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diff --git a/old/14000-h/14000-h.htm b/old/14000-h/14000-h.htm new file mode 100644 index 0000000..24b0aee --- /dev/null +++ b/old/14000-h/14000-h.htm @@ -0,0 +1,8200 @@ +<?xml version="1.0" encoding="utf-8"?> +<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" + "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> +<html xmlns="http://www.w3.org/1999/xhtml"> +<head> +<meta name="generator" content= +"HTML Tidy for Windows (vers 1st August 2004), see www.w3.org" /> +<title>The Project Gutenberg eBook of Six Lectures On Light, by +John Tyndall.</title> + +<style type="text/css"> +/*<![CDATA[ XML blockout */ +<!-- + body>p { margin-top: .75em; + text-align: justify; + text-indent: .75em; + margin-bottom: .75em; + } + + h1,h2,h3,h4,h5,h6 { + text-align: center; /* all headings centered */ + clear: both; + } + hr { width: 33%; + margin-top: 2em; + margin-bottom: 2em; + margin-left: auto; + margin-right: auto; + } + body{margin-left: 10%; + margin-right: 10%; + } + + table {margin-left: auto; margin-right: auto;} + + .linenum {position: absolute; top: auto; left: 4%;} + .pagenum {position: absolute; right: 92%; font-size: smaller; text-align: right;} /* page numbers */ + .sidenote {width: 20%; padding-bottom: .5em; padding-top: .5em; + padding-left: .5em; padding-right: .5em; margin-left: 1em; + float: right; clear: right; margin-top: 1em; + font-size: smaller; background: #eeeeee; border: dashed 1px;} + .blockquot {margin-left: 10%; margin-right: 10%; font-size: 0.9em;} + + .bb {border-bottom: solid 2px;} + .bl {border-left: solid 2px;} + .bt {border-top: solid 2px;} + .br {border-right: solid 2px;} + .bbox {border: solid 2px;} + + .center {text-align: center;} + + .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;} + + .footnotes {border: dashed 1px;} + .footnote {margin-left: 10%; margin-right: 10%; font-size: 0.9em;} + .footnote .label {position: absolute; right: 84%; text-align: right;} + .fnanchor {vertical-align: super; font-size: .7em; text-decoration: none;} + + .poem {margin-left:10%; margin-right:10%; text-align: left;} + .poem br {display: none;} + .poem .stanza {margin: 1em 0em 1em 0em;} + .poem span {display: block; margin: 0; padding-left: 3em; text-indent: -3em;} + .poem span.i2 {display: block; margin-left: 2em;} + .poem span.i4 {display: block; margin-left: 4em;} + + // --> + /* XML end ]]>*/ +</style> +</head> +<body> + + +<pre> + +The Project Gutenberg EBook of Six Lectures on Light, by John Tyndall + +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: Six Lectures on Light + Delivered In The United States In 1872-1873 + +Author: John Tyndall + +Release Date: November 10, 2004 [EBook #14000] + +Language: English + +Character set encoding: ISO-8859-1 + +*** START OF THIS PROJECT GUTENBERG EBOOK SIX LECTURES ON LIGHT *** + + + + +Produced by Clare Boothby, Stephen Schulze and the PG Online +Distributed Proofreading Team. + + + + + + +</pre> + +<h1>SIX LECTURES ON LIGHT</h1> +<h4>DELIVERED IN THE UNITED STATES</h4> +<h5>IN</h5> +<h4>1872-1873</h4> +<h3>BY</h3> +<h2>JOHN TYNDALL, D.C.L., LL,D., F.R.S.</h2> +<p class="center">LATE PROFESSOR OF NATURAL PHILOSOPHY IN THE ROYAL +INSTITUTION OF GREAT BRITAIN<br /> +<br /> +<br /></p> +<div class="figcenter" style="width: 505px;"><img src= +"images/frontispiece.jpg" width="505" height="659" alt= +"Sir Thomas Laurence PRA Pinx Henry Adlarc. Sc." title= +"Sir Thomas Laurence PRA Pinx Henry Adlarc. Sc." /></div> +<div class="figcenter" style="width: 420px;"><img src= +"images/sig.png" width="420" height="105" alt= +"(Signature) Thomas Young" title="" /></div> +<p class="center">London: Longmans & Co.</p> +<p class="center"><i>SIXTH IMPRESSION</i></p> +<p class="center">LONGMANS, GREEN, AND CO.</p> +<p class="center">39 PATERNOSTER ROW, LONDON</p> +<p class="center">NEW YORK AND BOMBAY</p> +<p class="center">1906</p> +<h3>PREFACE TO THE FOURTH EDITION.</h3> +<p>In these Lectures I have sought to render clear a difficult but +profoundly interesting subject. My aim has been not only to +describe and illustrate in a familiar manner the principal laws and +phenomena of light, but to point out the origin, and show the +application, of the theoretic conceptions which underlie and unite +the whole, and without which no real interpretation is +possible.</p> +<p>The Lectures, as stated on the title-page, were delivered in the +United States in 1872-3. I still retain a vivid and grateful +remembrance of the cordiality with which they were received.</p> +<p>My scope and object are briefly indicated in the 'Summary and +Conclusion,' which, as recommended in a former edition, might be, +not unfitly, read as an introduction to the volume.</p> +<p>J.T.</p> +<p style="text-align: right;">ALP LUSGEN: <i>October</i> 1885.</p> +<hr style="width: 65%;" /> +<h2><a name="CONTENTS" id="CONTENTS"></a>CONTENTS.</h2> +<div style="margin-left: 20%; margin-right: 20%"> +<p><a href="#LECTURE_I"><b>LECTURE I.</b></a></p> +<div style="font-size: smaller;"> +<ul> +<li>Introductory</li> +<li>Uses of Experiment</li> +<li>Early Scientific Notions</li> +<li>Sciences of Observation</li> +<li>Knowledge of the Ancients regarding Light</li> +<li>Defects of the Eye</li> +<li>Our Instruments</li> +<li>Rectilineal Propagation of Light</li> +<li>Law of Incidence and Reflection</li> +<li>Sterility of the Middle Ages</li> +<li>Refraction</li> +<li>Discovery of Snell</li> +<li>Partial and Total Reflection</li> +<li>Velocity of Light</li> +<li>Roemer, Bradley, Foucault, and Fizeau</li> +<li>Principle of Least Action</li> +<li>Descartes and the Rainbow</li> +<li>Newton's Experiments on the Composition of Solar Light</li> +<li>His Mistake regarding Achromatism</li> +<li>Synthesis of White Light</li> +<li>Yellow and Blue Lights produce White by their Mixture</li> +<li>Colours of Natural Bodies</li> +<li>Absorption</li> +<li>Mixture of Pigments contrasted with Mixture of Lights</li> +</ul> +</div> +<p><a href="#LECTURE_II"><b>LECTURE II.</b></a></p> +<div style="font-size: smaller;"> +<ul> +<li>Origin of Physical Theories</li> +<li>Scope of the Imagination</li> +<li>Newton and the Emission Theory</li> +<li>Verification of Physical Theories</li> +<li>The Luminiferous Ether</li> +<li>Wave-theory of Light</li> +<li>Thomas Young</li> +<li>Fresnel and Arago</li> +<li>Conception of Wave-motion</li> +<li>Interference of Waves</li> +<li>Constitution of Sound-waves</li> +<li>Analogies of Sound and Light</li> +<li>Illustrations of Wave-motion</li> +<li>Interference of Sound Waves</li> +<li>Optical Illustrations</li> +<li>Pitch and Colour</li> +<li>Lengths of the Waves of Light and Rates of Vibration of +the</li> +<li>Ether-particles</li> +<li>Interference of Light</li> +<li>Phenomena which first suggested the Undulatory Theory</li> +<li>Boyle and Hooke</li> +<li>The Colours of thin Plates</li> +<li>The Soap-bubble</li> +<li>Newton's Rings</li> +<li>Theory of 'Fits'</li> +<li>Its Explanation of the Rings</li> +<li>Overthrow of the Theory</li> +<li>Diffraction of Light</li> +<li>Colours produced by Diffraction</li> +<li>Colours of Mother-of-Pearl.</li> +</ul> +</div> +<p><a href="#LECTURE_III"><b>LECTURE III.</b></a></p> +<div style="font-size: smaller;"> +<ul> +<li>Relation of Theories to Experience</li> +<li>Origin of the Notion of the Attraction of Gravitation</li> +<li>Notion of Polarity, how generated</li> +<li>Atomic Polarity</li> +<li>Structural Arrangements due to Polarity</li> +<li>Architecture of Crystals considered as an Introduction to +their</li> +<li>Action upon Light</li> +<li>Notion of Atomic Polarity applied to Crystalline Structure</li> +<li>Experimental Illustrations</li> +<li>Crystallization of Water</li> +<li>Expansion by Heat and by Cold</li> +<li>Deportment of Water considered and explained</li> +<li>Bearings of Crystallization on Optical Phenomena</li> +<li>Refraction</li> +<li>Double Refraction</li> +<li>Polarization</li> +<li>Action of Tourmaline</li> +<li>Character of the Beams emergent from Iceland Spar</li> +<li>Polarization by ordinary Refraction and Reflection</li> +<li>Depolarization.</li> +</ul> +</div> +<p><a href="#LECTURE_IV"><b>LECTURE IV.</b></a></p> +<div style="font-size: smaller;"> +<ul> +<li>Chromatic Phenomena produced by Crystals in Polarized +Light</li> +<li>The Nicol Prism</li> +<li>Polarizer and Analyzer</li> +<li>Action of Thick and Thin Plates of Selenite</li> +<li>Colours dependent on Thickness</li> +<li>Resolution of Polarized Beam into two others by the +Selenite</li> +<li>One of them more retarded than the other</li> +<li>Recompounding of the two Systems of Waves by the Analyzer</li> +<li>Interference thus rendered possible</li> +<li>Consequent Production of Colours</li> +<li>Action of Bodies mechanically strained or pressed</li> +<li>Action of Sonorous Vibrations</li> +<li>Action of Glass strained or pressed by Heat</li> +<li>Circular Polarization</li> +<li>Chromatic Phenomena produced by Quartz</li> +<li>The Magnetization of Light</li> +<li>Rings surrounding the Axes of Crystals</li> +<li>Biaxal and Uniaxal Crystals</li> +<li>Grasp of the Undulatory Theory</li> +<li>The Colour and Polarization of Sky-light</li> +<li>Generation of Artificial Skies.</li> +</ul> +</div> +<p><a href="#LECTURE_V"><b>LECTURE V.</b></a></p> +<div style="font-size: smaller;"> +<ul> +<li>Range of Vision not commensurate with Range of Radiation</li> +<li>The Ultra-violet Rays</li> +<li>Fluorescence</li> +<li>The rendering of invisible Rays visible</li> +<li>Vision not the only Sense appealed to by the Solar and Electric +Beam</li> +<li>Heat of Beam</li> +<li>Combustion by Total Beam at the Foci of Mirrors and Lenses</li> +<li>Combustion through Ice-lens</li> +<li>Ignition of Diamond</li> +<li>Search for the Rays here effective</li> +<li>Sir William Herschel's Discovery of dark Solar Rays</li> +<li>Invisible Rays the Basis of the Visible</li> +<li>Detachment by a Ray-filter of the Invisible Rays from the +Visible</li> +<li>Combustion at Dark Foci</li> +<li>Conversion of Heat-rays into Light-rays</li> +<li>Calorescence</li> +<li>Part played in Nature by Dark Rays</li> +<li>Identity of Light and Radiant Heat</li> +<li>Invisible Images</li> +<li>Reflection, Refraction, Plane Polarization, Depolarization, +Circular Polarization, Double Refraction, and Magnetization of +Radiant Heat</li> +</ul> +</div> +<p><a href="#LECTURE_VI"><b>LECTURE VI.</b></a></p> +<div style="font-size: smaller;"> +<ul> +<li>Principles of Spectrum Analysis</li> +<li>Prismatic Analysis of the Light of Incandescent Vapours</li> +<li>Discontinuous Spectra</li> +<li>Spectrum Bands proved by Bunsen and Kirchhoff to be +characteristic of the Vapour</li> +<li>Discovery of Rubidium, Cæsium, and Thallium</li> +<li>Relation of Emission to Absorption</li> +<li>The Lines of Fraunhofer</li> +<li>Their Explanation by Kirchhoff</li> +<li>Solar Chemistry involved in this Explanation</li> +<li>Foucault's Experiment</li> +<li>Principles of Absorption</li> +<li>Analogy of Sound and Light</li> +<li>Experimental Demonstration of this Analogy</li> +<li>Recent Applications of the Spectroscope</li> +<li>Summary and Conclusion</li> +</ul> +</div> +<p><a href="#APPENDIX"><b>APPENDIX.</b></a></p> +<div style="margin-left: 2em;"> +<p><a href="#ON_THE_SPECTRA_OF_POLARIZED_LIGHT">On the Spectra of +Polarized Light</a></p> +<p><a href="#MEASUREMENT_OF_THE_WAVES_OF_LIGHT">Measurement of the +Waves of Light</a></p> +</div> +<p><a href="#INDEX"><b>INDEX.</b></a></p> +</div> +<div><a name="Page_1" id="Page_1"></a><span class="pagenum">[Pg +1]</span></div> +<hr style="width: 65%;" /> +<h1>ON LIGHT</h1> +<h2><a name="LECTURE_I" id="LECTURE_I"></a>LECTURE I.</h2> +<table border="0" cellpadding="0" cellspacing="0" summary=""> +<tr> +<td> +<div style="font-size: smaller;"> +<ul style="list-style: none;"> +<li>INTRODUCTORY</li> +<li>USES OF EXPERIMENT</li> +<li>EARLY SCIENTIFIC NOTIONS</li> +<li>SCIENCES OF OBSERVATION</li> +<li>KNOWLEDGE OF THE ANCIENTS REGARDING LIGHT</li> +<li>DEFECTS OF THE EYE</li> +<li>OUR INSTRUMENTS</li> +<li>RECTILINEAL PROPAGATION OF LIGHT</li> +<li>LAW OF INCIDENCE AND REFLECTION</li> +<li>STERILITY OF THE MIDDLE AGES</li> +<li>REFRACTION</li> +<li>DISCOVERY OF SNELL</li> +<li>PARTIAL AND TOTAL REFLECTION</li> +<li>VELOCITY OF LIGHT</li> +<li>ROEMER, BRADLEY, FOUCAULT, AND FIZEAU</li> +<li>PRINCIPLE OF LEAST ACTION</li> +<li>DESCARTES AND THE RAINBOW</li> +<li>NEWTON'S EXPERIMENTS ON THE COMPOSITION OF SOLAR LIGHT</li> +<li>HIS MISTAKE AS REGARDS ACHROMATISM</li> +<li>SYNTHESIS OF WHITE LIGHT</li> +<li>YELLOW AND BLUE LIGHTS PRODUCE WHITE BY THEIR MIXTURE</li> +<li>COLOURS OF NATURAL BODIES</li> +<li>ABSORPTION</li> +<li>MIXTURE OF PIGMENTS CONTRASTED WITH MIXTURE OF LIGHTS.</li> +</ul> +</div> +</td> +</tr> +</table> +<h3>§ 1. <i>Introduction</i>.</h3> +<p>Some twelve years ago I published, in England, a little book +entitled the 'Glaciers of the Alps,' and, a couple of years +subsequently, a second book, entitled 'Heat a Mode of Motion.' +These volumes were followed by others, written with equal +plainness, and with a similar aim, that aim being to develop and +deepen sympathy between science and the world outside of science. I +agreed with thoughtful men<a name="FNanchor_1_1" id= +"FNanchor_1_1"></a><a href="#Footnote_1_1" class="fnanchor">[1]</a> +who deemed it good for neither world to be isolated from the other, +<a name="Page_2" id="Page_2"></a><span class="pagenum">[Pg +2]</span>or unsympathetic towards the other, and, to lessen this +isolation, at least in one department of science, I swerved, for a +time, from those original researches which have been the real +pursuit and pleasure of my life.</p> +<p>The works here referred to were, for the most part, republished +by the Messrs. Appleton of New York,<a name="FNanchor_2_2" id= +"FNanchor_2_2"></a><a href="#Footnote_2_2" class="fnanchor">[2]</a> +under the auspices of a man who is untiring in his efforts to +diffuse sound scientific knowledge among the people of the United +States; whose energy, ability, and single-mindedness, in the +prosecution of an arduous task, have won for him the sympathy and +support of many of us in 'the old country.' I allude to Professor +Youmans. Quite as rapidly as in England, the aim of these works was +understood and appreciated in the United States, and they brought +me from this side of the Atlantic innumerable evidences of +good-will. Year after year invitations reached me<a name= +"FNanchor_3_3" id="FNanchor_3_3"></a><a href="#Footnote_3_3" class= +"fnanchor">[3]</a> to visit America, and last year (1871) I was +honoured with a request so cordial, signed by five-and-twenty +names, so distinguished in science, in literature, and in +administrative position, that I at once resolved to respond to it +by braving not only the disquieting oscillations of the Atlantic, +but the far more disquieting ordeal of appearing in person before +the people of the United States.</p> +<p>This invitation, conveyed to me by my accomplished friend +Professor Lesley, of Philadelphia, and preceded by a letter of the +same purport from your scientific Nestor, the celebrated Joseph +Henry, of <a name="Page_3" id="Page_3"></a><span class= +"pagenum">[Pg 3]</span>Washington, desired that I should lecture in +some of the principal cities of the Union. This I agreed to do, +though much in the dark as to a suitable subject. In answer to my +inquiries, however, I was given to understand that a course of +lectures, showing the uses of experiment in the cultivation of +Natural Knowledge, would materially promote scientific education in +this country. And though such lectures involved the selection of +weighty and delicate instruments, and their transfer from place to +place, I determined to meet the wishes of my friends, as far as the +time and means at my disposal would allow.</p> +<h3>§ 2. <i>Subject of the Course. Source of Light +employed.</i></h3> +<p>Experiments have two great uses—a use in discovery, and a +use in tuition. They were long ago defined as the investigator's +language addressed to Nature, to which she sends intelligible +replies. These replies, however, usually reach the questioner in +whispers too feeble for the public ear. But after the investigator +comes the teacher, whose function it is so to exalt and modify the +experiments of his predecessor, as to render them fit for public +presentation. This secondary function I shall endeavour, in the +present instance, to fulfil.</p> +<p>Taking a single department of natural philosophy as my subject, +I propose, by means of it, to illustrate the growth of scientific +knowledge under the guidance of experiment. I wish, in the first +place, to make you acquainted with certain elementary phenomena; +then to point out to you how the theoretical principles by <a name= +"Page_4" id="Page_4"></a><span class="pagenum">[Pg 4]</span>which +phenomena are explained take root in the human mind, and finally to +apply these principles to the whole body of knowledge covered by +the lectures. The science of optics lends itself particularly well +to this mode of treatment, and on it, therefore, I propose to draw +for the materials of the present course. It will be best to begin +with the few simple facts regarding light which were known to the +ancients, and to pass from them, in historic gradation, to the more +abstruse discoveries of modern times.</p> +<p>All our notions of Nature, however exalted or however grotesque, +have their foundation in experience. The notion of personal +volition in Nature had this basis. In the fury and the serenity of +natural phenomena the savage saw the transcript of his own varying +moods, and he accordingly ascribed these phenomena to beings of +like passions with himself, but vastly transcending him in power. +Thus the notion of <i>causality</i>—the assumption that +natural things did not come of themselves, but had unseen +antecedents—lay at the root of even the savage's +interpretation of Nature. Out of this bias of the human mind to +seek for the causes of phenomena all science has sprung.</p> +<p>We will not now go back to man's first intellectual gropings; +much less shall we enter upon the thorny discussion as to how the +groping man arose. We will take him at that stage of his +development, when he became possessed of the apparatus of thought +and the power of using it. For a time—and that historically a +long one—he was limited to mere observation, accepting what +Nature offered, and confining intellectual action to it alone. The +apparent motions of sun and stars first drew towards them the +questionings of the <a name="Page_5" id="Page_5"></a><span class= +"pagenum">[Pg 5]</span>intellect, and accordingly astronomy was the +first science developed. Slowly, and with difficulty, the notion of +natural forces took root in the human mind. Slowly, and with +difficulty, the science of mechanics had to grow out of this +notion; and slowly at last came the full application of mechanical +principles to the motions of the heavenly bodies. We trace the +progress of astronomy through Hipparchus and Ptolemy; and, after a +long halt, through Copernicus, Galileo, Tycho Brahe, and Kepler; +while from the high table-land of thought occupied by these men, +Newton shoots upwards like a peak, overlooking all others from his +dominant elevation.</p> +<p>But other objects than the motions of the stars attracted the +attention of the ancient world. Light was a familiar phenomenon, +and from the earliest times we find men's minds busy with the +attempt to render some account of it. But without +<i>experiment</i>, which belongs to a later stage of scientific +development, little progress could be here made. The ancients, +accordingly, were far less successful in dealing with light than in +dealing with solar and stellar motions. Still they did make some +progress. They satisfied themselves that light moved in straight +lines; they knew also that light was reflected from polished +surfaces, and that the angle of incidence was equal to the angle of +reflection. These two results of ancient scientific curiosity +constitute the starting-point of our present course of +lectures.</p> +<p>But in the first place it will be useful to say a few words +regarding the source of light to be employed in our experiments. +The rusting of iron is, to all intents and purposes, the slow +burning of iron. It develops <a name="Page_6" id= +"Page_6"></a><span class="pagenum">[Pg 6]</span>heat, and, if the +heat be preserved, a high temperature may be thus attained. The +destruction of the first Atlantic cable was probably due to heat +developed in this way. Other metals are still more combustible than +iron. You may ignite strips of zinc in a candle flame, and cause +them to burn almost like strips of paper. But we must now expand +our definition of combustion, and include under this term, not only +combustion in air, but also combustion in liquids. Water, for +example, contains a store of oxygen, which may unite with, and +consume, a metal immersed in it; it is from this kind of combustion +that we are to derive the heat and light employed in our present +course.</p> +<p>The generation of this light and of this heat merits a moment's +attention. Before you is an instrument—a small voltaic +battery—in which zinc is immersed in a suitable liquid. An +attractive force is at this moment exerted between the metal and +the oxygen of the liquid; actual combination, however, being in the +first instance avoided. Uniting the two ends of the battery by a +thick wire, the attraction is satisfied, the oxygen unites with the +metal, zinc is consumed, and heat, as usual, is the result of the +combustion. A power which, for want of a better name, we call an +electric current, passes at the same time through the wire.</p> +<p>Cutting the thick wire in two, let the severed ends be united by +a thin one. It glows with a white heat. Whence comes that heat? The +question is well worthy of an answer. Suppose in the first +instance, when the thick wire is employed, that we permit the +action to continue until 100 grains of zinc are consumed, the +amount of heat generated in the battery would be <a name="Page_7" +id="Page_7"></a><span class="pagenum">[Pg 7]</span>capable of +accurate numerical expression. Let the action then continue, with +the thin wire glowing, until 100 grains of zinc are consumed. Will +the amount of heat generated in the battery be the same as before? +No; it will be less by the precise amount generated in the thin +wire outside the battery. In fact, by adding the internal heat to +the external, we obtain for the combustion of 100 grains of zinc a +total which never varies. We have here a beautiful example of that +law of constancy as regards natural energies, the establishment of +which is the greatest achievement of modern science. By this +arrangement, then, we are able to burn our zinc at one place, and +to exhibit the effects of its combustion at another. In New York, +for example, we may have our grate and fuel; but the heat and light +of our fire may be made to appear at San Francisco.</p> +<div class="figcenter" style="width: 444px;"><img src= +"images/fig01.jpg" width="444" height="307" alt="Fig. 1." title= +"" /> <b>Fig. 1.</b></div> +<p>Removing the thin wire and attaching to the severed ends of the +thick one two rods of coke we obtain, on bringing the rods together +(as in fig. 1), a small star of <a name="Page_8" id= +"Page_8"></a><span class="pagenum">[Pg 8]</span>light. Now, the +light to be employed in our lectures is a simple exaggeration of +this star. Instead of being produced by ten cells, it is produced +by fifty. Placed in a suitable camera, provided with a suitable +lens, this powerful source will give us all the light necessary for +our experiments.</p> +<p>And here, in passing, I am reminded of the common delusion that +the works of Nature, the human eye included, are theoretically +perfect. The eye has grown for ages <i>towards</i> perfection; but +ages of perfecting may be still before it. Looking at the dazzling +light from our large battery, I see a luminous globe, but entirely +fail to see the shape of the coke-points whence the light issues. +The cause may be thus made clear: On the screen before you is +projected an image of the carbon points, the <i>whole</i> of the +glass lens in front of the camera being employed to form the image. +It is not sharp, but surrounded by a halo which nearly obliterates +the carbons. This arises from an imperfection of the glass lens, +called its <i>spherical aberration</i>, which is due to the fact +that the circumferential and central rays have not the same focus. +The human eye labours under a similar defect, and from this, and +other causes, it arises that when the naked light from fifty cells +is looked at the blur of light upon the retina is sufficient to +destroy the definition of the retinal image of the carbons. A long +list of indictments might indeed be brought against the +eye—its opacity, its want of symmetry, its lack of +achromatism, its partial blindness. All these taken together caused +Helmholt to say that, if any optician sent him an instrument so +defective, he would be justified in sending it back with the +severest censure. But the eye is not to be judged from the +standpoint <a name="Page_9" id="Page_9"></a><span class= +"pagenum">[Pg 9]</span>of theory. It is not perfect, but is on its +way to perfection. As a practical instrument, and taking the +adjustments by which its defects are neutralized into account, it +must ever remain a marvel to the reflecting mind.</p> +<h3>§ 3. <i>Rectilineal Propagation of Light. Elementary +Experiments. Law of Reflection.</i></h3> +<p>The ancients were aware of the rectilineal propagation of light. +They knew that an opaque body, placed between the eye and a point +of light, intercepted the light of the point. Possibly the terms +'ray' and 'beam' may have been suggested by those straight spokes +of light which, in certain states of the atmosphere, dart from the +sun at his rising and his setting. The rectilineal propagation of +light may be illustrated by permitting the solar light to enter, +through a small aperture in a window-shutter, a dark room in which +a little smoke has been diffused. In pure <i>air</i> you cannot see +the beam, but in smoky air you can, because the light, which passes +unseen through the air, is scattered and revealed by the smoke +particles, among which the beam pursues a straight course.</p> +<div class="figleft" style="width: 445px;"><img src= +"images/fig02.jpg" width="445" height="250" alt="Fig. 2." title= +"" /> <b>Fig. 2.</b></div> +<p>The following instructive experiment depends on the rectilineal +propagation of light. Make a small hole in a closed window-shutter, +before which stands a house or a tree, and place within the +darkened room a white screen at some distance from the orifice. +Every straight ray proceeding from the house, or tree, stamps its +colour upon the screen, and the sum of all the rays will, +therefore, be an image of the object. But, as the rays cross each +other at the orifice, the image is inverted. At <a name="Page_10" +id="Page_10"></a><span class="pagenum">[Pg 10]</span>present we may +illustrate and expand the subject thus: In front of our camera is a +large opening (L, fig. 2), from which the lens has been removed, +and which is closed at present by a sheet of tin-foil. Pricking by +means of a common sewing-needle a small aperture in the tin-foil, +an inverted image of the carbon-points starts forth upon the +screen. A dozen apertures will give a dozen images, a hundred a +hundred, a thousand a thousand. But, as the apertures come closer +to each other, that is to say, as the tin-foil between the +apertures vanishes, the images overlap more and more. Removing the +tin-foil altogether, the screen becomes uniformly illuminated. +Hence the light upon the screen may be regarded as the overlapping +of innumerable images of the carbon-points. In like manner the +light upon every white wall, on a cloudless day, may be regarded as +produced by the superposition of innumerable images of the sun.</p> +<div class="figright" style="width: 475px;"><img src= +"images/fig03.jpg" width="475" height="311" alt="Fig. 3." title= +"" /> <b>Fig. 3.</b></div> +<p>The law that the angle of incidence is equal to the angle of +reflection has a bearing upon theory, to be subsequently mentioned, +which renders its simple illustration here desirable. A straight +lath (pointing to <a name="Page_11" id="Page_11"></a><span class= +"pagenum">[Pg 11]</span>the figure 5 on the arc in fig. 3) is fixed +as an index perpendicular to a small looking-glass (M), capable of +rotation. We begin by receiving a beam of light upon the glass +which is reflected back along the line of its incidence. The index +being then turned, the mirror turns with it, and at each side of +the index the incident and the reflected beams (L <i>o</i>, +<i>o</i> R) track themselves through the dust of the room. The mere +inspection of the two angles enclosed between the index and the two +beams suffices to show their equality; while if the graduated arc +be consulted, the arc from 5 to <i>m</i> is found accurately equal +to the arc from 5 to <i>n</i>. The complete expression of the law +of reflection is, not only that the angles of incidence and +reflection are equal, but that the incident and reflected rays +always lie in a plane perpendicular to the reflecting surface.</p> +<p>This simple apparatus enables us to illustrate another law of +great practical importance, namely, that when a mirror rotates, the +angular velocity of a beam <a name="Page_12" id= +"Page_12"></a><span class="pagenum">[Pg 12]</span>reflected from it +is twice that of the reflecting mirror. A simple experiment will +make this plain. The arc (<i>m n</i>, fig. 3) before you is divided +into ten equal parts, and when the incident beam and the index +cross the zero of the graduation, both the incident and reflected +beams are horizontal. Moving the index of the mirror to 1, the +reflected beam cuts the arc at 2; moving the index to 2, the arc is +cut at 4; moving the index to 3, the arc is cut at 6; moving the +index at 4, the arc is cut at 8; finally, moving the index to 5, +the arc is cut at 10 (as in the figure). In every case the +reflected beam moves through twice the angle passed over by the +mirror.</p> +<p>One of the principal problems of science is to help the senses +of man, by carrying them into regions which could never be attained +without that help. Thus we arm the eye with the telescope when we +want to sound the depths of space, and with the microscope when we +want to explore motion and structure in their infinitesimal +dimensions. Now, this law of angular reflection, coupled with the +fact that a beam of light possesses no weight, gives us the means +of magnifying small motions to an extraordinary degree. Thus, by +attaching mirrors to his suspended magnets, and by watching the +images of divided scales reflected from the mirrors, the celebrated +Gauss was able to detect the slightest thrill of variation on the +part of the earth's magnetic force. By a similar arrangement the +feeble attractions and repulsions of the diamagnetic force have +been made manifest. The minute elongation of a bar of metal, by the +mere warmth of the hand, may be so magnified by this method, as to +cause the index-beam to move through 20 or 30 feet. The lengthening +of a bar of iron when it is magnetized may be also thus +demon<a name="Page_13" id="Page_13"></a><span class="pagenum">[Pg +13]</span>strated. Helmholtz long ago employed this method of +rendering evident to his students the classical experiments of Du +Bois Raymond on animal electricity; while in Sir William Thomson's +reflecting galvanometer the principle receives one of its latest +and most important applications.</p> +<h3>§ 4. <i>The Refraction of Light. Total +Reflection.</i></h3> +<p>For more than a thousand years no step was taken in optics +beyond this law of reflection. The men of the Middle Ages, in fact, +endeavoured, on the one hand, to develop the laws of the universe +<i>à priori</i> out of their own consciousness, while many +of them were so occupied with the concerns of a future world that +they looked with a lofty scorn on all things pertaining to this +one. Speaking of the natural philosophers of his time, Eusebius +says, 'It is not through ignorance of the things admired by them, +but through contempt of their useless labour, that we think little +of these matters, turning our souls to the exercise of better +things.' So also Lactantius—'To search for the causes of +things; to inquire whether the sun be as large as he seems; whether +the moon is convex or concave; whether the stars are fixed in the +sky, or float freely in the air; of what size and of what material +are the heavens; whether they be at rest or in motion; what is the +magnitude of the earth; on what foundations is it suspended or +balanced;—to dispute and conjecture upon such matters is just +as if we chose to discuss what we think of a city in a remote +country, of which we never heard but the name.'</p> +<p>As regards the refraction of light, the course of <a name= +"Page_14" id="Page_14"></a><span class="pagenum">[Pg 14]</span>real +inquiry was resumed in 1100 by an Arabian philosopher named +Alhazen. Then it was taken up in succession by Roger Bacon, +Vitellio, and Kepler. One of the most important occupations of +science is the determination, by precise measurements, of the +quantitative relations of phenomena; the value of such measurements +depending greatly upon the skill and conscientiousness of the man +who makes them. Vitellio appears to have been both skilful and +conscientious, while Kepler's habit was to rummage through the +observations of his predecessors, to look at them in all lights, +and thus distil from them the principles which united them. He had +done this with the astronomical measurements of Tycho Brahe, and +had extracted from them the celebrated 'laws of Kepler.' He did it +also with Vitellio's measurements of refraction. But in this case +he was not successful. The principle, though a simple one, escaped +him, and it was first discovered by Willebrord Snell, about the +year 1621.</p> +<p>Less with the view of dwelling upon the phenomenon itself than +of introducing it in a form which will render subsequently +intelligible to you the play of theoretic thought in Newton's mind, +the fact of refraction may be here demonstrated. I will not do this +by drawing the course of the beam with chalk on a black board, but +by causing it to mark its own white track before you. A shallow +circular vessel (RIG, fig. 4), half filled with water, rendered +slightly turbid by the admixture of a little milk, or the +precipitation of a little mastic, is placed with its glass front +vertical. By means of a small plane reflector (M), and through a +slit (I) in the hoop surrounding the vessel, a beam of light is +admitted in any required direction. It <a name="Page_15" id= +"Page_15"></a><span class="pagenum">[Pg 15]</span>impinges upon the +water (at O), enters it, and tracks itself through the liquid in a +sharp bright band (O G). Meanwhile the beam passes unseen through +the air above the water, for the air is not competent to scatter +the light. A puff of smoke into this space at once reveals the +track of the incident-beam. If the incidence be vertical, the beam +is unrefracted. If oblique, its refraction at the common surface of +air and water (at O) is rendered clearly visible. It is also seen +that <i>reflection</i> (along O R) accompanies refraction, the beam +dividing itself at the point of incidence into a refracted and a +reflected portion.<a name="FNanchor_4_4" id= +"FNanchor_4_4"></a><a href="#Footnote_4_4" class= +"fnanchor">[4]</a></p> +<div class="figright" style="width: 450px;"><img src= +"images/fig04.jpg" width="450" height="254" alt="Fig. 4." title= +"" /> <b>Fig. 4.</b></div> +<p>The law by which Snell connected together all the measurements +executed up to his time, is this: Let A B C D (fig. 5) represent +the outline of our circular vessel, A C being the water-line. When +the beam is incident along B E, which is perpendicular to A C, +there is no refraction. When it is incident along <i>m</i> E, there +is refraction: it is bent at E and strikes the <a name="Page_16" +id="Page_16"></a><span class="pagenum">[Pg 16]</span>circle at +<i>n</i>. When it is incident along <i>m'</i> E there is also +refraction at E, the beam striking the point <i>n'</i>. From the +ends of the two incident beams, let the perpendiculars <i>m</i> +<i>o</i>, <i>m'</i> <i>o'</i> be drawn upon B D, and from the ends +of the refracted beams let the perpendiculars <i>p</i> <i>n</i>, +<i>p'</i> <i>n'</i> be also drawn. Measure the lengths of <i>o +m</i> and of <i>p</i> <i>n</i>, and divide the one by the other. +You obtain a certain quotient. In like manner divide <i>m'</i> +<i>o'</i> by the corresponding perpendicular <i>p'</i> <i>n'</i>; +you obtain precisely the same quotient. Snell, in fact, found this +quotient to be <i>a constant quantity</i> for each particular +substance, though it varied in amount from one substance to +another. He called the quotient the <i>index of refraction</i>.</p> +<div class="figleft" style="width: 253px;"><img src= +"images/fig05.jpg" width="253" height="253" alt="Fig. 5" title= +"" /> <b>Fig. 5</b></div> +<p>In all cases where the light is incident from air upon the +surface of a solid or a liquid, or, to speak more generally, when +the incidence is from a less highly refracting to a more highly +refracting medium, the reflection is <i>partial</i>. In this case +the most powerfully reflecting substances either transmit or absorb +a portion of the incident light. At a perpendicular incidence +<a name="Page_17" id="Page_17"></a><span class="pagenum">[Pg +17]</span>water reflects only 18 rays out of every 1,000; glass +reflects only 25 rays, while mercury reflects 666 When the rays +strike the surface obliquely the reflection is augmented. At an +incidence of 40°, for example, water reflects 22 rays, at +60° it reflects 65 rays, at 80° 333 rays; while at an +incidence of 89½°, where the light almost grazes the +surface, it reflects 721 rays out of every 1,000. Thus, as the +obliquity increases, the reflection from water approaches, and +finally quite overtakes, the perpendicular reflection from mercury; +but at no incidence, however great, when the incidence is from air, +is the reflection from water, mercury, or any other substance, +<i>total</i>.</p> +<p>Still, total reflection may occur, and with a view to +understanding its subsequent application in the Nicol's prism, it +is necessary to state when it occurs. This leads me to the +enunciation of a principle which underlies all optical +phenomena—the principle of reversibility.<a name= +"FNanchor_5_5" id="FNanchor_5_5"></a><a href="#Footnote_5_5" class= +"fnanchor">[5]</a> In the case of refraction, for instance, when +the ray passes obliquely from air into water, it is bent +<i>towards</i> the perpendicular; when it passes from water to air, +it is bent <i>from</i> the perpendicular, and accurately reverses +its course. Thus in fig. 5, if <i>m</i> E <i>n</i> be the track of +a ray in passing from air into water, <i>n</i> E <i>m</i> will be +its track in passing from water into air. Let us push this +principle to its consequences. Supposing the light, instead of +being incident along <i>m</i> E or <i>m′</i> E, were incident +as close as possible along C E (fig. 6); suppose, in other words, +that it just grazes the surface before entering the water. After +refraction it will <a name="Page_18" id="Page_18"></a><span class= +"pagenum">[Pg 18]</span>pursue say the course E <i>n</i>″. +Conversely, if the light start from <i>n</i>″, and be +incident at E, it will, on escaping into the air, just graze the +surface of the water. The question now arises, what will occur +supposing the ray from the water to follow the course +<i>n</i>‴ E, which lies beyond <i>n</i>″ E? The answer +is, it will not quit the water at all, but will be <i>totally</i> +reflected (along E <i>x</i>). At the under surface of the water, +moreover, the law is just the same as at its upper surface, the +angle of incidence (D E <i>n</i>‴) being equal to the angle +of reflection (D E <i>x</i>).</p> +<div class="figright" style="width: 252px;"><img src= +"images/fig06.jpg" width="252" height="243" alt="Fig. 6" title= +"" /> <b>Fig. 6</b></div> +<p>Total reflection may be thus simply illustrated:—Place a +shilling in a drinking-glass, and tilt the glass so that the light +from the shilling shall fall with the necessary obliquity upon the +water surface above it. Look upwards through the water towards that +surface, and you see the image of the shilling shining there as +brightly as the shilling itself. Thrust the closed end of an empty +test-tube into water, and incline the tube. When the inclination is +sufficient, horizontal light falling upon the tube cannot enter the +air within it, but is totally reflected upward: when looked down +upon, such a tube looks quite as bright as burnished silver. Pour a +<a name="Page_19" id="Page_19"></a><span class="pagenum">[Pg +19]</span>little water into the tube; as the liquid rises, total +reflection is abolished, and with it the lustre, leaving a +gradually diminishing shining zone, which disappears wholly when +the level of the water within the tube reaches that without it. Any +glass tube, with its end stopped water-tight, will produce this +effect, which is both beautiful and instructive.</p> +<p>Total reflection never occurs except in the attempted passage of +a ray from a more refracting to a less refracting medium; but in +this case, when the obliquity is sufficient, it always occurs. The +mirage of the desert, and other phantasmal appearances in the +atmosphere, are in part due to it. When, for example, the sun heats +an expanse of sand, the layer of air in contact with the sand +becomes lighter and less refracting than the air above it: +consequently, the rays from a distant object, striking very +obliquely on the surface of the heated stratum, are sometimes +totally reflected upwards, thus producing images similar to those +produced by water. I have seen the image of a rock called Mont +Tombeline distinctly reflected from the heated air of the strand of +Normandy near Avranches; and by such delusive appearances the +thirsty soldiers of the French army in Egypt were greatly +tantalised.</p> +<p>The angle which marks the limit beyond which total reflection +takes place is called the <i>limiting angle</i> (it is marked in +fig. 6 by the strong line E <i>n</i>″). It must evidently +diminish as the refractive index increases. For water it is +48½°, for flint glass 38°41', and for diamond +23°42'. Thus all the light incident from two complete +quadrants, or 180°, in the case of diamond, is condensed into +an angular space of 47°22' (twice 23°42') by refraction. +Coupled with its great refraction, are <a name="Page_20" id= +"Page_20"></a><span class="pagenum">[Pg 20]</span>the great +dispersive and great reflective powers of diamond; hence the +extraordinary radiance of the gem, both as regards white light and +prismatic light.</p> +<h3>§ 5. <i>Velocity of Light. Aberration. Principle of least +Action.</i></h3> +<p>In 1676 a great impulse was given to optics by astronomy. In +that year Olav Roemer, a learned Dane, was engaged at the +Observatory of Paris in observing the eclipses of Jupiter's moons. +The planet, whose distance from the sun is 475,693,000 miles, has +four satellites. We are now only concerned with the one nearest to +the planet. Roemer watched this moon, saw it move round the planet, +plunge into Jupiter's shadow, behaving like a lamp suddenly +extinguished: then at the other edge of the shadow he saw it +reappear, like a lamp suddenly lighted. The moon thus acted the +part of a signal light to the astronomer, and enabled him to tell +exactly its time of revolution. The period between two successive +lightings up of the lunar lamp he found to be 42 hours, 28 minutes, +and 35 seconds.</p> +<p>This measurement of time was so accurate, that having determined +the moment when the moon emerged from the shadow, the moment of its +hundredth appearance could also be determined. In fact, it would be +100 times 42 hours, 28 minutes, 35 seconds, after the first +observation.</p> +<p>Roemer's first observation was made when the earth was in the +part of its orbit nearest Jupiter. About six months afterwards, the +earth being then at the opposite side of its orbit, when the little +moon ought to have made its hundredth appearance, it was found +<a name="Page_21" id="Page_21"></a><span class="pagenum">[Pg +21]</span>unpunctual, being fully 15 minutes behind its calculated +time. Its appearance, moreover, had been growing gradually later, +as the earth retreated towards the part of its orbit most distant +from Jupiter. Roemer reasoned thus: 'Had I been able to remain at +the other side of the earth's orbit, the moon might have appeared +always at the proper instant; an observer placed there would +probably have seen the moon 15 minutes ago, the retardation in my +case being due to the fact that the light requires 15 minutes to +travel from the place where my first observation was made to my +present position.'</p> +<p>This flash of genius was immediately succeeded by another. 'If +this surmise be correct,' Roemer reasoned, 'then as I approach +Jupiter along the other side of the earth's orbit, the retardation +ought to become gradually less, and when I reach the place of my +first observation, there ought to be no retardation at all.' He +found this to be the case, and thus not only proved that light +required time to pass through space, but also determined its rate +of propagation.</p> +<p>The velocity of light, as determined by Roemer, is 192,500 miles +in a second.</p> +<p>For a time, however, the observations and reasonings of Roemer +failed to produce conviction. They were doubted by Cassini, +Fontenelle, and Hooke. Subsequently came the unexpected +corroboration of Roemer by the English astronomer, Bradley, who +noticed that the fixed stars did not really appear to be fixed, but +that they describe little orbits in the heavens every year. The +result perplexed him, but Bradley had a mind open to suggestion, +and capable of seeing, in the smallest fact, a picture of the +largest. He was one day upon the <a name="Page_22" id= +"Page_22"></a><span class="pagenum">[Pg 22]</span>Thames in a boat, +and noticed that as long as his course remained unchanged, the vane +upon his masthead showed the wind to be blowing constantly in the +same direction, but that the wind appeared to vary with every +change in the direction of his boat. 'Here,' as Whewell says, 'was +the image of his case. The boat was the earth, moving in its orbit, +and the wind was the light of a star.'</p> +<p>We may ask, in passing, what, without the faculty which formed +the 'image,' would Bradley's wind and vane have been to him? A wind +and vane, and nothing more. You will immediately understand the +meaning of Bradley's discovery. Imagine yourself in a motionless +railway-train, with a shower of rain descending vertically +downwards. The moment the train begins to move, the rain-drops +begin to slant, and the quicker the motion of the train the greater +is the obliquity. In a precisely similar manner the rays from a +star, vertically overhead, are caused to slant by the motion of the +earth through space. Knowing the speed of the train, and the +obliquity of the falling rain, the velocity of the drops may be +calculated; and knowing the speed of the earth in her orbit, and +the obliquity of the rays due to this cause, we can calculate just +as easily the velocity of light. Bradley did this, and the +'aberration of light,' as his discovery is called, enabled him to +assign to it a velocity almost identical with that deduced by +Roemer from a totally different method of observation. Subsequently +Fizeau, and quite recently Cornu, employing not planetary or +stellar distances, but simply the breadth of the city of Paris, +determined the velocity of light: while Foucault—a man of the +rarest mechanical genius—solved the problem without quitting +<a name="Page_23" id="Page_23"></a><span class="pagenum">[Pg +23]</span>his private room. Owing to an error in the determination +of the earth's distance from the sun, the velocity assigned to +light by both Roemer and Bradley is too great. With a close +approximation to accuracy it may be regarded as 186,000 miles a +second.</p> +<p>By Roemer's discovery, the notion entertained by Descartes, and +espoused by Hooke, that light is propagated instantly through +space, was overthrown. But the establishment of its motion through +stellar space led to speculations regarding its velocity in +transparent terrestrial substances. The 'index of refraction' of a +ray passing from air into water is 4/3. Newton assumed these +numbers to mean that the velocity of light in water being 4, its +velocity in air is 3; and he deduced the phenomena of refraction +from this assumption. Huyghens took the opposite and truer view. +According to this great man, the velocity of light in water being +3, its velocity in air is 4; but both in Newton's time and ours the +same great principle determined, and determines, the course of +light in all cases. In passing from point to point, whatever be the +media in its path, or however it may be refracted or reflected, +light takes the course which occupies <i>least time</i>. Thus in +fig. 4, taking its velocity in air and in water into account, the +light reaches G from I more rapidly by travelling first to O, and +there changing its course, than if it proceeded straight from I to +G. This is readily comprehended, because, in the latter case, it +would pursue a greater distance through the water, which is the +more retarding medium.</p> +<div><a name="Page_24" id="Page_24"></a><span class="pagenum">[Pg +24]</span></div> +<h3>§ 6. <i>Descartes' Explanation of the Rainbow</i>.</h3> +<p>Snell's law of refraction is one of the corner-stones of optical +science, and its applications to-day are million-fold. Immediately +after its discovery Descartes applied it to the explanation of the +rainbow. A beam of solar light falling obliquely upon a rain-drop +is refracted on entering the drop. It is in part reflected at the +back of the drop, and on emerging it is again refracted. By these +two refractions, and this single reflection, the light is sent to +the eye of an observer facing the drop, and with his back to the +sun.</p> +<p>Conceive a line drawn from the sun, through the back of his +head, to the observer's eye and prolonged beyond it. Conceive a +second line drawn from the shower to the eye, and enclosing an +angle of 42½° with the line drawn from the sun. Along +this second line a rain-drop when struck by a sunbeam will send red +light to the eye. Every other drop similarly situated, that is, +every drop at an angular distance of 42½° from the line +through the sun and eye, will do the same. A circular band of red +light is thus formed, which may be regarded as the boundary of the +base of a cone, with its apex at the observer's eye. Because of the +magnitude of the sun, the angular width of this red band will be +half a degree.</p> +<p>From the eye of the observer conceive another line to be drawn, +enclosing an angle, not of 42½°, but of 40½°, +with the prolongation of the line drawn from the sun. Along this +other line a rain-drop, at its remote end, when struck by a solar +beam, will send violet light to the eye. All drops at the same +angular distance will do the same, and we shall therefore obtain a +band of violet light of the same width as the red band. <a name= +"Page_25" id="Page_25"></a><span class="pagenum">[Pg +25]</span>These two bands constitute the limiting colours of the +rainbow, and between them the bands corresponding to the other +colours lie.</p> +<p>Thus the line drawn from the eye to the <i>middle</i> of the +bow, and the line drawn through the eye to the sun, always enclose +an angle of about 41°. To account for this was the great +difficulty, which remained unsolved up to the time of +Descartes.</p> +<p>Taking a pen in hand, and calculating by means of Snell's law +the track of every ray through a raindrop, Descartes found that, at +one particular angle, the rays, reflected at its back, emerged from +the drop <i>almost parallel to each other</i>. They were thus +enabled to preserve their intensity through long atmospheric +distances. At all other angles the rays quitted the drop +<i>divergent</i>, and through this divergence became so enfeebled +as to be practically lost to the eye. The angle of parallelism here +referred to was that of forty-one degrees, which observation had +proved to be invariably associated with the rainbow.</p> +<p>From what has been said, it is clear that two observers standing +beside each other, or one above the other, nay, that even the two +eyes of the same observer, do not see exactly the same bow. The +position of the base of the cone changes with that of its apex. And +here we have no difficulty in answering a question often +asked—namely, whether a rainbow is ever seen reflected in +water. Seeing two bows, the one in the heavens, the other in the +water, you might be disposed to infer that the one bears the same +relation to the other that a tree upon the water's edge bears to +its reflected image. The rays, however, which reach an observer's +eye after reflection from the water, and which form a bow in the +<a name="Page_26" id="Page_26"></a><span class="pagenum">[Pg +26]</span>water, would, were their course from the shower +uninterrupted, converge to a point vertically under the observer, +and as far below the level of the water as his eye is above it. But +under no circumstances could an eye above the water-level and one +below it see the same bow—in other words, the self-same drops +of rain cannot form the reflected bow and the bow seen directly in +the heavens. The reflected bow, therefore, is not, in the usual +optical sense of the term, the <i>image</i> of the bow seen in the +sky.</p> +<h3>§ 7. <i>Analysis and Synthesis of Light. Doctrine of +Colours</i>.</h3> +<p>In the rainbow a new phenomenon was introduced—the +phenomenon of colour. And here we arrive at one of those points in +the history of science, when great men's labours so intermingle +that it is difficult to assign to each worker his precise meed of +honour. Descartes was at the threshold of the discovery of the +composition of solar light; but for Newton was reserved the +enunciation of the true law. He went to work in this way: Through +the closed window-shutter of a room he pierced an orifice, and +allowed a thin sunbeam to pass through it. The beam stamped a round +white image of the sun on the opposite wall of the room. In the +path of this beam Newton placed a prism, expecting to see the beam +refracted, but also expecting to see the image of the sun, after +refraction, still round. To his astonishment, it was drawn out to +an image with a length five times its breadth. It was, moreover, no +longer white, but divided into bands of different colours. Newton +saw immediately that solar light was <i>composite</i>, not simple. +His elongated image <a name="Page_27" id="Page_27"></a><span class= +"pagenum">[Pg 27]</span>revealed to him the fact that some +constituents of the light were more deflected by the prism than +others, and he concluded, therefore, that white light was a mixture +of lights of different colours, possessing different degrees of +refrangibility.