INSTRUMENTAL TRADITIONS AND THEORIES OF LIGHT

Science and Philosophy

VOLUME 9

Series Editor

Nancy J. Nersessian, Program in Cognitive Science, College ofComputing, and School ofPublic Policy, Georgia Institute ofTechnology, Atlanta

Editorial Advisory Board

Joseph Agassi, Department ofPhilosophy, York University and Tel Aviv University (Emeritus)Geoffrey Cantor, Department ofPhilosophy, University ofLeedsNancy Cartwright, Department ofPhilosophy, London School ofEconomicsJames T. Cushing, Department ofPhysics and Department ofPhilosophy, Notre Dame

UniversityLindley Darden, Committee on the History and Philosophy ofScience, University ofMarylandMax Dresden, Institute for Theoretical Physics, SUNY Stony Brook (Emeritus)Allan Franklin, Department ofPhysics, University ofColorado, BoulderMarjorie Grene, Department ofPhilosophy, University ofCalifornia, Davis (Emeritus)Adolf Griinbaum, Department ofPhilosophy, University ofPittsburghRichard Lewontin, Museum ofComparative Zoology, Harvard UniversityThomas Nickles, Department ofPhilosophy, University ofNevada, RenoDudley Shapere, Department ofPhilosophy, Wake Forest University

This series has been established as a forum for contemporary analysis of philosophical problemswhich arise in connection with the construction of theories in the physical and the biologicalsciences. Contributions will not place particular emphasis on anyone school of philosophicalthought. However, they will reflect the belief that the philosophy of science must be firmly rootedin an examination of actual scientific practice. Thus, the volumes in this series will include ordepend significantly upon an analysis of the history of science, recent or past. The Editors welcomecontributions from scientists as well as from philosophers and historians of science.

The titles published in this series are listed at the end ofthis volume.

INSTRUMENTAL TRADITIONS AND

THEORIES OF LIGHT

The U ses of Instruments in the Optical Revolution

by

XIANGCHEN California Lutheran University

SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.

A C.I.P. Ctalogue record for this book is available from the Library of Congress.

ISBN 978-94-010-5824-7 ISBN 978-94-011-4195-6 (eBook) DOI 10.1007/978-94-011-4195-6

Printed an acidjree paper

AII Rights Reserved

© 2000 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 2000

Softcover reprint of the hardcover l st edition 2000 No part of the material protected by this copyright notice may be reproduced or

utilized in any form Of by any means, electronic Of mechanical, including photocopying, recording or by any information storage and

retrieval system, without written permission from the copyright owner.

To LiLi,my "ultimate classmate ",

for her understanding and love

CONTENTS

List of Figures

Acknowledgments

Introduction

Chapter I. Comparisons of Explanatory PowerI. Introducing the wave theory to Britain2. Comparing the explanatory powers3. The reflection of a particle theorist4. Improving the explanatory power of the particle theory5. The problem of selective absorption

Chapter 2. Explanatory Power and ClassificationI. The Newtonian taxonomic systems2. Herschel's synthetic attempt3. Lloyd's dichotomous design

Chapter 3. Classification and the Use of InstrumentsI. Brewster's plate polarizers and crystal analyzers2. Fresnel's innovative uses of crystal analyzers3. Herschel's understanding of partial polarization4. Lloyd and conical polarization

Chapter 4. The Dispute over Dispersion1. Powell's formulas of dispersion2. Fraunhofer's theodolites and spectral lines3. Powell's hollow prisms and spectral lines4. Brewster's telescope and spectral lines5. The difficulties ofmaking gratings6. The impasse in the debate

Chapter 5. The Discovery of the "Polarity of Light"1. The discovery of the "polarity of light"2. Brewster's classification3. The wave explanations

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4. The setback of the wave theory 785. Powell's hollow prism 816. Stokes's solution 83

Chapter 6. The Measurements of the Intensity ofLight1. Potter's reflecting photometer 872. Potter's measurements ofmetallic mirrors 913. Potter's measurements of glass mirrors 934. Potter's comparative photometer 975. The debate on the reliability of the eye 996. Potter's attack on the wave account of diffraction 104

Chapter 7. Instrumental Traditions1. Optical instruments as image-making devices 1092. The eye as an optical instrument III3. Optical instruments as measuring devices 1144. Whewell on optical measurements 1185. The visual tradition 1216. The geometric tradition 125

Chapter 8. The Geometric Tradition and the Wave Theory ofLightI. Humboldtian sciences: measuring nature 1292. The shortage of scientific manpower in optics 1313. A new generation ofphysicists 1344. Stokes's experiments on fluorescence 1375. Measuring the velocity of light 1416. The status of the wave theory 144

Chapter 9. The Visual Tradition and the Closure of the Optical Revolution1. Stereoscopes and the studies of space perception 1472. Stroboscopes and the studies of visual persistence 1523. Kaleidoscopes and the making of "philosophical toys" 1564. Binocular cameras and the photographic industry 1605. The end of the optical revolution 164

Conclusion 167

Appendixes1.The intensity of light in Brewster's experiment of polarizationby successive refraction 175

2. Powell's calculation of refractive indices 1773. The relative error of Powell's measurements of refractive indices 1784. Powell's mathematical analysis of the "polarity oflight" 180

IX

5. A recalculation of the reflective power of glass without Potter'sapproximations 181

Notes 183

References 191

Name Index 201

Subject Index 205

LIST OF FIGURES

Figure 2.1 Brewster's taxonomy 16Figure 2.2 Herschel's taxonomy 18Figure 2.3 Lloyd's taxonomy 23

Figure 3.1 Brewster's plate polarizer and crystal analyzer 29Figure 3.2 Brewster's procedure for classifying polarization 32Figure 3.3 Arago's apparatus for interference ofpolarized light 34Figure 3.4 Fresnel's procedure for classifying polarization 36Figure 3.5 Herschel's apparatus for producing chromatic polarization 38Figure 3.6 Lloyd's apparatus for producing external conical refraction 42Figure 3.7 Lloyd's law of conical polarization 43

Figure 4.1 Fraunhofer's spectroscope 50Figure 4.2 Comparisons of Powell's calculations and Fraunhofer'smeasurements 52

Figure 4.3 Powell's spectroscope 54Figure 4.4 Brewster's apparatus for producing prismatic spectra 58Figure 4.5 Brewster's diffraction spectra 63

Figure 5.1 Talbot's apparatus for producing "Talbot's bands" 70Figure 5.2 Brewster's apparatus for producing the "polarity oflight" 71Figure 5.3 Relations between polarity and refrangibility 74Figure 5.4 Brewster's classification of polarization 75Figure 5.5 Powell's apparatus for producing the "polarity oflight" 82Figure 5.6 Stokes's apparatus for producing the "polarity of light" 85

Figure 6.1 William Herschel's apparatus for measuring reflective power 88Figure 6.2 Potter's reflecting photometer 90Figure 6.3 Potter's reflecting photometer (details) 91Figure 6.4 Comparisons between Potter's measurements and Fresnel'spredictions 95

Figure 6.5 Potter's measurements: A recalculation without the approximations 96Figure 6.6 Potter's comparative photometer 97Figure 6.7 Forbes's "thermal photometer" 101Figure 6.8 Forbes's proposed experiment 102

xi

xii FIGURES

Figure 7.1 Newton's apparatus for testing the sine law 115Figure 7.2 Brewster's apparatus for measuring refractive indices 117Figure 7.3 The visual tradition 124Figure 7.4 Rayleigh's interference refractometer 126Figure 7.5 The geometric tradition 128

Figure 8.1 Numbers of papers presented in Section A of the BritishAssociation, 1831-1855 132

Figure 8.2 Numbers of papers published by old-generation wave theorists 133Figure 8.3 Numbers ofpapers published by new-generation wave theorists 135Figure 8.4 Stokes's apparatus for detecting fluorescence 139Figure 8.5 Fizeau's apparatus for measuring the velocity of light 142Figure 8.6 Foucault's apparatus for measuring the velocity of light 144

Figure 9.1 Wheatstone's reflecting stereoscope 149Figure 9.2 Convergence of optic axes 151Figure 9.3 Brewster's lenticular stereoscope 152Figure 9.4 Faraday's anorthoscope 153Figure 9.5 Plateau's stroboscope 155Figure 9.6 Brewster's kaleidoscope 157Figure 9.7 Numbers of optical instrument makers in Britain, 1801-1850 159Figure 9.8 Single-lens stereoscopic camera, designed by T.H. Powell 161Figure 9.9 Double-lens stereoscopic camera, designed by Brewster 162

ACKNOWLEDGMENTS

Numerous people have helped to improve the arguments of this book. I especially thankPeter Barker, Jed Buchwald and Allan Franklin for their advice and criticisms on earlierdrafts of the manuscript. They do not entirely agree with my views, and I have, at best,answered only some of their questions. Thomas Nickles has read the manuscript word­by-word, and he has provided numerous comments that helped me strengthen thearguments and avoid many mistakes. I am grateful for the help and encouragement ofNancy Nersessian, who has taught me many things in the process of preparing apresentable manuscript. I have also benefitted from discussions, both formal andinformal, with many people over the years. They are Peter Achinstein, Hanne Andersen,Roger Ariew, Geoffrey Cantor, Larry Laudan, David Lux, Albert Moyer, AndyPickering, Joseph Pitt, and Sigmar Schwarz.Between 1998 and 1999, the Dibner Institute for the History of Science and

Technology at MIT offered me a superior research environment and resources tocomplete this book. I had an enormous amount of help there, both from the kindnessof the staff and from stimulating discussion with other Dibner fellows. I also had thesupport from California Lutheran University, which granted me sabbatical leave whileI was writing the manuscript.In a few sections of this book I have used revised parts of some previously

published articles: "Taxonomic Changes and the Particle-wave Debate in EarlyNineteenth-century Britain," Studies in History and Philosophy ofScience 26 (1995):251-271; "The Debate on the Polarity ofLight During the Optical Revolution," Archivefor History of Exact Sciences 50 (1997): 359-393; "Dispersion, ExperimentalApparatus, and the Acceptance of the Wave Theory of Light," Annals ofScience 55(1998): 401-420. I thank the editors of these journals for permission to draw on thesepublished articles.I thank my colleagues and friends at California Lutheran University for providing

me a pleasant environment to work on this project. Hall Stuart-Lovell has offeredprofessional help in editing the manuscript. Finally this book is dedicated to Li Li, mywife. Without her understanding, encouragement and love, I would have not been ableto complete this book.

Thousand Oaks, February 2000

xiii

INTRODUCTION

This book is about the relationship between optical instruments and optical theories inthe context of the debate between the particle and the wave theory of light in earlynineteenth-century Britain. Optical instruments themselves have drawn the attention ofmany scholars. Gerard Turner has offered us exceptionally rich information on thehistory of various optical instruments, from spectacles to telescopes and microscopes(Turner 1969). Henry King's work on the telescope and Jim Bennett's work onspectroscopes are also very instructive (King 1955; Bennett 1984). But most previousworks on optical instruments have focused on the technical aspects of instrumentation,such as materials, structures, designs, and underlying theoretical principles. Although,in general, the making of instruments required theoretical knowledge, neither theparticle nor the wave theories of light played any significant role in the design ofopticalinstruments in the specific context on which this book is to focus. If we limitedourselves to the technical aspects of instrumentation, we would find little that shedslight on the particle versus wave debate. To reveal the connections between opticalinstruments and optical theories and consequently the role ofoptical instruments in therevolutionary change, we need to focus on the procedural aspect of instrumentation -­how practitioners used optical instruments in their explorations of the world.For a long time, philosophers have recognized that there are fundamental

differences betWeen two kinds of intelligent activities: knowing that and knowing how.As noted by Gilbert Ryle more than forty years ago, knowing that involves intelligentoperations that require the observance of clearly articulated rules. Logical andmathematical analyses are good examples of this kind of intellectual activities in whichpeople act consciously according to well-explicated principles or criteria. But in otherintellectual activities, the rules are unformulated. People can act properly but do sowithout understanding the rules behind their acts, or without knowing how to articulatethose rules. For example, a wit knows how to make good jokes and how to detect badones, but he may not be able to tell us or even himself any recipes for doing so; or, awell-trained sailor can tie complex knots and discern whether someone else is tyingthem correctly, but he is probably incapable of describing in words how the knotsshould be tied. Ryle calls this kind of intellectual activity knowing how, which operatesin such a way that "efficient practice precedes the theory of it; . .. Some intelligentperformances are not controlled by any anterior acknowledgments of the principlesapplied to them"(Ryle 1949, 30).Recent cognitive studies have shed more light on the nature of knowing how.

According to the production system model, a well-received account, knowing how isthe result of skilled performance. With repeated practice, people can learn to process

xv

xvi INTRODUCTION

automatically, and can react to certain stimuli directly without retrieving the knowledgefrom the long-term memory that specifies conditions and actions for achieving a goal.Hence, knowing how need not be verbalizable nor open to conscious introspection(Masson 1990, 222-8; Barsalou 1992, 88). A good example is learning how to ride abike or, more precisely, how to keep one's balance while riding on a bike. Ourknowledge of physics teaches us that, in order to compensate for a given angle ofimbalance, we must take a curve on the side of the imbalance, and that the radius of thecurve should be proportional to the square of the velocity divided by the tangent of theangle of the imbalance. We may write down this requirement in the form of a rule, butlearning this rule does not help one know how to cycle. In fact, the majority of cyclistswould not be able to describe this rule in words, although they know quite well how tomaintain balance. The key to knowing how to cycle is to mastering the proceduresthrough repeated practice. Thus, knowing how is also called procedural knowledge.Many philosophers and historians ofscience realize that knowing how, or procedural

knowledge, holds a key for understanding the development of science. In his study ofthe history of electromagnetism, David Gooding gives detailed analysis of Faraday'sexperimental procedures as recorded in his notebooks, and shows convincingly how agroup of diverse investigators reached a consensus on electromagnetism not becausethey had similar perceptions or interpretations of the subject, but because Faraday'sprocedures made the hitherto unknown phenomenon assessable and replicable.According to Gooding, procedural knowledge is also the key to understanding howreality constrains the enterprise of science. The objectivity of science is rooted in thereproducibility of experiments, which requires transforming privately experiencedinteractions with the world into publicly accessible phenomena. By generating a set ofprotocols that others can employ, procedural knowledge facilitates the transformationfrom the private to the public domain and makes replications of experiments possible.But traditional analytic philosophy concentrates on the world of talk, thought andargument, and fails to recognize the pre-articulated or unarticulated aspect of science.This ignorance of procedural knowledge, according to Gooding, constitutes the real"neglect of experiment," which can eventually weaken our belief in science by denyingits objectivity (Gooding 1990).In this book, I introduce the notion "instrumental tradition" to capture the

procedural aspect of instrumentation. An instrumental tradition is a set of relativelystable procedures adopted by a community concerning the proper uses of instruments.In the early nineteenth century, there were two incompatible instrumental traditions inthe field of optics, each of which nurtured a body of practices that exemplified howoptical instruments should be operated, and particularly, how the eye should be usedin optical experiments. On the one side, there was a tradition rooted deeply in themetaphysical belief that the eye was an ideal optical instrument and thus should playan essential role in all optical experiments. Consequently, it regarded manmade opticalinstruments as aids to the eye, and evaluated them according to how good they were atproducing images suitable for the perception of the eye. In practice, this traditionnurtured a body of procedures that emphasized the proper uses of the eye. Since the eye

INTRODUCTION xvii

was an intrinsic element in all optical systems, this tradition insisted that we mustconduct optical experiments when the eye was in its best state, and that we must adoptspecial procedures to ensure that the eye was in its optimal conditions. I call this thevisual tradition because of its faith in the eye.On the other side, there was a tradition rooted in doubts about the reliability of the

eye in optical experiments, particularly in precise measurements. Consequently, it didnot regard the eye as the model ofmanmade optical apparatus, nor an intrinsic elementof any optical system. In practice, this tradition nurtured a body of procedures, botharticulated and tacit, that aimed at reducing the role of the eye in optical experiments.Among these procedures, the approach of converting optical effects to geometricparameters was essential, and it significantly decreased the impact of the eye on opticalmeasurements. I call this the geometric tradition because of its emphasis upon theconversion of optical images to geometric parameters.The notion of "instrumental tradition" is embedded in a specific understanding of

scientific practice. The exact meaning of scientific practice is controversial. Traditionalphilosophers of science, such as logical empiricists, emphasize the logical aspect ofscientific practice. For them, scientific practice consists in the appraisal of conceptualknowledge, an operation ideally governed by logic and methodology. Recently, somestudents of science have highlighted the temporal and contextual aspects of scientificpractice. For example, Barry Barnes holds that scientific practice is an open-endedprocess driven by scientists' interests -- they extend scientific knowledge to fit newcircumstances by seeing new situations as relevantly like old ones (Barnes 1982), andJoseph Rouse believes that scientific practice is a process always engaged in relationsofpower, because practice exists only against a background of resistance (Rouse 1996).My understanding of scientific practice draws primarily on Hubert Dreyfus's concepts,which emphasize its operational aspect (Dreyfus 1991; Dreyfus 1992). According toDreyfus, scientific practice is a skilled engagement with the world. A skilled interactionwith the world is a meaningful response to things, rather than an imposition ofmeaningon things. Thus, typical cases of scientific practice are neither linguistic nor perceptualrepresentations, but skilled bodily activities. Since skills embodied in practice areirreducible to articulated rules, the normative power of scientific practice does not comefrom rule-governed activities. In fact, all intelligent behavior, including scientIficpractice, "must be traced back to our sense ofwhat we are, which is ... something wecan never explicitly know" (Dreyfus 1979,56-7; original emphasis).!In the light of such a specific understanding of scientific practice, I emphasize

several general features of an "instrumental tradition." First, an instrumental traditionis not about the technical aspects of instrumentation, but about its operational aspect.Neither the material structures of optical instruments nor the theoretical principlesbehind their designs and functions are the references of this notion. In their technicalaspects, optical instruments are complexly heterogeneous. We classify some apparatus,such as telescopes, polarizers and photometers, as optical instruments because they aredesigned and built on the base of optical knowledge. But we classify some others, suchas theodolites, gratings and apertures, as optical instruments simply because they have

xviii INTRODUCTION

been used extensively in studying optical phenomena. There are few similaritiesbetween different kinds of optical instruments, even among those from the samecategory, for example, an extinction photometer and a shadow photometer. Butsimilarities and patterns emerge when we examine the procedural aspect ofinstrumentation. Different instrumental traditions consist in the distinct styles in whichpractitioners use optical instruments, particularly their ways ofusing the eye.Second, an instrumental tradition does not consist merely of articulated

methodological principles or imperatives. Unlike the doctrines of optical theories thatare clearly stated in a variety of literatures and openly debated in public, many practicesendorsed by instrumental traditions remain tacit. In the early nineteenth century,procedures of using optical instruments were rarely discussed openly -- most textbooksof optics concentrated on technical aspects, such as the materials and structures ofoptical instruments. This tacit feature often caused communication problems amongthose who belonged to different instrumental traditions, a phenomenon similar to theincommensurability experienced by those who belong to rival theoretical paradigms.However, communication problems associated with instrumental traditions do not resultfrom failures in translating or understanding terms used by the other side, but fromfailures in recognizing issues that remain unarticulated.Third, an instrumental tradition does not define the practice of a scientific

community by offering rigid imperatives, expressed in the form of a set of sufficientand necessary conditions. Instead, it influences the behavior of the members of thecommunity by developing exemplars of the proper procedures for operating the majorinstruments. Not everyone in the community always acts according to the betterexemplars set up by the tradition. Thus, we should understand the relations among thosewho belong to the same instrumental tradition as some sort of family resemblance.Similarly, the relations between rival instrumental traditions are not absolutelyexclusive. We should not be surprised to fmd someone who adopts procedures endorsedby one tradition in some cases, but switches to a different set of procedures belongingto another tradition under different circumstances.

* * *The development of optical theories has long been closely examined by the

historians of science. In Britain, the early 1830s was a critical period for opticaltheories. The particle theory of light, which defined light as a sequence of rapidlymoving particles subject to the law ofmechanics, had dominated the field of optics inBritain since Newton's endorsement, but this dominance became shaky at the beginningof the nineteenth century when Thomas Young discovered the principle of interference.In Britain, Young's works caused a revival of the wave theory oflight that regardedlight as a disturbance in an elastic medium called ether. In the late 1820s, a group ofBritish "gentlemen of science," including John Herschel, George Airy, Baden Powelland William Whewell, most of them trained at Cambridge, adopted the wave theory.Beginning in 1830, these newly committed wave theorists began publishing theirresearches, both theoretical and experimental, advocating the wave theory. Whatfollowed was a sequence of heated debates between the two sides, concerning not only

INTRODUCTION xix

the respective explanatory models (particle vs. wave), but also the closely relatedanalytic methods -- the ray analysis that treated light as countable objects (rays) and thewavefront analysis that utilized a group of entirety new concepts such as front andphase. The conflict between the rival analytic methods was more profound than thedebate regarding the explanatory models. Many wave theorists including Herschel, Airyand PoweIl who were not for some time fuIly able to embody their understanding oflight in a coherent manner frequently turned back to the ray method when theyencountered novel phenomena {Buchwald 1989: 291-96; Chen 1997}. Eventually, theparticle theory was replaced by the wave theory, and the ray analysis by the wavefrontanalysis. This was the so-caIled "optical revolution."2WheweIl provided the first historical survey of this revolutionary change in his

History ofthe Inductive Sciences, first published in 1837. In his philosophy of science,WheweIl conceptualized the development of science in three stages. The beginning wasa "prelude" when basic facts were found but no consensus on high level generalizations.FoIlow.ing the "prelude" was an "inductive epoch," in which a theory was establishedthrough an "inductive process." After that was a "sequel," in which the inductivelyestablished theory was extended and widely accepted (WheweIl 1967, vol. 1, 12). Usingthis schema, WheweIl divided the history ofoptics into three stages. The "prelude" layin the seventeenth and eighteenth centuries when the debate between the two rivaltheories of light emerged. The "inductive epoch" began in the early nineteenth centurywith the victory of the wave theory. According to WheweIl, the wave theory establishedits true status through its explanatory successes. Thanks to the works of Young andFresnel, the wave theory could explain a variety of optical phenomena using a simplemodel, provide quantitative accounts with elegant mathematical analysis, and makesuccessful predictions of hitherto unknown phenomena.3 WheweIl believed that theseexplanatory successes settled the debate and started the stage of "sequel" in the lateI820s, during which the community accepted the wave theory and concentrated on itsapplications to new domains (WheweIlI967, vol. 2, 312-73).In Britain, however, the debate between the particle and wave theories did not

disappear after the late 1820s. On the contrary, it continued into the early 1850s.Despite its explanatory successes, the wave theory did not immediately commandcomplete support from the optical community in Britain. Many particle theorists,including David Brewster, Henry Brougham, John Barton, and Richard Potter, neveraccepted the wave theory. This group ofwave opponents was not large, nor organized,but their voice was persistent. In a period lasting more than 30 years, they conductedmany experiments to expose the shortcomings of the wave theory, they publishednumerous articles in major scientific journals to chaIlenge the wave account, and theyprovoked several major debates in scientific societies such as the British Association.4

These challenges to the wave theory were not in vain. On more than one occasion, thewave opponents were able to sway the minds of some wave theorists, forcing them toopenly admit the defects of their theory.s Why did the explanatory successes of thewave theory fail to persuade its opponents? If the wave theory had established its truestatus in the late 1820s, why did the debate continue until the early 1850s? The superior

xx INTRODUCTION

explanatory power of the wave theory together with the longevity of the conflictbetween the particle and the wave theory in Britain constitutes what I call the "riddleof the optical revolution."One possible answer to the riddle is that the wave opponents were simply

unscientific and irrational. Some previous studies have suggested that the waveopponents might have recognized the explanatory superiority of the wave theory, butrefused to accept it for social, political, or personal reasons. These studies thus adopteda hostile tone to all wave opponents, accusing them of"ignorance as well as prejudice,"and calling them "reactionary," or simply "elderly holdouts" -- Brewster, Broughamand Potter all lived well to their eighties (WhewellI967, vol. 2, 347; Mach 1926,275;Worrall 1990). But by appealing to irrational factors, these previous studies overlookedmany significant developments in optics between the 1830s and the 1850s. The debateconcerning explanatory models and analytic methods in Britain stimulated manyimportant discoveries. In their search for evidence to contradict the wave theory, thewave opponents made contributions in their experimental investigations of refractiveindices, prismatic spectra and photometric phenomena. In their responses to thecriticisms, wave theorists also improved the theory by offering new accounts fordispersion, selective absorption, metallic reflection, and diffraction by a circularaperture. Using irrational factors to explain the longevity of the debate would cut offthe intellectual root of the historical process that constituted the foundation for thedevelopment of optics in the second half of the century.The riddle of the optical revolution, however, resulted from a narrow

historiographic perspective that limits its analysis of the optical revolution to opticaltheories and the associated explanatory power. In the early nineteenth century, practicein optics consisted not only in using theories to explain or predict optical phenomena,but also in manipulating optical instruments to explore the world. The optical revolutioninvolved heated disputes over the nature oflight, as well as rich discussions on the usesof a variety of optical instruments, an incomplete list ofwhich included spectroscopes,telescopes, polarizers, refractometers, photometers, gratings, prisms and apertures. Tosolve the riddle, I adopt a different historiographic perspective in this book by focusingon the role of optical instruments, which remained invisible behind the declarativeknowledge, that is, the explicit arguments regarding the nature of light. After we reviewhow the different uses of optical instruments, or more precisely, different instrumentaltraditions, affected the practitioners' positions in the particle versus wave debate andtheir judgments in daily practice, we will understand why the wave opponents refusedto accept the wave theory. Limited by the ways that they used optical instruments, theymay not have fully recognized the explanatory successes of their rivals. The long-termresistance to the wave theory might not be irrational in the contexts defined byinstrumentation.

* * *I will begin my discussion on the issue of comparing explanatory power. Chapter

1 will review the systematic comparisons of the rival optical theories presented byHerschel and Brewster at the dawn of the revolutionary change. Their comparisons

INTRODUCTION xxi

concentrated on the explanatory powers of the theories, but their judgments wereinconsistent. Herschel argued for the explanatory superiority of the wave theory, butBrewster insisted that the explanatory power of the particle theory could be as good asthat of the wave theory after the former assimilated the interference principle. Theseassessments did not settle the debate between the rival theories.We will see in Chapter 2 that the conflicting judgments ofexplanatory power made

by Herschel and Brewster resulted, in part, from differences in the classificationsystems that they adopted. Brewster adopted the Newtonian system, which dividedoptical phenomena into eight categories, and consequently highlighted the explanatorydeficiencies of the wave theory. Herschel, and later Lloyd, introduced classificationsystems with dichotomous structures. These new systems used the state of polarizationas the key, or even the only, classification standard, and maximized the explanatorymerits of the wave theory. Without these fundamental changes in classification systems,the explanatory superiority ofthe wave theory would have been unrecognizable.But their selections of classification systems were not arbitrary, as we willleam in

Chapter 3. Brewster could not accept a dichotomous classification system because ofthe procedures that he adopted in his polarization experiments. Employing an analyzerto vary the intensity of polarized light and using the eye to detect the intensity ofpolarized light directly, Brewster believed that successive refractions could completelypolarize a beam of light, and that partial polarization was an independent physical state.He consequently conceptualized polarization as a property of a collection of rays andthereby not a fundamental category. On the other hand, the dichotomous systemsproposed by Herschel and Lloyd had a different procedural basis. Using an analyzer toalter the planes of polarization, Fresnel had invented a new procedure to determine thestate of polarization and proposed a new taxonomy ofpolarization. This new taxonomyimplied that polarization was the property of an individual wavefront and described theessential feature ofwaves as transverse vibrations. Thus, to followers of Fresnel, it wasreasonable to use the state ofpolarization as the primary standard for classification andadopt a dichotomous system.In the next three chapters, I document how differences in the use of optical

instruments affected scientists' daily practice, such as data interpretation, experimentappraisal, and theory evaluation. Chapter 4 addresses the dispute over dispersion. In themid I830s, Powell proposed a wave account of dispersion and triggered a heated debatein which both sides utilized the same set of experimental data to test the proposedaccount of dispersion, but could not agree on how these data should be analyzed. Usinga theodolite as the key apparatus in spectral experiments, Powell measured the angularpositions of the spectral lines and interpreted the differences between prismatic anddiffraction spectra as optical effects. Employing the eye and a telescope with a highmagnification power as the key apparatus, Brewster counted the number of spectrallines and believed that the differences between prismatic and diffraction spectraoriginated from the interactions between light and matter. These differentunderstandings provoked conflicting judgments of the method for analyzing the rawdata. Instrumental obstacles further led the debate into an impasse, because high quality

xxii INTRODUCTION

gratings were unavailable for the necessary experimental replication.Chapter 5 discusses the debate over the anomaly called "polarity of light." In the

late 1830s, Brewster discovered this unexpected phenomenon and used it to challengethe wave theory. In his experiment, Brewster employed the pupil of the eye as theaperture, but the existence of the aperture was obscure because the role of the eye wasusually ignored in physical optics. Brewster's experimental results thus appeared to bedue to interference. Early wave accounts failed to explain the anomaly because theytreated it as interference, and wave theories suffered a setback in explanatory power.The correct explanation of the phenomenon did not appear until the late 1840s whenPowell introduced a new experimental design. Because he used the objective lens of atelescope as the aperture, the existence of the aperture became obvious, and Powell'sdesign exhibited strong similarities to diffraction experiments. After Stokes classifiedthe phenomenon correctly as diffraction, he developed a successful explanation andsettled the debate quickly.Chapter 6 covers the debate over photometric measurements. Armed with a

photometer originally designed for evaluating telescopes, Potter measured the reflectivepower of metallic and glass mirrors at various angles in the early 1830s. Because hefound significant discrepancies between his measurements and Fresnel's predictions,Potter developed a strong objection to the wave theory. However, Potter'smeasurements, particularly those used as the evidence to reject the wave theory, werecolored by a peculiar procedure. In order to protect the sensitivity of the eye, Pottermade a couple of approximations in the measuring process, which exaggerated thediscrepancies between the theory and the data. Potter's photometric measurementsreceived strong criticisms from wave theorists, not because they felt that they neededto defend their theory, but because they believed that Potter was wrong in using the eyeas an essential apparatus in the experiments.In the last three chapters of the book, I discuss how the procedural aspect of

instrumentation determined the pace of the optical revolution. The differences in the useof instruments during the optical revolution originated from two incompatibleinstrumental traditions, each of which endorsed a body of practices concerning howoptical instruments should be properly used. Chapter 7 gives a brief historical reviewof these instrumental traditions and outlines their key features. In their early years,optical instruments functioned primarily as visual aids to the eye, which was regardedas an ideal optical instrument. In these historical contexts, the visual tradition thataccepted the intrinsic role of the eye in all optical instruments was nurtured, and greatattention was paid to ensuring that the eye was in its optimal condition. Since the mid­eighteenth century, as more and more optical instruments were used as measuringdevices, the reliability ofthe eye became questionable. In the early nineteenth century,there emerged the geometric tradition that highlighted the defects of the eye inmeasurements, and proposed various procedures to reduce the role of the eye in opticalexperiments.Chapter 8 focuses on the influence of the geometric tradition. With their emphasis

upon accurate measurements of complex natural phenomena, Humboldtian sciences

INTRODUCTION xxiii

became the favorite research subjects of many wave theorists from the geometrictradition. The popularity of Humboldtian sciences however diverted the researchinterests ofthe wave camp, and the problem-solving ability of the wave theory becamestagnant. When the popularity of Humboldtian sciences waned in the early 1850s, anew generation of physicists revitalized the geometric tradition and the wave theory.The measurements of a couple of important optical parameters profoundly shaped thedevelopment of the wave theory in the second half of the nineteenth century. Amongthese measurements, the determination of the speed of light eventually offered thefoundation for the unification of physical optics and electromagnetism.Chapter 9 concentrates on the impact of the visual tradition. With its emphasis upon

the intrinsic role of the eye in optical experiments, the visual tradition nurtured a groupof interdisciplinary researches associated with the psychological aspect of vision,including physiological optics, photometry, photography, and the making of the so­called "philosophical toys." Due to the proliferation of specialization in the midnineteenth century, physical optics was no'ionger the single central domain in the fieldofoptics, and both sides in the debate became apathetic about the question of the natureof light. Thus, the debate between the particle and the wave theory was not settled butbecame unimportant and insignificant to the members of the optical community. Theclosure of the "optical revolution" took the form ofproliferation ofdisciplines, ratherthan a replacement of a theory by another.In the Conclusion, I offer a brief philosophical analysis of the paradigmatic role of

instrumental traditions. In many ways, instrumental traditions in the optical revolutionfunctioned as paradigms. Like theoretical paradigms, they shaped people's perspectivesand caused communication problems among people from different traditions. Butunlike theoretical paradigms, instrumental traditions were deeply attached to theprocedural aspect of instrumentation, which frequently remained tacit during thedebate.

CHAPTER 1

CONWAIDSONSOFEXPLANATORYPOwtR

After Newton's endorsement in the late seventeenth century, the particle theory oflightdominated the field of optics in Britain for more than a hundred years. Throughout theeighteenth century, optical researches in Britain were conducted within the particleframework, and considerable progress was made during this period (Steffens 1977;Cantor 1983; Pav 1964). Partially because ofNewton's support, and partially becauseof its explanatory successes, the dominance of the particle theory in Britain lasted wellinto the frrst quarter of the nineteenth century. But this dominance of the particle theorybecame shaky when John Herschel in 1827 circulated in the optical community anessay that offered a systematic review of the wave theory of light and argued for itssuperiority. In this way, the showdown between the particle theory and the wave theorybegan.

1. INTRODUCING THE WAVE THEORY TO BRITAIN

The wave theory of light was first introduced to Britain at the very beginning of thenineteenth century, but it encountered enormous resistance. When Thomas Youngpublished a series of papers between 1799 and 1803 advocating the wave theory, hewas immediately attacked by Henry Brougham. In three articles published inEdinburgh Review, Brougham accused Young of using a hypothesis that "is a work offancy, useless in science," and objected to the notion of ether by quoting Newton'sname (Brougham 1803,451,455). Brougham's attacks were disastrous to Young.Although Young later wrote a reply to Brougham, he had to publish his response in theform of a pamphlet (Young 1804), and only one copy of it was sold (Young 1855,215). According to many contemporaries, Brougham's attack virtually stopped thespread ofYoung's wave theory (WhewellI967, vol.2, 347-8; Peacock 1855, 182).\During the same period, the wave theory of light developed rapidly on the other

side of the channel. Due to the work of Dominique-Francois Arago and AugustinFresnel, the wave theory was widely accepted in France in the 1820s (Buchwald 1989).When the wave theory was reintroduced to Britain from France in the late 1820s, itstood on a much sounder footing than it had 20 years before.

It was John Herschel (1792-1871) who introduced the wave theory of light toBritain from France. As Sir William Herschel's only child, John Herschel's career

X. Chen, Instrumental Traditions and Theories of Light© Springer Science+Business Media Dordrecht 2000

2 CHAPTER I

choice was strongly influenced by his father. John Herschel devoted most ofhis life toastronomical study, but he took up this discipline out of a sense of "filial devotion": tocontinue his father's work. Optics, however, was a more attractive subject thanastronomy to John Herschel, at least when he was young. Herschel began his opticalresearch as early as 1808, when he was only 16 years old. He later recalled that "lightwas myfrrst love" (Buttmann 1970, 27).

In his early years, Herschel's understanding oflight was consistent with the particletradition, and he was particularly influenced by Jean-Baptiste Biot's version of theparticle theory. To explain polarization generated by doubly refracting crystals, Biotin 1812 proposed a "theory ofoscillations," or a theory of"mobile polarization" as helater labeled it, which accounted for the phenomenon in terms of the oscillations ofluminous particles caused by attractive and repulsive forces from the axes of thecrystals. Herschel fIrst learned of the outline of Biot's mobile polarization theory in1818, and later committed himself fully to this theory after he visited Biot in 1819.Herschel began to study polarization in biaxial crystals in 1819, and published an

extended paper on the subject in 1820. In that paper, Herschel reported a series ofexperiments in which he examined the colored fringes produced by biaxial crystals.2

He found that the patterns of these colored fringes were different from those observedby Newton, and were not accounted for by any existing theory, including Biot's.Herschel's solution was a revision of Biot's mobile polarization theory. Unlike Biotwho considered only a single set of crystal axes, Herschel proposed that particles ofdifferent colors were affected by different sets ofaxes in biaxial crystals and explainedthe deviations of the colored fringes in terms of the forces exerted from these axes(Herschel 1820, 62-73). Although Herschel attempted to use neutral language todescribe his analysis and even claimed that his explanation of the colored fringes ofbiaxial crystals was compatible with both the particle and the wave theories, his paperwas certainly not a neutral experimental report. By appealing to the concepts of opticalforces and the oscillations of luminous particles, Herschel clearly showed hisacceptance of the particle theory.However, Herschel was not a dogmatic follower of the particle theory. On the

contrary, he kept his eyes open to any new development in the fIeld of optics. Thesuccesses of Fresnel's wave theory in the early 1820s made a deep impression onHerschel, and around 1824, he decided to write an essay to review systematically thetwo existing theories of light. In his diary entry on October 27, 1824, Herschel wrotethat he "began an essay on physical optics" (Buttmann 1970,43).Herschel may well have been the only person in Britain able to give a thoughtful

review ofboth the particle and the wave theories oflight.3 He was undoubtedly familiarwith the particle theory as a result ofhis early optical research. On the other hand, withhis excellent education in mathematics, he did not have much diffIculty understandingand representing the wave theory with its sophisticated mathematical analyses. Beforehe completed his essay, Herschel even identifIed several problems related to doublerefraction that Fresnel had not fully explained. He then wrote to Fresnel, asking fordetails on the laws of double refraction in unpolarized and polarized light, and on the

EXPLANATORY POWER 3

intensity ofpartially reflected light on a crystalline or noncrystalline surface.4 Fresnellater cleared up these questions in his second memoir on double refraction publishedin 1827.On December 12,1827, Herschel fmishedhis essay, which was titled "Light" and

filled 245 quarto pages. He did not publish the essay immediately; instead, hecirculated it around the optical community.5 In the spring of 1828, Herschel sent copiesofhis essay to a number ofpeople, including WilliamWhewell, Thomas Young, DavidBrewster, George Airy, William Hamilton, and William Fox Talbot (Cantor 1983,162). Herschel did not anticipate that his essay would bring about any strong reaction,and thus was a little surprised when he found that his essay "has excited a much greatersensation than I expected it would" (Buttmann 1970,61). Neither did Herschel foreseethat his essay would provide a ground for a controversy on the nature of light thatlasted more than three decades in Britain.

2. COMPARING THE EXPLANATORY POWERS

In "Light," Herschel compared and evaluated the two existing theories of light. Hisevaluation standards came directly from his methodology consonant with the Scottishphilosophy, or, as some people called it, the Common Sensemethodology (Olson 1975,252-70). Inhis methodological manual, Preliminary Discourse on the Study o/NaturalPhilosophy, published in 1830 for the Cabinet Cyclopedia, Herschel expressed clearlyhis criteria for evaluating scientific theories or hypotheses.According to Herschel, a hypothesis is "a most real and important accession to our

knowledge" because "it serves to group together in one comprehensive point of viewa mass of facts almost infmite in number and variety, to reason from one to another,and to establish analogies and relations between them" (Herschel 1831 ,262). Throughproviding explanations for different kinds ofphenomena, a hypothesis could functionas a guide to understand "the mutual connection ... of two classes of individuals"(Herschel 1831, 101).Herschel also pointed out that science needed "the knowledge of the hidden

processes ofnature in their production." But obtaining this kind ofknowledge requiredthe discovery of the actual structures and mechanisms of the universe. Detection ofthese structures and mechanisms could go beyond our ability, because they were, forthe most part, "either on too large or too small a scale to be immediately cognizable byour senses" (Herschel 1831, 191). We might formulate hypotheses about these hiddenstructures and mechanisms, but only in a few cases were we able to know if ourspeculations truly represented all the facts.Nevertheless, Herschel was still confident about the positive functions of

hypotheses. He argued that, although hypotheses could not tell us about the truth ofhidden causes, they were able to supply us with valuable suggestions. The majorfunction ofhypotheses was to "serve as a scaffold for the erection ofgeneral laws." Hereminded his readers that "hypotheses have often an eminent use: and a faculty inframing them, if attended with an equal facility in laying them aside when they have

4 CHAPTER 1

served their tum, is one of the most valuable qualities a philosopher can process; while,on the other hand, a bigoted adherence to them, or indeed to peculiar view ofany kind,in opposition to the tenor of facts as they arise, is the bane ofall philosophy" (Herschel1831, 204). Thus, the value of hypotheses consisted in their explanatory power andsuggestiveness, but not in their certainty or truth. Given such an instrumentalistmethodology, Herschel concentrated his attention on explanatory power when heevaluated the particle and the wave theories.Herschel recognized the explanatory power of the particle theory. In "Light," he

carefully examined all the optical phenomena that the particle theory could explain,which included a group of phenomena already known in Newton's time, such asreflection and refraction, total reflection, double refraction, colors in thin plates, colorsin thick plates, colors of the sky, and colors ofnatural bodies. Herschel also noted that,at the beginning of the nineteenth century, the particle theory might continue toimprove its explanatory power to account for some newly discovered facts. Forexample, by using the principle of least action, Laplace could supply a particle accountof double refraction that explained the phenomenon quantitatively.But the particle theory of light had difficulties in explaining a very important group

ofoptical phenomena -- those involving diffraction. Herschel used a simple experimentto illustrate the problems of the particle theory. It was an experiment in whichdiffraction was produced by a small opaque body. When the distance between theopaque body and the light source decreased, the diffraction fringes expandedconsiderably. Herschel noted that this fact was evidently incompatible with the particleaccount, which attributed the cause of diffraction to the deflecting force emanatingfrom the opaque body and thus implied that the change in distance between the opaquebody and the light source would have no impact on the fringe pattern (Herschel 1827,481).The particle theory also had trouble explaining a series of optical phenomena just

discovered at the beginning of the nineteenth century, specifically those related topolarization. In "Light," Herschel drew the attention of his readers to the newlydiscovered phenomena of polarization. The particle theory was particularly weak onthis issue, according to Herschel. For most polarization effects, the particle theory couldnot provide any satisfactory account. Although some particle theorists could explaina few polarization effects by adding ad hoc hypotheses to their systems, such as Biot'sassumption that luminous molecules rotated about their axes, Herschel noted that theseparticle accounts were obtained "with a great sacrifice of clearness of conception"(Herschel 1827, 529).The wave theory, however, exhibited excellent explanatory power for the

phenomena that upset the particle theory, such as those related to diffraction andpolarization. For diffraction, the wave theory could explain perfectly every detail ofdiffraction fringes, including the distances from the fringes to the geometrical shadowand the distances between fringes. The ability to account for the alternations ofdiffraction fringes when the distance between the diffracting body and light sourcechanged was, according to Herschel, "the strongest fact in favour of the undulatory

EXPLANATORY POWER 5

doctrine" (Herschel 1827, 483). The wave theory's superiority in the field ofpolarization was even more evident, Herschel argued. Throughout the last part of hisessay, Herschel used wave language to describe and explain all kinds of polarizationeffects. The wave explanations of these phenomena, Herschel claimed, were "really themost natural," adapting themselves "with the least violence and obscurity to the facts"(Herschel 1827, 529).But the wave theory was not perfect. It still had notable difficulty in explaining

some optical phenomena, particularly the dispersion of light. According to the wavedoctrines, Herschel pointed out, the velocity of propagation of a light wave dependedsolely on the elasticity of the medium, having no relation to the original disturbance.Thus, the wave theory asserted that light of every color should travel with one and thesame velocity in a homogeneous medium. In the phenomenon of dispersion, however,the deviation of light by refraction indicated that light with different colors traveledwith different velocities in the refracting medium. "Now here arises, in limine, a greatdifficulty; and it must not be dissembled, that it is impossible to look on it in any otherlight than as a most formidable objection to the undulatory doctrine" (Herschel 1827,449-50).Although neither the particle theory nor the wave theory could "furnish that

complete and satisfactory explanation ofall the phenomena of light which is desirable"(Herschel 1827,450; original emphasis), Herschel certainly had a preference for thewave theory. At the same time, he did not regard the wave theory as really representingthe truth. The value of this theory consisted merely in its explanatory power, rather thanin representing physical facts. 6 Herschel did not fully commit himself to the wavetheory because of the problem of the ether. He believed that it was necessary for thewave theory to explain the production of our sensations, and consequently to answerquestions regarding the properties of the ether and its relationships with light vibrationsand with sense organs. But it was impossible to obtain reliable knowledge of the ether,because the particles of the ether were so tiny that they lay beyond the limit of directobservations. Every existing model of the ether involved defects, which more or lesscontradicted the existing mechanical knowledge. The existence of ethereal particles wasnot a demonstrated fact, but only a kind of locum teneus. Thus, the wave theory did notrepresent the underlying mechanisms and the hidden interactions, and fell short of thetruth.For a rather long period after he established his preference for the wave theory,

Herschel did not think that the particle theory should be totally rejected because of itsinferior explanatory power. On several occasions, he appealed to the particle theory toexplain phenomena that troubled the wave theory, and expressed hope that the particletheory could be improved and then revived. Herschel's judgment of the particle theorywas consistent with his instrumentalist methodology. According to Herschel,hypotheses were merely intellectual tools, or "scaffolds," for approaching physicalfacts. Consequently, although the "scaffold" provided by the particle theory was not asgood as the one provided by the wave theory, keeping it for a while might still bebeneficial and would not bring about any harm.

6 CHAPTER 1

3. THE REFLECTION OF A PARTICLE THEORIST

David Brewster (1781-1868), the son of a grammar school rector, entered theUniversity of Edinburgh at a very early age and pursued his studies under JohnRobinson, John Playfair, and Dugald Stewart. He attended Stewart's moral philosophyclass and read intensively from the Common Sense philosophers, including Stewart andThomas Reid. Brewster was thoroughly acquainted with the Scottish philosophicaltradition, and his methodology of science, which determined his positions in the laterparticle-wave controversy, was deeply shaped by the principal doctrines of theCommon Sense philosophy.Brewster began his optical experiments in about 1799 when he was still at the

University, probably due to the influence of his classmate Henry Brougham (Forbes1858, 113). In 1813, he published his first book, A Treatise ofNew PhilosophicalInstruments, in which he described many new and improved optical instruments andreported his measurements of the refractive and dispersive powers ofa great numberof substances. Just before he completed his book, Brewster learned about Malus'discovery ofpolarization by reflection and quickly devoted himself to this new field.Through a series of experiments, Brewster found that light was also polarized byrefraction. By the end of 1813, he had determined the law of polarization by successiverefraction (Brewster 1814,221). In 1814, Brewster investigated the law ofpolarizationby reflection, discovering the so-called Brewster law, namely that the angle ofpolarization by reflection is in proportion to the refractive index of the reflectingmaterial (Brewster 1815b, 126). The optical community soon recognized Brewster'sdiscoveries. The Royal Society ofLondon in 1815 awarded Brewster the Copley Medalfor his studies of polarization and elected him Fellow of the Society.?Brewster also conducted experiments to study metallic reflection, optical

mineralogy, and absorptive spectroscopy. In 1819, he received the Rumford medalfrom the Royal Society for his study of the interference pattern produced by polarizedlight through crystals. In 1830, he won another medal from the Royal Society for hisdiscoveries of the laws of polarization by refraction and by pressure. Through thesesuccesses, Brewster established his reputation. James Forbes complimented Brewster'soriginal discoveries in physical optics, claiming that "few people have made with theirown eyes so vast a number of independent observations more faithfully" than Brewsterdid (Forbes 1858, 118). And William Whewell, although he disliked Brewster'stheoretical viewpoint, still admitted that Brewster was "the father of modemexperimental optics" (WheweIl1967, vol. 2, 373).Brewster clearly committed himself to the particle theory in his early optical

researches. Following the particle tradition, he regarded all optical phenomena as theresult of the interactions between light and matter, and interpreted them in terms ofparticles and forces. He explained polarization by reflection and refraction, forexample, in terms of the "polarizing forces" that "rotated" the particles of light(Brewster 1815b, 149). For double refraction, Brewster attributed its cause to the

EXPLANATORY POWER 7

attractive forces that emanated from the axes and acted differentially on the ordinaryand extraordinary rays (Brewster 1822, 747). Also, Brewster accepted Newton's theoryof fits ofeasy reflection and transmission, calling it a "beautiful theory ..., by whichNewton was enabled to explain all the phenomena of the colours of thick and thinplates" (Brewster 1815a, 436), and conceived it as a descriptive law equal to the lawof interference formulated by Young. He later even tried to provide a theoretical basisfor Newton's theory of fits by assuming that the phenomena of fits were produced bythe rotations of particles with two opposite poles (Brewster 1831b, 79).Although Brewster accepted the basic particle doctrines, he was not a blind

believer of the theory. In an unpublished article written in 1802, Brewster criticizedNewton's theory of inflection (diffraction). He rejected Newton's account that regardedrepulsive forces as the cause of inflection, and argued that, according to hisexperimental results, inflection did not depend on the density of the diffracting material(Cantor 1984, 68). A few years later, Brewster restated his criticism in a paper read tothe Royal Society ofEdinburgh, claiming that "from the experiments on inflection, itfollows that the deviation which the rays experience, in passing by the edges ofbodies,is not produced by any force inherent in the bodies themselves, but that it is a propertyof the light itself, ..."8Brewster also openly expressed his dissatisfaction with Newton's accounts ofmany

other optical phenomena. He regarded Newton's explanation of double refraction as"absolutely incompatible with observations" (Brewster 1821, 129). He attackedNewton's theory of the solar spectrum, claiming that his experiments contradictedNewton's supposition (Brewster 1823,442). He also stated that Newton's theory of thecolors ofnatural bodies was "no longer admissible as a general truth" (Brewster 1831a,72), and proposed a new theory to replace it. Thus, at the very beginning of his opticalstudies, Brewster had already realized the defects of the particle theory and attemptedto correct these problems in his own way.

4. IMPROVING THE EXPLANATORY POWER OF THE PARTICLE THEORY

Brewster was one of the few people in Britain who paid attention to the wave theoryin the early 1820s. As early as 1820, he published an anonymous paper, introducingFresnel's discoveries on the inflection of light (Brewster 1820). Brewster also fullyrecognized the value and significance of Young's principle of interference. After anextended correspondence with Young, Brewster was convinced that the principle ofinterference had been confirmed by experiments, and he began to treat it as adescriptive law (Cantor 1984, 70).Brewster was particularly impressed by the ability of the interference principle to

explain the phenomena of diffraction. In his Treatise on Optics published in 1831,Brewster discussed the results of a series ofdiffraction experiments, including the factthat diffraction fringes were in proportion to the distance between the source and thediffracting body but independent of the density of the diffracting material, and that thelocus of each fringe, with respect to the diffracting body, was in a hyperbolic rather

8 CHAPTER 1

than a straight line (Brewster 1831a, 96-7). All of these facts contradicted theNewtonian account but comfortably fitted the interference principle.Brewster also compared the explanatory powers of the two existing theories of

light in handling other optical phenomena. He concluded that "each of these twotheories of light is beset with difficulties peculiar to itself; but the theory ofundulationshas made great progress in modern times, and derives such powerful support from anextensive class of phenomena, that it has been received by many of our mostdistinguished philosophers" (Brewster 1831a, 135). The explanatory power of the wavetheory was evidently superior, but he did not believe that meant that the wave theoryshould replace the particle theory. The major obstacle that prevented Brewster fromembracing the wave theory was a set of problems associated with the chemicalproperties of light. When Brewster began his optical research, he firmly believed thatthe alliance of chemistry with optics was essential because the forces of affinity werelikely to be responsible for the refraction, diffraction, and polarization of light(Brewster 1815c, 285-302). Brewster's later studies further confirmed his opinion thatthe wave theory failed to explain the phenomena associated with the chemicalproperties of light. He argued that rays of solar light possessed several remarkableproperties: they promoted chemical combinations, they affected chemicaldecompositions, they altered the colors of bodies, and they were necessary to thedevelopment ofplants and flowers. "It is impossible to admit for a moment that thesevaried effects are produced by a mere mechanical action, or that they arise from theagitation of the particles of bodies by the vibrations of the ether which is considered tobe the cause of light" (Brewster 1831b, 90).Brewster attributed the successes of the wave theory primarily to the interference

principle, which he conceived as a descriptive law compatible with both the wave andthe particle traditions. Although the interference principle was apparently a logicalderivation from the wave theory, Brewster hoped that he could also incorporate theinterference principle into the particle framework and thus improve the explanatorypower of the particle theory.In 1822, Brewster proposed a psychological interpretation of the interference

principle to reconcile it with the particle theory. He assumed that the vibrationsrequired by interference could be physiological; that is, they were vibrations of theretinal nerves excited by the particle of light. When two particles reached the nerveswith a time difference, they could generate effects interfering with each other. Thesecond particle could either enhance or destroy the vibrations excited by the otherparticle, depending upon when it reached the nerves (Brewster 1822, 685).Later Brewster continued his effort to incorporate the interference principle into

the particle framework. In 1831, he specifically tried to reconcile the interferenceprinciple with Newton's theory offits. Brewster noted the crucial role in interferenceofa quantity of distance. If the path difference of two intersecting rays was d, 2d, or 3d,etc., they reinforced each other. If the path difference was 'h.d, I 'h.d, or 2'h.d, etc., theydestroyed each other. But Brewster argued that the physical meaning of this crucialquantity could be interpreted in two equally sound ways. It could be interpreted as the

EXPLANATORY POWER 9

breadth of a wave of light, as the wave theory did, or as "double the interval of the fitsof easy reflexion and transmission" (Brewster 1831a, 134). Thus, the principle ofinterference was also compatible with the particle theory.Because Brewster was confident that the interference principle could be employed

equally well by both theories, he decided not to abandon the particle theory. Instead,he continued to devote his time and energy to improving the explanatory power of theparticle theory. In 1831, he proposed a new account of diffraction. Deviating from thetraditional particle theory that explained the phenomenon in terms of interactionsbetween the diffracting body and the particles, Brewster attributed diffraction solely tothe repulsive force of the particles. Thus he was able to explain why diffraction fringeswere in proportion to the distance between the source and the diffracting body butindependent of the density of the diffracting material, facts that had troubled thetraditional particle theory (Brewster 1831b, 105-6). Brewster's new account ofdiffraction represented a significant improvement of the particle theory in the earlynineteenth century. Although he did not further explore this theory of diffraction,probably due to his lack of mathematical skill, Brewster continued to proclaim itscorrectness until the late 1840s (Brewster 1848).

5. THE PROBLEM OF SELECTIVE ABSORPTION

The establishment ofthe British Association for the Advancement of Science in 1831provided a new platform for the controversy between the particle theory and the wavetheory. Vernon Harcourt was one of the founders of the British Association. When hefrrst sketched out his ideas about the organization, he suggested that it should be ableto "look over the map of science and to say 'here is a shore of which the soundingsshould be more accurately taken, there a line of coast along which a voyage ofdiscovery should be made'" (Harcourt 1831). Supported by Herschel and Whewell,Harcourt's suggestion soon developed into a course of action, commissioned reports.These reports were supposed to be written by well-qualified experts and to reviewrecent conditions and progress in different subjects of science.At the 1831 meeting of the British Association, a subcommittee for mathematics

and physical science was founded. Brewster, Hamilton, Baden Powell, and Whewellwere the members of this committee.9One of the responsibilities of this subcommitteewas to decide topics and authors of proposed reports. At the meeting, the committeerequested six reports for the next year: on physical astronomy, tides, meteorology, heat,thermo-electricity, and optics. The number of candidates able to make the report onoptics was limited. According to Whewell, only three persons, Airy, Herschel andBrewster, were qualified (Whewell 1831). Since Airy had been assigned the report onphysical astronomy and Herschel did not attend the meeting, Brewster became the onlyqualified and appropriate candidate. Hence, the committee requested Brewster "toprepare for the next meeting a report on the progress of optical science" (BritishAssociation 1831,52).In his "Report on the recent progress of optics," which was presented to the

10 CHAPTER I

mathematics and physical science section at the 1832 meeting of the BritishAssociation, Brewster provided a general review of the field. He began his report bylisting a series of important discoveries in optics during the first three decades of thecentury, including Brougham's and Young's works on inflection, Laplace's study ondouble refraction, Malus's discovery of polarization of reflected light, as well asFresnel's researches. Regarding more recent discoveries that were relatively unknown,Brewster pointed to the discoveries of Airy, including his works on ellipticalpolarization and Newton's rings. 10

After describing recent progress in optics, Brewster reported a number of unsolvedproblems. As a response to the increasing claims of the wave theory, Brewsterreminded his audience that "even the theory of undulations, with all its power and allits beauty, is still burthened with difficulties, and cannot claim our implicit assent"(Brewster 1832, 318). These difficulties, according to Brewster, included ellipticalpolarization, "from the rectilineal polarization of transparent bodies, to the almostcircular polarization of pure silver," and the relationship between polarization anddouble refraction (Brewster 1832, 318). And yet the most formidable challenge to thewave theory, Brewster said, lay in the domain of absorption, a phenomenon newlystudied and explored by him in a series of experiments. He thus devoted the last partof his report to this subject.Brewster began his studies of selective absorption as early as 1822, with an initial

purpose of creating monochromatic light sources. In his absorption experiments, heused a prism to produce a solar spectrum and then inserted a variety of materials,including colored glass, colored liquid, rock crystals and metallic films, between theprism and the eye to study the absorption effects. Brewster found that differentmaterials absorbed light in different parts of the spectrum; for example, a plate of blueglass absorbed a portion of the red, green and violet light in the spectrum but not therest, and a plate of yellow glass eliminated only the violet, blue and green light but therest remained untouched (Brewster 1823, 439-40).11 After several experiments,Brewster believed that he was able to distinguish different absorptive materials merelyby looking at the spectra they produced. Thus, Brewster thought that his study ofabsorption spectra could yield knowledge about the chemical composition ofmatter.He hoped that his absorption experiments could eventually lead to "the discovery of ageneral principle of chemical analysis, in which simple and compound bodies mightbe characterized by their action on definite parts of the spectrum" (Brewster 1834a,519).Brewster made his most important discovery in absorption when he turned his

attention to the absorption spectrum of "nitrous acid gas" (N02) in February or Marchof 1832. 12 Directing the light of a monochromatic lamp through a prism and thenthrough a vessel containing the "nitrous acid gas," Brewster found hundreds of darklines and bands in the absorption spectrum, sharp at the violet end but faint at the redend. When he increased the thickness of the gas, the lines became more and moredistinct in the yellow and red region of the spectrum. When he raised the temperatureof the gas, distinct lines even appeared at the red end of the spectrum. Finally, Brewster

EXPLANATORY POWER 11

was able to use the gas to produce more than a thousand dark lines in the spectrum ofordinary flames (Brewster 1834a, 521-2).Brewster immediately realized the theoretical implications of these experimental

results. He pointed out that his experiments had very strong bearing on the rivaltheories of light, because these two theories did not have equal ability to explain hisobservations. Brewster believed that the particle theory could easily offer anexplanation for the phenomenon. According to this theory, when a beam oflight wastransmitted through a certain thickness of a particular gas, some portions of the beamwould be stopped by a special action of the material atoms in the gas -- "the light isactually stopped by the particles of the body, and remains within it in the form ofimponderable matter" (Brewster 1831a, 138; original emphasis). By assuming that theparticles of light were identical with the molecules of the gas, Brewster even suggestedthat these similar particles would unite with each other when they were brought withinthe spheres of their mutual attraction.However, it was difficult for the wave theory to account for the same phenomenon.

The experiment showed that more than a thousand waves of light with differentwavelengths were incapable ofpropagating through the ether of a transparent gas. Butat the same time, all other waves with intermediate wavelengths freely passed throughthe same medium. According to Brewster, it was simply inconceivable to say thatwaves of red light with wavelengths of 25D-millionths and 252-millionths of an inchwere able to pass freely through the gas, but another red light with a wavelength of25 I-millionths of an inch was entirely stopped.Selective absorption also exposed a possible inconsistency within the wave theory,

Brewster claimed. The problem was that "there is no fact analogous to [selectiveabsorption] in the phenomena of sound" (Brewster 1832, 321). According to the wavetheory, both light and sound consisted of the waves of an elastic medium, andconsequently there should not be fundamental differences between them. If the wavetheory were right about the analogous relations between light and sound, Brewsterreasoned, selective absorption should also appear in the field of sound. But, Brewsternoted, "among the various phenomena of sound no such analogous fact exists, and wecan scarcely conceive an elastic medium so singularly constituted as to exhibit suchextraordinary effects. We might readily understand how a medium could transmitsounds of a high pitch, and refuse to transmit sounds of a low pitch; but it isincomprehensible how any medium could transmit two sounds of nearly adjacentpitches, and yet obstruct a sound of an intermediate pitch" (Brewster 1833,363).The fact that there were no phenomena analogous to selective absorption in sound

exposed a potential incoherence within the wave theory. If the wave assumption of theanalogy between light and sound was correct, then selective absorption of light oughtto be excluded from the domain of the wave theory. On the other hand, if a waveaccount of selective absorption was possible, then the wave theory had to give up theanalogy between light and sound. Hence, Brewster implied that a wave account ofabsorption either was impossible or would be inconsistent with the wave assumptionregarding the analogous relations between light and sound. This internal incoherence

12 CHAPTER 1

constituted a non-empirical or conceptual problem for the wave theory, which wasdifferent from those empirical difficulties created by the conflicts between the theoryand experimental results. IJ Because of this conceptual problem, Brewster concluded inhis report that selective absorption in gaseous media presented a formidable objectionto the wave theory.Brewster's belief that the wave theory was incapable of explaining selective

absorption was further confirmed when he continued his experiments. When he latercondensed the "nitrous acid gas" into a liquid state, all absorption lines disappeared.This fact was entirely at odds with the wave theory, Brewster claimed. "The aether inthe liquid undulates readily to all their rays, while the aether in the gas, in which weshould expect it to exist in a much freer state, has not the power of transmitting theundulations of two thousand portions ofwhite light" (Brewster 1833, 362-3; originalemphasis).Because of his work in selective absorption, Brewster changed his attitude toward

the wave theory. Until his discoveries of the absorptive power of "nitrous acid gas,"Brewster did not openly challenge the wave theory. Although he did not accept thetheory, he never publicly rejected it. Now, in a paper published in 1833, entitled"Observations on the absorption of specific rays, in reference to the wave theory,"Brewster expressed his first public disavowal of the wave theory. At beginning of thepaper, Brewster stated, "I have long been an admirer of the singular power of [wave]theory to explain some of the most perplexing phenomena of optics; ... The power ofa theory, however, to explain and predict facts, is by no means a test of its truth; ...Twenty theories, indeed, may all enjoy the merit of accounting for a certain class offacts, provided they have all contrived to interweave some common principle to whichthese facts are actually related" (Brewster 1833, 360-1). Here Brewster raised his mainmethodological objection to the wave theory. He insisted that great explanatory powerwas only a necessary condition but not a sufficient one for a theory to correctlyrepresent the phenomena. Although the wave theory could explain a great number ofphenomena related to polarization, double refraction, and diffraction, it did not touchthe problems of the nature of ponderable matter and of the interactions between matterand light, such as dispersion and absorption. Citing these reasons, Brewster assertedthat the wave theory was "defective as a physical representation of the phenomena oflight" (Brewster 1833, 361; original emphasis).

