John Herschel's optical researches and the development of his ideas on method and causality

GREGORY

GOOD”

JOHN HERSCHEL’S OPTICAL RESEARCHES AND THE DEVELOPMENT OF HIS IDEAS ON METHOD AND CAUSALITY I. Introduction:

Science and Method

THE MOST apparent fact about the optical research and methodological musings of Sir John Herschel (1792 - 1871) is their separation in time. Most of his investigations in optical properties of crystals were undertaken in 18 19 and 1820, when Herschel was in his late 20s. His magnum opus on method, The Preliminary Discourse on the Study of Natural Philosophy, was published in 1830, a full decade later.’ This seems to support the view that scientists reflect on their science long after the research is completed. That is, philosophy follows science. This is not strictly true for Herschel. It can be unequivocally established by an appeal to a broader range of his publications and manuscripts that Herschel’s curiosity about nature and about the nature of scientific investigations both appeared early. They developed side by side. Herschel developed his methodological guidelines while he practiced his science, and repeatedly applied them in carrying out his research. There are two sources for understanding a scientist’s methods: the scientific writings and the reflective ones. The scientist learns methodology likewise from two sources: from the practice of science and from the methodological doctrines in sources as diverse as Isaac Newton’s Principia and Thomas Reid’s An Inquiry into the Human Mind.2 This article heeds both sorts of sources.

*History of Science and Technology, West Virginia University, Morgantown, WV 26506, U.S.A. This article derives from my doctoral dissertation, written for the University of Toronto. A version was presented at the History of Science Society meeting in October 1983. I wish to thank T. H. Levere,. J. 2. Buchwald and Robert McRae (all at Toronto), Charles Jones (Ball State University). Robert Butts (Universitv of Western Ontario) and Paul Theerman (Smithsonian Institution) for useful comments and criticism. The illustrations are the work of Mark Kemp. Lastly, the librarians at these institutions greatly facilitated my research: Royal Society of London, University of Texas (Austin), Harvard University, St. John’s College (Cambridge). I appreciate the privilege of quoting documents in these collections. Received 1 March 1984; in revised form 15 October 1985. ‘Herschel, Preliminary Discourse on the Study of Natural Philosophy (London: Longman, Orme, Brown, Green, Longmans & Taylor, 1830), hereafter referred to as the Discourse. This work was “preliminary” to the Cabinet Cyclopaedia, edited by Dionysius Lardner. 21saac Newton, Mathematical Principles of Natural Philosophy translated into English by Andrew Motte in 1729, 2 vols (Berkeley: University of California Press, 1973); Thomas Reid, An Inquiry into the Human Mind (Glasgow: William Falconer, 1817). Stud. Hist. Phil. Sri., Vol. 18, No. 1, pp. l-41, Printed in Great Britain.

1987.

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John Herschel’s Discourse has been treated in isolation,3 with little effort to place it in the context of either the scientific or the methodological literature of the time. His debt to Newton, admittedly significant, has been emphasized at the expense of other potential sources on which he could have drawn.4 Herschel has, moreover, been seen through the important but partial perspective of his public debate with William Whewell, a notorious episode that has portrayed Herschel as an empiricist. This has restricted attention to the works in which this debate took place.5 Some recent works have pointed the way toward supplementing these perspectives. Richard Olson and Chaman La1 Jain, in particular, have interpreted Herschel’s methodology in light of the Scottish Common Sense school of philosophy that flourished in the late-eighteenth and earlynineteenth centuries.6 While Herschel certainly studied John Locke as a student at Cambridge (everyone did), he afterward concentrated on Thomas Reid, Dugald Stewart and Thomas Brown. By no means did he always agree with these writers, but he was familiar with the issues they debated. Olson has drawn our attention to the similarities between Herschel’s views on mathematics, causes and the roles of hypotheses, and those of Reid and Brown.’ Jain has carried the investigation further in a most thorough analysis of Herschel’s entire philosophy of science and has weighed his debts to Bacon, Newton, Hume, Reid and Kant.’ As important as Olson and Jain’s works are, they share two limitations. Like the other works mentioned above, these are based almost entirely on the Discourse and the 1841 review of Whewell. They do not examine the pre-1830 methodological writing of Herschel, nor do they look at Herschel’s scientific writings and manuscripts to see if he used any of the methodology he ‘Curt J. Ducasse, ‘John F. W. Herschel’s methods of experimental inquiry’ in: Ralph M. Blake, Curt J. Ducasse and Edward H. Madden (eds), Theories of Scientific Method: The Renaissunce through the Nineteenth Century (Seattle: University of Washington Press, 1966), pp. 153 - 182; Michael Partridge, ‘Introduction’ in: J. Herschel, Preliminary Discourse on the Study of Nuturul Philosophy (New York and London: Johnson Reprint Corporation, 1966). 4For example both David B. Wilson, ‘Herschel and Whewell’s version of Newtonianism’, Journal for the History of Ideas 35 (1974),79 - 97, and Vincent Carl Kavaloski, ‘The veru cuusu principle: a historic0 - philosophical study of a metatheoretical concept from Newton through Darwin’ (Ph.D. Thesis, University of Chicago, 1974), miss the Scottish philosophers almost altogether. ‘The discussions of Herschel in both articles in the preceding note are based on this debate. On Herschel’s side, the relevant works are the Discourse and ‘Whewell on the Inductive Sciences’, Quarterly Review 68 (1841), 177 - 238. 6Richard Olson, Scottish Philosophy and British Physics, 1750- 1880: A Study in the Foundations of the Victorian Scientific Style (Princeton: Princeton University Press, 1975); Chaman La1 Jam, ‘Methodology and epistemology: an examination of Sir John Frederick William Herschel’s philosophy of science with reference to his theory of knowledge’ (Ph.D. Thesis, Indiana University, 1975). ‘Olson, ‘Sir John Herschel’s Preliminary Discourse on the Study of Natural Philosophy and the Common Sense Tradition’ in: Scottish Philosophy ond British Physics, pp. 252 - 270. ‘Jain, ‘Methodology and epistemology’, pp. 31-53.

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propounded. We shall attempt partly to redress these deficiencies. The manuscript evidence establishes directly that Herschel read the Common Sense Philosophers. This article is intended to demonstrate not that Herschel’s methodology was the exclusive product of his scientific (and especially his optical) research, but that he had many of his methodological ideas at the time he was conducting this research. To use the phrase of Hannah Gay, the scientific and metascientific concepts “reciprocally illuminated” each other. Even in such a case study, it is most difficult to put one before the other. However, I believe it does show that for Herschel the interchange between science and metascience was one of mutual adjustment over many years.’

II. Analysis of Phenomena, Generalizations, and Physical Axioms This section examines the preliminaries to what Herschel later called the First Stage of Induction, namely the analysis of phenomena, the classification of phenomena according to general facts, and the analogy of physical science with abstract mathematics. Recent scholarship has begun to redirect attention away from issues surrounding hypotheses and theory choice and toward this equally important level of Herschel’s methodological theory. Although Olson, Jain and Vincent Carl Kavaloski have considered other sources for these ideas on procedures beyond the traditional Newton and Locke, many questions remain unanswered. This section discusses the development of Herschel’s doctrines of axiomatic structure, analysis, and generalization in three contexts: his mathematical interests, his optical research, and Scottish Common Sense philosophy. I intend minimally to establish the breadth and depth of the roots of Herschel’s methodological precepts. While Herschel’s methodology was partly inspired by Francis Bacon, he was in no sense a simple inductivist. This is seen in the earliest sections of his Discourse on the “Analysis of Phenomena”.” Notwithstanding Herschel’s assertion that experience is the “only ground of all physical enquiry” and his warning that we should “dismiss. . . any preconceived notion of what might or what ought to be the order of nature in any proposed case. . . ,” he also outlined the positive, active role of the investigator.” He called experiment “active observation” and compared the investigator with a lawyer:

9Hannah Gay, ‘The Dependence of Scientific Method on the History of Science’ presented at the 1984 meeting of the Canadian Society for the History and Philosophy of Science. My thanks to Prof. Gay for a typescript of this paper. “‘Herschel, Discourse, especially Part II, Chapters I and II, “Of Experience as the Source of Knowledge. . . “, pp. 75- 84, and “Of the Analysis of Phenomena”, pp. 85 - 103. “Ibid., pp. 79 - 80.

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. . . we cross-examine our witness, and by comparing one part of his evidence with the other, while he is yet before us, and reasoning upon it in his presence, [we] are enabled to put pointed and searching questions, the answer to which may at once enable us to make up our minds.‘*

He made plain the role of the scientist as interlocuter, not mere passive chronicler, in saying that mechanics is essentially experimental because it allows one to subject any suspected principle to “immediate and decisive trial.” Put simply, he allowed hypothetical principles to precede experimental trial. This is not the method of a naive inductivist.u Herschel emphasized his distance from inductivism in the next chapter of the Discourse, where he discussed the analysis of complex phenomena into simpler ones and, as he stated it, the raising of general physical axioms.14 He began the chapter by defining phenomena as the sensible results of hidden processes, processes which may be made sensible. This is what Herschel called analysis. I5 Rather than address the meaning of this term directly, Herschel chose to illustrate its meaning with extended examples. He “analysed” the complex phenomenon of sound into, first, six points in which all cases of the production of sound agree: the excitement of motion in the source of sound, the communication of that motion from the source to some medium, propagation of that motion through this medium, its transfer to the ear, its propagation within the ear to the nerves, and lastly, the production of the sensation. All but the last of these is a variety of the propagation of motion. Hence, the complex phenomenon of sound is analysed into the two simpler, or phenomena: the as Herschel allowed, “more general or elementary,” production of motion and the production of sensation. These cannot be analysed further and so are provisionally taken as “referable. . . to the immediate action of their causes.” This process, he said, leads next in two directions: to the study of the laws of the causes of motion and sensation, and to the recognition of the “ultimate phenomena” of the cohesion and elasticity of matter, which can be explained only by reference to their causes, attractive and repulsive force. l6 Such phenomena, Herschel hastened to say, are ultimate and beyond analysis only in the sense in which a chemist refers to an ingredient as an element: until it is shown to be the result of others more elementary.17 There is some evidence that Herschel read Reid and Brown’s accounts of analysis some time prior to writing the Discourse. Herschel’s main example of “Ibid., “Ibid.,

p. I?. p. 78.

140n raising

of physical

“Ibid., pp. 85 and 88. 161bid., pp. 88 - 90. “Ibid., p. 92.

axioms,

see, e.g. Ibid., pp. 98 - 99.

