251

TAXONOMY IN THE SCIENCE

Taxonomic Changes and the

Particle-Wave Debate in Early

Nineteenth-Century Britain Xiang Chen*

Introduction

In Britain, the early 1830s was a critical period for the development of optics. The

particle theory of light had dominated the field of optics in Britain since Newton's

endorsement, but this dominance became shaky at the beginning of the nineteenth

century when Thomas Young revived the wave theory by introducing the principle

of interference. In the late 1820s, a group of British "gentlemen of science," most

of whom were trained at Cambridge, adopted the wave theory. Beginning in 1830,

these newly committed wave theorists started to publish their researches, both

theoretical and experimental, advocating the wave theory. What followed was a

heated debate between the two sides, and eventually, a replacement of the particle

theory by the wave theory, or, the so-called "optical revolution".1

Historians have provided many detailed studies of this revolutionary change in

optics and the accompanying particle-wave debate. When historians explain the

victory of wave theorists in the debate and the replacement of the particle theory by

the wave theory, they agree that one of the crucial factors was the explanatory

successes of the wave theory, in the sense that it could explain more optical

phenomena than its rival, or provide quantitative accounts with elegant

mathematical analysis, or make successful predictions of hitherto unknown

phenomena.2

* Department of Philosophy, California Lutheran University, Thousand Oaks, CA

91360-2787, U.S.A.

Received 20 May 1994; in revised form 5 November 1994.

1 Kuhn first called the replacement of the particle theory by the wave theory a scientific revolution; see T. Kuhn, The Structure of Scientific Revolution (Chicago: The University of Chicago Press, 1970),

pp. 11-12. Recently, some historians further label it "the optical revolution"; see G. Cantor 'Physical

Optics', in R.C. Olby, G.N. Cantor, J.R. Christie, and M.J. Hodge (eds), Companion to the History of Modern Science (New York: Routledge, 1990), pp. 634-636.

2 In addition to explanatory success, many other factors, both cognitive and social, also

contributed to the victory of the wave theory. These factors include generational, institutional, regional, methodological, and metaphysical differences between the two theories, as well as their connections

with other disciplines in the field of physics. For a summary discussion of the roles of these factors,

see G. Cantor, Optics after Newton: Theories of Light in Britain and Ireland, 1704-1840 (Manchester: Manchester University Press, 1983), pp. 192-194.

252

However, historians also recognize that, despite its explanatory successes, the

wave theory did not immediately command complete support from the optical

community -- many particle theorists, such as Biot in France and Brewster in

Britain, did not accept the wave theory in their whole lives, and a heated

particle-wave debate lasted well up to the early 1850s.3

The superior explanatory power of the wave theory and the long span resistance

from its rivals raise interesting questions: Why did not the explanatory superiority

of the wave theory persuade such particle theorists as Brewster and Biot? How

could these particle theorists refuse to accept the wave theory despite its

explanatory successes. One possible answer is that these particle theorists were

simply unscientific and irrational.4 The presumption behind this answer is that

these particle theorists fully understood and recognized the wave theory's

explanatory superiority, but refused to accept it for social, political, or personal

reasons.

However, some particle theorists such as Brewster might not fully recognize the

explanatory successes of his rival. In some occasions, Brewster did admire the

merits of the wave theory in accounting for some optical phenomena, but he always

insisted that its explanatory power was not good enough to allow it to replace the

particle theory.5 To understand Brewster's judgment, we need to examine how

Brewster and other historical actors measured the explanatory power of the wave

theory. During the early nineteenth century, there was a consensus in the

scientific community that explanatory power consisted not only in the ability to

give accounts for numerous but, more importantly, various phenomena. If a

theory's successes are restricted in a few classes, its explanatory power is very

limited despite the number of its explanations. Herschel thus insisted that theories

should be evaluated with respect to facts "purposely selected so as to include every

variety of case."6 However, how many different classes of phenomena a theory

can explain also depends upon how the subject domain is classified, that is, upon

what kind of taxonomy is adopted, which provides a foundation for categorization

and classification. The measurement of a theory's explanatory power may vary

under different taxonomic systems, especially when a new taxonomic system

3 For studies of the debate in the 1840s and the early 1850s, see G. Cantor, Op. Cit., note 2, pp. 186-87, J. Buchwald, The Rise of the Wave Theory of Light, (Chicago: The University of Chicago Press,

1989), pp. 296-302; X. Chen and P. Barker, "Cognitive Appraisal and Power: David, Brewster, Henry

Brougham, and the Tactics of the Emission-Undulatory Controversy during the Early 1850s", Studies in the History and Philosophy of Science, 1992, 23: 75-101.

4 For an analysis of this possibility, see J. Worrall, 'Scientific Revolution and Scientific

Rationality: The Case of the Elderly Holdout', in C. Savage (ed), Scientific Theories (Minneapolis: University of Minnesota Press, 1990), pp. 341-350.

5 For example, Brewster in 1846 claimed that since the wave theory was still "incapable of

explaining whole classes of well-observed and distinctly marked phenomenon, ... [people] may be excused for ... not wholly abandoning older, though less popular, views". See D. Brewster, 'On A New

Polarity of Light', Report of the British Association 15 (1845), 7 (original emphasis).

6 J. Herschel, A Preliminary Discourse on the Study of Natural Philosophy (London: Longman, 1830), p. 208.

253

classifies previously homogeneous phenomena as different kinds or groups

previously different phenomena together under one category.

In this paper, I document an evolution of optical taxonomy accompanying the

dramatic changes of optical theory during the early 1830s. I trace the

development of optical taxonomy during the revolutionary change, and uncover

how these taxonomic shifts affected the evaluations of the two rival theories of light.

I particularly detail how particle theorists such as Brewster adopted a taxonomic

system developed from the Newtonian tradition, in which the explanatory

deficiencies of the wave theory were highlighted, and how wave theorists

introduced taxonomic systems with revolutionary structures, in which the

explanatory merits of their theory were emphasized to a maximum. The historical

narrative shows that, without the related taxonomic changes, the explanatory

superiority of the wave theory would have been unrecognizable, and the

replacement of the particle theory by the wave theory would have been impossible.

In the concluding remarks, I further reveal that the selections of taxonomic

systems by these historical actors were not arbitrary. Their selections of taxonomy

were not based upon social or rhetorical reasons, but reflected the experimental

techniques, including instruments and skills, they developed in their practices.

