.</p>
+
+<p>It is interesting to speculate whether the first visual impression of a
+new-born babe is &#8220;projected outward&#8221; or is perceived as in the eye. It is
+equally futile to conjecture in this manner because there is no
+<span class="pagenum"><a name="Page_18" id="Page_18">[Pg 18]</a></span>indication that the time will come when the baby can answer us
+immediately upon experiencing its first visual impression. The period of
+infancy increases with progress up the scale of animal life and this
+lengthening is doubtless responsible and perhaps necessary for the
+development of highly specialized sense-organs. Incidentally, suppose a
+blind person to be absolutely uneducated by transferred experience and
+that he suddenly became a normal adult and able to see. What would he say
+about his first visual impression? Apparently such a subject is
+unobtainable. The nearest that such a case had been approached is the case
+of a person born blind, whose sight has been restored. This person has
+acquired much experience with the external world through other senses. It
+has been recorded that such a person, after sight was restored, appeared
+to think that external objects &#8220;touched&#8221; the eyes. Only through visual
+experience is this error in judgment rectified.</p>
+
+<p>Man studies his kind too much apart from other animals and perhaps either
+underestimates or overestimates the amount of inherited, innate,
+instinctive qualities. A new-born chick in a few minutes will walk
+straight to an object and seize it. Apparently this implies perception of
+distance and direction and a co&ouml;rdination of muscles for walking and
+moving the eyes. It appears reasonable to conclude that a certain amount
+of the wealth of capacities possessed by the individual is partly
+inherited, and in man the acquired predominates. But all capacities are
+acquired, for even the inherited was acquired in ancestral experience.
+Even instinct (whatever that may be) must involve inherited<span class="pagenum"><a name="Page_19" id="Page_19">[Pg 19]</a></span> experience.
+These glimpses of the depths to which one must dig if he is to unearth the
+complete explanations of visual perception&mdash;and consequently of
+illusions&mdash;indicate the futility of treating the theories in the available
+space without encroaching unduly upon the aims of this volume.</p>
+
+<p>Certain defects of the optical system of the eye must contribute toward
+causing illusions. Any perfect lens of homogeneous material has at least
+two defects, known as spherical and chromatic aberration. The former
+manifests itself by the bending of straight lines and is usually
+demonstrated by forming an image of an object such as a wire mesh or
+checkerboard; the outer lines of the image are found to be very much bent.
+This defect in the eye-lens is somewhat counteracted by a variable optical
+density, increasing from the outer to the central portion. This results in
+an increase in refractive-index as the center of the lens is approached
+and tends to diminish its spherical aberration. The eye commonly possesses
+abnormalities such as astigmatism and eccentricity of the optical
+elements. All these contribute toward the creation of illusions.</p>
+
+<p>White light consists of rays of light of various colors and these are
+separated by means of a prism because the refractive-index of the prism
+differs for lights of different color or wave-length. This causes the blue
+rays, for example, to be bent more than the red rays when traversing a
+prism. It is in this manner that the spectrum of light may be obtained. A
+lens may be considered to be a prism of revolution and it thus becomes
+evident that the blue rays will be brought<span class="pagenum"><a name="Page_20" id="Page_20">[Pg 20]</a></span> to a focus at a lesser
+distance than the red rays; that is, the former are bent more from their
+original path than the latter. This defect of lenses is known as chromatic
+aberration and is quite obvious in the eye. It may be demonstrated by any
+simple lens, for the image of the sun, for example, will appear to have a
+colored fringe. A purple filter which transmits only the violet and red
+rays is useful for this demonstration. By looking at a lamp-filament or
+candle-flame some distance away the object will appear to have a violet
+halo, but the color of the fringe will vary with accommodation. On looking
+through a pin-hole at the edge of an object silhouetted against the bright
+sky the edge will appear red if the light from the pin-hole enters the
+pupil near its periphery. This optical defect of the eye makes objects
+appear more sharply defined when viewed in monochromatic light. In fact,
+this is quite obvious when using yellow glasses. The defect is also
+demonstrated by viewing a line-spectrum focused on a ground glass. The
+blue and red lines cannot be seen distinctly at the same distance. The
+blue lines can be focused at a much less distance than the red lines.
+Chromatic aberration can account for such an illusion as the familiar
+&#8220;advancing&#8221; and &#8220;retiring&#8221; colors and doubtless it plays a part in many
+illusions.</p>
+
+<p>The structure of the retina plays a very important part in vision and
+accounts for various illusions and many interesting visual phenomena. The
+optic nerve spreads out to form the retina which constitutes the inner
+portion of the spherical shell of the eye with the exception of the front
+part. Referring again to <a href="#fig1">Fig. 1</a>,<span class="pagenum"><a name="Page_21" id="Page_21">[Pg 21]</a></span> the outer coating of the shell is called
+the sclerotic. This consists of dense fibrous tissue known as the &#8220;white
+of the eye.&#8221; Inside this coating is a layer of black pigment cells termed
+the choroid. Next is the bacillary layer which lines about five-sixths of
+the interior surface of the eye. This is formed by closely packed &#8220;rods&#8221;
+and &#8220;cones,&#8221; which play a dominant role in the visual process. A
+light-sensitive liquid (visual purple) and cellular and fibrous layers
+complete the retinal structure.</p>
+
+<p>The place where the optic nerve enters the eye-ball and begins to spread
+out is blind. Objects whose images fall on this spot are invisible. This
+blind-spot is not particularly of interest here, but it may be of interest
+to note its effect. This is easily done by closing one eye and looking
+directly at one of two small black circles about two inches apart on white
+paper at a distance of about a foot from the eye. By moving the objects
+about until the image of the circle not directly looked at falls upon the
+blind-spot, this circle will disappear. A three-foot circle at a distance
+of 36 feet will completely disappear if its image falls directly upon the
+blind-spot. At a distance of 42 inches the invisible area is about 12
+inches from the point of sight and about 3 to 4 inches in diameter. At 300
+feet the area is about 8 feet in diameter. The actual size of the retinal
+blind-spot is about 0.05 inch in diameter or nearly 5 degrees. Binocular
+vision overcomes any annoyance due to the blind-spots because they do not
+overlap in the visual field. A one-eyed person is really totally blind for
+this portion of the retina or of the visual field.</p>
+
+<p><span class="pagenum"><a name="Page_22" id="Page_22">[Pg 22]</a></span>The bacillary layer consists of so-called rods and cones. Only the rods
+function under very low intensities of illumination of the order of
+moonlight. The cones are sensitive to color and function only at
+intensities greater than what may be termed twilight intensities. These
+elements are very small but the fact that they appear to be connecting
+links between the retinal image and visual perception, acuity or
+discrimination of fine detail is limited inasmuch as the elements are of
+finite dimensions. The smallest image which will produce a visual
+impression is the size of the end of a cone. The smallest distance between
+two points which is visible at five inches is about 0.001 inch. Two cones
+must be stimulated in such a case. Fine lines may appear crooked because
+of the irregular disposition of these elemental light-sensitive points.
+This apparent crookedness of lines is an illusion which is directly due to
+the limitations of retinal elements of finite size.</p>
+
+<p>The distribution of rods and cones over the retina is very important. In
+the fovea centralis&mdash;the point of the retina on the optical axis of the
+eye&mdash;is a slight depression much thinner than the remainder of the retina
+and this is inhabited chiefly by cones. It is this spot which provides
+visual acuteness. It is easily demonstrated that fine detail cannot be
+seen well defined outside this central portion of the visual field. When
+we desire to see an object distinctly we habitually turn the head so that
+the image of the object falls upon the fovea of each eye. Helmholtz has
+compared the foveal and lateral images with a finished drawing and a rough
+sketch respectively.</p>
+
+<p><span class="pagenum"><a name="Page_23" id="Page_23">[Pg 23]</a></span>The fovea also contains a yellow pigmentation which makes this area of the
+retina selective as to color-vision. On viewing certain colors a
+difference in color of this central portion of the field is often very
+evident. In the outlying regions of the retina, rods predominate and in
+the intermediate zone both rods and cones are found. Inasmuch as rods are
+not sensitive to color and cones do not function at low intensities of
+illumination it is obvious that visual impressions should vary, depending
+upon the area of the retina stimulated. In fact, many interesting
+illusions are accounted for in this manner, some of which are discussed
+later.</p>
+
+<p>It is well known that a faint star is seen best by averted vision. It may
+be quite invisible when the eye is directed toward it, that is, when its
+image falls upon the rod-free fovea. However, by averting the line of
+sight slightly, the image is caused to fall on a retinal area containing
+rods (sensitive to feeble light) and the star may be readily recognized.
+The fovea is the point of distinct focus. It is necessary for fixed
+thoughtful attention. It exists in the retina of man and of higher monkeys
+but it quickly disappears as we pass down the scale of animal life. It may
+be necessary for the safety of the lower animals that they see equally
+well over a large field; however, it appears advantageous that man give
+fixed and undivided attention to the object looked at. Man does not need
+to trust solely to his senses to protect himself from dangers. He uses his
+intellect to invent and to construct artificial defenses. Without the
+highly specialized fovea we might see equally<span class="pagenum"><a name="Page_24" id="Page_24">[Pg 24]</a></span> well over the whole retina
+but could not look attentively at anything, and therefore could not
+observe thoughtfully.</p>
+
+<p>When an image of a bright object exists upon the retina for a time there
+results a partial exhaustion or fatigue of the retinal processes with a
+result that an after-image is seen. This after-image may be bright for a
+time owing to the fact that it takes time for the retinal process to die
+out. Then there comes a reaction which is apparent when the eye is
+directed toward illuminated surfaces. The part of the retina which has
+been fatigued does not respond as fully as the fresher areas, with the
+result that the fatigued area contributes a darker area in the visual
+field. This is known as an after-image and there are many interesting
+variations.</p>
+
+<p>The after-image usually undergoes a series of changes in color as well as
+in brightness as the retinal process readjusts itself. An after-image of a
+colored object may often appear of a color complementary to the color of
+the object. This is generally accounted for by fatigue of the retinal
+process. There are many conflicting theories of color-vision but they are
+not as conflicting in respect to the aspect of fatigue as in some other
+aspects. If the eye is directed toward a green surface for a time and then
+turned toward a white surface, the fatigue to green light diminishes the
+extent of response to the green rays in the light reflected by the white
+surface. The result is the perception of a certain area of the white
+surface (corresponding to the portion of the field fatigued by green
+light) as of a color equal to white minus<span class="pagenum"><a name="Page_25" id="Page_25">[Pg 25]</a></span> some green&mdash;the result of which
+is pink or purple. This is easily understood by referring to the
+principles of color-mixture. Red, green, and blue (or violet) mixed in
+proper proportions will produce any color or tint and even white. Thus
+these may be considered to be the components of white light. Hence if the
+retina through fatigue is unable to respond fully to the green component,
+the result may be expressed mathematically as red plus blue plus reduced
+green, or synthetically a purplish white or pink. When fatigued to red
+light the after-image on a white surface is blue-green. When fatigued to
+blue light it is yellowish.</p>
+
+<p>Further mixtures may be obtained by directing the after-image upon colored
+surfaces. In this manner many of the interesting visual phenomena and
+illusions associated with the viewing of colors are accounted for. The
+influence of a colored environment upon a colored object is really very
+great. This is known as simultaneous contrast. The influence of the
+immediately previous history of the retina upon the perception of colored
+surfaces is also very striking. This is called successive contrast. It is
+interesting to note that an after-image produced by looking at a bright
+light-source, for example, is projected into space even with the eyes
+closed. It is instructive to study after-images and this may be done at
+any moment. On gazing at the sun for an instant and then looking away, an
+after-image is seen which passes in color from green, blue, purple, etc.,
+and finally fades. For a time it is brighter than the background which may
+conveniently be the sky. On<span class="pagenum"><a name="Page_26" id="Page_26">[Pg 26]</a></span> closing the eyes and placing the hands over
+them the background now is dark and the appearance of the after-image
+changes markedly. There are many kinds, effects, and variations of
+after-images, some of which are discussed in other chapters.</p>
+
+<p>As the intensity of illumination of a landscape, for example, decreases
+toward twilight, the retina diminishes in sensibility to the rays of
+longer wave-lengths such as yellow, orange, and red. Therefore, it becomes
+relatively more sensitive to the rays of shorter wave-length such as
+green, blue, and violet. The effects of this Purkinje phenomenon (named
+after the discoverer) may be added to the class of illusions treated in
+this book. It is interesting to note in this connection that moonlight is
+represented on some paintings and especially on the stage as greenish blue
+in color, notwithstanding that physical measurements show it to be
+approximately the color of sunlight. In fact, it is sunlight reflected by
+dead, frigid, and practically colorless matter.</p>
+
+<p>Some illusions may be directly traced to the structure of the eye under
+unusual lighting conditions. For example, in a dark room hold a lamp
+obliquely outward but near one eye (the other being closed and shielded)
+and forward sufficiently for the retina to be strongly illuminated. Move
+the lamp gently while gazing at a plain dark surface such as the wall.
+Finally the visual field appears dark, due to the intense illumination of
+the retina and there will appear, apparently projected upon the wall, an
+image resembling a branching leafless tree. These are really shadows of
+the blood vessels in the retina. The<span class="pagenum"><a name="Page_27" id="Page_27">[Pg 27]</a></span> experiment is more successful if an
+image of a bright light-source is focused on the sclerotic near the
+cornea. If this image of the light-source is moved, the tree-like image
+seen in the visual field will also move.</p>
+
+<p>The rate of growth and decay of various color-sensations varies
+considerably. By taking advantage of this fact many illusions can be
+produced. In fact, the careful observer will encounter many illusions
+which may be readily accounted for in this manner.</p>
+
+<p>It may be said that in general the eyes are never at rest. Involuntary
+eye-movements are taking place all the time, at least during
+consciousness. Some have given this restlessness a major part in the
+process of vision but aside from the correctness of theories involving
+eye-movements, it is a fact that they are responsible for certain
+illusions. On a star-lit night if one lies down and looks up at a star the
+latter will be seen to appear to be swimming about more or less jerkily.
+On viewing a rapidly revolving wheel of an automobile as it proceeds down
+the street, occasionally it will be seen to cease revolving momentarily.
+These apparently are accounted for by involuntary eye-movements which take
+place regardless of the effort made to fixate vision.</p>
+
+<p>If the eyelids are almost closed, streamers appear to radiate in various
+directions from a light-source. Movements of the eyelids when nearly
+closed sometimes cause objects to appear to move. These may be accounted
+for perhaps by the distortion of the moist film which covers the cornea.</p>
+
+<p><span class="pagenum"><a name="Page_28" id="Page_28">[Pg 28]</a></span>The foregoing are only a few of the many visual phenomena due largely to
+the structure of the eye. The effects of these and many others enter into
+visual illusions, as will be seen here and there throughout the chapters
+which follow.</p>
+
+
+<p>&nbsp;</p><p>&nbsp;</p>
+<hr style="width: 50%;" />
+<p><span class="pagenum"><a name="Page_29" id="Page_29">[Pg 29]</a></span></p>
+<h2><a name="III" id="III"></a>III<br />VISION</h2>
+
+<p class="dropcap"><span class="caps">A description</span> of the eye by no means suffices to clarify the visual
+process. Even the descriptions of various phenomena in the preceding
+chapter accomplish little more than to acquaint the reader with the
+operation of a mechanism, although they suggest the trend of the
+explanations of many illusions. At best only monocular vision has been
+treated, and it does not exist normally for human beings. A person capable
+only of monocular vision would be like Cyclops Polyphemus. We might have
+two eyes, or even, like Argus, possess a hundred eyes and still not
+experience the wonderful advantages of binocular vision, for each eye
+might see independently. The phenomena of binocular vision are far less
+physical than those of monocular vision. They are much more obscure,
+illusory, and perplexing because they are more complexly interwoven with
+or allied to psychological phenomena.</p>
+
+<p>The sense of sight differs considerably from the other senses. The sense
+of touch requires solid contact (usually); taste involves liquid contact;
+smell, gaseous contact; and hearing depends upon a relay of vibrations
+from an object through another medium (usually air), resulting finally in
+contact. However, we perceive things at a distance through vibration<span class="pagenum"><a name="Page_30" id="Page_30">[Pg 30]</a></span>
+(electromagnetic waves called light) conveyed by a subtle, intangible,
+universal medium which is unrecognizable excepting as a hypothetically
+necessary bearer of light-waves or, more generally, radiant energy.</p>
+
+<p>It also is interesting to compare the subjectiveness and objectiveness of
+sensations. The sensation of taste is subjective; it is in us, not in the
+body tasted. In smell we perceive the sensation in the nose and by
+experience refer it to an object at a distance. The sensation of hearing
+is objective; that is, we refer the cause to an object so completely that
+there is practically no consciousness of sensation in the ear. In sight
+the impression is so completely projected outward into space and there is
+so little consciousness of any occurrence in the eye that it is extremely
+difficult to convince ourselves that it is essentially a subjective
+sensation. The foregoing order represents the sense-organs in increasing
+specialization and refinement. In the two higher senses&mdash;sight and
+hearing&mdash;there is no direct contact with the object and an intricate
+mechanism is placed in front of the specialized nerve to define and to
+intensify the impression. In the case of vision this highly developed
+instrument makes it possible to see not only <i>light</i> but <i>objects</i>.</p>
+
+<p>As we go up the scale of vertebrate animals we find that there is a
+gradual change of the position of the eyes from the sides to the front of
+the head and a change of the inclination of the optical axes of the two
+eyes from 180 degrees to parallel. There is also evident a gradual
+increase in the fineness of the<span class="pagenum"><a name="Page_31" id="Page_31">[Pg 31]</a></span> bacillary layer of the retina from the
+margins toward the center, and, therefore, an increasing accuracy in the
+perception of form. This finally results in a highly organized central
+spot or fovea which is possessed only by man and the higher monkeys.
+Proceeding up the scale we also find an increasing ability to converge the
+optic axes on a near point so that the images of the point may coincide
+with the central spots of both retinas. These changes and others are
+closely associated with each other and especially with the development of
+the higher faculties of the mind.</p>
+
+<p>Binocular vision in man and in the higher animals is the last result of
+the gradual improvement of the most refined sense-organ, adapting it to
+meet the requirements of highly complex organisms. It cannot exist in some
+animals, such as birds and fishes, because they cannot converge their two
+optical axes upon a near point. When a chicken wishes to look intently at
+an object it turns its head and looks with one eye. Such an animal sees
+with two eyes independently and possibly moves them independently. The
+normal position of the axes of human eyes is convergent or parallel but it
+is possible to diverge the axes. In fact, with practice it is possible to
+diverge the axes sufficiently to look at a point near the back of the
+head, although, of course, we do not see the point.</p>
+
+<p>The movement of the eyes is rather complex. When they move together to one
+side or the other or up and down in a vertical plane there is no rotation
+of the optical axes; that is, no torsion. When the visual plane is
+elevated and the eyes move to the<span class="pagenum"><a name="Page_32" id="Page_32">[Pg 32]</a></span> right they rotate to the right; when
+they move to the left they rotate to the left. When the visual plane is
+depressed and the eyes move to the right they rotate to the left; when
+they move to the left they rotate to the right. Through experience we
+unconsciously evaluate the muscular stresses, efforts, and movements
+accompanying the motion of the eyes and thereby interpret much through
+visual perception in regard to such aspects of the external world as size,
+shape, and distance of objects. Even this brief glimpse of the principal
+movements of the eyes indicates a complexity which suggests the intricacy
+of the explanations of certain visual phenomena.</p>
+
+<p>At this point it appears advantageous to set down the principal modes by
+which we perceive the third dimension of space and of objects and other
+aspects of the external world. They are as follows: (1) extent; (2)
+clearness of brightness and color as affected by distance; (3)
+interference of near objects with those more distant; (4) elevation of
+objects; (5) variation of light and shade on objects; (6) cast shadows;
+(7) perspective; (8) variation of the visor angle in proportion to
+distance; (9) muscular effort attending accommodation of the eye; (10)
+stereoscopic vision; (11) muscular effort attending convergence of the
+axes of the eyes. It will be recognized that only the last two are
+necessarily concerned with binocular vision. These varieties of
+experiences may be combined in almost an infinite variety of proportions.</p>
+
+<p>Wundt in his attempt to explain visual perception considered chiefly three
+factors: (1) the retinal<span class="pagenum"><a name="Page_33" id="Page_33">[Pg 33]</a></span> image of the eye at rest; (2) the influence of
+the movements of one eye; and, (3) the additional data furnished by the
+two eyes functioning together. There are three fields of vision
+corresponding to the foregoing. These are the retinal field of vision, the
+monocular field, and the binocular field. The retinal field of vision is
+that of an eye at rest as compared with the monocular field, which is all
+that can be seen with one eye in its entire range of movement and
+therefore of experience. The retinal field has no clearly defined
+boundaries because it finally fades at its indefinite periphery into a
+region where sensation ceases.</p>
+
+<p>It might be tiresome to follow detailed analyses of the many modes by
+which visual perception is attained, so only a few generalizations will be
+presented. For every voluntary act of sight there are two adjustments of
+the eyes, namely, focal and axial. In the former case the ciliary muscle
+adjusts the lens in order to produce a defined image upon the retina. In
+axial adjustments the two eyes are turned by certain muscles so that their
+axes meet on the object looked at and the images of the object fall on the
+central-spots of the retina. These take place together without distinct
+volition for each but by the single voluntary act of <i>looking</i>. Through
+experience the intellect has acquired a wonderful capacity to interpret
+such factors as size, form, and distance in terms of the muscular
+movements in general without the observer being conscious of such
+interpretations.</p>
+
+<p>Binocular vision is easily recognized by holding a finger before the eyes
+and looking at a point beyond<span class="pagenum"><a name="Page_34" id="Page_34">[Pg 34]</a></span> it. The result is two apparently
+transparent fingers. An object is seen single when the two retinal images
+fall on corresponding points. Direction is a primary datum of sense. The
+property of corresponding points of the two retinas (binocular vision) and
+consequently of identical spatial points in the two visual fields is not
+so simple. It is still a question whether corresponding points (that is,
+the existence of a corresponding point in one retina for each point in the
+other retina) are innate, instinctive, and are antecedent of experience or
+are &#8220;paired&#8221; as the result of experience. The one view results in the
+<i>nativistic</i>, the other in the <i>empiristic</i> theory. Inasmuch as some
+scientists are arrayed on one side and some on the other, it appears
+futile to dwell further upon this aspect. It must suffice to state that
+binocular vision, which consists of two retinas and consequently two
+fields of view absolutely co&ouml;rdinated in some manner in the brain, yields
+extensive information concerning space and its contents.</p>
+
+<p>After noting after-images, motes floating in the field of view (caused by
+defects in the eye-media) and various other things, it is evident that
+what we call the field of view is the external projection into space of
+retinal states. All the variations of the latter, such as images and
+shadows which are produced in the external field of one eye, are
+faithfully reproduced in the external field of the other eye. This sense
+of an external visual field is ineradicable. Even when the eyes are closed
+the external field is still there; the imagination or intellect projects
+it outward. Objects at different distances cannot be<span class="pagenum"><a name="Page_35" id="Page_35">[Pg 35]</a></span> seen distinctly at
+the same time but by interpreting the eye-movements as the point of sight
+is run backward and forward (varying convergence of the axes) the
+intellect practically automatically appraises the size, form, and distance
+of each object. Obviously, experience is a prominent factor. The
+perception of the third dimension, depth or relative distance, whether in
+a single object or a group of objects, is the result of the successive
+combination of the different parts of two dissimilar images of the object
+or group.</p>
+
+<p>As already stated, the perception of distance, size, and form is based
+partly upon monocular and partly upon binocular vision, and the simple
+elements upon which judgments of these are based are light, shade, color,
+intensity, and direction. Although the interpretation of muscular
+adjustments plays a prominent part in the formation of judgments, the
+influences of mathematical perspective, light, shade, color, and intensity
+are more direct. Judgments based upon focal adjustment (monocular) are
+fairly accurate at distances from five inches to several yards. Those
+founded upon axial adjustment (convergence of the two axes in binocular
+vision) are less in error than the preceding ones. They are reliable to a
+distance of about 1000 feet. Judgments involving mathematical perspective
+are of relatively great accuracy without limits. Those arrived at by
+interpreting aerial perspective (haziness of atmosphere, reduction in
+color due to atmospheric absorption, etc.) are merely estimates liable to
+large errors, the accuracy depending largely upon experience with local
+conditions.</p>
+
+<p>The measuring power of the eye is more liable<span class="pagenum"><a name="Page_36" id="Page_36">[Pg 36]</a></span> to error when the distances
+or the objects compared lie in different directions. A special case is the
+comparison of a vertical distance with a horizontal one. It is not
+uncommon to estimate a vertical distance as much as 25 per cent greater
+than an actually equal horizontal distance. In general, estimates of
+direction and distance are comparatively inaccurate when only one eye is
+used although a one-eyed person acquires unusual ability through a keener
+experience whetted by necessity. A vertical line drawn perpendicular to a
+horizontal one is likely to appear bent when viewed with one eye. Its
+apparent inclination is variable but has been found to vary from one to
+three degrees. Monocular vision is likely to cause straight lines to
+appear crooked, although the &#8220;crookedness&#8221; may seem to be more or less
+unstable.</p>
+
+<p>The error in the estimate of size is in reality an error in the estimation
+of distance except in those cases where the estimate is based directly
+upon a comparison with an object of supposedly known size. An amusing
+incident is told of an old negro who was hunting for squirrels. He shot
+several times at what he supposed to be a squirrel upon a tree-trunk and
+his failure to make a kill was beginning to weaken his rather ample
+opinion of his skill as a marksman. A complete shattering of his faith in
+his skill was only escaped by the discovery that the &#8220;squirrel&#8221; was a
+louse upon his eyebrow. Similarly, a gnat in the air might appear to be an
+airplane under certain favorable circumstances. It is interesting to note
+that the estimated size of the disk of the sun or moon varies from the
+size of a saucer to that of the end of a barrel,<span class="pagenum"><a name="Page_37" id="Page_37">[Pg 37]</a></span> although a pine tree at
+the horizon-line may be estimated as 25 feet across despite the fact that
+it may be entirely included in the disk of the sun setting behind it.</p>
+
+<p>Double images play an important part in the comparison of distances of
+objects. The &#8220;doubling&#8221; of objects is only equal to the interocular
+distance. Suppose two horizontal wires or clotheslines about fifty feet
+away and one a few feet beyond the other. On looking at these no double
+images are visible and it is difficult or even impossible to see which is
+the nearer when the points of attachment of the ends are screened from
+view. However, if the head is turned to one side and downward (90 degrees)
+so that the interocular line is now at right angles (vertical) to the
+horizontal lines, the relative distances of the latter are brought out
+distinctly. Double images become visible in the latter case.</p>
+
+<p>According to Br&uuml;cke&#8217;s theory the eyes are continuously in motion and the
+observer by alternately increasing or decreasing the convergence of the
+axes of the eyes, combines successively the different parts of the two
+scenes as seen by the two eyes and by running the point of sight back and
+forth by trial obtains a distinct perception of binocular perspective or
+relief or depth of space. It may be assumed that experience has made the
+observer proficient in this appraisal which he arrives at almost
+unconsciously, although it may be just as easy to accept Wheatstone&#8217;s
+explanation. In fact, some experiences with the stereoscope appear to
+support the latter theory.</p>
+
+<p>Wheatstone discovered that the dissimilar pictures<span class="pagenum"><a name="Page_38" id="Page_38">[Pg 38]</a></span> of an object or scene,
+when united by means of optical systems, produce a visual effect similar
+to that produced by the actual solid object or scene provided the
+dissimilarity is the same as that between two retinal images of the solid
+object or scene. This is the principle upon which the familiar stereoscope
+is founded. Wheatstone formulated a theory which may be briefly stated as
+follows: In viewing a solid object or a scene two slightly dissimilar
+retinal images are formed in the two eyes respectively, but the mind
+completely fuses them into one &#8220;mental&#8221; image. When this mental fusion of
+the two really dissimilar retinal images is complete in this way, it is
+obvious that there cannot exist a mathematical coincidence. The result is
+a perception of depth of space, of solidity, of relief. In fact the third
+dimension is perceived. A stereoscope accomplishes this in essentially the
+same manner, for two pictures, taken from two different positions
+respectively corresponding to the positions of the eyes, are combined by
+means of optical systems into one image.</p>
+
+<p>Lack of correct size and position of the individual elements of
+stereoscopic pictures are easily detected on combining them. That is,
+their dissimilarity must exactly correspond to that between two views of
+an object or scene from the positions of the two eyes respectively (<a href="#fig2">Fig.
+2</a>). This fact has been made use of in detecting counterfeit notes. If two
+notes made from the same plate are viewed in a stereoscope and the
+identical figures are combined, the combination is perfect and the plane
+of the combined images is perfectly flat. If the notes are not made from
+the<span class="pagenum"><a name="Page_39" id="Page_39">[Pg 39]</a></span> same plate but one of them is counterfeit, slight variations in the
+latter are unavoidable. Such variations will show themselves in a wavy
+surface.</p>
+
+<p>The unwillingness of the visual sense to combine the two retinal images,
+if they are dissimilar to the extent of belonging to two different
+objects, is emphasized by means of colors. For example, if a green glass
+is placed over one eye and a red glass over the other, the colors are not
+mixed by the visual sense. The addition of these two colors results
+normally in yellow, with little or no suggestion of the components&mdash;red
+and green. But in the foregoing case the visual field does not appear of a
+uniform yellow. It appears alternately red and green, as though the colors
+were rivaling each other for complete mastery. In fact, this phenomenon
+has been termed &#8220;retinal rivalry.&#8221;</p>
+
+<p>The lenses of the stereoscope supplement eye-lenses and project on the
+retina two perfect images of a near object, although the eyes are looking
+at a distant object and are therefore not accommodated for the near one
+(the photographs). The lenses enlarge the images similar to the action of
+a perspective glass. This completes the illusion of an object or of a
+scene. There is a remarkable distinctness of the perception of depth of
+space and therefore a wonderful resemblance to the actual object or scene.
+It is interesting to note the effect of taking the two original
+photographs from distances separated by several feet. The effect is
+apparently to magnify depth. It is noteworthy that two pictures taken from
+an airplane at points fifty feet or so apart, when combined in the<span class="pagenum"><a name="Page_40" id="Page_40">[Pg 40]</a></span>
+stereoscope, so magnify the depth that certain enemy-works can be more
+advantageously detected than from ordinary photographs.</p>
+
+<p>Stereoscopic images such as represented in <a href="#fig2">Fig. 2</a> may be combined without
+the aid of the stereoscope if the optical axes of the eye can be
+sufficiently converged or diverged. Such images or pictures are usually
+upon a card and are intended to be combined beyond the plane of the card,
+for it is in this position that the object or scene can be perceived in
+natural perspective, of natural size, of natural form, and at natural
+distance. But in combining them the eyes are looking at a distant object
+and the axes are parallel or nearly so. Therefore, the eyes are focally
+adjusted for a distant object but the light comes from a very near
+object&mdash;the pictures on the card. Myopic eyes do not experience this
+difficulty and it appears that normal vision may be trained to overcome
+it. Normal eyes are aided by using slightly convex lenses. Such glasses
+supplement the lenses of the eye, making possible a clear vision of a near
+object while the eyes are really looking far away or, in other words,
+making possible a clear image of a near object upon the retina of the
+unadjusted eye. Stereoscopic pictures are usually so mounted that
+&#8220;identical points&#8221; on the two pictures are farther apart than the
+interocular distance and therefore the two images cannot be combined when
+the optical axes of the eyes are parallel or nearly so, which is the
+condition when looking at a distant object. In such a case the two
+pictures must be brought closer together.</p>
+
+<p><a name="fig2" id="fig2"></a>&nbsp;<span class="pagenum"><a name="Page_41" id="Page_41">[Pg 41]</a></span></p>
+<div class="figcenter"><img src="images/fig2.jpg" alt="" /></div>
+<p class="center">Fig. 2.&mdash;Stereoscopic pictures for combining by converging or diverging the optical axes.</p>
+<p><a name="fig3" id="fig3"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig3.jpg" alt="" /></div>
+<p class="center">Fig. 3.&mdash;Stereoscopic pictures.</p>
+<p>&nbsp;</p>
+
+<p>In <a href="#fig2">Figs. 2</a> and <a href="#fig3">3</a> are found &#8220;dissimilar&#8221; drawings of the correct
+dissimilarity of stereoscopic pictures. It is interesting and instructive
+to practice combining these with the unaided eyes. If <a href="#fig2">Fig. 2</a> is held at an
+arm&#8217;s length and the eyes are focused upon a point several inches distant,
+the axes will be sufficiently converged so that the two images are
+superposed. It may help to focus the eyes upon the tip of a finger until
+the stereoscopic images are combined. In this case of converging axes the
+final combined result will be the appearance of a hollow tube or of a
+shell of a truncated cone, apparently possessing the third dimension and
+being perceived as apparently smaller than the actual pictures in the
+background at arm&#8217;s length. If the two stereoscopic pictures are combined
+by looking at a point far beyond the actual position of <a href="#fig2">Fig. 2</a>, 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<span class="pagenum"><a name="Page_42" id="Page_42">[Pg 42]</a></span>
+diagrams. In the latter case the smaller end of the apparent solid appears
+to be nearer than the larger end, but in the former case the reverse is
+true, that is, the smaller end appears to be at a greater distance. The
+same experiments may be performed for <a href="#fig3">Fig. 3</a> with similar results
+excepting that this appears to be a shell under the same circumstances
+that <a href="#fig2">Fig. 2</a> appears to be a solid and vice versa. A few patient trials
+should be rewarded by success, and if so the reader can gain much more
+understanding from the actual experiences than from description.</p>
+
+<p>The foregoing discussion of vision should indicate the complexity of the
+visual and mental activities involved in the discrimination, association,
+and interpretation of the data obtained through the eye. The psychology of
+visual perception is still a much controverted domain but it is believed
+that the glimpses of the process of vision which have been afforded are
+sufficient to enable the reader to understand many illusions and at least
+to appreciate more fully those whose explanations remain in doubt.
+Certainly these glimpses and a knowledge of the information which visual
+perception actually supplies to us at any moment should convince us that
+the visual sense has acquired an incomparable facility for interpreting
+the objective world for us. Clearness of vision is confined to a small
+area about the point of sight, and it rapidly diminishes away from this
+point, images becoming dim and double. We sweep this point of sight
+backward and forward and over an extensive field of view, gathering all
+the distinct impressions into one mental image. In doing this the
+unconscious interpretation of the<span class="pagenum"><a name="Page_43" id="Page_43">[Pg 43]</a></span> muscular activity attending
+accommodation and convergence of the eyes aids in giving to this mental
+picture the appearance of depth by establishing relative distances of
+various objects. Certainly the acquired facility is remarkable.</p>
+
+
+<p>&nbsp;</p><p>&nbsp;</p>
+<hr style="width: 50%;" />
+<p><span class="pagenum"><a name="Page_44" id="Page_44">[Pg 44]</a></span></p>
+<h2><a name="IV" id="IV"></a>IV<br />SOME TYPES OF GEOMETRICAL ILLUSIONS</h2>
+
+<p class="dropcap"><span class="caps">No</span> simple classification of illusions is ample or satisfactory, for there
+are many factors interwoven. For this reason no claims are made for the
+various divisions of the subject represented by and in these chapters
+excepting that of convenience. Obviously, some divisions are necessary in
+order that the variegated subject may be presentable. The classification
+used appears to be logical but very evidently it cannot be perfectly so
+when the &#8220;logic&#8221; is not wholly available, owing to the disagreement found
+among the explanations offered by psychologists. It may be argued that the
+&#8220;geometrical&#8221; type of illusion should include many illusions which are
+discussed in other chapters. Indeed, this is perhaps true. However, it
+appears to suit the present purpose to introduce this phase of this book
+by a group of illusions which involve plane geometrical figures. If some
+of the latter appear in other chapters, it is because they seem to border
+upon or to include other factors beyond those apparently involved in the
+simple geometrical type. The presentation which follows begins (for the
+sake of clearness) with a few representative geometrical illusions of
+various types.</p>
+
+<p><i>The Effect of the Location in the Visual Field.</i>&mdash;One of the most common
+illusions is found in the<span class="pagenum"><a name="Page_45" id="Page_45">[Pg 45]</a></span> letter &#8220;S&#8221; or figure &#8220;8.&#8221; Ordinarily we are not
+strongly conscious of a difference in the size of the upper and lower
+parts of these characters; however, if we invert them <img src="images/eights.jpg" alt="" /> the
+difference is seen to be large. The question arises, Is the difference due
+fundamentally to the locations of the two parts in the visual field? It
+scarcely seems credible that visual perception innately appraises the
+upper part larger than the lower, or the lower smaller than the upper part
+when these small characters are seen in their accustomed position. It
+appears to be possible that here we have examples of the effect of
+learning or experience and that our adaptive visual sense has become
+accustomed to overlook the actual difference. That is, for some reason
+through being confronted with this difference so many times, the intellect
+has become adapted to it and, therefore, has grown to ignore it.
+Regardless of the explanation, the illusion exists and this is the point
+of chief interest. For the same reason the curvature of the retina does
+not appear to account for illusion through distortion of the image,
+because the training due to experience has caused greater difficulties
+than this to disappear. We must not overlook the tremendous &#8220;corrective&#8221;
+influence of experience upon which visual perception for the adult is
+founded. If we have learned to &#8220;correct&#8221; in some cases, why not in all
+cases which we have encountered quite generally?</p>
+
+<p><a name="fig4" id="fig4"></a>&nbsp;<span class="pagenum"><a name="Page_46" id="Page_46">[Pg 46]</a></span></p>
+<div class="figcenter"><img src="images/fig4.jpg" alt="" /></div>
+<p class="center">Fig. 4.&mdash;The vertical line appears longer than the equal horizontal line in each case.</p>
+<p>&nbsp;</p>
+
+<p>This type of illusion persists in geometrical figures and may be found on
+every hand. A perfect square when viewed vertically appears too high,
+although the illusion does not appear to exist in the circle. In <a href="#fig4">Fig. 4</a>
+the vertical line appears longer than the horizontal line of the same
+length. This may be readily demonstrated by the reader by means of a
+variety of figures. A striking case is found in <a href="#fig5">Fig. 5</a>, where the height
+and the width of the diagram of a silk hat are equal. Despite the actual
+equality the height appears to be much greater than the width. A pole or a
+tree is generally appraised as of greater length when it is standing than
+when it lies on the ground. This illusion may be demonstrated by placing a
+black dot an inch or so above another on a white paper. Now, at right
+angles to the original dot place another at a horizontal distance which
+appears equal to the vertical distance of the first dot above the
+original. On turning the paper through ninety degrees or by actual
+measurement, the extent of the illusion will become apparent. By doing
+this several times, using various distances, this type of illusion becomes
+convincing.</p>
+
+<p><a name="fig5" id="fig5"></a>&nbsp;<span class="pagenum"><a name="Page_47" id="Page_47">[Pg 47]</a></span></p>
+<div class="figcenter"><img src="images/fig5.jpg" alt="" /></div>
+<p class="center">Fig. 5.&mdash;The vertical dimension is equal to the horizontal one, but the former appears greater.</p>
+<p>&nbsp;</p>
+
+<p>The explanation accepted by some is that more effort is required to raise
+the eyes, or point of sight, through a certain vertical distance than
+through an equal horizontal distance. Perhaps we unconsciously appraise
+effort of this sort in terms of distance, but is it not logical to inquire
+why we have not through experience learned to sense the difference between
+the relation of effort to horizontal distance and that of effort to
+vertical distance through which the point of sight is moved? We are doing
+this continuously, so why do we not learn to distinguish; furthermore, we
+have overcome other great obstacles in developing our visual sense. In
+this complex field of physiological psychology questions are not only
+annoying, but often disruptive.</p>
+
+<p><span class="pagenum"><a name="Page_48" id="Page_48">[Pg 48]</a></span>As has been pointed out in Chapter II, images of objects lying near the
+periphery of the visual field are more or less distorted, owing to the
+structure and to certain defects of parts of the eye. For example, a
+checkerboard viewed at a proper distance with respect to its size appears
+quite distorted in its outer regions. Cheap cameras are likely to cause
+similar errors in the images fixed upon the photographic plate.