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analysis-the ringing of a bell- appeared in Brown’s Cause and Effect (1818),‘8 which Herschel read before 1833.19 Moreover, Herschel’s use of the term “proximate cause”, which is prominent in Brown’s book, appears in his correspondence as early as 1820 and was later central to his discussion of causality in the Discourse.2o The resolution or analysis of a subject into its attributes was one of the mental operations which, according to Reid, led to general conceptions. The other operation, generalization, is discussed below. He called this process abstraction.” Reid considered the ability to discern attributes, i.e. to analyse a subject, to be common to all humanity. He also thought that, as subjects have many attributes, they can be analysed in different ways, by different individuals. Reid meant these operations to apply to knowledge generally, and Herschel readily applied his discussion of analysis to natural science. As Reid considered “whiteness”, for example, to be an attribute of this sheet of paper, Herschel considered motion to be an attribute of sound. Of course, this was not exactly what Reid meant. But some of Herschel’s examples were more faithful to Reid’s intent, as will be seen in the case of chromatic polarization.” Reid drew several of his best examples of analysis from science. He thought this doctrine was relatively novel and compared it with the analysis “. . . which a Chemist makes of a compounded body into the ingredients which enter into its composition. . . .“23 Herschel, too, used chemical examples to make several points about analysis. Any phenomenon, like any substance, should be treated as an “elementary or simple one” till it is actually resolved into simpler ones. Also the complexity of a phenomenon may be recognized before analysis is possible, as sometimes happens with a chemical substance.24 To understand what Herschel meant by generalization, one must understand how he used “axiom” as a synonym for a general proposition that explains particular phenomena. In transferring this word from geometry to the physical

“Thomas Brown, Inquiry into the Relation of Cause and Effect, 3rd edn. (Andover, Massachusetts: Mark Newman, 1822), pp. 89 - 93. 19Herschel, Treatise on Astronomy (London: Longman, Rees, Orme, Brown, Green, Longmans & Taylor, 1833), p. 232. MLetter of Herschel to David Brewster, 3 February 1820, RSL.HS.20.84. This reference abbreviates: Royal Society of London, Herschel Collection. Herschel, Discourse, p. 144. Brown, Cause and Effect, p. 68. *‘Reid, Essays on the Powers of the Human Mind, Vol. 2, 120ff. u Herschel, Discourse, pp. 88 - 89. 23Reid, Essays on the Powers of the Human Mind, Vol. 2, pp. 128- 130. This example is interesting as Reid uses it to show the imperfections of the analogy. He was more positive in: An Inquiry into the Human Mind on the Principles of Common Sense (Glasgow: William Falconer, 1817), pp. 24-25, 53. 24Herschel, Discourse, pp. 92 - 94.

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sciences, Herschel followed a useage traceable to Bacon.*’ Notably, Reid did not agree entirely with this usage, saying that the term applied strictly only to self-evident propositions, not dependent upon any evidence or argument.26 However, Reid allowed that if one accepts the contingency of, for example, Newton’s pronouncements about the universality of inertia and gravitation, these may still be called axioms, because they serve as grounds for reasoning.*’ Herschel reinterpreted the term in the context of l&h-century mathematics and rational mechanics. He sometimes meant by axiom a general fact and sometimes a law of nature, terms which he thought differed only in degree of generality, not in kind. Axioms were “raised”, according to Herschel, from the stock of ultimate or elementary phenomena found in the analysis of nature’s many complex phenomena. With sound, the production and communication of motion constituted elementary phenomena. The relevant axioms were the laws of motion.” Herschel’s conception of scientific inquiry differed most clearly from naive inductivism in the role he attributed to general axioms. He argued that one can reason from these axioms to their consequences as one argues from the axioms of geometry. For example, axioms, abstracted from nature, contain all that is needed to explain motion and may be treated as “grounds of reasoning” or as “creatures of pure thought”.29 Herschel insisted that these axioms can be used to argue backwards from the general to the particular and in so doing one may derive both the complex phenomena from which the analysis began and other previously unknown phenomena: . . . and thus we are not only furnished with the explanation of all known facts, but with the actual discovery of such as were before unknown.‘O

One of his of light, in refraction. prediction,

examples was Augustin Fresnel’s apriori discovery that neither ray a doubly refracting medium actually follows the ordinary law of Herschel’s theory of method had roles for deductive reasoning and too.

25Sir Francis Bacon, The New Organon (New York: The Library of Liberal Arts, 1960), c.f. Aphorisms LXIX and LXX, pp. 66-69, and CIII to CVI, pp. 97-99. %Thomas Reid, E&ays on the Powers of the Human Mind: to which are prefixed, an Essay on Quantity, and m Analysis of Aristotle’s Logic, 3 vols (Edinburgh: Abernathy & Walker, 1819), 2: 267. 271bid., Vol. 2, pp. 272-280. 28Herschel, Discourse, pp. 94 - 96. ‘91bid., pp. 95 and 97. mIbid., p. 97.

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But how are these axioms obtained? In the Discourse Herschel turned from the lamentable lack of a method of analysis of phenomena, to a more pleasing prospect: In the important business of raising these axioms of nature, we are not, as in the analysis of phenomena, left wholly without a guide. The nature of abstract or general reasoning points out in a great measure the course we must pursue.

The ensuing discussion is so similar to Reid’s that it seems likely that Herschel formed his idea of abstract or general reasoning while reflecting on Reid’s Herschel advised the researcher to note the essay “Of Abstraction”.3’ “remarkable points” in which a class of phenomena agree, and to disregard their differences.32 For Reid, analysis was followed (or at least completed) by generalizing, or “observing one or more. . . attributes to be common to many subjects”.33 Ironically, where Reid seems to use “abstraction” in reference to those attributes chosen for generalization, Herschel uses it to mean those disregarded. Nonetheless, Herschel also explicitly adopted the aim of generalization to be the position stating that the shared property is a predicate of all appropriate subjects. This statement, he wrote, has “the character of a law of nature”.34 Herschel chose to exemplify generalization in the Discourse with his research on polarization and double refraction, perhaps hinting at the importance of optics in the elaboration of his ideas on method.35 Jain’s excellent re-examination of Herschel’s philosophy of science offers valuable perspective on this passage in the Discourse.36 Jain stresses the important point that Herschel used “analogy” in two ways in this example. First, analogy meant only a similarity of attributes, as in Reid’s “generalization”. Second, Herschel used it as a shorthand for “argument from analogy”, which has predictive force, unlike the first usage.37 Herschel explained in this example that many transparent materials display vividly colored bands when exposed to polarized light, and observed in a particular way. Because of its appearance, this phenomenon is called periodical colours. Of all substances, only transparent solids display this phenomenon. Herschel thus proposed a first generalization: “transparent solids exhibit periodical colours by exposure to polarized light.“3s However, there are exceptions to this statement, e.g. glass. By the nature of general “Reid, Essays on the Powers of the Human Mind, Vol. 2 pp. lOl- 187. “Herschel, Discourse, p. 98. “Reid, Essays on the Powers of the Human Mind, Vol. 2, p, 120. u Herschel, Discourse, p. 98. “‘Ibid., pp. 99- 102. 16Jain, ‘Methodology and epistemology’, pp. 142 - 153. “Ibid., pp. 143 - 146. ‘8Herschel, Discourse, p. 99.

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reasoning, one should then list all the transparent solids that exhibit these colours and search for other shared properties. A careful examination reveals that only one other property recurs unfailingly. All these substances are doubly refractive. Hence the law becomes: “Doubly refracting substances exhibit periodical colours by exposure to polarized light. . . .‘339 Since an extensive search never revealed one exception to this, Herschel claimed justification for calling it a general law of nature. According to Herschel, this example points out two important aspects about laws of nature. First, they serve to classify and tie together many particular instances. Secondly, by pricking our curiosity about why these properties are constantly conjoined, a law leads us to look for a causal link. In this example, the instances tied together include: calcite exhibits these properties, Rochelle salt exhibits them, etc. Likewise, one wonders about the mechanism that invariably displays both periodic colours and double refraction. One candidate was Jean-Baptiste Biot’s corpuscular theory, another was Fresnel’s undulatory theory. As Herschel summarized: it is thus, too, that phenomena assume their places under general points of resemblance; as in optics, those which refer themselves to the class of periodical colours, double refraction, etc.; and that resemblances themselves become traced, which it is the business of induction to generalize and include in abstract propositions.40

As Jain correctly notes, while the former sense of a law implies only analogy, the latter sense requires argument from analogy.4’ Analogy, he says, leads to general facts, while argument from analogy produces more general laws of nature, which might yield knowledge of a higher causal relationship. However, it must be noted that Herschel did not restrict his usage this way and he sometimes used “general fact” and “law of nature” interchangeably. These two terms were already part of his vocabulary in his 1820 article on chromatic polarization.42 Interesting as Herschel’s ideas about axioms in physical science were for 1830, he had expressed them in 1818 in an article on mathematics for David Herschel’s ideas on the relations of Brewster’s Edinburgh Encyclopaedia.43 experiment and theory owed much to a methodological tradition that had long

‘9rbid., p. 100. 4olbid., p. 141. ‘I Jain, ‘Methodology and epistemology’, pp. 148 - 150. “Herschel, ‘On the action of crystallized bodies on homogeneous light, and on the causes of the deviation from Newton’s scale in the tints which many of them develope on exposure to a polarised ray’, Philosophical Transactions 110 (1820), p. 49. 43John Herschel, ‘Mathematics’ in: Edinburgh Encyclopaediu (Edinburgh, 1830), Vol. 13, pp. 359- 383.

existed among mathematicians.~ For Herschel, physical science was ideally part of mixed mathematics, which differed from pure mathematics mainly in that its subject was nature. Even Aristotle used this distinction, but it had more recentIy been discussed in an article by Jean D’Alembert in the E~c~c~o~~di~.45

Mixed mathematics provided Herschel with the model of deductive argument from axioms. In his 1818 article, Herschel defined mathematics so as to include both the abstract reIations of number and magnitude and their application to natural science.46 In 1818 he did not elaborate on how the Iaws of nature-the axioms of physical science-are obtained. As he wrote, mixed mathematics [takes] for granted the truth of general Iaws deduced by legitimate induction from observations sufficiently numerous, supplies the hidden links which connect the cause with its remote effect and endeavours, from the intensity of one to estimate the magnitude of the other. Herschel denied that the certainty of mixed mathematics is vitiated by its foundation on ill-understood induction, which rests, he wrote, on unavoidable observational error. Deduction from general laws controls the magnitude of error. Errors due to observation, he wrote, “Iike the impurities fabled to have mixed themselves with the sacred river of antiquity”, can be followed through the reasoning and separated at the end.47 A main source of error in mixed mathematics was “over-hasty generalization”, which Herschel defined as “assuming Iaws to hold universally which have been verified by partial experience’“.48 Herschel might have been alerted to this aspect of science in Bacon’s writings, but he was to become aware of its importance and subtle forms in his optical research.4v When he wrote “Mathematics” he had done little mixed mathematical research and thought this problem had been vanquished from science, but this was far from true.50 The resolution of over-hasty generalizations was to assume an important role in Herschel’s optical research a few months later. Herschel had been developing his ideas on analysis of phenomena and on generalization since his early mathematical and chemical research. For

“See: Philip Enros, ‘The Analytical Society: mathematics at Cambridge University in the earlynineteenth century’ (Ph.D. Thesis, University of Toronto, 1979). “‘Jean D’Alembert, ‘Mathematique’ in: EncyclopPdie, 3rd edn, (Geneva, 17791, Vol. 21, pp. 141- 142. “Herschel, ‘Mathematics’, Vol. 13, p. 359. ” Ibid.

*Zbid., p. 360. “Francis Bacon, Novum Organurn, mHerschel, ‘Mathematics’, p. 360

Aphorism

XIV, p, 41.

