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| author | Roger Frank <rfrank@pglaf.org> | 2025-10-14 20:11:37 -0700 |
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| committer | Roger Frank <rfrank@pglaf.org> | 2025-10-14 20:11:37 -0700 |
| commit | 604420c6cbd4c34a91f5aa4deec653fc4705737b (patch) | |
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diff --git a/38984-h/38984-h.htm b/38984-h/38984-h.htm new file mode 100644 index 0000000..b14cf42 --- /dev/null +++ b/38984-h/38984-h.htm @@ -0,0 +1,6672 @@ +<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<HTML><HEAD> + <meta http-equiv="Content-type" content="text/html;charset=UTF-8"> + <meta http-equiv="Content-Style-Type" content="text/css"> + <title> + Colour Measurement And Mixture, by Captain W. De W. Abney. A Project Gutenberg eBook + </title> + <style type="text/css"> + + +body { + margin-left: 10%; + margin-right: 10%; +} + + h1,h2,h3 { + text-align: center; /* all headings centered */ + clear: both; +} + +p { + margin-top: .75em; + text-align: justify; + margin-bottom: .75em; +} +.smaller {font-size:small;} + +.larger {font-size:large;} + +.padtop {margin-top:4em;} + +.moustache {font-size: 400%; vertical-align: -0.7em;} +.moustachetp {font-size: 350%; vertical-align: 0.4em;} +.moustachesm {font-size: 250%; vertical-align: 0.4em;} + + +table { + margin-left: auto; + margin-right: auto; +} + +.pagenum { /* uncomment the next line for invisible page numbers */ + /* visibility: hidden; */ + position: absolute; + left: 92%; + font-size: smaller; + text-align: right; +} /* page numbers */ + +blockquote { + margin-left: 5%; + margin-right: 10%; + text-align: center; +} +.rtnote { + margin-left: 2em; + margin-bottom: 1em; + margin-top: 1em; + margin-right: 0; + padding: 0; + text-align: right; +} + +.sidenote { + width: 15%; + margin-left: 1em; + float: right; + clear: right; + color: black; +} + + +.smcap {font-variant: small-caps;} + + +.center {text-align: center;} + +.caption {font-weight: bold;} + +/* Images */ +.figcenter { + margin: auto; + text-align: center; +} + +.figleft { + float: left; + clear: left; + margin-left: 0; + margin-bottom: 1em; + margin-top: 1em; + margin-right: 1em; + padding: 0; + text-align: center; +} + +.figright { + float: right; + clear: right; + margin-left: 1em; + margin-bottom: + 1em; + margin-top: 1em; + margin-right: 0; + padding: 0; + text-align: center; +} + + + </style> + </head> +<body> + + +<pre> + +Project Gutenberg's Colour Measurement and Mixture, by W. de W. Abney + +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: Colour Measurement and Mixture + +Author: W. de W. Abney + +Release Date: February 26, 2012 [EBook #38984] + +Language: English + +Character set encoding: UTF-8 + +*** START OF THIS PROJECT GUTENBERG EBOOK COLOUR MEASUREMENT AND MIXTURE *** + + + + +Produced by Chris Curnow, Hazel Batey and the Online +Distributed Proofreading Team at https://www.pgdp.net (This +file was produced from images generously made available +by The Internet Archive) + + + + + + +</pre> + + + +<p>This E text uses UTF-8 (unicode) file encoding. If the apostrophes, +quotation marks and Greek text [ἀπολύτρωσις] in this paragraph appear as +garbage, you may have an incompatible browser or unavailable fonts. +First, make sure that your browser’s “character set” or “file encoding” +is set to Unicode (UTF-8). You may also need to change the default font.</p> +<a name="frontispiece" id="frontispiece"></a> +<div class="figcenter" style="width: 402px;"> +<img src="images/i_002.jpg" width="402" height="253" alt="" title=""> +<span class="caption">COLOUR-PATCH APPARATUS.</span> +</div><br> + + +<h2><i>THE ROMANCE OF SCIENCE.</i></h2> +<hr style="width: 95%;"> +<h1> COLOUR MEASUREMENT</h1> +<p class='center larger'> AND</p> +<h1>MIXTURE.</h1> + + +<p class='padtop center smaller'> <b>With Numerous Illustrations.</b></p> + + +<p class='padtop center smaller'> BY</p> +<p class='center larger'> CAPTAIN W. <span class="smcap">de W. ABNEY, c.b., r.e., d.c.l., f.r.s.</span></p> + + +<p class='padtop center smaller'> PUBLISHED UNDER THE DIRECTION OF THE COMMITTEE<br> + OF GENERAL LITERATURE AND EDUCATION APPOINTED BY THE<br> + SOCIETY FOR PROMOTING CHRISTIAN KNOWLEDGE.</p> + + +<p class='padtop center smaller'> SOCIETY FOR PROMOTING CHRISTIAN KNOWLEDGE.<br> + LONDON: NORTHUMBERLAND AVENUE, W.C.;<br> + 43, QUEEN VICTORIA STREET, E.C.<br> + BRIGHTON: 135, NORTH STREET.<br> + NEW YORK: E. & J. B. YOUNG & CO.<br> + 1891.</p><br> + + +<hr style="width: 65%;"> +<h2>PREFACE.</h2> + + +<p>Some ten years ago there were three measurements +of the spectrum which I set myself to carry +out; the last two, at all events, involving new +methods of experimenting. The three measurements +were: (1st) The heating effect; (2nd) the +luminosity; and (3rd) the chemical effect on various +salts, of the different rays of the spectrum. +The task is now completed, and it was in carrying +out the second part of it that General Festing, who +joined me in the research, and myself were led +into a wider study of colour than at first intended, +as the apparatus we devised enabled us to carry +out experiments which, whilst difficult under ordinary +circumstances, became easy to make. On +two occasions, at the invitation of the Society of +Arts, I have delivered a short course of lectures on +the subject of Colour, and naturally I chose to +treat it from the point of view of our own methods +of experimenting; and these lectures, expanded and +modified, form the basis of the present volume.</p> + +<p>As a treatise it must necessarily be incomplete, +as it scarcely touches on the history of the subject—a +part which must always be of deep interest. +The solely physiological aspect of colour has also +been scarcely dealt with; that part which the +physicist can submit to measurement being that +which alone was practicable under the circumstances.</p> + +<p class="rtnote"><span class="smcap">W. de W. Abney.</span></p> +<br> +<p><span style="margin-left: 2em;"><i>South Kensington,</i></span><br> +<span style="margin-left: 2em;"><i>1st May, 1891.</i></span><br> +</p> + + +<hr style="width: 65%;"> +<h2>CONTENTS.</h2> + + + +<h3><a href="#CHAPTER_I">CHAPTER I.</a></h3> + +<p> Sources of Light—Reflected Light—Reflection from Roughened + Surfaces—Colour Constants <span class="sidenote"><i>p.</i> 11</span></p> + + +<h3><a href="#CHAPTER_II">CHAPTER II.</a></h3> + +<p> A Standard of Light—Formation of the Spectrum by Prisms and by + the Diffraction Grating—Wave-lengths of the principal Fraunhofer + Line—Position of Colours in the Spectrum <span class="sidenote"><i>p.</i> 17</span></p> + + +<h3><a href="#CHAPTER_III">CHAPTER III.</a></h3> + +<p> The Visible and Invisible Parts of the Spectrum—Methods + for showing the Existence of the Invisible + Portions—Phosphorescence—Photography of the Dark + Rays—Thermo-Electric Currents <span class="sidenote"><i> p.</i> 30</span></p> + + +<h3><a href="#CHAPTER_IV">CHAPTER IV.</a></h3> + +<p> Description of Colour Patch Apparatus—Rotating Sectors—Method of + making a Scale for the Spectrum <span class="sidenote"><i>p.</i> 41</span></p> + + +<h3><a href="#CHAPTER_V">CHAPTER V.</a></h3> + +<p> Absorption of the Spectrum—Analysis of Colour—Vibrations of + Rays—Absorption by Pigments—Phosphorescence—Interference <span class="sidenote"><i>p.</i> 51</span></p> +<p><span class="pagenum">[Pg viii]</span></p> + +<h3><a href="#CHAPTER_VI">CHAPTER VI.</a></h3> + +<p> Scattered Light—Sunset Colours—Law of the Scattering by Fine + Particles—Sunset Clouds—Luminosities of Sunlight at different + Altitudes of the Sun <span class="sidenote"><i>p.</i> 62</span></p> + + +<h3><a href="#CHAPTER_VII">CHAPTER VII.</a></h3> + +<p> Luminosity of the Spectrum to Normal-eyed and Colour-blind + Persons—Method of determining the Luminosity of Pigments—Addition + of one Luminosity to another <span class="sidenote"><i>p.</i> 76</span></p> + + +<h3><a href="#CHAPTER_VIII">CHAPTER VIII.</a></h3> + +<p> Methods of Measuring the Intensity of the Different Colours of the + Spectrum, reflected from Pigmented Surfaces—Templates for + the Spectrum <span class="sidenote"><i>p.</i> 88</span></p> + + +<h3><a href="#CHAPTER_IX">CHAPTER IX.</a></h3> + +<p> Colour Mixtures—Yellow Spot in the Eye—Comparison of Different + Lights—Simple Colours by Mixing Simple Colours—Yellow and + Blue from White <span class="sidenote"><i>p.</i> 112</span></p> + + +<h3><a href="#CHAPTER_X">CHAPTER X.</a></h3> + +<p> Extinction of Colour by White Light—Extinction of White Light + by Colour <span class="sidenote"><i>p.</i> 126</span></p> + + +<h3><a href="#CHAPTER_XI">CHAPTER XI.</a></h3> + +<p> Primary Colours—Molecular Swings—Colour Sensations—Sensations + absent in the Colour-blind <span class="sidenote"><i>p.</i> 133</span></p> + + +<h3><a href="#CHAPTER_XII">CHAPTER XII.</a></h3> + +<p> Formation of Colour Equations—Kœnig's Curves—Maxwell's Apparatus + and Curves <span class="sidenote"><i>p.</i> 147</span></p> + + +<h3><a href="#CHAPTER_XIII">CHAPTER XIII.</a></h3> + +<p> Match of Compound Colours with Simple Colours—All Colours + reduced to Numbers—Method of Matching a Colour with a + Spectrum Colour and White Light <span class="sidenote"><i>p.</i> 156</span></p> +<p><span class="pagenum">[Pg ix]</span></p> + + +<h3><a href="#CHAPTER_XIV">CHAPTER XIV.</a></h3> + + <p>Complementary Colours—Complementary Pigment Colours—Measurement + of Complementary Colours <span class="sidenote"><i>p.</i> 167</span></p> + + +<h3><a href="#CHAPTER_XV">CHAPTER XV.</a></h3> + + <p>Persistence of Images on the Retina—The Use of Coloured Discs <span class="sidenote"><i>p.</i> 179</span></p> + + +<h3><a href="#CHAPTER_XVI">CHAPTER XVI.</a></h3> + + <p>Contrast Colours—Measurement of Contrast Colours—Fatigue of + the Eye—After-Images <span class="sidenote"><i>p.</i> 196</span></p> + + +<hr style="width: 65%;"> +<h2>LIST OF ILLUSTRATIONS.</h2> + +<div class="center"> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="right"> FIG.</td><td align="left"></td><td align="right">PAGE</td></tr> +<tr><td align="right"></td><td align="left">Colour-patch apparatus</td><td align="right"><i><a href="#frontispiece">Frontispiece</a></i></td></tr> +<tr><td align="right"> 1.</td><td align="left">Spectrum of sunlight</td><td align="right"><a href="#Page_18">18</a> </td></tr> +<tr><td align="right"> 2.</td><td align="left">Carbon poles of an electric light</td><td align="right"><a href="#Fig_2">20</a> </td></tr> +<tr><td align="right"> 3.</td><td align="left">Curve for converting prismatic spectrum into wave-lengths</td><td align="right"><a href="#Page_28">28</a> </td></tr> +<tr><td align="right"> 4.</td><td align="left">The thermopile</td><td align="right"><a href="#Fig_4">35</a> </td></tr> +<tr><td align="right"> 5.</td><td align="left">Heating effect of different sources of radiation</td><td align="right"><a href="#Page_38">38</a> </td></tr> +<tr><td align="right"> 6.</td><td align="left">Colour-patch apparatus</td><td align="right"><a href="#Page_42">42</a> </td></tr> +<tr><td align="right"> 7.</td><td align="left">Rotating sectors</td><td align="right"><a href="#Page_45">45</a> </td></tr> +<tr><td align="right"> 8.</td><td align="left">Spectrum of Carbon Sodium and Lithium</td><td align="right"><a href="#Page_48">48</a> </td></tr> +<tr><td align="right"> 9.</td><td align="left">Interference bands</td><td align="right"><a href="#Page_60">60</a> </td></tr> +<tr><td align="right"> 10.</td><td align="left">Absorption of rays by the atmosphere</td><td align="right"><a href="#Page_68">68</a> </td></tr> +<tr><td align="right"> 11.</td><td align="left">Luminosity curve of spectrum of the positive pole of the electric light</td><td align="right"><a href="#Page_79">79</a> </td></tr> +<tr><td align="right"> 12.</td><td align="left">Rectangles of white and vermilion</td><td align="right"><a href="#Page_82">82</a> </td></tr> +<tr><td align="right"> 13.</td><td align="left">Arrangement for measuring the luminosities of pigments</td><td align="right"><a href="#Fig_13">83</a> </td></tr> +<tr><td align="right"> 14.</td><td align="left">Measurement of the intensity of rays reflected from white and coloured surfaces</td><td align="right"><a href="#Page_88">88</a> </td></tr> +<tr><td align="right"> 15.</td><td align="left">Intensity of rays reflected from vermilion, emerald green, and French ultramarine</td><td align="right"><a href="#Page_92">92</a> <span class="pagenum">[Pg 10]</span></td></tr> +<tr><td align="right"> 16.</td><td align="left">Method of obtaining two patches of identical colour</td><td align="right"><a href="#Fig_16">95</a> </td></tr> +<tr><td align="right"> 17.</td><td align="left">Absorption by red, blue, and green glasses</td><td align="right"><a href="#Page_99">99</a> </td></tr> +<tr><td align="right"> 18.</td><td align="left">Light reflected from metallic surfaces</td><td align="right"><a href="#Page_100">100</a> </td></tr> +<tr><td align="right"> 19.</td><td align="left">Intensities of vermilion, carmine, mercuric iodide, and Indian red</td><td align="right"><a href="#Page_101">101</a> </td></tr> +<tr><td align="right"> 20.</td><td align="left">Intensities of gamboge, Indian yellow, cadmium yellow, and yellow ochre</td><td align="right"><a href="#Fig_20">101</a> </td></tr> +<tr><td align="right"> 21.</td><td align="left">Intensities of emerald green, chromous oxide, and terre verte</td><td align="right"><a href="#Page_103">103</a> </td></tr> +<tr><td align="right"> 22.</td><td align="left">Intensities of indigo, Antwerp blue, cobalt, and French ultramarine</td><td align="right"><a href="#Page_104">104</a> </td></tr> +<tr><td align="right"> 23.</td><td align="left">Method of obtaining a colour template</td><td align="right"><a href="#Fig_23">104</a> </td></tr> +<tr><td align="right"> 24.</td><td align="left">Template of carmine</td><td align="right"><a href="#Page_106">106</a> </td></tr> +<tr><td align="right"> 25.</td><td align="left">Template of luminosity of white light</td><td align="right"><a href="#Page_108">108</a> </td></tr> +<tr><td align="right"> 26.</td><td align="left">Absorption of transmitted and reflected light by Prussian blue and carmine</td><td align="right"><a href="#Page_107">107</a> </td></tr> +<tr><td align="right"> 27.</td><td align="left">Collimator for comparing the intensity of two sources of light</td><td align="right"><a href="#Page_109">109</a> </td></tr> +<tr><td align="right"> 28.</td><td align="left">Spectrum intensities of sunlight, gaslight, and blue sky</td><td align="right"><a href="#Fig_28">109</a> </td></tr> +<tr><td align="right"> 29.</td><td align="left">Comparison of sun and sky lights</td><td align="right"><a href="#Page_111">111</a> </td></tr> +<tr><td align="right"> 30.</td><td align="left">Slide with slits to be used in the spectrum</td><td align="right"><a href="#Page_113">113</a> </td></tr> +<tr><td align="right"> 31.</td><td align="left">Screen on which to match gamboge</td><td align="right"><a href="#Page_116">116</a> </td></tr> +<tr><td align="right"> 32.</td><td align="left">Diaphragm in front of prism</td><td align="right"><a href="#Page_128">128</a> </td></tr> +<tr><td align="right"> 33.</td><td align="left">Curve of sensitiveness of silver bromo-iodide</td><td align="right"><a href="#Page_136">136</a> </td></tr> +<tr><td align="right"> 34.</td><td align="left">Curves of colour sensations</td><td align="right"><a href="#Page_139">139</a> </td></tr> +<tr><td align="right"> 35.</td><td align="left">Kœnig's curves of colour sensations</td><td align="right"><a href="#Page_151">151</a> </td></tr> +<tr><td align="right"> 36.</td><td align="left">Maxwell's colour-box</td><td align="right"><a href="#Page_152">152</a> </td></tr> +<tr><td align="right"> 37.</td><td align="left">Maxwell's curves of colour sensations</td><td align="right"><a href="#Page_154">154</a> </td></tr> +<tr><td align="right"> 38.</td><td align="left">Chromatic circle</td><td align="right"><a href="#Page_168">168</a> </td></tr> +<tr><td align="right"> 39.</td><td align="left">Disc to cause alternate opening and closing of two slits</td><td align="right"><a href="#Page_179">179</a> </td></tr> +<tr><td align="right"> 40.</td><td align="left">Disc painted blue and red</td><td align="right"><a href="#Page_181">181</a> </td></tr> +<tr><td align="right"> 41.</td><td align="left">Electro-motor with discs attached</td><td align="right"><a href="#Page_183">183</a> </td></tr> +<tr><td align="right"> 42.</td><td align="left">Method of cutting disc to allow an overlap of a second disc</td><td align="right"><a href="#Fig_42">184</a> </td></tr> +<tr><td align="right"> 43.</td><td align="left">Arrangement to find value of gamboge in terms of emerald green and vermilion</td><td align="right"><a href="#Page_188">188</a> </td></tr> +<tr><td align="right"> 44.</td><td align="left">Disc arranged to give approximately all the spectrum colours</td><td align="right"><a href="#Page_192">192</a> </td></tr> +<tr><td align="right"> 45.</td><td align="left">Method of showing contrast colours</td><td align="right"><a href="#Page_196">196</a> </td></tr> +</table></div> +<p><span class="pagenum">[Pg 11]</span></p> + +<br> + +<hr style="width: 65%;"> +<h2>COLOUR MEASUREMENT</h2> +<p class='center smaller'>AND</p><h1>MIXTURE.</h1> + +<hr style="width: 25%;"> +<h3><a name="CHAPTER_I" id="CHAPTER_I"></a>CHAPTER I.</h3> + +<blockquote>Sources of Light—Reflected Light—Reflection from Roughened +Surfaces—Colour Constants. +</blockquote> + + +<p>There is nothing, perhaps, in our everyday life +which appeals more to the mind than colour, yet +so accustomed are the generality of mankind to +its influence that but few stop to inquire the "why +and wherefore" of its existence, or its cause. To +those few, however, there is a source of endless +and boundless enjoyment in its study; for in the +realms of physical and physiological science there +is perhaps no other subject in which experiments +give results so fascinating and often so beautiful. +Although its serious study must be undertaken +with a clear mind, a good eye, and a fair supply +<span class="pagenum">[Pg 12]</span> +of patience, yet a general idea of the subject may +be grasped by those who are possessed of but +ordinary intelligence.</p> + +<p>Colour phenomena are encountered nearly every +day of one's life, and the fact that they are so +frequently met with, prevents that attention to +them, or even their remark. Who amongst us, for +instance, has noticed the existence of what are +called positive and negative after images, after +looking at some strongly illuminated object, or +would have gauged the fact that a certain portion +of the nervous system can be fatigued by a colour, +and give rise to images of its complementary, had +not an enterprising advertiser, who manufactures +a household necessary, drawn attention to it in a +manner that could not be misunderstood.</p> + +<p>If on an autumn afternoon we pass through a +garden whilst it is still perfectly light, we can +notice the gorgeous colouring of the flowers, and +appreciate with the eyes the beauty of each tint. +As evening comes on the tints darken, the darkest-coloured +flowers begin to lose their colour, and +only the brightest strike the eye. When night +still further closes in every colour goes, though the +outlines of the flowers may still be distinguished; +and it would not be impossible, in some parts, to +see a tiny speck of pale light upon the ground +amongst them. This speck of light we should know +<span class="pagenum"><a name="Page_13" id="Page_13">[Pg 13]</a></span> +from experience to be the light from a glow-worm. +Why is it that we lose the colour of the flowers +and recognize the tiny light from this small worm? +The reason for the one is that in order for objects +which are not self-luminous to be seen at all, light +must fall on them and illuminate them, and the +light which they reflect may be coloured if they +possess the qualities to reflect coloured light. The +glow-worm's light is seen, not because it does not +emit light in the day-time, but because the eye, +being limited in sensitiveness, is unable to distinguish +it when it is flooded with the light of day. +The glow-worm, however, is self-luminous, as is +shown by the fact that it emits light in the dark, +the light itself being slightly coloured if compared +with that of day. That a candle-flame or the sun +is self-luminous is an axiom, and need not be +philosophised upon; but what must be impressed +on the reader is, that though an object which +requires to be illuminated to be seen, is not self-luminous, +yet when illuminated it does in fact +become a source of illumination to the eye, although +the light is only light reflected from its surface. It +is a point worth remembering that the rougher the +surface of an object, the brighter to the eye it will +be. That is, a coloured object when polished will +be a bad secondary source of illumination, as the +light incident upon it will be very nearly reflected +<span class="pagenum"><a name="Page_14" id="Page_14">[Pg 14]</a></span> +from the surface, according to the ordinary laws of +reflection; but if it be roughened it will become +a much better source, as the roughnesses, though +obeying the laws of reflection, will reflect light in +every direction. A good example of this is an +ordinary sheet of glass. Light from a source falling +on its surface is scarcely reflected in any direction +except in that determined by the ordinary laws of +reflection, and it will be scarcely visible to the eye. +Grind its surface, however, and the innumerable +facets caused by the grinding will reflect light back +to the eye in whatever position it be placed, and +will thus be distinctly seen.</p> + +<p>We may here premise that even the roughest +surface will reflect a greater percentage—varying +greatly according to the nature of the surface—of +light in the direction which it would do if it were +a smooth surface than in any other; and in taking +measurements of the light irregularly reflected +from a rough surface, this fact must be borne in +mind.</p> + +<p>Not only must we know how colour is produced, +but we must also be able to refer it to some +standard which shall be readily reproduced, and +which shall be unalterable. There are two variable +factors which have to be taken into account in +colour experiments: the first is the quality of +light which illuminates the object, and the second +<span class="pagenum"><a name="Page_15" id="Page_15">[Pg 15]</a></span> +is the sensitiveness of the eye which perceives it, +as light is only a sensation which is recognized by +the brain through the medium of the eye. We +shall, as we go on, see that different qualities of +light may cause objects to appear of different +hues, and further that eyes may vary in perceptive +power, to an extent of which the large majority of +people are not aware. Hence it becomes necessary +as far as possible to eliminate these variables.</p> + +<p>The task which we have set ourselves to perform +then, is first to find a suitable light for experimental +work, and next to endeavour to refer colour +to an eye which has no abnormal defects. This +being accomplished, we have then to find means to +measure the different constants which are involved +in colour, and to refer the measurements to some +standard. Colour constants are three, viz. hue, +luminosity, and purity; and it will be seen that +if these three are determined, the measurement of +the colour is complete.</p> + +<p>Perhaps the meaning of these terms may require +to be explained. The hue of a colour is what in +common parlance is often called the colour. Thus +we talk of rose, violet, magenta, emerald green, and +so on, but for measuring purposes the hue had best +be referred to the spectrum colours as a standard +(the means of doing so will be shortly explained), +for they are simple colours, which can be expressed +<span class="pagenum"><a name="Page_16" id="Page_16">[Pg 16]</a></span> +by numbers. Compound colours, which it may be +said are invariably to be found in nature, being +mixtures of simple colours, can be just as readily +referred to the spectrum. By the luminosity of a +colour we mean its brightness, the standard of reference +being the brightness of a white surface when +illuminated by the same white light. By the purity +of a colour we mean its freedom from admixture +with white light. An example of different degrees +of purity will be found in washes of water-colours +of different tenuity. Thus if we wash a sheet of +paper with a light tint of carmine, the whiteness +of the paper is not obliterated; if we pass another +wash over it the whiteness of the paper is lessened, +and so on. The lightest tint is that which is most +lacking in purity.</p><br> +<span class="pagenum"><a name="Page_17" id="Page_17">[Pg 17]</a></span> + + + + +<hr style="width: 65%;"> +<h2><a name="CHAPTER_II" id="CHAPTER_II"></a>CHAPTER II.</h2> + +<blockquote><p>A Standard Light—Formation of the Spectrum by Prisms and by the +Diffraction Grating—Wave-lengths of the principal Fraunhofer +Line—Position of Colours in the Spectrum.</p></blockquote> + + +<p>As we have to turn to the spectrum for pure and +simple colours, from which we may produce any +compound colour we may wish to deal with, we +will first consider the light with which we shall +form it. A spectrum may be produced from any +source of light, such as sunlight, limelight, the +electric light, gaslight, or incandescence electric +light, as also from incandescent vapours, or gases; +but it is only a solid which is, or is rendered incandescent, +that will give us a <i>continuous</i> spectrum, as +it is called, that is, a spectrum which is unbroken +by gaps of non-luminosity, or sudden change of +brightness, throughout its length.</p> + +<div class="figright" style="width: 78px;"> +<img src="images/i_018.jpg" width="78" height="392" alt="" title=""> +<span class="caption">Fig. 1.—Spectrum of Sunlight.</span> +</div> + +<p>The great desideratum for the study of colour +is a light which not only gives a practically +<span class="pagenum"><a name="Page_18" id="Page_18">[Pg 18]</a></span> +continuous spectrum, but one which is produced by +the radiation of matter which is black when cold, +and which can be kept at a constantly +high temperature. We +have purposely said "black" in +the sentence above, since it is +believed that differently coloured +bodies, when heated to equal +temperatures, might not give the +same relative intensities to the +different parts of the spectrum, +the variation being dependent on +the colour of the heated body. +A black body must always give +the same visible spectrum when +heated to the same temperature. +The spectrum of sunlight (<a href="#Page_18">Fig. +1</a>) is not continuous, as we find +it crossed by an innumerable +number of fine lines of varying +breadth and blackness. This +want of continuity would not +be fatal to its adoption were +it possible to use it outside +the limits of our atmosphere, +as then, unless the temperature of the sun itself +changed, the spectrum produced would be invariable; +but unfortunately the relative brightness or +<span class="pagenum"><a name="Page_19" id="Page_19">[Pg 19]</a></span> +luminosity of the different parts of the spectrum +varies from day to day, and hour to hour, according +to the height of the sun above the horizon (see +<a href="#CHAPTER_VI">Chap. VI</a>.); and its integral brightness varies according +to the clearness of the sky. It is evident +then, that, as a reference light, sunlight is most +unsuitable, so we may dismiss it from our possible +standards.</p> +<a name="Fig_2" id="Fig_2"></a> +<div class="figright" style="width: 150px;"> +<img src="images/i_020.png" width="150" height="269" alt="" title=""> +<span class="caption">Fig. 2.—The Carbon Poles +of an Electric Light.</span> +</div> + +<p>By the process of elimination we may arrive at +the light upon which we can rely, for the purpose +we have in view, viz. the production of a spectrum +of moderate size, and sufficiently bright to +be well viewed when projected upon a screen. +For some purposes, as for instance in becoming +acquainted with the general character of the +spectrum, a feebler light, such as gaslight, or light +from electrical glow lamps, may be employed, since +the spectrum may be viewed directly by the eye +without the intervention of a screen. They have +two drawbacks for our object: one being the want +of general intensity, and the other the feeble +luminosity of blue and violet rays in their spectrum +(see <a href="#Page_110">page 110</a>). The limelight we can also +dismiss for want of steadiness. Its whiteness and +luminosity varies according to the oxygen playing +on the lime cylinder, rendering the relative intensities +of the different parts of the spectrum so +erratic as to make it unreliable. This leaves the +<span class="pagenum"><a name="Page_20" id="Page_20">[Pg 20]</a></span> +(electric) arc-light as the only one which is really +available. Remember how the arc-light is produced. +A current of electricity passes between +the ends of two thick black carbon rods, or poles +as they are called, through an air space of small +interval, and the passage of the current renders the +tips of these rods white-hot (<a href="#Fig_2">Fig. 2</a>). The centre of +the end of one pole, called the +positive pole, where a crater-like +depression is formed, is the +part which attains the whitest +heat, and its temperature seems +to be constant, and to be that +of the volatilization of carbon. +Numerous experiments have +been made by the writer, and +he has found that the light +emitted by this crater in the +positive pole is, within the +limits of the error of observation, +always of the same whiteness, +and consequently gives a spectrum which is +unvarying in the proportionate intensities of the +different colours. When the experiments made to +determine the luminosity of the spectrum are described, +the method of ascertaining this will be +readily understood.</p> + +<p>In the spectrum produced by this light there are +<span class="pagenum"><a name="Page_21" id="Page_21">[Pg 21]</a></span> +two places in the violet where there are bands of +violet lines slightly brighter than the general spectrum. +They are principally due to the light emitted +from the incandescent vapour of carbon, which is +volatilized and plays between the two poles (see +<a href="#Fig_2">Fig. 2</a>); but as these bands are of but small +visual intensity, and situated towards the limit of +the visible spectrum, they do not interfere with +eye-measures of colours, though they do, to a +certain extent, to the analysis of radiation by +photography. If we throw the positive pole a +little behind the negative pole we can, however, +considerably mitigate this evil. We can separate +the carbon rods to such a degree that the white-hot +crater faces the observer, and a good deal of +the arc is hidden. This is well seen in the figure.</p> + +<p>We have now described the light we have +adopted, and the reasons for adopting it; and +having obtained our light, we can now consider by +what plan we shall form our spectrum. There are +two ways open to us—one by glass prisms, and +the other by a diffraction grating. Glass prisms +separate white light, or indeed any light, into its +components, from the fact that the refraction of +each coloured ray differs from every other. Thus +the red rays are least refracted, and the violet the +most, and the yellow, green and blue are intermediate +between them, being placed in the order +<span class="pagenum"><a name="Page_22" id="Page_22">[Pg 22]</a></span> +of least refrangibility. Between these there is of +course every shade of simple colour, one melting +into the other. In order to form a pure and +bright spectrum with prisms, in a room of limited +dimensions, we have to use certain auxiliary apparatus +which are not positively essential, though +convenient. The real essentials to form a spectrum +are a narrow slit, a glass prism, with perfectly plane +faces, and a lens. If this be the only apparatus +available, the slit must be placed at a long distance +from the prism, the beam of light must pass through +the slit on to the prism, and the lens must be placed +at such a distance from the slit that it forms a sharp +image on a screen. When the light passes through +the prism, the screen will have to be rotated in the +arc of a circle, so that its distance from the slit +measured along the line of the ray to the prism, +and from the prism to the screen, is the same as it +would be without the intervening prism. An apparatus +of this description is not convenient, however, +as it requires much more space than is often +available. If a lens be placed between the slit +and the prism, at exactly its focal length from the +former, the light entering the slit will, after passage +through the lens, emerge as parallel rays, that is, +they will emerge as they would do if the slit were +placed at an infinite distance from the observer.</p> + +<p>The focal length of this collimating lens need +<span class="pagenum"><a name="Page_23" id="Page_23">[Pg 23]</a></span> +not be greater than twelve to eighteen inches, so +that the great space required by the cruder +apparatus is very much curtailed. The lens and +slit are mounted one at each end of a tube of the +necessary length, and are thus handy to use.</p> + +<p>Instead of one prism two or three may be used, +giving an angular dispersion of the spectrum two +or three times respectively greater than that which +would be given by only one prism; consequently +to obtain a given length of spectrum with the increased +dispersion, the focal length of the lens used +to focus the image on the screen may be diminished.</p> + +<p>The drawback to the use of prisms is that the +dispersion of the red end of the spectrum is much +less than that of the blue end, and is apt to give a +false impression as to the relative luminosities of, +and length of spectrum occupied by, the different +colours. In some text-books it is told us that the +diffraction grating gives us a dispersion which is in +exact relation to the wave-length. This is not true, +however, as it can only give one small portion in +such relationship, and that only when it is specially +set for the purpose. The subject of diffraction is +one into which it would be foreign to our purpose +to wander. We may say that for measures such as +we shall make, it is handier to employ prisms, as +the prismatic spectrum is more intense than the diffraction +spectrum. This can be readily understood +<span class="pagenum"><a name="Page_24" id="Page_24">[Pg 24]</a></span> +when we consider the subject even superficially. +If we throw a beam of light on a grating which +contains perhaps some 14,000 parallel lines in the +space of one inch in width, the lines being ruled on +a plane and bright metallic surface, and receive the +reflected beam on a screen, the appearance that is +presented is a white central spot, together with six +or seven spectra of gradually diminishing brightness +on each side of it, all except the first pair +overlapping one another. That these different +spectra do exist can be readily shown by placing +in the beam a piece of red glass, when symmetrical +pairs of the red part of the spectrum will +be found, one of each pair being on opposite sides +of what will now be the central red spot. Half +the light falling on the grating is concentrated in +this central spot, and the remaining half goes to +form the spectra; the pair nearest the central spot +being the brightest. We thus are drawn to the +conclusion that at the outside we can only have +less than one-quarter of the incident light to form +the brightest spectrum we can use. With two good +prisms we use at last three-fourths of the incident +light, so that for the same length of spectrum we +can get at least three times the average brightness +that we should get were we to employ a diffraction +grating.</p> + +<p>We must now refresh the reader's memory with +<span class="pagenum">[Pg 25]</span> +a few simple facts about light, in order that our +meaning may be clear when we speak of rays of +different wave-lengths. Every colour in the spectrum +has a different wave-length, and it is owing +to this difference in wave-length that we are able +to separate them by refraction, or diffraction, and +to isolate them. Light, or indeed any radiation, is +caused by a rhythmic oscillation of the impalpable +medium which we, for want of a better term, call +ether, and the distance between two of these waves +which are in the same phase is called the wave-length +of the particular radiation. The extent of +the oscillation is called the amplitude, which when +squared is in effect a measure of the <i>intensity</i> of +the radiation. Thus at sea the distance between +the crests of two waves is the wave-length, and the +height from trough to crest the amplitude; and the +intensity, or power of doing work, of two waves +of the same wave-lengths but of different heights, +is as the square of their heights. Thus, if the +height of one were one unit, and of the other two +units, the latter could do four times more work than +the former. The waves of radiation which give the +sensation of colour in the spectrum vary in length, +not perhaps to the extent that might be imagined, +considering the great difference that is perceived +by the eye, but still they are markedly different. +The fact that the spectrum of sunlight is not continuous, +but is broken up by innumerable fine lines, +<span class="pagenum"><a name="Page_26" id="Page_26">[Pg 26]</a></span> +has already been alluded to. The position of these +lines is always the same, as regards the colour in +which they are situated, and is absolutely fixed +directly we know their wave-length; hence if we +know the wave-lengths of these lines, we can refer +the colour in which they lie to them. Now some +lines of the solar-spectrum are blacker and consequently +more marked than others, and instead of +referring the colours to the finer lines, we can refer +them to the distance they are from one or more of +these darker lines, where these latter are absolutely +fixed; in fact they act as mile-stones on a road.</p> + +<p>In the red we have three lines in the solar spectrum, +which for sake of easy reference are called A, +B and C; in the orange we have a line called D, in +the green a line called E, in the blue F, in the violet +G, and in the extreme violet H. These lines are +our fiducial lines, and all colours can be referred to +them. The following are the wave-lengths of these +lines, on the scale of <b>1/10,000,000</b> of a millimetre as a unit</p> + +<div class="center"> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="left"></td><td align="left">A</td><td align="left"> </td><td align="left">7594</td></tr> +<tr><td align="left"></td><td align="left">B</td><td align="left"></td><td align="left">6867</td></tr> +<tr><td align="left"></td><td align="left">C</td><td align="left"></td><td align="left">6562</td></tr> +<tr><td align="left"></td><td align="left">D</td><td align="left"></td><td align="left">5892</td></tr> +<tr><td align="left"></td><td align="left">E</td><td align="left"></td><td align="left">5269</td></tr> +<tr><td align="left"></td><td align="left">F</td><td align="left"></td><td align="left">4861</td></tr> +<tr><td align="left"></td><td align="left">G</td><td align="left"></td><td align="left">4307</td></tr> +<tr><td align="left"></td><td align="left">H</td><td align="left"></td><td align="left">3968</td></tr> +</table></div> + +<p>When the spectrum is produced by prisms the +intervals between these lines are not proportional +<span class="pagenum">[Pg 27]</span> +to the wave-lengths, and consequently if we measure +the distance of a ray in the spectrum from two of +these lines, we have to resort to calculation, or to +a graphically drawn curve, to ascertain its wave-length. +For the purpose of experiments in colour +the graphic curve from which the wave-length can +immediately be read off is sufficient. The following +diagram (<a href="#Page_28">Fig. 3</a>) shows how this can be done.</p> + +<p>The names and range of the principal colours +which are seen in the spectrum has been a matter +of some controversy. Professor Rood has, however, +made observations which may be accepted as correct +with a moderately bright spectrum. If the +spectrum be divided into 1000 parts between A in +the red, and H, the limit of the violet, he makes +the following table of colours.</p> + + +<div class="center"> +<table border="1" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="center">Scale.