+Photographs are interesting in connection with visual illusions, because
+of certain distortions and of the magnification of such aspects as
+perspective. Incidentally in looking for illusions, difficulty is
+sometimes experienced in seeing them when the actual physical truths are
+known; that is, in distinguishing between what is actually seen and what
+actually exists. The ability to make this separation grows with practice
+but where the difficulty is obstinate, it is well for the reader to try
+observers who do not suspect the truth.</p>
+
+<p><i>Illusions of Interrupted Extent.</i>&mdash;Distance and area appear to vary in
+extent, depending upon whether they are filled or empty or are only
+partially filled. For example, a series of dots will generally appear
+longer overall than an equal distance between two points. This may be
+easily demonstrated by arranging three dots in a straight line on paper,
+the two intervening spaces being of equal extent, say about one or two
+inches long. If in one of the spaces a series of a dozen dots is placed,
+this space will appear longer than the empty space. However, if only one
+dot is placed in the middle of one of the empty spaces, this space now is
+likely to appear of less extent than the<span class="pagenum"><a name="Page_49" id="Page_49">[Pg 49]</a></span> empty space. (See <a href="#fig7">Fig. 7</a>.) A
+specific example of this type of illusion is shown in <a href="#fig6">Fig. 6</a>. The filled
+or divided space generally appears greater than the empty or undivided
+space, but certain qualifications of this statement are necessary. In <i>a</i>
+the divided space unquestionably appears greater than the empty space.
+Apparently the filled or empty space is more important than the amount of
+light which is received from the clear spaces, for a black line on white
+paper appears longer than a white space between two points separated a
+distance equal to the length of the black line. Furthermore, apparently
+the spacing which is the most obtrusive is most influential in causing the
+divided space to appear greater for <i>a</i> than for <i>b</i>. The illusion still
+persists in <i>c</i>.</p>
+
+<p><a name="fig6" id="fig6"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig6.jpg" alt="" /></div>
+<p class="center">Fig. 6.&mdash;The divided or filled space on the left appears longer than the equal space on the right.</p>
+<p>&nbsp;</p>
+
+<p>An idea of the magnitude may be gained from certain experiments by Aubert.
+He used a figure similar to <i>a</i> <a href="#fig6">Fig. 6</a> containing a total of five short
+lines.<span class="pagenum"><a name="Page_50" id="Page_50">[Pg 50]</a></span> Four of them were equally spaced over a distance of 100 mm.
+corresponding to the left half of <i>a</i>, <a href="#fig6">Fig. 6</a>. The remaining line was
+placed at the extreme right and defined the limit of an empty space also
+100 mm. long. In all cases, the length of the empty space appeared about
+ten per cent less than that of the space occupied by the four lines
+equally spaced. Various experimenters obtain different results, and it
+seems reasonable that the differences may be accounted for, partially at
+least, by different degrees of unconscious correction of the illusion.
+This emphasizes the desirability of using subjects for such experiments
+who have no knowledge pertaining to the illusion.</p>
+
+<p><a name="fig7" id="fig7"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig7.jpg" alt="" /></div>
+<p class="center">Fig. 7.&mdash;The three lines are of equal length.</p>
+<p><a name="fig8" id="fig8"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig8.jpg" alt="" /></div>
+<p class="center">Fig. 8.&mdash;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.</p>
+<p>&nbsp;</p>
+
+<p>As already stated there are apparent exceptions to any simple rule, for,
+as in the case of dots cited in a preceding paragraph, the illusion
+depends upon the manner in which the division is made. For example, in
+<a href="#fig7">Fig. 7</a>, <i>a</i> and <i>c</i> are as likely to appear shorter than <i>b</i> as equal to
+it. It has been concluded by certain investigators that when subdivision
+of a line causes it to appear longer, the parts into which it is divided
+or some of them are likely to appear shorter than isolated lines of the
+same length. The reverse of this statement also appears to hold. For
+example in<span class="pagenum"><a name="Page_51" id="Page_51">[Pg 51]</a></span> <a href="#fig7">Fig. 7</a>, <i>a</i> appears shorter than <i>b</i> and the central part
+appears lengthened, although the total line appears shortened. This
+illusion is intensified by leaving the central section blank. A figure of
+this sort can be readily drawn by the reader by using short straight lines
+in place of the circles in <a href="#fig8">Fig. 8</a>. In this figure the space between the
+inside edges of the two circles on the left appears larger than the
+overall distance between the outside edges of the two circles on the
+right, despite the fact that these distances are equal. It appears that
+mere intensity of retinal stimulation does not account for these
+illusions, but rather the figures which we see.</p>
+
+<p><a name="fig9" id="fig9"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig9.jpg" alt="" /></div>
+<p class="center">Fig. 9.&mdash;Three squares of equal dimensions which appear different in area and dimension.</p>
+<p>&nbsp;</p>
+
+<p>In <a href="#fig9">Fig. 9</a> the three squares are equal in dimensions but the different
+characters of the divisions cause them to appear not only unequal, but no
+longer squares. In <a href="#fig10">Fig. 10</a><span class="pagenum"><a name="Page_52" id="Page_52">[Pg 52]</a></span> the distance between the outside edges of the
+three circles arranged horizontally appears greater than the empty space
+between the upper circle and the left-hand circle of the group.</p>
+
+<p><a name="fig10" id="fig10"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig10.jpg" alt="" /></div>
+<p class="center">Fig. 10.&mdash;The vertical distance between the upper circle
+and the left-hand<br />one of the group is equal to the overall length of the group of three circles.</p>
+<p>&nbsp;</p>
+
+<p><i>Illusions of Contour.</i>&mdash;The illusions of this type, or exhibiting this
+influence, are quite numerous. In <a href="#fig11">Fig. 11</a> there are two semicircles, one
+closed by a diameter, the other unclosed. The latter appears somewhat
+flatter and of slightly greater radius than the closed one. Similarly in
+<a href="#fig12">Fig. 12</a> the shorter portion of the interrupted circumference of a circle
+appears flatter and of greater radius of curvature than the greater
+portions. In <a href="#fig13">Fig. 13</a> the length of the<span class="pagenum"><a name="Page_53" id="Page_53">[Pg 53]</a></span> middle space and of the open-sided
+squares are equal. In fact there are two uncompleted squares and an empty
+&#8220;square&#8221; between, the three of which are of equal dimensions. However the
+middle space appears slightly too high and narrow; the other two appear
+slightly too low and broad. These figures are related to the well-known
+M&uuml;ller-Lyer illusion illustrated in <a href="#fig56">Fig. 56</a>. Some of the illusions
+presented later will be seen to involve the influence of contour. Examples
+of these are <a href="#fig55">Figs. 55</a> and <a href="#fig60">60</a>. In the former, the horizontal base line
+appears to sag; in the latter, the areas appear unequal, but they are
+equal.</p>
+
+<p><a name="fig11" id="fig11"></a><a name="fig12" id="fig12"></a>&nbsp;</p>
+<table border="0" cellpadding="0" cellspacing="5" summary="table">
+<tr><td align="center"><img src="images/fig11.jpg" alt="" /></td><td><span class="spacer">&nbsp;</span></td>
+    <td align="center"><img src="images/fig12.jpg" alt="" /></td></tr>
+<tr><td align="center">Fig. 11.&mdash;Two equal semicircles.</td><td>&nbsp;</td>
+    <td align="center">Fig. 12.&mdash;Arcs of the same circle.</td></tr></table>
+
+<p><a name="fig13" id="fig13"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig13.jpg" alt="" /></div>
+<p class="center">Fig. 13.&mdash;Three incomplete but equal squares.</p>
+<p>&nbsp;</p>
+
+<p><i>Illusions of Contrast.</i>&mdash;Those illusions due to brightness contrast are
+not included in this group,<span class="pagenum"><a name="Page_54" id="Page_54">[Pg 54]</a></span> for &#8220;contrast&#8221; here refers to lines, angles
+and areas of different sizes. In general, parts adjacent to large extents
+appear smaller and those adjacent to small extents appear larger. A simple
+case is shown in <a href="#fig14">Fig. 14</a>, where the middle sections of the two lines are
+equal, but that of the shorter line appears longer than that of the longer
+line. In <a href="#fig15">Fig. 15</a> the two parts of the connecting line are equal, but they
+do not appear so. This illusion is not as positive as the preceding one
+and, in fact, the position of the short vertical dividing line may appear
+to fluctuate considerably.</p>
+
+<p><a name="fig14" id="fig14"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig14.jpg" alt="" /></div>
+<p class="center">Fig. 14.&mdash;Middle sections of the two lines are equal.</p>
+<p><a name="fig15" id="fig15"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig15.jpg" alt="" /></div>
+<p class="center">Fig. 15.&mdash;An effect of contrasting areas (Baldwin&#8217;s figure).</p>
+<p>&nbsp;</p>
+
+<p><a href="#fig16">Fig. 16</a> might be considered to be an illusion of contour, but the length
+of the top horizontal line of the lower figure being apparently less than
+that of the top line of the upper figure is due largely to contrasting the
+two figures. Incidentally, it is difficult to believe that the maximum
+horizontal width of the lower figure is as great as the maximum height of
+the figure. At this point it is of interest to refer to other contrast
+illusions such as <a href="#fig20">Figs. 20</a>, <a href="#fig57">57</a>, and <a href="#fig59">59</a>.</p>
+
+<p><a name="fig16" id="fig16"></a>&nbsp;<span class="pagenum"><a name="Page_55" id="Page_55">[Pg 55]</a></span></p>
+<div class="figcenter"><img src="images/fig16.jpg" alt="" /></div>
+<p class="center">Fig. 16.&mdash;An illusion of contrast.</p>
+<p>&nbsp;</p>
+
+<p>A striking illusion of contrast is shown in <a href="#fig17">Fig. 17</a>, where the central
+circles of the two figures are equal, although the one surrounded by the
+large circles appears much smaller than the other. Similarly, in <a href="#fig18">Fig. 18</a>
+the inner circles of <i>b</i> and <i>c</i> are equal but that of <i>b</i> appears the
+larger. The inner circle of <i>a</i> appears larger than the outer circle of
+<i>b</i>, despite their actual equality.</p>
+
+<p><a name="fig17" id="fig17"></a>&nbsp;<span class="pagenum"><a name="Page_56" id="Page_56">[Pg 56]</a></span></p>
+<div class="figcenter"><img src="images/fig17.jpg" alt="" /></div>
+<p class="center">Fig. 17.&mdash;Equal circles which appear unequal due to contrast (Ebbinghaus&#8217; figure).</p>
+<p><a name="fig18" id="fig18"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig18.jpg" alt="" /></div>
+<p class="center">Fig. 18.&mdash;Equal circles appearing unequal owing to contrasting concentric circles.</p>
+<p>&nbsp;</p>
+
+<p>In <a href="#fig19">Fig. 19</a> the circle nearer the apex of the angle appears larger than the
+other. This has been presented as one reason why the sun and moon appear
+larger at the horizon than when at higher altitudes. This explanation must
+be based upon the assumption that we interpret the &#8220;vault&#8221; of the sky to
+meet <span class="pagenum"><a name="Page_57" id="Page_57">[Pg 57]</a></span>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&#8217;s horizon. If there were one in reality, it would not be seen in
+profile.</p>
+
+<p><a name="fig19" id="fig19"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig19.jpg" alt="" /></div>
+<p class="center">Fig. 19.&mdash;Circles influenced by position within an angle.</p>
+<p><a name="fig20" id="fig20"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig20.jpg" alt="" /></div>
+<p class="center">Fig. 20.&mdash;Contrasting angles.</p>
+<p>&nbsp;</p>
+
+<p>If two angles of equal size are bounded by small and large angles
+respectively, the apex in each case being common to the inner and two
+bounding angles, the effect of contrast is very apparent, as seen in <a href="#fig20">Fig.
+20</a>. In <a href="#fig57">Fig. 57</a> are found examples of effects of lines contrasted as to
+length.</p>
+
+<p><a name="fig21" id="fig21"></a>&nbsp;<span class="pagenum"><a name="Page_58" id="Page_58">[Pg 58]</a></span></p>
+<div class="figcenter"><img src="images/fig21.jpg" alt="" /></div>
+<p class="center">Fig. 21.&mdash;Owing to perspective the right angles appear oblique and vice versa.</p>
+<p>&nbsp;</p>
+
+<p>The reader may readily construct an extensive variety of illusions of
+contrast; in fact, contrast plays a part in most geometrical-optical
+illusions. The contrasts may be between existing lines, areas, etc., or
+the imagination may supply some of them.</p>
+
+<p><a name="fig22" id="fig22"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig22.jpg" alt="" /></div>
+<p class="center">Fig. 22.&mdash;Two equal diagonals which appear unequal.</p>
+<p>&nbsp;</p>
+
+<p><i>Illusions of Perspective.</i>&mdash;As the complexity of figures is increased the
+number of possible illusions is multiplied. In perspective we have the
+influences of various factors such as lines, angles, and sometimes contour
+and contrast. In <a href="#fig21">Fig. 21</a> the <span class="pagenum"><a name="Page_59" id="Page_59">[Pg 59]</a></span>suggestion due to the perspective of the
+cube causes right angles to appear oblique and oblique angles to appear to
+be right angles. This figure is particularly illusive. It is interesting
+to note that even an after-image of a right-angle cross when projected
+upon a wall drawn in perspective in a painting will appear oblique.</p>
+
+<p><a name="fig23" id="fig23"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig23.jpg" alt="" /></div>
+<p class="center">Fig. 23.&mdash;Apparent variations in the distance between two parallel lines.</p>
+<p>&nbsp;</p>
+
+<p>A striking illusion involving perspective, or at least the influence of
+angles, is shown in <a href="#fig22">Fig. 22</a>. Here the diagonals of the two parallelograms
+are of equal length but the one on the right appears much smaller. That
+<i>AX</i> is equal in length to <i>AY</i> is readily demonstrated by describing a
+circle from the center <i>A</i> and with a radius equal to <i>AX</i>. It will be
+found to pass through the point <i>Y</i>. Obviously, geometry abounds in
+geometrical-optical illusions.</p>
+
+<p><a name="fig24" id="fig24"></a>&nbsp;<span class="pagenum"><a name="Page_60" id="Page_60">[Pg 60]</a></span></p>
+<div class="figcenter"><img src="images/fig24.jpg" alt="" /></div>
+<p class="center">Fig. 24.&mdash;A striking illusion of perspective.</p>
+<p>&nbsp;</p>
+
+<p>The effect of contrast is seen in <i>a</i> in <a href="#fig23">Fig. 23</a>; that is, the short
+parallel lines appear further apart than the pair of long ones. By adding
+the oblique lines at the ends of the lower pair in <i>b</i>, these parallel
+lines now appear further apart than the horizontal parallel lines of the
+small rectangle.</p>
+
+<p>The influence of perspective is particularly apparent in <a href="#fig24">Fig. 24</a>, where
+natural perspective lines are drawn to suggest a scene. The square columns
+are of the same size but the further one, for example, being apparently
+the most distant and of the same<span class="pagenum"><a name="Page_61" id="Page_61">[Pg 61]</a></span> physical dimensions, actually appears
+much larger. Here is a case where experience, allowing for a diminution of
+size with increasing distance, actually causes the column on the right to
+appear larger than it really is. The artist will find this illusion even
+more striking if he draws three human figures of the same size but
+similarly disposed in respect to perspective lines. Apparently converging
+lines influence these equal figures in proportion as they suggest
+perspective.</p>
+
+<p><a name="fig25" id="fig25"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig25.jpg" alt="" /></div>
+<p class="center">Fig. 25.&mdash;Distortion of a square due to superposed lines.</p>
+<p>&nbsp;</p>
+
+<p>Although they are not necessarily illusions of perspective, <a href="#fig25">Figs. 25</a> and
+<a href="#fig26">26</a> are presented here because they involve similar influences. In <a href="#fig25">Fig. 25</a>
+the hollow square is superposed upon groups of oblique lines so arranged
+as to apparently distort the square.<span class="pagenum"><a name="Page_62" id="Page_62">[Pg 62]</a></span> In <a href="#fig26">Fig. 26</a> distortions of the
+circumference of a circle are obtained in a similar manner.</p>
+
+<p><a name="fig26" id="fig26"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig26.jpg" alt="" /></div>
+<p class="center">Fig. 26.&mdash;Distortion of a circle due to superposed lines.</p>
+<p>&nbsp;</p>
+
+<p>It is interesting to note that we are not particularly conscious of
+perspective, but it is seen that it has been a factor in the development
+of our visual perception. In proof of this we might recall the first time
+as children we were asked to draw a railroad track trailing off in the
+distance. Doubtless, most of us drew two parallel lines instead of
+converging ones.<span class="pagenum"><a name="Page_63" id="Page_63">[Pg 63]</a></span> A person approaching us is not sensibly perceived to
+grow. He is more likely to be perceived all the time as of normal size.
+The finger held at some distance may more than cover the object such as a
+distant person, but the finger is not ordinarily perceived as larger than
+the person. Of course, when we think of it we are conscious of perspective
+and of the increase in size of an approaching object. When a locomotive or
+automobile approaches very rapidly, this &#8220;growth&#8221; is likely to be so
+striking as to be generally noticeable. The reader may find it of interest
+at this point to turn to illustrations in other chapters.</p>
+
+<p>The foregoing are a few geometrical illusions of representative types.
+These are not all the types of illusions by any means and they are only a
+few of an almost numberless host. These have been presented in a brief
+classification in order that the reader might not be overwhelmed by the
+apparent chaos. Various special and miscellaneous geometrical illusions
+are presented in later chapters.</p>
+
+
+<p>&nbsp;</p><p>&nbsp;</p>
+<hr style="width: 50%;" />
+<p><span class="pagenum"><a name="Page_64" id="Page_64">[Pg 64]</a></span></p>
+<h2><a name="V" id="V"></a>V<br />EQUIVOCAL FIGURES</h2>
+
+<p class="dropcap"><span class="caps">Many</span> figures apparently change in appearance owing to fluctuations in
+attention and in associations. A human profile in intaglio (<a href="#fig72">Figs. 72</a> and
+<a href="#fig73">73</a>) may appear as a bas-relief. Crease a card in the middle to form an
+angle and hold it at an arm&#8217;s length. When viewed with one eye it can be
+made to appear open in one way or the other; that is, the angle may be
+made to appear pointing toward the observer or away from him. The more
+distant part of an object may be made to appear nearer than the remaining
+part. Plane diagrams may seem to be solids. Deception of this character is
+quite easy if the light-source and other extraneous factors are concealed
+from the observer. It is very interesting to study these fluctuating
+figures and to note the various extraneous data which lead us to judge
+correctly. Furthermore, it becomes obvious that often we see what we
+expect to see. For example, we more commonly encounter relief than
+intaglio; therefore, we are likely to think that we are looking at the
+former.</p>
+
+<p>Proper consideration of the position of the dominant light-source and of
+the shadows will usually provide the data for a correct conclusion.
+However, habit and probability are factors whose influence is difficult to
+overcome. Our perception is strongly<span class="pagenum"><a name="Page_65" id="Page_65">[Pg 65]</a></span> associated with accustomed ways of
+seeing objects and when the object is once suggested it grasps our mind
+completely in its stereotyped form. Stairs, glasses, rings, cubes, and
+intaglios are among the objects commonly used to illustrate this type of
+illusion. In connection with this type, it is well to realize how
+tenaciously we cling to our perception of the real shapes of objects. For
+example, a cube thrown into the air in such a manner that it presents many
+aspects toward us is throughout its course a cube.</p>
+
+<p><a name="fig27" id="fig27"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig27.jpg" alt="" /></div>
+<p class="center">Fig. 27.&mdash;Illustrating fluctuation of attention.</p>
+<p>&nbsp;</p>
+
+<p>The figures which exhibit these illusions are obviously those which are
+capable of two or more spatial relations. The double interpretation is
+more readily accomplished by monocular than by binocular vision. <a href="#fig27">Fig. 27</a>
+consists of identical patterns in black and white. By gazing upon this
+steadily it will appear<span class="pagenum"><a name="Page_66" id="Page_66">[Pg 66]</a></span> to fluctuate in appearance from a white pattern
+upon a black background to a black pattern upon a white background.
+Sometimes fluctuation of attention apparently accounts for the change and,
+in fact, this can be tested by willfully altering the attention from a
+white pattern to a black one. Incidentally one investigator found that the
+maximum rate of fluctuation was approximately equal to the pulse rate,
+although no connection between the two was claimed. It has also been found
+that inversion is accompanied by a change in refraction of the eye.</p>
+
+<p><a name="fig28" id="fig28"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig28.jpg" alt="" /></div>
+<p class="center">Fig. 28.&mdash;The grouping of the circles fluctuates.</p>
+<p>&nbsp;</p>
+
+<p>Another example is shown in <a href="#fig28">Fig. 28</a>. This may appear to be white circles
+upon a black background or a black mesh upon a white background. However,
+the more striking phenomenon is the change in the grouping of the circles
+as attention fluctuates. We may be conscious of hollow diamonds of
+circles, one inside the other, and then suddenly the pattern may change to
+groups of diamonds consisting of four<span class="pagenum"><a name="Page_67" id="Page_67">[Pg 67]</a></span> circles each. Perhaps we may be
+momentarily conscious of individual circles; then the pattern may change
+to a hexagonal one, each &#8220;hexagon&#8221; consisting of seven circles&mdash;six
+surrounding a central one. The pattern also changes into parallel strings
+of circles, triangles, etc.</p>
+
+<p><a name="fig29" id="fig29"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig29.jpg" alt="" /></div>
+<p class="center">Fig. 29.&mdash;Crossed lines which may be interpreted in two ways.</p>
+<p>&nbsp;</p>
+
+<p>The crossed lines in <a href="#fig29">Fig. 29</a> can be seen as right angles in perspective
+with two different spatial arrangements of one or both lines. In fact
+there is quite a tendency to see such crossed lines as right angles in
+perspective. The two groups on the right represent a simplified Z&ouml;llner&#8217;s
+illusion (<a href="#fig37">Fig. 37</a>). The reader may find it interesting to spend some time
+viewing these figures and in exercising his ability to fluctuate his
+attention. In fact, he must call upon his imagination in these cases.
+Sometimes the<span class="pagenum"><a name="Page_68" id="Page_68">[Pg 68]</a></span> changes are rapid and easy to bring about. At other moments
+he will encounter an aggravating stubbornness. Occasionally there may
+appear a conflict of two appearances simultaneously in the same figure.
+The latter may be observed occasionally in <a href="#fig30">Fig. 30</a>. Eye-movements are
+brought forward by some to aid in explaining the changes.</p>
+
+<p><a name="fig30" id="fig30"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig30.jpg" alt="" /></div>
+<p class="center">Fig. 30.&mdash;Reversible cubes.</p>
+<p>&nbsp;</p>
+
+<p>In <a href="#fig30">Fig. 30</a> a reversal of the aspect of the individual cubes or of their
+perspective is very apparent. At rare moments the effect of perspective
+may be completely vanquished and the figure be made to appear as a plane
+crossed by strings of white diamonds and zigzag black strips.</p>
+
+<p><span class="pagenum"><a name="Page_69" id="Page_69">[Pg 69]</a></span>The illusion of the bent card or partially open book is seen in <a href="#fig31">Fig. 31</a>.
+The tetrahedron in <a href="#fig32">Fig. 32</a> may appear either as erect on its base or as
+leaning backward with its base seen from underneath.</p>
+
+<p><a name="fig31" id="fig31"></a><a name="fig32" id="fig32"></a>&nbsp;</p>
+<table border="0" cellpadding="0" cellspacing="5" summary="table">
+<tr><td align="center"><img src="images/fig31.jpg" alt="" /></td><td><span class="spacer">&nbsp;</span></td>
+    <td align="center"><img src="images/fig32.jpg" alt="" /></td></tr>
+<tr><td align="center">Fig. 31.&mdash;The reversible &#8220;open book&#8221; (after Mach).</td><td>&nbsp;</td>
+    <td align="center">Fig. 32.&mdash;A reversible tetrahedron.</td></tr></table>
+<p>&nbsp;</p>
+
+<p>The series of rings in <a href="#fig33">Fig. 33</a> may be imagined to form a tube such as a
+sheet-metal pipe with its axis lying in either of two directions.
+Sometimes by closing one eye the two changes in this type of illusion are
+more readily brought about. It is also interesting to close and open each
+eye alternately, at the same time trying to note just where the attention
+is fixed.</p>
+
+<p>The familiar staircase is represented in <a href="#fig34">Fig. 34</a>. It is likely to appear
+in its usual position and then<span class="pagenum"><a name="Page_70" id="Page_70">[Pg 70]</a></span> suddenly to invert. It may aid in bringing
+about the reversal to insist that one end of a step is first nearer than
+the other and then farther away. By focusing the attention in this manner
+the fluctuation becomes an easy matter to obtain.</p>
+
+<p><a name="fig33" id="fig33"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig33.jpg" alt="" /></div>
+<p class="center">33.&mdash;Reversible perspective of a group of rings or of a tube.</p>
+<p><a name="fig34" id="fig34"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig34.jpg" alt="" /></div>
+<p class="center">Fig. 34.&mdash;Schr&ouml;der&#8217;s reversible staircase.</p>
+<p>&nbsp;</p>
+
+<p>In <a href="#fig35">Fig. 35</a> is a similar example. First one part will appear solid and the
+other an empty corner, then suddenly both are reversed. However, it is
+striking to note one half changes while the other remains <span class="pagenum"><a name="Page_71" id="Page_71">[Pg 71]</a></span>unchanged, thus
+producing momentarily a rather peculiar figure consisting of two solids,
+for example, attached by necessarily warped surfaces.</p>
+
+<p><a name="fig35" id="fig35"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig35.jpg" alt="" /></div>
+<p class="center">Fig. 35.&mdash;Thi&eacute;ry&#8217;s figure.</p>
+<p>&nbsp;</p>
+
+<p>Perhaps the reader has often witnessed the striking illusion of some
+portraits which were made of subjects looking directly at the camera or
+painter. Regardless of the position of the observer the eyes of the
+portrait appear to be directed toward him. In fact, as the observer moves,
+the eyes in the picture follow him so relentlessly as to provoke even a
+feeling of uncanniness. This fact is accounted for by the absence of a
+third dimension, for a sculptured model of a head does not exhibit this
+feature. Perspective plays a part in some manner, but no attempt toward
+explanation will be made.</p>
+
+<p><span class="pagenum"><a name="Page_72" id="Page_72">[Pg 72]</a></span>In <a href="#fig36">Fig. 36</a> are two sketches of a face. One appears to be looking at the
+observer, but the other does not. If the reader will cover the lower parts
+of the two figures, leaving only the two pairs of eyes showing, both pairs
+will eventually appear to be looking at the observer. Perhaps the reader
+will be conscious of mental effort and the lapse of a few moments before
+the eyes on the left are made to appear to be looking directly at him.
+Although it is not claimed that this illusion is caused by the same
+conditions as those immediately preceding, it involves attention. At
+least, it is fluctuating in appearance and therefore is equivocal. It is
+interesting to note the influence of the other features (below the eyes).
+The perspective of these is a powerful influence in &#8220;directing&#8221; the eyes
+of the sketch.</p>
+
+<p>In the foregoing only definite illusions have been presented which are
+universally witnessed by normal persons. There are no hallucinatory phases
+in the conditions or causes. It is difficult to divide these with
+definiteness from certain illusions of depth as discussed in Chapter VII.
+The latter undoubtedly are sometimes entwined to some extent with
+hallucinatory phases; in fact, it is doubtful if they are not always
+hallucinations to some degree. Hallucinations are not of interest from the
+viewpoint of this book, but illusions of depth are treated because they
+are of interest. They are either hallucinations or are on the border-line
+between hallucinations and those illusions which are almost universally
+experienced by normal persons under similar conditions. The latter
+statement does not hold for illusions of depth in <span class="pagenum"><a name="Page_73" id="Page_73">[Pg 73]</a></span>which objects may be
+seen alternately near and far, large and small, etc., although they are
+not necessarily pure hallucinations as distinguished from the types of
+illusions regarding which there is general perceptual agreement.</p>
+
+<p><a name="fig36" id="fig36"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig36tmb.jpg" alt="" /><br />
+<a href="images/fig36.jpg"><small>Larger Image</small></a></div>
+<p class="center">Fig. 36.&mdash;Illustrating certain influences upon the apparent direction of vision.<br />
+By covering all but the eyes the latter appear to be drawn alike in both sketches.</p>
+<p>&nbsp;</p>
+
+<p><span class="pagenum"><a name="Page_74" id="Page_74">[Pg 74]</a></span>In explanation of the illusory phenomena pertaining to such geometrical
+figures as are discussed in the foregoing paragraphs, chiefly two
+different kinds of hypotheses have been offered. They are respectively
+psychological and physiological, although there is more or less of a
+mixture of the two in most attempts toward explanation. The psychological
+hypotheses introduce such factors as attention, imagination, judgment, and
+will. Hering and also Helmholtz claim that the kind of inversion which
+occurs is largely a matter of chance or of volition. The latter holds that
+the perception of perspective figures is influenced by imagination or the
+images of memory. That is, if one form of the figure is vividly imagined
+the perception of it is imminent. Helmholtz has stated that, &#8220;Glancing at
+a figure we observe spontaneously one or the other form of perspective and
+usually the one that is associated in our memory with the greatest number
+of images.&#8221;</p>
+
+<p>The physiological hypotheses depend largely upon such factors as
+accommodation and eye-movement. Necker held to the former as the chief
+cause. He has stated that the part of the figure whose image lies near the
+fovea is estimated as nearer than those portions in the peripheral regions
+of the visual field. This hypothesis is open to serious objections. Wundt
+contends that the inversion is caused by changes in the points and lines
+of fixation. He says, &#8220;The image<span class="pagenum"><a name="Page_75" id="Page_75">[Pg 75]</a></span> of the retina ought to have a determined
+position if a perspective illusion is to appear; but the form of this
+illusion is entirely dependent on motion and direction.&#8221; Some hypotheses
+interweave the known facts of the nervous system with psychological facts
+but some of these are examples of a common anomaly in theorization, for
+facts plus facts do not necessarily result in a correct theory. That is,
+two sets of facts interwoven do not necessarily yield an explanation which
+is correct.</p>
+
+
+<p>&nbsp;</p><p>&nbsp;</p>
+<hr style="width: 50%;" />
+<p><span class="pagenum"><a name="Page_76" id="Page_76">[Pg 76]</a></span></p>
+<h2><a name="VI" id="VI"></a>VI<br />THE INFLUENCE OF ANGLES</h2>
+
+<p class="dropcap"><span class="caps">As</span> previously stated, no satisfactory classification of visual illusions
+exists, but in order to cover the subject, divisions are necessary. For
+this reason the reader is introduced in this chapter to the effects
+attending the presence of angles. By no means does it follow that this
+group represents another type, for it really includes many illusions of
+several types. The reason for this grouping is that angles play an
+important part, directly or indirectly, in the production of illusions.
+For a long time many geometrical illusions were accounted for by
+&#8220;overestimation&#8221; or &#8220;underestimation&#8221; of angles, but this view has often
+been found to be inadequate. However, it cannot be denied that many
+illusions are due at least to the presence of angles.</p>
+
+<p>Apparently Z&ouml;llner was the first to describe an illusion which is
+illustrated in simple form in <a href="#fig29">Fig. 29</a> and more elaborately in <a href="#fig37">Figs. 37 to
+40</a>. The two figures at the right of <a href="#fig29">Fig. 29</a> were drawn for another purpose
+and are not designed favorably for the effect, although it may be detected
+when the figure is held at a distance. Z&ouml;llner accidentally noticed the
+illusion on a pattern designed for a print for dress-goods. The illusion
+is but slightly noticeable in <a href="#fig29">Fig. 29</a>, but by multiplying the number of
+lines (and angles) the long parallel lines appear to diverge in<span class="pagenum"><a name="Page_77" id="Page_77">[Pg 77]</a></span> the
+direction that the crossing lines converge. Z&ouml;llner studied the case
+thoroughly and established various facts. He found that the illusion is
+greatest when the long parallel lines are inclined about 45 degrees to the
+horizontal. This may be accomplished for <a href="#fig37">Fig. 37</a>, by turning the page
+(held in a vertical plane) through an angle of 45 degrees from normal. The
+illusion vanishes when held too far from the eye to distinguish the short
+crossing lines, and its strength varies with the inclination of the
+oblique lines to the main parallels. The most effective angle between the
+short crossing lines and the main parallels appears to be approximately 30
+degrees. In <a href="#fig37">Fig. 37</a> there are two illusions of direction. The parallel
+vertical strips appear unparallel and the right and left portions of the
+oblique cross-lines appear to be shifted vertically. It is interesting to
+note that steady fixation diminishes and even destroys the illusion.</p>
+
+<p><a name="fig37" id="fig37"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig37.jpg" alt="" /></div>
+<p class="center">Fig. 37.&mdash;Z&ouml;llner&#8217;s illusion of direction.</p>
+<p>&nbsp;</p>
+
+<p><span class="pagenum"><a name="Page_78" id="Page_78">[Pg 78]</a></span>The maximum effectiveness of the illusion, when the figure is held so that
+the main parallel lines are at an inclination of about 45 degrees to the
+horizontal was accounted for by Z&ouml;llner as the result of less visual
+experience in oblique directions. He insisted that it takes less time and
+is easier to infer divergence or convergence than parallelism. This
+explanation appears to be disproved by a figure in which slightly
+divergent lines are used instead of parallel ones. Owing to the effect of
+the oblique crossing lines, the diverging lines may be made to appear
+parallel. Furthermore it is difficult to attach much importance to
+Z&ouml;llner&#8217;s explanation because the illusion is visible under the extremely
+brief illumination provided by one electric spark. Of course, the duration
+of the physiological reaction is doubtless greater than that of the spark,
+but at best the time is very short. Hering explained the Z&ouml;llner illusion
+as due to the curvature of the retina, and the resulting difference in the
+retinal images, and held that acute angles appear relatively too large and
+obtuse ones too small. The latter has been found to have limitations in
+the explanation of certain illusions.</p>
+
+<p>This Z&ouml;llner illusion is very striking and may be constructed in a variety
+of forms. In <a href="#fig37">Fig. 37</a> the effect is quite apparent and it is interesting to
+view the figure at various angles. For example, hold the figure so that
+the broad parallel lines are vertical. The illusion is very pronounced in
+this position; however, on tilting the page backward the illusion finally
+disappears. In <a href="#fig38">Fig. 38</a> the short oblique lines do not cross the long
+parallel lines and to make the<span class="pagenum"><a name="Page_79" id="Page_79">[Pg 79]</a></span> illusion more striking, the obliquity of
+the short lines is reversed at the middle of the long parallel lines.
+Variations of this figure are presented in <a href="#fig39">Figs. 39</a> and <a href="#fig40">40</a>. In this case
+by steady fixation the perspective effect is increased but there is a
+tendency for the parallel lines to appear more nearly truly parallel than
+when the point of sight is permitted to roam over the figures.</p>
+
+<p><a name="fig38" id="fig38"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig38.jpg" alt="" /></div>
+<p class="center">Fig. 38.&mdash;Parallel lines which do not appear so.</p>
+<p><a name="fig39" id="fig39"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig39.jpg" alt="" /></div>
+<p class="center">Fig. 39.&mdash;Wundt&#8217;s illusion of direction.</p>
+<p><a name="fig40" id="fig40"></a>&nbsp;<span class="pagenum"><a name="Page_80" id="Page_80">[Pg 80]</a></span></p>
+<div class="figcenter"><img src="images/fig40.jpg" alt="" /></div>
+<p class="center">Fig. 40.&mdash;Hering&#8217;s illusion of direction.</p>
+<p>&nbsp;</p>
+
+<p>Many investigations of the Z&ouml;llner illusion are recorded in the
+literature. From these it is obvious that the result is due to the
+additive effects of many simple illusions of angle. In order to give an
+idea of the manner in which such an illusion may be built up the reasoning
+of Jastrow<a href="#reference"><small>[1]</small></a> will be presented in condensed form. When two straight lines
+such as <i>A</i> and <i>B</i> in <a href="#fig41">Fig. 41</a> are separated by a space it is usually
+possible to connect the two mentally and to determine whether or not, if
+connected, they would lie<span class="pagenum"><a name="Page_81" id="Page_81">[Pg 81]</a></span> on a straight line. However, if another line is
+connected to one, thus forming an angle as <i>C</i> does with <i>A</i>, the lines
+which appeared to be continuous (as <i>A</i> and <i>B</i> originally) no longer
+appear so. The converse is also true, for lines which are not in the same
+straight line may be made to appear to be by the addition of another line
+forming a proper angle. All these variations cannot be shown in a single
+figure, but the reader will find it interesting to draw them. Furthermore,
+the letters used on the diagram in order to make the description clearer
+may be confusing and these can be eliminated by redrawing the figure. In
+<a href="#fig41">Fig. 41</a> the obtuse angle <i>AC</i> tends to tilt <i>A</i> downward, so apparently if
+<i>A</i> were prolonged it would fall below <i>B</i>. Similarly, <i>C</i> appears to fall
+to the right of <i>D</i>.</p>
+
+<p><a name="fig41" id="fig41"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig41.jpg" alt="" /></div>
+<p class="center">Fig. 41.&mdash;Simple effect of angles.</p>
+<p>&nbsp;</p>
+
+<p>This illusion apparently is due to the presence of<span class="pagenum"><a name="Page_82" id="Page_82">[Pg 82]</a></span> the angle and the
+effect is produced by the presence of right and acute angles to a less
+degree. The illusion decreases or increases in general as the angle
+decreases or increases respectively.</p>
+
+<p>Although it is not safe to present simple statements in a field so complex
+as that of visual illusion where explanations are still controversial, it
+is perhaps possible to generalize as Jastrow did in the foregoing case as
+follows: If the direction of an angle is that of the line bisecting it and
+pointing toward the apex, the direction of the sides of an angle will
+apparently be deviated toward the direction of the angle. The deviation
+apparently is greater with obtuse than with acute angles, and when obtuse
+and acute angles are so placed in a figure as to give rise to opposite
+deviations, the greater angle will be the dominant influence.</p>
+
+<p>Although the illusion in such simple cases as <a href="#fig41">Fig. 41</a> is slight, it is
+quite noticeable. The effect of the addition of many of these slight
+individual influences is obvious in accompanying figures of greater
+complexity. These individual effects can be so multiplied and combined
+that many illusory figures may be devised.</p>
+
+<p>In <a href="#fig42">Fig. 42</a> the oblique lines are added to both horizontal lines in such a
+manner that <i>A</i> is tilted downward at the angle and <i>B</i> is tilted upward
+at the angle (the letters corresponding to similar lines in <a href="#fig41">Fig. 41</a>). In
+this manner they appear to be deviated considerably out of their true
+straight line. If the reader will draw a straight line nearly parallel to
+<i>D</i> in <a href="#fig41">Fig. 41</a> and to the right, he will find it helpful.<span class="pagenum"><a name="Page_83" id="Page_83">[Pg 83]</a></span> This line
+should be drawn to appear to be a continuation of <i>C</i> when the page is
+held so <i>D</i> is approximately horizontal. This is a simple and effective
+means of testing the magnitude of the illusion, for it is measured by the
+degree of apparent deviation between <i>D</i> and the line drawn adjacent to
+it, which the eye will tolerate. Another method of obtaining such a
+measurement is to begin with only the angle and to draw the apparent
+continuation of one of its lines with a space intervening. This deviation
+from the true continuation may then be readily determined.</p>
+
+<p><a name="fig42" id="fig42"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig42.jpg" alt="" /></div>
+<p class="center">Fig. 42. The effect of two angles in tilting the horizontal lines.</p>
+<p><a name="fig43" id="fig43"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig43.jpg" alt="" /></div>
+<p class="center">Fig. 43. The effect of crossed lines upon their respective apparent directions.</p>
+<p>&nbsp;</p>
+
+<p>A more complex case is found in <a href="#fig43">Fig. 43</a> where the effect of an obtuse
+angle <i>ACD</i> is to make the continuation<span class="pagenum"><a name="Page_84" id="Page_84">[Pg 84]</a></span> of <i>AB</i> apparently fall below
+<i>FG</i> and the effect of the acute angle is the reverse. However, the net
+result is that due to the preponderance of the effect of the larger angle
+over that of the smaller. The line <i>EC</i> adds nothing, for it merely
+introduces two angles which reinforce those above <i>AB</i>. The line <i>BC</i> may
+be omitted or covered without appreciably affecting the illusion.</p>
+
+<p><a name="fig44" id="fig44"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig44.jpg" alt="" /></div>
+<p class="center">Fig. 44.&mdash;Another step toward the Z&ouml;llner illusion.</p>
+<p>&nbsp;</p>
+
+<p>In <a href="#fig44">Fig. 44</a> two obtuse angles are arranged so that their effects are
+additive, with the result that the horizontal lines apparently deviate
+maximally for such a simple case. Thus it is seen that the tendency of the
+sides of an angle to be apparently deviated toward the direction of the
+angle may result in an apparent divergence from parallelism as well as in
+making continuous lines appear discontinuous. The illusion in <a href="#fig44">Fig. 44</a> may
+be strengthened by adding more lines parallel to the oblique lines. This
+is demonstrated in <a href="#fig38">Fig. 38</a> and in other illustrations. In this manner
+striking illusions are built up.</p>
+
+<p><a name="fig45" id="fig45"></a><a name="fig46" id="fig46"></a>&nbsp;<span class="pagenum"><a name="Page_85" id="Page_85">[Pg 85]</a></span></p>
+<table border="0" cellpadding="0" cellspacing="5" summary="table">
+<tr><td align="center"><img src="images/fig45.jpg" alt="" /></td><td><span class="spacer">&nbsp;</span></td>
+    <td align="center"><img src="images/fig46.jpg" alt="" /></td></tr>
+<tr><td align="center">Fig. 45.&mdash;The two diagonals would<br />meet on the left vertical line.</td><td>&nbsp;</td>
+    <td align="center">Fig. 46.&mdash;Poggendorff&#8217;s illusion.<br />Which oblique line on the right is the<br />prolongation of the oblique line on the left?</td></tr></table>
+<p>&nbsp;</p>
+
+<p>If oblique lines are extended across vertical ones, as in <a href="#fig45">Figs. 45</a> and <a href="#fig46">46</a>,
+the illusion is seen to be very striking. In <a href="#fig45">Fig. 45</a> the oblique line on
+the right if extended would meet the upper end of the oblique line on the
+left; however, the apparent point of intersection is somewhat lower than
+it is in reality. In <a href="#fig46">Fig. 46</a> the oblique line on the left is in the same
+straight line with the lower oblique line on the right. The line drawn
+parallel to the latter furnishes an idea of the extent of the illusion.