</p> +<p>Let us reproduce this celebrated experiment. On the screen is +now stamped a luminous disk, which may stand for Newton's image of +the sun. Causing the beam (from the aperture L, fig. 7) which +produces the disk to pass through a lens (E), we form a sharp image +of the aperture. Placing in the track of the beam a prism (P), we +obtain Newton's coloured image, with its red and violet ends, which +he called a <i>spectrum</i>. Newton divided the spectrum into seven +parts—red, orange, yellow, green, blue, indigo, violet; which +are commonly called the seven primary or prismatic colours. The +drawing out of the white light into its constituent colours is +called <i>dispersion</i>.</p> +<div class="figcenter" style="width: 443px;"><img src= +"images/fig07.jpg" width="443" height="303" alt="Fig. 7." title= +"" /> <b>Fig. 7.</b></div> +<p>This was the first <i>analysis</i> of solar light by Newton; +<a name="Page_28" id="Page_28"></a><span class="pagenum">[Pg +28]</span>but the scientific mind is fond of verification, and +never neglects it where it is possible. Newton completed his proof +by <i>synthesis</i> in this way: The spectrum now before you is +produced by a glass prism. Causing the decomposed beam to pass +through a second similar prism, but so placed that the colours are +refracted back and reblended, the perfectly white luminous disk is +restored.</p> +<div class="figcenter" style="width: 430px;"><img src= +"images/fig08.jpg" width="430" height="321" alt="Fig. 8." title= +"" /> <b>Fig. 8.</b></div> +<p>In this case, refraction and dispersion are simultaneously +abolished. Are they always so? Can we have the one without the +other? It was Newton's conclusion that we could not. Here he erred, +and his error, which he maintained to the end of his life, retarded +the progress of optical discovery. Dollond subsequently proved that +by combining two different kinds of glass, the colours can be +extinguished, still leaving a residue of refraction, and he +employed this residue in the construction of achromatic +lenses—lenses yielding no colour—which Newton thought +an impossi<a name="Page_29" id="Page_29"></a><span class= +"pagenum">[Pg 29]</span>bility. By setting a +water-prism—water contained in a wedge-shaped vessel with +glass sides (B, fig. 8)—in opposition to a wedge of glass (to +the right of B), this point can be illustrated before you. We have +first of all the position (dotted) of the unrefracted beam marked +upon the screen; then we produce the narrow water-spectrum (W); +finally, by introducing a flint-glass prism, we refract the beam +back, until the colour disappears (at A). The image of the slit is +now <i>white</i>; but though the dispersion is abolished, there +remains a very sensible amount of refraction.</p> +<p>This is the place to illustrate another point bearing upon the +instrumental means employed in these lectures. Bodies differ widely +from each other as to their powers of refraction and dispersion. +Note the position of the water-spectrum upon the screen. Altering +in no particular the wedge-shaped vessel, but simply substituting +for the water the transparent bisulphide of carbon, you notice how +much higher the beam is thrown, and how much richer is the display +of colour. To augment the size of our spectrum we here employ (at +L) a slit, instead of a circular aperture.<a name="FNanchor_6_6" +id="FNanchor_6_6"></a><a href="#Footnote_6_6" class= +"fnanchor">[6]</a></p> +<div class="figcenter" style="width: 445px;"><img src= +"images/fig09.jpg" width="445" height="305" alt="Fig. 9." title= +"" /> <b>Fig. 9.</b></div> +<p><a name="Page_30" id="Page_30"></a><span class="pagenum">[Pg +30]</span>The synthesis of white light may be effected in three +ways, all of which are worthy of attention: Here, in the first +instance, we have a rich spectrum produced by the decomposition of +the beam (from L, fig. 9). One face of the prism (P) is protected +by a diaphragm (not shown in the figure), with a longitudinal slit, +through which the beam passes into the prism. It emerges decomposed +at the other side. I permit the colours to pass through a +cylindrical lens (C), which so squeezes them together as to produce +upon the screen a sharply defined rectangular image of the +longitudinal slit. In that image the colours are reblended, and it +is perfectly white. Between the prism and the cylindrical lens may +be seen the colours, tracking themselves through the dust of the +room. Cutting off the more refrangible fringe by a card, the +rectangle is seen red: cutting off the less refrangible fringe, the +rectangle is seen blue. By means of a thin glass prism (W), I +deflect one portion of the colours, and <a name="Page_31" id= +"Page_31"></a><span class="pagenum">[Pg 31]</span>leave the +residual portion. On the screen are now two coloured rectangles +produced in this way. These are <i>complementary</i> +colours—colours which, by their union, produce white. Note, +that by judicious management, one of these colours is rendered +<i>yellow</i>, and the other <i>blue</i>. I withdraw the thin +prism; yellow and blue immediately commingle, and we have +<i>white</i> as the result of their union. On our way, then, we +remove the fallacy, first exposed by Wünsch, and afterwards +independently by Helmholtz, that the mixture of blue and yellow +lights produces green.</p> +<p>Restoring the circular aperture, we obtain once more a spectrum +like that of Newton. By means of a lens, we can gather up these +colours, and build them together, not to an image of the aperture, +but to an image of the carbon-points themselves.</p> +<p>Finally, by means of a rotating disk, on which are spread in +sectors the colours of the spectrum, we blend together the +prismatic colours in the eye itself, and thus produce the +impression of whiteness.</p> +<p>Having unravelled the interwoven constituents of white light, we +have next to inquire, What part the constitution so revealed +enables this agent to play in Nature? To it we owe all the +phenomena of colour, and yet not to it alone; for there must be a +certain relationship between the ultimate particles of natural +bodies and white light, to enable them to extract from it the +luxury of colour. But the function of natural bodies is here +<i>selective</i>, not <i>creative</i>. There is no colour +<i>generated</i> by any natural body whatever. Natural bodies have +showered upon them, in the white light of the sun, the sum total of +all possible colours; and their action is limited to the sifting of +that total—<a name="Page_32" id="Page_32"></a><span class= +"pagenum">[Pg 32]</span>the appropriating or absorbing of some of +its constituents, and the rejecting of others. It will fix this +subject in your minds if I say, that it is the portion of light +which they reject, and not that which they appropriate or absorb, +that gives bodies their colours.</p> +<p>Let us begin our experimental inquiries here by asking, What is +the meaning of blackness? Pass a black ribbon through the colours +of the spectrum; it quenches all of them. The meaning of blackness +is thus revealed—it is the result of the absorption of all +the constituents of solar light. Pass a red ribbon through the +spectrum. In the red light the ribbon is a vivid red. Why? Because +the light that enters the ribbon is not quenched or absorbed, but +in great part sent back to the eye. Place the same ribbon in the +green of the spectrum; it is black as jet. It absorbs the green +light, and renders the space on which that light falls a space of +intense darkness. Place a green ribbon in the green of the +spectrum. It shines vividly with its proper colour; transfer it to +the red, it is black as jet. Here it absorbs all the light that +falls upon it, and offers mere darkness to the eye.</p> +<p>Thus, when white light is employed, the red sifts it by +quenching the green, and the green sifts it by quenching the red, +both exhibiting the residual colour. The process through which +natural bodies acquire their colours is therefore a <i>negative</i> +one. The colours are produced by subtraction, not by addition. This +red glass is red because it destroys all the more refrangible rays +of the spectrum. This blue liquid is blue because it destroys all +the less refrangible rays. Both together are opaque because the +light transmitted by the one is quenched by the other. In <a name= +"Page_33" id="Page_33"></a><span class="pagenum">[Pg 33]</span>this +way, by the union of two transparent substances, we obtain a +combination as dark as pitch to solar light. This other liquid, +finally, is purple because it destroys the green and the yellow, +and allows the terminal colours of the spectrum to pass unimpeded. +From the blending of the blue and the red this gorgeous purple is +produced.</p> +<p>One step further for the sake of exactness. The light which +falls upon a body is divided into two portions, one of which is +reflected from the surface of the body; and this is of the same +colour as the incident light. If the incident light be white, the +superficially reflected light will also be white. Solar light, for +example, reflected from the surface of even a black body, is white. +The blackest camphine smoke in a dark room, through which a sunbeam +passes from an aperture in the window-shutter, renders the track of +the beam white, by the light scattered from the surfaces of the +soot particles. The moon appears to us as if</p> +<div class="blockquot"> +<p>'Clothed in white samite, mystic, wonderful;'</p> +</div> +<p>but were it covered with the blackest velvet it would still hang +as a white orb in the heavens, shining upon our world substantially +as it does now.</p> +<h3>§ 8. <i>Colours of Pigments as distinguished from Colours +of Light</i>.</h3> +<p>The second portion of the incident light enters the body, and +upon its treatment there the colour of the body depends. And here a +moment may properly be given to the analysis of the action of +pigments upon light. They are composed of fine particles mixed with +a <a name="Page_34" id="Page_34"></a><span class="pagenum">[Pg +34]</span>vehicle; but how intimately soever the particles may be +blended, they still remain particles, separated, it may be, by +exceedingly minute distances, but still separated. To use the +scientific phrase, they are not optically continuous. Now, wherever +optical continuity is ruptured we have reflection of the incident +light. It is the multitude of reflections at the limiting surfaces +of the particles that prevents light from passing through snow, +powdered glass, or common salt. The light here is exhausted in +echoes, not extinguished by true absorption. It is the same kind of +reflection that renders the thunder-cloud so impervious to light. +Such a cloud is composed of particles of water, mixed with +particles of air, both separately transparent, but practically +opaque when thus mixed together.</p> +<p>In the case of pigments, then, the light is <i>reflected</i> at +the limiting surfaces of the particles, but it is in part +<i>absorbed</i> within the particles. The reflection is necessary +to send the light back to the eye; the absorption is necessary to +give the body its colour. The same remarks apply to flowers. The +rose is red, in virtue, not of the light reflected from its +surface, but of light which has entered its substance, which has +been reflected from surfaces within, and which, in returning +<i>through</i> the substance, has had its green extinguished. A +similar process in the case of hard green leaves extinguishes the +red, and sends green light from the body of the leaves to the +eye.</p> +<p>All bodies, even the most transparent, are more or less +absorbent of light. Take the case of water. A glass cell of clear +water interposed in the track of our beam does not perceptibly +change any one of the colours of the spectrum. Still absorption, +though <a name="Page_35" id="Page_35"></a><span class="pagenum">[Pg +35]</span>insensible, has here occurred, and to render it sensible +we have only to increase the depth of the water through which the +light passes. Instead of a cell an inch thick, let us take a layer, +ten or fifteen feet thick: the colour of the water is then very +evident. By augmenting the thickness we absorb more of the light, +and by making the thickness very great we absorb the light +altogether. Lampblack or pitch can do no more, and the only +difference in this respect between them and water is that a very +small depth in their case suffices to extinguish all the light. The +difference between the highest known transparency and the highest +known opacity is one of degree merely.</p> +<p>If, then, we render water sufficiently deep to quench all the +light; and if from the interior of the water no light reaches the +eye, we have the condition necessary to produce blackness. Looked +properly down upon, there are portions of the Atlantic Ocean to +which one would hardly ascribe a trace of colour: at the most a +tint of dark indigo reaches the eye. The water, in fact, is +practically <i>black</i>, and this is an indication both of its +depth and purity. But the case is entirely changed when the ocean +contains solid particles in a state of mechanical suspension, +capable of sending the light impinging on them back to the eye.</p> +<p>Throw, for example, a white pebble, or a white dinner plate, +into the blackest Atlantic water; as it sinks it becomes greener +and greener, and, before it disappears, it reaches a vivid blue +green. Break such a pebble, or plate, into fragments, these will +behave like the unbroken mass: grind the pebble to powder, every +particle will yield its modicum of green; and if the particles be +so fine as to remain suspended in the <a name="Page_36" id= +"Page_36"></a><span class="pagenum">[Pg 36]</span>water, the +scattered light will be a uniform green. Hence the greenness of +shoal water. You go to bed with the black water of the Atlantic +around you. You rise in the morning, find it a vivid green, and +correctly infer that you are crossing the Bank of Newfoundland. +Such water is found charged with fine matter in a state of +mechanical suspension. The light from the bottom may sometimes come +into play, but it is not necessary. The subaqueous foam, generated +by the screw or paddle-wheels of a steamer, also sends forth a +vivid green. The foam here furnishes a <i>reflecting surface</i>, +the water between the eye and it the <i>absorbing medium</i>.</p> +<p>Nothing can be more superb than the green of the Atlantic waves +when the circumstances are favourable to the exhibition of the +colour. As long as a wave remains unbroken no colour appears, but +when the foam just doubles over the crest like an Alpine +snow-cornice, under the cornice we often see a display of the most +exquisite green. It is metallic in its brilliancy. The foam is +first illuminated, and it scatters the light in all directions; the +light which passes through the higher portion of the wave alone +reaches the eye, and gives to that portion its matchless colour. +The folding of the wave, producing, as it does, a series of +longitudinal protuberances and furrows which act like cylindrical +lenses, introduces variations in the intensity of the light, and +materially enhances its beauty.</p> +<p>We are now prepared for the further consideration of a point +already adverted to, and regarding which error long found currency. +You will find it stated in many books that blue light and yellow +light mixed together, produce green. But blue and yellow have been +just proved to be complementary colours, pro<a name="Page_37" id= +"Page_37"></a><span class="pagenum">[Pg 37]</span>ducing white by +their mixture. The mixture of blue and yellow <i>pigments</i> +undoubtedly produces green, but the mixture of pigments is a +totally different thing from the mixture of lights.</p> +<p>Helmholtz has revealed the cause of the green produced by a +mixture of blue and yellow pigments. No natural colour is +<i>pure</i>. A blue liquid, or a blue powder, permits not only the +blue to pass through it, but a portion of the adjacent green. A +yellow powder is transparent not only to the yellow light, but also +in part to the adjacent green. Now, when blue and yellow are mixed +together, the blue cuts off the yellow, the orange, and the red; +the yellow, on the other hand, cuts off the violet, the indigo, and +the blue. Green is the only colour to which both are transparent, +and the consequence is that, when white light falls upon a mixture +of yellow and blue powders, the green alone is sent back to the +eye. You have already seen that the fine blue ammonia-sulphate of +copper transmits a large portion of green, while cutting off all +the less refrangible light. A yellow solution of picric acid also +allows the green to pass, but quenches all the more refrangible +light. What must occur when we send a beam through both liquids? +The experimental answer to this question is now before you: the +green band of the spectrum alone remains upon the screen.</p> +<p>The impurity of natural colours is strikingly illustrated by an +observation recently communicated to me by Mr. Woodbury. On looking +through a blue glass at green leaves in sunshine, he saw the +superficially reflected light blue. The light, on the contrary, +which came from the body of the leaves was crimson. On examination, +I found that the glass <a name="Page_38" id= +"Page_38"></a><span class="pagenum">[Pg 38]</span>employed in this +observation transmitted both ends of the spectrum, the red as well +as the blue, and that it quenched the middle. This furnished an +easy explanation of the effect. In the delicate spring foliage the +blue of the solar light is for the most part absorbed, and a light, +mainly yellowish green, but containing a considerable quantity of +red, escapes from the leaf to the eye. On looking at such foliage +through the violet glass, the green and the yellow are stopped, and +the red alone reaches the eye. Thus regarded, therefore, the leaves +appear like faintly blushing roses, and present a very beautiful +appearance. With the blue ammonia-sulphate of copper, which +transmits no red, this effect is not obtained.</p> +<p>As the year advances the crimson gradually hardens to a coppery +red; and in the dark green leaves of old ivy it is almost absent. +Permitting a beam of white light to fall upon fresh leaves in a +dark room, the sudden change from green to red, and from red back +to green, when the violet glass is alternately introduced and +withdrawn, is very surprising. Looked at through the same glass, +the meadows in May appear of a warm purple. With a solution of +permanganate of potash, which, while it quenches the centre of the +spectrum, permits its ends to pass more freely than the violet +glass, excellent effects are also obtained.<a name="FNanchor_7_7" +id="FNanchor_7_7"></a><a href="#Footnote_7_7" class= +"fnanchor">[7]</a></p> +<p><a name="Page_39" id="Page_39"></a><span class="pagenum">[Pg +39]</span>This question of absorption, considered with reference to +its molecular mechanism, is one of the most subtle and difficult in +physics. We are not yet in a condition to grapple with it, but we +shall be by-and-by. Meanwhile we may profitably glance back on the +web of relations which these experiments reveal to us. We have, +firstly, in solar light an agent of exceeding complexity, composed +of innumerable constituents, refrangible in different degrees. We +find, secondly, the atoms and molecules of bodies gifted with the +power of sifting solar light in the most various ways, and +producing by this sifting the colours observed in nature and art. +To do this they must possess a molecular structure commensurate in +complexity with that of light itself. Thirdly, we have the human +eye and brain, so organized as to be able to take in and +distinguish the multitude of impressions thus generated. The light, +therefore, at starting is complex; to sift and select it as they +do, natural bodies must be complex; while to take in the +impressions thus generated, the human eye and brain, however we may +simplify our conceptions of their action,<a name="FNanchor_8_8" id= +"FNanchor_8_8"></a><a href="#Footnote_8_8" class="fnanchor">[8]</a> +must be highly complex.</p> +<p><a name="Page_40" id="Page_40"></a><span class="pagenum">[Pg +40]</span>Whence this triple complexity? If what are called +material purposes were the only end to be served, a much simpler +mechanism would be sufficient. But, instead of simplicity, we have +prodigality of relation and adaptation—and this, apparently, +for the sole purpose of enabling us to see things robed in the +splendours of colour. Would it not seem that Nature harboured the +intention of educating us for other enjoyments than those derivable +from meat and drink? At all events, whatever Nature meant—and +it would be mere presumption to dogmatize as to what she +meant—we find ourselves here, as the upshot of her +operations, endowed, not only with capacities to enjoy the +materially useful, but endowed with others of indefinite scope and +application, which deal alone with the beautiful and the true.</p> +<hr style="width: 65%;" /> +<div><a name="Page_41" id="Page_41"></a><span class="pagenum">[Pg +41]</span></div> +<h2><a name="LECTURE_II" id="LECTURE_II"></a>LECTURE II.</h2> +<table border="0" cellpadding="0" cellspacing="0" summary=""> +<tr> +<td> +<div style="font-size: smaller;"> +<ul style="list-style: none;"> +<li>ORIGIN OF PHYSICAL THEORIES</li> +<li>SCOPE OF THE IMAGINATION</li> +<li>NEWTON AND THE EMISSION THEORY</li> +<li>VERIFICATION OF PHYSICAL THEORIES</li> +<li>THE LUMINIFEROUS ETHER</li> +<li>WAVE THEORY OF LIGHT</li> +<li>THOMAS YOUNG</li> +<li>FRESNEL AND ARAGO</li> +<li>CONCEPTION OF WAVE-MOTION</li> +<li>INTERFERENCE OF WAVES</li> +<li>CONSTITUTION OF SOUND-WAVES</li> +<li>ANALOGIES OF SOUND AND LIGHT</li> +<li>ILLUSTRATIONS OF WAVE-MOTION</li> +<li>INTERFERENCE OF SOUND-WAVES</li> +<li>OPTICAL ILLUSTRATIONS</li> +<li>PITCH AND COLOUR</li> +<li>LENGTHS OF THE WAVES OF LIGHT AND RATES OF VIBRATION OF</li> +<li>THE ETHER-PARTICLES</li> +<li>INTERFERENCE OF LIGHT</li> +<li>PHENOMENA WHICH FIRST SUGGESTED THE UNDULATORY THEORY</li> +<li>BOYLE AND HOOKE</li> +<li>THE COLOURS OF THIN PLATES</li> +<li>THE SOAP-BUBBLE</li> +<li>NEWTON'S RINGS</li> +<li>THEORY OF 'FITS'</li> +<li>ITS EXPLANATION OF THE RINGS</li> +<li>OVER-THROW OF THE THEORY</li> +<li>DIFFRACTION OF LIGHT</li> +<li>COLOURS PRODUCED BY DIFFRACTION</li> +<li>COLOURS OF MOTHER-OF-PEARL.</li> +</ul> +</div> +</td> +</tr> +</table> +<h3>§ 1. <i>Origin and Scope of Physical Theories</i>.</h3> +<p>We might vary and extend our experiments on Light indefinitely, +and they certainly would prove us to possess a wonderful mastery +over the phenomena. But the vesture of the agent only would thus be +revealed, not the agent itself. The human mind, however, is so +constituted that it can never rest satisfied with this outward view +of natural things. Brightness and freshness take possession of the +mind when it is crossed by the light of principles, showing the +facts of Nature to be organically connected.</p> +<p>Let us, then, inquire what this thing is that we have been +generating, reflecting, refracting and analyzing.</p> +<p><a name="Page_42" id="Page_42"></a><span class="pagenum">[Pg +42]</span>In doing this, we shall learn that the life of the +experimental philosopher is twofold. He lives, in his vocation, a +life of the senses, using his hands, eyes, and ears in his +experiments: but such a question as that now before us carries him +beyond the margin of the senses. He cannot consider, much less +answer, the question, 'What is light?' without transporting himself +to a world which underlies the sensible one, and out of which all +optical phenomena spring. To realise this subsensible world the +mind must possess a certain pictorial power. It must be able to +form definite images of the things which that world contains; and +to say that, if such or such a state of things exist in the +subsensible world, then the phenomena of the sensible one must, of +necessity, grow out of this state of things. Physical theories are +thus formed, the truth of which is inferred from their power to +explain the known and to predict the unknown.</p> +<p>This conception of physical theory implies, as you perceive, the +exercise of the imagination—a word which seems to render many +respectable people, both in the ranks of science and out of them, +uncomfortable. That men in the ranks of science should feel thus +is, I think, a proof that they have suffered themselves to be +misled by the popular definition of a great faculty, instead of +observing its operation in their own minds. Without imagination we +cannot take a step beyond the bourne of the mere animal world, +perhaps not even to the edge of this one. But, in speaking thus of +imagination, I do not mean a riotous power which deals capriciously +with facts, but a well-ordered and disciplined power, whose sole +function is to form such conceptions as the intellect imperatively +demands. Imagination, <a name="Page_43" id= +"Page_43"></a><span class="pagenum">[Pg 43]</span>thus exercised, +never really severs itself from the world of fact. This is the +storehouse from which its materials are derived; and the magic of +its art consists, not in creating things anew, but in so changing +the magnitude, position, grouping, and other relations of sensible +things, as to render them fit for the requirements of the intellect +in the subsensible world.<a name="FNanchor_9_9" id= +"FNanchor_9_9"></a><a href="#Footnote_9_9" class= +"fnanchor">[9]</a></p> +<p>Descartes imagined space to be filled with something that +transmitted light <i>instantaneously</i>. Firstly, because, in his +experience, no measurable interval was known to exist between the +appearance of a flash of light, however distant, and its effect +upon consciousness; and secondly, because, as far as his experience +went, no physical power is conveyed from place to place without a +vehicle. But his imagination helped itself farther by illustrations +drawn from the world of fact. 'When,' he says,' one walks in +darkness with staff in hand, the <a name="Page_44" id= +"Page_44"></a><span class="pagenum">[Pg 44]</span>moment the +distant end of the staff strikes an obstacle the hand feels it. +This explains what might otherwise be thought strange, that the +light reaches us instantaneously from the sun. I wish thee to +believe that light in the bodies that we call luminous is nothing +more than a very brisk and violent motion, which, by means of the +air and other transparent media, is conveyed to the eye, exactly as +the shock through the walking-stick reaches the hand of a blind +man. This is instantaneous, and would be so even if the intervening +distance were greater than that between earth and heaven. It is +therefore no more necessary that anything material should reach the +eye from the luminous object, than that something should be sent +from the ground to the hand of the blind man when he is conscious +of the shock of his staff.' The celebrated Robert Hooke at first +threw doubt upon this notion of Descartes, but he afterwards +substantially espoused it. The belief in instantaneous transmission +was destroyed by the discovery of Roemer referred to in our last +lecture.</p> +<h3>§ 2. <i>The Emission Theory of Light</i>.</h3> +<p>The case of Newton still more forcibly illustrates the position, +that in forming physical theories we draw for our materials upon +the world of fact. Before he began to deal with light, he was +intimately acquainted with the laws of elastic collision, which all +of you have seen more or less perfectly illustrated on a +billiard-table. As regards the collision of sensible elastic +masses, Newton knew the angle of incidence to be equal to the angle +of reflection, and he also knew that experiment, as shown in our +last lecture (fig. 3), had established <a name="Page_45" id= +"Page_45"></a><span class="pagenum">[Pg 45]</span>the same law with +regard to light. He thus found in his previous knowledge the +material for theoretic images. He had only to change the magnitude +of conceptions already in his mind to arrive at the Emission Theory +of Light. Newton supposed light to consist of elastic particles of +inconceivable minuteness, shot out with inconceivable rapidity by +luminous bodies. Optical reflection certainly occurred <i>as if</i> +light consisted of such particles, and this was Newton's +justification for introducing them.</p> +<p>But this is not all. In another important particular, also, +Newton's conceptions regarding the nature of light were influenced +by his previous knowledge. He had been pondering over the phenomena +of gravitation, and had made himself at home amid the operations of +this universal power. Perhaps his mind at this time was too freshly +and too deeply imbued with these notions to permit of his forming +an unfettered judgment regarding the nature of light. Be that as it +may, Newton saw in Refraction the result of an attractive force +exerted on the light-particles. He carried his conception out with +the most severe consistency. Dropping vertically downwards towards +the earth's surface, the motion of a body is accelerated as it +approaches the earth. Dropping downwards towards a horizontal +surface—say from air on to glass or water—the velocity +of the light-particles, when they came close to the surface, is, +according to Newton, also accelerated. Approaching such a surface +obliquely, he supposed the particles, when close to it, to be drawn +down upon it, as a projectile is deflected by gravity to the +surface of the earth. This deflection was, according to Newton, the +refraction seen in our last lecture (fig. 4). Finally, it <a name= +"Page_46" id="Page_46"></a><span class="pagenum">[Pg 46]</span>was +supposed that differences of colour might be due to differences in +the 'bigness' of the particles. This was the physical theory of +light enunciated and defended by Newton; and you will observe that +it simply consists in the transference of conceptions, born in the +world of the senses, to a subsensible world.</p> +<p>But, though the region of physical theory lies thus behind the +world of senses, the verifications of theory occur in that world. +Laying the theoretic conception at the root of matters, we +determine by deduction what are the phenomena which must of +necessity grow out of this root. If the phenomena thus deduced +agree with those of the actual world, it is a presumption in favour +of the theory. If, as new classes of phenomena arise, they also are +found to harmonise with theoretic deduction, the presumption +becomes still stronger. If, finally, the theory confers prophetic +vision upon the investigator, enabling him to predict the +occurrence of phenomena which have never yet been seen, and if +those predictions be found on trial to be rigidly correct, the +persuasion of the truth of the theory becomes overpowering.</p> +<p>Thus working backwards from a limited number of phenomena, the +human mind, by its own expansive force, reaches a conception which +covers them all. There is no more wonderful performance of the +intellect than this; but we can render no account of it. Like the +scriptural gift of the Spirit, no man can tell whence it cometh. +The passage from fact to principle is sometimes slow, sometimes +rapid, and at all times a source of intellectual joy. When rapid, +the pleasure is concentrated, and becomes a kind of ecstasy or +intoxication. To any one who has experienced this <a name="Page_47" +id="Page_47"></a><span class="pagenum">[Pg 47]</span>pleasure, even +in a moderate degree, the action of Archimedes when he quitted the +bath, and ran naked, crying 'Eureka!' through the streets of +Syracuse, becomes intelligible.</p> +<p>How, then, did it fare with the Emission Theory when the +deductions from it were brought face to face with natural +phenomena? Tested by experiment, it was found competent to explain +many facts, and with transcendent ingenuity its author sought to +make it account for all. He so far succeeded, that men so +celebrated as Laplace and Malus, who lived till 1812, and Biot and +Brewster, who lived till our own time, were found among his +disciples.</p> +<h3>§ 3. <i>The Undulatory Theory of Light</i>.</h3> +<p>Still, even at an early period of the existence of the Emission +Theory, one or two great men were found espousing a different one. +They furnish another illustration of the law that, in forming +theories, the scientific imagination must draw its materials from +the world of fact and experience. It was known long ago that sound +is conveyed in waves or pulses through the air; and no sooner was +this truth well housed in the mind than it became the basis of a +theoretic conception. It was supposed that light, like sound, might +also be the product of wave-motion. But what, in this case, could +be the material forming the waves? For the waves of sound we have +the air of our atmosphere; but the stretch of imagination which +filled all space with a <i>luminiferous ether</i> trembling with +the waves of light was so bold as to shock cautious minds. In one +of my latest conversations with Sir David Brewster, he <a name= +"Page_48" id="Page_48"></a><span class="pagenum">[Pg 48]</span>said +to me that his chief objection to the undulatory theory of light +was, that he could not think the Creator capable of so clumsy a +contrivance as the filling of space with ether to produce light. +This, I may say, is very dangerous ground, and the quarrel of +science with Sir David, on this point as with many estimable +persons on other points, is, that they profess to know too much +about the mind of the Creator.</p> +<p>This conception of an ether was advocated, and successfully +applied to various phenomena of optics, by the illustrious +astronomer, Huyghens. He deduced from it the laws of reflection and +refraction, and applied it to explain the double refraction of +Iceland spar. The theory was espoused and defended by the +celebrated mathematician, Euler. They were, however, opposed by +Newton, whose authority at the time bore them down. Or shall we say +it was authority merely? Not quite so. Newton's preponderance was +in some degree due to the fact that, though Huyghens and Euler were +right in the main, they did not possess sufficient data to +<i>prove</i> themselves right. No human authority, however high, +can maintain itself against the voice of Nature speaking through +experiment. But the voice of Nature may be an uncertain voice, +through the scantiness of data. This was the case at the period now +referred to, and at such a period, by the authority of Newton, all +antagonists were naturally overborne.</p> +<p>The march of mind is rhythmic, not uniform, and this great +Emission Theory, which held its ground so long, resembled one of +those circles which, according to your countryman Emerson, the +intermittent force of genius periodically draws round the +operations of the intellect, but which are eventually broken +through by <a name="Page_49" id="Page_49"></a><span class= +"pagenum">[Pg 49]</span>pressure from behind. In the year 1773 was +born, at Milverton, in Somersetshire, a circle-breaker of this +kind. He was educated for the profession of a physician, but was +too strong to be tied down to professional routine. He devoted +himself to the study of natural philosophy, and became in all its +departments a master. He was also a master of letters. Languages, +ancient and modern, were housed within his brain, and, to use the +words of his epitaph, 'he first penetrated the obscurity which had +veiled for ages the hieroglyphics of Egypt.' It fell to the lot of +this man to discover facts in optics which Newton's theory was +incompetent to explain, and his mind roamed in search of a +sufficient theory. He had made himself acquainted with all the +phenomena of wave-motion; with all the phenomena of sound; working +successfully in this domain as an original discoverer. Thus +informed and disciplined, he was prepared to detect any resemblance +which might reveal itself between the phenomena of light and those +of wave-motion. Such resemblances he did detect; and, spurred on by +the discovery, he pursued his speculations and experiments, until +he finally succeeded in placing on an immovable basis the +Undulatory Theory of Light.</p> +<p>The founder of this great theory was Thomas Young, a name, +perhaps, unfamiliar to many of you, but which ought to be familiar +to you all. Permit me, therefore, by a kind of geometrical +construction which I once ventured to employ in London, to give you +a notion of the magnitude of this man. Let Newton stand erect in +his age, and Young in his. Draw a straight line from Newton to +Young, tangent to the heads of both. This line would slope +downwards from Newton to <a name="Page_50" id= +"Page_50"></a><span class="pagenum">[Pg 50]</span>Young, because +Newton was certainly the taller man of the two. But the slope would +not be steep, for the difference of stature was not excessive. The +line would form what engineers call a gentle gradient from Newton +to Young. Place underneath this line the biggest man born in the +interval between both. It may be doubted whether he would reach the +line; for if he did he would be taller intellectually than Young, +and there was probably none taller. But I do not want you to rest +on English estimates of Young; the German, Helmholtz, a kindred +genius, thus speaks of him: "His was one of the most profound minds +that the world has ever seen; but he had the misfortune to be too +much in advance of his age. He excited the wonder of his +contemporaries, who, however, were unable to follow him to the +heights at which his daring intellect was accustomed to soar. His +most important ideas lay, therefore, buried and forgotten in the +folios of the Royal Society, until a new generation gradually and +painfully made the same discoveries, and proved the exactness of +his assertions and the truth of his demonstrations."</p> +<p>It is quite true, as Helmholtz says, that Young was in advance +of his age; but something is to be added which illustrates the +responsibility of our public writers. For twenty years this man of +genius was quenched—hidden from the appreciative intellect of +his country-men—deemed in fact a dreamer, through the +vigorous sarcasm of a writer who had then possession of the public +ear, and who in the <i>Edinburgh Review</i> poured ridicule upon +Young and his speculations. To the celebrated Frenchmen Fresnel and +Arago he was first indebted for the restitution of his rights; for +they, especi<a name="Page_51" id="Page_51"></a><span class= +"pagenum">[Pg 51]</span>ally Fresnel, independently remade and +vastly extended his discoveries. To the students of his works Young +has long since appeared in his true light, but these twenty blank +years pushed him from the public mind, which became in time filled +with the fame of Young's colleague at the Royal Institution, Davy, +and afterwards with the fame of Faraday. Carlyle refers to a remark +of Novalis, that a man's self-trust is enormously increased the +moment he finds that others believe in him. If the opposite remark +be true—if it be a fact that public disbelief weakens a man's +force—there is no calculating the amount of damage these +twenty years of neglect may have done to Young's productiveness as +an investigator. It remains to be stated that his assailant was Mr. +Henry Brougham, afterwards Lord Chancellor of England.</p> +<h3>§ 4. <i>Wave-Motion, Interference of Waves, 'Whirlpool +Rapids' of Niagara</i>.</h3> +<p>Our hardest work is now before us. But the capacity for hard +work depends in a great measure on the antecedent winding up of the +will; I would call upon you, therefore, to gird up your loins for +coming labours.</p> +<p>In the earliest writings of the ancients we find the notion that +sound is conveyed by the air. Aristotle gives expression to this +notion, and the great architect Vitruvius compares the waves of +sound to waves of water. But the real mechanism of wave-motion was +hidden from the ancients, and indeed was not made clear until the +time of Newton. The central difficulty of the subject was, to +distinguish between the motion <a name="Page_52" id= +"Page_52"></a><span class="pagenum">[Pg 52]</span>of the wave +itself, and the motion of the particles which at any moment +constitute the wave.</p> +<p>Stand upon the seashore and observe the advancing rollers before +they are distorted by the friction of the bottom. Every wave has a +back and a front, and, if you clearly seize the image of the moving +wave, you will see that every particle of water along the front of +the wave is in the act of rising, while every particle along its +back is in the act of sinking. The particles in front reach in +succession the crest of the wave, and as soon as the crest is past +they begin to fall. They then reach the furrow or <i>sinus</i> of +the wave, and can sink no farther. Immediately afterwards they +become the front of the succeeding wave, rise again until they +reach the crest, and then sink as before. Thus, while the waves +pass onwards horizontally, the individual particles are simply +lifted up and down vertically. Observe a sea-fowl, or, if you are a +swimmer, abandon yourself to the action of the waves; you are not +carried forward, but simply rocked up and down. The propagation of +a wave is the propagation of a <i>form</i>, and not the +transference of the substance which constitutes the wave.</p> +<p>The <i>length</i> of the wave is the distance from crest to +crest, while the distance through which the individual particles +oscillate is called the <i>amplitude</i> of the oscillation. You +will notice that in this description the particles of water are +made to vibrate <i>across</i> the line of propagation.<a name= +"FNanchor_10_10" id="FNanchor_10_10"></a><a href="#Footnote_10_10" +class="fnanchor">[10]</a></p> +<p><a name="Page_53" id="Page_53"></a><span class="pagenum">[Pg +53]</span>And now we have to take a step forwards, and it is the +most important step of all. You can picture two series of waves +proceeding from different origins through the same water. When, for +example, you throw two stones into still water, the ring-waves +proceeding from the two centres of disturbance intersect each +other. Now, no matter how numerous these waves may be, the law +holds good that the motion of every particle of the water is the +algebraic sum of all the motions imparted to it. If crest coincide +with crest and furrow with furrow, the wave is lifted to a double +height above its sinus; if furrow coincide with crest, the motions +are in opposition and their sum is zero. We have then <i>still</i> +water. This action of wave upon wave is technically called +<i>interference</i>, a term, to be remembered.</p> +<div class="figcenter" style="width: 438px;"><img src= +"images/fig10.jpg" width="438" height="443" alt="Fig. 10." title= +"" /> <b>Fig. 10.</b></div> +<p>To the eye of a person conversant with these principles, nothing +can be more interesting than the crossing of water ripples. Through +their interference the water-surface is sometimes shivered into the +most beautiful mosaic, trembling rhythmically as if with a kind of +visible music. When waves are skilfully generated in a dish of +mercury, a strong light thrown upon the shining surface, and +reflected on to a screen, reveals the motions of the liquid metal. +The shape of the vessel determines the forms of the figures +produced. In a circular dish, for example, a disturbance at the +centre propagates itself as a series of circular waves, which, +after reflection, again meet at the centre. If the point of +disturbance be a little way removed from the centre, the +interference of the direct and reflected waves produces the +magnificent chasing shown in the annexed <a name="Page_54" id= +"Page_54"></a><span class="pagenum">[Pg 54]</span>figure.<a name= +"FNanchor_11_11" id="FNanchor_11_11"></a><a href="#Footnote_11_11" +class="fnanchor">[11]</a> The light reflected from such a surface +yields a pattern of extraordinary beauty. When the mercury is +slightly struck by a needle-point in a direction concentric with +the surface of the vessel, the lines of light run round in mazy +coils, interlacing and unravelling themselves in a wonderful +manner. When the vessel is square, a splendid chequer-work is +produced by the crossing of the direct and reflected waves. Thus, +in the case of wave-motion, the most ordinary causes give rise to +most exquisite effects. The words of Emerson are perfectly +applicable here:—</p> +<div class="poem"> +<div class="stanza"><span>'Thou can'st not wave thy staff in the +air,<br /></span> <span class="i2">Or dip thy paddle in the +lake,<br /></span> <span>But it carves the brow of beauty +there.<br /></span> <span class="i2">And the ripples in rhymes the +oars forsake.'<br /></span></div> +</div> +<p><a name="Page_55" id="Page_55"></a><span class="pagenum">[Pg +55]</span>The most impressive illustration of the action of waves +on waves that I have ever seen occurs near Niagara. For a distance +of two miles, or thereabouts, below the Falls, the river Niagara +flows unruffled through its excavated gorge. The bed subsequently +narrows, and the water quickens its motion. At the place called the +'Whirlpool Rapids,' I estimated the width of the river at 300 feet, +an estimate confirmed by the dwellers on the spot. When it is +remembered that the drainage of nearly half a continent is +compressed into this space, the impetuosity of the river's escape +through this gorge may be imagined.</p> +<p>Two kinds of motion are here obviously active, a motion of +translation and a motion of undulation—the race of the river +through its gorge, and the great waves generated by its collision +with the obstacles in its way. In the middle of the stream, the +rush and tossing are most violent; at all events, the impetuous +force of the individual waves is here most strikingly displayed. +Vast pyramidal heaps leap incessantly from the river, some of them +with such energy as to jerk their summits into the air, where they +hang suspended as bundles of liquid pearls, which, when shone upon +by the sun, are of indescribable beauty.</p> +<p>The first impression, and, indeed, the current explanation of +these Rapids is, that the central bed of the river is cumbered with +large boulders, and that the jostling, tossing, and wild leaping of +the waters there are due to its impact against these obstacles. A +very different explanation occurred to me upon the spot. Boulders +derived from the adjacent cliffs visibly cumber the <i>sides</i> of +the river. Against these the water rises and sinks rhythmically but +violently, large waves being <a name="Page_56" id= +"Page_56"></a><span class="pagenum">[Pg 56]</span>thus produced. On +the generation of each wave there is an immediate compounding of +the wave-motion with the river-motion. The ridges, which in still +water would proceed in circular curves round the centre of +disturbance, cross the river obliquely, and the result is, that at +the centre waves commingle which have really been generated at the +sides. This crossing of waves may be seen on a small scale in any +gutter after rain; it may also be seen on simply pouring water from +a wide-lipped jug. Where crest and furrow cross each other, the +wave is annulled; where furrow and furrow cross, the river is +ploughed to a greater depth; and where crest and crest aid each +other, we have that astonishing leap of the water which breaks the +cohesion of the crests, and tosses them shattered into the air. The +phenomena observed at the Whirlpool Rapids constitute, in fact, one +of the grandest illustrations of the principle of interference.</p> +<h3>§ 5. <i>Analogies of Sound and Light.</i></h3> +<p>Thomas Young's fundamental discovery in optics was that the +principle of Interference was applicable to light. Long prior to +his time an Italian philosopher, Grimaldi, had stated that under +certain circumstances two thin beams of light, each of which, +acting singly, produced a luminous spot upon a white wall, when +caused to act together, partially quenched each other and darkened +the spot. This was a statement of fundamental significance, but it +required the discoveries and the genius of Young to give it +meaning. How he did so will gradually become clear to you. You know +that air is compressible: that by pressure it can be rendered more +<a name="Page_57" id="Page_57"></a><span class="pagenum">[Pg +57]</span>dense, and that by dilatation it can be rendered more +rare. Properly agitated, a tuning-fork now sounds in a manner +audible to you all, and most of you know that the air through which +the sound is passing is parcelled out into spaces in which the air +is condensed, followed by other spaces in which the air is +rarefied. These condensations and rarefactions constitute what we +call <i>waves</i> of sound. You can imagine the air of a room +traversed by a series of such waves, and you can imagine a second +series sent through the same air, and so related to the first that +condensation coincides with condensation and rarefaction with +rarefaction. The consequence of this coincidence would be a louder +sound than that produced by either system of waves taken singly. +But you can also imagine a state of things where the condensations +of the one system fall upon the rarefactions of the other system. +In this case (other things being equal) the two systems would +completely neutralize each other. Each of them taken singly +produces sound; both of them taken together produce no sound. Thus +by adding sound to sound we produce silence, as Grimaldi, in his +experiment, produced darkness by adding light to light.</p> +<p>Through his investigations on sound, which were fruitful and +profound, Young approached the study of light. He put meaning into +the observation of Grimaldi, and immensely extended it. With +splendid success he applied the undulatory theory to the +explanation of the colours of thin plates, and to those of striated +surfaces. He discovered and explained classes of colour which had +been previously unnoticed or unknown. On the assumption that light +was wave-motion, all his experiments on interference were accounted +for; <a name="Page_58" id="Page_58"></a><span class="pagenum">[Pg +58]</span>on the assumption that light was flying particles, +nothing was explained. In the time of Huyghens and Euler a medium +had been assumed for the transmission of the waves of light; but +Newton raised the objection that, if light consisted of the waves +of such a medium, shadows could not exist. The waves, he contended, +would bend round opaque bodies and produce the motion of light +behind them, as sound turns a corner, or as waves of water wash +round a rock. It was proved that the bending round referred to by +Newton actually occurs, but that the inflected waves abolish each +other by their mutual interference. Young also discerned a +fundamental difference between the waves of light and those of +sound. Could you see the air through which sound-waves are passing, +you would observe every individual particle of air oscillating to +and fro, <i>in the direction of propagation</i>. Could you see the +luminiferous ether, you would also find every individual particle +making a small excursion to and fro; but here the motion, like that +assigned to the water-particles above referred to, would be +<i>across</i> the line of propagation. The vibrations of the air +are <i>longitudinal</i>, those of the ether <i>transversal</i>.</p> +<p>The most familiar illustration of the interference of +sound-waves is furnished by the <i>beats</i> produced by two +musical sounds slightly out of unison. When two tuning-forks in +perfect unison are agitated together the two sounds flow without +roughness, as if they were but one. But, by attaching with wax to +one of the forks a little weight, we cause it to vibrate more +slowly than its neighbour. Suppose that one of them performs 101 +vibrations in the time required by the other to perform 100, and +suppose that <a name="Page_59" id="Page_59"></a><span class= +"pagenum">[Pg 59]</span>at starting the condensations and +rarefactions of both forks coincide. At the 101st vibration of the +quicker fork they will again coincide, that fork at this point +having gained one whole vibration, or one whole wavelength, upon +the other. But a little reflection will make it clear that, at the +50th vibration, the two forks condensation where the other tends to +produce a rarefaction; by the united action of the two forks, +therefore, the sound is quenched, and we have a pause of silence. +This occurs where one fork has gained <i>half a wavelength</i> upon +the other. At the 101st vibration, as already stated, we have +coincidence, and, therefore, augmented sound; at the 150th +vibration we have again a quenching of the sound. Here the one fork +is <i>three half-waves</i> in advance of the other. In general +terms, the waves conspire when the one series is an <i>even</i> +number of half-wave lengths, and they destroy each other when the +one series is an <i>odd</i> number of half-wave lengths in advance +of the other. With two forks so circumstanced, we obtain those +intermittent shocks of sound separated by pauses of silence, to +which we give the name of beats. By a suitable arrangement, +moreover, it is possible to make one sound wholly extinguish +another. Along four distinct lines, for example, the vibrations of +the two prongs of a tuning-fork completely blot each other +out.<a name="FNanchor_12_12" id="FNanchor_12_12"></a><a href= +"#Footnote_12_12" class="fnanchor">[12]</a></p> +<p>The <i>pitch</i> of sound is wholly determined by the rapidity +of the vibration, as the <i>intensity</i> is by the amplitude. What +pitch is to the ear in acoustics, colour is to the eye in the +undulatory theory of light. <a name="Page_60" id= +"Page_60"></a><span class="pagenum">[Pg 60]</span>Though never +seen, the lengths of the waves of light have been determined. Their +existence is proved <i>by their effects</i>, and from their effects +also their lengths may be accurately deduced. This may, moreover, +be done in many ways, and, when the different determinations are +compared, the strictest harmony is found to exist between them. +This consensus of evidence is one of the strongest points of the +undulatory theory. The shortest waves of the visible spectrum are +those of the extreme violet; the longest, those of the extreme red; +while the other colours are of intermediate pitch or wavelength. +The length of a wave of the extreme red is such, that it would +require 39,000 such waves, placed end to end, to cover one inch, +while 64,631 of the extreme violet waves would be required to span +the same distance.</p> +<p>Now, the velocity of light, in round numbers, is 186,000 miles +per second. Reducing this to inches, and multiplying the number +thus found by 39,000, we find the number of waves of the extreme +red, in 186,000 miles, to be four hundred and sixty millions of +millions. <i>All these waves enter the eye, and strike the retina +at the back of the eye in one second</i>. In a similar manner, it +may be found that the number of shocks corresponding to the +impression of violet is six hundred and seventy-eight millions of +millions.</p> +<p>All space is filled with matter oscillating at such rates. From +every star waves of these dimensions move, with the velocity of +light, like spherical shells in all directions. And in ether, just +as in water, the motion of every particle is the algebraic sum of +all the separate motions imparted to it. One motion does not blot +out the other; or, if extinction occur at one point, it is strictly +atoned for, by augmented motion, at some <a name="Page_61" id= +"Page_61"></a><span class="pagenum">[Pg 61]</span>other point. +Every star declares by its light its undamaged individuality, as if +it alone had sent its thrills through space.