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“The main Business of natural Philosophy” pp 179–224Cite as

Facing the Limits of Deductions from Phenomena: Newton’s Quest for a Mathematical-Demonstrative Optics

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Part of the book series: Archimedes ((ARIM,volume 29))

Abstract

In this chapter, I shall elaborate on the claims made by the late I. Bernard Cohen according to which Newton’s methodological ideal of “deducing causes from phenomena,” on which we have elaborated on in Chapters 2 and 3, was not equally attainable in the study of optical phenomena. If his suggestion is correct, then in The Opticks, the apex of his optical researches, which in fact contained a set of separate but interrelated theories, Newton failed to rigidly establish these theories in the same way as he had established the theory of universal gravitation in the Principia. By contrasting Newton’s methodology in the Principia, as previously characterized, to the method by which theoretical and causal conclusions are established in The Opticks, I shall attempt to explain why Newton was less successful to accommodate optical phenomena according to his own methodological desiderata of deducing causes from phenomena.

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Notes

  1. 1.

    First English edition: 1704; first Latin edition: 1706; second English edition: 1717 (reissued in 1718); second Latin edition: 1719; third English edition: 1721; fourth posthumous English edition: 1730.

  2. 2.

    CUL Add. Ms. 3975, ff. 1r–22r. This tract is transcribed in McGuire and Tamny, eds., Certain Philosophical Questions, pp. 466–489. Newton’s earlier Questiones quaedam philosophicae (= CUL Add. Ms. 3996, ff. 122r–124v [ca. 1664]) contained a number of short sections related to optics, which were primarily based on material from Robert Boyle’s Experiments and Considerations Touching Colours (1664) (Lohne, “Isaac Newton: The Rise of a Scientist, 1661–1671”).

  3. 3.

    Cohen, ed., Isaac Newton’s Papers and Letters on Natural Philosophy, pp. 47–59. The unedited version, which Newton sent to Henry Oldenburg on 6 February 1671/2, is to be found in Newton, Correspondence, I, pp. 92–107.

  4. 4.

    McGuire and Tamny, eds., Certain Philosophical Questions, p. 389.

  5. 5.

    When Newton became Lucasian Professor in 1669 he was required to submit a selection of 10 lectures he had given during the academic year for deposit in the University Library. The Lectiones opticae thus predate his first optical paper. Whilst Newton was working on his first optical paper in 1671/72, he had also begun on a revision (Optica) of the Lectiones opticae, which was published posthumously in 1729 (Newton, Lectiones opticae). The material related to Newton’s optical lectures can be found in two manuscripts: the Lectiones opticae proper (CUL Add. Ms. 4002) and Optica, the later variant of the Lectiones opticae (CUL Ms. Dd.9.67). Both are transcribed in Shapiro, The Optical Papers of Isaac Newton, I.

  6. 6.

    Cohen, ed., Isaac Newton’s Papers and Letters on Natural Philosophy, pp. 178–199; Newton, Correspondence, I, pp. 362–392.

  7. 7.

    OEL 1 , [iii]. Cf. Cohen, “Versions of Isaac Newton’s First Published Paper”, p. 359. For details on the composition of The Opticks, see especially: Shapiro, “Beyond the Dating Game: Watermark Clusters and the Composition of Newton’s Opticks”, pp. 198–226.

  8. 8.

    Cohen, “The Case of the Missing Author: The Title Page of Newton’s Opticks (1704)”, pp. 18–19.

  9. 9.

    Newton, Correspondence, III, p. 336.

  10. 10.

    Apart from two corrected calculations in Part I, Book I of The Opticks remained unchanged in all editions. With the exception of the introduction of an extra paragraph, which remained unchanged in all later editions, at the end of Proposition VIII of Part III in the second edition (OE 2, pp. 242–244), Book II of The Opticks remained nearly unchanged in all editions. Book III remained the same in all editions, except for the concluding Queries. In the first edition, The Opticks contained 16 Queries. In the second edition, Newton inserted 15 additional Queries – while also extending Queries 8, 10, 11, and 16 (ibid., pp. 313–382). The Queries added in the second edition remained unchanged in all later editions.

  11. 11.

    Cf. Westfall, Never at Rest, pp. 797–798. This is most certainly the case for the third book of which Newton himself admitted that the arguments contained in it were imperfect. In the introductory section to the Queries Newton, wrote: “And since I have not finish’d this part of my Design, I shall conclude with proposing only some Queries, in order to a farther search to be made by other.” (Newton, The Opticks, p. 339). Colin MacLaurin pointed out: “He [i.e., Newton] knew where to stop when experiments were wanting, and when the subtility of nature carried things out of his reach: nor would he abuse the great authority and reputation he had acquired, by delivering his opinion concerning these, otherwise than as matter of question.” (MacLaurin, An Account of Sir Isaac Newton’s Philosophical Discoveries, p. 10; cf. Desaguliers, A Course of Experimental Philosophy, vol. II, p. 403).