+This is the well-known Poggendorff illusion. The upper oblique line on the
+right actually appears to be approximately the continuation of the upper
+oblique line on the right. The explanation of this illusion on the simple
+basis of underestimation or overestimation of angles is open to criticism.
+If <a href="#fig46">Fig. 46</a> is held so that the intercepted line is horizontal or vertical,
+the illusion disappears or at least is greatly reduced. It is difficult to
+reconcile this disappearance of the illusion for certain positions of the
+figure with the theory that the illusion is due to an incorrect appraisal
+of the angles.</p>
+
+<p><a name="fig47" id="fig47"></a>&nbsp;<span class="pagenum"><a name="Page_86" id="Page_86">[Pg 86]</a></span></p>
+<div class="figcenter"><img src="images/fig47.jpg" alt="" /></div>
+<p class="center">Fig. 47.&mdash;A straight line appears to sag.</p>
+<p>&nbsp;</p>
+
+<p>According to Judd,<a href="#reference"><small>[2]</small></a> those portions of the parallels lying on the
+obtuse-angle side of the intercepted line will be overestimated when
+horizontal or vertical distances along the parallel lines are the subjects
+of attention, as they are in the usual positions of the Poggendorff
+figure. He holds further that the overestimation of this distance along
+the parallels (the two vertical lines) and the underestimation of the
+oblique distance across the interval are sufficient to provide a full
+explanation of the illusion. The disappearance and appearance of the
+illusion, as the position of the figure is varied appears to demonstrate
+the fact that lines produce illusions only when they have a direct
+influence on the direction in which the attention is turned. That is, when
+this Poggendorff figure is in such a position that the intercepted line is
+horizontal, the incorrect estimation of distance along the parallels has
+no direct bearing on the distance to which the attention is directed. In
+this case Judd holds that the entire influence of the parallels is
+absorbed in aiding the intercepted line in carrying the eye across the
+interval. For a detailed account the reader is referred to the original
+paper.</p>
+
+<p>Some other illusions are now presented to demonstrate further the effect
+of the presence of angles. Doubtless, in some of these, other causes
+contribute<span class="pagenum"><a name="Page_87" id="Page_87">[Pg 87]</a></span> more or less to the total result. In <a href="#fig47">Fig. 47</a> a series of
+concentric arcs of circles end in a straight line. The result is that the
+straight line appears to sag perceptibly. Incidentally, it may be
+interesting for the reader to ascertain whether or not there is any doubt
+in his mind as to the arcs appearing to belong to circles. To the author
+the arcs appear distorted from those of true circles.</p>
+
+<p><a name="fig48" id="fig48"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig48.jpg" alt="" /></div>
+<p class="center">Fig. 48.&mdash;Distortions of contour due to contact with other contours.</p>
+<p>&nbsp;</p>
+
+<p>In <a href="#fig48">Fig. 48</a> the bounding figure is a true circle but it appears to be
+distorted or dented inward where the angles of the hexagon meet it.
+Similarly, the sides of the hexagon appear to sag inward where the corners
+of the rectangle meet them.</p>
+
+<p>The influences which have been emphasized apparently are responsible for
+the illusions in <a href="#fig49">Figs. 49</a>, <a href="#fig50">50</a> and <a href="#fig51">51</a>. It is interesting to note the
+disappearance of the illusion, as the plane of <a href="#fig49">Fig. 49</a> is varied from<span class="pagenum"><a name="Page_88" id="Page_88">[Pg 88]</a></span>
+vertical toward the horizontal. That is, it is very apparent when viewed
+perpendicularly to the plane of the page, the latter being held
+vertically, but as the page is tilted backward the illusion decreases and
+finally disappears.</p>
+
+<p><a name="fig49" id="fig49"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig49.jpg" alt="" /></div>
+<p class="center">Fig. 49.&mdash;An illusion of direction.</p>
+<p><a name="fig50" id="fig50"></a>&nbsp;<span class="pagenum"><a name="Page_89" id="Page_89">[Pg 89]</a></span></p>
+<div class="figcenter"><img src="images/fig50.jpg" alt="" /></div>
+<p class="center">Fig. 50.&mdash;&#8220;Twisted-cord&#8221; illusion. These are straight cords.</p>
+<p><a name="fig51" id="fig51"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig51.jpg" alt="" /></div>
+<p class="center">Fig. 51.&mdash;&#8220;Twisted-cord&#8221; illusion. These are concentric circles.</p>
+<p>&nbsp;</p>
+
+<p>The illusions in <a href="#fig50">Figs. 50</a> and <a href="#fig51">51</a> are commonly termed &#8220;twisted cord&#8221;
+effects. A cord may be made by twisting two strands which are white and
+black (or any dark color) respectively. This may be superposed upon
+various backgrounds with striking results. In <a href="#fig50">Fig. 50</a> the straight &#8220;cords&#8221;
+appear bent in the middle, owing to a reversal of the &#8220;twist.&#8221; Such a
+figure may be easily made by using cord and a checkered cloth. In <a href="#fig51">Fig. 51</a>
+it is difficult to convince the intellect that the &#8220;cords&#8221; are not
+arranged in the form of concentric circles, but this becomes evident when
+one of them is traced out. The influence<span class="pagenum"><a name="Page_90" id="Page_90">[Pg 90]</a></span> of the illusion is so powerful
+that it is even difficult to follow one of the circles with the point of a
+pencil around its entire circumference. The cord appears to form a spiral
+or a helix seen in perspective.</p>
+
+<p><a name="fig52" id="fig52"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig52.jpg" alt="" /></div>
+<p class="center">Fig. 52.&mdash;A spiral when rotated appears to expand or contract, depending upon direction of rotation.</p>
+<p>&nbsp;</p>
+
+<p>A striking illusion is obtained by revolving the spiral shown in <a href="#fig52">Fig. 52</a>
+about its center. This may be considered as an effect of angles because
+the curvature and consequently the angle of the spiral is continually
+changing. There is a peculiar movement or progression toward the center
+when revolved in one direction. When the direction of rotation is reversed
+the movement is toward the exterior of the figure; that is, there is a
+seeming expansion.</p>
+
+<p>Angles appear to modify our judgments of the length of lines as well as of
+their direction. Of course, it must be admitted that some of these
+illusions might be classified under those of &#8220;contrast&#8221; and others. In
+fact, it has been stated that classification is difficult but it appears
+logical to discuss the effect of angles<span class="pagenum"><a name="Page_91" id="Page_91">[Pg 91]</a></span> in this chapter apart from the
+divisions presented in the preceding chapters. This decision was reached
+because the effect of angles could be seen in many of the illusions which
+would more logically be grouped under the classification presented in the
+preceding chapters.</p>
+
+<p><a name="fig53" id="fig53"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig53.jpg" alt="" /></div>
+<p class="center">Fig. 53.&mdash;Angles affect the apparent length of lines.</p>
+<p>&nbsp;</p>
+
+<p>In <a href="#fig53">Fig. 53</a> the three horizontal lines are of equal length but they appear
+unequal. This must be due primarily to the size of the angles made by the
+lines at the ends. Within certain limits, the greater the angle the
+greater is the apparent elongation of the central horizontal portion. This
+generalization appears to apply even when the angle is less than a right
+angle, although there appears to be less strength to the illusions with
+these smaller angles than with the larger angles. Other factors which
+contribute to the extent of the illusion are the positions of the figures,
+the distance between them, and the juxtaposition of certain lines. The
+illusion still exists if the horizontal lines are removed and also if the
+figures<span class="pagenum"><a name="Page_92" id="Page_92">[Pg 92]</a></span> are cut out of paper after joining the lower ends of the short
+lines in each case.</p>
+
+<p><a name="fig54" id="fig54"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig54.jpg" alt="" /></div>
+<p class="center">Fig. 54.&mdash;The horizontal line appears to tilt downward toward the ends.</p>
+<p><a name="fig55" id="fig55"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig55.jpg" alt="" /></div>
+<p class="center">Fig. 55.&mdash;The horizontal line appears to sag in the middle.</p>
+<p>&nbsp;</p>
+
+<p>In <a href="#fig54">Fig. 54</a> the horizontal straight line appears to consist of two lines
+tilting slightly upward toward the center. This will be seen to be in
+agreement with the general proposition that the sides of an angle are
+deviated in the direction of the angle. In this case it should be noted
+that one of the obtuse angles to be considered is <i>ABC</i> and that the
+effect of this is to tilt the line <i>BD</i> downward from the center. In <a href="#fig55">Fig.
+55</a> the horizontal line appears to tilt upward toward its extremities or to
+sag in the middle. The explanation in order to harmonize with the
+foregoing must be based upon the assumption that our judgments may be
+influenced by things not present but imagined. In this case only one side
+of each obtuse angle is present, the other side being formed by continuing
+the horizontal line both ways by means of the imagination. That we do this
+unconsciously is attested to by many experiences. For example, we often
+find ourselves imagining a horizontal, a vertical, or a center upon which
+to base a pending judgment.</p>
+
+<p><span class="pagenum"><a name="Page_93" id="Page_93">[Pg 93]</a></span>A discussion of the influence of angles must include a reference to the
+well-known M&uuml;ller-Lyer illusion presented in <a href="#fig56">Fig. 56</a>. It is obvious in <i>a</i>
+that the horizontal part on the left appears considerably longer than that
+part in the right half of the diagram. The influence of angles in this
+illusion can be easily tested by varying the direction of the lines at the
+ends of the two portions.</p>
+
+<p><a name="fig56" id="fig56"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig56.jpg" alt="" /></div>
+<p class="center">Fig. 56.&mdash;The M&uuml;ller-Lyer illusion.</p>
+<p>&nbsp;</p>
+
+<p>In all these figures the influence of angles is obvious. This does not
+mean that they are always solely or even primarily responsible for the
+illusion. In fact, the illusion of Poggendorff (<a href="#fig46">Fig. 46</a>) may be due to the
+incorrect estimation of certain linear distances, but the angles make this
+erroneous judgment possible, or at least contribute toward it. Many
+discussions of the theories or explanations of these figures are available
+in scientific literature of which one by Judd<a href="#reference"><small>[2]</small></a> may be taken as
+representative. He holds that the false estimation of angles in the
+Poggendorff figure is merely a secondary effect, not always<span class="pagenum"><a name="Page_94" id="Page_94">[Pg 94]</a></span> present, and
+in no case the source of the illusion; furthermore, that the illusion may
+be explained as due to the incorrect linear distances, and may be reduced
+to the type of illusion found in the M&uuml;ller-Lyer figure. Certainly there
+are grave dangers in explaining an illusion on the basis of an apparently
+simple operation.</p>
+
+<p>In <a href="#fig56">Fig. 56</a>, <i>b</i> is made up of the two parts of the M&uuml;ller-Lyer illusion. A
+small dot may be placed equally distant from the inside extremities of the
+horizontal lines. It is interesting to note that overestimation of
+distance within the figure is accompanied with underestimation outside the
+figure and, conversely, overestimation within the figure is accompanied by
+underestimation in the neighboring space. If the small dot is objected to
+as providing an additional M&uuml;ller-Lyer figure of the empty space, this dot
+may be omitted. As a substitute an observer may try to locate a point
+midway between the inside extremities of the horizontal lines. The error
+in locating this point will show that the illusion is present in this
+empty space.</p>
+
+<p>In this connection it is interesting to note some other illusions. In <a href="#fig57">Fig.
+57</a> the influence of several factors are evident. Two obviously important
+ones are (1) the angles made by the short lines at the extremities of the
+exterior lines parallel to the sides of the large triangle, and (2) the
+influence of contrast of the pairs of adjacent parallel lines. The effect
+shown in <a href="#fig53">Fig. 53</a> is seen to be augmented by the addition of contrast of
+adjacent lines of unequal length.</p>
+
+<p>An interesting variation of the effect of the presence<span class="pagenum"><a name="Page_95" id="Page_95">[Pg 95]</a></span> of angles is seen
+in <a href="#fig58">Fig. 58</a>. The two lines forming angles with the horizontal are of equal
+length but due to their relative positions, they do not appear so. It
+would be quite misleading to say that this illusion is merely due to
+angles. Obviously, it is due to the presence of the two oblique lines. It
+is of interest to turn to <a href="#fig25">Figs. 25</a>, <a href="#fig26">26</a> and various illusions of
+perspective.</p>
+
+<p><a name="fig57" id="fig57"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig57.jpg" alt="" /></div>
+<p class="center">Fig. 57.&mdash;Combined influence of angles and contrasting lengths.</p>
+<p><a name="fig58" id="fig58"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig58.jpg" alt="" /></div>
+<p class="center">Fig. 58.&mdash;Two equal oblique lines appear unequal because of their different positions.</p>
+<p>&nbsp;</p>
+
+<p>At this point a digression appears to be necessary and, therefore, <a href="#fig59">Fig. 59</a>
+is introduced. Here the areas of the two figures are equal. The judgment
+of area is likely to be influenced by juxtaposed lines and therefore, as
+in this case, the lower appears larger than the<span class="pagenum"><a name="Page_96" id="Page_96">[Pg 96]</a></span> upper one. Similarly two
+trapezoids of equal dimensions and areas may be constructed. If each is
+constructed so that it rests upon its longer parallel and one figure is
+above the other and only slightly separated, the mind is tempted to be
+influenced by comparing the juxtaposed base of the upper with the top of
+the lower trapezoid. The former dimension being greater than the latter,
+the lower figure appears smaller than the upper one. Angles must
+necessarily play a part in these illusions, although it is admitted that
+other factors may be prominent or even dominant.</p>
+
+<p><a name="fig59" id="fig59"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig59.jpg" alt="" /></div>
+<p class="center">Fig. 59.&mdash;An illusion of area.</p>
+<p>&nbsp;</p>
+
+<p>This appears to be a convenient place to insert an illusion of area based,
+doubtless, upon form, but angles must play a part in the illusions; at
+least they<span class="pagenum"><a name="Page_97" id="Page_97">[Pg 97]</a></span> are responsible for the form. In <a href="#fig60">Fig. 60</a> the five figures are
+constructed so as to be approximately equal in area. However, they appear
+unequal in this respect. In comparing areas, we cannot escape the
+influence of the length and directions of lines which bound these areas,
+and also, the effect of contrasts in lengths and directions. Angles play a
+part in all these, although very indirectly in some cases.</p>
+
+<p><a name="fig60" id="fig60"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig60.jpg" alt="" /></div>
+<p class="center">Fig. 60.&mdash;Five equal areas showing the influence of angles and contrasting lengths.</p>
+<p>&nbsp;</p>
+
+<p>To some extent the foregoing is a digression from the main intent of this
+chapter, but it appears worth while to introduce these indirect effects of
+the presence of angles (real or imaginary) in order to emphasize the
+complexity of influences and their subtleness. Direction is in the last
+analysis an effect of angle; that is, the direction of a line is measured
+by the angle it makes with some reference line, the latter being real or
+imaginary. In <a href="#fig61">Fig. 61</a>, the effect of diverting or directing attention by
+some subtle force, such as suggestion, is demonstrated. This &#8220;force&#8221;
+appears to contract or expand an area. The circle on the left appears
+smaller than the other. Of course there is the effect of empty space
+compared with partially filled space, but this cannot be avoided in<span class="pagenum"><a name="Page_98" id="Page_98">[Pg 98]</a></span> this
+case. However, it can be shown that the suggestions produced by the arrows
+tend to produce apparent reduction or expansion of areas. Note the use of
+arrows in advertisements.</p>
+
+<p><a name="fig61" id="fig61"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig61.jpg" alt="" /></div>
+<p class="center">Fig. 61.&mdash;Showing the effect of directing the attention.</p>
+<p>&nbsp;</p>
+
+<p>Although theory is subordinated to facts in this book, a glimpse here and
+there should be interesting and helpful. After having been introduced to
+various types and influences, perhaps the reader may better grasp the
+trend of theories. The perspective theory assumes, and correctly so, that
+simple diagrams often suggest objects in three dimensions, and that the
+introduction of an imaginary third dimension effects changes in the
+appearance of lines and angles. That is, lengths and directions of lines
+are apparently altered by the influence of lines and angles, which do not
+actually exist. That this is true may be proved in various cases. In fact
+the reader has doubtless<span class="pagenum"><a name="Page_99" id="Page_99">[Pg 99]</a></span> been convinced of this in connection with some
+of the illusions already discussed. Vertical lines often represent lines
+extending away from the observer, who sees them foreshortened and
+therefore they may seem longer than horizontal lines of equal length,
+which are not subject to foreshortening. This could explain such illusions
+as seen in <a href="#fig4">Figs. 4</a> and <a href="#fig5">5</a>. However this theory is not as easily applied to
+many illusions.</p>
+
+<p>According to Thi&eacute;ry&#8217;s perspective theory a line that appears nearer is
+seen as smaller and a line that seems to be further away is perceived as
+longer. If the left portion of <i>b</i>, <a href="#fig56">Fig. 56</a>, be reproduced with longer
+oblique lines at the ends but with the same length of horizontal lines, it
+will appear closer and the horizontal lines will be judged as shorter. The
+reader will find it interesting to draw a number of these portions of the
+M&uuml;ller-Lyer figure with the horizontal line in each case of the same
+length but with longer and longer obliques at the ends.</p>
+
+<p>The dynamic theory of Lipps gives an important role to the inner activity
+of the observer, which is not necessarily separated from the objects
+viewed, but may be felt as being in the objects. That is, in viewing a
+figure the observer unconsciously separates it from surrounding space and
+therefore creates something definite in the latter, as a limiting
+activity. These two things, one real (the object) and one imaginary, are
+balanced against each other. A vertical line may suggest a necessary
+resistance against gravitational force, with the result that the line
+appears longer than a horizontal one resting in peace.<span class="pagenum"><a name="Page_100" id="Page_100">[Pg 100]</a></span> The difficulty
+with this theory is that it allows too much opportunity for purely
+philosophical explanations, which are likely to run to the fanciful. It
+has the doubtful advantage of being able to explain illusions equally well
+if they are actually reversed from what they are. For example, gravity
+could either contract or elongate the vertical line, depending upon the
+choice of viewpoint.</p>
+
+<p>The confusion theory depends upon attention and begins with the difficulty
+of isolating from illusory figures the portions to be judged. Amid the
+complexity of the figure the attention cannot easily be fixed on the
+portions to be judged. This results in confusion. For example, if areas of
+different shapes such as those in <a href="#fig60">Fig. 60</a> are to be compared, it is
+difficult to become oblivious of form or of compactness. In trying to see
+the two chief parallel lines in <a href="#fig38">Fig. 38</a>, in their true parallelism the
+attention is being subjected to diversion, by the short oblique parallels
+with a compromising result. Surely this theory explains some illusions
+successfully, but it is not so successful with some of the illusions of
+contrast. The fact that practice in making judgments in such cases as
+<a href="#fig45">Figs. 45</a> and <a href="#fig56">56</a> reduces the illusion even to ultimate disappearance,
+argues in favor of the confusion theory. Perhaps the observer devotes
+himself more or less consciously to isolating the particular feature to be
+judged and finally attains the ability to do so. According to Auerbach&#8217;s
+indirect-vision theory the eyes in judging the two halves of the
+horizontal line in <i>a</i>, <a href="#fig56">Fig. 56</a>, involuntarily draw imaginary lines
+parallel to this line but above or below it. Obviously<span class="pagenum"><a name="Page_101" id="Page_101">[Pg 101]</a></span> the two parts of
+such lines are unequal in the same manner as the horizontal line in the
+M&uuml;ller-Lyer figure appears divided into two unequal parts.</p>
+
+<p>Somewhat analogous to this in some cases is Brunot&#8217;s mean-distance theory.
+According to this we establish &#8220;centers of gravity&#8221; in figures and these
+influence our judgments.</p>
+
+<p>These are glimpses of certain trends of theories. None is a complete
+success or failure. Each explains some illusions satisfactorily, but not
+necessarily exclusively. For the present, we will be content with these
+glimpses of the purely theoretical aspects of visual illusions.</p>
+
+
+<p>&nbsp;</p><p>&nbsp;</p>
+<hr style="width: 50%;" />
+<p><span class="pagenum"><a name="Page_102" id="Page_102">[Pg 102]</a></span></p>
+<h2><a name="VII" id="VII"></a>VII<br />ILLUSIONS OF DEPTH AND OF DISTANCE</h2>
+
+<p class="dropcap"><span class="caps">Besides</span> the so-called geometrical illusions discussed in the preceding
+chapters, there is an interesting group in which the perception of the
+third dimension is in error. When any of the ordinary criteria of relief
+or of distance are apparently modified, illusions of this kind are
+possible. There are many illusions of this sort, such as the looming of
+objects in a fog; the apparent enlargement of the sun and moon near the
+horizon; the flattening of the &#8220;vault&#8221; of the sky; the intaglio seen as
+relief; the alteration of relief with lighting; and various changes in the
+landscape when regarded with the head inverted.</p>
+
+<p>Although some of the criteria for the perception of depth or of distance
+have already been pointed out, especially in Chapter III, these will be
+mentioned again. Distance or depth is indicated by the distribution of
+light and shade, and an unusual object like an intaglio is likely to be
+mistaken for relief which is more common. An analysis of the lighting will
+usually reveal the real form of the object. (See <a href="#fig70">Figs. 70</a>, <a href="#fig71">71</a>, <a href="#fig72">72</a>,
+<a href="#fig73">73</a>, <a href="#fig76">76</a> and <a href="#fig77">77</a>.) In this connection it is interesting to compare photographic
+negatives with their corresponding positive prints.</p>
+
+<p>Distance is often estimated by the definition and color of objects seen
+through great depths of<span class="pagenum"><a name="Page_103" id="Page_103">[Pg 103]</a></span> air (aerial perspective). These distant objects
+are &#8220;blurred&#8221; by the irregular refraction of the light-rays through
+non-homogeneous atmosphere. They are obscured to some degree by the veil
+of brightness due to the illuminated dust, smoke, etc., in the atmosphere.
+They are also tinted (apparently) by the superposition of a tinted
+atmosphere. Thus we have &#8220;dim distance,&#8221; &#8220;blue peaks,&#8221; &#8220;azure depths of
+sky,&#8221; etc., represented in photographs, paintings, and writings.
+Incidentally, the sky above is blue for the same general reasons that the
+atmosphere, intervening between the observer and a distant horizon, is
+bluish. The ludicrous errors made in estimating distances in such regions
+as the Rockies is usually accounted for by the rare clearness and
+homogeneity of the atmosphere. However, is the latter a full explanation?
+To some extent we judge unknown size by estimated distance, and unknown
+distance by estimated size. When a person is viewing a great mountain peak
+for the first time, is he not likely to assume it to be comparable in size
+to the hills with which he has been familiar? Even by allowing
+considerable, is he not likely to greatly underestimate the size of the
+mountain and, as a direct consequence, to underestimate the distance
+proportionately? This incorrect judgment would naturally be facilitated by
+the absence of &#8220;dimness&#8221; and &#8220;blueness&#8221; due to the atmospheric haze.</p>
+
+<p>Angular perspective, which apparently varies the forms of angles and
+produces the divergence of lines, contributes much information in regard
+to relative and absolute distances from the eye of the various<span class="pagenum"><a name="Page_104" id="Page_104">[Pg 104]</a></span> objects or
+the parts of an object. For example, a rectangle may appear as a rhomboid.
+It is obvious that certain data pertaining to the objects viewed must be
+assumed, and if the assumptions are incorrect, illusions will result.
+These judgments also involve, as most judgments do, other data external to
+the objects viewed. Perhaps these incorrect judgments are delusions rather
+than illusions, because visual perception has been deluded by
+misinformation supplied by the intellect.</p>
+
+<p>Size or linear perspective is a factor in the perception of depth or of
+distance. As has been stated, if we know the size experience determines
+the distance; and conversely, if we know the distance we may estimate the
+size. Obviously estimates are involved and these when incorrect lead to
+false perception or interpretation.</p>
+
+<p>As an object approaches, the axes of the eyes converge more and more and
+the eye-lens must be thickened more and more to keep the object in focus.
+As stated in Chapter III, we have learned to interpret these accompanying
+sensations of muscular adjustment. This may be demonstrated by holding an
+object at an arm&#8217;s length and then bringing it rapidly toward the eyes,
+keeping it in focus all the time. The sensations of convergence and
+accommodation are quite intense.</p>
+
+<p>The two eyes look at a scene from two different points of view
+respectively and their images do not perfectly agree, as has been shown in
+<a href="#fig2">Figs. 2</a> and <a href="#fig3">3</a>. This binocular disparity is responsible to some degree for
+the perception of depth, as the stereoscope has<span class="pagenum"><a name="Page_105" id="Page_105">[Pg 105]</a></span> demonstrated. If two
+spheres of the same size are suspended on invisible strings, one at six
+feet, the other at seven feet away, one eye sees the two balls in the same
+plane, but one appears larger than the other. With binocular vision the
+balls appear at different distances, but judgment appraises them as of
+approximately equal size. At that distance the focal adjustment is not
+much different for both balls, so that the muscular movement, due to
+focusing the eye, plays a small part in the estimation of the relative
+distance. Binocular disparity and convergence are the primary factors.</p>
+
+<p>Some have held that the perception of depth, that is, of a relative
+distance, arises from the process of unconsciously running the point of
+sight back and forth. However, this view, unmodified, appears untenable
+when it is considered that a scene illuminated by a lightning flash (of
+the order of magnitude of a thousandth of a second) is seen even in this
+brief moment to have depth. Objects are seen in relief, in actual relation
+as to distance and in normal perspective, even under the extremely brief
+illumination of an electric spark (of the order of magnitude of one
+twenty-thousandth of a second). This can also be demonstrated by viewing
+stereoscopic pictures with a stereoscope, the illumination being furnished
+by an electric spark. Under these circumstances relief and perspective are
+quite satisfactory. Surely in these brief intervals the point of sight
+cannot do much surveying of a scene.</p>
+
+<p>Parallax aids in the perception of depth or distance. If the head be moved
+laterally the view or<span class="pagenum"><a name="Page_106" id="Page_106">[Pg 106]</a></span> scene changes slightly. Objects or portions of
+objects previously hidden by others may now become visible. Objects at
+various distances appear to move nearer or further apart. We have come to
+interpret these apparent movements of objects in a scene in terms of
+relative distances; that is, the relative amount of parallactic
+displacement is a measure of the relative distances of the objects.</p>
+
+<p>The relative distances or depth locations of different parts of an object
+can be perceived as fluctuating or even reversing. This is due to
+fluctuations in attention, and illusions of reversible perspective are of
+this class. It is quite impossible for one to fix his attention in perfect
+continuity upon any object. There are many involuntary eye-movements which
+cannot be overcome and under normal conditions certain details are likely
+to occupy the focus of attention alternately or successively. This applies
+equally well to the auditory sense and perhaps to the other senses.
+Emotional coloring has much to do with the fixation of attention; that
+which we admire, desire, love, hate, etc., is likely to dwell more in the
+focus of attention than that which stirs our emotions less.</p>
+
+<p>A slight suggestion of forward and backward movements can be produced by
+successively intercepting the vision of one eye by an opaque card or other
+convenient object. It has been suggested that the illusion is due to the
+consequent variations in the tension of convergence. Third dimensional
+movements may be produced for binocular or monocular vision during
+eye-closure. They are also produced by opening the eyes as widely as
+possible, by pressure on<span class="pagenum"><a name="Page_107" id="Page_107">[Pg 107]</a></span> the eye-balls, and by stressing the eyelids.
+However, these are not important and are merely mentioned in passing.</p>
+
+<p>An increase in the brightness of an object is accompanied by an apparent
+movement toward the observer, and conversely a decrease in brightness
+produces an apparent movement in the opposite direction. These effects may
+be witnessed upon viewing the glowing end of a cigar which is being smoked
+by some one a few yards away in the darkness. Rapidly moving thin clouds
+may produce such an effect by varying the brightness of the moon. Some
+peculiar impressions of this nature may be felt while watching the
+flashing light of some light-houses or of other signaling stations. It has
+been suggested that we naturally appraise brighter objects as nearer than
+objects less bright. However, is it not interesting to attribute the
+apparent movement to irradiation? (See Chapter VIII.) A bright object
+appears larger than a dark object of the same size and at the same
+distance. When the same object varies in brightness it remains in
+consciousness the same object and therefore of constant size; however, the
+apparent increase in size as it becomes brighter must be accounted for in
+some manner and there is only one way open. It must be attributed a lesser
+distance than formerly and therefore the sudden increase in brightness
+mediates a consciousness of a movement forward, that is, toward the
+observer.</p>
+
+<p>If two similar objects, such as the points of a compass, are viewed
+binocularly and their lateral distance apart is altered, the observer is
+conscious of<span class="pagenum"><a name="Page_108" id="Page_108">[Pg 108]</a></span> a third dimensional movement. Inasmuch as the accommodation
+is unaltered but convergence must be varied as the lateral distance
+between the two, the explanation of the illusion must consider the latter.
+The pair of compass-points are very convenient for making a demonstration
+of this pronounced illusion. The relation of size and distance easily
+accounts for the illusion.</p>
+
+<p>Obviously this type of illusion cannot be illustrated effectively by means
+of diagrams, so the reader must be content to watch for them himself. Some
+persons are able voluntarily to produce illusory movements in the third
+dimension, but such persons are rare. Many persons have experienced
+involuntary illusions of depth. Carr found, in a series of classes
+comprising 350 students, 58 persons who had experienced involuntary depth
+illusions at some time in their lives. Five of these also possessed
+complete voluntary control over the phenomenon. The circumstances
+attending visual illusions of depth are not the same for various cases,
+and the illusions vary widely in their features.</p>
+
+<p>Like other phases of the subject, this has been treated in many papers,
+but of these only one will be specifically mentioned, for it will suffice.
+Carr<a href="#reference"><small>[3]</small></a> has studied this type of illusion comparatively recently and
+apparently quite generally, and his work will be drawn upon for examples
+of this type. Apparently they may be divided into four classes: (1) Those
+of pure distance; that is, an object may appear to be located at varying
+distances from the observer, but no movement is perceived. For example, a
+person<span class="pagenum"><a name="Page_109" id="Page_109">[Pg 109]</a></span> might be seen first at the true distance; he might be seen next
+very close in front of the eyes; then he might suddenly appear to be quite
+remote; (2) illusions of pure motion; that is, objects are perceived as
+moving in a certain direction without any apparent change in location. In
+other words, they appear to move, but they do not appear to traverse
+space; (3) illusions of movement which include a change in location. This
+appears to be the most common illusion of depth; (4) those including a
+combination of the first and third classes. For example, the object might
+first appear to move away from its true location and is perceived at some
+remote place. Shortly it may appear in its true original position, but
+this change in location does not involve any sense of motion.</p>
+
+<p>These peculiar illusions of depth are not as generally experienced as
+those described in preceding chapters. A geometrical illusion, especially
+if it is pronounced, is likely to be perceived quite universally, but
+these illusions of depth are either more difficult to notice or more
+dependent upon psychological peculiarities far from universal among
+people. It is interesting to note the percentages computed from Carr&#8217;s
+statistics obtained upon interrogating 350 students. Of these, 17 per cent
+had experienced depth-illusions and between one and two per cent had
+voluntary control of the phenomenon. Of the 48 who had experienced
+illusions of this type and were able to submit detailed descriptions, 25
+per cent belonged to class (1) of those described in the preceding
+paragraph; 4 per cent to class (2); 52 per cent to class (3); and 17 per
+cent to class (4).</p>
+
+<p><span class="pagenum"><a name="Page_110" id="Page_110">[Pg 110]</a></span>Usually the illusion involves all objects in the visual field but with
+some subjects the field is contracted or the objects in the periphery of
+the field are unaffected. For most persons these illusions involve normal
+perceptual objects, although it appears that they are phases of
+hallucinatory origin.</p>
+
+<p>Inasmuch as these illusions cannot be illustrated diagrammatically we can
+do no better than to condense some of the descriptions obtained and
+reported by Carr.<a href="#reference"><small>[3]</small></a></p>
+
+<p>A case in which the peripheral objects remain visible and stationary at
+their true positions while the central portion of the field participates
+in the illusion is as follows:</p>
+
+<p class="blockquot">The observer on a clear day was gazing down a street which ended a
+block away, a row of houses forming the background at the end of the
+street. The observer was talking to and looking directly at a
+companion only a short distance away. Soon this person (apparently)
+began to move down the street, until she reached the background of
+houses at the end, and then slowly came back to her original position.
+The movement in both directions was distinctly perceived. During the
+illusory movement there was no vagueness of outline or contour, no
+blurring or confusion of features; the person observed, seemed
+distinct and substantial in character during the illusion. The
+perceived object moved in relation to surrounding objects; there was
+no movement of the visual field as a whole. The person decreased in
+size during the backward movement and increased in size during the
+forward return movement.</p>
+
+<p>With many persons who experience illusions of depth, the objects appear to
+move to, or appear at, some definite position and remain there until the
+illusion is voluntarily overcome, or until it disappears without voluntary
+action. A condensation of a typical<span class="pagenum"><a name="Page_111" id="Page_111">[Pg 111]</a></span> description of this general type
+presented by Carr is as follows:</p>
+
+<div class="blockquot"><p>All visual objects suddenly recede to the apparent distance of the
+horizon and remain in that position several minutes, returning at the
+end of this period to their original positions. This return movement
+is very slow at the beginning, but the latter phase of the movement is
+quite rapid. If the subject closes her eyes while the objects appear
+at their distant position she cannot even <i>imagine</i> those objects
+located anywhere except at their apparent distant position.</p>
+
+<p>In all cases (encountered by Carr) the motion in both directions is an
+actual experience reality and the subject was helpless as to
+initiating, stopping, or modifying the course of the illusion in any
+way. Objects and even visual images (which are subject to the same
+illusions) decrease in size in proportion to the amount of backward
+movement and grow larger again on their return movement. The objects
+are always clearly defined as if in good focus. In this particular
+case the illusion occurred about twice a year, under a variety of
+conditions of illumination, at various times of the day, but
+apparently under conditions of a rather pronounced fatigue.</p></div>
+
+<p>In regard to the variation in the size of objects, many who have
+experienced these illusions of depth testify that the size seems to change
+in proportion to the apparent distance, according to the law of
+perspective. Some persons appear in doubt as to this change and a few have
+experienced the peculiar anomaly of decreasing size as the objects
+apparently approached.</p>
+
+<p>Many persons who have experienced these peculiar illusions report no
+change in the distinctness of objects; almost as many are uncertain
+regarding this point; and as many report a change in distinctness.
+Apparently there are phases of hallucinatory origin<span class="pagenum"><a name="Page_112" id="Page_112">[Pg 112]</a></span> so that there is a
+wide variety of experiences among those subject to this type of illusion.</p>
+
+<p>According to Carr&#8217;s investigation internal conditions alone are
+responsible for the illusion with more persons than those due to external
+conditions alone. With some persons a combination of internal and external
+conditions seem to be a necessity. Fixation of vision appears to be an
+essential objective condition for many observers. That is, the illusion
+appeared while fixating a speaker or singer in a church or a theater. With
+others the illusion occurs while reading. Some reported that fixation upon
+checkered or other regularly patterned objects was an essential condition.
+Among the subjective conditions reported as essential are steady fixation,
+concentration of attention, complete mental absorption, dreamy mental
+abstraction, and fatigue.</p>
+
+<p>Ocular defects do not appear to be essential, for the illusions have been
+experienced by many whose eyes were known to be free from any
+abnormalities.</p>
+
+<p>Period of life does not appear to have any primary influence, for those
+who are subject to these peculiar illusions often have experienced them
+throughout many years. In some cases it is evident that the illusions
+occur during a constrained eye position, while lying down, immediately
+upon arising from bed in the morning, and upon opening the eyes after
+having had them closed for some time. However, the necessity for these
+conditions are exceptional.</p>
+
+<p>The control of these illusions of depth, that is, the ability to create or
+to destroy them, appears to be totally lacking for most of those who have
+<span class="pagenum"><a name="Page_113" id="Page_113">[Pg 113]</a></span>experienced them. Some can influence them, a few can destroy them, a few
+can indirectly initiate them, but those who can both create and destroy
+them appear to be rare.</p>
+
+<p>It may seem to the reader that the latter part of this chapter departs
+from the main trend of this book, for most of these illusions of depth are
+to a degree of hallucinatory origin. Furthermore it has been the intention
+to discuss only those types of illusions which are experienced quite
+uniformly and universally. The digression of this chapter is excused on
+the basis of affording a glimpse along the borderland of those groups of
+illusions which are nearly universally experienced. Many other phases of
+depth illusions have been recorded in scientific literature. The excellent
+records presented by Carr could be drawn upon for further glimpses, but it
+appears that no more space should be given to this exceptional type. The
+reader should be sufficiently forewarned of this type and should be able
+to take it into account if peculiarities in other types appear to be
+explainable in this manner. However, in closing it is well to emphasize
+the fact that the hallucinatory aspect of depth illusions is practically
+absent in types of illusions to which attention is confined in other
+chapters.</p>
+
+
+<p>&nbsp;</p><p>&nbsp;</p>
+<hr style="width: 50%;" />
+<p><span class="pagenum"><a name="Page_114" id="Page_114">[Pg 114]</a></span></p>
+<h2><a name="VIII" id="VIII"></a>VIII<br />IRRADIATION AND BRIGHTNESS-CONTRAST</h2>
+
+<p class="dropcap"><span class="caps">Many</span> interesting and striking illusions owe their existence to contrasts
+in brightness. The visual phenomenon of irradiation does not strictly
+belong to this group, but it is so closely related to it and so dependent
+upon brightness-contrast that it is included. A dark line or spot will
+appear darker in general as the brightness of its environment is
+increased; or conversely, a white spot surrounded by a dark environment
+will appear brighter as the latter is darkened. In other words, black and
+white, when juxtaposed, mutually reinforce each other. Black print on a
+white page appears much darker than it really is. This may be proved by
+punching a hole in a black velvet cloth and laying this hole over a
+&#8220;black&#8221; portion of a large letter. The ink which appeared so black in the
+print, when the latter was surrounded by the white paper, now appears only
+a dark gray. Incidentally a hole in a box lined with black velvet is much
+darker than a piece of the black velvet surrounding the hole.</p>
+
+<p>The effects of brightness-contrast are particularly striking when
+demonstrated by means of lighting, a simple apparatus being illustrated
+diagrammatically in <a href="#fig62">Fig. 62</a>. For example, if a hole <i>H</i> is cut in an
+opaque white blotting paper and a large piece of the white<span class="pagenum"><a name="Page_115" id="Page_115">[Pg 115]</a></span> blotting paper
+is placed at <i>C</i>, the eye when placed before the opening at the right will
+see the opening at <i>H</i> filled with the background <i>C</i>. The hole <i>H</i> may be
+cut in thin metal, painted a dull white, and may be of the shape of a
+star. This shape provides an intimacy between the hole and its environment
+which tends to augment the effects of contrasts. <i>R</i> and <i>F</i> are
+respectively the rear and front lamps. That is, the lamps <i>R</i> illuminate
+<i>C</i>, which &#8220;fills&#8221; the hole and apparently is the hole; and the lamps <i>F</i>
+illuminate the diffusing white environment <i>E</i>. The two sets of lamps may
+be controlled by separate rheostats, but if the latter are unavailable the
+lamps (several in each set) may be arranged so that by turning each one
+off or on, a range of contrasts in brightness between <i>E</i> and <i>H</i> (in
+reality <i>C</i>) may be obtained. (By using colored lamps and colored papers
+as discussed in Chapter IX the marvelous effects of color-contrast may be
+superposed upon those of brightness-contrast.)</p>
+
+<p><a name="fig62" id="fig62"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig62.jpg" alt="" /></div>
+<p class="center">Fig. 62.&mdash;Simple apparatus for demonstrating the remarkable effects of contrasts in brightness and color.</p>
+<p>&nbsp;</p>
+
+<p><span class="pagenum"><a name="Page_116" id="Page_116">[Pg 116]</a></span>If, for example, <i>C</i> is very feebly illuminated and <i>E</i> is very bright,
+<i>C</i> will be pronounced black; but when the lamps <i>F</i> are extinguished and
+no light is permitted to reach <i>E</i>, the contrast is reversed, and <i>C</i> may
+actually appear &#8220;white.&#8221; Of course, it is obvious that white and black are
+relative terms as encountered in such a case. In fact in
+brightness-contrasts relative and not absolute values of brightness are
+usually the more important. In order to minimize the stray light which
+emerges from <i>H</i>, it is well to paint the inside of both compartments
+black with the exception of sufficiently large areas of <i>C</i> and <i>E</i>. The
+use of black velvet instead of black paint is sometimes advisable. It is
+also well to screen the lamps as suggested in the diagram. This simple
+apparatus will demonstrate some very striking effects of contrasts in
+brightness and will serve, also, to demonstrate even more interesting
+effects of contrasts in color.</p>
+
+<p>Two opposite contrasts obtainable by means of a simple apparatus
+illustrated in <a href="#fig62">Fig. 62</a> may be shown simultaneously by means of white,
+black, and gray papers arranged as in <a href="#fig63">Fig. 63</a>. In this figure the gray is
+represented by the partially black <i>V</i>s, each of which contains equal
+amounts of black and of white. When held at some distance this serves as a
+gray and the same effect is apparent as is described for the case of
+actually gray <i>V</i>s. An excellent demonstration may be made by the reader
+by using two <i>V</i>s, cut from the same sheet of gray paper, and pasted
+respectively upon white and black backgrounds, as in <a href="#fig63">Fig. 63</a>. It will be
+apparent that the one amid the black environment<span class="pagenum"><a name="Page_117" id="Page_117">[Pg 117]</a></span> appears much brighter
+than the one (same gray) amid the white environment. This can be
+demonstrated easily to an audience by means of a figure two feet long. It
+is interesting to carry the experiment further and place a <i>V</i> of much
+darker gray on the black background than the <i>V</i> on the white background.