CHAPTER 2

EXPLANATORY POWER AND CLASSIFICATION

The general explanatory successes ofthe wave theory did not persuade Brewster, whoon many occasions admired the merits of the wave theory in accounting for someoptical phenomena, but always insisted that its explanatory power was not good enoughto allow it to replace the particle theory. To understand Brewster's judgment, we needto examine how Brewster and other historical actors measured the explanatory powerof the wave theory. During the early nineteenth century, there was a consensus in thescientific community that explanatory power consisted not only in the ability to giveaccounts for numerous phenomena but, more importantly, for various phenomena. Ifa theory's successes were restricted to a few classes, its explanatory power was verylimited, despite the number of its explanations. Herschel thus insisted that theoriesshould be evaluated with respect to facts "purposely selected so as to include everyvariety of case" (Herschel 1831, 208). However, how many different classes ofphenomena a theory can explain also depends upon how the subject domain isclassified, upon which kind of taxonomy is adopted to provide a foundation forcategorization and classification. The measurement of a theory's explanatory powermay vary under different taxonomic systems, especially when a new taxonomic systemclassifies previously homogeneous phenomena as different kinds, or groups previouslydifferent phenomena together into one category. This chapter documents an evolutionofoptical taxonomy accompanying the dramatic changes of optical theory during theearly 1830s. These taxonomic shifts affected evaluations of the two rival theories oflight. Without the introduction of taxonomic systems with revolutionary structures, theexplanatory merits of the wave theory would have gone unrecognized, and thereplacement ofthe particle theory by the wave theory would have been impossible.

1. THE NEWTONIAN TAXONOMIC SYSTEMS

Before the revolutionary change in optics, all dominant taxonomic systems in Britainwere developed within the Newtonian framework. The first Newtonian system wasproposed by Newton himself in his Opticks, published in 1704 (Newton 1979). Thesubtitle of the book, A Treatise ofthe Reflections, Refractions, Inflections, and ColorsofLight, displayed the basic structure of this system. In Book I of the Opticks, Newtonfocused on reflection and refraction, but he also discussed the production of spectra by

13

X. Chen, Instrumental Traditions and Theories of Light© Springer Science+Business Media Dordrecht 2000

14 CHAPTER 2

prisms and the compositions of colored and white light, phenomena called "differentrefrangibility of light" in his own words. Although these phenomena later becameindependent under the category of "dispersion," Newton regarded them as a specialcase of refraction. The focus ofBook II was the production of colors, later called theinterference of light. To explain these phenomena, Newton introduced the notion of"fits" of easy transmission and easy reflection. In Book III, Newton first reportedseveral experiments related to inflection (or diffraction), and tried to explain them interms of interactions between light particles and body particles. Newton also examineddouble refraction and several other optical phenomena, including thermal and chemicaleffects of light, because he believed that they all were caused by interactions betweenlight and materials. This arrangement of the subjects reflected a taxonomic system thatcontained four major categories: "reflection," "refraction," "diffraction," and "color oflight." Some optical categories that were important in the later debate, such as"dispersion," "double reflection," and "optico-chemical effects," were treated assubcategories in this system.Newton's classification was very influential during the whole of the eighteenth

century. Most taxonomic systems that emerged in this period were built uponNewton's, with a few minor revisions. The most common revisions among thoseeighteenth-century systems were the introduction of new optical categories by makingsome subcategories in Newton's system major categories. Such upgrades happened in"dispersion," "double refraction," and "optico-chemical effects" (Anonymous 1771,vol. 3, 417-41; Priestley 1772, xiv-xvi). As a result, most taxonomic systems in the lateeighteenth and early nineteenth century doubled and even tripled the number ofmajorcategories. An example of them was the one developed by Thomas Young in 1807,which included ten major categories. They are: "sources of light (thermal/mechanical/chemical)," "velocity of light," "aberration of light," "intensity of light," "reflectionand partial reflection," "dispersion," "refraction," "double refraction," "vision," and"colors in plates" (Young 1807, vol. 2, 97-8).A significant development of optical taxonomy within the Newtonian framework

occurred during the 1820s. This was a systematic classification of optical phenomenadesigned by Brewster, a fully committed particle theorist who witnessed therevolutionary change, but never accepted the wave theory although he lived until 1868.In 1822, Brewster published an essay titled "Optics" in the Edinburgh

Encyclopaedia (Brewster 1822). With more than 200 pages, he systematically reviewedthe history ofoptics, the theory of optics, the applications of optics to the explanationsof natural phenomena, as well as optical instruments themselves. When Brewsterintroduced the theory of optics, he adopted a taxonomic system that contained sevenmajor categories, but which had many similarities with those developed in theeighteenth century. He kept all four major categories in Newton's system ("reflection,""refraction," "colors of plates," and "diffraction"), and upgraded "dispersion" and"double refraction" to major categories. However, Brewster's system had some notabledifferences from older ones. First, he added a new category -- "polarization" -- that hadnever appeared in Newtonian systems. Polarization was a concept first adopted by

CLASSIFICAnON 15

Malus in 1808 that soon became the most exciting research subject of the next twodecades. The introduction of "polarization" was a significant development thatreflected the current state of optics. Second, Brewster further examined the internalstructures of these major optical categories by listing their subcategories. In particular,he provided 11 subcategories outlining the detailed structure of"polarization." Thesesubcategories of"polarization" first covered those phenomena caused by the deviationsof rectilinear propagation, such as polarization by double refraction, by reflection, byrefraction, and by crystallized plates. They also covered those phenomena associatedwith the emission and absorption of light by matter, such as polarization related tothermal and mechanical properties of crystallized media. As we will see in latersections, the introduction of "polarization" as a major category and the discussion ofits internal structure were very important in the evolution of optical taxonomy: theyprovided a basis for the later development of Herschel's and Lloyd's taxonomicsystems that classified optical phenomena primarily, or even solely, in terms of the stateof polarization.Just a few years after he adopted this seven-category system, Brewster introduced

another major category -- "absorption." In his 1822 essay, "absorption" was asubcategory under "polarization." However, Brewster began to treat "absorption" asa major category in the early 1830s due to his discoveries of the absorption spectrumof"nitrous acid gas." As we have seen, Brewster in a series of experiments found that"nitrous acid gas" could produce hundreds and even thousands of dark lines and bandsin its absorption spectrum. According to Brewster, the particle theory could easilyexplain these phenomena in tenus of the interactions between the particles of light andthose in the gas, but it was difficult for the wave theory to give any reasonable account(Brewster 1833). In 1831 when Brewster published his A Treatise on Optics, a revisionof his 1822 essay, he introduced a new chapter on absorption, upgrading it from asecondary category under "polarization" to a major category in its own right (Brewster1831a, 120-5). The following year, when he presented his "Report on the RecentProgress of Optics" to the 1832 meeting of the British Association for theAdvancement of Science, Brewster repeatedly emphasized the importance ofabsorption and called for immediate cooperation within the optical community toexplore this "extensive" but "almost untrodden" field (Brewster 1832, 319-22).At the eve of the revolutionary change, Brewster gradually developed a taxonomic

system that contained eight major categories (Figure 2.1). Due to Brewster's prestige,this system was widespread both in the optical community and among the generalscientific audience -- more than four thousands copies ofhis A Treatise on Optics weresold within the first year of publication (The House of Longman 1978). Brewster'staxonomic system became the most influential one developed from the Newtonianframework.For Brewster, this new taxonomic system not only functioned as a frame for

organizing his essay and book, but also provided a ground for comparing theexplanatory powers of the rival optical theories. The result of such a comparison,however, was not in favor of the wave theory. According to Brewster, the explanatory

16 CHAPTER 2

Light

Reflection

Refraction

Dispersion

Diffraction

Colors of Plates

Double Refraction

Polarization

Absorption

{By Plane MirrorsBy Convex MirrorsBy Concave Mirrors

-[ By Plane SurfacesBy Spherical Surfaces

-[ By Prisms (Spectrum)In Refracting Telescopes

{By Circular DiscsBy Circular ApertureThin Plates

{

Thick PlatesDouble PlatesMixed Plates

{

Crystals with One AxisCrystals with Two AxesCrystals with Three Axes

By Double RefractionBy ReflectionBy RefractionColors in Crys. PlatesCircular PolarizationBy Thermal EffectsBy Mechanical EffectsBy Total ReflectionBy Metals

{

By GlassesBy FluidsBy Gases

Figure 2. J Brewster:v taxonomy

powers of the two rivals were almost the same in "reflection" and "refraction": bothcould provide reasonable explanations for the phenomena (Brewster 1822,651-5, 662­4). "Dispersion," however, was a favorable category for the particle theory, because itcould explain the different refrangibilities of light simply in terms of different sizes oflight particles, while the wave theory did not have a satisfactory account (Brewster1822,681). In "diffraction" and "colors of plates," the wave theory was superior to itsrival, because with the help of the interference principle the wave theory could providebeautiful explanations for the phenomena of diffraction and colors in plates, while theNewtonian explanations were rather inaccurate (Brewster 1822, 613; Brewster 1831a,96-7). "Double refraction" and "polarization" were two other categories in which boththeories had acceptable explanations, although he thought the wave theory still hadproblems in accounting for elliptical polarization as well as the connection betweendouble refraction and polarization (Brewster 1822, 747-8; Brewster 1832, 308-22).Lastly, "absorption" was another formidable obstacle to the acceptance of the wavetheory, because the phenomenon could be intuitively explained in terms of theinteractions between the particles of light and those of the gas, but not by the vibrationsof the ether (Brewster 1832, 321-2).Therefore, according to Brewster's comparisons under his own taxonomic system,

the explanatory power of the wave theory was not considerably superior to that of the

CLASSIFICATION 17

particle theory. The wave theory had troubles in two major categories ("dispersion" and"absorption"), while its rival also experienced difficulties in other two major categories("diffraction" and "colors of plates"). With this result, Brewster could not see anyimmediate reason to replace the particle theory with the wave theory. In general, mostwave theorists agreed that their theory had fonnidable difficulties in "dispersion" and"absorption,"! although some did not accept Brewster's judgments about "doublerefraction" and "polarization."2 Thus, if one accepted Brewster's classifications, onehad no choice but to admit that the particle theory was in control of two majorcategories, and that the particle theory was still valuable and should not be abandonedcompletely.

2. HERSCHEL'S SYNTHETIC ATTEMPT

A new optical taxonomic system that was substantially different from those developedwithin the Newtonian framework emerged in 1827. This was a system designed byJohn Herschel and presented in his influential essay "Light."At the beginning of his essay, Herschel clearly stated his purpose, which was to

"give an account of the properties of light; of the physico-mathematical laws whichregulate the direction, intensity, state of polarization, colours, and interference of itsrays" (Herschel 1827, 341). To achieve this goal, Herschel divided his essay into fourparts. Part I was on the propagation and intensity of unpolarized light, including thephenomena and empirical laws of reflection, refraction, aberration, photometry andvision. Part II was about the colors of unpolarized light, or chromatics as he called it,covering dispersion and absorption by uncrystallized media. Part III was on theinterference of unpolarized light. According to Herschel, interference was aphenomenon that could "hardly be understood, or even described, without a referenceto some theoretical views" (Herschel 1827,439). He therefore, in this section, firstreviewed the basic doctrines of both the particle and wave theories, and then examinedtheir explanations ofdiffraction and colors of plates. The last part, on polarization, wasthe longest, 89 pages, and was indeed the most important one in the whole essay. In its15 sections, Herschel surveyed all phenomena related to polarization, most of whichhad been discovered recently. These phenomena included those generated by thedeviations of rectilinear propagation, such as polarization by double refraction,reflection, refraction, interference and in crystallized plates. But much like Brewster,Herschel also discussed those phenomena caused by the emission and absorption oflight by matter, such as absorption by crystallized media, and polarization related tothennal, mechanical and chemical properties of crystallized media. The structure ofHerschel's essay thus reflected a new taxonomic system with only four majorcategories: "direction/intensity of unpolarized light," "colors of unpolarized light,""interference of unpolarized light," and "polarization" (Figure 2.2).Herschel's new system was essentially different from those developed from the

Newtonian framework. The first distinctive feature of this taxonomic system was its

18 CHAPTER 2

Light

Direction/Intensityof Unpolarized Light

Color ofUnpolarized Light

Interference ofUnpolarized Light

Polarized Light

{

ReflectionRefractionPhotometryAberrationvision

{DispersionAbsorption

S Colors of Plates""L Diffraction

By Double RefractionBy ReflectionBy RefractionColors of Crys. PlatesInterferenceCircular PolarizationAbsorption by Crys. MediaThermal EffectsChemical EffectsColors of Natural BodiesSolar Spectrum

Figure 2.2 Herschel's taxonomy

effort to search for a synthesis of optical categories. In this system, Herschel grouped"reflection," "refraction," "photometry," and "aberration" together under one majorcategory, because they all manifested the direction and intensity oflight. Following thesame principle, he merged "dispersion" with "absorption" because they both illustratedthe colors of light, he unified "diffraction" with "colors of plates" because they werethe products of interference, and he treated "double refraction" as a subcategory under"polarization" because it also reflected the state of polarization. By identifying theunderlying connections among optical phenomena, Herschel reduced the number ofmajor categories to four. This attempt at synthesis was essentially different from thepractices of categorization within the traditional framework, which tended to increasethe number ofmajor optical categories by simply listing every discovered phenomenonaccumulatively.Another distinctive feature ofHerschel's system was its emphasis on polarization.

By examining every subcategory under "polarization," Herschel illustrated similaritiesbetween polarized and unpolarized light. On the one hand, unpolarized light possessedsuch properties as direction, intensity, color and interference; on the other hand,polarized light had all the corresponding properties, although they displayed themselvesin different ways. Herschel's discovery of the similarities between polarized andunpolarized light was another important step in the evolution ofoptical taxonomy. Withthese similarities, Herschel implicitly suggested that the state of polarization might bea more fundamental property of light than the others such as direction, intensity, colorand interference. This idea later became the foundation for Lloyd's dichotomoussystem that classified optical phenomena only in terms of the state of polarization.In addition to the tacit arguments embedded in the structure of his essay, Herschel

also gave two explicit reasons justifying the importance ofpolarization. His first reason

CLASSIFICATION 19

was practical. Between the 1810s and the 1820s, merely two decades after polarizationwas discovered, a large number ofnovel optical properties related to polarization werefound. But "the intricacy as well as variety of its phenomena, and the unexampledrapidity with which discoveries have succeeded each other in it, have hithertoprevented the possibility of embodying it satisfactorily in a systematic form" (Herschel1827, 503). An emphasis on polarization reflected an urgent need to search for asystematic understanding of a variety of phenomena related to polarization.Herschel's second reason for highlighting polarization was methodological. In his

early study ofpolarization in biaxial crystals, Herschel had found that polarizing angleson the surfaces of crystallized media were better than refracting angles for investigatingthe constitutions and structures of crystals (Herschel 1820, 45-100). With polarizedlight, Herschel believed, scientists could have access to the minute mechanisms of thematerial world, studying such features as the inclination of the optic axes in crystals andthe intrinsic refractive power of molecules (Herschel 1827, 568-79). Thus, Herschelclaimed that "polarized light is, in the hands of the natural philosopher, not merely amedium of vision; it is an instrument by which he may be almost said to feel theultimate molecules ofnatural bodies, to detect the existences and investigate the natureof powers and properties ascertainable only by this test, and connected with the moreimportant and intricate inquiries in the study of nature" (Herschel 1827, 34 I).Herschel's new taxonomic system also became a basis for comparing the

explanatory powers of the rival optical theories. The result of theory appraisal underHerschel's system, however, was not in favor of the particle theory. On the one hand,Herschel acknowledged most of the particle theory's explanatory successes claimed byits supporters. He admitted that "[the particle] hypothesis, which was discussed andreasoned upon by Newton in a manner worthy ofhimself, affords, by the applicationof the same dynamical laws which he had applied with so much success to theexplanation of the planetary motions, not merely a plausible, but a perfectly reasonableand fair explanation ofall the usual phenomena of light known in his time" (Herschel1831, 250-1; original emphasis). Here, "the usual phenomena" referred to those topicsassociated with reflection, refraction, dispersion and absorption, all of which wereincluded in the first two categories in his system, that is, "direction! intensity ofunpolarized light" and "colors of unpolarized light." On the other hand, the particletheory was particularly weak in the categories of"interference" and "polarization." Theparticle theory simply could not explain why the distance from the light source couldaffect the diffraction fringes, a very important effect associated with diffraction. Theparticle theory also failed to provide coherent explanations of polarization: althoughBiot and Brewster were able to explain a few polarization effects, their explanationswere built upon ad hoc hypotheses.In contrast, the wave theory exhibited excellent explanatory power in most of the

major optical categories, according to Herschel. It did not have any problem explainingreflection and refraction, and could give excellent accounts for all details ofinterference and diffraction fringes. It was particularly powerful in the field ofpolarization: it was able to explain every polarization effect, including polarization by

20 CHAPTER 2

reflection, refraction and double refraction, colors of polarized light, interference ofpolarized light, as well as circular polarization. However, Herschel noted that the wavetheory experienced difficulties in explaining dispersion and absorption. The problemsrelated to dispersion were particularly troublesome, because the wave theory predictedthat rays of all colors would refract equally and that no dispersion could happen.Although the wave theory could not explain every major category of optical

phenomena, Herschel insisted that under his taxonomic system it did exhibit superiorexplanatory power to that of its rival. The superiority of the wave theory consisted notonly of its ability to explain one more major category than its rival did, but also of itssuccesses in the most important optical category -- "polarization." Thus, Herschelconcluded that "we shall adopt ... the undulatory system, not as being at all satisfiedof its reality as a physicalfact, but regarding it as by far the simplest means yet devisedof grouping together, and representing not only all the phenomena explicable byNewton's doctrine, but a vast variety ofother classes of facts to which that doctrine canhardly be applied without great violence, and much additional hypothesis of a verygratuitous kind" (Herschel 1827, 475; original emphasis).This statement indicated that, when Herschel evaluated the two rival theories of

light under his taxonomic system, he did develop a preference for the wave theory, butwas reluctant to embrace it completely. The failure of the wave theory in one majorcategory still troubled Herschel and made him believe that the wave theory did notrepresent the "physical fact." At the same time, the explanatory successes of the particletheory in dispersion and absorption, although they were just qualitative, led Herschelto hold that the particle theory was still valuable. For a rather long period after heestablished his preference for the wave theory, Herschel did not believe that the particletheory should be totally abandoned. Instead, he suggested that the particle theoryshould be improved: "Still, it is by no means impossible that the Newtonian theory oflight, if cultivated with equal diligence with the Huyghenian, might lead to an equallyplausible explanation ofphenomena now regarded as beyond its reach" (Herschel 1831,262).3Herschel even devoted himself to a project of constructing a new particle theory of

light. Around 1832, he postulated a new particle theory, which included a revision ofBiot's notion of mobile polarization, and claimed that it could explain many opticalphenomena that troubled the Newtonian version, such as the interference of polarizedlight. He proposed that a ray of light was composed ofmany rotating spherical particlesat equal intervals. Every particle of light had two poles of opposite "qualities." If twoof these particles were side by side, they either reinforced or neutralized each other,depending on the cosine square of one half of the angle between their axes of rotation.The interference effect of polarized light was thus accounted for in terms of theinteractions of the particles of light. Thus, while he declared that the wave theory wassuperior in explanatory power, Herschel also admitted that "I should be sorry to haveexpressed myself in the language of a partisan, a character in my opinion incompatiblewith that of a philosopher" (Herschel 1832). Under his own taxonomic system,Herschel simply did not regard the replacement of the particle theory by the wave

CLASSIFICAnON

theory as necessary, nor could he conceive a revolutionary change in optics.

3. LLOYD'S DICHOTOMOUS DESIGN

21

In the early 1830s, the British Association was the major institutional forum in thedebate concerning the two rival theories of light. Its annual meetings and publicationsprovided a platform for the debate. More importantly, its official reports on recentconditions and progress in different scientific subjects became a powerful means forspreading a writer's personal views, with the impression of endorsement by theAssociation.Brewster presented the first report on optics at the 1832 British Association

meeting, in which he listed all the drawbacks of the wave theory and concluded that itwas far from an acceptable theory of light (Brewster 1832, 308-22). Not surprisingly,Brewster's report caused strong discontent among wave theorists, many ofwhom, likeWilliam Whewell and George Airy, were already elected to the committee preparingthe next Association meeting. These wave theorists did not agree with Brewster'sconclusion on the status of their theory, nor could they tolerate the spread of confusioncreated by Brewster's report, but they did not criticize him openly. Instead, they simplyrequested another report on optics at a future meeting "on the phenomena consideredas opposed to the undulatory theory."4 This was a very vague description, which couldbe interpreted in either way. However, those who made this request knew that theycould ensure that the new report would be written in the way they wanted by selectingan appropriate reporter. The selection of the reporter was made at the 1833 meeting ofthe British Association. A perfect candidate would be one who was not only acommitted advocate of the wave theory but also a qualified practitioner of optics, bothin theoretical analysis and in experimental operation.Because of his successful experiments on conical refraction, Humphrey Lloyd

(1800-1881), Professor ofNatural and Experimental Science at Trinity College, Dublin,emerged at this meeting as the candidate who perfectly fitted all these criteria. Thephenomena of conical refraction were first discussed by William Hamilton in 1832.With sophisticated mathematical analysis, Hamilton predicted two hitherto unobservedfeatures ofdouble refraction in biaxial crystals (called conical refraction) that had beenoverlooked by Fresnel. To confirm these predictions, Hamilton asked for help fromLloyd. Utilizing his delicate experimental skills, Lloyd was able to verify Hamilton'snovel predictions within a couple months.s Lloyd gave a brilliant performance at the1833 meeting of the British Association by presenting his experimental confirmationof conical refraction. His presentation demonstrated both his theoreticalaccomplishments in understanding Hamilton' s extremely abstract theory and hisexperimental skiIls in designing and conducting delicate experiments. Moreimportantly, it showed his commitment to the wave theory. Consequently, Lloyd wasselected as the reporter, and was requested to draw up a report on the recent progressof physical optics for the next British Association meeting.Lloyd's "Report on the progress and present state of physical optics" appeared in

22 CHAPTER 2

the 1834 issue of the Association report.6 In the report's 118 pages, Lloyd attemptedto show the superiority of the wave theory by making a systematic comparison of thetwo rivals' explanatory powers. His judgments of the two rivals' explanatory abilitiesin individual cases were virtually the same as Herschel's. However, by carefullydesigning the structure of his report, Lloyd presented a new taxonomic system thatrevealed the necessity of immediately abandoning the particle theory and adopting thewave theory.At the beginning of his report, Lloyd stated that, to prove the superiority of the

wave theory, "I have found it necessary to deviate from the arrangement which astrictly theoretical view of the subject would naturally suggest" (Lloyd 1834, 21). This"arrangement" from which Lloyd wanted to deviate was the tradition in opticalcategorization that classified optical phenomena in terms of the properties of light.According to this tradition, every principal property of light, such as direction,intensity, color, interference and the state of polarization, had a corresponding majorcategory, all of equal importance. Lloyd was discontent with this classification traditionbecause he did not believe that it was the way it was done in practice. The reality wasthat polarization had become the research frontier in the field, and a single property -­the state of polarization -- had drawn the attention ofmost researchers. According toLloyd, a taxonomic system should reflect the community's common practice. Hence,he claimed that, "the relation of theory to phenomena, which I propose to consider,obliges me to examine the latter in the groups in which they have been usually broughttogether, and under which their laws have been investigated. I propose, therefore, todivide the following Report into two parts, ofwhich the first will treat of unpolarized,and the second ofpolarized light" (Lloyd 1834, 21; original emphasis).Lloyd further divided the part of the report on unpolarized light into four sections.

The first section was titled "the propagation of light and the principle of interference"and covered the rectilinear propagation of light, the velocity of light, aberration andinterference. Section two was called "the reflection and refraction of light," whichincluded not only reflection and refraction, but also, surprisingly, dispersion,absorption, solar phosphorus and solar spectrum. The last two sections in this part wereabout diffraction and colors of plates, discussing the contents one would expect to findunder these two categories. Lloyd also divided the part on polarized light into foursections. The first one was titled "the polarization of light" and was primarily on theprinciple of transverse vibrations. Section two was called "the reflection and refractionof polarized light," covering polarization by reflection, refraction, total reflection andNewton's rings. Section three was "double refraction," discussing both doublerefraction and absorption by crystallized media. The last section was "the colors ofcrystallized plates," reviewing interference of polarized light, circular polarization anddepolarization.The structure ofLloyd's report reflected an entirely new taxonomic system with a

distinctive dichotomous structure (Figure 2.3). In this system, all optical phenomenawere first classified solely in terms of their states of polarization. "Polarized light" and"unpolarized light" were the only two major categories, and other categories treated as

Light

UnpolarizedUght

CLASSIFICATION

PropagationInterference

ReflectionRefraction

Diffraction

Color inPlates

Polarization

{Velocity of LightRectilinear PropagationAberration

[

ReflectionRefraction

_ DispersionAbsorptionSolar PhosphorusSolar Spectrum

{

By Opaque BodiesBy ApertureBy Straight EdgesBy Gratings

{

Thin PlatesDouble PlatesThick Plates

_ Transverse Vibrations

23

ReflectionRefraction

PolarizedLight

{

ReflectionRefractionNewlon's RingsTotal Reflection

. -[ Double RefractionDouble Refraction Absorption by Crys. Media

. { Colors of Crys. PlatesColor In Circular PolarizationCrystallized Plates Depolarization

Interference

Figure 2.3 Lloyd's taxonomy

major under old systems, such as "reflection," "refraction," "dispersion" and"diffraction," now became subcategories, or even sub-subcategories. To some degree,this dichotomous system reflected Lloyd's effort to continue a trend that existed in bothBrewster's and Herschel's classifications: recognizing and emphasizing the importanceof polarization. However, by making the state of polarization the only principalclassification standard and designing a dichotomous system that contained only"polarized light" and "unpolarized light" as the major categories, Lloyd emphasized thevalue of polarization to an extreme.In addition to the dichotomous structure, Lloyd's taxonomic system had two other

distinctive features. First, Lloyd organized the subcategories under "unpolarized light"in a very peculiar way. On the one hand, he used three subcategories ("propagation andinterference," "diffraction," and "colors in plates") to cover the phenomena related tointerference. On the other hand, he combined "reflection," "refraction," "dispersion,""absorption," "solar phosphorus" and "solar spectrum" under a single category:"reflection and refraction of unpolarized light." In this way, "dispersion" and"absorption," which were major categories in Brewster's system, or second-levelcategories in Herschel's system, became third-level categories. Second, Lloyd deletedall of the categories related to thermal, mechanical and chemical effects of crystallizedmedia, although they had appeared in both Brewster's and Herschel's systems. The

24 CHAPTER 2

reasons were, according to Lloyd, that these subjects were "as yet little understood,"and that they were "remotely connected with the leading object of the present Report,"that is, to prove the truth ofthe wave theory (Lloyd 1834,22,21).With this new taxonomic system, Lloyd was able to make a stronger and more

persuasive argument for the wave theory than had Herschel in his "Light." Lloydbelieved that the explanatory power of a theory was one of the most importantconditions for its truth: if a theory could explain various "leading classes of opticalphenomena," and its explanations could be "numerically compared with establishedfacts," then the truth of the theory should be "fully and finally ascertained" (Lloyd1834, 19).7 Lloyd insisted that this was exactly the achievement of the wave theory.Under his taxonomic system, the wave theory now was able to have total control of oneof the two major optical categories -- "polarized light" -- in which the particle theoryexperienced tremendous difficulties.8 In the other major category -- "unpolarized light"-- the wave theory had demonstrated its superiority in such secondary categories as"propagation of light and interference," "diffraction" and "colors of thin plates" for along time by giving not only numerical explanations but also striking predictions, whilethe particle theory had no currency at all without the interference principle (Lloyd1834,25-7, 58-65, 73-4).By listing the wave theory's explanatory successes in both major and secondary

categories, Lloyd showed its superiority to the particle theory. But Lloyd wanted more:he wanted to demonstrate that the wave theory was at a level "as advanced as that towhich the theory of universal gravitation was pushed by the single-handed efforts ofNewton" (Lloyd 1834, 20). To achieve this goal, he needed to discuss the difficultiesof the wave theory. Lloyd admitted that dispersion was "the most fonnidable obstacle"to the reception of the wave theory, and wave theorists were "still far from a precisetheory of absorption" (Lloyd 1834, 41, 46). But under his new dichotomous system,the troublesome cases of dispersion and absorption now became third-level categories,subsumed under "reflection and refraction of unpolarized light." Thus, the argumenttacitly implied by this taxonomic system was that dispersion and absorption were nolonger among the "leading classes of optical phenomena." Even though the wavetheory still had difficulties in dealing with these phenomena, these failures now becametrivial in comparison to the theory's successes in those important optical categories.With the help of a revolutionary taxonomic system, Lloyd could emphasize the

merits of the wave theory to a maximum both through making "polarized light" one ofthe two major categories as well as through using three subcategories to cover thephenomena related to interference. He was also able to reduce the defects of the wavetheory to a minimum by treating "dispersion" and "absorption" as third-levelcategories. Under his system, Lloyd also diminished the advantages of the particletheory in explaining dispersion, absorption and optico-chemical effects, by eitherdegrading the values of these phenomena or simply dropping them out of the game.Based upon these comparisons, Lloyd strongly objected to Herschel's view that theparticle theory might be revivable if it were cultivated with the same zeal and talent asits rival, calling Herschel's position "untenable" (Lloyd 1834,20). According to Lloyd,

CLASSIFICAnON 25

the particle theory should be totally abandoned, and the wave theory should be adoptedand advocated immediately. A revolution in optics •• replacing the particle theory withthe wave theory -- became necessary and urgent under Lloyd's dichotomous system.Lloyd's report was applauded by most wave theorists. Powell called it "the

completely and masterly report," James Forbes labeled it "an able and impartial reviewof the progress of science," and, according to Hamilton, its only fault was "its too greatmodesty." They complimented Lloyd, partly on his verdict for the wave theory andpartly on the taxonomy embedded in his report. In fact, the dichotomous structure ofLloyd's taxonomic system reflected a consensus among many wave theorists onclassification. A number ofwave theorists adopted similar dichotomous systems. Forexample, Airy in his Mathematical Tracts divided optical phenomena into two majorclasses: those related to polarization and those not (Airy 1831b, 249-409). Thus,because ofLloyd's report and other wave theorists' supports, a dichotomous taxonomicsystem became dominant within the wave camp. Many textbooks written by wavetheorists in this period adopted this dichotomous structure. Among them, Airy's Tracts,with three editions in three decades,9 was most influential, because it was the officialtext for the Cambridge's Mathematical Tripos. Lloyd himself also published twotextbooks in this period, both ofwhich were organized using the dichotomous structure(Lloyd 1841; Lloyd 1857).10With a delicate taxonomic system and convincing arguments, Lloyd's report held

a very important status in the debate. His report convinced supporters of the wavetheory, who controlled the British Association, that the damage caused by Brewster hadbeen remedied and the particle-wave controversy had been settled. After Lloyd'sreport, the British Association did not request any further report on optics for the nexttwo decades. The other two reports about optics in the nineteenth century were onepresented by George Stokes on double refraction in 1862 and one by Glazebrook onoptical theories in 1885, by which time the particle-wave controversy was no more anissue. Therefore, many historians agree that Lloyd's report represented a turning pointin the particle-wave debate. The publication of Lloyd's report indicated that the wavetheory had become orthodoxy in the British Association, and the particle tradition fellinto a defensive position (Morrell & Thackray 1981,469).The above analysis of the taxonomic evolution during the early nineteenth centUry

shows the dominant role of taxonomy in theory evaluation and scientific change. Theexplanatory superiority ofthe wave theory and the necessity of a revolutionary changein optics became evident and compelling only after the significant taxonomic shifts.Under a traditional taxonomic system, Brewster did not regard the wave theory assignificantly superior in explanatory power. Neither did Herschel recognize the needto immediately replace the particle theory with the wave theory under his new system,although he developed a preference for the latter. Only with a dichotomous system didLloyd fully understood the necessity of a revolutionary change in optics -- acceptinga new optical theory at the price of abandoning the old one.The vital role of taxonomic changes is rooted in the fact that a taxonomic system

functions as a framework of language learning and application for a scientific

26 CHAPTER 2

community. By providing a list of categories and revealing the similar and dissimilarrelationships among them, a taxonomic system defmes how a given category pertainsto a given kind of object or situation and how it is related to other categories.Taxonomic shifts then result in fundamental changes in the way in which people learnand apply taxonomic terms: some categories do not refer to the same kind of object orsituation and bear different relationships to others in a new taxonomic system. Forexample, "dispersion" in Brewster's taxonomic system referred to the phenomenoncaused by changes of a principal optical property -- refrangibility - and thus wastreated as one of the major categories, sharing the same status as "reflection" and"refraction." In Lloyd's system, however, the same category referred to the deviationsofrectilinear transmission and was put under "reflection and refraction." Thus, whethera theory can explain a particular phenomenon, or whether it can be justified by certainkind ofempirical evidence, depends on the underlying taxonomy, which classifies theresearch domain in a certain way. In this way, taxonomy preconditions the results oftheory evaluation, although a taxonomic system is in tum built upon a certaintheoretical framework.

CHAPTER 3

CLASSIFICATION AND THE USE OF INSTRUMENTS

If the taxonomic changes were the preconditions of the theory choice in the opticalrevolution, then what were the causes of these taxonomic changes? At first glance, itlooks as if these taxonomic changes were caused by some social or political motives:Brewster stuck with the old taxonomic system because he could downgrade the meritsofthe wave theory, Lloyd introduced a dichotomous system because he could make thewave theory look good, and these tactics were closely tied up with the politics at theBritish Association. This social or political interpretation, however, has a vital problem.If Brewster's persistence in using the traditional taxonomic system reflected only hishostile attitude toward the wave theory and ifLloyd's choice ofa dichotomous systemwas merely a rhetorical trick, then we should expect heated debates between the rivalson the legitimacy of their classifications, but that never happened. The silence ofparticle theorists suggested that they might have agreed with the main idea embeddedin Lloyd's system. Comparing the three major taxonomic systems during therevolution, we can see that the emphasis on polarization was a common theme, whichappeared first in Brewster's classification, was further elaborated in Herschel's, andfinally reached its climax in Lloyd's dichotomous system. This common themereflected the consensus shared by particle and wave theorists during this period thatpolarization was the most promising research topic. The common practice ofthe opticalcommunity may have been the foundation ofthese taxonomic changes, but why did notBrewster, who had recognized the importance ofpolarization much earlier than Lloyd,develop a dichotomous system? This chapter analyzes the cognitive basis fortaxonomic choices in the debate concerning the two rival theories of light, and arguesthat the selections of taxonomic systems by these historical actors were not arbitrary.Brewster stuck to the old Newtonian system not because he was unscientific orirrational, but because his experimental instruments and procedures preventedhim fromseeing polarization as the most important optical property. Similarly, Lloyd'sdichotomous system was not a rhetorical tactic, but a reflection of the improvement inexperimental instruments and procedures.

I. BREWSTER'S PLATE POLARIZERS AND CRYSTAL ANALYZERS

In 1808, Louis Malus discovered the phenomenon of polarization by reflection. In his

27

X. Chen, Instrumental Traditions and Theories of Light© Springer Science+Business Media Dordrecht 2000

28 CHAPTER 3

experiments on double refraction, he accidentally directed a prism of calcareous spartowards the windows of the Luxembourg Palace, and was surprised to see that theintensity of the two images of the windows varied as he rotated the prism, aphenomenon similar to those produced by a light beam passing through doublyrefractive crystals. Malus reasoned that the property of the light must be modified byreflection, and later he called this phenomenon "polarization." Malus also found that,at a particular reflection angle (now called the polarizing angle), the effect ofpolarization achieved its maximum, that is, the images of the reflected beam vanishedalternately during the rotation of the prism. Above or below this angle, Malusdiscovered, "a part of the rays is more or less modified, and in a manner analogous towhat takes place between two crystals whose principal sections are neither parallel norrectangular" (Brewster 1824, 93).Around 1811, Malus's discovery of polarization by reflection drew Brewster's

attention. He repeated Malus's experiments and measured the polarizing angles ofmany substances. After he confirmed Malus's discovery, Brewster decided to vary theexperiment. "I made a variety ofexperiments, with the view ofdiscovering ifa similarcharacter could be impressed upon light by its transmission through bodies, eitherwholly or imperfectly transparent" (Brewster 18Ba, 102; original emphasis).Brewster first used a thin plate ofagate as the refracting material. He passed a light

beam through the plate and examined the transmitted lightwith a prism ofIceland spar.By turning the Iceland spar around its axis, he observed that the two images of therefracted beam alternately vanished at every quarter of a revolution, which indicatedthat the refracted beam had been polarized (Brewster 18Ba, 102). Brewster latersubstituted a plate of crown glass for the plate of agate and found a similar effect,although the two images ofthe refracted beam never vanished. By adding one plate ofglass after another, Brewster saw that the polarization effect was enhanced by theaddition ofeach plate. He used a piece ofagate as the analyzer to examine the refractedlight passing through a pile of 15 glass plates and observed that, at an incident angleof about 70 degrees, the images of the refracted beam vanished completely when thelamina of the agate was parallel to the plane of refraction, and recovered their fullintensity when the axis of the agate was perpendicular to the plane of refraction.According to Brewster, this phenomenon indicated that, the refracted light wascompletely polarized by the refraction (Brewster 1814,219-20).After discovering polarization by successive refraction, Brewster began to search

for a quantitative formula describing the degree of polarization in relation to thenumber of plates and the angle of refraction. He collected 47 plates of crown glass(about three inches by one inch each), and put them together to form various bundleswith different numbers of plates, from 47 to eight. The light source was the flame ofa wax candle at a distance of 10 feet, and the state ofpolarization ofthe refracted beamwas determined by looking through a prism of Iceland spar. Using a theodolite,Brewster measured the angles at which a beam oflight was completely polarized afterbeing transmitted through a bundle of plates (Figure 3.1). After many experiments,Brewster found a regular progression in the relationships between number ofplates and

USE OF INSTRUMENTS

PolarizerAnalyzer

29

Figure 3.1 Brewster:S plate polarizer and crystal analyzer

angle of incidence: the less the angle the more plates that were needed for completepolarization. Further comparing the number of plates with the angles, Brewster foundthat the ratio ofany two numbers ofplates was always equal to the ratio ofthe tangentsof the corresponding angles. From this observation, Brewster proposed the followinglaw: "the number ofplates in any parcel multiplied by the tangent ofthe angle, at whichit polarises light, is a constant quantity" (Brewster 1814,221).To determine the value of the constant, Brewster used the data as the reference

from the experiment that employed a bundle with 18 plates. After a great number ofobservations, he determined that the refracted beam was completely polarized by thisbundle of plates at an incident angle of 66°43', and thereby the constant should be41.84 (18 x tan 66°43'). Brewster thus had the following empirical formula forpolarization by successive refraction:

tan e 41.84

m

Using this formula, Brewster calculated the angles of incidence at which refracted lightwould be completely polarized, and his calculations showed that light would becompletely polarized by passing through a single plate of crown glass at an incidenceof 88°38', or through 8,640,000 plates at an almost perpendicular angle (one arc­second). Brewster did not conduct new experiments to confirm his calculations;instead, he simply compared some of his calculations with his existing data, and theresults, according to Brewster, were quite satisfactory. "The differences are all withinthe limits of error, and are singularly small when we consider the difficulty ofobserving the complete extinction of a luminous object, when the light by which it isformed has traversed a great number of plates," he wrote (Brewster 1814,222).Brewster's formula for polarization by successive refraction was faulty: today we

know that light would never be completely polarized by refraction. For example, whena light beam passes through 18 plates ofcrown glass at an incident angle of66°43', thedegree ofpolarization is actually only about 77%.' However, considering the difficulty

30 CHAPTER 3

of"observing the complete extinction of a luminous object," we can understand whyBrewster made such a mistake.In his experiments, Brewster used a doubly refracting crystal as an analyzer to

determine the state and degree of polarization. The basic procedure of thismeasurement was to let the light to be examined pass through the crystal, and thenobserve the variation of the intensity while rotating the crystal. If the light beam werecompletely polarized, one of its images should vanish when the analyzer was turned toa certain angle. If the light beam were not completely polarized, the intensity of itsimageswould change as the crystal was rotated, but would never completely disappear.And, if the light were unpolarized, the intensity of its images would remain the sameduring the rotation. In this way, the intensity of light became the indicator of the stateand degree of polarization. After converting the state and degree of polarization tointensity variation, Br~wsterused the eye to sense the level ofbrightness. Thus, the eyewas essential in Brewster's determination and measurement of polarization. It is nowwell known that the eye does a very poor job in judging intensity variation. Forexample, studies of astronomical observations show that a normal observer cannotperceive brightness below the level of 10-8 candle/cm2 when the size ofthe illuminatedfield is as small as a few degrees (Hardy & Perrin 1932, 193-4). This minimumbrightness could well be the threshold that determined the range oferror in Brewster'sobservations. According to theoretical calculations, the intensity of the unpolarizedlight in Brewster's successive refraction experiments should never be zero, but it couldquite possibly be undetectable. The intensity of the incident light in Brewster'sexperiments was at the level of 10-5 candle/cm2 after traveling 10 feet from the source,a single candle. After the refraction caused by the 18 plates ofcrown glass, the intensityof the unpolarized light would further drop to the level of 10-8 candle/cm2 (seeAppendix 1). In practice, this level ofilluminationmight have been imperceivable. Thisprobably explains why Brewster reported in his experiments that one ofthe images ofthe refracted light vanished during the rotation ofthe crystal and thus reasoned that therefracted beam was completely polarized.Brewster's faulty beliefthat light could be completely polarized through successive

refraction substantially shaped his understanding of the phenomenon. If 18 plates ofglass were needed for completely polarizing a light beam at the angle of66°43', thenlight that passed through fewer than 18 plates would not achieve complete polarization.At the same time, it was no longer natural light. What was the nature of this kind ofincomplete polarization? In his studies of polarization by reflection, Malus alsodiscovered the phenomenon of incomplete polarization. He found that when light wasnot reflected at the polarizing angle, the polarization was only partial. But, accordingto Malus, incomplete polarization was a mixture oftwo independent physical states. Apartially polarized light beam in fact consisted of a certain quantity of completelypolarized light, while the rest was unmodified and preserved the characteristics ofnatural light.Brewster was suspicious of Malus's hypothesis about the nature of incomplete

polarization because he found that Malus's hypothesis was in conflict with his

USE OF INSTRUMENTS 31

experimental data. His experiments showed that 24 plates were needed to polarizecompletely a given light beam at the angle of 61 degrees. Consequently, Brewsterreasoned, 12 plateswould only partially polarize the light beam at the same angle. Nowassume that the unpolarized portion amounted to 20 rays out of 100. If these 20 rayswere absolutely unpolarized and in the same state as natural light, as Malus had said,they would have to pass through 24 plates at an angle of 61 degrees in order to bepolarizedcompletely. Butthe experiments provedthat they needed to pass through only12 plates at that angle in order to be polarized completely.To explain these experimental data, Brewster argued, it was necessary to assume

that the 20 rays had been half or partially polarized by the first 12 plates, and thatpolarization was completed by the other 12. He said, "when a pencil oflight is incidentat any angle except a right angle, upon the surface of a transparent body, a certainportion ofthe transmitted light is completely polarised, while the remaining portion hassuffered a physical change, approaching more or less to that of complete polarisation"(Brewster 1822, 720; original emphasis).2 In this way, Brewster conceptualizedincomplete polarization as a mixture ofcomplete polarization and partial polarization,which he believed to be two independent physical states.Brewster's analysis implied a new taxonomy of polarization. The taxonomy of

polarization derived from Malus's analysis divided all phenomena ofpolarization intotwo, and only two, groups: light was either completely polarized or completelyunpolarized. The phenomenon of incomplete polarization was treated by Malus as amixture ofthese two states. But now Brewster suggested classifying the phenomena ofpolarization into three different groups: completely polarized, completely unpolarized,and partially polarized light. Brewster's new taxonomy of polarization was not theresult of an arbitrary rearrangement of the field. Instead, this taxonomy had itsinstrumental basis and was derived from a specific experimental procedure for theanalysis of light. In this procedure, the state of polarization was determined by theoperation ofa specific instrument, an analyzer. When the light to be examined passedthrough a doubly refracting crystal, rotating the crystal generated signals in the formof intensity variation for distinguishing different states of polarization. While theanalyzer was rotating, the images ofthe refracted light would either vanish alternately,or vary but not completely disappear, or remain the same. These three signals indicatedthree different states ofpolarization, the foundation ofthe three subordinate categoriesin Brewster's taxonomy (Figure 3.2).In Brewster's taxonomy, the state ofpolarization was a matter ofdegree: different

levels of partially polarized light fall in a spectrum with completely polarized andnatural light as the two extremes. However, the notion of partial polarization could beconceptually problematic. Brewster knew that polarization was in essence a propertyof spatial asymmetry because polarized light had different properties with respect todifferent directions. But it was hard to imagine how spatial asymmetry could be amatterofdegree. An object could be either spatially symmetric or spatially asymmetric;its properties either changed or did not change with respect to spatial variations, butthere was nothing in between. Thus, a single ray, which possessed either an inherent

32

Superordinate Instrumentalcategory operation

CHAPTER 3

Signal Subordinatecategory

I ~ RotatingLight the

Analyzer

The ImagesVanish

The ImagesVary

The ImagesRemain

the Same

PolarizedLight

PartiallyPolarized Light

UnpolarizedLight

Figure 3.2 Brewster sprocedure for classifying polarization

asymmetry or an inherent symmetry, could not generate partially polarized light. Ofcourse, such a conceptual problem could have occurred only if polarization wasunderstood as the property of a single ray. This was never the case within theframework of the particle tradition, which always assumed that all optical phenomenawere caused by the collective properties or behaviors ofmicro particles. Thus, to avoidthe possible conceptual problem associated with the notion of partial polarization,Brewster had to stick to the tradition, maintaining the position that polarization was aproperty of a collection of rays.

Itwas this understanding ofpolarization that shaped Brewster's optical taxonomy,particularly his judgment of the importance and significance of the category of"polarization" in comparison with other optical categories. Since polarization was aproperty of a collection of rays, it depended upon the attributes of single rays.According to this understanding, "polarization" couldnot bemore important than thosecategories that revealed the attributes of a single ray, such as "reflection" and"refraction." Consequently, "polarization" could be one of the categories in thetaxonomy, but, strictly speaking, it could only be a secondary one. Brewster's reasonfor listing "polarization" as one of the major categories might have merely beenpragmatic: it was the most promising research direction in the early nineteenth century.Limited by his instruments, particularly his use of the analyzer, Brewster could nevercomprehend a dichotomous system that used the state of polarization as the onlyclassification standard.

2. FRESNEL'S INNOVATIVE USES OF CRYSTAL ANALYZERS

The investigation of polarization took a dramatic leap in France around 1816 whenArago and Fresnel decided to examine interference of polarized light. In his first

USE OF INSTRUMENTS 33

experiment, Arago put a thin plate of copper with two narrow slits in front of a lightsource to produce two unpolarized beams with a common origin. In front ofeach oftheslits, he employed a pile of 15 thin films of brown glass, which polarized the lightalmost completely at an incident angle of30 degrees. When the planes ofincidence onthe two piles were parallel to each other, Arago observed the interference fringes as ifthe light beams were in their natural state (Figure 3.3a). But when Arago turned one ofthe piles around until the planes of incidence on the piles were perpendicular to eachother, the interference fringes vanished. These two experiments proved, according toArago, that two beams of light polarized in the same plane interfered under the sameconditions as two similar beams ofunpolarized light, but two beams oflight polarizedinmutually perpendicular planes did not interfere under any condition. About the sametime, Fresnel also conducted a couple ofexperiments showing similar results.3

Ifbeing in the same plane of polarization was the precondition for two polarizedbeams to interfere, the interference fringes could be restored in Arago's secondexperiment by altering the polarization plane of one of the beams. To examine thispossibility, Arago and Fresnel conducted a new experiment. Beginning with the settingin which the planes of the two polarized beams were perpendicular, they put a doublyrefracting crystal behind one of the polarized beam, with its principal section 45degrees inclined to the polarization plane (Figure 3.3b). Light emerging from thecrystal was divided into two beams with planes of polarization that were no longerperpendicular to the beam from the other pile. Under these circumstances, interferencefringes should reappear, Arago and Fresnel reasoned. Yet no fringes were seen. Theexperiment thus showed that if two beams ofpolarized light were from an unpolarizedsource, they did not produce interference fringes even when their planes ofpolarizationwere no longer perpendicular to each other. Later Arago and Fresnel altered theexperimental setting. They used a beam ofpolarized light as the source, and behind thedouble slits, they put a doubly refracting crystal instead of piles of brown glass. Thecrystal produced four beams of light, two from each slit, with planes of polarizationperpendicular to each other. They used another doubly refracting crystal to alter thesebeams' planes ofpolarization and made some of them mutually parallel. This time, asexpected, they saw fringes of interference (Herschel 1827, 531). Based on thisexperiment, Arago and Fresnel concluded that if two beams of polarized light werefrom the same polarized source, they could produce interference fringes when theirplanes of polarization were not perpendicular to each other.Before Arago and Fresnel's experiments, it was a common belief that the state of

polarization was a matter of degree. Light could be polarized, unpolarized, and inbetween, partially polarized. ButArago and Fresnel's experiments showed that the stateof polarization was absolute. In their experimental setting, a light source could eitherproduce interference fringes or did not do so at all, but nothing in between. Ifinterference fringes appeared, then the incident ray was polarized; if not, then it wasunpolarized. Thus, there was a clear demarcation between polarized and unpolarizedlight.This novel statement regarding the state of polarization was built upon an

34 CHAPTER 3

innovative use of instruments, specifically the analyzers. All experiments onpolarization required using analyzers. Before Arago and Fresnel, the function of theanalyzers in Brewster's and Biot's experiments was to alter the intensity of polarizedbeams, and the variation of intensity was understood as the indicator of the degree ofpolarization. Since Brewster observed gradual changes in the intensity by viewing

Pofarizers(A)

Lightsource

(8) Pofarizers

lightsource

Screen

Figure 3.3 Aragos apparatllsfor interference ofpolarized light

USE OF INSTRUMENTS 35

through an analyzer, he reasonably believed that the state ofpolarization was a matterof degree. Such an understanding of polarization was limited by the use of the eye,which was incapable of judging the intensity of light accurately. Arago and Fresnelgave a new function to analyzers: they used them to alter the plane of polarizationrather than the image intensity. This inventive use of analyzers generated a differentkind of signal through a process of interference. When Arago and Fresnel rotated theanalyzer, they looked for interference fringes as the signals, which were interpreted asthe indicator of the existence of polarization. Since Arago and Fresnel's experimentclearly showed that interference fringes either appeared or disappeared according to thecondition of the incident ray, there was no evidence for the existence of partialpolarization. This understanding ofpolarization was no longer limited by the use oftheeye because the eye was reliable in detecting the existence of such geometric figuresas interference fringes.Since Huygens, wave theorists had always conceptualized waves as longitudinal

vibrations, which were in essence symmetric. To account for polarization, anasymmetric phenomenon, Fresnel at first tried to add transverse vibrations into thepicture, derming waves as the resultant ofboth longitudinal and transverse vibrations.This theoretical model of waves was compatible with the belief that the state ofpolarization was a matter of degree. According to this model, polarized light did notcontain a longitudinal component and thus was completely transverse, and unpolarizedlight either was completely longitudinal or contained equal transverse vibrations allaround its ray. However, these were extreme conditions. Logically speaking, there wasno reason to prohibit the combination of longitudinal and transverse vibrations. Thus,this theoretical model required the existence of partial polarization, which was themixture of longitudinal and transverse vibrations. However, the new discovery of theabsolute distinction between polarized and unpolarized light caused a problem.Fresnel solved this problem between 1819 and 1821 by proposing a simple

theoretical model: light contains only transverse vibrations (Buchwald 1989,226-31).Even natural light was always completely asymmetric at a given instant, but a momentlater the direction ofthe transverse vibrations changed. Since these changes succeededone after another so fast that the eye could not follow the rapid variations, no onewould find a trace ofpolarization. In otherwords, natural light was the rapid successionof waves polarized in all directions. This model implied a new conceptual tool toanalyze optical phenomena. Fresnel explained, "according to this way of looking atthings, the act of polarization consists not in creating transverse motions, but indecomposing them in two fixed, mutually perpendicular directions, and in separatingthe two components the one from the other; because, in each of them, the oscillatorymotions will always operate in the same plane" (Fresnel 1821,635-6).4 Light couldalways be decomposed into two orthogonal vibrations, whichwere, in general, differentin phase. Thus, to determine the direction and the magnitude of the resultant in thewavefront, two parameters were needed: the amplitudes of the orthogonal vibrationsand their phase difference.In terms of amplitude and phase difference, Fresnel offered a new interpretation

36

Superordinatecategory

Instrumentaloperation

CHAPTER 3

Signal Subordinatecategory

I' ~Rotating<light theAnalyzer

Rotatingthe ~-.

Analyzer

NoInterference

Fringes

InterferenceFringes

The ImagesVanish

The ImagesRemain

the Same

UnpolarizedLight

PlanePolarization

EllipticPolarization

CircularPolarization

Figure 3.4 Fresnel sprocedure for classifyingpolarization

of the difference between polarized and unpolarized light. Polarized light was a statein which the two orthogonal components had a fixed phase difference and a fixedamplitude ratio, and unpolarized light was a state where the phase difference and theamplitude ratio between the two orthogonal components varied over time. Using thesame parameters, Fresnel further divided polarization into three subcategories: plane,elliptical, and circular polarization. Among them, plane polarization was a state inwhich the orthogonal components had no phase difference, circular polarization wasa state in which the orthogonal components had a phase difference of 90 degrees butno difference in their amplitudes, and all other possibilities fell into the category ofelliptic polarization.This was a whole new taxonomy of polarization that originated from a specific

experimental procedure. Quite different from the procedure used by Brewster, Fresnel'scontained an innovative use of the analyzer. He continued to use a doubly refractingcrystal as the analyzer, but he used it to alter the plane of polarization rather than theintensity. The state of polarization was determined by rotating the analyzer, whichgenerated signals in the form of interference fringes. Whether interference fringesexisted or not indicated the state ofpolarization, the foundation of the two subordinatecategories -- "polarized light" and "unpolarized light." Furthermore, the degree ofpolarization was decided according to the intensity variation generated by the rotation

USE OF INSTRUMENTS 37

of another analyzer. If one of the images of a polarized light vanished when theanalyzer was turned to a certain position, then it was plane polarization; if it nevervanished, then circular polarization; and if it varied but never completely disappeared,then elliptic polarization (Figure 3.4). Fresnel's taxonomy ofpolarization once againdid not classify the phenomenon arbitrarily; instead, every step ofthe classification hadits own instrumental basis. Metaphorically speaking, it is the analyzer that functions asa sorting machine sitting in the node of the taxonomy, and thus provides an objectivefoundation for the taxonomy.The absolute distinction between polarized and unpolarized light had important

implications for the overall classification ofoptical phenomena. Since light was alwayspolarized, and unpolarized light was only a special distribution of asymmetries overtime, the state of polarization reflected the nature of light -- waves in fact weretransverse vibrations. Furthermore, the state of polarization also determined otheroptical properties. Knowing the direction ofthe plane ofpolarization was necessary fordetermining both the orientation and the magnitude ofawavefront. Thus, with this newunderstanding of polarization, it was reasonable to use the state of polarization as theprimary standard for classifying optical phenomena. Fresnel did not explore theimplications ofhis new notion ofpolarization for the taxonomy ofoptical phenomena,but these ideas resurfaced a few years later and profoundly affected some British wavetheorists.

3. HERSCHEL'S UNDERSTANDING OF PARTIAL POLARIZATION

Herschel began his studies of polarization in the late 1810s. In an article published in1820, Herschel reported his extensive research on colored rings produced by crystalplateswith polarized light, known as the phenomenon ofchromatic polarization. Aragofirst observed colored rings in 1811 by using a prism ofIceland spar to examine a verythin lamina ofmica under a skylight that, he later realized, was polarized. After that,Biot, Brewster and Fresnel also conducted experiments to study the colored ringsproduced by crystal plates when exposed to polarized light.In his experiments with chromatic polarization, Arago observed the colored rings

by bringing the eye close to the Island spar. This method, according to Herschel, hadits limits. Since the eye was so close to the Island spar, it was difficult to see a completepicture of the rings. To overcome this defect, Herschel designed a new instrument toproject the colored rings onto a screen. The instrument contained a brass tube, aboutfour inches long and two inches in diameter (Figure 3.5). At the left end of the brasstube, there was a double convex lens with a short focus, which would produce verystrong illumination. About 1.5 inches behind the lens was a plate oftourmaline, whichfunctioned as the polarizer. Herschel had learned that a plate of tourmaline withmoderate thickness could produce highly polarized light -- no light could pass twoplates of tourmaline with their optic axes perpendicular to each other. Immediatelybehind the plate of tourmaline was the crystal to be examined, placed in an azimuth of45 degrees with the plane of the polarized light. Finally, a second piece of tourmaline

38 CHAPTER 3

Crystal

Figure 3.5 Herschel's apparatus/or producing chromatic polarization

was used as the analyzer, placed immediately behind the crystal, with the plane ofpolarization perpendicular to that of the fIrst tourmaline plate.5

When he started the experiment, Herschel fIrst adjusted the positions of thecomponents (the lens, the crystal and the tourmaline plates) to make sure that the focusofthe lens fell exactly on the surface ofthe second tourmaline plate (the one behind thecrystal). Using sunlight as the source, Herschel projected the colored rings exhibitedin the crystal onto a screen about three inches behind the second tourmaline plate. Thismethod allowed Herschel to examine closely the details of the colored rings. Heclaimed that "I have thus, occasionally, examined the rings in a portion not exceedingthe hundredth of an inch in diameter" (Herschel 1820, 98). Herschel carefullyexamined the colored rings produced by several different crystals, such as sulphate ofbaryta and Rochelle salt, and described in detail the patterns of these rings.The colored rings that Herschel observed were fringes produced by interference of

polarized light. In Herschel's apparatus, the fIrst tourmaline plate generated polarizedlight, the crystal divided the polarized light to two separate beams, and the secondtourmaline plate altered the planes of polarization of these beams and inducedinterference. Inmany ways, Herschel's experimental design was identical to Arago andFresnel's fInal experiment on interference by polarized light as discussed in the lastsection. But in his experiment, Herschel was not interested in the conditions underwhich interference between polarized rays could occur. He concentrated on the patternsofthe interference fringes and their relations with the crystal. Because of this focusedinterest, Herschel never turned the crystal and the analyzer (the second tourmalineplate) around to examine the variation of the interference fringes. He always kept thecrystal and the second tourmaline plate in fIxed positions, which he believed wouldmake the color rings sharp and reduce the observation error.