These experimental instruments and skills restricted the ways these historical actors

made classifications. Thus, when we take the developments at this deeper level

into consideration, the long-term resistance of particle theorists finally becomes

comprehensible without referring solely to social or irrational factors.

1. The Newtonian Taxonomic Systems

Before the "optical revolution," all dominant taxonomic systems in Britain were

developed within the Newtonian framework. The first Newtonian system was

proposed by Newton himself in his Opticks published in 1704.7 The subtitle of the

book, A Treatise of the Reflections, Refractions, Inflections, and Colors of Light,

displayed the basic structure of this system. In Book I of the Opticks, Newton

focused on reflections and refractions, but he also discussed the production of

spectra by prisms and the compositions of colored and white light, phenomena

called "different refrangibility of light" in his own words. Although these

phenomena later became independent under the category of "dispersion," Newton

regarded them as a special case of refractions. The focus of Book II was the

production of colors, later called the interference of light. To explain these

phenomena, Newton introduced the notion of "fits" of easy transmission and easy

reflection. In Book III, Newton first reported several experiments related to

inflection (or diffraction), and tried to explain them in terms of interactions between

light particles and body particles. Newton also examined double refraction and

several other optical phenomena, including thermal and chemical effects of light,

because he believed that they all were caused by interactions between light and

7 I. Newton, Opticks (New York: Dover, 1979).

254

materials. This arrangement of the subjects reflected a taxonomic system that

contained four major categories: "reflection," "refraction," "diffraction," and "color

of light." Some optical categories that were important in the later "optical

revolution," such as "dispersion," "double reflection," and "optico-chemical

effects," were treated as subcategories in this system.

Newton's classification was very influential during the whole eighteenth century.

Most taxonomic systems emerged in this period were built upon Newton's one, with

a few minor revisions. The most common revisions among those eighteenth-century

systems were to introduce new optical categories by making some subcategories in

Newton's system major categories. Such upgrades happened in "dispersion,"

"double refraction," and "optico-chemical effects."8 As a result, most taxonomic

systems in the late eighteenth and early nineteenth century doubled and even tripled

the number of major categories. An example of them was the one developed by

Thomas Young in 1807, which included ten major categories.9

A significant development of optical taxonomy within the Newtonian

framework occurred during the 1820s. This was a systematic classification of

optical phenomena designed by David Brewster (1781-1868), a fully committed

particle theorist who witnessed the "optical revolution," but never accepted the

wave theory although he lived until 1868. Brewster began his optical experiments

about 1799 when he was still a student at the University of Edinburgh. In 1814,

he determined the law of polarization in successive refraction, and the law of

polarization by reflection -- the so-called Brewster law. The optical community

soon recognized his researches. The Royal Society of London in 1815 awarded

him the Copley Medal for his studies of polarization, and elected him Fellow of the

Royal Society. He received the Rumford medal from the Royal Society for his

study of the interference pattern produced by polarized light in 1819. Through

these successes, Brewster established his prestige in optics, especially in optical

experiments.

In 1822 Brewster published an essay titled "Optics" in the Edinburgh

Encyclopaedia. With more than two hundred pages, he systematically reviewed

the history of optics, the theory of optics, the applications of optics to the

explanations of natural phenomena, and optical instruments.10

When Brewster

introduced the theory of optics, he adopted a taxonomic system that contained

seven major categories. Brewster's system had many similarities with those

developed in the eighteenth century. He kept all four major categories in

Newton's system ("reflection," "refraction," "colors of plates," and "diffraction"),

and upgraded "dispersion" and "double refraction" to major categories. However,

8 See Anno., 'Optics', Encyclopaedia Britannica (Edinburgh: Bell & Macfarquhar, 1771), vol.3,

pp. 417-441; J. Priestley, The History and Present State of Discoveries Relating to Vision, Light, and

Colours (London: Johnson, 1772), pp. xiv-xvi. 9 They are: "sources of light (thermal/mechanical/ chemical)," "velocity of light," "propagation of

light (aberration)," "intensity of light," "reflection and partial reflection," "dispersion," "refraction,"

"double refraction," "vision," and "diffraction (colors in plates)." See T. Young, A Course of Lectures on Natural Philosophy and the Mechanical Arts, (New York: Johnson Reprint Corp., 1971), vol. 2, pp.

97-98.

10 D. Brewster, 'Optics', in Edinburgh Encyclopaedia (Edinburgh: Blackwood, 1830), vol. 15, pp. 589-798.

255

Brewster's system had a couple notable differences from those old ones. First, he

added a new category -- "polarization" -- that never appeared in Newtonian systems.

Polarization was the concept first adopted by Malus in 1808, and soon became the

most exciting research subject in the next two decades. The introduction of

"polarization" was a significant development that reflected the current state of

optics. Second, Brewster further examined the internal structures of these major

optical categories by listing their subcategories. In particular, he provided eleven

subcategories to outline the detailed structure of "polarization." These

subcategories of "polarization" first covered those phenomena caused by the

deviations of rectilinear propagation, such as polarization by double refraction, by

reflection, by refraction, and by crystallized plates. They also covered those

phenomena associated with the emission and absorption of light by matter, such as

polarization related to thermal and mechanical properties of crystallized media.

As we will see in the later sections, the introduction of "polarization" as a major

category and the discussion of its internal structure were very important in the

evolution of optical taxonomy: they provided a basis for the later developments of

Herschel's and Lloyd's taxonomic systems that classified optical phenomena mainly

or even only in terms of the state of polarization.