+The persistency of the illusion is found to be remarkable, for it will
+exist even when the one <i>V</i> is actually a much darker gray than the other.
+To become convinced that the two grays are of the same brightness in <a href="#fig63">Fig.
+63</a>, 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 <i>V</i>s when the card is laid upon <a href="#fig63">Fig. 63</a>. The grays in the holes should
+now appear alike because their environments are similar.</p>
+
+<p><a name="fig63" id="fig63"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig63.jpg" alt="" /></div>
+<p class="center">Fig. 63.&mdash;Illustrating brightness-contrast.</p>
+<p>&nbsp;</p>
+
+<p>The importance of contrasts in brightness and in color cannot be
+overemphasized, and it appears certain<span class="pagenum"><a name="Page_118" id="Page_118">[Pg 118]</a></span> that no one can fully realize
+their effectiveness without witnessing it in a manner similar to that
+suggested in <a href="#fig62">Fig. 62</a>.</p>
+
+<p><a name="fig64" id="fig64"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig64.jpg" alt="" /></div>
+<p class="center">Fig. 64.&mdash;An effect of brightness-contrast. Note the darkening of the intersections of the white strips.</p>
+<p>&nbsp;</p>
+
+<p>Many illusions of brightness-contrast are visible on every hand. For
+example, the point at which the mullions of a window cross will be seen to
+appear brighter than the remaining portions of them when viewed against a
+bright sky. Conversely, in <a href="#fig64">Fig. 64</a>, dark spots appear where the white bars
+cross. This is purely an illusion and the same type may be witnessed by
+the observant many times a day. In <a href="#fig64">Fig. 64</a> it is of interest to note that
+the illusion is weak for the crossing upon which the point of sight rests,
+but by averted vision the illusion is prominent for the<span class="pagenum"><a name="Page_119" id="Page_119">[Pg 119]</a></span> other crossings.
+This is one of the effects which depends upon the location in the visual
+field.</p>
+
+<p>No brightness-contrasts are seen correctly and often the illusions are
+very striking. If a series of gray papers is arranged from black to white,
+with the successive pieces overlapped or otherwise juxtaposed, a series of
+steps of uniform brightness is not seen. An instrument would determine the
+brightness of each as uniform, but to the eye the series would appear
+somewhat &#8220;fluted.&#8221; That is, where a light gray joined a darker gray the
+edge of the former would appear lighter than its actual brightness, and
+the edge of the darker gray would appear darker than it should. This may
+also be demonstrated by laying a dozen pieces of white tissue paper in a
+pile in such a manner that a series of 1, 2, 3, 4, etc., thickness would
+be produced. On viewing this by transmitted light a series of grays is
+seen, and the effect of contrast is quite apparent. Such a pattern can be
+made photographically by rotating before a photographic plate a disk with
+openings arranged properly in steps.</p>
+
+<p>Many demonstrations of the chief illusion of brightness-contrast are
+visible at night under glaring lighting conditions. It is difficult or
+impossible to see objects beyond automobile headlights, and adjacent to
+them, in the visual field. Objects similarly located in respect to any
+surface sufficiently bright are more or less obscured. Characters written
+upon a blackboard, placed between two windows, may be invisible if the
+surfaces seen through the window are quite bright, unless a sufficient
+quantity of light reaches the blackboard from other sources.
+Stage-settings have<span class="pagenum"><a name="Page_120" id="Page_120">[Pg 120]</a></span> been changed in perfect obscurity before an audience
+by turning on a row of bright lights at the edge of the stage-opening. The
+term &#8220;blinding light&#8221; owes its origin to this effect of
+brightness-contrast.</p>
+
+<p>The line of juncture between a bright and a dark surface may not be seen
+as a sharp line, but as a narrow band of gray. When this is true it is
+possible that an undue amount of area is credited to the white. In
+preceding paragraphs we have seen the peculiar effect at the border-lines
+of a series of grays. This may have something to do with the estimate;
+however, irradiation may be due to excitation of retinal rods and cones
+adjacent to, but not actually within the bright image.</p>
+
+<p>A remarkable effect which may be partially attributable to irradiation can
+be produced by crossing a grating of parallel black lines with an oblique
+black line. At the actual crossings the black appears to run up the narrow
+angle somewhat like ink would under the influence of surface tension. This
+is particularly striking when two gratings or even two ordinary
+fly-screens are superposed. The effect is visible when passing two
+picket-fences, one beyond the other. If a dark object is held so that a
+straight edge appears to cross a candle-flame or other light-source, at
+this portion the straight edge will appear to have a notch in it.</p>
+
+<p>Irradiation in general has been defined as the lateral diffusion of
+nervous stimuli beyond the actual stimulus. It is not confined to the
+visual sense but irradiation for this sense is a term applied to the
+apparent enlargement of bright surfaces at the <span class="pagenum"><a name="Page_121" id="Page_121">[Pg 121]</a></span>expense of adjacent darker
+surfaces. The crescent of the new moon appears larger in radius than the
+faint outline of the darker portion which is feebly illuminated chiefly by
+light reflected from the earth&#8217;s surface. A filament of a lamp appears to
+grow in size as the current through it is slowly increased from a zero
+value; that is, as it increases in brightness. In <a href="#fig65">Fig. 65</a> the small inner
+squares are of the same size but the white square appears larger than the
+black one. It seems that this apparent increase is made at the expense of
+the adjacent dark area. This phenomenon or illusion is strongest when the
+brightness is most intense, and is said to be greatest when the
+accommodation is imperfect. A very intense light-source may appear many
+times larger than its actual physical size.</p>
+
+<p><a name="fig65" id="fig65"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig65.jpg" alt="" /></div>
+<p class="center">Fig. 65.&mdash;The phenomenon of irradiation.</p>
+<p>&nbsp;</p>
+
+<p>Doubtless a number of factors may play a part in this phenomenon. It
+appears possible that there is a rapid spreading of the excitation over
+the retina <span class="pagenum"><a name="Page_122" id="Page_122">[Pg 122]</a></span>extending quite beyond the border of the more intensely
+stimulated region, but this must be practically instantaneous in order to
+satisfy results of experiments. Eye-movements may play some part for,
+despite the most serious efforts to fixate the point of sight, a fringe
+will appear on the borders of images which is certainly due to involuntary
+eye-movements.</p>
+
+<p>Irradiation has also been ascribed to spherical aberration in the eye-lens
+and to diffraction of light at the pupil. Printed type appears
+considerably reduced in size when the pupil is dilated with atropin and is
+restored to normal appearance when a small artificial pupil is placed
+before the dilated pupil. It has been suggested that chromatic aberration
+in the eye-lens is a contributory cause, but this cannot be very
+important, for the illusion is visible with monochromatic light which
+eliminates chromatic aberration. The experimental evidence appears to
+indicate that the phenomenon is of a physical nature.</p>
+
+<p>There are variations in the effects attributable to radiation, and it is
+difficult to reduce them to simple terms. Perhaps it may aid the reader to
+have before him the classification presented by Boswell.<a href="#reference"><small>[4]</small></a> He describes
+the varieties of irradiation as follows:</p>
+
+<div class="blockquot"><p>1. Very rapid spreading of the excitation over the retina extending
+far beyond the border of the stimulated region and occurring
+immediately upon impact of the stimulating light.</p>
+
+<p>2. Irradiation within the stimulated portion of the retina after the
+form of a figure becomes distinctly perceptible.</p>
+
+<p>3. Emanations of decreasing intensity extend themselves outward and
+backward from a moving image until lost in the darkness of the
+background.</p>
+
+<p>4. A well known form of irradiation which occurs when a<span class="pagenum"><a name="Page_123" id="Page_123">[Pg 123]</a></span> surface of
+greater intensity enlarges itself at the expense of one of less
+intensity.</p>
+
+<p>5. A form having many of the characteristics of the first type, but
+occurring only after long periods of stimulation, of the magnitude of
+30 to 60 seconds or more.</p></div>
+
+
+<p>&nbsp;</p><p>&nbsp;</p>
+<hr style="width: 50%;" />
+<p><span class="pagenum"><a name="Page_124" id="Page_124">[Pg 124]</a></span></p>
+<h2><a name="IX" id="IX"></a>IX<br />COLOR</h2>
+
+<p class="dropcap"><span class="caps">In</span> order to simplify the presentation of the general subject, discussions
+of color have been omitted in so far as possible from the preceding
+chapters. There are almost numberless phenomena involving color, many of
+which are illusions, or seemingly so. It will be obvious that many are
+errors of sense; some are errors of judgment; others are errors due to
+defects of the optical system of the eye; and many may be ascribed to
+certain characteristics of the visual process. It is not the intention to
+cover the entire field in detail; indeed, this could not be done within
+the confines of a large volume. However, substantial glimpses of the more
+important phases of color as related to illusions are presented in this
+chapter. In the early chapters pertaining to the eye and to vision some of
+the following points were necessarily touched upon, but the repetition in
+the paragraphs which follow is avoided as much as possible.</p>
+
+<p><i>Simultaneous Contrast.</i>&mdash;That the life of color is due to contrast is
+demonstrable in many ways. If a room is illuminated by deep red light, at
+first this color is very vivid in consciousness; however, gradually it
+becomes less saturated. After a half hour the color is apparently a much
+faded red but upon emerging from the room into one normally lighted, the<span class="pagenum"><a name="Page_125" id="Page_125">[Pg 125]</a></span>
+latter appears very markedly greenish in tint. The reason that the pure
+red light does not appear as strongly colored as it really is, is due to
+the lack of contrast. In a similar manner at night we see white objects as
+white even under the yellowish artificial light. The latter appears very
+yellow in color when it is first turned on as daylight wanes but as
+darkness falls and time elapses it gradually assumes a colorless
+appearance.</p>
+
+<p>An apparatus constructed after the plan of <a href="#fig62">Fig. 62</a> is very effective for
+demonstrating the remarkable effects of color-contrast but some additions
+will add considerably to its convenience. If the lamps <i>F</i> are divided
+into three circuits, each emitting, respectively, red, green, and blue
+primary colors, it is possible by means of controlling rheostats to
+illuminate <i>E</i>, the environment, with light of any hue (including purple),
+of any saturation, and of a wide range of intensities or resulting
+brightnesses. Thus we have a very simple apparatus for quickly providing
+almost numberless environments for <i>H</i>. The same scheme can be applied to
+lamps <i>R</i>, with the result that a vast array of colors may be seen through
+the hole <i>H</i>. If the hole is the shape of the star in <a href="#fig66">Fig. 66</a> it will be
+found very effective. The observer will actually see a star of any desired
+color amid an environment of any desired color. Care should be taken to
+have the star cut in very thin material in order to eliminate conspicuous
+boundary lines. It is quite satisfactory to use a series of colored papers
+on a slide at <i>C</i> and ordinary clear lamps at <i>R</i>. By means of this
+apparatus both contrasts&mdash;hue and brightness&mdash;may be <span class="pagenum"><a name="Page_126" id="Page_126">[Pg 126]</a></span>demonstrated. Of
+course, for black and white only brightness-contrast is present; but in
+general where there is color-contrast there is also brightness-contrast.
+The latter may be reduced or even eliminated if the brightness of the star
+and of its surroundings are made equal, but it is difficult to make a
+satisfactory balance in this respect. Assuming, however, that
+brightness-contrast is eliminated, we have left only hue and saturation
+contrast, or what will be termed (rather loosely, it is admitted)
+color-contrast.</p>
+
+<p><a name="fig66" id="fig66"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig66.jpg" alt="" /></div>
+<p class="center">Fig. 66.&mdash;An excellent pattern for demonstrating color-contrast.</p>
+<p>&nbsp;</p>
+
+<p>If the surroundings are dark and, for example, an orange star is seen
+alone, it does not appear very colorful. However, if the surroundings are
+now made bright with white light, the star appears quite saturated. With
+blue or green light the orange star appears even more intensely orange,
+but when the color-contrast is reduced, as in the case of yellow or red
+surroundings, the vividness of the orange star again decreases. This may
+be summarized by stating that<span class="pagenum"><a name="Page_127" id="Page_127">[Pg 127]</a></span> two widely different colors viewed in this
+manner will mutually affect each other so that they appear still more
+different in hue. If their hues are close together spectrally this effect
+is not as apparent. For example, if orange and green are contrasted, the
+orange will appear reddish in hue and the green will appear bluish.</p>
+
+<p>Let us now assume the star to be white, and that the surroundings are of
+any color of approximately the same brightness. The star which is really
+white will now appear decidedly tinted and of a hue approximately
+complementary to that of the surroundings. When the latter are of a green
+color the white star will assume a purplish tinge; when red the white star
+will appear of a blue-green tint; when yellow the white star will appear
+bluish. This is an illusion in any sense of the term.</p>
+
+<p>The strength of this illusion caused by simultaneous contrast is very
+remarkable. For example, if a grayish purple star is viewed amid intense
+green surroundings it will appear richly purple, but when the surroundings
+are changed to a rich purple the grayish purple star will even appear
+greenish. The apparent change of a color to its complementary by merely
+altering its environment is really a remarkable illusion.</p>
+
+<p>The importance of simultaneous contrast is easily demonstrated upon a
+painting by isolating any colored object from its surroundings by means of
+a hole in a gray card. For example, an orange flower-pot amid the green
+foliage of its surroundings will appear decidedly different in color and
+brightness than when<span class="pagenum"><a name="Page_128" id="Page_128">[Pg 128]</a></span> viewed through a hole in a white, black, or gray
+cardboard. By means of colored papers the same color may be placed in many
+different environments and the various contrasts may be viewed
+simultaneously. The extent of the illusion is very evident when revealed
+in this simple manner. However, too much emphasis cannot be given to <a href="#fig62">Figs.
+62</a> and <a href="#fig66">66</a> as a powerful means for realizing the greatest effects.</p>
+
+<p><i>After-images.</i>&mdash;After looking at bright objects we see after-images of
+the same size and form which vary more or less in color. These
+after-images are due to persistence or fatigue of the visual process,
+depending upon conditions. After looking at the sun for a moment a very
+bright after-image is seen. Undoubtedly this at first is due to a
+persistence of the visual process, but as it decays it continuously
+changes color and finally its presence is due to fatigue.</p>
+
+<p>After-images may be seen after looking intently at any object and then
+directing the eyes toward a blank surface such as a wall. A picture-frame
+will be seen as a rectangular after-image; a checkered pattern will be
+seen as a checkered after-image. When these after-images are projected
+upon other objects it is obvious that the appearance of the latter is
+apparently altered especially when the observer is not conscious of the
+after-image. The effects are seen in paintings and many peculiar phenomena
+in the various arts are directly traceable to after-<ins class="correction" title="original: imgaes">images</ins>.</p>
+
+<p>It appears unnecessary to detail the many effects for the explanations or
+at least the general principles of after-images are so simple that the
+reader should easily render an analysis of any given case.</p>
+
+<p><span class="pagenum"><a name="Page_129" id="Page_129">[Pg 129]</a></span>Let us assume that vision is fixed upon a green square upon a gray or
+white background. Despite the utmost effort on the part of the observer to
+gaze fixedly upon this green square, the latter will begin to appear
+fringed with a pinkish border. This is due to the after-image of the green
+square and it is displaced slightly due to involuntary eye-movements.
+After gazing as steadily as possible for a half minute, or even less, if
+the point of sight is turned to the white paper a pink square is seen upon
+it. Furthermore, this pink square moves over the field with the point of
+sight. This is the type most generally noticed.</p>
+
+<p>After-images have been classified as positive and negative. The former are
+those in which the distribution of light and shade is the same as in the
+original object. Those in which this distribution is reversed, as in the
+photographic negative, are termed &#8220;negative.&#8221; After-images undergo a
+variety of changes in color but in general there are two important states.
+In one the color is the same as in the original object and in the other it
+is approximately complementary to the original color. In general the
+negative after-image is approximately complementary in color to the color
+of the original object.</p>
+
+<p>After-images are best observed when the eyes are well rested, as in the
+morning upon awakening. With a little practice in giving attention to
+them, they can be seen floating in the air, in the indefinite field of the
+closed eyes, upon a wall, or elsewhere, and the changes in the brightness
+and color can be readily followed. Negative after-images are sometimes
+very persistent<span class="pagenum"><a name="Page_130" id="Page_130">[Pg 130]</a></span> and therefore are more commonly noticed than positive
+ones. The positive after-image is due to retinal inertia, that is, to the
+persistency of the visual process after the actual stimulus has been
+removed. It is of relatively brief duration. If an after-image of a window
+is projected on a white area it is likely to appear as a &#8220;negative&#8221; when
+projected upon a white background, and as a &#8220;positive&#8221; upon a dark
+background, such as is readily provided by closing the eyes. It may be of
+interest for the reader to obtain an after-image of a bright surface of a
+light-source and study its color changes with the eye closed. Upon
+repeating the experiment the progression of colors will be found to be
+always the same for the same conditions. The duration of the after-image
+will be found to vary with the brightness and period of fixation of the
+object.</p>
+
+<p>It is interesting to note that an after-image is seen with difficulty when
+the eyes are in motion, but it becomes quite conspicuous when the eyes are
+brought to rest.</p>
+
+<p>An after-image due to the stimulation of only one eye sometimes seems to
+be seen by the other eye. Naturally this has given rise to the suggestion
+that the seat of after-images is central rather than peripheral; that is,
+in the brain rather than at the retina. However, this is not generally the
+case and the experimental evidence weighs heavily against this conclusion.</p>
+
+<p>If <a href="#fig52">Fig. 52</a> is revolved about its center and fixated for some time striking
+effects are obtained upon looking away suddenly upon any object. The
+latter will<span class="pagenum"><a name="Page_131" id="Page_131">[Pg 131]</a></span> appear to shrink if the spiral has seemed to run outward, or
+to expand if the spiral has seemed to run inward. These are clearly
+after-images of motion.</p>
+
+<p>As stated elsewhere, we may have illusions of after-images as well as of
+the original images. For example, if a clearly defined plane geometrical
+figure such as a cross or square is bright enough to produce a strong
+after-image, the latter when projected upon a perspective drawing will
+appear distorted; that is, it is likely to appear in perspective.</p>
+
+<p>A simple way of demonstrating after-images and their duration is to move
+the object producing them. For example, extinguish a match and move the
+glowing end. If observed carefully without moving the eye a bluish
+after-image will be seen to follow the glowing end of the match. In this
+case the eyes should be directed straight ahead while the stimulus is
+moving and the observation must be made by averted or indirect vision.</p>
+
+<p><i>Growth and Decay of Sensation.</i>&mdash;Although many after-images may not be
+considered to be illusions in the sense in which the term is used here,
+there are many illusions in which they at least play a part. Furthermore,
+it is the intention throughout these chapters to adhere to a discussion of
+&#8220;static&#8221; illusions, it is difficult to avoid touching occasionally upon
+motion. The eyes are in motion most of the time, hence, certain effects of
+an illusory nature may be superposed upon stationary objects.</p>
+
+<p>The persistence of vision has been demonstrated by every small boy as he
+waved a glowing stick seized<span class="pagenum"><a name="Page_132" id="Page_132">[Pg 132]</a></span> from a bonfire. Fireworks owe much of their
+beauty to this phenomenon. A rapidly revolving spoked wheel may appear to
+be a more or less transparent disk, but occasionally when a rapid
+eye-movement moves the point of sight with sufficient speed in the
+direction of motion, the spokes reappear momentarily. Motion-pictures owe
+their success to this visual property&mdash;the persistence of vision. If a
+lantern-slide picture be focused upon black velvet or upon a dark doorway,
+the projected image will not be seen. However, if a white rod be moved
+rapidly enough in the plane of the image, the latter may be seen in its
+entirety. The mixture of colors, by rotating them on disks, owes its
+possibility to the persistence of the color-sensations beyond the period
+of actual stimulation. The fact that it takes time for sensations of light
+to grow and decay is not as important here as the fact that the rates of
+growth, and also of decay, vary for different colors. In general, the
+growth and the decay are not of similar or uniform rates. Furthermore, the
+sensation often initially &#8220;overshoots&#8221; its final steady value, the amount
+of &#8220;overshooting&#8221; depending upon the intensity and color of the stimulus.
+These effects may be witnessed in their extensive variety by rotating
+disks so constructed that black and various colors stimulate the retina in
+definite orders.</p>
+
+<p>An interesting case of this kind may be demonstrated by rotating the disk
+shown in <a href="#fig67">Fig. 67</a>. Notwithstanding the fact that these are only black and
+white stimuli, a series of colored rings is seen varying from a reddish
+chocolate to a blue-green. Experiment<span class="pagenum"><a name="Page_133" id="Page_133">[Pg 133]</a></span> will determine the best speed,
+which is rather slow under a moderate intensity of illumination. The
+reddish rings will be outermost and the blue-green rings innermost when
+the disk is rotated in one direction. Upon reversing the direction of
+rotation the positions of these colored rings will be reversed. By using
+various colors, such as red and green for the white and black
+respectively, other colors will be produced, some of which are very
+striking. The complete explanation of the phenomenon is not clear, owing
+to the doubt which exists concerning many of the phenomena of
+color-vision, but it appears certain that the difference in the rates of
+growth and decay of the various color-sensations (the white stimulus
+includes all the spectral hues of the illuminant) is at least partially,
+if not wholly, responsible.</p>
+
+<p><a name="fig67" id="fig67"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig67.jpg" alt="" /></div>
+<p class="center">Fig. 67.&mdash;By rotating this Mason (black and white) disk color-sensations are produced.</p>
+<p>&nbsp;</p>
+
+<p><span class="pagenum"><a name="Page_134" id="Page_134">[Pg 134]</a></span>An interesting effect, perhaps due wholly or in part to the differences in
+the rates of growth and decay of color-sensations, may be observed when a
+colored pattern is moved under a low intensity of illumination, the eyes
+remaining focused upon a point in space at about the same distance as the
+object. A square of red paper pasted in the center of a larger piece of
+blue-green paper is a satisfactory object. On moving this object gently,
+keeping the point of sight fixed in its plane of movement, the central red
+square will appear to shake like jelly and a decided trail of color will
+appear to cling to the lagging edge of the central square. Perhaps
+chromatic aberration plays some part in making this effect so conspicuous.</p>
+
+<p>A similar case will be noted in a photographic dark-room illuminated by
+red light upon observing the self-luminous dial of a watch or clock. When
+the latter is moved in the plane of the dial, the greenish luminous
+figures appear separated from the red dial and seem to lag behind during
+the movement. For such demonstrations it is well to experiment somewhat by
+varying the intensity of the illumination and the speed of movement.
+Relatively low values of each appear to be best.</p>
+
+<p>Although the various color-sensations grow and decay at different rates,
+the latter depend upon conditions. It appears that blue-sensation rises
+very rapidly and greatly overshoots its final steady value for a given
+stimulus. Red ranks next and green third in this respect. The overshooting
+appears to be greater for the greater intensity of the stimulus. The time
+required for the sensation to reach a steady value<span class="pagenum"><a name="Page_135" id="Page_135">[Pg 135]</a></span> depends both upon the
+spectral character and the brightness of the color but is usually less
+than a second.</p>
+
+<p><i>Chromatic Aberration.</i>&mdash;It is well known that the eye focuses different
+spectral colors at different points. This is true of any simple lens and
+the defect is overcome in the manufacture of optical instruments by
+combining two lenses consisting respectively of glasses differing
+considerably in refractive index. If a white object is viewed by the eye,
+it should appear with a purplish fringe; however, the effect is observed
+more readily by viewing a light-source through a purple filter which
+transmits only violet and red light. The light-source will have a red or a
+violet fringe, depending upon the accommodation or focus of the eye.</p>
+
+<p>This effect is perhaps best witnessed on viewing a line spectrum such as
+that of the mercury arc, focused upon a ground glass. The violet and blue
+lines are not seen in good focus when the eyes are focused upon the green
+and yellow lines. Furthermore, the former can be seen in excellent focus
+at a distance too short for accommodating the eyes to the green and the
+yellow lines. This experiment shows that the focal length of the optical
+system of the eye is considerably shorter for the spectral hues of shorter
+wave-length (violet, blue) than for those of longer wave-length (such as
+yellow). Narrow slits covered with diffusing glass and illuminated
+respectively by fairly pure blue, green, yellow, and red lights may be
+substituted.</p>
+
+<p>The effect may be demonstrated by trying to focus fine detail such as
+print when two adjacent areas are<span class="pagenum"><a name="Page_136" id="Page_136">[Pg 136]</a></span> illuminated by blue and red lights
+respectively. It is also observed when fine detail such as black lines are
+held close to the eye for colored fringes are seen. This optical defect is
+responsible for certain visual illusions.</p>
+
+<p>An excellent demonstration of chromatic aberration in the eye is found by
+viewing fine detail through a purple filter. Now if a red filter be
+superposed on the purple one only the red light is transmitted.
+Notwithstanding the decrease in illumination or rather of light reaching
+the eye, measurement shows that finer detail can be discriminated than in
+the first case. A similar result is found on superposing a blue filter
+upon the purple one.</p>
+
+<p><i>Retiring and Advancing Colors.</i>&mdash;For years the artist and the decorator
+have felt that certain colors seem to advance nearer than others or that
+the latter seem to retire more than the former. The author<a href="#reference"><small>[5]</small></a> obtained
+actual measurements of this phenomenon, but the evidence also indicated
+that the effects were not the same for all persons. The phenomenon is very
+noticeable in the case of the image of a colored lantern-slide projected
+upon a screen and is readily observed when the image consists of letters
+of various colors. In the case of red and green letters, for example, the
+former appear (to most persons) to be considerably nearer the observer
+than the green letters. It has appeared to the writer that the illusion is
+apparent even for white letters upon a dark background. In general, the
+colors whose dominant hues are of the shorter wave-lengths (violet, blue,
+blue-green, green) are retiring and those whose dominant<span class="pagenum"><a name="Page_137" id="Page_137">[Pg 137]</a></span> hues are of the
+longer wave-lengths (yellow, orange, red) are advancing.</p>
+
+<p><a name="fig68" id="fig68"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig68.jpg" alt="" /></div>
+<p class="center">Fig. 68.&mdash;For demonstrating retiring and advancing colors.</p>
+<p>&nbsp;</p>
+
+<p>In order to obtain experimental measurements two light-tight boxes, each
+containing a light-source, were arranged to run independently upon tracks.
+Over the front end of each a diaphragm was placed so that the observer saw
+two characters as in <a href="#fig68">Fig. 68</a>. A saturated red filter was placed over one
+and a saturated blue filter over the other. In a dark room the observer
+saw a blue <i>E</i> and a red <i>H</i> standing out in the darkness. One of these
+boxes was fastened so as to be immovable and the observer moved the other
+to and fro by means of a cord over pulleys until the two characters
+appeared equi-distant from him. This was done for a series of distances of
+the stationary box from the observer&#8217;s eye. Nearly all the observers
+(without being acquainted with the positions) were obliged to set the red
+<i>H</i> further behind the blue <i>E</i> in order that both appeared at the same
+distance. This added distance for the red <i>H</i> was as much as 2.4 feet when
+the blue <i>E</i> was at a distance of 24 feet. In other words the difference
+in the positions of the<span class="pagenum"><a name="Page_138" id="Page_138">[Pg 138]</a></span> two was as much as 10 per cent of the total
+distance in this case.</p>
+
+<p>Many other interesting data were obtained but most of these are not
+particularly of interest here. Some of the experiments tended to show the
+effect of certain optical defects in the eye and the variations and even
+reversal of the effect for some persons were accounted for by differences
+in the curvatures, etc., of certain eye-media for the observers. These
+details are not of interest here but it may be of interest to know that
+the phenomenon may be accounted for by the chromatic aberration in the
+eye. This may not be the true explanation, or it may be only partially
+correct. Perhaps some of the illusion is purely psychological in origin.
+Certainly the illusion is very apparent to most careful observers.</p>
+
+<p><i>Color-sensibility of the Retina.</i>&mdash;This aspect was touched upon in
+Chapter III, but the differences in the sensibility of various areas of
+the retina to various colors are of sufficient importance to be discussed
+further. The ability to distinguish light and color gradually fades or
+decreases at the periphery of the visual field, but the actual areas of
+the fields of perception vary considerably, depending upon the hue or
+spectral character of the light reaching the retina. The extreme
+peripheral region of the visual field is &#8220;color-blind&#8221;; that is, color
+ceases to be perceived before brightness-perception vanishes in the
+outskirts of the visual field. These fields for various colors depend in
+size and contour not only upon the hue or spectral character of the
+light-stimuli but also upon the intensity and perhaps upon the size of
+the<span class="pagenum"><a name="Page_139" id="Page_139">[Pg 139]</a></span> stimuli. There is some disagreement as to the relative sizes of these
+fields but it appears that they increase in size in the following order:
+green, red, blue, white (colorless). The performances of after-images, and
+the rates of growth and decay of sensation vary for different colors and
+for different areas of the retina, but it would be tedious to peruse the
+many details of these aspects of vision. They are mentioned in order that
+the reader may take them into account in any specific case.</p>
+
+<p>As already stated, the central part of the visual field&mdash;the fovea upon
+which we depend for acute vision&mdash;contains a yellowish pigmentation, which
+is responsible for the term &#8220;yellow spot.&#8221; This operates as a yellow
+filter for this central area and modifies the appearance of visual fields
+quite the same as if a similar yellow filter was placed in the central
+position of the field of vision. The effect of the selectivity of the
+&#8220;yellow spot&#8221; is noticeable in viewing certain colors.</p>
+
+<p><i>Purkinje Effect.</i>&mdash;The relative sensibility of the retina varies for
+different colors with a change in brightness; or it may be better to state
+that the relative sensations for various colors alters as the brightness
+values are reduced to a low intensity. For example, if a reddish purple
+(consisting of red and blue or violet rays) be illuminated in such a
+manner that the intensity of illumination, and consequently its
+brightness, may be reduced from normal to a low value (approximating
+moonlight conditions), it will be seen to vary from reddish purple to
+violet. In doing this its appearance changes through the range of<span class="pagenum"><a name="Page_140" id="Page_140">[Pg 140]</a></span> purples
+from reddish to violet. This can be accomplished by orientation of the
+purple surface throughout various angles with respect to the direction of
+light or by reducing the illumination by means of screens.</p>
+
+<p>In general the Purkinje effect may be described as an increasing
+sensibility of the retina for light of shorter wave-lengths (violet, blue,
+green) as the brightness decreases, or a corresponding decreasing
+sensibility for light of longer wave-lengths (yellow, orange, red). The
+effect may be seen on any colored surfaces at twilight illumination. A
+blue and a red flower, which appear of the same brightness before sunset
+will begin to appear unequal in this respect as twilight deepens. The red
+will become darker more rapidly than the blue if there are no appreciable
+changes in the color of the daylight. Finally all color disappears. It is
+better to perform this experiment under artificial light, in order that
+the spectral character of the illuminant may be certain to remain
+constant. In this case rheostats must not be used for dimming the light
+because of the attendant changes in color or quality of the light.</p>
+
+<p>The Purkinje effect may be noticed by the careful observer and it is
+responsible for certain illusions. Apparently it cannot operate over one
+portion of the retina, while the remainder is stimulated by normal
+intensities of light.</p>
+
+<p><i>Retinal Rivalry.</i>&mdash;Many curious effects may be obtained by stimulating
+the two retinas with lights, respectively different in color. For example,
+it is interesting to place a blue glass before one eye and a<span class="pagenum"><a name="Page_141" id="Page_141">[Pg 141]</a></span> yellow or
+red one before the other. The two independent monocular fields strive for
+supremacy and this rivalry is quite impressive. For a moment the whole
+field may appear of one color and then suddenly it will appear of the
+other color. Apparently the fluctuation of attention is a factor. Usually
+it does not seem to be possible to reach a quiescent state or a perfect
+mixture of the two colors in this manner. The dependence of one monocular
+field upon the other, and also their independence, are emphasized by this
+experiment. It is of interest to consider the illusions of reversible
+perspective and others in Chapter V in this connection.</p>
+
+<p><a name="fig69" id="fig69"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig69.jpg" alt="" /></div>
+<p class="center">Fig. 69.&mdash;By combining these stereoscopically the effect of metallic lustre<br />(similar to graphite in this case) is obtained.</p>
+<p>&nbsp;</p>
+
+<p>One of the interesting results of retinal rivalry is found in combining
+two stereoscopic pictures in black and white with the black and white
+reversed in one of them. The apparently solid object will appear to
+possess lustre. The experiment may be tried with <a href="#fig69">Fig. 69</a> by combining the
+two stereoscopic pictures by converging or diverging the axes of the eyes
+as described in connection with <a href="#fig2">Figs. 2</a> and <a href="#fig3">3</a>.</p>
+
+<p>It will be noted that in order for two stereoscopic pictures, when
+combined, to produce a perfect effect<span class="pagenum"><a name="Page_142" id="Page_142">[Pg 142]</a></span> of three dimensions their
+dissimilarity must be no more than that existing between the two views
+from the two eyes respectively. The dissimilarity in <a href="#fig69">Fig. 69</a> is correct as
+to perspective, but the reversal of white and black in one of them
+produces an effect beyond that of true third dimension. When the colors
+are so arranged in such pictures as to be quite different in the two the
+effects are striking. There is, in such cases, an effect beyond that of
+perfect binocular combination.</p>
+
+<p>By means of the stereoscope it is possible to attain binocular mixture of
+colors but this is usually difficult to accomplish. The difficulty
+decreases as the brightness and saturation of the colors decrease and is
+less for colors which do not differ much in hue and in brightness. These
+effects may be studied at any moment, for it is only necessary to throw
+the eyes out of focus for any object and to note the results. Many simple
+experiments may be arranged for a stereoscope, using black and white, and
+various combinations of colors. For example, <a href="#fig65">Fig. 65</a> may be combined by
+means of double images (produced by converging or diverging the optical
+axes) so that the two inner squares are coincident. Actual observation is
+much more satisfactory than a detailed description.</p>
+
+<p><i>Miscellaneous.</i>&mdash;There are many interesting effects due to diffraction of
+light by edges of objects, by meshes such as a wire screen or a
+handkerchief, by the eye-media, etc. On looking at a very bright small
+light-source it may be seen to be surrounded by many colors.</p>
+
+<p>Streamers of light appear to radiate from brilliant<span class="pagenum"><a name="Page_143" id="Page_143">[Pg 143]</a></span> sources and all
+bright areas colored or colorless, when viewed amid dark surroundings,
+appear to be surrounded by diffuse brushes of light. These brushes are
+likely to be of a bluish tint.</p>
+
+<p>Many of these phenomena are readily explained, but this cannot be done
+safely without knowing or recognizing all conditions. Many are not easily
+explained, especially when reported by others, who may not recognize
+certain important conditions. For example, authentic observers have
+reported that black letters on white paper appeared vivid red on a white
+background, under certain conditions. Of the latter, the apparently
+important one was &#8220;sun&#8217;s rays falling aslant the forehead.&#8221; When the eyes
+were shaded with the hand the letters immediately appeared black as they
+should.</p>
+
+<p>The influence of the color of an object upon its apparent weight is
+relatively slight, but there is evidence of a tendency to judge a red or
+black object to be slightly heavier than a yellow or blue object of the
+same weight. It appears that hue is a minor factor in influencing the
+judgment and that there is no correlation between the affective quality of
+a color and its influence upon apparent weight. Although the scanty
+evidence available attributes but a slight influence to color in this
+respect, it is of interest in passing as a reminder of the many subtle
+factors which are at work modifying our judgments.</p>
+
+
+<p>&nbsp;</p><p>&nbsp;</p>
+<hr style="width: 50%;" />
+<p><span class="pagenum"><a name="Page_144" id="Page_144">[Pg 144]</a></span></p>
+<h2><a name="X" id="X"></a>X<br />LIGHTING</h2>
+
+<p class="dropcap"><span class="caps">It</span> should be obvious by this time that the lighting of objects or of a
+scene can alone produce an illusion, and that it can in still more cases
+contribute toward an illusion. Furthermore, there are many cases of
+illusions in lighting due to brightness and color. Many effects of
+lighting have been described elsewhere with detailed analyses of the
+underlying principles, but a condensed survey applying particularly to
+illusions will be presented here.</p>
+
+<p>The comparison of intaglio with low relief has been mentioned several
+times in preceding chapters. Examples of these as related to lighting are
+found in <a href="#fig70">Figs. 70 to 73</a>. <a href="#fig70">Fig. 70</a> represents a bas-relief lighted from
+above and <a href="#fig71">Fig. 71</a> would ordinarily be taken to represent a bas-relief
+lighted from below. However, the latter was made from a photograph of the
+mold (intaglio) from which the bas-relief was made and <a href="#fig71">Fig. 71</a> really
+represents an intaglio lighted from above.</p>
+
+<p>Similarly <a href="#fig72">Fig. 72</a> represents the bas-relief lighted from the left and
+<a href="#fig73">Fig. 73</a> ordinarily would be taken to be a bas-relief lighted from the right.
+However, <a href="#fig73">Fig. 73</a> was made from a photograph of an intaglio lighted from
+the left. These amply demonstrate the effect of lighting as an influence
+upon the appearance<span class="pagenum"><a name="Page_145" id="Page_145">[Pg 145]</a></span> of objects and they indicate the importance of
+correct assumptions in arriving at a correct judgment. In these cases the
+concealment of the light-source and the commonness of bas-relief as
+compared with intaglio are the causes for the illusion or the error in
+judgment. Certainly in these cases the visual sense delivers its data
+correctly.</p>
+
+<p><a name="fig74" id="fig74"></a>&nbsp;</p>
+<table border="0" cellpadding="0" cellspacing="5" summary="table">
+<tr><td align="center"><img src="images/fig74a.jpg" alt="" /></td><td><span class="spacer">&nbsp;</span></td>
+    <td align="center"><img src="images/fig74b.jpg" alt="" /></td></tr>
+<tr><td align="center"><strong><i>a</i></strong></td><td>&nbsp;</td><td align="center"><strong><i>b</i></strong></td></tr>
+<tr><td colspan="3" align="center">Fig. 74.&mdash;<i>a.</i> A disk (above) and a sphere (below) lighted from overhead.<br />
+<i>b.</i> A disk and a sphere lighted by perfectly diffused light.</td></tr></table>
+
+<p><a name="fig70" id="fig70"></a>&nbsp;<span class="pagenum"><a name="Page_146" id="Page_146">[Pg 146]</a></span></p>
+<div class="figcenter"><img src="images/fig70.jpg" alt="" /></div>
+<p class="center">Fig. 70.&mdash;A bas-relief lighted from above.</p>
+<p><a name="fig71" id="fig71"></a>&nbsp;<span class="pagenum"><a name="Page_147" id="Page_147">[Pg 147]</a></span></p>
+<div class="figcenter"><img src="images/fig71.jpg" alt="" /></div>
+<p class="center">Fig. 71.&mdash;An intaglio lighted from above.</p>
+<p><a name="fig72" id="fig72"></a>&nbsp;<span class="pagenum"><a name="Page_148" id="Page_148">[Pg 148]</a></span></p>
+<div class="figcenter"><img src="images/fig72.jpg" alt="" /></div>
+<p class="center">Fig. 72.&mdash;A bas-relief lighted from the left.</p>
+<p><a name="fig73" id="fig73"></a>&nbsp;<span class="pagenum"><a name="Page_149" id="Page_149">[Pg 149]</a></span></p>
+<div class="figcenter"><img src="images/fig73.jpg" alt="" /></div>
+<p class="center">Fig. 73.&mdash;An intaglio lighted from the left.</p>
+<p>&nbsp;</p>
+
+<p><span class="pagenum"><a name="Page_150" id="Page_150">[Pg 150]</a></span>In <a href="#fig74">Fig. 74</a> the upper object is a disk
+and the lower is a sphere. In <i>a</i> <a href="#fig74">Fig. 74</a> the lighting is due to a source of light of rather small
+physical dimensions directly above the objects. The same objects
+illuminated by means of highly diffused light (that is, light from many
+directions and of uniform intensity) appear as in <i>b</i>. Both objects now
+appear as disks. It is obvious that under appropriate lighting a disk
+might be taken for a sphere and vice versa, depending upon which dominates
+the judgment or upon the formulation of the attendant assumptions.
