1548 lines
79 KiB
Plaintext
1548 lines
79 KiB
Plaintext
A HISTORY OF THE THEORIES OF AETHER AND ELECTRICITY : FROM THE AGE OF DESCARTES TO THE CLOSE OF THE NINETEENTH CENTURY
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E.T. (EDMUND TAYLOR) WHITTAKER
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A History of the Theories of Aether and Electricity : From the Age of Descartes to the Close of the Nineteenth Century
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E. T. (Edmund Taylor) Whittaker
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,NET
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HARDPRESS
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ISBN: 978129010626
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Published by:
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HardPress Publishing
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8345 NW 66TH ST #2561
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MIAMI FL 33166-2626
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Email: info@hardpress.net
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Web: http://www.hardpress.net
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X LI BR.I
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11
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11
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DU BL IN UN I VERSITY PRESS SERIES .
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.A HISTORY
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OF THE
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THEORIE OF AE'fHER AND ELECTRICITY
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FROM:: T HE AGE OF DE CARTE TO THE CLO E OF THE NT~~TEEXTH CENTeRY.
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BY
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H o/i . c. .D. (.Du hl. ) ; F.R. . ; Roycrl A s ronomt:t· of I rdand.
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LOXG~IAX , GREEX, A.._~D CO. ,
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39 PATERXO TER R O W , LONDON ,
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NEW YORK, BOMBAY, A..'lD CALCCTTA.
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HODGE , FIGGIS, , CO., LTn ., D"CBLIN. 1910.
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DUBLIN; PRINTBD A 'i . 'J HB UNI VB RSITY PRBSS,
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BY PONSONBY AND GIRRS.
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. . .
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....
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......"" :.,
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. -
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.
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:
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......:
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.. ,.
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:•-:.
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........
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THE author de ires to record hi gratitude to lV[r. , v. W.
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Ro SE B ALL, Fellow of Trin ity College, Cambridge., and to Profe or "\V. 1\1:cF. ORR, F.R.S., of the R oyal College of c1ence for I reland; these friends have read the proof- beets, and have made many helpful suggestions and criticism .
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Thank are also due to the BOARD OF TRINITY COLLEGE,. DUBLIN, for he financial assistance which made pos ible the publication of the work.
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236360
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CONTENTS.
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CHAPTER I.
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~ E THEORY OF THE AETHER IN THE SEVE..."'lTEENTH CE~TURY.
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l'tiatter and aether,
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The physical writings of Descartes,
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Early history of magnetism : Petrus Peregrinus, Gilbert, De:-;cartes,
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Fermat attacks Descartes' theory of light: the principle of least
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time,
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Hooke's undulat-n·y theory: the advance of wave-fronts,
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Newton overthrows Hooke's theory of colours,
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-Conception of the aether in the writings of Newton,
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Newton's theories of the periodicity of homogeneous light, and of
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fits of easy transmission,
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The velocity of light : Huygens' Traite de la
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Glua-hrnleieor,e:R• oheismtehre, ories
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of
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the
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propagation
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of
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waves, and of crystalline optics,
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•
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Newton shows that rays obtained by double refraction have sides
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his objections to the undulatory theory,
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Pag"'
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1 2 7
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10 11 15 17
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20 21
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22
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28
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CHAPTER II.
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ELECTRIC A.."JD 1\lAGNETIO SCIENCE, PRIOR TO THE INTRODUCTION OF THE POTENTIALS.
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The electrical researches of Gilbert : the theory of emanations,
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29
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State of physical science in the first half of the eighteenth century, 32
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Gray discovers electric conduction : Desaguliers, •
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•
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• 37
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The electric fluid,
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38
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Du Fay distinguishes vitreous and resinous electricity,
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39
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Nollet's effluent and affluent streams,
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40
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The Leyden phial,
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41
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The one-fluid theory: ideas of Watson and Franklin,
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42
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Final overthrow by Aepinus of the doctrine of effluvia,
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48
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Priestley discovers the law- of electrostatic force,
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50
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Vlll
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Contents.' · •J
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Cavendish,
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•
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Michell disoovers the law of magnetic force, .
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The two-fluid theory : Coulomb,
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Limited mobility of the magnetic fluids,
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Poisson's mathematical theory of electrostatics,
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The equivalent surface- and volume-distributions of magnetism:
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Poisson's theory of magnetic induction,
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Green's Nottingham memoir,
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Page-
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51 54 56 58 59
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64 65
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CHAPTER III.
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GALVANISM, FROM: GALVANI TO OHM.
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Sulzer's discovery,
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67
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G~~nic~~~~~-
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~
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Rival hypotheses regarding the galvanic fluid,
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70
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The voltaic pile,
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72
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Nicholson and Carlisle decompose water voltaically,
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75
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Davy's chemical theory of the pile,
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76
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Grothu" ss' chain,
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78
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De La.Rive's hypoth~~;ds,
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79
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Berzelius' scheme of electro-chemistry,
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80
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Early attempts _to discover .a connexion between electricity and
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magnetism,
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83
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Oersted's experiment: his explanation of it,
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85
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The law of Biot and Savart, .
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86
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The researches of Ampere on electrodynan1ics,
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87
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Seebeck's phenom"enon,
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90
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Davy's researches on conducting power,
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94
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Ohm's theory : electroscopic force,
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95
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CHAPTER IV.
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----- " THE LUMINIFEROUS MEDIUM' FR0l\l BRADLEY TO FRESNEL.
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Bradley discovers aberration, -John Bernoulli's model of the aether,
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Maupertuis and the principle of least action, Views of Euler, Courtivron, ·MelviU,
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Young defends the undulatory theory, and explains the colours of thin plates,
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Laplace supplies a corpuscular theory of double refraction, .
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99 100 102 104
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105 109
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Contents.
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Young proposes a dynamical theory of light in crystals, Researches of l\Ialus on polarization, Recognition of biaxal crystals, Fresnel successfully explains diffraction, His theory of the relatiV"e motion of aether and matter, Young suggests the transversality of the vibrations of light, Fresnel discusses the dynamics of transverse vibrations, Fresnel's theory of the propagation of light in crystal~, Hamilton predicts conical refraction, Fresnel's theory of reflexion,
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Page
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110 111 113 114 115 121 123 125 131 133
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.CHAPTER V.
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~THE AETHER AS A.,.'- ELASTIC S0L1n.
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Astronomical objection to the elastic-solid theory : Stokes'
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hypothesis.
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137
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Navier and Cauchy discover the equation of vibration of an elastic
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solid,
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139
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Poisson distinguishes condensational and distortional waves,
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Cauchy's first and second theories of light Ill crystals,
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141
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143
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Cauchy's first theory of reflexion,
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145
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His second theory of reflexion,
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147
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The theory of reflexion of J\IacCullagh and Neumann,
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148
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Green discovers the correct conditions at the boundaries,
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151
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Green's. theory of reflexion : objections to it,
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152
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:I\IacCullagh introduces a new type of elastic solid,
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,v. Thomson's model of a rotationally-elastic body,
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154 157
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Cauchy's third theory of reflexion: the contractile aether, .
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158
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Later work of W. Thomson and others on the contractile aether,
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159
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Green's first and second theories of light in crystals,
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161
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Influence of Green,
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167
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Researches of Stokes on the relation of the direction of vibration of
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light to its plane of polarization,
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168
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The hypothesis of aeolotropic inertia,
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171
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Rotation of the plane of polarization of light by active bodies,
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173
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l\IacCullagh's theory of natural rotatory power,
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175
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l\IacCullagh's and Cauchy's theory of metallic reflexion,
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177
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Extension of the elastic-solid theory to metals,
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179
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Lord Rayleigh's objection,
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181
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Cauchy's theory of dispersion,
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182
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Boussinesq's elastic-solid theory,
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185
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X
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Contents.
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CHAPTER VI.
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FARADAY.
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Discovery of induced currents: lines of magnetic force,
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Page
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.189
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Self-induction,
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193
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Identity of frictional and voltaic electricity: Faraday's views on the
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nature of electricity,
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194
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Electro-chemistry,
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197
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-Oontro·versy between the adherents of the chemical and contact
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hypotheses,
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201
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The properties of dielectrics, .
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206
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Theory of dielectric polarization: Faraday, ,v. Thomson, and
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Mossotti,
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211
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The connexion between magnetism and light,
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213
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Airy's theory of magnetic rotatory polarization,
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214
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Faraday's Thoughts on Ray- Vibrations,
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217
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Researches of Faraday and Plucker on diamagnetism,
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218
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CHAPTER VII.
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THE MATHEMATICAL ELECTRICIANS OF THE l\1IDDLE OF THE NINETEENTH CENTURY.
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F. Neumann's theory of induced currents the electrodynamic
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potential,
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W. Weber's theory of electrons,
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Riemann's law,
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.