USE OF INSTRUMENTS 39

Thus, Herschel did not acquire the technique of using an analyzer as a sortingmachine to distinguish between polarized and unpolarized light. Several years laterHerschel reviewed Arago and Fresnel's experiments with interference by polarizedlight, but he evidently did not fully understand the significance oftheirwork. He highlypraised the importance of Arago and Fresnel's work, but he limited its significancesolely to its explanatory success -- Arago and Fresnel's work offered "an explanationof the colours of crystalline plates," and thus supplied "the defective link in the chainwhich connects the doctrine ofundulations" with the phenomenon (Herschel 1827, 533,532). Herschel never mentioned the fact that Arago and Fresnel's experimental setupfunctioned as a sorting procedure that distinguished polarized from unpolarized light,nor did he discuss the associated theoretical implications about the nature ofpolarization.In this way, Herschel's apparatus for producing chromatic polarization -- in

particular, the way that he used his specially designed apparatus -- effectively limitedhis understanding of polarization. In his essay "Light," Herschel had clearly noticedand accepted Fresnel's interpretation of polarization based on the notion that waveswere transverse. He wrote: "According to [Fresnel's] doctrine, a polarized ray is onein which the vibration is constantly performed in one plane, ... An unpolarized raymay be regarded as one in which the plane of vibration is perpetually varying, ... ""Thus we must conceive polarization as a property or character not susceptible ofdegree, not capable ofexisting sometimes in a more, sometimes in a less, intense state.A single elementary ray is either wholly polarized or not at all" (Herschel 1827, 534,509; original emphasis). So far, Herschel accurately represented Fresnel's notion ofpolarization. But he continued to write in the same paragraph: "A beam composed ofmany coincident rays may be partially polarized, inasmuch as some of its componentrays only may be polarized, and the rest not so. This distinction once understood,however, we shall continue to speak of a ray as wholly or partially polarized, inconformity with common language" (Herschel 1827,509; original emphasis). Here,Herschel interpreted the notion of "partial polarization" as being in a framework ofcollective rays, an understanding inconsistent with Fresnel's idea based on anindividual wavefront. It seems that Herschel did not fully understand Fresnel's notionof polarization; otherwise, he would not have put two fundamentally contradictoryinterpretations together in the same paragraph. However, it is not too difficult tounderstand why Herschel made such a mistake. As discussed in the last section,Fresnel's dichotomous classification of polarization was closely associated with anexperimental procedure, specifically his innovative use of an analyzer as a sortingmachine to distinguish polarized from unpolarized light. Without acquiring thisexperimental procedure and specific use of the analyzer, it would be difficult, if notimpossible, for Herschel to fully grasp the meaning of polarization.Herschel was familiar with the other experimental procedures used by Malus and

Brewster to determine the degree of polarization. In "Light," he gave a description ofsuch a procedure: "If a ray be reflected at an angle greater or less than the polarizingangle, it is partially polarized, that is to say, when received at the polarizing angle on

40 CHAPTER 3

another reflecting surface, which is made to revolve round the reflected ray withoutaltering its inclination to it, the twice reflected ray never vanishes entirely, butundergoes alternations of brightness, ... " (Herschel 1827,509; original emphasis).This description was accurate, indicating that Herschel either had carried out theseprocedures himself or learned them from reliable sources, which may also have givenHerschel reason to accept the notion of partial polarization.Herschel also recognized the different interpretations ofpartial polarization given

by Malus and Brewster. He accepted Malus's interpretation and rejected Brewster's.To justify his choice, Herschel gave the following analysis. "We may conceive apartially polarized ray to consist of two unequally intense portions; one completelypolarized, the other not at all. It is evident that the former, periodically passing fromevanescence to total brightness, during the rotation ofthe tourmaline or reflector, whilethe later remains constant in all positions, will give rise to the phenomenon in question"(Herschel 1827, 509). Here, Herschel attempted to use an experimental procedure toillustrate andjustifyMalus's interpretation ofpartial polarization. Apparently, however,Herschel did not actually carry out the procedure because, if he had, he should haveseen quite a different result. Decomposing light, including partially polarized, or moreprecisely, elliptical polarized light, into two orthogonal vibrations, is an effectivemathematical analysis for computational purposes. However, such a decomposition isnot physically operational. No instrument, at least no doubly refractive analyzer, is ableto sort a partially polarized light into a completely polarized and a completelyunpolarized portion. Thus, ifHerschel had examined a polarized light through a crystal,he would have seen two images (due to double refraction), both ofwhich would varyas the crystal was rotated but never completely disappear.Without acquiring Fresnel's experimental procedure or his specific use of the

analyzer to distinguish different kinds of polarized light, Herschel did not fullyunderstand Fresnel. He was confused when he tried to interpret the meaning and natureofpolarization, and his remarks on polarization were incoherent, consistent neitherwiththe newly emerged wave framework, nor with the traditional one (Buchwald 1989,295). This confusion made it impossible for him to explore the implications fromFresnel's notion of polarization, which suggested a dichotomous classification foroptical phenomena. Although Herschel did emphasize the importance of polarizationin his synthesized classification system, he appealed to its practical orpragmatic values.Thus, limited by his instruments and his skills for operating a certain experimentalprocedure, Herschel could only comprehend and construct a compromised system inhis attempt at synthesis.

4. LLOYD AND CONICAL POLARIZAnON

Huygens discovered double refraction in biaxial crystals such as Iceland spar andquartz in the seventeenth century, and explained the phenomenon by assigning differentforms to the two wavefronts in the crystals, a sphere for the ordinary and a spheroid forthe extraordinary. The majority of the optical community at the time, however, did not

USE OF INSTRUMENTS 41

accept Huygens' explanation. In the early 1820s, Fresnel developed a new account ofdouble refraction by assuming that the elasticities ofthe ethereal mediumwithin biaxialcrystals were unequal in three perpendicular axes. He demonstrated that the surface ofthe wavefront in biaxial crystals was neither a sphere nor a spheroid, but a complicatedform consisting oftwo sheets with different shapes. Consequently, neither the ordinarynor the extraordinary rays obeyed the law ofHuygens. However, Fresnel's new accountcontinued to imply that a single ray, when entering into a biaxial crystal and refractedin the direction ofthe optical axis, would necessarily be divided into two, and only two,rays.William Hamilton turned his attention to double refraction in 1832. Between the

late 1820s and the early 1830s, Hamilton developed a series of new concepts in hisstudies of geometrical optics. Among them the most significant one was the notion of"characteristic function," which represented the geometrical length ofa ray regardlessofwhether the ray consisted ofparticles or ofwaves (Hamilton 1830). When applyingthis new concept to analysis of Fresnel's wave surface in biaxial crystals, Hamiltondiscovered something that had been overlooked by Fresnel. He showedmathematicallythat a single ray, when entering into a biaxial crystal and refracted in the direction ofthe optical axis, could be divided into not just two, but an infmite number of rays.Based on his mathematical analysis, Hamilton predicted two hitherto unobserved

optical phenomena in an article presented to the Royal Irish Academy in 1832. First,a pencil of unpolarized light, when entering a biaxial crystal and refracted in thedirection of the optic axis, would be divided into an infmite number of rays,constituting a conical surface within the crystal. Hamilton called this "internal conicalrefraction." Second, a pencil of light, when passing through a biaxial crystal in aparticular direction, would be divided after emerging at the crystal surface into aninfinite number of rays, forming a cylindrical cone. Hamilton called this "externalconical refraction" (Hamilton 1837b, 136). Hamilton announced his theoreticaldiscoveries at the Royal Irish Academy on October 22, 1832. On the same day, heasked his colleague and friend Lloyd to conduct the necessary experiments to confirmhis predictions.Lloyd immediately undertook the task ofconfirming Hamilton's predictions, and

decided first to demonstrate the existence ofexternal conical refraction. The crystal thathe used in his experiments was a specimen ofarragonite (CaC03), the three elasticitiesofwhich had been determined by Rudberg. Lloyd placed two plates ofthin metal, eachhaving a small aperture, on the two surfaces of the crystal. The line connecting theapertures was in the direction of the optic axis. He used a lens of short focus toconverge a beam ofunpolarized light on the aperture at the upper surface, and used aground glass screen to observe the shape of the emergent light (Figure 3.6). Afterseveral trials, Lloyd successfully produced external conical refraction on December 14,1832. With sunlight as the source, he was able to show that, while the incident light wasrefracted as a single ray within the crystal, it became a hollow cone after emerging fromthe second aperture. He reported that the section of the cone on the screen was as largeas two inches in diameter (Lloyd 1833a, 115-6).

42 CHAPTER 3

Arragonitecrystal

Figure 3.6 Lloyd's apparatus for producing extemal conical refraction

Although Lloyd demonstrated the existence of external conical refraction, hisinitial measurements did not conform very well to Hamilton's theoretical predictions.According to Hamilton's calculation, the angular size of the cone in external conicalrefraction should be about three arc-degrees. In Lloyd's experiments, however, theangular size ofthe angle appeared to be 6 0 14', doubling the theoretical calculation. Ittook Lloyd a while to explain the discrepancy between the observational result and thetheoretical prediction. In a paper published in the February issue of PhilosophicalMagazine, Lloyd reported his experimental discoveries of external conical refraction,and attributed the discrepancy between his observation and Hamilton's prediction tothe effect of diffraction -- the cone appeared to be larger because of the surroundingdiffraction fringes. Lloyd noted that, after the effect of diffraction was taken intoaccount, the angular size of the cone was only one half of the gross value. Heconcluded that the observed angular size of the cone should have a mean value of3 0 47', which nearly corresponded to Hamilton's prediction (Lloyd 1833a, 118-20).Lloyd continued his experimental exploration to verify internal conical refraction

and succeeded in producing the phenomenon in January of 1833. Lloyd employed alamp placed at some distance from the crystal as the light source. In order to obtain anincident ray as small as possible, he made the light pass through two small apertures,one ofwhich was in a screen near the lamp and the other in a thin plate ofmetal on theupper surface ofthe crystal. After observing that the incident ray was generally dividedinto two beams within the crystal, Lloyd altered the direction of incidence by turningthe crystal slowly. After several trials, he obtained an incidence at which the two beams

USE OF INSTRUMENTS 43

were seen to spread into a continuous circle, which emerged as a hollow cylinder at thesecond surface ofthe crystal. After carefullymeasuring the angle ofthe cylinder, Lloydreported that it was about 1°50', only differing by five arc-minutes from the valuepredicted by Hamilton (Lloyd 1833b, 209-210).Lloyd did not limit himself simply to searching for evidence supportive of

Hamilton's predictions. When he conducted the experiment on external conicalrefraction, he also carefully examined the state ofpolarization ofthe emergent cone byusing a plate of tourmaline as an analyzer. He was surprised to see that, in any givenposition ofthe tourmaline plate, only one point in the section ofthe cone vanished. Thisobservation suggested to Lloyd that rays in the cone were polarized and that only oneofthese polarized rays had a plane ofpolarization perpendicular to the optic axis ofthetourmaline plate. By turning the tourmaline plate around its axis by 90 degrees, heobserved that the dark spot gradually moved along the circumference of the cone by180 degrees, to the other side ofthe circle. From these observations, Lloyd concludedthat "all the rays of the cone are polarized in different planes" (Lloyd 1833a, 116).After repeated observations, Lloyd summarized his discovery in the format of anempirical law. He claimed: "On examining this curious phenomenon more attentively,I discovered the remarkable law, -- that 'the angle between the planes of polarizationof any two rays of the cone is half the angle contained by the planes passing throughthe rays themselves and its axis'" (Lloyd 1833a, 116-7). Put in other words, Lloyd'slaw states that for rays that are opposite to each other in the cone, that is, 180 degreesapart, their planes of polarization are perpendicular to each other (Figure 3.7). This isthe so-called law of conical polarization, which was subsequently "introduced" byHamilton in a paper published in 1837 (Hamilton l837b). Hamilton did not predict thelaw ofconical polarization in his report to the Royal Irish Academy in 1832, but when

Planes of polarization

Figure 3.7 Lloyd s law ofconical polarization

44 CHAPTER 3

he in 1837 published his report with the title "Third Supplement to an Essay on theTheory ofSystem ofRays", he treated conical polarization as if it had been predictedby him in the same way as conical refraction (Hamilton 1837a).Lloyd's observations ofconical polarization were crucial for his understanding of

light. Just a few years before he discovered conical polarization, Lloyd still embraceda collective notion of rays, just as many of his fellow British scientists did. Forexample, in the book he published in 1831, titled "A Treatise on Light and Vision," hecontinued to conceptualize light as something consisting of"separable and independentparts" (Lloyd 1831, 1). But the phenomenon of conical polarization was clearly inconflict with the collective vision of ray. From a collective point of view, the cone inLloyd's experiments should be unpolarized as awhole, because rays that were oppositeto each other in the cone had equal but orthogonal vibrations and thus the combinationofthem was mathematically equivalent to an unpolarized beam. The whole cone wasan assembly of this kind ofunpolarized beams. If the cone was unpolarized, then theray within the crystal must also be unpolarized because emergence from the crystalwould not generate polarization. But the ray within the crystal could not beunpolarized, because light had to become polarized when passing through the doublyrefracting crystal. Thus, to make sense ofconical polarization, Lloyd had to give up thecollective interpretation ofray. Consequently, he embraced the notion that polarizationwas the state of an individual wavefront, not a property of collective rays.Lloyd's discovery ofconical polarization thus provides a clue to explain his correct

understanding of the wave theory when he prepared the report to the BritishAssociation in 1833. In the report, Lloyd correctly comprehended the most essentialpoint of Fresnel's notion of polarization. He never adopted the notion of partialpolarization. Although he gave a thorough review of Malus's analysis of partialpolarization, he carefully kept a distance from Malus's position and never offered anyendorsement (Lloyd 1834, 88-9). At the same time, Lloyd adopted Fresnel's taxonomyof polarization without any hesitation and applied the notions of plane, elliptic andcircular polarization as the main classification categories in his discussion.Lloyd was excited by his successes in verifying Hamilton's novel predictions, and

he wanted to use these successes as evidence to prove the superiority of the wavetheory over the particle theory. In an article published in Philosophical Magazine in1833, Lloyd wrote that "Here then are two singular and unexpected consequences ofthe undulatory theory, not only unsupported by any phenomena hitherto noticed, buteven opposed to all the analogies derived from experience. Ifconfirmed by experiment,they would furnish a new and almost convincing proofof the truth of that theory; andif disproved, on the other hand, it was evident that the theory must be abandoned ormodified" (Lloyd 1833a, 114). Lloyd here tried to present his experiments on conicalrefraction as a crucial test for the truth of the wave theory. He made the abovestatement after he had discovered external conical refraction and was confident that hewould find internal conical refraction soon. However, he dramatized the situation byclaiming that if Hamilton's predictions were disproved, the theory "must beabandoned," even though he knew that such a scenario would never happen. This was

USE OF INSTRUMENTS 45

a rhetorical trick that exaggerated the importance of the experiments on conicalrefraction by deliberately inventing a scenario of the potential disconfrrmation of thewave theory.In fact, Hamilton's predictions of conical refraction, based upon his theory of

characteristic function and a new understanding of the structure of the wave surfacewithin biaxial crystals, were directly in contrast to Fresnel's theory ofdouble refraction,rather than with any particle account. The successes ofHamilton's predictions provedthe superiority ofHamilton's version ofdouble refraction theory over Fresnel's. SinceHamilton's double refraction theory was still built upon the wave doctrines, thepredictive successes could also provide a limited support for the wave theory, in thesense of improving its explanatory ability though not proving its truth. If thepredictions had failed, Hamilton's special double refraction theory would have bornethe blame, while Fresnel's theory as well as the general wave doctrines would haveremained undamaged. Thus, Hamilton's predictions ofconical refraction could hardlybe a crucial test for the wave theory.Although mostwave theorists expressed their cautious welcome to Hamilton's and

Lloyd's discoveries, they did not regard the confrrmation of conical refraction as aconclusive triumph of the wave theory. Even Hamilton himself did not interpret theverifications ofhis own predictions in the way Lloyd did. In a letter written to Herschelin 1833, Hamilton denied that the verifications ofhis predictions could be used to testthe two rival theories of light. He told Herschel that "you are aware that thefundamental principle ofmy optical methods does not essentially require the adoptionof either of the two great theories of light in preference to other" (Hamilton 1832).Hamilton believed that he could apply his theory ofcharacteristic function equally wellto both accounts of light, either particle or wave, and he regarded his work on conicalrefraction as merely an application of his optical methods to biaxial crystals. Thediscoveries ofconical refraction could indeed provide another bit ofevidence for wavetheory, but Hamilton never expected that it could become a life or death test.Nevertheless, the confirmation of conical refraction was crucial to Lloyd on a

personal level because Lloyd himselfmust have fmally adopted the wave theory as aresult of this confrrmation. Itwas evident that Lloyd had not completely committed tothe wave theory in 1831 when he published his treatise on light, in which he tried topresent both the particle and the wave theory with a neutral tone (Lloyd 1831, 5-7).Between 1831 and 1832, Lloyd did not conduct any other optical research except theexperiments on conical refraction. It is highly possible that the successes in confirmingHamilton's predictions changed Lloyd's evaluation of the rival theories of light andfmally made him a committed wave theorist in early 1833.Furthermore, Lloyd's discovery ofconical polarization during his confirmation of

conical refraction also helped him understand Fresnel's notion ofpolarization. He wasable to do a much better job than Herschel in introducing Fresnel's wave theory to theEnglish-speaking audience, and his report to the British Association in 1834 definitelycontained a more accurate interpretation of Fresnel's theory than Herschel's "Light"had. More importantly, Lloyd was capable of exploring the implications of Fresnel's

46 CHAPTER 3

notion of polarization. After fully understanding the absolute distinction betweenpolarized and unpolarized light, and after interpreting the state of polarization as theessential feature oflight, it was simply logical for Lloyd to use the state ofpolarizationas the primary standard for classifying optical phenomena when he prepared his reportto the British Association in 1833. Thus it was Lloyd rather than Herschel who wasable to construct the dichotomous taxonomy essential to the revolutionary change.

CHAPTER 4

THE DISPUTE OVER DISPERSION

Although by the early 1830s the wave theory of light had demonstrated its superiorexplanatory power in accounting for many optical phenomena, it was not withoutobstacle. The phenomenon of dispersion (light of different colors'suffering differentdegrees of refraction in a prism) was still problematic for the wave theory. Accordingto the doctrines outlined by Augustin Fresnel, the velocity of light as well as itsrefractive index depended solely upon the elasticity of the medium transmitting it.Light of every color should travel with the same velocity and have only one refractiveindex in a homogeneous medium. But experiment showed that light beams traveledwith different velocities and had difference refractive indices within a prism accordingto their colors. However, such negative evidence from dispersion experiments did notbecome an obstacle to the acceptance of the wave theory. Why did dispersionexperiments not play any decisive role in the evaluation of the wave theory of light?Those who continued to embrace the wave theory perhaps did so because they gavemore weight to the other explanatory successes of the wave theory, or because they didnot believe that the rival particle theory could explain the phenomenon. I But it isdifficult to understand the reaction of the opponents of the wave theory. They shouldhave seized this opportunity to expose the explanatory inadequacy of the rival, as theyhad done in many other cases. Why did they not take advantage of the issue ofdispersion?This chapter concentrates on a debate over dispersion in the second half of the

1830s, in which both sides utilized the same set of experimental data to test a proposedwave account of dispersion, but could not agree on how these data should be analyzed.This conflict regarding experimental data was caused by differences in the use ofinstruments. Instrumental obstacles led the debate further into an impasse, especiallysince no apparatus was available for the necessary experimental replication. Becauseof unreconcilable differences regarding experimental evidence, the wave theory'sfailure in explaining dispersion did not become an obstacle to its acceptance.

1. POWELL'S FORMULAS OF DISPERSION

Wave theorists in Britain made various attempts to overcome the difficulty posed bythe phenomenon ofdispersion. One of the earliest attempts was Thomas Young's brief

47

X. Chen, Instrumental Traditions and Theories of Light© Springer Science+Business Media Dordrecht 2000

48 CHAPTER 4

account in 1807. He speculated that both the particles of the refracting materials andthose of the ether were vibrating, and that the vibrations ofthe particles could affect thevibrations ofthe ether according to the frequency of the latter (Young 1807, 623). LaterJames Challis adopted Young's hypothesis and developed a similar account with somedetailed analysis (Challis 1830). In 1831, George Airy offered a different account ofdispersion, one based on thermal effects. According to Airy, the vibrations of etherparticles could produce latent heat by compression, and the amount of the latent heatmight depend upon the duration of the compression process, which was related to thewave's frequency. Thus, the elasticity of the ether should vary according to the amountof the latent heat, and thereby cause dispersion (Airy 183Ia).Both Young's and Airy's accounts of dispersion were merely qualitative. Neither

of them was able to deduce a quantitative description of the phenomenon that couldeventually be tested experimentally. This failure to explain dispersion deeply perplexedthe British wave commimity. John Herschel openly admitted that dispersion was a mostformidable objection to the wave theory, but he asked members of the opticalcommunity to suspend their condemnation of the wave theory until they had "becomeacquainted with the immense variety and complication of the phenomenon" (Herschel1827, 450). Many prominent wave theorists in Britain agreed with Herschel thatdispersion constituted a major problem for the wave theory, but at the same time theyinsisted that this problem should not affect the acceptance of the wave theory. Some,like Humphrey Lloyd, even suggested eliminating the problem ofdispersion by alteringthe classification system (Lloyd 1834, 295-413VIn France, wave theorists attacked the problem of dispersion using a different

approach. Fresnel in 1822 stated that the difficulty in accounting for dispersion mightresult from the mistaken assumption that the range of the molecular force in themedium was much smaller than the length of the wave. Fresnel believed that, on thebasis of ether dynamics, he could prove that the velocity of the wave could increasewith the length of the wave even in a homogeneous medium, if the range of themolecular force was comparable to the wavelength. Fresnel mentioned this proofmorethan once in his writing, but he never put it in print. A few years later, the Frenchmathematician Augustin Cauchy carried out Fresnel's research program and provideda detailed but faulty demonstration. In many ways, Cauchy's ether dynamics was acontinuation of Fresnel's work, but, unlike Fresnel's general equation of motion,Cauchy's allowed every ether particle to be displaced, and he calculated the net forceon any given particle caused by the displacements.3 Armed with a new general equationof motion, Cauchy attempted to show that, if the range of the molecular force werecomparable to the wavelength, the degree of refraction would depend essentially on theratio of the wavelength to the range of the molecular force; on the other hand, if therange of the molecular force were much smaller than the wavelength in the void, thendispersion would not occur.Cauchy's ether dynamics became influential in Britain by the mid 1830s, mainly

because for the first time it offered British wave theorists tools to deduce quantitativeaccounts for various optical phenomena (Buchwald 1981, 225). Baden Powell, Savilian

DISPERSION 49

Professor of Geometry at Oxford, was a major advocate of Cauchy's approach.Although he was a professor ofgeometry, Powell was the most active proponent of thewave theory. From the 1820s to the 1850s, he published more than 70 scientific paperson physical optics and involved himself in almost every debate regarding the wavetheory.4 Beginning in 1835, Powell published a series of papers in which he developeda wave account of dispersion based on the elaborate equation of motion alreadyproduced by Cauchy (Powell 1835a). After a lengthy mathematical analysis thatinvolved many approximations, Powell managed to derive a dispersion formula,showing that light with different wavelengths (A) could have different refractive indices(J-l):

1 =!... sin (.E!A.)

!J h .E!..1.

where h, and ~ are constants determined by the properties of the medium (Powell1835b,250).Powell's formula gained immediate attention from the British wave community. In

the same year, William Hamilton went over Powell's mathematical analysis and foundthat Powell had assumed that the molecular force of the medium extended onlybetween contiguous molecules. Hamilton kindly suggested to Powell some ways to fixthis problem. With Hamilton's help, Powell abandoned the problematic assumption andin 1836 derived a different formula in the form of a Taylor series (Powell 1836b):

where Ao, AI and 1\ are also constants needed to be determined empirically. Thisformula was identical to the one independently obtained by Cauchy about the sametime, which is now called the Cauchy equation in contemporary textbooks.According to Powell, his formula of dispersion indicated "a relation between the

length ofa wave and the velocity of its propagation," and provided "a reason why rayswhose waves are of different lengths should be unequally refracted" (Powell 1835a,266). Thus, if this formula were confirmed experimentally, it could offer a reasonablewave account for the phenomenon, and finally eliminate the difficulty of explainingdispersion that had perplexed the wave community for a long time.

2. FRAUNHOFER'S THEODOLITES AND SPECTRAL LINES

Powell did not immediately conduct his own experiments to test his formulas ofdispersion. He instead used the measurements already produced by Joseph Fraunhofer:the refractive indices of seven spectral lines as seen in prismatic spectra and theirwavelengths obtained from diffraction spectra.Fraunhofer's measurements of the refractive indices and the wavelengths of spectral

50 CHAPTER 4

Achromatic telescope

Figure 4. J Fraunhofer sspectroscope

lines originated from his work on glass manufacturing. As the technical director of theOptical Institute at Benediktbeuem, Fraunhofer's day-to-day responsibility was to makeachromatic lenses used in astronomical and surveying instruments such as telescopesand theodolites. Since both spherical and chromatic aberration could be corrected bya convex-concave doublet made of flint and crown glass with carefulIy selecteddispersive powers, Fraunhofer needed to measure the refractive indices of glass atdifferent wavelengths (Jackson 1996).In 1814, Fraunhofer conducted a series of experiments to measure the refractive

indices ofdifferent colored beams in a solar spectrum produced by a prism. The basicidea behind these experiments was not new -- the generation of colors by a prism hadbeen known since antiquity -- but Fraunhofer's precision instruments and sophisticateddesign produced something unanticipated. Two pieces of apparatus were crucial. ThefIrst was the prism, which was made ofhighly homogeneous flint glass manufacturedby his own company. The other was a modifIed theodolite equipped with an 18-inchachromatic telescope (with a magnifying power of 30 or 50) and a large dividing circle,ruled on silver at 10 arc-second intervals (Figure 4.1). Sunlight was transmitted througha slit of IS arc-seconds, and felI into the prism that was 24 feet away. The combinationof the high-quality prism and the achromatic telescope alIowed Fraunhofer to fIndhundreds of spectral lines across the whole solar spectrum. By his own count he saw574 spectral lines; to the most prominent ones he assigned letter names, A, a, B, C, D,E, b, F, G, H, I, from red to violet (Fraunhofer 1817,4-6).5 At the same time, using the

DISPERSION 51

dividing circle, together with a pair of vernier protractors, Fraunhofer preciselymeasured the refractive angles of these spectral lines, and computed their refractiveindices according to a standard formula in geometric optics:

sin ({}+iP}1211 = ---'----'--

sin (@'2)

Here ~ is the index of refraction, e is the angle of refraction, and cI> is the angle of theprism. Before the discovery of the spectral lines, it was impossible to determineprecisely the refractive index of each color, because there are no clear demarcationlines between colors. The discovery of the spectral lines thus dramatically improved themeasurements of refractive indices. Using these spectral lines as the natural reference,Fraunhofer was able to determine precisely the index of refraction for each color andto improve their accuracy by two orders of magnitude.Fraunhofer's measurements ofwavelengths came from his work on diffraction. He

devoted his attention first to diffraction by a single slit, then double slits, and [mallymultiple slits, that is, a grating. When he used a grating to generate diffraction,Fraunhofer saw many spectra symmetrically on both sides of the image of the aperture.When the number ofopenings in the grating increased, distinct spectral lines emergedfrom these spectra. Using a formula introduced by Thomas Young, Fraunhofer realizedthat he could determine the wavelengths of these spectral lines by means of their anglesof incidence and diffraction (Fraunhofer 1823,51). To obtain the measurements ofthese two angular parameters, Fraunhofer again deployed a modified theodolite similarto the one used in his prismatic experiments. This theodolite had a lower dividing circlewith a least count of four arc-seconds for measuring the angles of diffraction. The tablein front of the telescope was also equipped with a small dividing circle with 10 arc­second least intervals, which, together with a telescope ruler, measured the angles ofincidence. Armed with this sophisticated theodolite, Fraunhofer accurately measuredthe wavelengths of six spectral lines (e, D, E, F, G, and H). According to Fraunhofer'sown estimation, the relative error ofhis calculations was about 0.1%, and all his values,except for line G, lie in that range (Leitner 1975, 59-68).To connect the measurements of refractive indices and those of wavelengths,

Fraunhofer needed to establish a one-to-one correspondence between the spectral linesin prismatic spectra and those in diffraction spectra. This was not an easy task becausespectral lines in prismatic spectra are dispersed in a quite different pattern from thosein diffraction spectra. For example, spectral lines spread out much more at the violetend than at the red end in prismatic spectra, but spread evenly across diffractionspectra. Fraunhofer immediately recognized this "striking difference between thespectra produced by the grating and the prism" (Fraunhofer 1822, 23).Fraunhofer's aim in his prismatic and diffraction experiments was always to obtain

angular measurements, specifically, the angular positions of the spectral lines, so thathe could determine their refractive indices and wavelengths. To increase the accuracyof these angular measurements, Fraunhofer realized that he needed to increase the

52 CHAPTER 4

angular size of the spectra. He learned that the angular size of a spectrum wasdetermined by the quality of the instruments -- the refractive angle and the refractiveindex in prisms or the density of lines in gratings. He then reasoned that the "strikingdifference" between the two sets of spectral lines must also be caused by theinstruments. Because prisms had a higher dispersive power than gratings, particularlyin the area near the violet end, spectral lines in prismatic spectra spread out in a patterndifferent from that in diffraction spectra. Since the instruments only relocated spectrallines, correspondence between these two sets of spectral lines could exist. Thus,Fraunhofer worked hard to establish a one-to-one correspondence between somespectral lines in the two spectra. He carefully compared the relative intensity of theselines and their arrangements, and identified seven lines in diffraction spectra as thecounterparts of the seven prominent spectral lines in prismatic spectra. He used thesame letters (B, C, D, E, F, G, and H) to label them.

3. POWELL'S HOLLOW PRISMS AND SPECTRAL LINES

Powell used Fraunhofer's measurements of refractive indices and wavelengths directlyto test his formula of dispersion. Since his original formula contained two empiricalconstants (h and ~), Powell had to use the data of two spectral lines to determine thevalues of these constants. He selected the two extreme lines, the B and the H lines, asthe reference points, leaving only five for testing his formula (Powell 1835b, 251-2).6After a cumbersome process of trial and error, Powell determined the values of the twoconstants, and then deduced the refractive indices of the remaining five spectral linesaccording to his formula (see Appendix 2). Finally, he compared the calculated valuesof the refractive indices with Fraunhofer's measurements (Figure 4.2). According toPowell, the results of the comparisons were impressive: all the calculated refractiveindices were either identical or very close to Fraunhofer's measurements. In most cases,the agreement was accurate to the third decimal place. Consequently Powell claimedthat "we are thus, I think, justified in concluding, that for all the substances examinedby Fraunhofer, viz. for four kinds of flint glass, three ofcrown glass, for water, solutionof potash, and oil of turpentine, the refractive indices observed for each of the seven

~ Powell's calculations Fraunhofer's meastrements Error(%)

B 1.6275 1.627749 -.015

C 1.6299 1.629681 .013

D 1.6355 1.635036 .028

E 1.6426 1.642024 .035

F 1.6486 1.648260 .021

G 1.6609 1.660285 .037

H 1.6711 1.671062 .002

Figure 4.2 ComJX1risons ofPowell's calculations and Fraunhofer s measurements(Flint glass, No. 13)

DISPERSION 53

defmite rays are related to the lengths ofwaves for the same rays, as nearly as possibleaccording to the fonnula above deduced from M. Cauchy's theory." He concludedthat, for all the media that had been examined, the wave theory of light was able tosupply "at once both the law and the explanation of the phenomena ofdispersion"(Powell 1835b, 254; original emphasis).Powell also compared his fonnula with the measurements made by Frederik

Rudberg, who had detennined the refractive indices of the seven spectral lines in somecrystals. The agreement between the data and the fonnula, according to Powell, wasagain sufficiently close (Powell 1836c, 17-9). But Powell was not yet completelysatisfied with the results of these comparisons because he realized that all ofFraunhofer's and Rudberg's data were from media with relatively low dispersivepower. To test his fonnula and eventually to verify the wave account of dispersion, heneeded a variety of data, especially those from media with high dispersive power.Powell first wanted to measure the refractive indices of the spectral lines in the

spectra produced by the chromate of lead, which was known to have very highdispersive power. He obtained a good specimen of this crystal and cut it to fonn aprism with a small angle. But due to defects in the specimen such as veins and cracks,which were common among crystals, the appearance of the spectrum was confused andno spectral lines were measurable (Powell 1839c, 5). To circumvent this problem,Powell decided to use fluids as the refracting media, since fluids always havehomogeneous structure and some of them have relatively high dispersive power.In 1836, Powell conducted a series ofexperiments to measure the refractive indices

ofvarious fluids. His experimental design was similar to Fraunhofer's, with a prism anda modified theodolite as the key apparatus. In order to hold the fluid, the prism washollow, made of two pieces of plate glass with truly parallel surfaces. Hollow prismswere not Powell's invention. For example, Fraunhofer had employed hollow prisms toproduce colored rays. But Powell was probably the first who used hollow prisms filledwith highly refractive fluids to generate spectra. Since highly refractive fluids are alsovery absorptive, Powell sometimes had to use hollow prisms with very small angles.He made several hollow prisms with different angles, ranging from about 60 degreesto only about seven degrees, but the one that he used most was about 30 degrees. Thetheodolite was manufactured and installed by William Simms, who owned one of thebest mathematical instrument shops in London (King 1955,237-8). The dividing circleof the theodolite, which was put vertically, was ten inches in diameter and ruled onsilver to 10 arc-minutes (Figure 4.3). With the help of two opposite vernier protractorsequipped with lenses, it could be read with an accuracy of 10 arc-seconds. The hollowprism was placed at the center of the dividing circle, and a thennometer was insertedinto the prism to measure the temperature of the fluid. An achromatic telescope witha magnifying power of 10 was directed toward the prism and fixed in an arm moveablearound the center of the circle. In these experiments, Powell set the width of the slit,from which the light originated, to I120th of an inch (about one arc-minute), and thedistance of the slit to the prism was about 12 feet (Powell 1836a, 9-10).Using hollow prisms and the theodolite, Powell measured the refractive indices of

54 CHAPTER 4

Figure 4.3 Powell's spectroscope

Theodolite

the seven spectral lines in the spectra of 32 fluids, including oil of cassia, oil of anise­seed, and sulphuret of carbon. The accuracy ofPowell's measures was not comparablewith Fraunhofer's. By using prisms with smaller angles, Powell's measures becamemore sensitive to the error in the angle ofthe prism. Even ifwe give Powell the benefitof the doubt by assuming that his measurements of refractive angles and prism angleswere as good as Fraunhofer's, the range of the relative error in his measurements ofrefractive indices was still three to eight times that of Fraunhofer's (see Appendix 3).Worst of all, Powell was not able to control the heat impact of the sunlight, whichdramatically affected the refractive power of the fluid as the experiment proceeded. He

DISPERSION 55

simply took the mean of several observations under different temperatures. Powellopenly admitted that the accuracy of his measurements was inferior to Fraunhofer's,but he insisted that a lower level of precision was still acceptable since his task was totest the theory. He claimed that "my object was, in the ftrst instance, to obtain somedata which might be admitted as approximate values subject to correction fromsubsequent repetitions: principally with a view to the comparison of observation withtheory" (Powell I836a, 8).When Powell examined the spectra of the highly dispersive media, he discovered

something unexpected. He found that some spectral lines, which were single inFraunhofer's prismatic and diffraction experiments, apparently became multiple. Forexample, in the spectrum of anise-seed oil, it seemed that the H line expanded to twowidely separated bands, one with an angular position of 47.33 degrees and the other47.47 degrees. Similarly, the G line appeared to include a mass of small lines closetogether. This newly found one-to-many correspondence between the spectral lines inFraunhofer's spectra and those in his prismatic spectra created a big problem forPowell. To test his formula, he needed a one-to-one correspondence between the twosets of spectral lines and between the related refractive indices and wavelengths. Tosolve this problem, Powell tried to attribute the apparent discrepancies between thesetwo sets of spectral lines to the difference in the dispersive power of the instruments,assuming that an increase in dispersive power should accompany an increase inresolving power. According to Powell, spectral lines in diffraction spectra, whichusually had lower dispersive and resolving power than prismatic spectra, appeared "ina form far more closely condensed together (especially towards the blue end) than theyappear even in the least dispersed of the refraction-spectra." In prismatic spectra,however, the spectral lines "are not only far more widely separated, but those whichappear single in the [diffraction spectra], and even in the lower dispersive media, areresolved into assemblages of several lines in the higher" (Powell 1838b, 841; originalemphasis). In hindsight, it is clear that Powell's explanation of the apparent one-to­many correspondence was mistaken. His hollow prisms did have higher dispersivepower because of the highly dispersive fluids; for example, the dispersive power of theprism ftlled with sulphuret of carbon was about 80% higher than that of Fraunhofer'sflint glass prism. But the increase ofdispersive power does not bring about an increasein resolving power, which is in proportion to the size of a prism's base. Due to theirsmaller angles, Powell's hollow prisms in fact had shorter bases than Fraunhofer's flintglass prism and, thereby, lower resolving power. Thus, Powell's hollow prisms,together with those highly dispersive fluids, could only displace the existing spectrallines and enlarge the angular size of the spectrum, but could not increase the numberof spectral lines.To Powell, giving an explanation of the one-to-many correspondence was not

enough. He needed a solution to reinstall the one-to-one correspondence between hisprismatic and Fraunhofer's diffraction spectral lines. But which one of the H lines inhis prismatic spectra corresponded to the single line in Fraunhofer's diffraction spectra?Or which one of the G lines in his prismatic spectra matched with the wavelength of

56 CHAPTER 4

G given by Fraunhofer? According to Powell, every one of them should correspond toa single line because they all originated from that single line due to the increase inresolving power. The solution then was to take the mean of these small lines torepresent the whole group, so that a one-to-one correspondence could be maintainedfor the purpose ofcalculation. "It appeared to me the only fair and reasonable method,to take the mean of the expanded set oflines as corresponding to the value of the wave­length, given for the condensed line," he claimed (Powell 1838b, 841; originalemphasis).Powell soon reported the results of his measurements to the scientific community,

first to the Ashmolean Society at Oxford in May 1836 and later to the 1836 meeting ofthe British Association. His report to the latter drew the attention of David Brewsterand initiated a heated debate.Brewster's initial reaction toward Powell's work on refractive indices was positive.

Brewster, who always emphasized the importance of experimental investigations,believed that to measure refractive indices was one of the most important tasks inoptics. In his 1832 report on optics presented to the British Association, Brewster hadlisted the detennination of"the refractive and dispersive powers of ordinary solid andfluid bodies" as the problem to which "we would call the attention ofyoung and activeobservers" (Brewster 1832, 319). Following Brewster's suggestion, the BritishAssociation in 1833 put the measurements of refractive and dispersive indices into itslist of recommendations for optical studies (British Association 1833). When Powelldecided to pick up this research topic, the British Association in 1835 provided him asmall grant to carry on the experiments (Powell 1839c, 2).But Brewster soon developed doubt about Powell's capacity to make accurate

measurements of refractive indices. A couple of observations triggered Brewster'ssuspicion. In his presentation at the 1836 meeting of the British Association, Powelladmitted that he had difficulties in producing distinct spectral lines when he usedprisms made of crystals with high dispersive power. Hearing PowelI's difficulties,Brewster gave Powell some tips at the meeting to overcome these problems. Brewster'ssuggestions included using ink to cover the defects of the crystals, inserting a thin plateof glass between the crystal and the eye to make the spectral lines visible, and selecting'an appropriate angle of the incidence (Anonymous 1836). But Powell did not adopt anyofBrewster's suggestions and continued to report difficulties in using highly dispersivecrystals to produce prismatic spectra with distinct spectral lines (Powell 1838a, 6-7).Brewster was clearly disappointed when he found that Powell had not followed hissuggestions. At the 1838 meeting of the British Association, Brewster remarked that,using those techniques he had suggested to Powell, he never had any difficulty inobtaining distinct spectral lines when using prisms with high refractive power. Powell'sfailure, Brewster implied, showed that he had not learned the necessary skills formeasuring the refractive indices ofmaterials with high dispersive power (Anonymous1838).In addition to casting doubt on Powell's skills in handling prismatic experiments,

Brewster later concentrated his criticisms on Powell's method of taking the mean. At

DISPERSION 57

the 1838 meeting of the British Association, Brewster expressed his objections toPowell's method. Brewster fIrst stated that, as he knew from daily observations, boththe G and H lines were remarkably distinct and easily recognized in prismatic spectra.He brought a map ofa prismatic spectrum to the meeting, on a scale of about fIve feet,to illustrate that the G and H lines remained as single lines in a spectrum with a veryhigh resolving power (Anonymous 1838). This large-scale map was the product ofBrewster's longtime study of absorption spectra.

4. BREWSTER'S TELESCOPE AND SPECTRAL LINES

Brewster began his studies of absorption in the early 1820s and made a signifIcantbreakthrough in 1832 by using "nitrous acid gas" (N02) as the absorptive material togenerate a spectrum. In this experiment, the light of a powerful monochromatic lampfIrst passed through a prism and then through a layer of "nitrous acid gas." The resultof this experiment was unanticipated. Brewster reported that "I was surprised toobserve the spectrum crossed with hundreds of lines or bands, far more distinct thanthose of the solar spectrum" (Brewster 1834a, 522). By adjusting the thickness of thegas, Brewster fmally produced a spectrum with more than a thousand dark lines.Brewster immediately realized the value of his discovery. Compared to

Fraunhofer's spectra with only a few hundred lines, Brewster's gaseous spectrum withmore than a thousand spectral lines could defInitely generate a dramatic effect. Moreimportantly, unlike Fraunhofer's prismatic experiments, Brewster's absorptionexperiments could be replicated easily. To repeat Fraunhofer's prismatic experiments,very delicate instruments were needed; for example, the prism had to be made ofsufficiently pure glass. On the contrary, instrumental requirements were relatively lowfor producing a gaseous spectrum with a large number of distinct lines -- a prism withordinary purity would do the job. Brewster thus suggested that his gaseous spectracould substitute for Fraunhofer's prismatic spectra for studying the properties of light.But evidently the difference between Fraunhofer's prismatic and Brewster's

gaseous spectrum was signifIcant: the latter contained more than 1,000 lines while theformer had only about 500. To compare the two spectra accurately, Brewster formeda prismatic and a gaseous spectrum with the same light source (sunlight), and hemanaged to superimpose the two so that their coincidences and differences could beexamined. The result showed that although some spectral lines in the gaseous spectrumcoincided with some in the prismatic spectrum, in many cases faint and narrow linesin one spectrum corresponded with strong and broad lines in the other. Even worse,many strong gaseous lines had no counterpart in the prismatic spectrum. Thesediscrepancies forced Brewster either to abandon his hope of establishing the identityof the two spectra or to increase the resolution of the prismatic spectrum by alteringFraunhofer's original experimental design.At fIrst Brewster was reluctant to challenge Fraunhofer's authority in prismatic

spectra. He later explained that "the magnifIcence of Fraunhofer's instruments, -- themeans of nice observation which he had at his command, -- and his great skill as an

58 CHAPTER 4

observer, were considerations which long deterred me from even attempting to repeathis examination of the spectrum." But he soon found a solution by adopting WilliamFox Talbot's suggestion that "a change might have taken place in the light of the sunitself' (Brewster 1834a, 526). Thus, whatever he found in his prismatic experimentwould not be in conflict with Fraunhofer's.Brewster managed to get hold of many fme instruments for the experiment,

including several high quality prisms, one ofwhich was manufactured by Fraunhofer'scompany, an achromatic telescope made by Dollond for viewing spectra, a wiremicroscope for measuring the distance between lines, a brass stand with a variableaperture, and a stage for holding the prism. Brewster's experimental design was similarto Fraunhofer's -- a prism was used to refract the sunlight emitted through an adjustableslit, and an achromatic telescope was used to view the prismatic spectrum. UnlikeFraunhofer, however, Brewster did not use a theodolite. The prism, telescope and otherapparatus were all independent and separated (Figure 4.4).It is important to understand why Brewster did not use a theodolite. He knew the

basic arrangement of Fraunhofer's prismatic experiment, and a theodolite was notdifficult to find. So, Brewster's decision not to use a theodolite must have beendeliberate. His goal in the experiment was not to conduct measurements, but to increasethe number of spectral lines so that he could establish the identity of absorption andprismatic spectra. Today we know that an effective way to see more spectral lines is toimprove the resolving power of the telescope, which is defined by the diameter of theobjective (the size of the aperture). Usually, the larger the aperture the higher theresolving power. But the notion of resolving power was not available until 1840 whenAiry studied diffraction by circular apertures. Thus, Brewster's solution was intuitive:he wanted to improve the magnifying power of the achromatic telescope, hoping thathe could identify more spectral lines by enlarging the spectrum. The magnifying powerofa telescope is defmed by the ratio between the focal lengths of the objective and theeyepiece; usually the longer a telescope, the greater its magnifying power. In hisexperiment, Brewster employed a five-foot achromatic telescope with a magnifyingpower about 200, which was four times of the magnifying power of Fraunhofer's

Slit Prism Telescope

Figure 4.4 Brewster sapparatus for producing prismatic spectra

DISPERSION 59

telescope. The size of this telescope generated a problem, because it was difficult, atleast from a fmancial perspective, to fmd a theodolite to hold such a big telescope. Thisprobably explains why Brewster did not use a theodolite in his prismatic experiments.This five-foot telescope turned out to be critical, but not in the way that Brewster

had expected. The increase of the magnifying power could not do anything useful,because it could not improve the quality of the spectral image. But the telescopeBrewster selected happened to have a larger aperture. It was one of the Dollond's five­foot telescopes armed with a 3.75 inch objective.? Compared to Fraunhofer's telescope,the aperture of which was less than two inches,8 Brewster's five-footer had a higherresolving power. Thus, Brewster saw more details of the prismatic spectrum, madesome fuzzed spectral lines countable, and found many new lines as he had hoped. Hereported that he could count more than 2,000 lines in his prismatic spectrum, many ofwhich did not exist in Fraunhofer's original map. He drew a map five feet long tooutline the detail of this spectrum, and later presented the map to the 1838 meeting ofthe British Association. He was happy to report that "after a little practice in theobservation of the solar spectrum, I discovered most of the lines, which I had in vainsought for in Fraunhofer's map, as the counterpart ofthose in the gaseous spectrum"(Brewster 1834a, 527).Although he had employed many fine instruments, Brewster's observations of

prismatic spectra were still constrained by the state of his eye. Brewster's goal in hisprismatic experiments was to count the number of the spectral lines. Unlike measuringthe angular positions of the spectral lines, which can be very objective and reliable withthe help of a theodolite, how many spectral lines one can see in a spectrum dependsupon the resolving power of the whole optical system, which includes the prism, thetelescope, and the eye. The resolving power of the eye is not stable. Under normalcircumstance, the eye can distinguish two spectral lines if their angular separation is notsmaller than one arc-minute. But the resolving power of the eye is determined by thediameter of the pupil, which changes constantly according to the brightness of thebackground and the physiological state of the observer. Thus, the eye was an intrinsicapparatus in Brewster's measurement of the number of spectral lines and directlyaffected his observations.The discovery ofthousands of spectral lines renewed Brewster's interest in studying

the chemical nature of spectra. Brewster had long been speculating that those lines inspectra were caused by the absorption effects of the particles in the absorptivematerials. Specifically, some particles of light must have been stopped by the materialatoms in the absorptive materials, but others had gone through. According to Brewster,"such a specific affinity between definite atoms and definite rays, though we do notunderstand its nature, is yet perfectly conceivable" (Brewster 1832, 321 ).9 Thus, asingle spectral line could reveal the existence of a specific chemical element in theabsorptive materials.Brewster conducted several studies to reveal the chemical origins of spectral lines.

First, he noted that some spectral lines in the prismatic spectrum became broader andsome new lines emerged in the morning and late afternoon. These changes, according

60 CHAPTER 4

to Brewster, must be caused by the increased absorptive action exerted by the earth'satmosphere -- sunlight passed through thicker atmosphere during these periods. Thus,some spectral lines in the prismatic spectrum were caused by the chemical elements inthe earth's atmosphere. Second, according to Fraunhofer's observations, prismaticspectra produced by different fixed stars were not identical. This implied that theterrestrial atmosphere was not the only absorptive material; otherwise, all stellar spectrawould have been the same. Brewster then argued that some spectral lines in theprismatic spectrum must be caused by the chemical elements in the solar atmosphere.Finally, the resemblance between the gaseous and the prismatic spectrum allowedBrewster to speculate that "the same absorptive elements which exist in nitrous acid gasexist also in the atmospheres of the sun and of the earth" (Brewster l834a, 530).In retrospect, Brewster's effort to identify chemical substances by examining

absorption spectra was fruitless. Indeed, all attempts at chemical spectroscopic analysisbefore 1860 similarly failed (James 1983). Nevertheless, Brewster's inclination to usespectra as a means of chemical analysis deeply influenced his understanding of therelationship between spectral lines from different spectra. He was more interested inthe chemical origin of spectral lines than in their geometrical positions, and he tried toexplain the apparent differences between spectra (the number and the distribution ofspectral lines) in terms of those chemical origins. For example, according to Brewster,the increase in the number of spectral lines in the gaseous spectrum was caused by thenew absorptive material, that is, the N02 gas. Similarly, the discrepancies betweendiffraction and prismatic spectra reported by Powell must also reflect differences in thechemical nature of their absorptive materials. In the case ofPowell's experiment, thosefine lines around G and H must have their own chemical origins. Instead of using aregular glass prism, Powell employed a hollow prism filled with liquid, which wasprobably the origin of those newly found fine lines. 10 Because of different chemicalorigins, there was no reason to group these fine lines together by the method of takingthe mean, no matter how close to one another these lines were located. Brewsterinsisted that "the wave length of (G) belongs positively and rigorously to the standardray or line (G), distinctly marked in Fraunhofer's map, and distinctly characterized byprecise numbers in his table; and it has nothing whatever to do with any lines or groupof lines near (G). In the like manner the wave length of (H) belongs positively andrigorously to the band (H), similarly marked and similarly characterized inFraunhofer's map and tables, and it has nothing whatever to do with the band similarto (H), ofwhich Fraunhofer has neither given the wave lengths nor measured the indexof refraction" (Brewster 1838c, 876; original emphasis). This explains why Brewsterstrongly objected to Powell's taking the mean: this method was fundamentally wrongbecause it mixed up spectral lines that had distinct chemical natures.Brewster further remarked that taking the mean also failed to provide accurate

measurements. Powell took the average of a group of small fine lines as representingthe G line. However, Brewster insisted, the real position of the G line, according toFraunhofer's description, was not in the center of the group but closer to the red endof the spectrum. A similar problem occurred when Powell took the mean of two

DISPERSION 61

separate bands as the precise position of the H line. In Fraunhofer's original map, theH line was the least refrangible one of the two that Powell referred to. Therefore,Brewster claimed, all of Powell's measurements of the refractive indices of 0 and Hwere "too great." Since the values ofrefractive indices derived from Powell's formulawere always larger than his measurements, taking the mean would "offer fewerdiscrepancies with the undulatory theory" and create an illusion that Powell's formulawas supported by the measurements (Brewster 1838d, 826).Worse than that, Brewster noted, Powell had used the refractive index of H to

determine the values of the constants when he applied Hamilton's method to derivereflective indices from his formula. Hence, the error in the measurement ofH affectedthe calculations of the refractive indices in C, D, E and 0 (Brewster l838c, 876). Sinceboth the measurements and the theoretical calculations of refractive indices wereproblematic, the coincidence between them became insignificant and Powell's formulathat specified a relationship between refractive index and wavelength also had to beconsidered unfounded. Brewster thus rejected Powell's undulatory account ofdispersion.

5. THE DIFFICULTIES OF MAKINO ORATINOS

The dispute between Powell and Brewster boiled down to a simple question: did the 0and H lines in Fraunhofer's diffraction spectrum correspond, as Powell claimed, togroups of small lines in the prismatic spectrum or, as Brewster insisted, to single lines?During the debate, neither side had given any experimental evidence to support theirpositions. Powell simply assumed that all discrepancies between prismatic anddiffraction spectra were caused by differences in the dispersive power of theinstruments, and that a single line would expand into a group of small lines when thedispersive power of the instrument increased. On the other hand, Brewster attributedthe differences between the two spectra to chemical effects and hypothesized that thenumber ofspectral lines in a spectrum was determined by the interactions between lightand absorptive materials, and thus each spectral line had its own chemical origins.Both Powell and Brewster bore the burden of offering experimental evidence to

support their positions, and their dispute could have been settled by carefully designedexperiments. For example, Powell's position implied that new spectral lines in adiffraction spectrum would emerge from the expansion of a nearby existing line whenthe dispersive power of the grating increased, while Brewster suggested that they wouldspring out independently when new interactions between light and absorptive materialsoccurred, such as when sunlight passed through thicker layers of atmosphere. Thesepredictions could have been tested by examining the structures and positions of spectrallines in diffraction spectra under different conditions such as using gratings withdifferent dispersive powers, or inserting different absorptive materials between thegrating and the eye. In theory, the dispute between PoweIl and Brewster could alsohave been settled by examining what happened if the number of spectral lines in theprismatic spectrum decreased. According to Powell, some of them should gradually

62 CHAPTER 4

condense to nearby lines when the dispersive power of the prism decreased. But,according to Brewster, they should simply disappear when different absorptivematerials were used. In practice, however, it was impossible to reduce the resolutionof prismatic spectra -- the whole set of spectral lines would have disappeared if thedispersive power of the prism was below a certain level. Thus, replicating Fraunhofer'sexperiments on diffraction spectra, perhaps with some minor adjustments in theexperimental design, such as using gratings with higher dispersive power or introducingnew absorptive materials, became a necessary step to resolve the dispute betweenPoweIl and Brewster.Replicating Fraunhofer's diffraction experiment in the 1830s was not an easy task.

The key obstacle was the extremely complicated technique ofmaking gratings. It tookmany years for Fraunhofer to learn how to make gratings that could produce distinctspectral lines so that their wavelengths could be measured accurately. He first usedparaIlel stretched wires' to make gratings, the best ofwhich had 260 lines (openings) atabout 170 lines per inch. Diffraction spectra produced by this grating were rather smaIl-- the angular size of the first-order spectra was only 17 arc-minutes (Fraunhofer 1822,22 & 26). Although spectral lines appeared, they could not be measured with certainty.Fraunhofer later developed a new technique using a diamond to rule fine lines in thesurface of a glass plate covered by a layer of grease. He was able to make a gratingwith 3,601 lines at 8,176 lines per inch. With this grating, he obtained diffractionspectra (the first order) with an angular size of 4.5 degrees, from which thewavelengths of the six spectral lines could be measured (Fraunhofer 1823,45).The number of lines was not the only issue that determined the acceptability of

gratings. Fraunhofer also noticed that all lines in an acceptable grating must beidentical, and that the key to ruling identical lines was the shape of the diamond point.But what should a proper diamond point look like? Fraunhofer was not sure even usingthe most powerful microscopes. He admitted that "even with the most powerfulmicroscope one cannot be sure whether the point is suited to rule proper lines. Adiamond which appears less pointed than another often rules the finer lines; andtherefore a suitable point can be found by experiment only" (Fraunhofer 1823,44). Tohim, the selection of a proper diamond point depended partly upon experience andpartly upon luck. In fact, until Friedrich Nobert in the second half of the centurydescribed in detail how the shape and weight of a diamond would affect the quality ofgratings, the process ofmaking gratings remained a secret craft (Dorries 1994).The delicacy of gratings, together with the unarticulated features of the grating­

making technique, must have deterred many in the 1830s from replicating Fraunhofer'sdiffraction experiment. Gratings became an obstacle that made the replicationextremely difficult, if not impossible. This probably explains why PoweIl did notrespond to the chaIlenge of improving the resolution ofdiffraction spectra. In his studyofTalbot bands, PoweIl reported that he had produced diffraction spectra by foIlowingFraunhofer's method, but he made no effort to improve the experiment. II He did not

DISPERSION 63

Diffraction spectra

~Diffraction spectra

.,Aperture Image

Figure 4.5 Brewster sdiffraction spectra

provide any details of his instruments, nor the result of his experiment. Since thepurpose of the experiment was to see if spectral lines in a diffraction spectrum woulddisappear altogether when a thin plate of glass was inserted to cover a certain area ofthe spectrum, Powell did not require accurate measurement of the positions of thespectral lines. Available documents suggest that Powell's diffraction spectra did notreach the sophisticated level of Fraunhofer's.Brewster also conducted his own diffraction experiments but, unlike Powell, he did

provide some detailed descriptions of the experimental results. Brewster began hisdiffraction experiments in 1822, when he obtained from John Barton some finespecimens of steel with grooved surfaces. Using a delicate ruling machine, Barton

64 CHAPTER 4

succeeded in cutting parallel grooves with 500 to 10,000 lines per inch on the surfacesof steel (Grodzinski 1947). Originally people used these grooved surfaces to makebuttons or articles of ornament, but Brewster employed them as reflection gratings togenerate diffraction spectra. With an experimental setup similar to Fraunhofer's,Brewster obtained diffraction spectra containing all the prismatic colors and theprominent spectral lines, but their angular sizes were rather small. Brewster did notreport the actual sizes of these spectra, but he was so disappointed with the results thathe decided to give up the research. Later he recalled, "having found that M. Fraunhoferwas actively engaged in the very same research, with all the advantages of the [rnestapparatus and materials, I abandoned the subject, though with some reluctance, to hissuperior powers and means of investigation" (Brewster 1829,301).Later Brewster found something new by altering the experimental setup. Instead of

using a narrow slit to regulate the incident light, he employed a long rectangularaperture formed by nearly closing the window-shutters. The length of this aperture wasabout 35 arc-degrees, and its width was about one arc-degree (measured from thegrating).'2 Using a grooved surface with 1,000 lines per inch as a reflection grating,Brewster obtained a sequence of diffraction spectra (Figure 4.5). Because the sourceslit had a width of one degree, Brewster's diffraction spectra no longer contained anydistinct spectral lines -- according to Fraunhofer only a few lines remained visible if thewidth of the slit exceeded one minute of arc (Fraunhofer 1817,4). But Brewster'sdiffraction spectra contained something new: there were many dark lines crossing thespectra obliquely. Brewster shared his novel discoveries with someone who wasfamiliar with Fraunhofer's work and was assured that the phenomena he observed "hadentirely escaped the notice" of Fraunhofer (Brewster 1829,301). Only after receivingthis assurance did Brewster decide to publish his [mdings and continue his study of thesubject.To study further the nature of these oblique dark lines, Brewster felt that he needed

a better grating that could improve the quality of the spectra. He had several options.For example, he could increase the density of lines in a grating by reducing the widthof the openings and the distance between openings, which would significantly enlargethe horizontal size of the spectra. This result, however, was not attractive to Brewsterbecause he could easily expand the spectra vertically by increasing the length of theaperture. Another option was to reduce the distance between openings while keepingthe width of the openings unchanged, and consequently enhance the intensity of thespectra. For the purpose ofstudying those oblique dark lines, the intensity of the spectrabecame far more important than their angular sizes. Brewster thus asked Barton tomake a grating containing 2,000 grooves per inch, in which the distance betweengrooves was reduced to a minimum. Barton at first agreed to make Brewster such agrooved surface, but something unexpected happened: Barton's "diamond point,however, having unfortunately broken before he had executed any considerable space[sic], I was unable to make all the experiments with it which I could have wished"(Brewster 1829, 304). In this way, a new apparatus -- a rectangular aperture -- ledBrewster to study an entirely different kind of diffraction spectrum, but problems in

DISPERSION 65

getting a necessary apparatus, that is, an improved grating, soon forced Brewster togive up his pursuit.

6. THE IMPASSE IN THE DEBATE

Because of the obstacles in obtaining or making high quality gratings, in the late 1830sneither Powell nor Brewster was able to replicate Fraunhofer's experiments ondiffraction spectra so that they could resolve their differences. Probably as a result ofhaving realized the difficulties in producing diffraction spectra, both Powell andBrewster shifted their focus later in the debate to the graphic presentations of prismaticspectra. In 1839, Powell presented a report to the meeting of the British Association,in which he raised doubt about Brewster's maps ofprismatic spectra. Although Powellhad conducted his own experiments on prismatic spectra, he realized that hisinstruments were not as sophisticated as Fraunhofer's, and thus he used Fraunhofer'smaps as the standard. He referred to Fraunhofer's original map of the prismaticspectrum printed in Munich Transactions in 1817. According to Powell, Fraunhofer'smap was superior "in delicacy of representation," because it used shading to capture"the relative intensity of the different parts of the spectrum." Fraunhofer's map clearlyshowed "the appearance of the numerous lines about G" and "two small groups of linesbetween and below the bands at H" (Powell 1839c, 4). Thus, he believed that one-to­many correspondence existed between lines in prismatic and diffraction spectra, andthe method of taking the mean was correct. After appraising Fraunhofer's work, Powellturned to criticize Brewster. He targeted a map of the prismatic spectrum that Brewsterhad printed in Edinburgh Encyclopedia in the 1820s. This map, according to Powell,was copied from Fraunhofer's original one, but the copying job was poorly done. It lostseveral crucial features captured by Fraunhofer's map; for example, the G line inBrewster's map became a distinct line, and the H line was "distinctly marked at thepoint midway between the two bands, instead of being opposite the lower" (Powell1839c, 4). This inaccurate map, Powell implied, contributed to Brewster's mistakenbelief that a one-to-one correspondence existed between lines in prismatic anddiffraction spectra.In the eyes of Brewster, Powell's remarks on his map of the prismatic spectrum

were completely inappropriate because Powell had ignored his recent work onprismatic spectra. At the 1840 meeting of the British Association, Brewster respondedto Powell's attack. He presented to the meeting two partial spectral maps, each ofwhich contained the areas near the G and H lines respectively. These two partial mapswere taken from a map of the prismatic spectrum about five feet long and with morethan 2,000 distinguishable lines, a product of his latest work on gaseous spectra. Thefirst diagram illustrated the group of lines around G, and Brewster pinpointed a singleone near the least refrangible side of the diagram as the real position of the G line. Thesecond diagram contained two bands with no fewer than 14 stripes in between, andBrewster insisted that the least refrangible one was the real position of the H line(Brewster 1840,5).

66 CHAPTER 4

In this way, Powell and Brewster shifted the focus of their debate from the relationsbetween prismatic and diffraction spectra to the graphic presentations of prismaticspectra. But they simply missed the point. The crucial issue in the debate was whethersingle lines in diffraction spectra corresponded to groups of small lines in prismaticspectra. No one could answer this question by merely examining prismatic spectra.Unfortunately, neither Powell nor Brewster was capable of replicating Fraunhofer'sdiffraction experiment, a necessary step to bring their dispute to a close. Thus, thedispute between Powell and Brewster fell into an impasse -- neither side was able toprovide evidence to verify its position, and all exchanges became primarily rhetorical.Evidently, Powell's account of dispersion, particularly his tests and "confirmation"

ofhis formula for dispersion, was very problematic. Even Powell himself admitted thatthe method he used to fix the constants was questionable, because it was equivalent toassuming the formula at two points and interpolating it to the intermediate values(Powell 1838c, 67-72). Even worse, when Powell accepted Hamilton's suggestions tochange his formula to the format of a Taylor series, he had to use the data of threespectral lines to determine the values ofthe three constants, leaving only four lines fortesting purposes (Powell 1836b, 204-210).Even many wave theorists remained skeptical toward Powell's work on dispersion.

For example, James MacCullagh questioned the legitimacy of Powell's explanation ofdispersion because it was based upon extensive constant fixing. According toMacCullagh, it was always possible to reach any desirable conclusion throughmanipulating constants, and he used Cauchy's account ofdouble refraction to illustratethe problems of fIXing constants. Cauchy's theory of double refraction contained nineconstants, three from each differential equation. In his early version, Cauchy simplysupposed three out of the nine constants to vanish, and assigned three very specificrelations among the rest six constants. By means of these relations, he was able toderive equations similar to Fresnel's law. But Cauchy's early theory of doublerefraction implied that the vibrations of a polarized ray were parallel to its plane ofpolarization, which was at odd with the common knowledge. Later, in 1836, Cauchychanged his suppositions regarding the constants -- he reinstated the constants that hehad before supposed to vanish. After changing the constants, he arrived at thecontradictory conclusion that the vibrations ofa polarized ray were perpendicular to theplane of polarization. This example, according to MacCullagh, demonstrated thearbitrary nature of constant fixing (MacCullagh 1841). Humphrey Lloyd was alsocritical ofPowell's work. According to Lloyd, a complete account of dispersion oughtto reveal the physical meaning of those constants, and Powell's formula went only avery little way toward a satisfactory explanation of the phenomenon. Disappointed byPowell's failure, Lloyd himself spent some time trying to provide physicalinterpretations of the constants in Powell's formula, but soon admitted that it wasimpossible to do so (Powell 1838c, 7).Although Powell's explanation of dispersion was full of problems and Brewster

wanted to exploit the issue of dispersion, Brewster failed to justify his criticisms ofPowell's work with experimental evidence. Brewster's objection thus did not constitute

DISPERSION 67

a real threat against Powell's work, and Powell won a chance to keep his account ofdispersion alive. In 1841, Powell simply disregarded Brewster's criticisms andannounced that the problem ofdispersion had been solved in his hands (Powell 1841).While this might have reflected only Powell's personal opinion and not convincedmany contemporaries, Powell's work at least made it reasonable to suspend judgmenton the wave theory regarding dispersion, just as Herschel had asked in the late 1820s.The impasse in the debate between Powell and Brewster explains why the Britishoptical community disregarded the negative evidence from dispersion experiments and,in particular, why the opponents of the wave theory could not take advantage of thedispersion issue to challenge their rival.