+Incidentally an appearance quite similar to that of <i>a</i>, <a href="#fig74">Fig. 74</a> is
+obtained when the light-source is near the observer; that is, when it lies
+near the line of sight.</p>
+
+<p><a name="fig75" id="fig75"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig75.jpg" alt="" /></div>
+<p class="center">Fig. 75.&mdash;A concave hemispherical cup on the left and a convex hemisphere on the right<br />
+lighted by a light-source of large angle such as a window.</p>
+<p>&nbsp;</p>
+
+<p>Somewhat similar to the confusion of intaglio with bas-relief is the
+confusion of the two hemispherical objects illustrated in <a href="#fig75">Fig. 75</a>. The one
+on the left is concave toward the observer. In other words, both could be
+hemispherical shells&mdash;one a mold for the other. Under the lighting which
+existed when the original photographs were made they could both be taken
+for hemispheres. The lighting was due to a large light-source at the left,
+but if the object<span class="pagenum"><a name="Page_151" id="Page_151">[Pg 151]</a></span> on the left is assumed (incorrectly) to be a hemisphere
+convex toward the observer or a sphere, it must be considered to be
+lighted from the right, which is also an incorrect assumption. Obviously,
+if the direction of the dominant light is clear to the observer, he is not
+likely to make the error in judgment. Incidentally the object on the right
+might be assumed to be a sphere because a sphere is more commonly
+encountered than a hemisphere.</p>
+
+<p><a name="fig76" id="fig76"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig76.jpg" alt="" /></div>
+<p class="center">Fig. 76.&mdash;The same as <a href="#fig75">Fig. 75</a>, but lighted by a very small light-source.</p>
+<p>&nbsp;</p>
+
+<p>The same objects are represented in <a href="#fig76">Fig. 76</a> lighted from the left by means
+of a light-source of relatively small dimensions; that is, a source
+subtending a relatively small solid-angle at the objects. In this case the
+sharp shadow due to the edge of the hemispherical cup (on the left) is
+likely to cause the observer to inquire further before submitting his
+judgment. The more gradual modulation of light and shade as in the case of
+a sphere or a hemisphere convex toward the observer is not present in the
+case of the cup. This should be sufficient information for the careful
+observer to guide him, or at least to prevent<span class="pagenum"><a name="Page_152" id="Page_152">[Pg 152]</a></span> him from arriving at the
+definite conclusion that the left-hand object is a hemisphere with its
+convex side toward him. Furthermore it should be noted that we often jump
+at the conclusion that an object is a sphere even though we see with one
+eye practically only a hemisphere and with two eyes hardly enough more to
+justify such a conclusion. However, spheres are more commonly encountered
+than hemispheres, so we take a chance without really admitting or even
+recognizing that we do.</p>
+
+<p>The foregoing figures illustrate several phases which influence our
+judgments and the wonder is that we do not make more errors than we do. Of
+course, experience plays a large part and fortunately experience can be
+depended upon in most cases; however, in the other cases it leads us
+astray to a greater extent than if we had less of it.</p>
+
+<p>The photographer, perhaps, recognizes more than anyone else the pitfalls
+of lighting but it is unfortunate that he is not better acquainted with
+the fundamentals underlying the control of light. Improper lighting does
+produce apparent incongruous effects but adequately controlled it is a
+powerful medium whose potentiality has not been fully realized. The
+photographer aims to illuminate and to pose the subject with respect to
+the source or sources of light so that undesirable features are suppressed
+and desirable results are obtained.</p>
+
+<p>Finally his work must be accepted by others and the latter, being human,
+possess (unadmittedly of course) a desire to be &#8220;good looking.&#8221; Lighting
+may be a powerful flatterer when well controlled<span class="pagenum"><a name="Page_153" id="Page_153">[Pg 153]</a></span> and may be a base
+revealer or even a creator of ugliness.</p>
+
+<p>Incidentally, the photographer is always under the handicap of supplying a
+&#8220;likeness&#8221; to an individual who perhaps never sees this same &#8220;likeness&#8221; in
+a mirror. In other words, the image which a person sees of himself in a
+mirror is not the same in general that the photographer supplies him in
+the photographic portrait. The portrait can be a true likeness but the
+mirrored image in general cannot be. In the mirror there is a reversal of
+the parts from right to left. For example, a scar on the right cheek of
+the actual face appears on the left cheek in the mirror. Faces are not
+usually symmetrical and this reversal causes an individual to be familiar
+with his own facial characteristics in this reversed form. This influence
+is very marked in some cases. For example, suppose the left side of a
+companion&#8217;s face to be somewhat paralyzed on one side due to illness. We
+have become more or less oblivious to the altered expression of the left
+side by seeing it so often. However, if we catch a glimpse of this
+companion&#8217;s face in the mirror and the altered expression of the left side
+now appears upon the right side of the face, the contrast makes the fact
+very conspicuous. Perhaps this accounts for the difference which exists
+between the opinions of the photographer (or friends) and of the subject
+of the portrait.</p>
+
+<p>All the illusions of brightness-contrast may be produced by lighting.
+Surfaces and details may appear larger or smaller, harsh or almost
+obliterated, heavy or light; in fact, lighting plays an important<span class="pagenum"><a name="Page_154" id="Page_154">[Pg 154]</a></span> part in
+influencing the mood or expression of a room. A ceiling may be &#8220;lifted&#8221; by
+light or it may hang low and threatening when dark, due to relatively
+little light reaching it. Columns may appear dark on a light background or
+vice versa, and these illustrate the effects of irradiation. A given room
+may be given a variety of moods or expressions by varying the lighting and
+inasmuch as the room and its physical characteristics have not been
+altered, the various moods may be considered to be illusions. It should be
+obvious that lighting is a potent factor.</p>
+
+<p>In connection with lighting it should be noted that contrasts play a
+prominent r&ocirc;le as they always do. These have been discussed in other
+chapters, but it appears advantageous to recall some of the chief
+features. The effect of contrast is always in the direction of still
+greater contrast. That is, black tends to make its surroundings white; red
+tends to make its surroundings blue-green (complementary), etc. The
+contrast-effect is greatest when the two surfaces are juxtaposed and the
+elimination of boundary lines of other colors (including black or white)
+increases its magnitude. The contrast-effect of colors is most conspicuous
+when there is no brightness-contrast, that is, when the two surfaces are
+of equal brightness and therefore differ chiefly in hue. This effect is
+also greatest for saturated colors. It has been stated that cold colors
+produce stronger contrast-effects than warm colors, but experimental
+evidence is not sufficiently plentiful and dependable to verify this
+statement.</p>
+
+<p>As the intensity of illumination increases, colors<span class="pagenum"><a name="Page_155" id="Page_155">[Pg 155]</a></span> appear to become less
+saturated. For example, a pure red object under the noonday sun is likely
+to be painted an orange red by the artist because it does not appear as
+saturated as it would under a much lower intensity of illumination. In
+general, black and white are the final appearances of colors for
+respectively very low and very high brightness. As the intensity of
+illumination decreases, hue finally disappears and with continued decrease
+the color approaches black. Conversely, as the intensity of illumination
+increases, a color becomes apparently less and less saturated and tends
+toward white. For example, on viewing the sun through a colored glass the
+sun appears of a much less saturated color than the haze near the sun or a
+white object illuminated by sunlight.</p>
+
+<p>Visual adaptation also plays a prominent part, and it may be stated that
+all sensations of light tend toward a middle gray and all sensations of
+color tend toward neutrality or a complete disappearance of hue. The
+tendency of sensations of light toward a middle gray is not as easily
+recognized as changes in color but various facts support this conclusion.
+In lighting it is important to recognize the tendency of color toward
+neutrality. For example, a warm yellow light soon disappears as a hue and
+only its subtle influence is left; however, a yellow vase still appears
+yellow because it is contrasted with objects of other colors. In the case
+of colored light the light falls upon everything visible, and if there is
+no other light-source of another color with which to contrast it, its
+color appears gradually to fade. This is an excellent example<span class="pagenum"><a name="Page_156" id="Page_156">[Pg 156]</a></span> of the
+tremendous power and importance of contrast. It is the life of color and
+it must be fully appreciated if the potentiality of lighting is to be
+drawn upon as it should be.</p>
+
+<p>Physical measurements are as essential in lighting as in other phases of
+human endeavor for forming a solid foundation, but in all these activities
+where visual perception plays an important part judgment is finally the
+means for appraisal. Wherever the psychological aspect is prominent
+physical measurements are likely to be misleading if they do not agree
+with mental appraisals. Of course the physical measurements should be made
+and accumulated but they should be considered not alone but in connection
+with psychological effects.</p>
+
+<p>The photometer may show a very adequate intensity of illumination;
+nevertheless seeing may be unsatisfactory or even impossible. An
+illumination of a few foot-candles under proper conditions at a given
+surface is quite adequate for reading; however, this surface may appear
+quite dark if the surroundings are bright enough. In such a case the
+photometer yielded results quite likely to be misinterpreted as
+satisfactory. It should be obvious that many illusions discussed in
+preceding chapters are of interest in this connection.</p>
+
+<p>An interesting example of the illusion of color may be easily demonstrated
+by means of a yellow filter. For this purpose a canary glass is quite
+satisfactory. When such a filter is placed before the eyes a daytime scene
+outdoors, for example, is likely to appear to be illuminated to a greater
+intensity than<span class="pagenum"><a name="Page_157" id="Page_157">[Pg 157]</a></span> when the eyes are not looking through the filter. This is
+true for a glass used by the author notwithstanding the fact that the
+filter transmits only about one-half as much light as a perfectly clear
+colorless glass. In other words, the brightnesses of objects in the scene
+are reduced on the average about fifty per cent, still the subject is
+impressed with an apparent <i>increase</i> in the intensity of illumination
+(and in brightness) when the filter is placed before the eyes. Of course,
+the actual reduction in brightness depends upon the color of the object.</p>
+
+<p>In such a case as the foregoing, true explanations are likely to involve
+many factors. For this reason explanations are usually tedious if they are
+to be sufficiently qualified to be reasonably near completeness. In this
+case it appears that the yellow filter may cause one to appraise the
+intensity of illumination as having increased, by associating such an
+influence as the sun coming out from behind a cloud. If we look into the
+depths where light and color accumulated their psychological powers, we
+are confronted on every hand by associations many of which are more or
+less obscure, and therefore are subtly influential.</p>
+
+<p>The psychological powers of colors could have been discussed more
+generally in the preceding chapter, but inasmuch as they can be
+demonstrated more effectively by lighting (and after all the effect is one
+of light in any case) they will be discussed briefly here. They have been
+presented more at length elsewhere.</p>
+
+<p>It is well known that the artist, decorator, and<span class="pagenum"><a name="Page_158" id="Page_158">[Pg 158]</a></span> others speak of warm and
+cold colors, and these effects have a firm psychological foundation. For
+example, if a certain room be illuminated by means of blue light, it does
+seem colder. A theater illuminated by means of bluish light seems
+considerably cooler to the audience than is indicated by the thermometer.
+If this lighting is resorted to in the summer time the theater will be
+more inviting and, after all, in such a case it makes little difference
+what the thermometer indicates. The &#8220;cold&#8221; light has produced an illusion
+of coolness. Similarly &#8220;warm&#8221; light, such as yellow or orange, is
+responsible for the opposite feeling and it is easily demonstrated that an
+illusion of higher temperature may be produced by its use. As already
+stated, color-schemes in the decorations and furnishings produce similar
+effects but in general they are more powerful when the primary light is
+colored. In the latter case no object is overlooked for even the hands and
+faces of the beings in the room are colored by the light. In the case of
+color-schemes not all objects are tinged with the desired &#8220;warm&#8221; or &#8220;cold&#8221;
+color.</p>
+
+<p>In the foregoing, associations play a prominent r&ocirc;le. The sky has been
+blue throughout the numberless centuries during which the human organism
+evolved. The blue-sky during all these centuries has tinged the shadows
+outdoors a bluish color. That shade is relatively cool we know by
+experience and perhaps we associate coolness or cold with the aerial
+realm. These are glimpses of influences which have co&ouml;perated toward
+creating the psychological effect of coldness in the case of bluish light.
+By contrast<span class="pagenum"><a name="Page_159" id="Page_159">[Pg 159]</a></span> with skylight, sunlight is yellowish, and a place in the sun
+is relatively warm. South rooms are usually warmer than north rooms in
+this hemisphere when artificial heat is absent and the psychological
+effect of warmth has naturally grown out of these and similar influences.</p>
+
+<p>We could go further into the psychology of light and color and conjecture
+regarding effects directly attributable to color, such as excitement,
+depression, and tranquillity. In so doing we would be led far astray from
+illusions in the sense of the term as used here. Although this term as
+used here is still somewhat restricted, it is broader in scope than in its
+usual applications. However, it is not broad enough to lead far into the
+many devious highways and byways of light and color. If we did make these
+excursions we would find associations almost universally answering the
+questions. The question would arise as to innate powers of colors and we
+would find ourselves wondering if all these powers were acquired (through
+associations) and whether or not some were innate. And after many
+interesting views of the intricate subject we would likely conclude that
+the question of the innateness of some of the powers of color must be left
+unanswered.</p>
+
+<p>As an example let us take the case of the restfulness or depression due to
+blue. We note that the blue sky is quite serene or tranquil and we find
+that the delicate sensibilities of poets verify this impression. This
+association could account for the impression or feeling of tranquillity
+associated with blue. On proceeding further, we would find nature&#8217;s
+<span class="pagenum"><a name="Page_160" id="Page_160">[Pg 160]</a></span>solitudes often tinged with the blue skylight, for these solitudes are
+usually in the shade. Thus their restfulness or even depressiveness may be
+accounted for&mdash;partially at least. These brief glimpses are presented in
+order that they may suggest to the reader another trend of thought when
+certain illusions of light and color are held up for analysis. Besides
+these our individual experiences which have molded our likes and dislikes
+must be taken into account. This phase of light and color has been treated
+elsewhere.<a href="#reference"><small>[6]</small></a></p>
+
+<p>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 (<a href="#fig77">Fig. 77</a>). For years the apparent ending has more or less
+carelessly been attributed to the diminution of the density of atmospheric
+fog or haze, but recently Karrer<a href="#reference"><small>[13]</small></a> has suggested what appears to be the
+correct explanation.</p>
+
+<p>When the beam of light from a powerful searchlight is directed into space,
+its path is visible owing to the scattering of some of the light by dust
+and moisture particles and the molecules of the air itself. While
+obviously the beam itself must go on indefinitely, its luminous path
+appears to end abruptly at no very great distance from the source. This is
+true whether the beam is photographed or viewed with the naked eye.</p>
+
+<p><a name="fig77" id="fig77"></a>&nbsp;<span class="pagenum"><a name="Page_161" id="Page_161">[Pg 161]</a></span></p>
+<div class="figcenter"><img src="images/fig77.jpg" alt="" /></div>
+<p class="center">Fig. 77.&mdash;Apparent ending of a searchlight beam.</p>
+<p>&nbsp;</p>
+
+<p>The fact that the appearance of the beam is no different when it is
+directed horizontally than when directed vertically proved that the common
+assumption pertaining to the ending of the haze or fog is untenable.
+Furthermore, photometric measurements on the different portions of the
+beam as seen from a position near the searchlight show that the beam is
+actually brighter at its outer termination than near its origin. Again,
+the apparent length of the beam<span class="pagenum"><a name="Page_162" id="Page_162">[Pg 162]</a></span> varies with the position of the observer,
+and bears a direct ratio to his distance from the searchlight.</p>
+
+<p>The fact is, that the luminous path of the beam has no definite ending,
+and extends to a very great distance&mdash;practically to infinity. It appears
+to be sharply cut off for the same reason that the boundary between earth
+and sky in a flat landscape is a sharp line. Just as the horizon recedes
+when the landscape is viewed from an elevation, so the beam appears longer
+when one&#8217;s distance from it is increased. The outer portion appears
+brighter, because here the line of sight pierces it to great depth.</p>
+
+<p>That the ending of the beam appears <i>close at hand</i> is no doubt partly due
+to the brightness distribution, but is also a matter of perspective
+arising from the manner in which the beam is adjusted. Searchlight
+operators in the army were instructed to adjust the light to throw a
+parallel beam. Accordingly, the adjustments were so made that the beam
+appeared the same width at its outer extremity as at its base. The result
+seems to be a short parallel shaft of light, but is really a divergent
+cone of infinite extent, its angle of divergence being such as exactly to
+offset the effects of perspective.</p>
+
+<p>If the beam were a truly parallel one it would seem to come to a point,
+just as the edges of a long straight stretch of country road seem to meet
+at the horizon. If the sides of the road were not parallel, but diverged
+from the observer&#8217;s eye at exactly the rate at which they ordinarily would
+appear to converge, then the road would seem to be as wide where it passed
+out at the horizon as at the observer&#8217;s feet. If there were<span class="pagenum"><a name="Page_163" id="Page_163">[Pg 163]</a></span> no other
+means in the landscape of judging the distance of the horizon than by the
+perspective afforded by the road, it would likely be inferred that the
+road only extended a short distance on the level, and then went down a
+hill, that is, passed abruptly from the observer&#8217;s view.</p>
+
+<p>These conditions obtain ideally in the case of the searchlight beam. There
+is no other means of judging the position in space of the &#8220;end&#8221; of an
+unobstructed searchlight beam than by the perspective of the beam itself,
+and the operator in adjusting it to appear parallel eliminates the
+perspective.</p>
+
+<p>The angle at which the beam must diverge to appear parallel to an observer
+depends upon the distance of the observer from the searchlight. A beam
+which seems parallel to a person close to it will not appear so at a
+distance. This fact probably accounts for the difficulties encountered
+during &#8220;searchlight drill&#8221; in the army in getting a beam which satisfied
+both the private operating the lamp and the officer down the field as to
+its parallelity.</p>
+
+<p>To summarize, the apparent abrupt ending of a searchlight beam is purely
+an optical illusion. It really has no ending; it extends to infinity.</p>
+
+
+<p>&nbsp;</p><p>&nbsp;</p>
+<hr style="width: 50%;" />
+<p><span class="pagenum"><a name="Page_164" id="Page_164">[Pg 164]</a></span></p>
+<h2><a name="XI" id="XI"></a>XI<br />NATURE</h2>
+
+<p class="dropcap"><span class="caps">Visual</span> illusions abound everywhere, and there are a number of special
+interest in nature. Inasmuch as these are representative of a wide range
+of conditions and are usually within the possible experience of nearly
+everyone daily, they appear worthy of special consideration. Some of these
+have been casually mentioned in other chapters but further data may be of
+interest. No agreement has been reached in some cases in the many
+suggested explanations and little or no attempt of this character will be
+made in the following paragraphs. Many illusions which may be seen in
+nature will be passed by because their existence should be obvious after
+reading the preceding chapters. For example, a tree appears longer when
+standing than after it has been felled for the same reason that we
+overestimate vertical lines in comparison with horizontal ones. The
+apparent movement of the sun, moon, and stars, when clouds are floating
+past, is a powerful, though commonplace, illusion but we are more
+specifically interested in static illusions. However, it is of interest to
+recall the effect of involuntary eye-movements or of fluctuation in
+fixation because this factor in vision is important in many illusions. It
+is demonstrated by lying face upward on a starlit night and<span class="pagenum"><a name="Page_165" id="Page_165">[Pg 165]</a></span> fixing the
+gaze upon a star. The latter appears to move more or less jerkily over its
+dark background. The magnitude and involuntary nature of these
+eye-movements is demonstrated in this manner very effectively.</p>
+
+<p>The effect sometimes known as aerial perspective has been mentioned
+heretofore. The atmosphere is not perfectly transparent or colorless and
+is not homogeneous from an optical standpoint. It scatters rays of the
+shorter wave-lengths more than those of the longer wave-lengths. Hence it
+appears of a bluish tint and anything seen through great distances of it
+tends toward a reddish color. The blue sky and the redness of the setting
+sun are results of this cause. Distant signal-lights are reddened, due to
+the decrease in the rays of shorter wave-length by scattering. Apparently
+we have come to estimate distance to some extent through the amount of
+blurring and tinting superposed upon the distant scene.</p>
+
+<p>In the high Rockies where the atmosphere is unusually clear, stretches of
+fifty miles of atmosphere lying between the observer and the distant peaks
+will show very little haze. A person inexperienced in the region is likely
+to construe this absence of haze as a shorter distance than the reality
+and many amusing incidents and ludicrous mistakes are charged against the
+tenderfoot in the Rockies. After misjudging distance so often to his own
+discomfiture a tourist is said to have been found disrobing preparatory to
+swimming across an irrigation ditch. He had lost confidence in his
+judgment of distance and was going to assume the risk of jumping across
+what appeared to be a ditch but what might be a broad<span class="pagenum"><a name="Page_166" id="Page_166">[Pg 166]</a></span> river. Of course,
+this story might not be true but it serves as well as any to emphasize the
+illusion which arises when the familiar haze is not present in strange
+territory.</p>
+
+<p>It is a common experience that things &#8220;loom in a fog,&#8221; that is, that they
+appear larger than they really are. An explanation which has been offered
+is that of an &#8220;excess of aerial perspective&#8221; which causes us to
+overestimate distance and therefore to overestimate size. If this
+explanation is correct, it is quite in the same manner that in clear
+atmosphere in the mountains we underestimate distance and, consequently,
+size. However, another factor may enter in the latter case, for the
+illusion is confined chiefly to newcomers; that is, in time one learns to
+judge correctly. On entering a region of real mountains the first time,
+the newcomer&#8217;s previous experience with these formations is confined to
+hills relatively much smaller. Even allowing considerably for a greater
+size when viewing the majestic peaks for the first time, he cannot be
+expected to think in terms of peaks many times larger than his familiar
+hills. Thus underestimating the size of the great peaks, he underestimates
+the distance. The rarity of the atmospheric haze aids him in making this
+mistake. This is not offered as a substitute for aerial perspective as the
+primary cause of the illusion but it appears to the author that it is a
+cause which must be taken into account.</p>
+
+<p>The apparent form of the sky has attracted the attention of many
+scientific investigators for centuries. There are many conflicting
+opinions as to the causes<span class="pagenum"><a name="Page_167" id="Page_167">[Pg 167]</a></span> of this appearance of form, but there is
+general agreement that the sky appears usually as a flattened vault. The
+sky is bright, due to scattering of light by actual particles of solid
+matter and moisture and possibly by molecules of gas. Lack of optical
+homogeneity due to varying refractive index is likely to be partially
+responsible. Usually a prominent layer of haze about a mile in thickness
+(although this varies considerably) lies next to the earth&#8217;s surface. The
+top of this haze is fairly well defined as aerial travelers know, but the
+sky above is still far from black, indicating scattered light and
+illuminated particles still higher. As one continues to ascend, thereby
+leaving more and more of the luminous haze behind, the sky becomes darker
+and darker. Often at altitudes of four or five miles the sky is very dark
+and the sun is piercingly bright. Usually there is little or no bright
+haze adjacent to the sun at these high altitudes as is commonly seen from
+the earth&#8217;s surface. At these high altitudes the author is not conscious
+of a flattened vault as at the earth&#8217;s surface but the illusion of a
+hemispherical dome still persists.</p>
+
+<p>There is some agreement that the dome of the sky appears less depressed at
+the zenith by night than by day. This is in accord with the author&#8217;s
+observation at very high altitudes on occasions when the sky was much
+darker than when viewed from the earth&#8217;s surface. Dember and Uibe assumed
+the apparent shape as a part of a sphere (justifying this assumption to
+their satisfaction) and obtained estimates of the apparent depression at
+the zenith. They estimated the middle point of the arc from the zenith<span class="pagenum"><a name="Page_168" id="Page_168">[Pg 168]</a></span> to
+the horizon and then measured the angular altitude of that point. They
+found that the degree of clearness of the sky has considerable influence
+upon the apparent height and they state that the sky appears higher in the
+sub-tropics than in Germany. On very clear moonless nights they found that
+the shape of the sky-dome differs little from that of a hemisphere. They
+concluded that the phenomenon is apparently due to optical conditions of
+the atmosphere which have not been determined.</p>
+
+<p>It is of interest to note the appearance of the sky when cumulus clouds
+are present. The bases of these vary in height, but are found at altitudes
+from three to five thousand feet. They appear to form a flat roof of
+clouds bending downward at the horizon, thus giving the appearance of a
+vaulted but flattened dome. This apparent shape does not differ much in
+clear weather, perhaps due largely to the accustomedness of the eye and to
+the degradation of color from blue to gray toward the horizon. Furthermore
+the lower sky is usually much brighter than the zenith and the latter
+being darker appears to hang lower. It is of interest to note how
+persistent is the illusion of a flattened dome, for when one rises rapidly
+in the air and, within a few minutes, is on the level with the clouds or
+the dense low-lying haze, he is mildly surprised to find these are levels
+and not vaulted roofs. Despite the fact that by many previous experiences
+he has learned what to expect, the feeling of mild surprise is born each
+time on ascending rapidly.</p>
+
+<p>The appearance of the flattened vault of the sky is held by some to
+account for the apparent enlargement<span class="pagenum"><a name="Page_169" id="Page_169">[Pg 169]</a></span> of the sun, moon, and the
+constellations at the horizon. That is, they appear more distant at the
+horizon and we instinctively appraise them as being larger than when they
+are at higher altitudes. It is certain that these heavenly bodies do
+appear much larger when they are rising or setting than when they are
+nearer the zenith. In fact, this is one of the most remarkable and
+surprising illusions which exist. Furthermore this apparent enlargement
+has been noted universally, still many persons have attributed it to an
+actual optical magnification. Although we are more familiar with this
+enlargement in connection with the sun and moon, it still persists with
+the constellations. For example, Orion is apparently very large; in fact,
+this is the origin of the name. That this enlargement is an illusion can
+be shown in several ways but that it is solely due to the influence of the
+apparent flattened form of the sky may be doubted. Certainly the moon
+appears greatly enlarged while near the horizon, even when there is doubt
+as to an appreciable appearance of flattening of the sky-dome.</p>
+
+<p>Many peculiar conditions and prejudices must be taken into account. For
+example, if various persons are asked to give an idea of how large is the
+disk of the sun or moon, their answers would vary usually with the head of
+a barrel as the maximum. However, the size of a tree at a distant sky-line
+might unhesitatingly be given as thirty feet. At the horizon we
+instinctively compare the size of the sun, moon, and constellations with
+hills, trees, houses, and other objects, but when the former are high
+toward the<span class="pagenum"><a name="Page_170" id="Page_170">[Pg 170]</a></span> zenith in the empty sky we may judge them in their isolated
+position to be nearer, hence smaller.</p>
+
+<p>Normally the retinal image grows larger as the object approaches, but this
+same sensation also arises when an object grows in size without altering
+its distance. If the moon be viewed through field-glasses the image is
+larger than in the case of the unaided eyes, but it is quite common for
+observers to state that it appears smaller. The enlargement may be
+interpreted as approach and inasmuch as we, through habit, allow for
+enlargement as an object approaches, we also must reduce it in our
+imagination to its natural size. Perhaps in this case we overdo this
+reduction.</p>
+
+<p>James states that the increased apparent size of the moon near the horizon
+&#8220;is a result of association and probability. It is seen through vaporous
+air and looks dimmer and duskier than when it rides on high; and it is
+seen over fields, trees, hedges, streams, and the like, which break up the
+intervening space and makes us the better realize the latter&#8217;s extent.&#8221;
+Both these causes may make the moon seem more distant when it is at low
+altitudes and as its visual angle grows less, we may think that it must be
+a larger body and we so perceive it. Certainly it looks particularly large
+when a well-known object is silhouetted against its disk.</p>
+
+<p>Before proceeding further with explanations, it may be of interest to turn
+to <a href="#fig78">Fig. 78</a> which is an accurate tracing of the path of the moon&#8217;s image
+across a photographic plate. The camera was placed in a fixed position and
+the image of the moon&#8217;s disk on rising was accurately focused on a
+panchromatic plate.<span class="pagenum"><a name="Page_171" id="Page_171">[Pg 171]</a></span> A dense red filter was maintained over the lens
+throughout in order to eliminate the effect of selective absorption of the
+atmosphere. But the slightest enlargement was detected in the width of the
+path near the horizon as compared with that at the highest altitude. This
+copy was made because it was thought better for reproduction than the
+photograph which would require a half-tone. This is positive evidence that
+the phenomenon is an illusion.</p>
+
+<p><a name="fig78" id="fig78"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig78.jpg" alt="" /></div>
+<p class="center">Fig. 78.&mdash;An accurate tracing from a photograph (continual exposure) of the moon rising.</p>
+<p>&nbsp;</p>
+
+<p>Similarly <a href="#fig79">Fig. 79</a> is a copy of a negative of several exposures of the sun.
+Owing to the greater brightness, continuous exposure was not considered
+feasible. A panchromatic plate and red filter was used as in the case of
+the moon. The various exposures were<span class="pagenum"><a name="Page_172" id="Page_172">[Pg 172]</a></span> made without otherwise adjusting the
+camera. Again no enlargement at the horizon was found.</p>
+
+<p><a name="fig79" id="fig79"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig79.jpg" alt="" /></div>
+<p class="center">Fig. 79.&mdash;Accurate tracings from a photograph (short exposures at intervals) of the sun setting.</p>
+<p>&nbsp;</p>
+
+<p>Although the foregoing is conclusive evidence of the illusory character of
+the enlargement there are other ways of making measurements. On viewing
+the sun at the horizon a bright after-image is obtained. This may now be
+projected upon the sky as a background at any desired altitude. It will
+appear much smaller at the zenith than the sun appears at the horizon.
+Certainly this is a simple and conclusive demonstration of the illusion.
+In this case the after-image of the sun or the sun itself will usually
+appear at least twice as large as the after-image at the zenith.</p>
+
+<p><span class="pagenum"><a name="Page_173" id="Page_173">[Pg 173]</a></span>If the variation in the position of the eyes is held to account for the
+illusion, this explanation may be supported by using a horizontal
+telescope with adjustable cross-hairs, and a mirror. By varying the
+position of the latter the disk of the sun may be measured at any altitude
+without varying the position of the eye. When everything is eliminated
+from the field but the moon&#8217;s disk, it is found to be constant in size.
+However, this is not conclusive evidence that the variation in the
+position of the line of sight accounts for the illusion.</p>
+
+<p>As a demonstration of the absence of enlargement of the size of the moon
+near the horizon some have brought forward measurements of the lunar
+circles and similar phenomena. These are said to be unaffected by the
+altitude of the moon except for refraction. But even this does not change
+the horizontal diameter and actually diminishes the vertical one. The moon
+is further away when near the horizon than when at the zenith, the maximum
+increase in distance being one-half the diameter of the earth. This would
+make the moon appear about one-sixtieth, or one-half minute of arc smaller
+at the horizon than at the zenith. This is not only in the wrong direction
+to aid in accounting for the apparent enlargement, but it is so slight as
+to be imperceptible to the unaided eye.</p>
+
+<p>Nearly two centuries ago Robert Smith and his colleagues concluded that
+the sky appears about three times as far away at the horizon as at the
+zenith. They found that the relative apparent diameters of the sun and of
+the moon varied with altitude as follows:</p>
+
+<p><span class="pagenum"><a name="Page_174" id="Page_174">[Pg 174]</a></span></p>
+
+<table border="0" cellpadding="0" cellspacing="5" summary="table">
+<tr><td colspan="3" align="center">Altitude</td>
+    <td><span class="spacer">&nbsp;</span></td>
+    <td align="center">Relative apparent diameter</td></tr>
+<tr><td align="right">0</td><td>deg.</td><td>(horizon)</td>
+    <td>&nbsp;</td>
+    <td align="center">100</td></tr>
+<tr><td align="right">15</td><td align="center">"</td><td>&nbsp;</td>
+    <td>&nbsp;</td>
+    <td align="center"><span style="margin-left: .5em;">68</span></td></tr>
+<tr><td align="right">30</td><td align="center">"</td><td>&nbsp;</td>
+    <td>&nbsp;</td>
+    <td align="center"><span style="margin-left: .5em;">50</span></td></tr>
+<tr><td align="right">45</td><td align="center">"</td><td>&nbsp;</td>
+    <td>&nbsp;</td>
+    <td align="center"><span style="margin-left: .5em;">40</span></td></tr>
+<tr><td align="right">60</td><td align="center">"</td><td>&nbsp;</td>
+    <td>&nbsp;</td>
+    <td align="center"><span style="margin-left: .5em;">34</span></td></tr>
+<tr><td align="right">75</td><td align="center">"</td><td>&nbsp;</td>
+    <td>&nbsp;</td>
+    <td align="center"><span style="margin-left: .5em;">31</span></td></tr>
+<tr><td align="right">90</td><td align="center">"</td><td>(zenith)</td>
+    <td>&nbsp;</td>
+    <td align="center"><span style="margin-left: .5em;">30</span></td></tr></table>
+
+<p><a name="fig80" id="fig80"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig80.jpg" alt="" /></div>
+<p class="center">Fig. 80.&mdash;Explanation offered by Smith of the apparent enlargement of heavenly bodies near the horizon.</p>
+<p>&nbsp;</p>
+
+<p>They also found a similar relation between the altitude and the apparent
+size of constellations. <a href="#fig80">Fig. 80</a> is a reproduction of a diagram which Smith
+submitted as illustrating the cause of the illusion of apparent
+enlargement of heavenly bodies near the horizon. If the sky seems to be a
+flattened vault, the reason for the apparent decrease in the size of the
+sun, the moon, or the constellations, as they approach the zenith, is
+suggested by the diagram.</p>
+
+<p>It has also been suggested that such illusions as those shown in <a href="#fig10">Figs. 10</a>
+and <a href="#fig19">19</a> are associated with that of apparent enlargement of heavenly bodies
+near<span class="pagenum"><a name="Page_175" id="Page_175">[Pg 175]</a></span> the horizon. It will be left to the reader to decide whether or not
+there is any similarity or relation.</p>
+
+<p>Zoth appears to have proved, to his own satisfaction at least, that the
+chief factors are not aerial perspective, the apparent curvature or form
+of the sky, and the comparison of the sun or moon with objects of known
+size. He maintained that the illusion of apparent decrease in size as
+these bodies increase in altitude is due to the necessary elevation of the
+eye. No available experimental evidence seems to refute his statement. In
+fact, Guttman&#8217;s experiments seem to confirm it to some extent. The latter
+found that there was an apparent diminution in the size of objects of
+several per cent, in objects slightly more than a foot distant from the
+eyes, as they were raised so that the line of vision changed from
+horizontal to an angle of forty degrees. The magnitude of this diminution
+is not sufficient to promote the acceptance of elevation of the eyes as a
+primary cause of the illusion in respect to the heavenly bodies.</p>
+
+<p>Notwithstanding arguments to the contrary, it is difficult to eliminate
+aerial perspective and the apparent form of the sky as important factors.
+That no explanation of this illusion has been generally accepted indicates
+the complexity of the causes. Certainly the reddish coloration of the sun
+and moon near the horizon and the contrast with the misty atmosphere
+combined with the general vague aspect of the atmosphere contribute
+something if no more than a deepening of the mystery. Variations in the
+transparency and brightness of the air must play some part.</p>
+
+<p><span class="pagenum"><a name="Page_176" id="Page_176">[Pg 176]</a></span>In discussing the great illusions of nature, it appears appropriate to
+introduce the mirage. This is not due to an error of sense of judgment.
+The eye sees what is presented but the inversions and other peculiar
+effects are due to variations in the refractive index of the atmosphere.
+These variations account for the appearance of &#8220;lakes&#8221; in arid deserts, of
+the inverted images of ships and icebergs on the sea and of &#8220;pools of
+water&#8221; on pavements. The refractive index of the atmosphere is continually
+changing, but the changes are chiefly of two types: (1) those due to
+irregular heating and (2) those due to normal variation with altitude. The
+former type are particularly responsible for mirages.</p>
+
+<p><a name="fig81" id="fig81"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig81.jpg" alt="" /></div>
+<p class="center">Fig. 81.&mdash;Explanation of a common mirage.</p>
+<p>&nbsp;</p>
+
+<p>A common type of mirage is illustrated in <a href="#fig81">Fig. 81</a>. This is often visible
+on deserts where the hot sand causes the adjacent layer of air to expand
+and therefore, the refractive index to increase. This layer of air then
+may be considered to operate like an inverted prism. The rays of light
+close to the earth are bent convex to the earth and the curvature of those
+higher up may be reversed. The reason that an object may<span class="pagenum"><a name="Page_177" id="Page_177">[Pg 177]</a></span> appear double,
+or as if mirrored by the surface of a nearby pond, is clearly shown in the
+illustration.</p>
+
+<p>Similar atmospheric conditions are found sometimes over pavements and over
+bodies of water. As one rides along in an automobile ascending an incline,
+if he closely observes at the moment the line of sight is just on the
+level of the pavement, he will often be rewarded by the sight of a mirage.
+An approaching pedestrian may have no feet (they are replaced by a bit of
+sky) and the distant pavement will appear to contain pools of water on its
+surface.</p>
+
+<p>Sometimes on deserts, over ice fields, or on northern seas, mirages are of
+the inverted type. A horseman or ship may appear suspended in the air in
+an inverted position. When the density of the air is great enough so that
+only the upper rays reach the eye, the object will be seen inverted and
+far <ins class="correction" title="original: bove">above</ins> the surface upon which nothing is seen. Many modifications of
+these types are possible through variations in the refractive indices of
+various strata of air. Sometimes the air is stratified horizontally and
+even vertically, which results in magnification as well as other peculiar
+effects.</p>
+
+<p>As one rides over the desert in a rapidly moving train or automobile these
+vagaries of nature are sometimes very striking, because the speed of
+motion will make the effects of the varying refractive indices more
+marked. A distant foothill may appear to float in the air or to change its
+shape very rapidly. An island surrounded by quiet air and water may appear
+like a huge mushroom barely supported by a stem.</p>
+
+<p><span class="pagenum"><a name="Page_178" id="Page_178">[Pg 178]</a></span>Arctic mirages are no less wonderful than those of the hot barren deserts.
+While traveling along over the ice and snow distant white peaks may assume
+the most fantastic shapes. At first they may appear flattened like a
+table-land and then suddenly they may stretch upward like spires. They may
+shrink then spread like huge mushrooms supported by the stalk-like bases
+and stretching out laterally. Suddenly they may shoot upward into another
+series of pinnacles as if another range had suddenly arisen. Such antics
+may go on for hours as one travels along a frozen valley. Even a change of
+position of the eyes accompanying a change from erect to lying down may
+cause remarkable contortions of the distant mountains and one is reminded
+of the psalmist&#8217;s query, &#8220;Why hop ye so, ye hills?&#8221;</p>
+
+<p>Although not an illusion but a physical reality, it is of interest in
+passing to note the colored halo or aureole surrounding the shadows of
+objects cast by the sun against a cloud, fog, or jet of steam. The most
+wonderful effects are seen by the aerial traveler over a bank of clouds
+when the upper sky is clear. For example, the shadow of the aircraft cast
+by the sun upon a dense layer of clouds is surrounded by a halo or aureole
+of the colors of the rainbow. The phenomenon is purely optical, involving
+diffraction of light. A well-known example of this is the &#8220;Spectre of the
+Brocken.&#8221;</p>
+
+
+<p>&nbsp;</p><p>&nbsp;</p>
+<hr style="width: 50%;" />
+<p><span class="pagenum"><a name="Page_179" id="Page_179">[Pg 179]</a></span></p>
+<h2><a name="XII" id="XII"></a>XII<br />PAINTING AND DECORATION</h2>
+
+<p class="dropcap"><span class="caps">In</span> the arts where colors, brightnesses, contrasts, lines, forms, and
+perspectives mean so much, it is obvious that visual illusions are
+important. Sometimes they are evils which must be suppressed; in some
+cases they are boons to the artist if he is equal to the task of
+harnessing them. Ofttimes they appear unheralded and unexpected. The
+existence of visual illusions is sufficient to justify the artist&#8217;s pride
+in his &#8220;eye&#8221; and his dependence upon his visual judgment rather than upon
+what he knows to be true. However true this may be, knowledge is as useful
+to the artist as to anyone else. The artist, if he is to produce art, is
+confronted with the tremendous task of perfecting an imperfect nature and
+he is handicapped with tools inferior to those which nature has at her
+disposal. He must deal with reflected lights from earthly materials.