Just a few years after he adopted this seven-category system, Brewster

introduced another major category -- "absorption." In his 1822 essay,

"absorption" was a subcategory under "polarization." However, Brewster began to

treat "absorption" as a major category in the early 1830s due to his discoveries of

the absorptive spectrum of "nitrous acid gas" (nitrogen dioxide). In a series of

experiments, Brewster found that "nitrous acid gas" could produce hundreds and

even thousands of dark lines and bands in its absorptive spectrum. As a

committed particle theorist, Brewster immediately realized the theoretical

implications of these experimental results. According to Brewster, the particle

theory could easily explain these phenomena in terms of the interactions between

the particles of light and those in the gas, but it was difficult for the wave theory to

give any reasonable account.11

When Brewster published his A Treatise on Optics

in 1831, which was a revision of his 1822 essay, he introduced a new chapter on

absorption, upgrading it from a secondary category under "polarization" to a major

one.12

Next year when he presented his "Report on the Recent Progress of Optics"

to the 1832 meeting of the British Association for the Advancement of Science,

Brewster repeatedly emphasized the importance of absorption, and called for

immediate cooperation within the optical community to explore this "extensive" but

"almost untrodden" field.13

11 D. Brewster, 'Observations on the Absorption of Specific Rays, in Reference to the Undulatory Theory', Philosophical Magazine 2 (1833), 360-363.

12 D. Brewster, A Treatise on Optics (Philadelphia: Carey, Lea, & Blanchard, 1835), pp. 120-125.

13 D. Brewster, 'Report on the Recent progress of Optics', Report of the British Association 2 (1832), 319-322.

256

At the eve of the "optical revolution," Brewster gradually developed a

taxonomic system that contained eight major categories (see Fig.1). Due to

Brewster's prestige, this system was widespread both in the optical community and

among the general scientific audience -- more than four thousands copies of his A

Treatise on Optics were sold within the first year of publication.14

Brewster's

taxonomic system became the most influential one developed from the Newtonian

framework.

For Brewster, this new taxonomic system not only functioned as a frame for

organizing his essay and book, but also provided a ground for comparing the

explanatory powers of the rival optical theories. The result of such a comparison,

however, was not in favor of the wave theory. According to Brewster, the

explanatory powers of the two rivals were almost the same in "reflection" and

"refraction": both could provide reasonable explanations for the phenomena.15

14 See The House of Longman, Archives of the House of Longman, 1794-1914 (Cambridge:

Longman, 1978), D8. 15 Op. Cit., note 10, pp. 651-655, 662-664.

257

"Dispersion," however, was a favorable category for the particle theory, because it

could explain the different refrangibilities of light simply in terms of different sizes

of light particles while the wave theory did not have a satisfactory account.16

In

"diffraction" and "colors of plates," the wave theory was superior to its rival,

because the wave theory could provide beautiful explanations for the phenomena of

diffraction and colors in plates with the help of the interference principle, while the

Newtonian explanations were rather inaccurate.17

"Double refraction" and

"polarization" were other two categories in which both theories had acceptable

explanations, although he thought the wave theory still had problems in accounting

for elliptical polarization and the connection between double refraction and

polarization.18

Lastly, "absorption" was another formidable objection to the wave

theory, because the phenomenon could be intuitively explained in terms of the

interactions between the particles of light and those of the gas, but not by the

vibrations of the ether.19

Therefore, according to Brewster's comparisons under his own taxonomic

system, the explanatory power of the wave theory was not considerably superior to

that of the particle theory. The wave theory had troubles in two major categories

("dispersion" and "absorption"), while its rival also experienced difficulties in other

two major categories ("diffraction" and "colors of plates"). With this result,

Brewster could not see any reason to replace the particle theory with the wave

theory immediately. In general, most of wave theorists agreed that their theory

had formidable difficulties in "dispersion" and "absorption,"20

although some did

not accept Brewster's judgments in "double refraction" and "polarization."21

Thus, if one accepted Brewster's classification, one would have no choice but admit

that the particle theory was in control of two major categories, and that the particle

theory was still valuable and should not be abandoned completely.

2. Herschel's Synthetic Attempt

A new optical taxonomic system that was substantially different from those

developed within the Newtonian framework emerged in 1827. This was a system

designed by John Herschel (1792-1871), one of the most prestigious "gentlemen of

science" in early nineteenth-century Britain. Herschel began his optical research

16 Op. Cit., note 10, p. 681.

17 Op. Cit., note 10, p. 613; Op. Cit., note 12, pp. 96-97. 18 Op. Cit., note 10, pp. 747-748; Op. Cit., note 13, pp. 308-322.

19 Op. Cit., note 13, pp. 321-22.

20 Most wave theorists recognized these problems, and their tactics in the early 1830s was either only to argue for the possibilities of wave accounts for dispersion and absorption in the future, or simply

to deny them as legitimate topics of physical optics. See J. Herschel, 'On the Absorption of Light by

Coloured Medium, Viewed in Connexion with the Undulatory Theory', Philosophical Magazine 3 (1833), 401-412, and G. Airy, 'Remarks

on Sir Brewster's Paper "On the Absorption of Specific Rays, &c"', Philosophical magazine 2 (1833),

419-424. 21 For example, Herschel believed that the wave theory was slightly better than its rival in

explaining these two categories, because the particle explanations required too many ad hoc hypotheses.

See J. Herschel, 'Light', in P. Barlow (ed), The Encyclopaedia of Mechanical Philosophy (London: Griffin, 1854), p. 529.

258

as early as 1808, when he was only 16 years old. Under the dominance of the

particle theory, it was not a surprise that Herschel's early optical research was done

within the Newtonian framework. However, Herschel was not a dogmatic

follower of this tradition, and he kept his eyes open to every development in the

field. The explanatory successes of Fresnel's wave theory in the early 1820s made

a deep impression on Herschel, and around 1824, he decided to write an essay

systematically to review the two theories of light.

On December 12, 1827, Herschel finished his essay, which filled 245 quarto

pages, and titled it "Light." Although the essay was not published until 1845 in

the Encyclopaedia Metropolitana,22

it was privately circulated in the optical

community immediately after it was completed. From the spring of 1828,

Herschel sent copies of his essay to a number of people, including William

Whewell, Thomas Young, David Brewster, George Airy, William Hamilton, and

William Fox Talbot.

At the beginning of his essay, Herschel clearly stated his purpose, which was to

"give an account of the properties of light; of the physico-mathematical laws which

regulate the direction, intensity, state of polarization, colours, and interference of its

rays."23

To achieve this goal, Herschel divided his essay into four parts. Part I

was on the propagation and intensity of unpolarized light, including the phenomena

and empirical laws of reflection, refraction, aberration, photometry, and vision.