CHAPTERS

THE DISCOVERY OF THE "POLARITY OF LIGHT"

Although the wave theory had established its dominance by the mid 1830s, itsopponents in Britain did not immediately surrender to the new orthodoxy. On thecontrary, they continued to resist the wave theory. During the late 183Os and the entire1840s, opponents of the wave theory in Britain kept throwing up all kinds ofobservational and experimental data that the wave theory at that time did not orapparently could not explain, initiating many debates with wave theorists, who foughthard to minimize the damage. Among these debates, perhaps the one initiated byBrewster in 1837 on the "polarity of light" was most significant, both because of itsscale -- it involved almost every first-rank wave theorists in Britain -- and because ofits duration -- it lasted more than a decade, during which wave theorists failed toexplain the phenomenon.This chapter focuses on the role of instruments in the debate over the "polarity of

light." The temporary setback of the wave theory in accounting for the "polarity oflight" was related to how instruments were used to generate the anomalousphenomenon. The early wave account of the phenomenon was constrained by a specificexperimental design, which appeared to be strikingly similar to interferenceexperiments. This anomaly, however, could not be accounted for in terms of theinterference principle. The correct explanation of the anomaly was not achieved untilthe late 1840s when a new experimental design was developed that used a hollow prismas the key apparatus and exhibited strong similarities to diffraction experiments. Afterthe anomaly was categorized correctly as diffraction, its explanation becametransparently evident, and the debate was settled quickly.

1. THE DISCOVERY OF THE "POLARITY OF LIGHT"

William Fox Talbot discovered an interesting phenomenon in prismatic spectra in 1837.In his experiment, Talbot used a prism with moderate dispersive power to produce aspectrum. Instead of observing the spectrum directly, he inserted a circular aperture ofthe size of the pupil just in front of the eye, and he covered one halfof the aperture witha thin plate of glass (Figure 5.1). When he viewed the prismatic spectrum in this way,Talbot saw a group ofparallel dark bands crossing throughout the spectrum, similar tothose produced by absorption. As a wave theorist, Talbot attributed this novel

69

X. Chen, Instrumental Traditions and Theories of Light© Springer Science+Business Media Dordrecht 2000

70 CHAPTER 5

Thin plate

~Prism

The eye

-+---0/

Aperture

Figure 5.1 Talbot's apparatus/or producing "Talbot's bands"

phenomenon to interference. Relying on Huygens's principle, Talbot reasoned thatevery point in the spectrum acted as a new source, emitting homogeneous rays thatwere focused by the crystalline lens of the eye onto the retina. Since the rays passingthrough the upper half of the lens experienced retardation caused by the plate, theycould interfere with the unretarded rays that pass through the other half of the lens.When the retardation, which varied according to the color ofa ray, was an odd numberof half wavelength, the light would be extinguished by interference. The spectrumwould thereby be interrupted by a number of dark bands (Talbot 1837, 364).1 Talbotdid not, however, attempt to produce a quantitative account.Talbot's discovery was published in Philosophical Magazine in 1837, and it drew

the attention ofBrewster. Although his early optical researches were deeply influencedby the particle tradition, Brewster never publicly admitted that he was a particletheorist, nor was he willing to give a straightforward answer to the question ofwhetherlight is particles or waves (Brewster 1831a, 1-2). Brewster's optical researches,however, always contained an implicit element that was thoroughly consonant with theparticle tradition: he always conceptualized light as rays, and he analyzed opticalphenomena in terms of the properties of rays, occasionally thinking in terms of thedeflection of rays by forces emanating from material bodies.2

Brewster repeated Talbot's experiment, but with two significant revisions. First,instead of using the naked eye, he examined the spectrum formed at the focus of anachromatic telescope, thereby producing a distinct and sharp spectral image. Theexistence of dark bands in prismatic spectra was well-known in the 1830s. Using atelescope to view the spectrum, Fraunhofer in the 1820s had reported the existence ofmore than 500 dark lines in the light from the sun. Since these dark lines could not beseen by the naked eye, the telescope was taken to be a standard device for spectralexperiments. Brewster thus added an achromatic telescope to Talbot's design. Because

POLARITY OF LIGHT 71

TelescopePrism

the object lens of the telescope in itself functioned as an aperture limiting the amountof light allowed to pass, Brewster did not use Talbot's circular aperture. He kept thethin plate of glass directly in front of his eye, covering one half of the pupil (Figure5.2). In this way, Brewster was able to make Talbot's dark bands more intense anddistinct.Brewster's second modification to Talbot's design was to rotate the thin plate

during the experiment. In his early experiments on polarization by refraction,conducted in the mid 1810s, Brewster found that observational results varied when theanalyzer was rotated: some images disappeared altogether when the analyzer wasturned to a particular angle with the plane of refraction (Brewster 1814,220). Giventhe experience learned from his earlier work on polarization, Brewster decided to tryrotating the thin plate in the modified Talbot experiment. This produced an entirelynovel phenomenon, one that had not been found by Talbot. When he held the thin platein its original position (covering the violet end of the spectrum), intensely dark bandsappeared. However, when Brewster rotated the thin plate in its own plane, the darkbands became less and less distinct as the angle between the edge of the plate and thelines of the spectrum increased. When the angle was 180 degrees, that is, when the thinplate covered the red end of the spectrum, the dark bands completely disappeared(Brewster 1837,12-3; Brewster 1838b, 13-4).Brewster's persistent search for experimental facts unfavorable to the wave theory

made him especially sensitive to every anomaly. He immediately realized that the wavetheory might not be able to explain why the dark bands disappeared when the thin platecovered the red end of the spectrum. The account given by Talbot attributed the bandsto interference. But according to the wave theory, interference in this experimentshould occur no matter what the orientation of the thin plate might be, and, therefore,the dark bands should never disappear on this account. Brewster did not want to missthis opportunity to embarrass the wave theory. He immediately reported his discoveriesat the 1837 meeting of the British Association, characterizing the peculiar phenomenonhe had found as "a very curious and entirely inexplicable property of light." (Brewster1837,12-3)Brewster's report did not produce the kind of reaction from the audience that he

expected. Whewell and Lloyd were present when Brewster read his report, but these

Thin plate

The eye

~---+-+-()Figure 5.2 Brewster sapparatus for producing the "polarity oflight"

72 CHAPTER 5

two wave theorists tried to reduce the impact of his discovery. Whewell simply deniedthat there was any new property of light involved in Brewster's discovery, although hewas not quite sure about the details of the experiment. Lloyd admitted that he could notat the present imagine any probable way ofexplaining the fact, but he insisted that theas-yet unexplained phenomenon should not compel people to adopt the conclusion that"the time of an undulation of light could, under certain circumstances, be altered"(Anonymous 1837, 719V These wave theorists, secure in their new-found dominanceof optics, argued that, though Brewster's discovery might not yet be explained, it wastrivial and should not affect confidence in the wave theory.

2. BREWSTER'S CLASSIFICAnON

Brewster did not give up despite the disappointing response at the 1837 meeting. Hecontinued to make changes in the experiment and brought up the topic again at the1838 meeting, where he did not simply describe his empirical findings; he alsoprovided theoretical analyses.Brewster first told his audience about a new observation. Instead of using just one

plate, he had let one half of the light beam pass through a series of thin plates, each thesame thickness but having different widths, piled up so that different parts of the lightbeam suffered different degrees of retardation. On looking through this pile of thinplates, Brewster said that he was surprised to observe a multitude ofsplendid bands anddark lines crossing the entire spectrum, which looked "as if it had been acted upon byabsorbing media." The different degrees of retardation caused by the plate suggested,Brewster reasoned, that "we have here dark lines and the effects of local absorptionsproduced by the interference of an unretarded pencil with different other pencils,proceeding in the same path with different degrees of retardation" (Brewster 1838b, 13­4; original emphasis). Brewster continued to agree with Talbot that the formation of thebands was caused by interference.Brewster next returned to the major point that he had made the year before, now

emphasized by the multitude of new bands, and he made it the centerpiece of a newassertion. He reminded his audience that this "local absorption produced byinterference" had a very peculiar feature. The bands appeared only when the thin platecovered the violet end ofthe spectrum, but they disappeared when the plate covered thered end. Interference alone could not explain this asymmetric phenomenon, andBrewster now argued that the phenomenon might be caused by a new kind of luminousasymmetry or polarity that worked to alter the conditions under which interferencecould occur.In the early 1830s, polarization was the only asymmetry recognized by the optical

community, and it was accordingly possible that the new phenomenon was somehowthe result of the known interference properties of polarized light, with which Brewsterwas familiar, most likely having read about them in Herschel's "Light." He knew thatrays of light polarized in the same plane would interfere with each other in the sameway as natural light, but that rays polarized at right angles to each other produced no

POLARITY OF LIGHT 73

fringes (Brewster 1831a, 179-81). Polarization could be used in explaining Brewster'snew phenomenon if the two beams of light were in fact polarized. Brewster had tocounter this possibility before he could argue for an altogether new asymmetry.Brewster already knew that a light beam's polarization could not be rotated through

a right angle by passing through thin plates, which spoke powerfully against theproperty being involved. To prove directly that polarization was not responsible,Brewster later replaced the thin plate of glass in the original experiment with a pieceof doubly refracting crystal. He now saw two systems of dark bands in the spectrumwhen the crystal covered the violet end, one produced by the ordinary rays and theother by the extraordinary rays. However, all these bands disappeared when the crystalcovered the red end. The observation of double refraction proved that all the light(retarded as well as unretarded) in his original experiment was in fact unpolarized.Furthermore, the disappearance of dark lines produced by both the ordinary andextraordinary rays implied that the polarity phenomenon also existed in polarized light.Brewster accordingly claimed that "I have no hesitation in considering this property oflight as indicating a new species ofpolarity in the simple elements of light, whetherpolarized or unpolarizecf' (Brewster 1838b, 13; original emphasis).According to Brewster, as well as to others who deployed ray conceptions,

polarization as an observable phenomenon was caused by a special property of the raysof light, namely that a ray had sides (Brewster 1815b, 149-51; Brewster 1830b, 176-7).On this basis, Brewster was able to provide explanations for many phenomena relatedto polarization, and this confirmed for him the exemplary power of ray analysis.Brewster often attributed novel optical phenomena to correspondingly novel propertiesof rays. Although this might seem to be a clear case of introducing ad hoc assumptions,the procedure was in fact quite powerful since it could and did have broader empiricalimplications than those for which it had been designed. Furthermore, assigning newproperties to rays had the virtue of leaving intact their identity as individual objects,and it was precisely this identity that permitted Brewster and those who thought likehim to consider rays collectively. For example, when Brewster in the early 1830sdiscovered two new species of polarization -- elliptic and circular -- in his metallicreflection experiments, he was able to explain the phenomena with impressivequantitative detail by ascribing to rays a new property linked to a specific notion of"phase."4Brewster thought that the newly discovered asymmetry was tightly bound to a ray's

refrangibility. The bands appeared when the plate covered the more refrangible end ofthe spectrum (the violet end), or "when the least refrangible side of the retarded ray istowards the most refrangible side of the spectrum, or towards to most refrangible sideof the unretarded ray." The bands disappeared altogether when the plate covered theless refrangible end (the red end), or "when the most refrangible side of the retarded rayis towards the least refrangible side of the unretarded ray" (Figure 5.3). Hence Brewsterconcluded that "the different sides of the rays of homogeneous light have differentproperties when they are separated by prismatic refraction ... , -- that is, these rays

74 CHAPTER 5

High refrangibility (violet)

(A) When the most refrangible side ofthe retarded ray is towards the leastrefrangible side of the unretarded ray.

Unretarded ray

Retarded ray

~Thin plate

Thin plate

~

Retarded ray

Unretarded ray

(B) When the least refrangible side ofthe retarded ray is towards the mostrefrangible side of the unretarded ray.

Low refrangibility (red)

Figure 5.3 Relations between polarity and refrangibility

have polarity" (Brewster 1838b, 13-4; original emphasis).More specifically, Brewster thought that his polar refrangibility was produced by

a process of ray-sorting that occurred when rays interacted with material particles."When," he wrote, "light is rendered as homogeneous as possible by absorption, orwhen it is emitted in the most homogeneous state by certain coloured flames, it exhibitsnone of the indications of polarity above mentioned. The reason of this is, that the moreor less refrangible sides of the rays lie in every direction, but as soon as these sides arearranged in the same direction by prismatic refraction or by diffraction, the lightdisplays the same properties as if it had originally formed part of a spectrum" (Brewster1838b, 14). This process of ray-sorting was similar to the one that occurred inpolarization, which was, obviously, Brewster's model (although the latter has nothingto do with refrangibility).Brewster might have developed a quantitative explanation of his experimental

findings on this basis. Given his spatially-directed conception of polar refrangibility,he would have needed two additional assumptions to provide a mathematics for hissystem, one assumption to specify how the thin plate alters the direction of a ray's polarrefrangibility, and another to specify the conditions for interference between rays withdifferent polar refrangibilities.sBut Brewster did not work out such a scheme. Instead,he never openly described how his assumption of polar refrangibility could be used toexplain the experiment. Given the situation that Brewster faced in the late 1830s, it ishardly surprising that he cautiously decided not to present a theoretical account of theexperiment. With the wave theory's dominance, no theoretical account with traces ofthe particle theory, which the notion of a ray-linked refrangibility inevitably implies,could possibly be accepted by wave theorists. Instead, presenting apparently neutralexperimental results that could not be explained by either theory effectively weakenedthe dominant system, provided nobody denied the value of the experiments. Brewster

POLARITY OF LIGHT 75

accordingly adopted a careful strategy: in the fIrst stage, he presented new facts thatneither the particle nor the wave theory could cover and that accordingly challengedthe latter's completeness. After these facts were widely accepted, a second campaignfor the downfall of the wave theory could be launched.6

Presenting unexplained observational facts raised problems. Wave theorists coulddismiss the anomalies by treating them as trivial, at least until they appeared in manydifferent experimental settings. Brewster therefore needed to show that his fIndingswere not artifIcial, but that they reflected the existence of anew, general opticalproperty. Brewster, thus, tried to convince others that what he had found was notsimply a novel, possibly singular phenomenon, but a "new species of polarity." Hewanted to categorize the polarity phenomenon as a new kind of optical asymmetrysimilar to polarization. Indeed, there were parallels between polarization andBrewster's polar refrangibility. First, both were caused by orderly arrangements of aparticular property of rays, which was the side of rays in polarization and therefrangibility of rays in the other. Random arrangements of these properties in bothkinds resulted in the disappearance of asymmetry. Second, both kinds of asymmetrycould prevent two light beams from interfering with each other, though they requireddifferent specifIc conditions. Thus, Brewster's "new species of polarity" tacitly implieda taxonomy for the phenomena of optical asymmetry, which included, in addition tothe existing category of polarization, a new one called "polar refrangibility" (Figure5.4). The introduction of"polar frangibility" as a major category of asymmetry similarto "polarization" was crucial to Brewster's argument. If this taxonomy for opticalasymmetry were accepted, then his experimental discovery would not be trivial becauseit would imply a new classifIcation for light itself, in which case the wave theory would

Light with PolarRefrangibility

«orderlya"angement

Unpolarized Light of rays' refrangibility)(Random a"angementof rays' side) Light without Polar

Refrangibility(Random a"angementof rays' refrangibility)

Light

Polarized Light <(Orderly a"angementof rays' side)

Light with PolarRefrangibility(Orderlya"angementof rays' refrangibility)

Light without PolarRefrangibility(Random a"angementofrays' refrangibility)

Figure 5.4 Brewster :s classification ofpolarization

76 CHAPTERS

fail not in a single case but in a whole range ofphenomena.Brewster's strategy was apparently successful. His discussions drew the attention

of the audience at the 1838 meeting of the British Association. Both Whewell andLloyd were again present when Brewster made his report. This time, however, thesetwo wave theorists no longer denied the significance of Brewster's findings. Theyasked Brewster many questions about the experimental design, but did not raise anysubstantial objections. John Herschel also listened to Brewster's report, and his reactionwas quite positive. After admitting that the wave theory was not able to explain thephenomenon described by Brewster, Herschel praised the "indefatigable zeal andindustry" ofBrewster in these experiments, and asserted that Brewster's works "openedan entirely new field of optical discovery" (Anonymous 1838,625). Herschel's praisegave Brewster renewed confidence. When William Hamilton said that he "did notdespair" of seeing the phenomenon brought into the wave theory's dominion, Brewsterdid not hesitate to assert that he saw no way whatsoever ofdoing so (Anonymous 1838,625).

3. THE WAVE EXPLANATIONS

After the mid 1830s when the wave theory became dominant in Britain, its proponentswere usually not taken aback by new observational and experimental results that theirrivals claimed could not be explained by the wave system. They simply played downthe value or significance of the experiments, sometimes just by remaining silent. Thisoccurred, for example, at the same 1838 meeting of the British Association. In additionto the problem raised by his new "polarity oflight," Brewster had also presented therethree other papers on several new diffraction phenomena that, he asserted, Fresnel'stheory could not explain. Wave theorists at the meeting did not say a word in reply.Their silence embarrassed even Herschel, who was sympathetic to Brewster(Anonymous 1838,675).Brewster's new polarity, however, was dangerous, primarily because he claimed

general significance for it. The urgency stemmed from Brewster's implied taxonomy.Ifhis system of new optical categories were accepted, then the wave theory's failureto account for an entire key category could not be counted as trivial. To make mattersworse, Brewster had introduced a highly contentious notion that implicated the ray­based concept of refrangibility, with its close association to the particle tradition.Baden Powell supplied the first wave-based explanation of Brewster's novel

discovery. He turned his attention to the Talbot-Brewster experiments during thesummer of 1839, and after conducting several experiments of his own, he brieflyreported his results at the 1839 meeting of the British Association (Powell 1839a, 1).Like both Talbot and Brewster, Powell believed that the new dark bands in thespectrum were caused by interference between "the two halves of the parallel pencil ofeach ray, which converges in the eye, and whose breath is equal to the aperture of thepupil" (Powell 1839a, 1). Powell however revised Talbot's wave account by importinginto it elements of ray analysis. The key to Powell's explanation was considering the

POLARITY OF LIGHT 77

retarding effect caused by the prism. Powell noted that, because of prismatic aberration,all of the light of any given color emanating from a point source would spread out intoa patch after passing through the prism. Of course, dispersion could create overlappingpatches of different colors, but at this point in his reasoning, Powell's interest involvedthe light in any single, homogeneously-colored patch.Powell next argued that the different parts of each patch had to have been produced

by rays that had undergone different degrees of retardation in the prism. The half of thehomogeneous patch that lay near the violet end suffered more retardation than thepatch's other half simply because it had passed through a thicker part of the prism.Powell now added in a bit ofwave-front analysis. He assumed that every point in

each homogeneous patch itself acted as a new source for waves, all of which finallyconverged onto a single point of the retina after being refracted by the eye's lens. Theseconverging waves would then interfere with one another (because they all derived fromhomogeneous light that had originally emanated from a single point). Using a retardingplate to cover one half of the beam from a patch would produce differences inretardation between the light that had passed through the plate and the light that hadnot. These differences would vary, however, according to whether the plate covered thered or the violet end of the spectrum because, as we will see in a moment, theinterference pattern depended on altering the differences in retardation between theviolet- and red-tending rays in a given patch, whereas the plate affected only one suchgroup. If the plate lay near the violet end, then it would exacerbate an alreadyconsiderable difference in retardation between light from different parts of the patch,thereby making interference bands visible. On the other hand, if the plate covered thered end, then its effect would be to decrease an already small difference in retardation,in which case no visible interference bands would result.7

For unknown reasons, Powell delayed publishing details of his explanation.However, when he later learned that Airy had conducted research on the same topic andhad produced many new conclusions, Powell became anxious to put his own work onrecord, and so he sent in a paper to Philosophical Magazine (Powell 1840, 81-5).8 Here,Powell reported a new observation. He found that the retarding plate must have acertain minimum thickness in order to produce the polarity phenomenon. If the platewere thinner than the lower limit, then bands continued to exist even though the platecovered the red end of the spectrum. Powell believed that his discovery, together withthe polarity phenomenon noted by Brewster, could be explained by the account he hadpresented at the 1839 meeting, namely, by considering both the retardation producedby the plate and that by the prism in the following way.If, Powell reasoned, the plate covered the violet end, then the path differences

between the two halves of a circular patch that passed through the prism would be:

(Rv;o,prism + Rvio,pla,d - Rred.prism = (Rvio,prh-m - Rred,pri.w,J + Rvio,pJate

Here, Rvio,prism, Rred.prism, Rvio,plate respectively denote the retardation caused by the prismin a given patch near the violet and the red ends ofthe spectrum, and the retardation

78 CHAPTERS

produced in the plate on the violet-tending ray. No tenn for retardation by the plate onthe red-tending ray (Rroo,plate) appeared because this ray escaped the plate altogether. Inconsequence, the path difference became equal to the sum of the original pathdifference caused by the prism and the new one imposed by the plate on the violet­tending light.If, on the other hand, the plate covered the red end of the spectrum, then the path

difference between the two involved light pencils would be:

Rvio,prism - (Rred,prism + Rred,platJ = (Rvio,prism - Rred,prisrrJ - Rvio,plate

In this case, the violet-tending light escaped the plate, with the result that his expressionhad become the difference between the prism-produced difference in retardation andthe red-tending one produced by the plate.Powell thought that he had here an explanation for his discovery concerning the

effect of plate thickness. If a plate covering the red end of the spectrum had a properthickness so that the retardation produced by it alone was close in magnitude to thedifference produced in the prism between the violet- and red-tending rays in a givenpatch, then that difference would effectively be annulled and interference would notoccur, On the other hand, if the plate was extremely thin, Rred,pla,e would be too smallto create any effect, and the bands would continue to exist.9

Powell's explanation did not satisfy Brewster because, according to the latter, itrested on an unacceptable approximation. Powell, Brewster noted, had assumed that anentire half of a circular patch suffered the same degree of retardation from the prism.This assumption was grossly inaccurate, for Brewster remarked, "every elementary partof the spectrum consists of rays which have passed through all the different thicknessesof that portion of the prism which receives that incident beam ofwhite light" (Brewster1839, 781). Different parts of a patch suffered different degrees of retardation causedby the prism, in which case Powell's account could only explain the vanishing of somedark bands but not the disappearance of the whole set. In any case, Brewster's mostdevastating point was that the phenomenon did not require a prism -- it only needed aspectrum. He had observed the same polarity phenomenon by using an interferencespectrum, which was not produced by a prism but rather by a number of parallelgrooves cut on a polished steel surface. This experimental fact showed that the"polarity of light" resulted from something other than the retardation of a prism, inwhich case Powell's account failed (Brewster 1839, 781),10

4. THE SETBACK OF THE WAVE THEORY

Brewster's successes in exposing the difficulties and problems in Powell's accountencouraged him to launch a full-scale attack against the wave theory, and this attackstirred up heated debates at the British Association. Although in these debates Brewsterfaced alone almost all ofthe fIrst-rank wave theorists in Britain, including Airy, Powell,Herschel, Hamilton, MacCullagh, Challis, and Lloyd, he made his point so successfully

POLARITY OF LIGHT 79

that, in the end, he actually convinced some of his rivals that the polarity problemremained unsolved.Brewster did not concentrate his rhetoric entirely on the wave theory's specific

failures here or elsewhere. Instead, he proposed a discussion of the general merits ofthe wave theory at both the 1842 and the 1845 meetings of the British Association,though it had dominated the field for more than a decade. Brewster insisted that thetheory still failed to explain entire classes of well-observed and distinctly markedphenomena. One of these was his own recently discovered "polarity of light," whichremained unexplained despite the best efforts of Powell and other wave theorists. Thesecond class of unexplained phenomena was the one he had discovered more than adecade ago: the phenomenon of selective reflection by grooved surfaces. Here, apolishedmetallic surface with equal and equidistant grooves was incapable ofreflectinga single ray of homogeneous light at several angles of the incidence, whereas itreflected that ray freely at intermediate angles (Brewster 1829, 301-16).11 Explanationsof these "extraordinary facts," Brewster asserted, were beyond the power of the wavetheory. Its failures here gave Brewster sufficient reason to reject the theory altogether:"Notwithstanding the great power of the Undulatory Theory in explaining phenomena,and its occasional success in predicting them, I have never been able to consider it asa representation of that interesting assemblage of facts which constitute PhysicalOptics" (Brewster 1845, 7).Brewster should have expected nothing but fierce counterattacks from the wave

camp because he was openly challenging the status of the already-influential wavetheory. Nevertheless, he received a qualifiedly sympathetic response from a wavetheorist, namely James MacCullagh, Professor of Mathematics at Trinity College,Dublin. Educated at Trinity, Dublin, MacCullagh had completely endorsed Fresnel'swave theory in his early optical researches. His faith in wave principles did not,however, also extend to the theory's physical foundation, which he began to explorein the late 1830s. MacCullagh decided that he could not develop a workable accountofcrystalline reflection using the kinds of assumptions that had been put to use (withonly partial success in any case) by Fresnel for ordinary reflection. He instead soughtto develop a general account, or what he termed a "dynamical theory," ofreflection andrefraction, by working with a potential function for an elastic solid (MacCullagh 1839,187-217). MacCullagh found that he had to dispense with terms in the generalexpression for the potential that had been developed by George Green, the implicationbeing that the appropriate medium could not be considered elastic in the usual sense.In a letter to Herschel in 1846, MacCullagh wrote that "I have thought a good deal (asyou may suppose) on the subject - but have not succeeded in acquiring any definitemechanical conception. .. One thing only I am persuaded of, that the constitution ofthe ether if it ever should be discovered, will be found to be quite different from anything that we are in the habit of conceiving, though at the same time very simple andvery beautiful" (MacCullagh 1846; original emphasis). Because he failed to establisha mechanical basis within the generally-accepted wave framework, MacCullagh's viewof the theory's integral structure became more skeptical, as he insisted -- based on his

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own experience -- that much remained to be worked out.After listening to Brewster's complaints at the 1842 meeting of the British

Association, MacCullagh expressed his sympathy and acknowledged that wavetheorists still "knew so little of the undulatory theory." The major problem, asMacCullagh admitted, consisted in the theory's obscure physical foundation, forwithout a fInn ground in physical reality the theory relied entirely on the applicationof the principle of interference. Bereft of any "physical foundation," MacCullaghargued, wave theorists "knew nothing absolutely of the undulatory theory," althoughthey were able to use it to explain many things in a very beautiful way. He went on tosuggest that perhaps the research style of the theory, namely, its employment of purelymathematical investigation, was responsible for the neglect of physical inquiry(Anonymous I842a, 662; Anonymous 1842b, 534)"2Agreeing with MacCullagh, on this point at any rate, Brewster expressed his strong

discontent with the cUll-ent tendency in the fIeld to overlook the importance and valueof experimental inquiry. The wave theory had explained several "grosser phenomena,"but had been supported in a way that held back optical science by discouraging allexperimental research. People who knew very little of the subject had praised thetheory as perfect, and had even ventured to place it on the same level as the theory ofuniversal gravitation. 13 These people, Brewster continued, held up those facts explainedby the theory as great discoveries, while they ignored other far more interesting andvaluable facts simply because they were either hostile to, or unexplained by, the theory(Anonymous 1842b, 534).To support his criticism that wave theorists discouraged experimental researches,

Brewster complained to the audience about one of his recent experiences. In 1841, hehad submitted a paper primarily containing experimental results on polarization to theRoyal Society, but the Council of the Society rejected its publication. As one of theoldest members of the society, and author of more than 30 papers in PhilosophicalTransactions, Brewster felt humiliated. He believed that the Council had rejected thepaper solely because it was experimental and contained results and views hostile to thewave theory. This rejection was a clear indicator that the process of discouragingexperimental researches had spread to such an extent that "even learned societies wereso completely under the incubus of the undulatory theory."14Among the wave theorists who listened to Brewster's attack, MacCullagh was the

only one who was sympathetic. Most could accept neither Brewster's critiques nor thedoubt cast on the theory. Nevertheless, they admitted, as Brewster had claimed, that the"polarity of light" was still a problem for the wave theory. What they did was to reducethe damage, arguing that this was a purely local, minor failure. For example, Herschelasked the audience to suspend their judgment, not to put the theory on life-or-death trialbased solely upon Brewster's discovery. Similarly, Hamilton reminded the audiencethat, although wave theorists considered Brewster's discovery to be (at present)inexplicable, "it would not be supposed that the wave men were wavering, or that theundulatory theory was at all undulatory in their minds." Hamilton remarked that theDublin wave men at least retained as strong a conviction as ever of the substantial truth

POLARITY OF LIGHT 81

of the wave theory (Anonymous 1842a, 662; Anonymous 1842b, 534).Even the most stubborn wave theorists such as Airy and Powell recognized the

compelling power of Brewster's critique. Although they did not accept Brewster'scharge and felt that they had been able to explain the phenomenon, they knew that theirarguments were weak. Indeed, after Brewster presented his critique at the 1845 meetingof the British Association, Airy was clearly not willing to pursue the debate. Hecomplained that he was not aware ofBrewster's plan to discuss the subject until he sawthe announcement about half an hour before the meeting began, and he said that hismemory on the subject was so imperfect that he did not even remember the details ofhis own account. Airy accordingly declared that under these circumstances he wastotally unprepared to debate the matter, and he refused to have any substantialdiscussion with Brewster (Anonymous 1845a, 699).

5. POWELL'S HOLLOW PRISM

Brewster's victory at the 1842 and 1845 meetings of the British Association made theproblem of the "polarity of light" a significant, recognized issue and forced wavetheorists to continue their researches on the matter. Powell continued to work in thisperiod on the "polarity" problem. Around 1847, he developed a new experimentalapparatus that, he felt, could lead to a better understanding of the issue. The keycomponent of this apparatus was a hollow glass prism containing highly refractive anddispersive liquid. In his earlier study of reflective indices, Powell had learned that aneffective way to have a better observation of a spectrum was to increase the dispersivepower of the prism. Since it was difficult to fmd glass prisms with high dispersivepower, a hollow prism filled with highly dispersive liquid became a convenientsubstitute. Apparently, Powell hoped that he could have a better look of thephenomenon by using a hollow prism.In his experiments, Powell inserted a plate of glass into the hollow prism vertically,

covering the upper half of the liquid. When light from a narrow slit passed through thehollow prism and the glass plate, a number of dark bands crossing throughout thespectrum appeared (Figure 5.5). Powell believed that the dark bands generated by hisapparatus were the same kind as those reported by Talbot and Brewster. His apparatuswas similar to the one used by Brewster: he changed only the position of the thin plate,moving it from in front of the eye to within the prism. Although he did not use atelescope to view the spectrum as Brewster had, he apparently believed that thesealterations did not result in important differences.Powell's new apparatus, however, revealed something new. Unlike Brewster's

experimental setup, where the position of the glass plate was the operational parameter,Powell's apparatus involved different manipulations. The fact that the plate wasinserted into the hollow prism made it difficult to rotate the glass plate. However, usinga hollow prism made the refractive index of the liquid a controllable parameter. Thus,in his experiments Powell tried various combinations of liquids and plates withdifferent thicknesses, and he found that in some combinations the dark bands appeared

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Refractiveliquid

CHAPTER 5

Thin plate.----The eye

Figur 5.5 Powell sapparatus for producing the "polarity oflight"

quite vivid and distinct, while in some other combinations they were too fme to beseen. With some very specific combinations, such as glass with water, or glass with oilof turpentine, the dark bands disappeared entirely, just as Brewster had discoveredwhen the plate covered the red end of the spectrum. This discovery suggested that theappearance and disappearance of the dark bands could hardly be attributed to anyspatial factor, nor to any "polarity."On the basis ofhis experiments, Powell developed a quantitative analysis to account

for the phenomenon. He continued to believe that interference between the retarded andunretarded rays originating from the same homogeneous colored patch was the causeof the dark bands. "For an explanation of the general phenomena of the formation ofbands under the conditions specified," he claimed, "the simple interference-theorysuffices" (powell 1848, 215; original emphasis). But in contrast to his earlier qualitativeaccount, Powell now considered only the retardation caused by the plate. He beganwith two equations that represented the disturbances caused by the retarded andunretarded rays, from which he derived a formula representing the intensity of light inthe spectrum. But, deviating from standard wave analysis, Powell did not use themethod of integration to determine the intensity of light. He simply derived the formulaby adding up the squares of the coefficients in the two equations that represented singlerays, a clear indication that Powell did not grasp the method ofwavefront analysis. Theformula, however, showed that the intensity of light in the spectrum changedperiodically, from zero to four times of the incident intensity. It changed according tothe wavelength of the ray and the retardation caused by the plate, which could bedetermined based on the thickness ofthe plate and the difference between the refractiveindices of the plate and the liquid medium. Specifically, the formula showed that, whenthe ratio of the retardation to the wavelength was an even number, the intensity of lightdecreased to zero and a dark band appeared. When the ratio did not satisfy thiscondition, no dark bands were visible (See Appendix 4). Considering the retardationof the plate alone, Powell believed that his formula revealed the causes of theappearance and disappearance of the dark bands, and thus offered an explanation for

POLARITY OF LIGHT 83

the polarity phenomenon.In addition to accounting for the formation of the dark bands, Powell's formula

could also predict the precise number of bands in an interval between any two spectrallines. For example, when the liquid medium was oil of sassafras and the plate was apiece of.4 inch crown glass, Powell's formula showed that there should be five darkbands in the region between the B and the D lines, 15 between the D and the F lines,18 between the F and the G lines, and 25 between the G and the H lines. The totalnumber of dark bands in the spectrum, that is, between the B and the H lines, shouldbe 65 according to Powell's calculation.To test these predictions, Powell conducted a series of experiments to count the

actual number of dark bands in the spectrum. Because he used a hollow prism filledwith highly dispersive liquid, the dark bands in the spectrum were well defined. Theresults ofhis observations were, according to Powell's own judgment, very satisfactory.For example, Powell reported that, in the arrangement where oil of sassafras and apiece of.4 inch crown glass plate were used, there were six dark bands between the Band D lines, 14 between the D and F lines, 21 between the F and the G lines, and 24between the G and the H lines. All these observations were very close to thepredictions. Even more impressively, he reported that the total number of the darkbands in the whole spectrum was 65, exactly the same as the formula predicted. Powellthus declaimed that his formula was confirmed by the observations. He said, "the moreprecise comparison of the number of bands formed throughout the spectrum, or withcertain defmite spaces of it, though in some cases unavoidably imperfect from thedifficulty of distinguishing the bands, yet upon the whole gives accordances as goodas perhaps can be expected" (powell 1848, 216; original emphasis).After he believed that his formula was confirmed, Powell sent a paper to the Royal

Society reporting his discovery. Since he classified his finding as a rather simple caseof the well-known phenomenon of interference, he had to justify the significance ofhiswork. At the beginning ofhis paper, Powell admitted that, given the advanced state ofthe theory of light, his topic -- a case of interference ofunpolarized light -- could hardlybe deemed of sufficient importance to form the subject of a paper for the Society.However, Powell claimed that the matter he was going to discuss was a case "which byno means stands isolated, but offers analogies with other classes of phenomena whichhave excited considerable interest and discussion, especially with regard to what hasbeen termed, perhaps improperly, a 'polarity' in the prismatic rays" (Powell 1848,213). Apparently Powell believed that he had successfully defused the "polarity bomb"set up by Brewster.

6. STOKES'S SOLUTION

Powell's research drew the attention ofGeorge Stokes, one of the most skillful wavetheorists of the day. Stokes had graduated from Cambridge in 1842, and he was one ofa new generation ofwave proponents who had received their education after the wavetheory was already embedded in university curricula in Britain. He had not himself

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experienced the conversion from the old theoretical framework to the new one. Withhis superb mathematical skills, Stokes was able to handle very complicated opticalphenomena that had been beyond the powers ofhis predecessors. In his correspondencewith Powell between 1847 and 1848, Stokes gave a detailed mathematical treatment ofthe "polarity" phenomenon. His analysis was so fertile that Powell later complained ofan "embarras de richesses" and suggested that Stokes write a separate, summary paper(Stokes 1907, 115). Accepting Powell's suggestion, Stokes wrote a paper summarizinghis analysis and sent it to the Royal Society (Stokes 1848,227-42).

In the fIrst section ofhis paper, Stokes reviewed several existing explanations of thepolarity phenomenon, primarily Powell's and Airy's account. According to Stokes,both Powell and Airy analyzed the polarity phenomenon in terms of rays, adding onlythe principle of interference. They had also assumed that modifications occurred onlywhen rays passed the prism and the retarding plate, and that the form and magnitudeof the aperture (that is, the object lens of the telescope or the pupil ofthe eye) need notbe taken into consideration. They accordingly attributed the phenomenon to theinterference between retarded and unretarded rays (Stokes 1848,228-30).Stokes labeled both Powell's and Airy's accounts an "imperfect theory of

interference." Their problems, as Stokes remarked, lay in two unacceptableassumptions. First, the Powell-Airy accounts assumed an annihilation of light when thephases of two interfering rays were in opposition. According to Stokes, "light is neverlost by interference . .. The effect of interference has been, not to annihilate any light,but only to alter the 'distribution of the illumination'" (Stokes 1848,234-5; originalemphasis). Thus, bright bands would also appear in the spectrum if interference werereally the cause, but that had not been seen in the experiment. Second, the Powell-Airyaccounts supposed that the light wave, after passing through the lens of either the eyeor the telescope, still had an unbroken front. They had accordingly treated waves asthough they were rays following the courses given. them by geometrical optics, andthey had attributed the phenomenon to the interference between two or a finite numberof rays. However, Stokes argued, it was mistaken to ignore the role ofthe aperture inthese experiments because both the object lens of the telescope and the pupil of the eyecould alter the shape of the front. With broken fronts, waves could not be treated asrays, and the cause of the polarity phenomenon could no longer be interference.To unpack the "polarity" phenomenon on correct grounds, Stokes first replicated

the experiment. He improved Powell's design by using a telescope behind the retardingplate but in front of the eye to view the spectrum (Figure 5.6). This new experimentaldesign did not yield any new result, but it demonstrated that the object lens of thetelescope played a very important role, since it functioned like a diffracting aperture.An aperture had also existed in Powell's experiment, but that was the pupil of the eye.Brewster's experiment had employed a telescope, but it had been put in front of theretarding plate. According to Stokes, only the aperture behind the retarding plate wascritical in altering light distribution. Thus, it was again the eye's pupil that functionedas an aperture in Brewster's experiment. The crucial role of the aperture in Brewster'sand Powell's experiments, as Stokes saw it, had been ignored because the effect of the

Refractiveliquid

POLARITY OF LIGHT

Thin plate

/

Telescope

The eye

85

Figure 5.6 Stokes:S apparatus for producing the "polarity oflight"

eye's pupil was usually overlooked. Brewster's experiment accordingly exhibited manysimilarities to an exemplary case of interference -- Young's double slit experiment, twoexperiments in which the light from a single source was split into two parts and thenrecombined, and apertures played no role. But when Stokes employed a telescope andput it behind the retarding plate, the function of the object lens as an aperture wasclearly brought out. This arrangement exhibited strong similarities to an exemplary caseof diffraction -- Fresnel's experiment with a circular aperture. Stokes thus argued thatboth the formation of the dark bands and their disappearance were the results of theredistribution of illumination triggered by the retarding plate and the object lens: "theexplanation of the polarity of the bands depends on diffraction"(Stokes 1848,229).In the second section of his paper, Stokes calculated the distribution of light in the

experiment on the basis of the integral formulation originally developed by Fresnel.Starting with a point source emitting homogeneous light, Stokes first determined thedisturbances produced by the unretarded and retarded fronts after passing through theaperture, as well as the intensity of light caused by these disturbances when thespectrum was viewed in focus. Next, he calculated the intensity of light when thesource was a line of homogeneous light by integrating the intensities caused by allluminous points on the line. Finally, Stokes determined the intensity of light with aspectrum as the source by integrating the intensities caused by all homogeneous linesin the spectrum. ISThe results of these calculations were very impressive. Stokes was able to derive

a formula which showed that, when the retarding plate covered the violet end of thespectrum, the intensity of light at the retina was a trigonometric function of the distanceto the retina center, in such a manner that dark bands appeared alternately. The formulaalso showed that, when the retarding plate covered the red end of the spectrum, theintensity was constant and no dark band could be seen, whatever the size ofthe aperture(pupil or object lens) might be. This result exactly accommodated Brewster'sexperiments and corrected one of the mistakes made by Airy, whose mathematical

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analysis implied that, under certain conditions, dark bands could appear when the platecovered the red end of the spectrum.After his temporary victory at the 1845 meeting ofthe British Association, Brewster

had continued to keep his eye on the issue ofpolarity, and he did not miss Powell's andStokes's fmdings. Brewster might not have fully understood Stokes's mathematicalanalysis, but he defmitely grasped the implications of Powell's experimentaldiscoveries, which contradicted Brewster's understanding of the phenomenon. The factthat the dark bands disappeared at certain combinations of the retarding medium andthe liquid conflicted with Brewster's notion of polarity, which referred to an opticalasymmetry sensitive only to spatial variation. Brewster's taxonomy of opticalasymmetry could not incorporate this new experimental discovery, and so Powell'sexperimental apparatus stimulated Brewster to develop a new conception. In 1847,Brewster found that the edges of thin plates could produce diffraction bands similar tothose in the polarity experiment (Brewster 1847,33). Powell's experimental apparatus,in which the thin plate was inserted in a hollow prism filled with liquid, now suggestedto Brewster that the dark bands in the polarity experiments might actually be caused bythe edge of the thin plate. After carefully studying the internal diffraction fringesproduced by fme objects such as a needle, Brewster finally convinced himself that thephenomenon he had believed indicated a new species of polarity of light was merelythe internal diffraction fringes produced by the edge of the thin plate, and renderedvisible by the action of the prism. Brewster openly announced this new view at the1852 meeting of the British Association and in his 1853 edition ofA Treatise on Optics(Brewster 1852b, 24-5; Brewster 1853, 170). After more than ten years of heateddispute involving almost every major actor in the field of physical optics, the debateon the polarity of light finally ended in 1852 when Brewster openly admitted that thephenomenon was not a problem for the wave theory, although he still did not acceptthe current wave explanation, which attributed the polarity phenomenon to thediffraction produced by the aperture.

CHAPTER 6

THE MEASUREMENTSOF THE INTENSITY OF LIGHT

The wave theory's ability to explain diffraction had long been considered one ofthemost important facts in favor of the theory. Even some opponents of the wave theory,such as Brewster, had to admit the advantage of the wave theory in explaining thisphenomenon. Although diffraction seemed to be the last area where disputes betweenthe two rival theories of light could occur, the wave account of diffraction was stillchallenged in the early 1840s. It was Richard Potter, Professor ofNatural Philosophyand Astronomy at University College, London, who launched a series of attacks, basedon his photometric experiments. The debate between Potter and wave theorists wasquite unusual because it centered on diffraction, the stronghold of the wave theory.This chapter describes how instruments and experimental procedures affected

Potter's judgment of the wave account of diffraction. Armed with a photometeroriginally designed for evaluating telescopes, Potter measured the reflective power ofmetallic and glass mirrors in the early 1830s. Because he found significantdiscrepancies between his measurements and Fresnel's predictions, Potter developeddoubts about the wave theory and, eventually, objections to the wave account ofdiffraction. However, Potter's photometric measurements were colored by a peculiarexperimental procedure. In order to protect the sensitivity of the eye during theexperiments, Potter made a couple of approximations in the measuring process thatexaggerated the discrepancies between the theory and the data.

1. POTTER'S REFLECTING PHOTOMETER

In his earlier years when he was still a merchant in Manchester, Potter had built areflecting telescope. I This was a Newtonian telescope, which used a concave metallicmirror to produce images, and a small plane metallic mirror, inclined 45 degrees to theaxis, to reflect images to a side for observation. According to the available data,Potter's reflecting telescope clearly belonged to the amateur class. The diameter of theconcave mirror was only 5.5 inches, with a focal length about 50 inches. The smallplane mirror was about one by 1.25 inches. With two different eyepieces, the telescopecould have two levels ofmagnification, either 100 or 150.The key to constructing a reflecting telescope was to obtain high-quality metallic

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X. Chen, Instrumental Traditions and Theories of Light© Springer Science+Business Media Dordrecht 2000

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llIUT..LIDrrfllTXIDn:mScreen A

Mirror

mirrors. Potter spent his leisure time for more than ten years acquiring and improvinghis skill at making metallic mirrors. He fIrst asked a local bell-maker to cast the mirrorsfor him, but later he learned to cast the mirrors himself. The most difficult part inmaking the mirrors, Potter recalled, was the task of polishing. At the beginning, Potterused the common polishing powder available in shops, such as putty (oxide of tin) androuge (oxide of iron), but he soon found them unsatisfactory. For example, thecommercial oxide of iron was always mixed with carbonate of iron, which corroded thesurfaces and reduced the quality of the polishing results. In order to prepare betterpolishing powder, Potter spent two years studying chemistry with John Dalton as histutor.2 Finally, Potter learned a method for producing pure oxide of iron from copperas(sulphate of iron) and obtained satisfactory mirrors (potter 1831c). After many years'practice, Potter believed that he had attained some profIciency in this difficult art. Inearly 1829, he became interested in evaluating the quality of his telescope.The need for evaluating the telescope triggered Potter's photometric research. By

the late eighteenth century, it had become a common knowledge that, for the purposeof astronomical observations, magnifIcation power was not the only standard forevaluating telescopes. A good telescope should allow observers to detect faint objectsregardless of its magnification power. William Herschel called this capacity "space­penetrating power," and it depended upon three factors. The first was the aperture ofthe observer's pupil, which directly determined the amount oflight reaching the retina.The second was the diameter of the concave mirror in a reflecting telescope or of the

crr

Figure 6.1 rVilliam Hersche I 's apparalusfor measuring refleclive power

INTENSITY OF LIGHT 89

objective lens in a refracting telescope. The last factor was the so-called illuminatingpower of the telescope, that is, the percentage ofiight that was transmitted through theoptical system, which depended upon the reflective power of metallic mirrors or thetransmitting power of glass lenses (Herschel 1800b, 49-65).To determine the "space-penetrating power" for his own reflecting telescopes,

around 1799 Herschel conducted a series of photometric experiments to measure thereflective power of the mirrors that he used. Unlike the Newtonian reflectingtelescopes, Herschel's telescopes employed only a single convex mirror that reflectedlight at normal, and the observer obtained the image by sitting in front of the telescope.So Herschel needed to measure the reflective power ofthe mirror at a reflection angleof zero degree, and he used a method proposed by Pierre Bouguer in the mid­eighteenth century (Bouguer 1961, 28-9).Figure 6.1 illustrates the setup ofHerschel's experiments. He placed the mirror to

be measured halfway between two identical reflecting screens, and a lamp somewherebetween the screens, along the line AB. From point 0, he could see the image of thelamp in screen A directly and the image of the lamp in the other screen through thereflection from the mirror. He then adjusted the position of the lamp until the brightnessof the two images, the direct and the reflected one, appeared to be equal. Finally, hemeasured the distances of the lamp to the two screens, and, according to the inversesquare law, calculated the reflective power ofthe mirror by means of the ratio of thedistance squares.3 The result showed that the reflective power ofhis metallic mirror was67.262% (Herschel 1800b, 64-5).After he learned of Herschel's photometric research, Potter began a series of

experiments to determine the reflective power of the mirrors used in his telescope.Potter did not, however, adopt Herschel's method that could measure only the reflectivepower at near zero degrees. Because his telescope employed two mirrors, one reflectinglight at normal and the other at 45 degrees, Potter needed to determine the reflectivepower at various angles of reflection. To achieve this task, Potter designed a specialinstrument, a reflecting photometer (Figure 6.2).The main components ofthis photometer were an upright screen with an aperture

(four inches by 2.5 inches) and a horizontal board (4.5 inches by 50 inches) divided bya blackened partition. Unlike Herschel, who used a single lamp, Potter employed tWoidentical lamps, each ofwhich was put on the end of a slide and placed on either sideof the partition. To determine the reflective power at various angles, Potter added acouple of special devices to the photometer. He fixed the mirror to be measured to anarm, which could be turned around an axis attached to the right-hand slide (Figure 6.3).To intercept alternately the direct and reflected light, Potter installed two uprightpartitions perpendicular to each other. When the partitions were in the direct lightposition as shown in Figure 6.3, they intercepted the reflected light; when the partitionswere turned 90 degrees clockwise to the reflected light position, they stopped the directlight.This photometer allowed Potter to measure directly the reflective power at 45

90 CHAPTER 6

Lamp

Aperture

/Mirror

Figure 6.2 Potter sreflecting photometer

degrees, but not at zero degrees, that is, when the incident light and the mirror were atnormal. Potter used an indirect method to determine the latter. He first measured thereflective power at various reflection angles, from 10, 20, up to 80 degrees, and thenderived the value at zero by interpolation. To obtain the preset reflection angles, headjusted the location of the lamp and the angular position of the mirror until he wasable to see the image of the lamp at the center of the mirror through a hole at the centerof the right-hand aperture. He then determined the reflection angle by trigonometriccalculations. After repeating these steps many times, he determined the positions of thelamp corresponding to all preset reflection angles and marked them in the slide.4

Potter later recalled that one of the major difficulties that he experienced in theseexperiments arose from "the fatigue of the eye experienced by looking long andintently at bright objects surrounded by darkness, which prevents it after some timejudging accurately of very small differences [in brightness]"(Potter 1830,279). Toreduce the fatigue of the eye, Potter covered the aperture with semi-translucent paper,which reduced the contrast between the light sources and the background. Potter alsoinvented several "remote-control" devices, which allowed him to conduct theexperiments without exposing himself under the direct light from the lamps. Forexample, he put the lamps on moveable slides, and because the ends of these slides

INTENSITY OF LIGHT

Figure 6.3 Potter sreflecting photometer (details)

91

extended over the screen, he could adjust the distances to the lamps by simply pullingor pushing the slides while staying behind the screen. He marked the right-hand slidewith divisions, in .25 inch intervals, so that he could determine the distance betweenthe lamp and the screen by simply reading off the divisions. By attaching strings to thecomers of the perpendicular partitions, he could tum them in either direction withoutleaving his seat behind the screen.

2. POTTER'S MEASUREMENTS OF METALLIC MIRRORS

Using the specially designed photometer, Potter began to measure the reflective powerof several metallic mirrors, one composed of cast steel and the rest of tin-copper alloy.The crucial step in Potter's measuring process was to use the eye to match brightnesson the aperture. The accuracy of this procedure obviously relied upon the sensitivityof the eye, which, according to Bouguer, could detect differences in brightness as smallas 1.5% (Bouguer 1961, 50-1).5 To begin with, Potter put the right-hand lamp and themirror in preset positions and turned the perpendicular partitions to stop the reflectedlight. He then made the ftrst brightness match, adjusting the left-hand lamp until equalbrightness appeared in the aperture, and measuring the distance between the right-handlamp and the screen (the distance of the direct light). Next, he turned the partitions to

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stop the direct light, and made the second brightness match by pulling the right-handslide together with the lamp and the mirror closer to the screen until equal brightnessappeared in the aperture. He again measured the distance between the right-hand lampand the screen (the distance of the reflected light). Finally, with the distance of thedirect light (Ddir) and the distance of the reflected light (I~f)' he calculated thereflective power (P) by using the following equation derived from the inverse squarelaw:

Dp=[ relf

D dir

Among these operations, the measurements of distances deserve our attention.Potter's measurement of the distance of the direct light was straightforward. Heobtained this parameter by simply reading offthe divisions on the slide. But Potter'smethod ofmeasuring the distance of the reflected light was peculiar. This parameteris the sum of the distance from the lamp to the mirror (LM in Figure 6.3) and thedistance from the mirror to the center of the aperture (MS). The value of LM wasavailable before the experiment from the preset positions of the lamp and the mirror,but the value of MS was not because, after the second brightness matching, thereflected light no longer fell into the center of the aperture. Potter made it clear that hedid not actually measure MS. "[Because] it will be seen that the divisions commencingonly at the thicker piece ofwood, the distance of the lamp in the direct measurements,and the sum of the distances of the lamp to the mirror, and the mirror to thecommencement of the divisions, must be added afterwards in the reflected ones," hesaid (P-otter 1830,286). In other words, Potter made an approximation by substitutingfor MS the horizontal span between the mirror and the screen (MH), which wasavailable by reading off the slide. His reason for making this approximation was toprotect the eye. If Potter measured MS directly, he would have exposed himselfto thedirect light from the lamps and quickly developed eye fatigue. This approximation,however, did not have any notable effect on the measurements of metallic mirrors.Because metals had relatively high reflective power, the right-hand lamp was still quitefar away from the screen after the second brightness matching, usually more than 30inches. Potter's approximation of distance caused only about .1% deviation in the finalmeasurements.Potter's calculations also deserve our attention. Potter knew that, if the light from

the source did not fall onto a surface perpendicularly, the illumination of the surfacewas also proportional to the cosine of the incident angle a. This was the cosine law ofillumination found by Johann Lambert in the late eighteenth century. In Potter'sexperiments, the reflected light was not perpendicular to the screen. Thus, the reflectivepower should have been calculated by using the following equation:

INTENSITY OF LIGHT

p = _1_ x [ D ref )2COS « D dir

93

where a is the angle between the reflected light and the normal of the screen. Butsimilar to MS, a had to be measured experimentally. For the same reason of protectingthe eye, Potter made another approximation: he completely ignored the incident anglein his calculations. Fortunately, this approximation of the angle also did not causesignificant degradation of the accuracy in the metallic experiments. Due to the highreflective power of metals, the incident angles in Potter's metallic experiments werealways close to zero.Potter frrst determined the reflective power of an alloy mirror at 45 degrees. After

18 measurements, he averaged the findings, which yielded a quantity of 64.9%. Todetermine the reflective power at zero degree, Potter first took the measurements atthose preset angles and then used interpolation to obtain the net(ded quantity. Theresults showed that the reflective power of the alloy mirror was 72.3% when theincident light was perpendicular to the mirror. These results were consistent with thosegiven by Bouguer and Herschel.6 According to these measurements, Potter estimatedthat his reflecting telescope was able to transmit about 43% of the incoming light, thesame level as other Newtonian-type telescopes.Potter's photometric measurements immediately drew the attention of many in the

optical community. Brewster first heard of Potter's measurements in 1830, andimmediately invited Potter to publish the results in The Edinburgh Journal ofScience(Smith 1874). Apparently, Brewster believed that Potter's measurements were usefulfor constructing reflecting telescopes. In his A Treatise on Optics printed in 1831,Brewster cited Potter's results in the section on reflecting telescopes, and proposed touse an achromatic prism to replace the plane metallic mirror in the traditional reflectingtelescopes (Brewster 1831a).However, the impact of Potter's metallic measurements went beyond telescopic

design. Repeating his measurements with different metallic mirrors, Potter found thatmetals reflected less light when the reflection angle increased. For example, thereflective power ofa steel mirror was 57.19% at 10 degrees, dropped to 55.52% at 20degrees, further to 53.29% at 50 degrees, but rebounded to 54.67% at 60 degrees.7 Thiswas a novel discovery, which invalidated the received view that, similar to othersubstances, metals reflected more light when the reflection angle increased. Potter'sdiscovery stimulated MacCullagh to study metallic reflection and to discover in 1836an empirical law to describe the reflective power ofmetals (MacCullagh 1836,61).8

3. POTIER'S MEASUREMENTS OF GLASS MIRRORS

Once he knew the illuminating power ofhis reflecting telescope, Potter wanted to makegeneral comparisons of the quality of reflecting telescopes and that of refractingtelescopes. He claimed that "I feel it incumbent upon me, ... , to remove a veryincorrect idea which is universal in the scientific world on the comparative illuminating

94 CHAPTER 6

powers ofreflecting and refracting telescopes" (potter 1831c, 25). The traditional beliefat the time was that a reflecting telescope with two metallic mirrors had only about one­half of the illuminating power of an achromatic refracting telescope with the sameaperture size. According to Potter, this belief resulted from an overestimation of glass'scapacity to transmit light. To correct this misconception, Potter found a six-footachromatic telescope made by Dollond and measured the amount of light transmittedthrough its objective lens. Using the same photometer, Potter began with a setting inwhich light from both lamps fell directly on the aperture and generated equalbrightness. He then placed the objective lens ofthe Dollond telescope on the left-handboard, between the lamp and the screen. The inserted lens absorbed and reflected some

I

portion of the light, so that the right-hand lamp had to be pushed away a little in orderto maintain equal brightness on the aperture. With the original and adjusted distancesof the right-hand lamp to the screen, Potter used the inverse square law to calculate thepercentage of light transmitted through the lens. The result showed that a significantamount of light was lost due to reflection and absorption and that the lens transmittedonly about 66% of the incoming light, about the same as the amount reflected by ametallic mirror. Potter thus concluded that, "an achromatic telescope with one objectand one eye-glass has no advantage over a reflector in respect of light, with onespeculum and one eye-glass of the same quantity of available reflecting aperture, whichit has of refracting" (Potter 1831c, 26). Since it was relatively easy and inexpensive toincrease the diameter ofmetallic mirrors, which was another factor affecting the space­penetrating power, Potter concluded that reflecting telescopes, particularly Herschel'sfront-view type that used only one concave mirror, were better choices than refractingtelescopes for astronomical observations.9

The measurements of the achromatic lens drew Potter's attention to the absorptionof glass. To determine the role of absorption in affecting the quality of lenses, heneeded to know the amount of light reflected by glass. Thus, in later 1830 Potter starteda new series of experiments to measure the reflective power of glass.Potter used the same photometer and followed essentially the same procedures as

those adopted in the metallic experiments. In the glass experiments, however, he hadto place the right-hand lamp very close to the screen during the second brightnessmatching because of the low reflective power of glass. A significant amount of lightscattered by the parts surrounding the lamp reached the aperture and inflated themeasurements. Thus, Potter added a new procedure to estimate the amount of thescattered light and then subtract it from the gross readings including both the reflectedand the scattered light. He started with a setting in which light reflected by the glassmirror and scattered by the surrounding parts all reached the aperture. He attached aroughly ground glass plate in front of the left-hand lamp, and adjusted the luminousarea of the plate (by covering it with black paper) until equal brightness appeared in theaperture. Next, he removed the glass mirror from the photometer so that only scatteredlight reached the aperture, and reduced the luminous area of the glass plate in the left­hand side until equal brightness appeared. Finally, he used the ratios between the twoluminous areas to determine the amount of the scattered light.

INTENSITY OF LIGHT 95

In a paper published in 1831, Potter reported his measurements of the reflectivepower of plate, crown and flint glass at various reflection angles, from 10 to 80degrees. His fmdings revealed several interesting features of the reflective power ofglass. First, the reflective power of glass was in proportion to the angle of reflection,which was opposite to the pattern found in metals. Moreover, the reflective power ofglass at small reflection angles was very low, only about 3 to 4%. Finally, the reflectivepower ofglass remained low and changed very little when the reflection angle was lessthan 60 degrees, but went up rapidly afterwards.Unlike metallic reflection, for which no theoretical account was available in the

early I830s, reflection of transparent materials had been well within the domain of thewave theory since the late I820s. According to the basic doctrine of the wave theory,Fresnel deduced the following formula for calculating the amount of light (I) reflectedby transparent materials:

I = i [sin2(8-fI) + tan

2(8-fI) 12 sin2(8+fI) tan2(8+fI)

where e is the angle of the reflected light, and e' is the angle of the refracted light.Thus, Potter immediately realized the theoretical implications of his photometricmeasurements. In late 1831, Potter published another paper in Edinburgh Journal ofScience, in which he claimed that, "on repetition of the experiments, I awoke to the fullvalue of a discovery perhaps of equal importance in physical optics with any of latedate, and ofwhich I have just reason to be highly proud, and this on several accounts;fIrst, that I believe it is the experiment to settle the question of the rival theories on thenature of light, as to whether it is an emitted matter, or only consists of undulations orvibration in a subtitle ether" (Potter 1831b, 322).To test the wave theory, Potter used Fresnel's formula to calculate the reflective

power ofglass, and then compared the theoretical predictions with his measurements.The results showed that Fresnel's predictions were always higher than themeasurements. For example, Fresnel's formula predicted that the reflective power ofplate glass would be 4.23% at 10 degrees, 4.37% at 30 degrees, 6.02% at 50 degrees,and 17.41% at 70 degrees, but Potter's measurements were 3.66%, 4.09%, 5.57%, and14.06% respectively. In most cases, the discrepancies were more than 10 percent(Figure 6.4). Because of these discrepancies, Potter concluded that "if the formulre

Plate glass Angle of reflection

(n=1.517) IO 20 30 40 50 60 70 &l

Potter's measurements 3.66 3.74 4.09 4.40 5.57 8.0 14.06 34.57

Fresnel's predictions 4.225 4.248 4.370 4.808 6.016 9.198 17.41 39.05

Discrepan~ (%) 15.31 13.5 6.9 9.2 7.9 14.9 23.9 12.9

Figure 6. 4Comparisons between Potter 's meCEurements and Fresnel's predictions

96

Plate glass

(n=1.517) 10

CHAPTER 6

Angle of reflection

~ 30 40 50

Potter's rreasuremerts

Withwt approximations

Fresnel's predictions

Original discrepancy (%)

Adjusted discrepancy (%)

3.66

3.944

4.225

15.3

7.1

3.74 4.09 4.40

3.954 4.278 4.583

4.248 4.3~ 4.&>8

13.5 6.9 9.2

7.4 2.2 4.9

5.57

5.763

6.016

7.9

4.4

Figure 6.5 Potter's mzasureM!nts: A recalculation without the approximations

which they have deduced from the undulatory hypothesis are found to give results atvariance with observed phenomena, we are justly entitled to draw an argument fromit, against the hypothesis from which they emanated, as being also at variance withfact"(potter 1831b, 323).Potter believed that his measurements could offer a crucial test for the wave theory.