</td><td align="center">Colour.</td></tr> +<tr><td align="left"> 0 to 149</td><td align="left"> Red.</td></tr> +<tr><td align="left"> 149 to 194</td><td align="left">Orange red.</td></tr> +<tr><td align="left"> 194 to 210</td><td align="left">Orange.</td></tr> +<tr><td align="left"> 210 to 230</td><td align="left">Orange yellow.</td></tr> +<tr><td align="left"> 230 to 240</td><td align="left">Yellow.</td></tr> +<tr><td align="left"> 240 to 344</td><td align="left">Yellow green and green yellow.</td></tr> +<tr><td align="left"> 344 to 447</td><td align="left">Green and blue green.</td></tr> +<tr><td align="left"> 447 to 495</td><td align="left">Azure blue.</td></tr> +<tr><td align="left"> 495 to 806</td><td align="left">Blue and blue violet.</td></tr> +<tr><td align="left"> 806 to 1000</td><td align="left">Violet. </td></tr> +</table></div> +<br> +<p><span class="pagenum"><a name="Page_28" id="Page_28">[Pg 28]</a></span></p> + +<div class="figcenter" style="width: 350px;"> +<img src="images/hb028.png" width="401" height="182" alt="" title=""> +<span class="caption">Fig. 3.—Curve for converting the Prismatic Spectrum into Wave-lengths. +</span> +</div><p><br><span class="pagenum"><a name="Page_29" id="Page_29">[Pg 29]</a></span></p> + +<p>In the above scale (Fig. 3) A = 0, B = 74·0, C = +112·7, D = 220·3, E = 363·1, F = 493·2, G = 753·6, +H = 1000.</p> + +<p>These are the main subdivisions of colour, but it +must be recollected that one melts into the other. +When the spectrum is very bright the colours +tend to alter in hue; thus the orange becomes +paler, and the yellow whiter, and the blue paler. +On the other hand, if the spectrum be diminished +in brightness the tendency is for the colours to +change in the opposite direction. Thus the yellow +almost disappears and becomes of a green hue, +whilst the orange becomes redder, and the spectrum +itself becomes shorter to the eye than before.</p> + +<p>Let us strictly guard ourselves, however, from +the criticism that all eyes see not alike. Suffice +it to say that the above table is correct for the +ordinary or normal eye, and does not necessarily +apply to those who have defective vision as regards +colour sensation.</p><br> +<span class="pagenum"><a name="Page_30" id="Page_30">[Pg 30]</a></span> + +<hr style="width: 65%;"> +<h2><a name="CHAPTER_III" id="CHAPTER_III"></a>CHAPTER III.</h2> + +<blockquote><p>The Visible and Invisible Parts of the Spectrum—Methods for showing +the Existence of the Invisible +Portions—Phosphorescence—Photography of the Dark +Rays—Thermo-Electric Currents.</p></blockquote> + + +<p>We are apt to forget, when looking at the spectrum, +that what the eye sees is not all that is to +be found in the prismatic analysis of light. The +spectrum, it must be recollected, is not limited to +those rays which the eye perceives. There are rays +both beyond the extreme violet and below the extreme +red, which exist and which exercise a marked +effect on the world's economy. Thus, rays beyond +the violet are those which with the violet and the +blue rays principally affect vegetation, enabling +certain chemical changes to take place which are +necessary for its growth and health; whilst the +rays below the red are those possessing the +greatest amount of energy, and if they fall upon +bodies which absorb them, as very nearly all +<span class="pagenum"><a name="Page_31" id="Page_31">[Pg 31]</a></span> +bodies do to a certain extent, they heat them. +The warmth we feel from sunlight is principally +due to the dark rays which lie below the red of +the spectrum.</p> + +<p>The existence of both kinds of these dark rays +may be demonstrated in a very simple manner +by the effect that they produce on certain bodies. +For instance, there is a yellow dye with which +cheap ribbon is dyed, which if placed in the +spectrum and beyond the violet causes a visible +prolongation of the spectrum. The light in the +newly-seen and once invisible part of the spectrum +is yellow, the colour of the ribbon itself. In fact, +the whole of that part of the spectrum, which on +the white screen is seen as blue and violet, becomes +yellow, the red and green remaining unchanged. +This change in colour is due to fluorescence, a +phenomenon of light which Sir G. Stokes found +was caused by an alteration in the lengths of the +waves of light when reflected from certain bodies. +It is not meant to imply by this that the wave-length +of any ray falling on a body can be altered +by reflection, but only that the body itself on +which the rays fall emits rays of light which are +not of the same wave-length as those which fall +upon it. Now it is a fact that the rays that lie +beyond the violet, and which are ordinarily invisible, +are shorter than the violet rays, and that these are +<span class="pagenum"><a name="Page_32" id="Page_32">[Pg 32]</a></span> +shorter than the yellow rays. It follows therefore +that when, what we may now call, the ultra-violet +rays fall on the yellow dyed ribbon, the waves +emitted by it are so lengthened that they appear +yellow to the eye instead of dark, violet, or blue.</p> + +<p>We can also brush a solution of quinine on the +screen, and immediately the place where the ultra-violet +rays fall is illuminated by a violet light. We +do not see the ultra-violet rays themselves, but only +the rays of increased wave-length, which are emitted +by their effect on the sulphate of quinine. Common +machine oil as used for engines also emits greenish +rays when excited by the ultra-violet rays, and a very +beautiful colour it is. Fluorescence then is one means +of demonstrating the existence of the ultra-violet +rays—or Ritter's rays as they were formerly called, +after their discoverer—in a very simple manner. +The method of rendering the effects of the infra-red +rays visible to the eye is also interesting. All, or at +all events most, of our readers have seen Balmain's +luminous paint. A glass or card coated with this +substance, which is essentially a sulphide of calcium, +when exposed to the light of the sun, or of the electric +arc, and then taken into comparative darkness, is +seen to shine with a peculiar violet-coloured light. +If when thus excited we place it in a bright spectrum +for some little time, we shall find on shutting +off the light that where the ultra-violet and blue +<span class="pagenum"><a name="Page_33" id="Page_33">[Pg 33]</a></span> +fell on it, the violet light is intenser than the light +of the main part of the screen; where the yellow +fell there is neither increase or diminution in brightness; +but that in the red it becomes darker, and +also beyond the limit of the visible spectrum, indicating +the existence of rays beyond, which through +their greater length have not the power of affecting +the eye. If the spectrum be shut off, however, very +soon after it falls on the plate, it has been asserted +that the red and infra-red rays have increased the +brightness of that particular part of the plate on +which they fell. At first these two observations +seem to contradict one another; they do not in +reality. We may expose a tablet of Balmain's +paint to light, and place a heated iron in contact +with the back of the plate; we shall then find that +the iron produces a bright image of its surface on +a less bright background. This bright image will +gradually fade away, and the same space will +eventually become dark compared with the rest +of the plate. The reason of this is clear. When +light excites the paint a certain amount of energy +is poured into it, which it radiates out slowly as +light. When the hot iron is placed in contact with +it, the heat causes the light to radiate more rapidly, +and consequently with greater intensity, at the part +where its surface touches, and the energy of that +particular portion becomes used up. When the +<span class="pagenum"><a name="Page_34" id="Page_34">[Pg 34]</a></span> +energy of radiation of this part becomes less than +that of the rest of the tablet, its light must of +necessity be of less brightness than that of the +background, with which the heated iron has had +no contact. For this reason the image of the iron +subsequently appears dark. We shall see presently, +and as before stated, that the principal heating +effect of the spectrum lies in the red and infra-red, +and it is owing to the heating of the paint by these +rays that the image might be at first slightly brighter +than the background, and subsequently darker.</p> + +<p>There is another way in which the existence of +both the ultra-violet and infra-red rays can be +demonstrated, and that is by means of photography. +If we place an ordinary photographic plate in +the spectrum and develop it, we shall find that +besides being affected by the blue and violet rays, +it is also affected by the rays beyond the violet, +the energy of these rays being capable of causing a +decomposition of the sensitive silver salt. If quartz +prisms and lenses be used, and the electric light +be the source of illumination, the ultra-violet spectrum +will extend to an enormous extent. A more +difficult, but perhaps even more interesting means +of illustrating the existence of the infra-red rays, +and first due to the writer, can be made by means +of photography. It is possible to prepare a photographic +plate with bromide of silver, which is so +<span class="pagenum"><a name="Page_35" id="Page_35">[Pg 35]</a></span> +molecularly arranged that it becomes capable of +being decomposed not only by the violet and blue +rays, but also by the red rays, and by those rays +which have wave-lengths of nearly three times that +of the red rays. It would be inappropriate to +enter into a description of the method of the preparation +of these plates. Those who are curious +as to it will find a description in the Bakerian +lecture published in the Philosophical Transactions +of the Royal Society for 1881. With plates so +prepared it has been found possible to obtain impressions +in the dark with the rays coming from a +black object, heated to only a black heat.</p> + +<p>That these dark rays possess greater energy or +capacity for doing work of some kind than any +other rays of the spectrum, can be shown by means +of a linear thermopile (<a name="Fig_4" id="Fig_4"></a>Fig. 4), if it be so arranged +as to allow only a narrow vertical slice of light to +reach its face.</p> + +<div class="figcenter" style="width: 350px;"> +<img src="images/i_044.png" width="350" height="463" alt="" title=""> +<span class="caption">Fig. 4.—The Thermopile. +</span> +</div> + +<p>The principle of the thermopile we need not +describe in detail. Suffice it to say that the heating +of the soldered junctions of two dissimilar +metals (there are ten pairs of antimony and bismuth +in the above instrument) produces a feeble +current of electricity, which, however, is sufficient +to cause a deflection to the suspended needle of +a delicate galvanometer. To the needle is attached +a mirror weighing a fraction of a grain, and the +<span class="pagenum"><a name="Page_36" id="Page_36">[Pg 36]</a></span> +deflections are made visible by the reflection from +it of a beam of light issuing from a fixed point +along a scale. The greater the heating of the +junctions of the thermopile, within limits which +in these cases are never exceeded, the greater +is the current produced, and consequently the +<span class="pagenum">[Pg 37]</span> +greater is the deflection of the mirror-bearing +needle, and of the beam of light along the scale. +In order to get a comparative measure of the +energies of the different rays, it is necessary that +they should be completely absorbed. Now the +junctions themselves of the pile being metal, and +therefore more or less bright, will not absorb completely, +but if they be coated with a fine layer of +lamp-black, the rays falling on the pile will be +absorbed by this substance, and their absorption +will cause a rise in temperature in it, and the heat +will be communicated to the thermopile.</p> + +<p>If we make a bright spectrum, and one not too +long, say three inches in length, and pass the linear +thermopile through its length, we shall find that +when the galvanometer is attached, the galvanometer +needle will be differently deflected in its +various parts. The deflection will be almost insensible +in the violet, but sensible in the blue, rather +more in the green, still more in the yellow, and +it will further increase in the red. When, however, +the slit of the thermopile is placed beyond the limit +of the visible spectrum, the deflection enormously +increases, and will increase till a position is reached +as far below the red as the yellow is above it. +After this maximum is reached, by moving the +pile still further from the red, the galvanometer +needle will travel towards its zero, and finally +<span class="pagenum"><a name="Page_38" id="Page_38">[Pg 38]</a></span> +all deflection will cease. At this point we may suppose +we have reached the limit of the spectrum, +but if rock-salt prisms and lenses be used, the limit +will be increased. What the real limit of the +spectrum is, is at present unknown; Mr. Langley +with his bolometer, and rock-salt prisms, an instrument +more sensitive than the thermopile, must +have nearly reached it.</p> + +<div class="figcenter" style="width: 401px;"> +<img src="images/i_038.png" width="401" height="404" alt="" title=""> +<span class="caption">Fig. 5.—Heating effect of different Sources of Radiation. +</span> +</div> +<p>The above figure is a graphic representation +of the heating effect of the spectrum of the electric +<span class="pagenum">[Pg 39]</span> +light, sunlight, and the incandescence electric light, +on the lamp-black coating of the thermopile, as +shown by the galvanometer. The vast difference +between the heating effect of the visible rays of +the first two sources compared with the last is +clearly indicated.</p> + +<p>Since every ray may be taken as totally absorbed, +the heating of the lamp-black is a measure +of the energy or the capacity of performing work +of some description, which they possess. Waves +of the sea do work when they beat against the +shore, and they do work when they lift a vessel. +If we notice a ship at anchor we shall find that +behind the vessel and towards the shore the waves +are lowered in height or amplitude; the energy +which they have expended in raising the vessel of +necessity causes this lowering. In the same way +the waves of light, after falling on matter whose +molecules or atoms are swinging in unison with +them, are destroyed, and the energy is spent in +either decomposing the matter into a simpler form +at first—though the subsequent form may be more +complex—or in raising its temperature. As lamp-black +or carbon is in its simplest form, the only +work done upon it by the energy of radiation is the +raising of its temperature, and it is for this reason +that this material is so excellent for covering the +junctions of the pile. The eye evidently does not +<span class="pagenum">[Pg 40]</span> +absorb all rays, since only a limited part of the +spectrum is visible, and it would be useless to +take a measure of the heating effect of lamp-black +for the visible part of the spectrum as a measure +of its luminosity, since the latter fades off in the +red—the very place in which the heat curve rises +rapidly.</p><br> +<span class="pagenum"><a name="Page_41" id="Page_41">[Pg 41]</a></span> + + + +<hr style="width: 65%;"> +<h2><a name="CHAPTER_IV" id="CHAPTER_IV"></a>CHAPTER IV.</h2> + +<blockquote><p>Description of Colour Patch Apparatus—Rotating Sectors—Method of +making a Scale for the Spectrum.</p></blockquote> + + +<p>Before proceeding further we must describe somewhat +in detail two or three pieces of apparatus to +be used in the experiments we shall make.</p> + +<p>The first piece was devised by the writer a few +years ago, and has got rid of several objections +which existed in older pieces of apparatus. It is +not only useful for lecture purposes, but also for +careful laboratory work. The ordinary lecture +apparatus for throwing a spectrum on the screen +is of too crude a form to be effective for the purpose +we have in view; the purity of the colours +seen on the screen is more than doubtful, and this +alone unfits it for our experiments. If we want +to form a pure spectrum we must have a narrow +slit, prisms with true, flat surfaces, and lenses of +proper curvature. As a rule the ordinary lecture +<span class="pagenum"><a name="Page_42" id="Page_42">[Pg 42]</a></span> +apparatus for forming the spectrum lacks all of +these requisites.</p> + +<div class="figcenter" style="width: 401px;"> +<img src="images/i_042.png" width="401" height="474" alt="" title=""> +<span class="caption">Fig. 6.—Colour Patch Apparatus. +</span> +</div> +<p>The accompanying diagram (Fig. 6) will give an +idea of the apparatus we shall employ. On the usual +slit S₁ of a collimator C is thrown, by means of a +<span class="pagenum">[Pg 43]</span> +condensing lens L₁, a beam of light, which emanates +from the intensely white-hot carbon positive pole +of the electric light. The focus is so adjusted +that an image of the crater is formed on the +slit. The collimating lens L₂ is filled by this +beam, and the rays issue parallel to one another +and fall on the prisms P₁ and P₂, which disperse +them. The dispersed beam falls on a corrected +photographic lens L₃, attached to a camera in the +ordinary way. It is of slightly larger diameter +than the height of the prisms, and a spectrum is +formed on the focusing-screen D, which is slewed +at a slight angle with the perpendicular to the axis +of the lens L₃. This is necessary, because the focus +of the least refrangible or red rays is longer than +that of the more refrangible or blue rays. By +slewing the focusing-screen as shown, a very good +general focus for every ray may be obtained. When +the focusing-screen is removed, the rays form a +confused patch of parti-coloured light on a white +screen F, placed some four feet off the camera. +The rays, however, can be collected by a lens L₄, +of about two feet focus, placed near the position +of the focusing-screen, and slightly askew. This +forms an image on the screen of the near surface +of the last prism P₂; and if correctly adjusted, the +rectangular patch of light should be pure and without +any fringes of colour. The card D slides into +<span class="pagenum">[Pg 44]</span> +the grooves which ordinarily take the dark slide. +In it will be seen a slit S₂, the utility of which will +be explained later on.</p> + +<p>We shall usually require a second patch of white +light, with which to compare the first patch. Now, +although the light from the positive pole of the +carbons is uniform in quality, it sometimes varies in +quantity, as it is difficult to keep its image always +in exactly the centre of the slit. If we can take one +part of the light coming through the slit to form +the spectrum, and another part to form the second +patch of white light, then the brightness of the +two will vary together. At first sight this might +appear difficult to attain; but advantage is taken +of the fact that from the first surface of the first +prism P₁ a certain amount of light is reflected. +Placing a lens L₅, and a mirror G, in the path of +this reflected beam, another square patch of light +can be thrown on the same screen as that on which +the first is thrown, and this second patch may be +made of the same size as the first patch, if the lens +L₅ be of suitable focus, and it can be superposed +over the first patch if required; or, as is useful in +some cases, the two patches may be placed side +by side, just touching each other.</p> + +<p>We are thus able to secure two square white +patches upon the screen F, one from the re-combination +of the spectrum, and one from the reflected +<span class="pagenum"><a name="Page_45" id="Page_45">[Pg 45]</a></span> +beam. If a rod be placed in the path of these +two beams when they are superposed, each beam +will throw a shadow of the rod upon the screen. +The shadow cast by the integrated spectrum will +be illuminated by the reflected beam, and the +shadow cast by the latter will be illuminated by +the former. In fact we have an ordinary Rumford +photometer, and the two shadows may be caused +to touch one another by moving the rod towards +or from the screen. When the illumination of the +two shadows by the white light is equal, the whole +should appear as <i>one</i> unbroken gray patch. To +prevent confusion to the eye a black mask is +placed on the screen F with a square aperture cut +out of it, on which the two shadows are caused to +fall. If it be desired to diminish the brightness of +either patch, it can be accomplished by the introduction +of rotating sectors M, which can be opened +and closed at pleasure during rotation, in the path +of one or other of the beams.</p> + +<div class="figcenter" style="width: 350px;"> +<img src="images/i_046.png" width="350" height="286" alt="" title=""> +<span class="caption">Fig. 7.—Rotating Sectors. +</span> +</div> +<p>The annexed figure (Fig. 7) is a bird's-eye view of +the instrument. A A are two sectors, one of which +is capable of closing the open aperture by means +of a lever arrangement C, which moves a sleeve in +which is fixed a pin working in a screw groove, +which allows the aperture in the sectors to be +opened and closed at pleasure during their revolution; +D is an electro-motor causing the sectors +<span class="pagenum"><a name="Page_46" id="Page_46">[Pg 46]</a></span> +to rotate. To show its efficiency, if two strips of +paper, one coated with lamp-black and the other +white, are placed side by side on the screen, and if +one shadow from the rod falls on the white strip, +and the other shadow on the black strip of paper, +and the rotating sectors are interposed in the path +of the light illuminating the shadow cast on the +white strip, the aperture of the sectors can be +closed till the white paper appears absolutely +blacker than the black paper. White thus becomes +darker than lamp-black, owing to the want +<span class="pagenum"><a name="Page_47" id="Page_47">[Pg 47]</a></span> +of illumination. This is an interesting experiment, +and we shall see its bearings as we proceed, as it +indicates that even lamp-black reflects a certain +amount of white or other light.</p> + +<p>Having thus explained the main part of the +apparatus with which we shall work, we can go on +and show how monochromatic light of any degree +of purity can be produced on the screen. If the +slit in the cardboard slide D be passed through +the spectrum when it has been focused on the +focusing-screen, only one small strip of practically +monochromatic light will reach the screen, and +instead of the white patch on the screen we shall +have a succession of coloured patches, the colour +varying according to the position the slit occupies +in the spectrum. It should be noted that the +purity of the colour depends on two things—the +narrowness of the slit S₁ of the collimator, and of +the slit S₂ in the card. If two slits be cut in the +card D, we shall have two coloured patches overlapping +one another, and if the reflected beam +falls on the same space we shall have a mixture +of coloured light with white light, and either the +coloured light or the white light can be reduced +in brightness by the introduction of the rotating +sectors. If the rod be introduced in the path of +the rays we shall have two shadows cast, one illuminated +with coloured light, monochromatic or +<span class="pagenum"><a name="Page_48" id="Page_48">[Pg 48]</a></span> +compound, and the other with white light, and +these can be placed side by side, and surrounded +by the black mask as before described.</p> + +<div class="figright" style="width: 78px;"> +<img src="images/i_048.png" width="75" height="303" alt="" title=""> +<span class="caption">Fig. 8.—Spectrum of Sodium Lithium and Carbon. +</span> +</div> +<p>There is one other part of the apparatus which +may be mentioned, and that +is the indicator, which tells +us what part of the spectrum +is passing through the slit. +Just outside the camera, and +in a line with the focusing-screen, +is a clip carrying a +vertical needle. A small beam +of light passes outside the +prism P₁; this is caught by +a mirror attached to the side +of the apparatus, and is reflected +so as to cast a shadow +of the needle on to the back +of the card D, on which a +carefully divided scale of +twentieths of an inch is +drawn. To fix the position +of the slit the poles of the +electric light are brushed over +with a solution of the carbonates +of sodium and lithium in +hydrochloric acid, and the image of the arc is +thrown on the slit. This gets rid of the continuous +<span class="pagenum"><a name="Page_49" id="Page_49">[Pg 49]</a></span> +spectrum, and only the bright lines due to the incandescent +vapours appear on the focusing-screen +(Fig. 8). Amongst other lines we have the red +and blue lines due to the vapour of lithium; the +orange, yellow (D), and green lines of sodium, +together with the violet lines of calcium (these +last due to the impurities of the carbons forming +the poles). These lines are caused successively to +fall on the centre of the slit by moving the card +D, which for the nonce is covered with a piece of +ground glass, and the position of the shadow of the +needle-point on the scale is registered for each. A +further check can be made by taking a photograph +of these lines, or of the solar spectrum, and having +fixed accurately on the scale any one of these lines +already named, the position of the others on the +scale may be ascertained by measurement from +the photograph. Now the wave-lengths of these +bright lines have been most accurately ascertained, +in fact as accurately as the dark lines in +the solar spectrum. Thus the scale on the card +is a means of localizing the colour passing through +the slit or slits. Should more than one slit be used +in the spectrum the positions of each can be determined +in exactly the same way. The most tedious +part of the whole experimental arrangement with +this apparatus is what may be called the scaling +of the spectrum.</p> +<span class="pagenum">[Pg 50]</span> + +<p>A fairly large spectrum may be formed upon the +screen without altering any arrangement of the +apparatus, when it has been adjusted to form colour +patches. If a lens L₆ (see <a href="#Page_42">Fig. 6</a>) of short focus +be placed in front of L₄ (the big combining lens), +an enlarged spectrum will be thrown upon the screen +F, and if slits be placed in the spectrum the images +of their apertures are formed by the respective +coloured rays passing through them, so that the +colours which are combined in the patch can be +immediately seen.</p><br> +<span class="pagenum"><a name="Page_51" id="Page_51">[Pg 51]</a></span> + + + +<hr style="width: 65%;"> +<h2><a name="CHAPTER_V" id="CHAPTER_V"></a>CHAPTER V.</h2> + +<blockquote><p>Absorption of the Spectrum—Analysis of Colour—Vibrations of +Rays—Absorption by Pigments—Phosphorescence—Interference.</p></blockquote> + + +<p>We must now briefly consider what is the origin, +or at all events the cause, of the colour which +we see in objects. It is not proposed to enter into +this by any means minutely, but only sufficiently +to enable us to understand the subject which is to +be brought before you. What for instance is the +cause of the colour of this green solution of +chlorophyll, which is an extract of cabbage leaves? +If we place it in the front of the spectrum apparatus +and throw the spectrum on the screen, we +find that while there is a certain amount of blue +transmitted, the green is strong, and there are red +bands left, but a good deal of the spectrum is +totally absorbed. Forming a colour patch of this +absorption spectrum on the screen, we see that it +is the same colour as the chlorophyll solution, and +<span class="pagenum"><a name="Page_52" id="Page_52">[Pg 52]</a></span> +of this we can judge more accurately by using +the reflected beam, and placing the rod in position +to cast shadows. (The light of the reflected beam +is that of the light entering the slit.) The colour +then of the chlorophyll is due to the absence of +certain colours from the spectrum of white light. +When white light passes through it, the material +absorbs, or filters out, some of the coloured rays, +and allows others to pass more or less unaffected, +and it is the re-combination of these last which +makes up the colour of the chlorophyll. We have +a green dye which to the eye is very similar in +colour to chlorophyll, but putting a solution of it +in front of the spectrum, we see that it cuts off +different rays to the latter. It would be quite +possible to mistake one green for the other, but +directly we analyze the white light which has +filtered through each by means of the spectrum, +we at once see that they differ. Hence the +spectrum enables the eye to discriminate by +analysis what it would otherwise be unable to do. +Any coloured solution or transparent body may +be analyzed in the same way, and, as we shall +see subsequently, the intensity of every ray after +passing through it can be accurately compared +with the original incident light. There are some +cases, indeed the majority of cases, in which the +colour transmitted through a small thickness of +<span class="pagenum"><a name="Page_53" id="Page_53">[Pg 53]</a></span> +the material is different to that transmitted through +a greater thickness. For instance, a weak solution +of litmus in water is blue when a thin layer is examined, +and red when it is a thicker or more concentrated +layer. Bichromate of potash is more ruddy +as the thickness increases. This can be readily +understood by a reference to the law of absorption. +Suppose we have a thin layer of a liquid which +gives a purple colour when two simple colours, +red and blue, pass through it, and that this thin +layer cuts off one-quarter of the red and one-half +of the blue incident on it, another layer of equal +thickness will cut off another quarter of the three-quarters +of red passing through the first layer, and +half of the one-half left of the blue; we shall thus +have nine-sixteenths of the red passing and only a +quarter of the blue. With a third layer we shall +have twenty-seven sixty-fourths of red and only +one-eighth of blue left, showing that as the thickness +of the liquid is increased the blue rapidly disappears, +leaving the red the dominant colour. Now +what is true of two simple colours is equally true of +any number of them, where the rates of absorption +differ from one another, and what is true for a +solution is true for a transparent solid. In some +opaque bodies, such as rocks, the reflected colour +often differs slightly from that of the same when +they are cut into thin and polished slices, through +<span class="pagenum"><a name="Page_54" id="Page_54">[Pg 54]</a></span> +which the light can pass. The reason is that when +opaque, light penetrates to a very small distance +through the surface, and is reflected back, whilst in +these layers the colour has to struggle through more +coloured matter, and emerges of a different hue.</p> + +<p>The question why substances transmit some rays +and quench others, brings us into the domain of +molecular physics. Of all branches of physical +science this is perhaps the most fascinating and +the most speculative, yet it is one which is being +built up on the solid foundations of experiment +and mathematics, till it has attained an importance +which the questions depending on it fully +warrants. We have to picture to ourselves, in the +case in point, molecules, and the atoms composing +them, of a size which no microscope can bring to +view, vibrating in certain definite periods which are +similar to the periods of oscillation of the waves +of light. At page 26 we have given the lengths +of some of the waves which give the sensation of +coloured light. Now as light, of whatever colour +it may be, is practically transmitted with the same +velocity through air which has the same density +throughout, it follows that the number of vibrations +per second of each ray can be obtained by +dividing the velocity of light in any medium by +the wave-length. The following table gives roughly +the number of vibrations per second of the ether +<span class="pagenum"><a name="Page_55" id="Page_55">[Pg 55]</a></span> +giving rise to the colours fixed by the dark solar +lines.</p> + + +<div class="center"> +<table border="1" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="left"><span class="smcap">Name of Line.</span></td><td align="left"><span class="smcap">Millions of Millions of; Vibrations per Second.</span></td></tr> +<tr><td align="left"> A in the Red </td><td align="left"> 395 </td></tr> +<tr><td align="left"> B " " </td><td align="left"> 437 </td></tr> +<tr><td align="left"> C " " </td><td align="left"> 458 </td></tr> +<tr><td align="left"> D " Orange</td><td align="left"> 510 </td></tr> +<tr><td align="left"> E " Green</td><td align="left"> 570 </td></tr> +<tr><td align="left"> F " Blue</td><td align="left"> 618 </td></tr> +<tr><td align="left"> G " Violet</td><td align="left"> 697 </td></tr> +<tr><td align="left"> H " Ultra-Violet</td><td align="left"> 757 </td></tr> +</table></div> + +<p>If we endeavour to gauge what this rate of oscillation +means we shall scarcely be able to realize it, +even by a comparison with some physically measurable +rate of vibration. A tuning-fork, for instance, +giving the middle C, vibrates 528 times per second. +Compare this with the number of vibrations of the +waves of light, and we still are as far as ever from +realizing it, yet the velocity of light, and the +lengths of the different waves have been accurately +determined; the latter, although the much smaller +quantity, with even greater accuracy than the first. +These rates of vibration must therefore be—cannot +help being—at all events approximately true. This +being so, we know that some of the atoms of the +molecules at least, and perhaps in some cases the +<span class="pagenum"><a name="Page_56" id="Page_56">[Pg 56]</a></span> +molecules themselves, are vibrating at the same +rate as those waves of light, which they refuse to +allow to pass. If we have a child's swing beginning +to oscillate, we know that it is only by well-timed +blows that the extent of the swing is permanently +increased, and the energy exerted by the person +who gives the well-timed blow is expended on producing +the increased amplitude. In the same way +if the rate of vibration of a wave of light is in accord +with that of a molecule or atom, the amplitude or +swing of the atom or molecule is increased, and the +energy of the wave and therefore its amplitude is +totally or partially destroyed; and as the amplitude +is a function of the intensity of the light, the +ray fails to be seen at all, or else is diminished in +brightness.</p> + +<p>In what way the atoms vibrate where more than +one ray is absorbed is still a matter of speculation, +but no doubt as experimental methods are more +fully developed, and mathematicians investigate the +results of such experiments, we shall be able to +form a picture of the vibrations themselves. At +page 137 a speculation as to the reason why solids +or liquids can absorb more waves of light than one +which are adjacent to each other is put forward, +but it does not deal with the absorptions which +occupy various parts of the spectrum. Again, +too, we have the fact that the energy absorbed by +<span class="pagenum"><a name="Page_57" id="Page_57">[Pg 57]</a></span> +these atoms and molecules from the waves of light, +must show itself as work done on them—it may +be as heat or as chemical action. We shall see +by and by that in some cases, no doubt, at least +a part is expended in the latter form of work.</p> + +<p>Perhaps this mode of looking at the question of +colour in objects may make the subject more +interesting to the reader than it at first appears to +be deserving. The whole subject is one which +enlarges the faculty of making mental pictures, +and this is one of the most useful forms of +scientific education.</p> + +<p>But how can we distinguish between pigments +which to the eye are apparently the same? If +we dye paper with the green dye referred to, we +can place it in the spectrum, and we shall see that +the dye reflects differently to the white paper. In +fact we shall find that it refuses to reflect in those +parts of the spectrum which the transparent solution +refused to transmit. So long as the light +passes through the dye-stuff, it is indifferent, as +regards the colour produced, whether the colouring +matter be at a distance from the paper or whether +the latter be dyed with it, as we can see at once. +If we place the solution of the dye in the reflected +beam of the apparatus and form a patch on the +screen, and alongside throw the patch of white +light from the integrated or recombined spectrum +<span class="pagenum"><a name="Page_58" id="Page_58">[Pg 58]</a></span> +upon the dyed paper, it will be found that the +two colours are alike; that is, the green-coloured +light on the white paper, or the white light on the +green paper are the same. Similarly we may +experiment on other dyes, such as magenta, log-wood, +&c., and we shall see that like results are +obtained. It should be said, however, that when +the paper is dyed with the colouring matter a +<i>small quantity</i> of white light will be reflected from +the surface of the paper itself. We may now say +that the general colour is given to a body by its +refusal to transmit or reflect, more or less completely, +certain rays of the spectrum. Should the +solvent form a compound with the dye, perhaps +this would not be absolutely true, but in the large +majority of cases the statement is correct. When +we have bodies which are also fluorescent, this +statement would also have to be modified, but we +need not consider these for the present.</p> + +<p>Another source of colour in objects, though very +rarely met with, and which for our object we need +not stay to explain in detail, is the interference of +light. Such is seen in soap-bubbles. Briefly it may +be said that the colours are due to rays of light +reflected from the inner surface of the film, which +quench other rays of light of the same wave-length +reflected from the outer surface. If two series of +waves of the same wave-length are going in the same +<span class="pagenum"><a name="Page_59" id="Page_59">[Pg 59]</a></span> +direction and from the same source, each of which +has the same intensity as the other, that is, having +the same amplitude, and it happens that the one +series is exactly half a wave-length behind the other, +then the crest of one wave in the first series will fill +up the trough of the other in the second series, and +no motion would result, and this lack of motion +means darkness, since it is the wave motion which +gives the sensation of light. If then we have white +light falling on two reflecting surfaces, such as the +front and back of a soap-film, part of the light will +be reflected from each, and if the film be of such +a thickness that the latter reflects light exactly ½ +wave-length, 3/2 or 5/2 wave-length, &c., of some colour +behind the former, the colour due to that particular +wave-length will be absent from the reflected white +light, and instead of white light we shall have +coloured light, due to the combination of all the +colours less this colour, which is quenched.</p> + +<p>A very pretty experiment to make is to throw +the image of a soap film on the screen, and to +watch the change in the colours of the film. Their +brilliancy increases as the film becomes thinner, +and the bands, which first appear close to each +other, separate, and then we see a large expanse +of changing colour. A soap solution should be +made according to almost any of the published +formulæ, and a piece of flat card be dipped in it, +<span class="pagenum"><a name="Page_60" id="Page_60">[Pg 60]</a></span> +and be drawn across a ring of wire some inch in +diameter, or—what the writer prefers best—the +stop of a photographic lens. A film will form and +fill the aperture. The ring or stop may be placed +vertically in a clamp, and a beam of light caused +to fall at an angle of about 45 degrees on to the +film. If a lens be placed in the path of the reflected +beam to form an image of the aperture, the +colours which the film shows can be exhibited to +an audience, if the diameter of the image be made +four or five feet. Instead of this large image, a +small image may be thrown on the slit of the +spectroscope, by using a lens of a greater focal +length, and if the beam be so directed that it falls +on the axis of the collimator, a very fairly bright +spectrum may be also thrown on the screen. The +appearance of the spectrum is somewhat like that +shown in the above diagram (Fig. 9).