  12. 12.

    Newton, The Opticks, cxxi. For the reasons prodding Newton to publish The Opticks, see: Cohen, “Versions of Isaac Newton’s First Published Paper”, pp. 359–361. After the publication of the first edition The Opticks, Newton commissioned Samuel Clarke to make a Latin translation which appeared in 1706 as Optice. After having praised Newton for his experimental-mathematical method of demonstration in the Principia by which Newton had dispensed with “fictitious hypotheses” and “capricious conjectures” (OEL 1 , [i]), Samuel Clarke pointed out in his Præfatio Interpretis that the Latin translation was begun by the order of the author and absolutely approved by the same person (“Id hic certior faciendus est Lector, hanc Versionem & Authoris jussu incoeptam, & eodem approbante absolutam” (ibid., [ii])).

  13. 13.

    Newton, The Opticks, p. 1.

  14. 14.

    Cohen, “The Case of the Missing Author”, pp. 18–23.

  15. 15.

    Shapiro, “Newton’s Experimental Investigation of Diffraction for the Opticks: A Preliminary Study”, pp. 63, 70.

  16. 16.

    Ibid., pp. 317–338.

  17. 17.

    CUL Add. Ma. 3970, f. 244v, cf. f. 286r [ca. 1700–1704].

  18. 18.

    Ibid., f. 242r [ca. 1700–1704]. Newton was not simply “propounding Hypotheses” but offering “Quaeres to be examined by experiments” (Newton, “Manuscript in Miracles”, Lehigh University Libraries, Bethlehem (Pennsylvania), f. 1v; quoted from: Dobbs, The Janus Faces of Genius, p. 230). Cf. [Newton], “An Account of the Book entitled Commercium Epistolium”, p. 222. On the evolution of “queries” in Newton’s thought, see Anstey, “The Methodological Origins of Newton’s Queries”.

  19. 19.

    Cohen, “The Case of the Missing Author”, pp. 22–23.

  20. 20.

    Cohen, Franklin and Newton, p. 192.

  21. 21.

    See Guerlac, Essays and Papers in the History of Modern Science, pp. 212–215 for related objections against Cohen’s assessment.

  22. 22.

    Newton, The Opticks, Book I, Part I, Proposition I, pp. 20–72.

  23. 23.

    Ibid., p. 405.

  24. 24.

    Cohen, The Newtonian Revolution, pp. 134–135, cf. pp. 136, 141.

  25. 25.

    Cohen, “The Case of the Missing Author”, p. 41.

  26. 26.

    Shapiro, Fits, Passions, and Paroxysms, pp. 22–23.

  27. 27.

    Cf. “While he [= Newton] considered causal explanations to be desirable, they never play an essential or necessary role in his science.” (Shapiro, “Newton’s Optics and Atomism”, p. 228).

  28. 28.

    Hakfoort, “Newton’s Opticks and the Incomplete Revolution”, p. 103.

  29. 29.

    Ibid., p. 109.

  30. 30.

    See Section 4.6 in this chapter.

  31. 31.

    Shapiro, “Newton’s Optics and Atomism” and Westfall, Never at Rest, pp. 159–163. For Newton’s early corpuscular model see: Bechler, “Newton’s Search for a Mechanistic Model of Colour Dispersion” and id., “Newton’s Laws of Forces which are Inversely as Mass”.

  32. 32.

    E.g., McGuire and Tamny, eds., Certain Philosophical Questions, p. 585. On CUL Add. Ms. 3970, f. 289r, Newton wrote: “I have therefore proposed the Question whether the rays of light may not be small bodies emitted by shining substances” (cf. ibid., f. 299r). He added furthermore that the resemblance between rays and bodies is “very great:” “For such ↓such↓ bodies will pass through uniform Mediums in right lines without bending into the shadow wch is the property of the rays of light.” (ibid., f. 289r).

  33. 33.

    Shapiro, Fits, Passions, and Paroxysms, pp. 12–40; Ihmig, “Newton’s Program of Mathematizing Nature”. In Query 31 Newton wrote: “Even the Rays of Light seem to be hard Bodies; for otherwise they would not retain different Properties in their different Sides.” (Newton, The Opticks, p. 389).

  34. 34.

    Shapiro, Fits, Passions, and Paroxysms, pp. 77–78. In the same period Newton came to accept non-mechanical “vegetable spirits” (Dobbs, “Newton’s Alchemy and His Theory of Matter”, p. 515).

  35. 35.