His confidence came partly from his trust in his instrument, which had yielded reliablemeasurements in his metallic experiments, and partly from the extent of thediscrepancies. As shown by Bouguer, photometric measurements always had theirlimits because the eye could not detect differences in brightness smaller than 1.5%.Since Potter's measuring procedures involved two brightness matching operations,Potter's measurements had a minimal error margin of 3%. But Potter's data showedthat the discrepancies between the measurements and the predictions persisted evenafter the instrumental errors were taken into consideration.It is important to note that a peculiar procedure that Potter first adopted in the

metallic experiments and carried over to the glass experiments directly caused thelower measuring results. Potter continued to make the approximations of the reflecteddistance and the incident angle. In the metallic experiments, the impact of theapproximations was negligible, but their consequences became significant in the glassexperiments. Due to its low reflective power at small reflection angles, Potter had topull the glass to be measured very close to the aperture in the second brightnessmatching, for instance, only about six inches away from the aperture at 10 degrees. Inthis setting, the approximation of the reflected distance was about 2% lower than thetrue value, and the incident angle was more than 13 degrees. Thus, without theapproximations, Potter's glass measurements would have been higher. Using theexperimental data offered by Potter, we can estimate the true values of the reflecteddistance and the incident angle, and then recalculate the reflective power at variousangles. 10Our recalculations show that the discrepancies between Potter's measurementsand Fresnel's predictions would have been smaller if Potter had not made theapproximations. In the case of plate glass, the discrepancies should have dropped from15% to 7% at 10 degrees, from 7% to 2% at 30 degrees, and from 8% to 4% at 50degrees (Figure 6.5). With a minimal error margin of 3% associated with Potter'smeasurements, the reductions of the discrepancies could have substantially affected

INTENSITY OF LIGHT 97

Potter's argument against the wave theory, because some of the adjusted measurementswere consistent with the predictions. Thus, Potter's measuring procedures defmitelytainted his evaluation of the wave theory. Without the approximations, Potter might nothave had a case to challenge the wave theory.

4. POTTER'S COMPARATIVE PHOTOMETER

After measuring the reflective power of glass at various reflection angles, Potterinterpolated the data and obtained an empirical formula that described the reflectivepower ofglass at any particular angle. Using this formula, Potter was able to use glassas a calibrated standard to estimate the reflective power of other materials. For thispurpose, in 1832 he constructed a comparative photometer. The key element of thisphotometer was a semicircular pasteboard that functioned as a large and uniform lightsource by reflecting sunlight on a cloudy or misty day (Figure 6.6). At the center of thepasteboard, there was a vertical pin, upon which turned two movable arms. Potter hadone quadrant around the pin graduated so that he could determine the angular positionsof both arms. He attached a piece of crown glass with known reflective power to theright arm, and the material to be examined to the other. By looking through a viewingtube attached to the pasteboard, Potter could compare the intensities of the reflected

Crownglass

Othermatenal

Movablearms

VIewingtube

Figure 6. 6 Paller S comparative photometer

98 CHAPTER 6

lights from the crown glass and the other material. Since the pasteboard was uniformlyilluminated and its distance to the two surfaces was constant, the intensity of lightreflected from either surface depended only on the reflection angle, that is, theinclination between a surface and the viewing tube. By turning an arm around, Pottercould easily adjust the reflection angle, and thus the intensity. Potter began themeasuring process by setting the material to be measured at a specific angle, and thenadjusting the reflection angle ofthe crown glass until he saw from the viewing tube thatthe brightness ofthe two surfaces appeared to be equal. He then measured the reflectionangle of the crown glass and, according to his empirical formula, determined itsreflective power, which was equal to the reflective power of the material to beexamined (Potter 1832b, 175-6).Compared to the reflecting photometer, the measuring process of the comparative

photometer was much simpler. Using this new instrument, Potter was able to measurequickly the reflective power of many materials, including diamond, mica, selenite,Iceland spar, rock crystal, amethyst, emerald, and antimony glass. His measurementsagain were significantly smaller than the predictions of the wave theory. For example,Potter reported that the reflective power of diamond at 10 degrees was about 10%,while the Fresnel's prediction was 18%, an 80% discrepancy. If Potter's measurementshad been accurate, they would have offered even more powerful evidence against thewave theory.The huge discrepancies between Potter's measurements and the wave theory's

predictions resulted, in part, from his empirical formula, which had underestimated thereflective power ofglasses. But the structure of Potter's comparative photometer alsoaffected the measuring results. A peculiar feature of Potter's photometer was itssemicircular light source, which allowed Potter to adjust the reflective power of thecrown glass continuously, a critical step in his measuring procedure. But thesemicircular light source caused uneven distribution of brightness at the reflectingsurfaces. In the surface of the diamond attached to the left-hand arm, its right edge (theedge in contact with the crown glass) appeared to be brighter than its left edge, becausethe reflection angle decreased from the right to the left. The eye, however, can onlysense the average intensity of light in a sizable area. When Potter determined thebrightness of the diamond, he could only measure the average intensity, but what thewave theory predicted was the intensity at the right edge, which was higher than theaverage. This partially explains why Potter's measurements were lower than the wavetheory's predictions. IIIn addition to using the comparative photometer as an efficient means to collect

data, Potter also employed the newly invented instrument to explore a new subject. Heattempted to use the comparative photometer to determine the intensity ratio of the darkfringes to the bright fringes in Newton's rings, a measurement that no one had beenable to accomplish. Newton's rings were a set of dark and bright fringes, whichappeared when a beam ofhomogeneous light fell on a combination of two glass plates,the upper one with one convex surface and the bottom one with a plane surface. Thesefringes were called Newton's rings because Newton was the first to note the

INTENSITY OF LIGHT 99

phenomenon. According to Potter, Newton's rings were among the most importantphenomena in optics. If an optical theory really represented "the true law" in the field,it ought to be able to explain the phenomenon. Newton had tried to explain thephenomenon in terms of his doctrine of fits of easy reflection and transmission, but,according to Potter, Newton's explanation was unsatisfactory. The wave theory, on theother hand, was able to offer a quantitative account of the phenomenon in terms of theprinciple of interference. According to Herschel's calculation based upon a formuladeveloped from Fresnel's theory, the intensity ratio of the dark fringes to the brightfringes in Newton's rings should be 1 to 1.1538 (Herschel 1827, 469-73).To measure the intensity ratio, Potter frrst set up a device that could produce

Newton's rings and kept the device next to the comparative photometer. He made someminor changes in the photometer. For example, he installed two identical crown glassmirrors in the movable arms. Each mirror was covered with a piece ofblackened paperwith a narrow opening slit. He also colored the pasteboard of the photometer the samecolor as the homogeneous light used to produce Newton's rings. Looking at Newton'srings and the reflecting mirrors in the photometer alternately, Potter adjusted thereflection angles of the mirrors until their relative intensities appeared to be the sameas the relative intensities between the dark and the bright fringes in Newton's rings. Bymeasuring the reflection angles of both mirrors, Potter could determine the intensityratio according to his empirical formula.Potter conducted his measurements under a variety of conditions, first using

homogeneous green light and then homogeneous red light. He found that the intensityratio of the dark fringes to the bright fringes was about 1 to 2.36 when homogeneousgreen light was used, and was about 1 to 3.21 when red light was used. Bothmeasurements were significantly higher than Herschel's theoretical calculation.Because of these discrepancies, Potter concluded that the wave theory's account ofNewton's rings must be wrong. He claimed, "the great difference in intensity betweenthe dark and the bright rings which we here fmd, is certainly not to be accounted foron any principles of interference yet proposed; and it furnishes a very strong argumentagainst the undulatory theory, in which the effects o'finterference are supposed to beperfectly determinate when we know the circumstances of the interfering pencils"(Potter 1832b, 178).

5. THE DEBATE ON THE RELIABILITY OF THE EYE

Potter's criticisms of the wave theory immediately caused strong reactions from wavetheorists. The first response from the wave camp occurred in 1834 when Lloydpresented his "Report on Physical Optics" to the British Association. In the report,Lloyd briefly mentioned Potter's photometric measurements and cast doubts on theiraccuracy. Without replicating Potter's experiments, Lloyd did not have solid evidence,but he raised reasonable doubt by questioning the reliability of the eye at matchingbrightness, which was the crucial procedure in all photometric measurements (Lloyd1834, 74-5).

100 CHAPTER 6

In a paper presented to the 1838 meeting of the British Association, Powell pickedup the issue raised by Lloyd and continued questioning the accuracy of Potter'sphotometric measurements. Powell used a "thought experiment" to reveal the problemsof photometric experiments. He asked the audience to imagine the result of a simpleexperiment in which the light from a candle first fell onto a screen directly, and thena thin and clear glass plate was inserted between the candle and the screen. Sincereflection took place at both surfaces of the plate, more than one half of the incidentlight was reflected. Ifthe eye was reliable, Powell reasoned, we should have seen a neartwo-to-one difference caused by the glass plate. But Powell noted that, in our dailyexperience, we did not perceive such a dramatic difference. Thus, he concluded that,because the eye could not accurately judge the intensity of light, photometricmeasurements were unreliable and should not be used to test the wave theory (Powell1838a, 7). But apparently Powell did not fully comprehend the procedures ofphotometric measurements. In the "thought experiment," he "compared" thebrightnesses consecutively -- he first observed the illumination of the direct light andthen the illumination after the reflection. This procedure violated an essentialrequirement of photometry, namely that illuminations must be comparedsimultaneously.The major challenge to Potter came from James Forbes, Professor of Natural

Philosophy at the University of Edinburgh. In a paper presented to the Royal Societyof Edinburgh in 1838, Forbes questioned the reliability of Potter's photometricmeasurements with experimental evidence. Again, he did not replicate Potter'sexperiments. Instead, Forbes built his criticisms on experiments in which he used adifferent kind of"photometer" to measure the reflection ofheat, assuming that the lawsof reflection for heat and those for light, if not identical, would at least be analogous.Forbes's "photometer" was in principle similar to the one designed by John Leslie, whoused an air differential thermometer to measure the quantity of reflected light (Leslie1824). Unlike Leslie, Forbes employed an electric thermometer, consisting of athermoelectric pile and a galvanometer (Figure 6.7). The pile contained 30 pairs ofbismuth-antimony bars that generated electricity when they were heated. Thegalvanometer consisted ofa magnetic needle hung over a flattened coil of silver-wire,and it measured the electric current in terms of the angular deviation of the needle. Theextent of the angular deviation was read off in reference to the attached divided circle.With the help ofa small telescope that focused upon the divided circle, Forbes was ableto observe angular deviations of the needle as small as six arc-minutes, whichamounted to a sensitivity of .005 centigrade degrees (Forbes 1835, 134-40).Forbes used this "thermal photometer" in 1837 to measure the intensity of heat

reflected by glass and found that about 8% of the heat was reflected at 55 degrees, aresult close to the prediction given by Fresnel's formula (7%), assuming that Fresnel'sformula could be applied to the reflection of heat. But Forbes soon realized that hismeasurement was invalid because he had not excluded the reflection from the secondsurface of the glass. Forbes improved his experiment in 1838, in which he used wedges

INTENSITY OF LIGHT 101

Figure 6. 7Forbes' "thermal photometer"

of plate glass to exclude the reflection from the second surface. He also constructedsquare tubes to guide the heat rays and to reduce the impact of scattered heat from thebackground. Using the "thermal photometer" to measure the intensity of the source andthat of the reflected heat directly, Forbes determined the reflective power of glass. Hereported that the reflective power of plate glass was 4% at 10 degrees, 5.1% at 30degrees, 7.6% at 50 degrees, and 18.5% at 70 degrees (Forbes 1851). Except for theone at 10 degrees, all of these measurements were significantly higher than Fresnel'spredictions. Forbes could not say that his measuring results verified Fresnel's formula,but he compared his fmdings with Potter's measurements and claimed that Potter musthave underestimated the reflective power ofglass.Forbes also measured the intensity of heat reflected by metallic mirrors at various

angles and compared his thermal measurements with Potter's photometric ones, againunder the assumption that reflections of light and heat were analogous. Forbes foundthat his measurements verified Potter's observations that metallic reflection was lessintense when the angle of reflection increased. However, Forbes also reported that theamounts of heat reflected from metallic surfaces were significantly higher than thosereported by Potter. "The quantity ofheat reflected by the metals is so much greater thanMr. Potter's estimate for light, as to lead me to suspect that his photometric ratios areall too small, which would nearly account for their deviation from Fresnel's law," heclaimed (Forbes 1839,480).To explain the discrepancies between his measurements and Fresnel's predictions,

Forbes blamed the impact of scattered heat from the background. Because scattered

102 CHAPTER 6

heat was distributed unevenly in the background, the directed heat rays from the sourceand the reflected heat rays from the glass could have mixed with different levels ofscattered heat once they took different paths. To control the scattered heat, Forbesdesigned a new experiment, in which he transmitted the direct and the reflected heatrays along the same path.The key to Forbes's proposed design was measuring the intensity ofpolarized heat

by reflection. Partially polarized heat, or, more precisely, elliptically polarized heat,could be mathematically decomposed into two components with their planes ofpolarization perpendicular to one another. The two fractions in Fresnel's formulacorresponded to the intensities of these two components. Fresnel's formula could thenbe tested by measuring difference in intensity of polarized heat between the twocomponents after reflection. Forbes proposed the following experiment. A beam ofheatwas fIrst passed through a pile of mica sheets, which rendered the heat polarized bysuccessive refraction. The heat rays then reached a wedge of plate glass, whichreflected the incident rays to a "thermal photometer" (Figure 6.8). According toFresnel's formula, the intensity of the reflected heat should be:

m sin2(8-8)

2 sin2(8+8)

Thermalphotometer__--------=

Wedge of glass

Figure 6.8 Forbes' proposed experiment

INTENSITY OF LIGIIT 103

Here, m and n were the relative intensities of the two perpendicular components in thepolarized incident rays (m was the one with the plane of polarization parallel to theplane ofreflection). In his previous studies, Forbes had detennined that the ratio ofmto n was 100 to 27 in the polarized rays that passed through the mica pile (Forbes 1838,551).12 After the intensity of the reflected heat was recorded, Forbes rotated the pile ofmica 90 degrees and made a new measurement. Because turning the mica pile did notalter the path of the heat rays, the impact of scattered heat was effectively controlled.Now, according to Fresnel's fonnula, the intensity of the reflected heat should become:

I = ~ sin2(8-fi) + m tan2(8-fi)

2 2 sin2(8+fi) 2 tan2(8+fi)

The difference between these two measurements was:

II -12

= (m -n) [sin2(8-fi) _ tan

2(8-fi) J

2 sin2(8+fi) tan2(8+fi)

Since the values ofm and n were already known, Fresnel's fonnula could then be testedby comparing the difference between the two fractions with the difference between thetwo measurements.Forbes's design was beautiful, but he could not carry out the experiment. The

obstacle was the intensity level of the reflected heat, which was too weak to bemeasured after both refraction and reflection. "I fear we must wait for yet more delicateinstruments to measure it," he conceded (Forbes 1839, 480). Nevertheless Forbesinsisted that his approach was better than Potter's direct visual method. Although his"thennal photometer" only measured the reflection of heat, and his verification ofFresnel's fonnula could only be analogical, his approach was reliable; on the contrary,"photometric methods are so very imperfect as I still consider them to be, howeverdexterously employed" (Forbes 1840, 103). The reliability of his thennal approachcame from the measuring procedure, which converted the thennal effect to angulardeviation and thus reduced the dependence upon the eye to a minimum. In contrast,although Potter's visual photometer measured the reflection oflight directly, it reliedupon the eye to match brightness and thus was in essence unreliable no matter how itwas carefully operated.The criticisms from wave theorists prompted a quick response from Potter. In

1840, he published a paper in Philosophical Magazine defending his photometricresearch. Potter apparently did not understand why his critics questioned the reliabilityof the eye, and he did not offer any argument or evidence to justify the extensive useof the eye in his photometer. He instead accused his critics, particularly Lloyd andPowell, of ignorance. "As Professors Lloyd and Powell did not think it necessary tomake themselves acquainted with the subject they undertook to discuss," he claimed,"their observations do not call for any further notice in this place" (potter 1840a, 17-8).Potter devoted most of his paper to answering Forbes's criticisms. He first

104 CHAPTER 6

questioned the reliability of Forbes's measurements of reflected heat. Withoutexperience in dealing with heat phenomena, nor the necessary skills of operating the"thennal photometer," Potter was unable to replicate Forbes's experiments and couldonly play with rhetoric. Since Forbes admitted that he had experienced many"unforseen difficulties" in his experiments, Potter seized this chance and insisted thatbecause of these "unforseen difficulties" Forbes's method s "are not likely to furnishresults accurate enough for testing important laws of nature" (Potter 1840a, 19).Responding to Forbes's suspicion that his photometric measurements were all toosmall, Potter offered some empirical evidence by citing the work ofMichael Faraday.He gave details ofFaraday's photometric measurements presented in the 1830 BakerianLecture on the manufacture ofoptical glass, in which Faraday measured the reflectivepower ofplate, crown and flint glass at 45 degrees. Faraday's measurements were alsoat odds with Fresnel's fonnula, and more importantly, Faraday's measurements wereeven smaller than Potter's. For example, Faraday reported that the reflective power ofhis No.6 crown glass at 45 degrees was 4.52%, much smaller than the prediction fromFresnel's fonnula (5.366%). By pointing out the consistency between Faraday's andhis own measurements, Potter claimed that the discrepancies between Fresnel'spredictions and photometric measurements were substantial. Furthennore, Potter notedthat, in effect, Faraday's photometric measurements could be used as an experimentacrucis to test the wave theory, because "in high refracting bodies the discordance ofFresnel's fonnula with experiments is palpable, for it gives results frequently one-halfmore, to twice as much as experiment"(Potter I840a, 20).

In the same paper, Potter also complained bitterly that his critics had ignored thesignificance of his photometric experiments and decried the criticisms of hisphotometric measurements as a sign ofa trend in optics that blindly admired Fresnel'stheory but overlooked the value ofexperimentation. He complained that, "The fashionofpinning their faith on Fresnel's sleeve having become general amongst the influentialin learned societies, and amongst the most eminent in mathematical attainments, ...""My objections to Fresnel's fonnula for the intensity of light reflected and transmittedby transparent bodies, although founded on laborious and careful experimentalresearches, have been treated as though other men's guesses were more worth than myexperiments" (Potter 1840a, 16-7). With a desire to fmd out "the truth according to theprinciples laid down by Lord Bacon," Potter asserted that photometry should be anexperimental foundation for physical optics and proclaimed that he would continue touse this method to expose the wave theory's problems.

6. POTTER'S ATTACK ON THE WAVE ACCOUNT OF DIFFRACTION

Potter's judgment of the wave theory was firmly shaped by his early photometricresearch, and he never changed his mind regarding the wave theory even after he hada chance to study it at Cambridge. After he graduated from Cambridge and held theprofessorship at University College, Potter continued to use photometric measurementsto challenge the wave theory. In 1840, he published an article in Philosophical

INTENSITY OF LIGHT 105

Magazine criticizing Huygens's principle, a fundamental doctrine of the wave theory.Huygens's principle stated that each point of a wavefront could be considered as a newsource of wave motions. Using Huygens's principle and the interference principle,wave theorists had successfully explained a large number of optical phenomena,including the linear propagation of light, which had been a formidable difficulty to thetheory before Fresnel. However, Potter argued in this paper that Huygens's principlewas problematic because he was able to derive several obviously absurd consequencesfrom it, all ofwhich were related to the intensity oflight.

In his analysis, Potter examined two cases that had not been touched by the wavetheory: the intensity of light in the diffraction fringes produced by a circular apertureand by a circular disc. Starting from Huygens's principle and the general equation ofwave propagation adopted by the wave theory, Potter derived a formula that describedthe intensity of light in the diffraction fringes along a straight line behind a circularaperture. This formula, however, implied that the intensity of light along this line wasalways the same, regardless ofwhether the shape of the aperture was a complete circleor just a portion of it. For the diffraction fringes produced by a circular disc, Potter alsodeduced a formula with meaningless implications. Instead of predicting slowlydiminishing intensity behind the disc, it gave a series of maximum and minimumintensity that stretched along the line to an infinite extent. These implications couldonly be possible by assuming that light traveled like sound. Potter thus claimed that"The result of the [Huygens's] principle is therefore that light ought to bend into theshadows of bodies to an indefinite extent, as sound is known to pass through allapertures, and bend round all obstacles" (Potter I840b, 246). But this assumption wasobviously absurd, and so was Huygens's principle, Potter implied.Potter's challenge to the wave theory stimulated immediate responses from wave

theorists. The first reaction came from John Tovey. Just two months after Potterpublished his paper, Tovey sent a short remark to Philosophical Magazine, claimingthat Potter's analysis of Huygens's principle was completely wrong. According toTovey, when Potter derived his formulas that described the intensity of light in thediffraction fringes produced by a circular aperture and by a circular disc, he onlyconsidered a luminous line connecting a single point at the wavefront and a single pointin the fringes. Potter had not taken other lines that originated from other points o(thewavefront into account. A single luminous line, however, was merely a geometricalconception, from which no interference could develop, nor any diffraction fringes.Thus Tovey concluded that "it appears then that Mr. Potter has mistaken a luminousline for a luminous space; and consequently, that his conclusions have, in reality, nofoundation" (Tovey 1840,432; original emphasis).Another reaction to Potter's challenge came from Airy. In 1841, Airy published a

paper in Philosophical Magazine entitled "On the diffraction of an annular aperture."At the beginning of this paper, Airy stated, "I had no wish to make a communicationto you which should assume the form of a discussion with Mr. Potter, and I proposed,therefore, in adverting to the subject to which Mr. Potter has alluded in your Numberof October last, rather to add something to the investigation of a point which has

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perhaps been passed over too lightly by writers on the Undulatory Theory, than toemploy myself specially in indicating what I consider to be failing steps in Mr. Potter'sreasoning" (Airy 1841, I). Airy did not analyze in his paper where Potter's analysiswent wrong. Rather, he devoted the whole paper to developing a comprehensive theoryon the diffraction produced by a circular aperture and by a circular disc. Airy believedthat he could effectively eliminate the confusions created by Potter by offering a correctwave based account of the phenomena.Unlike Potter, who only considered the intensity of light along one geometrical

line, Airy took the whole space behind a circular aperture or behind a circular disc intoaccount. Starting from the equation of wave propagation, through a sophisticatedmathematical analysis, Airy obtained a formula for the intensity of light in thediffraction fringes produced by a circular aperture or by a circular disc. This formulaindicated that, in the diffraction fringes caused by a circular aperture, there should bea bright spot at the center of the fringes, surrounded by a series ofdark and bright rings.The intensity of the bright spot was double that ofthe source. In the fringes caused bya circular disc, there should be a bright spot at the center of the shadow, and theintensity of the bright spot should be equal to that of the uninterrupted light. Thesurrounding rings were much feebler, and their intensities decreased rapidly until theybecame insensible (Airy 1840,9). Airy believed that all these implications regardingthe diffraction fringes of circular aperture and circular disc were in agreement withobservations. He thus concluded that, despite Potter's objection, both the wave theoryin general and Huygens's principle in particular stood "as firmly as they did before,"and "perhaps even more firmly" (Airy 1840, 10).Airy's comprehensive analysis of the diffraction fringes of circular apertures and

circular discs did not silence Potter. In June 1941, Potter published a paper inPhilosophical Magazine in which he narrowed his focus to the diffraction fringes of acircular disc and reported several photometric experiments that were apparentlyinconsistent with Airy's predictions. Potter's experimental setting was simple. Usinga lathe, he prepared several circular discs of brass with diameters of 1120, 1110,2110,3110, 4/10, and 7110 of an inch. The light source was a beam of sunlight formed by alens at 60 inches from a circular disc. He put an eyepiece 60 inches behind the disc toobserve the diffraction fringes. Looking through the eyepiece, Potter saw a bright spotat the center of the shadow cast by the disc, surrounded by a number of colored rings.Using a 1/20 inch disc, Potter reported that the central bright spot in the shadow waslarge, and so bright that "at the first view it would have been taken to be equally brightwith the light which had passed uninterruptedly" (Potter 1841, 154). From hisexperience in photometric experiments, however, Potter soon realized that the spot wasnot so bright as it looked. Since the bright spot was surrounded by a dark ring, itappeared to be brighter than it was due to contrast.Potter invented a special technique to eliminate the effect of contrast. Using a fine

needle, he punched a number of small circular holes of different sizes in a thin sheetofbrass. The brass sheet was placed in the focus of the eyepiece so that one ofthe holeswas exactly behind the central part of the bright spot. Through the hole, Potter was able

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to observe the central spot without the effect of contrast. Potter used another hole ofequal diameter to observe the uninterrupted light and compared its intensity with thatof the central spot. He immediately found that the brightness of the central spot wasmuch less intense than that of the uninterrupted light. After repeating the observationsusing discs of different sizes, Potter found that the larger the disc, the greater thedifference between the intensity of the central spot and that of the uninterrupted light.To estimate the intensity of the central spot generated by the 1/20 of an inch disc,

Potter used a simple extinction photometer. He prepared a number of thin mica platesof identical thickness and then placed them before the uninterrupted light to see howmany plates were needed to reduce the light's intensity to a level equal to the centralspot. After many trials, he concluded that four mica plates produced the mostsatisfactory result. To estimate the extinction effect of the four mica platesquantitatively, Potter obtained a standard two-to-one intensity ratio by using an Icelandspar to partially overlap two bright spots. Through experimentation, he found that theintensity ratio of the light passing through three mica plates to incident light was almostidentical to the standard two-to-one ratio, that is, three mica plates transmitted about50% ofthe incident light. This fmding implied that a single mica plate transmitted lessthan 80% of the incidence, and four mica plates allowed about one-third of the incidentlight to pass through. Thus, the intensity of the central spot in the diffraction fringesproduced by a 1/20 of an inch disc was about one-third of the original. Thisexperimental result, according to Potter, contradicted Airy's theoretical prediction thatthe brightness of the central spot should be equal to that of the uninterrupted light forall sizes of discs.Thus, Potter claimed that he had found another fact in conflict with the wave

theory. Although his photometric methods were constantly challenged by his rivals,Potter was quite confident in the reliability ofhis experimental results and believed thathis experimental results could playa decisive role in the dispute between the two rivaltheories of light. At the end of his paper, he claimed, "I must be allowed to state, thatI consider the controversy, as to the undulatory theory being the physical theory oflight, to be nearly terminated; and that the experiments necessary for completing thebasis of a physical theory are those now most desirable to be undertaken" (Potter 1841,155). So Potter continued his battle against the wave theory, even after Brewster gaveup his objections. In 1859, Potter even published a textbook with the title Physicaloptics: The corpuscular theory of light, discussed mathematically, in which heproposed a new particle theory to replace the well-established wave theory (Potter1859).

CHAPTER 7

INSTRUMENTAL TRADITIONS

During the optical revolution, there were different styles of operating opticalinstruments, and their impact on the dispute between the two rival theories of light wasevident. The differences in the use ofoptical instruments during the optical revolutionoriginated from two incompatible instrumental traditions. This chapter begins with abrief historical review of these instrumental traditions. In their early years, opticalinstruments functioned primarily as visual aids to the eye, which was regarded as anideal optical instrument. But when more and more optical instruments were used asmeasuring devices, the reliability of the eye came into question. In this context, thereemerged two incompatible instrumental traditions, each ofwhich endorsed a body ofpractices, both articulated and tacit, that defined how optical instruments should beoperated, and particularly, how the eye should be used in optical experiments.

I. OPTICAL INSTRUMENTS AS IMAGE-MAKING DEVICES

One of the oldest optical instruments is spectacles, or eyeglasses, which consist of twoconcave lenses, one for each eye, mounted in a hand-frame. Spectacles first appearedin Italy around the end of the thirteenth century, and their inventor was probably aglass-worker of Pisa who kept his method secret for trade reasons (Rosen 1956).Originally, spectacles were observing devices, helping people with poor eye sight. Butthe knowledge ofmaking and improving spectacles eventually led to the invention ofthe most important optical instrument in the early modem age: the refracting telescope.Most historians believe that Hans Lippershey, a spectacle maker in Holland,

invented the first refracting telescope in 1608. After learning ofLippershey's invention,Galileo started to construct his own telescope in 1609. He obtained two eyeglasses froma spectacle maker, one convex and the other concave, and fitted them into the ends ofa tube. "Then, applying my eye to the concave glass," he later recalled, "I saw objectssatisfactorily large and close. Indeed, they appeared three times closer and nine timeslarger than when observed with natural vision only" (Galileo 1989, 37). Galileo neverclaimed that he was the inventor ofthe telescope, and often referred the credit to the"Dutchman." But he was the first person who pointed it to the heavens. With the helpof the telescope, Galileo saw that the surface of the Moon was not smooth, nor evenperfectly spherical, which contradicted the beliefs held by many natural philosophers.

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X. Chen, Instrumental Traditions and Theories of Light© Springer Science+Business Media Dordrecht 2000

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He also saw that Jupiter was surrounded by a round disk, which consisted of four smallstars. Observations over the next few months showed further that these newly foundstars always wandered around Jupiter -- they were the moons of Jupiter. At that time,a major difficulty of the Copernican theory was to explain why, if the Earth were aplanet, it seemed to be the only one to have a moon rotating around it. The discoveryof Jupiter's moons thus answered a major criticism of the Copernican theory: theuniverse in fact has more than one center ofmotion, and the Earth is not the only planetto have a moon. Galileo's telescopic observations offered the hard evidence to supporta new way of thinking in astronomy. As pointed out by many historians, it is hard tooverstate the importance ofGalileo's telescopic observations. I

In his telescopic exploration, Galileo used the telescope primarily as an imagemagnifier, which enlarged optical images for better perception by the eye. As an imageamplifier, the magnifying power of a telescope became the most important factor inevaluating its quality. Galileo quickly became unsatisfied with his first telescope, whichhad a magnification power of three. He made a great effort to search for methods ofmaking more powerful telescopes. 1 He soon learned that to increase the magnifyingpower, he needed to "grind the concave lens deeper than is done for spectacles to aidthe nearsighted and to shape the convex lens to the radius of a very large sphere"(Drake 1983, 10). To keep the secret of his discovery, Galileo decided to make thelenses himself. Because the local spectacle shops could not supply him the appropriateglass, which must be hard and clear and of a certain thickness, Galileo ordered itdirectly from Florence. After several months of hard labor, Galileo made anothertelescope with a magnifying power of eight, then another of 20 magnification power,and finally one of30 magnification power.Isaac Newton was the first person who systematically applied optical instruments

to the study of light. Among Newton's apparatus, the central piece was the prism.Unlike lenses, prisms did not play any significant role in early astronomicalobservations. They were originally used to make chandeliers or as entertaining devicesto generate prismatic colors (Schaffer 1988, 73). But in the early seventeenth century,natural philosophers such as Descartes and Boyle began to use prisms in theirinvestigations. To illustrate the formation of the rainbow, Descartes used a prism toshow how colors formed at the boundary between light and dark. Boyle also used aprism to produce a colored spot, and then cast the colored spot upon a colored object.With this experiment, he showed that the Aristotelian distinction between the colors ofbodies and the colors of light was wrong, because prismatic colors combined with"real" colors in the same way as "real" colors did with each other. Newton learned ofthese experiments with prisms from his readings of Descartes, Boyle, and othermechanical philosophers.In the summer of 1664, Newton obtained his first prism, perhaps at Stourbridge Fair

in Cambridge. He bought another one from the same place in 1665 in order to checkDescartes's hypothesis of colors (Mills 1981, 14). Eventually, he accumulated severalprisms with different angles, including 60 degrees, 62.5 degrees, 63.5 degrees, and 64degrees. Later he also constructed a hollow prism, made of four pieces of polished

INSTRUMENTAL TRADITIONS 111

plane glass and filled with water. The first thing Newton did with the prism was simplyto look at objects through it. He saw that straight lines parallel to the axis of the prismno longer appeared straight. He then set up an experiment in which he painted a slip ofpaper halfblue and half red and looked at the slip through a prism. He saw that the blueportion of the slip appeared to be higher than the red one, which indicated that the bluerays were refracted more than the red rays (Hall 1993, 36-7).To demonstrate the unequal refraction ofdifferent colors, Newton in 1666 carefully

designed an experiment in which a beam of sunlight went through a triangular prismand projected an image onto a screen. Before Newton, della Porta and de La Chambrehad conducted similar prismatic experiments, but they saw only a circular white imagesurrounded by colored fringes because both of them had placed the screen just a fewfeet away from the prism (Shapiro 1996,69). Newton, however, set the screen 22 feetfrom the prism and obtained a completely different result. The'image was a fullycolored and elongated spectrum: its breadth was less than three inches, but its lengthwas almost 14 inches. This spectrum, according to Newton, "definitely appears toestablish that at equal incidence some rays undergo a greater refraction than other"(Newton 1984,53). In other words, the prism clearly proved the unequal refrangibilityof light. In this way, Newton's prism became an optical apparatus that, he thought,could reveal the nature of light.

In the hands ofNewton and other seventeenth-century mechanical philosophers, thefunctions of optical instruments gradually evolved. In Galileo's telescopicinvestigation, he used the telescope primarily as a visual aid to magnify existing opticalimages for better perception by the eye. But Newton and his contemporaries usedoptical instruments, particularly the prism, in a different way. They used the prism togenerate optical effects that were not available in nature or not perceivable directly bythe naked eye. Without the prism we would never be able to see an elongated spectrum.Thus, after the seventeenth century, optical instruments were assigned a new function:they were not just image detectors but also image generators. This new role of opticalinstruments eventually transformed optics from an observational to an experimentalscience.

2. THE EYE AS AN OPTICAL INSTRUMENT

Before the invention of the telescope, the eye was known to be the most complexoptical system, and it had been carefully studied since antiquity. Around theseventeenth century, associated with the trend of the "mathematization of nature," amechanistic hypothesis became dominant in the study ofvision. This mechanistic view,first advocated by Kepler, interpreted the eye simply as a camera obscura, a machinefor taking pictures of the external world. To be more precise, the eye was seen as anoptical instrument with an aperture, a concave lens, and a screen. By arguing that themechanism of the eye was the same as those operating in the mechanical world, Keplertried to show that the eye was in fact a dead organ (Crombie 1967,52-63). Later,Descartes further enhanced this mechanical interpretation ofvision by arguing that not

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only was the eye a dead apparatus, but also that the whole body was a dead machine.Following this mechanistic hypothesis, Kepler offered an account for the perception ofdistance. He believed that we estimated the distance to an object by implicitly drawinga triangle with its apex in the object and its base in the pupils. We then determined thedistance to the object through geometric calculation: the smaller the degree ofdivergency, the longer the distance. By the end of the seventeenth century, thedominant beliefamong natural philosophers was that the eye was a passive receiver thatcould be analyzed and understood solely in geometric terms.At the beginning of the eighteenth century, however, George Berkeley began to

challenge this mechanistic view of vision. In his Essays Towards a New Theory ofVision, Berkeley developed his criticisms of the mechanistic view by analyzing theperception of distance. According to Berkeley, the mechanistic interpretation of visionthat used such geometric parameters as lines and angles in its analysis had a seriousproblem: we did not have direct perception of angles nor lengths. Berkeley insistedthat, "Those lines and angles have no real existence in nature, being only a hypothesisframed by the mathematicians, and by them introduced into optics that they might treatof that science in a geometrical way (Berkeley 1963,23). Thus, we could not acquirethe perception of distance by using geometric calculations; instead, we did so byappealing to our past experience. To account for vision, Berkeley proposed a newmodel based on a metaphor of language acquisition. The way that we determined thedistance of an object, he said, "is the same with that of languages and signs of humanappointment; which do not suggest the things signified by any likeness or identity ofnature, but only by a habitual connection that experience has made us to observebetween them" (Berkeley 1963, 92). The objects of vision were not images, butlanguages that we learned through experience. Consequently, we used not just the eye,but also the mind to form visual perception. For this reason, Berkeley insisted thatgeometric optics was inappropriate for the study of vision.Berkeley's theory ofvision caused strong reactions among many eighteenth-century

natural philosophers. There were three different attitudes in responding to Berkeley(Cantor 1990, 435-46). The first one, represented by Benjamin Martin, Samuel Dunn,Joseph Harris and William Porterfield, opposed Berkeley and continued to accept thegeometric approach. Another one, represented by Fran~oisVoltaire, Adam Smith andDavid Hartley, supported Berkeley and adopted the language metaphor of vision. Thelast one, which is most interesting for our discussion, held a compromise position. Arepresentative of this attitude was Thomas Reid, one of the most influential figures inthe school of Scottish commonsense philosophy. Reid, on the one hand, adoptedBerkeley's language metaphor extensively and recognized the roles of experiences andcustoms in perception, and he praised the ''just and important observation of the BishopofCloyne, that the visible appearance of objects is a kind of language used by nature,to inform us of their distance, magnitude and figure" (Reid 1997, 82). On the otherhand, Reid believed that geometry could still be useful in representing the relationshipbetween an object and its sign, and he devised a "geometry ofvisibles" solely for thepurpose of analyzing visual phenomena. Reid's solution to Berkeley's challenge was

INSTRUMENTAL TRADITIONS 113

to divide the phenomena of vision into two separated fields: one corresponding togeometric optics where geometrical analysis was effective, and the other topsychological optics where images and experiences were the main concerns.The philosophical understanding ofvision profoundly affected how the practitioners

in optics handled the relationships between the eye and other optical instruments. Longbefore Berkeley introduced his theory of vision, it was common knowledge that visioncould be deceptive. But those who adopted the mechanistic interpretation believed thatthey could fix the defects of the eye by mechanical means so long as the defects couldbe accounted for by geometric principles. Galileo's solution to visual illusionsexemplified this approach. In his telescopic observations, Galileo found that thetelescope did not enlarge the images of the stars in the same proportion as it did theimage of the Moon. He noted that a telescope capable ofmultiplying other objects 100times barely enlarged the images of the stars by four to five times. At first glance, thisstrange phenomenon seemed to suggest that the telescope was defective, but Galileoinsisted that the problem was actually rooted in another component of the opticalsystem -- the eye. He explained, "The reason for this is that when the stars are observedwith the naked eye, they do not show themselves according to their simple and, so tospeak, naked size, but rather surrounded by a certain brightness and crowned bytwinkling rays, especially as the night advances. Because of this they appear muchlarger than if they were stripped of these extraneous rays, for the visual angle isdetermined not by the primary body of the star but by the widely surroundingbrilliance" (Galileo 1989,57). Because the images ofthe stars were always surroundedby luminous circles, they appeared to be deceptively large.2

Galileo went on to explain how the eye generated these luminous circles. He firstpointed out the subjective nature of these circles. They were visual illusions, similar tothe halo around a candle perceived by someone with a particular illness. Galileo thenoffered an account for these luminous circles in terms of geometric optics byidentifying two causes: they were made either "by refraction in the moist surface of theeye," or by "reflection of the primary rays in the moisture at the edges of the eyelids,and it extends over the convexity of the pupil" (Galileo 1623,319). Unlike those visualillusions associated with illness, the luminous circles surrounding the images of thestars were accounted for by geometric principles -- they resulted from the angulardeviation of the light beams.Thus, we could in principle eliminate these luminous circles by mechanical means,

with the help of a carefully designed optical instrument. Galileo noted that we usuallydid not see luminous circles when looking at the Moon. He speculated that the reasonwas that the image of the Moon was big enough to fill the whole eye, leaving the eyeno room for the luminous circles. Thus, the key to eliminating those luminous circlessurrounding the images of stars was to enlarge the images of the stars so that they werebig enough to fill the whole eye. A telescope with an appropriate magnification powercould easily achieve this goal. By enlarging the images, the telescope simply "takesaway the borrowed and accidental brightness from the stars and thereupon it enlargestheir simple globes (if indeed their figures are globular), and therefore they appear

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increased by a much smaller ratio" (Galileo 1989, 58). In this way, an opticalinstrument, the operation of which was fully accounted for in terms of geometricprinciples, corrected an inherent defect of the eye. Surely the telescope was alsoimperfect, but, according to Galileo, it was much superior to the eye in the observationof stars. Thus, Galileo implied that the key to a reliable optical system was not the eye,but a well designed optical instrument, such as his telescope.Those who were sympathetic to Berkeley's view of vision, however, handled the

relationship between the eye and other optical instruments in a substantially differentway. To illustrate the differences, let us briefly take a look ofthe development of thecamera obscura. Many natural philosophers frequently used the camera obscura as amodel to illustrate the mechanical nature of the eye, but, ironically, the camera obscurawas also the optical instrument that in many ways imitated the structure of the eye.An Arabic scholar invented the camera obscura around the tenth century; it was

simply a dark room with a tiny hole in the wall projecting the view outside to a whitescreen.3 Later, the structure ofthe camera obscura gradually evolved, accompanied bya better understanding of the eye's anatomy. Around the sixteenth century, convexlenses were used to replace the hole. Soon, diaphragms, like the pupil, were adoptedto sharpen the image. And later, in the seventeenth century, Hooke introduced curvedscreens because he realized that the retina was also curved. During the cameraobscura's evolution, the eye was often used as the ideal that determined its quality.Perhaps the most vivid example is the invention of the scioptric ball. This was awooden ball with a hole drilled through its axis and a lens fitted at each end of the hole.When fixed into an opening in the wall and capable of free rotation, the ball greatlyextended the field of view in all directions. To make sure that this optical device wasreliable, its inventors actually used an eye as the standard, an ox eye to be exact. Theyput an ox eye in the hole of the wall, and then observed the image on the retina. Theywanted to prove the reliability of the artificial device by showing the identity of theimage produced by the ball and the one in the eye of an ox (Gemsheim & Gemsheim1955,8).The evolution of the camera obscura illustrates a different attitude toward the

relationship between the eye and other optical instruments. From this perspective, allman-made optical devices were inherently imperfect. The eye, however, was an idealoptical instrument, superior to all other man-made devices. Thus, an effective way toimprove the quality ofman-made optical instruments was simply to imitate the eye, andto use the eye to calibrate man-made devices.

3. OPTICAL INSTRUMENTS AS MEASURING DEVICES

Although the phenomenon of refraction was known in antiquity, the quantitative lawof refraction was not discovered until the seventeenth century. Descartes in 1637derived the sine-law (sin J / sin r = k. where J is the angle of incidence and r the angleof refraction) through kinematic analysis, assuming that light increased its speed whenit traveled from a thin to a dense optical medium.4 To test the sine-law, it became

INSTRUMENTAL TRADITIONS 115

necessary to measure accurately the angles of incidence and refraction. For practicalreasons, fluids were usually used as the medium. Ptolemy's method ofmeasuring therefraction of fluids was still popular in the early seventeenth century. The apparatuswas a circular disk graduated along its circumference, placed vertically in the fluid withthe lower half submerged. The observer determined the angles of incidence andrefraction by looking at a marker on the submerged part of the disk through a sight onthe upper part.s This method, however, could not measure the angle of refractionaccurately because, due to unequal refrangibility, the refracted beam spread out into aspectrum. According to Newton, the Ptolemaic method was "more troublesome thanwas necessary and perhaps more prone to errors than if it were freed from the entireapparatus" (Newton 1984, 173).Newton believed that, to improve the measurements, the key was to choose a

middle point in the refracted beam as the reference to determine the angle of refraction.To do so, in the mid 1660s he designed a special instrument, a refractometer (Figure7.1). It consisted of a solid beam (about nine feet) and two upright plates, one nearlyat the lower end of the beam and the other about four inches from the upper end. Asmall cylindrical vessel was placed over the upper plate, and a small hole was piercedin the base of the vessel and the plate. A piece of glass was inserted between the plateand the vessel so that the vessel remained impervious. To begin the measurement,

Quadrant

Quadrant

Figure 7.1 Newton's apparatus/or testing the sine law

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Newton filled the vessel with water and placed it under the sun. He adjusted thedirection of the beam until the refracted rays emerged from the hole perpendicularlyand proceeded toward the lower plate. Due to dispersion, the refracted rays fonned asmall spectrum, with red falling at R and purple at P. Newton further adjusted theinclination of the beam until the boundary between blue and green, the middle point ofthe refracted beam, fell at B, a point exactly opposite to the hole. This step was crucialfor the accuracy of the measurements, but difficult because the boundary between blueand green was not clear cut. Newton's solution was to increase the length of the beam.The nine-foot beam effectively enlarged the size of the spectrum in the plate so that itwas easier for him to locate the boundary of blue and green more accurately. Afterlocating the boundary, Newton used two quadrants to measure the angular parameters,one attached to the beam for measuring the refraction angle and the other for theincidence. His measurements fmally confInned the sine law.Newton and many other natural philosophers in the seventeenth century measured

refraction for testing the sine law, but there was another group of people with adifferent purpose interested in the same issue. They were makers of telescopes.Galileo's refracting telescopes had two major defects: spherical and chromaticaberration. Spherical aberration is caused by the fact that rays passing through theperiphery of a spherical lens focus at a point closer to the lens than those through thecenter, so that light from a point source does not fonn a point image. Chromaticaberration is due to the unequal refrangibility of different colors, namely that red raysalways have a longer focal length than violet ones. To reduce these defects, telescopemakers in the seventeenth century discovered a simple remedy. They found that byincreasing the focal length of the objective lens to about 150 times its aperture, theycould almost eliminate spherical aberration and reduce chromatic aberration tosomething less noticeable. Thus, refracting telescopes became longer and longer in thesecond half of the seventeenth century. The most extreme example was the telescopemade by Hevelius, with a length of 150 feet (King 1955,50-4).Newton had noticed the phenomenon of chromatic aberration, but he concluded

that, since refraction was always accompanied by dispersion, chromatic aberration wasunavoidable. No one questioned Newton's view on chromatic aberration until thebeginning of the eighteenth century when people began to realize the achromatic natureof the eye. The complex structure of the eye, consisting of different media withdifferent shapes, suggested that achromatic lenses could be created by combining lenseswith different optical properties. Following this idea, John Dollond, an instrumentmaker in London, successfully made an achromatic lens in 1757 by combining aconcave flint lens and a convex crown lens.6 But Dollond's lenses were still imperfect,partly because of the limited dispersive power of the flint glass. To make betterachromatic lenses, opticians in the late eighteenth century began to search fortransparent materials with high dispersive power, and some of them, like Robert Blair,ended up using fluids, some of which were highly dispersive. All these efforts atmaking achromatic lenses required better measurements of the optical properties of thematerials, such as their refractive power and dispersive power. Consequently, there was

INSTRUMENTAL TRADITIONS 117

a strong demand for precise optical measurements from those making achromaticlenses.In the early nineteenth century, Brewster made the first attempt to measure the

refractive indices of more than a hundred transparent substances.? Brewster'smeasuring method was similar to the one suggested by Euler. The apparatus was in facta modified compound microscope, consisting of an objective lens, a field lens, and aneyepiece (Figure 7.2). Brewster first looked through the optical system at an object andadjusted the position of the object until a distinct image of it fonned at P. He theninserted the transparent fluid to be examined between the objective lens and a thin glassplate. The fluid fonned a plano-concave lens, which decreased the magnification powerof the system and increased its focal length. To maintain the distinctness of the image,the object had to be moved from its original position M to a new position N. Bymeasuring the distance between M and N, Brewster could calculate the refractive indexof the fluid.8

Maintaining the eye in its optimal condition was the key to obtaining accuratemeasurements with Brewster's apparatus. The crucial steps in Brewster's measurementswere the operations that adjusted the position of the object to fonn a distinct image atP. Brewster relied upon the eye to detennine the distinctness of the image, but the focallength of the eye could vary, and so did its judgment. Brewster recognized thisproblem, and he invented a special technique to stabilize the focal length of the eye. Heexplained, "in order to prevent any error in judging of the instant of distinct vision,from a variation in the focal length of the eye, a delicate fibre of glass, with atransparent axis, was stretched across the diaphragm, at the anterior focus of the eye­glass" (Brewster 1813b, 250). By looking at the fibre, the observer could fix the focusof his eye in the same place during the measuring process and avoid misjudgment ofthe distinctness of the image.In addition to the practical needs of making achromatic lenses, there was another

source in the early nineteenth century that nurtured the development of precisemeasurements in optics. Although optics had been in the domain ofmixed mathematicssince Newton's time, it only used geometry, trigonometry and algebra, and it couldonly offer mathematical treatments to a limited number of optical phenomena such as

Eyepiece

Field lens

Fluid

M N

Figure 7.2 Brewster sapparatus for measuring refractive indices

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reflection, refraction and Newton's rings. But Fresnel and his followers, such asCauchy, substantially changed the relationship between optics and mathematics. Usingsuch powerful analytic tools as differential and integral equations, Fresnel and hisfollowers were able to provide quantitative analyses for most of the known opticalphenomena. Wave theorists frequently cited the capacity of making quantitativeaccounts as the key evidence for their theory. For example, in his 1834 report to theBritish Association on physical optics, Lloyd stated that "in making [the comparisonbetween the wave and the particle theories of light] it is not enough to rest in vagueexplanations which may be moulded to suit any theory. Whatever be the apparentsimplicity ofan hypothesis -- whatever its analogy to known laws -- it is only when itadmits of mathematical expression, and when its mathematical consequences can benumerically compared with established facts, that its truth can be fully and [mallyascertained" (Lloyd 1834, 19). Nevertheless, no one could deny that the fate oftheories, including those highly mathematicized, must eventually be detennined on anexperimental basis. Thus, quantitative theories required numerical data, and highlymathematicized theories such as the wave theory of light needed evidence from precisemeasurements. When the wave theory was able to make numerical predictionsexpressed in precise quantities, experimental opticians felt the pressure to offermeasurements with similar accuracy levels to either support or disprove the theory.

4. WHEWELL ON OPTICAL MEASUREMENTS

The need for precise numerical data stimulated reflections and discussions in the opticalcommunity on the methodology of optical measurements. In his Philosophy of theInductive Science, Whewell offered an interesting analysis of optical measurements.Whewell started his analysis from the demarcation between the so-called primary

and secondary qualities, proposed first by John Locke in the seventeenth century.According to Locke, primary qualities such as shapes, sizes, motion, and postures "areutterly inseparable from the body, in what estate soever it be; ... such as senseconstantly [mds in every particle ofmatter which has bulk enough to be perceived, themind finds inseparable from every particle ofmatter, though less than to make itselfsingly perceived by our sense." Secondary qualities such as colors, sounds and tastes,however, "are nothing in the objects themselves, but powers to produce varioussensations in us by their primary qualities, Le. by the bulk, figure, texture, and motionof their insensible parts" (Locke 1823, vol. 1, 119-20). Most British naturalphilosophers accepted the distinction between primary and secondary qualities, but noteveryone agreed with Locke's specific interpretation.According to Whewell, the distinction between primary and secondary qualities was

plain and clear. He believed that such a distinction "is assented to by all, with aconviction so finn and indestructible, that there must be some fundamental principleat the bottom of the belief' (Whewell 1847, vol. 1,279). There were many ways todistinguish primary and secondary qualities. For example, we could perceive primaryqualities directly and immediately, but could only perceive secondary qualities through

INSTRUMENTAL TRADITIONS 119

media. But with respect to the issue of measurement, Whewell claimed that theirdifferences consisted mainly in their ways of inducing measuring units.To measure an object, Whewell explained, we needed a measuring unit, which

could be a yardstick in length measurements or a standard weight in weightmeasurements. By dividing the object to be measured by the measuring unit, we gaineda quantitative result. Obviously, we did not have a universal unit that could fit alldifferent kinds ofmeasurements; different kinds ofobjects required different measuringunits. To measure a primary quality, however, acquiring a proper measuring unit wasstraightforward, because we could always use a part of the object to be measured as themeasuring unit. This feature resulted from the fact that primary qualities weremeasurable of themselves. The magnitudes of primary qualities always changed byaddition or reduction ofextension. For example, a space was doubled when we placedanother equal space by its side, and ifwe put a weight on top of another their weightwas made up of the sum ofthe two. The same was also true along the opposite directionof reduction. Primary qualities "can at will be resolved into the parts of which theywere originally composed, or any other which the nature of their extension admits; theirproportion is apparent; they are directly and at once subject to the relations ofnumber"(Whewell 1847, vol. 1, 320). Thus, to measure the length of a room, we could use anylinear interval within the room as the yardstick. Similarly, to measure the weight of anobject, we could use the heaviness of any of its parts as the unit. A primary qualityusually offered us more than one measuring unit, but all of these units were objectivebecause they were parts of the objects. Consequently, the measurements of primaryqualities could be reliable, in the sense that we should in principle be able to agree witheach other on the measuring results if we followed the proper measuring procedure.Of course, not all units for measuring primary qualities were equal, Whewell

reminded us. We frequently used some rather arbitrary units to measure primaryqualities. In measurements of linear space, for example, many measuring units adoptedin the past were merely conventional, such as a foot, a cubit or a fathom, all ofwhichoriginated from parts of human bodies. Even among those who adopted "foot" as theunit, there were still a great number of different standards in Europe, such as theEnglish foot, the Paris foot and the Rhenish foot, just to mention a few. Using them asthe measuring units, people frequently ended up with different results even though theywere measuring the same object. On the other hand, some measuring units were"natural" and not arbitrary. For example, in the measurement of angular space, acommon practice was to divide the whole circumference into 360 parts or degrees andto use one of these parts as the unit to measure the arc of a circle. This angularmeasuring unit was different from all others used in linear measurements, Whewellsaid, "for there is a natural unit, the total circumference, to which all arcs may bereferred" (WhewellI847, vol. 2, 340; original emphasis). Thus, to obtain accurate andreliable measurements for primary qualities, Whewell recommended that we shouldadopt natural measuring units like arc-degree whenever it was possible.Unlike primary qualities, secondary qualities were not measurable of themselves,

because the magnitudes of secondary qualities changed by increase or decrease of

120 CHAPTER 7

intensity. Although we might increase the magnitude of a secondary quality bycombining one with another, "the increase is absorbed into the previous amount, andis no longer in evidence as a part of the whole" (Whewell 1847, vol. 1, 320). Forexample, we could not double the temperature ofwater by adding an equal amount ofwater with the same temperature, nor could we duplicate the intensity of light throughimposing one bright spot on another. Similar problems also occurred along thedirection of reduction. Secondary qualities "cannot be resolved into smallermagnitudes; we can see that they differ, but we cannot tell in what proportion; we haveno direct measure of their quantity"(WheweIl1847, vol. 1,320). Thus, we could notuse a part of the object as the unit when measuring secondary qualities. To determinethe quantity of a secondary quality, we must introduce a conventional unit, such as acentigrade scale in temperature measurements or a set of color terms in colormeasurements. These units were not objective, because they were not parts ofsecondary qualities. Consequently, measurements of secondary qualities would neverbe as reliable and accurate as those of primary qualities. We might not be able to agreewith each other on the measuring results even if we followed correct measuringprocedures.To illustrate the correct procedure for measuring secondary qualities, Whewell

offered a detailed analysis of the measurements ofrefractive indices. A popular methodwas the one used by Newton, who measured refractive indices, or the refractiveproperty of transparent media, by directly observing the deviation of the refracted rays.Due to dispersion, the refracted rays always spread out to form a spectrum, and itbecame necessary to select a reference point in the spectrum to represent the deviation.Locating the reference point required the spectrum to be divided into several areasaccording to some standard. A common method was to divide the spectrum accordingto a group ofconventional color terms, such as red, orange, yellow, green, indigo, blueand violet. This was exactly how Newton selected the reference point in hismeasurements: he located the point at the boundary of blue and green. But inWhewell's view, Newton's selection of the reference point was entirely subjective andarbitrary because the distinctions between colors depend upon the physiological andpsychological state of the observer. "What one person calls bluish green another callsgreenish blue. Nobody can say what is the precise boundary between red and orange.Thus the prismatic scale of colour was incapable ofmathematical exactness, and thisinconvenience was felt up to our own times" (Whewell 1847, vol. 1,327-8; originalemphasis).A fundamentally different method of measuring refractive indices was the one

proposed by Fraunhofer. Instead of directly measuring the deviation of the refractedrays, Fraunhofer used a prism and an achromatic telescope to convert the optical effect(the refrangibility of light) to a primary quality: the locations of a group of spectrallines. He treated these spectral lines as pure geometric entities, that is, they were lineswithout width. With the help of a theodolite, Fraunhofer was able to determineprecisely the angular positions of these geometric lines, and subsequently calculatetheir refractive indices. Using the spectral lines, Fraunhofer eliminated the subjective

INSTRUMENTAL TRADITIONS 121

and arbitrary reference used in the previous measurements, and his measuring resultsno longer relied upon the physiological and psychological state of the observer.Because of Fraunhofer's discovery, "we have now no uncertainty as to what colouredlight we are speaking of, when we describe it as that part of the spectrum in whichFraunhofer's line C or D occurs. And thus, by this discovery, the prismatic spectrumof sunlight became, for certain purposes, an exact Chromatometer" (WhewellI847,vol. 1, 328; original emphasis).According to Whewell, Fraunhofer's procedure of measuring refractive indices

established an exemplar for precise optical measurements. To measure an optical effectin an accurate manner, Whewell suggested that we should first search for a way toconvert the optical effect to a primary quality, ideally the angular positions of ageometric object, and then measure the geometric parameter by means of its naturalunit. Converting a secondary quality to a primary quality required the help ofappropriate instruments. In the case ofFraunhofer, this was the combination ofa prism,an achromatic telescope and a theodolite. But many other instruments could alsoperform the same conversion. For example, a combination of a plane and a thinconcave lens could also transform the refrangibility of light to a primary quality -- thepositions of a group of interference fringes (Newton's rings). Thus, it was crucial to useproper optical instruments, which converted optical images into geometric signals andprovided the proper measuring scale. "We cannot obtain any sciential truths respectingthe comparison of sensible qualities, till we have discovered measures and scales of thequalities which we have to consider; and accordingly, some of the most important stepsin such sciences have been the establishment of such measures and scales, and theinvention of the requisite instruments" (Whewell 1847, vol. 1,321).