</p> + +<div class="figcenter" style="width: 300px;"> +<img src="images/i_060.png" width="300" height="133" alt="" title=""> +<span class="caption">Fig. 9.—Interference Bands. +</span> +</div> +<p>If we take a horizontal line across the spectrum, +<span class="pagenum">[Pg 61]</span> +we shall see what particular colours are missing +from the reflected light which falls on the part of +the slit corresponding to that line. The colours +of some objects, such as of the opal, and the lovely +colouring of some feathers are due to interference +of light. The partial scattering of different rays +by small particles will also cause light to be +coloured, as we shall see in the experiments we +shall make to imitate the colour of sunlight at +various altitudes of the sun. We may, however, +take it as a rule that the colour of objects is +produced by the greater or less absorption of some +rays, and the reflection in the case of opaque bodies, +or the transmission, in the case of transparent +bodies, of the remainder.</p><br> +<span class="pagenum"><a name="Page_62" id="Page_62">[Pg 62]</a></span> + + + +<hr style="width: 65%;"> +<h2><a name="CHAPTER_VI" id="CHAPTER_VI"></a>CHAPTER VI.</h2> + +<blockquote><p>Scattered Light—Sunset Colours—Law of the Scattering by Fine +Particles—Sunset Clouds—Luminosities of Sunlight at different +Altitudes of the Sun.</p></blockquote> + + +<p>It is probable that we should be able to ascertain +approximately the true colour of sunlight (if we +may talk of the colour of white light) if we could +collect all the light from a cloudless sky, and condense +it on a patch of sunlight thrown on a screen. +For skylight is, after all, only a portion of the light +of the sun, scattered from small particles in the +atmosphere, part of the light being scattered into +space, and part to our earth. The small particles +of water and dust—and when we say small we +mean small when measured on the same scale as we +measure the lengths of waves of light—differentiate +between waves of different lengths, and scatter the +blue rays more than the green, and the green than +the red; consequently what the sun lacks in blue +and green is to be found in the light of the sky. +<span class="pagenum"><a name="Page_63" id="Page_63">[Pg 63]</a></span> +The effect that small water particles have upon +light passing through them can be very well seen in +the streets of London at night, when the atmosphere +is at all foggy. Gaslights at the far end of a street +appear to become ruby red and dim, and half-way +down only orange, but brighter, whilst close to they +are of the ordinary yellow colour, and of normal +brightness. When no fog is present the gas-lights in +the distance and close to are of the same colour and +brightness, showing that their change in appearance +is simply due to the misty atmosphere intervening +between them and the observer. We can imitate +the light from the sun, after its passage through +various thicknesses of atmosphere, in a very perfect +manner in the lecture-room, using the electric light +as a source. A condensing lens is put in front of +the lamp, and in front of that a circular aperture in +a plate. Beyond that again is a lens which throws +an enlarged image of the aperture on the screen, +which we may call our mock sun. If we place a +trough of glass, in which is a dilute solution of +hyposulphite of soda, carefully filtered from motes +as far as possible, in front of the aperture, we +have an image of the aperture unaffected by the +insertion of the solution. The white disc on the +screen will, as we have said before, be a close +approximation to sunlight on a May-day about +noon, when the sky is clear. By dropping into +<span class="pagenum"><a name="Page_64" id="Page_64">[Pg 64]</a></span> +the trough a little dilute hydrochloric acid, a change +will be found to come over the light of the mock +sun; a pale yellow colour will spread over its +surface, and this will give way to an orange tint, +and at the same time its brightness will diminish. +Gradually the orange will give place to red, the +luminosity will be very small, being of the same +hue as that seen in the sun when viewed through +a London fog. Finally the last trace of red will +so mingle with the scattered white light that the +image will disappear, and then the experiment is +over.</p> + +<p>If we track the cause of this change of colour +in our artificial sun, we shall find that it is due +to minute particles of sulphur separating out +from the solution of hyposulphite, and the longer +the time that elapses the more turbid the dilute +solution will become. This experiment exemplifies +the action of small particles on light. +Examining the trough it will be found that whilst +the light which passes <i>through the solution</i> principally +loses blue rays, the light which is scattered +from the sides is almost cerulean in blue, and can +well be compared with the light from the sky. We +can analyze the transmitted light very readily by +focusing the beam from the positive pole of the +electric light on to the slit of our colour apparatus, +and placing the lens L₆ (<a href="#Page_42">Fig. 6</a>) in position +<span class="pagenum">[Pg 65]</span> +to form the large spectrum on the screen. We can +also show the colour of the light which goes to +form the spectrum, by sending the patch of light +reflected from the first surface of the first prism +just above it. We thus have the spectrum and +the light forming the spectrum to compare with +one another. Using this apparatus and inserting +the trough of dilute hyposulphite in the beam, +the spectrum is of the character usually seen with +the electric light; but on dropping the dilute +hydrochloric acid into the solution the same hues +fall on the slit of the spectroscope which fell upon +the screen to form the mock sun, and the spectrum +is seen to change as the light changes from white +to yellow, and from yellow to red. First the violet +will disappear, the blue and the green being +dimmed, the former most however; then the blue +will vanish to the eye, the green becoming still +less luminous, and the yellow also fading; the +green and yellow will successively disappear, +leaving finally on the screen a red band alone, +which will be a near match to the colour of the +unanalyzed light, as may be seen by comparing it +with the adjacent patch formed from the reflected +beam.</p> + +<p>We have here a proof that the succession of +phenomena is caused by a scattering of the shorter +wave-lengths of light, and that the shorter the +<span class="pagenum"><a name="Page_66" id="Page_66">[Pg 66]</a></span> +waves are the more they are scattered. It has +been found theoretically by Lord Rayleigh that +the scattering takes place in inverse proportion to +the fourth power of the wave-length; thus, if two +wave-lengths, which may be waves in the green +and violet, are in the proportion of three to four, +the former will be scattered as 1/3⁴ to 1/4⁴, or as 256 +to 81, which is approximately as three to one. +Consequently if the green in passing through a +certain thickness of a turbid medium loses one-half +the violet in passing through the same thickness +will lose five-sixths of its luminosity. The inverse +fourth powers of the following wave-lengths, which +are within the limits of the whole visible spectrum, +are shown below.</p> + + +<div class="center"> +<table border="1" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="left"> λ</td><td align="left"> 7000</td><td align="left"> 6000</td><td align="left"> 5000</td><td align="left"> 4000</td></tr> +<tr><td align="left"> 1/λ⁴</td><td align="right"> 1</td><td align="left"> ·504</td><td align="left"> ·260</td><td align="left"> ·107</td></tr> +</table></div> + +<p>Supposing λ7000 by the scattering of small +particles loses one-tenth of its luminosity, then +λ6000 would have ·454 of its original brightness; +λ5000, ·234; and λ4000, ·095; that is, whilst λ7000 +would lose one-tenth only of its luminosity, λ4000 +in the violet would retain not quite one-hundredth +of its brightness.</p> + +<p>During the years 1885, 1886, and 1887, the writer measured the +luminosity of the solar spectrum at <span class="pagenum"><a name="Page_67" id="Page_67">[Pg 67]</a></span> different times of the +year, and at different hours of the day (see <i>Phil. Trans.</i> 1887: +"Transmission of Sunlight through the Earth's Atmosphere"), and from the +results he found that the smallest coefficient of scattering for one +atmosphere at sea-level for each wave-length was ·0013, when λ⁻⁴ was for +convenience sake multiplied by 10¹⁷ (thus λ6000⁻⁴ on this scale was +77·2), and that the mean was ·0017.</p> + + +<div class="center"> +<table border="1" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="left" rowspan="2">Line.</td><td align="left" rowspan="2"> Wave-length.</td><td align="left" rowspan="2"><u> 1 </u><br>λ⁻⁴<br>× 10¹⁷</td><td align="left" colspan="10"> Light after passing through atmospheres of the following thicknesses.</td></tr> +<tr><td align="right">0</td><td align="right"> 1</td><td align="right"> 2</td><td align="right"> 3</td><td align="right"> 4</td><td align="right"> 5</td><td align="right"> 6</td><td align="right"> 7</td><td align="right"> 8</td><td align="right"> 32</td></tr> +<tr><td align="left">A</td><td align="right"> 7594</td><td align="right"> 30</td><td align="right">1</td><td align="right"> ·955</td><td align="left"> ·908</td><td align="right"> ·857</td><td align="left"> ·815</td><td align="right"> ·775</td><td align="right"> ·736</td><td align="right"> ·707</td><td align="right"> ·665</td><td align="right"> ·107</td></tr> +<tr><td align="left">B</td><td align="right"> 6867</td><td align="right"> 45</td><td align="right">1</td><td align="right"> ·926</td><td align="left"> ·858</td><td align="right"> ·795</td><td align="left"> ·735</td><td align="right"> ·684</td><td align="right"> ·632</td><td align="right"> ·583</td><td align="right"> ·542</td><td align="right"> ·086</td></tr> +<tr><td align="left">C</td><td align="right"> 6562</td><td align="right"> 54</td><td align="right">1</td><td align="right"> ·912</td><td align="left"> ·832</td><td align="right"> ·759</td><td align="left"> ·693</td><td align="right"> ·632</td><td align="right"> ·576</td><td align="right"> ·526</td><td align="right"> ·480</td><td align="right"> ·019</td></tr> +<tr><td align="left">D</td><td align="right"> 5892</td><td align="right"> 83</td><td align="right">1</td><td align="right"> ·868</td><td align="left"> ·754</td><td align="right"> ·655</td><td align="left"> ·569</td><td align="right"> ·494</td><td align="right"> ·428</td><td align="right"> ·372</td><td align="right"> ·323</td><td align="right"> ·001</td></tr> +<tr><td align="left">E</td><td align="right"> 5269</td><td align="right"> 129</td><td align="right">1</td><td align="right"> ·803</td><td align="left"> ·644</td><td align="right"> ·518</td><td align="left"> ·427</td><td align="right"> ·334</td><td align="right"> ·268</td><td align="right"> ·216</td><td align="right"> ·173</td><td align="right"> —</td></tr> +<tr><td align="left">F</td><td align="right"> 4861</td><td align="right"> 179</td><td align="right">1</td><td align="right"> ·738</td><td align="left"> ·544</td><td align="right"> ·402</td><td align="left"> ·296</td><td align="right"> ·219</td><td align="right"> ·161</td><td align="right"> ·119</td><td align="right"> ·088</td><td align="right"> —</td></tr> +<tr><td align="left">G</td><td align="right"> 4307</td><td align="right"> 291</td><td align="right">1</td><td align="right"> ·609</td><td align="left"> ·367</td><td align="right"> ·220</td><td align="left"> ·137</td><td align="right"> ·084</td><td align="right"> ·051</td><td align="right"> ·031</td><td align="right"> ·019</td><td align="right"> —</td></tr> +<tr><td align="left">H</td><td align="right"> 3968</td><td align="right"> 403</td><td align="right">1</td><td align="right"> ·506</td><td align="left"> ·254</td><td align="right"> ·128</td><td align="left"> ·071</td><td align="right"> ·033</td><td align="right"> ·016</td><td align="right"> ·008</td><td align="right"> ·004</td><td align="right"> —</td></tr> +</table></div> +<p>The following table shows the loss of light for the rays denoted by the +principal lines given at page 26, using this last coefficient for +different air thicknesses. This is equivalent to giving the intensity of +the rays of sunlight when the sun is at different altitudes.</p> +<span class="pagenum"><a name="Page_68" id="Page_68">[Pg 68]</a></span> + +<p>The sun traverses the following thicknesses of +atmosphere when it is at the angles shown above +the horizon.</p> + + +<div class="center"> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="left">1</td><td align="left"> atmosphere </td><td align="left">90°</td></tr> +<tr><td align="left">2</td><td align="center"> "</td><td align="left">30°</td></tr> +<tr><td align="left">3</td><td align="center"> "</td><td align="left">19·30</td></tr> +<tr><td align="left">4</td><td align="center"> "</td><td align="left">14·30</td></tr> +<tr><td align="left">5</td><td align="center"> "</td><td align="left">11·30</td></tr> +<tr><td align="left">6</td><td align="center"> "</td><td align="left"> 9·30</td></tr> +<tr><td align="left">7</td><td align="center"> "</td><td align="left"> 8·30</td></tr> +<tr><td align="left">8</td><td align="center"> "</td><td align="left"> 7·30</td></tr> +</table></div> + +<div class="figcenter" style="width: 401px;"> +<img src="images/i_069.png" width="401" height="269" alt="" title=""> +<span class="caption">Fig. 10.—Absorption of Rays by the Atmosphere. +</span> +</div> +<p>It traverses thirty-two atmospheres when it is +very nearly setting. Bougier and Forbes have +calculated that the extreme thickness of the</p> + +<p><span class="pagenum"><a name="Page_69" id="Page_69">[Pg 69]</a></span> +atmosphere, traversed by its light when the sun is +on the horizon, is approximately 35½ atmospheres. +The absorption shown by 32 atmospheres will +therefore be very close to that which would be +observed at sunset on an ordinary day, and it +will be seen that practically all rays have been +scattered from the light, except the red, and a little +bit of the orange.</p> + +<p>As to the luminosity of the sun at these different +altitudes, we can easily find it by reducing the +luminosity curve of the sun at some known altitude +by the factors in the table just given, for as +many wave-lengths as we please, and thus construct +another curve. The area of the figure thus +obtained would be a measure of the total luminosity +on the same scale as the area of the luminosity +curve from which it was derived.</p> + +<p>The following are the approximate luminosities +of the sun when the light shines</p> + + +<div class="center"> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="center">through</td><td align="center"> 0</td><td align="center"> atmospheres </td><td align="center"> 1</td></tr> +<tr><td align="center">"</td><td align="center"> 1</td><td align="center"> "</td><td align="center">·840</td></tr> +<tr><td align="center">"</td><td align="center"> 2</td><td align="center"> "</td><td align="center">·705</td></tr> +<tr><td align="center">"</td><td align="center">3</td><td align="center"> "</td><td align="center"> ·594</td></tr> +<tr><td align="center">"</td><td align="center"> 4</td><td align="center"> "</td><td align="center"> ·496</td></tr> +<tr><td align="center">"</td><td align="center"> 5</td><td align="center"> "</td><td align="center"> ·417</td></tr> +<tr><td align="center">"</td><td align="center"> 6</td><td align="center"> "</td><td align="center"> ·303</td></tr> +<tr><td align="center">"</td><td align="center">7</td><td align="center"> "</td><td align="center"> ·256</td></tr> +<tr><td align="center">"</td><td align="center"> 8</td><td align="center"> "</td><td align="center"> ·215</td></tr> +<tr><td align="center">"</td><td align="center"> 32</td><td align="center"> "</td><td align="center"> ·002</td></tr> +</table></div> +<p><span class="pagenum">[Pg 70]</span></p> + +<p>It will thus be seen that the sun is 420 times less +bright just at sunset than it is if it were to shine +directly overhead, and about 350 times brighter +than it is for a winter sun in a cloudless and mistless +sky at twelve o'clock, for the altitude of the +sun in our latitude is about 30° at that time, and +corresponds with a thickness of two atmospheres, +through which the sun has to shine. We all know +that to look at the sun at any time near noon in a +cloudless sky dazzles the eyes, but that near sunset +it may be looked at with impunity. The reduction +in luminosity explains this fact.</p> + +<p>The distribution of the scattering particles in +the atmosphere is very far from regular. As we +ascend, the particles get more sparse, as is shown +by the less scattering that takes place of the blue +rays compared with the red. Thus at an altitude +of some 8000 feet the mean coefficient of scattering +is about ·0003, instead of ·0017, which it is at +sea-level. It must be recollected that there is only +about three-fourths of the air above us at 8000 +feet, and it is less dense. There will therefore be a +diminution of particles not only because there is less +air, but because the air itself is less capable of keeping +them in suspension. Up to 3000 or 4000 feet +there is no very great marked difference in the scattering +of light, as observations carried on during five +years have shown; but above that the scattering +<span class="pagenum">[Pg 71]</span> +rapidly diminishes, and at 20,000 feet it must be +very small indeed, if the diminution increases as +rapidly as has been found it does at the altitude of +8000 feet.</p> + +<p>We must repeat once more that the blue of the +sky is principally if not entirely due to the presence +of these particles, the rays scattered by them, +which are principally the blue rays, being reflected +back from them, giving the sensation of blue which +we know as sky-blue. The greater the number of +these fine particles that are encountered by sunlight, +the greater the scattering will be, and the +bluer the sky. It is more than probable that the +blue sky of Italy, so proverbial for being beautiful, +is due to this cause, since from its geographical +position the small particles of water must be very +abundant there.</p> + +<p>Carrying this argument further, we should expect +that as we mount higher the blue would become +more fully mixed with the darkness of space, and +this Alpine travellers will tell you is the case. At +heights of 12,000 feet or more, on a clear day, the +sky seems almost black, and it is no uncommon +thing to see this admirably rendered in photographs +of Alpine scenery when taken at a height. Many +of the late Mr. Donkin's photographs show this in +great perfection, as also Signor Sella's.</p> + +<p>Before quitting this subject we may call attention +<span class="pagenum"><a name="Page_72" id="Page_72">[Pg 72]</a></span> +not only to the colour of the sun itself at sunset, +but also to the colouring of the sky which accompanies +the sun as it sinks. This colouring is often +different to the colour that the sun itself assumes; +but we can easily show that the effects so wonderfully +beautiful are entirely dependent on this +scattering of light by these small intervening particles +in the air. We often see a ruddy sun, and +perhaps nearly in the zenith, or even further away +from the sun, clouds of a beautiful crimson hue, +lying on a sky which appears almost pea-green, +whilst nearer to the sun the sky is a brilliant +orange, which artists imitate with cadmium yellow. +Let us fix our attention first on the crimson cloud. +The clouds of which the colouring is so gorgeous +are often not 1000 feet above us, and were we to be +at that altitude we should see the sun not quite so +ruddy as we see it from the earth, and the cloud +would consequently be illuminated by the sun with +a more orange tint; but the light reflected from the +cloud to our eyes has to pass through, say 1000 feet +of dense atmosphere, and thus the total atmosphere +that the light traverses in the latter case is always +greater than the air thickness through which the +direct light from the sun has to pass; hence more +orange is cut off, and the light reflected from the +cloud is redder. This red, however, will not account +for the brilliant crimson and purples which we so +<span class="pagenum"><a name="Page_73" id="Page_73">[Pg 73]</a></span> +often see. It has to be remembered that not sunlight +alone illumines the cloud, but also the blue +light of the sky. The feebler the intensity of the +red, the more will the blue of the sky be felt in +the mixture of light which reaches our eyes, and +consequently we may have any tint ranging from +crimson to purple, since red and blue make these +hues, according to the proportions in which they +are mixed.</p> + +<p>Now let us see how we get the brilliant orange +of the sky itself. When the evening is perfectly +clear and free from mist and cloud, the orange in +the sky is very feeble, showing that the intensity +depends upon their presence. Now a look at the +table will show that the sun is very close to the +horizon when it becomes ruddy under normal conditions; +but that when the light traverses a thickness +of eight atmospheres, the blue and violet, and +most of the green, are absent, leaving a light of +yellowish colour. To traverse eight atmospheres +the light has only to come from a point some eight +degrees above the horizon. When the sun is near +the horizon, it sends its rays not only to us and over +us, but in every direction; and an eye placed some +few thousand feet above the earth would see the +sun almost of its midday colour, for sunset colours +of the gorgeous character that we see at sea-level +are almost absent at high altitudes. If a cloud or +<span class="pagenum"><a name="Page_74" id="Page_74">[Pg 74]</a></span> +mist were at such an altitude the sunlight would +strike it, and whilst only a small portion would be +selectively scattered, owing to the general grossness +of the particles, the major part would be reflected +back to our eyes, and come from an altitude of +over eight to ten degrees, and would therefore, +after traversing the intervening atmosphere, reach +us as the orange-coloured light of which we +have just spoken. The clouds which are orange +when near the sun, are usually higher than those +which are simultaneously red or purple. The +pea-green colour of the sky is often due to contrast, +for the contrast colour to red is green, and +this would make the blue of the sky appear decidedly +greener. Sometimes, however, it is due to +an absolute mixture of the blue of the sky and +the orange light which illuminates the same haze. +In the high Alps it is no uncommon occurrence +for the snow-clad mountains to be tipped with +the same crimson we have described as colouring +the clouds, and this is usually just after sunset, +when the sun has sunk so low beneath the +horizon that the light has to traverse a greater +thickness of dense air, and consequently to pass +through a larger number of small particles than it +has when just above the horizon. In this case +the red of the sunlight mixes with blue light of the +sky, and gives us the crimson tints. The deeper +<span class="pagenum">[Pg 75]</span> +and richer tints of the clouds just after sunset +are also due to the same cause, the thickness of +air traversed being greater.</p> + +<p>It is worth while to pause a moment and think +what extraordinary sensual pleasure the presence +of the small scattering particles floating in the air +causes us; that without them the colouring which +impresses itself upon us so strongly would have +been a blank, and that artists would have to rely +upon form principally to convey their feelings of +art. Indeed without these particles there would +probably be no sky, and objects would appear of +the same hard definition as do the mountains in +the atmosphereless moon. They would be only +directly illuminated by sunlight, and their shadows +by the light reflected from the surrounding bright +surfaces.</p><br> +<span class="pagenum"><a name="Page_76" id="Page_76">[Pg 76]</a></span> + + + +<hr style="width: 65%;"> +<h2><a name="CHAPTER_VII" id="CHAPTER_VII"></a>CHAPTER VII.</h2> + +<blockquote><p>Luminosity of the Spectrum to Normal-eyed and Colour-blind +Persons—Method of determining the Luminosity of Pigments—Addition +of one Luminosity to another.</p></blockquote> + + +<p>The determination of the luminosity of a coloured +object, as compared with a colourless surface +illuminated by the same light, is the determination +of the second colour constant. We will +first take the pure spectrum colours, and show +how their luminosity or relative brightness can be +determined. Viewing a spectrum on the screen, +there is not much doubt that in the yellow there +is the greatest brightness, and that the brightness +diminishes both towards the violet and red. Towards +the latter the luminosity gradient is evidently +more rapid than towards the former. This being the +case, it is evident that, except at the brightest part +there are always two rays, one on each side of the +yellow, which must be equally luminous. If the +spectrum be recombined to form a white patch +<span class="pagenum"><a name="Page_77" id="Page_77">[Pg 77]</a></span> +upon the screen, and the slide with the slit be +passed through it, patches of equal area of the +different colours will successively appear; but the +yellow patch will be the brightest patch. If the +patch formed by the reflected beam be superposed +over the colour patch, and the rod be interposed, +we get a coloured stripe alongside a white stripe, +and by placing our rotating sectors in the path +of the reflected beam, the brightness of the latter +can be diminished at pleasure. Suppose the sectors +be set at 45°, which will diminish the reflected beam +to one-quarter of its normal intensity, we shall find +some place in the spectrum, between the yellow +and the red, where the white stripe is evidently less +bright than the coloured stripe, and by a slight +shift towards the yellow, another place will be +found where it is more bright. Between these two +points there must be some place where the brightness +to the eye is the same. This can be very +readily found by moving the slit rapidly backwards +and forwards between these two places of +"too dark" and "too light," and by making the path +the slit has to travel less and less, a spot is finally +arrived at which gives equal luminosities. The +position that the slit occupies is noted on the scale +behind the slide, as is also the opening of the +sectors, in this case 45°. As there is another position +in the spectrum between the yellow and the +<span class="pagenum">[Pg 78]</span> +violet, which is of the same intensity, this must be +found in the same manner, and be similarly noted. +In the same way the luminosities of colours in the +spectrum, equivalent to the white light passing +through other apertures of sectors, can be found, +and the results may then be plotted in the form +of a curve. This is done by making the scale of +the spectrum the base of the curve, and setting up +at each position the measure of the angular aperture +of the sector which was used to give the equal +luminosity or brightness to the white. By joining +the ends of these ordinates by lines a curve is +formed, which represents graphically the luminosity +of the spectrum to the observer. In Fig. 11 the +maximum luminosity was taken as 100, and the +other ordinates reduced to that scale. The outside +<span class="pagenum"><a name="Page_79" id="Page_79">[Pg 79]</a></span> +curve of the figure was plotted from observations +made by the writer, who has colour vision +which may be considered to be normal, as it coincides +with observations made by the majority of +persons. The inner curve requires a little explanation, +though it will be better understood when the +theory of colour vision has been touched upon.</p> + +<div class="figcenter" style="width: 401px;"> +<img src="images/i_079.png" width="401" height="271" alt="" title=""> +<span class="caption">Fig. 11.—Luminosity Curve of the Spectrum of the Positive Pole +of the Electric Light. +</span> +</div> + +<p>The observer in this case was colour-blind to the +red, that is, he had no perception of red objects as +red, but only distinguished them by the other colours +which were mixed with the red. This being +premised, we should naturally expect that his +perception of the spectrum would be shortened, +and this the observations fully prove. If it +happened that his perceptions of all other colours +were equally acute with a normal-eyed person, then +his illumination value of the part of the spectrum +occupied by the violet and green ought to be the +same as that of the latter. The diagram shows +that it is so, and the amount of red present in +each colour to the normal-eyed observer is shown +by the deficiency curve, which was obtained by subtracting +the ordinates of colour-blind curve from +those of the normal curve. There are other persons +who are defective in the perception of green, and +they again give a different luminosity curve for the +spectrum. These variations in the perception of +the luminosity of the different colours are very +<span class="pagenum"><a name="Page_80" id="Page_80">[Pg 80]</a></span> +interesting from a physiological point of view, and +this mode of measuring is a very good test as to +defective colour vision. We shall allude to the +subject of colour-blindness in a subsequent chapter.</p> + +<p>The following are the luminosities for the +colours fixed by the principal lines of the solar +spectrum, and for the red and blue lines of +lithium, to which reference has already been +made.</p> + +<div class="center"> +<table border="1" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="left" rowspan="2">Line.</td><td align="left" rowspan="2">Colour.</td><td align="center" colspan="2">Luminosity.</td></tr> +<tr><td align="left"> Normal Eye.</td><td align="left"> Red Colour Blind.</td></tr> +<tr><td align="left">A</td><td align="left"> Very dark Red </td><td align="right">—</td><td align="right">—</td></tr> +<tr><td align="left">B</td><td align="left"> Red (Crimson) </td><td align="right">1·0</td><td align="right"> 0</td></tr> +<tr><td align="left">Red Lithium </td><td align="left"> Red (Crimson) </td><td align="right"> 8·5 </td><td align="right"> ·5</td></tr> +<tr><td align="left">C</td><td align="left"> Red (Scarlet) </td><td align="right"> 20·6 </td><td align="right"> 2·1</td></tr> +<tr><td align="left">D</td><td align="left"> Orange</td><td align="right"> 98·5 </td><td align="right"> 53·0</td></tr> +<tr><td align="left">E</td><td align="left"> Green </td><td align="right"> 50·0 </td><td align="right"> 49·0</td></tr> +<tr><td align="left">F</td><td align="left"> Blue Green </td><td align="right"> 7·0 </td><td align="right"> 7·0</td></tr> +<tr><td align="left">Blue Lithium</td><td align="left"> Blue </td><td align="right"> 1·9 </td><td align="right"> 1·9</td></tr> +<tr><td align="left">G</td><td align="left"> Violet</td><td align="right"> ·6 </td><td align="right"> ·6</td></tr> +<tr><td align="left">H</td><td align="left"> Faint Lavender</td><td align="right"> — </td><td align="right"> —</td></tr> +</table></div> + +<p>The failure of the red colour-blind person to +perceive red is very well shown from this table. +It will for instance be noticed that he perceives +about one-tenth of the light at C which the normal-eyed +person perceives.</p> +<p><span class="pagenum"><a name="Page_81" id="Page_81">[Pg 81]</a></span> +</p> +<p>A modification of this plan can be employed for +measuring the luminosity of the spectrum, and it is +<i>excessively</i> useful, because we can adapt it to the +measurement of colours other than these simple +ones. In the plan already explained it was the +colour in the patch that was altered, to get an +equal luminosity with a certain luminosity of white +light. In the modified plan the luminosity of the +white light is altered, for the luminosity of the +shadow illuminated by the reflected beam can +be altered rapidly at will by opening or closing +the apertures of the sectors whilst it is rotating. +The slit in the slide is placed in the spectrum at +any desired point, and the aperture of the sectors +altered till equal luminosities are secured. The +readings by this plan are very accurate, and give +the same results as obtained by the previous +method employed.</p> + +<p>It must be remembered that we have so far +dealt with colours which are spectrum colours, +and which are intense because they are colours +produced by the spectrum of an intensely bright +source of light. By an artifice we can deduce +from this curve the luminosity curve of the spectrum +of any other source of light. If by any +means we can compare, <i>inter se</i>, the intensity of the +same rays in two different sources of light, one +being the electric light, we can evidently from the +<span class="pagenum"><a name="Page_82" id="Page_82">[Pg 82]</a></span> +above figure deduce the luminosity curve of the +spectrum of the other source of light (see <a href="#Page_109">p. 109</a>).</p> + +<p>We can now show how we can adapt the last +method to the measurement of the luminosity of +the light reflected from pigments.</p> + +<div class="figright" style="width: 200px;"> +<img src="images/i_083.jpg" width="200" height="201" alt="" title="" > +<span class="caption">Fig. 12.—Rectangles of White and Vermilion.</span> +</div> +<a name="Fig_13" id="Fig_13"></a> +<div class="figright" style="width: 251px;"> +<img src="images/i_084.jpg" width="251" height="101" alt="" title=""> +<span class="caption">Fig. 13.—Arrangement for measuring the Luminosities of Pigments.</span> +</div> + +<p>Suppose the luminosity of a vermilion-coloured surface had to be +compared with a white surface when both were illuminated, say by +gaslight, the following procedure is adopted. A rectangular space is cut +out of black paper (Fig. 12) of a size such that its side is rather less +than twice the breadth of the rod used to cast a shadow: a convenient +size is about one inch broad by three-quarters of an inch in height. +One-half of the aperture is filled with a white surface, and the other +half with the vermilion-coloured surface. The light L (Fig. 13) +illuminates the whole, and the rod R, a little over half an inch in +breadth, is placed in such a position that it casts a shadow on the +white surface, the edge of the shadow being placed accurately at the +junction of the vermilion and white surface. A flat silvered mirror M is +placed at such a distance and at such an angle that the light it +reflects casts a second shadow +<span class="pagenum">[Pg 83]</span> +on the vermilion surface. Between R and L are placed the rotating +sectors A. The white strip is caused to be evidently too dark and then +too light by altering the aperture of the sectors, and an oscillation of +diminishing extent is rapidly made till the two shadows appear equally +luminous. A white screen is next substituted for the vermilion and again +a comparison made. The mean of the two sets of readings of angular +apertures gives the relative value of the two luminosities. It must be +stated, however, that any diffused light which might be in the room +would relatively illuminate the white surface more than the coloured +one. To obviate this the receiving screen is placed in a box, in the +front of which a narrow aperture is cut just wide enough to allow the +two beams to reach the screen. An aperture is also cut at the front +angle of the box, through which the observer can see the screen. When +this apparatus is adopted, its efficiency is seen from the fact that +when the apertures of the rotating sectors are closed the shadow on the +white surface appears quite black, which it would not have done had +there been +<span class="pagenum">[Pg 84]</span> +diffused light in any measurable quantity present within the box. The +box, it may be stated, is blackened inside, and is used in a darkened +room. The mirror arrangement is useful, as any variation in the direct +light also shows itself in the reflected light. Instead of gaslight, +reflected skylight or sunlight can be employed by very obvious +artifices, in some cases a gaslight taking the place of the reflected +beam. When we wish to measure luminosities in our standard light, viz. +the light emitted from the crater of the positive pole of the arc-light, +all we have to do is to place the pigment in the white patch of the +recombined spectrum, and illuminate the white surface by the reflected +beam, using of course the rod to cast shadows, as just described. The +rotating sectors must be placed in either one beam or the other, +according to the luminosity of the pigment.</p> + +<p>The luminosities of the following colours were taken by the above +method, and subsequently we shall have to use their values.</p> + +<div class="center"> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="right" colspan="2"> <span class="smcap">Electric Light.</span></td></tr> +<tr><td align="left"> White</td><td align="left">100</td></tr> +<tr><td align="left"> Vermilion</td><td align="left"> 36</td></tr> +<tr><td align="left"> Emerald Green</td><td align="left"> 30</td></tr> +<tr><td align="left"> Ultramarine</td><td align="left"> 4·4</td></tr> +<tr><td align="left"> Orange</td><td align="left"> 39·1</td></tr> +<tr><td align="left"> Black</td><td align="left"> 4</td></tr> +<tr><td align="left"> " (different surface)</td><td align="left"> 5·1</td></tr> +</table></div> +<p><span class="pagenum"><a name="Page_85" id="Page_85">[Pg 85]</a></span></p> + +<p>Suppose we have two or more colours of the +spectrum whose luminosities have been found, the +question immediately arises, as to whether, when +these two colours are combined, the luminosity of +the compound colour is the sum of the luminosities +of each separately. Thus suppose we have a slide +with two slits placed in the spectrum, and form a +colour patch of the mixture of the two colours +and measure its luminosity, and then measure the +luminosity of the patch first when one slit is +covered up, and then the other. Will the sum of +the two latter luminosities be equal to the measure +of the luminosity of the compounded colour +patch? One would naturally assume that it would, +but the physicist is bound not to make any assumptions +which are not capable of proof; and the truth +or otherwise is perfectly easy to ascertain, by employing +the method of measurement last indicated. +Let us get our answer from such an experiment.</p> + + +<div class="center"> +<table border="1" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="left"> <span class="smcap">Colours Measured.</span></td><td align="left"> Observed Luminosity.</td></tr> +<tr><td align="left"> R</td><td align="left"> 203·0</td></tr> +<tr><td align="left"> G</td><td align="left"> 38·5</td></tr> +<tr><td align="left"> V</td><td align="left"> 8·5</td></tr> +<tr><td align="left"> (R + G)</td><td align="left"> 242</td></tr> +<tr><td align="left"> (G + V)</td><td align="left"> 45</td></tr> +<tr><td align="left"> (R + V)</td><td align="left"> 214</td></tr> +<tr><td align="left"> (R + G + V)</td><td align="left"> 250</td></tr> +</table></div> +<p><span class="pagenum">[Pg 86]</span></p> + +<p>Three apertures were employed, one in the red, +another in the green, and the third in the violet, +and the luminosity was taken of each separately, +next two together, and then all three combined, +with the results given above.</p> + +<p>The accuracy of the measurements will perhaps be +best shown by adding the single colours together, +the pairs and the single colours, and comparing +these values with that obtained when the three +colours were combined. When the pairs are shown +they will be placed in brackets; thus (R + G) +means that the luminosity of the compound colour +made by red and green are being considered.