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example, in 1814, he discussed generalizing and simplifying mathematical notation.51 He also criticized those chemists who prematurely made oxygen the basis of all explanation of combustion and he wrote to Charles Babbage: “III have generalized 1817 he had thought

my ideas very much lately enough about generalization

on. . .combustion.“‘* to chastize Babbage

By for

discussing the use of analogy or induction in mathematics.53 Herschel began his optical research while he was writing “Mathematics” in 1818, and once again he was pre-occupied with generalization. During the summer he repeated some of the easier polarization experiments of Brewster and Biot, and was drawn into some original observations of his own. In August he wrote to his Cambridge friend William Whewell about this work. After four pages of experimental detail and some slight speculation, Herschel wrote:

It will be long before I can generalize sufficiently to discover, but if I only open my eyes I may observe. The credit of mere observer however is not exactly what I aim at.54

He said he had first to become familiar with the known phenomena and the experimental techniques before attempting to discover. In reply to this or a later (lost) descriptive letter, Whewell told Herschel not to be reluctant to look for higher laws.55 During the height of his optical research, Herschel explicitly addressed generalization several times. He told his correspondents in 1819 that he was busy correcting over-hasty generalizations. 56 His most revealing statement came when Babbage admitted analogy seemed to shade into

in 1820 that induction, generalization and one another.57 For Herschel the differences

were clear:

I tell you as plainly as man can speak that induction is an operation of the mind sui generis-if operation it can be called-and whosoever maintains the contrary is a damnable heretic and will fry for it. - It is a mere passive habit acquired by the repetition of the same identical impression on the mind which leads to the

“Letter of Herschel to Babbage, 52Letterof Herschel to Babbage, “Letter of Herschel criticism is not clear. “Letter of Herschel “Letter of Whewell 56Letter of Herschel “Letter of Babbage

to Babbage,

25 October 1814, RSL.HS.20.20. 4 August 1814, RSL.HS.20.17. 15 May 1817, RSL.HS.20.43. What Herschel

to to to to

19 August 1818, RSL.HS.20.56. 1 November 1818, RSL.HS.18.160. 1 December 1819, RSL.HS.20.77. 1 December 1819, RSL.HS.20.77.

Whewell, Herschel, Whewell, Whewell,

meant

by this

Herschel’s

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Optical Researches

expectation of its future recurrence. Analogy is always the result of an effort of the imagination. The poetical powers are brought into action. But generalization 0 Lord 0 Lord has no more to do with it than the man in the moon. Why the mind of a man generalizing is all in a state of active inflammation. - It is in a ravenous and hungry mood grasping swallowing digesting and assimilating all that comes near it and condensing and pocketing all that is over and above (like Sancho Panca at the wedding feast) for future use. I should like to see some of the transition rocks on which your discernment seems to have been in danger of splitting.j8

Clearly, he had been reading one of the Common Sense Philosophers. Induction was a mental faculty, analogy an actively inventive comparison of instances, and generalization the gathering of an array of experiences. This schema is not identical to Reid’s discussion of analysis, generalization and accumulation of categories of shared attributes, but it is compatible with it. By these terms, Herschel was mainly generalizing in 18 19 and 1820. He was performing the same dozen or so observations on every crystal he could obtain from nature or the laboratory: What are its form, its structure, its cleavage planes and polish? Does it have one, two, or more optic axes?5g He began to

look closely at a polarization phenomenon, the production of colours by thin plates of crystalline material placed in a particular experimental situation. This phenomenon, called chromatic polarization, came in many forms. Herschel and others tried to classify the sorts of polarization effects observed. It was noted that crystals which produce one kind of polarization effect consistently produce a particular sort of double refraction effect. No one really knew why; that is, no one had an adequate theory to explain the connection between double refraction and polarization in all its manifestations. Herschel tried to find the connection through generalization, i.e. through classifying the sorts of polarization phenomena and relating them to the classes of double refraction phenomena. He proceeded partly by tearing down other people’s classifications (e.g. Brewster’s conflation of rotatory polarization with the anomalous tints produced by crystals with two axes) and partly by building up his own. This is discussed in detail in Section III. III. Prelude in Optics: Polarization

and Double Refraction

To appreciate the connection between Herschel’s method and his optics requires a preliminary understanding of the lively research on the nature of light that was underway in the 1810s. Much of Herschel’s earliest optical research was well-trodden ground, as indicated by his notes on problems in

J8Letter of Herschel to Babbage,

19 March 1820, RSL.HS.2.130. J9A large collection of Herschel’s research notes on these questions at the University of Texas at Austin, UT.W0281-354.

survives among

his archives

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refraction.60

Studies in History and Philosophy of Science However,

even his most elementary

higher than a school boy’s exercises. Herschel’s most important and original and 1820, was dedicated can deduce

the peculiarly

to discovering coloured

optical

work hinted research,

the physical

patterns

produced

axioms

that he aimed

conducted

in 1819

from which one

when polarized

light is

transmitted through crystals with one or two optic axes. He believed that these laws, like those he wrote about in the “Mathematics” article, should be simple. Indeed they were. His main difficulties were in finding ways to discuss the laws analytically and in verifying them. This effort was intricate, but the structure of the ultimate derivation was simply that of any mixed mathematical argument. The phenomenon of double refraction was first noted by Erasmus Bartholin in 1669. He observed that an incident ray of light is split into two distinct rays in crystals of calcite. One of these rays seemed to follow the same law of refraction as does a ray incident on a homogeneous material such as glass and was termed the ordinary ray. A law for the other, or extraordinary, ray was discussed in 1690 by Christiaan Huygens. Newton, also interested in this unusual phenomenon, commented that these two rays appeared to have “several sides, endued with several original Properties”. But it was not until 1808 that Etienne Louis Malus found that this was a general property of light and called it polarization.61 Prior to the 182Os, optical scientists suspected that double refraction and polarization in crystals were closely related, but there was no consensus on the nature of the connection. The best-known theory was that of mobile or alternate polarization, a corpuscular theory which was elaborated by Biot in This theory was intended to explain the his Trait& de physique of 1816.62 coloured rings produced when polarized light traverses a thin crystalline plate, usually along a particular direction, called the optic axis (see Fig. 1). Biot proposed, first, that some light corpuscles of every colour, upon entering a

@‘Herschel manuscripts, Houghton Library, Harvard University, 67M-67(110), Vol. 1, p. 433; St. John’s College, Cambridge University, James 508. 6’Erasmus Bartholin, Experimenta crystalli, Islandici disdiaclastici quibus mire et insolita refract0 detegitur (Hafniae, 1669); Christiaan Huygens, Trait6 de la /umit?re (Leiden, 1690). English translation by Sylvanus P. Thompson, Treatise on Light, 2nd edn (Chicago, 1950); and Isaac Newton, Opticks, or A Treatise on the Reflections, Refractions, Infections & Colours of Light (New York: Dover, 1952), Queries 25 and 26, pp. 354- 361. The Dover edition of Newton’s Opticks was based on the fourth edition, London, 1730. The best discussion of the history of the ‘Experimental investigations in double law of extraordinary refraction is Jed Z. Buchwald, refraction from Huygens to Malus’, Arch. Htit. Exact Sci. 22 (1980), 311-373. 62Jean-Baptiste Biot, Traite’dephysique, matheinatique et exp&imentale (Paris, 1816); Eugene Frankel. ‘Jean-Baotiste Biot’ (Ph.D. dissertation, Princeton University, 1972). This is the best account of Biot’s researches.‘Herschel’s extension of Biot’s theory is discussed at length in Gregory Good, ‘J.F.W. Herschel’s Optical Researches: A study in Method’ (Ph.D. dissertation, University of Toronto, Canada, 1982). See especially chapters 3 and 4.

Herschel’s Optical Researches

13

crystal are made to oscillate “like the balance wheel of a watch”63 (see Fig. 2). He also postulated a force of polarization, proportional to the angle between the plane of primitive polarization and the principal section of the crystal. Hence, light corpuscles originally polarized in this direction maintain their primitive orientation, i.e. they do not oscillate as do corpuscles oriented differently. Lastly, he assumed that the ordinary ray was composed entirely of non-oscillating corpuscles and that the extraordinary ray was composed entirely of oscillating ones (see Fig. 3). In the usual experimental arrangement, the plane of polarization of these corpuscles was assumed to pass between the primitive plane and one perpendicular to it.@ Moreover, the length of an oscillation was thought to be shorter in crystals with a more intense polarizing force. The oscillation was supposed to continue until the corpuscle left the crystalline plate, at which point it would remain in one of these two azimuths. If it was in the primitive plane, it would be unable to traverse the analyser. But perpendicular to it, the corpuscle would be oriented in exactly the correct direction for transmission. Hence, no part of the ordinary ray traverses the analyser in Biot’s theory of alternate polarization, and only those

Fig. 1. Rings produced

by a uniaxial

crystal

between

crossed

polarizers.

63Quoted in Frankel, ‘Biot’ p. 250. @In this set-up, the polarizer and analyser are “crossed”, i.e. light transmitted by the one is stopped by the other. Also, the plate of the sample crystal has its principal section at 45”. mid-way between the polarizer and analyser. The law proposed by Biot was that the light corpuscles are made to oscillate between the principal section and twice the aximuth angle, i.e. 2i= 2. (45’) = 90”. where i is the azimuth angle.

14

Fig. 2. Simplified

Studies

view of oscillating

in History

corpuscles in the extraordinary of mobile polarization.

and Philosophy

ray according

of Science

to Biot’s theory

extraordinary corpuscles which have made an odd multiple of half-oscillations do so. If one observes the colours at a series of distances in the rings and one knows the distances traversed by successive rays within the crystalline plate, the “periods of alternate polarization” for the various colours can easily be calculated. Biot concluded that these periods, actually lengths, were proportional to the fit-lengths Newton had calculated in his famous experiments on rings produced by homogeneous matter. This is not surprising, since the crystals Biot used produced rings nearly identical with those in Newton’s experiments. Biot’s law therefore became known as “the law of proportionality” .65 But not all patterns were coloured in this way and not all were exactly circular. In 1818 Brewster announced his discovery of biaxial crystals. These produce an elongated pattern, with two foci corresponding to the two axes along which the ordinary and extraordinary rays are not separated (see Fig. 4). Also, in analogy with his theory for uniaxial crystals, Biot concluded that along these directions the incident light corpuscles are not made to oscillate and their passage should be blocked by the analyser. These two foci should therefore appear black.@ “While Biot’s final theory was presented in the TruitP de physique, its development can be followed in his Recherche expdrimentales et mathkmatique sur les mole’cules de la IumiPre, autour de leur centre de gravitP(Paris, 1814). This reprints most of his memoirs on the subject. The only accurate and useful account of Biot’s theory in English is in Herschel, ‘Light’, Encyclopaediu Metropolituna (London, 1845), Vol. 4, pp. 533 - 545. This discussion is also of interest because it is Herschel’s textbook discussion of the problem of biaxial dispersion and because he no longer believed Biot’s theory to be the only alternative. He discussed the use of Fresnel’s theory in explaining phenomena of polarization in Vol. 4, pp. 533 - 545. Although this publication is listed as published in 1845, the articles were distributed as they left the press. Herschel finished ‘Light’ in 1827 (Diary, 19 December 1827, UT.WOOO9). “David Brewster, ‘On the laws of polarisation and double refraction in regular crystallised bodies’, Philosophical Transactions 108 (1818). 199- 273. N.B. Brewster never used Biot’s oscillating corpuscles. I only mention them at this point to indicate how they can be reconciled with Brewster’s discovery. Herschel and Biot soon did so.