    For instance, Abdelhamid I. Sabra has claimed that Newton’s rays were always those of the corpuscular theory and that a wave interpretation was denied a priori (Sabra, Theories of Light from Descartes to Newton, p. 288, cf. p. 284).

  36. 36.

    Cohen, ed., Isaac Newton’s Papers and Letters on Natural Philosophy, p. 179; Newton, Correspondence, I, p. 363. Cf. Westfall, “The Development of Newton’s Theory of Color”, pp. 352–353.

  37. 37.

    CUL Add. Ms. 3970, f. 296r [ca. 1700–1704; italics added].

  38. 38.

    Newton, The Principia, p. 626 [italics added].

  39. 39.

    Newton, The Opticks, pp. 1–2.

  40. 40.

    Laymon, “Newton’s Experimentum Crucis and the Logic of Idealization and Theory Refutation”, p. 61.

  41. 41.

    Hooke to Oldenburg, 15 February 1671/2, Newton, Correspondence, I, p. 114; Hooke, Micrographia, p. 57.

  42. 42.

    Hooke, Lampas, p. 39.

  43. 43.

    Shapiro, “Kinematic Optics”, p. 194.

  44. 44.

    Hooke, Lampas, p. 39.

  45. 45.

    Hooke to Oldenburg, 15 February 1671/2, Newton, Correspondence, I, p. 114. See Laymon, “Newton’s Experimentum Crucis”, pp. 64–65 for an opposing view.

  46. 46.

    Shapiro, “The Evolving Structure of Newton’s Theory of White Light and Color”, p. 208 [italics added].

  47. 47.

    Ibid., p. 196. Huygens’ optical theory for instance was compatible with Newton’s definition, for Huygens’ principle is compatible with Newton’s criteria of successiveness and contemporaneity.

  48. 48.

    We know that in these early years Newton read Kepler’s Paralipomena (1604), Descartes’ optics (La Dioptrique and Météores (1637)), Isaac Vossius’ De lucis natura et proprietate (1662), Robert Boyle’s Considerations of Colours (1664), Robert Hooke’s Micrographia (1665), Francisco M. Grimaldi’s Physico-mathesis de lumine, coloribus, et iride (1665) and Isaac Barrow’s Lectiones LVIII and his Lectiones Geometricae. On 7 July 1670, Barrow sent Newton the published copies of his Lectiones XVIII and his Lectiones Geometricae, which Newton had previously proofread – they were bound together as one copy (Wren Library, NQ.16.181). The former contains signs of dog-earing on: pp. 24, 32, 40, 70, 72, 78, 80, 83, 88, 94, 96, 102, 104, 110, 112, 118–120 and one correction on p. 25. The latter contains signs of dog-earing on: [p. i], pp. 6, 8, 38, 40, 46, 48, 50, 51, 54, 56, 89, 91–92. Newton did not read Marcus Marci’s Thaumantias, Liber de arcu cœlesti deque colorum apparentium natura, ortu, & causis (1648) which was not available to him. For a recent and interesting piece on Marci, who came close to endorsing a theory similar to Newton’s, see: Garber, “Chymical Wonders of Light: J. Marcus Marci’s Seventeenth-century Bohemian Optics”. In his Physiologia Epicuro-Gassendo-Charletoniana or A Fabrick of Science Natural, Upon the Hypothesis of Atoms, which Newton had read, Walter Charleton defended a corpuscular account of light in the chapter entitled “The Nature of Light.”

  49. 49.

    Newton to Oldenburg, 6 February 1671/2, Newton, Correspondence, I, p. 93; Cohen, ed., Isaac Newton’s Papers and Letters on Natural Philosophy, p. 49; cf. Newton, The Opticks, p. 28.

  50. 50.

    On an interesting note, see Topper, “Newton on the Number of Colours in the Spectrum”.

  51. 51.

    E.g., Westfall, “The Development of Newton’s Theory of Color”, p. 341; Shapiro, “Kinematic Optics”, p. 190. Shapiro notes that: “Descartes’s refraction model, which was based solely on mechanical parameters – the velocities of the light corpuscles and “impulses” normal to the refracting surface – made a profound and enduring impression on Newton, both as a persuasive example of how all nature might be reduced to similar mechanical principles and also in its own right as a mathematical model of a general optical law, which Newton quickly incorporated into his own investigations of refraction and dispersion.” (Shapiro, ed., The Optical Papers of Isaac Newton, I, pp. 7–8; Shapiro, Fits, Passions, and Paroxysms, p. 8). On Descartes’ optical research, see Buchwald, “Descartes’ Experimental Journey Past the Prism and through the Invisible World”.

  52. 52.