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~oposals to modify the law of gravitation, .
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Weber's theory of paramagnetism and diamagnetis1n: later theories,
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Joule's law: energetics of the voltaic cell,
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Researches of Helmholtz on electrostatic and electrodynam.ic energy,
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W. Thomson distinguishes the circuital and irrotational magnetic
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vectors,
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•
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His theory of magnecrystallic action,
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His formula for the energy of a magnetic field,
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_
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Extension of this formula to the case of fields produced by currents,
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Kirchhoff identifies Ohm's electroscopic force with electrostatic
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potential,
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The discharge of a Leyden jar: W. Thomson's theory,
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The velocity of electricity and the propagation of telegraphic signals,
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Clausius' law of force between electric charges: crucial experiments,
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Nature of the current,
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•
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•
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•
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•
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•
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The thermo-electric researches of Peltier and W. Thomson,
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•
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222 225 231 232 234 239 242
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244 245 247 249
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251 253 254 261 263 264
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C ont"ents.
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Xl
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CHAPTER VIII.
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·Gauss and Riemann on the propagation of electric actions, .
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Analogies suggested by \V. Thomson,
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l\Iaxwell's hydrodynamical analogy, .
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The vector potential,
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Linear and rotatory interpretations of n1agnetism,
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l\Iaxwell's mechanical model of the electromagnetic field,
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Electric displacement,
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Similarity of electric vibrations to those of light.
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Connexion of refractive index and specific inductive capacity,
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l\Iaxwell's _memoir of 1864,
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·The propagation of electric disturbances in crystals and in metals, .
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Anomalous dispersion,
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•
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The 1\laxwell-Sellmeier theory of dispersion,
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Imperfections of the electromagnetic theory of light,
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The theory of L. Lorenz,
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1Haxwell's theory of stress in the electric field,
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The pressure of radiation,
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l\Iaxwell's theory of the magnetic rotation of light, . •
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Page
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268 269 271 273 274 276 279 281 283 284 288 291 292 295 297
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300
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303 307
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CHAPTER IX.
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l\foDELS OF THE AETHER.
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Analogies in which a rotatory character is attributed to magnetism, 1\.1:odels in which magnetic force is represented as a linear velocity, Researches of "\V. Thomson, Bjerknes, and Leahy, on pulsating and
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oscillating bodies, l\IacCullagh's quasi-elastic solid as a model of the electric medium, The Hall effect. 1\Iodels of Riemann and Fitz Gerald, Vortex-atoms,
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The vortex-sponge theory of the aether: researches of ,v. Thomson,
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Fitz Gerald, and Hicks, ~
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310 311
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316 318 320 324 326
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327
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CHAPTER X.
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THE FOLLOWERS OF l\IAXWELL.
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Helmholtz and H. A. Lorentz supply an electromagnetic theory of reflexion,
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Crucial experin1ents of Helmholtz and Schiller,
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337
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338
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Xll
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Contents.
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Convection-currents: Rowland's experiments,
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The moving cha1:ged sphere: researches of J. J. Thomson, Fitz Gerald,
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and Heaviside,
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Conduction of rapidly-alternating currents, .
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Fitz Gerald devises the magnetic radiator,
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Poynting's theorem,
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Poynting and J. J. Thomson develop the theory of moving lines of
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force,
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•
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Mechanical momentum in the electromagnetic . field,
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New derivation of Maxwell's equations by Hertz,
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Hertz's assumptions and Weber's theory,
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E::itperiments of Hertz on electric ·waves,
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The memoirs of Hertz and Heaviside on fields in which material
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bodies are in motion,
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The current of dielectric convection, .
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Kerr's magne.to-optic phenomenon,
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Rowland's theory of magneto-optics,
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The rotation of the plane of polarization in naturally active bodies,
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Page
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339
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340 344 345 347
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349 352 353 356 357
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365 367 368 369 370·
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CHAPTER XI.
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CONDUCTION IN SOLUTIONS AND GASES, FROI\.I FARADAY TO
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J. J. THOMSON.
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The hypothesis of Williamson and Clausius, Migration of the ions, The researches of Hittorf and Kohlrausch, Polarization of electrodes, Electrocapillarity, Single differences of potential, Helmholtz' theory of concentration-cells, Arrhenius' hypothesis. The researches of N ernst, Earlier investigations of the discharge in rarefied gases, Faraday observes the dark space, Researches of Plucker, Hittorf, Goldstein, and Varley, on the
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cathode rays, Crookes and the fourth state of matter, Objections and alternatives to the charged-particle theory of
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cathode rays, Giese's and Schuster's ionic theory of conduction in gases, J ..J. Thomson measures the velocity of cathode rays,
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372 373 374 375 376 379 381 383 386 390 391
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393 394
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395 397 400
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Conte>,ts.
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Discovery of X-rays: hypotheses regarding them, Further researches of J. J. Thon1son on cathode rays: the _ratio -rn/e, Vitreous and resinous electricity,
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Determination of the ionic charge by J. J. Thomson,
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|
Becquerel's radiation: discovery of radio-active substances,
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Xlll
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P a g·e
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401 404 406 407 408
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CHAPTER XII.
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THE THEORY OF AETHER AND ELECTRONS IN THE CLOSING YEARS OF THE NINETEENTH CENTURY.
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Stokes' theory of aet-hereal motion near moving bodies,
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Astronomical phenomena in which the velocity of light is involved,
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Crucial experiments relating to the optics of 1noving bodies,
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Lorentz' theory of electrons, .
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.
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The current of dielectric convection: Rontgen's experiment,
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The electronic theory of dispersion, .
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Deduction of Fresnel's formula from the theory of electrons,
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Experimental verification of Lorentz' hypothesis,
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Fitz Gerald's explanation of l\Iichelson's experiment,
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Lorentz' treatise of 1895,
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Expression of the potentials in terms of the electronic charges,
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Further experiments on the relative motion of earth and aether,
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Extension of Lorentz' transformation : Larmor discovers its
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connexion with Fitz Gerald's hypothesis of contraction,
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Examination of the supposed primacy of the original variables
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fixity relative to the aether: the principle of relativity.
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The phenomenon of Zeeman,
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Connexion of Zeeman's effect with the magnetic rotation of light,
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The optical properties of 1netals,
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The electronic theory of metals,
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Thermionics,
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411 413 416 419 426
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428
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430 431 432 433 436 437
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440
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444
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449
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452 454 456 464
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INDEX,
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470
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l\IE1\1ORANDU1'f ON NOTATION.
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VECTORS are denoted by letters in clarendon type, as E .
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The three components of a vector E a1·e denoted by E,0 E,,, E,.;: and the magnitude of the vector is denoted by E, so that
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E 2 = E",,2 + E,,2 + E,.2 •
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The -vector product of two vectors E and H, which is denoted by [E . HJ, is the vector whose components are (E,,Ka - :I!,,"$,,, E,.Hs - E$,., E$,, - E,,Hz)- Its direction is at right angles to the direction of E and H, and its magnitude is represented by twice the area of the triangle formed by them.
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The scalar product of E and H is E:,,;ll"" + E,,H,, + E..Hz. It 0 is denoted by (E. H).
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The quantity
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is denoted by div E.
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The vector whose components are
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( oE,, oy
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_
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oE,, os'
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oE"" _ oE,.
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oy ox'
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oE,,
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ox
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is denoted by curl E.
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_or) If Vdenote a scalar quantity, the vector whose components ru·e
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(
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-
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av
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ox'
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av
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- oy'
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oz is denoted by grad V.
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The symbol V is used to denote the vector operator whose-
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o oo
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components are
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Differentiation with respect to the time is frequently indicated by a dot placed over the symbol of the ,ariable which is differentiated.
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~
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~
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..,
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J,#
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-,IJJ..,
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0
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J _,,J .., ..
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--
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.., ~ .....,.., ..,
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.., .>
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,
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.., ..
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.,#
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,,
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.,#..,
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..,
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..,
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•
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THEORIES OF AE'fHER AND ELEC'fRICITY.
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-·•o+o-
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CHAPTER I.
|
|
THE THEORY OF THE AETHER IN THE SEVENTEENTH CENTURY.
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|
THE observation of the heavens, which has been pursued continually from the earliest ages, revealed to the ancients the regularity of the planetary motions, and gave rise to the conception of a universal order. l\1odern research, building on this foundation, has shO'wn how intimate is the connexion between the different celestial bodies. They are formed of the same kind of matter; they are similar in origin and history; and across the vast spaces which divide them they hold perpetual intercourse.
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Until the seventeenth century the only influence which was known to be capable of passing from star to star was that of light. Newton added to this the force of gravity; and it is now recognized that the power of communicating across vacuous regions is possessed also by the electric and magnetic attractions.