Herschel’s Optical Researches

15

Brewster’s discovery of biaxial crystals Huygens’ law of extraordinary refraction calcite and four other minerals, general: in Herschel’s lexicon, claim,

since Huygens’

biaxial. that:

He called

challenged Malus’ verification for calcite. From experiments

Malus had earlier concluded Huygens’ law was a physical axiom. Brewster criticized Malus’

law did not apply to two of these minerals,

Malus’

of on

experiments

“decidedly

erroneous”

which were and

warned

generalization, however ingeniously managed, has been carried on too rapidly, and has far outrun the progress of observation and experimenL6’

To Brewster, no one could support this claim cautious spirit of inductive philosophy.”

who was “imbued

with the

Herschel agreed with Brewster that the process of generalizing had been carried on too rapidly in crystalline-optics, and he wrote that the discovery of biaxial crystals called for a “far more extensive scale of investigation”. He told Whewell that he was cleaning up “over-hasty generalizations, a nuisance too common in optical science”.68 The term over-hasty generalization had

ANALYZER (VERTICAL)

SAMPLE (PRINCIPAL SECTION,

ORDINARY EXTRAORDINARY Fig. 3. Separation

49)

RAY RAY

POLARIZER (HORIZONTAL)

(NOT -.

-.

-a

of the rays according

OSCILLATING)

(OSCILLATING to Biot’s theory

1 of mobile

polarization.

671bid., pp. 201-220, 210. The two minerals were aragonite and barium sulphate. “Herschel, ‘On the action of crystallized bodies on homogeneous light’, p. 45. Letter Herschel to Whewell, 1 December 1819, RSL.HS.20.77.

of

16

Studies in History and Philosophy of Science

Fig. 4. Rings produced by a biaxial crystal between crossed polarizers [from Norman Holt Hartshorne and A. Stuart, Practical Optical Crystallography (New York: American Elsevier, 1969), p.2131.

article, and signalled here appeared previously in Herschel’s “Mathematics” that he saw this as something more methodologically complex than a lack of inductive caution. Brewster asked Herschel if he had been unfair to Malus.69 Herschel’s reply is an interesting elaboration of his conception of the relation of law to observation in mixed mathematics. He was more restrained than Brewster in his judgement of Malus’ claim for the generality of the law of extraordinary refraction and he replied, in effect, that Malus’ conclusion was justifiable within the limits of mixed mathematics. There were two instances, he wrote, in which Malus could not have distinguished between uniaxial and biaxial crystals by direct observation: when the axes are too close together and when the double refracting force “is but feeble. . . “.” compounded of the two axes would In the former case, the “spheroid” differ only slightly from the Huygenian spheroid. Hence the separation of the ordinary and extraordinary rays could follow the Huygenian law within the limits of observational error. In the latter case, the slight separation of the two pencils should make the discovery of the correct law unlikely. Indeed,

69Letter of Brewster “Letter of Herschel

to Herschel, to Brewster,

7 November 1819, RSL.HS.4.248. 24 November 1819, RSL.HS.20.76.

17

Herschel’s Optical Researches

Herschel wrote, it would be difficult in this case even to discover the directions of the axes. Herschel advised Brewster: . . . perhaps his experiments (I say nothing of his conclusions) can hardly be reprobated as “decidedly erroneous” till it has been shown by calculations (for which we now have all the requisite data) that the action of this cause ought to have become sensible in his observations if made with proper care, and that he overlooked it, or confounded it with errors of obs[ervatioln.

Whether Brewster’s criticism was valid depended on the limits of observation and calculation in Malus’ time, according to Herschel. As these capabilities expanded, so did the ability of mixed mathematics to recognize error. To Herschel this explained how the valid generalizations of one generation might become the over-hasty generalizations of the next.” While Brewster pursued Malus’ over-hasty generalization of the law of extraordinary refraction, Herschel took up the law of proportionality, which Biot had asserted to be general. Contrary to his expectation from this law, Herschel saw that the colours in the rings of biaxial crystals usually deviate from that order in Newton’s rings. In the article he was completing at the time of his correspondence with Brewster, Herschel wrote: Ever since I first engaged in experimental enquiries on the polarisation of light I was struck by the very considerable deviation from the succession of colours of thin laminae, as observed by Newton, which many crystals exhibit when cut into plates perpendicular to one of their axes.‘* He continued in the article to say that he felt compelled to look for the cause of these deviations in tints since they “began to assume the form of a radical and unanswerable objection to the theory of M. Biot”. In his effort to resolve this objection, Herschel discovered two new properties of biaxial crystals: the fanlike dispersion of the axes for differently coloured rays and a marked deviation from Biot’s law of proportionality (see Fig. 5). Both of these new properties will be discussed at length in the next sections. However, our interest is not in the discoveries themselves, but in the ideas on method by which Herschel structured his research. Given a complex phenomenon, how did he try to explain it? IV. Discovery

of the First Cause of Deviant Tints

Herschel divided research into two complementary processes of identifying and verifying causes. He said discovery was like a kaleidoscope, consisting “in

“Ibid. ‘*Herschel, ‘On the action of crystallized bodies on homogeneous

light’, p. 48.

Studies in History and Philosophy of Science

18

rapidity and variety of combination”.73 True to this dictum, Herschel considered many possible causes of the deviation of tints. The place for exacting standards was not in suggesting causes, but in testing them. Consequently, while Herschel’s candidate explanations appeared quickly, months of experiments and calculations passed before he accepted them. Herschel’s search for the two causes of tint variation began in April 1819 and was his main occupation until his third memoir on the topic was completed in 182 1.74 His use of Biot’s theory indicates the subtleties possible for the role of physical axioms in his science. He said he had no “definite or accurate ideas on the polar[izatioln of light. . . ” until he discussed the phenomena with Biot in January 1819.75 When he began his research in April, he was simultaneously exploring the phenomena and Biot’s theory. Could oscillating optical corpuscles produce a pattern like the one exhibited by biaxial crystals? This required both a mathematical statement of Biot’s theory and a quantitative description of biaxial rings.

Blue Axis Red Axes Blue AXIS

Fig. 5. Dispersion

of the axes for differently

colored

rays in a biaxial

crystal.

“Letter of Herschel to Babbage, 27 April 1818, RSL.HS.2.92. Babbage replied that “The local Kaleidoscope of analysis is functions for functions produce them all [i.e. porisms, theorems].” April 1818, RSL.HS.2.93. “The first is cited in note 42. The others are: ‘On certain remarkable instances of deviation from Newton’s scale in the tints developed by crystals, with one axis of double refraction, on exposure to polarized light’, Cambridge Philosophicof Society Transactions 1(1822), 2l- 42; and ‘On a remarkable peculiarity in the law of the extraordinary refraction of differently-coloured rays exhibited by certain varieties of apophyllite’, Cambridge Philosophical Society Transactions 1 (1822), 242-248. Herschel wrote five other optical memoirs during this period, but they are not directly relevant to this discussion. 75Letter to Brewster, 24 November 1819, RSL.HS.20.76.

Herschel’s Optical Researches

Fig. 6. John

19

Herschel’s

sketch

of a biaxial

ring pattern

These explorations survive in an interesting manuscript.76 In it, Herschel imagined a crystal with slightly separated axes and an intense polarizing force. He intended to find the algebraic relationships between the lengths of oscillations and the ring pattern. He thought the biaxial rings were similar to lemniscates, and he guessed that their equation would be “a faithful representation to the eye of the Isochromatic bands”. Faithful mathematical representation was a minimal requirement in his mixed mathematics. Next Herschel explored the mathematical possibilities of Biot’s theory. In the theory, each band in the pattern represented a locus of directions in the crystal over which all the corpuscles of a given colour underwent the same number of oscillations. At some determinate small angle, different for each direction from a pole, the corpuscles in a ray underwent half an oscillation and exited the crystalline plate polarized similarly to the analyser. Such rays appeared as bright points in the pattern. At a slightly greater distance from the poles, the corpuscles returned to their primitive orientation and were blocked by the analyser in the same way as rays along the axes, producing a dark ring. Herschel easily interpreted the parameters in the equation of the lemniscate: PM - P’M = ba described successive rings close to the poles. In it the left-hand factors were the distances from the two poles P and P’ to a point M in the rings, “a” was half

‘6‘On the general SJC.James.516.

laws of the isochromatic

bands

in chrystals

(sic) with 2 axes’, 17 April 1819,

20

Studies in History and Philosophy of Science between the poles and “b” was an integer that increased from one ring to the next (see Fig. 6). At greater distances sines

the distance arithmetically were substituted

for arcs and the equation

became

sin 6 . sin 6’ = ba

@I

which was exactly the “law of with a law he had verified for angles between the path of the But what did this law mean?

tints” Biot had recently suggested an analogy uniaxial crystals, in which 8 and 8’ were arc ray and the two axes. How could it be rectified with the corpuscular

theory Herschel then used? Near the end of the manuscript Herschel concluded that the polarizing force must be “some functlioln of sin f3 * sin 8 ” and that the length of oscillation must be a function of this too. Herschel went on to conclude that the length of an oscillation is inversely proportional to sin e . sin 0’ and that the number of oscillations performed is directly proportional to this factor. With the existing sources we cannot be sure when Herschel learned of Biot’s law of tints or if he discovered it independently. The utility of the factor sin 8 - sin et, already evident in the above manuscript, was brought forth again in a letter from Biot to Herschel on 2 May 1819.” In it, Biot reported his law for the difference between the velocities of the ordinary and extraordinary rays in biaxial crystals, which also incorporated this factor. Biot’s suggested

(cl Biot claimed

law was

ve2 - vo2= k - sin 8 - sin 8’.

that it was a “representation

parfaitement”

and Herschel

it as a “simple and beautiful analytical expression”.78 Because Herschel did not know this law for the velocities

praised

of the two rays

while composing the April manuscript, it is not surprising that some of the details of its conclusions were incorrect. Moreover, Herschel did not even demonstrate the exact fit of a lemniscate to the observed curves until five months later.” Nonetheless, with some confidence in the physical hypothesis Herschel quickly traced out its and in its mathematical development, consequences. Verifying its many details was to be a much longer process.

“RSL.HS.4.184. 78Letter of Herschel to Brewster, 1.5 May 1819, RSL.HS.20.70. ‘9UT.W0338. The sketch is still among the experimental notes.

Herschel’s

21

Optical Researches

V. Verification

of the First Cause

Having satisfied himself at least tentatively that he could represent the basic properties of biaxial rings, Herschel was ready to tackle the deviations of tints, such as the unexpectedly coloured poles. He had guessed at the first two causes right away: The two axes for the different colours are dispersed fan-like in a plane. The first mention of this cause preceded his manuscript on the equations of the isochromatic bands by several days: “. . . the axes for red in Arragonite (sic) are less separated than for violet. . . “.*O This suggests that Herschel might have mathematized Biot’s theory on the 17th to see how well this discovery explained the deviant tints.” In testing this theory, Herschel found that while most of the deviation could be calculated from it, some deviation remained. Three months later this led him to the second cause, a peculiar variation in the law of lengths of oscillation, i.e. a deviation from Biot’s law of proportionality. The similarity of this approach to the successive identifications of perturbations of planetary orbits is suggestive of the frequent connection between practice in one science, astronomy, and general methodological precepts. Herschel later formalized this procedure and called it the “subduction of causes”.** This was a most important aspect of methodology derived from his mixed mathematical approach. In verifying these causes Herschel applied criteria that he later associated with the term vera causa. 83 Herschel was by no means the first person to use this concept. Bacon,84 Newton,85 ReidE6 and Brown” all used variations of it. Scholars have been interested in this methodological concept for some time. Both Ducasse@ and Partridge*9 devote considerable attention to it, but their

“Herschel manuscript, 13 April 1819, UT.WO281. *‘This is far from certain, given that he did not actively pursue the topic until three months later. “Herschel, Discourse, p. 156, rule 9. “See, e.g. Herschel, Discourse, pp. 144, 197, 202. LUBacon, New Organon, Aphorism LXX, p. 68. “Newton, Mathematical Principles of N&al Philosophy, 3rd edn, translated by Andrew Motte, edited and revised by Florian Cajori Universitv of California Press. 1966). ,. .D. - (Berkeley: . 398, rule 1. 86Reid, Philosophical Works, with notes & supplementary dissertations by William Hamilton, and an introduction by Harry M. Bracken, 2 vols (Hildesheim, Germany, 1967). Vol. 1, p. 261. This includes: An Inquiry into the Human Mind (1764), Essays on the Intellectual Powers if Man (1785), and Essays on the Active Powers of Man (1788). “Brown, Inquiry into the Relation of cause and Effect (Andover, Mass.: Mark Newman, 1822). This seems to be a reprint of the third edition. Brown did not use the words Vera causa or true cause, but he discussed most of the issues involved in some detail. “Curt. J. Ducasse, ‘Herschel’s methods of scientific inquiry’ especially p. 164ff. ‘Introduction’ to Johnson reprint of Herschel’s Discourse, especially a’Partridge, pp. xxix - xliii.