</p> + + +<div class="center"> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="left"> R + G + V</td><td align="left"> =</td><td align="left">250·0</td></tr> +<tr><td align="left"> (R + G) + V</td><td align="left"> =</td><td align="left">250·5</td></tr> +<tr><td align="left"> (R + V) + G</td><td align="left"> =</td><td align="left">252·5</td></tr> +<tr><td align="left"> (G + V) + R</td><td align="left"> =</td><td align="left">248·0</td></tr> +<tr><td align="left"> (R + G + V)</td><td align="left"> =</td><td align="left">250·0</td></tr> +</table></div> +<p>The mean of the first four is 250·25, which is +only 1/10% different from the value of 250 obtained +from the measurement of (R + G + V) combined. +Other measures fully bore out the fact that the +luminosity of the mixed light is equal to the sum +of the luminosities of its components. It is true +that we have here only been dealing with spectrum +colours, but we shall see when we come to deal +with the mixture of colours reflected from pigments +that the same law is universally true.</p> +<p><span class="pagenum">[Pg 87]</span></p> + +<p>It will be proved by and by that a mixture of +three colours, and sometimes of only two colours, +be they of the spectrum or of pigments, can +produce the impression of white light. If then we +measure all the components but one, and also the +white light produced by all, then the luminosity +of the remaining component can be obtained by +deducting the first measures from the last. For +instance, red, green and violet were mixed to form +white light. The luminosity of the white being +taken as 100, the red and violet were measured +and found to have a luminosity of 44·5 and 3 respectively. +This should give the green as having +a luminosity of 52·5. The green was measured +and found to be 53, whilst a measurement of the +red and green together gave a luminosity of 96·5 +instead of 97.</p><br> +<span class="pagenum"><a name="Page_88" id="Page_88">[Pg 88]</a></span> + + + +<hr style="width: 65%;"> +<h2><a name="CHAPTER_VIII" id="CHAPTER_VIII"></a>CHAPTER VIII.</h2> + +<blockquote><p>Methods of Measuring the Intensity of the Different Colours of the +Spectrum, reflected from Pigmented Surfaces—Templates for the +Spectrum.</p></blockquote> + +<div class="figcenter" style="width: 300px;"> +<img src="images/i_090.png" width="300" height="275" alt="" title=""> +<span class="caption">Fig. 14.—Measurement of the Intensity of Rays reflected from white +and coloured surfaces. +</span> +</div> +<p>We will now proceed to demonstrate how we can +measure the amount of spectral light reflected by +different pigments. Let us take a strip of card +painted with a paste of vermilion, leaving half the +breadth white; and similarly one with emerald +green. If we place the first in the spectrum so that +half its breadth falls on the red, and the other half +on the white card, we shall see that apparently the +red and orange rays are undiminished in intensity +by reflection from the vermilion, but that in the +green and beyond but very little of the spectrum is +reflected. With the emerald green placed similarly +in the spectrum, the red rays will be found to +be absorbed, but in the green rays the full intensity +of colour is found, fading off in the blue. +<span class="pagenum">[Pg 89]</span> +What we now have to do is to find a method +of comparing the intensities of the different rays +reflected from the pigments, with those from +the white surface. We will commence with the +second of the two methods which the writer devised +with this object, and then describe the first, which +is more complex. Suppose we have, say a card +disc three inches in diameter, painted with the pigment +whose reflective power has to be measured, +and place it on a rotating apparatus with black +and white sectors of say five inches diameter, and +capable of overlapping so as to show different proportions +of black to white (see <a href="#Fig_42">Fig. 42</a>). If we +throw a colour patch (shown in <a href="#Page_88">Fig. 14</a> as the area +inside the dotted square) on the combination of black +<span class="pagenum">[Pg 90]</span> +and white, and at the same time on the pigmented +disc, it is probable that either one or other will be +the brighter. By moving the slit along the spectrum +it is evident, however, that a colour can be found +which is equally reflected from them both whilst +rotating. Take as an example the sectors as set at +two parts white, to one part black, the centre disc +being vermilion, the slit is moved along the spectrum +until such a point is reached that the colour +reflected from the ring and the disc appears of the +same brightness, for it must be recollected that they +cannot differ in hue, as the light is monochromatic. +It will be found that the place where they match +in brightness is in the red, the exact position being +fixed by the scale at the back of the slide. Taking +the proportion of black to white as three to one, +the match will be found to take place in the orange. +Increasing the proportion of black more and more, +a point will be reached where the reflection takes +place uniformly along the blue end of the spectrum, +this will be from the green to the end of the violet. +By sufficiently increasing the number of matches +made, a curve of reflection can be made showing +the exact proportion of each ray of the spectrum +that is reflected. The uniform reflection along +the blue end of the spectrum shows that a certain +amount of white light is reflected from the +pigment.</p> +<span class="pagenum">[Pg 91]</span> + +<p>Next taking the emerald green disc, if we adopt +the same procedure it will be found that for some +shades of the ring there are two places in the +spectrum from which the colours reflected give the +same brightness. By plotting curves in exactly +the same way as that shown for the curve of luminosity +at page 78, substituting for the open aperture +of the sector the angular value of the white used, +we can show graphically the correct reflection +for each part of the spectrum. Sometimes three +places in the spectrum will be read, as giving +equal reflections from the coloured disc and the +grey ring.</p> + +<p>The accompanying figures show the results obtained +for reflection from vermilion, emerald green, +and French blue, after having made a correction +for the white by adding the amount which the +black reflects.</p> + +<p>The scale is that of the prismatic spectrum employed. On page 46 we +stated that a white surface could be made to appear darker than a black +surface, by illuminating the latter and cutting off the light from the +former. By placing the black surface in place of one of the coloured +ones, as shown in page 82, the luminosity of the black surface can be +ascertained. In this case it was found that almost exactly 5% of the +white light from the crater of the positive pole was reflected.In the +table the original measures are shown, and also the corrected measures, +and for convenience sake the intensity of every ray throughout the +length of the spectrum reflected from white, has been taken as 100. The +position of the reference lines on the scale (Fig. 15) are as +follows— +</p> + +<span class="pagenum"><a name="Page_92" id="Page_92">[Pg 92]</a></span> + +<div class="figcenter" style="width: 401px;"> +<img src="images/i_093.png" width="401" height="193" alt="" title=""> +<span class="caption">Fig. 15.—Intensity of Rays reflected from Vermilion, Emerald Green, and French Ultramarine. +</span> +</div><p><span class="pagenum"><a name="Page_93" id="Page_93">[Pg 93]</a></span></p> + +<p> +<span style="margin-left: 2em;">B=101, C=96·25, D=89, E=79·9, F=71·5, G=53·5.</span><br> +</p> + +<h3>VERMILION.</h3> + +<div class="center"> +<table border="1" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="left" colspan="4"> <span class="smcap">White Sectors.</span></td><td align="left" rowspan="3"> <span class="smcap">Reading of Spectrum Scale.</span></td></tr> +<tr><td align="left" colspan="2"> <span class="smcap">Original Setting.</span></td><td align="left" rowspan="2"><span class="smcap">White Corrected For Black.</span></td><td align="left" rowspan="2"><span class="smcap">Corrected White 100.</span></td></tr> +<tr><td align="left"> <span class="smcap">White.</span></td><td align="left"> <span class="smcap">Black.</span></td></tr> +<tr><td align="right"> 10</td><td align="right"> 350</td><td align="right"> 27·5</td><td align="right"> 7·65</td><td align="right"> 71½ </td></tr> +<tr><td align="right"> 20</td><td align="right"> 340</td><td align="right"> 37·0</td><td align="right"> 10·15</td><td align="right"> 84 </td></tr> +<tr><td align="right"> 30</td><td align="right"> 330</td><td align="right"> 46·5</td><td align="right"> 12·95</td><td align="right"> 86·2</td></tr> +<tr><td align="right"> 50</td><td align="right"> 310</td><td align="right"> 65·5</td><td align="right"> 18·10</td><td align="right"> 88·0</td></tr> +<tr><td align="right"> 70</td><td align="right"> 290</td><td align="right"> 84·5</td><td align="right"> 23·50</td><td align="right"> 88·7</td></tr> +<tr><td align="right"> 90</td><td align="right"> 270</td><td align="right"> 103·5</td><td align="right"> 29·7 </td><td align="right"> 89·5</td></tr> +<tr><td align="right"> 120</td><td align="right"> 240</td><td align="right"> 132·0</td><td align="right"> 37·2 </td><td align="right"> 90·3</td></tr> +<tr><td align="right"> 150</td><td align="right"> 210</td><td align="right"> 160·5</td><td align="right"> 45·0 </td><td align="right"> 91 </td></tr> +<tr><td align="right"> 180</td><td align="right"> 180</td><td align="right"> 189·0</td><td align="right"> 52·5 </td><td align="right"> 91·6</td></tr> +<tr><td align="right"> 210</td><td align="right"> 150</td><td align="right"> 217·5</td><td align="right"> 60·2 </td><td align="right"> 92·5</td></tr> +<tr><td align="right"> 220</td><td align="right"> 140</td><td align="right"> 227·0</td><td align="right"> 63·2 </td><td align="right"> 93·5</td></tr> +<tr><td align="right"> 230</td><td align="right"> 130</td><td align="right"> 236·5</td><td align="right"> 66·2 </td><td align="right"> 94·5</td></tr> +<tr><td align="right"> 240</td><td align="right"> 120</td><td align="right"> 246·0</td><td align="right"> 68·5 </td><td align="right"> 96 </td></tr> +<tr><td align="right"> 230</td><td align="right"> 130</td><td align="right"> 236·5</td><td align="right"> 66·2 </td><td align="right"> 97·7</td></tr> +<tr><td align="right"> 210</td><td align="right"> 150</td><td align="right"> 217·5</td><td align="right"> 60·2 </td><td align="right"> 100·0</td></tr> +</table></div> +<p><span class="pagenum"><a name="Page_94" id="Page_94">[Pg 94]</a></span></p> + +<h3>EMERALD GREEN.</h3> +<div class="center"> +<table border="1" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="left" colspan="4"> <span class="smcap">White Sectors.</span></td><td align="left" rowspan="3"> <span class="smcap">Reading of Spectrum Scale.</span></td></tr> +<tr><td align="left" colspan="2"> <span class="smcap">Original Setting.</span></td><td align="left" rowspan="2"><span class="smcap">White Corrected For Black.</span></td><td align="left" rowspan="2"><span class="smcap">Corrected White 100.</span></td></tr> +<tr><td align="left"> <span class="smcap">White.</span></td><td align="left"> <span class="smcap">Black.</span></td></tr> +<tr><td align="right"> 10</td><td align="right"> 350</td><td align="right"> 27·5</td><td align="right"> 7·65</td><td align="right"> 50 </td></tr> +<tr><td align="right"> 20</td><td align="right"> 340</td><td align="right"> 37·0</td><td align="right"> 10·15</td><td align="right"> 54 </td></tr> +<tr><td align="right"> 30</td><td align="right"> 330</td><td align="right"> 46·5</td><td align="right"> 12·95</td><td align="right"> 55 </td></tr> +<tr><td align="right"> 50</td><td align="right"> 310</td><td align="right"> 65·5</td><td align="right"> 18·10</td><td align="right"> 57·5</td></tr> +<tr><td align="right"> 70</td><td align="right"> 290</td><td align="right"> 84·5</td><td align="right"> 23·5 </td><td align="right"> 60·0</td></tr> +<tr><td align="right"> 90</td><td align="right"> 270</td><td align="right"> 103·5</td><td align="right"> 29·7 </td><td align="right"> 63·5</td></tr> +<tr><td align="right"> 110</td><td align="right"> 250</td><td align="right"> 122·5</td><td align="right"> 34·7 </td><td align="right"> 65·5</td></tr> +<tr><td align="right"> 130</td><td align="right"> 230</td><td align="right"> 141·5</td><td align="right"> 39·5 </td><td align="right"> 67·5</td></tr> +<tr><td align="right"> 150</td><td align="right"> 210</td><td align="right"> 160·5</td><td align="right"> 45·0 </td><td align="right"> 68·5</td></tr> +<tr><td align="right"> 170</td><td align="right"> 190</td><td align="right"> 179·5</td><td align="right"> 50·0 </td><td align="right"> 71 </td></tr> +<tr><td align="right"> 190</td><td align="right"> 170</td><td align="right"> 195·5</td><td align="right"> 54·7 </td><td align="right"> 73·5</td></tr> +<tr><td align="right"> 210</td><td align="right"> 150</td><td align="right"> 217·5</td><td align="right"> 60·2 </td><td align="right"> 75·0</td></tr> +<tr><td align="right"> 220</td><td align="right"> 140</td><td align="right"> 227 </td><td align="right"> 63·2 </td><td align="right"> 76 </td></tr> +<tr><td align="right"> 220</td><td align="right"> 140</td><td align="right"> 227 </td><td align="right"> 63·2 </td><td align="right"> 78 </td></tr> +<tr><td align="right"> 210</td><td align="right"> 150</td><td align="right"> 217·5</td><td align="right"> 60·2 </td><td align="right"> 80 </td></tr> +<tr><td align="right"> 190</td><td align="right"> 170</td><td align="right"> 198·5</td><td align="right"> 54·7 </td><td align="right"> 82 </td></tr> +<tr><td align="right"> 170</td><td align="right"> 190</td><td align="right"> 179·5</td><td align="right"> 50·0 </td><td align="right"> 83 </td></tr> +<tr><td align="right"> 150</td><td align="right"> 210</td><td align="right"> 160·5</td><td align="right"> 45·0 </td><td align="right"> 84 </td></tr> +<tr><td align="right"> 130</td><td align="right"> 230</td><td align="right"> 141·5</td><td align="right"> 39·5 </td><td align="right"> 85 </td></tr> +<tr><td align="right"> 110</td><td align="right"> 250</td><td align="right"> 122·5</td><td align="right"> 34·7 </td><td align="right"> 86·5</td></tr> +<tr><td align="right"> 90</td><td align="right"> 270</td><td align="right"> 103·5</td><td align="right"> 29·7 </td><td align="right"> 87·5</td></tr> +<tr><td align="right"> 70</td><td align="right"> 290</td><td align="right"> 84·5</td><td align="right"> 23·5 </td><td align="right"> 88·5</td></tr> +<tr><td align="right"> 50</td><td align="right"> 310</td><td align="right"> 65·5</td><td align="right"> 18·10</td><td align="right"> 90·0</td></tr> +<tr><td align="right"> 30</td><td align="right"> 330</td><td align="right"> 46·5</td><td align="right"> 12·95</td><td align="right"> 92 </td></tr> +<tr><td align="right"> 20</td><td align="right"> 340</td><td align="right"> 37·0</td><td align="right"> 10·15</td><td align="right"> 94 </td></tr> +<tr><td align="right"> 10</td><td align="right"> 350</td><td align="right"> 27·5</td><td align="right"> 7·65</td><td align="right"> 98 </td></tr> +</table></div> +<p><span class="pagenum"><a name="Page_95" id="Page_95">[Pg 95]</a></span></p> + +<h3>FRENCH ULTRAMARINE BLUE.</h3> +<div class="center"> +<table border="1" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="left" colspan="4"> <span class="smcap">White Sectors.</span></td><td align="left" rowspan="3"> <span class="smcap">Reading of Spectrum Scale.</span></td></tr> +<tr><td align="left" colspan="2"> <span class="smcap">Original Setting.</span></td><td align="left" rowspan="2"><span class="smcap">White Corrected For Black.</span></td><td align="left" rowspan="2"><span class="smcap">Corrected White 100.</span></td></tr> +<tr><td align="left"> <span class="smcap">White.</span></td><td align="left"> <span class="smcap">Black.</span></td></tr> +<tr><td align="right"> 0</td><td align="right"> 360</td><td align="right"> 18·0</td><td align="right"> 5·0</td><td align="right"> 84 </td></tr> +<tr><td align="right"> 10</td><td align="right"> 350</td><td align="right"> 27·5</td><td align="right"> 7·65</td><td align="right"> 80 </td></tr> +<tr><td align="right"> 20</td><td align="right"> 340</td><td align="right"> 37·0</td><td align="right"> 10·15</td><td align="right"> 77 </td></tr> +<tr><td align="right"> 30</td><td align="right"> 330</td><td align="right"> 46·5</td><td align="right"> 12·95</td><td align="right"> 75 </td></tr> +<tr><td align="right"> 40</td><td align="right"> 320</td><td align="right"> 56·0</td><td align="right"> 15·6 </td><td align="right"> 74 </td></tr> +<tr><td align="right"> 60</td><td align="right"> 300</td><td align="right"> 75·0</td><td align="right"> 20·7 </td><td align="right"> 72·5</td></tr> +<tr><td align="right"> 80</td><td align="right"> 280</td><td align="right"> 94·0</td><td align="right"> 25·5 </td><td align="right"> 70·5</td></tr> +<tr><td align="right"> 100</td><td align="right"> 260</td><td align="right"> 113·0</td><td align="right"> 32·5 </td><td align="right"> 68 </td></tr> +<tr><td align="right"> 120</td><td align="right"> 240</td><td align="right"> 132·0</td><td align="right"> 37·2 </td><td align="right"> 66·5</td></tr> +<tr><td align="right"> 140</td><td align="right"> 220</td><td align="right"> 151·0</td><td align="right"> 42·3 </td><td align="right"> 62·5</td></tr> +<tr><td align="right"> 160</td><td align="right"> 200</td><td align="right"> 170·0</td><td align="right"> 47·4 </td><td align="right"> 59·5</td></tr> +<tr><td align="right"> 170</td><td align="right"> 190</td><td align="right"> 179·5</td><td align="right"> 50·0 </td><td align="right"> 55 </td></tr> +<tr><td align="right"> 160</td><td align="right"> 200</td><td align="right"> 170·0</td><td align="right"> 47·4 </td><td align="right"> 51 </td></tr> +<tr><td align="right"> 140</td><td align="right"> 220</td><td align="right"> 151·0</td><td align="right"> 42·3 </td><td align="right"> 46 </td></tr> +<tr><td align="right"> 0</td><td align="right"> 360</td><td align="right"> 18·0</td><td align="right"> 5·0 </td><td align="right"> 95 </td></tr> +<tr><td align="right"> 10</td><td align="right"> 350</td><td align="right"> 27·5</td><td align="right"> 7·65</td><td align="right"> 98 </td></tr> +<tr><td align="right"> 20</td><td align="right"> 340</td><td align="right"> 37·0</td><td align="right"> 10·15</td><td align="right"> 99 </td></tr> +<tr><td align="right"> 30</td><td align="right"> 330</td><td align="right"> 46·5</td><td align="right"> 12·95</td><td align="right"> 110 </td></tr> +</table></div><br> + +<p>These three measurements have been given in +full, since they will be useful for reference when +other experiments are described.</p> +<a name="Fig_16" id="Fig_16"></a> +<div class="figcenter" style="width: 350px;"> +<img src="images/i_098.jpg" width="350" height="150" alt="" title=""> +<span class="caption">Fig. 16.—Method of obtaining two Patches of identical Colour. +</span> +</div> +<p>When we have to measure the colour transmitted +through coloured bodies, we have to adopt a slightly +different plan, which is extremely accurate. The +<span class="pagenum"><a name="Page_96" id="Page_96">[Pg 96]</a></span> +first thing necessary is to make some arrangement +whereby two beams of identical colour—that is, of +the same wave-length—reach the screen, one of +which passes through the transparent body to be +measured, and the other unabsorbed. If we in +addition have some means of equalizing the intensity +of the two beams, we can then tell the +amount cut off by the body through which one +beam passes. The method that would be first +thought of would be to use two spectra, from two +sources of light; but should we adopt that plan +there would be no guarantee that the spectra would +not vary in intensity from time to time. The point +then that had to be aimed at was to form two +spectra from the same source of light, and with the +same beam that passes through the slit of the +collimator. Here we are helped by the property +of Iceland spar, which is able to split up a ray into +two divergent rays. By placing what is called a +double-image prism of Iceland spar at the end of +the collimator, we get two divergent beams of light +falling on the prisms, and by turning the double-image +prism we are able to obtain two spectra on +the screen of the camera one above the other, and +if the slit of the slide be sufficiently long two beams +would issue through it of identical colour, and +separated from one another by a dark space, the +breadth of which depends on the length of the slit +<span class="pagenum">[Pg 97]</span> +of the collimator. It is to be observed that by this +arrangement we have exactly what we require: a +light from one source passes through the same +slit, is decomposed by the same prisms, and as the +beams diverge in a plane passing through the slit of +the collimator, the length of spectrum is the same. +The problem to solve is how to utilize these two +spectra now we have got them. We can make the +light from the top spectrum pass through the +coloured body by the following artifice. Let us +place a right-angled prism in front of the top slit, +reflecting say the beam to the right, and after it +has travelled a certain distance, catch it by another +right-angled prism, and thus reflect it on to the +screen. Already in the path of the ray, issuing +through the slit from the bottom spectrum, the lens +L₄ is placed, forming a square patch on the screen. +By placing a similar lens in the path of the other ray +after reflection from the second right-angled prism, +we can superpose a second patch of the same colour +<span class="pagenum">[Pg 98]</span> +over the first patch, and by putting a rod in the +path of the two beams we can have as before two +shadows side by side, but this time each illuminated +by the same colour. One shadow will be more +strongly illuminated than the other, owing to the +different intensities of beams into which the double-image +prism splits up the primary ray. The two, +however, can be equalized by placing a rotating +apparatus in the path of one of the beams. When +equalized the sector is read off, and tells us how +much brighter one spectrum is than the other. +Thus suppose in the direct beam the sectors had +to be closed to an angle of 80°, to effect this, the +bottom spectrum would be 180/80, or 2·25 times brighter +than the bottom spectrum. It should be noted +that as the two spectra are formed by the identical +quality of light, this same ratio will hold good +throughout their length. If it does not, it shows +that the double-image prism is not in adjustment, +and that the same rays are not coming through the +slit in the slide, and it must be rotated till the readings +throughout are the same. One of the most +sensitive tests for adjustment is to form a patch +with orange light, when the slightest deviation from +adjustment will be seen by the two patches differing +in hue.</p> + +<p>We can now place the coloured transparent +object in the path of the beam which is most +<span class="pagenum"><a name="Page_99" id="Page_99">[Pg 99]</a></span> +convenient, and by again equalizing the shadows, +measure the amount it cuts off; this we can do +for any ray we choose. As both right-angled prisms +can be attached to the card or slide which moves +across the spectrum, nothing besides the card need +be moved. In the following diagram we have the +proportion of rays transmitted by the three different +glasses, red, green, and blue, in terms of the +unabsorbed spectrum. Take for instance on the +scale of the spectrum the number 11. The curve +shows that at that particular part of the spectrum +which lies in the blue, the blue glass only allowed +4/100 or 1/25 of the ray to pass, whilst the green glass +allowed 10/100 or 1/10 to pass. So at scale No. 4 in the +orange, through the blue only 2% was transmitted, +through the green glass 4%, and through the +red 20%.</p> + +<div class="figcenter" style="width: 401px;"> +<img src="images/i_100.png" width="401" height="262" alt="" title=""> +<span class="caption">Fig. 17.—Absorption by Red, Blue, and Green Glasses. +</span> +</div><p><span class="pagenum"><a name="Page_100" id="Page_100">[Pg 100]</a></span> +</p> + +<div class="figcenter" style="width: 401px;"> +<img src="images/i_101.png" width="401" height="250" alt="" title=""> +<span class="caption">Fig. 18.—Light reflected from Metallic Surfaces. +</span> +</div> +<span class="pagenum"><a name="Page_101" id="Page_101">[Pg 101]</a></span> +<div class="figcenter" style="width: 401px;"> +<img src="images/i_102.png" width="401" height="335" alt="" title=""> +<span class="caption">1. Vermilion 2. Carmine. 3. Mercuric Iodide. +4. Indian Red.<br> Fig. 19. +</span> +</div> +<p>From such curves as these we can readily derive +the luminosity curves of the spectrum, after the +white light has passed through the coloured object. +All we have to do is to alter the ordinates of the +luminosity curve of white light in the proportion to +the intensities of the rays before and after passing +through the object. It will be seen that when the +luminosity curve of the spectrum of <i>any</i> source is +known, this method holds good.</p> +<a name="Fig_20" id="Fig_20"></a> +<div class="figcenter" style="width: 401px;"> +<img src="images/i_103.png" width="401" height="347" alt="" title=""> +<span class="caption">1. Gamboge. 2. Indian Yellow. 3. Cadmium Yellow. +4. Yellow Ochre.<br> Fig. 20. +</span> +</div> +<p>The intensity of the different rays of the spectrum +reflected from metallic surfaces can also be +measured, if for the first or second right-angled +<span class="pagenum">[Pg 102]</span> +prism a small piece of the metal is substituted, +using it as a reflecting surface, as can also the rays +reflected from any surface which is bright and +polished. In <a href="#Page_100">Fig. 18</a> the dotted curves show the +<i>luminosity</i> of the spectrum reflected from the different +metals, curve V being that of white light. +These curves are derived by reducing the ordinates +of curve V proportionately to the intensity curves. +Thus at 49 brass reflects 77% of the light, and the +luminosity of the white is 80. The luminosity of +the light from the brass is therefore 77/100 of 80, or +<span class="pagenum"><a name="Page_103" id="Page_103">[Pg 103]</a></span> +61. This shows the method which is adopted, of +deducing luminosities from intensities.</p> + +<div class="figcenter" style="width: 401px;"> +<img src="images/i_104.png" width="401" height="324" alt="" title=""> +<span class="caption">1. Emerald Green. 2. Chromous Oxide. 3. Terre Verte. +Fig. 21.</span></div> + +<p>The light reflected from pigments can also be +measured by the same plan. The procedure +adopted is that carried out when measuring their +luminosities, viz. to cause the ray from one spectrum +to fall on a strip of a white surface, and that +from the other on a strip of the coloured surface +(see <a href="#Page_82">page 82</a>). This is a more convenient method +than that just described, when the coloured surface +is small. The annexed figures (Figs. 19, 20, 21, 22) +show the results obtained from various pigments.</p> +<p><span class="pagenum"><a name="Page_104" id="Page_104">[Pg 104]</a></span> +</p> +<div class="figcenter" style="width: 401px;"> +<img src="images/i_105.png" width="401" height="338" alt="" title=""> +<span class="caption">1. Indigo. 2. Antwerp Blue. 3. Cobalt. +4. French Ultramarine. Fig. 22.</span></div> +<a name="Fig_23" id="Fig_23"></a> +<div class="figright" style="width: 200px;"> +<img src="images/i_106.png" width="200" height="198" alt="" title=""> +<span class="caption">Fig. 23.—Method of obtaining a Colour +Template.</span></div> + +<p>From curves such as these we are able to produce +the colour of the pigment on the screen from the +spectrum itself. This is a useful proof of the truth +of the measurements made. To do this we must +mark off on a card (Fig. 23) the absolute scale of +the spectrum along the radius of a circle, and draw +circles at the various points of the scale from its +centre. From the same centre we must draw lines +at angles to the fixed radius corresponding to the +various apertures of the sectors required at the +various points of the scale to measure the light +<span class="pagenum">[Pg 105]</span> +reflected from a pigment. Where each radial line +cuts the circle drawn through the particular point +of the scale to which its angle has reference, gives +us points which joined give a curved figure. Such +a figure, when cut +out and rotated +in front of the +spectrum in the +proper position +(as for instance +by making the D +sodium line correspond +with that +on the scale), will +cut off exactly the +same proportion +of each colour +that the pigment +absorbs. The spectrum, when recombined, should +give a patch of the exact colour of that measured. +The spectrum must be made narrow, as the template +is only theoretically correct for a spectrum +of the width of a line, as can be readily seen.</p> + +<p>Templates like these will always enable any +colour to be reproduced on the screen, and if the +light be used for the spectrum in which the colour +has to be viewed, be it sunlight, gaslight, starlight—whatever +light it is—the colour obtained will be +<span class="pagenum"><a name="Page_106" id="Page_106">[Pg 106]</a></span> +that which the pigment would reflect if it were +viewed in that light.</p> + +<p>The identity of the colour produced on the +screen by this plan with that measured, can be +readily seen by placing the latter in the reflected +beam of white light alongside the coloured patch +formed on the white surface.</p> + +<div class="figcenter" style="width: 300px;"> +<img src="images/i_107.jpg" width="300" height="297" alt="" title=""> +<span class="caption">Fig. 24.—Template of Carmine. +</span> +</div> +<p>In Fig. 24 we have a mask or template of +carmine, which was used for determining if the +measurements were right. The black fingerlike-looking +space on the right was the amount of +red reflected light, and the other that of the blue +<span class="pagenum"><a name="Page_107" id="Page_107">[Pg 107]</a></span> +and violet; scarcely any light at all was reflected +from the green part of the spectrum.</p> + +<div class="figcenter" style="width: 401px;"> +<img src="images/i_108.png" width="401" height="263" alt="" title=""> +<span class="caption">Fig. 26.—Absorption of transmitted and reflected Light by Prussian +Blue and Carmine. +</span> +</div> +<p>On page 108 we have given the diagram of the +luminosity of the spectrum in reference to a +standard white light. It will bring this luminosity +more home if, in a similar manner to that described +above, we make a template of this curve (<a href="#Page_108">Fig. 25</a>). +We can place a narrow slit horizontally in front +of the condensing lens of the optical lantern, and +throw an image of it on to the screen. If in +close contact with this slit we rotate the template, +we shall have on the screen a graduated strip of +white light, giving in black and white the apparent +luminosity of the spectrum as seen by the eye.</p><p> +<span class="pagenum"><a name="Page_108" id="Page_108">[Pg 108]</a></span> +</p> +<div class="figcenter" style="width: 401px;"> +<img src="images/i_109.png" width="401" height="225" alt="" title=""> +<span class="caption">Fig. 25.—Template of Luminosity of White Light. +</span> +</div><p> +<span class="pagenum"><a name="Page_109" id="Page_109">[Pg 109]</a></span> +</p> +<p>It has been stated in chapter V., that it is +generally immaterial whether a pigment is in contact +with the paper or away from it, so long as +the light passes through the pigment. The above +figure (<a href="#Page_107">Fig. 26</a>) shows the truth of this assertion. +I. and II. are the curves taken of the light transmitted +by Prussian blue and carmine respectively, +and III. and IV., from the light reflected from these +colours on paper.</p> + +<div class="figright" style="width: 200px;"> +<img src="images/i_110.png" width="200" height="187" alt="" title=""> +<span class="caption">Fig. 27.—Collimator for comparing +the intensity of two sources of Light. +</span> +</div> +<p>To measure the difference in the intensities of +the rays of different sources +of light we can use a spectroscopic +arrangement with +two slits (S) (Fig. 27) placed +in a line at right angles to +the axis of the collimator. +One slit is a little below the +other, the rays being reflected +to the collimating lens L, by +means of two right-angled +prisms P, and two spectra are formed, one above +the other. By placing the rotating sectors in front +of one of the sources, the intensities of the different +parts of the spectrum can be equalized and measured.</p> +<a name="Fig_28" id="Fig_28"></a> +<div class="figcenter" style="width: 401px;"> +<img src="images/i_111.png" width="401" height="287" alt="" title=""> +<span class="caption">Fig. 28.—Spectrum Intensities of Sunlight, Gaslight, and Blue Sky. +</span> +</div> +<p>The curves for the annexed figure (Fig. 28) were +derived from measures taken in this manner. If the +rays of a May-day sun are taken at 100, it will be +seen what a rapid diminution there is in the green +<span class="pagenum"><a name="Page_110" id="Page_110">[Pg 110]</a></span> +and the blue rays in gaslight. Gaslight only +possesses about 20% of the green rays, whilst of +the violet hardly 5%. On the other hand the +light which comes to us from the sky shows a very +marked falling off in the yellow and red rays. +A very easy experiment will convince us of the +difference in colour between skylight and gaslight. +If we let a beam of daylight fall on a sheet of +paper at the end of a blackened box, and cast +a shadow with a rod by such a beam, and then +bring a lighted candle or gas-flame so that it casts +another shadow of the rod alongside, one shadow +will be illuminated by the artificial light, and the +other by the daylight. The difference in colour +will be most marked: the blue of the latter light +<span class="pagenum"><a name="Page_111" id="Page_111">[Pg 111]</a></span> +and the yellow of the former being intensified +by the contrast (see <a href="#Page_198">page 198</a>).</p> + +<div class="figright" style="width: 200px;"> +<img src="images/i_112.png" width="200" height="227" alt="" title=""> +<span class="caption">Fig. 29.—Comparison of Sun and +Sky Lights. +</span> +</div> +<p>By a little trouble the blue light from the sky +may be compared with sunlight. A beam of light B +(Fig. 29) is reflected by +a silvered glass mirror +from the blue sky into +the box HH, at the end +of which is a screen E. +Another mirror A, which +is preferably of plain +glass, reflects light from +the sun on to a second +unsilvered mirror G +(shown in the figure as +a prism), which again +reflects it on to the +screen, and each of these lights casts a shadow +from the rod D; K are rotating sectors to diminish +the sunlight, and we can make two equally bright +shadows alongside one another. The bluer colour +of the sky will be very evident.</p><br> +<span class="pagenum"><a name="Page_112" id="Page_112">[Pg 112]</a></span> + + + +<hr style="width: 65%;"> +<h2><a name="CHAPTER_IX" id="CHAPTER_IX"></a>CHAPTER IX.</h2> + +<blockquote><p>Colour Mixtures—Yellow Spot in the Eye—Comparison of Different +Lights—Simple Colours by mixing Simple Colours—Yellow and Blue +form White. +</p></blockquote> + + +<p>The colour of an object in nature, without exception +we might almost say, is due, not to one +simple spectrum colour, or even to a mixture of +two or three of them, but to the whole of white +light, from which bands of colour are more or +less abstracted, the absorption taking place over +a considerable portion or portions of the spectrum. +Notwithstanding this we shall now experimentally +show that every colour can be formed +by the simple admixture of not more than three +simple colours, if they be rightly chosen, and from +this we shall make a deduction regarding vision +itself. We are in a position to obtain three simple +colours by means of a slide containing three slits. +Now for our purpose we require that the three +slits can be placed in any part of the spectrum, +<span class="pagenum"><a name="Page_113" id="Page_113">[Pg 113]</a></span> +and that they can be narrowed or widened at +pleasure. Instead of a card the writer uses a +metal slide, as shown in Fig. 30.</p> + +<div class="figcenter" style="width: 300px;"> +<img src="images/i_114.png" width="300" height="177" alt="" title=""> +<span class="caption">Fig. 30.—Slide with slits to be used in the Spectrum. +</span> +</div> +<p>It will be seen that the three slits can be closed +or opened from the centre by a parallel motion. +They also slide in a couple of grooves, so that they +can be moved along the frame into any position. +The position they occupy is indicated by a scale +engraved on the front of the slide. Behind the +grooves in which the slits move are another pair of +grooves, into which small pieces of card CCCC +can slide, and thus close the apertures between the +slits. By this arrangement all rays except those +coming through the slits themselves are cut off. The +metal frame fits on to an outer wooden frame, which +slides in the grooves used with the card in the +apparatus as already described. It is convenient +always to keep the scale on the back of this wooden +slide in the same position as regards the shadow of +<span class="pagenum"><a name="Page_114" id="Page_114">[Pg 114]</a></span> +the needle-point used for registering the position, +and to move the slits along their grooves when a +change in position is required. Using these three +slits three different colours can be thrown on the +same square patch on the screen.</p> + +<p>A very crucial experiment is to see if we +can make white light by the admixture of three +colours, for if this can be done it almost follows +that any colour can be formed. We must use the +colour patch apparatus, and begin with placing one +slit in the violet near the line G, another between +E and F, and a third between B and C of the +solar spectrum, and fill up the gaps between them +with cards as shown in the figure. For our present +purpose it is better to make the colour patch and +the white patch touch each other, not using the rod, +as by this means we avoid fringes of colour. We +shall find that the aperture of the slits can be so +altered that we can produce a perfect match with +the white reflected light. By placing the rotating +sectors in front of the reflected beam we can +reduce its intensity, so that the two patches are +equally bright. By a tapering wedge we can +measure the width of the slits, and thus get the +proportions of these three different colours which +must be used to give the white. This is a sample +of the method that we employ when we match +any other colour. Suppose, for instance, it be +<span class="pagenum"><a name="Page_115" id="Page_115">[Pg 115]</a></span> +wished to measure the colour of a solution of +bichromate of potash; it is placed in the path +of the reflected light, and we have an orange +strip of light which we have to match. In this case +it will be found that the slit in the blue has to be +closed entirely, and only the green and red slits +opened. The intensities of the two lights are +equalized by the rotating sectors as before. So +again with a solution of permanganate of potash. +In this instance no green light will be required +(or if any of it but a trifle), and the colour of the +permanganate will be formed by the rays coming +through the blue and red slits.</p> + +<p>This plan is a very useful one for measuring all +kinds of transparent colours in terms of three rays. +The method of finding the intensity of any ray +of the spectrum transmitted by any such medium +has already been explained. The latter has one +advantage over the former, in that the measurements +by it are exact, whatever source of light be +used to form the spectrum. By the method now +described this is not the case. For instance, the +colour of permanganate of potash may be matched +in the electric light with the red and blue slits. +If the limelight were substituted for the electric +light, it would be found that the slits would require +other apertures, not proportional to those already +formed, to match the colour of this substance.</p><p> +<span class="pagenum"><a name="Page_116" id="Page_116">[Pg 116]</a></span> +</p> +<div class="figright" style="width: 60px;"> +<img src="images/i_117.jpg" width="60" height="62" alt="" title=""> +<span class="caption">Fig. 31.