    Newton to Oldenburg, 6 February 1671/2, Newton, Correspondence, I, p. 92; Cohen, ed., Isaac Newton’s Papers and Letters on Natural Philosophy, p. 48.

  53. 53.

    Newton, The Opticks, p. 31.

  54. 54.

    In his Lectiones Opticae, which were inaccessible outside Cambridge at the time, Newton made this point more explicit, and offered a geometrical demonstration of equality of shape between the optical source and the refracted image (Shapiro, ed., The Optical Papers of Isaac Newton, I, pp. 53–61, pp. 285–293), which was accompanied by an illustration (ibid., I, p. 52 and 286 [for the illustration]). In the fourth and posthumous edition of The Opticks references to Newton’s Lectiones opticae were added. In The Opticks Newton did not emphasize the certainty of the outcome of the experimentum crucis as he had done in his first optical paper (Shapiro, “The Evolving Structure of Newton’s Theory of White Light and Color”, pp. 216–217).

  55. 55.

    Shapiro, ed., The Optical Papers of Isaac Newton, I, pp. 62–65; Newton, The Opticks, Proposition II, Book I, Part I, pp. 38–40.

  56. 56.

    Lohne, “Newton’s Experimentum Crucis”, pp. 172–173; Kuhn, “Newton’s Optical Papers”, pp. 34–35.

  57. 57.

    See, furthermore, Raftopoulos, “Newton’s Experimental Proofs as Eliminative Reasoning”.

  58. 58.

    Newton to Oldenburg, 6 February 1671/2, Newton, Correspondence, I, p. 93; Cohen, ed., Isaac Newton’s Papers and Letters on Natural Philosophy, p. 48; Shapiro, ed., The Optical Papers of Isaac Newton, I, pp. 74–75, 304–306.

  59. 59.

    Newton to Oldenburg, 6 February 1671/2, Newton, Correspondence, I, p. 93; Cohen, Isaac Newton’s Papers and Letters on Natural Philosophy, p. 48; cf. Shapiro, ed., The Optical Papers of Isaac Newton, I, pp. 74–75.

  60. 60.

    Newton to Oldenburg, 6 February 1671/2, Newton, Correspondence, I, p. 93; Cohen, ed., Isaac Newton’s Papers and Letters on Natural Philosophy, pp. 49–50.

  61. 61.

    Newton to Oldenburg, 6 February 1671/2, Newton, Correspondence, I, p. 94; Cohen, ed., Isaac Newton’s Papers and Letters on Natural Philosophy, p. 50.

  62. 62.

    See, e.g., Westfall, Never at Rest, pp. 213–214; Newton, The Opticks, pp. 46–48; Shapiro, “The Evolving Structure of Newton’s Theory of White Light and Color”; and, esp. Mills, “Newton’s Prisms and his Experiments on the Spectrum”. Again, it should be stressed that the experiment is idealised. As Laymon has pointed out, Newton assumed that the rays refracted by the second prism were of a single colour (Laymon, “Newton’s Experimentum Crucis”, pp. 51–77, 53, 56; cf. Newton to Oldenburg, 6 February 1671/2, Newton, Correspondence, I, p. 102; Cohen, ed., Isaac Newton’s Papers and Letters on Natural Philosophy, p. 59). This will be the case only if the ray has an equal breadth as the hole in the second board. The conclusion of the experimentum crucis in support of a one-to-one correspondence between colour and a specific degree of refrangibility succeeds on the assumption that an idealised description of the resultant image is used (ibid., pp. 69–70). The term experimentum crucis was first used by Boyle (Robert Boyle, Defence against Linus (1662), in: Boyle, The Works of Robert Boyle, III, p. 50), who derived it from Bacon’s instantia crucis (Bacon, The Works of Francis Bacon, I, Instauratio magna, Novum Organon., II.xxxvi, p. 436). Hooke had used the term experimentum crucis in his An Attempt to prove the Motion of the Earth from Observation, p. 2 and in his Micrographia, p. 54.

  63. 63.

    Newton’s first optical paper did not contain a figure of the experimentum crucis, which added to difficulty of understanding the configuration of the experiment. In fact, even Henry Oldenburg and Samuel Horsley gave mistaken figures to illustrate the experimentum crucis (Lohne, “The Increasing Corruption of Newton’s Diagrams”, pp. 72–73).

  64. 64.

    Schaffer, “Glass Works: Newton’s Prisms and the Uses of Experiment”, p. 74; Westfall, “The Development of Newton’s Theory of Color”, p. 341; Shapiro, Fits, Passions, and Paroxysms, pp. 6–8. Newton’s underlying premise is that radiant colours have a conceptual primacy over those of natural bodies (Shapiro, Fits, Passions, and Paroxysms, pp. 6–7).