22

Studies in History and Philosophy of Science

discussions have largely been superceded by those of Kavaloski” and William Wallace.” Wallace’s discussion is particularly valuable, as he examines Reid’s use of the term, as well as Herschel’s.92 Their views are discussed in Section VII below. This section’s purpose is to discuss Herschel’s use of a form of the vera cau.sa concept in his 1819 optical research. As Herschel applied it in 1819 in his experiments and in writing the memoir, establishing a [true] cause entailed two steps: demonstration that a candidate cause actually exists and demonstration that it is sufficient to produce the observed phenomenon. In the memoir he stated that he would demonstrate that a particular “law of action” “must really exist. . . “.93 In another place, having demonstrated the existence of a particular candidate cause, he wrote: We must now show that this supposition is sufficient [my emphasis1 to represent the phenomena correctly.94

It is important to note that Herschel was not discussing the establishment of higher generalizations such as the wave or corpuscular hypotheses as verae catme. He instead was dealing with lower level generalizations: if phenomenon x is present, phenomenon y will be present, too. Other restrictions are needed to define the causal relationship, but Herschel did not concern himself with them in this optical memoir. The reality of a cause can only be demonstrated experimentally. Regarding biaxial dispersion, Herschel asserted by August that the colour observed in the axis of no polarization “proves positively that the axis is not the same for all luminous molecules”. He soon devised better experiments using prisms and filters to observe the positions of the axes in different homogeneous colours. They were indeed dispersed in a plane. This candidate was a real phenomenon.95 The proof of the adequacy of this dispersion in explaining deviant tints required experimental testing combined with theoretical development. This process took months to complete. Both in his research notes and in his memoir of the adequacy of the Herschel began with “an ocular demonstration

90Kavaloski, ‘The vera cuusu principle’, note 4, pp. 39- 77. 9’Wallace, Cuusuljry and Scientific Explanation, (Univ. of Michigan

Press,

197%

Vol. 2, PP.

96- 110. “Ibid., Vol. 2, pp. 44-51. 93Herschel ‘On the action of crystallized bodies on homogeneous light. . . ‘, p. 63. %Ibid., p.‘68. 9’Herschel manuscript, 6 August 1819, UT.WO297, p. 5. On 12 August Herschel experimented with another crystal and was led to state his discovery in the form of a proposition. He also commented enigmatically that “The consequences deducible from this are obvious and most important”. UT.WO300.

Herschel’s

Optical Researches

23

concerned two white spots which explanation. . . ” .% This demonstration often appear in line with the poles or centres of the rings, sometimes between them and sometimes outside. He called these virtual poles. In the test, he fixed a plate of biaxial crystal so its rings could be projected onto a screen. He then used a prism to throw successively the parts of the solar spectrum onto the plate. The rings formed as expected. However, as the light on the sample shifted from red to violet, the ring dimensions not only decreased, but their poles moved apart. The experiment was first performed on nitre on 13 August 1819.97 Whether the real poles move toward or away from each other as the illumination changes from red to violet depends on the crystal. In Rochelle salt and mica the red poles are outermost, in nitre the violet are. Herschel noted that at a certain point the rings of all colours coincided, at the approximate spot where the virtual poles were formed in white light. This constituted a rough experimental verification to Herschel that biaxial dispersion explained an important special case of deviant tints. Herschel introduced a variation of the experiment on 17 August. In it he simultaneously projected the rings of two or more colours. An order of these rings always intersected at the virtual poles. He said the purpose of this experiment was to make biaxial dispersion evident to the common observer.98 Another qualitative test of the sufficiency of biaxial dispersion was its ability to explain the tints produced in white illumination. Near the virtual poles, for example, the tints follow Newton’s scale pretty nearly. Herschel discussed these tints in detail and explained qualitatively how they corresponded with expectations from Biot’s theory and biaxial dispersion. At the virtual poles, a maximum of the extreme rays red and violet must coincide. But because the length of oscillation is greater for red than for violet, the rings will not generally match in other orders. Hence at the next violet minimum beyond the virtual poles, some red will remain in the extraordinary ray, a little less orange, etc. At the second violet minimum, more red will remain, more orange, etc. At higher orders, the mixture is not so clear, but it can easily be calculated. Expectations did indeed match the observed colours.99 A more general test of the adequacy of biaxial dispersion demanded a quantitative treatment in the form of an analytical expression for the tints,

%Herschel, ‘On the action of crystallized bodies on homogeneous light. ‘, p. 75. “Herschel manuscript, UT.WO297. p8Herschel manuscript, UT.WO300. He called this a “very pleasing experiment”. %Herschel, ‘On the action of crystallized bodies on homogeneous light. . . ‘, p. 70. I must note that this argument does not appear in the research notes, but only in the memoir. However, since it would have been familiar to anyone conversant with Newton’s rings, as Herschel was, I strongly suspect he knew of it earlier.

24

Studies in History and Philosophy of Science

relating

the

parameters colour

number

of oscillations

of a lemniscate.

The number

and serves as an indicator

(4

performed

n =

of tint.

by a ray

of oscillations Herschel

to measureable

clearly

derived

varies

with

the expression

$-& . “f(e,e’)

in which k is a polarizing force (the inverse of I, similar to a wave number), t is the plate thickness, e indicates the obliquity of the ray to the plate, andf(8,8’) attenuates the polarizing force as the ray approaches either axis. The latter function is in fact sin O-sin 0’. Clearly the thickness and obliquity are independent of colour, as Herschel also thought the polarizing force to be. Herschel thought that onlyf(B,O’) could be colour-dependent. Since 8 and 8’ measure the angles from the ray to the two axes, this means that the positions of the axes must change with colour. Herschel concluded:

In order to render the theory of alternations applicable, we must admit the angle between the axes of double refraction to differ in the same crystal for differently coloured rays.‘”

As he stated, this made it possible to use Biot’s theory to further test the candidate cause. But it did not yet provide that general proof of sufficiency. Herschel took a long stride toward this general proof with his first quantitative tests. This instance is characteristically Herschellian, resting as it does on the psychological impact of an unexpected result: a scientist’s method does not always satisfy the philosopher in us. Herschel noted that in the formula which expresses the coincidence of red and violet maxima (i.e. the equation of condition for the virtual poles), the thickness of the sample plate does not appear:

k r cos

er

. sin 8, - sin 8,’

= - kv - sin 0, - sin 0,’ cos ev

That is, the position of the virtual poles is independent of plate thickness. This theoretical consequence contradicted the results of Herschel’s first experimental trials on nitre, in which he had thought the virtual poles were

ImHerschel, ‘On the action of crystallized sign is + for a ray outside the axes and -

bodies on homogeneous for one within.

light.

. ‘, pp. 67 - 68. The

Herschel’s

25

Optical Researches Colncldent Extraordlnary

Fig. 7. Production of the virtual pole by the coincidence of extreme rays.

closer to the real poles in thinner plates.“’ As Herschel wrote much later in a related context, there are instances of “theory actually remanding back experiment to read her lesson anew. . . “.I’* He carefully verified this prediction during August and September and gave these results a prominent place in his first memoir in December. He measured the angles of the virtual poles for nitre, barytes and Rochelle salt. In each case, he began with a thick plate and, between trials, he ground it to a new thickness. Herschel’s last and most demanding test of the general sufficiency of biaxial dispersion rested on a formula relating the value of the dispersion to certain theoretical and experimental parameters. Could Biot’s theory, from which the formula was derived, predict the actual angle between the red and violet axes? This formula was

in which P, and !, are the lengths of oscillations of red and violet rays. To test this, Herschel computed the values of 8, 8’ and 2a from two measurements: the position of the red axes (in red light) and of the virtual poles (in white light) (see Fig. 7). The lengths of oscillation were assumed to the proportional to Newton’s fit lengths, as Biot had recommended. The calculated value of the right side was then compared with the dispersion found by direct observation

““Herschel manuscript, 10 August 1819, UT.WO338, pp. 2-3. ImHerschel, ‘Whewell review’, Quarterly Review, June 1841, p. 223. He was here referring to William Rowan Hamilton’s discovery of conical refraction in 1833.

26

Studies in History and Philosophy of Science

in red and violet homogeneous light. Agreement was especially close for gypsum and mica. With barytes, the predicted apparent separation (in air) was l”59’20” and the observed value was 2”01’30”. As he wrote, regarding one specimen, “a more exact coincidence could not be wished”.‘03 Herschel confidently announced the discovery and verification of biaxial dispersion in letters to Babbage and Brewster at the end of the summer.‘04 In the December memoir, he reported the above results to be a “striking verification of the theory” and called biaxial dispersion “a simple and general fact” and a “principle” which explained many complex phenomena. He placed this conclusion in the context of mixed mathematics, saying, We have here then a new element, which for the future must enter into all formulae of double refraction pretending to rigour. . . .I”’

This concluded Herschel’s arguments for the reality and sufficiency of biaxial dispersion as a cause of deviation of tints in biaxial crystals. It had met the criteria for a vera causa. VI. Residual

Phenomena

and Verification

of the Second Cause

While verifying this vera cau.sa Herschel discovered that it did not account entirely for the deviant tints in all minerals. He had suspected this when he noted that the virtual poles of Rochelle salt exhibit a slight tint. From this he concluded that in Rochelle salt, the maxima of all rays do not coincide as they do in, for example, barytes and nitre.lM The law of this dispersion of axes, he reasoned, does not always exactly counter the law of the magnitudes of differently coloured rings. Because his research showed the axes of different colours to be dispersed regularly, he suspected the tints of the virtual poles to be due to an unusual variation in the law of the magnitude of the rings. That is, the lengths of alternate polarization for different colours did not appear to be proportional to the corresponding fit-lengths: Biot’s assumed law of proportionality was not generally valid. Hence, while verifying the first cause, Herschel had discovered a second in the violation of this assumption. Indeed, Biot’s law was the over-hasty generalization of which he complained to Whewell in December 18 19.

“‘Herschel manuscripts, 27 August 1819, UT.WO290 and 6 and 11 September 1819, UT.WO297. For mica Herschel observed a separation of 0 30’ in homogeneous light. The calculated value was 0 27’ 37”. The remarkable care exercised in these measurements cannot be overemphasized. l”Letter of Herschel to Babbage, no date [September or October 18191, RSL.HS.2.121; to Brewster, 30 September 1819, RSL.HS.20.74. ‘“Herschel, ‘On the action of crystallized bodies on homogeneous light. ‘, pp. 49 - 50. INIbid., p. 69.