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It is thus erroneous to regard the heavenly bodies as isolated in vacant space; around and bet,veen them is an incessant conveyance and transformation. of energy. To the vehicle of this activity the name aether has been given.
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|
The aether is the solitary tenant of the universe, save for that infinitesimal fraction of space ·which is occupied by ordinary matter. Hence arises a problem which has long engaged attention, and is not yet completely solved: What relation. subsists between the medium ,vhich fills the interstellar void and the condensations of matter that are scattered throughout it?
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B
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The history of this problem may be traced back continuously to the earlier half of the seventeenth century. It first emerged clearly in that reconstruction of ideas regarding the physical universe which ·was effected by Rene Descartes.
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Descartes was born in 1596, the son of Joachim.· D ·escartes, Counsellor to the Parliament of Brit~any. As a young man he followed the profession of arms, and served in the campaigns of Maurice of Nassau, and the Emperor; but his twenty:..fourth year brought a profound mental crisis, apparently not unlike those which have been recorded of many religious leaders; and he resolved to devote himself thenceforward to the study of philosophy.
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The age which preceded the birth of Descartes, and that i:n which he lived, "'.,.ere marked by events which greatly altered the prevalent conceptions of the world. The discovery of America, the circumnavigation of the globe by Drake, the overthrow of the Ptolemaic system of astronomy, and the invention of the telescope, all helped to loosen the old foundations and to 1nake plain the need for a new structure. It was this that Descartes set himself to erect. His aim was the most ambitious that can be conceived; it was nothing less than to create ·from
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the beginning a complete system of human knowledge.
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Of such a system the basis must necessarily be metaphysical; and this part of Descartes' work is that by which he •is most widely known. But his efforts were also largely devoted to the mechanical explanation of nature, which indeed he regarded~as one of the chief ends of Philosophy.•
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The general character of his writings may be illustrated by a comparison with those of his most celebrated contemporary.t Bacon clearly defined the end to be sought for, and laid down the method by which it ·was to be attained; then, recognizing that to discover all the la,vs of nature is a task beyond the
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'# Of the works which bear on our present subject, the .Dioptt·ique and the .Meteorea were published at Leyden in 1638, and the Principia Philosophiae at Amsterdam in 1644, six years before the death of its author.
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T The principal philosophical -works of Bacon were written about eighteen years
|
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before those of Descartes.
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' in the Seventeenth Century.
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3
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po,vers o'f one man or one generation, he left to posterity the ,vork of filling in the framework_ which he had designed. Descartes, on the other hand, desired to leave as little as possible for his successors to do ; his was a theory of the universe, worked out as far as possible in every detail. It is, however, impossible to ·derive such a theory inductively unless there are at h_and sufficient observational data on ·which to base the induction; and as such data ,vere not available in the age of Descartes, he ,vas compelled to deduce phenomena from preconceived principles and causes, after the fashion of the older philosophers. To the inherent ,veakness of this method may be traced the -errors that at last brought his scheme to ruin.
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The contrast bet,veen the systems of Bacon and Descartes is not unlike that bet,veen the Roman republic and the empire of Alexander. In the one case we have a career of aggrandizement pursued with patience for centuries ; in the other a growth of fungus-like rapidity, a speedy dissolution, and an iinmense influence long exerted by the disunited fragments. The _grandeur of Descartes~ plan, and the boldness of its execution, stimulated scientific thought to a degree before unparalleled; and it was largely from its ruins that later philosophers constructed those more valid theories ,vhich have endured to .our own time.
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Descartes regarded the ,vorld as an immense machine, operating by the motion and pressure of matter. ~, Give me matter and motion," he cried, "and I will construct the universe." A peculiarity which distinguished his system from that which afterwards sprang from its decay was the rejection of all forms of action at a distance; he assumed that force cannot be communicated except by actual pressure or impact. By this a.ssumption he ·was compelled· to provide an explicit mechanism in order to account for each of the -known forces of nature-a task evidently much more difficult than that •which lies before those who are ·willing to admit action at a distance as an ultiinate property of matter.
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• Since the sun. interacts ·with the planets, in sending them B2
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4
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The Theory o/ the Aether
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light and heat and influencing their motions, it followed from Descartes· principle that interplanetary space must be a plenun1.,. occupied by 1natter imperceptible to the touch but capable of serving as the vehicle of force and light. This conclusion in turn determined the view which he adopted on the all-important. question of the nature of matter.
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l\1atter, in the Cartesian philosophy, is characterized not Ly impenetrability, or by any quality recognizable by the senses,, but simply by extension; extension constitutes matter, and matter constitutes space. The basis of all things is a primitive,. elementary, unique type of matter, boundless in extent and infinitely divisible. .In the process of evolution of the universe. three distinct forms of this matter have originated, corresponding respectively to the luminous matter of the sun, the. transparent matter of interplanetary space, and the dense,. opaque matter of the earth. cc The first is constituted by what. has been scraped off the other particles of matter when they were rounded; it moves with so much velocity that when it. meets other bodies the force of its agitation causes it to be. broken and divided by them into a heap of small particles thatare of such a figure as to fill exactly all the holes and s1nall interstices which they find around these bodies. The next type includes most of the rest of matter; its particles are spherical,. and are very small compared with the bodies we see on the earth; but nevertheless they have a finite magnitude, so that. they can be divided into others yet smaller. There exists in addition a third type exemplified by some kinds of matternamely, those ·which, on account of their size and figure, cannot be so easily moved as the preceding. I will endeavour to show that. all the bodies of the visible world are co1nposed of these three forms of matter, as of three distinct ele1nents ; in fact, that the sun and the fixed stars are formed of the first of these elements, the interplanetary spaces of the second, and the earth, with the planets and co1nets, of the third. For, seeing that the sun and the fixed stars emit light, the heavens transmit it, and the earth,. the planets, and the comets reflect it, it appears to me that there
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.........
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in the Seventeenth Century.
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5
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is ground for using these three qualities of luminosity, transparence, and opacity, in order to distinguish the three elements of the visible ·world.>!<
|
|
According to Descartes' theory, the sun is the centre of an
|
|
inunense vortex formed of the first or subtlest kind of matter.t
|
|
The vehicle of light in interplanetary space is 1natter of the second kind or element, composed of a closely packed assen1blage of globules ·whose size is intermediate between that of the vortex-matter and that of ponderable matter. The globules of ±he second element, and all the matter of the first element, are .constantly straining a-way from the centres around ,vhich they turn, owing to the centrifugal force of the vortices ;+ so that the globules are pressed in contact ,vith each other, and tend to move outwards, although they do not actually so mo,re.§ It is the transmission of this pressure ·which constitutes light; the action of light therefore extends on all sides round the sun and fixed stars, and travels instantaneously to any distance.If In the .Dioptri,q_iw,9iT vision is compared to the perception of the presence of objects ,vhich a blind man obtains by the use of his stick ; the transmission of pressure along the stick from the object to the hand being analogous to the transmission of pressure from a luminous object to the eye by the second kind of matter.
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Descartes supposed the "diversities of colour and light " to be due to the different ,vays in ·which the matter moves.•• In the JJ.feteores,tt the various colours are connected ,vith different rotatory velocities of the globules, the particles ,vhich rotate most rapidly giving the sensation of red, the slo,ver ones of yellow, and the slo,vest of green and blue-the order of colours being taken from the rainbow. The assertion of the dependence of colour
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• .Principia, Part iii, § 52.
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t It is curious to specula te on the impression which would have been produced
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liad the spirality of ue::bulre been discovered before the overthro'\\· of the Cartesian
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theory of vortices.
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! Ibid., §§ 55-59.
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§ Ibid., ~ 63.
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II Ibid., § 64.
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"IT .Discours p1·emier.
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•• P,·incipia, Pa1·t iv, § 195.
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ti" Discoiws Huitieme.
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6
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The Theory of the Aether
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on periodic time is a curious foreshadowing of one of the
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great discoveries of N e--wton. The general explanati0n of light on these principles ,vas
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|
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a1nplified by a more particular discussion of reflexion and
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refraction. The la·w of reflexion-that the angles of incidence
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and refraction are equal-had been kno·wn to the Greeks; but-
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the la,v of refraction-that the sines of the angles of incidence·
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and refraction are to each other in a ratio depending on the
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media-was now published for the first ti1ne.• Descartes gave
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it as his o,vn; but he seen1s to have been under considerable
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obligations to Willebrord Snell (b. 1591, d. 1626), Professor of
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Mathematics at Leyden, ,vho had discovered it experin1entally
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(though not in the form in ·which Descartes gave it) about-
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1621. Snell did not publish his result, but co1n1nunicated it in
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manuscript to several persons, an9- Huygens affirms that this-
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n1anuscript had been seen by ])escartes.
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Descartes presents the law as a deduction from theory.