5. THE VISUAL TRADITION

In the late eighteenth and early nineteenth centuries, there was a widely held belief thatthe eye was a fme and complex optical instrument. Most textbooks of optics publishedduring this period included a chapter on the eye in the section on optical instruments.But some natural philosophers took one step further to argue that the eye was not onlya delicate, but in fact an ideal optical instrument. For example, Reid believed that '(thestructure of the eye, and of all its appurtenances, the admirable contrivance of naturefor performing all its various external and internal motions, and the variety in the eyesofdifferent animals, suited to their several natures and ways of life, clearly demonstratethis organ to be a masterpiece ofNature's work" (Reid 1997, 77). Some even arguedthat the eye was the perfect sense organ because it was designed by the Creator. PeterRoget, for example, claimed that "On none of the works of the Creator, which we arepermitted to behold, have the characters of intention been more deeply and legiblyengraved than in the organ of vision ...; and the most profound scientificinvestigations of the anatomy and physiology of the eye concur in showing that thewhole of its structure is most accurately and skillfully adapted to the physical laws oflight, and that all its parts are finished with that mathematical exactness which the

122 CHAPTER 7

precision of the effect requires" (Roget 1836, vol. 2, 316).No one denied that the eye could be deceptive. But for those who had strong faith

in the eye, the defects associated with vision were extrinsic and accidental. They werecaused by imperfect physiological or psychological conditions that prevent the eyefrom functioning normally and properly. For example, the eye could lose its sensitivity,could be out of focus, and could even experience all kinds of false illusion. But thesedefects were preventable by taking proper procedures to ensure the eye was in itsoptimal condition.Such a strong faith in the eye entailed special relationships between the eye and

man-made optical apparatus. Since the eye was an ideal optical instrument, it offereda model for the perfection ofman-made apparatus. Such a belief shaped the evolutionof the camera obscura and created the hope of making achromatic lenses. Anotherexample came from photography in its early years. In the mid nineteenth century,photographers tended to use large apertures (usually between two to six inches) in theircameras, due to the low speed of the photochemical processes. Brewster was veryunhappy with this practice because these oversize apertures greatly deviated from theirmodel, the pupil of the human eye. He remarked that, "when we use lenses of two, four,or six inches in diameter, we obtain, though a common eye may not discover it,monstrous representations of humanity, which no eye and no pair of eyes ever saw orcan see" (Brewster 1852a, 183). So, Brewster suggested that photographers should useapertures as small as the pupil, that is, about 2/10 of an inch in diameter.The eye also offered criteria for evaluating and comparing man-made optical

instruments. The functions ofman-made optical apparatus were to be aids to the eyeby generating and improving optical images suitable for perception. Thus, the value ofa particular optical instrument depended upon the quality of the images that itproduced, and the quality of the images further depended upon how appropriate theywere for the eye. These were exactly Herschel's concerns when he began to studydouble refraction and polarization (Chapter 3). There were two approaches availablefor studying double refraction and polarization. The fIrst one was Malus's directmethod, which used a device called Borda's repeating circle to measure the angulardeviation of the extraordinary ray (Buchwald 1989,33). The other was Arago's indirectmethod, which used a doubly refracting crystal to generate interference between theordinary and extraordinary rays, thus producing colored fringes of interference forobservation. According to Herschel, although Malus's device was able to producenumerical data, Arago's instrument was better because it could generate colorful,splendid phenomena that were easy for the eye to see. He claimed that "the power ofthis [Arago's] mode of observation affords of copying our outline fresh from nature,and from the general impression of the phenomena, brought at once under our view,is an advantage not to be despised" (Herschel 1820, 47). To Herschel, the standard forevaluating the effectiveness of optical instruments was whether the observationalresults could be presented with easily distinguishable cues such as color and shape.The understanding of the eye and its relations with other man-made apparatus

inevitably affected the practice of using optical instruments. If the eye was an ideal

INSTRUMENTAL TRADITIONS 123

optical instrument, it was logical to use it as an essential component in opticalexperiments. This was exactly what Potter did in his photometric experiments (Chapter6), in which he used the eye to match brightness, the most critical step in his measuringprocess. Similarly, Brewster used the eye to count the number of spectral lines in hisprismatic experiments (Chapter 4), and his measuring results (the number of thespectral lines) depended greatly upon the resolving power of the eye, that is, thediameter of the pupil.9 The eye also functioned as a critical component in Brewster'sexperiments of polarization by successive refraction, in which he used the eye to judgethe intensity of the polarized light, and consequently the nature of polarization (Chapter3).Neither Potter nor Brewster blindly worshiped the eye. They clearly recognized the

potential shortcomings of the eye if it was not used properly, and in practice theyadopted many special techniques to ensure that the eye was used in its optimalcondition. We have seen in Chapter 6 that Potter adopted some peculiar measuringprocedures in his photometric measurements. To avoid being exposed to the directlight, he did not measure two important parameters in his experiments. Instead, hemade approximations, replacing them with substitutes that he could easily measure byreading off the slide. These approximations were consistent with many otherprocedures that Potter carefully adopted in order to protect the sensitivity of the eye,including employing the remote-control devices and reducing the contrast between thelight source and the background.Potter was not in fact the only person with great concern over the sensitivity of the

eye. In their photometric experiments conducted during the late eighteenth and earlynineteenth centuries, Bouguer, Lambert, Rumford, and William Herschel all adoptedsimilar procedures to reduce the fatigue of the eye and to maintain its sensitivity. Forinstance, Bouguer took great care in his experiments to adjust the distance between thematching fields because he found that, to minimize visual fatigue, the ideal distanceshould reflect the anatomical features of the observer's eyes (Bouguer 1961, 27). Muchlike Potter, William Herschel used remote-control devices in his later photometricexperiments in order to avoid exposure to the direct light from the lamp (Herschel1800a, 528-30). Similar concern over the proper use of the eye existed outsidephotometry. When Brewster measured refractive indices, he paid great attention toprevent the eye from going out offocus. Using a special device, he fixed the focus ofthe eye at the proper place so that it could correctly judge the distinctness of theimages.In addition to the techniques for ensuring the best condition of the eye, there was

another set of skills used to improve the quality of images. Enlargement was a popularmethod to reveal details of an image when the eye had reached its limits. That wasexactly what Newton did in his refraction experiment. By using a large apparatus, hewas able to increase the size of the spectrum and obtain a precise reference for themeasurement. Similarly, Herschel in his experiments with chromatic polarizationprojected the fringes to a screen so that he could have a large image to examine. Whentelescopes were used, the technique ofenlargement took a specific form: increasing the

124 CHAPTER 7

magnifying power of the telescope. This was exactly the procedure used by Brewsterin his experiments with prismatic spectra. The five-foot telescope enabled him to seemore than two thousand spectral lines.All these experimental techniques, procedures, and skills exemplified an

instrumental tradition with a distinctive concern with the use of optical instruments.This was a tradition rooted deeply in the metaphysical or theological belief that the eyewas an ideal optical instrument and thus should play an essential role in all opticalexperiments. Consequently, it regarded man-made optical instruments as aids to theeye, and evaluated them according to how well they produced images suitable for theperception of the eye. In practice, this tradition nurtured a body of practices, botharticulated and tacit, that illustrated how optical instruments should be operated, andparticularly, how the eye should be used in optical experiments. Since the eye was anintrinsic element in all optical systems, it was important to conduct optical experimentswhen the eye was in its best state, and it was necessary to adopt special procedures toensure that the eye was in its optimal condition. Because of its faith in the eye, let uscall it the visual tradition.The techniques, procedures and skills practiced by the visual tradition were not

always articulated, but after carefully analyzing the instrumental operations andexperimental processes employed by the practitioners ofthis tradition, we can explicatea general procedure that represents the central tenet of the visual tradition (Figure 7.3).According to the visual tradition, we should use optical instruments in the followingway. When the optical effect to be studied does not exist in a natural state (e.g.polarization), we should first use a "generator" (for example, a polarizer) to create theeffect. Because not every optical image created by a "generator" is perceivable, weneed a "detector" (for example, an analyzer) to make the optical effect observable.Sometimes, although the optical effect is in principle observable, we still needinstruments to improve the optical image so that it becomes suitable for the perceptionofthe eye. Finally, the optical images caught and improved by the "detector" come tothe eye, which technically functions as a "receiver." But in essence, the eye representsthe goal of the whole optical system. We do not always need a "generator," nor a"detector," but it is inconceivable that there could be an optical system without the eye.Thus, the eye is the most important component, or the very soul, of opticalexperiments.

IGenerator I

1Optical I I h Optical I IEffect --.. Detector --.... Image --........ The Eye

Figure 7. 3 The visllal tradition

INSTRUMENTAL TRADITIONS

6. THE GEOMETRIC TRADITION

125

In contrast to the belief that the eye was an ideal optical instrument, a strong doubtabout the reliability of the eye in optical experiments and measurements emerged in theearly nineteenth centuries. Whewell's analysis of the demarcation between primary andsecondary qualities represented a philosophical reflection of the eye's role in opticalexperiments. Whewell emphasized that the distinction between primary and secondaryqualities was inherent in their ways of inducing measuring units. If secondary qualitieswere not measurable of themselves as Whewell argued, then the defects of the eye wereno longer extrinsic nor accidental. We might be able to employ various techniques toensure that the eye was in its optimal condition, but we could not change the fact that,because optical phenomena did not come with their own measuring' units, the eye couldnever "measure" an optical property without influence from the observer'sphysiological and psychological condition. Using the eye alone, it was impossible tohave consensus on whether an object was really red, whether two surfaces were exactlyequal in their brightness, or how many dark lines a spectrum actually had. The defectof the eye was intrinsic and unavoidable. To have accurate optical measurements, theonly solution was to reduce and eventually eliminate the role of the eye in opticalexperiments.Such a doubt over the eye's role logically implied relationships between the eye and

other man-made optical apparatus in direct contrast to those assumed by the visualtradition. For those who shared Whewell's concerns over the eye, man-made opticalapparatus no long functioned as an aid to the eye, nor did the eye offer a model for theperfection ofman-made instruments. The model of performance for optical apparatuswas instead those instruments used in the mechanical sciences such as astronomy andmechanics, which solely manipulated primary qualities. A general approach toimproving optical instruments was to reduce the role of optical operations and employmore mechanical processes. In the nineteenth century, the development ofthe apparatusfor measuring refractive indices basically followed this pattern. Although Fraunhofer'sspectroscopy effectively reduced the role of the eye by converting optical images togeometric signals, it still relied greatly on the optical quality of the prism. If the prismwas not optically homogenous, it was impossible to see any spectral lines. Thisrequirement for a high quality prism limited the applications of Fraunhofer' s approachin the early nineteenth century.Partly as a response to this difficulty, a new kind of refractometer appeared in the

second half of the nineteenth century. It was constructed first by Jules Jamin and thenimproved by John Rayleigh. This new refractometer converted the refrangibility oflight to the displacement of interference fringes. Figure 7.4 is a diagram of arefractometer designed by Rayleigh to measure refractive indices of gases. Rayleighpassed two light beams through two separated tubes, and then made them interfere witheach other by means of a double slit. At the beginning of the experiment, the gas to be

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Lightource

CHAPTER 7

Double slit

Gas

Viewing field

Figure 7.4 Rayleigh S interference refractometer

measured entered one of the tubes through an outlet. The gas gradually altered theoptical path ofone of the interfering beams and caused displacement of the interferencefringes. By counting the number of fringes that crossed the field of view during theperiod between the time the gas entered the tube and when it reached the desiredpressure and temperature, Rayleigh could calculate the refractive index according tothe principle of interference (Rayleigh 1896). In this way, Rayleigh's refractometersignificantly reduced requirements for the optical component, and exhibited moresimilarities to a typical mechanical device.The doubts about the eye's ability also significantly altered the practice of using

optical instruments. If it was impossible to correct the defects of the eye, it was logicalto minimize its role in optical experiments. Thus, we have seen in Chapter 3 thatFresnel did not use the intensity of light as the indication of polarization becauseobserving the intensity of light required an extensive use of the eye. He instead usedthe interference fringes as the reference for the state of polarization, and thus hisinterpretation ofpolarization was immune to the physiological conditions of the eye.We have also seen in Chapter 4 that Fraunhofer and Powell did not attempt to count thenumber of spectral lines in their prismatic experiments. Instead they measured theangular positions of some of the spectral lines, and the accuracy of their measurementsdepended primarily upon the theodolites, rather than the psychological features of theobservers. In the debate over the reliability of photometric measurements (Chapter 6),Forbes adopted exactly the same approach. He did not measure the intensity ofreflected light directly. Instead he used a "thermal photometer" to measure thereflection of heat, assuming that it was similar to the reflection of light. In this way,

INSTRUMENTAL 'TRADITIONS 127

Forbes merely used the eye to read the scale of the galvanometer, reducing its influenceto a minimum.The successes in reducing the role of the eye relied upon a group of special

techniques to convert optical images to geometric parameters. The one cited mostfrequently was Fraunhofer's procedure, in which he used the combination of a fmeprism and an achromatic telescope to transform the refrangibility of light to thepositions ofa group of geometric lines and then measured their angular positions witha theodolite. The method that utilized the principle of interference was also popular. Anexample of it was the procedure embedded in Rayleigh's refractometer, whichconverted the refrangibility of light to the displacement of interference fringes, andproduced results that depended primarily upon the accuracy of the mechanicalapparatus. Another technique that was not only widely used but also associated withmany important discoveries was the crossed prisms method fIrst proposed by Newtonin his investigation of the refrangibility of solar light. In Newton's original design, thecrossed-prism apparatus consisted of two glass prisms, the fIrst one with its refractiveedge horizontal and pointing downwards and the second one with its refractive edgevertical and pointing to the left of the observer (Newton 1979,35-45). When a beamof sunlight passed through this apparatus, the fIrst prism alone should form a verticalspectrum with the violet uppermost and the red below, and the second prism shoulddisplace the vertical spectrum horizontally in proportion to the color, that is, movingthe violet most and the red least. The end result was a continuous curve, showing thechange of refractive indices and their relationships to wavelengths in the form ofgeometric displacement. Using this method, in 1852 George Stokes converted therefrangibility of fluorescent light to two spectra with distinct geometric features, oneoblique and the other horizontal, and consequently discovered the law offluorescence. 10 Using the same method with a minor revision, in 1872 August Kundttransformed the phenomenon ofanomalous dispersion to two disconnected curves andrevealed the connection between dispersion and selective absorption (Chen 1999).Associated with the techniques of converting optical images to geometric

parameters, there were complementary procedures aimed at improving the quality ofgeometric signals. Unlike optical images, the quality ofgeometric signals could not beimproved by enlargement. To improve the accuracy of spectroscopic measurements,for example, the key was not to enlarge the overall size of the spectrum, but to increasethe dispersive power of the prism so that more lines became distinguishable. A directway to increase the dispersive power of a prism was to fInd one made of highlydispersive material, which, however, was very diffIcult to acquire in the nineteenthcentury due to technological limits. To overcome this diffIculty, many specialtechniques emerged. For example, Kirchhoff used a series of four prisms to increasethe dispersive power of his spectroscope (Bennett 1984,7), while Powell, as we haveseen, adopted a different approach using hol1ow prisms fIlled with highly refractivefluids.Al1 these experimental techniques, procedures and skills exemplified a different

instrumental tradition that was in many aspects incompatible with the visual tradition.

128 CHAPTER 7

IGenerator I

~Optical J H I Geometric J . IEffect --rDetector Convertor --.. Signal ~ Receiver

Figure 7.5 The geometric tradition

This was a tradition rooted in the doubts over the reliability of the eye in opticalexperiments. Consequently, the eye was no longer the model of man-made opticalapparatus, nor would it be an intrinsic element of any optical system. This traditionnurtured a body ofpractices, both articulated and tacit, that aimed at reducing the roleof the eye in optical experiments. Among these practices, the procedure of convertingoptical effects to geometric parameters, which trivialized. the impact of the eye inoptical measurements, was essential. Because of its trust in the reliability of geometricparameters, let us call this the geometric tradition.After carefully analyzing the instrumental operations and experimental processes

conducted by the practitioners, we can also explicate a general procedure thatrepresents the central tenets of the geometric tradition (Figure 7.5). According to thegeometric tradition, we should use optical instruments in the following way. Weusually need a "generator" and a "detector" to create and improve optical images, butwe should not use our eye to observe the optical images directly. To obtain reliableobservations and precise measurements, we should use a "convertor" to transform theoptical image to a geometric signal. After the transformation, we also need a"reference" that offers the measuring unit associated with the geometric parameter. Atthe end, we still need a "receiver" to pick up the signal, but it need not necessarily bethe eye. We often use the eye as a "receiver," not because it is necessary, but becauseit is convenient. To obtain more reliable measurements, we should eventually replacethe eye with other objective devices, such as using photoelectric cells in photometry.

CHAPTER 8

THE GEOMETRIC TRADITIONAND THE WAVE THEORY OF LIGHT

With its emphasis on accurate measurements, the geometric tradition should haveenhanced the status of the wave theory in the ongoing debate by offering numericaldata to test and to confmn the theory's quantitative accounts. However, such asupportive relationship between the geometric tradition and the wave theory did notexist in the 1830s and 1840s. This chapter begins with an examination of the impact ofHumboldtian sciences, which highlighted the importance ofmeasuring complex naturalphenomena. Because they became favorite research subjects ofmany wave theorists,Humboldtian sciences diverted the research interests, resources and manpower of thewave camp, and consequently the problem-solving ability ofthe wave theory stagnated.When the popularity of Humboldtian sciences waned in the early 1850s, a newgeneration of physicists revitalized the geometric tradition and the wave theory. Themeasurements of a couple of important optical parameters had a profound effect on thestatus of the wave theory in the second half of the nineteenth century.

1. HUMBOLDTIAN SCIENCES: MEASURING NATURE

Alexander von Humboldt, a German naturalist and scientific traveler, was a veryimportant figure in the development of physical geography and biogeography. Duringhis college years, Humboldt developed strong interests in botany, mineralogy andgeology, and collecting plants and mineral specimens became his hobby. But he soonfound that the countryside ofGermany did not give him much stimulus, so he beganto dream of journeys to more exotic lands. In 1798, he obtained permission from theSpanish government to make an expedition to the Spanish colonies in Central andSouth America. On June 5, 1799, he was bound for South America, beginning a five­year scientific expedition.Between 1799 and 1804, Humboldt traveled a wide expanse of the Central and

South American continent, from Venezuela to Colombia, then to Ecuador and Mexico.Covering more than 6,000 miles on foot, on horseback and in canoes, Humboldt hadthe opportunity to study a new world in detail. Unlike earlier explorers, Humboldt notonly recorded novel phenomena on his expedition but also conducted very accuratemeasurements. To conduct these measurements, he carried an impressive set of

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130 CHAPTER 8

instruments, including two chronometers, two telescopes, two microscopes, twosextants, one theodolite, one graphometor, one magnetometer, four barometers, severalthermometers, two hygrometers, two eletrometers, one cyanometer, and many more. l

Armed with the latest instruments, Humboldt was able to accurately measure a largerange ofnatural phenomena that had either been unknown or inaccurately reported byearlier explorers. When he returned, he brought back an enormous amount ofinformation. In addition to a huge collection of new plants, there were determinationsof longitudes and latitudes, measurements of the earth's geomagnetic field,observations of temperatures and barometric pressure, and statistical data on the socialand economic conditions ofMexico (Kellner 1963,3-65).After fmishing his American expedition, in 1814 Humboldt published a three­

volume book in French describing his discoveries. Later he expanded it to sevenvolumes in an English translation published from 1814 to 1829 under the title PersonalNarrative ofTravels to the Equinoctial Regions ofthe New Continent during the Years1799 - 1804. The tremendous number of detailed and accurate descriptions thatHumboldt included in his book impressed British readers immediately. One reviewerin Quarterly Reviewwrote, "[Humboldt's] great merit, however, is that of seeing everything, and leaving nothing unsaid ofwhat he sees; -- not a rock nor a thicket, a pool ora rivulet, -- say, not a plant nor an insect, from the lofty palm and the ferociousalligator, to the humble lichen and half-animated polypus, escapes his scrutinizing eye,and they all fmd a place in his book" (Anonymous 1818, 136). A "Humboldtian spirit"began to emerge and became popular in the British scientific community (Cannon1978, 73-110).Beginning in the late 1820s, the admiration for Humboldt's research style caused

an explosion of interest in the studies of the earth and its environment. FollowingHumboldt, these studies attempted to measure nature accurately and systematically andproduce quantitative data, often in the forms of charts and graphs. Subjects of thesestudies included tidology, meteorology, terrestrial magnetism, physical geology, fossilzoology, marine biology and the works of astronomical reductions,2 all ofwhich canbe categorized under the heading of "Humboldtian sciences" (Morrell & Thackray1981,512-3).In addition to his American expedition, Humboldt's work in organizing scientific

societies and scientific conferences also deeply impressed the British scientificcommunity. In 1828, Humboldt organized an international scientific conference inBerlin, the meeting of the Society ofNaturalists and Natural Philosophers. With morethan six hundred people present, the meeting was a great success. As the president ofthe meeting, Humboldt delivered an opening address, in which he declared that "themain purpose of this society is the personal contact ofmen who work in the same field,an oral and thus more stimulating exchange of ideas, they may be facts, opinions ordoubts; the forming of friendly relations which light up the sciences, give charm of lifeand gentleness and tolerance to intercourse ..." (Kellner 1963, 119).Among Humboldt's audience was Charles Babbage, Lucasian professor of

mathematics at Cambridge. Babbage was impressed by the success of the conference

THE GEOMETRIC TRADITION 131

and particularly inspired by Humboldt's speech. He immediately translated Humboldt'sspeech into English and published it with a report of the conference in EdinburghJournal o/Science (Babbage 1829). Humboldt's views on science and his success inorganizing a scientific society induced a strong interest among some British "gentlemenofscience," such as Babbage and Brewster, in establishing a scientific institution likethe one in Germany. Humboldt's example became one of the main factors leading upto the founding of the British Association for the Advancement of Science.3 It is notsurprising that the first meeting of the British Association, in 1831, was modeled onHumboldt's conference.

2. THE SHORTAGE OF SCIENTIFIC MANPOWER IN OPTICS

Humboldt's influence significantly shaped the research pattern of the BritishAssociation's members. Within the Mathematics and Physical Sciences Section oftheAssociation, researches that belonged to Humboldtian sciences constituted themainstream for a long period. The most vivid example ofHumboldt's influence wasthe "magnetism crusade," a project to establish a global network of geomagneticobservatories. Inspired by Humboldt's successes in observing and measuring terrestrialmagnetism, in the early 1830s Lloyd, John Herschel and Edward Sabine advocated theimportance of large-scale geomagnetic measurements, typifying the Humboldtianpassion for data collection. In the mid-1830s, the advocates of the geomagneticresearch project began to lobby the British gov~rnment, asking it to supply fmancialsupport for building stationary observatories in the southern polar region. Among thesupporters of the magnetic lobby, there were Lloyd, Herschel, Whewell, Airy andForbes, the principal members of the wave camp. The first attempt of the magneticlobby failed, primarily because at the time the Royal Society did not endorse theproject. Upon the request of Sabine, Humboldt wrote a letter to the Royal Society in1836, asking the Society's and the British government's support in establishingmagnetic observatories in the colonies. Because of the prestige ofHumboldt, the RoyalSociety changed its position and, together with the British Association, successfullypersuaded the British government to supply the financial support (Cawood 1979,494­505).In addition to the "magnetism crusade," Humboldtian sciences pursued by the

members of the British Association included tidology, meteorology, physical geologyand astronomical reductions. The works on tides, largely done by Whewell and JohnLubbock, consisted ofobserving the variations of tides in different locations, the effectsof the moon's declination and parallax on tides, and the effects of solar parallax andbarometric pressure on tides. The researches on meteorology, pursued by Forbes andWilliam Harris, included projects on atmospheric waves, on meteorologicalobservations and on improving the instruments used for meteorological measurements.The astronomical reductions conducted by Airy and Francis Baily produced star andplanet catalogues that provided corrected positions of a large number of fixed stars andplanets (Morrell & Thackray 1981, 509-17). All these works required large-scale

132 CHAPTER 8

observations, tremendous data collection and laborious calculation, and typified theresearch style practiced by Humboldt.Because of the large scale ofwork demanded by Humboldtian sciences, the British

Association in its first fifteen years spent a large amount of its fmancial resourcessupporting projects inspired by the "Humboldtian spirit." The distribution of researchgrants in the British Association was absolutely disproportionate. Although themembership included thousands, 14 people received over half of the research moneyduring the period between 1833 and 1844, £6681 out of £11784. Among these 14research projects supported by the Association, eight belonged to Humboldtiansciences, including astronomical reductions (Baily), tidology (Whewell and Lubbock),meteorology (Harris and Herschel), natural history (Owen and Agassiz) and marinebiology (Edward Forbes). In terms of money, these eight Humboldtian projectsconsisted of over 70 percent of the grants that the 14 major grantees had drawn(Morrell & Thackray 1981,551).The investment in Humboldtian sciences induced a large number of research papers.

In the Section A of the British Association, papers on Humboldtian sciencesdramatically increased after the mid 1830s. Between 1836 and 1850, papers onHumboldtian sciences actually outnumbered those on physical sciences, includingdynamics, optics, heat, electricity and magnetism. During this period, papers onHumboldtian sciences constituted almost a half of the works presented in Section A,while papers on the physical sciences dropped to about 30% (Figure 8.1). Such a largepercentage of publications in Humboldtian sciences must have required the membersof the Association to spend a substantial amount of time in these fields. Humboldtiansciences usually required laborious measuring, counting, reducing, tabulating andgraphing of data. The expenditure of manpower in these fields would have beenconsiderable. Thus, the popularity of Humboldtian sciences not only drained a largeportion of the financial resources ofthe British Association, but also, more importantly,a great amount of the scientific manpower of the scientific community.

In the first half of the nineteenth century, the opportunities for scientific researchin Britain were limited. Without support from the government, positions for scientific

1831-35 1836-40 1841-45 1846-50 1851-55

Mathematics 8 (7%) 12 (6%) 17 (1<Jl/o) 6 (3%) 7(4%)

Astronomy 3 (3%) 9(5%) IS (8%) 20 (9%) 23 (12%)

Physics 67(57%) 63 (34%) 53 (3<Jl/o) 92 (39%) 95 (49%)

Humboldtian Sciences 30 (26%) 84 (45%) 82 (46%) 101 (43%) 58 (30%)

Others 10 (8%) 18 (l<JlIo) II (6%) 14 (6%) 9(5%)

Total 117 186 178 233 192

Figwe 8.1 Number ofJX1pers presented in Section A ofthe British Association, 1831-1855

THE GEOMETRIC TRADITION 133

research were only available at universities and in industry. However, professorshipsin natural science at British universities were few, and openings for scientists inindustry were rare, with the probable exception of the chemical industry. For manypeople with scientific training, moving to the Dominions and South American countrieswas more attractive than remaining in Britain, and this brought about a "brain-drain"of scientific manpower (Roderick & Stephens 1974, 58). Under these circumstances,a shortage of scientific manpower developed in the field of physics (Cannon 1978,126). Very few people were capable of doing physical investigations, and thosequalified had diverse interests, covering fields not only within but outside the domainof physics. Through further diversifying the interests of the researchers, the popularityof Humboldtian sciences made the shortage of scientific manpower in physics evenworse.

In the field of optics, for example, only about a dozen people were involved whenthe particle-wave debate began, three on the particle side and about ten on the waveside. On the partiCle side were Barton, Brewster and Potter. On the other side wereAiry, Challis, Forbes, Hamilton, Herschel, Lloyd, MacCullagh, Powell, Talbot andWhewell, the old-generation wave theorists. With the exception of Brewster andPowell, most participants only spent a slight fraction of their time on optics.Consequently, the number of publications on optics was not very high, with an averageof 10 papers each year in the 1830s. When Humboldtian sciences became the newfashion, the time and manpower spent in optics inevitably decreased. This had asignificant impact on the debate, especially on the wave camp. After 1835, most wavetheorists were no longer interested in optical phenomena. Except in responding torivals' attacks, they seldom conducted original optical researches, and the number oftheir publications on optics also dropped significantly (Figure 8.2). After the mid

1830s 1840s 1850s

Optics Humboldtian Optics Humboldtian Optics Humboldtian

Airy 15 1 7 9 3

Challis 3 1 8 7

Forbes 4 12 1 33 1 IO

Hamilton 8 5 1 1

Herschel 1 4 2 9 3

Lloyd 4 13 2 20 1 13

MacCullag/1 13 8

Powell 27 26 4 4 12

Talbot IO 1

Whewell 1 19 9 1 2

Total 82 40 (j) 85 15 43

Figure 8.2 Number ofpapers published by old-generation wave theorists

134 CHAPTER 8

1830s, the most influential wave theorists who had played critical roles in theestablishment of the dominance of the wave theory in Britain, such as Herschel, Airyand Lloyd, turned their attention to new Humboldtian sciences. In the 1840s and 1850s,for instance, Lloyd published 33 papers on Humboldtian sciences, but only three onoptics. Although Airy maintained his interests in astronomy, his papers onHumboldtian sciences in the 1840s still outnumbered those on optics, and most of hisoptical papers (six out of seven) were merely reactions to Brewster's and Potter'sattacks. Similarly, Herschel published nine papers on Humboldtian sciences in contrastto two on optics in the entire 1840s. In fact, after 1835, only two wave theorists, Powelland MacCullagh, maintained their focus on optics, and the latter, unfortunately, diedyoung in 1847.Despite the wave theory having a relatively large number of supporters in Britain,

the actual scientific manpower spent on its development was limited after 1835. Thewave theory was relatively stagnant, in comparison to its achievements in the frrst halfof the 1830s, not to mention those accomplished by Fresnel in the 1820s. Until the lateI840s, the wave theory still had difficulties in explaining a variety of opticalphenomena, especially those deliberately uncovered by its opponents. Consequently,the wave theory's failure to solve these problems not only gave its opponents chancesto continue their challenges, but also stirred up discontent among some wave theoristssuch as MacCullagh. As we have seen in Chapter 5, the wave theorists' doubts abouttheir own theory furthered its opponents' illusion that the wave theory could bedefeated and the particle theory revived. In this way, the life of the particle-wave debatewas significantly lengthened.

3. A NEW GENERAnON OF PHYSICISTS

The number of research papers on Humboldtian sciences presented to the Britishassociation decreased substantially at the beginning of the 1850s, and the enthusiasmfor this research approach among British physicists fmally died out. At the same time,a new historical process began: a new generation of physicists emerged.In the field of optics, a fundamental transition occurred around the mid nineteenth

century. Those wave theorists who were actively involved in the particle-wave debatein the 1830s and the 1840s gradually disengaged. The time that they spent in opticalresearch and the papers that they published on optical problems diminishedsignificantly after 1845. These wave theorists, who had received their college educationbefore the wave theory became dominant in Britain and had thereby personallyexperienced a conversion from the particle to the wave tradition, constituted an oldgeneration in the wave camp. During the same period, however, a new group ofwavetheorists gradually emerged and replaced the old generation. The main figures in thisnew generation included Harvey Goodwin, Samuel Haughton, Philip Kelland, MatthewO'Brien, William Rankine, Archibald Smith, George Stokes and William Swan. Exceptfor Kelland who was trained in the late I820s at Cambridge, which had already beena stronghold of the wave tradition by that time, all these new-generation wave theoristsreceived their college education after the wave theory controlled the curricula ofBritain

THE GEOMETRIC TRADITION 135

universities. These young wave theorists were directly trained by old-generation wavetheorists and had accepted the theory from the very beginning of their intellectualcareers, without the experience of a conversion from an old theoretical framework toa new one. These young wave theorists began their optical researches in the late 1830s.The time that they spent in optical research and the papers they published on opticalproblems rapidly increased in the following years. Beginning in the second half of the1840s, the optical papers from the new generation outnumbered those from the oldgeneration, and these young wave theorists replaced their predecessors to become theprincipal force of the wave camp.One ofthe fundamental differences between these two generations ofwave theorists

was their attitude toward Humboldtian sciences. Unlike the old generation, wavetheorists from the new generation did not have strong interests in Humboldtian sciencesand had very few publications in these fields (Figure 8.3). Wave theorists from the oldgeneration had very diyerse interests and seldom specialized in a narrow field. Someof them even opposed the process of specialization. Up to 1835, for instance, Herschelstill regarded specialization as regrettable, complaining that "such is science now-a­day. No man can now hope to know more than one part of one science" (Herschel1835). This attitude partly explained why old-generation wave theorists were attractedby Humboldtian sciences. Compared with their predecessors, the intellectual interestsof the new generation were relatively narrow and highly specialized. Most of themwere only interested in a very narrow range of subjects, primarily mathematics andthose physical investigations to which they could directly apply mathematical analysis,and they seldom said anything on such complex subjects as tidology, meteorology, orterrestrial magnetism. The emergence of this new generation indicated that the processof specialization had greatly advanced and that around the mid-nineteenth centuryphysics had begun to become an independent discipline.Accompanying the emergence of these new-generation physicists, the general

1830s 1840s 1850s

Optics Htnnboldtian Optics Humboldtian Optics Humboldtian

Goodwin 14

Haughton 4 9 42

Kelland 4 19 3

O'Brien 1 12 4

Rankine 4 37 2

Smith 17 9 1

Stokes 36 29

Swan 4 4 3

Total 22 102 86 48

Figure 8.3 Number ofpapers published by fJ!w-generation wave theorists

136 CHAPTER 8

attitude ofthe physics community toward experimentation also changed fundamentally.The image popular in the frrst half of the nineteenth century pictured the physicalsciences as a spectrum -- ranging from mathematical dynamics at the one end toexperimental chemistry at the other. According to Herschel, since dynamics displayedthe closest alliance with mathematics, it was "placed at the head of all the sciences"(Herschel 1831, 96). Chemistry, on the other hand, "is, of all the sciences, perhaps, themost completely an experimental one; . .. [its theories] demand no intenseconcentration of thought, and lead to no profound mathematical researches" (Herschel1831, 299). Thus, Herschel put experimental chemistry at the bottom of the spectrum.Between dynamics and experimental chemistry, there were other physical sciences -­astronomy, optics, heat, electricity and magnetism -- arranged between the two endsaccording to their degrees ofmathematicization. The closer to dynamics, or the higherthe degree ofmathematicization, the more advanced the discipline. In this view of thephysical sciences, the degree of sophistication in instrumentation and experimentalskills played no role in the advancement of science. The tendency to ignoreexperimentation was further reinforced when Humboldtian sciences became popularin Britain, though for an entirely different reason. One of the methodological featuresof Humboldtian sciences was their emphasis upon accurate and systematicmeasurements of real and complex phenomena. Compared to this, studying nature insimplified or idealized situations through experiments in a laboratory came to seem old­fashioned (Cannon 1978, 105).All ofthese factors explained the underdevelopment of physics experiments and

physics laboratories in Britain during the frrst half of the century. There was no physicslaboratory in Britain during the frrst three decades of the nineteenth century. In fact, thefrrst physics laboratory originated from a chemistry laboratory when Faraday changedhis personal interests from chemical phenomena to electricity in the 1830s. However,the underdevelopment began to change in the 1840s and the early 1850s, when severalprivate physics laboratories appeared in major universities such as Cambridge,Edinburgh, and University of Glasgow. At Cambridge, Stokes established the firstprivate physics laboratory in 1849, using it not only for his own research but forteaching demonstrations (Sviedrys 1976, 409).Accompanying the development of physics laboratories, the system of academic

examinations at Cambridge also underwent an important transformation. In the firsthalf of the century, the academic examinations at Cambridge were the MathematicalTripos and the Smith Examination, both ofwhich emphasized mathematical analysisand excluded many physical subjects that were in principle experimental. This situationchanged at mid-century. In 1851, the University ofCambridge adopted a new academicexamination, the Natural Science Tripos. The content ofthe Natural Science Tripos wasprimarily experimental physics, covering the subjects of heat, electricity, magnetismand the related chemical phenomena (Wilson 1982, 341). The introduction of theNatural Science Tripos at Cambridge and the emergence of physics laboratories inmajor universities were indicators of a changing attitude toward experimentation.The new attitude toward experimentation was also evident in the researches

THE GEOMETRIC TRADITION 137

conducted by new-generation wave theorists. Stokes's works, for example, exhibitedan excellent integration ofmathematical analysis and experimental exploration. In hisresearch on optical phenomena, Stokes conducted a large number of very skillfulexperiments, including those on diffraction (Stokes 1849), on the Haidinger's brushes(Stokes l850b), on phase differences in streams of polarized light reflected frommetallic surfaces (Stokes 1850a), and on the colors of thick plates (Stokes 1851).Stokes even invented and constructed his own instruments in his optical experiments,as in 1851 he made an instrument for analyzing elliptically polarized light (Parkinson1975,77).This new attitude toward experimentation had a profound impact on the debate. The

reason why Brewster for a rather long period had been respected as "the father ofoptical experiments" lay not only in his own personal achievements, but also in the factthat his contemporaries were reluctant to spend more time on optical experiments.Brewster's prestige in optical experiments was crucial for the longevity of the debate.Brewster's prestige not only forced wave theorists to listen seriously to every critiquethat he raised, but also gave him self-confidence to continue his lonely fight against themajority of the optical community. However, when the new-generation wave theoristsemerged with equal or even superior skills in optical experiments, the hard currency inBrewster's hands suddenly vanished, and the particle theorists realized that their chanceofwinning the battle had become infinitesimal.

4. STOKES'S EXPERIMENTS ON FLUORESCENCE

Among the experimental investigations conducted by the new-generation wavetheorists, perhaps the most important one was Stokes's work on fluorescence. In 1845Herschel first reported observations of a phenomenon now known as fluorescence. Inhis experiments, Herschel transmitted a beam of sunlight through a solution of sulphateof quinine, and found that a vivid blue color appeared at the surface of the perfectlytransparent liquid. He also found that the blue color existed only in a stratum of theliquid next to the surface by which the light entered, and that, after passing through thisstratum, the incident light lost the power to produce the same effect. Herschelintroduced a term "epipolic dispersion" to describe the phenomenon, believing thafhewas dealing with a new type of polarization from the incident beam -- the light onentering the solution became "epipolarized," and this epipolarized light was incapableof producing further epipolic dispersion (Herschel 1845a; Herschel 1845b). Havingheard ofHerschel's experimental results, Brewster noted in 1848 that he had obtainedsimilar experimental results both in a solution of sulphate of quinine and in fluorsparmore than ten years before. In his own experiments, Brewster used an achromatic lensto produce an intense beam of light as the source, and he saw that the blue colormarked the entire path of the beam. Brewster concluded that the phenomenon was notpolarization but simply a new kind of dispersion caused by the incident beam, andaccordingly labeled it "internal dispersion" (Brewster 1849).Herschel's and Brewster's discoveries later drew Stokes's attention. He conducted

138 CHAPTER 8

numerous experiments to investigate the phenomenon, and in 1852 he published inPhilosophical Transactions a lOO-page paper on fluorescence, in which he offered acomprehensive description ofthe phenomenon as well as its relationships to absorption,polarization, heat and many other issues. In effect, Stokes's paper opened new fieldsof research in physics, especially, thermodynamics and chemistry. But to physicaloptics, the significance of this paper consisted not in its experimental details, but, asreflected in its title "On the Change of Refrangibility of Light," in its revision of afundamental principle ofNewtonian mechanics.When he started his investigation, Stokes took for granted that the fluorescent light

could only have arisen from light of the same color in the incident beam, an idea sharedby both Herschel and Brewster, but he soon gave up this assumption (Stokes 1907, vol.1, 8). Stokes later reasoned that the incident rays and the fluorescent rays must havebeen different because the former coexisted with the latter only in a stratum of thesolution. According to the wave theory, the nature of light was completely defined byits state of polarization and its refrangibility. So, fluorescence could be accounted foreither in terms of changes in the state of polarization, or in terms of changes ofrefrangibility. Stokes frrst contemplated the possibility that fluorescence was related tothe state of polarization, but he quickly realized that this hypothesis was "utterlyextravagant" -- it contradicted the fundamental doctrines of the wave theory (Stokes1853,261). He was then led to study the possibility ofa change of refrangibility.In his first experiment, Stokes employed a simple apparatus to control the

refrangibility of the incident light and that of the transmitting light. He prepared twopieces of colored glass. The first one was violet and transmitted only light with highrefrangibility (blue and violet) and absorbed the rest, and the other was yellow andtransmitted only light with low refrangibility (green, yellow and red). These two piecesof glass together were practically opaque even to a fairly strong light. When theexperiment began, Stokes threw an intense beam of sunlight on a solution of sulphateof quinine, and fluorescent light appeared at the surface of the solution. He theninserted the violet glass in front of the solution and the yellow glass behind it. Lookingthrough the yellow glass, he found that the fluorescent light continued to be visible. Butwhen he reversed the positions of the colored glasses, that is, the yellow glass in frontof the solution and the violet glass behind it, the fluorescent light disappeared (Stokes1852a, 466-7).These experimental results clearly indicated that fluorescence could not arise from

light with the same refrangibility, because no light from the incident beam could passthrough the combination of the two pieces of colored glass. Fluorescence must benewly created by the solution, which frrst absorbed some ofthe incident light and thendischarged it. The experimental results also indicated that only light with highrefrangibility could cause fluorescence because fluorescent light was visible only whenthe violet glass was in front of the solution. A change of refrangibility occurred whenmore refrangible light was absorbed and less refrangible light was emitted. Stokes thusbelieved that "to my own mind these experiments were conclusive as to the fact of achange of refrangibility" (Stokes I852a, 467; emphasis added). But Stokes did not stop

THE GEOMETRIC TRADITION 139

here. To convince others that fluorescence involved a change of refrangibility, he knewthat he needed a more sophisticated experimental design. In the 1850s, the ideal methodfor studying the refrangibility oflight was Fraunhofer's approach, which converted therefrangibility of light to the locations of spectral lines so that the observations were nolonger related to the physiological and psychological state of the observer. In Stokes'sexperiment, however, the refrangibility oflight was measured in terms of colors, andthe existence of fluorescence relied heavily upon the sensitivity of the eye, especiallywhen the intensity of the incident light was weak.To demonstrate the change of refrangibility in fluorescence in a precise manner,

Stokes designed a new experiment, which employed a pair of crossed prisms. He threwa beam of intense sunlight through a prism placed vertically (with its refractive edgevertical) and obtained a horizontal spectrum on a regular screen. Observing thespectrum with another prism held closely to the eye, with its refractive edge horizontal,Stokes saw an oblique spectrum -- the second prism displaced the horizontal spectrumvertically in proportion to the colors (Figure 8.4). Now, Stokes replaced the regularscreen with a piece of paper washed with sulphate of quinine, which should exhibitfluorescence when it was illuminated by the incident light. Examining the paperthrough the second prism, Stokes found something striking. He saw not just the obliquespectrum that resulted from the reflection of the incident light, but also a newhorizontal spectrum that resulted from the fluorescent light. As shown in Figure 8.4,the oblique spectrum RV contained the natural colors of the solar spectrum that runvertically from red to violet, and the fluorescent spectrum BY contained colors betweenblue and yellow arranged horizontally (Stokes 1852a, 507).The discovery of the fluorescent spectrum was a significant breakthrough. With the

crossed-prisms method, fluorescence could be detected with much higher certainty, and

Obliquespectrum

Screen

Verticalprism

_<l'~~_IIIII~Fluorescent.....---- spectrum

y

Figure 8.4 Stokes' apparatus/or detectingfluorescence

140 CHAPTER 8

the judgment depended much less upon the sensitivity of the eye. Stokes's crossed­prism experiment also revealed the change of refrangibility in fluorescence vividly, interms of the relative locations of the two spectra. Stokes found the properties of thefluorescent spectrum, including its size, both vertical and horizontal, and its colors,varied according to the nature of the fluorescent materials. But one thing was certain:"Whatever be the screen, the horizontal band is always situated below the oblique,since there appears to be no exception to the law, that when the refrangibility of lightis changed in this manner it is always lowered' (Stokes 1853,263; original emphasis).The fluorescent spectrum appeared always on the right-hand side of the obliquespectrum, and always in a position lower than the oblique spectrum. Since the spectrallines in the oblique spectrum offered a scale to estimate refrangibility, the relativelylow position of the fluorescent spectrum proved that the fluorescent light was lessrefrangible than the incident light. Thus, Stokes came to the conclusion that, influorescence, incident light with greater refrangibility was always transformed into lightwith lesser refrangibility, and never in the reverse direction. This is Stokes's law offluorescence. 4

Stokes was very pleased with his new discovery. He later recalled that "ifwe maysuppose the blue light given out by the solution to be an effect of the rays of higherrefrangibility incident upon it, everything would fall into its place, and the whole of thephenomenon be explained in the simplest manner" (Stokes 1907, vol. 1, 8). ButStokes's law of fluorescence had a profound theoretical implication. The change ofrefrangibility implied changes of wavelengths or changes of the periodicity of theether's vibrations. A fundamental principle in Newtonian mechanics was that, withoutoutside interference, vibrations in a mechanical system always retained their periodicitythrough all the modifications that they may undergo. To suppose that refrangibilitycould change was equivalent to supposing that vibrations of one period could give riseto vibrations of a different period, a supposition that involved a great mechanicaldifficulty. Stokes thus came to a dilemma, either giving up a beautiful wave accountof fluorescence or abandoning a principle ofNewtonian mechanics. Facing this criticalchoice, Stokes clearly put more weight on his wave account of fluorescence, which hebelieved had been proved to be true by his experimental investigations, and he declaredthat "it seems to me less improbable that the refrangibility should have changed, thanthat the undulatory theory should have been found at fault" (Stokes 1852a, 466).Stokes's decision to retain his account of fluorescence clearly indicated a lessening

of his commitment to the Newtonian tradition. Before Stokes, essentially all wavetheorists in Britain were Newtonian. For example, Young's optical investigations wereoverwhelmingly an extension rather than a refutation ofNewton's optical works. Laterstrong supporters of the wave theory in Britain such as Airy and Herschel were alsostrong advocates of Newtonianism. For a rather long period, one of the mostembarrassing problems for wave theorists was the nature of the ether, but it wastroublesome only within the Newtonian framework that required transverse waves tobe transmitted in an elastic solid. Stokes thus represented a new generation of wavetheorists who gradually distanced themselves from the Newtonian tradition.

THE GEOMETRIC TRADITION 141

The new critical attitude toward the Newtonian tradition created a conceptualobstacle in the communication between the two generations ofwave theorists. The oldgeneration experienced more and more difficulties in understanding the methods andthe concepts used by those who belonged to the new generation. Herschel, for instance,had great difficulty in the late 1850s in comprehending the principle of the conservationofenergy entertained by the younger generation (James 1985,33-4). Not surprisingly,the conceptual obstacles between old-fashioned particle theorists and new-generationwave theorists were even greater. Because Brewster was not proficient in mathematics,he had difficulties in following the sophisticated mathematical analyses presented bynew-generation wave theorists, not to mention their physical concepts. On the otherhand, since new-generation wave theorists had embraced the wave theory from the verybeginning of their careers, they were not familiar with the particle tradition and werenot interested in understanding it. The increasing incommensurability between thesegroups explains, in part, why the intensity of the debate concerning the rival theoriesof light died down in the 1850s.

5. MEASURING THE VELOCITY OF LIGHT

The wave theory of light experienced further fundamental changes when precisemeasurements of the velocity of light became available in the second half of thenineteenth century. For a long time, the wave theory had predicted that light traveledmore slowly in dense media such as water than in rare media such as air. Because theparticle theory had predicted the opposite, that is, light traveled faster in water than inair, some wave theorists believed that measuring the velocity oflight in different mediacould be a crucial experiment for testing the rival theories. But wave theorists wereunable to verify their predictions regarding the velocity of light, despite theirimpressive successes in explaining and predicting other optical phenomena. Before1850, no one was able to measure the velocity oflight accurately.Ole Romer, a Danish astronomer, proposed a method in 1675 to estimate the

velocity of light by observing the eclipses of the first satellite of Jupiter. Since thesatellite rotated around Jupiter with a constant velocity, it entered the shadow of theplanet at regular intervals, and the times of the eclipses should be predictable with greataccuracy. But Romer found that the intervals between successive eclipses variedgradually, ranging up to about 10 minutes during a period of a year. He further foundthat these eclipses occurred either earlier or later than the calculated time, according towhether the earth and Jupiter were on the same or opposite sides of the sun. Romerreasoned that these irregularities might be due to the varying time taken for light totravel to the earth. According to his observations, Romer estimated the time for lightto travel the semi-diameter of the earth's orbit as 11 minutes, and deduced that thevelocity oflight in air was 225,000,000 meters per second.5 Romer's value was about24% lower than the modem one given by the same astronomical method, and hisestimation of the time for light to travel the semi-diameter of the earth's orbit was about30% higher than it should be. These errors resulted largely from the uncertainty of his

142 CHAPTER 8

observations. Itwas difficult to determine precisely when an eclipse began and whenit finished. Judgments of this kind relied heavily upon the sensitivity of the eye indetecting the intensity of optical images.Romer's measuring error resulted also from difficulties in obtaining accurate

astronomical parameters, such as the diameter of the earth's orbit. To avoid this kindof difficulty, Galileo proposed a terrestrial method to measure the velocity of light,which in essence tried to determine the time for light to travel a certain distance directly(Galileo 1914,42-3). Due to the enormous velocity of light, Galileo's method failedeven when the distance was increased up to 10 miles. The first successful terrestrialmethod for measuring the velocity of light did not appear until 1849 when HippolyteFizeau invented the rotating-teeth method.In his experiment, Fizeau passed a beam of light from the source to the rim of a

toothed wheel by means of a semi-transparent reflector (Figure 8.5). After passingbetween the teeth of the wheel, the light beam fell upon a reflecting mirror placed along distance away (about 8,000 meters), and then returned to the wheel and reachedthe observer. Fizeau increased the rotating speed of the wheel gradually. When thespeed was low, he could see light reflected from the mirror. But when the speedreached a particular point, the reflected light disappeared because the light that passedthrough a given space of the wheelwas interrupted on its return by a tooth that hadmoved into the previous position of the space. Given the rotating speed of the wheeland the distance between the wheel and the reflecting mirror, Fizeau determined thatthe velocity of light was 315,000,000 meters per second (Fizeau 1849). This was arather accurate measurement, only about 5% higher than the modem value(299,910,000 meters per second). Despite its technical sophistication, however,Fizeau's method was still similar to Romer's in one aspect. The key operation inFizeau's method continued to use the eye to detect the intensity of optical images. Butthe image of the reflected light in Fizeau's experiment was never bright, and the light

Toothedwheel

Mirror Reflector

Lightsource

Figure 8.5 Fizeau sapparatus for measuring the velocity oflight

THE GEOMETRIC TRADITION 143

reflected from the teeth of the wheel caused a general illumination in the whole field.Thus, Fizeau experienced great difficulty in determining the exact moment when thereflected light disappeared, which inevitably affected the accuracy ofhis measurement.A different method for determining the velocity of light was developed by Charles

Wheatstone, Professor of Experimental Philosophy at King's College, London, who in1834 used a rotating mirror to determine the velocity of electricity. Wheatstone passeda current through a long copper wire, with spark gaps at each end. Since electricity hada fmite velocity, he expected that sparks from these gaps would not occursimultaneously. To determine the time difference between these sparks, Wheatstoneused a rotating mirror with a constant speed to reflect the sparks to a screen. Becauseof the angular movement of the mirror, two sparks that occurred at different timeswould project two bright spots in the screen with an angular distance. By measuringthis angular distance, Wheatstone could determine the time elapsed between the twosparks, and consequently the velocity of electricity in the copper. wire (Wheatstone1834).6

Fran~ois Arago picked up Wheatstone's idea in 1838 and designed a device thatused a rotating mirror to compare the velocities of light in different media. However,his attempt to carry out the experiment was unsuccessful, and his failing eyesightfmally forced him to give it up. Itwas Leon Foucault who, in 1850, carried out Arago'sscheme with significant modifications and successfully determined the relativevelocities oflight in air and in water. The key apparatus of Foucault's experiment wasa mirror rotating at 800 revolutions per second. A beam of light from the source wasreflected by the rotating mirror to a fixed reflector placed four meters away (Figure8.6). The light beam reflected from the reflector came back to the rotating mirror alongthe same path, but, since the mirror had a small angular displacement, it was deflectedby the mirror and formed a deflected image a l . In addition, the light beam was alsoreflected by the rotating mirror to another fixed reflector, going through a water-filledtube and forming another deflected image a2' Since the velocity of light was inverselyproportional to the displacement, the relative velocities of light in air and in water couldthen be determined by comparing the distance of aal and that of a~. Because aa\ wassmaller than aa2' Foucault concluded that light must travel more slowly in water thanin air (Foucault 1850). Unlike Fizeau's method that replied upon the sensitivity of theeye, Foucault's method was consistent with the approach endorsed by the geometrictradition. In his experiment, Foucault did not use the eye to detect the variation ofintensity. By means of the rotating mirror, he converted the optical property to bemeasured (the velocity of light) to a geometric parameter: the positions of the reflectedimages. In this way, his measurement no longer depended upon the physiological andpsychological status of the observer.Foucault's original investigation of the velocities of light in different media was

purely qualitative, yielding no values for light's velocity in either air or in water. Thedifficulty was determining the displacements of the deflected images, which were toosmall to be measured precisely. In 1862, Foucault improved the apparatus, replacingthe fixed reflector with a set of five mirrors. He arranged the mirrors in such a way that

144

Rotatingmirror

CHAPTER 8

Tube filledwith water

Reflector 2

Lightsource

Figure 8.6 Foucault sapparatus/or measuring the velocity 0/light

the light beam was reflected back and forth, and that the total path was expanded to 20meters (Foucault 1862). In this way he was able to make the displacements of thedeflected images measurable (up to 0.7 millimeter), and, accordingly, determine thatthe precise value of the velocity of light in air was 298,000,000 meters per second.Foucault's measurement corrected the overestimated value given by Fizeau a decadebefore and was soon adopted as the standard by the Royal Astronomical Society.

6. THE STATUS OF THE WAVE THEORY

Fizeau's and Foucault's measurements of the velocity of light did not immediatelydraw attention from the optical community. Although the velocity of light in air wasan important parameter, itwas not directly related to any particular optical theory. EvenFoucault's comparison of the velocities of light in different media did not settle thedebate. Brewster, for example, was not persuaded by Foucault's claim that hisexperiment proved the wave theory and discredited its rival.7Brewster did not questionFoucault's experimental findings that light traveled faster in air than in water, but hestrongly disagreed with anyone who attempted to use Foucault's experiment as acrucial test of the two rival theories of light. He conceded that Foucault's experimentreally supported the wave theory, but he insisted that there should be an essentialdifference between confirming a theory and demonstrating its truth. He argued that"Arago himselfnever even asserted that the undulatory theory was demonstrated evenby his own early experiments and those ofFresnel. He for twelve years looked forward

THE GEOMETRIC TRADITION 145

to the experiment of Foucault as a confirmation of his views; and were he alive, hewould tell us, with his usual candour, that something more is wanting to make theprevailing theory of light a theory of universal and necessary faith" (Brewster 1854,262; original emphasis).Brewster had long been claiming that explaining and predicting facts were by no

means a test of a theory's truth. According to his philosophical standpoint, ahypothesis, no matter how successful and useful, was essentially different from thelaws ofnature. In order to prove the truth of a hypothesis, it was necessary to show thatthe hypothesis had revealed a true cause ofnature, and this was exactly what the wavetheory failed to achieve. Brewster insisted that, although the wave theory could explaina considerably large number of optical phenomena and even could predict some newfacts, the theory did not correctly reveal the true causes of optical phenomena. He said,"Now, though the undulatory theory does assume an ether, invisible, intangible,imponderable, inseparable from all bodies, and extending from our own eye to theremotest verge of the starry heavens; yet, as the expounder of phenomena the mostcomplex, and otherwise inexplicable; and as the predicter of highly important facts, itmust contain, among its assumptions, (though, as a physical theory, it may still be false)some principle which is inherent in, and inseparable from, the real producing cause ofthe phenomena of light; and to this extent it is worthy of our adoption as a valuableinstrument of discovery, and of our admiration, as an ingenious and fertilephilosophical conception" (Brewster 1838a, 162; original emphasis). Thus, Foucault'sexperiment could improve the explanatory power ofthe wave theory but not its abilityto reveal the true causes of optical phenomena.Moreover, Brewster indicated that it was possible to explain Foucault's experiment

in terms ofan early version of the particle theory. Newton in his second paper on colorand light, read to the Royal Society in 1675, proposed a theory of light in which hecombined some principles of the particle theory and some of the wave theory. Newtonassumed the existence of both the particles of light and the ether, and explained a seriesof optical phenomena by the supposition that "light and ether mutually act upon oneanother, ether in refracting light, and light in warming ether" (Newton 1675,255).Brewster believed that "with that theory, which we do not adopt, the great experimentof Foucault is not at variance" (Brewster 1854, 263). Thus, Foucault's experimentshould not be used as a crucial test either to justify the truth of the wave theory or toprove the falsehood of the particle theory.The impact of Foucault's and Fizeau's measurements on physical optics was

indirect, not through tipping the balance in the debate between the two rival theoriesof light, but through offering evidence for the unification of physical optics andelectromagnetism. From his mathematical analysis, James Maxwell in the 1850s hadderived the velocity of the transverse waves propagating through the electromagneticether (310,740,000 meters per second). Maxwell learned of Fizeau's measurement in1861 and subsequently of Foucault's in 1862, and he was amazed to see thecoincidence between the experimental measurements and his theoretical calculation.He then reasoned that "the velocity of transverse undulations in our hypothetical

146 CHAPTER 8

medium, calculated from the electro-magnetic experiments ofKohlrausch and Weber,agrees so exactly with the velocity of light calculated from the optical experiments ofM. Fizeau that we can scarcely avoid the inference that light consists in the transverseundulations of the same medium which is the cause of electric and magneticphenomena" (Maxwell 1965, vol. 1,500; original emphasis).8 Maxwell's belief in theidentity ofoptical and electromagnetic phenomena opened up a new research directionthat eventually led to the unification ofthe wave theory oflight and the electromagnetictheory.9The unification with the electromagnetic theory affected the wave theory of light

profoundly. The most significant change was the improvement of its explanatorypower. The wave theory had been handling optical phenomena, such as reflection,refraction and double refraction, inconsistently, but, after the unification it was able toexplain them coherently in terms of the variation in the same property of the medium(the inductive capacity). More importantly, a couple of anomalies that had perplexedwave theorists for several decades, such as dispersion and selective absorption, now forthe first time were accounted for within the electromagnetic framework. Thus, in his1885 British Association Report on optical theories, Glazebrook proclaimed that "theelectro-magnetic theory, if we accept its fundamental hypotheses, is thus seen to becapable ofexplaining in a fairly satisfactory manner most of the known phenomena ofoptics" (Glazebrook 1885,260). But the improvement of the explanatory power hada price. After the unification with the electromagnetic theory, the wave theory of lightlost its independent status. At the end ofhis 1885 report, Glazebrook concluded that inthe future "we should then have a complete electro-magnetic theory ofoptics, or rathera complete theory of the ether embracing electro-magnetism and optics" (Glazebrook1885, 261). In this way, physical optics, represented by the wave theory of light,became a part of radiation physics. As pointed out by Vasco Ronchi, "the study ofphysical light, or lumen in the medieval sense, thereby entirely lost its specific character. .. Optics no longer had any reason to exist as a chapter ofmodem physics. Just assound had become a part ofmechanics, so optics was absorbed by electromagnetism"(Ronchi 1957, 19; original emphasis).

CHAPTER 9

THE VISUAL TRADITION AND THE CLOSURE OFTHE OPTICAL REVOLUTION

This chapter examines how the optical revolution ended. The visual tradition playeda critical role in bringing the optical revolution to a close, but not through settling thedebate. With its emphasis upon the intrinsic role of the eye in optical experiments, thevisual tradition nurtured a group of interdisciplinary researches within the field ofoptics, including physiological optics, photometry, photography and the making of so­called "philosophical toys." Due to the proliferation of specializations around the midnineteenth century, physical optics was no longer the central domain ofoptics, and bothsides in the debate became apathetic about the question of the nature of light. Thedebate between the particle and the wave theory was not settled but becameunimportant and insignificant to the members of the optical community, and closureof the "optical revolution" took the form of proliferation of disciplines.

1. STEREOSCOPES AND THE STUDIES OF SPACE PERCEPTION

The visual perception of depth and distance had long been controversial. As we havebriefly discussed before, in the seventeenth century Descartes attempted to explain theperception of depth and distance in terms ofgeometric principles. He believed that theeyes determined the distance to an object according to the convergence of their opticaxes, just as a blind man might feel out a distance with two sticks, one in each hand. Inthe early eighteenth century, Berkeley rejected Descartes's geometric account, notingthat "when we look at a near object with both eyes, according as it approaches orrecedes from us, we alter the disposition of our eyes, by lessening or widening theinterval between the pupils. This disposition or tum of the eyes is attended with asensation, which seems to me to be that which is the case brings the idea of greater orlesser distance into the mind . .. The mind has, by constant experience, found thedifferent sensations corresponding to the different dispositions of the eyes to beattended each with a different degree ofdistance in the object" (Berkeley 1963,23-4).The differences between Descartes's and Berkeley's accounts of space perception werefundamental, but these two accounts remained purely speculative -- neither Descartesnor Berkeley could test their theories by observation or experiment.The studies of space perception took a significant tum in the early nineteenth

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X. Chen, Instrumental Traditions and Theories of Light© Springer Science+Business Media Dordrecht 2000

148 CHAPTER 9

century. Coming from the visual tradition, Brewster had long been interested in thevisual perception ofdepth and distance. In 1826, he published an article in EdinburghJournal o/Science discussing a phenomenon of spatial deception. The fIrst report ofthis kind of deception appeared at the 1744 meeting of the Royal Society, when acompound microscope was exhibited. When the members looked through themicroscope at a coin, some of them perceived the head of the coin as depressed, butothers saw it as elevated. Brewster used a much simpler arrangement to replicate thephenomenon. He used an engraved seal (a cameo), illuminated by a candle a few inchesaway. Viewing the seal with an eyepiece, Brewster immediately experienced theillusion that the depressions of the seal rose to elevations. In other words, he saw aconversion ofcameos into intaglios. According to Brewster, this conversion occurredbecause the eyepiece inverted the image of the seal, including the relative location ofthe shadow inside the seal, upon which we made the distinction between cameos andintaglios. Brewster concluded that "it cannot therefore be doubted, that the opticalillusion ofthe conversion of a cameo into an intaglio, and ofan intaglio into a cameo,by an inverting eye-piece, is the result of an operation ofour own minds, whereby wejudge of the forms ofbodies by the knowledge we have acquired oflight and shadow"(Brewster 1826, 103).Brewster's account ofthe illusion, which appealed to our experience andknowledge

of shadows and thus was in many ways similar to Berkeley's position, was criticizedby Wheatstone. In an article published in Philosophical Transactions in 1838,Wheatstone reported that he was able to observe the same illusion without using aneyepiece, which was crucial in Brewster's experimental arrangement, for it caused theinversion ofthe image. Wheatstone observed that the same conversion ofcameos intointaglios took place when the objectwas viewed through an open tube without any lens.So, Brewster's explanation in terms of the experience and knowledge of shadows didnot reveal the cause of the illusion. To account for the phenomenon, Wheatstoneproposed a totally different hypothesis. He said, "ifwe suppose a cameo and an intaglioofthe same object, the elevations ofthe one corresponding exactly to the depressionsof the other, it is easy to show that the projection ofeither on the retina is sensibly thesame. When the cameo or the intaglio is seen with both eyes, it is impossible to mistakean elevation for a depression" (Wheatstone 1838, 384). In other words, the illusiveconversion of cameos into intaglios came from the defIciency of using a single eye.This hypothesis further implied that the perception of depth and distance requiresbinocular vision.To prove his hypothesis, Wheatstone invented a special instrument called a

stereoscope, in which two boards were set up vertically at each end ofa horizontal bar,facing a pair of plane mirrors between them (Figure 9.1). These mirrors were aboutfour inches square, and adjusted so as to form a right angle to each other. WheatstonefIxed on the boards a pair of outline figures, which were different projections of thesame object from two points ofsight separated by an interval ofabout 2.5 inches (equal

THE VISUAL TRADITION 149

to the distance between the eyes). Placing his eye as near as possible to the mirrors,Wheatstone was able to see the reflected images ofthe figures simultaneously, each eyeseeing only one image. In this way, he perceived a three-dimensional image by meansof the two dissimilar outline figures projected on the two retinas. Wheatstone triedmany different geometric figures such as cubes, cones and pyramids, and all these two­dimensional imageswere turned into three-dimensional solidbodies by the stereoscope.On the basis ofthese experiments, Wheatstone was confident that he had successfullyproved his hypothesis. "The preceding experiments render it evident," he said, "thatthere is an essential difference in the appearance of objects when seen with two eyes,and when only one eye is employed, and that the most vivid beliefof the solidity ofanobject ofthree dimensions arises from two different perspective projections of it beingsimultaneously presented to the mind" (Wheatstone 1838,380).Wheatstone demonstrated his stereoscope at the 1838 meeting of the British

Association. Brewster's initial reaction to Wheatstone's device was very enthusiastic.He appraised Wheatstone's report at the meeting as "one of the most valuable opticalpapers which had been presented to the Section" (Anonymous 1838, 650). On hisreturn to Scotland after the meeting, Brewster immediately ordered a stereoscope fromAndrew Rose, the London optical instrument maker, and began his own stereoscopicexperiments. After repeating many ofWheatstone's experiments, Brewster confirmedthat binocular vision did generate the perception of depth and distance. Brewster alsofound that some ofthe stereoscopic effects described by Wheatstone did not exist. Forexample, Wheatstone reported that he was able to use his stereoscope to superimposethe images of two figures with significant differences, such as lines with differentlengths or different orientations, and still obtain stereoscopic effects. But Brewster wasnever able to obtain the same results and thus insisted that the stereoscopic effectsreported by Wheatstone were illusions (Brewster 1844,439-44).

