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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Potter, Richard. (I 840b). "On the Application of Huygens's Principle in Physical Optics." PhilosophicolMagazine 17: 243-248.

Potter, Richard. (1841). "On the Phenomena of Diffraction in the Centre of the Shadow of a Circular Disc,Placed Before a Luminous Point, as Exhibited Be Experiment." Philosophical Magazine 19: 151-155.

Potter, Richard. (1859). Physical Optics. PartII. The Corpuscular TheoryofLight. DiscussedMathematically.Cambridge: Deighton, Bell and Co.

Powell, Baden. (1835a). "An Abstract ofthe Essential Principles ofCauchy's View ofthe Undulatory Theory,Leading to an Explanation of the Dispersion of Light." Philosophical Magazine 6: 16-25 107-113,189-193, 262-267.

Powell, Baden. (I 835b). "Researches Towards Establishing aTheory ofthe DispersionofLight. "PhilosophicalTransactions ofthe Royal Society ofLondon 124: 249-254.

Powell, Baden. (I 836a). "Observations for Determiningthe Refractive Indices forthe StandardRays ofthe SolarSpectrum in Various Media." Transactions ofthe Ashmolean Society I: 1-24.

Powell, Baden. (1836b). "On the Formula for the Dispersion of Light Derived from M. Cauchy's Theory."Philosophical Magazine 8: 204-210.

Powell, Baden. (I 836c). "Researches Towards Establishing a Theory of the Dispersion of Light, No.II."Philosophical Transactions ofthe Royal Society ofLondon 126: 17-19.

Powell, Baden. (1838a). "On Some Points Connected with the Theory ofLight."AnnualReports ofthe BritishAssociation 8: 6-7.

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Powell, Baden. (1840). "On the Theory of Dark Bands Formed in the Spectrum from Partial Interruption byTransparent Plates." Philosophical Magazine 17: 81-85.

Powell, Baden. (1841). "On the Theoretical Computation ofRefractive Indices."Annual Reports ofthe BritishAssociation II: 24-25.

Powell, Baden. (1848). "On a New Case ofthe Interference ofLight."Philosophical Transactions ofthe RoyalSociety ofLondon 138: 213-226.

Priestley, Joseph. (1772). The History andPresent State ofDiscoveries Relating to Vision. Light. and Colours.London: 1. Johnson.

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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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