+Nature has these besides the great primary light-sources&mdash;the sun, the
+moon, the stars, and, we might say, the sky. She also has the advantage of
+overwhelming magnitudes.</p>
+
+<p>These are only a few of the disadvantages under which the artist works,
+but they indicate that he must grasp any advantage here and there which he
+may. Knowledge cannot fail him; still, if he fears that it will take him
+out of his &#8220;dream world&#8221; and taint<span class="pagenum"><a name="Page_180" id="Page_180">[Pg 180]</a></span> him with earthliness, let him ponder
+over da Vinci, Rembrandt, and such men. These men <i>knew</i> many things. They
+possessed much knowledge and, after all, the latter is nothing more nor
+less than science when its facts are arranged in an orderly manner. If the
+arts are to speak &#8220;a noble and expressive language&#8221; despite the handicaps
+of the artist, knowledge cannot be drawn upon too deeply.</p>
+
+<p>Perhaps in no other art are the workmen as little acquainted with their
+handicaps and with the scientific facts which would aid them as in
+painting. Painters, of course, may not agree as to this statement, but if
+they wish to see how much of the science of light, color, lighting, and
+vision they are unacquainted with, let them invade the book-shelves. If
+they think they know the facts of nature let them paint a given scene and
+then inquire of the scientist regarding the relative values (brightnesses)
+in the actual scene. They will usually be amazed to learn that they cannot
+paint the lights and shadows of nature excepting in the feeblest manner.
+The range of contrast represented by their entire palette is many thousand
+times less than the range of values in nature. In fact exclusive of
+nature&#8217;s primary light-sources, such as the sun, she sometimes exhibits a
+range of brightness in a landscape a million times greater than the
+painter can produce with black and white pigments. This suggests that the
+artist is justified in using any available means for overcoming the
+handicap and among his tools, visual illusions are perhaps the most
+powerful.</p>
+
+<p>A painting in the broadest sense is an illusion,<span class="pagenum"><a name="Page_181" id="Page_181">[Pg 181]</a></span> for it strives to
+present the three-dimensional world upon plane areas of two dimensions.
+Through representation or imitation it creates an illusion. If the
+artist&#8217;s sensibility has been capable of adequate selection, his art will
+transmit, by means of and through the truths of science, from the region
+of perception to the region of emotion. Science consists of knowing; art
+consists of doing. If the artist is familiar with the facts of light,
+color, lighting, and vision, he will possess knowledge that can aid him in
+overcoming the great obstacles which are ever-present. A glimpse of visual
+illusions should strengthen him in his resolution to depend upon visual
+perception, but he can utilize these very illusions. He can find a use for
+facts as well as anyone. Facts as well as experience will prepare him to
+do his work best.</p>
+
+<p>The artist may suggest brilliant sunlight by means of deep shadow. The old
+painters gained color at the expense of light and therefore lowered the
+scale of color in their representations of nature. It is interesting to
+see how increasing knowledge, as centuries passed, directed painters as it
+did others onward toward the truth. Turner was one of the first to abandon
+the older methods in an attempt to raise the scale of his paintings toward
+a brilliance more resembling nature. By doing this he was able to put
+color in shadows as well as in lights. Gradually paintings became more
+brilliant. Monet, Claude, and others worked toward this goal until the
+brightnesses of paintings reached the limits of pigments. The
+impressionists, in their desire to paint nature&#8217;s<span class="pagenum"><a name="Page_182" id="Page_182">[Pg 182]</a></span> light, introduced
+something which was nothing more nor less than science. All this time the
+true creative artist was introducing science&mdash;in fact, illusions&mdash;to
+produce the perfect illusion which was his goal. A survey of any
+representative paintings&#8217; gallery shows the result of the application of
+more and more knowledge, as the art of painting progressed through the
+centuries. Surely we cannot go back to the brown shadows and sombre
+landscapes of the past.</p>
+
+<p>In the earliest art, in the efforts of children, in the wall-paintings of
+the Egyptians, and in Japanese representation of nature, the process is
+selective and not imitative. Certain things are chosen and everything else
+is discarded. In such art selection is carried to the extreme. Much of
+this simplicity was due to a lack of knowledge. Light and shade, or
+shading, was not introduced until science discovered and organized its
+facts. Quite in the same manner linear and aerial perspective made their
+appearances until in our present art the process of selection is complex.
+In our paintings of today objects are modeled by light and shade; they are
+related by perspective; backgrounds and surroundings are carefully
+considered; the proper emphasis of light, shade and color are given to
+certain details. The present complexity provides unprecedented
+opportunities for the application of knowledge pertaining to illusions but
+it should be understood that this application tends only toward realism of
+external things. Idealism in art and realism of character and expression
+are accomplished by the same tools&mdash;pigments and brushes&mdash;as realism of
+objective details is attained and<span class="pagenum"><a name="Page_183" id="Page_183">[Pg 183]</a></span> there is nothing mysterious in the
+masterpieces of this kind. Mystery in art as in other activities is merely
+lack of understanding due to inadequate knowledge. Mysteries of today
+become facts tomorrow. Science moves with certainty into the unknown,
+reaping and binding the facts and dropping them behind where they may be
+utilized by those who will.</p>
+
+<p>The painter can imitate aerial perspective although many centuries elapsed
+before mankind was keen enough to note its presence in nature. The
+atmospheric haze diminishes the brightness of very bright objects and
+increases that of dark objects. It blurs the distant details and adds a
+tinge of blue or violet to the distance. In painting it is a powerful
+illusion which the painter has learned to employ.</p>
+
+<p>The painter can accurately imitate mathematical or linear perspective but
+the art of early centuries does not exhibit this feature. In a painting a
+tremendously powerful illusion of the third dimension is obtained by
+diminishing the size of objects as they are represented in the distance.
+Converging lines and the other manifold details of perspective are aiding
+the artist in his efforts toward the production of the great illusion of
+painting.</p>
+
+<p>The painter cannot imitate focal perspective or binocular perspective. He
+can try to imitate the definition in the central portion of the visual
+field and the increased blurring toward the periphery. Focal perspective
+is not of much importance in painting, because it is scarcely perceptible
+at the distances at which paintings are usually viewed. However<span class="pagenum"><a name="Page_184" id="Page_184">[Pg 184]</a></span> the
+absence of binocular perspective in painting does decrease the
+effectiveness of the illusion very markedly. For this reason a painting is
+a more successful illusion when viewed with one eye than with two eyes. Of
+course, in one of nature&#8217;s scenes the converse is true because when
+viewing it with both eyes all the forms of perspective co&ouml;perate to the
+final end&mdash;the true impression of three dimensions.</p>
+
+<p>The painter may imitate the light and shade of solid forms and thereby
+apparently model them. In this respect a remarkable illusion of solid form
+or of depth may be obtained. For example, a painted column may be made to
+appear circular in cross-section or a circle when properly shaded will
+appear to be a sphere. Both of these, of course, are pure illusions. Some
+stage paintings are remarkable illusions of depth, and their success
+depends chiefly upon linear perspective and shadows. However, the illusion
+which was so complete at a distance quite disappears at close range.</p>
+
+<p>The inadequate range of brightnesses or values obtainable by means of
+pigments has already been discussed. The sky in a landscape may be
+thousands of times brighter than a deep shadow or a hole in the ground. A
+cumulus cloud in the sky may be a hundred thousand times brighter than the
+deepest shadow. However, the artist must represent a landscape by means of
+a palette whose white is only about thirty times brighter than its black.
+If the sun is considered we may have in a landscape a range of brightness
+represented by millions.</p>
+
+<p>This illustrates the pitiable weakness of pigments<span class="pagenum"><a name="Page_185" id="Page_185">[Pg 185]</a></span> alone as
+representative media. Will not light <i>transmitted</i> through media some day
+be utilized to overcome this inherent handicap of reflecting media? To
+what extent is the success of stained glass windows due to a lessening of
+this handicap? The range of brightness in this case may be represented by
+a black (non-transmitting) portion to the brightness of the background
+(artificial or sky) as seen through an area of clear glass. Transparencies
+have an inherent advantage over ordinary paintings in this respect and
+many effective results may be obtained with them even in photography.</p>
+
+<p>It is interesting to study the effect of greatly increasing the range of
+values or brightnesses in paintings by utilizing non-uniform distributions
+of light. Let us take a given landscape painting. If a light-source be so
+placed that it is close to the brighter areas (perhaps clouds and sky near
+the sun) it will illuminate this brighter portion several times more
+intensely than the more distant darker portions of the picture (foreground
+of trees, underbrush, deep shadows, etc.). The addition to the
+effectiveness of the illusion is quite perceptible. This effect of
+non-uniform lighting may be carried to the extreme for a painting by
+making a positive lantern-slide (rather contrasty) of the painting and
+projecting this slide upon the painting in accurate superposition. Now if
+the painting is illuminated solely by the &#8220;lantern-slide&#8221; the range of
+contrast or brightness will be enormously increased. The lightest portions
+of the picture will now be illuminated by light passing through the almost
+totally transparent portions of the slide<span class="pagenum"><a name="Page_186" id="Page_186">[Pg 186]</a></span> and the darkest portions by
+light greatly reduced by passing through the nearly opaque portions of the
+slide. The original range of contrast in the painting, perhaps twenty to
+one, is now increased perhaps to more than a thousand to one. This
+demonstration will be surprising to anyone and will emphasize a very
+important point to the painter.</p>
+
+<p>The painter has at his disposal all the scientific facts of light, color,
+and vision. Many of these have been presented elsewhere,<a href="#reference"><small>[9]</small></a> and those
+pertaining to illusions have been discussed in preceding chapters. These
+need not be repeated here excepting a few for the purpose of reminding the
+reader of the wealth of material available to the painter and decorator.
+Many tricks may be interjected into the foreground for their effect upon
+the background and vice versa. For example, a branch of a tree drooping in
+the foreground apparently close to the observer, if done well, will give a
+remarkable depth to a painting. Modeling of form may be effected to some
+extent by a judicious use of the &#8220;retiring&#8221; and &#8220;advancing&#8221; colors. This
+is one way to obtain the illusion of depth.</p>
+
+<p>After-images play many subtle parts in painting. For example, in a
+painting where a gray-blue sky meets the horizon of a blue-green body of
+water, the involuntary eye-movements may produce a pinkish line just above
+the horizon. This is the after-image of the blue-green water creeping
+upward by eye-movements. Many vivid illusions of this character may be
+deliberately obtained by the artist. Some of the peculiar restless effects
+obtained in impressionistic painting (stippling of small areas with
+<span class="pagenum"><a name="Page_187" id="Page_187">[Pg 187]</a></span>relatively pure hues) are due to contrasts and after-images.</p>
+
+<p>A painting came to the author&#8217;s notice in which several after-images of
+the sun, besides the image of the sun itself, were disposed in various
+positions. Their colors varied in the same manner as the after-image of
+the sun. Doubtless the painter strove to give the impression which one has
+on gazing at the sun. Whether or not this attempt was successful does not
+matter but it was gratifying to see the attempt made.</p>
+
+<p>There are many interesting effects obtainable by judicious
+experimentation. For example, if a gray medium be sprayed upon a landscape
+in such a manner that the material dries in a very rough or diffusing
+surface some remarkable effects of fog and haze may be produced. While
+experimenting in this manner a very finely etched clear glass was placed
+over a landscape and the combined effect of diffusely reflected light and
+of the slight blurring was remarkable. By separating the etched glass from
+the painting a slight distance, a very good imitation &#8220;porcelain&#8221; was
+produced. The optical properties of varnishes vary and their effect varies
+considerably, depending upon the mode of application. These and many other
+details are available to the painter and decorator. An interesting example
+among many is a cellulose lacquer dyed with an ordinary yellow dye. The
+solution appears yellow by transmitted light or it will color a surface
+yellow. By spraying this solution on a metallic object such as a
+nickel-plated piece, in a manner that leaves the medium rough<span class="pagenum"><a name="Page_188" id="Page_188">[Pg 188]</a></span> or
+diffusing, the effect is no longer merely a yellow but a remarkable lustre
+resembling gilt. Quite in the same manner many effects of richness, depth
+of color, haziness, etc., are obtainable by the artist who is striving to
+produce a great illusion.</p>
+
+<p>All the means for success which the painter possesses are also available
+to the decorator; however, the latter may utilize some of the illusions of
+line, form, irradiation, etc., which the architect encounters. The
+decorator&#8217;s field may be considered to include almost all of the painter&#8217;s
+and much of the architect&#8217;s. This being the case, little space will be
+given to this phase of the subject because painting and architecture are
+separately treated. The decorator should begin to realize more fully the
+great potentiality of lighting in creating moods or in giving expression
+to an interior. The psychology of light and the use of lighting as a mode
+of expression have barely been drawn upon by the decorator. Lighting has
+already been discussed so it will be passed by at this point.</p>
+
+<p>The practice of hanging pictures on walls which are brilliantly colored is
+open to criticism. There are galleries in existence where paintings are
+hung on brilliant green or rose walls. The changes in the appearance of
+the object due to these highly colored environments are easily
+demonstrated by viewing a piece of white paper pinned upon the wall. On
+the green wall, the white paper appears pinkish; on the rose wall, it
+appears bluish or greenish. A portrait or a picture in which there are
+areas of white or delicate tints is subject to considerable distortions in
+the appearance of its colors. Similarly, if a woman must<span class="pagenum"><a name="Page_189" id="Page_189">[Pg 189]</a></span> have a colored
+background, it is well to choose one which will induce the more desirable
+tints in her appearance. The designer of gowns certainly must recognize
+these illusions of color which may be desirable or undesirable.</p>
+
+<p>The lighting of a picture has already been mentioned, but the discussion
+was confined solely to distribution of light. The quality of the light
+(its spectral character) may have an enormous influence upon the painting.
+In fact with the same painting many illusions may be produced by lighting.
+In general, paintings are painted in daylight and they are not the same in
+appearance under ordinary artificial light. For this reason the artist is
+usually entitled to the preservation of the illusion as he completed it.
+By using artificial daylight which has been available for some years, the
+painting appears as the artist gave it his last touch. Of course, it is
+quite legitimate to vary the quality of light in case the owner desires to
+do so, but the purpose here is to emphasize the fact that the quality of
+light is a powerful influence upon the appearance of the painting. The
+influence is not generally enough recognized and its magnitude is
+appreciated by relatively few persons.</p>
+
+<p>All other considerations aside, a painting is best hung upon a colorless
+background and black velvet for this purpose yields remarkable results.
+Gray velvet is better, when the appearance of the room is taken into
+consideration, as it must be. However, the influence of dark surroundings
+toward enhancing the illusion is well worth recognizing. In the case of a
+special picture or a special occasion, a painting may<span class="pagenum"><a name="Page_190" id="Page_190">[Pg 190]</a></span> be exhibited in a
+booth&mdash;a huge shadow-box not unlike a show-window in which the
+light-sources are concealed. Such experiments yield many interesting data
+pertaining to the illusions which the painter strives to obtain.</p>
+
+<p><a name="fig82" id="fig82"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig82tmb.jpg" alt="" /><br />
+<a href="images/fig82.jpg"><small>Larger Image</small></a></div>
+<p class="center">Fig. 82.&mdash;Illustrating the apparent distortion of a picture frame in which the grain of the wood is visible.</p>
+<p>&nbsp;</p>
+
+<p>Incidentally on viewing some picture frames in which the grain of the wood
+was noticeable, the frames did not appear to be strictly rectangular. The
+illusions were so strong that only by measuring the frames could one be
+convinced that they were truly rectangular and possessed straight sides.
+Two of these are represented in <a href="#fig82">Figs. 82</a> and <a href="#fig83">83</a>. In the former, the
+horizontal sides appear bent upward in the middle and the two vertical
+sides appear bowed toward the right. In <a href="#fig83">Fig. 83</a>, the frame appears
+considerably narrower at the left end than at the right. Both these frames
+were represented in the original drawings by true rectangles.</p>
+
+<p><span class="pagenum"><a name="Page_191" id="Page_191">[Pg 191]</a></span>Many illusions are to be seen in furniture and in other woodwork in which
+the grain is conspicuous. This appears to the author to be an objection in
+general to this kind of finish. In <a href="#fig84">Fig. 84</a> there is reproduced a
+photograph of the end of a board which was plane or straight
+notwithstanding its warped, or bowed, appearance. The original photographs
+were placed so as to be related as shown in the figure. Various degrees of
+the illusion are evident. The reader will perhaps find it necessary to
+convince himself of the straightness of the horizontal edges by applying a
+straight edge. These are examples of the same illusion as shown in <a href="#fig37">Figs. 37 to 40</a>.</p>
+
+<p><a name="fig83" id="fig83"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig83tmb.jpg" alt="" /><br />
+<a href="images/fig83.jpg"><small>Larger Image</small></a></div>
+<p class="center">Fig. 83.&mdash;Another example similar to <a href="#fig82">Fig. 82</a>.</p>
+<p>&nbsp;<span class="pagenum"><a name="Page_192" id="Page_192">[Pg 192]</a></span></p>
+<p><a name="fig84" id="fig84"></a></p>
+<div class="figcenter"><img src="images/fig84tmb.jpg" alt="" /><br />
+<a href="images/fig84.jpg"><small>Larger Image</small></a></div>
+<p class="center">Fig. 84.&mdash;From actual photographs of the end-grain of a board.</p>
+<p>&nbsp;</p>
+
+<p><span class="pagenum"><a name="Page_193" id="Page_193">[Pg 193]</a></span>Perhaps a brief statement regarding the modern <i>isms</i> in art may be of
+interest. In considering some of the extreme examples, we must revise our
+idea that art is or should be always beautiful. The many definitions of
+art would lead us too far afield to discuss them here but in its most
+extended and popular sense, art may be considered to mean everything
+which we distinguish from nature. Certainly art need not be beautiful,
+although it does seem that the world would welcome the beautiful and would
+get along contentedly without art that is ugly or repulsive. The modern
+<i>isms</i> must be viewed with consideration, for there are many impostors
+concealing their inabilities by flocking to these less understood fields.
+However, there are many sincere workers&mdash;research artists&mdash;in the modern
+<i>isms</i> and their works may best be described at present as experiments in
+the psychology of light, shade, and color. They have cast aside or reduced
+in importance some of the more familiar components such as realism and are
+striving more deeply to utilize the psychology of light and color. Some of
+them admit that they strive to paint through child&#8217;s eyes and mind&mdash;free
+from experience, prejudice, and imitation. These need all the scientific
+knowledge which is available&mdash;and maybe more.</p>
+
+<p>In closing this chapter, it appears necessary to remind the artist and
+others that it is far from the author&#8217;s intention to subordinate the
+artist&#8217;s sensibility to the scientific facts or tools. Art cannot be
+manufactured by means of formulae. This would not be true if we knew a
+great deal more than we do pertaining to the science of light, color, and
+vision. The artist&#8217;s fine sensibility will always be the dominating
+necessity in the production of art. He must possess the ability to compose
+exquisitely; he must be able to look at nature through a special
+temperament; he must be gifted in eye and in hand; he<span class="pagenum"><a name="Page_194" id="Page_194">[Pg 194]</a></span> must be master of
+unusual visual and intellectual processes. But knowledge will aid him as
+well as those in other activities. A superior acquaintance with scientific
+facts lifted past masters above their fellows and what helped Leonardo da
+Vinci, Rembrandt, Velasquez, Turner, Claude, Monet, and other masters will
+help artists of today. What would not those past masters have accomplished
+if they had available in their time the greater knowledge of the present!</p>
+
+
+<p>&nbsp;</p><p>&nbsp;</p>
+<hr style="width: 50%;" />
+<p><span class="pagenum"><a name="Page_195" id="Page_195">[Pg 195]</a></span></p>
+<h2><a name="XIII" id="XIII"></a>XIII<br />ARCHITECTURE</h2>
+
+<p class="dropcap"><span class="caps">Many</span> illusions are found in architecture and, strangely enough, many of
+these were recognized long before painting developed beyond its primitive
+stages. The architecture of classic Greece displays a highly developed
+knowledge of many geometrical illusions and the architects of those
+far-off centuries carefully worked out details for counteracting them.
+Drawings reveal many illusions to the architect, but many are not
+predicted by them. The ever-changing relations of lines and forms in
+architecture as we vary our viewpoint introduce many illusions which may
+appear and disappear. No view of a group of buildings or of the components
+of a single structure can be free from optical illusions. We never see in
+the reality the same relations of lines, forms, colors, and brightnesses
+as indicated by the drawings or blue-prints. Perhaps this is one of the
+best reasons for justifying the construction of expensive models of our
+more pretentious structures.</p>
+
+<p>No detailed account of the many architectural illusions will be attempted,
+for it is easy for the reader to see many of the possibilities suggested
+by preceding chapters. However, a few will be touched upon to reveal the
+magnitude of the illusory effect and to<span class="pagenum"><a name="Page_196" id="Page_196">[Pg 196]</a></span> aid the observer in looking for
+or recognizing them, or purely for historical interest. In architecture
+the eye cannot be wholly satisfied by such tools as the level, the square,
+and the plumb-line. The eye is satisfied only when the <i>appearance</i> is
+satisfactory. For the purpose of showing the extent of certain
+architectural illusions, the compensatory measures applied by the Greeks
+are excellent examples. These also reveal the remarkable application of
+science to architecture as compared with the scanty application in
+painting of the same period.</p>
+
+<p>During the best period of Grecian art many refinements were applied in
+order to correct optical illusions. It would be interesting to know to
+what extent the magnitude of the illusions as they appeared to many
+persons were actually studied. The Parthenon of Athens affords an
+excellent example of the magnitude of the corrections which the designer
+thought necessary in order to satisfy the eye. The long lines of the
+architrave&mdash;the beam which surmounts the columns or extends from column to
+column&mdash;would appear to sag if it were actually straight. This is also
+true of the stylobate, or substructure of a colonnade, and of pediments
+and other features. These lines were often convex instead of being
+straight as the eye desires to see them.</p>
+
+<p>In the Parthenon, the stylobate has an upward curvature of more than four
+inches on the sides of the edifice and of more than two and a half inches
+on the east and west fronts. Vertical features were made to incline inward
+in order to correct the common appearance of leaning outward at the top.
+In<span class="pagenum"><a name="Page_197" id="Page_197">[Pg 197]</a></span> the Parthenon, the axes of the columns are not vertical, but they are
+inclined inward nearly three inches. They are said also to be inclined
+toward each other to such a degree that they would meet at an altitude of
+one mile above the ground. The eleven-foot frieze and architrave is
+inclined inward about one and one-half inches.</p>
+
+<p>In <a href="#fig85">Fig. 85</a>, <i>a</i> represents the front of a temple as it should appear; <i>b</i>
+represents its appearance (exaggerated) if it were actually built like <i>a</i>
+without compensations for optical illusions; <i>c</i> represents it as built
+and showing the physical corrections (exaggerated) in order that it may
+appear to the eye as <i>a</i> does.</p>
+
+<p>Tall columns if they are actually straight are likely to appear somewhat
+shrunken in the middle; therefore they are sometimes made slightly swollen
+in order to appear straight. This outward curvature of the profile is
+termed an entasis and in the Parthenon column, which is thirty-four feet
+in height, amounted to about three-fourths of an inch. In some early
+Grecian works, it is said that this correction was overdone but that its
+omission entirely is quite unsatisfactory. Some authorities appear to
+believe that an excellent compromise is found in the Parthenon columns.</p>
+
+<p><a name="fig85" id="fig85"></a>&nbsp;<span class="pagenum"><a name="Page_198" id="Page_198">[Pg 198]</a></span></p>
+<div class="figcenter"><img src="images/fig85tmb.jpg" alt="" /><br />
+<a href="images/fig85.jpg"><small>Larger Image</small></a></div>
+<p class="center">Fig. 85.&mdash;Exaggerated illusions in architecture.</p>
+<p>&nbsp;</p>
+
+<p>One of the conditions which is responsible for certain illusions and has
+been compensated for on occasions is represented in <a href="#fig86">Fig. 86</a>. On the left
+are a series of squares of equal size placed in a vertical row. If these
+are large so that they might represent stories in a building they will
+appear to decrease in size from the bottom upward, because of the
+decreasing<span class="pagenum"><a name="Page_199" id="Page_199">[Pg 199]</a></span> projection at the eye. This is obvious if the eye is
+considered to be at the point where the inclined lines meet. In order to
+compensate for the variation in visual angle, there must be a series of
+rectangles increasing considerably in height toward the top. The
+correction is shown in the illustration. It is stated that an inscription
+on an ancient temple was written in letters arranged vertically, and in
+order to make them appear of equal size they were actually increased in
+size toward the top according to the law represented in <a href="#fig86">Fig. 86</a>. Obviously
+a given correction would be correct only for one distance in a given
+plane.</p>
+
+<p><a name="fig86" id="fig86"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig86.jpg" alt="" /></div>
+<p class="center">Fig. 86.&mdash;Illustrating the influence of visual angle upon apparent vertical height.</p>
+<p>&nbsp;</p>
+
+<p>In Chapter VIII the phenomenon of irradiation was discussed and various
+examples were presented. It exerts its influence in the arts as elsewhere.
+Columns viewed against a background of white sky<span class="pagenum"><a name="Page_200" id="Page_200">[Pg 200]</a></span> appear of smaller
+diameter than when they are viewed against a dark background. This is
+illustrated in <a href="#fig87">Fig. 87</a> where the white and the black columns are supposed
+to be equal in diameter.</p>
+
+<p>The careful observer will find numberless optical illusions and
+occasionally he will recognize an attempt on the part of the architect to
+apply an illusory effect to his advantage. In <a href="#fig88">Fig. 88</a> some commonplace
+illusions are presented, not for what they are worth, but to suggest how
+prevalent they may be. Where the pole or column intersects the arches or
+circle, there is an apparent change in the direction of the curved lines.
+The different types of arches show different degrees of the illusion. It
+may be of interest for the reader to refer to preceding chapters and to
+ascertain what types of illusions are involved.</p>
+
+<p><a name="fig87" id="fig87"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig87.jpg" alt="" /></div>
+<p class="center">Fig. 87.&mdash;Irradiation in architecture.</p>
+<p>&nbsp;</p>
+
+<p>If a high wall ends in a series of long horizontal steps at a slightly
+inclined sidewalk, the steps are not likely to appear horizontal.</p>
+
+<p>Some remarkable illusions of depth or of solid form are given to flat
+surfaces when snow is driven against them so as to adhere in decreasing
+amounts similar to shading.</p>
+
+<p>A suggestion of augmented height may be given<span class="pagenum"><a name="Page_201" id="Page_201">[Pg 201]</a></span> to a low tower by
+decreasing the size of its successive portions more rapidly than demanded
+by perspective alone. The same principal can be applied in many ways. For
+example, in <a href="#fig89">Fig. 89</a> the roof appears quite extensive when viewed so that
+the end-walls of the structure are not seen. Such illusions find
+applications in the moving-picture studio where extensive interiors, great
+fortresses, and even villages must be erected within small areas.
+Incidentally the camera aids to create the illusion of magnitude in
+photographs because it usually magnifies perspective, thereby causing
+scenes to appear more extensive in the photographs than in the reality.</p>
+
+<p><a name="fig88" id="fig88"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig88.jpg" alt="" /></div>
+<p class="center">Fig. 88.&mdash;Some simple geometrical-optical illusions in architecture.</p>
+<p>&nbsp;</p>
+
+<p>Balance in architecture is subject to illusions and might be considered an
+illusion itself. For example, our judgment of balance is based largely
+upon mechanical laws. A composition must appear to be stable; that is, a
+large component such as a tower must not be situated too far from what we
+take as a center of<span class="pagenum"><a name="Page_202" id="Page_202">[Pg 202]</a></span> gravity, to appear capable of tipping the remainder
+of the structure. In physics we would apply the term &#8220;moment.&#8221; Each mass
+may be multiplied by its distance from the center of gravity, thus
+determining its moment. For a building or other composition to appear
+stable the sum of these moments must be zero; that is, those tending to
+turn the figure in one direction must be counterbalanced by those tending
+to turn it in another direction. In appraising a composition, our
+intellect summates the effects of different parts somewhat in this manner
+and if satisfactory, balance is considered to have been attained. The
+colors of the various components exert an influence in this respect, so it
+is seen that illusions may have much to do with the satisfactoriness of
+architectural compositions.</p>
+
+<p><a name="fig89" id="fig89"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig89.jpg" alt="" /></div>
+<p class="center">Fig. 89.&mdash;By decreasing the exposed length of shingles toward the top a greater apparent expanse is obtained.</p>
+<p>&nbsp;</p>
+
+<p><span class="pagenum"><a name="Page_203" id="Page_203">[Pg 203]</a></span>Various illusions of height, of ceiling, composedness, etc., may be
+obtained by the color of the ceiling. A dark cornice in an interior may
+appear to be unsupported if the walls below are light in color, without
+any apparent vertical supports for the cornice. We are then subjected to
+the illusion of instability or incongruity. Dark beams of ceilings are not
+so obtrusive because our intellect tells us that they are supports passing
+over the top of the walls and are therefore able to support themselves.
+Color and brightness in such cases are very important.</p>
+
+<p>The architectural details on exteriors evolved under daylighting outdoors
+so that their form has been determined by the shadows desired. The
+architect leads his lights and shadows around the building modeling it as
+he desires. An offset here and a depression there models the exterior in
+light and shade. The forms must be powerful enough to resist the
+obliterating effect of overcast skies but notwithstanding all precautions
+the expression of an exterior varies considerably with nature&#8217;s lighting.
+Indoors the architect has a powerful controllable medium in artificial
+light which he may draw upon for producing various expressions or moods in
+rooms. The effect of shadows is interesting when viewing some structures
+flood-lighted at night. In those cases where the light is directed upward
+there is a reversal of shadows which is sometimes very unsatisfactory.</p>
+
+<p>It is interesting to experiment with various ornamental objects lighted
+from various directions. For example, a Corinthian capital lighted from
+below<span class="pagenum"><a name="Page_204" id="Page_204">[Pg 204]</a></span> may produce an unpleasant impression upon the observer. We do not
+like to have the dominant light from below, perhaps because it is annoying
+to the eyes. Possibly this is an instinct acquired by experience in
+snow-fields or on the desert, or it may be a heritage of ancestral
+experience gained under these glaring conditions. This dislike manifests
+itself when we appraise shadow-effects and therefore our final impression
+is tempered by it.</p>
+
+<p>All sculptured objects depend for their appearance upon the lighting, and
+they are greatly influenced by it. In sculpture, in a strict sense,
+illusions play a lesser part than in other arts. Perhaps in those of very
+large proportions various corrections have been applied. A minor detail of
+interest is the small cavity in the eye, corresponding to a reversed
+cornea. This depression catches a shadow which gives considerable
+expression to the eye.</p>
+
+
+<p>&nbsp;</p><p>&nbsp;</p>
+<hr style="width: 50%;" />
+<p><span class="pagenum"><a name="Page_205" id="Page_205">[Pg 205]</a></span></p>
+<h2><a name="XIV" id="XIV"></a>XIV<br />MIRROR MAGIC</h2>
+
+<p class="dropcap"><span class="caps">Strictly</span> speaking there are fewer illusions found in the practice of the
+magician than is generally supposed; that is, the eye usually delivers
+correctly to the intellect, but the judgment errs for various reasons. The
+&#8220;illusion&#8221; is due to false assumptions, to the distracting words, to
+unduly accented superfluous movements of the magician; or in general to
+downright trickery. Much of the magician&#8217;s success is due to glibness of
+tongue and deftness of fingers, but many of the more notable &#8220;tricks&#8221; were
+those involving the use of mirrors and the control of light. Black
+curtains, blackened assistants, and controlled light have played prominent
+parts in the older magic, but the principles of these are easily
+understood. However, the mirror perhaps has done more to astound the
+audience than any other device employed by the magician. For this reason,
+and because its effects are commonly termed illusions, some representative
+examples will be presented.</p>
+
+<p>In a previous chapter attention was called to the simple but usually
+overlooked fact that, for example, the image of a face in a mirror is
+reversed as to right and left. When this fact is overlooked we may be
+astonished at the changed expression of an intimate friend as we view the
+face (reversed) in the mirror.<span class="pagenum"><a name="Page_206" id="Page_206">[Pg 206]</a></span> Similarly our own features are reversed as
+to right and left and we are acquainted with this reversed image rather
+than the appearance of our face as it is. Inasmuch as faces are not
+accurately symmetrical and many are quite unsymmetrical the effects of the
+mirror are sometimes startling. It might be of interest for the reader to
+study his face in the mirror and note that the right ear is the left ear
+of the image which he sees. He will also find it of interest to compare
+the face of a friend as viewed directly with the appearance of its image
+in the mirror. If he desires to see himself as others see him, he can
+arrange two mirrors vertically almost at a right-angle. By a little
+research he will find an image of his own face, which is not reversed;
+that is, an image whose right ear is really his right ear.</p>
+
+<p>A famous &#8220;illusion&#8221; which astounded audiences was the sphinx illustrated
+in <a href="#fig90">Fig. 90</a>. The box was placed upon a table and when opened there was
+revealed a Sphinxian head, but why it was called a Sphinx is clothed in
+mystery because upon some occasions it talked. As a matter of fact it
+belonged to a body which extended downward from the table-top and this
+kneeling human being was concealed from the audience by two very clean
+plate-glass mirrors <i>M</i> shown in the accompanying diagram. The table
+actually appeared to have three legs but the audience if it noticed this
+at all assumed the fourth leg was obscured by the foremost leg. The walls,
+floor, and ceiling of the box-like recess in which the table was placed
+were covered with the same material. It is seen by the diagram that the
+mirrors <i>M</i> reflected<span class="pagenum"><a name="Page_207" id="Page_207">[Pg 207]</a></span> images of the side walls <i>W</i> and these images were
+taken by the audience to be portions of the rear wall <i>W</i>. Thus the table
+appeared to be open underneath and the possibilities of the apparatus are
+evident.</p>
+
+<p><a name="fig90" id="fig90"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig90.jpg" alt="" /></div>
+<p class="center">Fig. 90.&mdash;An example of a &#8220;mirror&#8221; illusion.</p>
+<p>&nbsp;</p>
+
+<p>The magician with a fine flow of language could dwell at length upon the
+coming to life of the head of an ancient statue which he had in the box in
+his hand. Walking to the table he could place the box over a trap-door and
+by the time he had unlatched the door of the box, the assistant kneeling
+under the table could have his head thrust upward through the trap-door of
+the table-top into the box. After a few impressive words, supposed to be
+Hindoo but in reality were Hoodoo, presto! and the Sphinx was revealed.<span class="pagenum"><a name="Page_208" id="Page_208">[Pg 208]</a></span>
+It conversed after a period of silence extending back to the days of
+Rameses when a wrathful god condemned an unfortunate king to imprisonment
+in the stone statue. The original trick awed audiences for many nights and
+defied explanation until one night a keen observer noted finger-prints on
+what proved to be a mirror. Doubtless a careless accomplice lost his job,
+but the damage had been done, for the trick was revealed. This &#8220;illusion&#8221;
+is so effective that it, or variations of it, are still in use.</p>
+
+<p><a name="fig91" id="fig91"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig91.jpg" alt="" /></div>
+<p class="center">Fig. 91.&mdash;Another example of &#8220;mirror magic.&#8221;</p>
+<p>&nbsp;</p>
+
+<p>Another simple case is illustrated in <a href="#fig91">Fig. 91</a>. A large plate-glass mirror
+<i>M</i> was placed at an angle of approximately 45 degrees from the floor.
+Through a hole in it an assistant&#8217;s head and shoulders projected and the
+edge of the opening was covered with a draped cloth. The audience saw the
+image of the ceiling <i>C</i> of the alcove reflected by the mirror but being
+<span class="pagenum"><a name="Page_209" id="Page_209">[Pg 209]</a></span>ignorant of the presence of the mirror, assumed this image to be the rear
+wall. This trick was effective for many years. Obviously the mirrors must
+be spotlessly clean and the illuminations of the walls, ceiling, and in
+some cases, the floor must be very uniform. Furthermore, no large
+conspicuous pattern could be used for lining the box-like recess.</p>
+
+<p>The foregoing examples illustrate the principles involved in the
+appearance of ghosts on the stage and of a skeleton or other gruesome
+object in place of a human being. The possibilities of mirrors in such
+fields are endless and they can be studied on a small scale by anyone
+interested. The pseudoscope which produces effects opposite to those of
+the stereoscope is an interesting device.</p>
+
+<p>The foregoing is the faintest glimpse of the use of the mirror, but it
+does not appear advisable to dwell further upon its use, for after all the
+results are not visual illusions in the sense of the term as usually
+employed throughout this book.</p>
+
+
+<p>&nbsp;</p><p>&nbsp;</p>
+<hr style="width: 50%;" />
+<p><span class="pagenum"><a name="Page_210" id="Page_210">[Pg 210]</a></span></p>
+<h2><a name="XV" id="XV"></a>XV<br />CAMOUFLAGE</h2>
+
+<p class="dropcap"><span class="caps">Illusions</span> played many roles in the science and art of deception during the
+World War, but they served most prominently in the later stages of the war
+upon the sea. Inasmuch as the story of the science of camouflage is not
+generally available, it appears worth while to present it briefly. Besides
+being of interest, it will reveal to the reader the part that the science
+of light, color, lighting, and vision played in deception. Furthermore,
+the reader will sense the numberless illusions which are woven into
+camouflage as developed in nature, and in human activities. The word
+<i>camouflage</i> by origin does not include all kinds of deception; however,
+by extension it may and will here signify almost the entire art and
+science of deception as found in nature and as practiced in the World War.</p>
+
+<p><i>Terrestrial Camouflage.</i>&mdash;Camouflage is an art which is the natural
+outgrowth of our instinct for concealment and deception when pitting our
+wits against those of a crafty prey or enemy. It is an art older than the
+human race, for its beginnings may be traced back to the obscurity of the
+early ages of the evolution of animal life. The name was coined by the
+French to apply to a definite art which developed during the Great War to
+a high state, as many other arts developed by drawing deeply upon the
+resources of scientific<span class="pagenum"><a name="Page_211" id="Page_211">[Pg 211]</a></span> knowledge. With the introduction of this specific
+word to cover a vast field of activity in scientifically concealing and
+deceiving, many are led to believe that this is a new art, but such is not
+the case. However, like many other arts, such as that of flying, the
+exigencies of modern warfare have provided an impetus which has resulted
+in a highly developed art.</p>
+
+<p>Scientists have recognized for many years, and perhaps more or less
+vaguely for centuries, that Nature exhibits wonderful examples of
+concealment and deception. The survival of the fittest, as Darwin
+expressed his doctrine, included those individuals of a species who were
+best fitted by their markings and perhaps by peculiar habits to survive in
+the environment in which they lived. Naturally, markings, habits, and
+environment became more and more adapted to each other until the species
+became in equilibrium with Nature sufficiently to insure its perpetuity.
+If we look about us upon animal life we see on every hand examples of
+concealing coloration and attitudes designed to deceive the prey or enemy.
+The rabbit is mottled because Nature&#8217;s infinite variety of highlights,
+shadows, and hues demand variety in the markings of an animal if the
+latter is to be securely hidden. Solid color does not exist in Nature&#8217;s
+landscapes in large areas. The rabbit is lighter underneath to compensate
+for the lower intensity of illumination received on these portions. As
+winter approaches, animals in rigorous climates need warmer coats, and the
+hairs grow longer. In many cases the color of the hairs changes to gray or
+white, providing a better coating for the winter environment.</p>
+
+<p><span class="pagenum"><a name="Page_212" id="Page_212">[Pg 212]</a></span>Animals are known to mimic inanimate objects for the sake of safety. For
+example, the bittern will stand rigid with its bill pointed skyward for
+many minutes if it suspects an enemy. Non-poisonous snakes resemble
+poisonous ones in general characteristics and get along in the world on
+the reputation of their harmful relatives. The drone-bee has no sting, but
+to the casual observer it is a bee and bees generally sting. Some animals
+have very contrasting patterns which are conspicuous in shape, yet these
+very features disguise the fact that they are animals. Close observation
+of fishes in their natural environment provides striking examples of
+concealing coloration. Vast works have been written on this subject by
+scientists, so it will only be touched upon here.</p>
+
+<p>There are many examples of &#8220;mobile&#8221; camouflage to be found in Nature.