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This, however, he is -able to do only by the aid of analogy;:
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when rays meet ponderable bodies, "they are liable to be
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deflected or stopped in the same ,vay as the motion of a ball or-
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a stone impinging on a body " ; for "it is easy to believe that
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the action or inclination to move, ·which I have said must be
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taken for light, ought to follow in this the same lavvs as-
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motion."t Thus he replaces light, whose velocity of propagation
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he believes to be always infinite, by a projectile whose velocity
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varies from one medium to another. The law of refraction is
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then proved as ·follows+ : -
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Let a ball thro,vn fro1n A meet at B a cloth CBE, so weak
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that the ball is able to break through it and pass beyond, but.
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with its resultant velocity reduced in some definite proportion,.
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say 1 : k. Then if BI be a length measured on the refracted ray
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equal to AB, the projectile will take l..: times as long to
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describe BI as it took to describe AB. But the co1nponent-
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* .IJiopt,rique, .IJiscours second.
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t- 1 bid., .IJiscmtt"s premier.
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! .Ibid., .IJiscours second.
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in the Sevenlleuth Century.
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7
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of velocity parallel to the cloth must be unaffected by the impact; and therefore the projection BE of the refracted ray must be k times as long as the projection BC of the incident
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F.
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E
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I
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ray. So if i and r denote the angles of incidence and refraction,.
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·we ha-ve
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. , BE
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BC
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. .
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sin r = BI = k . BA = k sin -i,,
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or the sines of the angles of incidence and refraction are 1n a constant ratio; this is the law of refraction.
|
|
Desiring to include all kno,vn phenomena 111. his system,. Descartes devoted some attention to a class of effects which ,vere at that time little thought of, but which were destined to play a great part in the subsequent development of Physics.
|
|
The ancients ,vere acquainted ·wit:;h the curious properties possessed by t,vo minerals, amber (fJAE1erpov) and magnetic iron ore (11 A.l0o,;; Ma-yvijr,~). The former, when rubbed, attracts light bodies : the latter has the power of attracting iron.
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The use of the magnet for the purpose of indicating direction at sea does not seem to have been derived from classical antiquity; but it ·was certainly kno,vn in the time of the Crusades. Indeed, magnetism ·was one of the few sciences ,vhich progressed during the l\:1iddle Ages; for in the thirteenth century Petrus Pe~egrinus,• a native of ~faricourt in Picardy, made a discovery of fundamental importance.
|
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Taking a natural magnet or lodestone, which had been rounded into a globular form, he laid it on a needle, and marked
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• IIis Epistola was written in 1269.
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8
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The Theo1-y ef the Aether
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the line along which the needle set itself. Then laying the needle on other parts of the stone, he obtained more lines in
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the same way. When. the entire surface of the stone had been
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covered with such lines, their general disposition became evident;
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they formed circles, which girdled the stone in exactly the same way as meridians of longitude girdle the earth; and there were
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two points at opposite ends of the stone through which all the
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circles passed, just as all the meridians pass through the Arctic
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and Antarctic poles of the earth.* Struck by the analogy,
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Peregrinus proposed to call these t ·wo points the poles of the magnet: and he observed that the way in which magnets set
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themselves and attract each other depends solely on the position
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of their poles, as if these were the seat of the magnetic power.
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Such was the origin of those theories of poles and polarization
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which in later ages have played so great a part in Natura! Philosophy.
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The observations of Peregrinus were greatly extended not
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long before·the time of Descartes by William Gilberd or Gilbertt (b. 1540, d. 1603). Gilbert was born at Colchester: after
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studying at Cambridge, he took up medical practice in London,
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and had the honour of being appointed physician to Queen
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Elizabeth. In 1600 he published a work+ on Magnetism and
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Electricity, with which the modern history of both subjects begins.
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Of Gilbert's electrical researches we shall speak later: in
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magnetism he made the capital discovery of the reason why magnets set in definite orientations with respect to the earth;
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which is, that the earth is itself a great magnet, having one of
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its poles in high northern and the other in high southern
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latitudes. Thus the property of the compass was seen to be
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included in the general principle, that the north-seeking pole of
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*" Procul dubio omnes lineae hujusmodi in duo puncta concurrent si<:ut omnes
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orbes meridiani in duo concurrunt polos m.undi oppositos."
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1' The form. in the Colchester records is Gilberd.
|
|
t Guliehni Gilberti de l\Iagnete, l\Iagneticisque co1~rib11s, et de magno magnete
|
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tellure: London, 1600. An English translation by P. F. l\l'ottelay was published
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in 1893.
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in the Seventeenth Century.
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9
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eYery magnet attracts the south-seeking pole of every other magnet, and repels its north-seeking pole.
|
|
• Descartes attempted* to account for magnetic phenomena by his theory of vortices. A vortex of flu.id matter ,vas postulated round each magnet, the matter of the vortex entering by one pole and leaving by the other : this matter was supposed to act on iron and steel by virtue of a special resistance to its motion afforded by the molecules of those substances.
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Crude though the Cartesian system was in this and many other features, there is no doubt that by presenting definite conceptions of molecular activity, and applying them to so wide a range of phenomena, it stimulated the spirit of inquiry, and prepared the ,vay for the more accurate theories that came after. In it~ o,vn day it met with great acceptance: the confusion which had resulted from the destruction of the old order was now, as it seemed, ended by a reconstruction of knowledge in a system at once credible and complete. Nor did its influence quickly ,vane ; for even at Cambridge it was studied long after Newton
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had published his theory of gravitation ;t and in the middle of
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the eighteenth century Euler and two of the Bernoullis based the explanation of magnetism on the hypothesis of vortices.+
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Descartes' theory of light rapidly displaced the conceptions ,vhich had held sway in the ~liddle Ages. The validity of his explanation of refraction was, ho,vever, called m question by his fellow-countryman Pierre de Fermat (b. 1601, d. 1665),~ and a controversy ensued, which was kept up by the Cartesians long after the death of their master. :F'erm.at
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• Principia, Part iv, § 133 sqq.
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t Whiston has recorded that, -having 1·eturne<l to Cambridge after his
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ordination in 1693, he resumed his studies there, "'particularly the Mathematicks, and the Cartesian Philosophy: which was alone in Vogue with us at that Time. But it was not long b~fort' I, with immense Pains, but no .Assistance, set myself with the utmost Zeal to the study of Sir Isaac Xewton's wonderful Discoveries." - \\'histon's Memoirs (1749), i, p. 36.
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t Their memoirs shared a prize of the French Academy in 1743, and were
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printed in 1752 in the Recueil des pieces qui o1't remporte lea prix de l' .A.cad., tome v. § Renati Descartes Epistolae, Pars tertia ; Amstelodam.i, 1683. The Ferm.at
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correspondence is comptised in letters xx.ix to XLTX.
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10
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The Theory o_/ the Aether
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eventually introduced a new fundamental law, from which he proposed to deduce the paths of rays of light. This was the celebrated Principle of Least Time, enunciated* in the form, c, Nature always acts by the shortest course." Fro1n it the law of reflexion can readily be derived, since the path described by light bet·ween a point on the incident ray and a point on the reflected ray is the shortest possible consistent with the condition of meeting the reflecting surfaces.t In order to obtain the law of refraction, ~...ern1at assmned that "the resistance of the media is different," and applied his cc n1.ethod of maxima and
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minima " to find the path ·which ·would be described in the least tin1.e from a point of one medium to a point of the other. In :J_.661 he arrived at the solution.+ cc The result of my work," he ·writes, "has been the most extraordinary, the most unforeseen, and the happiest, that ever was; for, after having performed all the equations, multiplications, antitheses, and other operations of my 111.ethod, and having finally finished the problem, I haYe found that my principle gives exactly and precisely the same proportion for the refractions ·which l\1onsieur Descartes has established." His surprise ·was all the greater, as he had supposed light to 1nove 1nore slo·wly in dense than in rare media,. whereasDescartes had (as ·will be evident from the demonstration given above) been obliged to make the contrary supposition.
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Although Fermat's result ,vas correct, and, indeed, of high pennanent ·interest, the principles from ,vhich it ·was derived were .metaphysical rather than physical in character, and consequently were of little use for the purpose of framing a mechanical explanation of light. Descartes' theory therefore held the field until the publication in 1667~ of the Micrographia
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* Epist. XLII, written at Toulouse in August, 1657, to ~Ionsieur de la
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Chambre; 1·eprinted in CEui-Tes de Fermat (e<l. 1891), ii, p. 354.
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T That 1·eflected light follows the shortest path was no new result, for it had
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been affirmed (and attributed to Hero oi Alexandria) in the KE,Pa.\.a,a -r[;:v lnr-rH<wv of Heliodorns of Larissa, a work of ·which seven:1.l editions wen:' published in the seventeenth century.