Herschel’s Optical Researches

27

A more forceful illustration of the failure of Biot’s law came in Herschel’s tests of the law of biaxial dispersion expressed in equation (f). Herschel used this equation with specimens of Rochelle salt just as he had with other minerals. He measured the positions of the red axes and the virtual poles and calculated the values of 8, 8’ and 2~7.However, the calculation required him to assume 0, and P, to be proportional to Newton’s fit lengths, as Biot’s law recommended. In the case of Rochelle salt, the coupling of this assumption with the formula predicted a value of 6”Ol’ for the dispersion of the red and violet axes. The observed value of 9”46’ was clearly not close and led Herschel to doubt the presumed proportionality. The coefficient (P, - fV)/Pr in our formula being the only part not immediately deduced from observation, it is evident that the assumption must be widely erroneous. . . .I”

He concluded that the relation between the lengths of alternation and Newton’s fits was a residual phenomenon to be investigated, not assumed, for each crystal. In the memoir, Herschel called it a “secondary and subsidiary cause”.“* Herschel was satisfied by late September 1819 that this cause was real and in the publication he did not address the issue of reality at any length. Instead he concentrated on demonstrating the sufficiency of this cause to account for deviant tints not accounted for by biaxial dispersion. This cause was somewhat more difficult to study than was the first, as Herschel explained to Brewster, because the more powerful effect of biaxial dispersion “masked” it.‘@ Herschel considered different ways of studying this secondary cause. One way was to derive a formula which would allow the easy calculation of values of the lengths of oscillations for differently coloured rays, even in crystals with dispersed coloured axes. Herschel applied the formula

(g)

P = t-

sine - sine n - cos e

in an examination of Rochelle salt and concluded from the values of the lengths of oscillation obtained they were not proportional to Newton’s fits. It should also, he thought, be possible to cut biaxial plates to facilitate the investigation. ‘lo “‘Ibid., p. 88. l”Ibid., p. 91.

losHerschel to Brewster, 30 September 1819, RSL.HS.20.74. He used this phrase again in ‘On the action of crystallized “‘Ibid., pp. 88 - 90.

bodies

on homogeneous

light.

. . ‘, p. 51.

28

Studies in History and Philosophy

of Science

But the clearest way to demonstrate the action of the second cause would be to study a specimen in which the first cause did not act. Herschel found his opportunity in the mineral apophyllite. This was the only mineral known to him which exhibited deviation of tints but in which there was no biaxial dispersion. Indeed, apophyllite is uniaxial. As Herschel wrote to Biot, “it is only in crystals with a single axis that [the effect of the second cause1 can be By eliminating the effect of biaxial dispersion visible naturally.“” experimentally, as it were, Herschel stated “. . . the agency of this secondary cause is placed in the fullest evidence.““* Later, in 1830, Herschel called the unmasking of a secondary cause “subdu~tion”.‘~~ By this he meant that one took the effect of a known cause into account and then studied the remaining phenomenon as an indication of the action of the secondary cause. Subduction of biaxial dispersion in the mathematical argument had revealed the second cause. Apophyllite made it possible to subduct it experimentally. As Herschel advised in 1830, one should find an instance in which one cause is absent, in order to reveal the action of another suspected cause. Hence, while Herschel did not use the word subduction in 1819, he used the process in both its forms. As he had done for Rochelle salt, Herschel determined the lengths of alternate polarization in apophyllite for eight rays of standard colours. He found in one specimen that the lengths were nearly identical for all colours. Interestingly, however, the length of alternation for violet was slightly greater than that for red, the opposite of the relation in Newton’s fits.14 Herschel qualitatively demonstrated the sufficiency of the second cause in the same way as he had for biaxial dispersion: he explained the tints of apophyllite in white light. Exact identity of the lengths of alternations would produce successive black and white rings, stretching to infinity. Herschel therefore expected to see rings to a higher order, as he said, than usual. He counted alternate black and white rings to the 35th order and quit only because beyond that they were too close together to count.“’ Also, because these lengths differed slightly, he expected to see slightly tinted rings. Green was the shortest. This implied that it reached its first maximum before other rays. Longer lengths for indigo and violet indicated their first maxima should be outside those of other rays. Herschel observed exactly this with white illumination: a greenish-white ring at 13”50’, a pure,

“‘Letter of Herschel to Biot, 10 December 1819, RSL.HS.4.86. “2Herschel, ‘On the action of crystallized bodied on homogeneous light. . . ‘, p. 51. “3Herschel, Discourse, pp. 154- 158, rules 7 and 9. See the discussion of rules 7 and 9 of Herschel’s Preliminury Discourse, below. “4Herschel, ‘On the action of crystallized bodies on homogeneous light. . ‘, p. 92. “‘Ibid., p. 94.

Herschel’s Optical Researches

29

brilliant-white ring at 21”50’, and purplish-white one at 25”12’ ,‘I6 Likewise, as expected, the first over-all minimum was preceded by a sombre violet-blue and followed by an early increase of a pale yellow - green. The second cause was therefore sufficient as well as real. It, too, was a Vera causa.

VII. The Causal Relation

and the Criteria for verse causae in Reid and Brown

Nowhere in these optical memoirs or manuscripts did Herschel discuss methodological topics at any length. However, he was not only well-informed about philosophical issues relevant to his science, he was also deeply concerned about them. Jain may be correct in saying that Herschel’s daytime experiments and nighttime astronomical observations “left him little time to ponder over the fundamental problems of philosophy.““7 But he is wrong to say that Herschel showed no “. . . explicit awareness of philosophical issues relating to science. . . “. Herschel employed in his correspondence, research notes, and publications many terms found in the methodological literature of his time: axioms, mathematical representation, general facts, general laws, over-hasty generalization, etc. More importantly, he explicitly organized both his research and its presentation in terms of the reality and adequacy of a cause. This demonstrates Herschel’s early familiarity with the meta-scientific discussion. The highly complex optical research programme he developed in the late 1810s was his first sustained investigation outside of pure He revised and recombined various elements of mathematics.“’ metascientific discourse with the problems and puzzles of chromatic polarization daily before him. While he later refined his methodological doctrines in the contexts of other sciences such as uniformitarian geology, their basic outlines were already in hand by 1820. Herschel codified the procedures and standards of 1819 and 1820 in his Preliminary Discourse of 1830, especially in the section on the “First Stage of Induction”. The analysis of phenomena, the classification of phenomena according to general facts, and the analogy of physical science with abstract mathematics, discussed in Section II above, were essential aspects of this stage. Also central to this methodology was a wide-ranging and richly textured discourse on causality. It drew not only on the scientific literature of Newton

‘16Zbid.,p. 93. “‘Jain, ‘Methodology and epistemology’, pp. 16 - 17. ““His chemical investigations of the same period were also important in the development ideas on method, as discussed above. His astronomical research was only beginning.

of his

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and various astronomers, but also on the methodological literature. Especially important for Herschel were the works of Reid and Brown. Herschel’s debts to these writers have become a matter of some interest in recent years. Kavaloski not only traced the concept of vera causa to Newton’s first Rule of Reasoning, he also offered a most systematic analysis of its use by Newton, Herschel, Whewell, Mill, Lye11 and Darwin.“’ He is quite correct in pointing to the philosophical deficiencies of all these discussions. Wallace offers a very clear and adequate summary of Herschel’s standards for verae causae as expressed in the Discourse.‘20 But neither of these admirable works attempts to connect completely Herschel’s discussion to his actual sources, although they both mention his acknowledgements of Newton and Bacon, and Wallace also briefly refers to both Reid and Brown as holding views on causality related to Herschel’s.“’ Wallace puts Reid’s ideas on causality in the main context of his distinction between metaphysical and physical cause, which Reid calls “efficient” cause and “popular” cause.lz2 Hume had said that all we can know of a [physical] cause is that it constantly precedes its effect. This led Reid to trace some of the absurd conclusions regarding causes to which Hume’s definition necessarily leads us, such as that night causes day and that folly causes wisdom.‘23 Unfortunately, Wallace doesn’t tell us much about what positive suggestions Reid gave in place of Hume’s. Though he mentioned Reid’s approval of Newton’s first Rule of Reasoning and stated that Reid understood the term vera causa “to refer to observable entities or events that can be detected through patient observation and experimentation with nature”, this was not Wallace’s main concern. He does say that the basis for Reid’s faith that there is something more to causality than constant conjunction is the human experience of willed action, in which we act as the efficient cause. This is Reid’s metaphysical sense of cause and it presupposes the action of a Deity in effecting the events of the physical universe, as Wallace makes clear. But this is at best a peripheral issue in judging physical causation, which is something else entirely to Reid. In one passage Wallace has chosen, Reid equates physical cause with laws of nature, to which “we accordingly ascribe power, agency, efficiency”.lz4 In this passage Reid was not primarily concerned with offering his definition of physical cause or with outlining his criteria for recognizing such causes. He was primarily interested in the metaphysical basis of the physical world: the Deity as efficient cause. While “9Kavaloski, ‘The vem mum principle’. ‘“Wallace, Causality and Scientific Explanation, pp. 96“‘Ibid., p. 97 and p. 344, note 115. ‘=Ibid., pp. 44-51. l”Ibid., pp. 49-50. ‘“Ibid., p. 48.

118.

Herschel’s

Optical Researches

31

this aspect of Reid’s ideas on causality impact on Herschel’s methodological criteria

theology, regarding

is also important,

and had a significant

it is not relevant to the discussion of causes. Other passages in Reid’s writings,

not discussed by Wallace, do relate to this topic. Richard Olson places Herschel’s discussion of causality squarely in the lineage of Reid and Brown. He focuses his attention, as did Wallace, on Reid’s rejection of a search for efficient causes in science. For this reason, he stresses that “physical causes” implied to Reid no more than natural law, by which he understood contiguity in space and time and constant conjunction to be the only requirements. ‘25 To this extent, Reid agreed with Hume. Olson briefly addresses Reid’s criteria for true causes elsewhere, where he refers to Reid’s other sense of physical cause in considering his opinion that speculation is of limited utility in science.‘26 Reid accepted that one might speculate about a possible cause of a phenomenon. He required that before such a cause be accepted, it fulfill the familiar requirements of real existence and sufficiency of ,explanation. Here, unlike Herschel, Reid appears more concerned with the first than with the second condition, primarily because he had in mind causes like Descartes’ vortices, Newton’s ether and Hume’s ideas - all of which explained their respective effects well enough, but none of which had been shown to exist.12’ As Reid said, a cause whose existence cannot be demonstrated should be rejected “with disdain, as a fiction which ought to have no place in genuine philosophy”. Olson suggests that these requirements make no sense unless Reid intended the reality of a cause to be judged independently of the effect to be explained. To my knowledge, Reid never made this requirement explicit. In a most interesting passage in his Essays on the Intellectual Powers of Man, Reid used the phenomenon of falling bodies to indicate both what he meant by cause and what qualified as explanation in natural philosophy.“’ According to Reid, Galileo’s explanation of falling bodies was the first to “shew

the cause

of such

appearances,

or to account

for them.

. . “.