Part II was about the colors of unpolarized light, or chromatics as he called it,

covering dispersion and absorption by uncrystallized media. Part III was on the

interference of unpolarized light. According to Herschel, interference was a

phenomenon that could "hardly be understood, or even described, without a

reference to some theoretical views."24

He thereby in this part first reviewed the

basic doctrines of both the particle and the wave theory, then examined their

explanations of diffraction and colors of plates. The last part was the longest,

which counted 89 pages, and indeed the most important one in the whole essay. It

was on polarization. In its 15 sections, Herschel surveyed all phenomena related

to polarization, most of which were discovered recently. These phenomena

included those generated by the deviations of rectilinear propagation, such as

polarization by double refraction, reflection, refraction, interference, and in

crystallized plates. But similar to Brewster, Herschel also discussed those

phenomena caused by the emission and absorption of light by matter, such as

absorption by crystallized media, polarization related to thermal, mechanical, and

chemical properties of crystallized media. The structure of Herschel's essay thus

reflected a new taxonomic system with only four major categories:

"direction/intensity of unpolarized light," "colors of unpolarized light,"

"interference of unpolarized light," and "polarization" (see Fig.2).

22 This essay was later reprinted in P. Barlow (ed), The Encyclopaedia of Mechanical Philosophy (London: Griffin, 1854),

pp. 341-586. In this article all references to Herschel's "Light" are taken from this reprint.

23 Ibid., p. 341. 24 Ibid., p. 439.

259

Herschel's new system was essentially different from those developed from the

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

its effort in searching for a synthesis of optical categories. In this system,

Herschel grouped "reflection," "refraction," "photometry," and "aberration"

together under one major category, because they all manifested the direction and

intensity of light. Following the same principle, he merged "dispersion" with

"absorption" because they all illustrated the colors of light, he unified "diffraction"

with "colors of plates" because they were the products of interference, and he

treated "double refraction" as a subcategory under "polarization" because it also

reflected the state of polarization. By identifying the underneath connections

among optical phenomena, Herschel reduced the number of major categories into

four. This synthetic attempt was essentially different from the practices of

categorization within the traditional framework, which tended to increase the

number of major optical categories by simply listing every discovered phenomenon

accumulatively.

260

Another distinctive feature of Herschel's system was its emphasis on

polarization. By examining every subcategory under "polarization," Herschel

illustrated similarities between polarized and unpolarized light. On the one hand,

unpolarized light possessed such properties as direction, intensity, color, and

interference; on the other hand, polarized light had all the corresponding properties,

although they displayed themselves in different ways. Herschel's discovery of the

similarities between polarized and unpolarized light was another important step in

the evolution of optical taxonomy. With these similarities, Herschel implicitly

suggested that the state of polarization might be a more fundamental property of

light than the others such as direction, intensity, color, and interference. This idea

later became the foundation for Lloyd's dichotomous system that classified optical

phenomena only in terms of the state of polarization.

In addition to the tacit arguments embedded in the structure of his essay,

Herschel also gave two explicit reasons to justify the importance of polarization.

His first reason was practical. Between the 1810s and the 1820s, merely two

decades after polarization was discovered, a large number of novel optical

properties related to polarization was found. But "[t]he intricacy as well as variety

of its phenomena, and the unexampled rapidity with which discoveries have

succeeded each other in it, have hitherto prevented the possibility of embodying it

satisfactorily in a systematic form."25

An emphasis on polarization reflected an

urgent need to search for a systematic understanding of a variety of phenomena

related to polarization.

Herschel's second reason to highlight polarization was methodological. In his

early study of polarization in biaxial crystals, Herschel had found that polarizing

angles on the surfaces of crystallized media were better than refracting angles for

investigating the constitutions and structures of crystals.26

With polarized light,

Herschel believed, scientists could access to the minute mechanism of the material

world, studying such features as the inclination of the optic axes in crystals and the

intrinsic refractive power of molecules.27

Thus, Herschel claimed that "polarized

light is, in the hands of the natural philosopher, not merely a medium of vision; it is

an instrument by which he may be almost said to feel the ultimate molecules of

natural bodies, to detect the existences and investigate the nature of powers and

properties ascertainable only by this test, and connected with the most important

and intrinsic inquiries in the study of nature."28

Herschel's new taxonomic system also became a basis for comparing the

explanatory powers of the rival optical theories. The result of theory appraisal

under Herschel's system, however, was not in favor of the particle theory. On the

one hand, Herschel acknowledged most of the particle theory's explanatory

successes claimed by its supporters. He admitted that "[t]his [particle] hypothesis,

25 Ibid., p. 503.

26 J. Herschel, 'On the Action of Crystallized Bodies on Homogenous Light', Philosophical Transactions 110 (1820), 45-100.

27 Op. Cit., note 21, pp. 568-579. 28 Ibid., p. 341.

261

which was discussed and reasoned by Newton in a manner worthy of himself,

affords, by the application of the same dynamical laws which he had applied with

so much success to the explanation of the planetary motions, not merely a plausible,

but a perfectly reasonable and fair explanation of all the usual phenomena of light

known in his time."29

Here, "the usual phenomena" referred to those topics

associated with reflection, refraction, dispersion, and absorption, all of which were

under the first two categories in his system, i.e., "direction/ intensity of unpolarized

light" and "colors of unpolarized light." On the other hand, the particle theory was

particularly weak under the categories of "interference" and "polarization." The

particle theory simply could not explain why the distance of a light source could

affect the diffractive fringes, a very important effect associated with diffraction.30

The particle theory also failed to provide coherent explanations of polarization:

although Brewster was able to explain a few polarization effects by introducing ad

hoc hypotheses, Herschel noted that these accounts were obtained "with a great

sacrifice of clearness of conception."31

On the contrary, the wave theory exhibited an excellent explanatory power in

most of the major optical categories, according to Herschel. It did not have any

problem in explaining reflection and refraction, and could give excellent accounts

for all details of interference and diffractive fringes. It was particularly powerful

in the field of polarization. Throughout the last part of his essay, Herschel

provided most described polarization effects with wave accounts, which, he

claimed, were the best, in the sense that they had "the least violence and obscurity

to the facts."32

However, Herschel noted that the wave theory experienced

difficulties in explaining dispersion and absorption. The problems related to

dispersion was particularly desperate, because the wave theory predicted that rays

of all colors refracted equally and that no dispersion could happen. Herschel thus

admitted that "[n]ow here arises, in limine, a great difficulty; and it must not be

dissembled, that it is impossible to look on it in any other light than as a most

formidable objection to the undulatory doctrine."33

Although the wave theory could not explain every major category, Herschel

insisted that it did exhibit a superior explanatory power to its rival under his

taxonomic system. The superiority of the wave theory consisted not only in its

ability to explain one more major category than its rival did, but also in its

successes in the most important optical category -- "polarization." Thus, Herschel

concluded that "[w]e shall adopt . . . the undulatory system, not as being at all

satisfied of its reality as a physical fact, but regarding it as by far the simplest

means yet devised of grouping together, and representing not only all the

phenomena explicable by Newton's doctrine, but a vast variety of other classes of

facts to which that doctrine can hardly be applied without great violence, and much