</p> +<h3>§ 6. <i>Interference of Light</i>.</h3> +<div class="figleft" style="width: 465px;"><img src= +"images/fig11.jpg" width="465" height="150" alt="Fig. 11." title= +"" /> <b>Fig. 11.</b></div> +<p>The principle of interference, as just stated, applies to the +waves of light as it does to the waves of water and the waves of +sound. And the conditions of interference are the same in all +three. If two series of light-waves of the same length start at the +same moment from a common origin (say A, fig. 11), crest coincides +with crest, sinus with sinus, and the two systems blend together to +a single system (A <i>m</i> <i>n</i>) of double amplitude. If both +series start at the same moment, one of them being, at starting, a +whole wavelength in advance of the other, they also add themselves +together, and we have an augmented luminous effect. The same occurs +when the one system of waves is any <i>even</i> number of +semi-undulations in advance of the other. But if the one system be +half a wave-length (as at A' <i>a</i>', fig. 12), or any <i>odd</i> +number of half wavelengths, in advance, then the crests of the one +fall upon the sinuses of the other; the one system, in fact, tends +to <i>lift</i> the particles of ether at the precise places where +the other tends to <i>depress</i> them; hence, through the <a name= +"Page_62" id="Page_62"></a><span class="pagenum">[Pg +62]</span>joint action of these opposing forces (indicated by the +arrows) the light-ether remains perfectly still. This stillness of +the ether is what we call darkness, which corresponds with a dead +level in the case of water.</p> +<div class="figright" style="width: 480px;"><img src= +"images/fig12.jpg" width="480" height="88" alt="Fig. 12." title= +"" /> <b>Fig. 12.</b></div> +<p>It was said in our first lecture, with reference to the colours +produced by absorption, that the function of natural bodies is +selective, not creative; that they extinguish certain constituents +of the white solar light, and appear in the colours of the +unextinguished light. It must at once occur to you that, inasmuch +as we have in interference an agency by which light may be +self-extinguished, we may have in it the conditions for the +production of colour. But this would imply that certain +constituents are quenched by interference, while others are +permitted to remain. This is the fact; and it is entirely due to +the difference in the lengths of the waves of light.</p> +<h3>§ 7. <i>Colours of thin Films. Observations of Boyle and +Hooke</i>.</h3> +<p>This subject may be illustrated by the phenomena which first +suggested the undulatory theory to the mind of Hooke. These are the +colours of thin transparent films of all kinds, known as the +<i>colours of thin plates</i>. In this relation no object in the +world possesses a deeper scientific interest than a common +soap-bubble. And here let me say emerges one of the <a name= +"Page_63" id="Page_63"></a><span class="pagenum">[Pg +63]</span>difficulties which the student of pure science encounters +in the presence of 'practical' communities like those of America +and England; it is not to be expected that such communities can +entertain any profound sympathy with labours which seem so far +removed from the domain of practice as are many of the labours of +the man of science. Imagine Dr. Draper spending his days in blowing +soap-bubbles and in studying their colours! Would you show him the +necessary patience, or grant him the necessary support? And yet be +it remembered it was thus that minds like those of Boyle, Newton +and Hooke were occupied; and that on such experiments has been +founded a theory, the issues of which are incalculable. I see no +other way for you, laymen, than to trust the scientific man with +the choice of his inquiries; he stands before the tribunal of his +peers, and by their verdict on his labours you ought to abide.</p> +<p>Whence, then, are derived the colours of the soap-bubble? +Imagine a beam of white light impinging on the bubble. When it +reaches the first surface of the film, a known fraction of the +light is reflected back. But a large portion of the beam enters the +film, reaches its second surface, and is again in part reflected. +The waves from the second surface thus turn back and hotly pursue +the waves from the first surface. And, if the thickness of the film +be such as to cause the necessary retardation, the two systems of +waves interfere with each other, producing augmented or diminished +light, as the case may be.</p> +<p>But, inasmuch as the waves of light are of different lengths, it +is plain that, to produce extinction in the case of the longer +waves, a greater thickness of film is necessary than in the case of +the shorter ones. <a name="Page_64" id="Page_64"></a><span class= +"pagenum">[Pg 64]</span>Different colours, therefore, must appear +at different thicknesses of the film.</p> +<p>Take with you a little bottle of spirit of turpentine, and pour +it into one of your country ponds. You will then see the glowing of +those colours over the surface of the water. On a small scale we +produce them thus: A common tea-tray is filled with water, beneath +the surface of which dips the end of a pipette. A beam of light +falls upon the water, and is reflected by it to the screen. Spirit +of turpentine is poured into the pipette; it descends, issues from +the end in minute drops, which rise in succession to the surface. +On reaching it, each drop spreads suddenly out as a film, and +glowing colours immediately flash forth upon the screen. The +colours change as the thickness of the film changes by evaporation. +They are also arranged in zones, in consequence of the gradual +diminution of thickness from the centre outwards.</p> +<p>Any film whatever will produce these colours. The film of air +between two plates of glass squeezed together, exhibits, as shown +by Hooke, rich fringes of colour. A particularly fine example of +these fringes is now before you. Nor is even air necessary; the +rupture of optical continuity suffices. Smite with an axe the +black, transparent ice—black, because it is pure and of great +depth—under the moraine of a glacier; you readily produce in +the interior flaws which no air can reach, and from these flaws the +colours of thin plates sometimes break like fire. But the source of +most historic interest is, as already stated, the soap-bubble. With +one of the mixtures employed by the eminent blind philosopher, +Plateau, in his researches on the cohesion figures of thin films, +we obtain in still air a bubble ten or twelve <a name="Page_65" id= +"Page_65"></a><span class="pagenum">[Pg 65]</span>inches in +diameter. You may look at the bubble itself, or you may look at its +projection upon the screen; rich colours arranged in zones are, in +both cases, exhibited. Rendering the beam parallel, and permitting +it to impinge upon the sides, bottom, and top of the bubble, +gorgeous fans of colour, reflected from the bubble, overspread the +screen, rotating as the beam is carried round. By this experiment +the internal motions of the film are also strikingly displayed.</p> +<p>Not in a moment are great theories elaborated: the facts which +demand them become first prominent; then, to the period of +observation succeeds a period of pondering and of tentative +explanation. By such efforts the human mind is gradually prepared +for the final theoretic illumination. The colours of thin plates, +for example, occupied the attention of Robert Boyle. In his +'Experimental History of Colours' he contends against the schools +which affirmed that colour was 'a penetrative quality that reaches +to the innermost parts of the object,' adducing opposing facts. 'To +give you a first instance,' he says, 'I shall need but to remind +you of what I told you a little after the beginning of this essay, +touching the blue and red and yellow that may be produced upon a +piece of tempered steel; for these colours, though they be very +vivid, yet if you break the steel they adorn, they will appear to +be but superficial.' He then describes, in phraseology which shows +the delight he took in his work, the following beautiful +experiment:—</p> +<p>'We took a quantity of clean lead, and melted it with a strong +fire, and then immediately pouring it out into a clean vessel of +convenient shape and matter (we used one of iron, that the great +and sudden heat <a name="Page_66" id="Page_66"></a><span class= +"pagenum">[Pg 66]</span>might not injure it), and then carefully +and nimbly taking off the scum that floated on the top, we +perceived, as we expected, the smooth and glossy surface of the +melted matter to be adorned with a very glorious colour, which, +being as transitory as delightful, did almost immediately give +place to another vivid colour, and that was as quickly succeeded by +a third, and this, as it were, chased away by a fourth; and so +these wonderfully vivid colours successively appeared and vanished +till the metal ceasing to be hot enough to hold any longer this +pleasing spectacle, the colours that chanced to adorn the surface +when the lead thus began to cool remained upon it, but were so +superficial that how little soever we scraped off the surface of +the lead, we did, in such places, scrape off all the colour.' +'These things,' he adds, 'suggested to me some thoughts or ravings +which I have not now time to acquaint you with.'<a name= +"FNanchor_13_13" id="FNanchor_13_13"></a><a href="#Footnote_13_13" +class="fnanchor">[13]</a></p> +<p>He extends his observations to essential oils and spirits of +wine, 'which being shaken till they have good store of bubbles, +those bubbles will (if attentively considered) appear adorned with +various and lovely colours, which all immediately vanish upon the +retrogressing of the liquid which affords these bubbles their skins +into the rest of the oil.' He also refers to the colour of glass +films. 'I have seen one that was skilled in fashioning glasses by +the help of a lamp blowing some of them so strongly as to burst +them; whereupon it was found that the tenacity of the metal was +such that before it broke it suffered itself to be reduced into +films so extremely thin that they constantly showed upon their +surface the varying colours of the rainbow.'<a name= +"FNanchor_14_14" id="FNanchor_14_14"></a><a href="#Footnote_14_14" +class="fnanchor">[14]</a></p> +<p><a name="Page_67" id="Page_67"></a><span class="pagenum">[Pg +67]</span>Subsequent to Boyle the colours of thin plates occupied +the attention of Robert Hooke, in whose writings we find a dawning +of the undulatory theory of light. He describes with great +distinctness the colours obtained with thin flakes of 'Muscovy +glass' (talc), also those surrounding flaws in crystals where +optical continuity is destroyed. He shows very clearly the +dependence of the colour upon the thickness of the film, and proves +by microscopic observation that plates of a uniform thickness yield +uniform colours. 'If,' he says, 'you take any small piece of the +Muscovy glass, and with a needle, or some other convenient +instrument, cleave it oftentimes into thinner and thinner +laminæ, you shall find that until you come to a determinate +thinness of them they shall appear transparent and colourless; but +if you continue to split and divide them further, you shall find at +last that each plate shall appear most lovely tinged or imbued with +a determinate colour. If, further, by any means you so flaw a +pretty thick piece that one part begins to cleave a little from the +other, and between these two there be gotten some pellucid medium, +those laminated or pellucid bodies that fill that space shall +exhibit several rainbows or coloured lines, the colours of which +will be disposed and ranged according to the various thicknesses of +the several parts of the plate.' He then describes fully and +clearly the experiment with pressed glasses already referred +to:—</p> +<p>'Take two small pieces of ground and polished looking-glass +plate, each about the bigness of a shilling: take these two dry, +and with your forefingers and thumbs press them very hard and close +together, and you shall find that when they approach each other +<a name="Page_68" id="Page_68"></a><span class="pagenum">[Pg +68]</span>very near there will appear several irises or coloured +lines, in the same manner almost as in the Muscovy glass; and you +may very easily change any of the colours of any part of the +interposed body by pressing the plates closer and harder together, +or leaving them more lax—that is, a part which appeared +coloured with a red, may presently be tinged with a yellow, blue, +green, purple, or the like. 'Any substance,' he says, 'provided it +be thin and transparent, will show these colours.' Like Boyle, he +obtained them with glass films; he also procured them with bubbles +of pitch, rosin, colophony, turpentine, solutions of several gums, +as gum arabic in water, any glutinous liquor, as wort, wine, spirit +of wine, oyl of turpentine, glare of snails, &c.</p> +<p>Hooke's writings show that even in his day the idea that both +light and heat are modes of motion had taken possession of many +minds. 'First,' he says, 'that all kind <i>of fiery burning +bodies</i> have their parts in motion I think will be easily +granted me. That the spark struck from a flint and steel is in +rapid agitation I have elsewhere made probable;... that heat argues +a motion of the internal parts is (as I said before) generally +granted;... and that in all extremely hot shining bodies there is a +very quick motion that causes light, as well as a more robust that +causes heat, may be argued from the celerity wherewith the bodies +are dissolved. Next, it must be <i>a vibrative motion.'</i> His +reference to the quick motion of light and the more robust motion +of heat is a remarkable stroke of sagacity; but Hooke's direct +insight is better than his reasoning; for the proofs he adduces +that light is 'a vibrating motion' have no particular bearing upon +the question.</p> +<p><a name="Page_69" id="Page_69"></a><span class="pagenum">[Pg +69]</span>Still the Undulatory Theory had undoubtedly dawned upon +the mind of this remarkable man. In endeavouring to account for the +colours of thin plates, he again refers to the relation of colour +to thickness: he dwells upon the fact that the film which shows +these colours must be transparent, proving this by showing that +however thin an opaque body was rendered no colours were produced. +'This,' he says, 'I have often tried by pressing a small globule of +mercury between two smooth plates of glass, whereby I have reduced +that body to a much greater thinness than was requisite to exhibit +the colours with a transparent body.' Then follows the sagacious +remark that to produce the colours 'there must be a considerable +reflecting body adjacent to the under or further side of the lamina +or plate: for this I always found, that the greater that reflection +was the more vivid were the appearing colours. From which +observation,' he continues, 'it is most evident, <i>that the +reflection from the further or under side of the body is the +principal cause of the production of these colours.</i>'</p> +<p>He draws a diagram, correctly representing the reflection at the +two surfaces of the film; but here his clearness ends. He ascribes +the colours to a coalescence or confusion of the two reflecting +pulses; the principal of interference being unknown to him, he +could not go further in the way of explanation.</p> +<h3>§ 8. <i>Newton's Rings. Relation of Colour to Thickness of +Film</i>.</h3> +<div class="figright" style="width: 371px;"><img src= +"images/fig13.jpg" width="371" height="81" alt="Fig. 13" title= +"" /> <b>Fig. 13</b></div> +<p>In this way, then, by the active operation of different minds, +facts are observed, examined, and the precise <a name="Page_70" id= +"Page_70"></a><span class="pagenum">[Pg 70]</span>conditions of +their appearance determined. All such work in science is the +prelude to other work; and the efforts of Boyle and Hooke cleared +the way for the optical career of Newton. He conquered the +difficulty which Hooke had found insuperable, and determined by +accurate measurements the relation of the thickness of the film to +the colour it displays. In doing this his first care was to obtain +a film of variable and calculable depth. On a plano-convex glass +lens (D B E, fig. 13) of very feeble curvature he laid a plate of +glass (A C) with a plane surface, thus obtaining a film of air of +gradually increasing depth from the point of contact (B) outwards. +On looking at the film in monochromatic light he saw, with the +delight attendant on fulfilled prevision, surrounding the place of +contact, a series of bright rings separated from each other by dark +ones, and becoming more closely packed together as the distance +from the point of contact augmented (as in fig. 14). When he +employed red light, his rings had certain diameters; when he +employed blue light, the diameters were less. In general terms, the +more refrangible the light the smaller were the rings. Causing his +glasses to pass through the spectrum from red to blue, the rings +gradually contracted; when the passage was from blue to red, the +rings expanded. This is a beautiful experiment, and appears to have +given Newton the most lively satisfaction. When white light fell +upon, the glasses, inasmuch as the colours were not <a name= +"Page_71" id="Page_71"></a><span class="pagenum">[Pg +71]</span>superposed, a series <i>of iris-coloured</i> circles was +obtained. A magnified image of <i>Newton's rings</i> is now before +you, and, by employing in succession red, blue, and white light, we +obtain all the effects observed by Newton. You notice that in +monochromatic light the rings run closer and closer together as +they recede from the centre. This is due to the fact that at a +distance the film of air thickens more rapidly than near the +centre. When white light is employed, this closing up of the rings +causes the various colours to be superposed, so that after a +certain thickness they are blended together to white light, the +rings then ceasing altogether. It needs but a moment's reflection +to understand that the colours of thin plates, produced by white +light, are never unmixed or monochromatic.</p> +<div class="figleft" style="width: 278px;"><img src= +"images/fig14.jpg" width="278" height="275" alt="Fig. 14" title= +"" /> <b>Fig. 14</b></div> +<p>Newton compared the tints obtained in this way with the tints of +his soap-bubble, and he calculated the corresponding thickness. How +he did this may be thus made plain to you: Suppose the water of the +ocean to be absolutely smooth; it would then accurately represent +the earth's curved surface. Let a perfectly <a name="Page_72" id= +"Page_72"></a><span class="pagenum">[Pg 72]</span>horizontal plane +touch the surface at any point. Knowing the earth's diameter, any +engineer or mathematician in this room could tell you how far the +sea's surface will lie below this plane, at the distance of a yard, +ten yards, a hundred yards, or a thousand yards from the point of +contact of the plane and the sea. It is common, indeed, in +levelling operations, to allow for the curvature of the earth. +Newton's calculation was precisely similar. His plane glass was a +tangent to his curved one. From its refractive index and focal +distance he determined the diameter of the sphere of which his +curved glass formed a segment, he measured the distances of his +rings from the place of contact, and he calculated the depth +between the tangent plane and the curved surface, exactly as the +engineer would calculate the distance between his tangent plane and +the surface of the sea. The wonder is, that, where such +infinitesimal distances are involved, Newton, with the means at his +disposal, could have worked with such marvellous exactitude.</p> +<p>To account for these rings was the greatest optical difficulty +that Newton, ever encountered. He quite appreciated the difficulty. +Over his eagle eye there was no film—no vagueness in his +conceptions. At the very outset his theory was confronted by the +question, Why, when a beam of light is incident on a transparent +body, are some of the light-particles reflected and some +transmitted? Is it that there are two kinds of particles, the one +specially fitted for transmission and the other for reflection? +This cannot be the reason; for, if we allow a beam of light which +has been reflected from one piece of glass to fall upon another, +it, as a general rule, is also divided into a reflected and a +<a name="Page_73" id="Page_73"></a><span class="pagenum">[Pg +73]</span>transmitted portion. The particles once reflected are not +always reflected, nor are the particles once transmitted always +transmitted. Newton saw all this; he knew he had to explain why it +is that the self-same particle is at one moment reflected and at +the next moment transmitted. It could only he through <i>some +change in the condition of the particle itself</i>. The self-same +particle, he affirmed, was affected by 'fits' of easy transmission +and reflection.</p> +<h3>§ 9. <i>Theory of 'Fits' applied to Newton's +Rings</i>.</h3> +<p>If you are willing to follow me in an attempt to reveal the +speculative groundwork of this theory of fits, the intellectual +discipline will, I think, repay you for the necessary effort of +attention. Newton was chary of stating what he considered to be the +cause of the fits, but there can hardly be a doubt that his mind +rested on a physical cause. Nor can there be a doubt that here, as +in all attempts at theorising, he was compelled to fall back upon +experience for the materials of his theory. Let us attempt to +restore his course of thought and observation. A magnet would +furnish him with the notion of attracted and repelled poles; and he +who habitually saw in the visible an image of the invisible would +naturally endow his light-particles with such poles. Turning their +attracted poles towards a transparent substance, the particles +would be sucked in and transmitted; turning their repelled poles, +they would be driven away or reflected. Thus, by the ascription of +poles, the transmission and reflection of the self-same particle at +different times might be accounted for.</p> +<p><a name="Page_74" id="Page_74"></a><span class="pagenum">[Pg +74]</span>Consider these rings of Newton as seen in pure red light: +they are alternately bright and dark. The film of air corresponding +to the outermost of them is not thicker than an ordinary +soap-bubble, and it becomes thinner on approaching the centre; +still Newton, as I have said, measured the thickness corresponding +to every ring, and showed the difference of thickness between ring +and ring. Now, mark the result. For the sake of convenience, let us +call the thickness of the film of air corresponding to the first +dark ring <i>d</i>; then Newton found the distance corresponding to +the second dark ring 2 <i>d</i>; the thickness corresponding to the +third dark ring 3 <i>d</i>; the thickness corresponding to the +tenth dark ring 10 <i>d</i>, and so on. Surely there must be some +hidden meaning in this little distance, <i>d</i>, which turns up so +constantly? One can imagine the intense interest with which Newton +pondered its meaning. Observe the probable outcome of his thought. +He had endowed his light-particles with poles, but now he is forced +to introduce the notion of <i>periodic recurrence</i>. Here his +power of transfer from the sensible to the subsensible would render +it easy for him to suppose the light-particles animated, not only +with a motion of translation, but also with a motion of rotation. +Newton's astronomical knowledge rendered all such conceptions +familiar to him. The earth has such a double motion. In the time +occupied in passing over a million and a half of miles of its +orbit—that is, in twenty-four hours—our planet performs +a complete rotation; and in the time required to pass over the +distance <i>d</i>, Newton's light-particle might be supposed to +perform a complete rotation. True, the light-particle is smaller +than the planet, and the distance <i>d</i>, instead of being a +million <a name="Page_75" id="Page_75"></a><span class= +"pagenum">[Pg 75]</span>and a half of miles, is a little over the +ninety thousandth of an inch. But the two conceptions are, in point +of intellectual quality, identical.</p> +<p>Imagine, then, a particle entering the film of air where it +possesses this precise thickness. To enter the film, its attracted +end must be presented. Within the film it is able to turn +<i>once</i> completely round; at the other side of the film its +attracted pole will be again presented; it will, therefore, enter +the glass at the opposite side of the film <i>and be lost to the +eye</i>. All round the place of contact, wherever the film +possesses this precise thickness, the light will equally +disappear—we shall therefore have a ring of darkness.</p> +<p>And now observe how well this conception falls in with the law +of proportionality discovered by Newton. When the thickness of the +film is 2 <i>d</i>, the particle has time to perform, <i>two</i> +complete rotations within the film; when the thickness is 3 <i>d, +three</i> complete rotations; when 10 <i>d, ten</i> complete +rotations are performed. It is manifest that in each of these +cases, on arriving at the second surface of the film, the attracted +pole of the particle will be presented. It will, therefore, be +transmitted; and, because no light is sent to the eye, we shall +have a ring of darkness at each of these places.</p> +<p>The bright rings follow immediately from the same conception. +They occur between the dark rings, the thicknesses to which they +correspond being also intermediate between those of the dark ones. +Take the case of the first bright ring. The thickness of the film +is ½<i>d</i>; in this interval the rotating particle can +perform only half a rotation. When, therefore, it reaches the +second surface of the film, its repelled pole <a name="Page_76" id= +"Page_76"></a><span class="pagenum">[Pg 76]</span>is presented; it +is, therefore, driven back and reaches the eye. At all distances +round the centre corresponding to this thickness the same effect is +produced, and the consequence is a ring of brightness. The other +bright rings are similarly accounted for. At the second one, where +the thickness is 1½<i>d</i>, a rotation and a half is +performed; at the third, two rotations and a half; and at each of +these places the particles present their repelled poles to the +lower surface of the film. They are therefore sent back to the eye, +and produce there the impression of brightness. This analysis, +though involving difficulties when closely scrutinised, enables us +to see how the theory of fits may have grown into consistency in +the mind of Newton.</p> +<p>It has been already stated that the Emission Theory assigned a +greater velocity to light in glass and water than in air or stellar +space; and that on this point it was at direct issue with the +theory of undulation, which makes the velocity in air or stellar +space greater than in glass or water. By an experiment proposed by +Arago, and executed with consummate skill by Foucault and Fizeau, +this question was brought to a crucial test, and decided in favour +of the theory of undulation.</p> +<p>In the present instance also the two theories are at variance. +Newton assumed that the action which produces the alternate bright +and dark rings took place at a <i>single surface</i>; that is, the +second surface of the film. The undulatory theory affirms that the +rings are caused by the interference of waves reflected from both +surfaces. This also has been demonstrated by experiment. By a +proper arrangement, as we shall afterwards learn, we may abolish +reflection from one of <a name="Page_77" id= +"Page_77"></a><span class="pagenum">[Pg 77]</span>the surfaces of +the film, and when this is done the rings vanish altogether.</p> +<p>Rings of feeble intensity are also formed by <i>transmitted</i> +light. These are referred by the undulatory theory to the +interference of waves which have passed <i>directly</i> through the +film, with others which have suffered <i>two</i> reflections within +the film, and are thus completely accounted for.</p> +<h3>§ 10. <i>The Diffraction of Light</i>.</h3> +<p>Newton's espousal of the Emission Theory is said to have +retarded scientific discovery. It might, however, be questioned +whether, in the long run, the errors of great men have not really +their effect in rendering intellectual progress rhythmical, instead +of permitting it to remain uniform, the 'retardation' in each case +being the prelude to a more impetuous advance. It is confusion and +stagnation, rather than error, that we ought to avoid. Thus, though +the undulatory theory was held back for a time, it gathered +strength in the interval, and its development within the last half +century has been so rapid and triumphant as to leave no rival in +the field. We have now to turn to the investigation of new classes +of phenomena, of which it alone can render a satisfactory +account.</p> +<p>Newton, who was familiar with the idea of an ether, and who +introduced it in some of his speculations, objected, as already +stated, that if light consisted of waves shadows could not exist; +for that the waves would bend round the edges of opaque bodies and +agitate the ether behind them. He was right in affirming that this +bending ought to occur, but wrong <a name="Page_78" id= +"Page_78"></a><span class="pagenum">[Pg 78]</span>in supposing that +it does not occur. The bending is real, though in all ordinary +cases it is masked by the action of interference. This inflection +of the light receives the name of <i>Diffraction</i>.</p> +<p>To study the phenomena of diffraction it is necessary that our +source of light should be a physical point, or a fine line; for +when a luminous surface is employed, the waves issuing from +different points of the surface obscure and neutralize each other. +A <i>point</i> of light of high intensity is obtained by admitting +the parallel rays of the sun through an aperture in a +window-shutter, and concentrating the beam by a lens of short +focus. The small solar image at the focus constitutes a suitable +point of light. The image of the sun formed on the convex surface +of a glass bead, or of a watch-glass blackened within, though less +intense, will also answer. An intense <i>line</i> of light is +obtained by admitting the sunlight through a slit and sending it +through a strong cylindrical lens. The slice of light is contracted +to a physical line at the focus of the lens. A glass tube blackened +within and placed in the light, reflects from its surface a +luminous line which, though less intense, also answers the +purpose.</p> +<p>In the experiment now to be described a vertical slit of +variable width is placed in front of the electric lamp, and this +slit is looked at from a distance through another vertical slit, +also of variable aperture, and held in the hand.</p> +<p>The light of the lamp being, in the first place, rendered +monochromatic by placing a pure red glass in front of the slit, +when the eye is placed in the straight line drawn through both +slits an extraordinary appearance (shown in fig. 15) is observed. +Firstly, the slit <a name="Page_79" id="Page_79"></a><span class= +"pagenum">[Pg 79]</span>in front of the lamp is seen as a vivid +rectangle of light; but right and left of it is a long series of +rectangles, decreasing in vividness, and separated from each other +by intervals of absolute darkness.</p> +<p>The breadth of these bands is seen to vary with the width of the +slit held before the eye. When the slit is widened the bands become +narrower, and crowd more losely together; when the slit is +narrowed, the individual bands widen and also retreat from each +other, leaving between them wider spaces of darkness than +before.</p> +<div class="figcenter" style="width: 450px;"><img src= +"images/fig15.jpg" width="450" height="197" alt="Fig. 15." title= +"" /> <b>Fig. 15.</b></div> +<p>Leaving everything else unchanged, let a blue glass or a +solution of ammonia-sulphate of copper, which gives a very pure +blue, be placed in the path of the light. A series of blue bands is +thus obtained, exactly like the former in all respects save one; +the blue rectangles are <i>narrower</i>, and they are <i>closer +together</i> than the red ones.</p> +<p>If we employ colours of intermediate refrangibilities, which we +may do by causing the different colours of a spectrum to shine +through the slit, we obtain bands of colour intermediate in width, +and occupying intermediate positions, between those of the red and +blue. The aspect of the bands in red, green, and violet light is +<a name="Page_80" id="Page_80"></a><span class="pagenum">[Pg +80]</span>represented in fig. 16. When <i>white light</i>, +therefore, passes through the slit the various colours are not +superposed, and instead of a series of monochromatic bands, +separated from each other by intervals of darkness, we have a +series of coloured spectra placed side by side. When the distant +slit is illuminated by a candle flame, instead of the more intense +electric light, or when a distant platinum wire raised to a white +heat by an electric current is employed, substantially the same +effects are observed.</p> +<div class="figcenter" style="width: 496px;"><img src= +"images/fig16.jpg" width="496" height="208" alt="Fig. 16." title= +"" /> <b>Fig. 16.</b></div> +<h3>§ 11. <i>Application of the Wave-theory to the Phenomena +of Diffraction</i>.</h3> +<p>Of these and of a multitude of similar effects the Emission +Theory is incompetent to offer any satisfactory explanation. Let us +see how they are accounted for by the Theory of Undulation.</p> +<p>And here, with the view of reaching absolute clearness, I must +make an appeal to that faculty the importance of which I have dwelt +upon so earnestly here and elsewhere—the faculty of +imagination. Figure yourself upon the sea-shore, with a well-formed +wave advancing. Take a line of particles along the front of +<a name="Page_81" id="Page_81"></a><span class="pagenum">[Pg +81]</span>the wave, all at the same distance below the crest; they +are all rising in the same manner and at the same rate. Take a +similar line of particles on the back of the wave, they are all +falling in the same manner and at the same rate. Take a line of +particles along the crest, they are all in the same condition as +regards the motion of the wave. The same is true for a line of +particles along the furrow of the wave.</p> +<p>The particles referred to in each of these cases respectively, +being in the same condition as regards the motion of the wave, are +said to be in the same <i>phase</i> of vibration. But if you +compare a particle on the front of the wave with one at the back; +or, more generally, if you compare together any two particles not +occupying the same position in the wave, their conditions of motion +not being the same, they are said to be in different phases of +vibration. If one of the particles lie upon the crest, and the +other on the furrow of the wave, then, as one is about to rise and +the other about to fall, they are said to be in <i>opposite</i> +phases of vibration.</p> +<div class="figleft" style="width: 238px;"><img src= +"images/fig17.jpg" width="238" height="238" alt="Fig 17." title= +"" /> <b>Fig. 17.</b></div> +<p>There is still another point to be cleared up—and it is +one of the utmost importance as regards our present subject. Let O +(fig. 17) be a spot in still water which, when disturbed, produces +a series of circular waves: the disturbance necessary to produce +these waves is simply an oscillation up and down of the water at O. +Let <i>m</i> <i>n</i> be the position of the ridge of one of the +waves at any moment, and <i>m'</i> <i>n'</i> its position a second +or two afterwards. Now every particle of water, as the wave passes +it, oscillates, as we have learned, up and down. If, then, this +oscillation be a sufficient origin of wave-motion, each distinct +particle of the <a name="Page_82" id="Page_82"></a><span class= +"pagenum">[Pg 82]</span>wave <i>m</i> <i>n</i> ought to give birth, +to a series of circular waves. This is the important point up to +which I wish to lead you. Every particle of the wave <i>m</i> +<i>n</i> <i>does</i> act in this way. Taking each particle as a +centre, and surrounding it by a circular wave with a radius equal +to the distance between <i>m</i> <i>n</i> and <i>m'</i> <i>n'</i>, +the coalescence of all these little waves would build up the large +ridge <i>m'</i> <i>n'</i> exactly as we find it built up in nature. +Here, in fact, we resolve the wave-motion into its elements, and +having succeeded in doing this we shall have no great difficulty in +applying our knowledge to optical phenomena.</p> +<div class="figright" style="width: 343px;"><img src= +"images/fig18.jpg" width="343" height="253" alt="Fig. 18." title= +"" /> <b>Fig. 18.</b></div> +<p>Now let us return to our slit, and, for the sake of simplicity, +we will first consider the case of monochromatic light. Conceive a +series of waves of ether advancing from the first slit towards the +second, and finally filling the second slit. When each wave passes +through the latter it not only pursues its direct course to the +retina, but diverges right and left, tending to throw into motion +the entire mass of the ether behind the slit. In fact, as already +explained, <i>every point of <a name="Page_83" id= +"Page_83"></a><span class="pagenum">[Pg 83]</span>the wave which +fills the slit is itself a centre of a new wave system which is +transmitted in all directions through the ether behind the +slit</i>. This is the celebrated principle of Huyghens: we have now +to examine how these secondary waves act upon each other.</p> +<p>Let us first regard the central band of the series. Let AP (fig. +18) be the width of the aperture held before the eye, grossly +exaggerated of course, and let the dots across the aperture +represent ether particles, all in the same phase of vibration. Let +E T represent a portion of the retina. From O, in the centre of the +slit, let a perpendicular O R be imagined drawn upon the retina. +The motion communicated to the point R will then be the sum of all +the motions emanating in this direction from the ether particles in +the slit. Considering the extreme narrowness of the aperture, we +may, without sensible error, regard all points of the wave A P as +equally distant from R. No one of the partial waves lags sensibly +behind the others: hence, at R, and in its immediate neighbourhood, +we have no sensible reduction of the light by interference. This +<a name="Page_84" id="Page_84"></a><span class="pagenum">[Pg +84]</span>undiminished light produces the brilliant central band of +the series.</p> +<p>Let us now consider those waves which diverge laterally behind +the second slit. In this case the waves from the two sides of the +slit have, in order to converge upon the retina, to pass over +unequal distances. Let A P (fig. 19) represent, as before, the +width of the second slit. We have now to consider the action of the +various parts of the wave A P upon a point R' of the retina, not +situated in the line joining the two slits.</p> +<div class="figleft" style="width: 368px;"><img src= +"images/fig19.jpg" width="368" height="251" alt="Fig. 19." title= +"" /> <b>Fig. 19.</b></div> +<p>Let us take the particular case in which the difference of path +from the two marginal points A, P, to the retina is a whole +wave-length of the red light; how must this difference affect the +final illumination of the retina?</p> +<p>Let us fix our attention upon the particular oblique line that +passes through the <i>centre</i> O of the slit to the retina at R'. +The difference of path between the waves which pass along this line +and those from the two margins is, in the case here supposed, half +a wavelength. Make <i>e</i> R' equal to P R', join P and <i>e</i>, +and draw O <i>d</i> parallel to P e. A e is then the length of a +<a name="Page_85" id="Page_85"></a><span class="pagenum">[Pg +85]</span>wave of light, while A <i>d</i> is half a wave-length. +Now the least reflection will make it clear that not only is there +discordance between the central and marginal waves, but that every +line of waves such as <i>x</i> R', on the one side of O R', finds a +line <i>x</i>' R' upon the other side of O R', from which its path +differs by half an undulation—with which, therefore, it is in +complete discordance. The consequence is, that the light on the one +side of the central line will completely abolish the light on the +other side of that line, absolute darkness being the result of +their coalescence. The first dark interval of our series of bands +is thus accounted for. It is produced by an obliquity of direction +which causes the paths of the marginal waves to be <i>a whole +wave-length</i> different from each other.</p> +<p>When the difference between the paths of the marginal waves is +<i>half a wave-length,</i> a partial destruction of the light is +effected. The luminous intensity corresponding to this obliquity is +a little less than one-half—accurately 0.4—that of the +undiffracted light. If the paths of the marginal waves be three +semi-undulations different from each other, and if the whole beam +be divided into three equal parts, two of these parts will, for the +reasons just given, completely neutralize each other, the third +only being effective. Corresponding, therefore, to an obliquity +which produces a difference of three semi-undulations in the +marginal waves, we have a luminous band, but one of considerably +less intensity than the undiffracted central band.</p> +<p>With a marginal difference of path of four semi-undulations we +have a second extinction of the entire beam, because here the beam +can be divided into four <a name="Page_86" id= +"Page_86"></a><span class="pagenum">[Pg 86]</span>equal parts, +every two of which quench each other. A second space of absolute +darkness will therefore correspond to the obliquity producing this +difference. In this way we might proceed further, the general +result being that, whenever the direction of wave-motion is such as +to produce a marginal difference of path of an <i>even</i> number +of semi-undulations, we have complete extinction; while, when the +marginal difference is an <i>odd</i> number of semi-undulations, we +have only partial extinction, a portion of the beam remaining as a +luminous band.</p> +<p>A moment's reflection will make it plain that the wider the slit +the less will be the obliquity of direction needed to produce the +necessary difference of path. With a wide slit, therefore, the +bands, as observed, will be closer together than with a narrow one. +It is also plain that the shorter the wave, the less will be the +obliquity required to produce the necessary retardation. The maxima +and minima of violet light must therefore fall nearer to the centre +than the maxima and minima of red light. The maxima and minima of +the other colours fall between these extremes. In this simple way +the undulatory theory completely accounts for the extraordinary +appearance above referred to.</p> +<p>When a slit and telescope are used, instead of the slit and +naked eye, the effects are magnified and rendered more brilliant. +Looking, moreover, through a properly adjusted telescope with a +small circular aperture in front of it, at a distant point of +light, the point is seen encircled by a series of coloured bands. +If monochromatic light be used, these bands are simply bright and +dark, but with white light the circles display iris-colours. If a +slit be shortened so as to form a <a name="Page_87" id= +"Page_87"></a><span class="pagenum">[Pg 87]</span>square aperture, +we have two series of spectra at right angles to each other. The +effects, indeed, are capable of endless variation by varying the +size, shape, and number of the apertures through which the point of +light is observed. Through two square apertures, with their corners +touching each other as at A, Schwerd observed the appearance shown +in fig. 20. Adding two others to them, as at B, he observed the +appearance represented in fig. 21. The position of every band of +light and shade in such figures has been calculated from theory by +Fresnel, Fraunhofer, Herschel, Schwerd, and others, and completely +verified by experiment. Your eyes could not tell you with greater +certainty of the existence of these bands than the theoretic +calculation.</p> +<div class="figcenter" style="width: 381px;"><img src= +"images/fig20.jpg" width="381" height="416" alt="Fig. 20." title= +"" /> <b>Fig. 20.</b></div> +<p><a name="Page_88" id="Page_88"></a><span class="pagenum">[Pg +88]</span>The street-lamps at night, looked at through the meshes +of a handkerchief, show diffraction phenomena. The diffraction +effects obtained in looking through a bird's feathers are, as shown +by Schwerd, very brilliant. The iridescence of certain Alpine +clouds is also an effect of diffraction which may be imitated by +the spores of Lycopodium. When shaken over a glass plate these +spores cause a point of light, looked at through the dusted plate, +to be surrounded by coloured circles, which rise to actual +splendour when the light becomes intense. Shaken in the air the +spores produce the same effect. The diffraction phenomena obtained +during the artificial precipitation of clouds from the <a name= +"Page_89" id="Page_89"></a><span class="pagenum">[Pg +89]</span>vapours of various liquids in an intensely illuminated +tube are, as I have elsewhere shewn, exceedingly fine.</p> +<div class="figcenter" style="width: 382px;"><img src= +"images/fig21.jpg" width="382" height="442" alt="Fig. 21." title= +"" /> <b>Fig. 21.</b></div> +<p>One of the most interesting cases of diffraction by small +particles that ever came before me was that of an artist whose +vision was disturbed by vividly coloured circles. He was in great +dread of losing his sight; assigning as a cause of his increased +fear that the circles were becoming larger and the colours more +vivid. I ascribed the colours to minute particles in the humours of +the eye, and ventured to encourage him by the assurance that the +increase of size and vividness on the part of the circles indicated +that the diffracting particles were becoming <i>smaller</i>, and +that they might finally be altogether absorbed. The prediction was +verified. It is needless to say one word on the necessity of +optical knowledge in the case of the practical oculist.</p> +<p>Without breaking ground on the chromatic phenomena presented by +crystals, two other sources of colour may be mentioned here. By +interference in the earth's atmosphere, the light of a star, as +shown by Arago, is self-extinguished, the twinkling of the star and +the changes of colour which it undergoes being due to this cause. +Looking at such a star through an opera-glass, and shaking the +glass so as to cause the image of the star to pass rapidly over the +retina, you produce a row of coloured beads, the spaces between +which correspond to the periods of extinction. Fine scratches drawn +upon glass or polished metal reflect the waves of light from their +sides; and some, being reflected from the opposite sides of the +same scratch, interfere with and quench each other. But the +obliquity of reflection which extinguishes the shorter <a name= +"Page_90" id="Page_90"></a><span class="pagenum">[Pg +90]</span>waves does not extinguish the longer ones, hence the +phenomena of colours. These are called the colours of <i>striated +surfaces</i>. They are beautifully illustrated by mother-of-pearl. +This shell is composed of exceedingly thin layers, which, when cut +across by the polishing of the shell, expose their edges and +furnish the necessary small and regular grooves. The most +conclusive proof that the colours are due to the mechanical state +of the surface is to be found in the fact, established by Brewster, +that by stamping the shell carefully upon black sealing-wax, we +transfer the grooves, and produce upon the wax the colours of +mother-of-pearl.</p> +<hr style="width: 65%;" /> +<div><a name="Page_91" id="Page_91"></a><span class="pagenum">[Pg +91]</span></div> +<h2><a name="LECTURE_III" id="LECTURE_III"></a>LECTURE III.</h2> +<table border="0" cellpadding="0" cellspacing="0" summary=""> +<tr> +<td> +<div style="font-size: smaller;"> +<ul style="list-style: none;"> +<li>RELATION OF THEORIES TO EXPERIENCE</li> +<li>ORIGIN OF THE NOTION OF THE ATTRACTION OF GRAVITATION</li> +<li>NOTION OF POLARITY, HOW GENERATED</li> +<li>ATOMIC POLARITY</li> +<li>STRUCTURAL ARRANGEMENTS DUE TO POLARITY</li> +<li>ARCHITECTURE OF CRYSTALS CONSIDERED AS AN INTRODUCTION</li> +<li>TO THEIR ACTION UPON LIGHT</li> +<li>NOTION OF ATOMIC POLARITY APPLIED TO CRYSTALLINE STRUCTURE</li> +<li>EXPERIMENTAL ILLUSTRATIONS</li> +<li>CRYSTALLIZATION OF WATER</li> +<li>EXPANSION BY HEAT AND BY COLD</li> +<li>DEPORTMENT OF WATER CONSIDERED AND EXPLAINED</li> +<li>BEARINGS OF CRYSTALLIZATION ON OPTICAL PHENOMENA</li> +<li>REFRACTION</li> +<li>DOUBLE REFRACTION</li> +<li>POLARIZATION</li> +<li>ACTION OF TOURMALINE</li> +<li>CHARACTER OF THE BEAMS EMERGENT FROM ICELAND SPAR</li> +<li>POLARIZATION BY ORDINARY REFRACTION AND REFLECTION</li> +<li>DEPOLARIZATION</li> +</ul> +</div> +</td> +</tr> +</table> +<h3>§ 1. <i>Derivation of Theoretic Conceptions from +Experience.</i></h3> +<p>One of the objects of our last lecture, and that not the least +important, was to illustrate the manner in which scientific +theories are formed. They, in the first place, take their rise in +the desire of the mind to penetrate to the sources of phenomena. +From its infinitesimal beginnings, in ages long past, this desire +has grown and strengthened into an imperious demand of man's +intellectual nature. It long ago prompted Cæsar to say that +he would exchange his victories for a glimpse of the sources of the +Nile; it wrought itself into the atomic theories of Lucretius; it +impelled Darwin to those daring speculations which of late years +have so agitated the public mind. But in no case, while <a name= +"Page_92" id="Page_92"></a><span class="pagenum">[Pg +92]</span>framing theories, does the imagination <i>create</i> its +materials. It expands, diminishes, moulds, and refines, as the case +may be, materials derived from the world of fact and +observation.</p> +<p>This is more evidently the case in a theory like that of light, +where the motions of a subsensible medium, the ether, are presented +to the mind. But no theory escapes the condition. Newton took care +not to encumber the idea of gravitation with unnecessary physical +conceptions; but we know that he indulged in them, though he did +not connect them with his theory. But even the theory, as it +stands, did not enter the mind as a revelation dissevered from the +world of experience. The germ of the conception that the sun and +planets are held together by a force of attraction is to be found +in the fact that a magnet had been previously seen to attract iron. +The notion of matter attracting matter came thus from without, not +from within. In our present lecture the magnetic force must serve +as the portal into a new domain; but in the first place we must +master its elementary phenomena.</p> +<p>The general facts of magnetism are most simply illustrated by a +magnetized bar of steel, commonly called a bar magnet. Placing such +a magnet upright upon a table, and bringing a magnetic needle near +its bottom, one end of the needle is observed to retreat from the +magnet, while the other as promptly approaches. The needle is held +quivering there by some invisible influence exerted upon it. +Raising the needle along the magnet, but still avoiding contact, +the rapidity of its oscillations decreases, because the force +acting upon it becomes weaker. At the centre the oscil<a name= +"Page_93" id="Page_93"></a><span class="pagenum">[Pg +93]</span>lations cease. Above the centre, the end of the needle +which had been previously drawn towards the magnet retreats, and +the opposite end approaches. As we ascend higher, the oscillations +become more violent, because the force becomes stronger. At the +upper end of the magnet, as at the lower, the force reaches a +maximum; but all the lower half of the magnet, from E to S (fig. +22), attracts one end of the needle, while all the upper half, from +E to N, attracts the opposite end. This <i>doubleness</i> of the +magnetic force is called <i>polarity</i>, and the points near the +ends of the magnet in which the forces seem concentrated are called +its <i>poles</i>.</p> +<div class="figright" style="width: 160px;"><img src= +"images/fig22.jpg" width="160" height="306" alt="Fig. 22." title= +"" /> <b>Fig. 22.</b></div> +<p>What, then, will occur if we break this magnet in two at the +centre E? Shall we obtain two magnets, each with a single pole? No; +each half is in itself a perfect magnet, possessing two poles. This +may be proved by breaking something of less value than the +magnet—the steel of a lady's stays, for example, hardened and +magnetized. It acts like the magnet. When broken, each half acts +like the whole; and when <a name="Page_94" id= +"Page_94"></a><span class="pagenum">[Pg 94]</span>these parts are +again broken, we have still the perfect magnet, possessing, as in +the first instance, two poles. Push your breaking to its utmost +sensible limit—you cannot stop there. The bias derived from +observation will infallibly carry you beyond the bourne of the +senses, and compel you to regard this thing that we call magnetic +polarity as resident in the ultimate particles of the steel. You +come to the conclusion that each molecule of the magnet is endowed +with this polar force.</p> +<p>Like all other forces, this force of magnetism is amenable to +mechanical laws; and, knowing the direction and magnitude of the +force, we can predict its action. Placing a small magnetic needle +near a bar magnet, it takes a determinate position. That position +might be deduced theoretically from the mutual action of the poles. +Moving the needle round the magnet, for each point of the +surrounding space there is a definite direction of the needle and +no other. A needle of iron will answer as well as the magnetic +needle; for the needle of iron is magnetized by the magnet, and +acts exactly like a steel needle independently magnetized.</p> +<div class="figleft" style="width: 430px;"><img src= +"images/fig23.jpg" width="430" height="413" alt= +"Fig. 23. N is the nozzle of the lamp; M a plane mirror, reflecting the beam upwards. At P the magnets and iron filings are placed; L is a lens which forms an image of the magnets and filings; and R is a totally reflecting prism, which casts the image G upon the screen." +title="" /> <b>Fig. 23.<br /> +N is the nozzle of the lamp; M a plane mirror, reflecting the beam +upwards. At P the magnets and iron filings are placed; L is a lens +which forms an image of the magnets and filings; and R is a totally +reflecting prism, which casts the image G upon the +screen.</b></div> +<p>If we place two or more needles of iron near the magnet, the +action becomes more complex, for then the needles are not only +acted on by the magnet, but they act upon each other. And if we +pass to smaller masses of iron—to iron filings, for +example—we find that they act substantially as the needles, +arranging themselves in definite forms, in obedience to the +magnetic action.