View
7
Download
0
Category
Preview:
Citation preview
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.
Recommended