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t Epist. XLIII, ,vrittcn at Toulouse on Jan. 1, 1662; reprinted in <Eievres de
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Fennat. ii, p. 457 ; i, pp. 170, 173. § The imp1"imatu1· of Viscount Brouncker, P.R.s., is dated Nov. 23, 1664.
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'--:-,.._
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1n the Seventeenth Ce7! tur_y.
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11
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of Robert Hooke (b. 1635, d. 1703), one of the founders of the Royal Society, and at one time its Secretary.
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Hooke, ·who ,vas both an observer and a theorist, made t·wo experimental discoYeries which concern our present subject; but in both of these, as it appeared, he had been anticipated. The first• was the observation of the iridescent colours ·which are seen ·when light falls on a thin layer of air bet,veen two glass plates or lenses, or on a thin film of any transparent substance. These are generally known as the " colours of thin plates," or "Ne·wton's rings••; they had been previously observed by Boyle.t Hooke's second experimental discoYery,+ made after the date of the .1.liicrographia, ,vas that light in air is not propagated exactly in straight lines, but that there is some illumination within the geometrical shado,v of an opaque body. This observation had been published in 1665 in a posthumous ,vork§ of Francesco ~faria Grimaldi (b. 1618, d. 1663), who had giYen to the phenomenon the- name dijf'raction.
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Hooke's theoretical investigations on light ,vere of great importance, representing as they do the transition fro1n the Cartesian system to the fully developed theory of undulations. He begins by attac1'.--ing Descartes' proposition, that light is a tendency to motion rather than an actual motion. "-There is," he obserYes,11 "no luminous Body but has the parts of it in motion n1ore or less"; and this 1notion is "exceeding quick." l\foreoYer, since some bodies (e.g. the diamond ,vhen rubbed or heated in the dark) shine for a considerable time ,vithout being "·asted a,vay, it follo"·s that ,vhateYer is in motion is_not permanently lost to the body~ and therefore that the 1notion must be of a to-and-fro or vibratory character. The amplitude of the vibrations must be exceedingly sn1.all, since so.me h.uninous bodies (e.g. the diamond again) are very hard, and so cannot yield or bend to any sensible extent.
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,.. •.lliet·,_,g,·aphia, p. 47.
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-t Boyle's TVo,·ks (ed. 1772), j, p. 742.
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! Hooke's Postlunnous Wo,·ks, p. 186.
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§ Physico-~lfathesis de lmniue, coloribus, et i,·ide. Bologna, 1665 ; book i, prop. i.
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II ..,lficrog1·11phia, p. 55.
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12
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7lze Theory ef the Aether
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Concluding, then, that the condition associated with the emission of light by a luminous body is a rapid vibratory motion of very small amplitude, Hooke next inquires how light travels through space. " The next thing we are to consider," he says, " is the way or manner of the trajection of this motion through the interpos'd pellucid body to the eye: And here it will be easily granted-
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" First, that it must be a body susceptible and im,partible of this motion that will deserve the name of a Transparent; and next, that the parts of such a body must be h;;m,ogeneous, or of the same kind.
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"Thirdly, that the constitution and motion of the parts must be such that the appulse of the luminous body may be communicated or propagated through it to the greatest imaginable distance in the least imaginable time, though I see no reason to affirm that it must be in an instant.
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"Fourthly, that the motion is propagated every way through an Hom,ogeneoit,S medium, by direct or straight lines extended every way like .Rays from the centre of a Sphere.
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"Fifthly, in an Hom,ogeneous m,edium, this motion is propagated every way with equal velocity, whence necessarily every pulse or vibration of the luminous body will generate a Sphere, which will continually increase, and grow bigger, just after the same manner ( though indefinitely swifter) as the waves or rings on the surface of the water do swell into bigger and. bigger circles about a point of it, where by the sinking of a Stone the motion was begun, whence it necessarily follows, that all the parts of these Spheres undulated through an Homogeneous m,ediurn cut the Rays at right angles."
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Here we have a fairly definite mechanical conception. It resembles that of Descartes in postulating a medium as the vehicle of light; but according to the Cartesian hypothesis the disturbance is a statical pressure in this medium, while in Hooke's theory it is a rapid vibratory motion of small amplitude. In the above extract Hooke introduces, moreover, the idea of the wave-surfa,ce, or locus at any instant of a disturbance gene-
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in tlze Seventeenth Century.
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13
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rated originally at a point, and affirms that it is a sphere,. wh9se. centre is the point in question" and ·whose radii are
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the rays of light issuing from the point. Hooke's next effort was to produce a mechanical theory of
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refraction, to replace that given by Descartes. "Because," he says, "all transparent mediu1ns are not H01nogeneoits to one another, therefore we will next examine how this pulse or motion will be propagated through differingly transparent niediunis. And here, accorc!ing to the most acute and excellent Philosopher Des Cartes, I suppose the sine of the angle of inclination in the first medium to be to the sine of refraction in the second, as the density of the first to the density of the second. By density, I mean not the density in respect of gravity (with which the refractions or transparency of mediums hold no proportion), but in respect only to the trajection of the Rays of light, in ·which respect they only differ in this, that the one propagates the pulse more easily and ·weakly, the other more slowly, but more strongly. But as for the pulses themselves, they will by the refraction acquire another property, which we shall now
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endeavour to explicate. "We will suppose, therefore, in the first Figure, A OFD to be
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L
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0
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~
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a physical Ray, or ABOand DEF to be two mathematical Rays,. trajected from a very ren1ote point of a luminous body through
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1.4
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The 77ieory o_/ the Aether
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an H01nogeneous transparent mediun-1 LL, and .DA, EB, FC, to be small portions of the orbicular impulses which must therefore cut the Rays at right angles: these Rays meeting with the plain surface NO of a -mcdiu-m that- yields an easier transitu,s to the propagation of light, and falling obliquely on it, they will in the mediu1n ]_J,fM be refracted to,yards the perpendicular of the surface. And because this medium is more easily traJected than the former by a third, therefore the point U of the orbicular pulse P 7C will be moved to H four spaces in the same tin-le that F, the other end of it, is moved to three spaces, therefore the whole refracted pulse to H shall be oblique to the refracted Rays .CHK and GL"
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Although this is not in all respects successful, it represents a decided advance on the treatment of the same problem by Descartes, which rested on a mere analogy. Hooke tries to determine ·what happens to the ,vave-front when it meets the interface between two media; and for this end he introduces the correct principle that the side of the wave-front ,vhich first 1neets the interface will go forward in the second nJ.edium ,vith the velocity pr~per to that medium, while the other side of the wave-front which is still in the first medium is still moving with the old velocity: so that the wave-front ,vill be deflected in the transition from one medium to the other.
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This deflection of the "'\Vave-front was supposed by Hooke to be the origin of the prismatic colours. He regarded natural or ·white light as the simplest type of disturba_nce, being constituted by a si1nple and uniform pulse at right angles to the direction of propagation, .and inferred that colour is generated by the distortion to ·which this disturbance is subjected in the process of refraction. "The Ray,""" he says," is dispersed, split, and opened by its Refraction at the Superficies of a second medium, and from a line is opened into a diverging Superficies, and so obliquated, whereby the appearances of Colours are produced."
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• Hooke, Pv8tl,ionotes TVo,·ks, p. 82.
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in the Seveutanth Ceutur_y.
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15
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"Colour/' be says in another place,• " is not hing but the distur~ance of light by the communication of the pulse to other transparent mediums, that is by the refraction thereof.·• His precise hypothesis regarding the diffe_rent colours ·wast "that Blue is an impression on the Retina of an oblique and confus'd pulse of light, ·whose ·weakest part precedes, and whose strongest follows. ....-'\.nd, that red is an i1npression on the Retina of an oblique and confus'd pulse of light, whose strongest part precedes, and whose ·weakest follows."
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Hooke's theory of colour was completely overthrown., ·within a few years of its publication, by one of the earliest discoveries of Isaac Newton (b. 1642, d. 1727). Newton, ·who ·was elected a Fellow of Trinity College, Cambridge, in 1667, had in the beginning of 1666 obtained a triangular prism, "to try tbere,vith the celebrated Phaenomena of Colours.u For this purpose," having darkened my chamber, and made a small hole in my window-shuts, to let in a convenient quantity of the Sun's light, I placed my Prisme at his entrance, that it might be thereby refracted to the opposite ,vall. It was at first a very pleasing divertisement, to vie,v the vivid and intense colours produced thereby; but after a while applying myself to consider them more circumspectly, I became surprised to see them in an oblon,g form, which, according to the received laws of Refraction, I expected should have been circular." The length of the coloured spectrum was in fact about :fhTe times as great as its breadth.