</p> +<p>Placing a sheet of paper or glass over a bar magnet and +showering iron filings upon the paper, I notice a <a name="Page_95" +id="Page_95"></a><span class="pagenum">[Pg 95]</span>tendency of +the filings to arrange themselves in determinate lines. They cannot +freely follow this tendency, for they are hampered by the friction +against the paper. They are helped by tapping the paper; each tap +releasing them for a moment, and enabling them to follow their +tendencies. But this is an experiment which can only be seen by +myself. To enable you all to see it, I take a pair of small magnets +and by a simple optical arrangement throw the magnified images of +the magnets upon the screen. Scattering iron filings over the glass +plate to which the small magnets are attached, and tapping the +plate, you see the arrangement of the iron filings in those +magnetic <a name="Page_96" id="Page_96"></a><span class= +"pagenum">[Pg 96]</span>curves which have been so long familiar to +scientific men (fig. 23).</p> +<p>(By a very ingenious device, Professor Mayer, of Hoboken, has +succeeded in fixing and photographing the magnetic curves. I am +indebted to his kindness for the annexed beautiful illustration, +fig. 24.)</p> +<p>The aspect of these curves so fascinated Faraday that the +greater portion of his intellectual life was devoted to pondering +over them. He invested the space through which they run with a kind +of materiality; and the probability is that the progress of +science, by connecting the phenomena of magnetism with the +luminiferous ether, will prove these 'lines of force,' as Faraday +loved to call them, to represent a condition of this mysterious +substratum of all radiant action.</p> +<p>It is not, however, the magnetic curves, as such, but their +relationship to theoretic conceptions, that we have now to +consider. By the action of the bar magnet upon the needle we obtain +the notion of a polar force; by the breaking of the strip of +magnetized steel we attain the notion that polarity can attach +itself to the ultimate particles of matter. The experiment with the +iron filings introduces a new idea into the mind; the idea, namely, +of <i>structural arrangement</i>. Every pair of filings possesses +four poles, two of which are attractive and two repulsive. The +attractive poles approach, the repulsive poles retreat; the +consequence being a certain definite arrangement of the particles +with reference to each other.</p> +<h3>§ 2. <i>Theory of Crystallization.</i></h3> +<p>Now this idea of structure, as produced by polar force, opens a +way for the intellect into an entirely new <a name="Page_97" id= +"Page_97"></a><span class="pagenum">[Pg 97]</span><a name="Page_98" +id="Page_98"></a>region, and the reason you are asked to accompany +me into this region is, that our next inquiry relates to the action +of crystals upon light. Prior to speaking of this action, I wish +you to realise intellectually the process of crystalline +architecture. Look then into a granite quarry, and spend a few +minutes in examining the rock. It is not of perfectly uniform +texture. It is rather an agglomeration of pieces, which, on +examination, present curiously defined forms. You have there what +mineralogists call quartz, you have felspar, you have mica. In a +mineralogical cabinet, where these substances are preserved +separately, you will obtain some notion of their forms. You will +see there, also, specimens of beryl, topaz, emerald, tourmaline, +heavy spar, fluor-spar, Iceland spar—possibly a full-formed +diamond, as it quitted the hand of Nature, not yet having got into +the hands of the lapidary.</p> +<div class="figright" style="width: 428px;"><img src= +"images/fig24.jpg" width="428" height="912" alt="Fig. 24." title= +"" /> <b>Fig. 24.</b></div> +<p>These crystals, you will observe, are put together according to +law; they are not chance productions; and, if you care to examine +them more minutely, you will find their architecture capable of +being to some extent revealed. They often split in certain +directions before a knife-edge, exposing smooth and shining +surfaces, which are called planes of cleavage; and by following +these planes you sometimes reach an internal form, disguised +beneath the external form of the crystal. Ponder these beautiful +edifices of a hidden builder. You cannot help asking yourself how +they were built; and familiar as you now are with the notion of a +polar force, and the ability of that force to produce structural +arrangement, your inevitable answer will be, that those crystals +are built by the play of polar forces with which their molecules +are endowed. <a name="Page_99" id="Page_99"></a><span class= +"pagenum">[Pg 99]</span>In virtue of these forces, molecule lays +itself to molecule in a perfectly definite way, the final visible +form of the crystal depending upon this play of its ultimate +particles.</p> +<p>Everywhere in Nature we observe this tendency to run into +definite forms, and nothing is easier than to give scope to this +tendency by artificial arrangements. Dissolve nitre in water, and +allow the water slowly to evaporate; the nitre remains and the +solution soon becomes so concentrated that the liquid condition can +no longer be preserved. The nitre-molecules approach each other, +and come at length within the range of their polar forces. They +arrange themselves in obedience to these forces, a minute crystal +of nitre being at first produced. On this crystal the molecules +continue to deposit themselves from the surrounding liquid. The +crystal grows, and finally we have large prisms of nitre, each of a +perfectly definite shape. Alum crystallizes with the utmost ease in +this fashion. The resultant crystal is, however, different in shape +from that of nitre, because the poles of the molecules are +differently disposed. When they are <i>nursed</i> with proper care, +crystals of these substances may be caused to grow to a great +size.</p> +<p>The condition of perfect crystallization is, that the +crystallizing force shall act with deliberation. There should be no +hurry in its operations; but every molecule ought to be permitted, +without disturbance from its neighbours, to exercise its own +rights. If the crystallization be too sudden, the regularity +disappears. Water may be saturated with sulphate of soda, dissolved +when the water is hot, and afterwards permitted to cool. When cold +the solution is supersaturated; that is to say, <a name="Page_100" +id="Page_100"></a><span class="pagenum">[Pg 100]</span>more solid +matter is contained in it than corresponds to its temperature. +Still the molecules show no sign of building themselves +together.</p> +<p>This is a very remarkable, though a very common fact. The +molecules in the centre of the liquid are so hampered by the action +of their neighbours that freedom to follow their own tendencies is +denied to them. Fix your mind's eye upon a molecule within the +mass. It wishes to unite with its neighbour to the right, but it +wishes equally to unite with its neighbour to the left; the one +tendency neutralizes the other and it unites with neither. But, if +a crystal of sulphate of soda be dropped into the solution, the +molecular indecision ceases. On the crystal the adjacent molecules +will immediately precipitate themselves; on these again others will +be precipitated, and this act of precipitation will continue from +the top of the flask to the bottom, until the solution has, as far +as possible, assumed the solid form. The crystals here produced are +small, and confusedly arranged. The process has been too hasty to +admit of the pure and orderly action of the crystallizing force. It +typifies the state of a nation in which natural and healthy change +is resisted, until society becomes, as it were, supersaturated with +the desire for change, the change being then effected through +confusion and revolution.</p> +<p>Let me illustrate the action of the crystallizing force by two +examples of it: Nitre might be employed, but another well-known +substance enables me to make the experiment in a better form. The +substance is common sal-ammoniac, or chloride of ammonium, +dissolved in water. Cleansing perfectly a glass plate, the solution +of the chloride is poured over the glass, to <a name="Page_101" id= +"Page_101"></a><span class="pagenum">[Pg 101]</span>which when the +plate is set on edge, a thin film of the liquid adheres. Warming +the glass slightly, evaporation is promoted, but by evaporation the +water only is removed. The plate is then placed in a solar +microscope, and an image of the film is thrown upon a white screen. +The warmth of the illuminating beam adds itself to that already +imparted to the glass plate, so that after a moment or two the +dissolved salt can no longer exist in the liquid condition. +Molecule then closes with molecule, and you have a most impressive +display of crystallizing energy overspreading the whole screen. You +may produce something similar if you breathe upon the frost ferns +which overspread your window-panes in winter, and then observe +through a pocket lens the subsequent recongelation of the film.</p> +<p>In this case the crystallizing force is hampered by the adhesion +of the film to the glass; nevertheless, the play of power is +strikingly beautiful. Sometimes the crystals start from the edge of +the film and run through it from that edge; for, the +crystallization being once started, the molecules throw themselves +by preference on the crystals already formed. Sometimes the +crystals start from definite nuclei in the centre of the film, +every small crystalline particle which rests in the film furnishing +a starting-point. Throughout the process you notice one feature +which is perfectly unalterable, and that is, angular magnitude. The +spiculæ branch from the trunk, and from these branches others +shoot; but the angles enclosed by the spiculæ are +unalterable. In like manner you may find alum-crystals, +quartz-crystals, and all other crystals, distorted in shape. They +are thus far at the mercy of <a name="Page_102" id= +"Page_102"></a><span class="pagenum">[Pg 102]</span>the accidents +of crystallization; but in one particular they assert their +superiority over all such accidents—<i>angular magnitude</i> +is always rigidly preserved.</p> +<p>My second example of the action of crystallizing force is this: +By sending a voltaic current through a liquid, you know that we +decompose the liquid, and if it contains a metal, we liberate this +metal by electrolysis. This small cell contains a solution of +acetate of lead, which is chosen for our present purpose, because +lead lends itself freely to this crystallizing power. Into the cell +are dipped two very thin platinum wires, and these are connected by +other wires with a small voltaic battery. On sending the voltaic +current through the solution, the lead will be slowly severed from +the atoms with which it is now combined; it will be liberated upon +one of the wires, and at the moment of its liberation it will obey +the polar forces of its atoms, and produce crystalline forms of +exquisite beauty. They are now before you, sprouting like ferns +from the wire, appearing indeed like vegetable growths rendered so +rapid as to be plainly visible to the naked eye. On reversing the +current, these wonderful lead-fronds will dissolve, while from the +other wire filaments of lead dart through the liquid. In a moment +or two the growth of the lead-trees recommences, but they now cover +the other wire.</p> +<p>In the process of crystallization, Nature first reveals herself +as a builder. Where do her operations stop? Does she continue by +the play of the same forces to form the vegetable, and afterwards +the animal? Whatever the answer to these questions may be, trust me +that the notions of the coming generations regarding this +mysterious thing, which some have called 'brute <a name="Page_103" +id="Page_103"></a><span class="pagenum">[Pg 103]</span>matter,' +will be very different from those of the generations past.</p> +<p>There is hardly a more beautiful and instructive example of this +play of molecular force than that furnished by water. You have seen +the exquisite fern-like forms produced by the crystallization of a +film of water on a cold window-pane.<a name="FNanchor_15_15" id= +"FNanchor_15_15"></a><a href="#Footnote_15_15" class= +"fnanchor">[15]</a> You have also probably noticed the beautiful +rosettes tied together by the crystallizing force during the +descent of a snow-shower on a very calm day. The slopes and summits +of the Alps are loaded in winter with these blossoms of the frost. +They vary infinitely in detail of beauty, but the same angular +magnitude is preserved throughout: an inflexible power binding +spears and spiculæ to the angle of 60 degrees.</p> +<p>The common ice of our lakes is also ruled in its formation by +the same angle. You may sometimes see in freezing water small +crystals of stellar shapes, each star consisting of six rays, with +this angle of 60° between every two of them. This structure may +be revealed in ordinary ice. In a sunbeam, or, failing that, in our +electric beam, we have an instrument delicate enough to unlock the +frozen molecules, without disturbing the order of their +architecture. Cutting from clear, sound, regularly frozen ice, a +slab parallel to the planes of freezing, and sending a sunbeam +through such a slab, it liquefies internally at special points, +round each point a six-petalled liquid flower of exquisite beauty +being formed. Crowds of such flowers are thus produced. From an +ice-house we sometimes take blocks of ice presenting misty spaces +in the <a name="Page_104" id="Page_104"></a><span class= +"pagenum">[Pg 104]</span>otherwise continuous mass; and when we +inquire into the cause of this mistiness, we find it to be due to +myriads of small six-petalled flowers, into which the ice has been +resolved by the mere heat of conduction.</p> +<p>A moment's further devotion to the crystallization of water will +be well repaid; for the sum of qualities which renders this +substance fitted to play its part in Nature may well excite wonder +and stimulate thought. Like almost all other substances, water is +expanded by heat and contracted by cold. Let this expansion and +contraction be first illustrated:—</p> +<p>A small flask is filled with coloured water, and stopped with a +cork. Through the cork passes a glass tube water-tight, the liquid +standing at a certain height in the tube. The flask and its tube +resemble the bulb and stem of a thermometer. Applying the heat of a +spirit-lamp, the water rises in the tube, and finally trickles over +the top. Expansion by heat is thus illustrated.</p> +<p>Removing the lamp and piling a freezing mixture round the flask, +the liquid column falls, thus showing the contraction of the water +by the cold. But let the freezing mixture continue to act: the +falling of the column continues to a certain point; it then ceases. +The top of the column remains stationary for some seconds, and +afterwards begins to rise. The contraction has ceased, and +<i>expansion by cold</i> sets in. Let the expansion continue till +the liquid trickles a second time over the top of the tube. The +freezing mixture has here produced to all appearance the same +effect as the flame. In the case of water, contraction by cold +ceases, and expansion by cold sets in at the definite temperature +of 39° Fahr. Crystallization has <a name="Page_105" id= +"Page_105"></a><span class="pagenum">[Pg 105]</span>virtually here +commenced, the molecules preparing themselves for the subsequent +act of solidification, which occurs at 32°, and in which the +expansion suddenly culminates. In virtue of this expansion, ice, as +you know, is lighter than water in the proportion of 8 to +9.<a name="FNanchor_16_16" id="FNanchor_16_16"></a><a href= +"#Footnote_16_16" class="fnanchor">[16]</a></p> +<p>A molecular problem of great interest is here involved, and I +wish now to place before you, for the satisfaction of your minds, a +possible solution of the problem:—</p> +<p>Consider, then, the ideal case of a number of magnets deprived +of weight, but retaining their polar forces. If we had a mobile +liquid of the specific gravity of steel, we might, by making the +magnets float in it, realize this state of things, for in such a +liquid the magnets would neither sink nor swim. Now, the principle +of gravitation enunciated by Newton is that every particle of +matter, of every kind, attracts every other particle with a force +varying inversely as the square of the distance. In virtue of the +attraction of gravity, then, the magnets, if perfectly free to +move, would slowly approach each other.</p> +<p>But besides the unpolar force of gravity, which <a name= +"Page_106" id="Page_106"></a><span class="pagenum">[Pg +106]</span>belongs to matter in general, the magnets are endowed +with the polar force of magnetism. For a time, however, the polar +forces do not come sensibly into play. In this condition the +magnets resemble our water-molecules at the temperature say of +50°. But the magnets come at length sufficiently near each +other to enable their poles to interact. From this point the action +ceases to be solely a general attraction of the masses. Attractions +of special points of the masses and repulsions of other points now +come into play; and it is easy to see that the rearrangement of the +magnets consequent upon the introduction of these new forces may be +such as to require a greater amount of room. This, I take it, is +the case with our water-molecules. Like our ideal magnets, they +approach each other for a time <i>as wholes</i>. Previous to +reaching the temperature 39° Fahr., the polar forces had +doubtless begun to act, but it is at this temperature that their +claim to more room exactly balances the contraction due to cold. At +lower temperatures, as regards change of volume, the polar forces +predominate. But they carry on a struggle with the force of +contraction until the freezing temperature is attained. The +molecules then close up to form solid crystals, a considerable +augmentation of volume being the immediate consequence.</p> +<h3>§ 3. <i>Ordinary Refraction of Light explained by the Wave +Theory</i>.</h3> +<p>We have now to exhibit the bearings of this act of +crystallization upon optical phenomena. According to the undulatory +theory, the velocity of light in water and glass is less than in +air. Consider, then, a small por<a name="Page_107" id= +"Page_107"></a><span class="pagenum">[Pg 107]</span>tion of a wave +issuing from a point of light so distant that the minute area may +be regarded as practically plane. Moving vertically downwards, and +impinging on a horizontal surface of glass or water, the wave would +go through the medium without change of direction. As, however, the +velocity in glass or water is less than the velocity in air, the +wave would be retarded on passing into the denser medium.</p> +<div class="figleft" style="width: 446px;"><img src= +"images/fig25.jpg" width="446" height="256" alt="Fig. 25." title= +"" /> <b>Fig. 25.</b></div> +<p>But suppose the wave, before reaching the glass, to be +<i>oblique</i> to the surface; that end of the wave which first +reaches the medium will be the first retarded by it, the other +portions as they enter the glass being retarded in succession. It +is easy to see that this retardation of the one end of the wave +must cause it to swing round and change its front, so that when the +wave has fully entered the glass its course is oblique to its +original direction. According to the undulatory theory, light is +thus <i>refracted</i>.</p> +<p>With these considerations to guide us, let us follow the course +of a beam of monochromatic light through our glass prism. The +velocity in air is to its velocity in <a name="Page_108" id= +"Page_108"></a><span class="pagenum">[Pg 108]</span>glass as 3: 2. +Let A B C (fig. 25) be the section of our prism, and <i>a</i> +<i>b</i> the section of a plane wave approaching it in the +direction of the arrow. When it reaches <i>c</i> <i>d</i>, one end +of the wave is on the point of entering the glass. Following it +still further, it is obvious that while the portion of the wave +still in the air passes over the distance <i>c</i> <i>e</i>, the +wave in the glass will have passed over only two-thirds of this +distance, or <i>d</i> <i>f</i>. The line <i>e</i> <i>f</i> now +marks the front of the wave. Immersed wholly in the glass it +pursues its way to <i>g</i> <i>h</i>, where the end <i>g</i> of the +wave is on the point of escaping into the air. During the time +required by the end <i>h</i> of the wave to pass over the distance +<i>h</i> <i>k</i> to the surface of the prism, the other end +<i>g</i>, moving more rapidly, will have reached the point +<i>i</i>. The wave, therefore, has again changed its front, so that +after its emergence from the prism it will pass on to <i>l</i> +<i>m</i>, and subsequently in the direction of the arrow. The +refraction of the beam is thus completely accounted for; and it is, +moreover, based upon actual experiment, which proves that the ratio +of the velocity of light in glass to its velocity in air is that +here mentioned. It is plain that if the change of velocity on +entering the glass were greater, the refraction also would be +greater.</p> +<h3>§ 4. <i>Double Refraction of Light explained by the Wave +Theory</i>.</h3> +<p>The two elements of rapidity of propagation, both of sound and +light, in any substance whatever, are <i>elasticity</i> and +<i>density</i>, the speed increasing with the former and +diminishing with the latter. The enormous velocity of light in +stellar space is attainable because <a name="Page_109" id= +"Page_109"></a><span class="pagenum">[Pg 109]</span>the ether is at +the same time of infinitesimal density and of enormous elasticity. +Now the ether surrounds the atoms of all bodies, but it is not +independent of them. In ponderable matter it acts as if its density +were increased without a proportionate increase of elasticity; and +this accounts for the diminished velocity of light in refracting +bodies. We here reach a point of cardinal importance. In virtue of +the crystalline architecture that we have been considering, the +ether in many crystals possesses different densities, and different +elasticities, in different directions; the consequence is, that in +such crystals light is transmitted with different velocities. And +as refraction depends wholly upon the change of velocity on +entering the refracting medium, being greatest where the change of +velocity is greatest, we have in many crystals two different +refractions. By such crystals a beam of light is divided into two. +This effect is called <i>double refraction</i>.</p> +<p>In ordinary water, for example, there is nothing in the grouping +of the molecules to interfere with the perfect homogeneity of the +ether; but, when water crystallizes to ice, the case is different. +In a plate of ice the elasticity of the ether in a direction +perpendicular to the surface of freezing is different from what it +is parallel to the surface of freezing; ice is, therefore, a double +refracting substance. Double refraction is displayed in a +particularly impressive manner by Iceland spar, which is +crystallized carbonate of lime. The difference of ethereal density +in two directions in this crystal is very great, the separation of +the beam into the two halves being, therefore, particularly +striking.</p> +<p>I am unwilling to quit this subject before raising it to +unmistakable clearness in your minds. The <a name="Page_110" id= +"Page_110"></a><span class="pagenum">[Pg 110]</span>vibrations of +light being transversal, the elasticity concerned in the +propagation of any ray is the elasticity at right angles to the +direction of propagation. In Iceland spar there is one direction +round which the crystalline molecules are symmetrically built. This +direction is called the axis of the crystal. In consequence of this +symmetry the elasticity is the same in all directions perpendicular +to the axis, and hence a ray transmitted along the axis suffers no +double refraction. But the elasticity along the axis is greater +than the elasticity at right angles to it. Consider, then, a system +of waves crossing the crystal in a direction perpendicular to the +axis. Two directions of vibration are open to such waves: the ether +particles can vibrate parallel to the axis or perpendicular to it. +<i>They do both</i>, and hence immediately divide themselves into +two systems propagated with different velocities. Double refraction +is the necessary consequence.</p> +<h3>§ 4. <i>Double Refraction of Light explained by the Wave +Theory</i>.</h3> +<div class="figright" style="width: 453px;"><img src= +"images/fig26.jpg" width="453" height="290" alt="Fig. 26." title= +"" /> <b>Fig. 26.</b></div> +<p>By means of Iceland spar cut in the proper direction, double +refraction is capable of easy illustration. Causing <a name= +"Page_111" id="Page_111"></a><span class="pagenum">[Pg +111]</span>the beam which builds the image of our carbon-points to +pass through the spar, the single image is instantly divided into +two. Projecting (by the lens E, fig. 26) an image of the aperture +(L) through which the light issues from the electric lamp, and +introducing the spar (P), two luminous disks (E O) appear +immediately upon the screen instead of one.</p> +<p>The two beams into which the spar divides the single +incident-beam have been subjected to the closest examination. They +do not behave alike. One of them obeys the ordinary law of +refraction discovered by Snell, and is, therefore, called the +<i>ordinary ray</i>: its index of refraction is 1.654. The other +does not obey this law. Its index of refraction, for example, is +not constant, but varies from a maximum of 1.654 to a minimum of +1.483; nor in this case do the incident and refracted rays always +lie in the same plane. It is, therefore, called the +<i>extraordinary ray</i>. In calc-spar, as just stated, the +ordinary ray is the most refracted. One consequence of this merits +a passing notice. Pour water and bisulphide of carbon into two cups +of the same depth; the cup that contains the more strongly +refracting liquid will appear shallower than the other. Place a +piece of Iceland spar over a dot of ink; two dots are seen, the one +appearing nearer than the other to the eye. The nearest dot belongs +to the most strongly refracted ray, exactly as the nearest +cup-bottom belongs to the most highly refracting liquid. When you +turn the spar round, the extraordinary image of the dot rotates +round the ordinary one, which remains fixed. This is also the +deportment of our two disks upon the screen.<a name="Page_112" id= +"Page_112"></a><span class="pagenum">[Pg 112]</span></p> +<h3>§ 5. <i>Polarization of Light explained by the Wave +Theory</i>.</h3> +<p>The double refraction of Iceland spar was first treated in a +work published by Erasmus Bartholinus, in 1669. Huyghens sought to +account for this phenomenon on the principles of the wave theory, +and he succeeded in doing so. He, moreover, made highly important +observations on the distinctive character of the two beams +transmitted by the spar, admitting, with resigned candour, that he +had not solved the difficulty, and leaving the solution to future +times. Newton, reflecting on the observations of Huyghens, came to +the conclusion that each of the beams transmitted by Iceland spar +had two sides; and from the analogy of this <i>two-sidedness</i> +with the <i>two-endedness</i> of a magnet, wherein consists its +polarity, the two beams came subsequently to be described as +<i>polarized</i>.</p> +<p>We may begin the study of the polarization of light, with ease +and profit, by means of a crystal of tourmaline. But we must start +with a clear conception of an ordinary beam of light. It has been +already explained that the vibrations of the individual +ether-particles are executed <i>across</i> the line of propagation. +In the case of ordinary light we are to figure the ether-particles +as vibrating in all directions, or azimuths, as it is sometimes +expressed, across this line.</p> +<p>Now, in the case of a plate of tourmaline cut parallel to the +axis of the crystal, a beam of light incident upon the plate is +divided into two, the one vibrating parallel to the axis of the +crystal, the other at right angles to the axis. The grouping of the +<a name="Page_113" id="Page_113"></a><span class="pagenum">[Pg +113]</span>molecules, and of the ether associated with the +molecules, reduces all the vibrations incident upon the crystal to +these two directions. One of these beams, namely, that whose +vibrations are perpendicular to the axis, is quenched with +exceeding rapidity by the tourmaline. To such vibrations many +specimens of the crystal are highly opaque; so that, after having +passed through a very small thickness of the tourmaline, the light +emerges with all its vibrations reduced to a single plane. In this +condition it is what we call <i>plane polarized light</i>.</p> +<div class="figleft" style="width: 196px;"><img src= +"images/fig27.jpg" width="196" height="69" alt="Fig. 27." title= +"" /> <b>Fig. 27.</b></div> +<div class="figright" style="width: 150px;"><img src= +"images/fig28.jpg" width="150" height="200" alt="Fig. 28." title= +"" /> <b>Fig. 28.</b></div> +<p>A moment's reflection will show that, if what is here stated be +correct, on placing a second plate of tourmaline with its axis +parallel to the first, the light will pass through both; but that, +if the axes be crossed, the light that passes through the one plate +will be quenched by the other, a total interception of the light +being the consequence. Let us test this conclusion by experiment. +The image of a plate of tourmaline (<i>t</i> <i>t</i>, fig. 27) is +now before you. I place parallel to it another plate (<i>t'</i> +<i>t'</i>): the green of the <a name="Page_114" id= +"Page_114"></a><span class="pagenum">[Pg 114]</span>crystal is a +little deepened, nothing more; this agrees with our conclusion. By +means of an endless screw, I now turn one of the crystals gradually +round, and you observe that as long as the two plates are oblique +to each other, a certain portion of light gets through; but that +when they are at right angles to each other, the space common to +both is a space of darkness (fig. 28). Our conclusion, arrived at +prior to experiment, is thus verified.</p> +<p>Let us now return to a single plate; and here let me say that it +is on the green light transmitted by the tourmaline that you are to +fix your attention. We have to illustrate the two-sidedness of that +green light, in contrast to the all-sidedness of ordinary light. +The white light surrounding the green image, being ordinary light, +is reflected by a plane glass mirror in all directions; the green +light, on the contrary, is not so reflected. The image of the +tourmaline is now horizontal; reflected upwards, it is still green; +reflected sideways, the image is reduced to blackness, because of +the incompetency of the green light to be reflected in this +direction. Making the plate of tourmaline vertical, and reflecting +it as before, it is the light of the upper image that is quenched; +the side image now shows the green. This is a result of the +greatest significance. If the vibrations of light were +longitudinal, like those of sound, you could have no action of this +kind; and this very action compels us to assume that the vibrations +are transversal. Picture the thing clearly. In the one case the +mirror receives, as it were, the impact of the <i>edges</i> of the +waves, the green light being then quenched. In the other case the +<i>sides</i> of the waves strike the mirror, and the green light is +reflected. To <a name="Page_115" id="Page_115"></a><span class= +"pagenum">[Pg 115]</span>render the extinction complete, the light +must be received upon the mirror at a special angle. What this +angle is we shall learn presently.</p> +<p>The quality of two-sidedness conferred upon light by +bi-refracting crystals may also be conferred upon it by ordinary +reflection. Malus made this discovery in 1808, while looking +through Iceland spar at the light of the sun reflected from the +windows of the Luxembourg palace in Paris. I receive upon a plate +of window-glass the beam from our lamp; a great portion of the +light reflected from the glass is polarized. The vibrations of this +reflected beam are executed, for the most part, parallel to the +surface of the glass, and when the glass is held so that the beam +shall make an angle of 58° with the perpendicular to the glass, +the <i>whole</i> of the reflected beam is polarized. It was at this +angle that the image of the tourmaline was completely quenched in +our former experiment. It is called <i>the polarizing +angle</i>.</p> +<p>Sir David Brewster proved the angle of polarization of a medium +to be that particular angle at which the refracted and reflected +rays inclose a right angle.<a name="FNanchor_17_17" id= +"FNanchor_17_17"></a><a href="#Footnote_17_17" class= +"fnanchor">[17]</a> The polarizing angle augments with the index of +refraction. For water it is 52½°; for glass, as already +stated, 58°; while for diamond it is 68°.</p> +<p>And now let us try to make substantially the <a name="Page_116" +id="Page_116"></a><span class="pagenum">[Pg 116]</span>experiment +of Malus. The beam from the lamp is received at the proper angle +upon a plate of glass and reflected through the spar. Instead of +two images, you see but one. So that the light, when polarized, as +it now is by reflection, can only get through the spar in one +direction, and consequently can produce but one image. Why is this? +In the Iceland spar as in the tourmaline, all the vibrations of the +ordinary light are reduced to two planes at right angles to each +other; but, unlike the tourmaline, both beams are transmitted with +equal facility by the spar. The two beams, in short, emergent from +the spar, are polarized, their directions of vibration being at +right angles to each other. When, therefore, the light is first +polarized by reflection, the direction of vibration in the spar +which coincides with the direction of vibration of the polarized +beam, transmits the beam, and that direction only. Only one image, +therefore, is possible under the conditions.</p> +<p>You will now observe that such logic as connects our experiments +is simply a transcript of the logic of Nature. On the screen before +you are two disks of light produced by the double refraction of +Iceland spar. They are, as you know, two images of the aperture +through which the light issues from the camera. Placing the +tourmaline in front of the aperture, two images of the crystal will +also be obtained; but now let us reason out beforehand what is to +be expected from this experiment. The light emergent from the +tourmaline is polarized. Placing the crystal with its axis +horizontal, the vibrations of its transmitted light will be +horizontal. Now the spar, as already stated, has two directions of +vibration, one of which at the present <a name="Page_117" id= +"Page_117"></a><span class="pagenum">[Pg 117]</span>moment is +vertical, the other horizontal. What are we to conclude? That the +green light will be transmitted along the latter, which is parallel +to the axis of the tourmaline, and not along the former, which is +perpendicular to that axis. Hence we may infer that one image of +the tourmaline will show the ordinary green light of the crystal, +while the other image will be black. Tested by experiment, our +reasoning is verified to the letter (fig. 29).</p> +<div class="figcenter" style="width: 337px;"><img src= +"images/fig29.jpg" width="337" height="151" alt="Fig. 29." title= +"" /> <b>Fig. 29.</b></div> +<div class="figcenter" style="width: 333px;"><img src= +"images/fig30.jpg" width="333" height="151" alt="Fig. 30." title= +"" /> <b>Fig. 30.</b></div> +<p>Let us push our test still further. By means of an endless +screw, the crystal can be turned ninety degrees round. The black +image, as I turn, becomes gradually brighter, and the bright one +gradually darker; at an angle of forty-five degrees both images are +equally bright (fig. 30); while, when ninety degrees have been +obtained, the axis of the crystal being then vertical, the bright +and black images have changed places, exactly as reasoning would +have led us to suppose (fig. 31).<a name="Page_118" id= +"Page_118"></a><span class="pagenum">[Pg 118]</span></p> +<div class="figcenter" style="width: 357px;"><img src= +"images/fig31.jpg" width="357" height="150" alt="Fig. 31." title= +"" /> <b>Fig. 31.</b></div> +<div class="figcenter" style="width: 395px;"><img src= +"images/fig32.jpg" width="395" height="273" alt="Fig. 32." title= +"" /> <b>Fig. 32.</b></div> +<p>Considering what has been already said (p. 114) regarding the +reflection of light polarized by transmission through tourmaline, +you will readily foresee what must occur when we receive upon a +plate of glass, held at the polarizing angle, the two beams +emergent from our prism of Iceland spar. I cause both beams to pass +side by side through the air, catch them on a glass plate, and seek +to reflect them upwards. At the polarizing angle one beam only is +capable of being thus reflected. Which? Your prompt answer will be, +The beam whose vibrations are horizontal (fig. 32). I now turn the +glass plate and try to reflect both beams laterally. One of them +only is reflected; that, <a name="Page_119" id= +"Page_119"></a><span class="pagenum">[Pg 119]</span>namely, the +vibrations of which are vertical (fig. 33). It is plain that, by +means either of the tourmaline or the reflecting glass, we can +determine in a moment the direction of vibration in any polarized +beam.</p> +<div class="figcenter" style="width: 331px;"><img src= +"images/fig33.jpg" width="331" height="270" alt="Fig. 33." title= +"" /> <b>Fig. 33.</b></div> +<p>As already stated, the whole of a beam of ordinary light +reflected from glass at the polarizing angle is polarized; a word +must now be added regarding the far larger portion of the light +which is <i>transmitted</i> by the glass. The transmitted beam +contains a quantity of polarized light equal to the reflected beam; +but this is only a fraction of the whole transmitted light. By +taking two plates of glass instead of one, we augment the quantity +of the transmitted polarized light; and by taking <i>a bundle</i> +of plates, we so increase the quantity as to render the transmitted +beam, for all practical purposes, <i>perfectly</i> polarized. +Indeed, bundles of glass plates are often employed as a means of +furnishing polarized light. It is important to note that the plane +of vibration of this transmitted light is at right angles to that +of the reflected light.</p> +<p>One word more. When the tourmalines are crossed, <a name= +"Page_120" id="Page_120"></a><span class="pagenum">[Pg +120]</span>the space where they cross each other is black. But we +have seen that the least obliquity on the part of the crystals +permits light to get through both. Now suppose, when the two plates +are crossed, that we interpose a third plate of tourmaline between +them, with its axis oblique to both. A portion of the light +transmitted by the first plate will get through this intermediate +one. But, after it has got through, <i>its plane of vibration is +changed</i>: it is no longer perpendicular to the axis of the +crystal in front. Hence it will, in part, get through that crystal. +Thus, by pure reasoning, we infer that the interposition of a third +plate of tourmaline will in part abolish the darkness produced by +the perpendicular crossing of the other two plates. I have not a +third plate of tourmaline; but the talc or mica which you employ in +your stoves is a more convenient substance, which acts in the same +way. Between the crossed tourmalines, I introduce a film of this +crystal with its axis oblique to theirs. You see the edge of the +film slowly descending, and, as it descends, light takes the place +of darkness. The darkness, in fact, seems scraped away, as if it +were something material. This effect has been called, naturally but +improperly, <i>depolarization</i>. Its proper meaning will be +disclosed in our next lecture.</p> +<p>These experiments and reasonings, if only thoroughly studied and +understood, will form a solid groundwork for the analysis of the +splendid optical phenomena next to be considered.</p> +<hr style="width: 65%;" /> +<div><a name="Page_121" id="Page_121"></a><span class="pagenum">[Pg +121]</span></div> +<h2><a name="LECTURE_IV" id="LECTURE_IV"></a>LECTURE IV.</h2> +<table border="0" cellpadding="0" cellspacing="0" summary=""> +<tr> +<td> +<div style="font-size: smaller;"> +<ul style="list-style: none;"> +<li>CHROMATIC PHENOMENA PRODUCED BY CRYSTALS IN POLARIZED +LIGHT</li> +<li>THE NICOL PRISM</li> +<li>POLARIZER AND ANALYZER</li> +<li>ACTION OF THICK AND THIN PLATES OF SELENITE</li> +<li>COLOURS DEPENDENT ON THICKNESS</li> +<li>RESOLUTION OF POLARIZED BEAM INTO TWO OTHERS BY THE +SELENITE</li> +<li>ONE OF THEM MORE RETARDED THAN THE OTHER</li> +<li>RECOMPOUNDING OF THE TWO SYSTEMS OF WAVES BY THE ANALYZER</li> +<li>INTERFERENCE THUS RENDERED POSSIBLE</li> +<li>CONSEQUENT PRODUCTION OF COLOURS</li> +<li>ACTION OF BODIES MECHANICALLY STRAINED OR PRESSED</li> +<li>ACTION OF SONOROUS VIBRATIONS</li> +<li>ACTION OF GLASS STRAINED OR PRESSED BY HEAT</li> +<li>CIRCULAR POLARIZATION</li> +<li>CHROMATIC PHENOMENA PRODUCED BY QUARTZ</li> +<li>THE MAGNETIZATION OF LIGHT</li> +<li>RINGS SURROUNDING THE AXES OF CRYSTALS</li> +<li>BIAXAL AND UNIAXAL CRYSTALS</li> +<li>GRASP OF THE UNDULATORY THEORY</li> +<li>THE COLOUR AND POLARIZATION OF SKY-LIGHT</li> +<li>GENERATION OF ARTIFICIAL SKIES.</li> +</ul> +</div> +</td> +</tr> +</table> +<h3>§ 1. <i>Action of Crystals on Polarized Light: the Nicol +Prism.</i></h3> +<p>We have this evening to examine and illustrate the chromatic +phenomena produced by the action of crystals, and double-refracting +bodies generally, upon polarized light, and to apply the Undulatory +Theory to their elucidation. For a long time investigators were +compelled to employ plates of tourmaline for this purpose, and the +progress they made with so defective a means of inquiry is +astonishing. But these men had their hearts in their work, and were +on this account enabled to extract great results from small +instrumental appliances. For our present purpose we need far larger +apparatus; and, happily, in these later times this need has +<a name="Page_122" id="Page_122"></a><span class="pagenum">[Pg +122]</span>been to a great extent satisfied. We have seen and +examined the two beams emergent from Iceland spar, and have proved +them to be polarized. If, at the sacrifice of half the light, we +could abolish one of these, the other would place at our disposal a +beam of polarized light, incomparably stronger than any attainable +from tourmaline.</p> +<div class="figright" style="width: 170px;"><img src= +"images/fig34.jpg" width="170" height="368" alt="Fig. 34." title= +"" /> <b>Fig. 34.</b></div> +<p>The beams, as you know, are refracted differently, and from +this, as made plain in §4, Lecture I., we are able to infer +that the one may be totally reflected, when the other is not. An +able optician, named Nicol, cut a crystal of Iceland spar in two +halves in a certain direction. He polished the severed surfaces, +and reunited them by Canada balsam, the surface of union being so +inclined to the beam traversing the spar that the ordinary ray, +which is the most highly refracted, was totally reflected by the +balsam, while the extraordinary ray was permitted to pass on.</p> +<p>Let <i>b x, c y</i> (fig. 34) represent the section of an +elongated rhomb of Iceland spar cloven from the crystal. Let this +rhomb be cut along the plane <i>b c</i>; and the two severed +surfaces, after having been polished, reunited by Canada balsam. We +learned, in our first lecture, that total reflection only takes +place when a ray seeks to escape from a more refracting to a less +refracting medium, and that it always, under these circumstances, +takes place when the obliquity is sufficient. Now the refractive +index of Iceland spar is, for the extraordinary ray less, and for +the ordinary greater, than for Canada balsam. Hence, in passing +from the spar to the balsam, the extraordinary ray passes from a +less refracting to a more refracting medium, where total reflection +cannot occur; while the ordinary ray passes from a more <a name= +"Page_123" id="Page_123"></a><span class="pagenum">[Pg +123]</span>refracting to a less refracting medium, where total +reflection can occur. The requisite obliquity is secured by making +the rhomb of such a length that the plane of which <i>b c</i> is +the section shall be perpendicular, or nearly so, to the two end +surfaces of the rhomb <i>b x, c y</i>.</p> +<p>The invention of the Nicol prism was a great step in practical +optics, and quite recently such prisms have been constructed of a +size and purity which enable audiences like the present to witness +the chromatic phenomena of polarized light to a degree altogether +unattainable a short time ago.</p> +<p>(The two prisms employed in these experiments were lent to me by +my lamented friend Mr. William Spottiswoode, and they were +manufactured by Mr. Ahrens, an optician of consummate +skill.)<a name="Page_124" id="Page_124"></a><span class= +"pagenum">[Pg 124]</span></p> +<h3>§ 2. <i>Colours of Films of Selenite in Polarized +Light</i>.</h3> +<p>Two Nicol prisms play the same part as the two plates of +tourmaline. Placed with their directions of vibration parallel, the +light passes through both; while when these directions are crossed +the light is quenched. Introducing a film of mica between the +prisms, the light, as in the case of the tourmaline, is restored. +But notice, when the film of mica is <i>thin</i> you have sometimes +not only light, but <i>coloured</i> light. Our work for some time +to come will consist of the examination of such colours. With this +view, I will take a representative crystal, one easily dealt with, +because it cleaves with great facility—the crystal gypsum, or +selenite, which is crystallized sulphate of lime. Between the +crossed Nicols I place a thick plate of this crystal; like the +mica, it restores the light, but it produces no colour. With my +penknife I take a thin splinter from the crystal and place it +between the prisms; the image of the splinter glows with the +richest colours. Turning the prism in front, these colours +gradually fade and disappear, but, by continuing the rotation until +the vibrating sections of the prisms are parallel to each other, +vivid colours again arise, but these colours are complementary to +the former ones.</p> +<p>Some patches of the splinter appear of one colour, some of +another. These differences are due to the different thicknesses of +the film. As in the case of Hooke's thin plates, if the thickness +be uniform the colour is uniform. Here, for instance, is a stellar +shape, every lozenge of the star being a film of gypsum of uniform +thickness: each lozenge, you observe, shows a <a name="Page_125" +id="Page_125"></a><span class="pagenum">[Pg 125]</span>brilliant +and uniform colour. It is easy, by shaping our films so as to +represent flowers or other objects, to exhibit such objects in hues +unattainable by art. Here, for example, is a specimen of +heart's-ease, the colours of which you might safely defy the artist +to reproduce. By turning the front Nicol 90 degrees round, we pass +through a colourless phase to a series of colours complementary to +the former ones. This change is still more strikingly represented +by a rose-tree, which is now presented in its natural hues—a +red flower and green leaves; turning the prism 90 degrees round, we +obtain a green flower and red leaves. All these wonderful chromatic +effects have definite mechanical causes in the motions of the +ether. The principle of interference duly applied and interpreted +explains them all.</p> +<h3>§ 3. <i>Colours of Crystals in Polarized Light explained +by the Undulatory Theory</i>.</h3> +<p>By this time you have learned that the word 'light' may be used +in two different senses: it may mean the impression made upon +consciousness, or it may mean the physical cause of the impression. +It is with this cause that we have to occupy ourselves at present. +The luminiferous ether is a substance which fills all space, and +surrounds the atoms and molecules of bodies. To this inter-stellar +and inter-atomic medium definite mechanical properties are +ascribed, and we deal with it in our reasonings and calculations as +a body possessed of these properties. In mechanics we have the +composition and resolution of forces and of motions, extending to +the composition and resolution of <i>vibrations</i>. We treat the +luminiferous ether on mechanical principles, and, from <a name= +"Page_126" id="Page_126"></a><span class="pagenum">[Pg +126]</span>the composition and resolution of its vibrations we +deduce all the phenomena displayed by crystals in polarized +light.</p> +<div class="figleft" style="width: 261px;"><img src= +"images/fig35.jpg" width="261" height="120" alt="Fig. 35." title= +"" /> <b>Fig. 35.</b></div> +<p>Let us take, as an example, the crystal of tourmaline, with +which we are now so familiar. Let a vibration cross this crystal +oblique to its axis. Experiment has assured us that a portion of +the light will pass through. The quantity which passes we determine +in this way. Let A B (fig. 35) be the axis of the tourmaline, and +let <i>a</i> <i>b</i> represent the amplitude of an oblique +ethereal vibration before it reaches A B. From <i>a</i> and +<i>b</i> let the two perpendiculars <i>a</i> <i>c</i> and <i>b</i> +<i>d</i> be drawn upon the axis: then <i>c</i> <i>d</i> will be the +amplitude of the transmitted vibration.</p> +<p>I shall immediately ask you to follow me while I endeavour to +explain the effects observed when a film of gypsum is placed +between the two Nicol prisms. But, prior to this, it will be +desirable to establish still further the analogy between the action +of the prisms and that of the two plates of tourmaline. The +magnified images of these plates, with their axes at right-angles +to each other, are now before you. Introducing between them a film +of selenite, you observe that by turning the film round it may be +placed in a position where it has no power to abolish the darkness +of the superposed portions of the tourmalines. Why is this? The +answer is, that in the gypsum there are two direc<a name="Page_127" +id="Page_127"></a><span class="pagenum">[Pg 127]</span>tions, at +right angles to each other, in which alone vibrations can take +place, and that in our present experiment one of these directions +is parallel to one of the axes of the tourmaline, and the other +parallel to the other axis. When this is the case, the film +exercises no sensible action upon the light. But now I turn the +film so as to render its directions of vibration <i>oblique</i> to +the two tourmaline axes; then, you see it exercises the power, +demonstrated in the last lecture, of partially restoring the +light.</p> +<div class="figright" style="width: 380px;"><img src= +"images/fig36.jpg" width="380" height="270" alt="Fig. 36." title= +"" /> <b>Fig. 36.</b></div> +<p>Let us now mount our Nicol prisms, and cross them as we crossed +the tourmaline. Introducing our film of gypsum between them, you +notice that in one particular position the film has no power +whatever over the field of view. But, when the film is turned a +little way round, the light passes. We have now to understand the +mechanism by which this is effected.</p> +<p>First, then, we have a prism which receives the light from the +electric lamp, and which is called the <i>polarizer</i>. Then we +have the plate of gypsum (supposed to be placed at S, fig. 36), and +then the <a name="Page_128" id="Page_128"></a><span class= +"pagenum">[Pg 128]</span>prism in front, which is called the +<i>analyzer</i>. On its emergence from the first prism, the light +is polarized; and, in the particular case now before us, its +vibrations are executed in a horizontal plane. We have to examine +what occurs when the two directions of vibration in the interposed +gypsum are oblique to the horizon. Draw a rectangular cross (A B, C +D, fig. 37) to represent these two directions. Draw a line +(<i>a</i> <i>b</i>) to represent the amplitude of the horizontal +vibration on the emergence of the light from the first Nicol. Let +fall from each end of this line two perpendiculars (<i>a</i> +<i>c</i>, <i>a</i> <i>f</i>, <i>b</i> <i>d</i>, <i>b</i> <i>e</i>) +on the two arms of the cross; then the distances (<i>c</i> +<i>d</i>, <i>e</i> <i>f</i>) between the feet of these +perpendiculars represent the amplitudes of two rectangular +vibrations, which are the <i>components</i> of the first single +vibration. Thus the polarized ray, when it enters the gypsum, is +resolved into its two equivalents, which vibrate at right angles to +each other.</p> +<div class="figleft" style="width: 216px;"><img src= +"images/fig37.jpg" width="216" height="211" alt="Fig. 37." title= +"" /> <b>Fig. 37.</b></div> +<p>In one of these two rectangular directions the ether within the +gypsum is more sluggish than in the other; and, as a consequence, +the waves that follow this direction are more retarded than the +others. In both cases the undulations are shortened when they +<a name="Page_129" id="Page_129"></a><span class="pagenum">[Pg +129]</span>enter the gypsum, but in the one case they are more +shortened than in the other. You can readily imagine that in this +way the one system of waves may get half a wave-length, or indeed +any number of half wavelengths, in advance of the other. The +possibility of interference here at once flashes upon the mind. A +little consideration, however, will render it evident that, as long +as the vibrations are executed at right angles to each other, they +cannot quench each other, no matter what the retardation may be. +This brings us at once to the part played by the analyzer. Its sole +function is to recompound the two vibrations emergent from the +gypsum. It reduces them to a single plane, where, if one of them be +retarded by the proper amount, extinction will occur.</p> +<p>But here, as in the case of thin films, the different lengths of +the waves of light come into play. Red will require a greater +thickness to produce the retardation necessary for extinction than +blue; consequently when the longer waves have been withdrawn by +interference, the shorter ones remain, the film of gypsum shining +with the colours which the short waves confer. Conversely, when the +shorter waves have been withdrawn, the thickness is such that the +longer waves remain. An elementary consideration suffices to show, +that when the directions of vibration of the prisms and the gypsum +enclose an angle of forty-five degrees, the colours are at their +maximum brilliancy. When the film is turned from this direction, +the colours gradually fade, until, at the point where the +directions of vibration in plate and prisms are parallel, they +disappear altogether.