All

previous accounts had been “false and fictitious. . . ” Galileo’s explanation consisted of the two “principles” of inertia and of the constancy of the action of gravity. Reid stated these conclusions so as to equate these “causes assigned” with laws of nature, in the form of the propositions:

1z501son, Scottish Philosophy and British Physics, pp. 42 - 48.

i261bid., pp. 40 - 42. ‘*‘Ibid., p. 41. Here Olson quoted two passages from Reid: The Works of Thomas Reid, pp. 236 and 250. These examples do not appear in the quotations, but do appear in Reid, An Inquiry into the Human Mind (Glasgow, 1817), Vol. 1, p. 19 and pussim. ‘“This appears in Thomas Reid, Essays on the Powers of the Human Mind, to which are prefixed, An Essay on Quantity, and an Anafysis of Aristotle’s Logic, 3 vols (Edinburgh: 1819), Vol. 1, pp. 163- 167 (second pagination series). The example here traced accurate, but is yet indicative of Reid’s own understanding of the issues.

is not historically

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First, That bodies once put in motion retain their velocity and their direction, until it is changed by some force impressed upon them. Second/y, That the weight or gravitation

of a body is always the same.lz9

Leaving aside the imperfection of Reid’s science, note that he referred to these laws not only as causes, but as true causes.‘30 He applied the reality standard as confirmation by universal experience and also stated that these causes were “precisely adequate to the effect ascribed to them. . . “. This supports Olson’s characterization of Reid’s understanding of causation as Humean, if we allow that these laws are nothing more than statements of constant occurrence, a point not entirely clear in Reid’s corpus. Following this extended identification of cause with law, Reid surprisingly considered the ether as a possible cause of gravitation. With phenomena, causes and laws all conflated, Reid stated that the ether can be accepted as a cause only if its existence is proven, if its essential property elasticity is demonstrated, and if it is shown that the known properties of gravitation are its necessary consequences. Reid apparently intended the following. First, that both the entity (ether) and its behaviour must be demonstrated directly by observation. Second, that the laws describing the behaviour of the phenomenon to be explained must be deducible from the laws called causes. It is only fair to recall again that Reid was more concerned with issues other than the fine distinctions between causes and laws, and in particular, he wanted to reserve the final honour for efficient causality to God. A much more detailed examination of causality was undertaken by Thomas Brown, in his Inquiry into the Relation of Cause and Effect.13’ Brown, like Reid, went beyond Hume in allowing God to act as an efficient cause, but he stopped short of saying that our idea of causality originates in our own experience of willed action. Indeed, he argued at length against Reid’s position on this.‘32 Brown argued more forcefully than Reid against there being any mystery about physical causality, and insisted that it consists on/y in uniform antecedence and consequence. ‘33Although he was a Scot and a student of Dugald Stewart, Brown did not accept the positions of the Common Sense Philosophers unquestioningly. He considered Reid’s distinction between efficient and physical cause to be an illusion and thought the causal relation to be strictly subjective.‘34 ‘291bid., p. 165. l”Ibid., p. 166.

“‘I have examined the following editions: 3rd edn (Andover, Mass.: Mark Newman, 1822); 4th edn (London, 1835). The American edition appears to be a reprint of the 3rd edn (Edinburgh, 1818), which Herschel used. ‘32Brown, Cause and Effect, Andover edn, pp. 45 - 52. This is the point on which Herschel criticized Brown. See John Herschel, Treatise on Astronomy, p. 232 - 233, footnote. “3Brown, Andover edn, pp. 17 - 44, passim. ‘“Brown, London edn, 1835, pp. xi-xii.

Herschel’s Optical Researches

33

Nevertheless, Brown allowed that the word cause connotes not only constant conjunction, but a belief in the uniformity of this relation in past, present and future.13’ In this he certainly differed from Hume and was much more in line with Herschel’s position. He wrote that knowledge obtained through discreet perceptions is atemporal because of this uniformity. With the subtle introduction of this one word, uniform, Brown completely changed Hume’s definition of causality: It is this mere relation of uniform antecedence [of the cause], so important and so universally believed, which appears to me to constitute all that can be philosophically meant, in the words power and causation.‘36

Despite his argument against objective causality, Brown did occasionally come very close to accepting it in a limited form. Brown did not discuss verae causae, but he did discuss how one can recognize a cause. Beyond the essentials of the relation of causality already enumerated (precedence of cause, antecedence of effect), Brown echoed earlier writers’ requirement of spatial contiguity and insisted that the effect must invariably and immediately follow the cause.13’ Most importantly, however, Brown introduced the term “proximate cause,” saying: “There is, in strictness of language, but one cause, the proximate event, or the proximate combination of circumstances, in the order of priority. . . .“13* He allowed that some elements of these circumstances might act over a long period and others act only for a short while, the former being called predisposing causes and the latter occasional. However, he stated clearly that these were both part of the overall real cause, - the proximate event, of which alone the relation of invariable priority can be asserted, - being the whole aggregate of circumstances, thus combined, at the moment before the commencement of the change of which we speak.‘39

Despite Brown’s failure to address the issues of the reality and sufficiency of causes, he had introduced new dimensions to the discussion of causality at just the time that Herschel was beginning to refine his ideas on the topic. VIII. Causality in Herschel’s Optical Works of the 1820s Herschel borrowed extensively from both Reid’s and Brown’s ideas on causality. Some of this came very early, as in Herschel’s references to reality “‘Brown, Andover edn, p. 76. l”Brown, London edn, 1835, pp. 11 - 12. “‘Ibid., pp. 16 and 24. “‘Brown, Andover edn, 1822, pp. 67-68. ‘“Ibid., pp. 68 - 69.

34

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and sufficiency of causes in 1819, to proximate causes in 1820, and to what is essentially Brown’s predisposing causes also in 1820. Herschel used these ideas repeatedly in discussing optical issues following the paper on biaxial dispersion. While none of this constituted significant development of the methodological concepts, it at least illustrates Herschel’s continuing interest in metascience. Also, several of Herschel’s innovations regarding causation appeared in this period and he began to form positions which later appeared in the Preliminary Discourse in 1830. After the memoir on biaxial dispersion, Herschel did not incorporate metascientific concepts so directly into his presentation of scientific results. Nonetheless, he repeatedly hinted at his continuing concern with the issues surrounding causality and its demonstration. The research on biaxial dispersion led Herschel quickly into a closer examination of deviation of tints in uni-axial crystals, especially apophyllite. This sustained interest in the secondary cause of tint deviation produced two memoirs. 140 Herschel saw this research as leading to a “more intimate knowledge of the nature and laws of those forces by which the ultimate particles of matter act on light and on each other.“14’ He thought this optical character could help explain the internal structure of crystals. Continuing to speak of a law that “regulates the intensity” of a force, Herschel cautioned against “attempts to generalize antecedently to experience” in crystalline optics. 14*That is, Biot had again sinned with an over-hasty generalization. After a long rendering of experimental results, Herschel concluded again that this second cause-differences in the scale of action of a uniaxial crystal on differently coloured rays- certainly existed. It was just as he was finishing this article that Herschel wrote to Brewster: I ought to observe that prior to my receiving your letter. . . it was not possible for me to suppose from anything in your papers. . . that the real proximate causes of the deviation - (i.e. the separation of the axes, and the difference of the laws of action of diff’ crystals on the different colours) were known to you or any other observer. I43

“‘On certain remarkable instances of deviation from Newton’s scale in the tints developed by crystals, with one axis of double refraction, on exposure to polarized light’, Combridge Philosophical Society Transactions 1 (1822), 21- 42; ‘On a remarkable peculiarity in the law of the extraordinary refraction of differently-coloured rays exhibited by certain varieties of apophyllite’, Cambridge Philosophical Society Transactions 1 (1822), 242 - 248. “‘Ibid., Vol. 1, p. 21. “21bid., Vol. 1, pp. 23 - 24. “‘Letter of Herschel to Brewster, 3 February 1820. RSL.HS.20.84. Herschel considered this passage so important that he copied it into his diary, not his usual practice: UT.WOOO2.Herschel finished the article on 19 February. The Brewster letter referred to may be 9 December 1819, RSL.HS.4.250.

Herschel’s Optical Researches

35

Later that spring, Herschel again wrote to Brewster of what ought to be meant by analogy in physical speculations, of “some remote and general cause capable of producing” certain phenomena, and the “immediate cause” of a phenomenon. All these terms appear in Brown’s Cause and Effect, indicating that Herschel was weighing his and others’ optical research against this methodological background.14 In another crystalline-optical research regarding an optical property of quartz, demonstration of a causal relationship again claimed Herschel’s attention.14’ Biot had earlier discovered that the plane of polarization of light transmitted along the optical axis of a quartz plate rotates: clockwise in some crystals, counter-clockwise in others. Today called optical activity, this phenomenon was then termed “rotatory polarization”. Generally one cannot tell from looking at a crystal which direction it will rotate light. Herschel, however, discovered that in certain crystals, called plagiedral, a set of unusual faces may be used to predict this direction. The task of his investigation was to establish whether the plagiedral faces and the rotatory polarization share a common cause: “a cause constantly in action. . . “.‘46 Given what he called the “precise analogy” between them, Herschel already thought a common cause was probable. To demonstrate this, Herschel wrote, required an “invariable relation”. This was, of course, the standard advocated by Hume, Reid and Brown. Interestingly, Herschel mixed this standard with the requirement for the reality of a cause and claimed that testing of invariable relation was a way of “verifying or disproving the existence of such a cause. . . “.14’ His standards for reality of a cause were clearly broader than those of his predecessors, and unlike Hume and Brown, he interpreted constant conjunction as a sign of the objective existence of a cause. Herschel set about examining numerous specimens. Although the relation was indeed invariable, Herschel was cautious: The induction from so many instances without an exception seems conclusive, and we are authorized to state it [the invariable connection1 as a fact, general as far as our present observations go. . . “* The problem was how one transforms constant association in the past into a certain and timeless connection. Herschel took the options presented by Reid and Brown and simply accepted the uniformity of nature, calling induction ‘“Brown, Cause and Effect, Andover edn, 1822, pp. 68 - 69. “‘Herschel, ‘On the rotation impressed by plates of rock crystal on the planes of polarization of the rays of light, as connected with certain peculiarities in its crystallization’, Cambridge Philosophical Society Transactions 1 (1822), 43-52. This article was completed on I5 March 1820. l”Herschel, ‘Rotation’, p. 45. 14’Herschel, ‘Rotation’, pp. 47 - 48. IsHerschel, ‘Rotation’, p. 49.

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an operation of the mind. Past connection “leads to the expectation of . . . future recurrence.“‘49 But being a practicing scientist rather than a philosopher, Herschel needed a practical indicator of when he could legitimately make a general claim. He first multiplied his inductive base by examining numerous plates cut from eight different plagiedral crystals. Then he introduced a standard which was to become associated with his name: prediction. He predicted directions in which light would be rotated in some previously untried specimens. Confidence in this method rested on Herschel’s assurance of the uniformity of nature, which Brown had stressed.“’ Although Herschel published few optical memoirs after this series, he kept abreast of new work by Fresnel and others. His long article “Light” for the Encyclopedia Metropolitana, written between 1824 and 1827, required him to “feat-n at the same time that I teach”.“’ Much original research is in fact hidden in the dispassionate, third-person tone of this work. Herschel purposefully avoided any discussion of “misconceived facts and over-hasty generalizations” in “Light” and concentrated instead on the general facts and laws that were “well enough established. . . “.15’ But in fact he did not shy away from either theory or method. It was here that Herschel explicitly used the term Vera causa for the first time. Interestingly, he used it in his discussion of Fresnel’s undulatory explanation of the colours produced by polarized light in crystals: exactly the context in which he had originally used Biot’s corpuscular theory.‘53 Without detailing Fresnel’s theory, suffice it to say that Herschel protrayed certain of what were originally assumptions in Fresnel’s work as demonstrated facts. One he said could be made “a matter of ocular demonstration. . . “. Stated broadly, Fresnel’s theory supposed that crystalline plates change the polarization of the incident ray, breaking it into two rays polarized in opposite planes. “[Tlhis cause”, he wrote, “is what in Newton’s language would be termed a vera coma, a cause actually in existence. . . “. 154 Between about 1818 and 1827, optics was one of the most vibrant and quickly changing sciences. Herschel was one of the few scientists who actively participated in this research throughout the period and who was intimately aware of the details of both the corpuscular and the wave theories. Concurrently, he was becoming familiar with the metascientific discourse of lq9Letter of Herschel to Babbage, 19 March 1820, RSL.HS.2.130. His caution, of course, was born of constantly battling against over-hasty generalizations. ““Herschel, ‘Rotation’, p. 49. “‘Letter of Herschel to Francis Lunn, 5 January 1825, RSL.HS.11.412. Herschel, ‘Light’, Encyclopediu Metropofitano (London, 1845), Vol. 4, pp. 341- 586. Herschel began distributing copies of this in 1828. “‘Herschel, ‘Light’, p. 515. 15’Zbid.,pp. 524-525. ls4Zbid., p. 524.