  65. 65.

    In his Trinity Notebook in the section entitled “On Colours,” Newton had already pointed to the different refrangibility of light without proceeding further to the conclusion that white light consists of rays differently refrangible (McGuire and Tamny, eds., Certain Philosophical Questions, p. 468; CUL Add. Ms. 3996, f. 122v). The evidence adduced there was based on observations made by looking through a prism. See the editorial introduction to Shapiro, ed., The Optical Papers of Isaac Newton, I, pp. 1–25 for Newton’s early optical work.

  66. 66.

    Worrall, “The Scope, Limits, and Distinctiveness of the Method of ‘deduction from the phenomena’”, pp. 56–57.

  67. 67.

    Newton to Oldenburg, 6 February 1671/2, Newton, Correspondence, I, p. 95; Cohen, ed., Isaac Newton’s Papers and Letters on Natural Philosophy, p. 51.

  68. 68.

    Newton gave a total of 13 points (Newton to Oldenburg, 6 February 1671/2, Newton, Correspondence, I, pp. 97–100; Cohen, ed., Isaac Newton’s Papers and Letters on Natural Philosophy, pp. 53–57).

  69. 69.

    This sentence contains a criticism on the Aristotelian account of light according to which light is a quality (Shapiro, ed., The Optical Papers of Isaac Newton, I, pp. 78–85, 434–437; Cohen, “Versions of Isaac Newton’s First Published Paper”, pp. 364–366 and Mamiani, Isaac Newton filosofo della natura, pp. 39–67). Somewhat later in his paper Newton wrote: “These things being so, it can no longer be disputed, whether there be colours in the dark, nor whether they be the qualities of the objects we see, nor perhaps whether Light be a Body. For, since Colours are the qualities of Light, having its Rays for their intire and immediate subject, how can we think those Rays qualities also, unless one quality may be the subject of and sustain another; which in effect is to call it Substance. We should not know bodies for their substances, were it not for their sensible qualities, and the Principal of those being now found due to something else, we have good reason to believe that to be a Substance also.” (Cohen, ed., Isaac Newton’s Papers and Letters on Natural Philosophy, p. 57).

  70. 70.

    This sentence and the surrounding text were absent from the unedited version (6 February 1671/2, Newton, Correspondence, I, p. 97).

  71. 71.

    Cohen, ed., Isaac Newton’s Papers and Letters on Natural Philosophy, pp. 53–55; Newton to Oldenburg, 6 February 1671/2, Newton, Correspondence, I, p. 97–98.

  72. 72.

    Newton to Oldenburg, 6 February 1671/2, Newton, Correspondence, I, p. 97; Cohen, ed., Isaac Newton’s Papers and Letters on Natural Philosophy, p. 54. Newton’s ceteris paribus clause was not entirely empty, contrary to what Worrall has claimed (Worrall, “The Scope, Limits, and Distinctiveness of the Method of ‘deduction from the phenomena’”, p. 57, footnote 7). Newton did, however, not take into account other factors such as the temperature of the air or the glass, atmospheric conditions, etc.

  73. 73.

    Newton to Oldenburg, 6 February 1671/2, Newton, Correspondence, I, pp. 99–100; Cohen, ed., Isaac Newton’s Papers and Letters on Natural Philosophy, pp. 55–56. This seems to imply that Newton was thinking in terms of analysis-synthesis here: once the true causes have been established, they can be applied to phenomena that were not included in the original analysis. Similarly, in his Lectiones Opticae, Newton stated: “Thus far I have erected the foundations whereby the phenomena of colors produced in any way can be explained, but now I will describe individually the particular and immediate causes of the effects that I have not previously treated, not for the sake of the geometers (to whom, it will appear unnecessary) but for others.” (Shapiro, ed., The Optical Papers of Isaac Newton, I, p. 523; for Newton’s explanation of the rainbow, see ibid., pp. 593–601). Newton, furthermore, noted that in the first two books of The Opticks he proceeded by analysis and that he had provided an instance of synthesis at the end of the first book (Newton, The Opticks, p. 405). On CUL Add. Ms. 3790, f. 242v [ca. 1700–1704], Newton wrote: “Most of the second Book was written some years ↓before↓ after the ffirst & so is not in so good a method. However it proceeds by Analysis to discover the fits of easy reflexion & easy transmission of the rays, & thence ↓it is easy to compound↓ the explication of the colours of ↓bubbles & other↓ transparent plates, & ↓those of↓ feathers & tinctures ↓are easily compounded↓” (cf. ibid., f. 244r, cf. 292v).

  74. 74.