29 Ibid., pp. 250-251, original emphasis. 30 Ibid., p. 481.

31 Ibid., p. 529.

32 Ibid.. 33 Ibid., pp. 449-50.

262

additional hypothesis of a very gratuitous kind."34

This statement indicated that, when Herschel evaluated the two rival theories of

light under his taxonomic system, he did develop a preference for the wave theory,

but he was reluctant to embrace it completely. The failure of the wave theory in

one major category still troubled Herschel, and made him believe that the wave

theory did not represent the "physical fact." At the same time, the explanatory

successes of the particle theory in dispersion and absorption, although they were

just qualitative, led Herschel to hold that the particle theory was still valuable. In

a rather long period after he established his preference for the wave theory,

Herschel did not believe that the particle theory should be totally abandoned.

Instead, he suggested that the particle theory should be improved: "[I]t is by no

means impossible that the Newtonian theory of light, if cultivated with equal

diligence with the Huyghenian, might lead to an equally plausible explanation of

phenomena now regarded as beyond its reach."35

Herschel even devoted himself

to a project of constructing a new particle theory of light. Around 1832, he

postulated a new particle theory with a revision of Biot's notion of mobile

polarization, and claimed that it could explain many optical phenomena that

troubled the Newtonian version.36

Thus, under his own taxonomic system,

Herschel did not regard the replacement of the particle theory by the wave theory as

necessary, nor did he recognize the urgency of an "optical revolution."

3. Lloyd's Revolutionary Design

The taxonomic system that revealed the necessity of an "optical revolution" was

introduced in 1834 by Humphrey Lloyd (1800-1881), a professor of natural and

experimental science at Trinity College, Dublin. Lloyd developed a strong interest

in optics in the late 1820s, and became a committed wave theorist after he

performed the experiments of conical refraction between 1832 and 1833.

The phenomena of conical refraction were first discussed by William Hamilton

in 1832. With sophisticated mathematical analysis, Hamilton predicted two

hitherto unobserved features of double refraction in biaxial crystals (called conical

refraction) that had been overlooked by Fresnel. To confirm these predictions,

Hamilton asked helps from Lloyd. With delicate experimental skills, Lloyd was

able to verify Hamilton's novel predictions within a couple months.37

These

successes caused a great excitement in Lloyd, who now believed that the

verifications of Hamilton's predictions had proved the truth of the wave theory,

because Hamilton's predictions were built upon the wave doctrines. He claimed

that "[h]ere then are two singular and unexpected consequences of the undulatory

34 Ibid., p. 475, original emphasis.

35 J. Herschel, Preliminary Discourse on the Study of Natural Philosophy (London: Longman,

1830), p. 262. 36 See Herschel to Potter (April 20, 1832), Texas University, Herschel Collection, UT. L0315.

37 For details of Hamilton's theoretical analysis and Lloyd's experimental operations, see J. O'Hara,

'The Prediction and Discovery of Conical Refraction by William Rowan Hamilton and Humphrey Lloyd (1832-1833)', Proceedings of the Royal Irish Academy 82a (1982), 231-257.

263

theory, not only unsupported by any phenomena hitherto noticed, but even opposed

to all the analogies derived from experience. If confirmed by experiment, they

would furnish a new and almost convincing proof of the truth of that theory . . . "38

However, most wave theorists, including Hamilton himself, did not regard the

discovery of conical refraction as a conclusive triumph of the wave theory.39

The

confirmation of conical refraction did not, as Lloyd wished, become a crucial

evidence for the wave theory, but it did play a critical role in the particle-wave

debate in another way.

The major institutional forum in the particle-wave debate was the British

Association for the Advancement of Science found in 1831. Its annual meetings

and publications provided a platform for the debate. More importantly, its official

reports on the recent conditions and progress of different scientific subjects became

a powerful means to spread a writer's personal views, with the impressions of

endorsements by the Association.

Brewster presented the first report on optics at the 1832 British Association

meeting, in which he listed all the difficulties of the wave theory and concluded that

it was far from an acceptable theory of light.40

Without surprise, Brewster's report

caused strong discontent among wave theorists, many of whom, like William

Whewell and George Airy, were already elected to the committee preparing the

next Association meeting. These wave theorists did not agree with Brewster's

conclusion on the status of their theory, nor could they tolerate the spread of the

confusion created by Brewster's report, but they did not openly criticize him.

Instead, they simply requested another report on optics at a future meeting "on the

phenomena considered as opposed to the undulatory theory."41

This was a very

vague description, which could be interpreted in either way. However, those who

made this request knew that they could ensure the new report be written in the way

they wanted by selecting an appropriate reporter. The selection of the reporter

was made at the 1833 British Association meeting. A perfect candidate would be

one who was not only a committed advocate of the wave theory but also a qualified

practitioner of optics, both in theoretical analysis and in experimental operation.

Perhaps not by coincidence, Lloyd emerged at this meeting as the candidate

who perfectly fitted all these criteria. Lloyd gave a brilliant performance at this

meeting by presenting his experimental confirmation of conical refraction. His

presentation demonstrated both his theoretical accomplishments in understanding

Hamilton's extremely abstract theory and his experimental skills in designing and

conducting delicate experiments. More importantly, it showed his commitment to

the wave theory. Consequently, Lloyd was selected as the reporter, and was

38 H. Lloyd, 'On the Phenomena Presented by Light in Its Passage along the Axes of Biaxial

Crystals', Philosophical Magazine 2 (1833), 112-120. 39 In a letter to Herschel, Hamilton denied that the verification of conical refraction could be used

to test the two rival theories of light, because, he wrote, "the fundamental principle of my optical

methods does not essentially require the adoption of either of the two great theories of light in preference to other." See Hamilton to Herschel, (December 18, 1832), in R. Grave, The Life of Sir William Rowan

Hamilton (Dublin: Hodges & Figgis, 1882), vol.1, p. 627.