Herschel’s

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37

Newton, Reid and Brown. While he began by using the terms of this discourse exclusively with regard to general laws and the discovery of proximate causes, i.e. on what was to become his “First Level of Induction”, he came to apply it in more theoretical contexts, too. Consequently, Herschel formed his ideas on causality and on method generally in the context of the critical problems of chromatic polarization and double refraction. IX. Conclusion:

Herschel

on the Causal Relationship

and the Standards

for

verae causae This article has attempted to give a more complete interpretation of John Herschel’s ideas on method in three ways. First, it has placed his method in the context of his science, especially of his optics. Secondly, it has compared his early statements on method with those of figures whom we are reasonably certain he read. And it has, finally, paid particular attention to his ideas on method in the “First Stage of Induction,” i.e. in the discovery of new laws and proximate causes. This last emphasis is a particular benefit of having read Herschel’s scientific publications and manuscripts with method in mind. It is important that historians and philosophers of science shift some of their attention to this level of methodology, since so much scientific research has this character. Equally important, this level of methodology is intimately connected with the level relevant to high theories such as Lyellian geology or the wave theory of light. This examination of the relation of Herschel’s method and science may be completed with another look at his Discourse. His first self-consciously methodological work since “Mathematics” profited from over a decade of research experience. This experience particularly helped Herschel to elaborate his ideas on the causal relationship and on the standards for verae causae. As with other methodological issues, the Discourse was Herschel’s opportunity to temper philosopher’s pronouncements on causality with the lessons of the laboratory and the notepad. Wallace is quite correct to say that Herschel had a stronger notion of causality than did Hume, one more in line with Reid.155 Indeed, it was stronger even than Reid’s. Herschel fully believed in the objectivity of causality. In a famous passage, Herschel criticized those metaphysical writers who “reason away the connection of cause and effect, and fritter it down into the relation of habitual sequence. . . “. 156He was thinking particularly of Brown, not Hume or Auguste Comte. He continued, saying that we are as certain that the causal relation is “some more real and intimate connection” as ‘SJWallace, Causality and Scientific Explanation, p. 97. “6Herschel, A Treatise on Astronomy, p. 232. Thomas footnote on this page.

Brown

is discussed

in Herschel’s

38

Studies in History and Philosophy of Science

we are of the existence of an external world. He certainly did not agree with Reid’s assessment that causes are simply laws of nature. Laws and causes were distinct in Herschel’s lexicon. Herschel never doubted the objectivity of causality in the Discourse. Indeed, the philosopher’s first task when presented with a new phenomenon, he wrote, “is its explanation, or reference to an immediate producing cause”.‘57 In the first level of induction, Herschel allowed that science has two goals: laws of nature and proximate causes. Hence, although he disagreed with Brown over the objectivity of causation, he eagerly employed his concept. Science aimed at “the discovery of an adequate proximate cause. . . .“, and again, “antecedent phenomena, or causes (meaning at present merely proximate causes). . , “. This is the level at which Herschel primarily worked in 1819 and it was in this context that his first standards for verae causae were developed. In the Discourse, he explicitly equated his adequate proximate cause with Newton’s verae causae. Such a cause is a phenomenon, antecedent to the phenomenon to be explained, and adequate to its explanation. Like Reid, Herschel required verae causae to have a “real existence in nature” and not be “mere hypotheses or figments of the mind”.“’ Herschel chose his first two examples of verae causae from geology, perhaps because the recent publication of Charles Lyell’s Principles of Geology had attracted fresh attention to “this deservedly popular science. . . “.159 The first example was the occurrence of sea-shells on dry land, especially at high elevation. Herschel rejected as possible causes: a plastic virtue in the soil and celestial influence (both “figments of fancy”); being dropped by pilgrims (a “real cause”, but inadequate to explain the numbers of shells found), and fermentation (also a “real cause”, but never witnessed to produce such an effect). On the other hand, he accepted the death of shellfish, their falling to the ocean bottom and the gradual elevation of the sea bed as an event “witnessed so often, and on such a scale, as to qualify it for a vera causa..

.“.I@

The other geological phenomenon that required explanation was the apparent cooling of the earth’s climate over the eons. Herschel ruled out two candidate causes immediately because their existence was not demonstrated. No-one had shown that the earth cooled from “absolute fusion” to its present state, nor that the level of volcanic activity had decreased since primeval times. But he accepted as a Vera causa Lyell’s explanation that as continents erode and sea bottoms are elevated, the distribution of land masses can change climate. This cause, he wrote, is a “demonstrated fact” (i.e. it is real) and its “‘Herschel, Discourse, “‘Ibid. ‘J91bid.,p. 145. ‘@Ibid.

p. 144

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Herschel’s Optical Researches

influence on climate is “a perfectly fair conclusion, from what we know. . . by actual observation”.161 Even on this first level, however, there is an important nuance that scholars have not noted. Herschel did not maintain that the verue causae he discussed were beyond doubt the causes of the phenomena. Instead, they were causes “available in sound philosophy” and “on which a philosopher may consent to reason. . . “. He made this plain by considering an alternative Vera causa for climatic cooling. The earth’s orbit gradually is becoming more circular through the lengthening of its semi-minor axis. Hence, on average, the earth is further from the sun now than in former times and it should receive less solar heat. Here is a second Vera causu of cooling for philosophers to consider: it is an astronomical fact of “sufficient universality”; subject to exact estimation; and it acts in the right direction. But since Herschel explicitly stated that the adequacy of each of these causes was yet to be judged, he apparently had reduced verae causae to merely real causes.‘62 While in the first stage of induction, the evidence of the reality of a cause was in its direct observation, in the second stage Herschel employed other criteria. Indeed, it was here that Herschel’s Vera cm.~~adiffered most from Reid’s. The second stage was the realm of theory, where the “mind is more disencumbered of matter, and moves as it were in its own element”.‘63 Herschel’s consideration of theories such as the corpuscular and wave theories led him to place greater emphasis on the criterion of sufficiency and to replace the requirement of reality with one of analogy. Even in the 1819 research Herschel was concerned with the evaluation of higher level generalizations, in this case particularly the corpuscular theory. While most of the 1820 memoir was an effort to establish the two proximate causes of deviant tints, the investigation was largely motivated by Herschel’s familiarity with Biot’s theory that chromatic polarization phenomena are produced by the oscillations of luminous molecules. This last term occurs repeatedly in the memoir. Far from naive acceptance, Herschel saw that the anomalous tints of biaxial crystals presented an apparent “radical and unanswerable objection to the theory of M. Biot. . . “.la Demonstration of the reality and sufficiency of the lower level verue cuusae did not prove to him that light is indeed made of oscillating corpuscles. And Herschel had no way to show that these corpuscles were real. But this exercise did show that this hypothesis was adequate to the explanation - and the detailed calculation of the phenomena then known. As Herschel stated:

16’Ibid., pp. 145 - 147. ‘“Ibid., pp. 147- 148. ‘“Ibid., p. 190.

‘“Herschel,

‘On the action of crystallized

bodies on homogeneous

light’, p. 48.

40

Studies in History and Philosophy of Science . . by the easy and complete explanation affords of all the more perplexing anomalies

this principle [i.e. biaxial dispersion] in the tints, [Biot’sl theory of alternate

polarization. . . stands relieved from every difficulty, and may now be received as fully adequate to the representation of all the phenomena of the polarised rings.‘65

Herein lies the origin of Herschel’s attitudes towards both hypotheses standards for verue causae in higher level generalizations.

and the

In the Discourse, Herschel required that the agents or causes on which a theory is based not be “arbitrarily assumed”. He required explicitly that these agents be verae causae: “such as we have good inductive grounds to believe do exist in nature, and do perform a part in phenomena analogous to those we would render an account of. . . “.‘66 Despite the seeming certainty of this demand for verse causae, its criteria are somewhat relaxed from those of the first level. Reality is judged here on merely “good inductive grounds”, not ocular demonstration. This is clarified in the example of the ether, the primary agent of the wave theory. Herschel had no direct evidence of the existence of the ether, but he instanced three phenomena as indirect evidence. According to Joseph Fourier, the temperature of interplanetary space is higher than what the sun and the stars can cause. By analogy with other elastic media, however, Herschel supposed the ether to have a temperature and a specific heat.16’ This would explain the surplus temperature of space. His second phenomenon was the movement of Encke’s comet around its orbit. This comet, Herschel wrote, returns somewhat earlier than Newtonian planetary theory predicts it should. The resistance of an all pervasive ether could explain this anticipation. That is, it is sufficient to explain this phenomenon.‘68 But Herschel felt his strongest argument for the veru causa status of the ether lay in optical phenomena. The wave theory depended directly on this supposed cause. The most severe tests demonstrated the adequacy of this theory to account for optical phenomena. Moreover, as Herschel wrote

it may happen (and it has happened in the case of the undulatory doctrine of light) that such a weight of analogy and probability may become accumulated on the side of an hypothesis, that we are compelled to admit one of two things: either that it is an actual statement of what really passes in nature, or that the reality, whatever it

‘6’lbid., p. 50. It should be noted that while Herschel’s 1819 work was originally stated in corpuscular language, i? withstood the transition to Fresnel’s wave theory. Herschel interpreted these phenomena in terms of that theory in ‘Light’, p. 521. ‘“Herschel, Discourse, p. 197. 16’Ibid., pp. 157- 158. ‘“Ibid., pp. 156- 157.

Herschel’s Optical Researches

41

be, must run so close a parallel with it, as to admit of some mode of expression common to both, at least in so far as the phenomena actually known are concerned.‘@

If the supposed cause acted in close analogy with other known causes, and if it accounted for the phenomena, then Herschel called this cause true. His standards for verge causae were wider than Newton’s or Reid’s, and this was largely because of his optical investigations. This article has been an attempt to show the richness of Herschel’s ideas on causality and their roles in his methodology, and to indicate something of the importance both of his scientific practice and of the methodological literature in a long process of mutual development. It doesn’t answer every question about the relations of Herschel’s science and method, but it does, I think, show that the relationship cannot be ignored. Method as practiced tempers and informs our evaluation of method as preached. While the explicitly methodological literature is essential to the history of method, an overemphasis on metascientific writings, such as Brown’s Cause and Effect or Herschel’s Discourse, may produce over-hasty generalizations and false categorizations. The scientific writings provide one way to separate these impurities at least partially from the sacred river of antiquity to which Herschel referred.

‘“Zbid., pp.

196-

197.