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This puzzling fact he set himself to study ; and after more experiments the true explanation was discovered-namely, that ordinary white light is really a mixture of rays of eYery Yariety of colour, and that the elongation of the spectrum is due to the differences in. the refractive power of the glass for these different rays.
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" ...t. \..in.idst these thoughts," he tells us,! « I ,vas forced from
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• To the Royal Society, February 15, 1671-~. T .,_lfic,·ograpkia, p. 64.
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t Pl1il. Trans., :No. 80, February 19, 1671-2.
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16
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The Theory o_/- the Aether
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Cambridge by the intervening Plague"; this was in 1666, and his memoir on the subject was not presented to the Royal Society until five years later. In it he propounds a theory of colour directly opposed to that of Hooke. " Colours," he says, "are not Qualifications of light derived from Refractions, or Reflections of natural Bodies (as 'tis generally believed), but Original and connate p1~operties, which in divers Rays are divers. S01ne Rays are disposed to exhibit a red colour and no other: some a yellow and no other, some a green and no other, and so of the rest. Nor are there only Rays proper and particular to the more eminent colours, but even to all their intermediate gradations.
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" To the same degree of Refrangibility ever belongs the same colour, and to the same colour ever belongs the same degree of Refrangibility."
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" The species of colour, and degree of Refrangibility proper to any particular sort of Rays, is not n1.utable by Refraction, nor by Reflection from natural bodies, nor bl any other cause, that I could yet observe. When any one ,. sort of P'2.ys ha~h been well parted from those of other kinds, it hath afterwards ob~tinately retained its colour, notwithstanding my utmost endeavours to change it."
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The publication of the new theory gave rise to an acute controversy. A.s 1night have been expected, Hooke was foremost among the opponents, and led the attack with some degree of asperity. When it is re1nembered that at this tiine Newton was at the outset of his career, while Hooke was an older man, with _an established reputation, such harshness appears particularly ungenerous ; and it is likely that the unpleasant consequences which followed the announce1nent of his first great discovery had much to do with the reluctance which Newton ever afterwards showed to publish his results to the ·world.
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In the ·course of the discussion Newton found occasion to explain more fully the views which he entertained regarding the nature of light. Hooke charged him ·with holding the
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in the Seventeenth Century.
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17
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doctrine that light is a material substance. Now Ne,vton had, as a matter of fact, a great dislike of the more imaginative kind of hypotheses; be altogether renounced the attempt to construct the universe from its foundations after the fashion of Descartes, and aspired to nothing more than a formulation of the laws ,vhich directly govern the actual phenomena. His theory of gravitation, for example, is strictly an expression of the results of observation, and involves no hypothesis as to the cause of the attraction which subsists between ponderable bodies; and his own desire in regard to optics was to pi:_esent a theory free from speculation as to. the hidden mechanism of light. Accordingly, in reply to Hooke's criticism, he protested• that his views on colour ,vere in no way bound up with any particular conception of the ultimate nature of optical processes.
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Newton was, ho,vever, unable to carry out_ his plan of connecting together_ the phenomena of light into a coherent and reasoned ,vhole without having recourse to hypotheses. The hypothesis of Hooke, that light consists in vibrations of an aether, he rejected for reasons which at that time were perfectly cogent, and ,vhich indeed were not successfully refuted for over a century. One of these was the incompetence of the wavetheory to account for the rectilinear propagation of light,- and another was its inability to embrace the facts-discovered, as we shall presently see, by Huygens, and first interpreted correctly by Ne,vton himself-of polarization. On the ·whole, he seems to have favoured a scheme of ,vhich the following may
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be taken as a summaryt :All space is permeated by an elastic medium or aether, which
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1s capable of propagating vibrations in the same way as the
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• Phil. Trans. vii, 1672, p. 5086.
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-t Cf. Newton's memoir in Phil. Trans. vii, 1672; his memoir presented to the
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Royal Society in December, 1675, which is printed in Birch, iii, p. 247; bis Opticks, especially Queries 18, 19, 20, 21, 23, 29; the Scbolium at the end of the Principia; and a letter to Boyle, written in February, 1678-9, which is printed in Horsley's .JYewtoni Opera, p. 385.
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In. the Principia, Book I., section xiv, the analogy between rays of light and st-:-eams of corpuscles is indicated; but Xewton does not commit himself to any theory of light based on this.
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. The Theory ef the Aetlzer
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air propagates the vibrations of sound, but ,vith far greater velocity.
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This aether pervades the pores of all material bodies, a1id is the cause of their cohesion; its density varies from one body to another, being greatest in the free interplanetary spaces. It is not necessarily a single uniform substance: but just as air contains aqueous vapour, so the aether may contain various « aethereal spirits," adapted to produce the phenomena of electricity, magnetism, and gravitation.
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The vibrations of the aether cannot, for the reasons already mentioned, be supposed in themselves to constitute light. Light is therefore taken to be "something of a different kind, propagated from lucid bodies. They, that will, may suppose it an aggregate of various peripatetic qualities. Others may suppose it multitudes of unimaginable small and swift corpuscles of various sizes, springing from shining bodies at great distances one after another; but yet without any sensible interval of time, and continually urged forward by a principle of motion, which in the beginning accelerates them, till the resistance of the aethereal medium equals the force of that principle, much after the manner that bodies let fall in water are accelerated till the resistance of the water equals the force of gravity. But they, that like not this, may suppose light any other corporeal emanation, or any impulse or motion of any other medium or aethereal spirit diffused through the main body of aether, or what else they can imagine proper for this purpose. To avoid dispute, and make this hypothesis general~ let every man here take his fancy; only whatever light be, I suppose it consists of rays differing from one another in contingent circumstances, as bigness, form, or vigour."•
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In any case, light and aether are capable of mutual interaction; aether is in fact the interinediary between light and ponderable matter. When a ray of light meets a stratum of aether denser or rarer than that through which it has lately been passing, it is, in general, deflected from its rectilinear
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• Royal Society, Dec. 9, 1675.
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Ul the Seve1tleentlz Century.
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19
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.course; and differences of density of the aether between one mate!ial medium and another account on these principles for the reflexion and refraction of light. The condensation or rarefaction of the aether due to a material body extends to some little distance from the surface of the body, so that the inflexion due to it is really continuous, and not abrupt; and this further explains diffraction, ·which Newton took to be "' only a new kind of refraction, caused, perhaps, by the external aether's beginning to grow rarer a little before it came at the opake body, than it was in free spaces.''
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Although the regular vibrations of Newton's aether were not .supposed _to constitute light, its irregular turbulence seems to have represented fairly closely his conception of heat. He supposed that when light is absorbed by a material body, vibrations are set up in the aether, and are recognizable as the heat which is always generated in such cases. The .conduction of heat from hot bodies to contiguous cold ones he conceived to be effected by vibrations of the aether propagated between them; and he supposed that it is the violent agitation of aethereal motions which excites incandescent substances to emit light.
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Assu1ning with Newton that light is not actually constituted by the vibrations of an aether, even though such vibrations may exist in close connexion with it, the most definite and easily conceived supposition is that rays of light are streams of corpuscles emitted by luminous bodies. Although this was not the hypothesis of Descartes himself, it ,vas so thoroughly akin to his general scheme that the scientific men of Newton's generation, who were for the most part deeply imbued ·with the Cartesian philosophy, instinctively selected it from the wide choice of hypotheses which Newton had offered them; and by later writers it was generally associated with Xewton's name. A curious argument in its favour was drawn from a phenomenon ,vhich had then been known for nearly half a century: Vincenzo Cascariolo, a shoemaker of Bologna, had discovered, about 1630, that a substance, ,vhich afterwards
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C 2
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20
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The Theory ef the Aether
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received the name of Bologna stone or Bologna phosphorus, ha& the property of shining in the dark after it has been exposed for some time to sunlight; and the storage of light which seemed to be here involve.cl was n1.ore easily explicable on the corpuscular theory than on any other. The evidence in this quarter, however, pointed the other way when it was. found that phosphorescent substances do not necessarily emit the same kind of light as that which was used to stimulate them.
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In accordance with his earliest discovery, Newton considered colour to be an inherent characteristic of light, and inferred that it must be associated with some definite quality of the corpuscles or aether-vibrations. The corpuscles corresponding to different colours would, he remarked, like sonorous bodies of different pitch, excite vibrations of different .types in the aether; and "if by any means those [aether-vibrations] of unequal bignesses be separated from one another, the largest beget a Sensation of a Red colour, the least or shortest of a; deep Violet, and the intermediate ones, of intermediate colours; much after the manner that bodies, according to their several sizes, shapes, and motions, excite vibrations in the Air of various bignesses, which, according to those bignesses, make several Tones in Sound."*
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This sentence is the first enunciation of the great principle that homogeneous light is essentially pe1·iodic in its nature, and that differences of period correspond to differences of colour. The analogy with Sound is obvious ; and it may be remarked in passing that Newton's theory of periodic vibrations in an elastic · n1.edium, which he developedt in connexion with the explanation of Sound, would alone entitle him to a place among those who have exercised the greatest influence on the theory of light, even if he had made no direct contribution to the latter subject.