</p> +<p>(The best way of obtaining a knowledge of these phenomena is to +construct a model of thin wood or <a name="Page_130" id= +"Page_130"></a><span class="pagenum">[Pg 130]</span>pasteboard, +representing the plate of gypsum, its planes of vibration, and also +those of the polarizer and analyzer. Two parallel pieces of the +board are to be separated by an interval which shall represent the +thickness of the film of gypsum. Between them two other pieces, +intersecting each other at a right angle, are to represent the +planes of vibration within the film; while attached to the two +parallel surfaces outside are two other pieces of board, which +represent the planes of vibration of the polarizer and analyzer. On +the two intersecting planes the waves are to be drawn, showing the +resolution of the first polarized beam into two others, and then +the subsequent reduction of the two systems of vibrations to a +common plane by the analyzer. Following out rigidly the interaction +of the two systems of waves, we are taught by such a model that all +the phenomena of colour obtained by the combination of the waves, +when the planes of vibration of the two Nicols are parallel, are +displaced by the <i>complementary</i> phenomena, when the planes of +vibration are perpendicular to each other.)</p> +<p>In considering the next point, we will operate, for the sake of +simplicity, with monochromatic light—with red light, for +example, which is easily obtained pure by red glass. Supposing a +certain thickness of the gypsum produces a retardation of half a +wave-length, twice this thickness will produce a retardation of two +half wave-lengths, three times this thickness a retardation of +three half wave-lengths, and so on. Now, when the Nicols are +parallel, the retardation of half a wave-length, or of any +<i>odd</i> number of half wave-lengths, produces extinction; at all +thicknesses, on the other hand, which correspond to a retardation +of an <i>even</i> number of half <a name="Page_131" id= +"Page_131"></a><span class="pagenum">[Pg 131]</span>wave-lengths, +the two beams support each other, when they are brought to a common +plane by the analyzer. Supposing, then, that we take a plate of a +wedge form, which grows gradually thicker from edge to back, we +ought to expect, in red light, a series of recurrent bands of light +and darkness; the dark bands occurring at thicknesses which produce +retardations of one, three, five, etc., half wave-lengths, while +the bright bands occur between the dark ones. Experiment proves the +wedge-shaped film to show these bands. They are also beautifully +shown by a circular film, so worked as to be thinnest at the +centre, and gradually increasing in thickness from the centre +outwards. A splendid series of rings of light and darkness is thus +produced.</p> +<p>When, instead of employing red light, we employ blue, the rings +are also seen: but as they occur at thinner portions of the film, +they are smaller than the rings obtained with the red light. The +consequence of employing white light may be now inferred; inasmuch +as the red and the blue fall in different places, we have +<i>iris-coloured</i> rings produced by the white light.</p> +<p>Some of the chromatic effects of irregular crystallization are +beautiful in the extreme. Could I introduce between our two Nicols +a pane of glass covered by those frost-ferns which your cold +weather renders now so frequent, rich colours would be the result. +The beautiful effects of the irregular crystallization of tartaric +acid and other substances on glass plates now presented to you, +illustrate what you might expect from the frosted window-pane. And +not only do crystalline bodies act thus upon light, but almost all +bodies that possess a definite structure do the same. As a general +<a name="Page_132" id="Page_132"></a><span class="pagenum">[Pg +132]</span>rule, organic bodies act thus upon light; for their +architecture implies an arrangement of the molecules, and of the +ether associated with the molecules, which involves double +refraction. A film of horn, or the section of a shell, for example, +yields very beautiful colours in polarized light. In a tree, the +ether certainly possesses different degrees of elasticity along and +across the fibre; and, were wood transparent, this peculiarity of +molecular structure would infallibly reveal itself by chromatic +phenomena like those that you have seen.</p> +<h3>§ 4. <i>Colours produced by Strain and Pressure.</i></h3> +<p>Not only do natural bodies behave in this way, but it is +possible, as shown by Brewster, to confer, by artificial strain or +pressure, a temporary double refracting structure upon +non-crystalline bodies such as common glass. This is a point worthy +of illustration. When I place a bar of wood across my knee and seek +to break it, what is the mechanical condition of the bar? It bends, +and its convex surface is <i>strained</i> longitudinally; its +concave surface, that next my knee, is longitudinally +<i>pressed</i>. Both in the strained portion and in the pressed +portion of the wood the ether is thrown into a condition which +would render the wood, were it transparent, double-refracting. For, +in cases like the present, the drawing of the molecules asunder +longitudinally is always accompanied by their approach to each +other laterally; while the longitudinal squeezing is accompanied by +lateral retreat. Each half of the bar of wood exhibits this +antithesis, and is therefore double-refracting.</p> +<p><a name="Page_133" id="Page_133"></a><span class="pagenum">[Pg +133]</span>Let us now repeat this experiment with a bar of glass. +Between the crossed Nicols I introduce such a bar. By the dim +residue of light lingering upon the screen, you see the image of +the glass, but it has no effect upon the light. I simply bend the +glass bar with my finger and thumb, keeping its length oblique to +the directions of vibration in the Nicols. Instantly light flashes +out upon the screen. The two sides of the bar are illuminated, the +edges most, for here the strain and pressure are greatest. In +passing from longitudinal strain to longitudinal pressure, we cross +a portion of the glass where neither is exerted. This is the +so-called neutral axis of the bar of glass, and along it you see a +dark band, indicating that the glass along this axis exercises no +action upon the light. By employing the force of a press, instead +of the force of my finger and thumb, the brilliancy of the light is +greatly augmented.</p> +<p>Again, I have here a square of glass which can be inserted into +a press of another kind. Introducing the uncompressed square +between the prisms, its neutrality is declared; but it can hardly +be held sufficiently loosely in the press to prevent its action +from manifesting itself. Already, though the pressure is +infinitesimal, you see spots of light at the points where the press +is in contact with the glass. On turning a screw, the image of the +square of glass flashes out upon the screen. Luminous spaces are +seen separated from each other by dark bands.</p> +<div class="figright" style="width: 165px;"><img src= +"images/fig38.jpg" width="165" height="358" alt="Fig. 38" title= +"" /> <b>Fig. 38</b></div> +<p>Every two adjacent spaces are in opposite mechanical conditions. +On one side of the dark band we have strain, on the other side +pressure, the band marking the neutral axis between both. I now +tighten <a name="Page_134" id="Page_134"></a><span class= +"pagenum">[Pg 134]</span>the vice, and you see colour; tighten +still more, and the colours appear as rich as those presented by +crystals. Releasing the vice, the colours suddenly vanish; +tightening suddenly, they reappear. From the colours of a +soap-bubble Newton was able to infer the thickness of the bubble, +thus uniting by the bond of thought apparently incongruous things. +From the colours here presented to you, the magnitude of the +pressure employed might be inferred. Indeed, the late M. Wertheim, +of Paris, invented an instrument for the determination of strains +and pressures, by the colours of polarized light, which exceeded in +accuracy all previous instruments of the kind.</p> +<p>And now we have to push these considerations to a final +illustration. Polarized light may be turned to account in various +ways as an analyzer of molecular condition. It may, for instance, +be applied to reveal the condition of a solid body when it becomes +sonorous. A strip of glass six feet long, two inches wide and a +quarter of an inch thick, is held at the centre between the finger +and thumb. On sweeping a wet woollen rag over one of its halves, +you hear an acute sound due to the vibrations of the glass. What is +the condition of the glass while the sound is heard? This: its two +halves lengthen and shorten in quick succession. Its two ends, +therefore, are in a state of quick vibration; but at the centre the +pulses from the two ends alternately meet and retreat from each +other. Between their opposing actions, the glass at the centre is +kept motionless: but, on the other hand, it is alternately strained +and compressed. In fig. 38, A B may be taken to represent the glass +rectangle with its centre condensed; while A' B' represents the +same rectangle <a name="Page_135" id="Page_135"></a><span class= +"pagenum">[Pg 135]</span>with its centre rarefied. The ends of the +strip suffer neither condensation nor rarefaction.</p> +<p>If we introduce the strip of glass (<i>s</i> <i>s'</i>, fig. 39) +between the crossed Nicols, taking care to keep it oblique to the +directions of vibration of the Nicols, and sweep our wet rubber +over the glass, this is what may be expected to occur: At every +moment of compression the light will flash through; at every moment +of strain the light will also flash through; and these states of +strain and pressure will follow each other so rapidly, that we may +expect a permanent luminous impression to be made upon the eye. By +pure reasoning, therefore, we reach the conclusion that the light +will be revived whenever the glass is sounded. That it is so, +experiment testifies: at every sweep of the rubber (<i>h</i>, fig. +39) a fine luminous disk (O) flashes out upon the screen. The +experiment may be varied in this way: Placing in front of the +polarizer a plate of unannealed glass, <a name="Page_136" id= +"Page_136"></a><span class="pagenum">[Pg 136]</span>you have a +series of beautifully coloured rings, intersected by a black cross. +Every sweep of the rubber not only abolishes the rings, but +introduces complementary ones, the black cross being, for the +moment, supplanted by a white one. This is a modification of a +beautiful experiment which we owe to Biot. His apparatus, however, +confined the observation of it to a single person at a time.</p> +<div class="figcenter" style="width: 558px;"><img src= +"images/fig39.jpg" width="558" height="363" alt="Fig. 39." title= +"" /> <b>Fig. 39.</b></div> +<h3>§ 5. <i>Colours of Unannealed Glass</i>.</h3> +<p>Bodies are usually expanded by heat and contracted by cold. If +the heat be applied with perfect uniformity, no local strains or +pressures come into play; but, if one portion of a solid be heated +and another portion not, the expansion of the heated portion +introduces strains and pressures which reveal themselves under the +scrutiny of polarized light. When a square <a name="Page_137" id= +"Page_137"></a><span class="pagenum">[Pg 137]</span>of common +window-glass is placed between the Nicols, you see its dim outline, +but it exerts no action on the polarized light. Held for a moment +over the flame of a spirit-lamp, on reintroducing it between the +Nicols, light flashes out upon the screen. Here, as in the case of +mechanical action, you have luminous spaces of strain divided by +dark neutral axes from spaces of pressure.</p> +<div class="figleft" style="width: 197px;"><img src= +"images/fig40.jpg" width="197" height="198" alt="Fig. 40." title= +"" /> <b>Fig. 40.</b></div> +<div class="figright" style="width: 195px;"><img src= +"images/fig41.jpg" width="195" height="197" alt="Fig. 41." title= +"" /> <b>Fig. 41.</b></div> +<p>Let us apply the heat more symmetrically. A small square of +glass is perforated at the centre, and into the orifice a bit of +copper wire is introduced. Placing the square between the prisms, +and heating the wire, the heat passes by conduction to the glass, +through which it spreads from the centre outwards. You immediately +see four luminous quadrants and a dim cross, which becomes +gradually blacker, by comparison with the adjacent brightness. And +as, in the case of pressure, we produced colours, so here also, by +the proper application of heat, gorgeous chromatic effects may be +evoked. The condition necessary to the production of these colours +may be rendered permanent by first heating the glass sufficiently, +and then cooling it, so that the chilled mass <a name="Page_138" +id="Page_138"></a><span class="pagenum">[Pg 138]</span>shall remain +in a state of permanent strain and pressure. Two or three examples +will illustrate this point. Figs. 40 and 41 represent the figures +obtained with two pieces of glass thus prepared; two rectangular +pieces of unannealed glass, crossed and placed between the +polarizer and analyzer, exhibit the beautiful iris fringes +represented in fig. 42.</p> +<div class="figcenter" style="width: 444px;"><img src= +"images/fig42.jpg" width="444" height="442" alt="Fig. 42." title= +"" /> <b>Fig. 42.</b></div> +<h3>§ 6. <i>Circular Polarization.</i></h3> +<p>But we have to follow the ether still further into its +hiding-places. Suspended before you is a pendulum, which, when +drawn aside and liberated, oscillates to and fro. If, when the +pendulum is passing the middle point of its excursion, I impart a +shock to it tending to drive <a name="Page_139" id= +"Page_139"></a><span class="pagenum">[Pg 139]</span>it at right +angles to its present course, what occurs? The two impulses +compound themselves to a vibration oblique in direction to the +former one, but the pendulum still oscillates in <i>a plane</i>. +But, if the rectangular shock be imparted to the pendulum when it +is at the limit of its swing, then the compounding of the two +impulses causes the suspended ball to describe, not a straight +line, but an ellipse; and, if the shock be competent of itself to +produce a vibration of the same amplitude as the first one, the +ellipse becomes a circle.</p> +<p>Why do I dwell upon these things? Simply to make known to you +the resemblance of these gross mechanical vibrations to the +vibrations of light. I hold in my hand a plate of quartz cut from +the crystal perpendicular to its axis. The crystal thus cut +possesses the extraordinary power of twisting the plane of +vibration of a polarized ray to an extent dependent on the +thickness of the crystal. And the more refrangible the light the +greater is the amount of twisting; so that, when white light is +employed, its constituent colours are thus drawn asunder. Placing +the quartz plate between the polarizer and analyzer, this vivid red +appears; and, turning the analyzer in front from right to left, the +other colours of the spectrum appear in succession. Specimens of +quartz have been found which require the analyzer to be turned from +left to right to obtain the same succession of colours. Crystals of +the first class are therefore called right-handed, and of the +second class, left-handed crystals.</p> +<p>With profound sagacity, Fresnel, to whose genius we mainly owe +the expansion and final triumph of the undulatory theory of light, +reproduced mentally the mechanism of these crystals, and showed +their action to <a name="Page_140" id="Page_140"></a><span class= +"pagenum">[Pg 140]</span>be due to the circumstance that, in them, +the waves of ether so act upon each other as to produce the +condition represented by our rotating pendulum. Instead of being +plane polarized, the light in rock crystal is <i>circularly +polarized</i>. Two such rays, transmitted along the axis of the +crystal, and rotating in opposite directions, when brought to +interference by the analyzer, are demonstrably competent to produce +all the observed phenomena.</p> +<h3>§ 7. <i>Complementary Colours of Bi-refracting Spar in +Circularly Polarized Light. Proof that Yellow and Blue are +Complementary.</i></h3> +<div class="figright" style="width: 403px;"><img src= +"images/fig43.jpg" width="403" height="228" alt="Fig. 43." title= +"" /> <b>Fig. 43.</b></div> +<p>I now remove the analyzer, and put in its place the piece of +Iceland spar with which we have already illustrated double +refraction. The two images of the carbon-points are now before you, +produced, as you know, by two beams vibrating at right angles to +each other. Introducing a plate of quartz between the polarizer and +the spar, the two images glow with complementary colours. Employing +the image of an aperture instead of that of the carbon-points, we +have two coloured circles. As the analyzer is caused to rotate, the +colours pass through various changes: but they are always +complementary. When the one is red, the other is green; when the +one is yellow, the other is blue. Here we have it in our power to +demonstrate afresh a statement made in our first lecture, that +although the mixture of blue and yellow pigments produces green, +the mixture of blue and yellow lights produces white. By enlarging +our aperture, the two images produced by the spar are caused to +approach each other, and <a name="Page_141" id= +"Page_141"></a><span class="pagenum">[Pg 141]</span>finally to +overlap. The one image is now a vivid yellow, the other a vivid +blue, and you notice that where these colours are superposed we +have a pure white. (See fig. 43, where N is the end of the +polarizer, Q the quartz plate, L a lens, and B the bi-refracting +spar. The two images overlap at O, and produce white by their +mixture.)</p> +<h3>§ 8. <i>The Magnetization of Light.</i></h3> +<p>This brings us to a point of our inquiries which, though rarely +illustrated in lectures, is nevertheless so likely to affect +profoundly the future course of scientific thought that I am +unwilling to pass it over without reference. I refer to the +experiment which Faraday, its discoverer, called the 'magnetization +of light.' The arrangement for this celebrated experiment is now +before you. We have, first, our electric lamp, then a Nicol prism, +to polarize the beam emergent from the lamp; then an +electro-magnet, then a second Nicol, and finally our screen. At the +present moment the prisms are crossed, and the screen is dark. I +<a name="Page_142" id="Page_142"></a><span class="pagenum">[Pg +142]</span>place from pole to pole of the electro-magnet a cylinder +of a peculiar kind of glass, first made by Faraday, and called +Faraday's heavy glass. Through this glass the beam from the +polarizer now passes, being intercepted by the Nicol in front. On +exciting the magnet light instantly appears upon the screen. By the +action of the magnet upon the heavy glass the plane of vibration is +caused to rotate, the light being thus enabled to get through the +analyzer.</p> +<div class="figright" style="width: 430px;"><img src= +"images/fig44.jpg" width="430" height="283" alt="Fig. 44" title= +"" /> <b>Fig. 44</b></div> +<p>The two classes into which quartz-crystals are divided have been +already mentioned. In my hand I hold a compound plate, one half of +it taken from a right-handed, and the other from a left-handed +crystal. Placing the plate in front of the polarizer, I turn one of +the Nicols until the two halves of the plate show a common puce +colour. This yields an exceedingly sensitive means of rendering +visible the action of a magnet upon light. By turning either the +polarizer or the analyzer through the smallest angle, the +uniformity of the colour disappears, and the two halves of the +quartz show different colours. The magnet produces an effect +equivalent to this rotation. The puce-coloured circle is now before +you on the screen. (See fig. 44, where N is the nozzle of the lamp, +H the first Nicol, Q the biquartz plate, L a lens, M the +electro-magnet, with the heavy glass across its perforated poles, +and P the second Nicol.) Exciting the magnet, one half of the image +becomes suddenly red, the other half green. Interrupting the +current, the two colours fade away, and the primitive puce is +restored.</p> +<p>The action, moreover, depends upon the polarity of the magnet, +or, in other words, on the direction of the current which surrounds +the magnet. Reversing <a name="Page_143" id= +"Page_143"></a><span class="pagenum">[Pg 143]</span>the current, +the red and green reappear, but they have changed places. The red +was formerly to the right, and the green to the left; the green is +now to the right, and the red to the left. With the most exquisite +ingenuity, Faraday analyzed all those actions and stated their +laws. This experiment, however, long remained a scientific +curiosity rather than a fruitful germ. That it would bear fruit of +the highest importance, Faraday felt profoundly convinced, and +present researches are on the way to verify his conviction.</p> +<h3>§ 9. <i>Iris-rings surrounding the Axes of +Crystals.</i></h3> +<p>A few more words are necessary to complete our knowledge of the +wonderful interaction between ponderable molecules and the ether +interfused among them. Symmetry of molecular arrangement implies +symmetry on the part of the ether; atomic dissymmetry, on the other +hand, involves the dissymmetry of the ether, and, <a name= +"Page_144" id="Page_144"></a><span class="pagenum">[Pg +144]</span>as a consequence, double refraction. In a certain class +of crystals the structure is homogeneous, and such crystals produce +no double refraction. In certain other crystals the molecules are +ranged symmetrically round a certain line, and not around others. +Along the former, therefore, the ray is undivided, while along all +the others we have double refraction. Ice is a familiar example: +its molecules are built with perfect symmetry around the +perpendiculars to the planes of freezing, and a ray sent through +ice in this direction is not doubly refracted; whereas, in all +other directions, it is. Iceland spar is another example of the +same kind: its molecules are built symmetrically round the line +uniting the two blunt angles of the rhomb. In this direction a ray +suffers no double refraction, in all others it does. This direction +of no double refraction is called the <i>optic axis</i> of the +crystal.</p> +<p>Hence, if a plate be cut from a crystal of Iceland spar +perpendicular to the axis, all rays sent across this plate in the +direction of the axis will produce but one image. But, the moment +we deviate from the parallelism with the axis, double refraction +sets in. If, therefore, a beam that has been rendered +<i>conical</i> by a converging lens be sent through the spar so +that the central ray of the cone passes along the axis, this ray +only will escape double refraction. Each of the others will be +divided into an ordinary and an extraordinary ray, the one moving +more slowly through the crystal than the other; the one, therefore, +retarded with reference to the other. Here, then, we have the +conditions for interference, when the waves are reduced by the +analyzer to a common plane.</p> +<p>Placing the plate of Iceland spar between the crossed <a name= +"Page_145" id="Page_145"></a><span class="pagenum">[Pg +145]</span>Nicol prisms, and employing the conical beam, we have +upon the screen a beautiful system of iris-rings surrounding the +end of the optic axis, the circular bands of colour being +intersected by a black cross (fig. 45). The arms of this cross are +parallel to the two directions of vibration in the polarizer and +analyzer. It is easy to see that those rays whose planes of +vibration within the spar coincide with the plane of vibration of +<i>either</i> prism, cannot get through <i>both</i>. This complete +interception produces the arms of the cross.</p> +<div class="figcenter" style="width: 268px;"><img src= +"images/fig45.jpg" width="268" height="265" alt="Fig. 45." title= +"" /> <b>Fig. 45.</b></div> +<p>With monochromatic light the rings would be simply bright and +black—the bright rings occurring at those thicknesses of the +spar which cause the rays to conspire; the black rings at those +thicknesses which cause them to quench each other. Turning the +analyzer 90° round, we obtain the complementary phenomena. The +black cross gives place to a bright one, and every dark ring is +supplanted also by a bright one (fig. 46). Here, as elsewhere, the +different lengths of the light-<a name="Page_146" id= +"Page_146"></a><span class="pagenum">[Pg 146]</span>waves give rise +to iris-colours when white light is employed.</p> +<div class="figleft" style="width: 206px;"><img src= +"images/fig46.jpg" width="206" height="202" alt="Fig. 46." title= +"" /> <b>Fig. 46.</b></div> +<div class="figright" style="width: 278px;"><img src= +"images/fig47.jpg" width="278" height="210" alt="Fig. 47." title= +"" /> <b>Fig. 47.</b></div> +<p>Besides the <i>regular</i> crystals which produce double +refraction in no direction, and the <i>uniaxal</i> crystals which +produce it in all directions but one, Brewster discovered that in a +large class of crystals there are <i>two</i> directions in which +double refraction does not take place. These are called +<i>biaxal</i> crystals. When plates of these crystals, suitably +cut, are placed between the polarizer and analyzer, the axes (A A', +fig. 47) are seen surrounded, not by circles, but by curves of +another order and of a perfectly definite mathematical character. +Each band, as proved experimentally by Herschel, <a name="Page_147" +id="Page_147"></a><span class="pagenum">[Pg 147]</span>forms a +<i>lemniscata</i>; but the experimental proof was here, as in +numberless other cases, preceded by the deduction which showed +that, according to the undulatory theory, the bands must possess +this special character.</p> +<h3>§ 10. <i>Power of the Wave Theory</i>.</h3> +<p>I have taken this somewhat wide range over polarization itself, +and over the phenomena exhibited by crystals in polarized light, in +order to give you some notion of the firmness and completeness of +the theory which grasps them all. Starting from the single +assumption of transverse undulations, we first of all determine the +wave-lengths, and find that on them all the phenomena of colour are +dependent. The wavelengths may be determined in many independent +ways. Newton virtually determined them when he measured the periods +of his Fits: the length of a fit, in fact, is that of a quarter of +an undulation. The wave-lengths may be determined by diffraction at +the edges of a slit (as in the Appendix to these Lectures); they +may be deduced from the interference fringes produced by +reflection; from the fringes produced by refraction; also by lines +drawn with a diamond upon glass at measured distances asunder. And +when the length determined by these independent methods are +compared together, the strictest agreement is found to exist +between them.</p> +<p>With the wave-lengths once at our disposal, we follow the ether +into the most complicated cases of interaction between it and +ordinary matter, 'the theory is equal to them all. It makes not a +single new <a name="Page_148" id="Page_148"></a><span class= +"pagenum">[Pg 148]</span>physical hypothesis; but out of its +original stock of principles it educes the counterparts of all that +observation shows. It accounts for, explains, simplifies the most +entangled cases; corrects known laws and facts; predicts and +discloses unknown ones; becomes the guide of its former teacher +Observation; and, enlightened by mechanical conceptions, acquires +an insight which pierces through shape and colour to force and +cause.'<a name="FNanchor_18_18" id="FNanchor_18_18"></a><a href= +"#Footnote_18_18" class="fnanchor">[18]</a></p> +<p>But, while I have thus endeavoured to illustrate before you the +power of the undulatory theory as a solver of all the difficulties +of optics, do I therefore wish you to close your eyes to any +evidence that may arise against it? By no means. You may urge, and +justly urge, that a hundred years ago another theory was held by +the most eminent men, and that, as the theory then held had to +yield, the undulatory theory may have to yield also. This seems +reasonable; but let us understand the precise value of the +argument. In similar language a person in the time of Newton, or +even in our time, might reason thus: Hipparchus and Ptolemy, and +numbers of great men after them, believed that the earth was the +centre of the solar system. But this deep-set theoretic notion had +to give way, and the helio-centric theory may, in its turn, have to +give way also. This is just as reasonable as the first argument. +Wherein consists the strength of the present theory of gravitation? +Solely in its competence to account for all the phenomena of the +solar system. Wherein consists the strength of the theory of +undulation? Solely in its competence to disentangle and explain +phenomena a hundred-fold more complex <a name="Page_149" id= +"Page_149"></a><span class="pagenum">[Pg 149]</span>than those of +the solar system. Accept if you will the scepticism of Mr. +Mill<a name="FNanchor_19_19" id="FNanchor_19_19"></a><a href= +"#Footnote_19_19" class="fnanchor">[19]</a> regarding the +undulatory theory; but if your scepticism be philosophical, it will +wrap the theory of gravitation in the same or in greater +doubt.<a name="FNanchor_20_20" id="FNanchor_20_20"></a><a href= +"#Footnote_20_20" class="fnanchor">[20]</a></p> +<h3>§ 11. <i>The Blue of the Sky</i>.</h3> +<p>I am unwilling to quit these chromatic phenomena without +referring to a source of colour which has often come before me of +late in the blue of your skies at noon, and the deep crimson of +your horizon after the set of sun. I will here summarize and extend +what I have elsewhere said upon this subject. Proofs of the most +cogent description could be adduced to show that the blue light of +the firmament is reflected light. That light comes to us across the +direction of the solar rays, and even against the direction of the +solar rays; and this lateral and opposing rush of wave-motion can +only be due to the rebound of the waves from the air itself, or +from something suspended in the air. The solar light, moreover, is +not scattered by the sky in the proportions which produce white. +The sky is blue, which indicates an excess of the smaller waves. +The blueness of the air has been given as a reason for the blueness +of the sky; but then the question arises, How, if the air be blue, +can the light of sunrise and sunset, which travels through vast +distances of air, be yellow, orange, or even red? The passage of +the white solar light through a blue medium could by no <a name= +"Page_150" id="Page_150"></a><span class="pagenum">[Pg +150]</span>possibility redden the light; the hypothesis of a blue +atmosphere is therefore untenable. In fact, the agent, whatever it +be, which sends us the light of the sky, exercises in so doing a +dichroitic action. The light reflected is blue, the light +transmitted is orange or red, A marked distinction is thus +exhibited between reflection from the sky and that from an ordinary +cloud, which exercises no such dichroitic action.</p> +<p>The cloud, in fact, takes no note of size on the part of the +waves of ether, but reflects them all alike. Now the cause of this +may be that the cloud-particles are so large in comparison with the +size of the waves of ether as to scatter them all indifferently. A +broad cliff reflects an Atlantic roller as easily as it reflects a +ripple produced by a sea-bird's wing; and, in the presence of large +reflecting surfaces, the existing differences of magnitude among +the waves of ether may also disappear. But supposing the reflecting +particles, instead of being very large, to be very small, in +comparison with the size of the waves. Then, instead of the whole +wave being fronted and in great part thrown back, a small portion +only is shivered off by the obstacle. Suppose, then, such minute +foreign particles to be diffused in our atmosphere. Waves of all +sizes impinge upon them, and at every collision a portion of the +impinging wave is struck off. All the waves of the spectrum, from +the extreme red to the extreme violet, are thus acted upon; but in +what proportions will they be scattered? Largeness is a thing of +relation; and the smaller the wave, the greater is the relative +size of any particle on which the wave impinges, and the greater +also the relative reflection.</p> +<p>A small pebble, placed in the way of the ring-ripples <a name= +"Page_151" id="Page_151"></a><span class="pagenum">[Pg +151]</span>produced by heavy rain-drops on a tranquil pond, will +throw back a large fraction of each ripple incident upon it, while +the fractional part of a larger wave thrown back by the same pebble +might be infinitesimal. Now to preserve the solar light white, its +constituent proportions must not be altered; but in the scattering +of the light by these very small particles we see that the +proportions <i>are</i> altered. The smaller waves are in excess, +and, as a consequence, in the scattered light blue will be the +predominant colour. The other colours of the spectrum must, to some +extent, be associated with the blue: they are not absent, but +deficient. We ought, in fact, to have them all, but in diminishing +proportions, from the violet to the red.</p> +<p>We have thus reasoned our way to the conclusion, that were +particles, small in comparison to the size of the ether waves, sown +in our atmosphere, the light scattered by those particles would be +exactly such as we observe in our azure skies. And, indeed, when +this light is analyzed, all the colours of the spectrum are found +in the proportions indicated by our conclusion.</p> +<p>By its successive collisions with the particles the white light +is more and more robbed of its shorter waves; it therefore loses +more and more of its due proportion of blue. The result may be +anticipated. The transmitted light, where moderate distances are +involved, will appear yellowish. But as the sun sinks towards the +horizon the atmospheric distance increases, and consequently the +number of the scattering particles. They weaken in succession the +violet, the indigo, the blue, and even disturb the proportions of +green. The transmitted light under such circumstances must pass +from yellow through orange to red. This also is <a name="Page_152" +id="Page_152"></a><span class="pagenum">[Pg 152]</span>exactly what +we find in nature. Thus, while the reflected light gives us, at +noon, the deep azure of the Alpine skies, the transmitted light +gives us, at sunset, the warm crimson of the Alpine snows.</p> +<p>But can small particles be really proved to act in the manner +indicated? No doubt of it. Each one of you can submit the question +to an experimental test. Water will not dissolve resin, but spirit +will; and when spirit which holds resin in solution is dropped into +water, the resin immediately separates in solid particles, which +render the water milky. The coarseness of this precipitate depends +on the quantity of the dissolved resin. Professor Brücke has +given us the proportions which produce particles particularly +suited to our present purpose. One gramme of clean mastic is +dissolved in eighty-seven grammes of absolute alcohol, and the +transparent solution is allowed to drop into a beaker containing +clear water briskly stirred. An exceedingly fine precipitate is +thus formed, which declares its presence by its action upon light. +Placing a dark surface behind the beaker, and permitting the light +to fall into it from the top or front, the medium is seen to be of +a very fair sky-blue. A trace of soap in water gives it a tint of +blue. London milk makes an approximation to the same colour, +through the operation of the same cause: and Helmholtz has +irreverently disclosed the fact that a blue eye is simply a turbid +medium.</p> +<h3>§ 12. <i>Artificial Sky</i>.</h3> +<p>But we have it in our power to imitate far more closely the +natural conditions of this problem. We can generate in air +artificial skies, and prove their perfect <a name="Page_153" id= +"Page_153"></a><span class="pagenum">[Pg 153]</span>identity with +the natural one, as regards the exhibition of a number of wholly +unexpected phenomena. It has been recently shown in a great number +of instances by myself that waves of ether issuing from a strong +source, such as the sun or the electric light, are competent to +shake asunder the atoms of gaseous molecules. The apparatus used to +illustrate this consists of a glass tube about a yard in length, +and from 2½ to 3 inches internal diameter. The gas or vapour +to be examined is introduced into this tube, and upon it the +condensed beam of the electric lamp is permitted to act. The vapour +is so chosen that one, at least, of its products of decomposition, +as soon as it is formed, shall be <i>precipitated</i> to a kind of +cloud. By graduating the quantity of the vapour, this precipitation +may be rendered of any degree of fineness, forming particles +distinguishable by the naked eye, or particles which are probably +far beyond the reach of our highest microscopic powers. I have no +reason to doubt that particles may be thus obtained whose diameters +constitute but a very small fraction of the length of a wave of +violet light.</p> +<p>Now, in all such cases when suitable vapours are employed in a +sufficiently attenuated state, no matter what the vapour may be, +the visible action commences with the formation of a <i>blue +cloud</i>. Let me guard myself at the outset against all +misconception as to the use of this term. The blue cloud here +referred to is totally invisible in ordinary daylight. To be seen, +it requires to be surrounded by darkness, <i>it only</i> being +illuminated by a powerful beam of light. This cloud differs in many +important particulars from the finest ordinary clouds, and might +justly have assigned to it an <a name="Page_154" id= +"Page_154"></a><span class="pagenum">[Pg 154]</span>intermediate +position between these clouds and true cloudless vapour.</p> +<p>It is possible to make the particles of this <i>actinic +cloud</i> grow from an infinitesimal and altogether +ultra-microscopic size to particles of sensible magnitude; and by +means of these in a certain stage of their growth, we produce a +blue which rivals, if it does not transcend, that of the deepest +and purest Italian sky. Introducing into our tube a quantity of +mixed air and nitrite of butyl vapour sufficient to depress the +mercurial column of an air-pump one-twentieth of an inch, adding a +quantity of air and hydrochloric acid sufficient to depress the +mercury half an inch further, and sending through this compound and +highly attenuated atmosphere the beam of the electric light, within +the tube arises gradually a splendid azure, which strengthens for a +time, reaches a maximum of depth and purity, and then, as the +particles grow larger, passes into whitish blue. This experiment is +representative, and it illustrates a general principle. Various +other colourless substances of the most diverse properties, optical +and chemical, might be employed for this experiment. The +<i>incipient cloud</i>, in every case, would exhibit this superb +blue; thus proving to demonstration that particles of infinitesimal +size, without any colour of their own, and irrespective of those +optical properties exhibited by the substance in a massive state, +are competent to produce the blue colour of the sky.</p> +<h3>§ 13. <i>Polarization of Skylight</i>.</h3> +<p>But there is another subject connected with our firmament, of a +more subtle and recondite character <a name="Page_155" id= +"Page_155"></a><span class="pagenum">[Pg 155]</span>than even its +colour. I mean that 'mysterious and beautiful phenomenon,' as Sir +John Herschel calls it, the polarization of the light of the sky. +Looking at various points of the blue firmament through a Nicol +prism, and turning the prism round its axis, we soon notice +variations of brightness. In certain positions of the prism, and +from certain points of the firmament, the light appears to be +wholly transmitted, while it is only necessary to turn the prism +round its axis through an angle of ninety degrees to materially +diminish the intensity of the light. Experiments of this kind prove +that the blue light sent to us by the firmament is polarized, and +on close scrutiny it is also found that the direction of most +perfect polarization is perpendicular to the solar rays. Were the +heavenly azure like the ordinary light of the sun, the turning of +the prism would have no effect upon it; it would be transmitted +equally during the entire rotation of the prism. The light of the +sky may be in great part quenched, because it is in great part +polarized.</p> +<p>The same phenomenon is exhibited in perfection by our actinic +clouds, the only condition necessary to its production being the +smallness of the particles. In all cases, and with all substances, +the cloud formed at the commencement, when the precipitated +particles are sufficiently fine, is <i>blue</i>. In all cases, +moreover, this fine blue cloud polarizes <i>perfectly</i> the beam +which illuminates it, the direction of polarization enclosing an +angle of 90° with the axis of the illuminating beam.</p> +<p>It is exceedingly interesting to observe both the growth and the +decay of this polarization. For ten or fifteen minutes after its +first appearance, the light from <a name="Page_156" id= +"Page_156"></a><span class="pagenum">[Pg 156]</span>a vividly +illuminated incipient cloud, looked at horizontally, is absolutely +quenched by a Nicol prism with its longer diagonal vertical. But as +the sky-blue is gradually rendered impure by the introduction of +particles of too large a size, in other words, as real clouds begin +to be formed, the polarization begins to deteriorate, a portion of +the light passing through the prism in all its positions, as it +does in the case of skylight. It is worthy of note that for some +time after the cessation of perfect polarization the +<i>residual</i> light which passes, when the Nicol is in its +position of minimum transmission, is of a gorgeous blue, the whiter +light of the cloud being extinguished. When the cloud-texture has +become sufficiently coarse to approximate to that of ordinary +clouds, the rotation of the Nicol ceases to have any sensible +effect on the light discharged at right angles to the beam.</p> +<p>The perfection of the polarization in a direction perpendicular +to the illuminating beam may be also illustrated by the following +experiment, which has been executed with many vapours. A Nicol +prism large enough to embrace the entire beam of the electric lamp +was placed between the lamp and the experimental tube. Sending the +beam polarized by the Nicol through the tube, I placed myself in +front of it, the eyes being on a level with its axis, my assistant +occupying a similar position behind the tube. The short diagonal of +the large Nicol was in the first instance vertical, the plane of +vibration of the emergent beam being therefore also vertical. As +the light continued to act, a superb blue cloud visible to both my +assistant and myself was slowly formed. But this cloud, so deep and +rich when looked at from the positions mentioned, utterly +disappeared when <a name="Page_157" id="Page_157"></a><span class= +"pagenum">[Pg 157]</span>looked at vertically downwards, or +vertically upwards. Reflection from the cloud was not possible in +these directions. When the large Nicol was slowly turned round its +axis, the eye of the observer being on the level of the beam, and +the line of vision perpendicular to it, entire extinction of the +light emitted horizontally occurred when the longer diagonal of the +large Nicol was vertical. But a vivid blue cloud was seen when +looked at downwards or upwards. This truly fine experiment, which I +should certainly have made without suggestion, was, as a matter of +fact, first definitely suggested by a remark addressed to me in a +letter by Professor Stokes.</p> +<p>All the phenomena of colour and of polarization observable in +the case of skylight are manifested by those actinic clouds; and +they exhibit additional phenomena which it would be neither +convenient to pursue, nor perhaps possible to detect, in the actual +firmament. They enable us, for example, to follow the polarization +from its first appearance on the barely visible blue to its final +extinction in the coarser cloud. These changes, as far as it is now +necessary to refer to them, may be thus summed up:—</p> +<p>1. The actinic cloud, as long as it continues blue, discharges +polarized light in all directions, but the direction of maximum +polarization, like that of skylight, is at right angles to the +direction of the illuminating beam.</p> +<p>2. As long as the cloud remains distinctly blue, the light +discharged from it at right angles to the illuminating beam is +<i>perfectly</i> polarized. It may be utterly quenched by a Nicol +prism, the cloud from which it issues being caused to disappear. +Any deviation from <a name="Page_158" id= +"Page_158"></a><span class="pagenum">[Pg 158]</span>the +perpendicular enables a portion of the light to get through the +prism.</p> +<p>3. The direction of vibration of the polarized light is at right +angles to the illuminating beam. Hence a plate of tourmaline, with +its axis parallel to the beam, stops the light, and with the axis +perpendicular to the beam transmits the light.</p> +<p>4. A plate of selenite placed between the Nicol and the actinic +cloud shows the colours of polarized light; in fact, the cloud +itself plays the part of a polarizing Nicol.</p> +<p>5. The particles of the blue cloud are immeasurably small, but +they increase gradually in size, and at a certain period of their +growth cease to discharge perfectly polarized light. For some time +afterwards the light that reaches the eye, through the Nicol in its +position of least transmission, is of a magnificent blue, far +exceeding in depth and purity that of the purest sky; thus the +waves that first feel the influence of size, at both limits of the +polarization, are the shortest waves of the spectrum. These are the +first to accept polarization, and they are the first to escape from +it.</p> +<hr style="width: 65%;" /> +<div><a name="Page_159" id="Page_159"></a><span class="pagenum">[Pg +159]</span></div> +<h2><a name="LECTURE_V" id="LECTURE_V"></a>LECTURE V.</h2> +<table border="0" cellpadding="0" cellspacing="0" summary=""> +<tr> +<td> +<div style="font-size: smaller;"> +<ul style="list-style: none;"> +<li>RANGE OF VISION NOT COMMENSURATE WITH RANGE OF RADIATION</li> +<li>THE ULTRA-VIOLET BAYS</li> +<li>FLUORESCENCE</li> +<li>THE RENDERING OF INVISIBLE RAYS VISIBLE</li> +<li>VISION NOT THE ONLY SENSE APPEALED TO BY THE SOLAR AND ELECTRIC +BEAM</li> +<li>HEAT OF BEAM</li> +<li>COMBUSTION BY TOTAL BEAM AT THE FOCI OF MIRRORS AND LENSES</li> +<li>COMBUSTION THROUGH ICE-LENS</li> +<li>IGNITION OF DIAMOND</li> +<li>SEARCH FOR THE RAYS HERE EFFECTIVE</li> +<li>SIR WILLIAM HERSCHEL'S DISCOVERY OF DARK SOLAR RAYS</li> +<li>INVISIBLE RAYS THE BASIS OF THE VISIBLE</li> +<li>DETACHMENT BY A RAY-FILTER OF THE INVISIBLE RAYS FROM THE +VISIBLE</li> +<li>COMBUSTION AT DARK FOCI</li> +<li>CONVERSION OF HEAT-RAYS INTO LIGHT-RAYS</li> +<li>CALORESCENCE</li> +<li>PART PLAYED IN NATURE BY DARK RAYS</li> +<li>IDENTITY OF LIGHT AND RADIANT HEAT</li> +<li>INVISIBLE IMAGES</li> +<li>REFLECTION, REFRACTION, PLANE POLARIZATION, DEPOLARIZATION, +CIRCULAR<br /> + POLARIZATION, DOUBLE REFRACTION, AND +MAGNETIZATION OF RADIANT HEAT.</li> +</ul> +</div> +</td> +</tr> +</table> +<h3>§ 1. <i>Range of Vision and of Radiation</i>.</h3> +<p>The first question that we have to consider to-night is this: Is +the eye, as an organ of vision, commensurate with the whole range +of solar radiation—is it capable of receiving visual +impressions from all the rays emitted by the sun? The answer is +negative. If we allowed ourselves to accept for a moment that +notion of gradual growth, amelioration, and ascension, implied by +the term <i>evolution</i>, we might fairly conclude that there are +stores of visual impressions awaiting man, far greater than those +now in his possession. Ritter discovered in 1801 that beyond the +extreme violet of the spectrum there is a vast efflux of rays which +are totally useless as regards our present powers of vision. These +<a name="Page_160" id="Page_160"></a><span class="pagenum">[Pg +160]</span>ultra-violet waves, however, though incompetent to +awaken the optic nerve, can shake asunder the molecules of certain +compound substances on which they impinge, thus producing chemical +decomposition.</p> +<p>But though the blue, violet, and ultra-violet rays can act thus +upon certain substances, the fact is hardly sufficient to entitle +them to the name of 'chemical rays,' which is usually applied to +distinguish them from the other constituents of the spectrum. As +regards their action upon the salts of silver, and many other +substances, they may perhaps merit this title; but in the case of +the grandest example of the chemical action of light—the +decomposition of carbonic acid in the leaves of plants, with which +my eminent friend Dr. Draper (now no more) has so indissolubly +associated his name—the yellow rays are found to be the most +active.</p> +<p>There are substances, however, on which the violet and +ultra-violet waves exert a special decomposing power; and, by +permitting the invisible spectrum to fall upon surfaces prepared +with such substances, we reveal both the existence and the extent +of the ultraviolet spectrum.</p> +<h3>§ 2. <i>Ultra-violet Rays: Fluorescence</i>.</h3> +<p>The method of exhibiting the action of the ultraviolet rays by +their chemical action has been long known; indeed, Thomas Young +photographed the ultra-violet rings of Newton. We have now to +demonstrate their presence in another way. As a general rule, +bodies either transmit light or absorb it; but there is a third +case in which the light falling upon the body is neither +transmitted nor absorbed, but con<a name="Page_161" id= +"Page_161"></a><span class="pagenum">[Pg 161]</span>verted into +light of another kind. Professor Stokes, the occupant of the chair +of Newton in the University of Cambridge, has demonstrated this +change of one kind of light into another, and has pushed his +experiments so far as to render the invisible rays visible.</p> +<p>A large number of substances examined by Stokes, when excited by +the invisible ultra-violet waves, have been proved to emit light. +You know the rate of vibration corresponding to the extreme violet +of the spectrum; you are aware that to produce the impression of +this colour, the retina is struck 789 millions of millions of times +in a second. At this point, the retina ceases to be useful as an +organ of vision; for, though struck by waves of more rapid +recurrence, they are incompetent to awaken the sensation of light. +But when such non-visual waves are caused to impinge upon the +molecules of certain substances—on those of sulphate of +quinine, for example—they compel those molecules, or their +constituent atoms, to vibrate; and the peculiarity is, that the +vibrations thus set up are <i>of slower period</i> than those of +the exciting waves. By this lowering of the rate of vibration +through the intermediation of the sulphate of quinine, the +invisible rays are brought within the range of vision. We shall +subsequently have abundant opportunity for learning that +transparency to the visible by no means involves transparency to +the invisible rays. Our bisulphide of carbon, for example, which, +employed in prisms, is so eminently suitable for experiments on the +visual rays, is by no means so suitable for these ultra-violet +rays. Flint glass is better, and rock crystal is better than flint +glass. A glass prism, however, will suit our present purpose.</p> +<p><a name="Page_162" id="Page_162"></a><span class="pagenum">[Pg +162]</span>Casting by means of such a prism a spectrum, not upon +the white surface of our screen, but upon a sheet of paper which +has been wetted with a saturated solution of the sulphate of +quinine and afterwards dried, an obvious extension of the spectrum +is revealed. We have, in the first instance, a portion of the +violet rendered whiter and more brilliant; but, besides this, we +have the gleaming of the colour where, in the case of unprepared +paper, nothing is seen. Other substances produce a similar effect. +A substance, for example, recently discovered by President Morton, +and named by him <i>Thallene</i>, produces a very striking +elongation of the spectrum, the new light generated being of +peculiar brilliancy.</p> +<p>Fluor spar, and some other substances, when raised to a +temperature still under redness, emit light. During the ages which +have elapsed since their formation, this capacity of shaking the +ether into visual tremors appears to have been enjoyed by these +substances. Light has been potential within them all this time; +and, as well explained by Draper, the heat, though not itself of +visual intensity, can unlock the molecules so as to enable them to +exert their long-latent power of vibration. This deportment of +fluor spar determined Stokes in his choice of a name for his great +discovery: he called this rendering visible of the ultra-violet +rays <i>Fluorescence</i>.</p> +<p>By means of a deeply coloured violet glass, we cut off almost +the whole of the light of our electric beam; but this glass is +peculiarly transparent to the violet and ultra-violet rays. The +violet beam now crosses a large jar filled with water, into which I +pour a solution of sulphate of quinine. Clouds, to all appearance +opaque, instantly tumble downwards. Fragments of horse-<a name= +"Page_163" id="Page_163"></a><span class="pagenum">[Pg +163]</span>chestnut bark thrown upon the water also send down +beautiful cloud-like strife. But these are not clouds: there is +nothing precipitated here: the observed action is an action of +<i>molecules</i>, not of <i>particles</i>. The medium before you is +not a turbid medium, for when you look through it at a luminous +surface it is perfectly clear.</p> +<p>If we paint upon a piece of paper a flower or a bouquet with the +sulphate of quinine, and expose it to the full beam, scarcely +anything is seen. But on interposing the violet glass, the design +instantly flashes forth in strong contrast with the deep +surrounding violet. President Morton has prepared for me a most +beautiful example of such a design which, when placed in the violet +light, exhibits a peculiarly brilliant fluorescence. From the +experiments of Drs. Bence Jones and Dupré, it would seem +that there is some substance in the human body resembling the +sulphate of quinine, which causes all the tissues of the body to be +more or less fluorescent. All animal infusions show this +fluorescence. The crystalline lens of the eye exhibits the effect +in a very striking manner. When, for example, I plunge my eye into +this violet beam, I am conscious of a whitish-blue shimmer filling +the space before me. This is caused by fluorescent light generated +in the eye itself. Looked at from without, the crystalline lens at +the same time is seen to gleam vividly.</p> +<p>Long before its physical origin was understood this fluorescent +light attracted attention. Boyle describes it with great fulness +and exactness. 'We have sometimes,' he says, 'found in the shops of +our druggists certain wood which is there called <i>Lignum +Nephriticum,</i> because the inhabitants of the country where it +grows <a name="Page_164" id="Page_164"></a><span class= +"pagenum">[Pg 164]</span>are wont to use the infusion of it, made +in fair water, against the stone in the kidneys. This wood may +afford us an experiment which, besides the singularity of it, may +give no small assistance to an attentive considerer towards the +detection of the nature of colours. Take <i>Lignum, +Nephriticum</i>, and with a knife cut it into thin slices: put +about a handful of these slices into two or three or four pounds of +the purest spring water. Decant this impregnated water into a glass +phial; and if you hold it directly between the light and your eye, +you shall see it wholly tinted with an almost golden colour. But if +you hold this phial from the light, so that your eye be placed +betwixt the window and the phial, the liquid will appear of a deep +and lovely ceruleous colour.'