~Mirrors

.;::::::J

Figure OOJ DO rm Figure

~ ~ ~-.........:: ........./

Figure 9.1 Wheatstone:S reflecting stereoscope

150 CHAPTER 9

Brewster also disagreed with Wheatstone on the cause of spatial perception.Wheatstone believed that stereoscopic effects arosewhen themind incorporated imageswith different perspectives, but he did not offer any detailed account of theincorporation process. According to Brewster, Wheatstone's explanation appealed tosomething unobservable and untestable in principle. To avoid Wheatstone's problems,Brewster offered an explanation of spatial perception that appealed only to thefunctions of the eye. When we observed an object with both eyes, Brewster reasoned,we actually saw it in two different directions, and obtained two slightly differentimages on the retina. For example, when we looked at a section ofa cone (with its topcut off), two plane images appeared on the retina of the two eyes, equivalent to usingthe right eye to look at picture L and the left eye at picture R in Figure 9.2 respectively.But we saw a solid cone, due to the convergence of two sets of optic axes connectingeach eye with every visible point of the object. When we used both eyes to look at aparticular point of the cone, we converged upon it two optic axes from both eyes. Atthe intersection of the two optic axes, we saw a visible point single with two eyes, andthen experienced perception of space and distance. In the same manner, the eyesurveyed the whole object rapidly, seeing each point single and forming a three­dimensional image. 1

Brewster believed that the convergence of optic axes could explain how astereoscope generated three-dimensional images. Continue to use Figure 9.2, andsuppose that the right eye looked at picture L and the left eye at picture R. The opticaxes that connected each eye with a pair of corresponding points in the picturesconverged in a place between the pictures and the eyes. Repeating the convergenceprocess, a three-dimensional image of the cone appeared (Brewster 1844,444-55). InWheatstone's stereoscope, where the right eye looked at picture R and the left eye atpicture L, the convergence occurred behind the pictures. This explained why thedistance between the two pictures must be much smaller than the distance between theeyes in Wheatstone's stereoscope. With simple geometric analysis, Brewster provedthat the convergence would never occur ifthe distance between the pictures was equalto the distance between the eye. This set a limit to the size ofpictures that Wheatstone'sstereoscope could use.In addition to the size limit, Brewster identified several other defects of

Wheatstone's stereoscope. First, Wheatstone's stereoscope required complicatedoperations, including very cumbersome alignments ofthe positions ofthe mirrors, thepictures and the eyes. Because of that, Brewster called Wheatstone's stereoscope "aclumsy and unmanageable apparatus, rather than an instrument for general use"(Brewster 1856,62). Second, because Wheatstone used glass mirrors, more than 90percent of the incident light was lost after the reflection at 45 degrees, and the imagesthat appeared in the mirrors were always faint. Third, the eye was exposed to scatteredlight from the background. Because of the bright background and dim targets, the eyequickly lost its sensitivity and was unable to see distinct pictures with details. Thisexplained, according to Brewster, why it was very difficult to use Wheatstone'sstereoscope to generate three-dimension images from photographs.

Picture L

THE VISUAL TRADITION

Picture R

151

Figure 9.2 Convergence ofoptic axes

To overcome these problems, in 1849 Brewster designed a new stereoscope, whichused a pair of half lenses to generate stereoscopic effects. He called it a lenticularstereoscope, and it consisted ofa pyramidal box with two viewing tubes, each ofwhichheld a half lens inside (Figure 9.3). The pictures to be observed were put at the bottomof the pyramidal box. When the observer looked at the pictures through the viewingtubes, the two half lenses unified the images of the pictures through refraction andgenerated stereoscopic effects. Brewster's new design was very compact, and its

152 CHAPTER 9

Figure 9.3 Brewster :s lenticular stereoscope

operation merely required keeping the lenses in focus. More importantly, because itrelied on refraction, the images of the pictures were relatively bright. The use ofviewing tubes further reduced the exposure to scattered light and protected thesensitivity of the eye. As a result, Brewster's stereoscope could handle photographseasily and beautifully. Because of these advantages, Brewster's lenticular stereoscopewas quickly accepted and, as we will see later, became one of the most popular"philosophical toys" in the Victorian age.

2. STROBOSCOPES AND THE STUDIES OF VISUAL PERSISTENCE

Afterimage or visual persistence (persisting visual sensations after the visual stimuli)was another visual phenomenon that drew great attention from both the optical and thepsychological communities in the early nineteenth century. Jan Purkinje, the Czechphysiologist, made the first systematic reports of afterimages in 1825, and later, in1831, Wheatstone translated Purkinje's discoveries into English. Purkinje'sexperimental setup was very simple: he used only his own eyes and fingers as the"apparatus." In the experiment, he directed his eyes toward the sun, and quickly movedhis hand (with the fmgers spread) from one side to the other so that the fingersalternately intercepted the sunlight. At the beginning of the experiment, Purkinjereported that he perceived a yellow-red glare, later replaced by a beautiful and regularfigure. Continuing the experiment for some length of time, Purkinje was able todescribe in detail the shape ofthe figure, which appeared to consist of "small squares,chequered as in a chess board, and alternately bright and dark" (Wheatstone 1830,

THE VISUAL TRADITION 153

114).In the same year that Purkinje discovered the illusion caused by alternating light,

Roget published an article in Philosophical Transactions describing a different kind ofillusion. Rogel's discovery came from an observationwhile viewing a rotating carriagewheel through the intervals ofa series of vertical bars. Under these circumstances, thespokes of the wheel seemed to have a considerable degree ofcurvature. Except for thetwo spokes at the vertical position, all other spokes appeared curved (pointingdownward), and the spokes in the lower part of the wheel looked more curved thanthose in the upper part. Unlike Purkinje who gave only empirical descriptions, Rogettried to offer a qualitative explanation of the illusion. He believed that the illusion inprinciple resulted from the persistence ofvisual sensation, namely that "an impressionmade by a pencil of rays on the retina, if sufficiently vivid, will remain for a certaintime after the cause has ceased" (Roget 1825, 135). Specifically, the image of everyspoke would stay in the retina for a while because of visual persistence and then mixwith the subsequent images of the same spoke that had shifted to a different positiondue to the horizontal movement of the wheel and the upward or downward motion ofthe spoke. With mathematical analysis, Roget proved that the combination of theseimages could form the impression ofa curved spoke.2

Michael Faraday published a paper in 1831 on what he called "a peculiar class ofoptical deceptions" that he observed in a series of experiments. He designed a special

Figure 9.4 Faraday's anorthoscope

154 CHAPTER 9

apparatus for these experiments, which later was calIed anorthoscope. The keycomponents ofthis apparatus were two wheels made ofwhite cardboard, each ofwhichhad 12 rectangular teeth and 12 gaps of the same size. He mounted the wheels on thesame axis but on different axles (Figure 9.4). When a single wheel was rotating, it gavea uniform gray tint. The deceptive illusion appeared when the two wheels were rotatingin opposite directions. Viewing the wheels along the direction paralIel with the axis,Faraday saw a fixed wheel with twenty-four teeth. Like Roget, Faraday immediatelyattributed the cause ofthis illusion to the persistence of sensation. "The cause of theseappearances, when pointed out, is sufficiently obvious, . " The eye has the power, asit weII known, of retaining visual impressions for a sensible period of time;... Butduring such impressions, the eye, although to the mind occupied by an object, is stillopen, for a large proportion of time, to receive impressions from other sources; for theoriginal object looked at is not in the way to act as a screen, and shut out all else fromsight; the result is, that two or more objects may seem to exist before the eye at once,being visualIy superposed" (Faraday 1831,210-1). SpecificalIy, Faraday reasoned thatthe key to explain the ilIusion was the position and size of the gaps that separated theteeth. These gaps alIowed the eye to look through and see the dark background. Whena single wheel was rotating, the gaps between the teeth were moving constantly and nostable images appeared. But when two wheels were rotating, the teeth of the frontwheel obscured the gaps in the back wheel. If these wheels were rotating in oppositedirections, the two sets of teeth would repeatedly overlap each other and create spacesthat were exposed to and hidden from the eye alternately but which always stayed inthe same places. Because of visual persistence, the successive impulses from thebackground generated continuous sensation in the eye, and thus the eye saw a fixedwheel. With simple analysis, Faraday further showed that the size of these spacescreated by the opposite rotations of the wheels was only one half of the size of theoriginal gaps. Thus, the number of teeth in the illusive wheel was doubled.The discovery of visual persistence quickly led to the invention of several new

optical instruments, all ofwhich incorporated some element ofmotion to create visualillusions. John Paris, a physician in London, designed a very small instrument in 1825,calIed the thaumatrope, or the wonder turner. It consisted ofa circular piece ofcard andstrings attached to its opposite sides so that it could be twirled around quickly. On eachside ofthe card, there was a part ofa picture. When the card was rotating, both pictureswere seen superimposed, creating animated effects (Paris 1827). Joseph Plateau, theBelgian scientist who had made significant contributions to visual optics, designed adifferent device in 1830. The main component of Plateau's device was a diskcontaining 16 successive pictures ofa dancer and 16 rectangular slots (Figure 9.5). Hemounted the disk to an axis so that it could spin, and placed a mirror facing the picturedside of the disk. When the disk was rotating, Plateau stood behind the disk and lookedat the mirror through the slots. He saw successive images of the dancer, who appearedto move continuously due to visual persistence. Plateau named this device aphenakistoscope, or an "eye-deceiver," which today we calI a stroboscope.3 He sent hisfirst model to Faraday because he believed that his instrument r./)uld offer insight into

Disk withpictures

THE VISUAL TRADITION 155

Figure 9.5 Plateau sstroboscope

Faraday's wheel-and-spoke illusion (Boring 1942,590).Plateau's stroboscopes soon became a powerful tool for studying visual persistence.

Brewster picked up the issue ofafterimage caused by intermittent stimulation in 1834,apparently without knowing Purkinje's work. In an article published in PhilosophicalMagazine, Brewster described a series ofobservations related to visual persistence. Forexample, when he was walking beside a high iron railing, he directed his closed eye tothe sun so that its light was successively interrupted by the iron rails. The pattern thatBrewster sensed was similar to Purkinje's checkboard figures, except that Brewster'sfigures were colored.Brewsterwas not satisfied with these observations. To learnmore about the subje.ct,

Brewster designed an experiment, using the newly available stroboscope. "In order tomake light produce a series of successive impulses on the retina, and on the same partof it, I look through the openings ofthe revolving disc ofthe phenakistoscope with oneeye, and fix it steadily upon the same point ofthe luminous ground" (Brewster 1834b,242). With this set-up, Brewster was able to adjust the intervals between successiveimpulses of light by changing the speed of the disc. When the experiment began, thedisc was rotating at a great velocity. Brewster saw a very faint and uniform light overthe whole luminous surface. As he reduced the velocity of the disc, the light becameless uniform, and the luminous image began to flicker.Brewster tried to offer a quantitative account for the observations. He believed that

the key was the duration ofvisual impressions on the retina. Learning from the workof Jean D'Arcet, a French natural philosopher, Brewster knew that the impression of

156 CHAPTER 9

light continued on the retina about one eighth ofa second after the luminous body waswithdrawn (Brewster 1843,34). Thus, when the velocity of the disc was high, theinterval between successive impulses would be smaller than one eighth of a second.Consequently, the impression ofone impulse did not fade away before another impulsecreated a new impression, and discrete impulses would generate continuous sensation.But when the velocity of the disc was reduced, the interval between successiveimpulses would eventually increase to a point equal to the duration of visualimpressions. At this point, the impression of one impulse would fade away before anew impulse created another impression, and thus the eye saw a flickering image.Brewster also reported that he observed complex colored patterns when the rotation

speed ofthe disc was further reduced. He gave some detailed description ofthe pattern.The center of the pattern was a square, one ofwhose diagonals was vertical. Patchesofblue-purple color appeared in different parts of the field, forming a sort ofnetwork.But Brewster was never able to draw the pattern, because the elements of the pattern,including their colors, brightness and forms, were constantly changing. Brewsterbelieved thatthe unstable observation resulted from the defects ofthe eye. Specifically,he was suspicious that his age was a factor -- he was 53 years old by that time. Thus,Brewster pinned his faith on the new generations. He said that "I have no doubt thatobservers who have younger eyes than mine, and who shall have the courage to repeatthe experiments with the direct light ofthe sun, and with a disc having narrow slits, andrevolving upon a fixed axis so as to have its velocity uniform, will be able to obtain anaccurate representation of the pattern in question" (Brewster I834b, 243).

3. KALEIDOSCOPES AND THE MAKING OF "PHILOSOPHICAL TOYS"

Like the eye, man-made optical instruments also generated visual illusions. Since thesixteenth century, people had learned to generate multiple illusions by means of acombination of mirrors. For example, in 1558 Baptista Porta constructed a devicecalled a polyphaton, which employed two plane mirrors inclined to each other at acertain angle to generate multiple reflections. Later Athanasius Kircher in 1646described a similar device and specified the relationship between the inclination of themirrors and the number of the images (Brewster 1870,163-71). In the eighteenthcentury, a couple of similar instruments, like the Debusscope and polyscope, weremade, both ofwhich multiplied images placed between two inclined mirrors. Unlikeother optical instruments that were employed in the study of nature, devices likeDebusscopes and polyscopes remained "toys" for amusing natural philosophers.Brewster became interested in the phenomenon ofmultiple illusions in 1814 during

a series of experiments on the polarization of light by successive reflection. In theseexperiments, Brewster observed multiple images caused by repeated reflections atmirrors inclined to each other at a certain angle. In the subsequent years, Brewstercontinued to study this peculiar phenomenon and eventually realized that the number,form and orientation ofthe multiple images depended not just upon the angle betweenthe mirrors, but also upon the positions of the object and the eye. He found that to

THE VISUAL TRADITION 157

produce perfectly symmetrical forms by repeated reflections, the following conditionswere necessary. First, the mirrors must be placed at an angle that formed an exactmeasure ofacircle (an aliquot part ofa circle), such as 30 degrees (1112) or45 degrees(118); second, the object to be observed must be placed in contact with one end of themirrors; third, the eye must be at the other end, as near as possible to the connectingpoint of the two mirrors.Brewster constructed the fIrst kaleidoscope using these conditions. He put two

rectangularmetallic reflectors inside a tube, inclined to each other at 30 degrees (Figure9.6). At one end of the tube, he fIxed permanently pieces of colored glass and otherirregular objects. He showed this simplest form of kaleidoscope to some members ofthe Royal Society ofEdinburgh, who were much struck with the beauty ofthe multipleimages. Despite its initial successes, Brewster was not completely satisfIed with thiskaleidoscope. He soon replaced the fIxed colored glass with a transparent cell,containing pieces ofcolored glass that could move freely (Figure 9.6). In this way, newmultiple images appeared every time the tube was turned. To further increase the rangeof its application, Brewster later added a convex lens to the kaleidoscope. The convexlens, fIxed to a drawing tube, formed distinct images at the end of the reflectors forobjects otherwise too big to fIt in the triangular aperture or too far from the device.After these improvements, Brewster believed that his kaleidoscopewas [mally qualifIedto be a "general philosophical instrument ofuniversal application" (Brewster 1819,6).But the kaleidoscope was not designed for the purpose ofstudying nature. Brewster

believed that the functions and signifIcance of the kaleidoscope were different fromother philosophical instruments. He fIrst stressed the value of the kaleidoscope ingenerating symmetric images. According to Brewster, symmetrywas a common featurein nature, and thus an essential element of artistic beauty. In most forms ofart, exceptperhaps for those related to landscape, beauty arose directly from symmetry of forms.Thus, the kaleidoscope could be a valuable tool for artists who needed symmetricforms. Particularly in architectural ornamentation and decorative painting, whererepeated and symmetric forms were the dominant style, the kaleidoscope could be a

Transparent cellMetallic reflectors

,.''-:~~=-=:'.~~~== --=:::,.:~~:,:::'.:':.:::-.:::::::::=-

--_.._..__.._....__.•...__..._...._.._._.

Figure 9.6 Brewster skaleidoscope

158 CHAPTER 9

source of inspiration and a means of reducing labor (Brewster 1819, 113-28). It isdifficult to determine the extent of the actual use of the kaleidoscope in art. But itseems that Joseph Turner, a British landscape-painter, did use it because one criticspecifically criticized his Ulysses Deriding Polyphemus in 1829 for exhibiting "thevehement contrast of a Kaleidoscope or a Persian Carpet." William Hunt, a pre­Raphaelite painter, made at least one watercolor study of the view down akaleidoscope, and a critic specifically cited Brewster in connection with Hunt'sinnovatory style (Kemp 1994,215).Another important function of the kaleidoscope, according to Brewster, consisted

in its power of entertainment. Optical instruments, including telescopes andmicroscopes, often served different purposes in different hands. When they were usedby natural philosophers, these instruments were the means to explore nature, but whenthey were possessed ~y ordinary people, they became devices of amusement. Somesimply used optical instruments to generate astonishing images and to occupy theirleisure time in an amusingmanner. But inBrewster's judgement, neither telescopes normicroscopes could serve the entertainment needs effectively. Telescopes andmicroscopes were expensive, and their operations required considerable skill andcomplex preparations. On the contrary, the kaleidoscope could function as aninstrument of amusement in a very effective and efficient way. "The combination offme forms, and ever-varying tints, which [the kaleidoscope] presents in succession tothe eye, have already found, by experience, to communicate to those who have a tastefor this kind ofbeauty, a pleasure as intense and as permanent as that which the fmestear derives from musical sounds." And the preparation and operation of thekaleidoscope were easy -- "When it is once properly constructed, its effects areexhibited without either skill or labor" (Brewster 1819, 135).

It is important to note that there was a political agenda behind Brewster's emphasisof the amusing and entertaining functions of the kaleidoscope. For a long time,Brewster had been a passionate advocate ofthe role ofscience in society. As one ofthefounders ofthe BritishAssociation, Brewsterwas particularly concernedwith the statusofscience in society. He complained about the decline ofscience in Britain and the lackof government support for scientific research. According to Brewster, an effectivesolution to all these problems was education, which could improve the public'sunderstanding of nature and eventually promote the status of science. Thus, thefunctions and applications of scientific instruments consisted not just in exploringnature, but also in educating the public in the form of "instructing the young, orastonishing the ignorant."4Having realized the possible applications and potential value ofhis kaleidoscope,

Brewster patented his design in 1817 (Morrison-Low 1984, 84). But when he showedthe patented kaleidoscope to some of the London opticians, its remarkable, but at thesame time, simple, design became known, and overnight thousands of copies ofBrewster's kaleidoscope, many of which were poorly constructed, appeared in thestreets of London. In a letter he wrote in London to his wife in May 1818, Brewsterreported that "you can form no conception of the effect which the instrument

THE VISUAL TRADITION 159

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[kaleidoscope] excited in London; all that you have heard falls infmitely short of thereality. No book and no instrument in the memory of man ever produced such asingular effect. They are exhibited publicly on the streets for a penny, and I had thepleasure of paying this sum yesterday. These are about two feet long and foot wide.Infants are seen carrying them in their hands, and the coachmen on their boxes are busyusing them, and thousands of poor people make their bread by making and sellingthem" (Gordon 1870, 99). According to Brewster's own estimation, no fewer than200,000 kaleidoscopes were sold in London and Paris in three months.Makingkaleidoscopes then became a profitable business. Some opticians inBritain

not only made kaleidoscopes according to Brewster's design but also produced newmodels with significant improvements. Among them, Robert Bate, an optician inLondon, designed a polyangular kaleidoscope, which made the angle between the tworeflectors adjustable and therefore was able to generate more complicated patterns(Brewster 1819, 79-86). Another improvement was the parallel kaleidoscope designedby John Ruthven, an optician in Edinburgh. In the parallel kaleidoscope, the reflectorswere parallel to each other, generating repeated images along a straight line (Brewster1819, 90-2). Even Peter and George Dollond, the most prestigious optical instrumentmakers in Britain, jumped on the bandwagon ofmaking kaleidoscopes. They designeda universal kaleidoscope that united the properties ofthe common kaleidoscope and theparallel kaleidoscope (Brewster 1819, 87-90).In this way, the community of optical instrument makers, or opticians as they

labeled themselves, began to experience some fundamental changes.s Before thekaleidoscope, the demand for optical instruments was low -- only a few elites neededthem and could afford to pay for them. Accordingly, the community of optical

400

Figure 9.7 Number ofoptical instrument makers in Britain. 1801-1850

160 CHAPTER 9

instrumentmakers was small. But the invention ofthe kaleidoscope changed the wholepicture. The fact that 200,000 kaleidoscopes were sold within three months not onlymade many opticians rich, but also caused an expansion of the community. Figure 9.7lists the numbers of optical instrument makers in the British Isles between 1801 and1850.6 We see that the size of the community of optical instrument makers remainedrelatively stable in the fIrst 15 years of the nineteenth century, but it began to expandaround 1816 and 1817, coinciding with the invention of the kaleidoscope. After that,many new philosophical toys emerged and offered further stimuli to the growth of thecommunity. We have discussed Paris's thaumatrope (1825), Faraday's anorthoscope(1831) and Plateau's stroboscope (1833) in previous sections. Other philosophical toyssuch as the magic lantern, the phantasmagoria, the teinoscope, the static panorama, themultimedia diorama and the iconoscope, though not as dramatic and popular as thekaleidoscope, also created steady demand for the services ofopticians.7 By the end ofthe 1840s, Brewster's' lenticular stereoscope caused another round of expansion.According to Brewster's estimation, more than 500,000 lenticular stereoscopes weresold (Brewster 1856,36), and the number of optical instrument makers increased toaround three hundred. By the mid nineteenth century, the community of opticalinstrument makers had become a powerful player in the fIeld of optics.s

4. BINOCULAR CAMERAS AND THE PHOTOGRAPHIC INDUSTRY

Among the philosophical toys discussed above, the stereoscope deserves moreattention. Before the arrival of photography, the stereoscope was simply an intriguingphilosophical toy that could generate stereoscopic illusions, but the introduction oftheTalbotype process, published in the early 1840s by William Fox Talbot, gave thestereoscope a whole new life.Both Wheatstone and Brewster were keenly interested in the newly invented art of

photography. Because oftheir personal connections with Talbot and Herschel, the twopioneers ofphotography, they had been aware ofthe Talbotype process long before itsdetailswere published. Soon after learning ofTalbot's invention,Wheatstone requestedHenry Collen, one of the earliest photographers, to make pictures for his stereoscope.In 1841 Collen prepared for Wheatstone several pairs of stereoscopic pictures, thesubjects ofwhich included full-size statues, buildings and living persons (one ofthemwas Charles Babbage). All these photographs generated splendid three-dimensionalimages in Wheatstone's stereoscope after careful alignment. But due to the difficultyof alignment process, the newly discovered stereoscopic photography did notimmediately arouse public interest.Wheatstone gave detailed instructions for preparing stereoscopic pictures to be used

in his stereoscope. In general, each pair of stereoscopic pictures should be taken atdifferent positions by moving the same camera a few inches laterally. Sincestereoscopic pictures would be seen in Wheatstone's stereoscope at a distance ofeightinches before the eye, the convergence of the optic axes was about 18 degrees, giventhat the distance between the eyes was 2.5 inches. "To obtain the proper projections for

THE VISUAL TRADITION 161

this distance," Wheatstone suggested, "the camera must be placed, with its lensaccurately directed towards the object, successively in two points ofthe circumferenceof a circle ofwhich the object is the centre, and the points at which the camera is soplaced must have the angular distance of 18 0 from each other, exactly that ofthe opticaxes in the stereoscope" (Wheatstone 1852, 7). Ifpictures taken without following thisrule, stereoscopic images would be distorted. For example, if the angular distance ofthe camera's positions was larger than 18 degrees, the depth of the image would beexaggerated; if the angular distance was smaller than 18 degrees, the image wouldbecome flat.Later various stereoscopic cameraswere invented in accordancewithWheatstone's

instructions to simplify and speed up the process oftaking stereoscopic photograph. In1858, T.H. Powell designed a single-lens stereoscopic camera, in which the wholecamera was moveable laterally along a groove. After the fIrst picture had been takenon one halfof the plate, the camera was moved to a new location and the other halfofthe plate was then exposed. The range ofthe camera's lateralmovementwas 13 inches,which allowed the maximum distance between the lens and the object to be about 40inches (Figure 9.8).Through his personal correspondence with Talbot, Brewster also learned of the

invention of photography before its publication. He immediately introduced the newinvention to John Adamson, his colleague at St. AndrewsUniversity. UnderBrewster'sdirection, in May 1841 Adamson made a pair of stereoscopic portraits (using himselfas the subject) by means ofa single camera, the fIrst successful attempt in Scotland.Using a single camera to make stereoscopic pictures involved complicated

preparation. When Brewster invented his lenticular stereoscope, he immediatelyrealized that the same principle could be applied to the preparation of stereoscopicpictures. He then designed a binocular camera, which could have pictures taken

Figure 9.8 Sing/eo/ens stereoscopic camera, designed by TH. Powell

162 CHAPTER 9

Object

/ .... /. / ..... /.

Figure 9.9 Double-lens stereoscopic camera, design by Brewster

simultaneously by using two lenses (Figure 9.9). To ensure the quality ofstereoscopicpictures, Brewster instructed that the two lenses of a binocular camera should haveidentical properties, such as the same aperture and focal length. Because it was verydifficult, if not impossible, to grind and polish two lenses of exactly the same focallength, Brewster suggested to bisect a single lens, and construct the binocular camerawith semilenses that could give images of precisely the same size and defmition. Butmore importantly, Brewster insisted, the two semilenses must be placed at the distanceof2.5 inches, the average distance of the eyes in humans (Brewster 1851,260-2).Brewster believed that his method ofproducing stereoscopic pictures by using the

binocular camera was much better than Wheatstone's, which relied upon monocularcameras. Since there was no trouble of determining the angular distance, Brewsterclaimed that his method was more efficient than Wheatstone's. Brewster also arguedthatWheatstone's methodwas theoretically unsound. The key to Wheatstone'smethodwas keeping the angle of the optic axes constant, always at 18 degrees. But thisconstant was arbitrary because it came entirely from the structure of Wheatstone'sstereoscope. On the contrary, Brewster believed that his own method, which chose thedistance between the eyes as the constant, was natural and objective. Furthermore, inorder to maintain a fixed angular distance, Wheatstone had to place the camera inpositions that were far apart. Thus, Brewster claimed, "the picture taken by Mr.Wheatstone's rule is one which no man ever saw or can see, until he can place his eyesat the distance of twenty inches! It is, in short, the picture of a living doll, in whichparts are seen which are never seen in society, and parts hid which are always seen'(Brewster 1856, lSI; original emphasis).Brewster described his design for the binocular camera to the 1849 meeting of the

British Association, but for a while he had difficulties in turning his design intoproduction. He could not persuade British instrument makers to produce his binocularcamera. Even Lowdon, the optician of Dundee who was producing Brewster's

THE VISUAL TRADITION 163

lenticular stereoscope, was uninterested in Brewster's binocular camera. Brewster hadto appeal to the opticians on the other side ofthe channel. In 1850, he visited Paris anddescribed his design to many French opticians. As a result, Achille Quinet made abinocular camera of similar design to Brewster's, calling it the Quinetoscope. Quinetpresented his binocular camera to the Liverpool Photographic Society in 1853 andpatented his design in 1854.9

The fIrst binocular camera available for sale, however, was made by John Dancer,aManchesteroptician. Brewsterhad demonstrated the lenticular stereoscope toDancer.Struck by the three-dimensional images produced by the instrument, Dancerimmediately set to work to construct a camera for stereoscopic photography. Tocompare Wheatstone's and Brewster's designs, Dancer conducted many experimentsand fmally agreed with Brewster that "in order to get correct stereoscopic pictures, thecentres of the Camera lenses should be at the same distance apart as the Human eyes,or at all events not to exceed three inches in distance between the centre ofthe lenses"(Dancer 1964, 130). Dancer fIrst made a simple binocular camera in 1853, and laterpresented a more sophisticated model in 1856. 10

The combination of the stereoscope and photography started a whole new chapterin optics. The fIrst big success ofBrewster's lenticular stereoscope came at the GreatExhibition of1851, where a number ofstereoscopes were shown. Among them, the onemade by Dubosq, a French optician, won a Council medal. Together with a beautifulset of stereoscopic photographs, Brewster's lenticular stereoscope attracted theattention of Queen Victoria, who admired the presentation and praised Brewster'swork. Before the closing ofthe Exhibition, Brewsterpresented to the Queen a lenticularstereoscope made by Dubosq. At thatmoment, the craze for stereoscopic photographybegan.A huge public demand for stereoscopes and stereoscopic pictures generated the

need for mass production" and the technology, the process of Talbotype, made massproduction possible -- paper positives mounted on cardboard could be mass-producedand sold at a very low price. In 1854, George Nottage founded the LondonStereoscopic Company for the manufacture of lenticular stereoscopes and theproduction of stereoscopic pictures. 1I The slogan of the company was "no family orschool should be without a stereoscope," and it specially manufactured "a stereoscopefor the million" at a price of only two shilling and six pence. Within two years, thecompany sold a halfmillion stereoscopes all over the world. By 1858, the Companyadvertised a stock of 100,000 stereoscopic pictures of various subjects, sending staffphotographers around world. The prices of these pictures were between one and twoshillings, depending upon the subject. 12

In 1862, the London Stereoscopic Company paid 2,000 guineas for the exclusiveright to take photographs of the International Exhibition. It recorded the completehistory ofthe exhibition from the opening ceremony to the dismantling, and producedpictures of every court and almost every point of great interest. The quality of thepictures amazed the public. According to a reporter from Times, in some of thepictures, "such as the collection ofglass in the English and Austrian Courts, the effect

164 CHAPTER 9

is more than stereoscopic -- it is an optical delusion" (Timbs 1862, 137). Among thesepictures, the one of the statue called "Reading Girl" was most popular, as nearly 200copies were sold per week. During the exhibition (six months), the company sold300,000 stereoscopic pictures, and consumed 70 reams of paper, 200 gallons ofalbumen (from 32,000 eggs), 2,400 ounces of nitrate of silver, and 2,800 pounds offixing salt (Gernsheim & Gernsheim 1955, 193). With this scale of production,stereoscopic photography clearly had become a mass-production business.Accompanying this change, the making of optical instruments also evolved fromcraftsmanship into an industrial age. The manufacture ofoptical instruments, togetherwith photography, constituted the earliest trades of the optical industry.

5. THE END OF THE OPTICAL REVOLUTION

Before the nineteenth century, optics was a homogeneous field. There was no clearlydefmed specialization in the field, nor any sharp division of labor among thepractitioners. But specialization and sub-disciplines in optics began to emerge at thebeginning ofthe nineteenth century, when geometric and physical optics split. By themid nineteenth century, the field ofoptics had become far more diverse. The foundingof the first photographic society in 1853, the Photographic Society of London,indicated that photography and photochemistry had become an independent sub­discipline within optics. On the practical side, although optical instrument makers didnot have their own organization, the London Great Exhibition of 1851 and subsequenttrade fairs provided them with society-like gatherings. About the same time there wasa rapid growth of interest in physiological optics that undertook to examine thefunctions of the eye as an organ of the human body. Publications on physiologicaloptics increased threefold, from about 50 papers in the 1840s to about 150 papers in the1850s (Royal Society of London 1912, vol 3, 482-504). A similar publication patternalso existed in spectroscopy. Immediately after Kirchhoffs published his fIrst paper onspectroscopy in 1859, the number of publications in this field rose steeply, from about25 papers per year in the 1850s to about 75 papers per year in the 1860s, again athreefold increase (Sawyer 1963, 14). Even photometry began to obtain its own identityduring this time due to the birth and development of the gas industry. The Journal ofGas Lighting, where many articles on measuring the intensity of light were printed,appeared in 1849. Thus, by the mid nineteenth century, optics had becomeheterogeneous, including many semi-independent disciplines or specializations suchas geometric optics, physical optics, physiological optics, photography, spectroscopy,photometry and an industry ofmaking optical instruments.The proliferation of specialized disciplines within optics had a profound impact on

the debate between the two rival theories of light. Around the mid 1850s, Brewstergradually withdrew himself from the field of physical optics. However, in the lastdecade of his life, Brewster continued to immerse himself in optical research. From1860 to 1868, he published about 40 optical papers, the majority of which were onphotography and physiological optics, and only four of them covered the topics of

THE VISUAL TRADITION 165

physical optics (Morrison-Low & Christie 1984, 132-6). During this period, Brewsterfocused his attention on the "sanatory" aspect of light, studying the influence of lighton life, particularly on human beings. In public he did not raise any criticism againstthe wave theory and seemed not interested in the debate anymore. The bravest warriorof anti-undulationism, who had been fighting the wave theory for more than fourdecades, fmally put down his spear, not because he accepted the wave account, butbecause he felt that the topic was no longer interesting.By this time many wave theorists had also lost their interest in the debate. A good

example of their apathy was their reactions to Potter's books on physical optics. In1856, Potter published the second volume ofhis Physical Optics, in which he proposeda new particle theory oflight that he hoped could replace the dominant wave theory.The key of Potter's new particle theory was to define light as material particles, but atthe same time to admit that periodicity was an essential and inherent property of light.Potter also claimed that he was able to confirm his particle theory and disprove thewave theory by experiments with interference (Potter 1859, 1). Potter's bookconstituted a direct challenge to the wave theory, especially, his announcement that hisexperiments of interference had disproved the wave theory was novel -- hitherto, noone had challenged the wave theory with experiments of interference. But Potter'sprovocative announcement did not arouse any attention from the wave camp, and histwo-volume book on physical optics passed unnoticed in major scientific journals.Apparently, no wave theorists were interested in debating the nature of light, and noone was willing to spend time in replicating Potter's experiments. It seems that thesilence from his opponents disappointed Potter, and he soon gave up his plan ofreviving the particle theory. After the publication ofhis two-volume Physical Optics,Potter never again conducted optical research. With the withdrawal of Potter, astubborn particle theorist who had kept fighting against the wave theory for threedecades, the long-term confrontation between the particle theory and the wave theoryof light fmally ended in the last year of the 1850s.The debate concerning the two rival theories of light ended not because one side

had successfully convinced the other, but because both sides lost their interest in thesubject. This raises an interesting historiographical question. For a long time, historianshave depicted the optical revolution simply as a replacement of one scientific theoryby the other. We can trace this historiography of optics back to Kuhn's notion of"scientific revolution" as it appeared in his early writings, where scientific revolutionswere defined as episodes in the development ofa single science or scientific specialty.But Kuhn later admitted that this notion of"scientific revolution" was too limited. Tocorrect the problem, Kuhn suggested adopting an analogy between scientificdevelopment and biological evolution, both ofwhich have the same pattern ofgrowthin the form ofan evolutionary tree. The pattern ofknowledge growth is "the apparentlyinexorable (albeit ultimately self-limiting) growth in the number of distinct humanpractices or specialties over the course of human history" (Kuhn 1992, 15).Proliferation of specialized disciplines is the key feature of scientific progress.Scientific revolutions also play "a second, closely related, and equally fundamental

166 CHAPTER 9

role: they are often, perhaps always, associated with an increase in the number ofscientific specialties required for the continued acquisition of scientific knowledge"(Kuhn 1993, 336). Thus, the optical revolution needs to be understood in a morecomprehensive way. The replacement ofthe particle theory by the wave theory and thesubstitution of the ray analysis by the wavefront analysis were important, but theyrepresented only one interesting aspect ofthe revolutionary change. In addition to thedisruptive change regarding the explanatory model and the analytic apparatus, theoptical revolution also had an accumulative aspect -- the proliferation of specializeddisciplines in the field of optics. In this way, the optical revolution undoubtedlyrepresented progress in human knowledge, not only because it altered our point ofviewregarding the nature of light and changed the analytic apparatus for problem solving,but because it expanded our knowledge and skills to many new domains.

CONCLUSION

In The Structure of Scientific Revolutions, Thomas Kuhn defmed the concept"paradigm," the key notion ofhis theory of scientific revolutions, as an inclusive andheterogenous entity. Paradigms are "accepted examples ofactual scientific practice-­examples which include law, theory, application, and instrumentation together," that"providemodels from which spring particular coherent traditions ofscientific research"(Kuhn 1962, 10). By including instrumentation as an intrinsic part ofparadigms, Kuhnimplied that instruqlents could have a direct and crucial role in scientific revolutions,but he did not specify how they actually affect the revolutionary process. l

In a series of articles and manuscripts written in the late 1980s and early 1990s,Kuhn substantially revised his theory of scientific revolutions. As a response to thecharge of relativism, Kuhn limited meaning change, the key character of scientificrevolutions, to a restricted class ofterms. "Roughly speaking, they are taxonomic termsor kind terms" (Kuhn 1991, 4). These kind terms, together with their interconnections,form the taxonomy ofa speech community, and function as the common platform formutual communication and rational evaluation. In his new theory of scientificrevolutions, Kuhn focused on a limited class of linguistic entities rather than appealingto the notion of paradigm, and characterized scientific revolutions by changes intaxonomic systems (Chen 1997b).In his new theory of scientific revolutions, Kuhn offered a detailed analysis of

instruments. Consistent with his linguistic approach, Kuhn identified the role ofinstruments in the process of learning kind terms. He used the learning process of thenotion "force" in Newtonian mechanics to illustrate this point (Kuhn 1990,301-8).Because he adoptedWittgenstein's account offamily resemblance concepts, Kuhn

believed that "in the process through which the new terms are acquired, defmition playsa negligible role. Rather than being defined, these terms are introduced by exposure toexamples of their use, examples provided by someone who already belongs to thespeech community in which they are current" (Kuhn 1990, 302). These examples canbe introduced by actually exhibiting exemplary situations to which the terms inquestion can be properly applied, like demonstration experiments in science education,or by verbal descriptions of the exemplary situations. Through these processes, welearn not justmeaning ofthese terms, but how they are applied to a world in which theyfunction. 2

Differing from most terms used in our daily discourse, those important conceptsinNewtonianmechanics are quantitative. To learn these quantitative concepts, we needto know how to measure them. But due to the limits of our sense organs, we cannotreliably detect positions and movements for other than macroscopic bodies, and cannot

167

168 CONCLUSION

accurately notice changes of macroscopic bodies without referring to some kind ofmeasuring units. Tomake quantitative measurements, we then need instruments, whichconvert effects to be measured to positions or movements ofmacroscopic bodies andprovide measuring units for accurate counting. Instruments are inevitably involved inmeasurement, and in the process of learning quantitative concepts.Thus, the Newtonian concept "force" cannot be learned by referring to its

defmition -- Newton's second law. Nor can it be learned by using an example obtainedby direct observations such as a falling stone, which cannot illustrate the quantitativefeature ofthe term. To acquire the Newtonian notion of "force," we need exemplarysituations, usually demonstration experiments, in which forces are measured by properinstruments. These instruments can be as simple as a spring balance or some otherelastic devices. For example, we can acquire the notion by attaching a spring balanceto a heavy body and moving it along an inclined plane. Similarly, to acquire the term"mass," we need a centripetal-force apparatus, which can show that the mass ofa bodyis proportional to its acceleration under the influence ofa known force. To understandthe term "weight," we again need a spring balance, which, by yielding differentreadings from one location to another, proves that "weight" denotes a relative property.Kuhn insisted that the significance of instruments in the process of concept

acquisition is not simply pedagogical but conceptual, because using differentinstruments sometimes may affect the results of concept learning. In the seventeenthcentury, for example, the meaning of"force" might vary if different instruments wereused. Using a pan balance, a student in this historical period could only obtainexamples of a limited sort of force, the one caused by "weight." Without examplesfrom other sorts offorce, such as inertial forces and frictional forces, the student wouldacquire a notion of"force" quite different from the Newtonian one. Withweight-relatedforces as the only examples, the student could develop the idea that "force" was theelement that overcame "weight," and that a projectilewas the typical example offorcedmotion. This idea could reinforce the highly developed pre-Newtonian intuition thatconnected "force" with muscular exertion, and inevitably lead to an Aristotelianconcept of"force."After analyzing the learning processes of the notion "force" in Newtonian

mechanics, Kuhn had a second thought ofhow instruments affect scientific revolutions."My original discussion described non-linguistic as well as linguistic forms ofincommensurability. That I now take to have been an overextension resulting from myfailure to recognize how large a part of the apparently non-linguistic component wasacquired with language during the learning process," he said (Kuhn 1989, 10). Kuhnnow believed that the incompatible interpretations of "force" associated with panbalance and spring balance are merely the results of different processes of languageacquisition. Thus, according to Kuhn's latest linguistic theory ofscientific revolutions,instrumentation functions merely as an aid for learning kind terms, and its role inrevolutionary change is related to linguistic activities. Consequently, meaning changesofkind terms constitute the essence ofscientific revolutions, and instrumentation playsmerely an indirect and secondary role.

CONCLUSION 169

I believe that Kuhn's view on the role of instrumentation in scientific revolutionsis too narrow, because he limited his discussion to the process of concept acquisition.Linguistic activities, including representation and argumentation, constitute only oneaspect of science. Scientific practice obviously goes far beyond such linguisticactivities as concept acquisition and taxonomy construction. Science also has animportant aspect of doing, in which scientists interact with the world by usinginstruments. Many important concepts in science refer to things or effects that do notexhibit themselves in nature without human interference, and proper instruments areneeded to explore these objects. Through interactions with the world, we obtain notmerely the raw materials for concept acquisition, but also direct comprehension ofthesubject matter, because we can understand the world by knowing how things work. Asmany philosophers of science have correctly suggested, if we can produce an event,then we have already explained it, because we must identify the cause ofthe event andthe connections between the cause and the event in order to generate it. 3

* * *In previous chapters, we have seen that instrumental traditions played crucial roles

in determining a variety of non-linguistic activities during the optical revolution. Wehave seen how the uses of instruments affected observations (Chapter 4). Inhis spectralexperiments, Powell saw no substantial difference between prismatic and diffractionspectra, because he used a theodolite as the key apparatus, which restricted his attentionto angular parameters. On the other hand, Brewster observed fundamental differencesbetween prismatic and diffraction spectra, because he employed the eye and a telescopewith a high magnification power as the key apparatus, which allowed him to count agreat number of dark lines in prismatic spectra and led him to trace their chemicalorigins. Powell and Brewster had different observations of the same objects, simplybecause they used different instruments that confmed their perspectives in observations.We have also seen how the uses of instruments determined the operations of

experiments (Chapter 6). Because he used the eye as the apparatus to match brightness,Potter had to adopt a series of special procedures in order to protect the sensitivity ofthe eye in his measurements of reflective power, including those approximations thateventually exaggerated the discrepancies between his measurements and the wavetheory. Using a thermometer and a galvanometer as the apparatus, Forbes did notworryabout the sensitivity ofthe eye and measured reflective power in a totally different way.Here, Potter and Forbes interacted with the world differently because the instrumentsthat they employed had limited their options.Different uses of instruments affected observations and experiments, and, more

importantly, they altered the objective world directly. In Chapter 5, we have seen thatBrewster's experiment on the polarity oflight was classified as interference because heemployed the pupil of the eye as the aperture, and Powell's experiment that producedthe same effect was classified as diffraction because he used the objective lens of atelescope as the aperture. Here, the difference in classification reflected differences inthe objective world. Because of their material nature, instruments are a part of the

170 CONCLUSION

objective world. The practitioners in the debate on the polarity of light made differentclassifications not because they saw the same thing differently, but because they in factdealt with different phenomena.Thus, different uses of instruments, or more precise, different instrumental

traditions, can alter the results of observations, the process of experiments, and eventhe world itself. During the optical revolution, we have seen that the visual tradition andthe geometric tradition in many ways functioned just like the particle and the wavetheories, changing people's perspectives,judgments, and even world views. The visualtradition and the geometric tradition were also paradigmatic entities in the opticalrevolution. It is important to note that these instrumental traditions exerted theirparadigmatic functions without the medium of linguistic activities, and in waysessentially different from the theoretical paradigms such as the particle and the wavetheory.An essential difference between theoretical paradigms and instrumental traditions

consists in the fact that most components of a theoretical paradigm are articulated butmany elements of an instrumental tradition are not. The major components of atheoretical paradigm are concepts and the interconnections among concepts that formvarious theoretical principles and classification systems. These components must bearticulated explicitly and defined clearly in order for a theory to exert its paradigmaticfunctions. On the contrary, the main components of an instrumental tradition areprocedures, skills, techniques and protocols about the proper uses of instruments. Inpractice, these components need not be articulated, and some of them are even totallyunarticulated. They frequently remain hidden beneath explicit discussions abouttheoretical issues. Thus, instrumental traditions are tacit paradigms, different fromtheoretical paradigms, which are primarily declarative.4

Becauseofthe tacit nature, the relations between competing instrumental traditionsare significantly different from those between rival theoretical paradigms. Kuhn usesthe notion "incompatibility" to describe the relations between rival theoreticalparadigms: a theoretical paradigm always entails implications that are logicallycontradict those from the rival, so that "Einstein's [relativity] theory can be acceptedonly with the recognition that Newton's was wrong" (Kuhn 1962,98). But logicalrelations do not always exist between rival instrumental traditions, because most oftheir components were not articulated. The demarcation between the visual traditionand the geometric tradition in the optical revolution relied upon continuity inprocedures. Certain procedures continued within each tradition, such as those forprotecting the sensitivity of the eye in the visual tradition, and those for convertingoptical effects to geometric signals in the geometric tradition. Procedures from theother tradition did not transfer easily across the line, but the reason was practicalinstead of logical. In theory, it was not impossible to transfer one set of proceduresfrom one tradition to the other, but in practice, proficiency in mastering one set ofprocedures did not necessarily help improvement in learning the other. Knowing howto enlarge optical images usually did not lead to knowing how to improve the qualityof geometric signals, for example. Thus, it is not the case that the geometric tradition

CONCLUSION 171

could be accepted only with the recognition that the visual tradition was wrong. Rivalinstrumental traditions were simply separate, parallel but not contradictory.sKuhn also introduces the notion "incommensurability" to describe the relations

between rival theoretical paradigms. Two rival theoretical paradigms areincommensurable in the sense that there are communication obstacles between thecommunities that adopted the rival theories, because of the translation failures thatresult from the holistic nature ofparadigms (Kuhn 1962, 111-35). Without a taxonomynor internal logical relations, instrumental traditions are not holistic, and thus shouldnot cause communication problems related to translation difficulties. Butwp have seenmany communication failures and misunderstandings during the optical revolutionbetween thosewhobelonged to different instrumental traditions. These communicationfailures were in part caused by the tacit nature of instrumental traditions. People oftenmisunderstood each other simply because the issues with which they concerned werenot articulated. A good example is the debate between Potter and his critics onphotometric measurements. In hindsight, we know that the central issue in this debatewas Potter's peculiar procedures of making approximations, but the issue remainedtacit in the debate. Coming from the geometric tradition, the critics rejected Potter'sphotometric measurements because he used the eye as an essential element in themeasuring process, and they did not think that it was necessary to replicate Potter'sexperiments in order to discredit the data. Without replication, Potter's measuringprocedures, in particular those approximations, remained in the dark, and the criticsfailed to reveal why Potter'smeasurements were significantly lower than the theoreticalpredictions. The debate over the reliability of the eye, however, soon fell into animpasse. For those from the visual tradition, the essential role of the eye did notoriginate from a metaphysical belief that they could argue for, but rooted in thestructures ofthe instruments and the procedures ofthe experiments. Potter thus did notunderstand the criticisms against the use of the eye raised by the critics, and insteadinterpreted the criticisms in terms of the particle-wave division, accusing his critics ofworshiping the wave theory and overlooking experimentation. Without articulating thehidden issue regarding procedures, neither Potter nor his critics could successfullycommunicate with the other side in the debate.Even when procedures for using instruments are articulated, communication

obstacles can still exist between those who belong to different instrumental traditions.But misunderstanding between instrumental traditions under this circumstance isgenerated by a cognitive mechanism different from the one that causesincommensurability between rival theoretical paradigms. Since using instruments, aspecific kind of scientific practice, is a goal-oriented activity, describing processes forusing instruments involves many goal-derived concepts. Contrary to taxonomic termsthat refer to natural, artificial and social kinds, goal-derived concepts such as "thingsto eat on a diet," "things to take from one's home during a fire" and "birthday present"refer to goal-means relationships. Recent cognitive studies show that people'sunderstanding of goal-derived concepts is directly determined by their experience inachieving their goals with certain means, which includes their skills, expertise and

172 CONCLUSION

equipments. For instance, the notion "things to take from one's home during a fIre"reflects people's experienceofwhat kind ofmeans can serve the purpose ofminimizingloss. This experience includes people's capacity ofmoving heavy objects, the movingprocedure that they are going to adopt, and available moving tools (Barsalou 1985;Barsalou 1991).6 This fmding of cognitive studies can help us understand some of themiscommunication between those from the visual and the geometric traditions. Forexample, although both Potter and Forbes gave general descriptions oftheir proceduresfor measuring reflective power, they never fully comprehended the other'smethod. Thecause of this communication failure, however, had little to do with their capacities ofunderstanding the related theoretical notions and principles. Because of his previousexperience in astronomical observations, Potter trusted the visual approach because ofits effectiveness in handling light with low intensity, and he developed various skillsofprotecting the sensibility of the eye. However, with extensive experience with heatexperiments, particularly with skills in controlling scattered heat, Forbes was confIdentof the procedure that employed a thermal-electric pile as the key instrument. Theseprior experiences signifIcantly limited Potter's and Forbes's options when they tried tomeasure the reflective power of glass. Without the appropriate experience and skills,for example, it was very diffIcult, ifnot impossible, for Potter to replicate Forbes's heatexperiment, although he might have fully understood every word in Forbes'sdescription. Similarly, without experience in astronomical observation and the skillsofprotecting the eye in photometric experiments, it was diffIcult for Forbes to replicatePotter's procedure. The discrepancy of their prior experiences and skills formedobstacles of communication, which eventually led Potter and Forbes to interpret theirdifferences in political terms, a clear indication ofmiscommunication.?

* * *According to Kuhn's account of scientifIc revolutions, theoretical paradigms

always change in a discontinuous manner. Discontinuity is inevitable mainly becausea theoretical paradigm contains elements in two different abstract levels: concepts atthe lower level and a taxonomy at the higher one. At the level of concepts, anomaliesoccur discretely and responses to these anomalies are piecemeal. But according toKuhn, concepts are not learned through defInitions, and there is no a list of necessaryand suffIcient conditions that can or must be used to defme a concept.8 Differentindividuals, or the same individual in different situations, may use different standardsto identify the referents of a concept, and thus a single anomaly would not generateimmediate change at the level of taxonomy. A taxonomic change does not occur untilanomalies increase beyond a certain limit, or until the accumulation of anomaliesfInally causes a crisis and erodes people's faith in the existing taxonomy. The patternofparadigm shifts always begins with a crisis stage that destroys practitioners' faith inthe old tradition, followed by a period of confrontation between two incompatibleparadigms, leading to partial loss of communication between the communitiessupporting the paradigms, because ofthe incommensurability between their conceptualsystems.9

CONCLUSION 173

In terms of their level of abstraction, the elements of an instrumental tradition arehomogeneous. Procedures, skills, and techniques of using instruments are aboutoperations on the material world. Concepts are used to articulate these procedures, butthey are at the lowest level of abstraction. So, instrumental traditions do not containelements in two different abstract levels, and their development is seldom accomplishedin the form of discontinuity. Undoubtedly, anomalies occur daily in the uses ofinstruments, but usually they are addressed and resolved immediately. Changes ofinstrumental traditions are piecemeal. More important, there is no a crisis stage in thedevelopment of instrumental traditions. When practitioners encounter anomalies intheir uses of instruments, they frequently blame themselves rather than the tradition forthe failure, an attitude similar to the one when people encounter anomalies to atheoretical paradigm during the stage ofnormal science. For example, the practitionersin early nineteenth-century photometry were aware of the defect of using the eye tomatch brightness, but they attributed the defect to their own failures in conducting thematching operation in the optimal condition, and designing better matching fieldsbecame a major issue in the development of photometry. Furthermore, the evaluationof procedures, skills and techniques is always a matter of degree. People ask whethera particular procedure is effective or efficient in a specific context, not true or false ingeneral. Thus, competing procedures coexist, so do rival instrumental traditions. Thetechnique of using the eye to match brightness in photometry was never abandoned,even after a group of more advanced techniques such as photoelectric cells becameavailable. Even today, engineers in photometry continue to use the techniques involvedpsycho-physical analysis (Johnston 1996,293).After taking instrumental traditions, particularly their accumulative nature, into

consideration, we begin to see a new picture of the optical revolution. In addition toconcerns about the nature of light, the discussions, exchanges, and debates on the usesof instruments constituted another important issue during the optical revolution. So, theoptical revolution included development at two independent levels. At the level oftheory, there was a disrupt change in the understanding ofthe nature oflight, from theparticle model to the wave model. At the level of instrumentation, there were parallelevolutions of two instrumental traditions, each of which nurtured a distinct style ofusing optical instruments. Changes at these two levels were autonomous. There werestrong interactions between the theoretical paradigms and the instrumental traditions,but neither of them was privileged. Evolution at each level had its own pattern,determined by its own history of training, education, and practice. Consequently, thepaces of development at these two levels of intellectual activities did not alwayscoincide. The accumulative evolution at the level of instrumentation constituted thebasis for the continuity in the optical revolution.This new picture ofthe optical revolution is consistent with many recent historical

studies, which find that progress in science occurs at levels other than the articulatedone concerning concepts, theories and taxonomies. Underneath the theoretical level,the development of such elements as instrumentation and skill was frequently crucialin determining the pace ofscientific change. For example, Galison recently shows that

174 CONCLUSION

the history of microphysics consisted of three quasi-autonomous levels: theory,experimentation and instrumentation. Each of these levels carried their ownperiodization, and the local continuities were intercalated, that is, no abrupt changes oftheory, experimentation, and instrumentation occur simultaneously (Galison 1997).The multi-level picture ofthe optical revolution helps us understand the pattern of

the theoretical development. As we have seen in the previous chapters, at the level oftheory, the revolutionary change took the form of proliferation of specializeddisciplines. The replacement ofthe particle theory by the wave theory was only one ofthe many interesting themes in the optical revolution. But the proliferation inspecialization was driven by forces that existed outside the realm of theory. In fact, iftheory were the only element of science, it would be difficult to see how scientificprogress could take the form of specialization. As suggested by Kuhn, the criteria fortheory evaluation are accuracy, consistency, explanatory power, and simplicity (Kuhn1962, 153-9). Most ofthese criteria promote synthesis and reward theories that attemptto provide unified accounts. Evaluations of scientific instruments, however, havedistinct criteria. From a cognitive point of view, an instrument is an informationtransformer -- converting input information about the world to output information thatcan be conceived by our sense organs. So the key criterion for instrument evaluationis the reliability in this information transformation. A reliable instrument shouldpreserve the relations in inputs and reproduce themwith least distortion in outputs. Thehistory ofscientific instruments shows that a general approach to improve the reliabilityof an instrument is to narrow its application scope, that is, to make it special for alimited range ofsubjects. This is why the development ofmany scientific instruments,say, telescopes, shows a pattern of proliferation: from a single kind of telescope(optical) evolving into a big family, including radio, infrared, ultraviolet, gamma-ray,and x-ray telescopes, each ofwhich covers only a fraction of the light spectrum. Theproliferation of instruments provides one ofthe material bases for the specialization ofscience.Our new picture of the optical revolution also offers an explanation for the

longevity of the debate concerning the inconsistent explanatory models and the rivalanalytic methods. The opponents of the wave theory did not fully recognize theexplanatory successes of their rival because their perspectives, judgments and evenworld views were limited by the instrumental tradition to which they belonged. Theaccumulative development at the level of instrumentation continuously suppliedmaterials for the debate regarding the nature oflight. In fact, the longevity ofthe debateseemed to be inevitable because of the continuity of the revolution. Thus, we shouldunderstand the long-term debate between the particle and the wave theory in terms ofthe interplay between theory and instrumentation, not in terms ofconflicting personaltraits or any other irrational factors. Only after we go beyond a history of opticaltheories that hovers around physical models or explanatory power, and particularlyonly after we adopt an inclusive historiographical perspective that fully appreciates theinteractions between theory and instrumentation, can we finally have a full historicaland rational understanding ofthe history ofoptics, and in particular the replacement ofthe particle theory by the wave theory of light.

APPENDDCES

1. THE INTENSITY OF LIGHT IN BREWSTER'S EXPERIMENT OFPOLARIZATION BY SUCCESSIVE REFRACTION

In Brewster's experiment ofpolarization by successive refraction, the light source wasa single wax candle, 10 feet (about 3 meters) away from the refracting pile of glassplates.Assuming that the intensity ofthe source (Isuurce) was 1candle, we can determine the

illumination of the incidence at the surface of the glass pile according to the inversesquare law:

IE

source0---

y2= J X 10-5 candle I em 2

To calculate the illumination of the unpolarized light after transmitted through 18plates of crown glass at the angle of63 °43', fIrst we need to determine the intensity ofthe unpolarized light after transmitted through a single plate of glass.The natural incident light can be decomposed mathematically into two mutually

perpendicular plane-polarized light beams, I II and I.L. The former is parallel and thelatter perpendicular to the plane ofrefraction, and both have a single unit of intensity.At the fIrst surface of the glass, a portion of the incident beam is reflected. UsingFresnel's formulas, we can determine the intensity of the two components of thereflected light:

J sin2(0-e)I .1. =!.L x - = .2599

reflected (1) 2 sin2(0 +0)

where e is the angle of the incidence (66°43'), and e 'is the angle of refraction, whichis 37°2'. The value ofe 'is determined according to the following formula:

175

176 ApPENDIXES

. 01 sin 0Sin =--

Pg1ass

where ~glass is the refractive index of the crown glass (Pglass = 1.525).The plane ofpolarization in the refracted light is parallel to the plane of refraction,

and the unpolarized light exists only in the perpendicular component. The intensity ofthe unpolarized light is:

I refracted (I).L = I.L - Irejlected (I).L = .7401

At the second surface ofthe glass, a portion ofthe refracted light is reflected. Againusing Fresnel's formulas, we can determine the intensity of the perpendicularcomponents of the reflected light:

I .L = I .L X !.... sin](O-()? = .1924reflected (]) refracted (1) 2 sin](0 +B?

where e is the angle of the incidence (37°2'), and elis the angle of refraction (fromglass to air), which is 66°43' according to the relation: sin 0 I = sin 0 x Ilglas;-After two reflections, the intensity ofthe unpolarized light in the refracted beam is:

I refracted (2).L = Irefracted (J).L - Irejlected (2).L = .5477

Thus, the percentage of the unpolarized light after passing through one plate ofglass is:

P (I) = .5477

Using a formula proposed by John Herschel {Herschel 1827: 512}, we determinethe percentage of the unpolarized light after transmitting through 18 plates:

P (18) = P (1/8 = 2x/0-5

Finally, the illumination of the unpolarized light after passing through 18 platesof crown glass is:

E rmpolarized (18) =Eo x P (18) = 2 x/0-10 candle/cm2

In practice, this level of illumination may not be perceptible.

ApPENDIXES

2. POWELL'S CALCULATION OF REFRACTIVE INDICES

Powell stated his formula of dispersion as follows:

177

1

P

1 sin 4)h };

A

where J.l is the refractive index, Athe wavelength, h and ~ constants that depend uponthe nature of the medium and must be determined empirically.To determine these two constants, Powell used two extreme spectral lines, the B line

and the H line, as the reference points. According to Fraunhofer's measurements, therefractive indices ofthe B and the H lines in the spectrum produced by his #3 flint glasswere:

PB = 1.6020 PH = 1.6404

Also from Fraunhofer's measurements, the wavelengths ofthe B and the H lineswere:

AS = .00002541 (inch) AH = .00001464 (inch)

From the formula of dispersion, Powell obtained two equations:First, the ratio of the arcs (~/A) between the H line and the B line was equal to the

ratio of the respective wavelengths:

};

As AS AH =0.5762- -AH

}; ABAH

Second, the ratio of the arcs to their sins is equal to the ratio of the respectiverefractive indices:

sin As 1

B Ps PH= 1.024-- --

sin AH 1 PB---AH PH

To fmd the values ofAB and AH that satisfied the above two equations, Powell used

178 ApPENDIXES

the method of trial and error. After many trials, he found the following values:

As = 15 0 20' = .0857r AH = 26 039' = .1487r

With the value ofAH, Powell calculated the values ofh and~:

sin AH

-- = 1.6404 x .96433 = 1.582AH

() = AH X A.H = 6.8 xlO-6

Powell then derived the arcs for other rays:

(i = C, D, E, F, G)

With these values of arcs, Powell fmally deduced the values of refractive indicesfor the remaining five lines.

3. THE RELATIVE ERROR OF POWELL'S MEASUREMENTS OFREFRACTIVE INDICES

Both Fraunhofer and Powell used the following formula to compute the index ofrefraction in their measurements:

()+ifJsin -­

2

. ifJsm -

2

where ~ is the index ofrefraction, eis the angle of refraction, and <I> is the angle oftheprism. The accuracy of their measurements thus depended upon the ranges oferror inthe two angular parameters.Because the dividing circles in both Fraunhofer's and Powell's theodolites came

with a least count of 10 arc-seconds, their measurements of refractive angles had arange of error of 10 arc-seconds.Neither Fraunhofer nor Powell discussed the range of error in their measurements

of the prism angle, but we can derive this parameter from the available information.We can determine the range of error in Fraunhofer's measurements of refractive

indices by comparing his values with the modem ones. For the D line in the spectrumofwater, Fraunhofer's value was 1.333577, about .0 I% larger than the modem value(1.33336). Given the accuracies of ~ and e, we can calculate the accuracy of <I>according to the above formula. Such a calculation shows that, in order to achieve an

ApPENDIXES 179

accuracy level of.O I% in hismeasurements ofrefractive indices, Fraunhofermust havecontrolled the error in his measurements of the prism angle within I arc-minute.Now assume that the accuracy of Powell's measurements of the prism angle was

also I arc-minute.For Powell's hollow prism, (f) = 30°36'30".For the 0 line in the spectrum of anise-seed oil, e= 17°47'30".Assume that the true value of the prism angle is I arc-minute larger than the

observed value:

Assumed the true value of the refraction angle is 10 arc-seconds smaller than theobserved value:

The true value of Il is:

The observed value of Il is:

The relative error is:

o +if>. tr tr

SIn---2

if>• Ir

SIn-2

O+if>sin -­

2. if>

Sin ­2

= 1.5527

= 1.5531

Thus, the range oferror in Powell's measurements of refractive indices was aboutthree times ofFraunhofer' s. The errorofPowell'smeasurements was even higherwhenhe used prisms with smaller angles. For example, when (f) =7°42'30", £~ = .08%.