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* Phil. Trans. vii (1672), p. 5088.
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t Newton's Principia, Book ii., Props. xliii.-1.
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"'-
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in the Seventeenth Century.
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21
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Newton devoted considerable attention to the colours of thin . plates, and determined the empirical laws of the phenomena with great accuracy. In order to explain them, he supposed that " every ray of light, in its passage through any refracting surface, is put into a certain transient constitution or .state, which, in the progress of the ray, returns at equal -intervals, and disposes the ray, at every return, to be easily transmitted through the next refracting surface, and, between ·the returns, to be easily reflected by it_,,. The interval between two consecutive dispositions to easy transmission, or ~, length of fit," he supposed to depend on the colour, being greatest for red light_ and least for violet. If then a ray of homogeneous light falls on a ~hin plate, its fortunes as regards -transmission and reflexion at the two surfaces will depend on rthe relation which the length of fit bears to the thickness of the plate; and on this basis he built up a theory of the colours .of thin plates. It is evident that Newton's '' length of fit" eorresponds in some measure to the quantity which in the u.ndulatory theory is called the wave-length of the light; but the suppositions of easy transmission. and reflexion. were soon found inadequate to explain all N ewton.'s experimental results.at least without making other and more complicated additional
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.assumptions. At the time of the publication. of Hooke's Micrograpliia, and
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Newton.•s theory of colours, it was not known whether light is propagated instantaneously or not. An attempt to settle the question. experimentally had been made many years previously by Galileo,t who had stationed two men with ·1anterns at a considerable distance from each other; one of -.them was directed to observe when the other uncovered his light, and exhibit his own the moment he perceived it. But the interval of time required by the light for its journey was -.too small to be perceived in this ·way; and the discovery ·was
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• Optiel.:$, Book ii., Prop. 12.
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t IJiscoi·si e dimo:stra=ioni matematicke, p. 43 of the Elzevir edition of 1638.
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22
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The 7neory of the Aether
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ultimately made by an astronomer. It was observed in. 1675 by Olof Roemer• (b. 1644, d. 1710) that the eclipses of the first. satellites of Jupiter were apparently affected by an unknown disturbing cause; the time of the occurr~nce of the phenomenon was retarded when the earth and Jupiter, in the course of their orbital motions, happened to be most remote from each other, and accelerated in the contrary case. Roemer explained this by supposing that light requires a finite time for its propagation from the satellite to the earth; and by observations of eclipses, he calculated the interval required for its passage from the sun to the earth (the light-equation, as it is called) to be 11 minutes.t
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Shortly after Roemer's discovery, the wave-theory of light was greatly improved and extended by Christiaan Huygens (b. 1629, d. 1695). Huygens, who at the time was living in Paris, communicated his results in 1678 to Cassini, Roemer,. De la Hire, and the other physicists of the French Academy7. and prepared a manuscript of considerable length on the subject. This he proposed to translate into Latin, and to publish in that language together with a treatise on the Optics of Telescopes ; but the work of translation making little progress, after a delay of twelve years, he decided to print the work on wave-theory in its original form. In 1690 it appeared at Leyden,::: under the title Traite de la litnM·ere ou sont expliquees l es causes de ce qui luy ar11 i1:e dans la nijle:rion et dans la 11 ifraction. Et parti-
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-ii- Mem. de l' Acad. x. (1666-1699), p. 575.
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T It was soon recognized th1:1.t Roemel"s value was too large: and the astronomers of the succeeding half-century reduced it to 7 minutes. Delambre,
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by an investigation whose details appear to have been completely destroyed, pultlished in 1817 the value 493 ·2•, from a discussion of eclipses of Jupiter's satellites during the previous 150 years. Glasenapp, in an inaugural dissertation published in 1875, discussed the eclipses of the first satellite between 1848 and 1870, and derived, by different assumptions, values between 4965 and 5018 , the most probable vttlne being 500·8•. Sampson, in 1909, derived 498 ·648 from hisown readings of the Harvard Observations, and 498·79" from the Harvard readings, with probable errors of about± 0·02". The inequalities of Jupiter's surface giverise to some difficulty in exact determinations.
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:t Huygens had by this time returned to Holland.
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......
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in the Seventeenth Century.
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23
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culierement dans l'etrange rif1·acti"on du cristal d'Islande. Par C.H.D.Z.*
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The truth of Hooke's hypothesis, that light is essentially a
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form of motion, seemed to Huygens to be proved py the effects
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observed with burning-glasses; for in the combustion induced at the focus of the glass, the molecules of bodies are dissociated ; ·which, as he remarked, mus.t be taken as a certain sign of motion, if, in conformity to the Cartesian philosophy, we seek the cause of all natural phenomena in purely mechanical actions.
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The question then arises as to whether the motion is that of a medium, as is supposed in Hooke's theory, or whether it may be compared rather to that of a flight of arrows, as in the corpuscular theory. Huygens decided that the former alternative is the only tenable one, since beams of light proceeding in directions inclined to each other do not interfere with each other in any ,vay.
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Moreover, it had previously been shown by Torricelli that light is transmitted as readily through a vacuum as through air; and from this Huygens inferred that the medium or aether in which the propagation takes place must penetrate all matter, and be present even in all so-called vacua.
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The process of wave-propagation he discus:5ed by aid of a principle which was nowt introduced for the first time, and has since been generally known by his name. It may be stated thus : Consider a wave-front,+ or locus of disturbance, as it, exists at a definite instant t0 : then each surface-element of the wave-front may be regarded as the source of a secondary wave,. ,vhich in a homogeneous isotropic medium will be propagated outwards from the surface-element· in the form of a sphere
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whose radius at any subsequent instant t is proportional to
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(t-t0); and the wave-front which represents the whole distur-
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• i.e. Christiaan Huygens de Zuylicbem. The custom. of indicating names by
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initials was not unusual in that age.
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t- Traite de la lum., p. 17.
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t It m.ay be remarked that Huygens' " ·waves " are really what modern writers,
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following Hooke, call "pulses";. Huygens never considered true wave-trains
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having the property of periodicity. •
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•
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24
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The Theory ef the A ether
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bance -at the instant tis simply the envelope of the secondary waves which arise from the various surface elements of the original wave-front.* The introduction of this principle enabled Huygens to succeed where Hooke and other contemporary wave-theoristst had failed, in achieving the explanation of refraction and reflexion. His method was to combine his own principle with Hooke's device offollowing separately the fortunes of the right-hand and left-hand sides of a wave-front when it reaches the interface between two media. The actual explanation for the case of reflexion is as follows:-
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Let AB represent the interface at which reflexion takes place, AHO the incident wave-front at an instant t0, GMB the
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position which the wave-fron:t would occupy at a later instant t if the propagation were not interrupted by reflexion. Then by
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Huygens' principle the secondary wave from A is at the instant ta sphere RNS of radius equal to .AG: the disturbance from H, after meeting the interface at K, will generate a secondary wave TV of radius equal to KM, and similarly the secondary wave corresponding to any other element of the original wave-
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""- The justification for this was given long afterwards by Fresnel, Annales de .ckimie, xxi.
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• T e .g. Ignace Gaston Pardies and Pierre Ango, the latter of whom published
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a work on Optics at Paris:in 1682.
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' £n the Seventeeutfi Centur_y.
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25
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front can be found. It is obvious that the envelope of these secondary waves, which constitutes the final wave-front, will be .a plane BN, ·which will be inclined to AB at the same angle as AC. This gives the law of reflexion.
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The law of refraction is established by similar reasoning, -on the supposition that the velocity of light depends on the medium in ·which it is propagated. Since a ray ·which passes from air to glass is bent inwards towards the normal, it may be inferred that light travels more slowly in glass than in air.
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Huygens offered a physical explanation of the variation in velocity of light from one medium to another, by supposing that transparent bodies consist of hard particles which interact with the aethereal matter, modifying its elasticity. The -opacity of metals he explained by an extension of the same idea, supposing that some of the particles of metals are hard {these account for reflexion) and the rest soft: the latter destroy the luminous motion by damping it.
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The second half of the Theorie de la lumiere is concerned ·with .a phenomenon which had been discovered a few years previously by a Danish philosopher, Erasmus Bartholin (b. 1625, .d. 1698). A sailor had brought from Iceland to Copenhagen a number of beautiful crystals which he had coµ.ected in the Bay -0f Roerford. Bartholin, into whose hands they passed, noticed* that any small object viewed through one of these crystals .appeared double, and found the immediate cause of this in the fact that a ray of light entering the crystal gave rise in general to two refracted rays. One of these rays ·was subject to the ordinary law of refraction, while the other, which was called the e,xtraordinary ray, obeyed a different law, which Bartholin did not succeed in determining.