—Screen on which to match Gamboge. +</span> +</div> +<p>If we wish to register the tint of any pigment, +we have to slightly alter our mode of procedure. +Suppose, for instance, we wish to register the colour +of gamboge. In such a case we paint +a small bit of card (Fig. 31) with +the pigment, and divide the white +space on which the colour patches +are thrown into two parts, and cover +one-half with the pigmented card, +leaving the other half white. The +reflected beam illuminates the pigment, and the +spectrum patch the white. The widths of the +three slits are then altered till the two tints agree, +and the brightness matched by means of the +rotating sectors.</p> + +<p>There are certain sad and æsthetic colours which +it might be considered cannot be matched by a +mixture of three colours. A brown colour, or "eau +de nil," might appear to come out of the range of +matching. These colours, however, can be matched +in precisely the same manner as the brighter colours +are matched. Thus a brown pigment will be found +to require red and a little green, and a trifle of +blue; and the only difference between it and a +brighter shade of the same colour, is that more total +light has to be cut off from it to give the sombreness. +A sad colour only means a pigment or dye +which reflects but little light, and if that be so it +<span class="pagenum"><a name="Page_117" id="Page_117">[Pg 117]</a></span> +can naturally be matched by using but very small +quantities of the compounding colours.</p> + +<p>There is one curious phenomenon to which +attention may be called in this matching, which is +worthy of remark. The match will be found to +differ according as the patches are compared from a +distance of a couple of feet, or from a considerable +distance. More green will be required in the latter +case than in the former. If matched at a distance +of about six feet, and the eyes be then turned +so that the edge of the patch falls on their +centres, it will be noticed that the colour mixture +appears of a green hue. This last experiment +indicates that the retina is not equally sensitive +for all colours throughout its area. Physiologists +tell us that what is known as the yellow spot +occupies a central position in the retina, and that +it absorbs a part of the spectrum lying in the +green. Now when the eyes are close to the patch, +its image occupies a considerable part of the retina, +and the colour is compounded as it were of the +colour as seen on the yellow spot, and of that +beyond it, for the yellow spot will take in an image of +from six to eight degrees in angular measurement. +When viewed at a distance we have the image of the +patch falling almost entirely on the yellow spot, +and hence a greater quantity of green is required, +as it has to make up the deficiency caused by the +<span class="pagenum"><a name="Page_118" id="Page_118">[Pg 118]</a></span> +absorption. When the eyes are turned a little on +one side the image falls on the outside of the +yellow spot, and the patch illuminated by the +mixed light appears green, compared with the +patch illuminated with the white reflected beam.</p> + +<p>It is thus evident that when colour matches +have to be made, the distance of the eye from the +screen should always be stated, as also the dimensions +of the patches viewed. It may be fairly +asked why, if the half patch illuminated by the +mixed colours appears greener when the eye is +turned, the other should not equally do so. This +is a very fair question to ask. It must be remembered +that one strip is illuminated with white +light, in which every coloured ray of light is compounded, +whilst in the other only three rays are +blended. The green ray chosen happens to be +taken from that part of the spectrum which is +absorbed by the yellow spot; but all of the green +rays of the spectrum are not so much absorbed, +hence in ordinary white light, in which all the +green rays are present, only a small percentage +of the total green in the spectrum is absorbed, +compared with that absorbed from the single green +ray with which the match is made. No doubt both +patches are really greener when the eye receives +the impression of their images outside the yellow +spot, but one is much greener than the other, and +<span class="pagenum"><a name="Page_119" id="Page_119">[Pg 119]</a></span> +it is thus <i>comparatively</i> green. It is possible to +make a match with some colours with a blue-green +in which the phenomenon described does not appear; +but in cases where a match has to be made +with colours in which but little blue is required, it +would be impossible to make it, owing to the blue +existent in such a green-blue ray.</p> + +<p>We will now return to our compounding of three +colours to make white. Why have we chosen the +positions of the slits which we did in the spectrum +for its formation? Would not other positions +answer as well? Let us give our answer by experiment. +Let us move the slit which is now in +the green towards the red; we shall find that as +we do so—and keeping the blue slit of the same +width—that we shall have to close the red slit, and +alter the aperture of the green slit itself. If we +reason on this point we shall be forced to the conclusion +that the green slit lets through more red +light of some description, as less red from the red +slit is required to make the match. If we move +the green slit almost into the yellowish green, we +shall find that the red slit has to be entirely +closed, and that white light is formed of the two +colours, yellowish green and violet. This shows +us that the yellowish green colour here used is +formed by a mixture of the red and green rays +which passed through the two slits in their original +<span class="pagenum">[Pg 120]</span> +positions. If we replace the slits in these positions +and close the violet slit, we are at once able to +verify it.</p> + +<p>If we again form white light with the slits in +their original positions, and move the green slit +towards the blue, we shall find that, keeping the +red slit at a constant aperture, the blue slit will +have to be closed, and the green slit altered in +width. The necessity of lessening the aperture of +the blue slit shows that there is a certain amount +of blue light coming through the green slit. At +one point, when the slit has travelled into the blue-green, +the blue slit may be entirely closed, and +white light be formed of this and the red, showing +that the blue-green colour is composed of the +same proportions of blue and green which passed +through the blue and green slits in their original +position. The positions chosen were arrived at by +the writer from experiments made in this manner, +moving first one slit and then the others, and the +position of the green slit was confirmed by a consideration +of the neutral point which exists in a +green colour-blind person's spectrum.</p> + +<p>The method of mixing three colours together +gives us a means of imitating all kinds of white +light, as it does of coloured light. At page 110 +we have already given a diagram of the relative +amounts of spectrum colours in sunlight, skylight +<span class="pagenum"><a name="Page_121" id="Page_121">[Pg 121]</a></span> +and gaslight. If we by any means throw a patch +of the light which we wish to match on the patch +formed by the colour patch apparatus, and interpose +the rod, we can measure the apertures of the three +slits, and thus arrive at the relative proportions of +each colour present. In an experiment carried +out, sunlight, the electric arc-light, and gaslight were +compared in this manner. The following are the +results, the red being near the C line, the green +near the E line, and the violet near the G line of +the solar spectrum.</p> + + +<div class="center"> +<table border="1" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="right"></td><td align="center"> <span class="smcap">Sunlight.</span></td><td align="center"> <span class="smcap">Electric<br> Light.</span></td><td align="center"> <span class="smcap">Gaslight.</span></td><td align="center"> <span class="smcap">Skylight.</span></td></tr> +<tr><td align="right"> Red</td><td align="right"> 100</td><td align="right"> 100</td><td align="right"> 100</td><td align="right"> 100</td></tr> +<tr><td align="right"> Green</td><td align="right"> 193</td><td align="right"> 203</td><td align="right"> 95</td><td align="right"> 256</td></tr> +<tr><td align="right"> Violet</td><td align="right"> 228</td><td align="right"> 250</td><td align="right"> 27</td><td align="right"> 760</td></tr> +</table></div> +<p>Now from the above it might seem that as three +simple spectrum colours will give us the colour +of any pigment, that therefore two colours ought +to give us the same colour as any intermediate +simple colours in the spectrum which lie between +them; for instance, that the simple blue-green +ought to be obtained by mixing spectral green +and spectral violet together. This can be ascertained +with a single colour patch apparatus, by +cutting a slit in the card that fills up the aperture +between the two adjustable slits, and deflecting +<span class="pagenum">[Pg 122]</span> +the beam transmitted through it by a right-angled +prism, and back on to the screen through another +similar prism, as described in chapter VIII. It is +more convenient, however, to use a duplicate apparatus +precisely similar to the first, with the exception +that no collimator is required, placing them side by +side, and mirrors making the reflected beam from +the first traverse the second set of prisms. There +will be a reflected beam from the second apparatus, +which can be utilized in the same way as was that +from the first apparatus, and the two spectra will +vary together in brightness, as will also the new +reflected beam, since they all are formed by the +light coming through one slit. A patch of the +colour intermediate between the two is thrown on +the screen from the second apparatus, and the +second patch from the first apparatus overlaps it. A +rod placed in the usual manner throws two shadows, +which are illuminated by the two different beams. +If blue-green be a colour it is wished to match, it +will be found that no matter in what part of the +violet and green the slits are placed, no match can +be effected. But if some very small quantity of +red light be mixed with simple blue-green, that +then a colour identical in every respect as regards +the eye can be obtained from the violet and green +of the first apparatus. It must be remembered that +a mixture of red, green and violet form white, and +<span class="pagenum">[Pg 123]</span> +that they are mixed in definite proportions. No +matter how feeble in intensity the white may be, +the same proportions will still obtain. In the +above experiment, as the blue-green must contain +violet and green, the small quantity of red must +combine with the proper proportion of violet and +green, and will form white light, so that the match +is obtained by the residues of the violet and green +mixed with the small quantity of white light, of +which the red is the indicator.</p> + +<p>We can test the truth of this argument in a very +simple way. If we add to the colour with which +the match has to be made a small quantity of +white light from the reflected beam, cutting off +more or less by the rotating sectors, we can get the +exact hue of the impure blue-green made by the +mixture of the colours coming through the two +slits; and further we shall find that the amount of +white added corresponds with the amount of red +which would be required when the components of +the white light in the terms of the three colours +are taken into account. For spectrum colours +between the violet and the green it may therefore +safely be said that no match can be effected by +the mixture of violet and green light; but that it +always gives the intermediate colour diluted with +white light. For colours between the green and +the red of the spectrum, a very close, if indeed not +<span class="pagenum"><a name="Page_124" id="Page_124">[Pg 124]</a></span> +an exact match, can be made with the red and +green slits, without the addition of white.</p> + +<p>If we take from the second apparatus light from +above the position of the violet slit in the first +apparatus, that is, nearer the limit of visibility, it +will be found that a match is made, for at all events +a very considerable way with the violet slit alone, +by merely reducing the aperture, thus showing that +the colour is the same, only less intense. In the +same way it will be seen that the rays coming from +any point between the lower limit of the spectrum +to a little below the C line are identical in colour.</p> + +<p>As we have arrived at the fact that in colour +mixtures of violet and green, white light is to be +found in the colour produced, it follows that either +the violet or the green, or both, must themselves +contain some small proportion of white. It might +perhaps be said that violet is really a mixture of red +and blue, and hence the white in the mixture with +the green; but if in the first apparatus we place +one slit in the purest blue we can find, and the +other in the red, and throw a violet patch on the +screen from the second apparatus, we shall be unable +to form the same hue of violet by any means; +it will always be diluted with white. Now as the +very blue we are using, if matched as above by +green and violet, requires white light to be added +to it, and as to match the violet with the same blue +<span class="pagenum"><a name="Page_125" id="Page_125">[Pg 125]</a></span> +and red, white light has also to be added to it, it +follows that the violet must be freer from white +light at all events than the blue.</p> + +<p>There is one other experiment that must be +mentioned before leaving for a time this part of +our subject, viz. the formation of white by a mixture +of yellow and blue. If one of the slits be +placed in the yellow of the spectrum, a position will +be found in the blue where, if a second slit be +placed, and the apertures are adjusted, an absolute +match with the reflected white of the apparatus can +be secured. This experiment will be referred to later +on, when considering the question of primary colours.</p> + +<p>The above experiments have a great bearing on +the theory of colour vision, and should be considered +very carefully in connection with the shortened +spectrum which we have shown exists when red +colour-blind people are observing its luminosity.</p> + +<p>There is one point to be recollected in relation to +the mixtures of the three or two different colours +which make white light. If different coloured pigments +be illuminated by the "made" white light, +they will not appear of the same hues, as a rule, +as when viewed by ordinary white light. They +will vary not only in colour, but in brightness. +This might be expected when the spectral light +which they reflect is taken into account.</p><br> +<span class="pagenum"><a name="Page_126" id="Page_126">[Pg 126]</a></span> + + +<hr style="width: 65%;"> +<h2><a name="CHAPTER_X" id="CHAPTER_X"></a>CHAPTER X.</h2> + +<blockquote><p>Extinction of Colour by White Light—Extinction of White Light by +Colour.</p></blockquote> + + +<p>In the last chapter we have shown the impossibility +of matching the hue of the simple colours +between the violet and the green, unless a certain +and appreciable quantity of white light be added +to them. We will now turn to a phase of colour +measurement which will materially help us to see +why, in some cases, the addition of white light to +the simple spectrum colours, between the red and +green, does not appear necessary in order to make +a match with a mixture of red and green.</p> + +<p>We will ask ourselves two questions: one is, +whether any colour, and if so how much, can be +added to white without appearing to the eye? and +the other, if any, and if so how much, white light +can be added to a colour without its being +perceived?</p> +<span class="pagenum">[Pg 127]</span> + +<p>Perhaps one of the readiest methods of explaining +exactly what we mean is by a rotating disc. +Suppose we have a red disc, of nine or ten inches +in diameter, and at every one inch from the centre +paste on it a white wafer about one-eighth of an +inch in diameter, and cause it to rapidly rotate. +On examination we shall find that pink rings will +be formed by the combination of the white and +red near the centre, but that towards the margins +no rings will be visible, owing of course to more +red being combined with the same amount of +white. This shows that the eye is only sensitive +to a certain degree, and cannot distinguish a very +small diminution in colour purity. The intensity +of the light has something to do with the number +of these pink rings which are visible, as may +readily be tested in a room. If the rotating disc +be placed near a window, and the number of rings +visible be counted, a different number will be +visible when it is placed in a dark corner. A +kindred experiment is to place red circular wafers +upon a white disc, and note the rings visible. This +gives the sensitiveness of the eye for the diminution +in intensity at the other end of the scale. It will +be found that there is a marked difference between +the two.</p> + +<div class="figright" style="width: 60px;"> +<img src="images/i_129.jpg" width="60" height="57" alt="" title=""> +<span class="caption">Fig. 32.—Diaphragm in front of Prism. +</span> +</div> +<p>It is more instructive if we experiment with pure +colours, and so we must resort to our colour patch +<span class="pagenum"><a name="Page_128" id="Page_128">[Pg 128]</a></span> +apparatus described in <a href="#Page_42">Fig. 6</a>. If a small circular +aperture about quarter of an inch in diameter be cut +in a card, and placed in front of the prism nearest +the camera lens (Fig. 32), the colour patch, instead +of being an image of the face of the prism, will be +an image of the circular hole, +and when the slit is passed +through the spectrum we shall +have a coloured spot on the +screen, on which we can superpose +a patch of white light from +the reflected beam. There are +two ways in which we can reduce +the intensity of the spot, by narrowing the +slit through which the spectral ray passes or +by placing the rotating sectors in front of the +coloured beam. This last, perhaps, is the readiest +plan, as it only involves the reading of the sector. +We can then diminish the intensity of the coloured +spot to such a degree that by its dilution with +white light it will entirely disappear. It will be +found that red disappears at a different aperture +of sector to that required for the green, and the +green to that for the blue.</p> + +<p>From our previous experiments in chapter VII. +we know the luminosity of the spectrum to the +eye, and it will be of interest to see what relation +the luminosity at which the spots of different +<span class="pagenum">[Pg 129]</span> +colour disappear, when they are so diluted with +white light, bear to the total luminosity of these +rays.</p> + +<p>In a set of measurements made it was found that +the reduced angular apertures required for the +colours indicated by the following were:</p> + + +<div class="center"> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="right"> B</td><td align="center">required</td><td align="right">300°*</td><td align="center"> of aperture.</td></tr> +<tr><td align="right"> C</td><td align="center">"</td><td align="right">56° </td><td align="center">"</td></tr> +<tr><td align="right"> D</td><td align="center">"</td><td align="right">14° </td><td align="center">"</td></tr> +<tr><td align="right"> E</td><td align="center">"</td><td align="right">22° </td><td align="center">"</td></tr> +<tr><td align="right"> F</td><td align="center">"</td><td align="right">150° </td><td align="center">"</td></tr> +<tr><td align="right"> G</td><td align="center">"</td><td align="right">2100°*</td><td align="center">"</td></tr> +</table></div> +<p>The large numbers marked with an asterisk were +obtained by placing the rotating sectors in front of +the white reflected beam.</p> + +<p>The light of D had to be reduced to 14° before +it was extinguished; therefore to extinguish the +original light of this colour in the spectrum would +require 180/14, or 12·9 times the intensity of the white +light of the reflected beam. With the E light it +would take 180/22, or 8·2 times the white light to extinguish +it, and so on. If we tabulate the results +in this manner, and take the white light necessary +to extinguish the D light empirically as 98·5, +which is its percentage luminosity in the spectrum +of the electric light, we can then compare the +extinguishing factor with the luminosity in each +case.</p> +<span class="pagenum">[Pg 130]</span> + + +<div class="center"> +<table border="1" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="center"> <span class="smcap">Colour. </span></td> +<td align="center"><span class="smcap">White required<br> to extinguish<br> the Spectrum.</span></td> +<td align="center"> <span class="smcap">White required<br> to extinguish<br> the Spectrum,<br> with 50 as That<br> required at E.</span></td> +<td align="center"><span class="smcap">Luminosity<br> of<br> Spectrum.</span></td></tr> +<tr><td align="right"> near line B</td><td align="right"> ·6 </td><td align="right"> 3·9 </td><td align="right"> 4·9</td></tr> +<tr><td align="right"> C</td><td align="right"> 3·2 </td><td align="right"> 19·5 </td><td align="right"> 20·6</td></tr> +<tr><td align="right"> D</td><td align="right"> 12·9 </td><td align="right"> 78 </td><td align="right"> 98·5</td></tr> +<tr><td align="right"> E</td><td align="right"> 8·2 </td><td align="right"> 50 </td><td align="right"> 50 </td></tr> +<tr><td align="right"> F</td><td align="right"> 1·2 </td><td align="right"> 7·5 </td><td align="right"> 7·5</td></tr> +<tr><td align="right"> G</td><td align="right"> ·087</td><td align="right"> ·56</td><td align="right"> ·6</td></tr> +</table></div> +<p>The very close resemblance between the last two +columns indicates that the same luminosity of white +light is necessary to extinguish the same luminosity +of most colours, within the limits of observation that +is to say. Indeed the method of extinction was a +plan which Draper and Vierordt essayed, but the +results, tabulated from experiments made by them +with the apparatus they employed, give a curve +of intensity very unlike that given in Chapter VII. +In these experiments the luminosity of the orange +light corresponding to the D line coming through +the slit was measured, and it was found to be 37·5/180 of +the white light. Now according to the last table +but one 14/180 of this light was extinguished by the full +white light, consequently 37·5/180 × 14/180, or 1/62 of the orange +light was extinguished by the white light. In +other words, if white light be sixty-two times +<span class="pagenum"><a name="Page_131" id="Page_131">[Pg 131]</a></span> +latter when the two are mixed will be invisible. +The extinction of all colours requires somewhat +more light than this, and a calculation shows that +the extinction of every colour is effected by white +light, which is seventy-five times brighter than the +colour. Artists are well aware that a pale wash of +a pigment may be washed over drawing paper, and +when dry is invisible to the eye. The above experiments +fully account for it.</p> + +<p>The other experiment which was to be tried was +to see how much white light could be extinguished +by a colour. There are several ways by which this +can be effected. For instance we may superpose +a white dot on the colour patch by placing a card, +in which a circular hole is cut, in the reflected beam +near the prism, from which the reflection takes +place; or by putting a black circular disc of small +dimensions pasted on a glass in the same position, +by which means the white light is superposed over +the whole of the colour patch, with the exception +of what, when the colour is cut off, is a black spot; +or again by placing a rod to shade half the patch +from the white light, but leaving the whole of it +exposed to the coloured beam. All these methods +have been tried, and it appears that the size of the +piece of the patch over which the white light is +thrown may have some effect on the resulting +<span class="pagenum">[Pg 132]</span> +curve, but of one thing there is evidence, viz. that +a great deal more white light can be mixed unperceived +with orange light, than can be with the green, +blue, or violet. From one experiment it was found +that 1/36 part of white light of the same luminosity +as the orange could be mixed with the orange +and not be perceived; but that with the green light +at E 1/90 would just be visible, whilst at F in the blue-green +the 1/120 could be distinguished. Looking at +these results, and applying them in elucidating the +experiments in which it was attempted, but without +success, to match the intermediate colours between +violet and green (of which the light at F is a case +in point), by mixing them together, unless white +light were added to the simple colour; and the +success of the other experiment, in which orange +light could be obtained of the same hue as that at +D by a mixture of the red and green, it will be +noticed that 3·3 times more white light can be +added to the orange than to the green light at F, +without its perception. The white light produced +by the mixture in the first case might well show +when mixed with the green, but might pass wholly +unperceived when mixed with the orange.</p><br> +<span class="pagenum"><a name="Page_133" id="Page_133">[Pg 133]</a></span> + + + +<hr style="width: 65%;"> +<h2><a name="CHAPTER_XI" id="CHAPTER_XI"></a>CHAPTER XI.</h2> + +<blockquote><p>Primary Colours—Molecular Swings—Colour Sensations—Sensations +absent in the Colour-blind.</p></blockquote> + + +<p>For some purposes it is advantageous to show +experiments before indicating the deductions from +them which may lead to a theory. Those described +in Chapter IX. will enable us to treat the theory +of colour perception from a standpoint of some +advantage. How is it that the combination of +three colours suffices to form white, or to match +any colours we wish, be they spectrum colours +to which a little white is added, or the colours of +pigments? The most plausible theory that can be +advanced is that it is only necessary for the eye +to be furnished with a three-colour-perceiving +apparatus to give the impression of every colour, +and yet this would be somewhat difficult to +believe had we not had the experiments narrated +in that chapter before us. We should have almost +<span class="pagenum">[Pg 134]</span> +expected some machinery in the eye to exist, which +would answer to the rhythmic swing of the rays of +every wave-length which together make up white +light. But now we have to stand face to face +with the results of experiment, and we find that at +the most only three colours are necessary to make +up white light, and that from these three spectrum +colours we can form any others, with the limitation +already mentioned, when some simple colours are +in question.</p> + +<p>We must here digress for a moment, and notice +the fact that from our experiments we have derived +the three primary colours as they are called, viz. red, +violet, and green; the definition of a primary colour +being that it cannot be formed by the mixture of +any other colours. We have ascertained that yellow +and blue make white. It is therefore evident that +blue, yellow, and red cannot be primary colours, +since two of them form white; and we have moreover +shown that yellow can be made from green +and red; hence it might be fair to assume that the +three primary colours are red, green, and blue. +But blue, when mixed with a very small percentage +of white light, can be made by green and violet. +Hence, in the white light formed by the two colours +yellow and blue, we have the first made by green +and red, and the second by green and violet; +hence the three colours which really make the white +<span class="pagenum"><a name="Page_135" id="Page_135">[Pg 135]</a></span> +light are red, green, and violet. The approximate +positions of these three colours in the spectrum +are those already indicated; though, as we shall +presently see, it is highly improbable that any person +whose eyes are what are called normal, has +ever experienced the fundamental green sensation.</p> + +<p>The fact that red, yellow, and blue cannot be +primary colours has been mentioned, as even now +it is sometimes taught that they are so. As +long as the theory of colour principally lay with +artists there was reasonable ground for their assumption, +since they worked with impure colours, +viz. those of pigments; and as we shall see later on +the truth of the assumption agreed with such experiments +as they would make. When, however, +the question was taken up by the physicist with +more exact methods of experimenting, and with +pure colours, the falsity of the old triad was soon +capable of proof.</p> + +<p>To return from our digression: how it is that +three mixed colours can give the sensation of white +light is at first sight hard to understand; but a +reference to the action of light on a photographic +salt helps us in some degree. In the case of a +sensitive salt, such as the bromo-iodide of silver, +we find that a chemical decomposition is caused +by the violet end of the spectrum, and is only +feebly affected by any other part, though with +<span class="pagenum"><a name="Page_136" id="Page_136">[Pg 136]</a></span> +prolonged exposure even the red will cause it. The +annexed figure (Fig. 33) gives the idea of the relative +action of different parts of this violet portion.</p> + +<div class="figcenter" style="width: 401px;"> +<img src="images/i_137.png" width="401" height="330" alt="" title=""> +<span class="caption">Fig. 33.—Curve of Sensitiveness of Silver Bromo-iodide. +</span> +</div> +<p>The height of the curve shows the relative effects +produced. Now this curve is not symmetrical, but +has a maximum effect nearer to the violet end of +the spectrum than to the red. The atomic composition +of the silver bromo-iodide is probably two +atoms of silver and one of bromine and one of +iodine oscillating together, and we can conceive of +<span class="pagenum"><a name="Page_137" id="Page_137">[Pg 137]</a></span> +some one atom, the period of whose swings in +its molecule is isochronous with some wave-length +of light. Further, we can conceive that, like +a pendulum whose vibrations are increased in +magnitude by well-timed blows, the swing of +the atom is also increased, and that eventually it +gets beyond the sphere of the attraction of its +parent molecule, leaves it, and is attracted to +some neighbouring molecule of different constitution, +and that thus a chemical change is induced. +This we can conceive, but how can other +waves, which are not isochronous with the rhythmic +swing of the atoms, alter the composition of the +molecule? If we have an impulse given to a +pendulum exactly timed with the period of oscillation, +there is no doubt that the swing is increased. If +we have one nearly in accord, it will be found that +though the swings are not increased in amplitude +so greatly as when there is perfect accord, yet an +increased swing is given, and as exact accord is +removed further and further, so the increase in +the swing of the pendulum gets smaller and +smaller. In somewhat the same manner it is +possible that many series of waves, differing in +wave-length, and therefore in periods of oscillation, +may be capable of increasing the amplitude of a +swing, and with the photographic salt this probably +occurs, with the result which we see in the above +<span class="pagenum"><a name="Page_138" id="Page_138">[Pg 138]</a></span> +figure. Suppose in the eye we have three such +sensitive pendulums which are capable of responding +to the beats of waves of light, it requires +no great imagination to see that one such pendulum +will respond not only to that wave of +light which is isochronous with it, but also with +waves shorter and longer than that particular +wave. The same pendulum indeed may respond +to the whole of the visible spectrum, but when far +off from the maximum the response would be +very small indeed. We may therefore assume that +though each pendulum may have its maximum +increase of oscillation at one part of the spectrum, +yet at other parts not only it alone answers to the +beating of the waves, but that the other pendulums +are also affected by the same, and thus the whole +spectrum is recognized by the swings more or less +long, of either one, two, or of all three.</p> + +<p>To Thomas Young is usually attributed the +three-colour theory, though it seems to have been +promulgated in an incomplete state some time +before; Clark-Maxwell and Helmholtz revived it +in later years, and it is usually known as the +Young-Helmholtz theory. It should be remarked +that the three fundamental colour sensations are +not of necessity the same sensations as are given +by the three primary colours, as we shall see further +on. The following figure (Fig. 34) is taken from +<span class="pagenum"><a name="Page_139" id="Page_139">[Pg 139]</a></span> +Helmholtz's physiological optics, as diagrammatic +of the three sensations.</p> + +<div class="figright" style="width: 102px;"> +<img src="images/i_140.png" width="102" height="393" alt="" title=""> +<span class="caption">Fig. 34.—Curves of Colour Sensations. +</span> +</div> +<p>To this diagram there is an objection, in one +respect, viz. that it gives the +same luminosity-value to the +blue of the spectrum as it does +to the red and green. It has +been seen that if we call the +luminosity of the yellow 100, +that of the blue is about 5. +The objection does not hold +if it is remembered that the +three maxima of impressions +are taken as equal. If the +ordinates were increased, so +that the maxima were of the +same height as that of the +photographic curve, the resemblance +between them and this +last would be very marked. It +will be noticed that each of the +three colour sensations is not +only excited by a limited portion +of the spectrum, but by +all of it, the height of the +curves being a measure of their +response.</p> + +<p>Now assuming that this is the case, since a +<span class="pagenum"><a name="Page_140" id="Page_140">[Pg 140]</a></span> +certain degree of stimulation given simultaneously +to the three sensations causes an integral sensation +of white light, it follows that the colour perceived +in every part of the spectrum is due to the excess +of stimulation of either one or two of the fundamental +sensations, together with the sensation of +white light. If this diagram were correct, at no +point in the spectrum is one fundamental sensation +excited alone, but we believe that the diagram +obtained by Kœnig (<a href="#Page_151">Fig. 35</a>), from colour equations +(which will be explained in our next chapter), +is more exact, and that it is probable that in the +extreme violet and extreme red of the spectrum +the only sensations which are stimulated are the +violet and red respectively. Our measures in the +red and violet of the spectrum make it appear +that each of the two sensations can be perceived +unaccompanied by any others, and the +fact that the red colour blind person perceives a +shortened spectrum in the red end, is a further +proof of this deduction, so far as the red is +concerned.</p> + +<p>The colour which the fundamental green sensation +excites in the normal eye has probably never +been seen, nor can be seen. This is due to the fact +that all three sensations overlap in the green; that +is, that the pendulum which answers to the green +colour in the spectrum also affects, but with much +<span class="pagenum">[Pg 141]</span> +less energy, the other two pendulums, which +respond to the red and violet sensations.</p> + +<p>The word pendulum has been used advisedly, +for it may equally as well apply to a molecular +aggregation as to one which is visible and measurable. +Without entering into the physiological +structure of the eye, we may say that it has usually +been assumed that the pendulums are the ends of +nerves which vibrate with the waves of light; but +this seems rather doubtful. Gross matter, such as +these ends are, compared with the molecules of which +they are built up, cannot, as a rule, vibrate with waves +of light, and there seems to be no reason why there +should be an exception in the case of the eye. It +seems much more probable that a chemical decomposition +takes place in some substance attached to +them, and where such decomposition takes place +electricity of some kind must be produced. In +other sensations of the body the nerves act as +telegraph wires, carrying messages to the brain, +and it is not improbable that the nerves of the +eye are employed in somewhat the same manner. +Professor Dewar has shown that when light acts on +an extirpated eye, a current of electricity does +traverse the nerves, and of such an amount that it +can be shown to a large audience. This experiment +is not, however, conclusive, as the effect may +be mistaken for the cause. This idea, however, +<span class="pagenum"><a name="Page_142" id="Page_142">[Pg 142]</a></span> +is only hypothetical, as is indeed the hypothesis of +the mechanical action of light on the gross matter +of which the rods and cones attached to the retina +are composed.</p> + +<p>We have in a previous chapter stated that there +are some eyes in which the sensation of some +colour is altogether absent, and in others in which +it is more or less deficient. Thus some eyes appear +to be lacking wholly in the sensation of red, others of +green, and some very few of violet; and there have +been cases known in which two sensations, the red +and violet, have been totally absent. In the first +case, where the sensation of red is entirely absent, +what is known to the normal-eyed as white can be +matched with a mixture of blue and green, and +there is a place in the spectrum that is recognized +as white. Similarly white can be matched by a +green blind person with a mixture of red and +blue.</p> + +<p>To those who may be curious to see the colour +which red and green blind persons would call +white, a very simple means is at hand to demonstrate +it. Using the colour patch apparatus with +the three slits inserted in the slide, and in the +positions we have indicated in the violet, green, +and red, and forming white light for ourselves on +the screen, if we cover up the red slit entirely we +shall have a patch of sea-green colour, which a red +<span class="pagenum">[Pg 143]</span> +blind person would call white; and if we cover +the green slit, uncovering of course the red, we +shall have a brilliant purple, which to a green blind +person would be white. They both would call +white what the normal-eyed person sees as white, +for the simple reason that either the red or the +green mixed with the remaining colours would be +unperceived. The examination of colour-blind +people is of prime importance for testing any +theory of colour vision. For instance, if it were +asserted that the fundamental sensations did not +overlap as shown in the diagram above, then it +would follow that at some place in the spectrum +there would be a dark point. If they do overlap, +it must follow that both for the red and for +the green colour blind person there must be some +place in the spectrum where what is white light to +them is produced.</p> + +<p>Colour-blind people were tested with the colour +apparatus. The reflected beam and the colour +patch were made to cast shadows as before, and the +rotating sectors placed in the path of the former. +A slide with one slit was passed across the spectrum, +and the position noted where it was said that the +two shadows were illuminated with white light; to +the normal-eyed person one shadow of course +appeared illuminated with the sea-green colour, or +bluish green, according as the observer was red or +<span class="pagenum">[Pg 144]</span> +green colour blind. The ray in the spectrum +which to the red colour blind is white, has a wave-length +of about 4900, and that for the green colour +blind a wave-length of 5020, which corresponds to +the position in which we usually place the green +slit when a normal-eyed person is making colour +matches.</p> + +<p>It may be further remarked, that if the maxima +of all the three colour sensations are taken, as in the +diagram, as of equal value, that the place in the +spectrum where the white light is perceived by the +colour-blind is where the two sensations are of +equal strength, that is, where the two curves cut +one another, and are of equal height. By obtaining +the proportions of the different colours with colour-blind +persons which make up what to them is +white light, the curves for the two sensations can +be worked out in the form of simple equations.