180 ApPENDIXES

4. POWELL'S MATHEMATICAL ANALYSIS OF THE"POLARITY OF LIGHT"

Powell flIst used the standard wave equation to describe the disturbances caused by anunretarded ray and a retarded ray. The disturbance caused by an unretarded ray wasrepresented by:

. 271: ( xJsm T vt-

The disturbance caused by a retarded ray was represented by:

. 271: ( .1sm T v/-X-r/

From these two equations representing single rays, Powell determined the intensityoflight in the spectrum by simply taking the sum of the squares ofthe coefficients, andobtained the following formula:

2n:r1 = 2 (J + COST)

where r is the retardation caused by the thin plate, determined by the refractive indexofthe medium (Ilm), as well as the thickness (t) and the refractive index (Ilp) ofthe plate(r= ppr-Pmr).The formula showed that the intensity oflight in the spectrum changed periodically

according to the wavelengths and the retardation. Specifically, it showed that, whencos(2n:rIA)=-1, that is, when the ratio of the retardation to the wavelength was an evennumber, the intensity oflight was zero and a dark band appeared. When cos (2n:r1J..) "-1,that is, when the ratio ofthe retardation to the wavelength was not an even number, theintensity of light was not zero and no dark bands were visible.To simplify the analysis, Powell introduced p = 4r1A, and expressed the above

intensity formula as:

71:1 = 2 (J + cos-p)

2

The intensity oflight in the spectrum changed periodically according to the value ofp.Particularly, 1 reached its maximum and minimum under the following conditions:

for p (any even number),for p+1,forp+2,for p+3,

cos 7d2 P = -1,cos 71:/2 (p+ 1) = 0,cos 7d2 (p+2) = 1,cos 7d2 (p+3) = 0,

1=0;1=2;1=4;1=2;

forp+4,

ApPENDIXES

cos 7C!2 (p+4) =-1, /=0.

181

Thus, for any two values ofp, ifPI - p2=4, they corresponded to a change from onedark band to another. IfPI - pz =4n, n would be the number of bands in the intervalbetween two specific rays corresponding tOPI andp2 respectively.Since p=4r/A., Powell rewrote the retardation as:

p - p!!.. = ( p m) I

4 A

For any two rays whose refractive indices were !-Ipl and !-Ipz for the plate, !-Iml and!-1m2 for the medium, and whose wavelengths were Al and Az,

PrP2 = n = [(PpI-PmI) _ /P2-Pm2)} I4 Al A2

Here, n was the number of dark bands in the interval between the two rays.

5. A RECALCULATION OF THE REFLECTIVE POWER OF GLASSWITHOUT POTTER'S APPROXIMATIONS

Consider the reflection by plate glass at 30 degrees ( refer to Figure 6.3 for thesymbols).Potter in his article gave the values of the following parameters:

LM+MH=8.54SE = 1.25

MA = 1.5qJ = 45 0

Bymeans oftrigonometric analyses, we learn that the remained parameters shouldsatisfy the following conditions:

L1'vf = (SE+EHF + MB2

fJ - a = 60 0

tan a = (SE + EH) / MH

EH = MA - (MA x cos r)r = qJ - [30 0 + a}tanfJ = (SE + EH) / MB

Solving these equations, we obtain the values of the remained parameters:

MB = 0.4599BH= 6.7442a = 9.89 0

r = 5.11 0

Thus, the true value of the reflected distance is:

LM= 1.3376EH = 0.006fJ = 69.89 0

182 ApPENDIXES

Dre! = LM + [(MB+BH) 2 + (SE + EHy J* = 8.6504

The cosine of the incident angle is:

(MB+BH)cos a = -;::.======:::;::======:::::;J(MB +BHl + (SE +EHl

= 0.9851

Since Potter had given the value of the direct distance (40 inches), we canrecalculate the gross reflective powerwith the true values ofthe reflected distance andthe incident angle.

Pa=_1_ x [ Dre! l =4.7475%

cos a Ddir

Using Potter's estimation of the intensity of the scattered light (Ps = .47%), wehave the adjusted reflective power:

P = Pc - Ps = 4.278%

NOTES

Introduction

1. Dreyfus's argument draws on Wittgenstein's analysis of rule following (Wittgenstein 1958). Forconnections between the tacit nature of practice and Wittgenstein's notion of "form-of-Iife", see Collins(1990).2. Kuhn first called the replacement ofthe particle theory by the wave theory a scientific revolution; see

(Kuhn 1970, 11-2). Later, some historians further label it "the optical revolution"; see (Cantor 1990,634-6).3. Contemporary historians list many other factors, both cognitive and social, that were significant in

the victory of the wave theory. For example, David Wilson considers the greater simplicity of the wavetheory as another reason why' it was accepted by Cambridge physicists (Wilson 1968). Geoffrey Cantorbelieves that generational,. institutional, regional, methodological, and metaphysical differences between thetwo theories were also relevant (Cantor 1983). Jed Buchwald attributes the victory of the wave theory, inpart, to the way that it providedCambridge-trained mathematicians with a subject amenable to mathematicalanalysis (Buchwald 1989).4. For studies of the particle-wave debate in the 1840s and the early 1850s, see (Cantor 1983, 186-7),

(Buchwald 1989,296-302), (Chen & Barker 1992), (Chen 1997a), and (Chen 1998).5. For example, the criticisms from the rivals forced James MacCullage in 1845 to admit openly the

defects of the wave theory. For more about MacCullage's reflection of the wave theory, see Chapter 5. Amore drastic case was Herschel's reaction to the criticisms. Disappointed by the wave theory's failure inexplaining metallic reflection, Herschel in the 1845 meeting of the British Association publicly called forreviving the particle theory, by saying that "ifthe same amount ofanalytic skill had been expended upon thecorpuscular theory, perhaps more could be done with it than was at present believed" (Anonymous 1845b,640).

Chapter 1

1. For a different opinion of the effect of Brougham's attack, see (Worrall 1976, 107-10).2. For details ofHerschel's experiments, see Chapter 3.3. According to Brewster, Herschel was the only person in Europe who was able to do so; see (Brewster

1828).4. Herschel's questions appeared in Fresnel's reply, and a translation of these questions is provided by

Buchwald; see (Buchwald 1989,291).5. Herschel formally published his essay in 1845 as a part oftheEncyclopaedia Metropolitana. In this

book, all references to Herschel's "Light" are taken from the 1845 publication.6. Note that Herschel's instrumentalist interpretation of"explanatory power" is different from those

understood by many twentieth-century philosophers of science such as Hempel.7. Brewster also received one-halfofthe prize ofthree thousand francs from the France Institute in 1816

for his work on polarization, which was praised as one of the two most important discoveries in physicalscience made in Europe between 1814 to 1815.

8. An abstract ofthis paper was published in 1816 in The Quarterly Journal ofLiterature. Science andthe Arts; see (Morse 1972, 82).

9. The committee had total eight members. The other four were Thomas Brisbane, William Pearson,William Scoresby, andR.Willis; see (British Association 1831,46). Whewell was not present at the meetingalthough he was elected as a member of the committee.

10. Brewster also regarded Cauchy's explanation of dispersion as important, because if Cauchy'saccount was successful it could remove one of formidable difficulties of the wave theory. But Brewster

183

184 NOTES

admitted that he himselfwas unable to give a satisfactory review ofCauchy's work, probably because ofitssophisticated mathematical analysis. Hence he only briefly sketched Cauchy's account of dispersion(Brewster 1832,317).

II. For more on Brewster's search of monochromatic light sources and his subsequent study of thecolors of natural bodies, see (James 1985, 60; Shapiro 1993, 331-54).

12. In his 1832 report Brewster did not provide details of this experiment. He gave more informationabout it later in a paper read to the Royal Society ofEdinburgh in April 1833 (Brewster 1834a).

13. For more philosophical discussion of non-empirical or conceptual problems, see (BuchdahI1970;Buchdahl 1980; Laudan 1977,454-69).

Chapter 2

I. Mostwave theorists recognized these problems, and their tactic in the early 1830s was either to arguefor the possibility of wave accounts for dispersion and absorption in the future, or simply to deny them aslegitimate topics of physical optics; see (Herschel 1833, 401-12; Airy 1833,419-24).

2. For example, Herschel believed that the wave theory was slightly better than its rival in explainingthese two categories, because the particle explanations required too manyad hoc hypotheses; see (Herschel1827,529).

3. Although he was criticized by many wave theorists, Herschel upheld this view at least up to the1840s. In the 1845 British Association Meeting, he once again suggested to use an improved particle theoryto explain a phenomenon that troubled the wave theory (Anonymous 1845b, 640; Anonymous I845c, 416).

4. See Report ofthe British Association 2 (1832), 116.5. Formore on Hamilton's theoretical analysis, see (O'Hara 1982,231-57); see next chapter for details

ofLloyd's experiments on conical refraction.6. This report was later reprinted in Lloyd'sMiscellaneous Papers Connected with Physical Science

(1877). In this book, all references to Lloyd's "Report" are taken from this reprint.7. In his report, Lloyd also regarded internal coherence as another criterion for a true theory, but mainly

used this criterion to attack the particle theory. Formore discussion ofLloyd's view on the role ofconceptualcoherence in theory appraisal, see (Chen 1990, 665-76).

8. Although particle theorists did provide accounts for polarization, none of them were satisfactory,according to Lloyd. For example, Biot's explanation of reflection/refraction of polarized light could not becompared with experiments numerically; all particle accounts ofdouble refraction failed to cover the relatedpolarization effects; and Biot's theory ofcolors ofcrystallized plates was inconsistentwith experiments. See(Lloyd 1834, 92-132).

9. The second edition ofAiry'sTracts, which first included a section on optics, appeared in 1831. Later,two more editions were printed in the next two decades, one in 1842 and the other in 1858.

10. It is interesting to note that such a dichotomous structure gradually disappeared in textbooks aroundthe mid century, probably because while the debate concerning the two rival theories was dying down, therewas no need to advocate such a dichotomous structure that was inconvenient for instructional purposes.

Chapter 3

I. The degree ofpolarization is estimated according to the following formula given by Provostaye andDesaine:

Pm

m + ( 2n1

zJ1 - n

where m is the number of plates and n is the refractive index. This formula takes into account not onlyreflections at both surfaces of a plate, but also internal reflections that occur two or more times. But theformula does not consider the absorption effect (Jenkins & White 1957,493).

NOTES 185

2. Brewster later speculated that this kind of physical change was in fact displacements of thepolarization plane; see (Brewster 1830a; Brewster 1830b). From this hypothesis, he developed a notion ofphase, which allowed him to develop a quantitative theory of elliptical polarization around 1830. For adetailed analysis ofBrewster's theory of elliptical polarization, see (Buchwald 1989,404-8).

3. See (Buchwald 1989,203-4) for details ofFresnel's experiments.4. This quotation is taken from (Buchwald 1989,228-9).5. Herschel did not specified the physical dimension of his instrument, except saying that the focus of

the lens was about 2 inches. I estimate other parameters according the figure offered by Herschel.

Chapter 4

I. Brewster claimed that the particle theory could in principle explain dispersion by means ofdifferentsizes oflight particles, but he did not work out the details; see (Brewster 1822, 681).

2. For a discussion of the changes ofthe classification system during the optical revolution, see (Chen1995).

3. For a full account of Cauchy's ether dynamics and its differences from Fresnel's equation ofmotion,see (Buchwald 1980, 1981).

4. Among physicists in nineteenth-century Britain, Powell was second in the number of publishedoptical papers. Brewster was first, with more than 100 published papers on optics, and Stokes was third withabout 50. No other physicists published more than 30 papers on optics; see (Royal Society ofLondon 1870).

5. Fraunhofer was not the first person to discover the spectral lines in solar spectra. In 1802 WilliamWollaston reported that he saw dark lines in prismatic spectra. But probably because he used a rather widesource slit (about 1.25 arc-minutes), Wollaston saw only seven lines; see (Wollaston 1802,365).

6. Fraunhofer did not provide the wavelength of the B line because it could not be seen distinctly in theexperiment; see (Fraunhofer 1823, 51). The wavelength ofthe B line that Powell used in his test came fromhis own calculation, by using data that Fraunhofer obtained from a different experiment; see (Fraunhofer1822,26).

7. Brewster did not mention the aperture size of his telescope. But according to a broadside catalogissued by George Dollond around 1830, there was only one type offive-foot telescope available, which camewith an aperture of3.75 inches. See "A Catalogue ofOptical, Mathematical & Philosophical Instruments,Made by G. Dollond, Optician to His Majesty, 59 St. Paul's Church Yard, London". The original of thiscatalog is in the Whipple Museum ofthe History ofScience at Cambridge, U.K. lowe the discovery ofthiscatalog to Deborah Warner.

8. Fraunhofer did not mention the aperture size of his telescope either, but photos of his theodolite,together with the telescope, are available (Jackson 1996; Leitner 1975). According to these photos, thelength/diameter ratio of the telescope is about 10 to 1, which puts the size of its aperture at 1.8 inches.

9. Brewster's attempt to explain absorption by chemical affinities was unsuccessful-- it was difficultto imagine how a few elements could cause thousands of spectral lines. According to Shapiro, Brewster'sunsuccessful attempt to explain absorption by affinities represented the end of a long optical tradition thatappealed to chemical properties ofthe corpuscles ofmatter; see (Shapiro 1993,351).

10. lowe this analysis to Jed Buchwald.11. Talbot bands are optical phenomena in which spectral lines in a spectrum disappear altogether when

a thin plate of glass is inserted to cover one half of the spectrum, but the lines remain unchanged when thethin plate covers the other half. For Powell's experiment on diffraction spectra, see (Powell 1840, 82). Forthe debate over Talbot bands, see Chapter 5 and (Chen 1997a).

12. Brewster only reported the length of the aperture. The width of the aperture is estimated by usingthe diagram drawn by Brewster (Figure 4.5), in which the width/length ratio ofthe aperture's image is about1:37 according to the direct image of the aperture.

Chapter 5

I.Talbot's explanation was problematic, because it predicted the formation ofbright bands (due to theenhancements between rays), which had not been found in the experiment. Talbot probably based his

186 NOTES

explanation on the basis of Arago's account of stellar scintillation, which attributed the momentarydisappearance of starlight to interference between rays that passed the two halves of the eye's lens or thetelescope's objective.

2. Further analysis in this chapter will show that, in fact, even some wave theorists continued to applyray analysis tacitly in their researches though they had publicly declared their commitments to the wavetheory.

3. Lloyd's confidence in the wave theory came both from its various explanatory successes and fromits impressive quantitative ability; see (Lloyd 1834,295-413). A few other wave theorists, such as Airy andWhewell, also shared this opinion.

4. For detail ofBrewster's explanation, see (Buchwald 1992,50-4,67-74).5. For example, Brewster's experimental findings could be explained ifhe assumed that the retarding

plate altered the direction of polar refrangibility by 180 degrees, and that interference between two raysoccurred when their polar refrangibilities were heading at each other, but not the other way around.

6. Brewster continued this strategy in his later fights with the wave theory. For how he applied thisstrategy in the late I840s and the early 1850s, see (Chen & Barker 1992,78-81).

7. According to Powell, Lloyd also suggested a similar explanation for the phenomenon; see (PowellI839b, 795).

8. For details ofAiry's explanation and Brewster's response, see (Chen 1997a, 371-6).9. Powell's explanation is problematic, because it implies that bands would be visible with no plate

present. This problem was caused by his confusing combination of ray and wavefront analysis.10. Later Powell reported that he also found the polarity phenomenon in the interference spectrum; see

(Powell 1839b, 795).11. Brewster insisted that these selective reflections had nothing to do with interference and diffraction,

and remained problematic for both optical theories.12. Because oftheir conflicts in several priority issues, MacCullagh saw Hamilton as a competitor. His

commenton purely mathematical investigation might have been a criticism ofHamilton's research style. Formore about the personal relationship between MacCullagh and Hamilton, see (Hankins 1980,93-4,167-8).

13. Brewster here referred to Airy and Whewell.14. Brewster believed that Airy, who acting as referee ofPhilosophical Transactions, was responsible

for the rejection and had done this entirely from his personal feelings; see (Brewster 1841).15. For the detail of Stokes's integrations and the results, see (Chen 1997a, 388-91).

Chapter 6

I. Potter had been an amateur scientist for more than two decades since he graduated from grammarschool in 1815. He went to Cambridge to obtain formal education in 1835, and graduated in 1838 as a sixthwrangler. In 1841, he became the Professor ofNatural Philosophy and Astronomy at University College,London, and held that position until 1865.

2. Potter continued to have close contact with Dalton until he left for Cambridge in 1834. He acceptedmany ofDalton's opinions on scientific subjects, and shared more with chemists than physicists regardingthe nature of light. In his earlier years, for instance, he considered "light and caloric as the same matter indifferent circumstances, and reflection as caused by an atmosphere ofcaloric retained around bodies by thisattraction" (Potter 1831a, 54).

3. The inverse square law in photometry was first slated by Kepler in the seventeenth century. ButPierre Bouguer was the first one who applied this principle to measure the reflective power of variousmaterials around the mid-eighteenth century (Bouguer 1961,20-49)

4. The angle ofreflection would be affected by the variation in the distance of the mirror to the screenoccurred during the experiment. Potter probably used a method of trial and error to estimate this distancebefore he took the above steps to determine the reflection angles. In this way, later changes in the distanceof the mirror to the screen would only shift the focus of the reflected light out of the center of the aperturea little.

5. Helmholtz later found that, with better designed matching fields, the eye could detect a brightnessdifference as small as .075% (palaz 1896, II).

6. For example, Bouguer reported that the reflective power ofmercury was 66.6% at 21 degrees, and

NOTES 187

70% at three degrees (Bouguer 1961, 93, 53).7. Potter's measurements were surprisingly accurate. The discrepancies between Potter's measurements

and those obtained by Drude in the late nineteenth century are very small, usually less than 5%. For moreabout Drude's measurements, see (Ditchburn 1991,444,448).

8. Without making any specific theoretical assumption, MacCullagh was not able to explain metallicreflection. But itwas on his empirical law that later works built the theory which is now accepted. For moreon MacCullagh's work on metallic reflection and the later development, see (Whittaker 1951, 125-67).

9. Potter also used his photometric measurements to justify his specific design of the reflectingtelescope that used two metallic mirrors. In order to reduce the loss of light, Newton suggested using aconvex prism to replace the plane metallic mirror in reflecting telescopes. After conducting a series ofexperiments to measure the amount oflight transmitted through flint prisms, Potter concluded thatNewton'ssuggestion did not greatly surpass his design in terms of illuminating power, but came with a much higherprice tag (potter 1832a).

10. Assuming that Potter's measurements of the reflection angles were accurate, we can use Potter'sexperimental report to estimate the positions of the lamp and the glass by simple trigonometric analyses. Inthe recalculation of the reflective power, we use Lambert's version of the inverse square law, which takesthe role of the incident angle into consideration. For an example of the estimations and recalculation, seeAppendix 5.

11. In the crown glass, its left edge (the edge in contact with the diamond) appeared to be dimmer thanthe other edge. When Potter used his formula to determine the brightness ofthe crown glass, he only obtainedthe value at the left edge, which was lower than the average. In this way, he further underestimated thebrightness of the crown glass, and further lowered the measuring results.

12. To determine the ratio, Forbes passed a beam ofheat through two mica piles, and used the "thermalphotometer" to measure the intensities of the transmitted heat when the axes of the two mica piles wereparallel and perpendicular. He found that the ratio depended upon many factors, including the angle ofrefraction, the refracting medium, and the heat source.

Chapter 7

1. Instead ofmeasuring the focal lengths ofthe lenses, Galileo used an intuitive method to estimate themagnification power ofhis telescopes. He observed two circles ofdifferent sizes from a certain distance, thelarger one with a naked eye, and the smaller one with the other eye through a telescope. He adjusted the sizeofone ofthe circles until they appeared equal. Then the ratio ofthe circles' areas indicated the magnificationpower of the telescope (Galileo 1989,38).

2. This analysis was critical in the ongoing debate regarding the Copernican theory. A major difficultythat Copernicans encountered was to explain the apparent size ofMars. The Copernican theory implied that,when Mars was closest to the Earth, it should have appeared about 60 times as large as when it was mostdistant from the earth. But the best telescopic observations showed that the difference was only about fourtimes. By appealing to the defect ofthe eye, Galileo was able to neutralize the apparently negative evidenceagainst the Copernican theory. For more, see (Brown 1985).

3. For the history ofthe camera obscura, see (Gernsheim & Gernsheim 1955).4. This law was discovered by Harriot in 160 I, and rediscovered by Snell in the mid 1620s. Neither of

them published their discoveries.5. For details of Ptolemy's measuring device and procedure, see (Cohen & Drabkin 1958,274-5).6. According to King, David Gregory and Chester Hall were the first few persons who realized that

achromatic lenses were possible by drawing analogy to the eye. There are different accounts for howDollondleamed the idea ofmaking achromatic lenses. For details of Dollond's discovery, see (King 1955, 145-8).

7. Before Brewster, Wollaston had measured the refractive indices of 50 different substances, but hismeasurements, according to ThomasYoung and Brewster, were often inaccurate. See (Brewster 1813b, 245).

8. To calculate refractive indices, the radius of curvature of the objective lens must be determined.Because Brewster was not able to acquire this parameter with sufficient accuracy, he only offered themeasurements of the changed focal lengths, which were useful in ranking transparent substances accordingto their refractive power. Later, Young discovered a simple formula to convert Brewster's measurements toconventional refractive indices. For details ofYoung's analysis, see (Levene 1966,73-4).

188 NOTES

9. The resolving power of the eye (a) is defined by the following formula:a = 1.22AJD, where A. is thewavelength and D is the diameter of the pupil. Thus, the resolving power of the eye is in proportion to thediameter of the pupil.

10. See next Chapter for the details of Stoke's experimental procedure.

Chapter 8

1. Chronometers are used to keep accurate time in variations of temperature, graphometers areinstruments for measuring angles in surveying, and cyanometers are used to determine the intensity of theblue of the sky. For a complete list of the instruments that Humboldt used in his expedition, see (Humboldt1814-29, voU, 32-9).

2. The aim of astronomical reductions was to systematize the computations involved in reducing theapparent places of the fixed stars to their mean places, and to produce tables showing the corrections to bemade for the aberration of light, for precession and for nutation (Morrell & Thackray 1981, 510)

3. There are several different opinions on how the British Association was founded, but all of themagree that the successful exemplar set up by Humboldt was one of the important factors; see (Foote 1951;Williams 1961; Morrell 1971; Orange 1971; Cannon 1978, 181-96).

4. Stokes's law of fluorescence was not immediately accepted by the optical community. For moreabout the debate over Stokes's law in the second halfofthe nineteenth century, see (Malley 1991).

5. For more about Rllmer's determination of the velocity oflight, see (Cohen 1946).6. Because he found that the angular distance between the two bright spots was no more than half a

degree, Wheatstone estimated that the velocity ofelectricity was 288,000 miles per second. But he was notconfident in the accuracy of this measurement. For Wheatstone's concerns, see (Bowers 1975,44-51).

7. Brewster had witnessed Foucault's experiment, but he did not indicate the time and the place; see(Brewster 1854, 262).

8. According to Schaffer, Maxwell made a small error in transcribing Fizeau's value, which made himbelieve that the discrepancy between his calculation and Fizeau's measurement was only about 1%. Thediscrepancy between Maxwell's theoretical value and Foucault's measurement was more than 4%, whichforced Maxwell to recalculate the theoretical value; see (Schaffer 1990, 144-59).

9. For more about the theory unification achieved by Maxwell's electromagnetic theory, see (Morrison1992).

Chapter 9

1. Brewster believed that "the mind, residing, as it were, in every point of the retina, refers theimpression made upon it at each pointto a direction [ofthe optic axis]" (Brewster 1822,750). Thus, Brewsterexplanation of space perception also appealed to the mystical functions of the mind.

2. What Roget observed was not a simple stroboscopic phenomenon, which refers to effects in whicha discrete displacement ofthe stimulus gives rise to the perception of a single continuously moving objects.But in hindsight, Roget's work was particularly important, not only because he offered a theoretical accountof the phenomenon, but also because by focusing on circular motions, his work eventually led to theinvention of a new scientific instrument -- the stroboscope.

3. A few years later William Horner invented the cylindrical stroboscope, in which a sequence ofpictures showing a successive motion was put on the inner surface of a cylinder. The cylinder was mountedon a vertical axis so that it could spin around. Looking through the vertical slits in the upper part of thecylinder, a number ofobservers could see the motion ofthe pictures at the same time (Horner 1834). Hornernamed this device the daedeleum, which was renamed the zoetrope in the 1860s.

4. Brewster also wanted to use optical instruments as tools to reveal the beauty ofGod's creation; see(Kemp 1994, 206-9).

5. In the early nineteenth century, specialists in optical instruments often called themselves opticians.Not until the late nineteenth century did the term "optician" come to be used for those who made and soldglasses for the correction ofeye sight (Clifton 1995, xii).

6. Source: (Clifton 1995). Here, optical instrumentmakers include opticians, optical turners, and optical

NOTES 189

instrument manufactures.7. The magic lantern was an early fonn of slide projector. The phantasmagoria generated the illusion

ofmotion with a combination of a magic lantern and a movable screen. The teinoscope was a device thatused two prisms to magnify one dimension of the image while keeping the other dimension the same(Brewster 1822, 792). The static panorama was a device to show various parts of a picture in succession byarranging it on the inside ofa cylindrical surface. The dioramawas a mode ofscenic representation, in whichthe light source may be diminished or increased to represent the change from sunshine to cloudy weather.The iconoscope made three-dimension objects appear flat by suppressing binocular parallax.

8. The number ofoptical instrument makers reached its peak in 1851, when the Great Exhibition washeld in London. British opticians in the Exhibition demonstrated their superiority in the field. After that,large-scale factory production ofoptical instruments gradually replaced individual craftsmen, and the numberofoptical instrument makers decreased.

9. According to Brewster's own account, a small number ofbinocular cameras armed with semilenseswere made by Slater, a London optician, but all of them were sent to America (Brewster 1852a).

10. Another earlier binocular camera maker was Thomas Davidson, an Edinburgh optician, whosupplied Brewster a portrait camera armed with two achromatic lenses; see (Morrison-Low 1984,63).

II. Ofhumble origin and limited education, Nottage quickly became rich by making stereoscopes andstereoscopic pictures. In 1885 he was elected lord mayor ofLondon (Hope 1989, 1'5-6).

12. A catalogue ofbinocular pictures offered by the London Stereoscopic Company can be found in theappendix ofBrewster's The Stereoscope (Brewster 1856).

Conclusion

1. Some philosophers of science tried to interpret Kuhn's theory of scientific revolutions in a"conservative" way, which equates scientific revolutions with major conceptual and theoretical changes ina field. For a "radical" interpretation ofKuhn's theory of scientific revolutions, see (Rouse 1987).

2. Recent studies in cognitive psychology support Kuhn's analysis. Studies reveal that there are internalstructures (the so-called graded structures) in all terms, in the sense that referents vary in exemplifying theirterms. No definition expressed in the fonn ofsufficient and necessary conditions can account for differencesamong the referents ofa term. We acquire new concepts by identifying their exemplars or prototypes, whichrepresent the salient or central tendencies of the tenns in question. For more on the relations between thepsychological theory ofcategorization and Kuhn's theory ofscientific revolutions, see (Andersen, et al. 1996;Chen, et aI. 1998).

3. This is the so-called ontic conception of scientific explanation, in opposition to the epistemicconceptionwhich defines explanations as arguments on the basis ofthe relations oflogical necessity betweenexplanans-statements and explanandum-statements; see (Salmon 1984,84-123).

4. Theoretical paradigms also contain unarticulated procedures for analysis and calculation, such as theprocedure of ray analysis in the particle paradigm and the procedure of wavefront analysis in the waveparadigm. Thus, many implications derived from the tacit feature of instrumental traditions may also beapplied to theoretical paradigms.

5. We can find similar separate but non-contradictory relations between the image tradition and thelogical tradition in high energy physics; see (Galison 1997,20-1).

6. These cognitive studies are based upon experiments that used college students as the subjects, butthere are reasons to believe that these studies reveal some general features ofhuman cognition, and thus canshed light on historical studies. The key ofthis cognitive-historical analysis is to adopt a reflexive attitude-­we use cognitive theories to the extent that they help interpret the historical practices, while we test to whatextent current cognitive theories need refinement when they are applied to scientific thinking. For more onthe methodology of cognitive-historical analysis, see (Nersessian 1987; Nersessian 1995).

7. For more on incommensurability in the use ofgoal-derived concepts, and an extended analysis ofanexample of miscommunication caused by goal-derived concepts during the optical revolution, see (Chen1994).

8. Recent research in cognitive psychology supports Kuhn's theory of concepts, particularly hisrejection of the traditional view that concepts can be defined by necessary and sufficient conditions; see(Andersen, et al. 1996).

190 NOTES

9. Kuhn's analysis is based on a model of concept representation that defines concepts in terms of agroup ofunrelated features. But ifconcepts are represented by adifferentmodel that captures intraconceptualrelations, it is possible to show that even taxonomic change can occur in a continuous manner; see (Chen &Barker 2000).

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Stokes, George. (1848). "On the Theory ofCertain Bands Seen in the Spectrum." Philosophical Transactionsofthe Royal Society ofLondon 138: 227-242.

Stokes, George. (1849). "Onthe FormulationoftheCentral Spot ofNewton's Rings Beyond the Critical Angle."Transactions ofthe Cambridge Philosophical Society 8: 642.

Stokes, George. (1850a). "On a Fictitious Displacement of Fringes of Interference." Annual Reports oftheBritish Association 20: 20.

Stokes, George. (1850b). "On Metallic Reflexion." Annual Reports ofthe British Association 20: 19-20.Stokes, George. (1851). "On a New Elliptic Analyzer." Philosophical Magazine 2: 420.Stokes, George. (1853). "On the Changes ofRefrangibility ofLight, and theExhibitionThereby ofthe ChemicalRays." Notice ofthe Proceedings at the Meetings ofthe Members ofthe Royal Institution I: 259-264.

Stokes, George. (1854). "On the Change of Refrangibility of Light." Proceedings of the Royal Society ofLondon 6: 195-200.

Stokes, George. (I 907).Memoir andScientific Correspondence ofthe Late Sir George G. Stokes. Cambridge:Cambridge University Press.

Sviedrys, Romualdas. (1976). "TheRise ofPhysical Science at VictorianCambridge."Historical Studies in thePhysical Sciences 2: 127-151.

Talbot, William. (1837). "An Experiment on the Interference ofLight." Philosophical Magazine 10: 364.Timbs, John. (1862). Year-book ofFacts in the International Exhibition of1862. London: Lockwood.Tovey, John. (1840). "On Mr. Potter's Application ofHuygens's Principle in Physical Optics." Philosophical

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Wheatstone, Charles. (1852). "Contributions to the Physiology of Vision - Part the Second. On SomeRemarkable, and Hitherto Unobserved, Phenomena ofBinocular Vision." Philosophical Transactions ofthe Royal Society ofLondon 142: 1-17.

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Wittgenstein, Ludwig. (1958). Philosophical Investigations, 3rd Edition. Oxford: Basil Blackwell.Wollaston, William. (1802). "A Method of Examining Refractive and Dispersive Powers, by PrismaticReflection." Philosophical Transactions ofthe Royal Society ofLondon 92: 365.

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NAME INDEX

Agassiz, Jean. 132Airy, George. xix, 3, 9,10,21,25,48,58,77,79,

81,84,86,106,107,131,133,134,140,184, 186

Andersen, Hanne. 189Arago, Fran90is. 1,32-35,37,38, 122, 143, 186

Babbage, Charles. 130, 131, 160Baily, Francis. 131, 132Barker, Peter. 183, 186, 190Barsalou, Lawrence. xvi, 171, 172Barnes, Barry. xviiBarton, John. xx, 63, 64, 133Bennett, James. xvi, 127Berkeley, George. 112, 113, 148, 149Biot, Jean-Baptiste. 2,4,19,20,33,37, 184Blair, Robert. 116Bouguer, Pierre. 89,91,93,95, 123, 186Bowers, Brian. 188Boyle, Robert. 110Brewster, David. xx-xxii, 3, 6-17,19,21,23,25,

27-33, 36, 37, 39, 56-67, 69-83, 86, 87,93,107,117,122,123,131,133,137,138, 141, 144, 145, 149-151, 154-164,169,183-189

Brisbane, Thomas. 183Brougham, Henry. xx, xxi, 1,6,10,183Brown, Harold. 32, 33, 187Buchdahl, Gerd. 184Buchwald, Jed. xx, 1,35,40,48, 122, 183, 185,

186Buttmann, Guntner. 2, 3

Cannon, Susan. 130,133,136,188Cantor, Geoffrey. 1,3,7, 112, 183Cauchy, Augustin. 48, 49, 53,66,118,183-185Cawood, John. 131Challis, James. 48, 79, 133, 134Chambre, de La. 111Chen, Xiang. xx, 127, 167, 183-186, 189, 190Christie, J.R. 165Clifton, Gloria. 187Cohen, LB. 188Cohen, Morris. 188Collins, Henry. 183Crombie, Alistair. I 11Dalton, John. 88, 186Dancer, John. 163-164

201

Desaine, P. 184Descartes 110, Ill, 114, 147Ditchbum, R.W. 187Dollond, John. 116, 187Dollond, George. 58-59,94,160, 185Dollond, Peter. 159Dorries, Matthias. 62Drabkin, I.E. 187Dreyfus, Hubert. xviiDrude, P. 187Dunn, Samuel. 112

Faraday, Michael. xvii, 104, 136, 153,154,160Fizeau, Hippolyte. 142-144, 146, 188Foote, G. 188Forbes, Edward 132Forbes, James. 6, 25, 100-104, 126, 127,

131-134,169,172,187Foucault, Leon. 143-144, 188Fraunhofer, Joseph. 49-53, 56, 58, 60, 62, 64, 70,

120,121,126,179, 180,185Fresnel, Augustin. xx, xxii, 1-3, 21, 32-35, 37,

40,41,47,48,79,85,95,105,117,118,126, 134, 145

Galileo, Galilei. 109, 110, 113, 114, 142, 187Galison, Peter. 174, 189Gernsheim,Alison.114, 164, 187Gemsheim, Helmut. 114, 164, 187Glazebrook, Richard. 25, 146Gooding, David. xviGoodwin, Harvey. 134, 135Gordon, Margaret. 159Green, George. 79Gregory, David. 187Grodzinski, P. 64

Hall, A. Rupert. IIIHall, Chester. 187Hamilton, William. 3, 9, 21, 25, 40-43, 45, 49,

76,79-81,133,134,184,186Hankins, William. 186Harcourt, Vernon. 9Hardy, Arthur. 30Harriot, Thomas. 187Harris, Joseph. 112, 13 I, 132Hartley, David. 112Haughton, Samuel. 134, 135

202 NAME INDEX

Helmholtz, Hennann von. 186Hempel, Carl. 183Herschel, John. xix, xxi, xxii, 1-5,9, 13, 17-20,

24,25,33,37-40,45,48,67,76,79,80,88,89,93,99,122,123,131-138,140,141,161,177,183-185

Herschel, William. 88, 123Heve1ius, Johannes. 116Hooke, Robert. 114Hope, Valerie. 189Horner, William. 188Humboldt, Alexander von. 129-131, 188Huygens, Christian. 35,40, 105, 106

Jackson, Myles. 50, 185James, Frank. 60, 141, 184Jamin, Jules. 125Jenkins, Francis. 185Johnston, Sean. 173

Kelland, Philip. 134,135Kellner, L. 130Kepler, Johannes. 111, 112, 186Kemp, Martin. 158, 188King, Henry. xvi, 53, 116, 187Kirchhoff, Gustav von. 127Koh1rausch, Friedrich. 146Kuhn, Thomas. 166, 168, 170-172, 174, 183,

190Kundt, August. 127

Lambert, Johann. 92,123Laplace, Pierre. 4Laudan, Larry. 184Leitner, Alfred. 51, 185Leslie, John. 100Levene, John. 187Lippershey, Hans. 109Lloyd, Humphrey. xxii, 21-25, 27, 40-45, 48, 66,

72,76,79,100,104,118,131, 133, 134,184,186

Locke, John. 118Lubbock, John. 131, 132

MacCullagh, James. 66, 79, 80,93, 133, 134,186,187

Mach, Ernst. xxMalley, Marjorie. 188Malus, Louis. 10, 15,27,28,30,31,39,40,44,

122Masson, M. xviMartin, Benjamin. 112Maxwell, James. 145, 146, 188Mills, A.A. 110Morrell, Jack. 25,130-132,188Morrison, Margaret. 188Morrison-Low, AD. 159, 165, 189

Morse, Edgar. 183

Nersessian, Nancy. 189Newton, Isaac. xix, 1,2,4,7,8,10,13,14,19,

20,22,99,110,111,115,116,117,120,121, 123, 127, 140, 145, 169, 171, 187

Nobert, Friedrich. 62

O'Brien, Matthew. 134, 135O'Hara, 1. 184Olson, Richard. 3Orange, Derek. 188Owen, Richard. 132

Pa1az, Adrien. 186Paris, John. 155Parkinson, E. 137Pav, Peter. 1Peacock, George. 1Pearson, William. 183Perrin, Fred. 30P1ayfair, John. 6Porta, della. 11 I, 156Porterfield, William. 112Potter, Richard. xx, xxi, xxiii, 87-102, 100-108,

122,123,133,165,166,169,171,172,180,181,186,187

Powell, Baden. xix, xxii, xxiii, 9, 25, 48, 49,52-56,60-63,65-67,76-79,81-84, 100,104,126,127,133,134,162,170,178,179,181,182,185,186

Powell, T.H. 162Priestley, Joseph. 14Provostaye, F. 183Ptolemy 115 187

Rankine, William. 134, 135Rayleigh, John. 125, 126Reid, Thomas. 6, 112, 121Robinson, John. 6Roderick, Gordon. 133Roget, Peter. 121, 153-154, 188Romer, Ole. 141-142Ronchi, Vasco. 146Rosen, Edward. 109Rouse, Joseph. xvii, 189Rudberg, Frederik. 41, 53Rumford, Count. 123Ryle, Gilbert. xvSabine, Edward. 131Salmon, Wesley. 189Sawyer, Ralph. 164Schaffer, Simon. 110, 188Scoresby, William. 183Shapiro, Alan. 111, 184, 185Simms, William. 53Smith, Adam. 112

NAME INDEX

Smith, Archibald. 135Smith, Jeremiah. 93Snell,WilIebrord van. 187Steffens, Henry. 1Stephens, Michael. 133Stewart, Dugald. 6Stokes, George. xxiii, 25,83-85, 127, 134-140,

185, 186, 188Sviedrys, Romualdas. 136Swan, William. 135

Talbot, William. 3, 58, 62, 69-72, 76,81, 133,134, 161, 162, 185

Timbs, John. 164Thackray, Arnold. 25,130-132,188Tovey, John. 105, 106Turner, Gerard L'E. xvi, 154, 157

Voltaire, Franyois. 112

Warner, Deborah. 185Weber, Wilhelm. 146Wheatstone, Charles. 143, 148-150, 152, 160,

162, 188Whewell, William. xix-xxi, 1,3,6,9,21,72,76,

118-121,124,125,131-133,183,186White, Harvey. 184Whittaker, Edmund. 187Williams, Leslie. 188Willis, R. 183Wilson, David. 136, 183Wittgenstein, Ludwig. 183Wollaston, William. 185, 187Worrall, John, xxi, 183

Young, Thomas. xix, xx, 1-3,7,14,47,48,51,56,133,135,140,159,187

203

SUBJECT INDEX

aberration 17,22,50,77,116,188- chromatic 50, 116- spherical 50, 116

absorption xx, 9-12, 15, 17, 19,20,22,24,57-60,69,72,74,94,127,138,146,184,185- by nitrous acid gas 60• interactions between light and absorptivematerials 61

• selective xx, 9-12,127, 146absorption spectrum 10, 57,60absorptive material 57, 60absorptive spectroscopy 6ad hoc hypotheses 4,19,73, 184aether 12analytic method- rays analysis xxi, 32• wavefront analysis 77, 82

analyzer xxi, 27-34, 35·40, 42, 71,124- used by Brewster 28-30- used by Fresnel 33-35• used by Herschel 37-38- used by Lloyd 42-44

anorthoscope 153, 160aperture xviii, xx, 41, 42, 58, 85,105, 106, 122- circular xx, 69, 71, 85, 105, 106- diffracting 84

approximation xxii, 49, 87, 96, 97,123,169,171, 182

Arago's account ofstellar scintillation 186articulated element of science xv-xviii, 109, 124,128,170,171,174

Ashmolean Society 56astronomical reductions 130-132, 188

barometer 130biogeography 129biological evolution 166bismuth·antimony bars 100Borda's repeating circle 122Brewster's law 6British Association xx, 9, 10, I5, 2 I, 25, 27, 44,45,56,57,59,65,71,76,78-81,86,100,118,131,132,134,146,150,159,163,183,184,188· 1833 meeting 21- 1836 meeting 56- 1837 meeting 71

205

- 1838 meeting 56,57,59,76, 100, 149·1840 meeting 65- 1845 meeting 81,86, 184- 1849 meeting 162- 1852 meeting 86• Mathematics and Physical SciencesSection 131

- research grants 56, 132- "Report on the Progress and Present StateofPhysical Optics" 21,100

- "Report on the Recent Progress ofOptics"15

Cabinet Cyclopedia 3calculation, constant fixing 66Cambridge University xix, 83, 105, 110,130,135- 137, 183, 185, 186• Mathematical Tripos 25, 137- Natural Science Tripos 137· Smith Examination 137

camera 122, 160, 162, 189· binocular 161-163,189- stereoscopic 162

camera obscura Ill, 114, 122, 188categorization, ofoptical phenomena xxi, 13,14-19,22-24,26,31,32,36,44,76,184189. See also classification system

chemical spectroscopic analysis 60chemistry 8, 88, 135, 136, 138chronometer 130classification system xxi, 13-15, 18,22,23 25,26,27,32,36,37,39,40,44,45,48,72,75,76,86,170,171,172,173,185. Seealso categorization.• Airy 25- Brewster 14-17• dichotomous structure 22, 23, 25, 184- Herschel 17-19- Lloyd 22·24- Newton 13-14- Priestley 14- Young 14

cognitive studies ofscience xvi, 172, 173, 198color- Aristotle's theory of 110- Descartes's hypothesis I 10- ofnatural bodies 4, 7, 185- ofthe sky 4

206 SUBJECT INDEX

Common Sense methodology 3, 112communication problems xviii, xxiii, 172community, optical xvi, xviii, xix, xxiii, 1,3,6,13, 15,26,27,40,48,49,56,67,72,93,118,130,131,136,137,145,147,159,160,167,188

conceptual problem II, 31, 32conical polarization, Lloyd's law 43conical refraction 21,41-45,184-exrernaI41, 42,44- internal 42, 44

conservation of energy 141constant 49,52,61,66,178Copernican theory 110, 187Copley Medal 6crystal 2, 6, 10, 19,21,28,38,40,41,44,45,53,56- arragonite 41- biaxial 2, 19,21,40,41,44,45- chromate oflead 53- doubly refracting 2- Iceland spar 28, 37, 40, 97, 107- optic axes 19,37, 147, 150, 160, 162- rock 97

cyanometer 130

daedeleum 188Debusscope 156diffraction xx, xxii, 4, 7-9,12,14,16,17,19,22,41,49,51,52,55,56,58,60-66,69,74,76,85-87,105-107,137,170,185,186- intensity of light in the diffraction fringes105,106

- produced by a circular discs 106diffraction spectrum- produced by Brewster 63-64- produced by Fraunhofer 51- produced by Powell 62-63

diorama, multimedia 160dispersion xx-xxii, 5, 12, 17, 19,20,22,24,47-49,52,53,61,66,67,77,116,120,127,138,146,177,178,183-185- anomalous 127- epipolic. See fluorescence.- internal. See fluorescence.

dispersive power 6, 50, 56, 61dividing circle 50, 51, 53double refraction 2-4,6,7, 10, 12, 14-17,20-22,25,27,40,44,66,73,122,146,184- by biaxial crystals 21, 40- extraordinary rays 7, 40, 73, 122- ordinary rays 73

doublet, convex-concave 50dynamics 48,133, 136, 185

Edinburgh Encyclopaedia 14, 65

Edinburgh Journal a/Science 93, 95,131,148Edinburgh Review 1electromagnetism xvi, xxiii, 133, 136, 144, 145,188

e1etrometer 130epipolic dispersion. See fluorescence.error, relative 51, 54, 178, 179ether xix, 1,5,8,11, 16,48,79, 141, 145, 146,185

ether dynamics 48, 185experience7,44,62, 71,80,100,104,107,112,122,135,147,148,158,159,172,173

experiment replication xxii, 47, 62, 66,171experimenta crucis 104experimental evidence 47, 61, 66,100experimental procedure xvi, 31, 36, 39, 40, 87,188

experimentation, value 104explanatory power xx-xxii, 1,4,5,7-9, 12, 13,16,19,20,24,25,47,145,146,174,175

explanatory success xix-xxi, 1, 13, 19,20,24,47,174,186

eye xvii, xviii, xxi-xxiii, 10, 30, 34, 35, 37, 56,59,62,69-71,76,81,84,86,87,90-94,96,98,100,103,104,109-114,116,117,121-128, 130, 139, 140, 142, 143, 145,147.150,152,154-156,158,160,164,170.174,186-188- crystalline lens of 70- curved screen 114- diameter ofthe pupil 59, 123,188- diaphragm 114- fatigue 90, 92, 123-lens 77,186-retina 70, 77, 85, 88,114,148,150,153,155,188

-sensitivity of xxii, 87, 91,123,139,140,142,144,152,169,170

eyeglasses 109eyepiece 59, 106, 107, 117, 148

family resemblance xviii, 167fluorescence 127, 137-141, 188- Brewster's experiment 137- Herschel's experiment 137- Stokes's experiment 138-140

force- deflecting 4- molecular 48, 49- optical 2- attractive and repulsive 2

fossil zoology 130fringes- produced by biaxial crystals 2, 38- produced by diffraction 4, 7, 9, 19,41,86,105-107

SUBJECT INDEX 207

- produced by interference 32, 33, 35, 38,73,99, 121-123, 125-127

- produced by refraction III

g&vanometerIOO, 127, 169geometric parameter xvii, 112, 127, 128geometric tradition xvii, xxiii, 124, 128, 129,144,170,171

geometry 49,112,117glass- brown 32- colored glass 10, 138, 157- crown 28-30,50,53,83,97-99,104,176,177,187

- flint 50,52,53,55,94,104,116,178- ground 94- thin plate of56, 63, 69, 71, 73, 185-wedge 101

graphomotor 130grating xviii, xx, xxii, 51, 52, 61, 62,64,65- made by Barton 63- made by Fraunhofer 61-62- of par&lel stretched wires 62- ruled by a diamond 62

Great Exhibition of 1851 163-164,189

Haidinger's brushes 137Hamilton's characteristic function 44, 45heat 9, 48,55, 100-104, 126, 132, 136, 138,172,187- elliptically polarized 102- partially polarized 102- scattered 10 I, 102, 172

historiography 165Humboldtian sciences xxiii, 129, 131-136- papers of 132-134

Huygens's principle 70,105-106hygrometer 130hypothesis 1,3-5, 19,20,30,48,95, 110-112,118,138,145,146,149,150,184,185

iconoscope 160incommensurability xviii, 141, 169, 172, 173,189

index of refraction. See refractive index.industry ofmaking optical instruments 164inflection 7, 10, 14. See also diffraction.instrumental tradition xvi, xviii, 124, 127, 170,173, 174- the geometric tradition xvii, xxiii, 124,128,129,143,171,172

- the visual tradition xvii, xxiii, 121, 124,125,127,148,149,171,172

intensity ofheat 101, 102intensity oflight 18,30,34,82,85,87,97,98,100,104-106,120,126,164,175,180- in Newton's rings 99

- in prismatic spectra 64interaction between light and matter xxii, 6interference xix, xxi, xxii, 6-9,14,16-20,22-24,32,33,35,36,38,69-72,74,76-78,80,82-85,99,105, 121, 122, 125-127, 140,165, 169, 185, 186- colors ofplates 4,16, 137- fringes 2, 32, 33, 35,38,73,99, Ill,121-123,125-127

International Exhibition of 1862 163

Journal ofGas Lighting 164Jupiter- eclipses ofthe first satellite 141- moons of 110

kaleidoscope 156, 159, 160. See alsopolyphaton, polyscope, Quinetoscope.- applications in decorative painting 157- parallel 159

King's College, London 143knowing how xv, xvi, 169, 171. See alsoprocedural knowledge, tacit element.

lamp 10,42,57,89-92,94,123, 187language learning 25lathe 106lens- achromatic 50, 116, 117, 122, 187, 189- concave 109,110, 111, 117, 121- double convex 37- field lens 117- semilens 162, 189- transmitting power 89

light- "sanatory" aspect of 165- an&ogy between light and sound 11- analysis of31- as rays 70- chemical properties 8- homogeneous 73, 77, 79, 85, 99- nature of xx, xxiii, 3, 37, 95, Ill, 138,147,165,173,174,186

- optico-chemical effects 24- scattered 94, 150, 152, 182- thermal and chemical effects 14- velocity of 5, 14,22,47-49, 141-146,188

light source 4, 19,28,32,33,42,57,97,98,106, 123, 175- monochromatic 10, 184- semicircular 98

Liverpool Photographic Society 163Lloyd's law of conical polarization 43London Stereoscopic Company 163, 189lord mayor ofLondon 189

208 SUBJECT INDEX

magic lantern 160, 189magnetometer 130manpower, scientific 129, 131-134marine biology 130, 132Mars 188mass-production business 164mathematical analysis xix, 21, 40, 41, 49, 86,

106, 136-137, 146, 153, 180, 183, 184mathematics 2, 9, 74, 79, II7, II 8, 130-132,

134, 136, 141- algebra 117- differential and integral equations 118- integration 82- trigonometric calculation 85, 90, 117

measurement xvii, xxii, xxiii, 6, 41, 49, 51-56,58,60,61,87, 91-105,II5-121, 123-131,136,141,144-146,168,169,171,177-179,186,187- error 51,54,178,179- level ofprecision 55- angular 51

measuring device xxiii, 109, II4measuring refractive index- Brewster's method 117- Fraunhofer's method 49-51- Jamin's method 125-Newton's method II5-II6, 120- Powell's method 53-55- Ptolemy's method II5- Rayleigh's method 126- Whewell'smethod 121

measuring the intensity of light- Forbes's method 100-103- Potter's method 89-91- William Herschel's method 88

measuring the velocity oflight- Arago's method 143- Fizeau's method 142- Foucault's method 143-144- Galileo's method 142- Romer's method 141-142- Wheatstone's method 143

measuring unit 119, 128- arbitrary II9- conventional 120- cubit 119- English foot 119- fathom 119- foot 59, 94, II6, II9, 123, 130, 159, 185- naturallI9, 121- Paris foot 119- Rhenish foot 119

measuring wavelength, Fraunhofer's method 51,120-121

metallic mirror 88, 89,91-94, 101, 187- concave 87- oftin-copper alloy 91

metaphor of language acquisition 112meteorology 9, 130-132, 136method, trial and error 52, 178, 186mica 37,97, 102, 107, 187microscope xv, 62,130,158- compound II7, 148- wire 58

mirror, metallic 88, 89, 91-94, 10 I, 187Munich Transactions 65

natural philosophy 3, 87, 100, 136, 186Newton's rings 10,22, 99, II 7, 121Newton's theory offits 7,8, 14,99Newtonian mechanics 138, 140, 167, 168Newtonian taxonomic system xxi, 13,27

optical category 14, 15, 18, 19,24,32,76optical instrument xv, xvii, xviii, xx-xxiii, 6, 14,109-III, 113, II4, 121, 122, 124-126,128,154,156,158,159,164,165,173,188, 189. See also analyzer, aperture,Borda's repeating circle, crystal, disc,doublet, eye, eyeglasses, eyepiece, grating,lamp, lens, microscope, mirror,philosophical toy, photometer, polarizer,prism, refractometer, scioptric ball, sextant,slit, spectroscope, stand, telescope,theodolite, vernier protractor- as image magnifier II 0- entertaining functions 159- as observing devices 109

optical instrument maker 160, 161, 165, 188,189

optical mineralogy 6optical revolution xx, xxii, xxiii, 27,109, 148,164,166,169-171,173,174,185,189

optical theory xv, xviii, xx, xxi, 15, 19,25, 146,175, 186. See also particle theory oflight,wave theory oflight.

optical turner 189Optical Institute at Benediktbeuem 50optics xvii-xx, xxii, xxiii, 1,2,6-10,12-15,20,21,25,41,49,51,56,72,84,86,93,95,99,104, 107,III-II3, II7, II8, 121,131-136,138,144,145,147,154,160,163-165,174,184,185- geometric 51, II2, II3, 164- physical 164

Oxford University 49,56

panorama, static 160, 189paradigm, theoretical xviii, xxiii, 167, 170-173,

189particle theory oflight xv, xviii, xx, xxiii, 1,2,4,6,20,25,31,45,70,76,141,147,165,171,175

perception ofdepth and distance 112, 147-149,

SUBJECT INDEX 209

188phantasmagoria 160, 189phenakistoscope 154, 155philosophical toy. See anorthoscope, camera,camera obscura, daedeleum, Debusscope,iconoscope, kaleidoscope, magic lantern,phantasmagoria, phenakistoscope,polyphaton, polyscope, Quinetoscope, staticpanorama, stereoscope, stroboscope,teinoscope, thaumatrope, wonder turner,zoetrope

Philosophical Magazine 41, 44, 70, 77,104-106,155

photometer- comparative 96-99- extinction xviii, 107- reflecting 89-91- thermal 100-101

photometry- "remote-control" devices 90- distribution ofbrightness 98- Faraday's photometric measurements 104- Fresnel's formula 95,101-104- luminous asymmetry 72•matching brightness 91-92, 94, 96,103,123,169,173

- the cosine law ofillumination 92• the inverse square law 89, 92, 94, 176,186,187

physicist, new generation xxiii, 129, 134, 135,137,141

polarization- as deviations ofrectilinear transmission 26- chromatic 37, 39, 123- circular 10,20,22,35,36,44• conical 40, 43-45- ellipticallO, 16,36,185- Fresnel's interpretation 39- incomplete 30, 31- mobile 2, 20-partialxxi,30,31,32,35,37,39,40,44- phase differences in streams ofpolarizedlight 137

polarization, taxonomy of xxi, 31, 36, 44- Brewster's classification 31-32- Fresnel's classification 36, 44• Herschel's classification 39-40- Lloyd's classification 43-44• Malus's classification 30

polarizer xvii, xx, 27, 37, 124polishing powder- carbonate of iron 88- oxide of iron 88- sulphate of iron 88

polyphaton 156polyscope 156practice, scientific xvii, 167, 169, 171

primary qualities 118-120, 124prism- achromatic 93- convex 188- crossed-prisms 127, 139, 140- flint glass 55- hollow 53-55, 127- triangular III

prismatic spectrum- G line 55, 57, 61, 65- H line 55, 57, 61, 65,178- produced by Brewster 58-59- produced by Fraunhofer 49-51- produced by Powell 53-55- relationship to diffraction spectrum, 51,52,55,56,65

prismatic spectrum, graphic presentation 57, 65,66- Brewster's map 65- Fraunhofer's map 65

procedure• articulated xv, xvii-tacit. xvii, xviii, xxiii, 18, 109, 124, 128,

171,172,189. See also procedureknowledge, knowing how.

Quinetoscope 156

ray, side of75reflection- angle of95-97, 102, 186- by grooved surfaces 79- crystalline 79- metallic xx, 6, 73, 93, 95, 102, 183, 187

reflective power- Fresnel's prediction 97- ofamethyst 97- of antimony glass 97- of diamond 97-98, 187- of emerald 97- of glass mirror 93-95- ofmetallic mirror 91-93- ofselenite 97

refraction, offluorescent light 127refractive index 51, 179- ofanise-seed oil 55, 180- offluids 115- offluids 53-55, 115, 116, 127- of oil of anise-seed 54, 179- ofoil of cassia 54- ofoil ofsassafras 83- ofoil ofturpentine 53, 82- ofsulphate of quinine 137-138, 140- ofsulphuret ofearbon 54, 55

refractometer 126replicating Fraunhofer's diffraction experiment62,66

210 SUBmCT INDEX

resolving power- ofspectrom 55-57- oftelescope 58-59- ofthe eye 59, 123, 187

Royal Astronomical Society 144Royal Irish Academy 41,43Royal Society ofEdinburgh 7, 100, 157, 184Royal Society ofLondon 6, 7, 80, 83, 84, 100,131,145,148,157,164,185,186

ruling machine 63Rumford medal 6

scioptric ball 114Scottish commonsense philosophy 3, 112screen, semi-translucent 90Secondary qualities 118-120, 124sense organ 5, 168, 174sextant 130slit- single 51- double 33,51- multiple 51

Society ofNaturalists and Natural Philosophers131

solar phosphorus 22specialization xxiii, 135, 164, 174spectacles xv, 109, 110spectral line xxii, 49-64, 66, 83,120, 123, 125,126,139,140,177,185- oblique dark lines in diffraction spectrum64

spectroscopy 6, 125, 165spectrum 7,10,15,22,31,50,52,53,55,57-65,69-73,76-78,81-86, III, 115, 116,120, 121, 123, 125, 127, 136, 139, 140,174,177-180,185,186- by interference 78, 186. chemical nature 59- diffraction xxii, 49, 51, 52, 55, 56,61-66,170,185

- fluorescent 139, 140- gaseous 57, 60- solar 7,10,22,50,59, 139- stellar 60

stand, brass 58stereoscope 148-150, 152, 160-163, 188-lenticular 151, 152, 160-163- reflecting 151, 161, 163

stereoscopic camera- double-lens 162-163- single-lens 161

stereoscopic effects 149-151, 160-163, 188Stourbridge Fair 110stroboscope 152,154,155,160,188- cylindrical 189

stroboscopic phenomenon 188

tacit elements xvii, xviii, xxiii, 18, 109, 124,128,170,171,183,189. See alsoprocedure knowledge, knowing how.

Talbot bands 62, 185- produced by Brewster 72-73- produced by Powell 81-82- produced by Stokes 83-84- produced by Talbot 69

Talbotype process 160taxonomy, of optics xxi, 13-15, 18,25,26,27,31,32,36,37,44,45,75,76,86,167,169,171, 172. See also classification,categorization.

taxonomy, ofpolarization xxi, 31, 36, 44Taylor series 49, 66teinoscope 161, 189telescope xv, xviii, xx, xxii, 50, 57, 59, 87-89,93,94, 110, 116, 123, 130, 158, 174, 188- achromatic 50,53,58, 59,70,71,94,120, 121, 127

• diameter ofthe objective 58- elescope, Dollond's five-foot 59- focal lengths ofthe objective 58- gamma-ray 175- illuminating power 89, 93, 94, 188- infrared 175- magnifYing power xxii, 50,53, 58, 59,88,110,113,117,123,169,187

- Newtonian 87- objective lens xxii, 89, 94,116,117,170,187

- radio 175• space-penetrating power 94- ultraviolet 175- William Herschel's design 89- x-ray 175

telescope ruler 51terrestrial magnetism 130, 131, 136thaumatrope 155, 160theodolite xxii, xviii, 28, 49,50,51,53,54,58,59,126,120,121,127,130,169,179,185

theory evaluation xxi, 25, 26, 174thermo-electricity 9thermodynamics 138thermoelectric pile 100thermometer 53, 100, 169- air differential 100- electric 100

tides 9, 131tidology 130-132, 136Times 163total reflection 4, 22Trinity College, Dublin 21, 79truth 3-5, 12, 24, 44, 81, 104, 118, 145

Ulysses Deriding Polyphemus 158undulatory theory 21,44,79-81,99,106, 107,

SUBJECT INDEX

141,145. See also wave theory oflight.unification ofphysical optics andelectromagnetism xxiii, 146

University College, London 87, lOS, 186UniversnyofEdmburghl36University ofEdinburgh 6, 100University ofGlasgow 136unpolarized light 2, 17-19,22-24,30,33,35,37-39,41,45,83,175,177

vernier protractor 51, 53vision xxiii, 17, 19,43,109,111-114,117,121,122,148, 149- binocular 148, 149

visual aids, to the eye xxii, 109visual illusion 113, 154, 156- cameos into intaglios 148- spatial deception 148

visual persistence 152-155visual tradition xvii, xxiii, 121, 124,125,127,147,148,170,171• method, enlargement of image 123, 127

wave• amplitude 35, 36- as longitudinal vibrations 35- as transverse vibrations xxi, 22, 35, 37- phase xix, 35, 36, 137, 185

wave theorist- new generation xxiii, 129, 134, 135, 137,

141- old-generation 134-136

wave theory of light xv, xx, xix, xxiii, 1,45,47,53,118,129,141,145,147,165,170,174- Cauchy equation 49• crucial test for 45, 95• general equation ofmotion 48

wavefront xix, XXi, 32, 35, 37, 39, 40, 44, 51,69,71,77,81-82,84,89,94, 105, 138,154,166,186, 189

wonder turner 154

zoetrope 188

211

Science and Philosophy

Series Editor:

Nancy J. Nersessian, Program in Cognitive Science, Georgia Institute ofTechnology,Atlanta

1. N.J. Nersessian: Faraday to Einstein: Constructing Meaning in Scientific Theories.1984 ISBN Hb 90-247-2997-11 Pb (1990) 0-7923-0950-2

2. W. Bechtel (ed.): Integrating Scientific Disciplines. 1986 ISBN 90-247-3242-5

3. N.J. Nersessian (ed.): The Process of Science. Contemporary PhilosophicalApproaches to Understanding Scientific Practice. 1987 ISBN 90-247-3425-8

4. K. Gavroglu and Y. Goudaroulis: MethodologicalAspects ofthe Development ofLowTemperature Physics 1881-1956. Concepts out ofContext(s). 1989

ISBN 90-247-3699-4

5. D. Gooding: Experiment and the Making ofMeaning. Human Agency in ScientificObservation and Experiment. 1990 ISBN 0-7923-0719-4

6. J. Faye: Niels Bohr: His Heritage and Legacy. An Anti-realist View of QuantumMechanics. 1991 ISBN 0-7923-1294-5

7. D.A. Anapolitanos: Leibniz: Representation, Continuity and the Spatiotemporal.1999 ISBN 0-7923-5476-1

8. G. Chatelet: Figuring Space. Philosophy, Mathematics, and Physics. 2000ISBN 0-7923-5880-5

9. X. Chen: Instrumental Traditions and Theories ofLight. The Uses of Instruments inthe Optical Revolution. 2000 ISBN 0-7923-6349-3

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