+Seasonal changes have been cited in a foregoing paragraph. The chameleon
+changes its color from moment to moment. The flounder changes its color
+and <i>pattern</i> to suit its environment. It will even strive to imitate a
+black and white checkerboard.</p>
+
+<p>In looking at a bird, animal, insect, or other living thing it is
+necessary to place it in its natural environment at least in the
+imagination, before analyzing its coloration. For example, a male mallard
+duck hanging in the market is a very gaudy object, but place it in the
+pond among the weeds, the green leaves, the highlights, and the shadows,
+and it is surprisingly inconspicuous. The zebra in the zoo appears to be
+marked for the purpose of heralding its presence anywhere in the range of
+vision, but in its reedy, bushy,<span class="pagenum"><a name="Page_213" id="Page_213">[Pg 213]</a></span> grassy environment it is sufficiently
+inconspicuous for the species to survive in Nature&#8217;s continuous warfare.</p>
+
+<p>Thus studies of Nature reveal the importance of general hue, the necessity
+for broken color or pattern, the fact that black spots simulate shadows or
+voids, the compensation for lower illumination by counter-shading, and
+many other facts. The artist has aided in the development of camouflage,
+but the definite and working basis of all branches of camouflage are the
+laws and facts of light, color, and vision as the scientist knows them.</p>
+
+<p>Just as lower animal life has unconsciously survived or evolved by being
+fitted to do so, mankind has consciously, or at least instinctively,
+applied camouflage of various kinds to fool his prey or his enemy. Many of
+us in hunting ducks have concealed the bow of our sneak-boat with mud and
+weeds, or in the season of floating ice, with a white cloth. In our quest
+of water fowl we use decoys and grass suits. The Esquimau stalks his game
+behind a piece of ice. In fact, on every hand we find evidences of this
+natural instinct. The Indian painted his face and body in a variety of
+colors and patterns. Did he do this merely to be hideous? It seems very
+possible that the same instinct which made him the supreme master of
+wood-craft caused him to reap some of the advantages of concealment due to
+the painting of his face and body.</p>
+
+<p>In past wars there is plenty of evidence that concealment and deception
+were practiced to the full extent justifiable by the advantages or
+necessity. In the World War the advent of the airplane placed the<span class="pagenum"><a name="Page_214" id="Page_214">[Pg 214]</a></span> third
+dimension in reconnaissance and called for the application of science in
+the greatly extended necessity for concealment and deception. With the
+advent of the airplane, aerial photography became a more important factor
+than visual observation in much of the reconnaissance. This necessitated
+that camouflage in order to be successful had to meet the requirements of
+the photographic eye, as well as that of the human eye. In other words,
+the special characteristics of the colors used had to be similar to those
+of Nature&#8217;s colors. For example, chlorophyl, the green coloring matter of
+vegetation, is a peculiar green as compared with green pigments. When
+examined with a spectroscope it is seen to reflect a band of deep red
+light not reflected by ordinary pigments. In considering this aspect it is
+well to bear in mind that the eye is a synthetic apparatus; that is does
+not analyze color in a spectral sense. An artist who views color
+subjectively and is rarely familiar with the spectral basis may match a
+green leaf perfectly with a mixture of pigments. A photographic plate, a
+visual filter, or a spectroscope will reveal a difference which the
+unaided eye does not.</p>
+
+<p>Some time before the Great War began, it occurred to the writer that
+colored filters could be utilized in aiding vision by increasing the
+contrast of the object to be viewed against its surroundings.<a href="#reference"><small>[9]</small></a> Studies
+were made of various filters, made with the object of the experiment in
+mind, in viewing the uniforms of various armies. Further developments were
+made by applying the same principles to colored lights and painted
+pictures. Many of these have been<span class="pagenum"><a name="Page_215" id="Page_215">[Pg 215]</a></span> described elsewhere. With the
+development of the science of camouflage, filters came into use for the
+detection of camouflage. As a result of the demand for avoiding detection
+by photographic plates and by various colored filters, some paints
+provided for the camoufleur were developed according to the spectral
+requirements. Many other applications of science were developed so that
+camouflage can now be called an art based upon sound scientific
+principles.</p>
+
+<p>Natural lighting is so variable that it is often impossible to provide
+camouflage which will remain satisfactory from day to day; therefore, a
+broad knowledge of Nature&#8217;s lighting is necessary in order to provide the
+best compromise. There are two sources of light in the daytime, namely,
+the sun and the sky. The relative amounts of light contributed by these
+two sources is continually changing. The sky on cloudless days contributes
+from one-tenth to one-third of the total light received by a horizontal
+surface at noon. Light from the sky and light reflected from the
+surroundings illuminate the shadows. These shadows are different in color
+than highlights, although these finer distinctions may be ignored in most
+camouflage because color becomes less conspicuous as the distance of
+observation increases. In general, the distribution of brightness or light
+and shade is the most important aspect to be considered.</p>
+
+<p>The camoufleur worries over shadows more than any other aspect generally.
+On overcast days camouflage is generally much more successful than on
+sunny days. Obviously, counter-shading is resorted to in<span class="pagenum"><a name="Page_216" id="Page_216">[Pg 216]</a></span> order to
+eliminate shadows, and where this is unsuccessful confusion is resorted to
+by making more shadows. The shape and orientation of a building is very
+important to those charged with the problem of rendering it inconspicuous
+to the enemy, but little attention has been paid to these aspects. For
+example, a hangar painted a very satisfactory dull green will be
+distinguishable by its shape as indicated by its shadow and shaded sides.
+In this zone a hangar, for example, would be more readily concealed if its
+length lay north and south. Its sides could be brought with a gradual
+curve to the ground and its rear, which is during most of the day in
+shadow, could be effectively treated to conceal the shadow. A little
+thought will convince the reader of the importance of shape and
+orientation.</p>
+
+<p>Broken color or pattern is another fundamental of camouflage which, of
+course, must be adapted to its environment. For our trucks, cannon, and
+many other implements of war, dark green, yellow, dark blue, light gray,
+and other colors have been used in a jumble of large patterns. A final
+refinement is that of the blending of these colors at a distance, where
+the eye no longer resolves the individual patches, to a color which
+simulates the general hue of the surroundings. For example, red and green
+patches at a distance blend to yellow; yellow and blue patches blend to a
+neutral gray if suitably balanced, but if not, to a yellow-gray or a
+blue-gray; red, green, and blue if properly balanced will blend to a gray;
+black, white and green patches will blend to a green shade, and so on.
+These facts are simple to those who are<span class="pagenum"><a name="Page_217" id="Page_217">[Pg 217]</a></span> familiar with the science of
+light and color, but the artist, whose knowledge is based upon the mixture
+of pigments, sometimes errs in considering this aspect of color-blending
+by distance. For example, it is not uncommon for him to state that at a
+distance yellow and blue patches blend to make green, but the addition of
+lights or of juxtaposed colors is quite different in result from the
+addition of pigments by intimately mixing them.</p>
+
+<p>In constructing such a pattern of various colors it is also desirable to
+have the final mean brightness approximate that of the general
+surroundings. This problem can be solved by means of the photometer and a
+formula provided, which states, for example, that a certain percentage of
+the total area be painted in gray, another percentage in green, and so on.
+The photometer has played an important r&ocirc;le in establishing the scientific
+basis of camouflage. The size of the pattern must be governed by the
+distance at which it is to be viewed, for obviously if too small the
+effect is that of solid color, and if too large it will render the object
+conspicuous, which is a disadvantage ranking next to recognizable.</p>
+
+<p>Where the artist is concerned with a background which does not include the
+sky, that is, where he deals only with <i>illuminated</i> objects on the earth,
+his trained eye is valuable provided the colors used meet the demands made
+by photographic plates and visual color-filters. In other words, the sky
+as a background gives trouble to all who are unfamiliar with scientific
+measurements. The brightnesses of sky and clouds are outside the scale of
+brightnesses <span class="pagenum"><a name="Page_218" id="Page_218">[Pg 218]</a></span>ordinarily encountered in a landscape. Many interesting
+instances of the artist&#8217;s mistakes in dealing with these backgrounds could
+be presented; however, the artist&#8217;s trained eye has been a great aid in
+constructing patterns and various other types of camouflage. One of the
+most conspicuous aspects of the earth&#8217;s surface is its texture. From great
+heights it appears flat, that is, rolling land is ironed out and the
+general contour of the ground is flattened. However, the element of
+texture always remains. This is the chief reason for the extensive use of
+netting on which dyed raffia, foliage, pieces of colored cloth, etc., are
+tied. Such network has concealed many guns, headquarters, ammunition
+dumps, communication trenches, roadways, etc. When this has been well done
+the concealment is perfect.</p>
+
+<p>One of the greatest annoyances to the camoufleur is the lack of dullness
+or &#8220;flatness&#8221; of the paints, fabrics, and some of the other media used.
+When viewed at some angles the glint of highlights due to specular
+reflection renders the work very conspicuous. For this reason natural
+foliage or such material as dyed raffia has been very successful.</p>
+
+<p>Systems of network and vertical screens have been extensively employed on
+roadways near the front, not for the purpose of concealing from the enemy
+the fact that the roadways exist, but to make it necessary to shell the
+entire roadway continually if it is hoped to prevent its use.</p>
+
+<p>Although the camoufleur is provided with a vast amount of material for his
+work, many of his requirements are met by the material at hand.
+Obviously,<span class="pagenum"><a name="Page_219" id="Page_219">[Pg 219]</a></span> the most convenient method of providing concealment for a
+given environment is to use the materials of the environment. Hence,
+rubbish from ruined buildings or villages supplies camouflage for guns,
+huts, etc., in that environment. In woods the material to simulate the
+woods is at hand. Many of these aspects are so obvious to the reader that
+space will not be given to their consideration. The color of the soil is
+important, for if it is conspicuous the camoufleur must provide screens of
+natural turf.</p>
+
+<p>In this great game of hocus-pocus many deceptions are resorted to.
+Replicas of large guns and trenches are made; dummy soldiers are used to
+foil the sniper and to make him reveal his location, and papier-mach&eacute;
+horses, trees, and other objects conceal snipers and observers and afford
+listening posts. Gunners have been dressed in summer in green flowing
+robes. In winter white robes have been utilized. How far away from modern
+warriors are all the usual glitter and glamour of military impedimenta in
+the past parades of peace time! The armies now dig in for concealment. The
+artillery is no longer invisible behind yonder hill, for the eyes of the
+aerial observer of the camera reveal its position unless camouflaged for
+the third dimension.</p>
+
+<p>In the foregoing only the highlights of a vast art have been viewed, but
+the art is still vaster, for it extends into other fields. Sound must
+sometimes be camouflaged and this can only be done by using the same
+medium&mdash;sound. In these days of scientific warfare it is to be expected
+that the positions of enemy guns would be detected by other means than
+<span class="pagenum"><a name="Page_220" id="Page_220">[Pg 220]</a></span>employed in the past. A notable method is the use of velocity of sound.
+Records are made at various stations of the firing of a gun and the
+explosion of the shell. By trigonometric laws the position of the gun is
+ascertained. It is said that the Germans fired a number of guns
+simultaneously with the &#8220;75-mile&#8221; gun in order to camouflage its location.
+The airplane and submarine would gladly employ sound camouflage in order
+to foil the sound detector if practicable solutions were proposed.</p>
+
+<p>The foregoing is a brief statement of some of the fundamental principles
+of land camouflage. Let us now briefly consider the eyes of the enemy. Of
+course, much concealment and deception is devised to foil the observer who
+is on the ground and fairly close. The procedure is obvious to the average
+imagination; however, the reader may not be acquainted with the aerial
+eyes from which concealment is very important. As one ascends in an
+airplane to view a landscape he is impressed with the inadequacy of the
+eyes to observe the vast number of details and of the mind to retain them.
+Field glasses cannot be used as satisfactorily in an airplane as on solid
+ground, owing to vibration and other movements. The difference is not as
+great in the huge flying boats as it is in the ordinary airplane. The
+camera can record many details with higher accuracy than the eye. At an
+altitude of one mile the lens can be used at full aperture and thus very
+short exposures are possible. This tends to avoid the difficulty due to
+vibration. When the plates are developed for detail and enlargements are
+made, many<span class="pagenum"><a name="Page_221" id="Page_221">[Pg 221]</a></span> minute details are distinguishable. Furthermore, owing to the
+fact that the spectral sensibilities of photographic emulsions differ from
+that of the eye, contrasts are brought out which the eye would not see.
+This applies also to camouflage which is devised merely to suit the eye.
+Individual footprints have been distinguished on prints made from
+negatives exposed at an altitude of 6000 feet. By means of photography,
+daily records can be made if desired and these can be compared. A slight
+change is readily noted by such comparison by skilled interpreters of
+aerial photographs. The disappearance of a tree from a clump of trees may
+arouse suspicion. Sometimes a wilted tree has been noted on a photograph
+which naturally attracts attention to this position. It has been said that
+the belligerents resorted to transplanting trees a short distance at a
+time from day to day in order to provide clearance for newly placed guns.
+By paths converging toward a certain point, it may be concluded from the
+photographs that an ammunition dump or headquarters is located there even
+though the position itself was well camouflaged. Continuous photographic
+records may reveal disturbances of turf and lead to a more careful
+inspection of the region for sapping operations, etc. By these few details
+it is obvious that the airplane is responsible for much of the development
+of camouflage on land, owing to the necessity which it created for a much
+more extensive concealment. The entire story of land camouflage would
+overflow the confines of a volume, but it is hoped that the foregoing will
+aid the reader in visualizing the magnitude of the art and<span class="pagenum"><a name="Page_222" id="Page_222">[Pg 222]</a></span> the scientific
+basis upon which terrestial camouflage is founded.</p>
+
+<p><i>Marine Camouflage.</i>&mdash;At the time of the Spanish-American war, our
+battleships were painted white, apparently with little thought of
+attaining low visibility. Later the so-called &#8220;battleship gray&#8221; was
+adopted, but it has been apparent to close observers that this gray is in
+general too dark. Apparently it is a mixture of black and white. The ships
+of the British navy were at one time painted black, but preceding the
+Great War their coats were of a warm dark gray. Germany adopted dark gray
+before the close of the last century and Austria adopted the German gray
+at the outbreak of the war. The French and Italian fleets were also
+painted a warm gray. This development toward gray was the result of an aim
+toward attaining low visibility. Other changes were necessitated by
+submarine warfare which will be discussed later.</p>
+
+<p>In the early days of unrestricted submarine warfare many schemes for
+modifying the appearance of vessels were submitted. Many of these were
+merely wild fancies with no established reasoning behind them. Here again
+science came to the rescue and through research and consultation, finally
+straightened out matters. The question of low visibility for vessels could
+be thoroughly studied on a laboratory scale, because the seascape and
+natural lighting conditions could be reproduced very closely. Even the
+general weather conditions could be simulated, although, of course, the
+experiments could be prosecuted outdoors with small models, as indeed
+they<span class="pagenum"><a name="Page_223" id="Page_223">[Pg 223]</a></span> were. Mr.
+L. A. Jones<a href="#reference"><small>[10]</small></a> carried out an investigation on the shore
+of Lake Ontario, and laboratory experiments were conducted by others with
+the result that much light was shed on the questions of marine camouflage.
+This work confirmed the conclusion of the author and others that our
+battleship gray was too dark. Of course, the color best adapted is that
+which is the best compromise for the extreme variety in lighting and
+weather conditions. These vary in different parts of the world, so
+naturally those in the war zone were of primary importance. All camouflage
+generally must aim to be a compromise best suited for average or
+dominating conditions. For example, in foggy weather a certain paint may
+render a ship of low visibility, but on a sunny day the ship might be
+plainly visible. However, if ships are rendered of low visibility for even
+a portion of the time it is obvious that an advantage has been gained.
+Cloudiness increases generally from the equator northward, as indicated by
+meteorological annals.</p>
+
+<p>In order to study low visibility a scale of visibility must be
+established, and it is essential to begin with the fundamentals of vision.
+We distinguish objects by contrasts in brightness and in color and we
+recognize objects by these contrasts which mold their forms. In researches
+in vision it is customary to devise methods by which these contrasts can
+be varied. This is done by increasing or decreasing a veil of luminosity
+over the object and its surroundings and by other means. Much work has
+been done in past years in studying the minimum perceptible contrast, and
+it has been found to vary with hue, with the magnitude<span class="pagenum"><a name="Page_224" id="Page_224">[Pg 224]</a></span> of brightness, and
+with the size of the image, that is, with the distance of an object of
+given size. In such problems as this one much scientific work can be drawn
+upon. A simple, though rough, scale of visibility may be made by using a
+series of photographic screens of different densities. A photographic
+screen is slightly diffusing, still the object can be viewed through it
+very well. Such methods have been employed by various investigators in the
+study of visibility.</p>
+
+<p>Owing to the curvature of the earth, the distance at which a vessel can be
+seen on a clear day is limited by the height of the observer and of the
+ship&#8217;s superstructure. For an observer in a certain position the
+visibility range varies as the square root of the distance of the object
+from him. Such data are easily available, so they will not be given here.
+So far we have considered the ship itself when, as a matter of fact, on
+clear days the smoke cloud emitted by the ship is usually visible long
+before a ship&#8217;s superstructure appears on the horizon. This led to the
+prevention of smoke by better combustion, by using smokeless fuels, etc.</p>
+
+<p>The irregular skyline of a ship is perhaps one of the most influential
+factors which tend to increase its visibility. Many suggestions pertaining
+to the modification of the superstructure have been made, but these are
+generally impracticable. False work suffers in heavy seas and high winds.</p>
+
+<p>After adopting a suitable gray as, a &#8220;low-visibility&#8221; paint for ships,
+perhaps the next refinement was counter shading; that is, shadows were
+painted<span class="pagenum"><a name="Page_225" id="Page_225">[Pg 225]</a></span> a lighter color, or even white. The superstructure was painted in
+some cases a light blue, with the hope that it would fade into the distant
+horizon. However, the effectiveness of the submarine demanded new
+expedients because within its range of effectiveness no ingenuity could
+render its intended prey invisible. The effective gun-fire from submarines
+is several miles and torpedoes can be effective at these distances.
+However, the submarine prefers to discharge the torpedo at ranges within a
+mile. It is obvious that, in average weather, low visibility ceases to be
+very effective against the submarine. The movement of a target is of much
+less importance in the case of gun-fire than in the case of the torpedo
+with its relatively low velocity. The submarine gunner must have the
+range, speed, and course of the target in order to fire a torpedo with any
+hope of a hit. Therefore, any uncertainties that could be introduced
+pertaining to these factors would be to the advantage of the submarine&#8217;s
+prey. For example, low visibility gave way to confusibility in the
+discussions of defence against the submarine and the slogan, &#8220;A miss is as
+good as a mile&#8221; was adopted. The foregoing factors cannot be determined
+ordinarily with high accuracy, so that it appeared possible to add
+somewhat to the difficulties of the submarine commander.</p>
+
+<p>Many optical illusions have been devised and studied by scientists. In
+fact, some of these tricks are well known to the general reader. Straight
+lines may appear broken, convergent, or divergent by providing certain
+patterns or lines intermingled with<span class="pagenum"><a name="Page_226" id="Page_226">[Pg 226]</a></span> them. Many of these were applied to
+models in laboratory experiments and it has been shown that confusion
+results as to the course of the vessel. The application of these on
+vessels has resulted in the grotesque patterns to be seen on ships during
+the latter stage of the war. It is well known that these illusions are
+most effective when the greatest contrasts are used, hence black and white
+patterns are common. Color has not been utilized as definitely as pattern
+in confusibility, although there is a secondary aim of obtaining low
+visibility at a great distance by properly balancing the black, white, and
+other colors so that a blue-gray results at distances too great for the
+individual patterns to be resolved by the eye. Color could be used for the
+purpose of increasing the conclusion by apparently altering the
+perspective. For example, blue and red patterns on the same surface do not
+usually appear at the same distance, the red appearing closer than the
+blue.</p>
+
+<p><a name="fig92" id="fig92"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig92.jpg" alt="" /></div>
+<p class="center">Fig. 92.&mdash;A primary stage in the evolution of the use of geometrical-optical illusions on ships.</p>
+<p>&nbsp;</p>
+
+<p>Such apparently grotesque patterns aimed to distort the lines of the ship
+and to warp the perspective<span class="pagenum"><a name="Page_227" id="Page_227">[Pg 227]</a></span> by which the course is estimated. This was
+the final type of marine camouflage at the close of the war. Besides
+relying upon these illusions, ships zigzagged on being attacked and aimed
+in other ways to confuse the enemy. No general attempt was made to
+disguise the bow, because the bow-wave was generally visible. However,
+attempts have been made to increase it apparently and even to provide one
+at the stern. In fact, ingenuity was heavily drawn upon and many
+expedients were tried.</p>
+
+<p>After low-visibility was abandoned in favor of the optical illusion for
+frustrating the torpedo-attack by the submarine, there was a period during
+which merely a mottled pattern was used for vessels. Gradually this
+evolved toward such patterns as shown in <a href="#fig92">Fig. 92</a>. In this illustration it
+is seen that the optical-illusion idea has taken definite form. During the
+period of uncertainty as to the course the pattern should take, a
+regularity of pattern was tried, such as illustrated in <a href="#fig93">Figs. 93</a> and <a href="#fig94">94</a>.
+Finally, when it dawned more or less simultaneously upon various
+scientific men, who were studying the problems of protecting vessels upon
+the seas, that the geometrical-optical illusion in its well-known forms
+was directly adaptable, renewed impetus was given to investigation. The
+scientific literature yielded many facts but the problems were also
+studied directly by means of models. The latter study is illustrated by
+<a href="#fig95">Figs. 95</a> and <a href="#fig96">96</a>, the originals having been furnished by Mr. E. L.
+Warner,<a href="#reference"><small>[11]</small></a> who among others prosecuted a study of the application of
+illusions to vessels. The final results were gratifying, as shown to some
+extent in <a href="#fig97">Figs. 97</a> and <a href="#fig98">98</a>, also kindly furnished by Mr. Warner. It is
+seen that these patterns are really deceiving as to the course of the
+vessel.</p>
+
+<p>&nbsp;<span class="pagenum"><a name="Page_228" id="Page_228">[Pg 228]</a></span></p>
+<p><a name="fig93" id="fig93"></a></p>
+<div class="figcenter"><img src="images/fig93.jpg" alt="" /></div>
+<p><a name="fig94" id="fig94"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig94.jpg" alt="" /></div>
+<p class="center">Figs. 93 and 94.&mdash;Attempts at distortion of outline which preceded the adoption of geometrical-optical illusions for ships.</p>
+<p>&nbsp;</p>
+<p>&nbsp;<span class="pagenum"><a name="Page_229" id="Page_229">[Pg 229]</a></span></p>
+<p><a name="fig95" id="fig95"></a></p>
+<div class="figcenter"><img src="images/fig95.jpg" alt="" /></div>
+<p><a name="fig96" id="fig96"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig96.jpg" alt="" /></div>
+<p class="center">Figs. 95 and 96.&mdash;Illustrating the use of models by the Navy Department in developing the geometrical-illusion for ships.</p>
+<p>&nbsp;</p>
+
+<p><span class="pagenum"><a name="Page_230" id="Page_230">[Pg 230]</a></span>The convoy system is well known to the reader. This saved many vessels
+from destruction. Vessels of the same speed were grouped together and
+steamed in flocks across the Atlantic. Anyone who has had the extreme
+pleasure of looking down from an airplane upon these convoys led by
+destroyers and attended by chasers is strongly impressed with the old
+adage, &#8220;In unity there is strength.&#8221;</p>
+
+<p>Before the war began, a Brazilian battleship launched in this country was
+provided with a system of blue lights for use when near the enemy at
+night. Blue was adopted doubtless for its low range compared with light of
+other colors. We know that the setting sun is red because the atmospheric
+dust, smoke, and moisture have scattered and absorbed the blue and green
+rays more than the red and yellow rays. In other words the penetrating
+power of the red and yellow is greater than that of the blue rays. This
+country made use of this expedient to some extent. Of course, all other
+lights were extinguished and portholes were closed in ocean travel during
+the submarine menace.</p>
+
+<p>&nbsp;<span class="pagenum"><a name="Page_231" id="Page_231">[Pg 231]</a></span></p>
+<p><a name="fig97" id="fig97"></a></p>
+<div class="figcenter"><img src="images/fig97.jpg" alt="" /></div>
+<p><a name="fig98" id="fig98"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig98.jpg" alt="" /></div>
+<p class="center">Figs. 97 and 98.&mdash;Examples of the geometrical-optical illusion as finally applied.</p>
+<p>&nbsp;</p>
+
+<p>Naturally smoke-screens were adopted as a defensive measure on sea as well
+as on land. Destroyers belch dense smoke from their stacks in order to
+screen battleships. Many types of smoke-boxes have been devised or
+suggested. The smoke from these is produced chemically and the apparatus
+must be simple and safe. If a merchantman were attacked <span class="pagenum"><a name="Page_232" id="Page_232">[Pg 232]</a></span>by a submarine
+immediately smoke-boxes would be dumped overboard or some which were
+installed on deck would be put into operation and the ship would be
+steered in a zigzag course. These expedients were likely to render
+shell-fire and observations inaccurate. This mode of defense is obviously
+best suited to unarmed vessels. In the use of smoke-boxes the direction
+and velocity of the wind must be considered. The writer is unacquainted
+with any attempts made to camouflage submarines under water, but that this
+can be done is evident from aerial observations. When looking over the
+water from a point not far above it, as on a pier, we are unable to see
+into the water except at points near us where our direction of vision is
+not very oblique to the surface of the water. The brightness of the
+surface of water is due to mirrored sky and clouds ordinarily. For a
+perfectly smooth surface of water, the reflection factor is 2 per cent for
+perpendicular incidence. This increases only slightly as the obliquity
+increases to an angle of about 60 degrees. From this point the
+reflection-factor of the surface rapidly increases, becoming 100 per cent
+at 90 degrees incidence. This accounts for the ease with which we can see
+into the water from a position directly overhead and hence the airplane
+has been an effective hunter of submerged submarines. The depth at which
+an object can be seen in water depends, of course, upon its clarity. It
+may be surprising to many to learn that the brightness of water, such as
+rivers, bays, and oceans, as viewed perpendicularly to its surface, is
+largely due to light diffused within it. This point<span class="pagenum"><a name="Page_233" id="Page_233">[Pg 233]</a></span> became strikingly
+evident during the progress of work in aerial photometry.</p>
+
+<p>A submerged submarine may be invisible for two reasons: (1) It may be deep
+enough to be effectively veiled by the luminosity of the mass of water
+above it (including the surface brightness) or, (2) It may be of the
+proper brightness and color to simulate the brightness and color of the
+water. It is obvious that if it were white it would have to attain
+concealment by submerging deeply. If it were a fairly dark greenish-blue
+it would be invisible at very small depths. In fact, it would be of very
+low visibility just below the surface of the water. By the use of the
+writer&#8217;s data on hues and reflection-factors of earth and water areas it
+would be easy to camouflage submarines effectively from enemies overhead.
+The visibility of submarines is well exemplified by viewing large fish
+such as sharks from airships at low altitudes. They appear as miniature
+submarines dark gray or almost black amid greenish-blue surroundings.
+Incidentally, the color of water varies considerably from the dirty
+yellowish-green of shallow inland waters containing much suspended matter
+to the greenish-blue of deep clear ocean waters. The latter as viewed
+vertically are about one-half the brightness of the former under the same
+conditions and are decidedly bluer.</p>
+
+<p><i>The Visibility of Airplanes.</i>&mdash;In the Great War the airplane made its
+d&eacute;but in warfare and in a short time made a wonderful record, yet when
+hostilities ceased aerial camouflage had not been put on a scientific
+basis. No nation had developed this general<span class="pagenum"><a name="Page_234" id="Page_234">[Pg 234]</a></span> aspect of camouflage
+systematically or to an extent comparable with the developments on land
+and sea. One of the chief difficulties was that scientific data which were
+applicable were lacking. During the author&#8217;s activities as Chairman of the
+Committee on Camouflage of the National Research Council he completed an
+extensive investigation<a href="#reference"><small>[12]</small></a> of the fundamentals upon which the attainment
+of low visibility for airplanes must be based. Solutions of the problems
+encountered in rendering airplanes of low visibility resulted and various
+recommendations were made, but the experiences and data will be drawn upon
+here only in a general way. In this general review details would consume
+too much space, for the intention has been to present a broad view of the
+subject of camouflage.</p>
+
+<p>The visibility of airplanes presents some of the most interesting problems
+to be found in the development of the scientific basis for camouflage. The
+general problem may be subdivided according to the type of airplane, its
+field of operation, and its activity. For example, patrol craft which fly
+low over our own lines would primarily be camouflaged for low visibility
+as viewed by enemies above. (See <a href="#fig99">Fig. 99</a>.) High-flying craft would be
+rendered of low visibility as viewed primarily by the enemy below.
+Airplanes for night use present other problems and the visibility of
+seaplanes is a distinct problem, owing to the fact that the important
+background is the water, because seaplanes are not ordinarily high-flying
+craft. In all these considerations it will be noted that the activity of
+the airplanes is of primary importance,<span class="pagenum"><a name="Page_235" id="Page_235">[Pg 235]</a></span> because it determines the lines
+of procedure in rendering the craft of low visibility. This aspect is too
+complicated to discuss thoroughly in a brief r&eacute;sum&eacute;.</p>
+
+<p><a name="fig99" id="fig99"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig99.jpg" alt="" /></div>
+<p class="center">Fig. 99.&mdash;Representative earth backgrounds for an airplane (uncamouflaged) as viewed from above.</p>
+<p>&nbsp;</p>
+
+<p>The same fundamentals of light, color, and vision apply in this field as
+in other fields of camouflage, but different data are required. When
+viewing aircraft from above, the earth is the background of most
+importance. Cumulus clouds on sunny days are generally at altitudes of
+4000 to 7000 feet. Clouds are not always present and besides they are of
+such a different order of brightness from that of the earth that they
+cannot be considered in camouflage designed<span class="pagenum"><a name="Page_236" id="Page_236">[Pg 236]</a></span> for low visibility from
+above. In other words, the compromise in this case is to accept the earth
+as a background and to work on this basis. We are confronted with seasonal
+changes of landscape, but inasmuch as the summer landscape was of greatest
+importance generally, it was the dominating factor in considering low
+visibility from above.</p>
+
+<p>On looking down upon the earth one is impressed with the definite types of
+areas such as cultivated fields, woods, barren ground and water. Different
+landscapes contain these areas in various proportions, which fact must be
+considered. Many thousand determinations of reflection-factor and of
+approximate hue were made for these types of areas, and upon the mean
+values camouflage for low visibility as viewed from above was developed. A
+few values are given in the accompanying table, but a more comprehensive
+presentation will be found elsewhere.<a href="#reference"><small>[12]</small></a></p>
+
+
+<p class="center"><br /><i>Mean Reflection-Factors</i></p>
+
+<p>(From thousands of measurements made by viewing vertically downward during
+summer and fall from various altitudes.)</p>
+
+<table border="0" cellpadding="0" cellspacing="5" summary="table">
+<tr><td>&nbsp;</td><td><span class="spacer">&nbsp;</span></td><td align="center">Per Cent</td></tr>
+<tr><td>Woods</td><td>&nbsp;</td><td align="center"><span style="margin-left: .5em;">4.3</span></td></tr>
+<tr><td>Barren ground</td><td>&nbsp;</td><td align="center">13.0</td></tr>
+<tr><td>Fields (grazing land and growing crops)</td><td>&nbsp;</td><td align="center"><span style="margin-left: .5em;">6.8</span></td></tr>
+<tr><td>Inland water (rivers and bays)</td><td>&nbsp;</td><td align="center"><span style="margin-left: .5em;">6.8</span></td></tr>
+<tr><td>Deep ocean water</td><td>&nbsp;</td><td align="center"><span style="margin-left: .5em;">3.5</span></td></tr>
+<tr><td>Dense clouds</td><td>&nbsp;</td><td align="center">78.0</td></tr></table>
+
+<p>Wooded areas are the darkest general areas in a landscape and possess a
+very low reflection-factor. From above one sees the deep shadows
+interspersed among the highlights. These shadows and the trapping<span class="pagenum"><a name="Page_237" id="Page_237">[Pg 237]</a></span> of
+light are largely responsible for the low brightness or apparent
+reflection-factor. This is best illustrated by means of black velvet. If a
+piece of cardboard is dyed with the same black dye as that used to dye the
+velvet, it will diffusely reflect 2 or 3 per cent of the incident light,
+but the black velvet will reflect no more than 0.5 per cent. The velvet
+fibers provide many light traps and cast many shadows which reduce the
+relative brightness or reflection-factor far below that of the flat
+cardboard. Cultivated fields on which there are growing crops are nearly
+twice as bright as wooded areas, depending, of course, upon the denseness
+of the vegetation. Barren sunbaked lands are generally the brightest large
+areas in a landscape, the brightness depending upon the character of the
+soil. Wet soil is darker than dry soil, owing to the fact that the pores
+are filled with water, thus reducing the reflection-factor of the small
+particles of soil. A dry white blotting paper which reflects 75 per cent
+of the incident light will reflect only about 55 per cent when wet.</p>
+
+<p>Inland waters which contain much suspended matter are about as bright as
+grazing land and cultivated fields. Shallow water partakes somewhat of the
+color and brightness of the bed, and deep ocean water is somewhat darker
+than wooded areas. Quiet stagnant pools or small lakes are sometimes
+exceedingly dark; in fact, they appear like pools of ink, owing to the
+fact that their brightness as viewed vertically is almost entirely due to
+surface reflection. If it is due entirely to reflection at the surface,
+the brightness will be about 2 per cent of the brightness of the<span class="pagenum"><a name="Page_238" id="Page_238">[Pg 238]</a></span> zenith
+sky. That is, when viewing such a body of water vertically one sees an
+image of the zenith sky reduced in brightness to about 2 per cent.</p>
+
+<p>The earth patterns were extensively studied with the result that definite
+conclusions were formulated pertaining to the best patterns to be used.
+Although it is out of the question to present a detailed discussion of
+this important phase in this r&eacute;sum&eacute;, attention will be called to the
+manner in which the earth patterns diminish with increasing altitude. The
+insert in <a href="#fig100">Fig. 100</a> shows the actual size of an image of a 50-foot airplane
+from 0 to 16,000 feet below the observer as compared with corresponding
+images (to the same scale) of objects and areas on the earth&#8217;s surface
+10,000 feet below the observer.</p>
+
+<p>For simplicity assume a camera lens to have a focal length equal to 10
+inches, then the length <i>x</i> of the image of an object 100 feet long will
+be related to the altitude <i>h</i> in this manner:</p>
+
+<table border="0" cellpadding="0" cellspacing="5" summary="table">
+<tr><td align="center" class="botbor"><i>x</i></td>
+    <td rowspan="2" valign="middle">&nbsp; = &nbsp;</td>
+    <td align="center" class="botbor">100</td>
+    <td rowspan="2" valign="middle">&nbsp; or &nbsp; <i>xh</i> = 1000</td></tr>
+<tr><td align="center">10</td>
+    <td align="center"><i>h</i></td></tr></table>
+
+<p>By substituting the values of altitude <i>h</i> in the equation the values of
+the length <i>x</i> of the image are found. The following values illustrate the
+change in size of the image with altitude:</p>
+
+<table border="0" cellpadding="0" cellspacing="5" summary="table">
+<tr><td align="center">Altitude <i>h</i> in feet</td><td><span class="spacer">&nbsp;</span></td>
+    <td align="center">Size of image <i>x</i> in inches</td></tr>
+<tr><td align="center"><span style="margin-left: .5em;">1,000</span></td><td>&nbsp;</td>
+    <td align="center">1.00</td></tr>
+<tr><td align="center"><span style="margin-left: .5em;">2,000</span></td><td>&nbsp;</td>
+    <td align="center">0.50</td></tr>
+<tr><td align="center"><span style="margin-left: .5em;">3,000</span></td><td>&nbsp;</td>
+    <td align="center">0.33</td></tr>
+<tr><td align="center"><span style="margin-left: .5em;">4,000</span></td><td>&nbsp;</td>
+    <td align="center">0.25</td></tr>
+<tr><td align="center">10,000</td><td>&nbsp;</td>
+    <td align="center">0.10</td></tr>
+<tr><td align="center">20,000</td><td>&nbsp;</td>
+    <td align="center">0.05</td></tr></table>
+
+<p><span class="pagenum"><a name="Page_239" id="Page_239">[Pg 239]</a></span>It is seen that the image diminishes less rapidly in size as the altitude
+increases. For example, going from 1000 feet to 2000 feet the image is
+reduced to one-half. The same reduction takes place in ascending from
+10,000 to 20,000 feet. By taking a series of photographs and knowing the
+reduction-factor of the lens it is a simple matter to study pattern. An
+airplane of known dimensions can be placed in the imagination at any
+altitude on a photograph taken at a known altitude and the futility of
+certain patterns and the advantages of others are at once evident.</p>
+
+<p><a name="fig100" id="fig100"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/fig100.jpg" alt="" /></div>
+<p class="center">Fig. 100.&mdash;Illustrating the study of pattern for airplanes. The photograph was taken from an altitude of 10,000 feet.<br />
+The insert shows the relative lengths (<ins class="correction" title="original: verticle">vertical</ins> scale) of an airplane of 50-foot
+spread at various distances below the observer.</p>
+<p>&nbsp;</p>
+
+<p><span class="pagenum"><a name="Page_240" id="Page_240">[Pg 240]</a></span>It is impracticable to present colored illustrations in this r&eacute;sum&eacute; and
+values expressed in numbers are meaningless to most persons, so a few
+general remarks will be made in closing the discussion of low visibility
+as viewed from above in spring, summer and fall. A black craft is of much
+lower visibility than a white one. White should not be used. The paints
+should be very dark shades. The hues are approximately the same for the
+earth areas as seen at the earth&#8217;s surface. Inland waters are a dirty
+blue-green or bluish-green, and deep ocean water is a greenish-blue when
+viewed vertically, or nearly so. Mean hues of these were determined
+approximately.</p>
+
+<p>Before considering other aspects of camouflage it is well to consider such
+features as haze, clouds and sky. There appear to be two kinds of haze
+which the writer will arbitrarily call earth and high haze, respectively.
+The former consists chiefly of dust and smoke and usually extends to an
+altitude of about one mile, although it occasionally extends much higher.
+Its upper limit is very distinct, as seen by the &#8220;false&#8221; horizon. This
+horizon is used more by the pilot when flying at certain altitudes than
+the true horizon. At the top of this haze cumulus clouds are commonly seen
+to be poking out like nearly submerged icebergs. The upper haze appears
+somewhat whiter in color and appears to extend sometimes to altitudes of
+several or even many miles. The fact that the &#8220;earth&#8221; haze may be seen to
+end usually at about 5000 to 6000 feet and the upper haze to persist even
+beyond 20,000 feet has led the author to apply different names for
+convenience. The upper limit of the &#8220;earth&#8221;<span class="pagenum"><a name="Page_241" id="Page_241">[Pg 241]</a></span> haze is determined by the
+height of diurnal atmospheric convection. Haze aids in lowering the
+visibility of airplanes by providing a luminous veil, but it also operates
+at some altitudes to increase the brightness of the sky, which is the
+background in this case.</p>
+
+<p>The sky generally decreases considerably in brightness as the observer
+ascends. The brightness of the sky is due to scattered light, that is, to
+light being reflected by particles of dust, smoke, thinly diffused clouds,
+etc. By making a series of measurements of the brightness of the zenith
+sky for various altitudes, the altitude where the earth haze ends is
+usually plainly distinguishable. Many observations of this character were
+accumulated. In some extreme cases the sky was found to be only one-tenth
+as bright when observed at high altitudes of 15,000 to 20,000 feet as seen
+from the earth&#8217;s surface. This accounts partly for the decrease in the
+visibility of an airplane as it ascends. At 20,000 feet the sky was found
+to contribute as little as 4 per cent of the total light on a horizontal
+plane and the extreme harshness of the lighting is very noticeable when
+the upper sky is cloudless and clear.</p>
+
+<p>Doubtless, it has been commonly noted that airplanes are generally very
+dark objects as viewed from below against the sky. Even when painted white
+they are usually much darker than the sky. As they ascend the sky above
+them becomes darker, although to the observer on the ground the sky
+remains constant in brightness. However, in ascending, the airplane is
+leaving below it more and more luminous haze which acts as a veil in
+aiding to screen it until,<span class="pagenum"><a name="Page_242" id="Page_242">[Pg 242]</a></span> when it reaches a high altitude, the
+combination of dark sky behind it and luminous haze between it and the
+observer on the ground, it becomes of much lower visibility. Another
+factor which contributes somewhat is its diminishing size as viewed from a
+fixed position at the earth. The minimum perceptible contrast becomes
+larger as the size of the contrasting patch diminishes.</p>
+
+<p>Inasmuch as there is not enough light reflected upward from the earth to
+illuminate the lower side of an opaque surface sufficiently to make it as
+bright as the sky ordinarily, excepting at very high altitudes for very
+clear skies, it is necessary, in order to attain low visibility for
+airplanes as viewed from below, to supply some additional illumination to
+the lower surfaces. Computations have shown that artificial lighting is
+impracticable, but measurements on undoped airplane fabrics indicate that
+on sunny days a sufficient brightness can be obtained from direct sunlight
+diffused by the fabric to increase the brightness to the order of
+magnitude of the brightness of the sky. On overcast days an airplane will
+nearly always appear very much darker than the sky. That is, the
+brightness of the lower sides can in no other manner be made equal to that
+of the sky. However, low visibility can be obtained on sunny days which is
+an advantage over high visibility at all times, as is the case with
+airplanes now in use. Many observations and computations of these and
+other factors have been made, so that it is possible to predict results.