40 Op. Cit., note 13, pp. 308-322. 41 See Report of the British Association 2 (1832), 116.

264

requested to draw up for the next British Association meeting a report on the recent

progress of physical optics.

Lloyd's "Report on the progress and present state of physical optics" appeared in

the 1834 issue of the Association report.42

With a length of 118 pages, Lloyd

attempted to show the superiority of the wave theory by making a systematic

comparison of the two rivals' explanatory powers. His judgments of the two

rivals' explanatory abilities in individual cases were virtually the same as Herschel's.

But by carefully designing the structure of his report, Lloyd was able to make a

persuasive argument for the necessity of immediately abandoning the particle

theory and adopting the wave theory.

At the beginning of his report, Lloyd stated that, to prove the superiority of the

wave theory, "I have found it necessary to deviate from the arrangement which a

strictly theoretical view of the subject would naturally suggest."43

This

"arrangement" from which Lloyd wanted to deviate was the tradition in optical

categorization that classified optical phenomena in terms of the properties of light.

According to this tradition, every principal property of light, such as direction,

intensity, color, interference, and the state of polarization, had a corresponding

major category, sharing the same importance as others. Lloyd was discontent with

this classification tradition, because he did not believe that it was the way people

did in their practices. The reality was that polarization had become the research

frontier in the field, and a single property -- the state of polarization -- had drawn

the attention of most researchers. A taxonomic system should reflect this common

practice shared by the community, according Lloyd. Hence, he claimed that,

"[t]he relation of theory to phenomena, which I propose to consider, obliges me to

examine the latter in the groups in which they have been usually brought together,

and under which their laws have been investigated. I propose, therefore, to divide

the following Report into two parts, of which the first will treat of unpolarized, and

the second of polarized light."44

Lloyd further divided the part on unpolarized light into four sections. The first

section was tilted "the propagation of light and the principle of interference,"

covering the rectilinear propagation of light, the velocity of light, aberration, and

interference. Section two was called "the reflection and refraction of light," which

included not only reflection and refraction, but, surprisingly, dispersion, absorption,

solar phosphorus, and solar spectrum. The last two sections in this part were

about diffraction and colors of plates, discussing the regular contents usually under

these two categories. Lloyd also divided the part on polarized light into four

sections. The first one had a title "the polarization of light," mainly on the

principle of transverse vibrations. Section two was called "the reflection and

refraction of polarized light," covering polarization by reflection, refraction, total

reflection, and Newton's rings. Section three was "double refraction," discussing

42 This report was later reprinted in H. Lloyd, Miscellaneous Papers Connected with Physical Science (London: Longman, 1877), pp. 19-148. In this article all references to Lloyd's "Report" are

taken from this reprint.

43 Ibid., p. 21. 44 Ibid., p. 21, original emphasis.

265

both double refraction and absorption by crystallized media. The last section was

"the colors of crystallized plates," reviewing interference of polarized light, circular

polarization, and depolarization.

The structure of Lloyd's report reflected an entirely new taxonomic system with

a distinctive dichotomous structure (see Fig.3). In this system, all optical

phenomena were first classified solely in terms of their states of polarization.

"Polarized light" and "unpolarized light" were the only two major categories, and

other categories treated as major in those old systems, such as "reflection,"

"refraction," "dispersion," and "diffraction," now became subcategories, or even

sub-subcategories. In some degree, this dichotomous system reflected Lloyd's

effort to continue a trend that existed in both Brewster's and Herschel's

classifications: recognizing and emphasizing the importance of polarization. But

by making the state of polarization the only principal classification standard and

designing a dichotomous system that contained only "polarized light" and

"unpolarized light" as the major categories, Lloyd emphasized the value of

polarization to an extreme.

266

In addition to the dichotomous structure, Lloyd's taxonomic system had two

other distinctive features. First, Lloyd organized the subcategories under

"unpolarized light" in a very peculiar way. On the one hand he used three

subcategories ("propagation and interference," "diffraction," and "colors in plates")

to cover the phenomena related to interference. On the other hand, he combined

"reflection," "refraction," "dispersion," "absorption," "solar phosphorus," and "solar

spectrum" into a single category: "reflection and refraction of unpolarized light."

In this way, "dispersion" and "absorption," which were major categories in

Brewster's system, or second-level categories in Herschel's system, became

third-level categories. Second, Lloyd deleted all categories related to thermal,

mechanical, and chemical effects of crystallized media, although they had appeared

in both Brewster's and Herschel's systems. The reasons were, according to Lloyd,

that these subjects were "as yet little understood," and that they were "remotely

connected with the leading object of the present Report," that is, to prove the truth

of the wave theory.45

With this new taxonomic system, Lloyd was able to make a stronger and more

persuasive argument for the wave theory than did Herschel in his "Light." Lloyd

believed that the explanatory power of a theory was one of the most important

conditions for its truth: if a theory could explain various "leading classes of optical

phenomena," and its explanations could be "numerically compared with established

facts," then the truth of the theory should be "fully and finally ascertained."46

Lloyd insisted that this was exactly the achievement of the wave theory. Under

his taxonomic system, the wave theory now was able to have a total control of one

of the two major optical categories -- "polarized light," in which the particle theory

experienced tremendous difficulties.47

In the other major category -- "unpolarized

light," the wave theory had demonstrated its superiority in such secondary

categories as "propagation of light and interference," "diffraction," and "colors of

thin plates" for a long time by giving not only numerical explanations but also

striking predictions, while the particle theory had no currency at all without the

interference principle.48

By listing the wave theory's explanatory successes in both major and secondary

categories, Lloyd showed its superiority over the particle theory. But Lloyd

wanted more: he wanted to demonstrate that the wave theory was "as advanced as

that to which the theory of universal gravitation was pushed by the single-handed

45 Ibid., p. 22, 21.

46 Ibid., p. 19. 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. For more discussion of Lloyd's view

on the role of conceptual coherence in theory appraisal, see X. Chen, 'Young and Lloyd on the Particle

Theory of Light: A Response to Achienstein', Studies in History and Philosophy of Science 21 (1990), 665-676.