</p> + +<p>The experiments carried out with colour-blind +people are of the most interesting character, and a +good deal remains to be done with the data already +obtained from them.</p> + +<p>To the popular mind a colour-blind person is +usually thought a strange creature, and it is a +matter of wonderment, if not of amusement, that +they cannot distinguish between the red of cherries +and the leaves of the cherry tree. The physicist, +studying the theory of colour, views the matter quite +<span class="pagenum">[Pg 145]</span> +differently, and he looks upon an intelligent observer +of this class as a boon. It may be remarked that +both the red-blind and the green-blind persons +would be unable to distinguish between the cherries +and the leaves. The red-blind person would see +the cherries as green, as also the leaves; whilst the +green-blind person would see both as red. Without +regarding form it is probable that the red-blind +would see the leaves as a bright green, whilst the +green-blind would see them as darker red than the +cherries. Failure to distinguish between the two is +more likely to occur with the green of leaves, and +the red of such fruits as cherries, since the former +contains a marked proportion of red in it, and the +latter a small proportion of green.</p> + +<p>One highly-educated gentleman was led to know +his deficiency in colour sense, by hearing a companion +on a tour going into raptures over a sunset. +He saw but little difference between it and +that to be seen at midday. Testing his vision +it appeared that he was totally blind to the sensation +of green, and that white and purple would consequently +be mistaken by him for one another. +The crimson on the clouds, illuminated by the setting +sun, would appear to him as only slightly +different to the white clouds which he would see +at midday; in fact he would be always seeing +what to us would be a sunset. For this gentleman +<span class="pagenum">[Pg 146]</span> +to mix spectrum colours to match others would +evidently be no guide to normal-eyed persons.</p> + +<p>We believe that amongst us in our daily life +we have many persons who are blind to some +colour, but who are not aware of it, or if they are +aware of it, hide their defect as far as possible. +That some are ignorant of it to a late period of +their life we know.</p> + +<p>We have said that there are cases in which persons +are only defective in colour perceptions, and not +wanting in them altogether. The former are more +common than the latter, and to the experimenter +are by no means so interesting. They are only +alluded to here to indicate that there are degrees +in the defectiveness of eyes to colour. One point +which must be remembered here is that all colour +production for registration by the mixture of three +colours is delusive, unless the eye of the operator is +tested for its colour sense.</p><br> +<span class="pagenum"><a name="Page_147" id="Page_147">[Pg 147]</a></span> + + + +<hr style="width: 65%;"> +<h2><a name="CHAPTER_XII" id="CHAPTER_XII"></a>CHAPTER XII.</h2> + +<blockquote><p>Formation of Colour Equations—Kœnig's Curves—Maxwell's +Apparatus and Curves.</p></blockquote> + + +<p>The plan of obtaining colour equations will by +this time have become fairly evident. And we may +as well illustrate it by equations obtained with the +apparatus we have been using in our previous experiments. +Let us suppose we have an individual +who is desirous of having his eye-sight for colour +tested, and that we have the slide with the three +slits <i>in situ</i>. It will be found that when we alter +their width and form white light with them, matching +in purity the white light of the reflected beam, +that we shall have to reduce the intensity of the +latter very considerably, by means of the rotating +sectors. The aperture may sometimes be as small +as 4°, and at other times perhaps somewhere between +4° and 5°. Now the variation in aperture +between 4°, and say 4·7, is very considerable, but +it is highly probable that the latter might be +<span class="pagenum"><a name="Page_148" id="Page_148">[Pg 148]</a></span> +estimated as 4·6, since only degrees are marked +on the sectors. It therefore becomes essential +to use a less brilliant reflected beam for the comparison, +and this is secured by using as a mirror a +plain unsilvered glass. What before read 4 will +perhaps read 60, and 4·7 will be 70½, whilst 4·6 +would be 69, a difference easily read. We can +now commence operations. Let us then place the +red slit at say (35) of the scale, the green at (28), +and the violet at (17), and make white light of the +same intensity by altering the apertures of the slits. +Let us do the same with the slits at (34), (28), and +(17), instead of at (35), (28), and (17); and again +make white light, and similarly with the slits at (35), +(28), and (18); and let the following be the results—</p> + +<p class="center">(1) 20(35) + 60(28) + 40(17) = 100 W<br> +(2) 10(34) + 55(28) + 40(17) = 100 W<br> +(3) 20(35) + 59(28) + 10(18) = 100 W</p> + +<p>Subtracting (1) from (2) we get—</p> + +<p class="center"> + 10(34) = 20(35) + 5(28)<br> + or (34) = 2(35) + ¼(28) +</p> + +<p>which means that the colour sensation at (34) is +made up of two parts of the sensation of (35), +together with ¼ part of the sensation of (28).</p> + +<p>In the same way we find that the colour sensation +of (18) is made up of the sensations of (17) and (28).</p> + +<p class="center">(18) = 4(17) + 1/10(28).</p> +<p><span class="pagenum">[Pg 149]</span></p> + +<p>In this way all the different colour sensations +can be referred to the sensations which we may +happen to consider as best representing the fundamental +sensations. What these are is a matter still +unsettled; though from the equations formed by +colour-blind people, who only require really two +colours to form equations, their places are approximately +known; evidently as before said, the ray +in the spectrum which the green colour-blind person +sees as white light, is that where to the normal +eye the green fundamental sensation is purest, +being free from predominance of either of the +other two sensations, and might be taken as a +standard colour. Now if our luminosity curve is +correct, and if the sum of the luminosities of each +colour separately is equal to the luminosity of the +colours when mixed (which we have shown to be +the case in chapter VII.), it follows that the correctness +of the measures can be checked by using the +widths of the slits as multipliers of the luminosities. +These luminosities can then be added together, and +they should equal in luminosity the white light +with which the comparison was made. The results +can be compared together by reducing the equations +to the same standard of white light.</p> + +<p>The following is a set of observations which bear +this out.</p> + +<p>The red and violet slits in this case were kept at +<span class="pagenum">[Pg 150]</span> +35 and 17·8 on the scale, and the position of the +green slit altered.</p> + + +<div class="center"> +<table border="1" cellpadding="4" cellspacing="0" summary=""> +<tr> +<td align="center" colspan="3"> <span class="smcap">Position of Slits.</span></td> +<td align="center" colspan="3"> <span class="smcap">Aperture of Slits.</span></td> +<td align="center" colspan="3"> <span class="smcap">Luminosity of <br>Colour.</span></td> +<td align="center" rowspan="2"> <span class="smcap">Sum of the<br> Luminosity of<br> Each Colour<br> Multiplied by<br> the Aperture.</span></td></tr> +<tr><td align="center"> R</td><td align="center"> G</td><td align="center"> V</td><td align="center"> R</td><td align="center"> G</td><td align="center"> V</td><td align="center"> R</td><td align="center"> G</td><td align="center"> V</td></tr> +<tr><td align="right"> 35</td><td align="right"> 28·5 </td><td align="right"> 17·8</td><td align="right"> 115</td><td align="right"> 38</td><td align="right"> 112</td><td align="right"> 18·1</td><td align="right"> 73</td><td align="right"> ·65</td><td align="right"> 4930</td></tr> +<tr><td align="right"> 35</td><td align="right"> 28·0 </td><td align="right"> 17·8</td><td align="right"> 119</td><td align="right"> 45</td><td align="right"> 100</td><td align="right"> 18·1</td><td align="right"> 61·5</td><td align="right"> ·65</td><td align="right"> 4989</td></tr> +<tr><td align="right"> 35</td><td align="right"> 27·75</td><td align="right"> 17·8</td><td align="right"> 122</td><td align="right"> 52</td><td align="right"> 85</td><td align="right"> 18·1</td><td align="right"> 52</td><td align="right"> ·65</td><td align="right"> 4960</td></tr> +<tr><td align="right"> 35</td><td align="right"> 27·35</td><td align="right"> 17·8</td><td align="right"> 125</td><td align="right"> 65</td><td align="right"> 74</td><td align="right"> 18·1</td><td align="right"> 40</td><td align="right"> ·65</td><td align="right"> 4907</td></tr> +<tr><td align="right"> 35</td><td align="right"> 27·0 </td><td align="right"> 17·8</td><td align="right"> 128</td><td align="right"> 78</td><td align="right"> 67</td><td align="right"> 18·1</td><td align="right"> 33·2</td><td align="right"> ·65</td><td align="right"> 4954</td></tr> +<tr><td align="right"> 35</td><td align="right"> 26·3 </td><td align="right"> 17·8</td><td align="right"> 133</td><td align="right"> 125</td><td align="right"> 40</td><td align="right"> 18·1</td><td align="right"> 20·3</td><td align="right"> ·65</td><td align="right"> 4987</td></tr> +<tr><td align="right"> 35</td><td align="right"> 26·0 </td><td align="right"> 17·8</td><td align="right"> 134</td><td align="right"> 150</td><td align="right"> 10</td><td align="right"> 18·1</td><td align="right"> 16·7</td><td align="right"> ·65</td><td align="right"> 4952</td></tr> +<tr><td align="right"> 35</td><td align="right"> 25·85</td><td align="right"> 17·8</td><td align="right"> 135</td><td align="right"> 170</td><td align="right"> 0</td><td align="right"> 18·1</td><td align="right"> 15·0</td><td align="right">·65</td><td align="right"> 4993</td></tr> +<tr><td align="right"></td><td align="right"></td><td align="right"></td><td align="right"></td><td align="right"></td><td align="right"></td><td align="right"></td><td align="right"><td align="right"></td><td align="right"> Mean 4959</td></tr> +</table></div> +<p>The red slit was at a point in the spectrum +between C and the red lithium line, and excited +probably the fundamental sensation of red alone. +The violet slit was close to G, and probably in this +case the fundamental sensation of violet was almost +excited alone. With the green slit the reverse was +the case, all three fundamental sensations being +excited. At 26·3 the green sensation was probably +the fundamental sensation mixed with white light +alone, as at that point the green blind person saw +white light in the spectrum, on the red side of it +there being what he describes as a warm colour, +and on the violet side a cold colour.</p> + +<p>An inspection of the table will show how very +closely the sum of the luminosities agree amongst +<span class="pagenum"><a name="Page_151" id="Page_151">[Pg 151]</a></span> +themselves, the white light formed by them in each +case being of equal intensities. It must be recollected +that white light is not necessary to form +colour equations; colours may be mixed to form +any other colour, which may be taken as a standard. +This is often useful in the case of the light between +the violet and the blue, where the luminosities are +small compared with the luminosity in the green, +yellow, and red.</p> + +<div class="figcenter" style="width: 401px;"> +<img src="images/i_152.png" width="401" height="249" alt="" title=""> +<span class="caption">Fig. 35.—Kœnig's Curves of Colour Sensations. +</span> +</div> +<p>By taking a large number of colour equations, +Kœnig, who works in Helmholtz's laboratory, has +derived what he considers curves of the three +fundamental sensations in a normal-eyed person, +and also those of the colour-blind. It may be said +that with the colour-blind only two of the fundamental +sensations are seen, and therefore only two +<span class="pagenum"><a name="Page_152" id="Page_152">[Pg 152]</a></span> +curves are found, and that these agree in the main +with some two of the curves of the three belonging +to the normal-eyed.</p> + +<div class="figleft" style="width: 150px;"> +<img src="images/i_153.jpg" width="150" height="448" alt="" title=""> +<span class="caption">Fig. 36. Maxwell's Colour-box. +</span> +</div> + +<p>Maxwell was the first to +make a definite piece of apparatus +for the purpose of obtaining +colour equations, and +we reproduce from his paper in +the <i>Philosophical Transactions</i> +of the Royal Society for 18—, +a somewhat modified diagram +of it.</p> + +<p>This apparatus is often known +as Maxwell's colour-box, and is +in fact a spectroscope reversed. +With a collimator and prisms +we form a spectrum on the +focusing-screen of the camera +(<a href="#Page_42">Fig. 6</a>), by light coming through +the slit, and we can obtain light +on the distant screen, a patch of +any colour, by placing in the +spectrum slits as given at <a href="#Page_113">Fig. +30.</a> If we were to illuminate +the slits so placed with white +light, and look through the slit +of the collimator, we should see +the front surface of the first prism illuminated by +<span class="pagenum"><a name="Page_153" id="Page_153">[Pg 153]</a></span> +the mixture of the colours which would, when the +light illuminated the collimator slit, have formed +one colour patch on the screen. In Maxwell's +apparatus, the slits S₁, S₂, S₃ are illuminated by the +light reflected from a white card C, placed in the +sunshine, the rays passing through them fall on two +prisms P₁, P₂, are reflected back again through these +prisms by a concave mirror M₃, are received on +another mirror M, and fall at E on to the eye. At +A is an aperture in the box, letting through white +light on to a mirror M₁, which reflects it through a +lens L on to M₂, which again reflects it on to M, +and so to the eye at E. Thus at E an image of the +prisms, and an image of the aperture are seen, and +the white light of the latter can be compared with +the mixture of the colours formed by the prism +passing through S₁, S₂, and S₃.</p> + +<p>Suppose we have one slit S₁, the white light will +be decomposed by the prisms, and will be seen at +E as light of the same colour as would be seen at +S₁, if the light were sent from E to S₁, and so with +the other slits. Thus when two or three of the +slits are uncovered, the light falling on the eye at +E will be a mixture of two or three colours.</p> + +<p>There are two drawbacks to the mode of illumination +used, one being that the quality of sunlight +varies, and therefore colour equations will not be +accurately comparable one with the other; and +<span class="pagenum"><a name="Page_154" id="Page_154">[Pg 154]</a></span> +the second is that the light reflected from the card +is not absolutely the same in all directions, and it +cannot be perpendicularly placed to each of the +rays which strike the prisms, after passing through +the different slits. This latter is a small objection, +and is not of much account, but the first drawback +is a more serious one.</p> + +<div class="figcenter" style="width: 401px;"> +<img src="images/i_155.png" width="401" height="290" alt="" title=""> +<span class="caption">Fig. 37.—Maxwell's Curves of Colour Sensations. +</span> +</div> + +<p>With this apparatus, then, Maxwell formed +his colour equations, but he fixed as the colours +which may be called his standard colours, portions +of the spectrum which are certainly not pure, and +hence he got curves which are not as perfect as +those of Kœnig.</p><p> +<span class="pagenum">[Pg 155]</span> +</p> +<p>It will be seen, for instance, that his red and +violet curves do not overlap, but touch each other +near E. Were this true, the green colour-blind +person should see a dark space in the spectrum, +since the green sensation is missing in such eyes. +As a matter of fact the luminosity of the spectrum +is very considerable to such a person at this point.</p> + +<p>It will also be seen that some of his curves are +negative curves lying below the base. This shows +that the three standard colours he took are somewhat +wrong. The dotted curve gives the combination +of his three sensations at every point, and +should be the luminosity curve; but owing to his +having taken empirically certain standards of luminosity +for his three colours, it does not represent the +truth, as may be seen on comparison with <a href="#Page_79">Fig. 11</a>, +page 79.</p> + +<p>It must be recollected that since Maxwell's +observations the subject has been largely experimented +upon, and naturally improved appliances +and greater knowledge have enabled more nearly +correct views to be entertained regarding it.</p><br> +<span class="pagenum"><a name="Page_156" id="Page_156">[Pg 156]</a></span> + + + +<hr style="width: 65%;"> +<h2><a name="CHAPTER_XIII" id="CHAPTER_XIII"></a>CHAPTER XIII.</h2> + +<blockquote><p>Match of Compound Colours with Simple Colours—All Colours reduced +to Numbers—Method of matching a Colour with a Spectrum Colour and +White Light.</p></blockquote> + + +<p>If we place the solution of bichromate of potassium +in front of the slit of the collimator, we shall +see that on producing a spectrum on the screen, all +rays from the red to the yellow-green pass; hence +bichromate of potash transmits a colour which is a +compound colour.</p> + +<p>It has been shown that this orange colour and +the spectral yellow can be matched by mixing the +simple colours of red and green together; but it +will be instructive to see if a simple colour in the +spectrum itself can be found which can match such +a compound colour as that of the bichromate.</p> + +<p>If we place the bichromate in the reflected beam +of the colour patch apparatus and illuminate one +shadow cast by the rod with the light transmitted +by it, and pass a slit along the spectrum, to +<span class="pagenum"><a name="Page_157" id="Page_157">[Pg 157]</a></span> +produce monochromatic light, with which the other +shadow of the rod is illuminated, a position will be +found near the orange sodium line "D," where the +two colours apparently match in every respect; +when the intensities of the two illuminated shadows +are equalized as before by the rotating sectors. In +the same way by filling the part of the square +with the pigment on which the shadow illuminated +by the reflected beam falls, we can see if we can +match emerald green, cyanine blue, and other +coloured pigments.</p> + +<p>It will often be—more often than not—necessary, +however, to dilute the spectrum colour thrown on +the white half of the patch with a trace of white +light. By reference to our previous experiments we +arrive at what may appear an unlooked-for result, +that <i>no matter what the colour</i> may be, we can refer +it to one ray of the spectrum, together with a percentage +of added white light. It is worthy of +remark, that the place in the spectrum where the +simple and the compound colours match, varies +according to the kind of light with which the pigment +is illuminated. This we can show in a very +simple way.</p> + +<p>To persons who are totally colour-blind to one +sensation, viz. the green or the red, the matching +of a compound colour with a simple one in the +spectrum should possess no difficulties. Taking +<span class="pagenum">[Pg 158]</span> +the trichromic theory of three sensations for the +normal-eyed person, it is evident that only the +following classes of sensations are possible in the +normal-eyed, the green colour-blind and the red +colour-blind—</p> + + +<div class="center"> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="left"> Normal-eye.</td><td align="left">Green colour-blind.</td><td align="left">Red colour-blind.</td></tr> +<tr><td align="left"> Red</td><td align="left"> Red</td><td align="left">—</td></tr> +<tr><td align="left"> Green</td><td align="left"> —</td><td align="left">Green.</td></tr> +<tr><td align="left"> Violet</td><td align="left"> Violet</td><td align="left">Violet.</td></tr> +<tr><td align="left"> Mixtures of red and green</td><td align="left"> —</td><td align="left"> —</td></tr> +<tr><td align="left"> Mixtures of red and violet</td><td align="left"> Mixtures of red and violet</td><td align="left"> —</td></tr> +<tr><td align="left"> Mixtures of green and violet</td><td align="left"></td><td align="left"> Mixtures of green and violet.</td></tr> +<tr><td align="left"> Mixtures of red, green and violet</td><td align="left"></td><td align="left">—</td></tr> +</table></div> +<p>If we take as a type of colour-blindness the +green colour-blind person, we see that every colour +in the spectrum must be either pure red or violet, +or else these colours mixed with more or less white +light, since these two sensations when excited in +certain proportions give the sensation of white. At +one place, which is commonly called the neutral +point, the proportions of the two colours are such +that the impression there given is only white; hence +<span class="pagenum"><a name="Page_159" id="Page_159">[Pg 159]</a></span> +it follows that, between this neutral point and each +end of the spectrum, the rays are mixtures of +violet and white, or red and white, the dilution of +the colours varying from no white to all white. As +every compound colour must be a mixture of the +same two colours in certain proportions, it follows +that the green colour-blind person can match every +compound colour with some one ray of the spectrum, +and that every colour must to him be either +red or violet, diluted with different proportions of +white light.</p> + +<p>In the same way, a person who is colour-blind +to the red can also match any colour with a single +spectrum colour, and he will see it as green or +violet diluted with more or less white light. This +can be readily understood, but it is not quite so +plain how any colour sensation felt by the normal +eye can be referred to the spectrum.</p> + +<p>If we take three rays in the spectrum—one in +the red between C and the red Lithium line which +we will call <i>R</i>, another in the green between F and +<i>b</i> which we will call <i>G</i>, and a third in the violet +near G but on the <i>H</i> side of it, and which we may +call <i>V</i>—then by varying their intensities (which is +equivalent to varying the luminosities) and mixing +them, we can give the same impression to the eye +that any compound colour gives; and that any intermediate +simple spectrum colour gives, if very slightly +<span class="pagenum">[Pg 160]</span> +diluted with white light. With these same three +colours, but in different proportions, we can also +give the impression of white light to the eye. The +intermediate spectrum colours between the green +and the violet rays selected when slightly diluted +are imitated by mixing these rays together in +different proportions, and similarly those lying +between the red and the green by mixing together +these rays in different proportions—and there is +some ray present in the spectrum which, when +very slightly diluted with white light, has the same +colorific effect on the eye as the mixtures of the +pairs <i>v</i> and <i>b</i>, and <i>G</i> and <i>R</i>, in any proportions +whatever.</p> + +<p>Let the luminosities of the rays <i>R, G</i> and <i>V</i>, +which give the impression of white light, be <i>a</i>, <i>b</i> +and <i>c</i> units respectively, and <i>p</i>, <i>q</i> and <i>r</i> those which +give that of the colour which has to be registered +and reproduced. We then get the following equations—where +<i>W</i> is white, <i>w</i> its luminosity, <i>Z</i> the +colour, and <i>z</i> its luminosity—</p> + +<p class="center"><i>aR</i> + <i>bG</i> + <i>cV</i> = <i>wW</i>—(i.);<br> +<i>pR</i> + <i>qG</i> + <i>rV</i> = <i>zZ</i>—(ii.); +</p> + +<p>Then evidently—</p> + +<p class="center">(<i>a</i> + <i>b</i> + <i>c</i>) = <i>w</i>; and (<i>p</i> + <i>q</i> + <i>r</i>) = <i>z</i>.</p> + +<p class="center">Let <i>p</i> = ɑ<i>a</i>, <i>q</i> = β<i>b</i>, <i>r</i> = ɣ<i>c</i>,</p> + +<p>Then we may write (ii.) as—</p> + +<p class="center">α<i>aR</i> + β<i>bG</i> + ɣ<i>cV</i> = <i>zZ</i>—(iii.).</p> +<p><span class="pagenum">[Pg 161]</span> +Now either ɑ, β, or ɣ must be smaller than the +other two. As an example, if ɑ be the smallest, we +multiply (i.) by ɑ when we get—</p> + +<p class="center">ɑ<i>aR</i> + ɑ<i>bG</i> + ɑ<i>cV</i>= ɑ<i>wW</i>—(iv.) +<br> +Subtracting (iv.) from (iii.) and we get— +<br> +(β-ɑ)<i>bG</i> + (ɣ-ɑ)<i>cV</i> = <i>zZ</i> - ɑ<i>wW</i>. +</p> + +<p>Now it has already been stated that between <i>V</i> +and <i>G</i> there is some ray which gives the same +sensation of colour, mixed with a very small quantity +of white light, as the above mixture of <i>V</i> and +<i>G</i>—let us call it <i>X</i> and its luminosity <i>x</i> [<i>x</i> being +evidently equal to (β-ɑ)<i>b</i> + (ɣ-ɑ)<i>c</i>], and μ the +luminosity of the small quantity of white added.</p> + +<p>We then get <i>zZ</i> = <i>xX</i> + (μ + ɑ) <i>W</i>.</p> + +<p>Here we have the colour <i>Z</i> in terms of a single +ray, and of white light.</p> + +<p>This same holds good when in (ii.) ɣ is smaller +than ɑ and β; but it does not do so should it +happen that β is the smallest, for there is no part +of the spectrum which contains simple colours +giving the same sensation to the eye as mixtures +of red and blue. There is, however, a very simple +way in which the registration of such a colour (which +it must be remarked must be of a purple tone) can +be effected. It can be fixed by its complementary. +To do this we must add to (ii.) a certain amount +of <i>R</i> and <i>V</i>, which will make the whole white. +Thus, suppose in (iii.) ɑ to be larger than ɣ and ɣ +<span class="pagenum"><a name="Page_162" id="Page_162">[Pg 162]</a></span> +than β, then we must add ϕ<i>bG</i> + θ<i>cV</i> and we +have</p> + +<p class="center">ɑ<i>aR</i> + (β + ϕ)<i>bG</i> + (ɣ + θ)<i>cV</i> = <i>nW</i> = <i>Z</i> + ϕ<i>bG</i> + θ<i>cV</i>;<br> +but (β + ϕ), and (ɣ + θ) each equal ɑ ∴ <i>n</i> = ɑ<i>w</i>.<br> +∴ <i>Z</i> + ϕ<i>bG</i> + θ<i>cV</i>= ɑ<i>wW</i>. +</p> + +<p>Now between <i>V</i> and <i>G</i> in the spectrum there is +some single colour which gives the sensation of the +mixture of <i>G</i> and <i>V</i>. Let it be <i>X</i>´ with luminosity +<i>x</i>´, together with white whose luminosity is μ´, +which must equal (ϕ<i>b</i> + θ<i>c</i>).</p> + +<p class="center">∴ <i>Z</i> + <i>x´X´</i> + μ´<i>W</i> = ɑ<i>wW</i><br> +<i>Z</i> = (ɑ<i>w</i> - μ´)<i>W</i> - <i>x´X´</i> +</p> + +<p>which again is the colour expressed in terms of +white light less the complementary colour. We +have thus arrived at the very simple deduction that +the hue and luminosity of any colour, however +compounded, may be registered by a reference to +white light and a single ray of the spectrum.</p> + +<p>In practice this dominant ray is very easy to +find. Suppose we wish to determine numerically +the colour of a signal-green glass in the electric +light, we should proceed as follows—</p> + +<p>The colour patch apparatus (described in chapter +IV.) is employed, and the coloured glass is placed +between the silvered mirror which reflects the +beam already reflected from the first surface of +the first prism of the spectrum apparatus, and the +<span class="pagenum">[Pg 163]</span> +screen, and a square image of that surface of the +prism showing the tint of the glass is formed on +the screen by means of the lens. Touching this +image is a square patch of white light formed by +the re-combination of the spectrum by means of +another lens. An opaque slide containing an adjustable +slit is moved across the spectrum in the +manner described in the chapter referred to until +the colour of this last patch is approximately the +same hue as that of the glass.</p> + +<p>In the path of the reflected beam, but between +the prism and the silvered mirror, is inserted a piece +of plain glass which can be made to reflect part of +the beam into the spectrum patch of light, a square +patch of the white light being formed by means of +a third lens. We thus have monochromatic light +mixed with white light. The requisite intensity of +the added white light can be adjusted by means of +the rotating sectors, as described in the same +chapter, which open and close at will during rotation, +and the total luminosity of the mixed beams +can be altered by this, together with the adjustable +slit in the slide. The slit may probably have to be +moved in the spectrum to make the hue of these +mixed lights the same as that of the glass, but by +trial the position of the ray whose colour when +diluted with white makes the match is readily found. +The position of the slit in the spectrum is noted, as +<span class="pagenum">[Pg 164]</span> +also the aperture of the sectors. The relative luminosities +of the beam reflected from the plain glass +mirror and of the coloured ray is next measured by +placing a rod in the path of the two beams, and +equalizing by the sectors the luminosity of the +shadows which are illuminated, the one by the +spectral ray, and the other by the white light. +When the sector aperture is noted the registration +is complete, as far as hue is concerned, but the +luminosity of the ray transmitted through the glass +should be compared with that of the reflected +beam, and then the luminosity is also recorded.</p> + +<p>Should the colour of a pigment be in question, +the ray reflected from the silvered mirror is made +to fall on the pigmented surface and the same +procedure adopted.</p> + +<p>If a purple glass (say) has to be registered, we +proceed in a slightly different manner. The patch +of coloured light passing through the purple glass +is superposed over the spectrum patch, and the slit +in the slide is moved till a ray is found which will +make white light when superposed on the colour +of the glass. The luminosities of this white light, +of the reflected beam, and of the spectral colour +are compared "inter se," and there are then +sufficient data with which to make numerical +registration.</p> + +<p>Coloured glasses to be used at night with oil or +<span class="pagenum">[Pg 165]</span> +gas, or pigments to be viewed by these lights, must +be registered in these lights. As the spectrum +colours are always the same, it is convenient to use +the electric light spectrum, and the only alteration +in the apparatus is to use two gas-lights to illuminate +two square apertures, in front of one of which +the glass whose colour has to be measured is +placed. The images of these apertures are thrown +on the screen, the coloured image touching the +square image of the spectral colour patch, and +the naked image over the latter. The same +determinations are gone through as those just +described.</p> + +<p>The following are the determinations of some +glasses—</p> + + +<div class="center"> +<table border="1" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="center"> <span class="smcap">Glasses Measured.</span></td> +<td align="center"><span class="smcap">Wave-lengths of Dominant Ray.</span></td> +<td align="center"><span class="smcap">Percentage of White Light.</span></td> +<td align="center"> <span class="smcap">Percentage of Luminosity of Light Transmitted through the Glass.</span></td></tr> +<tr><td align="left"> Ruby</td><td align="right"> 6220</td><td align="right"> 2</td><td align="right"> 13·1 </td></tr> +<tr><td align="left"> Canary</td><td align="right"> 5850</td><td align="right"> 26</td><td align="right"> 82·0 </td></tr> +<tr><td align="left"> Bottle Green</td><td align="right"> 5510</td><td align="right"> 31</td><td align="right"> 10·6 </td></tr> +<tr><td align="left"> No. 1 Signal Green</td><td align="right"> 4925</td><td align="right"> 32</td><td align="right"> 6·9 </td></tr> +<tr><td align="left"> No. 2 Signal Green</td><td align="right"> 5100</td><td align="right"> 61</td><td align="right"> 19·4 </td></tr> +<tr><td align="left"> Cobalt</td><td align="right"> 4675</td><td align="right"> 42</td><td align="right"> 3·75</td></tr> +</table></div> +<p><span class="pagenum">[Pg 166]</span></p> + +<p>The following are determinations of some +coloured pigments—</p> + + +<div class="center"> +<table border="1" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="right"> <span class="smcap">Coloured Papers.</span></td><td align="right"><span class="smcap">Wave-lengths of Dominant Ray.</span></td><td align="right"><span class="smcap"> Percentage of White Light.</span></td><td align="right"> <span class="smcap">Percentage of Luminosity, White Paper being 100.</span></td></tr> +<tr><td align="right"> Vermilion</td><td align="right"> 6100</td><td align="right"> 2·5</td><td align="right"> 14·8</td></tr> +<tr><td align="right"> Emerald Green</td><td align="right"> 5220</td><td align="right"> 59·0</td><td align="right"> 22·7</td></tr> +<tr><td align="right"> French Ultramarine Blue</td><td align="right"> 4720</td><td align="right"> 61·0</td><td align="right"> 4·4</td></tr> +<tr><td align="right"> Brown Paper</td><td align="right"> 5940</td><td align="right"> 50·0</td><td align="right"> 25·0</td></tr> +<tr><td align="right"> Brown Paper</td><td align="right"> 5870</td><td align="right"> 67·0</td><td align="right"> 19·5</td></tr> +<tr><td align="right"> Orange</td><td align="right"> 5915</td><td align="right"> 4·0</td><td align="right"> 62·5</td></tr> +<tr><td align="right"> Chrome Yellow</td><td align="right"> 5835</td><td align="right"> 26·0</td><td align="right"> 77·7</td></tr> +<tr><td align="right"> Blue Green</td><td align="right"> 5005</td><td align="right"> 42·5</td><td align="right"> 14·8</td></tr> +<tr><td align="right"> Eosin Dye (<i>Sporting Times</i>)</td><td align="right"> 6400</td><td align="right"> 72·0</td><td align="right"> 44·7</td></tr> +<tr><td align="right"> Cobalt</td><td align="right"> 4820</td><td align="right"> 55·5</td><td align="right"> 14·5</td></tr> +</table></div><br> +<p><span class="pagenum"><a name="Page_167" id="Page_167">[Pg 167]</a></span></p> + + + +<hr style="width: 65%;"> +<h2><a name="CHAPTER_XIV" id="CHAPTER_XIV"></a>CHAPTER XIV.</h2> + +<blockquote><p>Complementary Colours—Complementary Pigment Colours—Measurement +of Complementary Colours.</p></blockquote> + +<p>We are now in a position to enter into the question +of complementary colours, which is one of supreme +interest to artists. A complementary colour, in its +strictest sense, may be described as the colour +which, combined with the colour whose complement +is required, makes up white. In this definition we +have three characteristics to take into account, viz. +hue and luminosity, and dilution with white light. +As an example of what we mean we refer to an +experiment which was made and described at page +125. It was said that if the violet slit was placed +in a certain position in the blue of the spectrum, it +was possible to move the green slit into a part of +the yellow, so that the two colours when mixed +together would form white. In that case the blue is +complementary to the yellow, and the yellow to the +<span class="pagenum"><a name="Page_168" id="Page_168">[Pg 168]</a></span> +blue, so long as the intensities are those which make +up white light. Again, if it requires the light coming +through the three slits to make up white light, be +it the white of the electric light or that of gaslight, +we can obtain the complementary colour of the light +issuing through any one of them by covering that +slit up. Thus suppose the slits to be in the normal +position the complementary colour of the red is a +green-blue, formed by the mixture of the violet and +green rays, the complementary colour of the green +is a purple, formed by the mixture of the red and +the violet light, whilst the complementary colour of +the violet is greenish yellow, formed by the mixture +of the red and green rays. It will be evident that +as the intensities of the three rays respectively will +be different according as the white light matched is +the electric light or gaslight, the complementary +colours in the former will be different in hue and +intensity to those in the latter.</p> + +<div class="figcenter" style="width: 300px;"> +<img src="images/i_170.jpg" width="300" height="297" alt="" title=""> +<span class="caption">Fig. 38.—Chromatic Circle. +</span> +</div> + +<p>Another couple of striking experiments which the +writer devised to show these colours can be made +with the colour patch apparatus, and on the same +principle as that used for obtaining the intensity of +the rays reflected from pigments, and transmitted +through coloured transparent bodies. Instead of the +small slit with a right-angled prism in front to deflect +the beam from the top spectrum, where two spectra +are produced (see <a href="#Fig_16">Fig. 16</a>, p. 95), a single spectrum +<span class="pagenum">[Pg 169]</span> +is used, with a right-angled prism of such a size +that it deflects half of it, which is again reflected on +to the screen by a mirror, and through a lens to +form a second patch of equal size as the undeflected +beam. A rod can be so placed in the path +of the beams that two coloured stripes are formed, +together with a white stripe caused by their overlapping. +The two coloured stripes are complementary +one to the other. By moving the prism +along the spectrum various coloured stripes can be +formed, in some cases one being much less luminous +than the other, and yet they are complementary. +If instead of the large right-angled prism a smaller +one be used, the complementary colour due to a +<span class="pagenum"><a name="Page_170" id="Page_170">[Pg 170]</a></span> +small part of the spectrum can be shown in the +same manner.</p> + +<p>It is customary to show the complementary +colours diagrammatically by what is known as the +chromatic circle. Roughly it is drawn as in the +above figure (<a href="#Page_168">Fig. 38</a>). The three colours, red, green +and blue, which are taken for primary colours, are +placed at 120° apart in a circle, and lines drawn from +them through the centre, at which white is supposed +to be situated. Where these lines cut the circumference +is placed the complementary colour. Other +colours can be placed round the circle with their +complementary colours opposite, and so a fairly +complete diagram of the spectrum can be made. +But it must be remembered that this is really of +no scientific value, as it conveys no idea of the +luminosity of the spectrum colours, nor of the +quantities which have to be mixed together to form +the complementaries. Such a circle is, however, +convenient as a sort of <i>memoria technica</i>, and can +be filled up according to the fancy of the observer.</p> + +<p>The following are pairs of most carefully selected +complementary colours of pigments, as adopted by +Professor Church.</p> + + +<div class="center"> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="right" rowspan="4"><span class="moustache">{</span></td><td align="center"><i>Complementaries.</i></td><td align="center"><i>Pigments.</i></td></tr> +<tr><td align="left" >Red</td><td align="left">Madder red or crimson vermilion.</td></tr> +<tr><td align="left"> and</td><td align="left"></td></tr> +<tr><td align="left">Green blue </td><td align="left">Viridian, the emerald oxide of chromium with a little cobalt.</td></tr> +<tr><td align="right" rowspan="4"><span class="moustache">{</span></td><td align="center"></td><td align="center"></td></tr> +<tr><td align="left" >Orange</td><td align="left">Cadmium yellow, of full orange hue.<span class="pagenum">[Pg 171]</span></td></tr> +<tr><td align="left"> and</td><td align="left"></td></tr> +<tr><td align="left">Greenish blue </td><td align="left">Cobalt green.</td></tr> +<tr><td align="right" rowspan="4"><span class="moustache">{</span></td><td align="center"></td><td align="center"></td></tr> +<tr><td align="left" >Orange yellow</td><td align="left">Cadmium yellow, or deep chrome.</td></tr> +<tr><td align="left"> and</td><td align="left"></td></tr> +<tr><td align="left">Turquoise </td><td align="left">Cœrulium, or cobalt blue, with a little emerald green.</td></tr> +<tr><td align="right" rowspan="4"><span class="moustache">{</span></td><td align="center"></td><td align="center"></td></tr> +<tr><td align="left" >Yellow</td><td align="left">Lemon yellow, pale chrome, or aureolin.<br></td></tr> +<tr><td align="left"> and</td><td align="left"></td></tr> +<tr><td align="left">Blue </td><td align="left">Ultramarine from lapis-lazuli.