</p> +<p>'These,' he continues, 'and other phenomena which I have +observed in this delightful experiment, divers of my friends have +looked upon, not without some wonder; and I remember an excellent +oculist, finding by accident in a friend's chamber a phial full of +this liquor, which I had given that friend, and having never heard +anything of the experiment, nor having anybody near him who could +tell him what this strange liquor might be, was a great while +apprehensive, as he presently afterwards told me, that some strange +new distemper was invading his eyes. And I confess that the +unusualness of the phenomenon made me very solicitous to find out +the cause of this experiment; and though I am far from pretending +to have found it, yet my enquiries have, I suppose, enabled me to +give such hints as may lead your greater sagacity to the discovery +of the cause of this wonder.'<a name="FNanchor_21_21" id= +"FNanchor_21_21"></a><a href="#Footnote_21_21" class= +"fnanchor">[21]</a></p> +<p><a name="Page_165" id="Page_165"></a><span class="pagenum">[Pg +165]</span>Goethe in his 'Farbenlehre' thus describes the +fluorescence of horse-chestnut bark:—'Let a strip of fresh +horse-chestnut bark be taken and clipped into a glass of water; the +most perfect sky-blue will be immediately produced.'<a name= +"FNanchor_22_22" id="FNanchor_22_22"></a><a href="#Footnote_22_22" +class="fnanchor">[22]</a> Sir John Herschel first noticed and +described the fluorescence of the sulphate of quinine, and showed +that the light proceeded from a thin stratum of the solution +adjacent to the surface where the light enters it. He showed, +moreover, that the incident beam, although not sensibly weakened in +luminous intensity, lost, in its transmission through the solution +of sulphate of quinine, the power of producing the blue fluorescent +light. Sir David Brewster also worked at the subject; but to +Professor Stokes we are indebted not only for its expansion, but +for its full and final explanation.</p> +<h3>§ 3. <i>The Heat of the Electric Beam. Ignition through a +Lens of Ice. Possible Cometary Temperature</i>.</h3> +<p>But the waves from our incandescent carbon-points appeal to +another sense than that of vision. They not only produce light, but +heat, as a sensation. The magnified image of the carbon-points is +now upon the screen; and with a suitable instrument the heating +power of the rays which form that image might be readily +demonstrated. In this case, however, the heat is spread over too +large an area to be very intense. Drawing out the camera lens, and +causing a movable screen to approach the lamp, the image is seen to +become smaller and smaller; the rays at the same time becoming more +and more concentrated, until finally <a name="Page_166" id= +"Page_166"></a><span class="pagenum">[Pg 166]</span>they are able +to pierce black paper with a burning ring. Pushing back the lens so +as to render the rays parallel, and receiving them upon a concave +mirror, they are brought to a focus; paper placed at that focus is +caused to smoke and burn. Heat of this intensity may be obtained +with our ordinary camera and lens, and a concave mirror of very +moderate power.</p> +<div class="figcenter" style="width: 365px;"><img src= +"images/fig48.jpg" width="365" height="268" alt="Fig. 48." title= +"" /> <b>Fig. 48.</b></div> +<p>We will now adopt stronger measures with the radiation. In this +larger camera of blackened tin is placed a lamp, in all particulars +similar to those already employed. But instead of gathering up the +rays from the carbon-points by a condensing lens, we gather them up +by a concave mirror (<i>m</i> <i>m'</i>, fig. 48), silvered in +front and placed behind the carbons (P). By this mirror we can +cause the rays to issue through the orifice in front of the camera, +either parallel or convergent. They are now parallel, and therefore +to a certain extent diffused. We place a convex lens (L) in the +path of the beam; the light is converged to a focus (C), and at +that focus paper is not only pierced, but it is instantly set +ablaze.</p> +<p><a name="Page_167" id="Page_167"></a><span class="pagenum">[Pg +167]</span>Many metals may be burned up in the same way. In our +first lecture the combustibility of zinc was mentioned. Placing a +strip of sheet-zinc at this focus, it is instantly ignited, burning +with its characteristic purple flame. And now I will substitute for +our glass lens (L) one of a more novel character. In a smooth iron +mould a lens of pellucid ice has been formed. Placing it in the +position occupied a moment ago by the glass lens, I can see the +beam brought to a sharp focus. At the focus I place, a bit of black +paper, with a little gun-cotton folded up within it. The paper +immediately ignites and the cotton explodes. Strange, is it not, +that the beam should possess such heating power after having passed +through so cold a substance? In his arctic expeditions Dr. Scoresby +succeeded in exploding gunpowder by the sun's rays, converged by +large lenses of ice; here we have succeeded in producing the effect +with a small lens, and with a terrestrial source of heat.</p> +<p>In this experiment, you observe that, before the beam reaches +the ice-lens, it has passed through a glass cell containing water. +The beam is thus sifted of constituents, which, if permitted to +fall upon the lens, would injure its surface, and blur the focus. +And this leads me to say an anticipatory word regarding +transparency. In our first lecture we entered fully into the +production of colours by absorption, and we spoke repeatedly of the +quenching of the rays of light. Did this mean that the light was +altogether annihilated? By no means. It was simply so lowered in +refrangibility as to escape the visual range. It was converted into +heat. Our red ribbon in the green of the spectrum quenched the +green, but if suitably examined its <a name="Page_168" id= +"Page_168"></a><span class="pagenum">[Pg 168]</span>temperature +would have been found raised. Our green ribbon in the red of the +spectrum quenched the red, but its temperature at the same time was +augmented to a degree exactly equivalent to the light extinguished. +Our black ribbon, when passed through the spectrum, was found +competent to quench all its colours; but at every stage of its +progress an amount of heat was generated in the ribbon exactly +equivalent to the light lost. It is only when <i>absorption</i> +takes place that heat is thus produced: and heat is always a result +of absorption.</p> +<p>Examine the water, then, in front of the lamp after the beam has +passed through it: it is sensibly warm, and, if permitted to remain +there long enough, it might be made to boil. This is due to the +absorption, by the water, of a certain portion of the electric +beam. But a portion passes through unabsorbed, and does not at all +contribute to the heating of the water. Now, ice is also in great +part transparent to these latter rays, and therefore is but little +melted by them. Hence, by employing the portion of the beam +transmitted by water, we are able to keep our lens intact, and to +produce by means of it a sharply defined focus. Placed at that +focus, white paper is not ignited, because it fails to absorb the +rays emergent from the ice-lens. At the same place, however, black +paper instantly burns, because it absorbs the transmitted +light.</p> +<p>And here it may be useful to refer to an estimate by Newton, +based upon doubtful data, but repeated by various astronomers of +eminence since his time. The comet of 1680, when nearest to the +sun, was only a sixth of the sun's diameter from his surface. +Newton estimated its temperature, in this position, to be more than +two thousand times that of molted iron. Now it <a name="Page_169" +id="Page_169"></a><span class="pagenum">[Pg 169]</span>is clear +from the foregoing experiments that the temperature of the comet +could not be inferred from its nearness to the sun. If its power of +absorption were sufficiently low, the comet might carry into the +sun's neighbourhood the chill of stellar space.</p> +<h3>§ 4. <i>Combustion of a Diamond by Radiant Heat</i>.</h3> +<p>The experiment of burning a diamond in oxygen by the +concentrated rays of the sun was repeated at Florence, in presence +of Sir Humphry Davy, on Tuesday, the 27th of March, 1814. It is +thus described by Faraday:—'To-day we made the grand +experiment of burning the diamond, and certainly the phenomena +presented were extremely beautiful and interesting. A glass globe +containing about 22 cubical inches was exhausted of air, and filled +with pure oxygen. The diamond was supported in the centre of this +globe. The Duke's burning-glass was the instrument used to apply +heat to the diamond. It consists of two double convex lenses, +distant from each other about 3½ feet; the large lens is +about 14 or 15 inches in diameter, the smaller one about 3 inches +in diameter. By means of the second lens the focus is very much +reduced, and the heat, when the sun shines brightly, rendered very +intense. The diamond was placed in the focus and anxiously watched. +On a sudden Sir H. Davy observed the diamond to burn visibly, and +when removed from the focus it was found to be in a state of active +and rapid combustion.'</p> +<p>The combustion of the diamond had never been effected by radiant +heat from a terrestrial source. I tried to accomplish this before +crossing the Atlantic, and succeeded in doing so. The small diamond +now in my hand is held by a loop of platinum wire. To <a name= +"Page_170" id="Page_170"></a><span class="pagenum">[Pg +170]</span>protect it as far as possible from air currents, and +also to concentrate the heat upon it, it is surrounded by a hood of +sheet platinum. Bringing a jar of oxygen underneath, I cause the +focus of the electric beam to fall upon the diamond. A small +fraction of the time expended in the experiment described by +Faraday suffices to raise the diamond to a brilliant red. Plunging +it then into the oxygen, it glows like a little white star; and it +would continue to burn and glow until wholly consumed. The focus +can also be made to fall upon the diamond in oxygen, as in the +Florentine experiment: the result is the same. It was simply to +secure more complete mastery over the position of the focus, so as +to cause it to fall accurately upon the diamond, that the mode of +experiment here described was resorted to.</p> +<h3>§ 5. <i>Ultra-red Rays: Calorescence</i>.</h3> +<p>In the path of the beam issuing from our lamp I now place a cell +with glass sides containing a solution of alum. All the +<i>light</i> of the beam passes through this solution. This light +is received on a powerfully converging mirror silvered in front, +and brought to a focus by the mirror. You can see the conical beam +of reflected light tracking itself through the dust of the room. A +scrap of white paper placed at the focus shines there with dazzling +brightness, but it is not even charred. On removing the alum cell, +however, the paper instantly inflames. There must, therefore, be +something in this beam besides its light. The <i>light</i> is not +absorbed by the white paper, and therefore does not burn the paper; +but there is something over and above the light which <i>is</i> +absorbed, and which provokes combustion. What is this +something?</p> +<p><a name="Page_171" id="Page_171"></a><span class="pagenum">[Pg +171]</span>In the year 1800 Sir William Herschel passed a +thermometer through the various colours of the solar spectrum, and +marked the rise of temperature corresponding to each colour. He +found the heating effect to augment from the violet to the red; he +did not, however, stop at the red, but pushed his thermometer into +the dark space beyond it. Here he found the temperature actually +higher than in any part of the visible spectrum. By this important +observation, he proved that the sun emitted heat-rays which are +entirely unfit for the purposes of vision. The subject was +subsequently taken up by Seebeck, Melloni, Müller, and others, +and within the last few years it has been found capable of +unexpected expansions and applications. I have devised a method +whereby the solar or electric beam can be so <i>filtered</i> as to +detach from it, and preserve intact, this invisible ultra-red +emission, while the visible and ultra-violet emissions are wholly +intercepted. We are thus enabled to operate at will upon the purely +ultra-red waves.</p> +<p>In the heating of solid bodies to incandescence, this non-visual +emission is the necessary basis of the visual. A platinum wire is +stretched in front of the table, and through it an electric current +flows. It is warmed by the current, and may be felt to be warm by +the hand. It emits waves of heat, but no light. Augmenting the +strength of the current, the wire becomes hotter; it finally glows +with a sober red light. At this point Dr. Draper many years ago +began an interesting investigation. He employed a voltaic current +to heat his platinum, and he studied, by means of a prism, the +successive introduction of the colours of the spectrum. His first +colour, as here, was red; then came orange, <a name="Page_172" id= +"Page_172"></a><span class="pagenum">[Pg 172]</span>then yellow, +then green, and lastly all the shades of blue. As the temperature +of the platinum was gradually augmented, the atoms were caused to +vibrate more rapidly; shorter waves were thus introduced, until +finally waves were obtained corresponding to the entire spectrum. +As each successive colour was introduced, the colours preceding it +became more vivid. Now the vividness or intensity of light, like +that of sound, depends not upon the length of the wave, but on the +amplitude of the vibration. Hence, as the less refrangible colours +grew more intense when the more refrangible ones were introduced, +we are forced to conclude that side by side with the introduction +of the shorter waves we had an augmentation of the amplitude of the +longer ones.</p> +<p>These remarks apply not only to the visible emission examined by +Dr. Draper, but to the invisible emission which precedes the +appearance of any light. In the emission from the white-hot +platinum wire now before you, the lightless waves exist with which +we started, only their intensity has been increased a thousand-fold +by the augmentation of temperature necessary to the production of +this white light. Both effects are bound up together: in an +incandescent solid, or in a molten solid, you cannot have the +shorter waves without this intensification of the longer ones. A +sun is possible only on these conditions; hence Sir William +Herschel's discovery of the invisible ultra-red solar emission.</p> +<p>The invisible heat, emitted both by dark bodies and by luminous +ones, flies through space with the velosity of light, and is called +<i>radiant heat</i>. Now, radiant heat may be made a subtle and +powerful explorer of molecular condition, and, of late years, it +has given a new <a name="Page_173" id="Page_173"></a><span class= +"pagenum">[Pg 173]</span>significance to the act of chemical +combination. Take, for example, the air we breathe. It is a mixture +of oxygen and nitrogen; and it behaves towards radiant heat like a +vacuum, being incompetent to absorb it in any sensible degree. But +permit the same two gases to unite chemically; then, without any +augmentation of the quantity of matter, without altering the +gaseous condition, without interfering in any way with the +transparency of the gas, the act of chemical union is accompanied +by an enormous diminution of its <i>diathermancy</i>, or +perviousness to radiant heat.</p> +<p>The researches which established this result also proved the +elementary gases, generally, to be highly transparent to radiant +heat. This, again, led to the proof of the diathermancy of +elementary liquids, like bromine, and of solutions of the solid +elements sulphur, phosphorus, and iodine. A spectrum is now before +you, and you notice that the transparent bisulphide of carbon has +no effect upon the colours. Dropping into the liquid a few flakes +of iodine, you see the middle of the spectrum cut away. By +augmenting the quantity of iodine, we invade the entire spectrum, +and finally cut it off altogether. Now, the iodine, which proves +itself thus hostile to the light, is perfectly transparent to the +ultra-red emission with which we have now to deal. It, therefore, +is to be our ray-filter.</p> +<p>Placing the alum-cell again in front of the electric lamp, we +assure ourselves, as before, of the utter inability of the +concentrated light to fire white paper-Introducing a cell +containing the solution of iodine, the light is entirely cut off; +and then, on removing the alum-cell, the white paper at the dark +focus is instantly set on fire. Black paper is more absorbent than +white <a name="Page_174" id="Page_174"></a><span class= +"pagenum">[Pg 174]</span>for these rays; and the consequence is, +that with it the suddenness and vigour of the combustion are +augmented. Zinc is burnt up at the same place, magnesium bursts +into vivid combustion, while a sheet of platinized platinum, placed +at the focus, is heated to whiteness.</p> +<p>Looked at through a prism, the white-hot platinum yields all the +colours of the spectrum. Before impinging upon the platinum, the +waves were of too slow recurrence to awaken vision; by the atoms of +the platinum, these long and sluggish waves are broken up into +shorter ones, being thus brought within the visual range. At the +other end of the spectrum, by the interposition of suitable +substances, Professor Stokes <i>lowered</i> the refrangibility, so +as to render the non-visual rays visual, and to this change he gave +the name of <i>Fluorescence</i>. Here, by the intervention of the +platinum, the refrangibility is <i>raised</i>, so as to render the +non-visual visual, and to this change I have given the name of +<i>Calorescence</i>.</p> +<p>At the perfectly invisible focus where these effects are +produced, the air may be as cold as ice. Air, as already stated, +does not absorb radiant heat, and is therefore not warmed by it. +Nothing could more forcibly illustrate the isolation, if I may use +the term, of the luminiferous ether from the air. The wave-motion +of the one is heaped up to an extraordinary degree of intensity, +without producing any sensible effect upon the other. I may add +that, with suitable precautions, the eye may be placed in a focus +competent to heat platinum to vivid redness, without experiencing +any damage, or the slightest sensation either of light or heat.</p> +<p>The important part played by these ultra-red rays <a name= +"Page_175" id="Page_175"></a><span class="pagenum">[Pg +175]</span>in Nature may be thus illustrated: I remove the iodine +filter, and concentrate the total beam upon a test tube containing +water. It immediately begins to splutter, and in a minute or two it +<i>boils</i>. What boils it? Placing the alum solution in front of +the lamp, the boiling instantly ceases. Now, the alum is pervious +to all the luminous rays; hence it cannot be these rays that caused +the boiling. I now introduce the iodine, and remove the alum: +vigorous ebullition immediately recommences at the invisible focus. +So that we here fix upon the invisible ultra-red rays the heating +of the water.</p> +<p>We are thus enabled to understand the momentous part played by +these rays in Nature. It is to them that we owe the warming and the +consequent evaporation of the tropical ocean; it is to them, +therefore, that we owe our rains and snows. They are absorbed close +to the surface of the ocean, and warm the superficial water, while +the luminous rays plunge to great depths without producing any +sensible effect. But we can proceed further than this. Here is a +large flask containing a freezing mixture, which has so chilled the +flask, that the aqueous vapour of the air of this room has been +condensed and frozen upon it to a white fur. Introducing the +alum-cell, and placing the coating of hoar-frost at the intensely +luminous focus of the electric lamp, not a spicula of the dazzling +frost is melted. Introducing the iodine-cell, and removing the +alum, a broad space of the frozen coating is instantly melted away. +Hence we infer that the snow and ice, which feed the Rhone, the +Rhine, and other rivers with glaciers for their sources, are +released from their imprisonment upon the mountains by the +invisible ultra-red rays of the sun.<a name="Page_176" id= +"Page_176"></a><span class="pagenum">[Pg 176]</span></p> +<h3>§ 6. <i>Identity of Light and Radiant Heat. Reflection +from Plane and Curved Surfaces. Total Reflection of Heat</i>.</h3> +<p>The growth of science is organic. That which today is an +<i>end</i> becomes to-morrow a <i>means</i> to a remoter end. Every +new discovery in science is immediately made the basis of other +discoveries, or of new methods of investigation. Thus about fifty +years ago Œrsted, of Copenhagen, discovered the deflection of +a magnetic needle by an electric current; and about the same time +Thomas Seebeck, of Berlin, discovered thermoelectricity. These +great discoveries were soon afterwards turned to account, by Nobili +and Melloni, in the construction of an instrument which has vastly +augmented our knowledge of radiant heat. This instrument, which is +called a <i>thermo-electric pile</i>, or more briefly a +thermo-pile, consists of thin bars of bismuth and antimony, +soldered alternately together at their ends, but separated from +each other elsewhere. From the ends of this 'thermo-pile' wires +pass to a galvanometer, which consists of a coil of covered wire, +within and above which are suspended two magnetic needles, joined +to a rigid system, and carefully defended from currents of air.</p> +<p>The action of the arrangement is this: the heat, falling on the +pile, produces an electric current; the current, passing through +the coil, deflects the needles, and the magnitude of the deflection +may be made a measure of the heat. The upper needle moves over a +graduated dial far too small to be directly seen. It is now, +however, strongly illuminated; and above it is a lens which, if +permitted, would form an image of the <a name="Page_177" id= +"Page_177"></a><span class="pagenum">[Pg 177]</span>needle and dial +upon the ceiling. There, however, it could not be conveniently +viewed. The beam is therefore received upon a looking-glass, placed +at the proper angle, which throws the image upon a screen. In this +way the motions of this small needle may be made visible to you +all.</p> +<p>The delicacy of this apparatus is such that in a room filled, as +this room now is, with an audience physically warm, it is +exceedingly difficult to work with it. My assistant stands several +feet off. I turn the pile towards him: the heat radiated from his +face, even at this distance, produces a deflection of 90°. I +turn the instrument towards a distant wall, a little below the +average temperature of the room. The needle descends and passes to +the other side of zero, declaring by this negative deflection that +the pile has lost its warmth by radiation against the cold wall. +Possessed of this instrument, of our ray-filter, and of our large +Nicol prisms, we are in a condition to investigate a subject of +great philosophical interest; one which long engaged the attention +of some of our foremost scientific workers—the substantial +<i>identity of light and radiant heat</i>.</p> +<p>That they are identical in <i>all</i> respects cannot of course +be the case, for if they were they would act in the same manner +upon all instruments, the <i>eye</i> included. The identity meant +is such as subsists between one colour and another, causing them to +behave alike as regards reflection, refraction, double refraction, +and polarization. Let us here run rapidly over the resemblances of +light and heat. As regards reflection from plane surfaces, we may +employ a looking-glass to reflect the light. Marking any point in +the track of the reflected beam, cutting off the light by the +dissolved <a name="Page_178" id="Page_178"></a><span class= +"pagenum">[Pg 178]</span>iodine, and placing the pile at the marked +point, the needle immediately starts aside, showing that the heat +is reflected in the same direction as the light. This is true for +every position of the mirror. Recurring, for example, to the simple +apparatus employed in our first lecture (fig. 3, p. 11); moving the +index attached to the mirror along the divisions of our graduated +arc (<i>m</i> <i>n</i>), and determining by the pile the positions +of the invisible reflected beam, we prove that the angular velocity +of the heat-beam, like that of the light-beam, is twice that of the +mirror.</p> +<div class="figcenter" style="width: 425px;"><img src= +"images/fig49.jpg" width="425" height="288" alt="FIG 49." title= +"" /> <b>FIG 49.</b></div> +<p>As regards reflection from curved surfaces, the identity also +holds good. Receiving the beam from our electric lamp on a concave +mirror (<i>m</i> <i>m</i>, fig. 49), it is gathered up into a cone +of reflected light rendered visible by the floating dust of the +air; marking the apex of the cone by a pointer, and cutting off the +light by the iodine solution (T), a moment's exposure of the pile +(P) at the marked point produces a violent deflection of the +needle.</p> +<p><a name="Page_179" id="Page_179"></a><span class="pagenum">[Pg +179]</span>The common reflection and the total reflection of a beam +of radiant heat may be simultaneously demonstrated. From the nozzle +of the lamp (L, fig. 50) a beam impinges upon a plane mirror (M N), +is reflected upwards, and enters a right-angled prism, of which +<i>a</i> <i>b</i> <i>c</i> is the section. It meets the hypothenuse +at an obliquity greater than the limiting angle,<a name= +"FNanchor_23_23" id="FNanchor_23_23"></a><a href="#Footnote_23_23" +class="fnanchor">[23]</a> and is therefore totally reflected. +Quenching the light by the ray-filter at F, and placing the pile at +P, the totally reflected heat-beam is immediately felt by the pile, +and declared by the galvanometric deflection.</p> +<div class="figcenter" style="width: 500px;"><img src= +"images/fig50.jpg" width="500" height="310" alt="Fig. 50." title= +"" /> <b>Fig. 50.</b></div> +<h3>§ 7. <i>Invisible Images formed by Radiant Heat.</i></h3> +<p>Perhaps no experiment proves more conclusively the substantial +identity of light and radiant heat, than the formation of invisible +heat-images. Employing the mirror already used to raise the beam to +its highest <a name="Page_180" id="Page_180"></a><span class= +"pagenum">[Pg 180]</span>state of concentration, we obtain, as is +well known, an inverted image of the carbon points, formed by the +light rays at the focus. Cutting off the light by the ray-filter, +and placing at the focus a thin sheet of platinized platinum, the +invisible rays declare their presence and distribution, by stamping +upon the platinum a white-hot image of the carbons. (See fig. +51.)</p> +<div class="figcenter" style="width: 219px;"><img src= +"images/fig51.jpg" width="219" height="215" alt="Fig. 51." title= +"" /> <b>Fig. 51.</b></div> +<h3>§ 8. <i>Polarization of Heat</i>.</h3> +<p>Whether radiant heat be capable of polarization or not was for a +long time a subject of discussion. Bérard had announced +affirmative results, but Powell and Lloyd failed to verify them. +The doubts thus thrown upon the question were removed by the +experiments of Forbes, who first established the polarization and +'depolarization' of heat. The subject was subsequently followed up +by Melloni, an investigator of consummate ability, who sagaciously +turned to account his own discovery, that the obscure rays of +luminous sources are in part transmitted by black glass. +Intercepting by a plate of this glass the light from an oil flame, +and operating upon the transmitted invisible heat, he <a name= +"Page_181" id="Page_181"></a><span class="pagenum">[Pg +181]</span>obtained effects of polarization, far exceeding in +magnitude those which could be obtained with non-luminous sources. +At present the possession of our more perfect ray-filter, and more +powerful source of heat, enables us to pursue this identity +question to its utmost practical limits.</p> +<div class="figcenter" style="width: 421px;"><img src= +"images/fig52.jpg" width="421" height="296" alt="Fig. 52." title= +"" /> <b>Fig. 52.</b></div> +<p>Mounting our two Nicols (B and C, fig. 52) in front of the +electric lamp, with their principal sections crossed, no light +reaches the screen. Placing our thermo-electric pile (D) behind the +prisms, with its face turned towards the source, no deflection of +the galvanometer is observed. Interposing between the lamp (A) and +the first prism (B) our ray-filter, the light previously +transmitted through the first Nicol is quenched; and now the +slightest turning of either Nicol opens a way for the transmission +of the heat, a very small rotation sufficing to send the needle up +to 90°. When the Nicol is turned back to its first position, +the needle again sinks to zero, thus demonstrating, in the plainest +manner, the polarization of the heat.</p> +<p><a name="Page_182" id="Page_182"></a><span class="pagenum">[Pg +182]</span>When the Nicols are crossed and the field is dark, you +have seen, in the case of light, the effect of introducing a plate +of mica between the polarizer and analyzer. In two positions the +mica exerts no sensible influence; in all others it does. A +precisely analogous deportment is observed as regards radiant heat. +Introducing our ray-filter, the thermo-pile, playing the part of an +eye as regards the invisible radiation, receives no heat when the +eye receives no light; but when the mica is so turned as to make +its planes of vibration oblique to those of the polarizer and +analyzer, the heat immediately passes through. So strong does the +action become, that the momentary plunging of the film of mica into +the dark space between the Nicols suffices to send the needle up to +90°. This is the effect to which the term 'depolarization' has +been applied; the experiment really proving that with both light +and heat we have the same resolution by the plate of mica, and +recompounding by the analyzer, of the ethereal vibrations.</p> +<p>Removing the mica and restoring the needle once more to 0°, +I introduce between the Nicols a plate of quartz cut perpendicular +to the axis; the immediate deflection of the needle declares the +transmission of the heat, and when the transmitted beam is properly +examined, it is found to be circularly polarized, exactly as a beam +of light is polarized under the same conditions.</p> +<h3>§ 9. <i>Double Refraction of Heat</i>.</h3> +<p>I will now abandon the Nicols, and send through the piece of +Iceland spar (B, fig. 53), already employed (in Lecture III.) to +illustrate the double refraction <a name="Page_183" id= +"Page_183"></a><span class="pagenum">[Pg 183]</span>of light, our +sifted beam of invisible heat. To determine the positions of the +two images, let us first operate upon the luminous beam. Marking +the places of the light-images, we introduce between N and L our +ray-filter (not in the figure) and quench the light. Causing the +pile to approach one of the marked places, the needle remains +unmoved until the place has been attained; here the pile at once +detects the heat. Pushing the pile across the interval separating +the two marks, the needle first falls to 0°, and then rises +again to 90° in the second position. This proves the double +refraction of the heat.</p> +<div class="figcenter" style="width: 408px;"><img src= +"images/fig53.jpg" width="408" height="383" alt="Fig. 53." title= +"" /> <b>Fig. 53.</b></div> +<p>I now turn the Iceland spar: the needle remains fixed; there is +no alteration of the deflection. Passing the pile rapidly across to +the other mark, the deflection is maintained. Once more I turn the +spar, but now the needle falls to 0°, rising, however, again +<a name="Page_184" id="Page_184"></a><span class="pagenum">[Pg +184]</span>to 90° after a rotation of 360°. We know that in +the case of light the extraordinary beam rotates round the ordinary +one; and we have here been operating on the extraordinary +heat-beam, which, as regards double refraction, behaves exactly +like a beam of light.</p> +<h3>§ 10. <i>Magnetization of Heat</i>.</h3> +<p>To render our series of comparisons complete, we must +demonstrate the magnetization of heat. But here a slight +modification of our arrangement will be necessary. In repeating +Faraday's experiment on the magnetization of light, we had, in the +first instance, our Nicols crossed and the field rendered dark, a +flash of light appearing upon the screen when the magnet was +excited. Now the quantity of light transmitted in this case is +really very small, its effect being rendered striking through +contrast with the preceding darkness. When we so place the Nicols +that their principal sections enclose an angle of 45°, the +excitement of the magnet causes a far greater positive augmentation +of the light, though the augmentation is not so well <i>seen</i> +through lack of contrast, because here, at starting, the field is +illuminated.</p> +<p>In trying to magnetize our beam of heat, we will adopt this +arrangement. Here, however, at the outset, a considerable amount of +heat falls upon one face of the pile. This it is necessary to +neutralize, by permitting rays from another source to fall upon the +opposite face of the pile. The needle is thus brought to zero. +Cutting off the light by our ray-filter, and exciting the magnet, +the needle is instantly deflected, proving that the magnet has +opened a door for the heat, exactly as <a name="Page_185" id= +"Page_185"></a><span class="pagenum">[Pg 185]</span>in Faraday's +experiment it opened a door for the light. Thus, in every case +brought under our notice, the substantial identity of light and +radiant heat has been demonstrated.</p> +<p>By the refined experiments of Knoblauch, who worked long and +successfully at this question, the double refraction of heat, by +Iceland spar, was first demonstrated; but, though he employed the +luminous heat of the sun, the observed deflections were exceedingly +small. So, likewise, those eminent investigators De la Povostaye +and Desains succeeded in magnetizing a beam of heat; but though, in +their case also, the luminous solar heat was employed, the +deflection obtained did not amount to more than two or three +degrees. With <i>obscure</i> radiant heat the effect, prior to the +experiments now brought before you, had not been obtained; but, +with the arrangement here described, we obtain deflections from +purely invisible heat, equal to 150 of the lower degrees of the +galvanometer.</p> +<h3>§ 11. <i>Distribution of Heat in the Electric +Spectrum</i>.</h3> +<p>We have finally to determine the position and magnitude of the +invisible radiation which produces these results. For this purpose +we employ a particular form of the thermo-pile. Its face is a +rectangle, which by movable side-pieces can be rendered as narrow +as desirable. Throwing a small and concentrated spectrum upon a +screen, by means of an endless screw we move the rectangular pile +through the entire spectrum, and determine in succession the +thermal power of all its colours.</p> +<div class="figcenter" style="width: 600px;"><img src= +"images/fig54.jpg" width="600" height="287" alt= +"SPECTRUM OF ELECTRIC LIGHT." title="" /> <b>SPECTRUM OF ELECTRIC +LIGHT.</b></div> +<p>When this instrument is brought to the violet end <a name= +"Page_186" id="Page_186"></a><span class="pagenum">[Pg +186]</span><a name="Page_187" id="Page_187"></a>of the spectrum, +the heat is found to be almost insensible. As the pile gradually +moves from the violet towards the red, it encounters a gradually +augmenting heat. The red itself possesses the highest heating power +of all the colours of the spectrum. Pushing the pile into the dark +space beyond the red, the heat rises suddenly in intensity, and at +some distance beyond the red it attains a maximum. From this point +the heat falls somewhat more rapidly than it rose, and afterwards +gradually fades away.</p> +<p>Drawing a horizontal line to represent the length of the +spectrum, and erecting along it, at various points, perpendiculars +proportional in length to the heat existing at those points, we +obtain a curve which exhibits the distribution of heat in the +prismatic spectrum. It is represented in the adjacent figure. +Beginning at the blue, the curve rises, at first very gradually; +towards the red it rises more rapidly, the line C D (fig. 54, +opposite page) representing the strength of the extreme red +radiation. Beyond the red it shoots upwards in a steep and massive +peak to B; whence it falls, rapidly for a time, and afterwards +gradually fades from the perception of the pile. This figure is the +result of more than twelve careful series of measurements, from +each of which the curve was constructed. On superposing all these +curves, a satisfactory agreement was found to exist between them. +So that it may safely be concluded that the areas of the dark and +white spaces, respectively, represent the relative energies of the +visible and invisible radiation. The one is 7.7 times the +other.</p> +<p>But in verification, as already stated, consists the strength of +science. Determining in the first place <a name="Page_188" id= +"Page_188"></a><span class="pagenum">[Pg 188]</span>the total +emission from the electric lamp, and then, by means of the iodine +filter, determining the ultra-red emission; the difference between +both gives the luminous emission. In this way, it is found that the +energy of the invisible emission is eight times that of the +visible. No two methods could be more opposed to each other, and +hardly any two results could better harmonize. I think, therefore, +you may rely upon the accuracy of the distribution of heat here +assigned to the prismatic spectrum of the electric light. There is +nothing vague in the mode of investigation, or doubtful in its +conclusions. Spectra are, however, formed by <i>diffraction</i>, +wherein the distribution of both heat and light is different from +that produced by the prism. These diffractive spectra have been +examined with great skill by Draper and Langley. In the prismatic +spectrum the less refrangible rays are compressed into a much +smaller space than in the diffraction spectrum.</p> +<hr style="width: 65%;" /> +<div><a name="Page_189" id="Page_189"></a><span class="pagenum">[Pg +189]</span></div> +<h2><a name="LECTURE_VI" id="LECTURE_VI"></a>LECTURE VI.</h2> +<table border="0" cellpadding="0" cellspacing="0" summary=""> +<tr> +<td> +<div style="font-size: smaller;"> +<ul style="list-style: none;"> +<li>PRINCIPLES OF SPECTRUM ANALYSIS</li> +<li>PRISMATIC ANALYSIS OF THE LIGHT OF INCANDESCENT VAPOURS</li> +<li>DISCONTINUOUS SPECTRA</li> +<li>SPECTRUM BANDS PROVED BY BUNSEN AND KIRCHHOFF TO BE +CHARACTERISTIC</li> +<li>OF THE VAPOUR</li> +<li>DISCOVERY OF RUBIDIUM, CAESIUM, AND THALLIUM</li> +<li>RELATION OF EMISSION TO ABSORPTION</li> +<li>THE LINES OF FRAUNHOFER</li> +<li>THEIR EXPLANATION BY KIRCHHOFF</li> +<li>SOLAR CHEMISTRY INVOLVED IN THIS EXPLANATION</li> +<li>FOUCAULT'S EXPERIMENT</li> +<li>PRINCIPLES OF ABSORPTION</li> +<li>ANALOGY OF SOUND AND LIGHT</li> +<li>EXPERIMENTAL DEMONSTRATION OF THIS ANALOGY</li> +<li>RECENT APPLICATIONS OF THE SPECTROSCOPE</li> +<li>SUMMARY AND CONCLUSION.</li> +</ul> +</div> +</td> +</tr> +</table> +<p>We have employed as our source of light in these lectures the +ends of two rods of coke rendered incandescent by electricity. Coke +is particularly suitable for this purpose, because it can bear +intense heat without fusion or vaporization. It is also black, +which helps the light; for, other circumstances being equal, as +shown experimentally by Professor Balfour Stewart, the blacker the +body the brighter will be its light when incandescent. Still, +refractory as carbon is, if we closely examined our voltaic arc, or +stream of light between the carbon-points, we should find there +incandescent carbon-vapour. And if we could detach the light of +this vapour from the more dazzling light of the solid points, we +should find its spectrum not only less brilliant, but of a totally +different character from the spectra that we have already seen. +Instead of being an unbroken succession of colours from red to +violet, <a name="Page_190" id="Page_190"></a><span class= +"pagenum">[Pg 190]</span>the carbon-vapour would yield a few bands +of colour with spaces of darkness between them.</p> +<p>What is true of the carbon is true in a still more striking +degree of the metals, the most refractory of which can be fused, +boiled, and reduced to vapour by the electric current. From the +incandescent vapour the light, as a general rule, flashes in groups +of rays of definite degrees of refrangibility, spaces existing +between group and group, which are unfilled by rays of any kind. +But the contemplation of the facts will render this subject more +intelligible than words can make it. Within the camera is now +placed a cylinder of carbon hollowed out at the top; in the hollow +is placed a fragment of the metal thallium. Down upon this we bring +the upper carbon-point, and then separate the one from the other. A +stream of incandescent thallium-vapour passes between them, the +magnified image of which is now seen upon the screen. It is of a +beautiful green colour. What is the meaning of that green? We +answer the question by subjecting the light to prismatic analysis. +Sent through the prism, its spectrum is seen to consist of a single +refracted band. Light of one degree of refrangibility—that +corresponding to this particular green—is emitted by the +thallium-vapour.</p> +<p>We will now remove the thallium and put a bit of silver in its +place. The are of silver is not to be distinguished from that of +thallium; it is not only green, but the same shade of green. Are +they then alike? Prismatic analysis enables us to answer the +question. However impossible it is to distinguish the one +<i>colour</i> from the other, it is equally impossible to confound +the <i>spectrum</i> of incandescent silver-vapour with that of +<a name="Page_191" id="Page_191"></a><span class="pagenum">[Pg +191]</span>thallium. In the case of silver, we have two green bands +instead of one.</p> +<p>If we add to the silver in our camera a bit of thallium, we +shall obtain the light of both metals. After waiting a little, we +see that the green of the thallium lies midway between the two +greens of the silver. Hence this similarity of colour.</p> +<p>But why have we to 'wait a little' before we see this effect? +The thallium band at first almost masks the silver bands by its +superior brightness. Indeed, the silver bands have wonderfully +degenerated since the bit of thallium was put in, and for a reason +worth knowing. It is the <i>resistance</i> offered to the passage +of the electric current from carbon to carbon, that calls forth the +power of the current to produce heat. If the resistance were +materially lessened, the heat would be materially lessened; and if +all resistance were abolished, there would be no heat at all. Now, +thallium is a much more fusible and vaporizable metal than silver; +and its vapour facilitates the passage of the electricity to such a +degree, as to render the current almost incompetent to vaporize the +more refractory silver. But the thallium is gradually consumed; its +vapour diminishes, the resistance rises, until finally you see the +two silver bands as brilliant as they were at first.<a name= +"FNanchor_24_24" id="FNanchor_24_24"></a><a href="#Footnote_24_24" +class="fnanchor">[24]</a></p> +<p>We have in these bands a perfectly unalterable characteristic of +the two metals. You never get other bands than these two green ones +from the silver, never other than the single green band from the +thallium, never other than the three green bands from the mixture +of both metals. Every known metal has its <a name="Page_192" id= +"Page_192"></a><span class="pagenum">[Pg 192]</span>own particular +bands, and in no known case are the bands of two different metals +alike in refrangibility. It follows, therefore, that these spectra +may be made a sure test for the presence or absence of any +particular metal. If we pass from the metals to their alloys, we +find no confusion. Copper gives green bands; zinc gives blue and +red bands; brass—an alloy of copper and zinc—gives the +bands of both metals, perfectly unaltered in position or +character.</p> +<p>But we are not confined to the metals themselves; the +<i>salts</i> of these metals yield the bands of the metals. +Chemical union is ruptured by a sufficiently high heat; the vapour +of the metal is set free, and it yields its characteristic bands. +The chlorides of the metals are particularly suitable for +experiments of this character. Common salt, for example, is a +compound of chlorine and sodium; in the electric lamp it yields the +spectrum of the metal sodium. The chlorides of copper, lithium, and +strontium yield, in like manner, the bands of these metals.</p> +<p>When, therefore, Bunsen and Kirchhoff, the illustrious founders +of <i>spectrum analysis</i>, after having established by an +exhaustive examination the spectra of all known substances, +discovered a spectrum containing bands different from any known +bands, they immediately inferred the existence of a new metal. They +were operating at the time upon a residue, obtained by evaporating +one of the mineral waters of Germany. In that water they knew the +unknown metal was concealed, but vast quantities of it had to be +evaporated before a residue could be obtained sufficiently large to +enable ordinary chemistry to grapple with the metal. They, however, +hunted it down, and <a name="Page_193" id= +"Page_193"></a><span class="pagenum">[Pg 193]</span>it now stands +among chemical substances as the metal <i>Rubidium</i>. They +subsequently discovered a second metal, which they called +<i>Cæsium</i>. Thus, having first placed spectrum analysis on +a sure foundation, they demonstrated its capacity as an agent of +discovery. Soon afterwards Mr. Crookes, pursuing the same method, +discovered the bright green band of <i>Thallium</i>, and obtained +the salts of the metal which yielded it. The metal itself was first +isolated in ingots by M. Lamy, a French chemist.</p> +<p>All this relates to chemical discovery upon earth, where the +materials are in our own hands. But it was soon shown how spectrum +analysis might be applied to the investigation of the sun and +stars; and this result was reached through the solution of a +problem which had been long an enigma to natural philosophers. The +scope and conquest of this problem we must now endeavour to +comprehend. A spectrum is <i>pure</i> in which the colours do not +overlap each other. We purify the spectrum by making our beam +narrow, and by augmenting the number of our prisms. When a pure +spectrum of the sun has been obtained in this way, it is found to +be furrowed by innumerable dark lines. Four of them were first seen +by Dr. Wollaston, but they were afterwards multiplied and measured +by Fraunhofer with such masterly skill, that they are now +universally known as Fraunhofer's lines. To give an explanation of +these lines was, as I have said, a problem which long challenged +the attention of philosophers, and to Professor Kirchhoff belongs +the honour of having first conquered this problem.</p> +<p>(The positions of the principal lines, lettered according to +Fraunhofer, are shown in the annexed sketch <a name="Page_194" id= +"Page_194"></a><span class="pagenum">[Pg 194]</span>(fig. 55) of +the solar spectrum. A is supposed to stand near the extreme red, +and J near the extreme violet.)</p> +<div class="figleft" style="width: 82px;"><img src= +"images/fig55.jpg" width="82" height="600" alt="Fig. 55." title= +"" /> <b>Fig. 55.</b></div> +<p>The brief memoir of two pages, in which this immortal discovery +is recorded, was communicated to the Berlin Academy on October 27, +1859. Fraunhofer had remarked in the spectrum of a candle flame two +bright lines, which coincide accurately, as to position, with the +double dark line D of the solar spectrum. These bright lines are +produced with particular intensity by the yellow flame derived from +a mixture of salt and alcohol. They are in fact the lines of sodium +vapour. Kirchhoff produced a spectrum by permitting the sunlight to +enter his telescope by a slit and prism, and in front of the slit +he placed the yellow sodium flame. As long as the spectrum remained +feeble, there always appeared two bright lines, derived from the +flame, in the place of the two dark lines D of the spectrum. In +this case, such absorption as the flame exerted upon the sunlight +was more than atoned for by the radiation from the flame. When, +however, the solar spectrum was rendered sufficiently intense, the +bright bands vanished, and the two dark Fraunhofer lines appeared +with much greater sharpness and distinctness than when the flame +was not employed.</p> +<p>This result, be it noted, was not due to any real quenching of +the bright lines of the flame, but to the augmentation of the +intensity of the adjacent spectrum. The <a name="Page_195" id= +"Page_195"></a><span class="pagenum">[Pg 195]</span>experiment +proved to demonstration, that when the white light sent through the +flame was sufficiently intense, the quantity which the flame +absorbed was far in excess of that which it radiated.</p> +<p>Here then is a result of the utmost significance. Kirchhoff +immediately inferred from it that the salt flame, which could +intensify so remarkably the dark lines of Fraunhofer, ought also to +be able to <i>produce</i> them. The spectrum of the Drummond light +is known to exhibit the two bright lines of sodium, which, however, +gradually disappear as the modicum of sodium, contained as an +impurity in the incandescent lime, is exhausted. Kirchhoff formed a +spectrum of the limelight, and after the two bright lines had +vanished, he placed his salt flame in front of the slit. The two +dark lines immediately started forth. Thus, in the continuous +spectrum of the lime-light, he evoked, artificially, the lines D of +Fraunhofer.</p> +<p>Kirchhoff knew that this was an action not peculiar to the +sodium flame, and he immediately extended his generalisation to all +coloured flames which yield sharply defined bright bands in their +spectra. White light, with all its constituents complete, sent +through such flames, would, he inferred, have those precise +constituents absorbed, whose refrangibilities are the same as those +of the bright bands; so that after passing through such flames, the +white light, if sufficiently intense, would have its spectrum +furrowed by bands of darkness. On the occasion here referred to +Kirchhoff also succeeded in reversing a bright band of lithium.</p> +<p>The long-standing difficulty of Fraunhofer's lines fell to +pieces in the presence of facts and reflections like these, which +also carried with them an immeasurable <a name="Page_196" id= +"Page_196"></a><span class="pagenum">[Pg 196]</span>extension of +the chemist's power. Kirchhoff saw that from the agreement of the +lines in the spectra of terrestrial substances with Fraunhofer's +lines, the presence of these substances in the sun and fixed stars +might be immediately inferred. Thus the dark lines D in the solar +spectrum proved the existence of sodium in the solar atmosphere; +while the bright lines discovered by Brewster in a nitre flame, +which had been proved to coincide exactly with certain dark lines +between A and B in the solar spectrum, proved the existence of +potassium in the sun.</p> +<p>All subsequent research verified the accuracy of these first +daring conclusions. In his second paper, communicated to the Berlin +Academy before the close of 1859, Kirchhoff proved the existence of +iron in the sun. The bright lines of the spectrum of iron vapour +are exceedingly numerous, and 65 of them were subsequently proved +by Kirchhoff to be absolutely identical in position with 65 dark +Fraunhofer's lines. Ångström and Thalén pushed +the coincidences to 450 for iron, while, according to the same +excellent investigators, the following numbers express the +coincidences, in the case of the respective metals to which they +are attached:—</p> +<table border="0" cellpadding="2" cellspacing="0" summary=""> +<tr> +<td align='left'>Calcium</td> +<td align='right'>75</td> +</tr> +<tr> +<td align='left'>Barium</td> +<td align='right'>11</td> +</tr> +<tr> +<td align='left'>Magnesium</td> +<td align='right'>4</td> +</tr> +<tr> +<td align='left'>Manganese</td> +<td align='right'>57</td> +</tr> +<tr> +<td align='left'>Titanium</td> +<td align='right'>118</td> +</tr> +<tr> +<td align='left'>Chromium</td> +<td align='right'>18</td> +</tr> +<tr> +<td align='left'>Nickel</td> +<td align='right'>33</td> +</tr> +<tr> +<td align='left'>Cobalt</td> +<td align='right'>19</td> +</tr> +<tr> +<td align='left'>Hydrogen</td> +<td align='right'>4</td> +</tr> +<tr> +<td align='left'>Aluminium</td> +<td align='right'>2</td> +</tr> +<tr> +<td align='left'>Zinc</td> +<td align='right'>2</td> +</tr> +<tr> +<td align='left'>Copper</td> +<td align='right'>7</td> +</tr> +</table> +<p>The probability is overwhelming that all these substances exist +in the atmosphere of the sun.</p> +<p>Kirchhoff's discovery profoundly modified the conceptions +previously entertained regarding the constitution of the sun, +leading him to views which, though <a name="Page_197" id= +"Page_197"></a><span class="pagenum">[Pg 197]</span>they may be +modified in detail, will, I believe, remain substantially valid to +the end of time. The sun, according to Kirchhoff, consists of a +molten nucleus which is surrounded by a flaming atmosphere of lower +temperature. The nucleus may, in part, be <i>clouds</i>, mixed +with, or underlying true vapour. The light of the nucleus would +give us a continuous spectrum, like that of the Drummond light; but +having to pass through the photosphere, as Kirchhoff's beam passed +through the sodium flame, those rays of the nucleus which the +photosphere emit are absorbed, and shaded lines, corresponding to +the rays absorbed, occur in the spectrum. Abolish the solar +nucleus, and we should have a spectrum showing a bright line in the +place of every dark line of Fraunhofer, just as, in the case of +Kirchhoff's second experiment, we should have the bright sodium +lines of the flame if the lime-light were withdrawn. These lines of +Fraunhofer are therefore not absolutely dark, but dark by an amount +corresponding to the difference between the light intercepted and +the light emitted by the photosphere.