47 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 be compared with experiments numerically; all particle accounts of double refraction

failed to cover the related polarization effects; and Biot's theory of colors of crystallized plates was

inconsistent with experiments. See Op. Cit., note 42, pp. 92-132. 48 Ibid., pp. 25-27, 58-65, 73-74.

267

efforts of Newton."49

To achieve this goal, he needed to discuss the difficulties of

the wave theory. Lloyd admitted that dispersion was "the most formidable

obstacle" to the reception of the wave theory, and wave theorists were "still far

from a precise theory of absorption."50

But under his new dichotomous system,

the troublesome cases of dispersion and absorption now became third-level

categories, under "reflection and refraction of unpolarized light." Thus, the tacit

argument implied by this taxonomic system was that dispersion and absorption

were no longer the "leading classes of optical phenomena." Even though the wave

theory might still have difficulties in dealing with these phenomena, these failures

now became trivial in comparison to the theory's successes in those important

optical categories.

With the help of a revolutionary taxonomic system, Lloyd could emphasize the

merits of the wave theory to a maximum through both making "polarized light" one

of the two major categories and using three subcategories to cover the phenomena

related to interference. He was also able to reduce the defects of the wave theory

to a minimum by treating "dispersion" and "absorption" as third-level categories.

Under his system, Lloyd also diminished the advantages of the particle theory in

explaining dispersion, absorption, and optico-chemical effects, by either degrading

the values of these phenomena or simply dropping them out of the game. Based

upon such a comparison, Lloyd strongly objected to Herschel's view that the

particle theory might be revivable if it had been cultivated with the same zeal and

talent as its rival, calling Herschel's position "untenable."51

According to Lloyd,

the particle theory should be totally abandoned, and the wave theory should be

adopted and advocated immediately. A revolution in optics, this is, replacing the

particle theory by the wave theory, became necessary and urgent under Lloyd's

dichotomous system.

Lloyd's report was applauded by most wave theorists. Powell called it "the

completely and masterly report", Forbes labeled it "an able and impartial review of

the progress of science", and, according to Hamilton, its only fault was "its too

great modesty." They complimented Lloyd partly on his verdict for the wave

theory, and partly on the taxonomy embedded in his report. In fact, the

dichotomous structure of Lloyd's taxonomic system reflected a consensus among

many wave theorists on classification. In addition to Lloyd, some other wave

theorists also adopted a similar dichotomous system. For example, Airy in his

Mathematical Tracts also divided optical phenomena into two major classes: those

related to polarization and those not.52

Thus, because of Lloyd's report and other

wave theorists' supports, a dichotomous taxonomic system became dominant within

the wave camp. Many textbooks written by wave theorists in this period adopted

this dichotomous structure. Among them, Airy's Tracts, with three editions in

49 Ibid., pp. 19-20.

50 Ibid., p. 41, 46. 51 Ibid., p. 20.

52 G. Airy, Mathematical Tracts on the Lunar and Planetary Theories, the Figure of the Earth,

Precession and Nutation, the Calculus of Variations, and the Undulatory Theory of Optics (Cambridge: Deighton, 1831), pp. 249-409.

268

three decades,53

was the most influential one, because it was the official text for the

Cambridge's Mathematical Tripos. Lloyd himself also published two textbooks in

this period, both of which used the dichotomous structure to organize materials.54

With a delicate taxonomic system and convincing arguments, Lloyd's report

held a very important status in the particle-wave debate. His report convinced

those supporters of the wave theory who controlled the British Association that the

damages caused by Brewster had been remedied and the particle-wave controversy

had been settled. After Lloyd's report, the British Association did not request any

further report on optics in the next two decades. The two other reports about

optics in the nineteenth century were presented by George Stokes on double

refraction in 1862 and by Glazebrook on optical theories in 1885, in which the

particle-wave controversy was no more an issue. Therefore, many historians agree

that Lloyd's report represented a turning point in the "optical revolution." The

publication of Lloyd's report indicated that the wave theory had become the

orthodox in the British Association and the particle tradition fell into a defensive

position.55

4. Conclusion

The above analysis of the taxonomic evolution during the early nineteenth

century shows the dominant role of taxonomy in theory evaluation and scientific

change. The explanatory superiority of the wave theory and the necessity of a

revolutionary change in optics became evident and compelling only after the

significant taxonomic shifts. Under a traditional taxonomic system, Brewster did

not regard the wave theory as significantly superior in explanatory power. Neither

did Herschel recognize the need of immediately replacing the particle theory with

the wave theory under his new system, although he developed a preference for the

latter. Only with a dichotomous system did Lloyd fully understood the necessity

of a revolutionary change in optics -- accepting a new optical theory at the price of

abandoning the old one.

The vital role of taxonomic changes roots in the fact that a taxonomic system

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

community. By providing a list of categories and revealing the

similarity/difference relationships among them, a taxonomic system defines how a

given category pertains to a given kind of object or situation and how it is related to

other categories. Taxonomic shifts then result in fundamental changes in the way

through which people learn and apply taxonomic terms: some categories do not

53 The second edition of Airy's Tracts, 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. 54 H. Lloyd, Lectures on the Wave-Theory of Light, (Dublin: Andrew Milliken, 1841); Elementary

Treatise on the Wave-Theory of Light, (London: Longman, 1857). It is interesting to note that such a

dichotomous structure gradually disappeared in textbooks around the mid century, probably because while the particle-wave debate was dying down, there was no need to advocate such a dichotomous

structure that was inconvenient for instructional purposes.

55 For example, see J. Morrell and A. Thackray, Gentlemen of Science (Oxford: Clarendon, 1981), p. 469.

269

refer to the same kind of object or situation and bear different relations with the

others in a new taxonomic system. For example, "dispersion" in Brewster's

taxonomic system referred to the phenomenon caused by changes of a principal

optical property -- refrangibility, and thus was treated as one of the major categories,

sharing the same status as "reflection" and "refraction." In Lloyd's system,

however, the same category referred to the deviations of rectilinear transmission,

and was put under "reflection and refraction." Thus, whether a theory can explain

a particular phenomenon, or whether it can be justified by certain kind of empirical

evidence, depends on the underlying taxonomy, which classifies the research

domain in a certain way. In this way, taxonomy preconditions the results of

theory evaluation, although a taxonomic system is in turn built upon certain

theoretical framework.