+Transparent media have obvious advantages, but no satisfactory ones are
+available at present.</p>
+
+<p><span class="pagenum"><a name="Page_243" id="Page_243">[Pg 243]</a></span>Having considered low visibility of aircraft as viewed from above and from
+below, respectively, it is of interest to discuss briefly the possibility
+of attaining both of these simultaneously with a given airplane. Frankly,
+it is not practicable to do this. An airplane to be of low visibility
+against the earth background must be painted or dyed very dark shades of
+appropriate color and pattern. This renders it almost opaque and it will
+be a very dark object when viewed against the sky. If the lower surfaces
+of the airplane are painted as white as possible the airplane still
+remains a dark object against the blue sky and a very dark object against
+an overcast sky, except at high altitudes. In the latter cases the
+contrast is not as great as already explained. A practicable method of
+decreasing the visibility of airplanes at present as viewed from below is
+to increase the brightness by the diffuse transmission of direct sun-light
+on clear days. On overcast days clouds and haze must be depended upon to
+screen the craft.</p>
+
+<p>In considering these aspects it is well to recall that the two sources of
+light are the sun and the sky. Assuming the sun to contribute 80 per cent
+of the total light which reaches the upper side of an opaque horizontal
+diffusing surface at midday at the earth and assuming the sky to be
+cloudless and uniform in brightness, then the brightness of the horizontal
+upper surface will equal 5 <i>RB</i>, where <i>R</i> is the reflection-factor of the
+surface and <i>B</i> is the brightness (different in the two cases) of the sky.
+On a uniformly overcast day the brightness of the surface would be equal
+<span class="pagenum"><a name="Page_244" id="Page_244">[Pg 244]</a></span>to <i>RB</i>. Now assuming <i>R<sub>e</sub></i> to be the mean reflection-factor of the
+earth, then the lower side of a horizontal opaque surface suspended in the
+air would receive light in proportion to <i>R<sub>e</sub>B</i>. If this lower surface
+were a perfect mirror or a perfectly reflecting and diffusing surface its
+brightness would equal 5 <i>R<sub>e</sub>B</i> on the sunny day and <i>R<sub>e</sub>B</i> on the
+overcast day where <i>B</i> is the value (different in the two cases) of the
+brightness of the uniform sky. The surface can never be a perfect
+reflector, so on an overcast day its brightness will be a fraction
+(<i>RR<sub>e</sub></i>) of the brightness <i>B</i> of the uniform sky. Inasmuch as <i>R<sub>e</sub></i>
+is a very small value it is seen that low visibility of airplanes as
+viewed from below generally cannot be attained on an overcast day. It can
+be approached on a sunny day and even realized by adopting the expedient
+already mentioned. Further computations are to be found elsewhere.<a href="#reference"><small>[12]</small></a></p>
+
+<p>Seasonable changes present no difficulties, for from a practical
+standpoint only summer and winter need be generally considered. If the
+earth is covered with snow an airplane covered completely with white or
+gray paint would be fairly satisfactory as viewed from above, and if a
+certain shade of a blue tint be applied to the lower surfaces, low
+visibility as viewed from below would result. The white paint would
+possess a reflection-factor about equal to that of snow, thus providing
+low visibility from above. Inasmuch as the reflection-factor of snow is
+very high, the white lower sides of an airplane would receive a great deal
+more light in winter than they would in summer. Obviously, a blue tint is
+necessary for low visibility against the sky, but color has not been
+primarily considered in the preceding paragraphs because the chief
+difficulty<span class="pagenum"><a name="Page_245" id="Page_245">[Pg 245]</a></span> in achieving low visibility from below lies in obtaining
+brightness of the proper order of magnitude. In winter the barren ground
+would be approximately of the same color and reflection-factor as in
+summer, so it would not be difficult to take this into consideration.</p>
+
+<p>Seaplanes whose backgrounds generally consist of water would be painted of
+the color and brightness of water with perhaps a slight mottling. The
+color would generally be a very dark shade, approximating blue-green in
+hue.</p>
+
+<p>Aircraft for night use would be treated in the same manner as aircraft for
+day use, if the moonlight is to be considered a dominant factor. This is
+one of the cases where the judgment must be based on actual experience. It
+appears that the great enemy of night raiders is the searchlight. If this
+is true the obvious expedient is to paint the craft a dull jet black.
+Experiments indicate that it is more difficult to pick up a black craft
+than a gray or white one and also it is more difficult to hold it in the
+beam of the searchlight. This can be readily proved by the use of black,
+gray, and white cards in the beam of an automobile head-light. The white
+card can be seen in the outskirts of the beam where the gray or black
+cannot be seen, and the gray can be picked up where the black one is
+invisible. The science of vision accounts for this as it does for many
+other questions which arise in the consideration of camouflage or low
+visibility.</p>
+
+<p>Some attempts have been made to apply the principle of confusibility to
+airplanes as finally developed for vessels to circumvent the submarine,
+but the<span class="pagenum"><a name="Page_246" id="Page_246">[Pg 246]</a></span> folly of this appears to be evident. Air battles are conducted at
+terrific speeds and with skillful maneuvering. Triggers are pulled without
+computations and the whole activity is almost lightning-like. To expect to
+confuse an opponent as to the course and position of the airplane is
+folly.</p>
+
+<p>The camouflage of observation balloons has not been developed, though
+experiments were being considered in this direction as the war closed.
+Inasmuch as they are low-altitude crafts it appears that they would be
+best camouflaged for the earth as a background. Their enemies pounce down
+upon them from the sky so that low visibility from above seems to be the
+better choice.</p>
+
+<p>In the foregoing it has been aimed to give the reader the general
+underlying principles of camouflage and low visibility, but at best this
+is only a r&eacute;sum&eacute;. In the following references will be found more extensive
+discussions of various phases of the subject.</p>
+
+
+<p><a name="reference" id="reference"></a>&nbsp;</p><p>&nbsp;</p>
+<p class="center"><span class="large">REFERENCES</span></p>
+
+<div class="note">
+<p class="hang">1. A Study of Z&ouml;llner&#8217;s Figures and Other Related Figures, J. Jastrow,
+Amer. Jour. of Psych. 1891, 4, p. 381.</p>
+
+<p class="hang">2. A Study of Geometrical Illusions, C. H. Judd, Psych. Rev. 1899, 6, p. 241.</p>
+
+<p class="hang">3. Visual Illusions of Depth, H. A. Carr, Psych. Rev. 1909, 16, p. 219.</p>
+
+<p class="hang">4. Irradiation of Light, F. P. Boswell, Psych. Bul. 1905, 2, p. 200.</p>
+
+<p class="hang">5. Retiring and Advancing Colors, M. Luckiesh, Amer. Jour. Psych. 1918, 29, p. 182.</p>
+
+<p class="hang">6. The Language of Color, 1918, M. Luckiesh.</p>
+
+<p class="hang">7. Apparent Form of the Dome of the Sky, Ann. d. Physik, 1918, 55, p. 387;
+Sci. Abs. 1918, No. 1147.</p>
+
+<p><span class="pagenum"><a name="Page_247" id="Page_247">[Pg 247]</a></span></p>
+
+<p class="hang">8. Course on Optics, 1738, Robert Smith.</p>
+
+<p class="hang">9. Color and Its Applications, 1915 and 1921; Light and Shade and Their Applications, 1916, M. Luckiesh.</p>
+
+<p class="hang">10. Report of The Submarine Defense Association, L. T. Bates and L. A. Jones.</p>
+
+<p class="hang">11. Marine Camouflage Design, E. L. Warner, Trans. I. E. S. 1919, 14, p. 215.</p>
+
+<p class="hang">12. The Visibility of Airplanes, M. Luckiesh, Jour. Frank. Inst. March and
+April, 1919; also Aerial Photometry, Astrophys. Jour. 1919, 49, p. 108.</p>
+
+<p class="hang">13. Jour. Amer. Opt. Soc., E. Karrer, 1921.</p></div>
+
+<p>The foregoing are only a few references indicated in the text. Hundreds of
+references are available and obviously it is impracticable to include such
+a list. The most fruitful sources of references are the general works on
+psychology. E. B. Titchener&#8217;s Experimental Psychology (vol. 1) contains an
+excellent list. A chapter on Space in William James&#8217; Principles of
+Psychology (vol. II) will be found of interest to those who wish to delve
+deeper into visual perception. Other general references are Elements of
+Physiological Psychology by Ladd and Woodworth; the works of Helmholtz; a
+contribution by Hering in Hermann&#8217;s Handb. d. Phys. Bk. III, part 1;
+Physiological Psychology by Wundt; E. B. Delabarre, Amer. Jour. Psych.
+1898, 9, p. 573; W. Wundt, T&auml;uschungen, p. 157 and Philos. Stud. 1898, 14,
+p. 1; T. Lipps, Raumaesthetik and Zeit. f. Psych. 1896, 12, 39.</p>
+
+<p><span class="pagenum"><a name="Page_248" id="Page_248">[Pg 248]</a></span></p>
+
+
+<p>&nbsp;</p><p>&nbsp;</p>
+<hr style="width: 50%;" />
+<p><span class="pagenum"><a name="Page_249" id="Page_249">[Pg 249]</a></span></p>
+<h2>INDEX</h2>
+
+
+<p class="index">
+Aberration, <a href="#Page_19">19</a><br />
+<span style="margin-left: 1em;">spherical, <a href="#Page_122">122</a></span><br />
+<span style="margin-left: 1em;">chromatic, <a href="#Page_135">135</a></span><br />
+<br />
+Aerial perspective, <a href="#Page_165">165</a>, <a href="#Page_183">183</a><br />
+<br />
+After-images, <a href="#Page_24">24</a>, <a href="#Page_25">25</a>, <a href="#Page_59">59</a>, <a href="#Page_128">128</a>, <a href="#Page_186">186</a><br />
+<span style="margin-left: 1em;">positive and negative, <a href="#Page_129">129</a></span><br />
+<br />
+Airplanes, visibility of, <a href="#Page_233">233</a><br />
+<span style="margin-left: 1em;">camouflage for different types, <a href="#Page_234">234</a></span><br />
+<span style="margin-left: 1em;">size of image at various altitudes, <a href="#Page_238">238</a></span><br />
+<span style="margin-left: 1em;">camouflage for various conditions, <a href="#Page_240">240</a></span><br />
+<br />
+Alhazen, <a href="#Page_8">8</a><br />
+<br />
+Angles, influence of, <a href="#Page_76">76</a><br />
+<span style="margin-left: 1em;">various effects of, <a href="#Page_81">81</a></span><br />
+<span style="margin-left: 1em;">contours and, <a href="#Page_87">87</a></span><br />
+<span style="margin-left: 1em;">apparent effect on length, <a href="#Page_91">91</a></span><br />
+<span style="margin-left: 1em;">theories, <a href="#Page_98">98</a></span><br />
+<br />
+Animals, protective coloration, <a href="#Page_211">211</a><br />
+<br />
+Architecture, <a href="#Page_195">195</a><br />
+<span style="margin-left: 1em;">balance in, <a href="#Page_201">201</a></span><br />
+<br />
+Arcs, circular, illusions due to, <a href="#Page_86">86</a><br />
+<br />
+Areas, juxtaposed, illusions of, <a href="#Page_96">96</a><br />
+<br />
+Artist, <a href="#Page_179">179</a><br />
+<br />
+Attention, fluctuation of, <a href="#Page_65">65</a>, <a href="#Page_106">106</a>, <a href="#Page_141">141</a>, <a href="#Page_164">164</a><br />
+<br />
+Aubert, <a href="#Page_49">49</a><br />
+<br />
+Auerbach&#8217;s indirect vision theory, <a href="#Page_100">100</a><br />
+<br />
+Aureole, <a href="#Page_178">178</a><br />
+<br />
+<br />
+Balance in architecture, <a href="#Page_201">201</a><br />
+<br />
+Bas-relief, <a href="#Page_143">143</a><br />
+<br />
+Battleships, <a href="#Page_222">222</a><br />
+<br />
+Binocular disparity, <a href="#Page_105">105</a><br />
+<br />
+Binocular vision, <a href="#Page_29">29</a>, <a href="#Page_31">31</a><br />
+<br />
+Blending of colors in camouflage, <a href="#Page_216">216</a><br />
+<br />
+Blind spot, <a href="#Page_21">21</a><br />
+<br />
+Blue light on war-vessels, <a href="#Page_230">230</a><br />
+<br />
+Boswell, varieties of irradiation, <a href="#Page_122">122</a><br />
+<br />
+Brightness,<br />
+<span style="margin-left: 1em;">illusions due to</span><br />
+<span style="margin-left: 2em;">variations in, <a href="#Page_107">107</a></span><br />
+<span style="margin-left: 2em;">and color contrasts, <a href="#Page_114">114</a></span><br />
+<span style="margin-left: 2em;">apparatus, <a href="#Page_115">115</a></span><br />
+<span style="margin-left: 2em;">and hue, <a href="#Page_125">125</a></span><br />
+<span style="margin-left: 2em;">sky, <a href="#Page_241">241</a></span><br />
+<br />
+Brucke&#8217;s theory, <a href="#Page_37">37</a><br />
+<br />
+Brunot&#8217;s mean distance theory, <a href="#Page_101">101</a><br />
+<br />
+<br />
+Camouflage, <a href="#Page_210">210</a><br />
+<span style="margin-left: 1em;">terrestrial, <a href="#Page_210">210</a></span><br />
+<span style="margin-left: 1em;">detection of, <a href="#Page_215">215</a></span><br />
+<span style="margin-left: 1em;">marine, <a href="#Page_222">222</a></span><br />
+<span style="margin-left: 1em;">airplane, <a href="#Page_234">234</a></span><br />
+<br />
+Carr, observations on distance illusions, <a href="#Page_108">108</a><br />
+<br />
+Chromatic aberration, <a href="#Page_19">19</a>, <a href="#Page_135">135</a><br />
+<br />
+Chlorophyl, <a href="#Page_214">214</a><br />
+<br />
+Circle, <a href="#Page_11">11</a><br />
+<span style="margin-left: 1em;">arcs of, illusion, <a href="#Page_86">86</a></span><br />
+<span style="margin-left: 1em;">contracting and expanding illusion, <a href="#Page_98">98</a></span><br />
+<br />
+Clouds, <a href="#Page_235">235</a><br />
+<br />
+Color, <a href="#Page_124">124</a><br />
+<span style="margin-left: 1em;">after-images, <a href="#Page_128">128</a></span><br />
+<span style="margin-left: 1em;">blending in camouflage, <a href="#Page_216">216</a></span><br />
+<span style="margin-left: 1em;">contrasts and brightness, <a href="#Page_114">114</a></span><br />
+<span style="margin-left: 1em;">growth and decay of sensation, <a href="#Page_131">131</a></span><br />
+<span style="margin-left: 1em;">illusions of, <a href="#Page_156">156</a></span><br />
+<span style="margin-left: 1em;">retiring and advancing, <a href="#Page_138">138</a></span><br />
+<span style="margin-left: 1em;">saturation, <a href="#Page_154">154</a></span><br />
+<span style="margin-left: 1em;">sensibility of retina, <a href="#Page_138">138</a></span><br />
+<span style="margin-left: 1em;">warm and cold, <a href="#Page_158">158</a></span><br />
+<br />
+Confusability, <a href="#Page_226">226</a><br />
+<br />
+Confusion theory of angular illusions, <a href="#Page_100">100</a><br />
+<br />
+Contour, illusions of, <a href="#Page_52">52</a><br />
+<span style="margin-left: 1em;">and angles, illusions, <a href="#Page_87">87</a></span><br />
+<span class="pagenum"><a name="Page_250" id="Page_250">[Pg 250]</a></span><br />
+Contracting and expanding circles, illusion of, <a href="#Page_98">98</a><br />
+<br />
+Contrasts, illusions of, <a href="#Page_53">53</a><br />
+<span style="margin-left: 1em;">simultaneous, <a href="#Page_124">124</a>, <a href="#Page_154">154</a></span><br />
+<span style="margin-left: 1em;">apparatus for, <a href="#Page_115">115</a>, <a href="#Page_125">125</a></span><br />
+<span style="margin-left: 1em;">color, <a href="#Page_114">114</a>, <a href="#Page_154">154</a>, <a href="#Page_188">188</a></span><br />
+<span style="margin-left: 1em;">brightness, <a href="#Page_114">114</a></span><br />
+<br />
+Convergence, illusions of, <a href="#Page_108">108</a>, <a href="#Page_191">191</a><br />
+<br />
+Cord, twisted, illusion, <a href="#Page_88">88</a><br />
+<br />
+<br />
+Daylight, artificial, <a href="#Page_189">189</a><br />
+<br />
+Decoration, painting and, <a href="#Page_179">179</a><br />
+<br />
+Decorator, <a href="#Page_188">188</a><br />
+<br />
+Dember, <a href="#Page_167">167</a><br />
+<br />
+Depth and distance, illusions, <a href="#Page_102">102</a><br />
+<br />
+Direction, illusions of<br />
+<span style="margin-left: 1em;">Z&ouml;llner&#8217;s, <a href="#Page_76">76</a></span><br />
+<span style="margin-left: 1em;">Wundt&#8217;s, <a href="#Page_79">79</a></span><br />
+<span style="margin-left: 1em;">Hering&#8217;s, <a href="#Page_80">80</a></span><br />
+<br />
+Disk, Mason, <a href="#Page_132">132</a><br />
+<br />
+Distance and depth, illusions, <a href="#Page_102">102</a><br />
+<span style="margin-left: 1em;">and size, <a href="#Page_35">35</a>, <a href="#Page_104">104</a>, <a href="#Page_166">166</a></span><br />
+<br />
+Distance illusions, Carr&#8217;s observations, <a href="#Page_108">108</a><br />
+<br />
+Double images, <a href="#Page_37">37</a><br />
+<br />
+Dynamic theory of angular illusions, <a href="#Page_99">99</a><br />
+<br />
+<br />
+Enlargement of sun and moon at horizon, apparent, <a href="#Page_169">169</a><br />
+<br />
+Equivocal figures, <a href="#Page_64">64</a><br />
+<br />
+Euclid, <a href="#Page_8">8</a><br />
+<br />
+Extent, interrupted, illusions of, <a href="#Page_48">48</a><br />
+<br />
+External image, <a href="#Page_15">15</a>, <a href="#Page_17">17</a>, <a href="#Page_34">34</a><br />
+<br />
+Eye, physiology, <a href="#Page_13">13</a><br />
+<span style="margin-left: 1em;">position, <a href="#Page_30">30</a></span><br />
+<span style="margin-left: 1em;">adjustments, <a href="#Page_33">33</a></span><br />
+<span style="margin-left: 1em;">defects, <a href="#Page_19">19</a></span><br />
+<br />
+<br />
+Fatigue, <a href="#Page_128">128</a><br />
+<br />
+Field, visual, effect of location in, <a href="#Page_44">44</a><br />
+<br />
+Figures, equivocal, <a href="#Page_64">64</a><br />
+<br />
+Filters, color, <a href="#Page_214">214</a><br />
+<br />
+Fluctuation of attention, <a href="#Page_65">65</a>, <a href="#Page_106">106</a>, <a href="#Page_141">141</a>, <a href="#Page_164">164</a><br />
+<br />
+Focusing, <a href="#Page_14">14</a><br />
+<br />
+
+Form of sky, apparent, <a href="#Page_166">166</a><br />
+<br />
+Fovea centralis, <a href="#Page_22">22</a>, <a href="#Page_23">23</a>, <a href="#Page_139">139</a><br />
+<br />
+Frames, picture, effect of wood grain, <a href="#Page_190">190</a><br />
+<br />
+<br />
+Geometrical illusions, <a href="#Page_44">44</a><br />
+<br />
+Glare, <a href="#Page_119">119</a><br />
+<br />
+Grain of wood, apparent distortions due to, <a href="#Page_190">190</a><br />
+<br />
+Grecian art, <a href="#Page_196">196</a><br />
+<br />
+Growth and decay of <ins class="correction" title="original: colo">color</ins> sensation, <a href="#Page_131">131</a><br />
+<br />
+Guttman, <a href="#Page_175">175</a><br />
+<br />
+<br />
+Hallucination, <a href="#Page_4">4</a>, <a href="#Page_72">72</a><br />
+<br />
+Halo, <a href="#Page_178">178</a><br />
+<br />
+Haze, illusions, etc., <a href="#Page_103">103</a>, <a href="#Page_166">166</a>, <a href="#Page_183">183</a><br />
+<span style="margin-left: 1em;">earth and high, <a href="#Page_240">240</a></span><br />
+<br />
+Helmholtz, <a href="#Page_13">13</a>, <a href="#Page_74">74</a><br />
+<br />
+Hering, <a href="#Page_74">74</a><br />
+<span style="margin-left: 1em;">illusion of direction, <a href="#Page_80">80</a></span><br />
+<br />
+Hue and brightness, <a href="#Page_125">125</a><br />
+<br />
+<br />
+Illusions, geometrical, <a href="#Page_44">44</a><br />
+<span style="margin-left: 1em;">equivocal figures, <a href="#Page_64">64</a></span><br />
+<span style="margin-left: 1em;">influence of angles, <a href="#Page_76">76</a></span><br />
+<span style="margin-left: 1em;">of depth and distance, <a href="#Page_102">102</a></span><br />
+<span style="margin-left: 1em;">irradiation and brightness contrast, <a href="#Page_114">114</a></span><br />
+<span style="margin-left: 1em;">color, <a href="#Page_124">124</a></span><br />
+<span style="margin-left: 1em;">light and shadows, <a href="#Page_144">144</a></span><br />
+<span style="margin-left: 1em;">in nature, <a href="#Page_164">164</a></span><br />
+<span style="margin-left: 1em;">in painting and decoration, <a href="#Page_179">179</a></span><br />
+<span style="margin-left: 1em;">mirror, <a href="#Page_205">205</a></span><br />
+<span style="margin-left: 1em;">camouflage, <a href="#Page_210">210</a></span><br />
+<br />
+Image<br />
+<span style="margin-left: 1em;">after-, <a href="#Page_24">24</a>, <a href="#Page_25">25</a>, <a href="#Page_59">59</a>, <a href="#Page_128">128</a>, <a href="#Page_129">129</a>, <a href="#Page_186">186</a></span><br />
+<span style="margin-left: 1em;">double, <a href="#Page_37">37</a></span><br />
+<span style="margin-left: 1em;">external, <a href="#Page_15">15</a>, <a href="#Page_17">17</a>, <a href="#Page_34">34</a></span><br />
+<span style="margin-left: 1em;">retinal, inversion of, <a href="#Page_16">16</a></span><br />
+<span style="margin-left: 1em;">of airplane, size at various altitudes, <a href="#Page_238">238</a></span><br />
+<br />
+Indirect vision theory, Auerbach&#8217;s, <a href="#Page_100">100</a><br />
+<br />
+Intaglio, <a href="#Page_143">143</a><br />
+<br />
+Interrupted extent, illusions of, <a href="#Page_48">48</a><br />
+<br />
+Iris, <a href="#Page_15">15</a><br />
+<br />
+<span class="pagenum"><a name="Page_251" id="Page_251">[Pg 251]</a></span>Irradiation, <a href="#Page_120">120</a><br />
+<span style="margin-left: 1em;">and brightness contrast, <a href="#Page_114">114</a></span><br />
+<span style="margin-left: 1em;">varieties of (Boswell), <a href="#Page_122">122</a></span><br />
+<span style="margin-left: 1em;">in architecture, <a href="#Page_199">199</a></span><br />
+<br />
+<br />
+James, <a href="#Page_170">170</a><br />
+<br />
+Jastrow, <a href="#Page_80">80</a><br />
+<br />
+Jones, L. A., <a href="#Page_223">223</a><br />
+<br />
+Judd, <a href="#Page_86">86</a>, <a href="#Page_93">93</a><br />
+<br />
+Judgment, <a href="#Page_1">1</a><br />
+<br />
+<br />
+Karrer, <a href="#Page_160">160</a><br />
+<br />
+Kepler, <a href="#Page_8">8</a><br />
+<br />
+<br />
+Light, effect of spectral character, <a href="#Page_189">189</a><br />
+<br />
+Lighting, illusions of depth and distance due to, <a href="#Page_102">102</a><br />
+<span style="margin-left: 1em;">contrasts, <a href="#Page_154">154</a></span><br />
+<span style="margin-left: 1em;">diffusion, effect of, <a href="#Page_145">145</a></span><br />
+<span style="margin-left: 1em;">direction, effect of, <a href="#Page_144">144</a>, <a href="#Page_151">151</a></span><br />
+<span style="margin-left: 1em;">ending of searchlight beam, <a href="#Page_160">160</a></span><br />
+<span style="margin-left: 1em;">warm and cold colors, <a href="#Page_158">158</a></span><br />
+<br />
+Lipps, <a href="#Page_10">10</a>, <a href="#Page_11">11</a><br />
+<span style="margin-left: 1em;">dynamic theory of, <a href="#Page_99">99</a></span><br />
+<br />
+Location in visual field, effect, <a href="#Page_44">44</a><br />
+<br />
+<br />
+Mean distance theory, Brunot&#8217;s, <a href="#Page_101">101</a><br />
+<br />
+Mechanical, esthetic unity, <a href="#Page_11">11</a><br />
+<br />
+Magician, <a href="#Page_3">3</a><br />
+<br />
+Magic, mirror, <a href="#Page_205">205</a><br />
+<br />
+Marine camouflage, <a href="#Page_222">222</a><br />
+<br />
+Mason disk, <a href="#Page_132">132</a><br />
+<br />
+Mirage, <a href="#Page_3">3</a>, <a href="#Page_176">176</a><br />
+<br />
+Mirror magic, <a href="#Page_205">205</a><br />
+<br />
+Miscellaneous color effects, <a href="#Page_140">140</a><br />
+<br />
+Moon, apparent size at horizon, <a href="#Page_8">8</a>, <a href="#Page_36">36</a>, <a href="#Page_169">169</a><br />
+<span style="margin-left: 1em;">theories of, <a href="#Page_173">173</a></span><br />
+<span style="margin-left: 1em;">apparent radius of crescent, <a href="#Page_121">121</a></span><br />
+<br />
+M&uuml;ller-Lyer illusion, <a href="#Page_53">53</a>, <a href="#Page_93">93</a><br />
+<br />
+<br />
+National Research Council, Committee on Camouflage, <a href="#Page_234">234</a><br />
+<br />
+Nature, <a href="#Page_164">164</a><br />
+<br />
+Necker, <a href="#Page_74">74</a><br />
+<br />
+<br />
+Oppel, <a href="#Page_9">9</a><br />
+<br />
+<br />
+Painting and decoration, <a href="#Page_179">179</a><br />
+<br />
+Painter, <a href="#Page_2">2</a>, <a href="#Page_179">179</a>, <a href="#Page_186">186</a><br />
+<br />
+Parallax, <a href="#Page_105">105</a><br />
+<br />
+Parthenon of Athens, <a href="#Page_196">196</a><br />
+<br />
+Persistence of vision, <a href="#Page_131">131</a><br />
+<br />
+Perspective, <a href="#Page_58">58</a><br />
+<span style="margin-left: 1em;">in architecture, <a href="#Page_198">198</a></span><br />
+<span style="margin-left: 1em;">aerial <a href="#Page_165">165</a>, <a href="#Page_183">183</a></span><br />
+<span style="margin-left: 1em;">theory, <a href="#Page_98">98</a></span><br />
+<br />
+Photographer, <a href="#Page_152">152</a><br />
+<br />
+Photography, use in detection of camouflage, <a href="#Page_220">220</a><br />
+<br />
+Photometer, <a href="#Page_156">156</a>, <a href="#Page_217">217</a><br />
+<br />
+Pigments, <a href="#Page_184">184</a><br />
+<br />
+Poggendorff illusion, <a href="#Page_85">85</a><br />
+<br />
+Protective coloration, animals, <a href="#Page_211">211</a><br />
+<br />
+Psychology, <a href="#Page_2">2</a>, <a href="#Page_6">6</a>, <a href="#Page_157">157</a><br />
+<span style="margin-left: 1em;">of light, <a href="#Page_193">193</a></span><br />
+<br />
+Purkinje phenomenon, <a href="#Page_26">26</a>, <a href="#Page_139">139</a><br />
+<br />
+<br />
+Reflection-factors, <a href="#Page_236">236</a><br />
+<br />
+Retina, <a href="#Page_14">14</a>, <a href="#Page_20">20</a><br />
+<span style="margin-left: 1em;">inertia, <a href="#Page_130">130</a></span><br />
+<span style="margin-left: 1em;">color sensibility, <a href="#Page_138">138</a></span><br />
+<br />
+Retinal rivalry, <a href="#Page_140">140</a><br />
+<br />
+Retiring and advancing colors, <a href="#Page_136">136</a><br />
+<br />
+Reversal of mirror image, <a href="#Page_205">205</a><br />
+<br />
+Rods and cones, <a href="#Page_21">21</a><br />
+<br />
+<br />
+Schr&ouml;der&#8217;s staircase, <a href="#Page_70">70</a><br />
+<br />
+Sculpture, <a href="#Page_204">204</a><br />
+<br />
+Searchlight beam, ending of, <a href="#Page_160">160</a><br />
+<br />
+Sensation, color, growth and decay, <a href="#Page_131">131</a><br />
+<br />
+Sense, <a href="#Page_1">1</a><br />
+<br />
+Shading, counter, for vessels, <a href="#Page_224">224</a><br />
+<br />
+Shadows, importance in camouflage, <a href="#Page_215">215</a><br />
+<br />
+Size and distance, <a href="#Page_35">35</a>, <a href="#Page_36">36</a><br />
+<span style="margin-left: 1em;">illusions of, <a href="#Page_104">104</a>, <a href="#Page_166">166</a></span><br />
+<br />
+Sky<br />
+<span style="margin-left: 1em;">apparent form of, <a href="#Page_166">166</a></span><br />
+<span style="margin-left: 1em;">brightness, <a href="#Page_241">241</a></span><br />
+<br />
+Skylight and sunlight, relative proportions of, <a href="#Page_215">215</a>, <a href="#Page_243">243</a><br />
+<br />
+Smith, Robert, <a href="#Page_173">173</a><br />
+<br />
+Smoke-screens, <a href="#Page_230">230</a><br />
+<span class="pagenum"><a name="Page_252" id="Page_252">[Pg 252]</a></span><br />
+Spectral character of light, <a href="#Page_189">189</a><br />
+<br />
+Sphere, illusions, <a href="#Page_145">145</a>, <a href="#Page_150">150</a>, <a href="#Page_151">151</a><br />
+<br />
+Spherical aberration, <a href="#Page_19">19</a><br />
+<br />
+Sphinx illusion, <a href="#Page_206">206</a><br />
+<br />
+Spiral illusions, <a href="#Page_90">90</a><br />
+<br />
+Spraying, paint, <a href="#Page_187">187</a><br />
+<br />
+Stereoscope, <a href="#Page_39">39</a>, <a href="#Page_142">142</a><br />
+<br />
+Stereoscopic vision, <a href="#Page_38">38</a>, <a href="#Page_41">41</a>, <a href="#Page_141">141</a><br />
+<br />
+Submarines, <a href="#Page_225">225</a><br />
+<span style="margin-left: 1em;">camouflage for, <a href="#Page_232">232</a></span><br />
+<br />
+Sun, apparent enlargement at horizon, <a href="#Page_169">169</a><br />
+<br />
+Sunlight and skylight, relative proportions in nature, <a href="#Page_215">215</a>, <a href="#Page_243">243</a><br />
+<br />
+<br />
+Terrestrial camouflage, <a href="#Page_210">210</a><br />
+<br />
+Theory of influence of angles, <a href="#Page_98">98</a><br />
+<span style="margin-left: 1em;">perspective, <a href="#Page_98">98</a></span><br />
+<span style="margin-left: 1em;">dynamic, <a href="#Page_99">99</a></span><br />
+<span style="margin-left: 1em;">confusion, <a href="#Page_100">100</a></span><br />
+<span style="margin-left: 1em;">indirect vision, <a href="#Page_100">100</a></span><br />
+<span style="margin-left: 1em;">mean distance, <a href="#Page_101">101</a></span><br />
+<br />
+Thi&eacute;ry&#8217;s figure, <a href="#Page_71">71</a><br />
+<br />
+Thi&eacute;ry&#8217;s perspective theory, <a href="#Page_99">99</a><br />
+<br />
+Transparencies, <a href="#Page_185">185</a><br />
+<br />
+Twisted cord illusions, <a href="#Page_88">88</a><br />
+<br />
+<br />
+Uibe, <a href="#Page_167">167</a><br />
+<br />
+<br />
+Vertical vs. horizontal distances, <a href="#Page_11">11</a>, <a href="#Page_36">36</a>, <a href="#Page_46">46</a><br />
+<br />
+Visibility, low, for vessels, <a href="#Page_222">222</a><br />
+<span style="margin-left: 1em;">of airplanes, <a href="#Page_233">233</a></span><br />
+<br />
+Vision, <a href="#Page_29">29</a><br />
+<span style="margin-left: 1em;">persistence of, <a href="#Page_131">131</a></span><br />
+<span style="margin-left: 1em;">stereoscopic, <a href="#Page_38">38</a></span><br />
+<br />
+Visual perception, <a href="#Page_32">32</a>, <a href="#Page_33">33</a><br />
+<br />
+<br />
+Warm and cold colors, <a href="#Page_158">158</a><br />
+<br />
+Warner, E. L., <a href="#Page_227">227</a><br />
+<br />
+Wheatstone, <a href="#Page_37">37</a><br />
+<br />
+Wood grain, illusions caused by, <a href="#Page_191">191</a><br />
+<br />
+World War, <a href="#Page_213">213</a><br />
+<br />
+Wundt, <a href="#Page_10">10</a>, <a href="#Page_11">11</a>, <a href="#Page_32">32</a>, <a href="#Page_74">74</a><br />
+<span style="margin-left: 1em;">illusion of direction, <a href="#Page_79">79</a></span><br />
+<br />
+<br />
+Yellow spot, <a href="#Page_139">139</a><br />
+<br />
+<br />
+Z&ouml;llner&#8217;s illusion, <a href="#Page_67">67</a>, <a href="#Page_76">76</a><br />
+<br />
+Zoth, <a href="#Page_175">175</a><br />
+</p>
+
+
+<p>&nbsp;</p><p>&nbsp;</p>
+<hr style="width: 50%;" />
+<div class="verts">
+<p class="center"><span class="large">OTHER BOOKS</span><br />
+BY<br />
+<span class="huge">M. LUCKIESH</span></p>
+
+<p>&nbsp;</p>
+<p class="center"><strong>COLOR AND ITS APPLICATIONS</strong></p>
+<p class="center">Second Edition, Revised and Enlarged.</p>
+<p class="center">6 x 9, 150 illustrations, 4 color plates, 431 pages.<span class="spacer">&nbsp;</span>$4.50</p>
+
+<p>The object of this treatise is not only to discuss the many applications
+of color, but to establish a sound scientific basis for these
+applications. The book is authoritative, well illustrated, and contains
+many references and a wealth of new material. It was written by an
+investigator in the general field of color and is therefore not narrowly
+limited in scope. It fills a distinct gap that has existed on the book
+shelves.</p>
+
+<p>&nbsp;</p>
+<p class="center"><strong>LIGHT AND SHADE AND THEIR APPLICATIONS</strong></p>
+<p class="center">6 x 9, 135 illustrations, 277 pages<span class="spacer">&nbsp;</span>$3.00</p>
+
+<p>The book is a condensed record of several years&#8217; research by the author in
+the science of light and shade. It is the first published work which deals
+with the science of light and shade in a complete and analytical manner.
+The author has the faculty of bringing forth scientific facts in such a
+manner as to be helpful to those interested in the various arts. The book
+is of extremely wide interest because it deals with the appearances of
+objects and hence with vision and with lighting. It is well illustrated
+and represents the first elaborate attempt to formulate the science of
+light and shade and to correlate it with various arts.</p>
+
+<p>&nbsp;</p>
+<p class="center"><strong>ULTRAVIOLET RADIATION,</strong> Its Properties, Production, Measurement and Applications.</p>
+<p class="center">6 x 9, 12 plates, 270 pages<span class="spacer">&nbsp;</span>$3.50</p>
+
+<p>It is the primary aim of this book to present authentic data of such scope
+as to be useful to the chemist, physicist, engineer, biologist,
+ophthalmologist and physician and others interested in ultraviolet
+radiation. Theory has been subordinated to experimental facts because the
+latter are not affected by the inevitable changes in theory. 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 factors. From this mass of isolated material the
+author has co&ouml;rdinated much valuable data. The many references which are
+included increase the usefulness of the book.</p>
+
+<p>&nbsp;</p>
+<p class="center"><strong>LIGHTING THE HOME</strong></p>
+<p class="center">5 x 7&#189;, illustrated, 289 pages<span class="spacer">&nbsp;</span>$2.00</p>
+
+<p>This is a pioneer book. It ranks with books on interior decoration and
+furniture as a help toward transforming a house into a home. It is
+practical in that it offers advice on all sorts of lighting problems and
+it is fascinating reading as well.</p>
+
+<p>&nbsp;</p>
+<p class="center"><strong>ARTIFICIAL LIGHT, ITS INFLUENCE ON CIVILIZATION</strong></p>
+<p class="center">6 x 9, illustrated, 366 pages<span class="spacer">&nbsp;</span>$3.00</p>
+
+<p>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 formulae, but who looks with admiration upon the huge signs
+which flash and sparkle above the crowds on the Great White Way, who
+marvels at the colors and brilliance of a spectacular theatrical
+production and desires to know how it is accomplished, and who takes a
+natural delight in hearing about scientific discoveries when they are
+explained in the simple, vivid language he understands best.</p>
+
+<p>&nbsp;</p>
+<p class="center"><strong>THE LIGHTING ART, ITS PRACTICE AND POSSIBILITIES</strong></p>
+<p class="center">6 x 9, illustrated, 229 pages<span class="spacer">&nbsp;</span>$2.50</p>
+
+<p>This book discusses lighting as engineering plus art, and treats the
+subject as a branch of interior and exterior decoration. The technical
+aspect of the subject is not neglected, but the main emphasis is upon the
+&#8220;why&#8221; and not merely the &#8220;how&#8221; of lighting.</p>
+
+<p>&nbsp;</p>
+<p class="center"><strong>THE LANGUAGE OF COLOR</strong></p>
+<p class="center">6 x 9, illustrated, 282 pages<span class="spacer">&nbsp;</span>$2.00</p>
+
+<p>A practical volume on color, the various fields in which it is used and
+its importance in portraying the ideas that make for progress. A book of
+special interest to all those who deal in color schemes and values.</p>
+
+<p>&nbsp;</p>
+<p class="center"><strong>THE BOOK OF THE SKY</strong></p>
+<p class="center">6 x 9, illustrated, 236 pages<span class="spacer">&nbsp;</span>$3.50</p>
+
+<p>&#8220;The beauties, wonders, awesome spectacles, inspiring panoramas, and
+extensive ranges of vision which await the aerial traveler, make of
+cloudland a veritable fairyland if he will open his consciousness to them.
+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 fly,
+or would fly, to the variety of interest which air travel affords.&#8221;</p></div>
+
+
+<p>&nbsp;</p><p>&nbsp;</p>
+<div class="vertsbox">
+<p class="center"><span class="huge"><i>The</i><br />
+Literature of Engineering<br />
+and the Industries</span></p>
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+
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+
+<p>&nbsp;</p>
+<div class="figcenter"><img src="images/ad_image.jpg" alt="" /></div>
+<p>&nbsp;</p>
+
+<p class="center">D. Van Nostrand Company<br />
+<i>PUBLISHERS AND BOOKSELLERS</i><br />
+8 WARREN STREET<span class="spacer">&nbsp;</span>NEW YORK</p></div>
+
+
+<p>&nbsp;</p><p>&nbsp;</p>
+<hr style="width: 50%;" />
+<p><strong>Transcriber&#8217;s Notes:</strong></p>
+
+<p>Images have been moved from the middle of a paragraph to a nearby paragraph break.</p>
+
+<p>Other than the corrections noted by hover information, inconsistencies in
+spelling and hyphenation have been retained from the original.</p>
+
+
+
+
+
+
+
+
+<pre>
+
+
+
+
+
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+</html>
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