</td></tr> +<tr><td align="right" rowspan="4"><span class="moustache">{</span></td><td align="center"></td><td align="center"></td></tr> +<tr><td align="left" >Greenish yellow</td><td align="left"> Aureolin with a little viridian.<br></td></tr> +<tr><td align="left"> and</td><td align="left"></td></tr> +<tr><td align="left">Violet blue</td><td align="left">French ultramarine.</td></tr> +<tr><td align="right" rowspan="4"><span class="moustache">{</span></td><td align="center"></td><td align="center"></td></tr> +<tr><td align="left" >Green yellow</td><td align="left">Lemon yellow, with some emerald green.<br></td></tr> +<tr><td align="left"> and</td><td align="left"></td></tr> +<tr><td align="left">Violet</td><td align="left">French ultramarine with madder carmine.</td></tr> +<tr><td align="right" rowspan="4"><span class="moustache">{</span></td><td align="center"></td><td align="center"></td></tr> +<tr><td align="left" >Yellowish green</td><td align="left">Lemon yellow with much emerald green.</td></tr> +<tr><td align="left"> and</td><td align="left"></td></tr> +<tr><td align="left">Purplish violet</td><td align="left"> Madder carmine with French ultramarine.</td></tr> +<tr><td align="right" rowspan="4"><span class="moustache">{</span></td><td align="center"></td><td align="center"></td></tr> +<tr><td align="left" >Green</td><td align="left">Emerald green with lemon yellow.</td></tr> +<tr><td align="left"> and</td><td align="left"></td></tr> +<tr><td align="left">Purple</td><td align="left"> Madder carmine with French ultramarine.</td></tr> +<tr><td align="right" rowspan="4"><span class="moustache">{</span></td><td align="center"></td><td align="center"></td></tr> +<tr><td align="left" >Emerald green</td><td align="left">Emerald green alone.</td></tr> +<tr><td align="left"> and</td><td align="left"></td></tr> +<tr><td align="left">Reddish purple</td><td align="left">Madder carmine with a little French ultramarine.</td></tr> +</table></div><br> +<p><span class="pagenum">[Pg 172]</span></p> + +<p>As these pairs of pigments are complementary, +it follows that if rotated together in proper proportions, +they should make a grey which will be indistinguishable +from a grey formed by rotating +black and white sectors together. (See <a href="#CHAPTER_XV">chap. XV.</a>)</p> + +<p>It will probably happen that a good deal more of +one of the pairs of the colours is required in the disc +than of the other, and supposing that the two are +each used of the full brightness which the pigments +are capable of giving, it follows that in a diagram +where equal areas are filled with the pigments as +complementary, some means must be adopted to +give the true depth of tone to each. The mixture +of white will heighten the luminosity of either, or +the admixture of black will lower it, but often +alters the hue.</p> + +<p>One of the most beautiful methods of observing +complementary colours is by means of the polarization +of light, which we need not describe in detail. +What is known as Brücke's schistoscope is perhaps +one of the most convenient. Dove's Iceland spar +prism is also useful, when two pigments have to be +worked on to paper, so as to be complementary. +The two squares of pigmented paper are placed +side by side, and two images of each are formed. +One image of one colour can be caused to overlap +the second of the other, and if the two when +superposed appear of a grey they are complementary +<span class="pagenum"><a name="Page_173" id="Page_173">[Pg 173]</a></span> +one to the other. If too much of one +colour appears, it must be toned down till the grey +is formed. This is a very simple piece of apparatus, +and for experiments with pigments will be found to +be very handy. When the right tint of each is +secured in this manner, a further test may be made +by making the pigmented surfaces into sectors, and +rotating them together, when if the double-image +prism gives correct results, the angular aperture of +the sectors should be 180° each, to match a grey +produced by a mixture by rotation of black and +white.</p> + +<p>We have already shown how the complementaries +of the spectrum colours can be found; the question +is can we find the complementaries of pigments by +the spectrum? There is one very self-evident way. +We can place the three slits in the spectrum as +given in chapter IX., and match in intensity the +white light of the reflected beam, and note the +apertures of the slits. We must then in the +reflected beam place the pigment whose complementary +colour is required, and match its colour +with the light from the three slits, keeping, for +the sake of convenience, the white light falling on +the pigmented surface of unaltered intensity, and +again note the apertures. If we deduct the last +measures from the first, the difference of aperture +will give the complementary colour. Thus it was +<span class="pagenum">[Pg 174]</span> +found that with slits in a certain position in the +spectrum, to make white light the following apertures +in hundredths of a millimetre were required:</p> + + + +<div class="center"> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="left" rowspan="4">(1)</td> +<td align="left" rowspan="4"><span class="moustache">{</span></td><td align="left"></td><td align="right"></td></tr> +<tr><td align="left">Red </td><td align="right">165</td></tr> +<tr><td align="left">Green </td><td align="right">60</td></tr> +<tr><td align="left">Violet </td><td align="right">100</td></tr> +</table></div> + +<p>Emerald green was placed in the patch and was +matched by the light from the three slits, when it +was found that it required</p> + +<div class="center"> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="left" rowspan="4">(2)</td> +<td align="left" rowspan="4"><span class="moustache">{</span></td><td align="left"></td><td align="right"></td></tr> +<tr><td align="left">Red </td><td align="right">4</td></tr> +<tr><td align="left">Green </td><td align="right">35</td></tr> +<tr><td align="left">Violet </td><td align="right">25</td></tr> +</table></div> + +<p>Deducting one from the other we get as the +complementary colour,</p> + + +<div class="center"> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="left" rowspan="4">(3)</td> +<td align="left" rowspan="4"><span class="moustache">{</span></td><td align="left"></td><td align="right"></td></tr> +<tr><td align="left">Red </td><td align="right">125</td></tr> +<tr><td align="left">Green </td><td align="right">25</td></tr> +<tr><td align="left">Violet </td><td align="right">75</td></tr> +</table></div> + +<p>This is a complementary colour, but like the green +itself it is mixed with white light; but we can +easily deduce what is the simplest complementary +colour; for we have only to deduct the possible +white light from the second measure. Now evidently +the greatest amount of white light is when +the whole of the green is taken as forming part of +it, with the proper proportions of red and violet, +<span class="pagenum">[Pg 175]</span> +and these we can obtain by taking the proportions +of the colours in (1); therefore deduct—</p> + +<div class="center"> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="left" rowspan="4">(4)</td> +<td align="left" rowspan="4"><span class="moustache">{</span></td><td align="left"></td><td align="right"></td></tr> +<tr><td align="left">Red </td><td align="right">69 </td></tr> +<tr><td align="left">Green </td><td align="right">25 </td></tr> +<tr><td align="left">Violet </td><td align="right">41.5</td></tr> +</table></div> + +<p>and this would leave as the complementary colour +without any admixture of white—</p> +<div class="center"> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="left" rowspan="3">(5)</td> +<td align="left" rowspan="3"><span class="moustache">{</span></td><td align="left"></td><td align="right"></td></tr> +<tr><td align="left">Red </td><td align="right">56 </td></tr> +<tr><td align="left">Violet </td><td align="right">33.5</td></tr> +</table></div> + +<p>which is a purple as would be expected.</p> + +<p>Now to give the same dilution of white to the +complementary that the emerald green has, we +must take away from the emerald green all the +white mixed with it, and add that quantity to +the complementary. The white in the emerald +green can be found by treating the whole of the +red as going to form the white; we then have +from (1)—</p> + +<div class="center"> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="left" rowspan="4">(6)</td> +<td align="left" rowspan="4"><span class="moustache">{</span></td><td align="left"></td><td align="right"></td></tr> +<tr><td align="left">Red </td><td align="right">40 </td></tr> +<tr><td align="left">Green </td><td align="right">14.4</td></tr> +<tr><td align="left">Violet </td><td align="right">24 </td></tr> +</table></div> + +<p>Deducting these from (2), we find that the colour +of emerald green, less the white light, is 20·6 of +green mixed with 1 of violet. To find the proper +dilution of the complementary colour we must add +the above proportions of the three colours, and as +<span class="pagenum">[Pg 176]</span> +our final result we find the complementary colour, +of equal impurity, is a mixture of—</p> + +<div class="center"> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="left" rowspan="4">(7)</td> +<td align="left" rowspan="4"><span class="moustache">{</span></td><td align="left"></td><td align="right"></td></tr> +<tr><td align="left">Red </td><td align="right">96 </td></tr> +<tr><td align="left">Green </td><td align="right">14.4</td></tr> +<tr><td align="left">Violet </td><td align="right">57.5</td></tr> +</table></div> + +<p>The slits may be set at these apertures and a colour +patch thrown on the screen, and we shall find it of +a delicate pink. The truth of this can be seen by +using a double-image prism to view the pigmented +surface, illuminated by the same white light as that +in which it was measured, and the colour patch +on the screen by its side. The two colours may +be caused to overlap, when it will be seen that +white is produced.</p> + +<p>Another example was an orange pigment, and +this we will work out in the form of colour equation. +The same mixture gave white, viz.:</p> + +<p class="center">165 R + 60 G + 100 V = W<br> +165 R + 42 G = O<br> +∴ the complementary colour, which is<br> +W - O = 18 G + 100 V,</p> + +<p>or a dark-blue colour. In this case there was +apparently no white light reflected from the orange. +It was slightly glossy, and as polarized light was +used for the reflected beam, it was probably somewhat +quenched; but what is more probable is that +<span class="pagenum">[Pg 177]</span> +the green contains some violet as well as red, for +the reasons given in chapter XI. The reason we +have been particular in showing to what extent +complementary colours must be diluted with white +to the same proportion that the colour itself is +diluted, will be apparent if considered for a +moment. A deep brown is in reality orange, +much degraded in tone, and can be produced as a +colour patch on the screen if a bright orange pigment +be placed in the reflected beam of the colour patch, +and the light nearly shut off by the rotating sectors. +Now the same complementary colour will be found +for both, but if we were to use the bright complementary +colour which we obtained with the orange +for the brown, and endeavoured to obtain a white +with it by means of the double-image prism we +should fail, as the complementary colour would +predominate. Complementary colours can always +be formed by a mixture of only two rays, and +although the overlapping images may form white, +yet when the two are placed side by side, it often +will be found that the complementary, unless +diluted with white, is evidently too dark to be +satisfactory, but the luminosity may be increased +by adding white to it, as any amount of white may +be added to the mixture of the two rays which +form the complementary, and of course white will +still be formed with the original colour. It is thus +<span class="pagenum">[Pg 178]</span> +quite feasible to give the complementary the same +luminosity as the latter by adding white light to +it. Like the colour itself, the complementary +colour can always be expressed either by a single +ray of the spectrum, or by white light from which +a single ray is deducted. (See chapter XIII.)</p><br> +<span class="pagenum"><a name="Page_179" id="Page_179">[Pg 179]</a></span> + + + +<hr style="width: 65%;"> +<h2><a name="CHAPTER_XV" id="CHAPTER_XV"></a>CHAPTER XV.</h2> + +<blockquote><p>Persistence of Images on the Retina—The Use of Coloured Discs.</p></blockquote> + +<div class="figcenter" style="width: 300px;"> +<img src="images/i_181.jpg" width="300" height="296" alt="" title=""> +<span class="caption">Fig. 39.—Disc to cause alternate opening and closing of two Slits. +</span> +</div> + +<p>By this time we must be thoroughly convinced +that by throwing one coloured patch over another a +compound colour can be formed; our next business +is to demonstrate that the same effect can be produced +by successive images of these same colours. +Thus we can show that as a mixture of red and +blue produces purple, when the two lights are +superposed, so precisely the same purple can be +produced by allowing the same two colours to strike +the eye alternately, and in very rapid succession. +We can make a match of the beautiful purple of permanganate +of potash as before upon the screen, by +placing one adjustable slit in the red and the other +in the violet. If we place in front of the slits a disc +cut out with equal angular apertures (<a href="#Page_179">Fig. 39</a>), the +slit S₁ will be covered when the slit S₂ is open, +<span class="pagenum">[Pg 180]</span> +and <i>vice versâ</i>, and the two will never be uncovered +at the same time when the card is turning round its +centre. When this disc is caused to rotate rapidly, +we shall have first a patch formed by the light +coming through one slit, and then another formed +by that coming through the other slit, thrown on the +screen on the same place in rapid succession, and +the effect on the eye should be precisely the same +as if the disc was not there, save in the matter of +intensity. Applying this artifice experimentally to +the two slits which were used to give the colour of +permanganate, the experiment tells us that such is +the case. It would be going away from the intention +<span class="pagenum"><a name="Page_181" id="Page_181">[Pg 181]</a></span> +of this work were the physiological aspect of this +experiment dwelt upon; it need only be stated that +an impression on the retina lasts an appreciable +time, though short, and that the impression made +by the blue patch has not had time to disappear +before there is an impression made by the red +patch, and so on. As the retina retains these two +impressions together, they produce the impression +of purple.</p> + +<div class="figright" style="width: 251px;"> +<img src="images/i_182.jpg" width="251" height="252" alt="" title=""> +<span class="caption">Fig. 40.—Disc painted Blue and Red. +</span> +</div> +<p>For experiments in colour this duration of +impressions is of great value, for we can take +advantage of it to compound +the colours of +pigments together in a +very simple manner. +For instance, we can +take a circular disc +painted in sectors with +blue and red (Fig. 40), +and produce a purple by +causing it to rotate round +its centre. Small discs +of two inches in diameter may be painted +with different coloured sectors, and if a pin be +passed through the centre, a smart movement +of a finger at the periphery will cause it to +rotate sufficiently quickly to make the colours +blend. A more convenient plan for exact work +<span class="pagenum"><a name="Page_182" id="Page_182">[Pg 182]</a></span> +is, however, to have an electro-motor similar to +that which moves the rotating movable sectors +(<a href="#Page_183">Fig. 41</a>), and at the end of the spindle to fix a cap +with a screw and nut attached. The disc, perforated +<span class="pagenum"><a name="Page_183" id="Page_183">[Pg 183]</a></span> +at the centre with a clean-cut hole, can be +slipt over the screw, and fastened by the circular +nut. When the armature rotates, the disc also +rotates at the same speed, and the colours thus +blend without any exertion on the part of the +observer. Ordinary tops can also be used, but it +is somewhat fatiguing to have to wind them up +and start them afresh for each experiment. The +motor shown in the figure rotates sufficiently +rapidly, with discs of eight inches in diameter, to +blend colours. It may here be remarked that the +stronger the light in which such sectors rotate, the +quicker the rotation should be. Too slow a rotation +allows a scintillation which is destructive of accuracy +of reading. To blend some colours together +also requires more rapid rotation than with others. +The brighter the colour the more rapid it should be. +We learn from this that the diminution of the more +intense impressions on the retina is more rapid at +first than of the feebler.</p> + +<div class="figcenter" style="width: 450px;"> +<img src="images/i_183.jpg" width="450" height="276" alt="" title=""> +<span class="caption">Fig. 41.—Electro-motor with Discs attached. +</span> +</div><br> +<a name="Fig_42" id="Fig_42"></a> +<div class="figright" style="width: 150px;"> +<img src="images/i184.jpg" width="150" height="150" alt="" title=""> +<span class="caption">Fig. 42.—Method of cutting +Disc to allow an overlap of a second Disc.</span> +</div> + +<p>Very convenient discs for producing colours by +rotation of sectors may be made by the following: +vermilion (V), emerald green (E), French ultramarine +blue (U), chrome yellow (Y), lamp-black +(X), and (zinc) white (W). With these nearly every +colour can be produced, or its value derived. The +chrome yellow disc is somewhat superfluous, but is +sometimes useful. The alteration in the proportions +<span class="pagenum"><a name="Page_184" id="Page_184">[Pg 184]</a></span> +of the colours can be readily made by Clark-Maxwell's +plan. From the circumference to the centre +he cut the discs open, as at <i>ab</i> (<a href="#Fig_42">Fig. 42</a>). Any +moderate number of discs, similarly cut, may be +slipt over one another, and +only a sector of each is left +visible. It should be remarked +that this necessitates the rotating +apparatus being viewed +with a direct light, as in the +case of two or three overlapping +discs it is impossible +to keep them entirely flat, and +shades are apt to be introduced. +If we wish to produce a white, or rather a grey, +from three colours, we can take three small discs +of V, E and U, of equal diameter, and behind +them place discs of black and white, of larger +diameter, rotating the whole five on a common +centre. We shall find that by altering the proportions +of the three first we can get a grey +which can be exactly matched by a mixture of +black and white, X and W. It has already +been shown that even lamp-black reflects a certain +amount of white light, so this amount of reflected +white light has to be added to the white in +the outside sectors. In the sectors used in the +following experiments it was found that the +<span class="pagenum">[Pg 185]</span> +following proportions of the three colours were +required—</p> + + +<div class="center"> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="right">V</td><td align="right">=</td><td align="right"> 124°</td></tr> +<tr><td align="right">E</td><td align="right">=</td><td align="right"> 143°</td></tr> +<tr><td align="right">U</td><td align="right">=</td><td align="right"> <u> 93°</u></td></tr> +<tr><td align="right"></td><td align="right"></td><td align="right">360°</td></tr> +</table></div> + +<p>and to make the same grey it required</p> + + +<div class="center"> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="right">X</td><td align="right">=</td><td align="right"> 278°</td></tr> +<tr><td align="right">W</td><td align="right">=</td><td align="right"><u> 82°</u></td></tr> +<tr><td align="right"></td><td align="right"></td><td align="right">360°</td></tr> +</table></div> + +<p>Now the black reflected 3·4% of white light, so +that really the proportions of black and white were</p> + + +<div class="center"> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="right">X</td><td align="right">=</td><td align="right"> 268·6</td></tr> +<tr><td align="right">W</td><td align="right">=</td><td align="right"><u> 91·4</u></td></tr> +<tr><td align="right"></td><td align="right"></td><td align="right">360·0</td></tr> +</table></div> + +<p>These matches were made in the light emitted by +the crater of the positive pole of the electric light, +and are correct only for this light. The greys here +are dark greys, and such greys can be matched +exactly by throwing the white light in which the +comparisons were made on a white card, and reducing +the intensity by means of the rotating sectors. +We can prove whether our matches are fairly correct +from our previous measures of the luminosity +of these three colours, in comparison with that of +white. The luminosities of V, E, and U, as found +<span class="pagenum">[Pg 186]</span> +from the measures (<a href="#Page_93">pp. 93-95</a>), are 36, 30, and 4·4, +white being 100; 124 of V would have a luminosity +of (124×36)/360, or 12·4; 143 of E would have 11·92; and 93 +of U would have 1·14; which, added to either, give +a luminosity of 25·46. The luminosity of 91·4/360 of +white, which is that of the mixture of black and +white, comes to 25·39, so that we may assume our +observations have been fairly correct.</p> + +<p>The influence of the kind of light in which the +match was made is well exemplified by taking the +matched discs whilst rotating into a room illuminated +by the light from the sky, when it is seen +that the grey of the outer discs is bluish; or again, +if the matched discs be examined in gaslight, the +inner grey will be found too blue.</p> + +<p>The match of grey in this last light was found +to be</p> + + +<div class="center"> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="right">V</td><td align="right">=</td><td align="right"> 119°</td></tr> +<tr><td align="right">E</td><td align="right">=</td><td align="right"> 148°</td></tr> +<tr><td align="right">U</td><td align="right">=</td><td align="right"> <u> 93°</u></td></tr> +<tr><td align="right"></td><td align="right"></td><td align="right">360°</td></tr> +<tr><td align="right">which matched with</td></tr> +<tr><td align="right">X</td><td align="right">=</td><td align="right"> 244°</td></tr> +<tr><td align="right">W</td><td align="right">=</td><td align="right"> 116°</td></tr> +</table></div> + +<p>(In this case the black and white are the corrected +black and white.)</p> + +<p>The importance of making matches in a uniform +<span class="pagenum">[Pg 187]</span> +light is fairly demonstrated by this experiment, and +we cannot be wrong in asserting that as skylight +and sunlight and cloudlight (the last being often +a mixture of the two first), are so variable no +measures made on one day can be fairly compared +with those made on another, more especially if +the observers are different. With an emerald green, +a vermilion, an ultramarine, a white, and a black +disc any colour may be reproduced in the rotation +apparatus, the three first nearly matching what we +have already stated to be the three primary colours.</p> + +<p>It may seem curious that both black and white +may have to be mixed with the colours, to produce +a pigment colour; but a little reflection will +show how it is. For instance, suppose we want to +know the colour composition of gamboge (Y) in +terms of vermilion (V), emerald green (E), and +ultramarine blue (U). We must make a disc +painted with gamboge, and also a black and a +white disc of the same diameter, but rather larger +than the other three discs, and place them on the +spindle of the electro-motor (<a href="#Page_188">Fig. 43</a>). We shall +soon see on rotating them that no blue is required +in the inner disc, and that all that remains to do +is to use the red and the green. Mix these two, +however, in whatever proportions we may, the +mixture will never attain the same luminosity, +consequently we must darken the yellow with +<span class="pagenum"><a name="Page_188" id="Page_188">[Pg 188]</a></span> +black. Even then we shall find that, add what +black we may, the rotating red and green sectors +will always be a little less saturated with colour; +which means that on rotation they produce a +certain quantity of white light mixed with the +yellow. This we might expect, for as emerald +green, besides green and red, also contains a fair +proportion of blue, and as red, green and blue +when mixed give white, it follows that when V and +E are rotated together, a grey or subdued white +light must be mixed with the colour produced. +Turning back to Chapter XIII. we also see that as +the emerald green is expressible by a single ray of +the spectrum, mixed with white light this result +might have been foretold.</p> + +<div class="figcenter" style="width: 300px;"> +<img src="images/i_189.jpg" width="300" height="290" alt="" title=""> +<span class="caption">Fig. 43.—Arrangement to find value of Gamboge in terms of +Emerald Green and Vermilion.</span> +</div><p> + +<span class="pagenum"><a name="Page_189" id="Page_189">[Pg 189]</a></span> +</p> +<p>This necessitates adding some white to the rotating +sectors of the yellow and black, as the yellow +reflects but little white light, and finally we shall +get an absolute match, of which the final results +are</p> + +<p class="center">172 V + 188 E = 75 Y + 45 W + 240 X.</p> + +<p>This equation is full of meaning. It tells us in +the first place what we have already known, that V +and E are one or both impure colours, and that when +rotated together in the proportions indicated, they +produce at least a luminosity of white equal to 53/360 of +a white disc (as the black used reflected just 3·4% of +white light). Further, it tells us that we can obtain +the luminosity of Y, when we know the luminosities +of V and E. At page 186, the luminosities of these +colours are given as 36 and 30 respectively, white +being 100. This makes the luminosity of the +colours on the left hand of the equation 17·2 + 15·67, +or 32·87, and on the right <b>75/360</b> Y + 14·76, and consequently +the luminosity of Y = 86·9. In the +same way we can obtain any other colour in terms +of these standards.</p> + +<p>We may here show how we can obtain the +luminosity of any colour by means of the three +inner discs, and the black and white outer discs. +We have already shown that any colour may be +matched by the combination of not more than two +simple colours, after deducting white from it; and +<span class="pagenum"><a name="Page_190" id="Page_190">[Pg 190]</a></span> +from this we deduce that any coloured pigment +will form a grey with some two of the three +coloured discs, V, E, and U; and this being done +we can then calculate the luminosity. For instance, +with an orange-coloured pigment we should +proceed to make a disc of the same diameter +as that of the three above; an inspection would +show us that in this colour red predominates, and +therefore we could do without the red disc. We +should then alter the proportions of V, U, and O, +till they gave a match which was the same as that +of a grey given by the rotating black and white +sectors.</p> + +<p>In an experiment with an orange of this kind, +the following results were obtained—</p> +<div class="center"> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="right">E<br>U<br>O</td><td align="right"> 115°<br>150°<br>95°</td> +<td align="right"></td> +<td align="right" rowspan="4"><span class="moustachetp">}</span></td> +<td align="center" rowspan="4">=</td> +<td align="center" rowspan="4"><span class="moustachesm">{</span></td> +<td align="right"> W<br>X</td><td align="right"> 85°<br>275°</td></tr> +</table></div> + +<p>We can now from these deduce the luminosity +of the orange employed in this case.</p> + +<p>The luminosities of E and U, as already found, +were 30 and 4·4, whilst the black (X) reflected +3·4% of white light; we thus get the following +equations—</p> + +<p class="center">115 × 30 + 150 × 4·4 + 95 O = (85 + 3·4 × 275) 100.<br> +This gives 95 O = 9435 - (3450 + 660).<br> +O = 56. +</p> +<p><span class="pagenum"><a name="Page_191" id="Page_191">[Pg 191]</a></span> +</p> +<p>That is, the luminosity of the orange is ·56 that +of white; by direct measurement it was ·57.</p> + +<p>In a similar way the luminosity of chrome yellow +(Y) is found. In this case—</p> + +<div class="center"> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="right">E<br>U<br>O</td><td align="right"> 35<br>204<br>121</td><td align="right"></td><td align="right" rowspan="4"><span class="moustachetp">}</span></td><td align="center" rowspan="4">=</td><td align="center" rowspan="4"><span class="moustachesm">{</span></td> +<td align="right"> W<br>X</td><td align="right"> 101<br>259</td></tr> +</table></div> + + +<p>Similar equations were formed as the above.</p> + +<p class="center">35 × 30 + 204 × 4·4 + 121 Y = (101 + 3·4 × 259) 100<br> +whence Y = 77·6. +</p> + +<p>That is, the luminosity of the chrome yellow is +·78; the same as was obtained by direct measurement.</p> + +<p>In the same manner the luminosity of any colour +can be found. Thus that of a purple, or of green, +can be ascertained; of the former by using the +green disc with either the red or the blue disc, and +the latter by the red and blue disc. From this it is +apparent that we can check the luminosities derived +from other means by this plan.</p> + +<p>A taking experiment can be made with colour +discs to imitate all the colours of the spectrum in +their proper order, though diluted more or less by +white light. This can be done by rotating V, E, and +U together; but in order to get additional luminosity +in the yellow, we can use chrome yellow as well. +If a disc be made as in the figure (Fig. 44), it will on +rotating give a fair imitation of the spectrum, if it +be viewed through a slit held in front of the disc.</p><p> +<span class="pagenum"><a name="Page_192" id="Page_192">[Pg 192]</a></span> +</p> +<div class="figcenter" style="width: 300px;"> +<img src="images/i_193.jpg" width="300" height="300" alt="" title=""> +<span class="caption">Fig. 44.—Disc arranged to give approximately all the Spectrum +Colours.</span></div> + +<p>The mixture of colours by means of rotating +sectors is one which the artist cannot use for artistic +purposes, and it might seem that for him any +deductions made from this method are useless; but +it is not so. Suppose we take black lines ruled +closely together on paper, and examine the surface +from such a distance that the lines are no longer +distinguishable it will appear of a grey; and if we +take the amount of black on the paper and amount +of white, and prepare two sectors of black and +white, whose angles are in these proportions, and +rotate them alongside the ruled surface, it will be +<span class="pagenum">[Pg 193]</span> +found that the grey of one matches the grey of the +other. If instead of lines of black and white we +have them of light yellow and cobalt blue, a grey is +also produced when the surface covered by the +blue is to that covered by the yellow in correct +proportions, and may be matched by rotating +sectors containing merely black and white. Now +some artists employ stippling, filling up cross-hatching +of one colour with dots of a totally +different colour, or they place dots side by side. +When seen from the distance at which the picture +should be viewed, these various colours blend one +into another, and form a tint which is the same +as that which would be obtained by rotating these +colours together in the proportion in which they +cover the ground. Artists, however, generally mix +their pigments together on the palette, and the +resulting mixtures are often totally unlike those +which are obtained by rotating the same colours +together, a noteworthy example is that of yellow +and blue. By rotation, and when in proper proportion, +these two give a white, but when mixed +on the palette a green results. What causes this +difference? Experimental proof is always the +most satisfactory proof, so let us have recourse +to the spectrum apparatus to obtain an answer. +Let a spectrum be thrown on the screen, and in +it place a strip of paper painted with the yellow, +<span class="pagenum">[Pg 194]</span> +and then another with the blue. With the first it +will be seen that the blue rays are not reflected, +but only the green and yellow and red, taking the +spectrum as roughly made up of these four colours. +With the latter the yellow is not reflected, and +but very little red, but the blue and the green are +reflected strongly. Now we have already said that +the reflection of colour from a surface is indicative +of the colours the particles of pigments when taken +thin enough to be transparent would transmit; +hence we may take it that the yellow pigment +transmits the red, yellow, and green, and the blue +pigment scarcely anything but blue and green. +When we have a mixture of these fine particles +of pigment on paper, some will underlie the others. +But let us pay attention to what would happen if a +yellow particle were at the top, and a blue one +beneath it. White light would impinge on the yellow +particle, but only red, yellow, and green would pass +out or be reflected from it. This sifted light would +next fall on the blue particle and—as we have +seen—only blue and green can pass through or +be reflected from it; but as the yellow particle has +already deprived the white light of its blue component, +the green light alone would pass to the +paper, and be reflected either direct from the surface +of the paper, or through the particles themselves +to the eye. If the blue particle were on the top, +<span class="pagenum"><a name="Page_195" id="Page_195">[Pg 195]</a></span> +precisely the same effect would be produced; it +would only allow blue and green to pass to the +yellow particle, and as the yellow is opaque to the +blue, only green light again would pass. Similarly +if side by side the same phenomena would occur, +since the light reflected from one on to the other +would be deprived of all colour except the green. +A very pretty experimental proof of this is to place +a yellow solution of dye in front of the slit of the +colour apparatus, and having formed the yellow +colour patch to place in it a piece of paper covered +with a blue pigment: the latter becomes green. By +placing a blue solution in front of the slit, and using +a piece of yellow pigmented paper, the same result +is obtained. The artist therefore in mixing his +pigments calls into play the law of absorption, and +from his mixtures very naturally assumes that blue +and yellow make green. He makes a neutral tint +of blue, red, and yellow, and as the red cuts off the +green, this naturally follows from the above. Such +experiments as these led him to the conclusion that +red, yellow, and blue are the three primary colours, +an assumption which had he used simple spectrum +colours instead of compound colours, such as pigments, +he would not have ventured to make.</p><br> +<span class="pagenum"><a name="Page_196" id="Page_196">[Pg 196]</a></span> + + + +<hr style="width: 65%;"> +<h2><a name="CHAPTER_XVI" id="CHAPTER_XVI"></a>CHAPTER XVI.</h2> + +<blockquote><p>Contrast Colours—Measurement of Contrast Colours—Fatigue of the +Eye—After-Images.</p></blockquote> + +<div class="figright" style="width: 200px;"> +<img src="images/i197.jpg" width="200" height="178" alt="" title=""> +<span class="caption">Fig. 45.—Method of showing +Contrast Colours.</span> +</div> + +<p>There is a phenomenon in colour which must be +alluded to, and which possesses more than a passing +interest to the art world, and that is colour contrast. +Perhaps one of the best methods of showing this is +by our colour patch apparatus. If we throw the +reflected beam and the colour +patch on a square as before, +and place a rather thinner +rod in front, so that the two +shadows lie on a background +of the combined white light +and spectral colours, on passing +a slit through the spectrum, +the shadow which is +illuminated by white light will appear anything +but white. Thus if we allow yellow spectral light +to illuminate one shadow, the other will appear +<span class="pagenum"><a name="Page_197" id="Page_197">[Pg 197]</a></span> +decidedly of a blue hue; if a green ray it will be of +a ruddy hue; if a blue ray of a yellow hue; that is, +all the contrast hues will appear to the eye to tend +towards a complementary tone to the spectral light. +The kind of white light illuminating the shadow has +a marked effect on the tone, as might be expected. +The following table shows the contrast colour of the +white illuminated shadow when the white light used +was that of a candle.</p> + + +<div class="center"> +<table border="1" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="left"><span class="smcap">Spectrum Colour.</span></td><td align="left"><span class="smcap">Contrast Colours in Electric light.</span></td><td align="left"><span class="smcap">Spectrum Colour.</span></td><td align="left"> <span class="smcap">Contrast Colours in Gaslight.</span></td></tr> +<tr><td align="left">Cherry red </td><td align="left"> Green gray</td><td align="left"> Cherry red </td><td align="left"> Green gray</td></tr> +<tr><td align="left">Scarlet</td><td align="left"> Bluish green gray</td><td align="left"> Scarlet</td><td align="left"> Sap green</td></tr> +<tr><td align="left">Terra-cotta</td><td align="left"> Blue gray </td><td align="left"> Light red </td><td align="left"> Green gray</td></tr> +<tr><td align="left">Raw sienna</td><td align="left"> Light blue gray </td><td align="left"> Olive green </td><td align="left"> Pink gray</td></tr> +<tr><td align="left">Olive green</td><td align="left"> Umber</td><td align="left"> Apple green </td><td align="left"> Mauve & black</td></tr> +<tr><td align="left">Emerald green</td><td align="left"> Pinkish lavender </td><td align="left"> Emerald green</td><td align="left"> Pink terra-cotta</td></tr> +<tr><td align="left">Grass green</td><td align="left"> Light pink</td><td align="left"> Emerald green</td><td align="left"> Pink terra-cotta</td></tr> +<tr><td align="left">Bluish green</td><td align="left"> Dark pink </td><td align="left"> Bluish green </td><td align="left"> Pinker terra-cotta</td></tr> +<tr><td align="left">Signal green</td><td align="left"> Salmon </td><td align="left"> Peacock blue </td><td align="left"> Salmon</td></tr> +<tr><td align="left">Cyanine blue</td><td align="left"> Yellow ochre</td><td align="left"> Prussian blue</td><td align="left"> Reddish yellow</td></tr> +<tr><td align="left">Ultramarine</td><td align="left"> Raw sienna</td><td align="left"> Ultramarine </td><td align="left"> Raw sienna</td></tr> +<tr><td align="left">Violet blue</td><td align="left"> Brownish yellow</td><td align="left"> Violet blue </td><td align="left"> Brownish orange</td></tr> +<tr><td align="left">Blue violet </td><td align="left"> Green yellow brown</td><td align="left"> Blue violet </td><td align="left"> Brownish yellow</td></tr> +<tr><td align="left">Violet</td><td align="left"> Burnt sienna</td><td align="left"> Violet</td><td align="left"> Yellow ochre</td></tr> +</table></div> + +<p>The contrasts here shown are not so visible when +the two shadows of the rod occupy the whole of +<span class="pagenum"><a name="Page_198" id="Page_198">[Pg 198]</a></span> +the white square, but are decidedly increased by the +shadows occupying only a part of the field, the +margins being illuminated with a mixture of the +two lights. Not only are there contrasts with +coloured light and white, but the relative position +of one colour to another may alter the hue of +each to the eye. The following experiments indicate +what change can be expected in contrasted +colours. The double colour apparatus was used as +described at page 122, and a slit was placed in four +different positions in the spectrum, viz. in the red, +orange, green, and violet, to form patches, and +another slit was placed in the same four positions +in the other spectrum, and the contrasts noted.</p> + +<div class="center"> +<table border="1" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="center" colspan = "2"><span class="smcap">Original Colours.</span></td><td align="center" colspan="2"><span class="smcap">Change due to Contrast.