</p> +<p>Almost every great scientific discovery is approached +contemporaneously by many minds, the fact that one mind usually +confers upon it the distinctness of demonstration being an +illustration, not of genius isolated, but of genius in advance. +Thus Foucault, in 1849, came to the verge of Kirchhoff's discovery. +By converging an image of the sun upon a voltaic arc, and thus +obtaining the spectra of both sun and arc superposed, he found that +the two bright lines which, owing to the presence of a little +sodium in the carbons or in the air, are seen in the spectrum of +the arc, coincide with the dark lines D of the solar spectrum. The +lines D <a name="Page_198" id="Page_198"></a><span class= +"pagenum">[Pg 198]</span>he found to he considerably strengthened +by the passage of the solar light through the voltaic arc.</p> +<p>Instead of the image of the sun, Foucault then projected upon +the arc the image of one of the solid incandescent carbon points, +which of itself would give a continuous spectrum; and he found that +the lines D were thus <i>generated</i> in that spectrum. Foucault's +conclusion from this admirable experiment was 'that the arc is a +medium which emits the rays D on its own account, and at the same +time absorbs them when they come from another quarter.' Here he +stopped. He did not extend his observations beyond the voltaic arc; +he did not offer any explanation of the lines of Fraunhofer; he did +not arrive at any conception of solar chemistry, or of the +constitution of the sun. His beautiful experiment remained a germ +without fruit, until the discernment, ten years subsequently, of +the whole class of phenomena to which it belongs, enabled Kirchhoff +to solve these great problems.</p> +<p>Soon after the publication of Kirchhoff's discovery, Professor +Stokes, who also, ten years prior to the discovery, had nearly +anticipated it, borrowed an illustration from sound, to explain the +reciprocity of radiation and absorption. A stretched string +responds to aërial vibrations which synchronize with its own. +A great number of such strings stretched in space would roughly +represent a medium; and if the note common to them all were sounded +at a distance they would take up or absorb its vibrations.</p> +<p>When a violin-bow is drawn across this tuning-fork, the room is +immediately filled with a musical sound, which may be regarded as +the <i>radiation</i> or <i>emission</i> of sound from the fork. A +few days ago, on sound<a name="Page_199" id= +"Page_199"></a><span class="pagenum">[Pg 199]</span>ing this fork, +I noticed that when its vibrations were quenched, the sound seemed +to be continued, though more feebly. It appeared, moreover, to come +from under a distant table, where stood a number of tuning-forks of +different sizes and rates of vibration. One of these, and one only, +had been started by the sounding fork, and it was the one whose +rate of vibration was the same as that of the fork which started +it. This is an instance of the <i>absorption</i> of the sound of +one fork by another. Placing two unisonant forks near each other, +sweeping the bow over one of them, and then quenching the agitated +fork, the other continues to sound; this other can re-excite the +former, and several transfers of sound between the two forks can be +thus effected. Placing a cent-piece on each prong of one of the +forks, we destroy its perfect synchronism with the other, and no +such communication of sound from the one to the other is then +possible.</p> +<p>I have now to bring before you, on a suitable scale, the +demonstration that we can do with <i>light</i> what has been here +done with sound. For several days in 1861 I endeavoured to +accomplish this, with only partial success. In iron dishes a +mixture of dilute alcohol and salt was placed, and warmed so as to +promote vaporization. The vapour was ignited, and through the +yellow flame thus produced the beam from the electric lamp was +sent; but a faint darkening only of the yellow band of a projected +spectrum could be obtained. A trough was then made which, when fed +with the salt and alcohol, yielded a flame ten feet thick; but the +result of sending the light through this depth of flame was still +unsatisfactory. Remembering that the direct combustion of sodium in +a Bunsen's <a name="Page_200" id="Page_200"></a><span class= +"pagenum">[Pg 200]</span>flame produces a yellow far more intense +than that of the salt flame, and inferring that the intensity of +the colour indicated the copiousness of the incandescent vapour, I +sent through the flame from metallic sodium the beam of the +electric lamp. The success was complete; and this experiment I wish +now to repeat in your presence.<a name="FNanchor_25_25" id= +"FNanchor_25_25"></a><a href="#Footnote_25_25" class= +"fnanchor">[25]</a></p> +<p>Firstly then you notice, when a fragment of sodium is placed in +a platinum spoon and introduced into a Bunsen's flame, an intensely +yellow light is produced. It corresponds in refrangibility with the +yellow band of the spectrum. Like our tuning-fork, it emits waves +of a special period. When the white light from the electric lamp is +sent through that flame, you will have ocular proof that the yellow +flame intercepts the yellow of the spectrum; in other words, that +it absorbs waves of the same period as its own, thus producing, to +all intents and purposes, a dark Fraunhofer's band in the place of +the yellow.</p> +<p>In front of the slit (at L, fig. 56) through which the beam +issues is placed a Bunsen's burner (<i>b</i>) protected by a +chimney (C). This beam, after passing through a lens, traverses the +prism (P) (in the real experiment there was a pair of prisms), is +there decomposed, and forms a vivid continuous spectrum (S S) upon +the screen. Introducing a platinum spoon with its pellet of sodium +into the Bunsen's flame, the pellet first fuses, colours the flame +intensely yellow, and at length bursts into violent combustion. At +the same <a name="Page_201" id="Page_201"></a><span class= +"pagenum">[Pg 201]</span>moment the spectrum is furrowed by an +intensely dark band (D), two inches wide and two feet long. +Introducing and withdrawing the sodium flame in rapid succession, +the sudden appearance and disappearance of the band of darkness is +shown in a most striking manner. In contrast with the adjacent +brightness this band appears absolutely black, so vigorous is the +absorption. The blackness, however, is but relative, for upon the +dark space falls a portion of the light of the sodium flame.</p> +<div class="figright" style="width: 441px;"><img src= +"images/fig56.jpg" width="441" height="252" alt="Fig. 56." title= +"" /> <b>Fig. 56.</b></div> +<p>I have already referred to the experiment of Foucault; but other +workers also had been engaged on the borders of this subject before +it was taken up by Bunsen and Kirchhoff. With some modification I +have on a former occasion used the following words regarding the +precursors of the discovery of spectrum analysis, and solar +chemistry:—'Mr. Talbot had observed the bright lines in the +spectra of coloured flames, and both he and Sir John Herschel +pointed out the possibility of making prismatic analysis a chemical +test of exceeding delicacy, though not of entire certainty. More +than a quarter of a century ago Dr. Miller gave drawings and +<a name="Page_202" id="Page_202"></a><span class="pagenum">[Pg +202]</span>descriptions of the spectra of various coloured flames. +Wheatstone, with his accustomed acuteness, analyzed the light of +the electric spark, and proved that the metals between which the +spark passed determined the bright bands in its spectrum. In an +investigation described by Kirchhoff as "classical," Swan had shown +that 1/2,500,000 of a grain of sodium in a Bunsen's flame could be +detected by its spectrum. He also proved the constancy of the +bright lines in the spectra of hydrocarbon flames. Masson published +a prize essay on the bands of the induction spark; while Van der +Willigen, and more recently Plücker, have also given us +beautiful drawings of spectra obtained from the same source.</p> +<p>'But none of these distinguished men betrayed the least +knowledge of the connexion between the bright bands of the metals +and the dark lines of the solar spectrum; nor could spectrum +analysis be said to be placed upon anything like a safe foundation +prior to the researches of Bunsen and Kirchhoff. The man who, in a +published paper, came nearest to the philosophy of the subject was +Ångström. In that paper, translated by myself, and +published in the "Philosophical Magazine" for 1855, he indicates +that the rays which a body absorbs are precisely those which, when +luminous, it can emit. In another place, he speaks of one of his +spectra giving the general impression of the <i>reversal</i> of the +solar spectrum. But his memoir, philosophical as it is, is +distinctly marked by the uncertainty of his time. Foucault, +Thomson, and Balfour Stewart have all been near the discovery, +while, as already stated, it was almost hit by the acute but +unpublished conjecture of Stokes.'</p> +<p><a name="Page_203" id="Page_203"></a><span class="pagenum">[Pg +203]</span>Mentally, as well as physically, every year of the +world's age is the outgrowth and offspring of all preceding years. +Science proves itself to be a genuine product of Nature by growing +according to this law. We have no solution of continuity here. All +great discoveries are duly prepared for in two ways; first, by +other discoveries which form their prelude; and, secondly, by the +sharpening of the inquiring intellect. Thus Ptolemy grew out of +Hipparchus, Copernicus out of both, Kepler out of all three, and +Newton out of all the four. Newton did not rise suddenly from the +sea-level of the intellect to his amazing elevation. At the time +that he appeared, the table-land of knowledge was already high. He +juts, it is true, above the table-land, as a massive peak; still he +is supported by the plateau, and a great part of his absolute +height is the height of humanity in his time. It is thus with the +discoveries of Kirchhoff. Much had been previously accomplished; +this he mastered, and then by the force of individual genius went +beyond it. He replaced uncertainty by certainty, vagueness by +definiteness, confusion by order; and I do not think that Newton +has a surer claim to the discoveries that have made his name +immortal, than Kirchhoff has to the credit of gathering up the +fragmentary knowledge of his time, of vastly extending it, and of +infusing into it the life of great principles.</p> +<p>With one additional point we will wind up our illustrations of +the principles of solar chemistry. Owing to the scattering of light +by matter floating mechanically in the earth's atmosphere, the sun +is seen not sharply defined, but surrounded by a luminous glare. +Now, a loud noise will drown a whisper, an intense <a name= +"Page_204" id="Page_204"></a><span class="pagenum">[Pg +204]</span>light will overpower a feeble one, and so this +circumsolar glare prevents us from seeing many striking appearances +round the border of the sun. The glare is abolished in total +eclipses, when the moon comes between the earth and the sun, and +there are then seen a series of rose-coloured protuberances, +stretching sometimes tens of thousands of miles beyond the dark +edge of the moon. They are described by Vassenius in the +'Philosophical Transactions' for 1733; and were probably observed +even earlier than this. In 1842 they attracted great attention, and +were then compared to Alpine snow-peaks reddened by the evening +sun. That these prominences are flaming gas, and principally +hydrogen gas, was first proved by M. Janssen during an eclipse +observed in India, on the 18th of August, 1868.</p> +<p>But the prominences may be rendered visible in sunshine; and for +a reason easily understood. You have seen in these lectures a +single prism employed to produce a spectrum, and you have seen a +pair of prisms employed. In the latter case, the dispersed white +light, being diffused over about twice the area, had all its +colours proportionately diluted. You have also seen one prism and a +pair of prisms employed to produce the bands of incandescent +vapours; but here the light of each band, being absolutely +monochromatic, was incapable of further dispersion by the second +prism, and could not therefore be weakened by such dispersion.</p> +<p>Apply these considerations to the circumsolar region. The glare +of white light round the sun can be dispersed and weakened to any +extent, by augmenting the number of prisms; while a monochromatic +<a name="Page_205" id="Page_205"></a><span class="pagenum">[Pg +205]</span>light, mixed with this glare, and masked by it, would +retain its intensity unenfeebled by dispersion. Upon this +consideration has been founded a method of observation, applied +independently by M. Janssen in India and by Mr. Lockyer in England, +by which the monochromatic bands of the prominences are caused to +obtain the mastery, and to appear in broad daylight. By searching +carefully and skilfully round the sun's rim, Mr. Lockyer has proved +these prominences to be mere local juttings from a fiery envelope +which entirely clasps the sun, and which he has called the +<i>Chromosphere</i>.</p> +<p>It would lead us far beyond the object of these lectures to +dwell upon the numerous interesting and important results obtained +by Secchi, Respighi, Young, and other distinguished men who have +worked at the chemistry of the sun and its appendages. Nor can I do +more at present than make a passing reference to the excellent +labours of Dr. Huggins in connexion with the fixed stars, nebulae, +and comets. They, more than any others, illustrate the literal +truth of the statement, that the establishment of spectrum +analysis, and the explanation of Fraunhofer's lines, carried with +them an immeasurable extension of the chemist's range. The truly +powerful experiments of Professor Dewar are daily adding to our +knowledge, while the refined researches of Capt. Abney and others +are opening new fields of inquiry. But my object here is to make +principles plain, rather than to follow out the details of their +illustration.<a name="Page_206" id="Page_206"></a><span class= +"pagenum">[Pg 206]</span></p> +<h3>SUMMARY AND CONCLUSION.</h3> +<p>My desire in these lectures has been to show you, with as little +breach of continuity as possible, something of the past growth and +present aspect of a department of science, in which have laboured +some of the greatest intellects the world has ever seen. I have +sought to confer upon each experiment a distinct intellectual +value, for experiments ought to be the representatives and +expositors of thought—a language addressed to the eye as +spoken words are to the ear. In association with its context, +nothing is more impressive or instructive than a fit experiment; +but, apart from its context, it rather suits the conjurer's purpose +of surprise, than the purpose of education which ought to be the +ruling motive of the scientific man.</p> +<p>And now a brief summary of our work will not be out of place. +Our present mastery over the laws and phenomena of light has its +origin in the desire of man to <i>know</i>. We have seen the +ancients busy with this problem, but, like a child who uses his +arms aimlessly, for want of the necessary muscular training, so +these early men speculated vaguely and confusedly regarding natural +phenomena, not having had the discipline needed to give clearness +to their insight, and firmness to their grasp of principles. They +assured themselves <a name="Page_207" id= +"Page_207"></a><span class="pagenum">[Pg 207]</span>of the +rectilineal propagation of light, and that the angle of incidence +was equal to the angle of reflection. For more than a thousand +years—I might say, indeed, for more than fifteen hundred +years—the scientific intellect appears as if smitten with +paralysis, the fact being that, during this time, the mental force, +which might have run in the direction of science, was diverted into +other directions.</p> +<p>The course of investigation, as regards light, was resumed in +1100 by an Arabian philosopher named Alhazen. Then it was taken up +in succession by Roger Bacon, Vitellio, and Kepler. These men, +though failing to detect the principles which ruled the facts, kept +the fire of investigation constantly burning. Then came the +fundamental discovery of Snell, that cornerstone of optics, as I +have already called it, and immediately afterwards we have the +application, by Descartes, of Snell's discovery to the explanation +of the rainbow. Following this we have the overthrow, by Roemer, of +the notion of Descartes, that light was transmitted instantaneously +through space. Then came Newton's crowning experiments on the +analysis and synthesis of white light, by which it was proved to be +compounded of various kinds of light of different degrees of +refrangibility.</p> +<p>Up to his demonstration of the composition of white light, +Newton had been everywhere triumphant—triumphant in the +heavens, triumphant on the earth, and his subsequent experimental +work is, for the most part, of immortal value. But infallibility is +not an attribute of man, and, soon after his discovery of the +nature of white light, Newton proved himself human. He supposed +that refraction and chromatic dispersion <a name="Page_208" id= +"Page_208"></a><span class="pagenum">[Pg 208]</span>went hand in +hand, and that you could not abolish the one without at the same +time abolishing the other. Here Dollond corrected him.</p> +<p>But Newton committed a graver error than this. Science, as I +sought to make clear to you in our second lecture, is only in part +a thing of the senses. The roots of phenomena are embedded in a +region beyond the reach of the senses, and less than the root of +the matter will never satisfy the scientific mind. We find, +accordingly, in this career of optics the greatest minds constantly +yearning to break the bounds of the senses, and to trace phenomena +to their subsensible foundation. Thus impelled, they entered the +region of theory, and here Newton, though drawn from time to time +towards truth, was drawn still more strongly towards error; and he +made error his substantial choice. His experiments are +imperishable, but his theory has passed away. For a century it +stood like a dam across the course of discovery; but, as with all +barriers that rest upon authority, and not upon truth, the pressure +from behind increased, and eventually swept the barrier away.</p> +<p>In 1808 Malus, looking through Iceland spar at the sun, +reflected from the window of the Luxembourg Palace in Paris, +discovered the polarization of light by reflection. As stated at +the time, this discovery ushered in the darkest hour in the +fortunes of the wave theory. But the darkness did not continue. In +1811 Arago discovered the splendid chromatic phenomena which we +have had illustrated by the deportment of plates of gypsum in +polarized light; he also discovered the rotation of the plane of +polarization by quartz-crystals. In 1813 Seebeck discovered the +<a name="Page_209" id="Page_209"></a><span class="pagenum">[Pg +209]</span>polarization of light by tourmaline. That same year +Brewster discovered those magnificent bands of colour that surround +the axes of biaxal crystals. In 1814 Wollaston discovered the rings +of Iceland spar. All these effects, which, without a theoretic +clue, would leave the human mind in a jungle of phenomena without +harmony or relation, were organically connected by the theory of +undulation.</p> +<p>The wave theory was applied and verified in all directions, Airy +being especially conspicuous for the severity and conclusiveness of +his proofs. A most remarkable verification fell to the lot of the +late Sir William Hamilton, of Dublin, who, taking up the theory +where Fresnel had left it, arrived at the conclusion that at four +special points of the 'wave-surface' in double-refracting crystals, +the ray was divided, not into two parts but into an infinite number +of parts; forming at these points a continuous conical envelope +instead of two images. No human eye had ever seen this envelope +when Sir William Hamilton inferred its existence. He asked Dr. +Lloyd to test experimentally the truth of his theoretic conclusion. +Lloyd, taking a crystal of arragonite, and following with the most +scrupulous exactness the indications of theory, cutting the crystal +where theory said it ought to be cut, observing it where theory +said it ought to be observed, discovered the luminous envelope +which had previously been a mere idea in the mind of the +mathematician.</p> +<p>Nevertheless this great theory of undulation, like many another +truth, which in the long run has proved a blessing to humanity, had +to establish, by hot conflict, its right to existence. Illustrious +names were arrayed against it. It had been enunciated by Hooke, it +had <a name="Page_210" id="Page_210"></a><span class="pagenum">[Pg +210]</span>been expounded and applied by Huyghens, it had been +defended by Euler. But they made no impression. And, indeed, the +theory in their hands lacked the strength of a demonstration. It +first took the form of a demonstrated verity in the hands of Thomas +Young. He brought the waves of light to bear upon each other, +causing them to support each other, and to extinguish each other at +will. From their mutual actions he determined their lengths, and +applied his knowledge in all directions. He finally showed that the +difficulty of polarization yielded to the grasp of theory.</p> +<p>After him came Fresnel, whose transcendent mathematical +abilities enabled him to give the theory a generality unattained by +Young. He seized it in its entirety; followed the ether into the +hearts of crystals of the most complicated structure, and into +bodies subjected to strain and pressure. He showed that the facts +discovered by Malus, Arago, Brewster, and Biot were so many +ganglia, so to speak, of his theoretic organism, deriving from it +sustenance and explanation. With a mind too strong for the body +with which it was associated, that body became a wreck long before +it had become old, and Fresnel died, leaving, however, behind him a +name immortal in the annals of science.</p> +<p>One word more I should like to say regarding Fresnel. There are +things better even than science. Character is higher than +Intellect, but it is especially pleasant to those who wish to think +well of human nature when high intellect and upright character are +found combined. They were combined in this young Frenchman. In +those hot conflicts of the undulatory theory, he stood forth as a +man of integrity, claiming no more than his right, and ready to +concede their <a name="Page_211" id="Page_211"></a><span class= +"pagenum">[Pg 211]</span>rights to others. He at once recognized +and acknowledged the merits of Thomas Young. Indeed, it was he, and +his fellow-countryman Arago, who first startled England into the +consciousness of the injustice done to Young in the 'Edinburgh +Review.'</p> +<p>I should like to read to you a brief extract from a letter +written by Fresnel to Young in 1824, as it throws a pleasant light +upon the character of the French philosopher. 'For a long time,' +says Fresnel, 'that sensibility, or that vanity, which people call +love of glory has been much blunted in me. I labour much less to +catch the suffrages of the public, than to obtain that inward +approval which has always been the sweetest reward of my efforts. +Without doubt, in moments of disgust and discouragement, I have +often needed the spur of vanity to excite me to pursue my +researches. But all the compliments I have received from Arago, De +la Place, and Biot never gave me so much pleasure as the discovery +of a theoretic truth or the confirmation of a calculation by +experiment.'</p> +<hr style='width: 45%;' /> +<p>This, then, is the core of the whole matter as regards science. +It must be cultivated for its own sake, for the pure love of truth, +rather than for the applause or profit that it brings. And now my +occupation in America is well-nigh gone. Still I will bespeak your +tolerance for a few concluding remarks, in reference to the men who +have bequeathed to us the vast body of knowledge of which I have +sought to give you some faint idea in these lectures. What was the +motive that spurred them on? What urged them to those battles and +those victories over reticent Nature, which have become the +heritage of the human race? It is never to be <a name="Page_212" +id="Page_212"></a><span class="pagenum">[Pg 212]</span>forgotten +that not one of those great investigators, from Aristotle down to +Stokes and Kirchhoff, had any practical end in view, according to +the ordinary definition of the word 'practical.' They did not +propose to themselves money as an end, and knowledge as a means of +obtaining it. For the most part, they nobly reversed this process, +made knowledge their end, and such money as they possessed the +means of obtaining it.</p> +<p>We see to-day the issues of their work in a thousand practical +forms, and this may be thought sufficient to justify, if not +ennoble, their efforts. But they did not work for such issues; +their reward was of a totally different kind. In what way +different? We love clothes, we love luxuries, we love fine +equipages, we love money, and any man who can point to these as the +result of his efforts in life, justifies these results before all +the world. In America and England, more especially, he is a +'practical' man. But I would appeal confidently to this assembly +whether such things exhaust the demands of human nature? The very +presence here for six inclement nights of this great audience, +embodying so much of the mental force and refinement of this vast +city,<a name="FNanchor_26_26" id="FNanchor_26_26"></a><a href= +"#Footnote_26_26" class="fnanchor">[26]</a> is an answer to my +question. I need not tell such an assembly that there are joys of +the intellect as well as joys of the body, or that these pleasures +of the spirit constituted the reward of our great investigators. +Led on by the whisperings of natural truth, through pain and +self-denial, they often pursued their work. With the ruling passion +strong in death, some of them, when no longer able to hold a pen, +dictated to their friends <a name="Page_213" id= +"Page_213"></a><span class="pagenum">[Pg 213]</span>the last +results of their labours, and then rested from them for ever.</p> +<p>Could we have seen these men at work, without any knowledge of +the consequences of their work, what should we have thought of +them? To the uninitiated, in their day, they might often appear as +big children playing with soap-bubbles and other trifles. It is so +to this hour. Could you watch the true investigator—your +Henry or your Draper, for example—in his laboratory, unless +animated by his spirit, you could hardly understand what keeps him +there. Many of the objects which rivet his attention might appear +to you utterly trivial; and if you were to ask him what is the +<i>use</i> of his work, the chances are that you would confound +him. He might not be able to express the use of it in intelligible +terms. He might not be able to assure you that it will put a dollar +into the pocket of any human being present or to come. That +scientific discovery <i>may</i> put not only dollars into the +pockets of individuals, but millions into the exchequers of +nations, the history of science amply proves; but the hope of its +doing so never was, and it never can be, the motive power of the +investigator.</p> +<p>I know that some risk is run in speaking thus before practical +men. I know what De Tocqueville says of you. 'The man of the +North,' he says, 'has not only experience, but knowledge. He, +however, does not care for science as a pleasure, and only embraces +it with avidity when it leads to useful applications.' But what, I +would ask, are the hopes of useful applications which have caused +you so many times to fill this place, in spite of snow-drifts and +biting cold? What, I may ask, is the origin of that kindness which +drew me from <a name="Page_214" id="Page_214"></a><span class= +"pagenum">[Pg 214]</span>my work in London to address you here, and +which, if I permitted it, would send me home a millionaire? Not +because I had taught you to make a single cent by science am I here +to-night, but because I tried to the best of my ability to present +science to the world as an intellectual good. Surely no two terms +were ever so distorted and misapplied with reference to man, in his +higher relations, as these terms useful and practical. Let us +expand our definitions until they embrace all the needs of man, his +highest intellectual needs inclusive. It is specially on this +ground of its administering to the higher needs of the intellect; +it is mainly because I believe it to be wholesome, not only as a +source of knowledge but as a means of discipline, that I urge the +claims of science upon your attention.</p> +<p>But with reference to material needs and joys, surely pure +science has also a word to say. People sometimes speak as if steam +had not been studied before James Watt, or electricity before +Wheatstone and Morse; whereas, in point of fact, Watt and +Wheatstone and Morse, with all their practicality, were the mere +outcome of antecedent forces, which acted without reference to +practical ends. This also, I think, merits a moment's attention. +You are delighted, and with good reason, with your electric +telegraphs, proud of your steam-engines and your factories, and +charmed with the productions of photography. You see daily, with +just elation, the creation of new forms of industry—new +powers of adding to the wealth and comfort of society. Industrial +England is heaving with forces tending to this end; and the pulse +of industry beats still stronger in the United States. And yet, +when <a name="Page_215" id="Page_215"></a><span class="pagenum">[Pg +215]</span>analyzed, what are industrial America and industrial +England?</p> +<p>If you can tolerate freedom of speech on my part, I will answer +this question by an illustration. Strip a strong arm, and regard +the knotted muscles when the hand is clenched and the arm bent. Is +this exhibition of energy the work of the muscle alone? By no +means. The muscle is the channel of an influence, without which it +would be as powerless as a lump of plastic dough. It is the +delicate unseen nerve that unlocks the power of the muscle. And +without those filaments of genius, which have been shot like nerves +through the body of society by the original discoverer, industrial +America, and industrial England, would be very much in the +condition of that plastic dough.</p> +<p>At the present time there is a cry in England for technical +education, and it is a cry in which the most commonplace intellect +can join, its necessity is so obvious. But there is no such cry for +original investigation. Still, without this, as surely as the +stream dwindles when the spring dies, so surely will 'technical +education' lose all force of growth, all power of reproduction. Our +great investigators have given us sufficient work for a time; but +if their spirit die out, we shall find ourselves eventually in the +condition of those Chinese mentioned by De Tocqueville, who, having +forgotten the scientific origin of what they did, were at length +compelled to copy without variation the inventions of an ancestry +wiser than themselves, who had drawn their inspiration direct from +Nature.</p> +<p>Both England and America have reason to bear those things in +mind, for the largeness and nearness of <a name="Page_216" id= +"Page_216"></a><span class="pagenum">[Pg 216]</span>material +results are only too likely to cause both countries to forget the +small spiritual beginnings of such results, in the mind of the +scientific discoverer. You multiply, but he creates. And if you +starve him, or otherwise kill him—nay, if you fail to secure +for him free scope and encouragement—you not only lose the +motive power of intellectual progress, but infallibly sever +yourselves from the springs of industrial life.</p> +<p>What has been said of technical operations holds equally good +for education, for here also the original investigator constitutes +the fountain-head of knowledge. It belongs to the teacher to give +this knowledge the requisite form; an honourable and often a +difficult task. But it is a task which receives its final +sanctification, when the teacher himself honestly tries to add a +rill to the great stream of scientific discovery. Indeed, it may be +doubted whether the real life of science can be fully felt and +communicated by the man who has not himself been taught by direct +communion with Nature. We may, it is true, have good and +instructive lectures from men of ability, the whole of whose +knowledge is second-hand, just as we may have good and instructive +sermons from intellectually able and unregenerate men. But for that +power of science, which corresponds to what the Puritan fathers +would call experimental religion in the heart, you must ascend to +the original investigator.</p> +<p>To keep society as regards science in healthy play, three +classes of workers are necessary: Firstly, the investigator of +natural truth, whose vocation it is to pursue that truth, and +extend the field of discovery for the truth's own sake and without +reference to practical ends. Secondly, the teacher of natural +truth, whose <a name="Page_217" id="Page_217"></a><span class= +"pagenum">[Pg 217]</span>vocation it is to give public diffusion to +the knowledge already won by the discoverer. Thirdly, the applier +of natural truth, whose vocation it is to make scientific knowledge +available for the needs, comforts, and luxuries of civilized life. +These three classes ought to co-exist and interact. Now, the +popular notion of science, both in this country and in England, +often relates not to science strictly so called, but to the +applications of science. Such applications, especially on this +continent, are so astounding—they spread themselves so +largely and umbrageously before the public eye—that they +often shut out from view those workers who are engaged in the +quieter and profounder business of original investigation.</p> +<p>Take the electric telegraph as an example, which has been +repeatedly forced upon my attention of late. I am not here to +attenuate in the slightest degree the services of those who, in +England and America, have given the telegraph a form so wonderfully +fitted for public use. They earned a great reward, and they have +received it. But I should be untrue to you and to myself if I +failed to tell you that, however high in particular respects their +claims and qualities may be, your practical men did not discover +the electric telegraph. The discovery of the electric telegraph +implies the discovery of electricity itself, and the development of +its laws and phenomena. Such discoveries are not made by practical +men, and they never will be made by them, because their minds are +beset by ideas which, though of the highest value from one point of +view, are not those which stimulate the original discoverer.</p> +<p>The ancients discovered the electricity of amber; and Gilbert, +in the year 1600, extended the discovery <a name="Page_218" id= +"Page_218"></a><span class="pagenum">[Pg 218]</span>to other +bodies. Then followed Boyle, Von Guericke, Gray, Canton, Du Fay, +Kleist, Cunæus, and your own Franklin. But their form of +electricity, though tried, did not come into use for telegraphic +purposes. Then appeared the great Italian Volta, who discovered the +source of electricity which bears his name, and applied the most +profound insight, and the most delicate experimental skill to its +development. Then arose the man who added to the powers of his +intellect all the graces of the human heart, Michael Faraday, the +discoverer of the great domain of magneto-electricity. Œrsted +discovered the deflection of the magnetic needle, and Arago and +Sturgeon the magnetization of iron by the electric current. The +voltaic circuit finally found its theoretic Newton in Ohm; while +Henry, of Princeton, who had the sagacity to recognize the merits +of Ohm while they were still decried in his own country, was at +this time in the van of experimental inquiry.</p> +<p>In the works of these men you have all the materials employed at +this hour, in all the forms of the electric telegraph. Nay, more; +Gauss, the illustrious astronomer, and Weber, the illustrious +natural philosopher, both professors in the University of +Göttingen, wishing to establish a rapid mode of communication +between the observatory and the physical cabinet of the university, +did this by means of an electric telegraph. Thus, before your +practical men appeared upon the scene, the force had been +discovered, its laws investigated and made sure, the most complete +mastery of its phenomena had been attained—nay, its +applicability to telegraphic purposes demonstrated—by men +whose sole reward for their labours was the noble <a name= +"Page_219" id="Page_219"></a><span class="pagenum">[Pg +219]</span>excitement of research, and the joy attendant on the +discovery of natural truth.</p> +<p>Are we to ignore all this? We do so at our peril. For I say +again that, behind all our practical applications, there is a +region of intellectual action to which practical men have rarely +contributed, but from which they draw all their supplies. Cut them +off from this region, and they become eventually helpless. In no +case is the adage truer, 'Other men laboured, but ye are entered +into their labours,' than in the case of the discoverer and applier +of natural truth. But now a word on the other side. While practical +men are not the men to make the necessary antecedent discoveries, +the cases are rare, though, in our day, not absent, in which the +discoverer knows how to turn his labours to practical account. +Different qualities of mind and habits of thought are usually +needed in the two cases; and while I wish to give emphatic +utterance to the claims of those whose position, owing to the +simple fact of their intellectual elevation, is often +misunderstood, I am not here to exalt the one class of workers at +the expense of the other. They are the necessary complements of +each other. But remember that one class is sure to be taken care +of. All the material rewards of society are already within their +reach, while that same society habitually ascribes to them +intellectual achievements which were never theirs. This cannot but +act to the detriment of those studies out of which, not only our +knowledge of nature, but our present industrial arts themselves, +have sprung, and from which the rising genius of the country is +incessantly tempted away.</p> +<p>Pasteur, one of the most illustrious members of the Institute of +France, in accounting for the disastrous <a name="Page_220" id= +"Page_220"></a><span class="pagenum">[Pg 220]</span>overthrow of +his country, and the predominance of Germany in the late war, +expresses himself thus: 'Few persons comprehend the real origin of +the marvels of industry and the wealth of nations. I need no +further proof of this than the employment, more and more frequent, +in official language, and in writings of all sorts, of the +erroneous expression <i>applied science</i>. The abandonment of +scientific careers by men capable of pursuing them with +distinction, was recently deplored in the presence of a minister of +the greatest talent. The statesman endeavoured to show that we +ought not to be surprised at this result, because <i>in our day the +reign of theoretic science yielded place to that of applied +science</i>. Nothing could be more erroneous than this opinion, +nothing, I venture to say, more dangerous, even to practical life, +than the consequences which might flow from these words. They have +rested in my mind as a proof of the imperious necessity of reform +in our superior education. There exists no category of the +sciences, to which the name of applied science could be rightly +given. <i>We have science, and the applications of science</i>, +which are united together as the tree and its fruit.'</p> +<p>And Cuvier, the great comparative anatomist, writes thus upon +the same theme: 'These grand practical innovations are the mere +applications of truths of a higher order, not sought with a +practical intent, but pursued for their own sake, and solely +through an ardour for knowledge. Those who applied them could not +have discovered them; but those who discovered them had no +inclination to pursue them to a practical end. Engaged in the high +regions whither their thoughts had carried them, they hardly +perceived these practical <a name="Page_221" id= +"Page_221"></a><span class="pagenum">[Pg 221]</span>issues though +born of their own deeds. These rising workshops, these peopled +colonies, those ships which furrow the seas—this abundance, +this luxury, this tumult—all this comes from discoveries in +science, and it all remains strange to the discoverers. At the +point where science merges into practice they abandon it; it +concerns them no more.'</p> +<p>When the Pilgrim Fathers landed at Plymouth Rock, and when Penn +made his treaty with the Indians, the new-comers had to build their +houses, to cultivate the earth, and to take care of their souls. In +such a community science, in its more abstract forms, was not to be +thought of. And at the present hour, when your hardy Western +pioneers stand face to face with stubborn Nature, piercing the +mountains and subduing the forest and the prairie, the pursuit of +science, for its own sake, is not to be expected. The first need of +man is food and shelter; but a vast portion of this continent is +already raised far beyond this need. The gentlemen of New York, +Brooklyn, Boston, Philadelphia, Baltimore, and Washington have +already built their houses, and very beautiful they are; they have +also secured their dinners, to the excellence of which I can also +bear testimony. They have, in fact, reached that precise condition +of well-being and independence when a culture, as high as humanity +has yet reached, may be justly demanded at their hands. They have +reached that maturity, as possessors of wealth and leisure, when +the investigator of natural truth, for the truth's own sake, ought +to find among them promoters and protectors.</p> +<p>Among the many problems before them they have <a name="Page_222" +id="Page_222"></a><span class="pagenum">[Pg 222]</span>this to +solve, whether a republic is able to foster the highest forms of +genius. You are familiar with the writings of De Tocqueville, and +must be aware of the intense sympathy which he felt for your +institutions; and this sympathy is all the more valuable from the +philosophic candour with which he points out not only your merits, +but your defects and dangers. Now if I come here to speak of +science in America in a critical and captious spirit, an invisible +radiation from my words and manner will enable you to find me out, +and will guide your treatment of me to-night. But if I in no +unfriendly spirit—in a spirit, indeed, the reverse of +unfriendly—venture to repeat before you what this great +historian and analyst of democratic institutions said of America, I +am persuaded that you will hear me out. He wrote some three and +twenty years ago, and, perhaps, would not write the same to-day; +but it will do nobody any harm to have his words repeated, and, if +necessary, laid to heart.</p> +<p>In a work published in 1850, De Tocqueville says: 'It must be +confessed that, among the civilized peoples of our age, there are +few in which the highest sciences have made so little progress as +in the United States.'<a name="FNanchor_27_27" id= +"FNanchor_27_27"></a><a href="#Footnote_27_27" class= +"fnanchor">[27]</a> He declares his conviction that, had you been +alone in the universe, you would soon have discovered that you +cannot long make progress in practical science without cultivating +theoretic science at the same time. But, according to De +Tocqueville, you are not thus alone. He refuses to separate America +from its ancestral home; <a name="Page_223" id= +"Page_223"></a><span class="pagenum">[Pg 223]</span>and it is +there, he contends, that you collect the treasures of the +intellect, without taking the trouble to create them.</p> +<p>De Tocqueville evidently doubts the capacity of a democracy to +foster genius as it was fostered in the ancient aristocracies. 'The +future,' he says, 'will prove whether the passion for profound +knowledge, so rare and so fruitful, can be born and developed as +readily in democratic societies as in aristocracies. For my part,' +he continues, 'I can hardly believe it.' He speaks of the unquiet +feverishness of democratic communities, not in times of great +excitement, for such times may give an extraordinary impetus to +ideas, but in times of peace. There is then, he says, 'a small and +uncomfortable agitation, a sort of incessant attrition of man +against man, which troubles and distracts the mind without +imparting to it either loftiness or animation.' It rests with you +to prove whether these things are necessarily so—whether +scientific genius cannot find, in the midst of you, a tranquil +home.</p> +<p>I should be loth to gainsay so keen an observer and so profound +a political writer, but, since my arrival in this country, I have +been unable to see anything in the constitution of society, to +prevent a student, with the root of the matter in him, from +bestowing the most steadfast devotion on pure science. If great +scientific results are not achieved in America, it is not to the +small agitations of society that I should be disposed to ascribe +the defect, but to the fact that the men among you who possess the +endowments necessary for profound scientific inquiry, are laden +with duties of administration, or tuition, so heavy as to be +utterly incompatible with the continuous and tranquil meditation +which original <a name="Page_224" id="Page_224"></a><span class= +"pagenum">[Pg 224]</span>investigation demands. It may well be +asked whether Henry would have been transformed into an +administrator, or whether Draper would have forsaken science to +write history, if the original investigator had been honoured as he +ought to be in this land. I hardly think they would. Still I do not +imagine this state of things likely to last. In America there is a +willingness on the part of individuals to devote their fortunes, in +the matter of education, to the service of the commonwealth, which +is probably without a parallel elsewhere; and this willingness +requires but wise direction to enable you effectually to wipe away +the reproach of De Tocqueville.</p> +<p>Your most difficult problem will be, not to build institutions, +but to discover men. You may erect laboratories and endow them; you +may furnish them with all the appliances needed for inquiry; in so +doing you are but creating opportunity for the exercise of powers +which come from sources entirely beyond your reach. You cannot +create genius by bidding for it. In biblical language, it is the +gift of God; and the most you could do, were your wealth, and your +willingness to apply it, a million-fold what they are, would be to +make sure that this glorious plant shall have the freedom, light, +and warmth necessary for its development. We see from time to time +a noble tree dragged down by parasitic runners. These the gardener +can remove, though the vital force of the tree itself may lie +beyond him: and so, in many a case you men of wealth can liberate +genius from the hampering toils which the struggle for existence +often casts around it.</p> +<p>Drawn by your kindness, I have come here to give these lectures, +and now that my visit to America has <a name="Page_225" id= +"Page_225"></a><span class="pagenum">[Pg 225]</span>become almost a +thing of the past, I look back upon it as a memory without a single +stain. No lecturer was ever rewarded as I have been. From this +vantage-ground, however, let me remind you that the work of the +lecturer is not the highest work; that in science, the lecturer is +usually the distributor of intellectual wealth amassed by better +men. And though lecturing and teaching, in moderation, will in +general promote their moral health, it is not solely or even +chiefly, as lecturers, but as investigators, that your highest men +ought to be employed. You have scientific genius amongst +you—not sown broadcast, believe me, it is sown thus +nowhere—but still scattered here and there. Take all +unnecessary impediments out of its way. Keep your sympathetic eye +upon the originator of knowledge. Give him the freedom necessary +for his researches, not overloading him, either with the duties of +tuition or of administration, nor demanding from him so-called +practical results—above all things, avoiding that question +which ignorance so often addresses to genius: 'What is the use of +your work?' Let him make truth his object, however unpractical for +the time being it may appear. If you cast your bread thus upon the +waters, be assured it will return to you, though it be after many +days.</p> +<div><a name="Page_226" id="Page_226"></a><span class="pagenum">[Pg +226]</span></div> +<hr style="width: 65%;" /> +<div><a name="Page_227" id="Page_227"></a><span class="pagenum">[Pg +227]</span></div> +<h2><a name="APPENDIX" id="APPENDIX"></a>APPENDIX.</h2> +<h3><a name="ON_THE_SPECTRA_OF_POLARIZED_LIGHT" id= +"ON_THE_SPECTRA_OF_POLARIZED_LIGHT"></a>ON THE SPECTRA OF POLARIZED +LIGHT.</h3> +<p>Mr. William Spottiswoode introduced some years ago to the +members of the Royal Institution, in a very striking form, a series +of experiments on the spectra of polarized light. With his large +Nicol prisms he in the first place repeated and explained the +experiments of Foucault and Fizeau, and subsequently enriched the +subject by very beautiful additions of his own. I here append a +portion of the abstract of his discourse:—</p> +<div class="blockquot"> +<p>'It is well known that if a plate of selenite sufficiently thin +be placed between two Nicol's prisms, or, more technically +speaking, between a polarizer and analyzer, colour will be +produced. And the question proposed is, What is the nature of that +colour? is it simply a pure colour of the spectrum, or is it a +compound, and if so, what are its component parts? The answer given +by the wave theory is in brief this: In its passage through the +selenite plate the rays have been so separated in the direction of +their vibrations and in the velocity of their transmission, that, +when re-compounded by means of the analyzer, they have in some +instances neutralized one another. If this be the case, the fact +ought to be visible when the beam emerging from the analyzer is +dispersed by the prism; for then we have the rays of all the +different colours ranged side by side, and, if any be wanting, +their <a name="Page_228" id="Page_228"></a><span class= +"pagenum">[Pg 228]</span>absence will be shown by the appearance of +a dark band in their place in the spectrum. But not only so; the +spectrum ought also to give an account of the other phenomena +exhibited by the selenite when the analyzer is turned round, viz. +that when the angle of turning amounts to 45°, all trace of +colour disappears; and also that when the angle amounts to 90°, +colour reappears, not, however, the original colour, but one +complementary to it.</p> +<p>'You see in the spectrum of the reddish light produced by the +selenite a broad but dark band in the blue; when the analyzer is +turned round the band becomes less and less dark, until when the +angle of turning amounts to 45° it has entirely disappeared. At +this stage each part of the spectrum has its own proportional +intensity, and the whole produces the colourless image seen without +the spectroscope. Lastly, as the turning of the analyzer is +continued, a dark band appears in the red, the part of the spectrum +complementary to that occupied by the first band; and the darkness +is most complete when the turning amounts to 90°. Thus we have +from the spectroscope a complete account of what has taken place to +produce the original colour and its changes.</p> +<p>'It is further well known that the colour produced by a +selenite, or other crystal plate, is dependent upon the thickness +of the plate. And, in fact, if a series of plates be taken, giving +different colours, their spectra are found to show bands arranged +in different positions. The thinner plates show bands in the parts +of the spectrum nearest to the violet, where the waves are shorter, +and consequently give rise to redder colours; while the thicker +show bands nearer to the red, where the waves are longer and +consequently supply bluer tints.</p> +<p>'When the thickness of the plate is continually increased, so +that the colour produced has gone through the complete cycle of the +spectrum, a further increase of thickness causes a reproduction of +the colours in the same order; but it will be noticed that at each +recurrence of the cycle the tints <a name="Page_229" id= +"Page_229"></a><span class="pagenum">[Pg 229]</span>become paler, +until when a number of cycles have been performed, and the +thickness of the plate is considerable, all trace of colour is +lost. Let us now take a series of plates, the first two of which, +as you see, give colours; with the others which are successively of +greater thickness the tints are so feeble that they can scarcely be +distinguished. The spectrum of the first shows a single band; that +of the second, two; showing that the second series of tints is not +identical with the first, but that it is produced by the extinction +of two colours from the components of white light. The spectra of +the others show series of bands more and more numerous in +proportion to the thickness of the plate, an array which may be +increased indefinitely. The total light, then, of which the +spectrum is deprived by the thicker plates is taken from a greater +number of its parts; or, in other words, the light which still +remains is distributed more and more evenly over the spectrum; and +in the same proportion the sum total of it approaches more and more +nearly to white light.</p> +<p>'These experiments were made more than thirty years ago by the +French philosophers, MM. Foucault and Fizeau.</p> +<p>'If instead of selenite, Iceland spar, or other ordinary +crystals, we use plates of quartz cut perpendicularly to the axis, +and turn the analyzer round as before, the light, instead of +exhibiting only one colour and its complementary with an +intermediate stage in which colour is absent, changes continuously +in tint; and the order of the colour depends partly upon the +direction in which the analyzer is turned, and partly upon the +character of the crystal, <i>i.e.</i> whether it is right-handed or +left-handed. If we examine the spectrum in this case we find that +the dark band never disappears, but marches from one end of the +spectrum to another, or <i>vice versâ</i>, precisely in such +a direction as to give rise to the tints seen by direct +projection.</p> +<p>'The kind of polarization effected by the quartz plates is +called circular, while that effected by the other class of <a name= +"Page_230" id="Page_230"></a><span class="pagenum">[Pg +230]</span>crystals is called plane, on account of the form of the +vibrations executed by the molecules of æther; and this leads +us to examine a little more closely the nature of the polarization +of different parts of these spectra of polarized light.