    Newton to Oldenburg, 6 February 1671/2, Newton, Correspondence, I, p. 97; Cohen, ed., Isaac Newton’s Papers and Letters on Natural Philosophy, p. 51. Cf. Shapiro, ed., The Optical Papers of Isaac Newton, I, pp. 433, 525, 603. In The Opticks, immediately after his famous exposition of the methods of analysis and synthesis, Newton declared that he used the method of analysis to discover and prove the “original Differences of the Rays of Light in respect of their Refrangibility, Reflexibility, and Colour, and their alternate Fits of easy Reflection and easy Transmission, and the Properties of Bodies both opake and pellucid, on which their Reflexions and Colours depend.” (Newton, The Opticks, p. 405; for other causal statements on this matter see, e.g., ibid., pp. 57, 113, 119, 244).

  75. 75.

    Newton to Oldenburg, 11 June 1672, Newton, Correspondence, I, p. 174, cf. Newton’s second optical paper (ibid., I, pp. 373–374).

  76. 76.

    Ibid., I, p. 264.

  77. 77.

    Shapiro, ed., The Optical Papers of Isaac Newton, I, p. 129.

  78. 78.

    However it is useful to keep in mind Laymon’s remark to which I referred to in footnote 62.

  79. 79.

    Cf. Newton, The Opticks, Book I, Part II, pp. 113–191, cf. p. 244.

  80. 80.

    Ibid., pp. 55–56 [italics added]; Shapiro, ed., The Optical Papers of Isaac Newton, I, pp. 142–142. This statement was identical in all versions of The Opticks (OE 1, p. 38; OE 2, p. 46; OE 3, p. 46; OE 4, p. 46). On Newton’s non-modificationist account of light see furthermore Newton, The Opticks, Proposition II, Book I, Part II, p. 124, Proposition VII, Book I, Part II, pp. 158–161 and Book II, Part II, p. 244.

  81. 81.

    Cf. Worrall, “The Scope, Limits, and Distinctiveness of the Method of ‘deduction from the phenomena’”, p. 59. According to modern wave optics, which is based on Fourier analysis, it makes no sense to claim that white light initially contains homogeneous colours, since it consists of completely random phase and frequency variations together with restricted randomness in amplitude. From the perspective of wave optics, what happens during the experimentum crucis is the following. The first prism contains oscillators which form sets with specific eigenfrequencies. These are stimulated by the passing white light so that each kind of oscillator emits radiation of its own eigenfrequency. The latter interferes with the stimulating radiation, which after sequential such shifts by successive oscillators produce a slowing down of the velocity in the prism, and, hence, refraction. The second prism is then struck by the specific frequency of the radiation generated by one such oscillator set in the first prism and the effect repeats. Therefore, according to wave optics, the causal process is exactly the same, but the object on which they operate is different in the two cases. I am indebted to Jed Z. Buchwald for illuminating discussion on this matter.

  82. 82.

    In manuscript material Newton also entertained such line of reasoning in his discussion of the double refraction of island spar (CUL Add. Ms. 3970, f. 298r).

  83. 83.

    Hooke claimed that his pulse hypothesis could equally account for the experimental results without requiring the heterogeneity of white light (Sabra, Theories of Light from Descartes to Newton, pp. 233–234; Hooke to Oldenburg, 15 February 1671/2, Newton Correspondence, I, pp. 110–116). Ideas similar to Hooke’s were later reintroduced in the nineteenth century by G. L. Gouy who demonstrated that white light can be represented as the superposition of an infinite number of waves (Sabra, Theories of Light from Descartes to Newton, pp. 280–281).

  84. 84.

    Shapiro, ed., The Optical Papers of Isaac Newton, I, pp. 128–145; Shapiro, “The Evolving Structure of Newton’s Theory of White Light and Color”, pp. 231–234.

  85. 85.

    Newton first introduced this particular argument in Proposition 6 of his reply to the criticisms raised by Huygens, which stated that the “rays of light do not act upon one another in passing through the same Medium” (Newton to Oldenburg, 23 June 1673, Newton, Correspondence, I, p. 293).

  86. 86.

    Shapiro, “The Evolving Structure of Newton’s Theory of White Light and Color”, pp. 230–232.

  87. 87.

    Ibid., p. 232; Newton, The Opticks, pp. 153–154.

  88. 88.

    This is, nevertheless, what Shapiro has suggested (Shapiro, Fits, Passions, and Paroxysms, pp. 47–48, cf. p. 118).

  89. 89.

    Cf. Shapiro, “The Evolving Structure of Newton’s Theory of White Light and Color”, p. 216.

  90. 90.