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The matter had arrived at this stage when it ·was taken up byHuygens. Since in his conception each ray of light corresponds to the propagation of a wave-front, the two rays in Iceland spar must correspond to two different wave-fronts propagated
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• E.xpe,·ime11ta criatalli Islandici disdiaclastici: 1669.
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26
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The Theory o/ the Aetlzer
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simultaneously. In this idea he found no difficulty ; as he says : "It is certain that a space occupied by more than one kind of matter may permit the propagation of several kinds of waves,. different in velocity; for this actually happens in air mixed with aethereal matter, where sound-waves and light-waves are propagated together."
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Accordingly he supposed that a light-disturbance generated at any spot within a crystal of Iceland spar spreads out in the form of a ·wave-surface, composed of a sphere and a spheroid having the origin of disturbance as centre. The spherical ·wavefront corresponds to the ordinary ray, and the spheroid to the extraordinary ray; and the direction in which the extraordinary ray is refracted may be determined by a geometrical construction, in which the spheroid takes the place which in the· ordinary construction is taken by the sphere.
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Thus, _let the plane of the figure be at right angles to the intersection of the wave-front with the surface of the crystal;. let AB represent the trace of the incident wave-front; and suppose that in unit tim~ the disturbance from B reaches the interface at T. In this unit-interval of time the disturbance from A will have spread out within the crystal into a sphere and spheroid: so • the wave-front corresponding to the,
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ordinary ray ·will be the tangent-plane to the sphere through the line whose trace is T, while the wave-front correspondingto the extraordinary ray will be the tangent-pl.,~e to the spheroid through the same line. The points of contact N
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' 1n tile Sc'llenteent/z. C entur_y.
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27
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and .LlI will determine the directions AN and .A.lJf of the t·worefracted rays• within the crystal.
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Huygens did not in the Theorie de la luniiere attempt a detailed physical explanation of the spheroidal wave, but communicated one later in a letter to Papin,t written in December, 1690. '' As to the kinds of matter contained in Iceland crystal,,, he says,. "I suppose one composed of small spheroids, and another which occupies the interspaces around these spheroids, and which serves to bind them together. Besides these, there is the matter of aether permeating all the crystal, both bet"\veen. and within the parcels of the two kinds of matter just mentioned ; for I suppose both· the little spheroids, and the matter which occupies the intervals around them, to be composed of small fixed particles, amongst which are diffused in. perpetual motion. the still fin.er particles of the aether. There is now no reason why the ordinary ray in the crystal should not be due to waves propagated in this aethereal matter. To account for the extraordinary refraction, I conceive another kind of waves, which have for vehicle both the aethereal matter and the two other kinds of matter constituting the crystal. Of these latter, I suppose that the matter of the small spheroids transmits the waYes a little more quickly than the aethereal matter, while that around the spheroids transmits these waves a little more slowly than the same aethereal matter. . . . These same waves, when they traYel in the direction of the breadth of the spheroids, meet with more of the matter of the spheroids, or at least pass ·with less obstruction, and so are propagated a little more quickly in this sense than in the other; thus the light-disturbance is propagated as a spheroidal sheet."
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Huygens made another discovery+ of capital importance when
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• The word nry in the -wave-theory is always applied to the line which goes from the centre of a wave (i.e. the origin of the disturb:ince) to a point on its surface, whatever may be the inclination of this line to the stu-face-element on which it abuts; for this line has the optical properties of the " rays" of the emission theory.
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-t Huygens' (E,w,·es, ed. 1905, x., p. 177.
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! Theorie de la /umiere, p. 89.
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28 Theory ef the Aether £n the Seventeenth Century.
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experimenting with the Iceland crystal. He observed that the
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two rays which are obtained by the double refraction of a single ray afterwards behave in a way different from ordinary light
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which has not experienced double refraction; and in particular,
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if one of these rays is incident on a second crystal of Iceland spar., it gives rise in. some circumstances to two, and in others
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to only one, refracted ray. The behaviour of the ray at this
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second refraction can be altered by simply rotating the second crystal about the direction of the ray as axis; the ray under-
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going the ordinary or extraordinary refraction according as the principal section of the crystal is in a certain direction or in the
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direction at right angles to this.
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The first stage in the explanation of Huygen~' observation was reached by Newton, who in 1717 showed~ that a ray
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obtained by double refraction differs from a ray of ordinary
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light in the same way that a long rod whose cross-section is a rectangle differs from a long rod whose cross-_section is a circle:
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mother words, the properties of a ray of ordinary -light are the
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same with respect to all directions at right angles to its direction
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of propagation, whereas a ray obtained by double refraction
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must be supposed to have sides, or properties related to special
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directions at right angles to its own direction. The refraction
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of such a ray at the surface of a crystal depends on the relation
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of its sides to the principal plane of the crystal.
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That a ray of light should possess such properties seemed to Newtont an insuperable objection to the hypothesis ·which
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regarded waves of light as analogous to waves of sound. On
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this point he wa·s in the right: his objections are perfectly
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valid against the wave-theory as it was understood by his
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.contemporaries+, although not against the theory§ which was put
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forward a century later by Young and Fresnel.
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• The second edition of Newton's Opticks, Quei-y 26.
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t Opticks, Query 28.
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:t In which the oscillations are performed in the direction in which the wave
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.-advances.
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§ In which the oscillations are performed in a direction at right angles to that
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in which the wave a.,lvances.
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CHAPTER II.
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ELECTRIC AND MAGNETIC SCIENCE PRIOR TO THE INTRODUCTION OF THE POTENTIALS.
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THE magnetic discoveries of Peregrinus and Gilbert, and the vortex-hypothesis by which Descartes had attempted to explain them,• had raised magnetism to the rank of a separate science by the middle of the seventeenth century. The kindred science of electricity ·was at that time in a less developed state; but it had been considerably advanced by Gilbert, whose researches in this direction will now be noticed.
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For two thousand years the attractive po"\ver of amber had been regarded as a virtue peculiar to that substance, or possessed by at most one or two others. Gilbert proYedt this view to be mistaken, showing that the same effects are induced by friction in quite a large class of .bodies ; among which he mentioned glass, sulpliur, sealing-wax, and various precious stones.
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A force which was manifested by so many different kinds of matter seemed to need a name of its own ; and accordingly Gilbert gave to it the name electric, which it has ever since retained.
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Between the magnetic and electric forces Gilbert remarked many distinctions. The lodestone requires no stimulus of friction such as is needed to stir glass and sulphur into activity. The lodestone attracts only magnetizable substances, ·whereas electrified bodies attract everything. The magnetic attraction between two bodies is not affected by interposing a sheet of paper, or a linen cloth, or by immersing the bodies in water;. whereas the electric attraction is readily destroyed by screens. Lastly, the magnetic force tends to arrange bodies in definite
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-A<- Cf. pp. 7-9.
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+ .De ll£f1gnete, lib. ii .. cap. 2.
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.30
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Electric and .llfagnetic Sci"ence
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-orientations; while the electric force merely tends to heap them together in shapeless clusters.
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These facts appeared to Gilbert to indicate that electric phenomena are due to something of a material nature, ·which under the influence of ·friction is liberated from the glass or .amber in which under ordinary circumstances it is imprisoned. In support of this vie-w he adduced _evidence from other quarters. Being a physician, he was ·well acquainted with the doctrine that the human body contains various humours or kinds of moisture-phlegm, blood, choler, and melancholy,-which, as they predominated, were supposed to determine the temper of mind; and when he observed that electrifiable bodies ·were almost all hard and transparent, and therefore (according to the ideas of that time) formed by the consolidation of watery liquids, he concluded that the common menstruum of these liquids must be a particular kind of humour, to the possession of which the electrical properties of bodies were to be referred. Friction might be supposed to warm or otherwise excite or liberate the p.umour, ·which would then issue from the body as an effluvium and form an atmosphere around it. The effluvium must, he remarked, be very attenuated, for its emission cannot be detected by the senses.
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The existence of an atmosphere of effluvia round every electrified body might indeed have been inferred, according to Gilbert's ideas, from the single fact of electric attraction. For he believed that matter cannot act where it is not; and hence if a body acts on all surrounding objects without appearing to touch them, something must have proceeded out of it unseen.
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The whole phenomenon appeared to h:iin to be analogous to the attraction which is exercised by the earth on falling bodies. For in the latter case he conceived of the atmospheric air as the effluvium by which the earth draws all things downwards to itself. •
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Gilbert's theory of electrical emanations commended itself generally to such of the natural philosophers of the seventeenth century as were interested in the subject; among ·whom ·were
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