If the taxonomic changes were the preconditions of the theory choice in the

revolutionary change of optics, then what were the causes of these taxonomic

changes? At the first glance, it looks like that these taxonomic changes were

caused by some social or irrational motives: Brewster stuck with the old taxonomic

system because he could downgrade the merits of the wave theory, Lloyd

introduced a dichotomous system because he could make the wave theory look

good, and all these tactics were closely tied up to the politics at the British

Association. This social or political interpretation, however, has a vital problem.

If Brewster's persistence of a traditional taxonomic system only reflected his hostile

attitude toward the wave theory and if Lloyd's choice of a dichotomous system was

merely a rhetorical trick, then we should expect heated debates between the rivals

on the legitimacy of their classifications, but that never happened. The silence of

particle theorists indicated that they might have agreed with the main idea

embedded in Lloyd's system. Comparing the three major taxonomic systems

during the revolution, we can see that the emphasis of polarization was a common

theme, which appeared first in Brewster's classification, then further elaborated in

Herschel's one, and finally reached its climax in Lloyd's dichotomous system.

This common theme reflected a consensus shared by both particle and wave

theorists during this period that polarization was the most promising research topic.

The common practice of the optical community may have been the foundation of

these taxonomic changes.

But why did not Brewster, who had recognized the importance of polarization

much earlier than Lloyd did, develop a dichotomous system? Or, in general, what

was the ground for taxonomy choices during the "optical revolution?" To answer

these questions, we need to examine how Brewster acquired the category

"polarization" at the eve of the "optical revolution." Brewster began his research

of polarization in 1813 by conducting a series of experiments about polarization by

refraction and by reflection. In these experiments, Brewster found that, although a

beam of light could only be partially polarized by a single refraction, it could be

completely polarized by successive refractions. He also discovered that a beam of

light could only be completely polarized by a single reflection at a particular

incident angle, and, beside this angle, it had to go through a number of successive

270

reflections in order to be polarized completely.56

From these successive reflection

and successive refraction experiments, Brewster reasoned that the asymmetry of a

given light beam must have two different states: either completely or partially

polarized. In other words, the state of polarization was a matter of degree:

different degrees of partial polarization fell in a spectrum with polarization and

non-polarization as two extremes. Consequently, polarization must be a property

of a collection of rays, because a single ray, which possessed an inherent

asymmetry and was always asymmetric, could not generate partly polarized and

unpolarized light. Since polarization was the property of a collection of rays, it

depended upon the attributes of single rays. According to this understanding,

"polarization" could not be more important than those categories that revealed the

attributes of a single ray, such as "reflection" and "refraction." Brewster's reason

to list "polarization" as one of the major categories might have merely been

pragmatic: it was the most productive research frontier in the early nineteenth

century. Thus, limited by his experiments, Brewster could never comprehend a

dichotomous system that used the state of polarization as the only classification

standard.

The new understanding of polarization underneath Lloyd's revolutionary

taxonomic system required new experiments, which were designed and conducted

by Fresnel in the late 1810s. Instead of using successive reflections and

refractions, Fresnel produced polarization by total reflections. With a new

instrument called a "Fresnel rhomb," which could generate a 90-degree phase

difference between two perpendicular periodic motions of a luminous ray by two

internal total reflections, Fresnel found that the state of polarization fell into two

groups. The first group was polarized light, which obtained a fixed phase

difference when passing through a rhomb and produces interference fringes when

passing through an analyzer. The other was unpolarized light, which had random

phase differences and did not cause interference fringes.57

With new experimental

instruments and skills, Fresnel revealed that the state of polarization was absolute:

light was either polarized or unpolarized, and nothing between. The so-called

partially polarized light would disappear if it went through a rhomb and an analyzer,

becoming either polarized or unpolarized light. The absolute state of polarization

implied that it must be the property of a single luminous ray. Light was always

completely asymmetric or "polarized," that is, light consisted of transverse waves.

Unpolarized light was only a special distribution of asymmetries over time, in

which the two perpendicular periodic motions did not interfere with each other due

to a lack of a fixed phase difference. The state of polarization now reflected the

nature of light -- transverse waves, and determined other properties such as the

direction and magnitude of a luminous ray. With this new comprehension of

56 D. Brewster, 'On the Polarization of Light by Oblique Transmission through All Bodies,

Whether Crystallized or Uncrystallized', Philosophical Transactions 104 (1814), 219-230; and 'On the Laws Which Regulate the Polarization of Light by Reflexion from Transparent Bodies', Philosophical

Transactions 105 (1815), 125-159.

57 See J. Buchwald, The Rise of the Wave Theory of Light (Chicago: The University of Chicago Press, 1989), pp. 226-231.

271

"polarization," it was reasonable to use the state of polarization as the primary

standard for classification, and to treat other optical properties as secondary.

Thus, the selections of taxonomic systems by historical actors were not arbitrary.

Brewster resisted the wave theory not because he was unscientific or irrational, but

because his experimental instruments and skills prevented him from seeing

polarization as the most important optical property. Similarly, Lloyd's

dichotomous system was not the product of a rhetorical tactics, but a reflection of

the improvement of experimental instruments and skills. The taxonomic shifts

during the revolutionary change of optics reflected developments at a deeper level:

the level of experimental instrument and skill.

In short, the particle-wave debate in early nineteenth- century Britain was not

simply about explanatory power. The wave theory's superiority in explanation

would have not been appreciated without a revolutionary shift in taxonomy. The

particle-wave debate was also about classification. This classification was in turn

related to experimentation: the experimental instruments, techniques and skills

historical actors developed in their practices could restrict the ways they

categorized and classified the research domain. Therefore, this historical episode

vividly shows that the result of a scientific debate does not always coincide with the

judgments of the explanatory power of corresponding scientific theories, and that

two other aspects of scientific practices, classification and experimentation, are

critical for understanding theory evaluation and scientific change.

Acknowledgements – I would like to thank Peter Barker and Jed Buchwald for their

helpful comments on earlier drafts of this article. I also thank the anonymous

reviewers who helped me strengthen the arguments and avoid a number of

mistakes.