    The criticism to which Newton was exposed must have really annoyed him and it is important to understand Newton’s reluctance to go in print (see especially Westfall, “Newton and his Critics on the Nature of Colors”, pp. 47–58). In a letter to Oldenburg on 6 July 1672 Newton noted that he wished that “all objections were suspended, taken from Hypotheses” – a remark that vaguely foreshadowed his fourth regula philosophandi (Newton, Correspondence, I, p. 210). In a letter to Henry Oldenburg on 8 March 1672/3, he wrote as follows: “Sr I desire that you will procure that I may be put out from being any longer fellow of ye R. Society. For though I honour that body, yet since I see I shall neither profit from them nor (by reason of this distance) can partake of the advantage of their Assemblies, I desire to withdraw.” (ibid., I, p. 262–263). In Optica Newton had declared: “I seem to have lingered too long on these matters, and consequently I have now decided to turn to the more abstract parts of mathematics” (Shapiro, ed., The Optical Papers of Isaac Newton, I, p. 603). In a letter to Oldenburg on 5 December 1674, Newton pointed out that: “I am sorry you put yourself to ye trouble of transcribing Fr. Linus’s conjecture, since (besides yt it needs no answer) I have long since determined to concern myself no further about ye promotion of Philosophy” (Newton, Correspondence, I, p. 328; cf. Newton to Oldenburg, 13 November 1675, ibid., I, p. 358). On 18 August 1676 in a response to a letter from Anthony Lucas containing several “experimentall exceptions” to Newton’s theory of light (sent on 17 May 1676), Newton put an end to all criticism: “seeing that I am well assured of ye truth & exactness of my own observation I shall be unwilling to be diverted by any other experiments from having a fair end made of this in ye first place” (ibid., II, p. 81; see, furthermore, Westfall, “Newton Defends his first Publication: The Newton Lucas Correspondence”). On 13 October 1676 Newton received another letter from Lucas (Newton, Correspondence, II, pp. 104–108). Newton wrote back to Oldenburg on 18 November that year as follows: “I promised you an answer to Mr Lucas this next Tuesday but I find I shall scarce finish what I have designed, so as to get a copy taken of it by that time, & therefore I beg your patience a week longer. I see I have made my self a slave to Philosophy, but if I get free of Mr Linus’s buissiness I will resolutely bid adew to it eternally, excepting what I do for my privat satisfaction or leave to come after me. For I see a man must either resolve to put out nothing new or to become a slave to defend it.” (ibid., II, pp. 182–183). On 28 November of that year, Newton responded that he “will not run into any other dispute till I see a full end of what relates to Mr Linus” (ibid., II, p. 183). When Lucas kept on sending further criticisms to Oldenburg, one to Hooke for Newton, and yet another one to Newton himself, Newton responded to Hooke that he wanted to rid himself from “this frivolous dispute & stop their clamouring against Oldenburg” and that he had answered Lucas’ letters sufficiently (ibid., II, p. 253). On 5 March 1677/8 Newton finally replied in two letters to Lucas. In the second of these letters, Newton wrote: “I forbeare to explain these things further for I do not think this a fit Subject to dispute about, & therefore have given these hints only in a private Letter” (ibid., II, p. 263).

    Prima facie one might wonder why Newton ever bothered to publish his second optical paper. In his second optical paper “An Hypothesis explaining the Properties of Light, discoursed in my several Papers” (1675), however, Newton made it clear that his findings were hypotheses so that he did not have to enter a new battle to defend his views against vehement criticism (Cohen, ed., Isaac Newton’s Papers and Letters on Natural Philosophy, pp. 177–235; Newton to Oldenburg, 7 December 1675, Newton, Correspondence, I, pp. 362–389). In the opening section of the second optical paper, in which Newton introduced the hypothesis that “agitated parts of bodies according to their severall sizes, figure and motions, doe excite Vibrations in the Æther of various depths and bignesses”, he asserted: “Sir, I had formerly purposed never to write any hypothesis of light and colours, fearing it might be a means to engage me in vain disputes: but I hope a declared resolution to answer nothing, that looks like a controversy, unless possibly at my own time upon some by-occasion, may defend me from that fear.” (Cohen, ed., Isaac Newton’s Papers and Letters on Natural Philosophy, p. 178). He emphasized that: “And though I shall not assume either this of any other hypothesis, not thinking it necessary to concern myself, whether the properties of light, discovered by me, be explained by this, of Mr. Hooke’s [which consisted in nothing more than in changing “Des Cartes’s pressing or progressive motion of the medium to a vibrating one” (ibid., p. 209; cf. Shapiro, ed., The Optical Papers of Isaac Newton, I, p. 161)], or any other hypothesis compatible of explaining them; yet while I am describing this, I shall sometimes, to avoid circumlocution, and to represent it more conveniently, speak of it, as if I assumed it, and propounded it to be believed. This I thought fit to express, that no man may confound this with my other discourses, or measure the certainty of one by the other, or think me obliged to answer objections against this script: for I desire to decline being involved in such troublesome and insignificant disputes.” (Cohen, ed., Isaac Newton’s Papers and Letters on Natural Philosophy, p. 179 [italics added]; Newton, Correspondence, I, pp. 363–364).