</p> +<p>'Now, two things are clear: first, that if the light be +plane-polarized—that is, if all the vibrations throughout the +entire ray are rectilinear and in one plane—they must in all +their bearings have reference to a particular direction in space, +so that they will be differently affected by different positions of +the analyzer. Secondly, that if the vibrations be circular, they +will be affected in precisely the same way (whatever that may be) +in all positions of the analyzer. This statement merely +recapitulates a fundamental point in polarization. In fact, +plane-polarized light is alternately transmitted and extinguished +by the analyzer as it is turned through 90°; while circularly +polarized light [if we could get a single ray] remains to all +appearance unchanged. And if we examine carefully the spectrum of +light which has passed through a selenite, or other ordinary +crystal, we shall find that, commencing with two consecutive bands +in position, the parts occupied by the bands and those midway +between them are plane-polarized, for they become alternately dark +and bright; while the intermediate parts, <i>i.e.</i> the parts at +one-fourth of the distance from one band to the next, remain +permanently bright. These are, in fact, circularly polarized. But +it would be incorrect to conclude from this experiment alone that +such is really the case, because the same appearance would be seen +if those parts were unpolarized, <i>i.e.</i> in the condition of +ordinary lights. And on such a supposition we should conclude with +equal justice that the parts on either side of the parts last +mentioned (e.g. the parts separated by eighth parts of the interval +between two bands) were partially polarized. But there is an +instrument of very simple construction, called a +"quarter-undulation plate," a plate usually of mica, whose +thickness is an odd multiple of a quarter of a wave-length, which +enables us to discriminate between light unpolarized <a name= +"Page_231" id="Page_231"></a><span class="pagenum">[Pg +231]</span>and circularly polarized. The exact mechanical effect +produced upon the ray could hardly be explained in detail within +our present limits of time; but suffice it for the present to say +that, when placed in a proper position, the plate transforms plane +into circular and circular into plane polarization. That being so, +the parts which were originally banded ought to remain bright, and +those which originally remained bright ought to become banded +during the rotation of the analyzer. The general effect to the eye +will consequently be a general shifting of the bands through +one-fourth of the space which separates each pair.</p> +<p>'Circular polarization, like circular motion generally, may of +course be of two kinds, which differ only in the direction of the +motion. And, in fact, to convert the circular polarization produced +by this plate from one of these kinds to the other (say from +right-handed to left-handed, or <i>vice versâ</i>), we have +only to turn the plate round through 90°. Conversely, +right-handed circular polarization will be changed by the plate +into plane-polarization in one direction, while left-handed will be +changed into plane at right angles to the first. Hence if the plate +be turned round through 90° we shall see that the bands are +shifted in a direction opposite to that in which they were moved at +first. In this therefore we have evidence not only that the +polarization immediately on either side of a band is circular; but +also that that immediately on the one side is right-handed, while +that immediately on the other is left-handed<a name= +"FNanchor_28_28" id="FNanchor_28_28"></a><a href="#Footnote_28_28" +class="fnanchor">[28]</a>.</p> +<p>'If time permitted, I might enter still further into detail, and +show that the polarization between the plane and the circular is +elliptical, and even the positions of the longer and shorter axes +and the direction of motion in each case. But sufficient has, +perhaps, been said for our present purpose.</p> +<p><a name="Page_232" id="Page_232"></a><span class="pagenum">[Pg +232]</span>'Before proceeding to the more varied forms of spectral +bands, which I hope presently to bring under your notice, I should +like to ask your attention for a few minutes to the peculiar +phenomena exhibited when two plates of selenite giving +complementary colours are used. The appearance of the spectrum +varies with the relative position of the plates. If they are +similarly placed—that is, as if they were one plate of +crystal—they will behave as a single plate, whose thickness +is the sum of the thicknesses of each, and will produce double the +number of bands which one alone would give; and when the analyzer +is turned, the bands will disappear and re-appear in their +complementary positions, as usual in the case of +plane-polarization. If one of them be turned round through 45°, +a single band will be seen at a particular position in the +spectrum. This breaks into two, which recede from one another +towards the red and violet ends respectively, or advance towards +one another according to the direction in which the analyzer is +turned. If the plate be turned through 45° in the opposite +direction, the effects will be reversed. The darkness of the bands +is, however, not equally complete during their whole passage. +Lastly, if one of the plates be turned through 90°, no bands +will be seen, and the spectrum will be alternately bright and dark, +as if no plates were used, except only that the polarization is +itself turned through 90°.</p> +<p>'If a wedge-shaped crystal be used, the bands, instead of being +straight, will cross the spectrum diagonally, the direction of the +diagonal (dexter or sinister) being determined by the position of +the thicker end of the wedge. If two similar wedges be used with +their thickest ends together, they will act as a wedge whose angle +and whose thickness is double of the first. If they be placed in +the reverse position they will act as a flat plate, and the bands +will again cross the spectrum in straight lines at right angles to +its length.</p> +<p>'If a concave plate be used the bands will dispose themselves in +a fanlike arrangement, their divergence depending upon the distance +of the slit from the centre of concavity.</p> +<p><a name="Page_233" id="Page_233"></a><span class="pagenum">[Pg +233]</span>'If two quartz wedges, one of which has the optic axis +parallel to the edge of the refractory angle, and the other +perpendicular to it, but in one of the planes containing the angle +(Babinet's Compensator), the appearances of the bands are very +various.</p> +<p>'The diagonal bands, besides sometimes doubling themselves as +with ordinary wedges, sometimes combine so as to form longitudinal +(instead of transverse) bands; and sometimes cross one another so +as to form a diaper pattern with bright compartments in a dark +framework, and <i>vice versâ</i>, according to the position +of the plates.</p> +<p>'The effects of different dispositions of the interposed +crystals might be varied indefinitely; but enough has perhaps been +said to show the delicacy of the method of spectrum analysis as +applied to the examination of polarized light.'</p> +</div> +<hr style='width: 45%;' /> +<p>The singular and beautiful effect obtained with a circular plate +of selenite, thin at the centre, and gradually thickening towards +the circumference, is easily connected with a similar effect +obtained with Newton's rings. Let a thin slice of light fall upon +the glasses which show the rings, so as to cover a narrow central +vertical zone passing through them all. The image of this zone upon +the screen is crossed by portions of the iris-rings. Subjecting the +reflected beam to prismatic analysis, the resultant spectrum may be +regarded as an indefinite number of images of the zone placed side +by side. In the image before dispersion we have <i>iris-rings</i>, +the extinction of the light being nowhere complete; but when the +different colours are separated by dispersion, each colour is +crossed transversely by its own system of dark interference bands, +which become gradually closer with the increasing refrangibility of +the light. The complete spectrum, <a name="Page_234" id= +"Page_234"></a><span class="pagenum">[Pg 234]</span>therefore, +appears furrowed by a system of continuous dark bands, crossing the +colours transversely, and approaching each other as they pass from +red to blue.</p> +<p>In the case of the plate of selenite, a slit is placed in front +of the polarizer, and the film of selenite is held close to the +slit, so that the light passes through the central zone of the +film. As in the case of Newton's rings, the image of the zone is +crossed by iris-coloured bands; but when subjected to prismatic +dispersion, the light of the zone yields a spectrum furrowed by +bands of complete darkness exactly as in the case of Newton's rings +and for a similar reason. This is the beautiful effect described by +Mr. Spottiswoode as the fanlike arrangement of the bands—the +fan opening out at the red end of the spectrum.</p> +<hr style='width: 45%;' /> +<h3><a name="MEASUREMENT_OF_THE_WAVES_OF_LIGHT" id= +"MEASUREMENT_OF_THE_WAVES_OF_LIGHT"></a><i>MEASUREMENT OF THE WAVES +OF LIGHT.</i></h3> +<p>The diffraction fringes described in Lecture II., instead of +being formed on the retina, may be formed on a screen, or upon +ground glass, when they can be looked at through a magnifying lens +from behind, or they can be observed in the air when the ground +glass is removed. Instead of permitting them to form on the retina, +we will suppose them formed on a screen. This places us in a +condition to understand, even without trigonometry, the solution of +the important problem of measuring <i>the length</i> of a wave of +light.</p> +<div class="figright" style="width: 313px;"><img src= +"images/fig57.jpg" width="313" height="196" alt="Fig. 57." title= +"" /> <b>Fig. 57.</b></div> +<p>We will suppose the screen so distant that the rays falling upon +it from the two margins of the slit are sensibly parallel. We have +learned in Lecture II. that the first of the dark bands corresponds +to a difference of marginal path of one undulation; the second dark +band to a difference of path of two undulations; the third dark +band to a differ<a name="Page_235" id="Page_235"></a><span class= +"pagenum">[Pg 235]</span>ence of three undulations, and so on. Now +the angular distance of the bands from the centre is capable of +exact measurement; this distance depending, as already stated, on +the width of the slit. With a slit 1.35 millimeter wide,<a name= +"FNanchor_29_29" id="FNanchor_29_29"></a><a href="#Footnote_29_29" +class="fnanchor">[29]</a> Schwerd found the angular distance of the +first dark band from the centre of the field to be 1'38"; the +angular distances of the second, third, fourth dark bands being +twice, three times, four times this quantity.</p> +<p>Let A B, fig. 57, be the plate in which the slit is cut, and C D +the grossly exaggerated width of the slit, with the beam of red +light proceeding from it at the obliquity corresponding to the +first dark band. Let fall a perpendicular from one edge, D, of the +slit on the marginal ray of the other edge at <i>d</i>. The +distance, C <i>d</i>, between the foot of this perpendicular and +the other edge is the length of a wave of the light. The angle C D +<i>d</i>, moreover, being equal to R C R', is, in the case now +under consideration, 1'38". From the centre D, with the width D C +as radius, describe a semicircle; its radius D C being 1.35 +millimeter, the length of this semicircle is found by an easy +calculation to be 4.248 millimeters. The length C <i>d</i> is so +small that it sensibly coincides with the arc of the circle. Hence +the length of the semicircle is to the length C <i>d</i> of the +wave as 180° to <a name="Page_236" id= +"Page_236"></a><span class="pagenum">[Pg 236]</span>1'38", or, +reducing all to seconds, as 648,000" to 98". Thus, we have the +proportion—</p> +<div class="blockquot"> +<p>648,000 : 98 :: 4.248 to the wave-length C <i>d</i>.</p> +</div> +<p>Making the calculation, we find the wave-length for this +particular kind of light to be 0.000643 of a millimeter, or +0.000026 of an inch.</p> +<div class="footnotes"> +<p class="center">FOOTNOTES:</p> +<div class="footnote"> +<p><a name="Footnote_1_1" id="Footnote_1_1"></a><a href= +"#FNanchor_1_1"><span class="label">[1]</span></a> Among whom may +be especially mentioned the late Sir Edmund Head, Bart., with whom +I had many conversations on this subject.</p> +</div> +<div class="footnote"> +<p><a name="Footnote_2_2" id="Footnote_2_2"></a><a href= +"#FNanchor_2_2"><span class="label">[2]</span></a> At whose hands +it gives me pleasure to state I have always experienced honourable +and liberal treatment.</p> +</div> +<div class="footnote"> +<p><a name="Footnote_3_3" id="Footnote_3_3"></a><a href= +"#FNanchor_3_3"><span class="label">[3]</span></a> One of the +earliest of these came from Mr. John Amory Lowell of Boston.</p> +</div> +<div class="footnote"> +<p><a name="Footnote_4_4" id="Footnote_4_4"></a><a href= +"#FNanchor_4_4"><span class="label">[4]</span></a> It will be +subsequently shown how this simple apparatus may be employed to +determine the 'polarizing angle' of a liquid.</p> +</div> +<div class="footnote"> +<p><a name="Footnote_5_5" id="Footnote_5_5"></a><a href= +"#FNanchor_5_5"><span class="label">[5]</span></a> From this +principle Sir John Herschel deduces in a simple and elegant manner +the fundamental law of reflection.—See <i>Familiar +Lectures</i>, p. 236.</p> +</div> +<div class="footnote"> +<p><a name="Footnote_6_6" id="Footnote_6_6"></a><a href= +"#FNanchor_6_6"><span class="label">[6]</span></a> The low +dispersive power of water masks, as Helmholtz has remarked, the +imperfect achromatism of the eye. With the naked eye I can see a +distant blue disk sharply defined, but not a red one. I can also +see the lines which mark the upper and lower boundaries of a +horizontally refracted spectrum sharp at the blue end, but +ill-defined at the red end. Projecting a luminous disk upon a +screen, and covering one semicircle of the aperture with a red and +the other with a blue or green glass, the difference between the +apparent sizes of the two semicircles is in my case, and in +numerous other cases, extraordinary. Many persons, however, see the +apparent sizes of the two semicircles reversed. If with a spectacle +glass I correct the dispersion of the red light over the retina, +then the blue ceases to give a sharply defined image. Thus +examined, the departure of the eye from achromatism appears very +gross indeed.</p> +</div> +<div class="footnote"> +<p><a name="Footnote_7_7" id="Footnote_7_7"></a><a href= +"#FNanchor_7_7"><span class="label">[7]</span></a> Both in foliage +and in flowers there are striking differences of absorption. The +copper beech and the green beech, for example, take in different +rays. But the very growth of the tree is due to some of the rays +thus taken in. Are the chemical rays, then, the same in the copper +and the green beech? In two such flowers as the primrose and the +violet, where the absorptions, to judge by the colours, are almost +complementary, are the chemically active rays the same? The general +relation of colour to chemical action is worthy of the application +of the method by which Dr. Draper proved so conclusively the +chemical potency of the yellow rays of the sun.</p> +</div> +<div class="footnote"> +<p><a name="Footnote_8_8" id="Footnote_8_8"></a><a href= +"#FNanchor_8_8"><span class="label">[8]</span></a> Young, +Helmholtz, and Maxwell reduce all differences of hue to +combinations in different proportions of three primary colours. It +is demonstrable by experiment that from the red, green, and violet +<i>all</i> the other colours of the spectrum may be obtained.</p> +<p>Some years ago Sir Charles Wheatstone drew my attention to a +work by Christian Ernst Wünsch, Leipzig 1792, in which the +author announces the proposition that there are neither five nor +seven, but only three simple colours in white light. Wünsch +produced five spectra, with five prisms and five small apertures, +and he mixed the colours first in pairs, and afterwards in other +ways and proportions. His result is that red is a <i>simple</i> +colour incapable of being decomposed; that orange is compounded of +intense red and weak green; that yellow is a mixture of intense red +and intense green; that green is a <i>simple</i> colour; that blue +is compounded of saturated green and saturated violet; that indigo +is a mixture of saturated violet and weak green; while violet is a +pure <i>simple</i> colour. He also finds that yellow and indigo +blue produce <i>white</i> by their mixture. Yellow mixed with +bright blue (Hochblau) also produces white, which seems, however, +to have a tinge of green, while the pigments of these two colours +when mixed always give a more or less beautiful green, Wünsch +very emphatically distinguishes the mixture of pigments from that +of lights. Speaking of the generation of yellow, he says, 'I say +expressly <i>red and green light</i>, because I am speaking about +light-colours (Lichtfarben), and not about pigments.' However +faulty his theories may be, Wünsch's experiments appear in the +main to be precise and conclusive. Nearly ten years subsequently, +Young adopted red, green, and violet as the three primary colours, +each of them capable of producing three sensations, one of which, +however, predominates over the two others. Helmholtz adopts, +elucidates, and enriches this notion. (<i>Popular Lectures</i>, p. +249. The paper of Helmholtz on the mixture of colours, translated +by myself, is published in the <i>Philosophical Magazine</i> for +1852. Maxwell's memoir on the Theory of Compound Colours is +published in the <i>Philosophical Transactions</i>, vol. 150, p. +67.)</p> +</div> +<div class="footnote"> +<p><a name="Footnote_9_9" id="Footnote_9_9"></a><a href= +"#FNanchor_9_9"><span class="label">[9]</span></a> The following +charming extract, bearing upon this point, was discovered and +written out for me by my deeply lamented friend Dr. Bence Jones, +when Hon. Secretary to the Royal Institution:—</p> +<div class="blockquot"> +<p>'In every kind of magnitude there is a degree or sort to which +our sense is proportioned, the perception and knowledge of which is +of the greatest use to mankind. The same is the groundwork of +philosophy; for, though all sorts and degrees are equally the +object of philosophical speculation, yet it is from those which are +proportioned to sense that a philosopher must set out in his +inquiries, ascending or descending afterwards as his pursuits may +require. He does well indeed to take his views from many points of +sight, and supply the defects of sense by a well-regulated +imagination; nor is he to be confined by any limit in space or +time; but, as his knowledge of Nature is founded on the observation +of sensible things, he must begin with these, and must often return +to them to examine his progress by them. Here is his secure hold: +and as he sets out from thence, so if he likewise trace not often +his steps backwards with caution, he will be in hazard of losing +his way in the labyrinths of Nature.'—(<i>Maclaurin: An +Account of Sir I. Newton's Philosophical Discoveries. Written 1728; +second edition</i>, 1750; pp. 18, 19.)</p> +</div> +</div> +<div class="footnote"> +<p><a name="Footnote_10_10" id="Footnote_10_10"></a><a href= +"#FNanchor_10_10"><span class="label">[10]</span></a> I do not wish +to encumber the conception here with the details of the motion, but +I may draw attention to the beautiful model of Prof. Lyman, wherein +waves are shown to be produced by the <i>circular</i> motion of the +particles. This, as proved by the brothers Weber, is the real +motion in the case of water-waves.</p> +</div> +<div class="footnote"> +<p><a name="Footnote_11_11" id="Footnote_11_11"></a><a href= +"#FNanchor_11_11"><span class="label">[11]</span></a> Copied from +Weber's <i>Wellenlehre</i>.</p> +</div> +<div class="footnote"> +<p><a name="Footnote_12_12" id="Footnote_12_12"></a><a href= +"#FNanchor_12_12"><span class="label">[12]</span></a> See +<i>Lectures on Sound</i>, 1st and 2nd ed., Lecture VII.; and 3rd +ed., Chap. VIII. Longmans.</p> +</div> +<div class="footnote"> +<p><a name="Footnote_13_13" id="Footnote_13_13"></a><a href= +"#FNanchor_13_13"><span class="label">[13]</span></a> <i>Boyle's +Works</i>, Birch's edition, p. 675.</p> +</div> +<div class="footnote"> +<p><a name="Footnote_14_14" id="Footnote_14_14"></a><a href= +"#FNanchor_14_14"><span class="label">[14]</span></a> Page 743.</p> +</div> +<div class="footnote"> +<p><a name="Footnote_15_15" id="Footnote_15_15"></a><a href= +"#FNanchor_15_15"><span class="label">[15]</span></a> The beautiful +plumes produced by water-crystallization have been successfully +photographed by Professor Lockett.</p> +</div> +<div class="footnote"> +<p><a name="Footnote_16_16" id="Footnote_16_16"></a><a href= +"#FNanchor_16_16"><span class="label">[16]</span></a> In a little +volume entitled 'Forms of Water,' I have mentioned that cold iron +floats upon molten iron. In company with my friend Sir William +Armstrong, I had repeated opportunities of witnessing this fact in +his works at Elswick, 1863. Faraday, I remember, spoke to me +subsequently of the perfection of iron castings as probably due to +the swelling of the metal on solidification. Beyond this, I have +given the subject no special attention; and I know that many +intelligent iron-founders doubt the fact of expansion. It is quite +possible that the solid floats because it is not <i>wetted</i> by +the molten iron, its volume being virtually augmented by capillary +repulsion. Certain flies walk freely upon water in virtue of an +action of this kind. With bismuth, however, it is easy to burst +iron bottles by the force of solidification.</p> +</div> +<div class="footnote"> +<p><a name="Footnote_17_17" id="Footnote_17_17"></a><a href= +"#FNanchor_17_17"><span class="label">[17]</span></a> This +beautiful law is usually thus expressed: <i>The index of refraction +of any substance is the tangent of its polarizing angle</i>. With +the aid of this law and an apparatus similar to that figured at +page 15, we can readily determine the index of refraction of any +liquid. The refracted and reflected beams being visible, they can +readily be caused to inclose a right angle. The polarizing angle of +the liquid may be thus found with the sharpest precision. It is +then only necessary to seek out its natural tangent to obtain the +index of refraction.</p> +</div> +<div class="footnote"> +<p><a name="Footnote_18_18" id="Footnote_18_18"></a><a href= +"#FNanchor_18_18"><span class="label">[18]</span></a> Whewell.</p> +</div> +<div class="footnote"> +<p><a name="Footnote_19_19" id="Footnote_19_19"></a><a href= +"#FNanchor_19_19"><span class="label">[19]</span></a> Removed from +us since these words were written.</p> +</div> +<div class="footnote"> +<p><a name="Footnote_20_20" id="Footnote_20_20"></a><a href= +"#FNanchor_20_20"><span class="label">[20]</span></a> The only +essay known to me on the Undulatory Theory, from the pen of an +American writer, is an excellent one by President Barnard, +published in the Smithsonian Report for 1862.</p> +</div> +<div class="footnote"> +<p><a name="Footnote_21_21" id="Footnote_21_21"></a><a href= +"#FNanchor_21_21"><span class="label">[21]</span></a> <i>Boyle's +Works</i>, Birch's edition, vol. i. pp, 729 and 730.</p> +</div> +<div class="footnote"> +<p><a name="Footnote_22_22" id="Footnote_22_22"></a><a href= +"#FNanchor_22_22"><span class="label">[22]</span></a> <i>Werke</i>, +B. xxix. p. 24.</p> +</div> +<div class="footnote"> +<p><a name="Footnote_23_23" id="Footnote_23_23"></a><a href= +"#FNanchor_23_23"><span class="label">[23]</span></a> Defined in +Lecture I.</p> +</div> +<div class="footnote"> +<p><a name="Footnote_24_24" id="Footnote_24_24"></a><a href= +"#FNanchor_24_24"><span class="label">[24]</span></a> This +circumstance ought not to be lost sight of in the examination of +compound spectra. Other similar instances might be cited.</p> +</div> +<div class="footnote"> +<p><a name="Footnote_25_25" id="Footnote_25_25"></a><a href= +"#FNanchor_25_25"><span class="label">[25]</span></a> The dark band +produced when the sodium is placed within the lamp was observed on +the same occasion. Then was also observed for the first time the +magnificent blue band of lithium which the Bunsen's flame fails to +bring out.</p> +</div> +<div class="footnote"> +<p><a name="Footnote_26_26" id="Footnote_26_26"></a><a href= +"#FNanchor_26_26"><span class="label">[26]</span></a> New York: for +more than a decade no such weather had been experienced. The snow +was so deep that the ordinary means of locomotion were for a time +suspended.</p> +</div> +<div class="footnote"> +<p><a name="Footnote_27_27" id="Footnote_27_27"></a><a href= +"#FNanchor_27_27"><span class="label">[27]</span></a> 'Il faut +reconnaître que parmi les peuples civilisés de nos +jours il en est pen chez qui les hautes sciences aient fait moins +de progrès qu'aux États-Unis, ou qui aient fourni +moins de grands artistes, de poëtes illustres et de +célèbres écrivains.' (<i>De la +Démocratie en Amérique</i>, etc. tome ii. p. 36.)</p> +</div> +<div class="footnote"> +<p><a name="Footnote_28_28" id="Footnote_28_28"></a><a href= +"#FNanchor_28_28"><span class="label">[28]</span></a> At these +points the two rectangular vibrations into which the original +polarized ray is resolved by the plates of gypsum, act upon each +other like the two rectangular impulses imparted to our pendulum in +Lecture IV., one being given when the pendulum is at the limit of +its swing. Vibration is thus converted into rotation.</p> +</div> +<div class="footnote"> +<p><a name="Footnote_29_29" id="Footnote_29_29"></a><a href= +"#FNanchor_29_29"><span class="label">[29]</span></a> The +millimeter is about 1/25th of an inch.</p> +</div> +</div> +<hr style="width: 65%;" /> +<div><a name="Page_237" id="Page_237"></a><span class="pagenum">[Pg +237]</span></div> +<h2><a name="INDEX" id="INDEX"></a>INDEX.</h2> +<div>Absorption, principles of, <a href="#Page_199">199</a><br /> +<br /> +Airy, Sir George, severity and conclusiveness of his proofs, +<a href="#Page_209">209</a><br /> +<br /> +Alhazen, his inquiry respecting light, <a href="#Page_14">14</a>, +<a href="#Page_207">207</a><br /> +<br /> +Analyzer, polarizer and, <a href="#Page_127">127</a><br /> +——recompounding of the two systems of waves by the +analyzer, <a href="#Page_129">129</a><br /> +<br /> +Ångström, his paper on spectrum analysis, <a href= +"#Page_202">202</a><br /> +<br /> +Arago, François, and Dr. Young, <a href= +"#Page_50">50</a><br /> +——his discoveries respecting light, <a href= +"#Page_208">208</a><br /> +<br /> +Atomic polarity, <a href="#Page_93">93-96</a><br /> +<br /> +Bacon, Roger, his inquiry respecting light, <a href= +"#Page_14">14</a>, <a href="#Page_207">207</a><br /> +<br /> +Bartholinus, Erasmus, on Iceland spar, <a href= +"#Page_112">112</a><br /> +<br /> +Bérard on polarization of heat, <a href= +"#Page_180">180</a><br /> +<br /> +Blackness, meaning of, <a href="#Page_32">32</a><br /> +<br /> +Boyle, Robert, his observations on colours, <a href= +"#Page_65">65</a>, <a href="#Page_66">66</a><br /> +——his remarks on fluorescence, <a href= +"#Page_163">163</a>, <a href="#Page_164">164</a><br /> +<br /> +Bradley, James, discovers the aberration of light, <a href= +"#Page_21">21</a>, <a href="#Page_22">22</a><br /> +<br /> +Brewster, Sir David, his chief objection to the undulatory theory +of light, <a href="#Page_47">47</a><br /> +<br /> +Brewster, Sir David, his discovery in biaxal crystals, <a href= +"#Page_209">209</a><br /> +<br /> +Brougham, Mr. (afterwards Lord), ridicules Dr. T. Young's +speculations, <a href="#Page_50">50</a>, <a href= +"#Page_51">51</a><br /> +<br /> +Cæsium, discovery of, <a href="#Page_193">193</a><br /> +<br /> +Calorescence, <a href="#Page_174">174</a><br /> +<br /> +Clouds, actinic, <a href="#Page_152">152-154</a><br /> +——polarization of, <a href="#Page_155">155</a><br /> +<br /> +Colours of thin plates, <a href="#Page_64">64</a><br /> +——Boyle's observations on, <a href="#Page_65">65</a>, +<a href="#Page_66">66</a><br /> +——Hooke on the colours of thin plates, <a href= +"#Page_67">67</a><br /> +——of striated surfaces, <a href="#Page_89">89</a>, +<a href="#Page_90">90</a><br /> +<br /> +Comet of 1680, Newton's estimate of the temperature of, <a href= +"#Page_168">168</a><br /> +<br /> +Crookes, Mr., his discovery of thallium, <a href= +"#Page_193">193</a><br /> +<br /> +Crystals, action of, upon light, <a href="#Page_98">98</a><br /> +——built by polar force, <a href="#Page_98">98</a><br /> +——illustrations of crystallization, <a href= +"#Page_99">99</a><br /> +——architecture of, considered as an introduction to +their action upon light, <a href="#Page_98">98</a><br /> +——bearings of crystallization upon optical phenomena, +<a href="#Page_106">106</a><br /> +<br /> +Crystals, rings surrounding the axes of, uniaxal and biaxal, +<a href="#Page_145">145</a><br /> +<br /> +Cuvier on ardour for knowledge, <a href="#Page_220">220</a><br /> +<br /> +De Tocqueville, writings of, <a href="#Page_215">215</a>, <a href= +"#Page_222">222</a>, <a href="#Page_223">223</a><br /> +<a name="Page_238" id="Page_238"></a><span class="pagenum">[Pg +238]</span><br /> +Descartes, his explanation of the rainbow, <a href= +"#Page_24">24</a>, <a href="#Page_25">25</a><br /> +——his ideas respecting the transmission of light, +<a href="#Page_43">43</a><br /> +——his notion of light, <a href= +"#Page_207">207</a><br /> +<br /> +Diamond, ignition of a, in oxygen, <a href= +"#Page_169">169</a><br /> +<br /> +Diathermancy, <a href="#Page_173">173</a><br /> +<br /> +Diffraction of light, phenomena of, <a href="#Page_78">78</a><br /> +——bands, <a href="#Page_78">78</a>, <a href= +"#Page_79">79</a><br /> +——explanation of, <a href="#Page_80">80</a><br /> +——colours produced by, <a href="#Page_89">89</a><br /> +<br /> +Dollond, his experiments on achromatism, <a href= +"#Page_28">28</a><br /> +<br /> +Draper, Dr., his investigation on heat, <a href= +"#Page_172">172</a><br /> +<br /> +Drummond light, spectrum of, <a href="#Page_195">195</a><br /> +<br /> +<br /> +Earth, daily orbit of, <a href="#Page_74">74</a><br /> +<br /> +Electric beam, heat of the, <a href="#Page_168">168</a><br /> +<br /> +Electricity, discoveries in, <a href="#Page_217">217</a>, <a href= +"#Page_218">218</a><br /> +<br /> +Emission theory of light, bases of the, <a href= +"#Page_45">45</a><br /> +——Newton espouses the theory, and the results of this +espousal, <a href="#Page_77">77</a><br /> +<br /> +Ether, Huyghens and Euler advocate and defend the conception of an, +<a href="#Page_48">48</a>, <a href="#Page_58">58</a><br /> +——objected to by Newton, <a href= +"#Page_58">58</a><br /> +<br /> +Euler espouses and defends the conception of an ether, <a href= +"#Page_48">48</a>, <a href="#Page_58">58</a><br /> +<br /> +Eusebius on the natural philosophers of his time, <a href= +"#Page_13">13</a><br /> +<br /> +Expansion by cold, <a href="#Page_104">104</a><br /> +<br /> +Experiment, uses of, <a href="#Page_3">3</a><br /> +<br /> +Eye, the, its imperfections, grown for ages towards perfection, +<a href="#Page_8">8</a><br /> +——imperfect achromatism of the, <a href= +"#Page_29">29</a>, <a href="#Footnote_6_6"><i>note</i></a><br /> +<br /> +<br /> +Faraday, Michael, his discovery of magneto-electricity, <a href= +"#Page_218">218</a><br /> +<br /> +'Fits,' theory of, <a href="#Page_73">73</a><br /> +——its explanation of Newton's rings, <a href= +"#Page_74">74</a><br /> +——overthrow of the theory, <a href= +"#Page_77">77</a><br /> +<br /> +Fizeau determines the velocity of light, <a href= +"#Page_22">22</a><br /> +<br /> +Fluorescence, Stokes's discovery of, <a href= +"#Page_161">161</a><br /> +——the name, <a href="#Page_174">174</a><br /> +<br /> +Forbes, Professor, polarizes and depolarizes heat, <a href= +"#Page_180">180</a><br /> +<br /> +Foucault, determines the velocity of light, <a href= +"#Page_22">22</a><br /> +——his experiments on absorption, <a href= +"#Page_197">197</a>, <a href="#Page_198">198</a><br /> +<br /> +Fraunhofer, his theoretical calculations respecting diffraction, +<a href="#Page_87">87</a><br /> +——his lines, <a href="#Page_193">193</a><br /> +———their explanation by Kirchhoff, <a href= +"#Page_193">193</a><br /> +<br /> +Fresnel, and Dr. Young, <a href="#Page_50">50</a><br /> +——his theoretical calculations respecting diffraction, +<a href="#Page_87">87</a><br /> +——his mathematical abilities and immortal name, +<a href="#Page_210">210</a><br /> +<br /> +<br /> +Goethe on fluorescence, <a href="#Page_165">165</a><br /> +<br /> +Gravitation, origin of the notion of the attraction of, <a href= +"#Page_92">92</a><br /> +——strength of the theory of, <a href= +"#Page_148">148</a><br /> +<br /> +Grimaldi, his discovery with respect to light, <a href= +"#Page_56">56</a><br /> +<a name="Page_239" id="Page_239"></a><span class="pagenum">[Pg +239]</span> ——Young's generalizations of, <a href= +"#Page_56">56</a><br /> +<br /> +<br /> +Hamilton, Sir William, of Dublin, his discovery of conical +refraction, <a href="#Page_209">209</a><br /> +<br /> +Heat, generation of, <a href="#Page_6">6</a><br /> +——Dr. Draper's investigation respecting, <a href= +"#Page_171">171</a><br /> +<br /> +Helmholtz, his estimate of the genius of Young, <a href= +"#Page_50">50</a><br /> +——on the imperfect achromatism of the eye, <a href= +"#Page_29">29</a>, <a href="#Footnote_6_6"><i>note</i></a>, +<a href="#Page_31">31</a><br /> +——reveals the cause of green in the case of pigments, +<a href="#Page_37">37</a><br /> +<br /> +Henry, Professor Joseph, his invitation, <a href= +"#Page_2">2</a><br /> +<br /> +Herschel, Sir John, his theoretical calculations respecting +diffraction, <a href="#Page_87">87</a><br /> +——first notices and describes the fluorescence of +sulphate of quinine, <a href="#Page_165">165</a><br /> +——his experiments on spectra, <a href= +"#Page_201">201</a><br /> +<br /> +Herschel, Sir William, his experiments on the heat of the various +colours of the solar spectrum, <a href="#Page_171">171</a><br /> +<br /> +Hooke, Robert, on the colours of thin plates, <a href= +"#Page_67">67</a><br /> +——his remarks on the idea that light and heat are modes +of motion, <a href="#Page_68">68</a><br /> +<br /> +Horse-chestnut bark, fluorescence of, <a href= +"#Page_165">165</a><br /> +<br /> +Huggins, Dr., his labours, <a href="#Page_205">205</a><br /> +<br /> +Huyghens advocates the conception of ether, <a href= +"#Page_48">48</a>, <a href="#Page_58">58</a><br /> +——his celebrated principle, <a href= +"#Page_83">83</a><br /> +<br /> +Huyghens on the double refraction of Iceland spar, <a href= +"#Page_112">112</a><br /> +<br /> +<br /> +Iceland spar, <a href="#Page_109">109</a><br /> +——double refraction caused by, <a href= +"#Page_110">110</a><br /> +——this double refraction first treated by Erasmus +Bartholinus, <a href="#Page_112">112</a><br /> +——character of the beams emergent from, <a href= +"#Page_114">114</a><br /> +——tested by tourmaline, <a href= +"#Page_116">116</a><br /> +——Knoblauch's demonstration of the double refraction +of, <a href="#Page_185">185</a><br /> +<br /> +Ice-lens, combustion through, <a href="#Page_167">167</a><br /> +<br /> +Imagination, scope of the, <a href="#Page_42">42</a><br /> +——note by Maclaurin on this point, 43 <i>note</i><br /> +<br /> +<br /> +Janssen, M., on the rose-coloured solar prominences, <a href= +"#Page_204">204</a><br /> +<br /> +Jupiter, Roemer's observations of the moons of, <a href= +"#Page_20">20</a><br /> +<br /> +Jupiter's distance from the sun, <a href="#Page_20">20</a><br /> +<br /> +<br /> +Kepler, his investigations on the refraction of light, <a href= +"#Page_14">14</a>, <a href="#Page_207">207</a><br /> +<br /> +Kirchhoff, Professor, his explanation of Fraunhofer's lines, +<a href="#Page_193">193</a><br /> +——his precursors, <a href="#Page_201">201</a><br /> +——his claims, <a href="#Page_203">203</a><br /> +<br /> +Knoblauch, his demonstration of the double refraction of heat of +Iceland spar, <a href="#Page_185">185</a><br /> +<br /> +<br /> +Lactantius, on the natural philosophers of his time, <a href= +"#Page_13">13</a><br /> +<br /> +Lamy, M., isolates thallium in ingots, <a href= +"#Page_193">193</a><br /> +<a name="Page_240" id="Page_240"></a><span class="pagenum">[Pg +240]</span><br /> +Lesley, Professor, his invitation, <a href="#Page_2">2</a><br /> +<br /> +Light familiar to the ancients, <a href="#Page_5">5</a><br /> +——generation of, <a href="#Page_6">6</a>, <a href= +"#Page_7">7</a><br /> +——spherical aberration of, <a href= +"#Page_8">8</a><br /> +——the rectilineal propagation of, and mode of producing +it, <a href="#Page_9">9</a><br /> +——illustration showing that the angle of incidence is +equal to the angle of reflection, <a href="#Page_10">10</a>, +<a href="#Page_11">11</a><br /> +——sterility of the Middle Ages, <a href= +"#Page_13">13</a><br /> +——history of refraction, <a href= +"#Page_14">14</a><br /> +——demonstration of the fact of refraction, <a href= +"#Page_14">14</a><br /> +——partial and total reflection of, <a href= +"#Page_16">16-20</a><br /> +——velocity of, <a href="#Page_20">20</a><br /> +——Bradley's discovery of the aberration of light, +<a href="#Page_21">21</a>, <a href="#Page_22">22</a><br /> +——principle of least time, <a href= +"#Page_23">23</a><br /> +——Descartes and the rainbow, <a href= +"#Page_24">24</a><br /> +——Newton's analysis of, <a href="#Page_26">26</a>, +<a href="#Page_27">27</a><br /> +——synthesis of white light, <a href= +"#Page_30">30</a><br /> +——complementary colours, <a href= +"#Page_31">31</a><br /> +——yellow and blue lights produce white by their +mixture, <a href="#Page_31">31</a><br /> +——what is the meaning of blackness? <a href= +"#Page_32">32</a><br /> +——analysis of the action of pigments upon, <a href= +"#Page_33">33</a><br /> +——absorption, <a href="#Page_34">34</a><br /> +——mixture of pigments contrasted with mixture of +lights, <a href="#Page_37">37</a><br /> +——Wünsch on three simple colours in white light, +<a href="#Page_39">39</a> <a href= +"#Footnote_8_8"><i>note</i></a><br /> +——Newton arrives at the emission theory, <a href= +"#Page_45">45</a><br /> +——Young's discovery of the undulatory theory, <a href= +"#Page_49">49</a><br /> +——illustrations of wave-motion, <a href= +"#Page_58">58</a><br /> +——interference of sound-waves, <a href= +"#Page_58">58</a><br /> +——velocity of, <a href="#Page_60">60</a><br /> +——principle of interference of waves of, <a href= +"#Page_61">61</a><br /> +——phenomena which first suggested the undulatory theory +<a href="#Page_62">62-69</a><br /> +——soap-bubbles and their colours, <a href= +"#Page_62">62-65</a><br /> +——Newton's rings, <a href="#Page_77">69-77</a><br /> +——his espousal of the emission theory, and the results +of this espousal, <a href="#Page_77">77</a><br /> +——transmitted light, <a href="#Page_77">77</a><br /> +——diffraction, <a href="#Page_77">77</a>, <a href= +"#Page_89">89</a><br /> +——origin of the notion of the attraction of +gravitation, <a href="#Page_92">92</a><br /> +——polarity, how generated, <a href= +"#Page_93">93</a><br /> +——action of crystals upon, <a href= +"#Page_98">98</a><br /> +——refraction of, <a href="#Page_106">106</a><br /> +——elasticity and density, <a href= +"#Page_108">108</a><br /> +——double refraction, <a href="#Page_109">109</a><br /> +——chromatic phenomena produced by crystals in +polarized, <a href="#Page_121">121</a><br /> +——the Nicol prism, <a href="#Page_122">122</a><br /> +——mechanism of, <a href="#Page_125">125</a><br /> +——vibrations, <a href="#Page_125">125</a><br /> +——composition and resolution of vibrations, <a href= +"#Page_128">128</a><br /> +——polarizer and analyzer, <a href= +"#Page_127">127</a><br /> +——recompounding the two systems of waves by the +analyzer, <a href="#Page_129">129</a><br /> +——interference thus rendered possible, <a href= +"#Page_131">131</a><br /> +——chromatic phenomena produced by quartz, <a href= +"#Page_139">139</a><br /> +——magnetization, of, <a href="#Page_141">141</a><br /> +——rings surrounding the axes of crystals, <a href= +"#Page_143">143</a><br /> +——colour and polarization of sky, <a href= +"#Page_149">149</a>, <a href="#Page_154">154</a><br /> +——range of vision incommensurate with range of +radiation, <a href="#Page_159">159</a><br /> +——effect of thallene on the spectrum, 162<br /> +<a name="Page_241" id="Page_241"></a><span class="pagenum">[Pg +241]</span> ——fluorescence, <a href= +"#Page_162">162</a><br /> +——transparency, <a href="#Page_167">167</a><br /> +——the ultra-red rays, <a href="#Page_170">170</a><br /> +——part played in Nature by these rays, <a href= +"#Page_175">175</a><br /> +——conversion of heat-rays into light-rays, <a href= +"#Page_176">176</a><br /> +——identity of radiant heat and, <a href= +"#Page_177">177</a><br /> +——polarization of heat, <a href= +"#Page_180">180</a><br /> +——principles of spectrum analysis, <a href= +"#Page_189">189</a><br /> +——spectra of incandescent vapours, <a href= +"#Page_190">190</a><br /> +——Fraunhofer's lines, and Kirchhoff's explanation of +them, <a href="#Page_193">193</a><br /> +——solar chemistry, <a href= +"#Page_195">195-197</a><br /> +——demonstration of analogy between sound and, <a href= +"#Page_198">198</a>, <a href="#Page_199">199</a><br /> +——Kirchhoff and his precursors, <a href= +"#Page_201">201</a><br /> +——rose-coloured solar prominences, <a href= +"#Page_204">204</a><br /> +——results obtained by various workers, <a href= +"#Page_205">205</a><br /> +——summary and conclusion, <a href= +"#Page_206">206</a><br /> +——polarized, the spectra of, <a href= +"#Page_227">227</a><br /> +——measurement of the waves of, <a href= +"#Page_234">234</a><br /> +<br /> +Lignum Nephriticum, fluorescence of, <a href= +"#Page_164">164</a><br /> +<br /> +Lloyd, Dr., on polarization of heat, <a href="#Page_180">180</a>, +<a href="#Page_209">209</a><br /> +<br /> +Lockyer, Mr., on the rose-coloured solar prominences, <a href= +"#Page_205">205</a><br /> +<br /> +Lycopodium, diffraction effects caused by the spores of, <a href= +"#Page_88">88</a><br /> +<br /> +<br /> +Magnetization of light, <a href="#Page_141">141</a><br /> +<br /> +Malus, his discovery respecting reflected light through Iceland +spar, <a href="#Page_115">115</a><br /> +——discovers the polarization of light by reflection, +<a href="#Page_208">208</a><br /> +<br /> +Masson, his essay on the bands of the induction spark, <a href= +"#Page_202">202</a><br /> +<br /> +Melloni, on the polarization of heat, <a href= +"#Page_180">180</a><br /> +<br /> +Metals, combustion of, <a href="#Page_5">5</a>, <a href= +"#Page_6">6</a><br /> +——spectrum analysis of, <a href= +"#Page_190">190</a><br /> +——spectrum bands proved by Bunsen and Kirchhoff to be +characteristic of the vapour of, <a href="#Page_192">192</a><br /> +<br /> +Mill, John Stuart, his scepticism regarding the undulatory theory, +<a href="#Page_149">149</a><br /> +<br /> +Miller, Dr., his drawings and descriptions of the spectra of +various coloured flames, <a href="#Page_201">201</a><br /> +<br /> +Morton, Professor, his discovery of thallene, <a href= +"#Page_162">162</a><br /> +<br /> +Mother-of-pearl, colours of, <a href="#Page_90">90</a><br /> +<br /> +<br /> +Nature, a savage's interpretation of, <a href="#Page_4">4</a><br /> +<br /> +Newton, Sir Isaac, his experiments on the composition of solar +light, <a href="#Page_26">26</a><br /> +——his spectrum, <a href="#Page_27">27</a><br /> +——dispersion, <a href="#Page_27">27</a><br /> +——arrives at the emission theory of light, <a href= +"#Page_45">45</a><br /> +——his objection to the conception of an ether espoused +and defended by Huyghens and Euler, <a href="#Page_58">58</a><br /> +——his optical career, <a href="#Page_70">70</a><br /> +——his rings, <a href="#Page_69">69-77</a><br /> +——his rings explained by the theory of 'fits,' <a href= +"#Page_73">73</a><br /> +——espouses the emission theory, <a href= +"#Page_77">77</a><br /> +——effects of this espousal, <a href= +"#Page_77">77</a><br /> +——his idea of gravitation, <a href= +"#Page_92">92</a><br /> +——his errors, <a href="#Page_208">208</a><br /> +<br /> +Nicol prism, the, <a href="#Page_122">122</a><br /> +<br /> +<br /> +Ocean, colour of the, <a href="#Page_35">35</a><br /> +<a name="Page_242" id="Page_242"></a><span class="pagenum">[Pg +242]</span><br /> +Œrsted, discovers the deflection of a magnetic needle by an +electric current, <a href="#Page_176">176</a><br /> +<br /> +Optics, science of, <a href="#Page_4">4</a><br /> +<br /> +<br /> +Pasteur referred to, <a href="#Page_219">219</a><br /> +<br /> +Physical theories, origin of, <a href="#Page_41">41-44</a><br /> +<br /> +Pigments, analysis of the action of, upon light, <a href= +"#Page_33">33</a><br /> +——mixture of, contrasted with mixture of lights, +<a href="#Page_37">37</a><br /> +——Helmholtz reveals the cause of the green in the case +of mixed blue and yellow pigments, <a href="#Page_37">37</a><br /> +——impurity of natural colours, <a href= +"#Page_37">37</a><br /> +<br /> +Pitch of sound, <a href="#Page_59">59</a><br /> +<br /> +Plücker, his drawings of spectra, <a href= +"#Page_202">202</a><br /> +<br /> +Polariscope, stained glass in the, 130,<a href= +"#Page_131">131</a><br /> +——unannealed glass in the, <a href= +"#Page_136">136</a><br /> +<br /> +Polarity, notion of, how generated, <a href="#Page_93">93</a><br /> +——atomic, <a href="#Page_93">93-96</a><br /> +——structural arrangements due to, <a href= +"#Page_96">96</a><br /> +——polarization of light, <a href= +"#Page_112">112</a><br /> +——tested by tourmaline, <a href= +"#Page_116">116</a><br /> +——and by reflection and refraction, <a href= +"#Page_119">119</a><br /> +——depolarization, <a href="#Page_120">120</a><br /> +<br /> +Polarization of light, <a href="#Page_112">112</a><br /> +——circular, <a href="#Page_140">140</a><br /> +——sky-light, <a href="#Page_149">149</a>, <a href= +"#Page_157">157</a><br /> +——of artificial sky, <a href="#Page_156">156</a><br /> +——of radiant heat, <a href="#Page_180">180</a><br /> +<br /> +Polarizer and analyzer, <a href="#Page_127">127</a><br /> +<br /> +Poles of a magnet, <a href="#Page_93">93</a><br /> +<br /> +Powell, Professor, on polarization of heat, <a href= +"#Page_180">180</a><br /> +<br /> +Prism, the Nicol, <a href="#Page_122">122</a><br /> +<br /> +<br /> +Quartz, chromatic phenomena produced by, <a href= +"#Page_139">139</a><br /> +<br /> +<br /> +Radiant heat, <a href="#Page_172">172</a><br /> +——diathermancy, or perviousness to radiant heat, +<a href="#Page_173">173</a><br /> +——conversion of heat-rays into light rays, <a href= +"#Page_174">174</a><br /> +——formation of invisible heat-images, <a href= +"#Page_179">179</a><br /> +——polarization of, <a href="#Page_180">180</a><br /> +——double refraction, <a href="#Page_182">182</a><br /> +——magnetization of, <a href="#Page_184">184</a><br /> +<br /> +Rainbow, Descartes' explanation of the, <a href= +"#Page_24">24</a><br /> +<br /> +Refraction, demonstration of, <a href="#Page_14">14</a><br /> +<br /> +Refraction of light, <a href="#Page_106">106</a><br /> +——double, <a href="#Page_109">109</a><br /> +<br /> +Reflection, partial and total, <a href="#Page_20">16-20</a><br /> +<br /> +Respighi, results obtained by, <a href="#Page_205">205</a><br /> +<br /> +Ritter, his discovery of the ultraviolet rays of the sun, <a href= +"#Page_159">159</a><br /> +<br /> +Roemer, Olav, his observations of Jupiter's moons, <a href= +"#Page_20">20</a><br /> +——his determination of the velocity of light, <a href= +"#Page_21">21</a><br /> +<br /> +Rubidium, discovery of, <a href="#Page_193">193</a><br /> +<br /> +Rusting of iron, what it is, <a href="#Page_5">5</a><br /> +<br /> +<br /> +Schwerd, his observations respecting diffraction, <a href= +"#Page_87">87</a><br /> +<br /> +Science, growth of, <a href="#Page_176">176</a>, <a href= +"#Page_203">203</a><br /> +<br /> +Scoresby, Dr., succeeds in exploding gunpowder by the sun's rays +conveyed by large lenses of ice, <a href="#Page_167">167</a><br /> +<br /> +Secchi, results obtained by, <a href="#Page_205">205</a><br /> +<br /> +Seebeck, Thomas, discovers thermo-electricity, <a href= +"#Page_176">176</a><br /> +——discovers the polarization of light by tourmaline, +<a href="#Page_208">208</a><br /> +<br /> +Selenite, experiments with thick and thin plates of, <a href= +"#Page_124">124</a><br /> +<a name="Page_243" id="Page_243"></a><span class="pagenum">[Pg +243]</span><br /> +Silver spectrum, analysis of, <a href="#Page_190">190</a>, <a href= +"#Page_191">191</a><br /> +<br /> +Sky-light, colour and polarization of, <a href="#Page_149">149</a>, +<a href="#Page_154">154</a><br /> +——generation of artificial skies, <a href= +"#Page_152">152</a><br /> +<br /> +Snell, Willebrord, his discovery, <a href="#Page_14">14</a><br /> +——his law, <a href="#Page_15">15</a>, <a href= +"#Page_24">24</a><br /> +<br /> +Soap-bubbles and their colours, <a href="#Page_63">63</a>, <a href= +"#Page_65">65</a><br /> +<br /> +Sound, early notions of the ancients respecting, <a href= +"#Page_51">51</a><br /> +——interference of waves of, <a href= +"#Page_58">58</a><br /> +——pitch of, <a href="#Page_59">59</a><br /> +——analogies of light and, <a href= +"#Page_56">56</a><br /> +——demonstration of analogy between, and light, <a href= +"#Page_198">198</a>, <a href="#Page_199">199</a><br /> +<br /> +Sonorous vibrations, action of, <a href="#Page_134">134</a><br /> +<br /> +Spectrum analysis, principles of, <a href="#Page_189">189</a><br /> +<br /> +Spectra of incandescent vapours, <a href="#Page_190">190</a><br /> +——discontinuous, <a href="#Page_191">191</a>, <a href= +"#Page_192">192</a><br /> +——of polarized light, <a href="#Page_227">227</a><br /> +<br /> +Spectrum bands proved by Bunsen and Kirchhoff to be characteristic +of the vapour, <a href="#Page_192">192</a><br /> +——its capacity as an agent of discovery, <a href= +"#Page_193">193</a><br /> +——analysis of the sun and stars, <a href= +"#Page_193">193</a><br /> +<br /> +Spottiswoode, Mr. William, <a href="#Page_123">123</a>, <a href= +"#Page_227">227</a><br /> +<br /> +Stewart, Professor Balfour, <a href="#Page_202">202</a><br /> +<br /> +Stokes, Professor, results of his examination of substances excited +by the ultra-violet waves, <a href="#Page_161">161</a><br /> +——his discovery of fluorescence, <a href= +"#Page_162">162</a><br /> +——on fluorescence, <a href="#Page_165">165</a><br /> +——nearly anticipates Kirchhoff's discovery, <a href= +"#Page_198">198</a>, <a href="#Page_202">202</a><br /> +<br /> +Striated surfaces, colours of, <a href="#Page_89">89</a><br /> +<br /> +Sulphate of quinine first noticed and described by Sir John +Herschel, <a href="#Page_165">165</a><br /> +<br /> +Sun, chemistry of the, <a href="#Page_195">195</a><br /> +<br /> +Sun, rose-coloured solar prominences, <a href= +"#Page_204">204</a><br /> +<br /> +<br /> +Talbot, Mr., his experiments, <a href="#Page_201">201</a><br /> +<br /> +Tartaric acid, irregular crystallization of, and its effects, +<a href="#Page_131">131</a><br /> +<br /> +Thallene, its effect on the spectrum, <a href= +"#Page_162">162</a><br /> +<br /> +Thallium, spectrum analysis of, <a href="#Page_190">190</a>, +<a href="#Page_191">191</a><br /> +——discovery of, <a href="#Page_193">193</a><br /> +——isolated in ingots by M. Lamy, <a href= +"#Page_193">193</a><br /> +<br /> +Theory, relation of, to experience, <a href="#Page_91">91</a><br /> +<br /> +Thermo-electric pile, <a href="#Page_176">176</a><br /> +<br /> +Thermo-electricity, discovery of, <a href="#Page_176">176</a><br /> +<br /> +Tombeline, Mont, inverted image of, <a href="#Page_19">19</a><br /> +<br /> +Tourmaline, polarization of light by means of, <a href= +"#Page_112">112</a><br /> +<br /> +Transmitted light, reason for, <a href="#Page_77">77</a><br /> +<br /> +Transparency, remarks on, <a href="#Page_167">167</a><br /> +<br /> +<br /> +Ultra-violet sun-rays, discovered by Ritter, <a href= +"#Page_159">159</a><br /> +——effects of, <a href="#Page_160">160</a><br /> +<br /> +Ultra-red rays of the solar spectrum, <a href= +"#Page_171">171</a><br /> +——part played by the, <a href="#Page_173">173</a><br /> +<br /> +Undulatory theory of light, bases of the, <a href= +"#Page_47">47</a><br /> +——Sir David Brewster's chief objection to the, <a href= +"#Page_47">47</a><br /> +<br /> +Undulatory theory of light, Young's foundation of the, <a href= +"#Page_49">49</a><br /> +<a name="Page_244" id="Page_244"></a><span class="pagenum">[Pg +244]</span> ——phenomena which first suggested the, +<a href="#Page_62">62</a>, <a href="#Page_69">69</a><br /> +——Mr. Mill's scepticism regarding the, <a href= +"#Page_143">143</a><br /> +——a demonstrated verity in the hands of Young, <a href= +"#Page_210">210</a><br /> +<br /> +<br /> +Vassenius describes the rose-coloured solar prominences in 1733, +<a href="#Page_204">204</a><br /> +<br /> +Vitellio, his skill and conscientiousness, <a href= +"#Page_14">14</a><br /> +——his investigations respecting light, <a href= +"#Page_207">207</a><br /> +<br /> +Voltaic battery, use of, and its production of heat, <a href= +"#Page_6">6</a>, <a href="#Page_7">7</a><br /> +<br /> +<br /> +Water, deportment of, considered and explained, <a href= +"#Page_105">105</a>, <a href="#Page_106">106</a><br /> +<br /> +Waves of water, <a href="#Page_51">51</a><br /> +——length of a wave, <a href="#Page_52">52</a><br /> +——interference of waves, <a href= +"#Page_53">53-55</a><br /> +<br /> +Wertheim, M., his instrument for the determination of strains and +pressures by the colours of polarized light, <a href= +"#Page_134">134</a><br /> +<br /> +Wheatstone, Sir Charles, his analysis of the light of the electric +spark, <a href="#Page_202">202</a><br /> +<br /> +Whirlpool Rapids, illustration of the principle of the interference +of waves at the, <a href="#Page_55">55</a><br /> +<br /> +Willigen, Van der, his drawings of spectra, <a href= +"#Page_202">202</a><br /> +<br /> +Wollaston, Dr., first observes lines in solar spectrum, <a href= +"#Page_193">193</a><br /> +——discovers the rings of Iceland spar, <a href= +"#Page_209">209</a><br /> +<br /> +Woodbury, Mr., on the impurity of natural colours, <a href= +"#Page_37">37</a><br /> +<br /> +Wünsch, Christian Ernst, on the three simple colours in white +lights, <a href="#Page_39">39</a> <a href= +"#Footnote_8_8"><i>note</i></a><br /> +——his experiments, <a href="#Page_39">39</a> <a href= +"#Footnote_8_8"><i>note</i></a><br /> +<br /> +<br /> +Young, Dr. Thomas, his discovery of Egyptian hieroglyphics, +<a href="#Page_49">49</a><br /> +——and the undulatory theory of light, <a href= +"#Page_49">49</a><br /> +——Helmholtz's estimate of him, <a href= +"#Page_50">50</a><br /> +——ridiculed by Brougham in the 'Edinburgh Review,' +<a href="#Page_50">50</a><br /> +——generalizes Grimaldi's observation on light, <a href= +"#Page_56">56</a>, <a href="#Page_57">57</a><br /> +——photographs the ultra-violet rings of Newton, +<a href="#Page_160">160</a><br /></div> + + + + + + + +<pre> + + + + + +End of the Project Gutenberg EBook of Six Lectures on Light, by John Tyndall + +*** END OF THIS PROJECT GUTENBERG EBOOK SIX LECTURES ON LIGHT *** + +***** This file should be named 14000-h.htm or 14000-h.zip ***** +This and all associated files of various formats will be found in: + https://www.gutenberg.org/1/4/0/0/14000/ + +Produced by Clare Boothby, Stephen Schulze and the PG Online +Distributed Proofreading Team. + + +Updated editions will replace the previous one--the old editions +will be renamed. + +Creating the works from public domain print editions means that no +one owns a United States copyright in these works, so the Foundation +(and you!) can copy and distribute it in the United States without +permission and without paying copyright royalties. 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