</span></td></tr> +<tr><td align="left"> Red</td><td align="left"> Orange</td><td align="left"> Red became yellower</td><td align="left"> Orange became green grey</td></tr> +<tr><td align="left"> Red</td><td align="left"> Green</td><td align="left"> Red unaltered, but brighter</td><td align="left"> Green unaltered, but brighter</td></tr> +<tr><td align="left"> Red</td><td align="left"> Blue</td><td align="left"> Red became more orange</td><td align="left"> Blue became greener</td></tr> +<tr><td align="left"> Red</td><td align="left"> Violet</td><td align="left"> Red became orange</td><td align="left"> Violet, no marked change</td></tr> +<tr><td align="left"> Green</td><td align="left"> Orange</td><td align="left"> Green became bluer</td><td align="left"> Orange became yellower</td></tr> +<tr><td align="left"> Green</td><td align="left"> Blue</td><td align="left"> Green became olive</td><td align="left"> Blue became more violet</td></tr> +<tr><td align="left"> Green</td><td align="left"> Violet</td><td align="left"> Green became yellower</td><td align="left"> Violet became bluer</td></tr> +<tr><td align="left"> Orange</td><td align="left"> Blue</td><td align="left"> Orange became redder</td><td align="left"> Blue became bluer</td></tr> +<tr><td align="left"> Orange</td><td align="left"> Violet</td><td align="left"> Orange became greener</td><td align="left"> Violet became bluer</td></tr> +<tr><td align="left"> Violet</td><td align="left"> Blue</td><td align="left"> Hardly altered</td><td align="left"> Hardly altered</td></tr> +</table></div> +<p><span class="pagenum">[Pg 199]</span></p> + +<p>These contrasts were in most cases very marked, +as would be seen by causing the same colours to +fall on a different part of the screen, outside that +on which the comparisons were made.</p> + +<p>This phenomenon of contrast is one which is most +valuable for artistic purposes, for it gives a power +of increasing the value of the colour of pigments +which is used by the artist almost intuitively. Thus +he can heighten the tone of his orange pigment, +with which he makes a sunset sky, by placing in +juxtaposition with it some bit of blue coloured space. +The blue becomes bluer, and the orange more +orange, by this artifice. All these artifices—or +rather we should say intuitive applications of science—are +most necessary when the small range of +luminosity of colours with which he has to deal is +taken into account. For instance, in a picture of a +sun-lighted snow mountain and deep pine forests, +the utmost luminosity he can give to the former is +that of white paper when seen in the shade, which, +in comparison with what he sees, is really a mixture +of 90% of black with the light from the snow, so +that his range of luminosity is only nine-tenths of +that which occurs in nature. It is in adapting this +low scale to his picture that true genius of the +artist is seen.</p> + +<p>It might seem that these contrast colours being +only a physiological effect, could not be accurately +<span class="pagenum"><a name="Page_200" id="Page_200">[Pg 200]</a></span> +measured, but such is not the case, if a little artifice +be employed. If we use the second colour +patch apparatus side by side with the first, we can +very readily and with very close approximation +determine the contrast colours we see. Suppose by +the second apparatus we form a colour patch of say +red, and place a thin rod in the beam of this ray +and of the reflected beam, and about six inches +from it form another patch with the first apparatus, +using the three slits to make colour mixtures; by +first noting the contrast colour, and then approximating +in the second patch to what the eye perceives, +we can little by little get a fairly exact match to the +contrast colour, and can definitely note it. We now +give the results of three measures made for the contrast +colours which presented themselves to the eye +when they were caused by a red ray near the +lithium line, another near the E line in the green, +and the third near the G line in the violet.</p> + +<p>To make white light and the contrast colours, the +slits had to be of the following apertures—</p> + +<div class="center"> +<table border="1" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="left"><span class="smcap">Colour.</span></td><td align="right"><span class="smcap">Red.</span></td><td align="right"><span class="smcap">Green.</span></td><td align="right"><span class="smcap">Violet.</span></td></tr> +<tr><td align="left"> White light</td><td align="right">15·7</td><td align="right"> 6·5</td><td align="right"> 9·8</td></tr> +<tr><td align="left"> Contrast to Red</td><td align="right">13·5</td><td align="right">11·8</td><td align="right">22·5</td></tr> +<tr><td align="left"> Contrast to Green</td><td align="right">15·8</td><td align="right"> 5·1</td><td align="right"> 4·8</td></tr> +<tr><td align="left"> Contrast to Violet</td><td align="right">15·9</td><td align="right"> 7·2</td><td align="right"> 4·2</td></tr> +</table></div> + +<p>Thus to form the contrast to red took 13·5 of red, +<span class="pagenum">[Pg 201]</span> +11·8 of green, and 22·5 of violet. Now from each of +these there can be deducted the amount of white +light, which will leave only two colours mixed. +Calculating this out we find that the contrasts +are—</p> + + +<div class="center"> +<table border="1" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="right"> <span class="smcap">Contrast Colour to</span></td><td align="right"><span class="smcap">Red.</span></td><td align="right"> <span class="smcap">Green.</span></td><td align="right"> <span class="smcap">Violet.</span></td></tr> +<tr><td align="left">Red</td><td align="center">—</td><td align="center"> 3·5</td><td align="center"> 16·7</td></tr> +<tr><td align="left">Green</td><td align="center"> 15·7</td><td align="center"> 3·2</td><td align="center"> —</td></tr> +<tr><td align="left">Violet</td><td align="center"> 19·4</td><td align="center"> 9·5</td><td align="center"> —</td></tr> +</table></div> + +<p>If the contrasts were exactly complementary +colours, the proportions of the two colours left +should be the same as those of the same colours as +given, which with the original colour make white +light. It will be seen that such is not the case. +A very simple way of testing this is to form a +patch of white light with the three slits in the first +apparatus, and then to obtain the contrasts by the +other apparatus, with the same colours one after +the other that pass through the three slits. If +now we cover up the slit in the first apparatus +through which the colour whose contrast in the +second apparatus is sought passes, we may dilute +it with white light as we will, but in no case has +the writer found that an exact match to the contrast +colour can be obtained in this way. Thus, +supposing we wanted to try the experiment with +<span class="pagenum"><a name="Page_202" id="Page_202">[Pg 202]</a></span> +the same red light as that which comes through +the red slit, we should use that same light in the +second apparatus, and form the contrast colour +with the white beam, and then in the first apparatus +cover up the red slit, leaving the violet and green to +form a patch on the screen. We should then dilute +the colour of this patch with white light, and note +if it appeared the same as the contrast colour.</p> + +<p>Another phenomenon which presents itself is the +fatigue of the colour-sensation apparatus of the +eye, induced by looking at a bright object. For +instance, if we look at a crimson wafer or spot for +some time, and then turn the eye so that it rests +on a grey surface, an image of the spot will still +be seen, but as of a greenish-blue colour. This +is due to the fact that the red-seeing apparatus is +fatigued and exhausted, whilst the green and violet-seeing +machinery has not been largely exercised. +Consequently when looking at grey paper the grey +of the paper is seen in the retina at all parts as grey, +except in the small part of the retina which has got +diminished power of perceiving a red sensation; +hence a sea-green image will be seen until the +fatigue has passed away. This colour can be reproduced +with very fair accuracy by allowing only +one eye to be fatigued, and then using the other +to obtain a colour mixture corresponding to it. It +will then be found that the colour is the same as +<span class="pagenum"><a name="Page_203" id="Page_203">[Pg 203]</a></span> +the complementary colour, much diluted with white +light.</p> + +<p>To the same cause may be traced positive and +negative after-images, as they are called. If we +look at a strongly-illuminated coloured form, such +as a church window, and close the eyes, the window +will still be seen, at first of its original colour (a +positive after-image), and it will then fade and be +seen in its complementary colours (a negative after-image). +The positive image is due to the persistence +of what we may call nerve irritation, whilst +the negative image is due to the physiological +excitation of all the nerve fibrils, which ordinarily +speaking give the sensation of a very dull white +light. The previous fatigue of one set of fibrils, +however, prevents them being excited to the same +degree as the others, hence we get a complementary +image. It would be out of place to +pursue this subject further, as we have only dealt +with the physical measurement of colour-sensations, +and these are beyond it.</p><br> +<span class="pagenum">[Pg 205]</span> + + + +<hr style="width: 65%;"> +<h2>INDEX.</h2> + + +<div class="center"> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="left">Absorption by red, blue, and green glasses,</td><td align="right"><a href="#Page_53">53</a> </td></tr> +<tr><td align="left">Absorption of light in the earth's atmosphere,</td><td align="right"> <a href="#Page_67">67</a> </td></tr> +<tr><td align="left">Absorption, reference to law of,</td><td align="right"><a href="#Page_53">53</a> </td></tr> +<tr><td align="left">After-glow,</td><td align="right"><a href="#Page_74">74</a> </td></tr> +<tr><td align="left">Arc light,</td><td align="right"><a href="#Page_20">20</a> </td></tr> +<tr><td align="left">Artists and colours,</td><td align="right"> <a href="#Page_195">195</a> </td></tr> +<tr><td align="left">Balmain's paint,</td><td align="right"><a href="#Page_33">33</a> </td></tr> +<tr><td align="left">Black body,</td><td align="right"><a href="#Page_18">18</a> </td></tr> +<tr><td align="left">Blindness to green,</td><td align="right"> <a href="#Page_142">142</a> </td></tr> +<tr><td align="left">Blindness to red,</td><td align="right"><a href="#Page_79">79-142</a></td></tr> +<tr><td align="left">Bromo-iodide of silver,</td><td align="right"><a href="#Page_136">136</a> </td></tr> +<tr><td align="left">Carbon poles,</td><td align="right"><a href="#Page_20">20</a> </td></tr> +<tr><td align="left">Carmine, light reflected from,</td><td align="right"> <a href="#Page_107">107</a> </td></tr> +<tr><td align="left">" template,</td><td align="right"><a href="#Page_106">106</a> </td></tr> +<tr><td align="left">Chlorophyll, green solution of,</td><td align="right"><a href="#Page_51">51</a> </td></tr> +<tr><td align="left">Collimating lens, focal length of,</td><td align="right"><a href="#Page_22">22</a> </td></tr> +<tr><td align="left">Colour, analysis of,</td><td align="right"><a href="#Page_52">52</a> </td></tr> +<tr><td align="left">Colour-blind, red and green,</td><td align="right"><a href="#Page_79">79</a> , <a href="#Page_80">80</a> </td></tr> +<tr><td align="left">Colour-blindness,</td><td align="right"><a href="#Page_142">142-146</a>, <a href="#Page_157">157</a> , <a href="#Page_159">159</a> </td></tr> +<tr><td align="left">Colour constants,</td><td align="right"><a href="#Page_15">15</a> </td></tr> +<tr><td align="left">Colour equations, formation of,</td><td align="right"><a href="#Page_147">147</a> , <a href="#Page_148">148</a> </td></tr> +<tr><td align="left">Colour, extinction of, by white light,</td><td align="right"><a href="#Page_126">126</a> </td></tr> +<tr><td align="left">Colour mixtures,</td><td align="right"><a href="#Page_113">113</a> </td></tr> +<tr><td align="left">Colour patch apparatus,</td><td align="right"><a href="#Page_41">41-52</a> </td></tr> +<tr><td align="left">Colour sensation of the eye,</td><td align="right"><a href="#Page_202">202</a> </td></tr> +<tr><td align="left">Coloured discs, use of,</td><td align="right"><a href="#Page_189">189</a> </td></tr> +<tr><td align="left">Coloured glasses, measurement of,</td><td align="right"><a href="#Page_162">162</a> </td></tr> +<tr><td align="left">Colours, complementary of pigments,</td><td align="right"><a href="#Page_170">170-172</a> </td></tr> +<tr><td align="left">Colours, complementary of spectrum,</td><td align="right"><a href="#Page_167">167</a> </td></tr> +<tr><td align="left">Colours, how matched,</td><td align="right"><a href="#Page_156">156</a> , <a href="#Page_157">157</a> </td></tr> +<tr><td align="left">Complementary colours, measurement of,</td><td align="right"><a href="#Page_173">173-178</a> </td></tr> +<tr><td align="left">Compound colours, definition of,</td><td align="right"><a href="#Page_16">16</a> </td></tr> +<tr><td align="left">Continuous spectrum,</td><td align="right"><a href="#Page_17">17</a> </td></tr> +<tr><td align="left">Contrast colours,</td><td align="right"><a href="#Page_196">196-200</a> </td></tr> +<tr><td align="left">Diffraction gratings,</td><td align="right"><a href="#Page_23">23</a> </td></tr> +<tr><td align="left">" spectra,</td><td align="right"><a href="#Page_24">24</a> </td></tr> +<tr><td align="left">Dimness and brightness of spectrum,</td><td align="right"><a href="#Page_29">29</a> </td></tr> +<tr><td align="left">Discs, spinning,</td><td align="right"><a href="#Page_182">182</a> </td></tr> +<tr><td align="left">Dust, particles of,</td><td align="right"><a href="#Page_62">62</a> </td></tr> +<tr><td align="left">Electric light, contrast colours in,</td><td align="right"><a href="#Page_197">197</a> </td></tr> +<tr><td align="left">Electric light, crater of positive pole of,</td><td align="right"><a href="#Page_20">20</a> </td></tr> +<tr><td align="left">Emerald green, light reflected from,</td><td align="right"><a href="#Page_94">94</a> <span class="pagenum">[Pg 206]</span></td></tr> +<tr><td align="left">Equations, colour,</td><td align="right"><a href="#Page_147">147</a> </td></tr> +<tr><td align="left">Essentials of spectrum,</td><td align="right"><a href="#Page_22">22</a> </td></tr> +<tr><td align="left">Extraction of colour by white light,</td><td align="right"><a href="#Page_126">126</a> </td></tr> +<tr><td align="left">Extraction of white light by colour,</td><td align="right"><a href="#Page_131">131</a> </td></tr> +<tr><td align="left">Eye, sensitiveness of,</td><td align="right"><a href="#Page_15">15</a> </td></tr> +<tr><td align="left">Fatigue of the retina,</td><td align="right"><a href="#Page_202">202</a> </td></tr> +<tr><td align="left">Fluorescence,</td><td align="right"><a href="#Page_31">31</a> </td></tr> +<tr><td align="left">Fundamental sensations,</td><td align="right"><a href="#Page_140">140</a> </td></tr> +<tr><td align="left">Gamboge, matching,</td><td align="right"><a href="#Page_189">189</a> </td></tr> +<tr><td align="left">Glass, light from sheet of,</td><td align="right"><a href="#Page_14">14</a> </td></tr> +<tr><td align="left">Glass prisms,</td><td align="right"><a href="#Page_21">21</a> , <a href="#Page_22">22</a> </td></tr> +<tr><td align="left">Glow-worm,</td><td align="right"><a href="#Page_13">13</a> </td></tr> +<tr><td align="left">Green colour-blindness,</td><td align="right"><a href="#Page_142">142</a> </td></tr> +<tr><td align="left">Heating effect of radiation,</td><td align="right"><a href="#Page_38">38</a> </td></tr> +<tr><td align="left">Hue,</td><td align="right"><a href="#Page_15">15</a> </td></tr> +<tr><td align="left">Images, after,</td><td align="right"><a href="#Page_202">202</a> </td></tr> +<tr><td align="left">Images, persistence of, on retina,</td><td align="right"><a href="#Page_179">179</a> </td></tr> +<tr><td align="left">Impurity of simple colours,</td><td align="right"><a href="#Page_124">124</a> </td></tr> +<tr><td align="left">Indicator of sectors,</td><td align="right"><a href="#Page_48">48</a> </td></tr> +<tr><td align="left">Infra-red rays,</td><td align="right"><a href="#Page_32">32</a> </td></tr> +<tr><td align="left">" photography with,</td><td align="right"><a href="#Page_34">34</a> </td></tr> +<tr><td align="left">Insensitiveness of the yellow spot to green,</td><td align="right"><a href="#Page_118">118</a> </td></tr> +<tr><td align="left">Intensities of limelight, gaslight, and blue sky compared,</td><td align="right"><a href="#Page_110">110</a> , <a href="#Page_121">121</a> </td></tr> +<tr><td align="left">Interference,</td><td align="right"><a href="#Page_58">58</a> , <a href="#Page_59">59</a> </td></tr> +<tr><td align="left">Interference bands on soap film,</td><td align="right"><a href="#Page_60">60</a> </td></tr> +<tr><td align="left">Invisible spectrum, methods for showing existence of,</td><td align="right"><a href="#Page_32">32</a> , <a href="#Page_33">33</a> </td></tr> +<tr><td align="left">Kœnig's curves,</td><td align="right"><a href="#Page_151">151</a> </td></tr> +<tr><td align="left">Kœnig's experiments,</td><td align="right"><a href="#Page_140">140</a> </td></tr> +<tr><td align="left">Law of the scattering by fine particles,</td><td align="right"><a href="#Page_66">66</a> </td></tr> +<tr><td align="left">Light from sun, imitation of,</td><td align="right"><a href="#Page_63">63</a> </td></tr> +<tr><td align="left">Light, quality of, illumining object,</td><td align="right"><a href="#Page_14">14</a> </td></tr> +<tr><td align="left">Light scattered,</td><td align="right"><a href="#Page_62">62</a> </td></tr> +<tr><td align="left">Limelight,</td><td align="right"><a href="#Page_19">19</a> </td></tr> +<tr><td align="left">Lines in solar spectrum,</td><td align="right"><a href="#Page_26">26</a> </td></tr> +<tr><td align="left">Luminosity,</td><td align="right"><a href="#Page_13">13</a> </td></tr> +<tr><td align="left">Luminosity, addition of one to another,</td><td align="right"><a href="#Page_85">85-87</a> </td></tr> +<tr><td align="left">Luminosity of colour,</td><td align="right"><a href="#Page_16">16</a> </td></tr> +<tr><td align="left">Luminosity of pigments, methods of determining,</td><td align="right"><a href="#Page_81">81</a> , <a href="#Page_82">82</a> </td></tr> +<tr><td align="left">Luminosity of spectrum to normal-eyed and colour-blind persons,</td><td align="right"><a href="#Page_76">76-78</a> </td></tr> +<tr><td align="left">Luminosity of sun at different altitudes,</td><td align="right"><a href="#Page_69">69-71</a> </td></tr> +<tr><td align="left">Maxwell's colour-box,</td><td align="right"><a href="#Page_152">152</a> , <a href="#Page_153">153</a> </td></tr> +<tr><td align="left">Maxwell's discs,</td><td align="right"><a href="#Page_184">184-186</a> </td></tr> +<tr><td align="left">Measurement of amount of light reflected by different pigments,</td><td align="right"><a href="#Page_88">88-92</a> </td></tr> +<tr><td align="left">Metals, light reflected from,</td><td align="right"><a href="#Page_100">100</a> </td></tr> +<tr><td align="left">Mock suns, cause of change of colour in,</td><td align="right"><a href="#Page_64">64</a> </td></tr> +<tr><td align="left">Molecular physics,</td><td align="right"><a href="#Page_54">54</a> </td></tr> +<tr><td align="left">Molecular swings,</td><td align="right"><a href="#Page_136">136</a> , <a href="#Page_137">137</a> </td></tr> +<tr><td align="left">Monochromatic light,</td><td align="right"><a href="#Page_47">47</a> </td></tr> +<tr><td align="left">Negative images,</td><td align="right"><a href="#Page_203">203</a> </td></tr> +<tr><td align="left">Normal vision,</td><td align="right"><a href="#Page_77">77</a> </td></tr> +<tr><td align="left">Orange, finding luminosity of,</td><td align="right"><a href="#Page_190">190</a> </td></tr> +<tr><td align="left">Percentages of skylight, sunlight, and gaslight,</td><td align="right"><a href="#Page_110">110</a> , <a href="#Page_111">111</a> </td></tr> +<tr><td align="left">Phosphorescence,</td><td align="right"><a href="#Page_32">32</a> , <a href="#Page_56">56</a> </td></tr> +<tr><td align="left">Pigments, absorption by,</td><td align="right"><a href="#Page_57">57</a> , <a href="#Page_58">58</a> </td></tr> +<tr><td align="left">Plan of forming spectrum,</td><td align="right"><a href="#Page_21">21</a> </td></tr> +<tr><td align="left">Polished and uneven surfaces,</td><td align="right"><a href="#Page_13">13</a> </td></tr> +<tr><td align="left">Primary colours, definition of,</td><td align="right"><a href="#Page_133">133-</a> <a href="#Page_135">135</a> </td></tr> +<tr><td align="left">Prism, Iceland spar,</td><td align="right"><a href="#Page_96">96</a> <span class="pagenum">[Pg 207]</span></td></tr> +<tr><td align="left">Prismatic spectrum into wave-lengths, conversion of,</td><td align="right"><a href="#Page_28">28</a> </td></tr> +<tr><td align="left">Prisms, drawback to use of,</td><td align="right"><a href="#Page_23">23</a> </td></tr> +<tr><td align="left">Prussian blue template,</td><td align="right"><a href="#Page_107">107</a> </td></tr> +<tr><td align="left">" " light reflected from,</td><td align="right"><a href="#Page_107">107</a> </td></tr> +<tr><td align="left">Purity of colour,</td><td align="right"><a href="#Page_16">16</a> </td></tr> +<tr><td align="left">Rays, infra-red,</td><td align="right"><a href="#Page_34">34</a> </td></tr> +<tr><td align="left">Rays, photography of dark,</td><td align="right"><a href="#Page_34">34</a> </td></tr> +<tr><td align="left">Rays, ultra-violet,</td><td align="right"><a href="#Page_34">34</a> </td></tr> +<tr><td align="left">Registering tint of pigments,</td><td align="right"><a href="#Page_116">116</a> </td></tr> +<tr><td align="left">" " colours,</td><td align="right"><a href="#Page_156">156</a> </td></tr> +<tr><td align="left">Retina, persistence of images on,</td><td align="right"><a href="#Page_179">179</a> </td></tr> +<tr><td align="left">Ritter's rays,</td><td align="right"><a href="#Page_32">32</a> </td></tr> +<tr><td align="left">Rood's colour scale,</td><td align="right"><a href="#Page_26">26</a> </td></tr> +<tr><td align="left">Rotating sectors,</td><td align="right"><a href="#Page_46">46</a> </td></tr> +<tr><td align="left">Scaling of spectrum,</td><td align="right"><a href="#Page_49">49</a> </td></tr> +<tr><td align="left">Sectors, rotating,</td><td align="right"><a href="#Page_46">46</a> </td></tr> +<tr><td align="left">Simple colours, how obtained,</td><td align="right"><a href="#Page_112">112</a> , <a href="#Page_113">113</a> </td></tr> +<tr><td align="left">Slits placed in spectrum,</td><td align="right"><a href="#Page_113">113</a> </td></tr> +<tr><td align="left">Soap-bubbles,</td><td align="right"><a href="#Page_58">58</a> , <a href="#Page_59">59</a> </td></tr> +<tr><td align="left">Soap-films,</td><td align="right"><a href="#Page_59">59</a> </td></tr> +<tr><td align="left">Spectrum, absorption of,</td><td align="right"><a href="#Page_51">51</a> , <a href="#Page_52">52</a> </td></tr> +<tr><td align="left">Spectrum of sunlight,</td><td align="right"><a href="#Page_18">18</a> </td></tr> +<tr><td align="left">Sun, mock,</td><td align="right"><a href="#Page_64">64</a> </td></tr> +<tr><td align="left">Sunset clouds,</td><td align="right"><a href="#Page_68">68</a> , <a href="#Page_69">69</a> , <a href="#Page_72">72</a> , <a href="#Page_73">73</a> </td></tr> +<tr><td align="left">Sunset sky,</td><td align="right"><a href="#Page_72">72</a> , <a href="#Page_73">73</a> </td></tr> +<tr><td align="left">Thermopile, heating effects of,</td><td align="right"><a href="#Page_36">36</a> </td></tr> +<tr><td align="left">Thermopile, principle of,</td><td align="right"><a href="#Page_35">35</a> </td></tr> +<tr><td align="left">Ultramarine, light reflected from,</td><td align="right"><a href="#Page_95">95</a> </td></tr> +<tr><td align="left">Ultra-violet rays,</td><td align="right"><a href="#Page_31">31</a> </td></tr> +<tr><td align="left">Vermilion, light reflected from,</td><td align="right"><a href="#Page_93">93</a> </td></tr> +<tr><td align="left">Vibrations of rays per second,</td><td align="right"><a href="#Page_55">55</a> </td></tr> +<tr><td align="left">Violet bands, brightness of,</td><td align="right"><a href="#Page_21">21</a> </td></tr> +<tr><td align="left">Visible and invisible parts of spectrum,</td><td align="right"><a href="#Page_30">30</a> </td></tr> +<tr><td align="left">Water, particles of,</td><td align="right"><a href="#Page_62">62</a> </td></tr> +<tr><td align="left">Wave-length of lines in solar spectrum,</td><td align="right"><a href="#Page_26">26</a> </td></tr> +<tr><td align="left">White light and contrast colours,</td><td align="right"><a href="#Page_200">200-202</a> </td></tr> +<tr><td align="left">White light, extinction of by colour,</td><td align="right"><a href="#Page_131">131</a> </td></tr> +<tr><td align="left">White light, formation of by mixture of yellow and blue,</td><td align="right"><a href="#Page_125">125</a> </td></tr> +<tr><td align="left">White light, how made,</td><td align="right"><a href="#Page_114">114</a> , <a href="#Page_115">115</a> , <a href="#Page_119">119-123</a> </td></tr> +<tr><td align="left">White light, impression of,</td><td align="right"><a href="#Page_81">81</a> </td></tr> +<tr><td align="left">Yellow and blue make white,</td><td align="right"><a href="#Page_125">125</a> </td></tr> +<tr><td align="left">Yellow, chrome, luminosity of,</td><td align="right"><a href="#Page_191">191</a> </td></tr> +<tr><td align="left">Yellow spot,</td><td align="right"><a href="#Page_117">117</a> </td></tr> +<tr><td align="left">Young-Helmholtz theory,</td><td align="right"><a href="#Page_138">138</a> </td></tr> +</table></div> + + + +<p>THE END.</p><p> +<span class="pagenum">[Pg 208]</span> +</p> + + + +<p> +<span class="smcap">Richard Clay & Sons, Limited,<br> +London & Bungay.</span><br> +</p> +<p><span class="pagenum">[Pg 209]</span></p> + + + +<hr style="width: 65%;"> +<h2>PUBLICATIONS + +<br>OF THE + +<br>Society for Promoting Christian Knowledge.</h2> + + +<h3>THE ROMANCE OF SCIENCE.</h3> + +<p class='center'>A series of books which shows that science has for the masses as great +interest as, and more edification than, the romances of the day.</p> + +<p class='center'><i>Small Post 8vo, Cloth boards.</i></p> + +<blockquote><p><b>Coal, and what we get from it.</b> Expanded from the Notes of a Lecture +delivered at the London Institution. By Professor <span class="smcap">Raphael Meldola</span>, +F.R.S., F.I.C. With several Illustrations. 2<i>s.</i> 6<i>d.</i></p> + +<p><b>Colour Measurement and Mixture.</b> By Captain <span class="smcap">W. de W. Abney</span>, L.B., +R.E., F.R.S. With Numerous Illustrations. 2<i>s.</i> 6<i>d.</i></p> + +<p><b>The Making of Flowers.</b> By the Rev. Professor <span class="smcap">George Henslow</span>, M.A., +F.L.S., F.G.S. With Several Illustrations. 2<i>s.</i> 6<i>d.</i></p> + +<p><b>The Birth and Growth of Worlds.</b> A Lecture by Professor <span class="smcap">A. H. Green</span>, +M.A., F.R.S. 1<i>s.</i></p> + +<p><b>Soap-Bubbles, and the Forces which Mould Them.</b> A course of Lectures +by <span class="smcap">C. V. Boys</span>, A.R.S.M., F.R.S. With numerous diagrams. 2<i>s.</i> 6<i>d.</i></p> + +<p><b>Spinning Tops.</b> By Professor <span class="smcap">J. Perry</span>, M.E., D.Sc., F.R.S. With +numerous diagrams. 2<i>s.</i> 6<i>d.</i></p> + +<p><b>Diseases of Plants.</b> By Professor <span class="smcap">Marshall Ward</span>. With Numerous +Illustrations. 2<i>s.</i> 6<i>d.</i></p> + +<p><b>The Story of a Tinder-Box.</b> A course of Lectures by <span class="smcap">Charles Meymott +Tidy</span>, M.B., M.S., F.C.S. With Numerous Illustrations. 2<i>s.</i></p> + +<p><b>Time and Tide.</b> A Romance of the Moon. By Sir <span class="smcap">Robert S. Ball</span>, LL.D., +Royal Astronomer of Ireland. With Illustrations. 2<i>s.</i> 6<i>d.</i> +</p></blockquote> +<p><span class="pagenum">[Pg 210]</span></p> + +<br> +<h3>MANUALS OF HEALTH.</h3> + +<p class='center'><i>Fcap. 8vo, 128 pp., limp cloth, price 1s. each.</i></p> + +<blockquote><p><b>Health and Occupation.</b> By <span class="smcap">B. W. Richardson</span>, Esq., F.R.S., M.D.</p> + +<p><b>Habitation in Relation to Health (The).</b> By F. S. B. <span class="smcap">Chaumont</span>, M.D., +F.R.S.</p> + +<p><b>On Personal Care of Health.</b> By the late <span class="smcap">E. A. Parkes</span>, M.D., F.R.S.</p> + +<p><b>Water, Air, and Disinfectant.</b> By <span class="smcap">W. Noel Hartley</span>, Esq., King's +College. +</p></blockquote> + +<br> +<h3>MANUALS OF ELEMENTARY SCIENCE.</h3> + +<p class='center'><i>Fcap. 8vo, 128 pp., with Illustrations, limp cloth, 1s. each.</i></p> + +<blockquote><p><b>Physiology.</b> By <span class="smcap">F. le Gros Clarke</span>, F.R.S., St. Thomas's Hospital.</p> + +<p><b>Geology.</b> By the Rev. <span class="smcap">T. G. Bonney</span>, M.A., F.G.S., Fellow and late +Tutor of St. John's College, Cambridge.</p> + +<p><b>Chemistry.</b> By <span class="smcap">Albert J. Bernays</span>.</p> + +<p><b>Astronomy.</b> By <span class="smcap">W. H. M. Christie</span>, M.A., the Royal Observatory, +Greenwich.</p> + +<p><b>Botany.</b> By <span class="smcap">Robert Bentley</span>, Professor of Botany in King's College, +London.</p> + +<p><b>Zoology.</b> By <span class="smcap">Alfred Newton</span>, M.A., F.R.S., Professor of Zoology and +Comparative Anatomy in the University of Cambridge.</p> + +<p><b>Matter and Motion.</b> By the late <span class="smcap">J. Clerk Maxwell</span>, M.A., Trinity +College, Cambridge.</p> + +<p><b>Spectroscope and its Work (The).</b> By the late <span class="smcap">Richard A. Proctor</span>.</p> + +<p><b>Crystallography.</b> By <span class="smcap">Henry Palin Gurney</span>, M.A., Clare College, +Cambridge.</p> + +<p><b>Electricity.</b> By the late Professor <span class="smcap">Fleeming Jenkin</span>.</p></blockquote> +<p><span class="pagenum">[Pg 211]</span></p> + +<br> +<h3>The Fathers for English Readers.</h3> + +<p class='center'><i>A series of Monograms on the Chief Fathers of the Church, the Fathers +selected being centres of influence at important periods of Church History +and in important spheres of action.</i></p> + +<p class='center'>Fcap. 8vo, cloth, boards, 2s. each.</p> + +<p> +<span style="margin-left: 2em;"><i>Leo the Great.</i></span><br> +<span style="margin-left: 4em;">By the Rev. <span class="smcap">Charles Gore</span>, M.A.</span><br> +<br> +<span style="margin-left: 2em;"><i>Gregory the Great.</i> </span><br> +<span style="margin-left: 4em;">By the Rev. <span class="smcap">J. Barmby</span>, B.D.</span><br> +<br> +<span style="margin-left: 2em;"><i>Saint Ambrose</i>: his Life, Times, and Teaching. </span><br> +<span style="margin-left: 4em;">By the Rev. <span class="smcap">Robinson Thornton</span>, D.D.</span><br> +<br> +<span style="margin-left: 2em;"><i>Saint Athanasius</i>: his Life and Times.</span><br> +<span style="margin-left: 4em;">By the Rev. <span class="smcap">R. Wheler Bush</span>. (2<i>s.</i> 6<i>d.</i>)</span><br> +<br> +<span style="margin-left: 2em;"><i>Saint Augustine.</i> </span><br> +<span style="margin-left: 4em;">By the Rev. <span class="smcap">E. L. Cutts</span>, B.A.</span><br> +<br> +<span style="margin-left: 2em;"><i>Saint Basil the Great.</i> </span><br> +<span style="margin-left: 4em;">By the Rev. <i>Richard T. Smith</i>, B.D.</span><br> +<br> +<span style="margin-left: 2em;"><i>Saint Bernard</i>: Abbot of Clairvaux, <span class="smcap">A.D.</span> 1091-1153.</span><br> +<span style="margin-left: 4em;"> By the Rev. <span class="smcap">S. J. Eales</span>, M.A., D.C.L. (2<i>s.</i> 6<i>d.</i>)</span><br> +<br> +<span style="margin-left: 2em;"><i>Saint Hilary of Poitiers, and Saint Martin of Tours.</i> </span><br> +<span style="margin-left: 4em;">By the Rev. <span class="smcap">J. Gibson Cazenove</span>, D.D.</span><br> +<br> +<span style="margin-left: 2em;"><i>Saint Jerome.</i> </span><br> +<span style="margin-left: 4em;">By the Rev. <span class="smcap">Edward L. Cutts</span>, B.A.</span><br> +<br> +<span style="margin-left: 2em;"><i>Saint John of Damascus.</i> </span><br> +<span style="margin-left: 4em;">By the Rev. <span class="smcap">J. H. Lupton</span>, M.A.</span><br> +<br> +<span style="margin-left: 2em;"><i>Saint Patrick</i>: his Life and Teaching. </span><br> +<span style="margin-left: 4em;">By the Rev. <span class="smcap">E. J. Newell</span>, M.A. (2<i>s.</i> 6<i>d.</i>)</span><br> +<br> +<span style="margin-left: 2em;"><i>Synesius of Cyrene</i>, Philosopher and Bishop. </span><br> +<span style="margin-left: 4em;">By <span class="smcap">Alice Gardner</span>.</span><br> +<br> +<span style="margin-left: 2em;"><i>The Apostolic Fathers.</i> </span><br> +<span style="margin-left: 4em;">By the Rev. <span class="smcap">H. S. Holland</span>.</span><br> +<br> +<span style="margin-left: 2em;"><i>The Defenders of the Faith</i>; </span><br> +<span style="margin-left: 2em;">or, The Christian Apologists of the Second and Third Centuries. </span><br> +<span style="margin-left: 4em;">By the Rev. <span class="smcap">F. Watson</span>, M.A.</span><br> +<br> +<span style="margin-left: 2em;"><i>The Venerable Bede.</i> </span><br> +<span style="margin-left: 4em;">By the Rev. <span class="smcap">G. F. Browne</span>.</span><br> +</p> +<p><span class="pagenum">[Pg 212]</span></p> + +<br> +<h3>MISCELLANEOUS PUBLICATIONS.</h3> +<div class="center"> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="left"></td><td align="left"></td><td align="left"> <i>s.</i> <i>d. </i></td></tr> +<tr><td align="left"><i>Animal Creation (The).</i> A popular Introduction to Zoology. By the late <span class="smcap">Thomas Rymer Jones</span>, F.R.S. With 488 Woodcuts. Post 8vo.</td><td align="left"><i>Cloth boards</i> </td><td align="right">7 6</td></tr> +<tr><td align="left"><i>Beauty in Common Things.</i> Illustrated by 12 Drawings from Nature, by Mrs. J. W. Whymper, and printed in Colours, with descriptions by the Author of "Life Underground," &c. 4to.</td><td align="left"><i>Cloth boards</i> </td><td align="right">10 6</td></tr> +<tr><td align="left"><i>Birds' Nests and Eggs.</i> With 22 coloured plates of Eggs. Square 16mo.</td><td align="left"><i>Cloth boards</i> </td><td align="right">3 0</td></tr> +<tr><td align="left"><i>British Birds in their Haunts.</i> By the late Rev. <span class="smcap">C. A. Johns</span>, B.A., F.L.S. With 190 engravings by Wolf and Whymper. Post 8vo.</td><td align="left"><i>Cloth boards</i> </td><td align="right">6 0</td></tr> +<tr><td align="left"><i>Evenings at the Microscope</i>; or, Researches among the Minuter Organs and Forms of Animal Life. By <span class="smcap">Philip H. Gosse</span>, F.R.S. With 112 woodcuts. Post 8vo.</td><td align="left"><i>Cloth boards</i> </td><td align="right">4 0</td></tr> +<tr><td align="left"><i>Fern Portfolio (The).</i> By <span class="smcap">Francis G. Heath</span>, Author of "Where to find Ferns," &c. With 15 plates, elaborately drawn life-size, exquisitely coloured from Nature, and accompanied with descriptive text.</td><td align="left"><i>Cloth boards</i> </td><td align="right">8 0</td></tr> +<tr><td align="left"><i>Fishes, Natural History of British</i>: their Structure, Economic Uses, and Capture by Net and Rod. By the late <span class="smcap">Frank Buckland</span>. With numerous illustrations. Crown 8vo.</td><td align="left"><i>Cloth boards</i> </td><td align="right">5 0</td></tr> +<tr><td align="left"><i>Flowers of the Field.</i> By the late Rev. C. A. <span class="smcap">Johns</span>, B.A., F.L.S. With numerous woodcuts. Post 8vo.</td><td align="left"><i>Cloth boards</i> </td><td align="right">5 0<span class="pagenum">[Pg 213]</span></td></tr> +<tr><td align="left"><i>Forest Trees (The) of Great Britain.</i> By the late Rev. <span class="smcap">C. A. Johns</span>, B.A., F.L.S. With 150 woodcuts. Post 8vo. </td><td align="left"><i>Cloth boards</i> </td><td align="right">5 0</td></tr> +<tr><td align="left"><i>Freaks and Marvels of Plant Life</i>; or, Curiosities of Vegetation. By <span class="smcap">M. C. Cooke</span>, M.A., LL.D. With numerous illustrations. Post 8vo.</td><td align="left"><i>Cloth boards</i> </td><td align="right">6 0</td></tr> +<tr><td align="left"><i>Man and his Handiwork.</i> By the late Rev. J. G. <span class="smcap">Wood</span>, Author of "Lane and Field," &c. With about 500 illustrations. Large Post 8vo.</td><td align="left"><i>Cloth boards</i> </td><td align="right">10 6</td></tr> +<tr><td align="left"><i>Natural History of the Bible (The).</i> By the Rev. <span class="smcap">Canon Tristram</span>, Author of "The Land of Israel," &c. With numerous illustrations. Crown 8vo.</td><td align="left"><i>Cloth boards</i> </td><td align="right">5 0</td></tr> +<tr><td align="left"><i>Nature and her Servants</i>; or, Sketches of the Animal Kingdom. By the Rev. <span class="smcap">Theodore Wood</span>. With numerous woodcuts. Large Post 8vo.</td><td align="left"><i>Cloth boards</i> </td><td align="right">5 0</td></tr> +<tr><td align="left"><i>Ocean (The).</i> By <span class="smcap">Philip Henry Gosse</span>, F.R.S., Author of "Evenings at the Microscope." With 51 illustrations and woodcuts. Post 8vo.</td><td align="left"><i>Cloth boards</i> </td><td align="right">3 0</td></tr> +<tr><td align="left"><i>Our Bird Allies.</i> By the Rev. <span class="smcap">Theodore Wood</span>. With numerous illustrations. Fcap. 8vo.</td><td align="left"><i>Cloth boards</i> </td><td align="right">2 6</td></tr> +<tr><td align="left"><i>Our Insect Allies.</i> By the Rev. <span class="smcap">Theodore Wood</span>. With numerous illustrations. Fcap. 8vo.</td><td align="left"><i>Cloth boards</i> </td><td align="right">2 6</td></tr> +<tr><td align="left"><i>Our Insect Enemies.</i> By the Rev. <span class="smcap">Theodore Wood</span>. With numerous illustrations. Fcap. 8vo.</td><td align="left"><i>Cloth boards</i> </td><td align="right">2 6</td></tr> +<tr><td align="left"><i>Our Island Continent.</i> A Naturalist's Holiday in Australia. By <span class="smcap">J. E. Taylor</span>, F.L.S., F.G.S. With Map. Fcap. 8vo. </td><td align="left"><i>Cloth boards</i> </td><td align="right">2 6 <span class="pagenum">[Pg 214]</span></td></tr> +<tr><td align="left"><i>Our Native Songsters.</i> By <span class="smcap">Anne Pratt</span>, Author of "Wild Flowers." With 72 coloured plates. 16mo.</td><td align="left"><i>Cloth boards</i> </td><td align="right">6 0</td></tr> +<tr><td align="left"><i>Selborne (The Natural History of).</i> By the Rev. <span class="smcap">Gilbert White</span>. With Frontispiece, Map, and 50 woodcuts. Post 8vo.</td><td align="left"><i>Cloth boards</i> </td><td align="right">2 6</td></tr> +<tr><td align="left"><i>Toilers in the Sea.</i> By <span class="smcap">M. C. Cooke</span>, M.A., LL.D. Post 8vo. With numerous illustrations. </td><td align="left"><i>Cloth boards</i> </td><td align="right">5 0</td></tr> +<tr><td align="left"><i>Wayside Sketches.</i> By <span class="smcap">F. Edward Hulme</span>, F.L.S., F.S.A. With numerous illustrations. Crown 8vo.</td><td align="left"><i>Cloth boards</i> </td><td align="right">5 0</td></tr> +<tr><td align="left"><i>Where to find Ferns.</i> By <span class="smcap">Francis G. Heath</span>, Author of "The Fern Portfolio," &c. With numerous illustrations. Fcap. 8vo. </td><td align="left"><i>Cloth boards</i> </td><td align="right">1 6</td></tr> +<tr><td align="left"><i>Wild Flowers.</i> By <span class="smcap">Anne Pratt</span>, Author of "Our Native Songsters," &c. With 192 coloured plates. In two volumes. 16mo. </td><td align="left"><i>Cloth boards</i></td><td align="right">12 0</td></tr> +</table></div><br> +<hr style="width: 45%;"> +<p class='center'>LONDON:</p> + +<p class='center'> +<span class="smcap">Northumberland Avenue, Charing Cross</span>, W.C.;<br> +43, <span class="smcap">Queen Victoria Street</span>, E.C.<br> +BRIGHTON: 135, <span class="smcap">North Street.</span><br> +</p> +<p><span class="pagenum">[Pg 215]</span> + +<h2>Transcribers Note</h2> +<p>On Page 162 the equation :</p> +<p class="center">∴ <i>Z</i> + <i>x´X´</i> + μ´<i>W</i> = ɑ<i>wW</i><br> +<i>Z</i> = (ɑ<i>w</i> - μ´)<i>W</i> - <i>x´X´</i> +</p> +<p>is printed as:</p> +<p class="center">∴ <i>Z</i> + <i>x₁X´</i> + μ´<i>W</i> = ɑ<i>wW</i><br> +<i>Z</i> = (ɑ<i>w</i> - μ´)<i>W</i> - <i>x´X´</i> +</p> + + + + + + + + +<pre> + + + + + +End of Project Gutenberg's Colour Measurement and Mixture, by W. de W. 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