  91. 91.

    In a letter to Oldenburg on 6 June 1672, Newton wrote concluding positively & directly (Newton, Correspondence, I, p. 209).

  92. 92.

    Newton to Oldenburg, 6 February 1671/2, Newton, Correspondence, I, pp. 96–97 [underscore added]; cf. Newton to Oldenburg, 11 June 1672, Newton, Correspondence, I, pp. 187–188.

  93. 93.

    See, furthermore, Section 4.8 in this chapter.

  94. 94.

    Cohen, ed., Isaac Newton’s Papers and Letters on Natural Philosophy, pp. 106, 109; Newton, Correspondence, I, p. 164.

  95. 95.

    CUL Add. Ms. 9597.2.8.1.19, [f. 1r]; cf. Newton, Correspondence, I, p. 209. In correspondence Newton tempered his position: “And the absolute certainty of a Science cannot exceed the certainty of its Principles. Now the evidence by wch I asserted the Propositions of colours is in the next words expressed to be from Experiments & so but Physicall: Whence the Propositions themselves can be esteemed no more than Physicall Principles of a Science. And if those Principles be such that on them a Mathematician may determin all Phænomena of colours that can de caused by refraction, & that by computing or demonstrating after what manner & how much those refractions doe separate or mingle the rays in wch severall colours are originally inherent; I suppose the Science of Colours will be granted Mathematicall & as certain as any part of Optiques. And that this may be done I have good reason to beleive because ever since I became first acquainted with these Principles, I have with constant successe in the events made use of them for this purpose.” (Newton to Oldenburg, 11 June 1672, Newton, Correspondence, I, p. 187). See, furthermore, the conclusions reached in Zemplén and Demeter, “Being Charitable to Scientific Controversies: On the Demonstrativity of Newton’s Experimentum Crucis” and Shapiro, Fits, Passions, and Paroxysms, pp. 37–38.

  96. 96.

    Guicciardini, Isaac Newton on Mathematical Certainty and Method, p. 21.

  97. 97.

    Because of his insistance on causes, Newton was seeking to innovate the mixed sciences (Dear, Discipline and Experience, p. 235).

  98. 98.

    Note that in Newton’s early optical work a general characterization of hypotheses or proper demonstrations was still absent.

  99. 99.

    See: Guicciardini, Newton on Mathematical Certainty and Method, esp. Chapter 2 and Mamiani, Isaac Newton filosofo della natura, pp. 34, 46, 65–67. It appears that in his early optical work, Newton was somewhat overconfident that nature would easily yield to his methodological ideal of explaining refraction by relying on a priori derived refractive indices and some basics mathematical rules alone. The following statement is typical in that respect: “Although I have not yet derived the certainty of this proposition [Newton’s a priori dispersion law] from experiments, nevertheless I do not doubt that it will satisfy all of them which it is possible to do with that respect to it.” (Shapiro, ed., Isaac Newton’s Optical Papers, I, p. 201). However, as Newton would learn early on, optical phenomena would not easily lend them to the deductive ideal he envisioned. In an unpublished manuscript letter (U.L.C. Add. 3970, f. 443r–444r), Newton tried to make a deductive model of refraction (Bechler, “‘A Less Agreeable Matter:’ The Disagreeable Case of Newton and Achromatic Refraction”). The experiment consisted in letting an uncoloured ray pass through a prismatic box ABC made of polished plates of glass cemented together at the edges, which is filled with water. In the box another prism DEF made of glass or crystal is placed upside down – so that the vertex of DEF points to the base of ABC. The bases of ABC and DEF are parallel to each other. The only relevant data were the refractive indices and dispersive powers of glass, water and air. Newton recorded that “for determining their refractions made in their passage out of any one into any other of these three medium glasse water & Air I made use of those proportions of the sines wch I have already mentioned” (CUL Add. Ms. 3970, f. 443r–v). Once these are known, the rest follows without further experimentation. The model predicted that, given equal contrary refractive indexes, colours would appear (ibid., f. 443r) (and that, given that the refractive index of the interior prism is less than that of the exterior one, no colours will appear (ibid., f. 443v)). In The Opticks we encounter the same experiment (Experiment 8, Part II, Book I) with only one significant difference: the conclusion was the exact opposite to Newton’s earlier model (Newton, The Opticks, pp. 129–130)! Newton now claimed that, given equal contrary refractive indexes, light continues “ever after to be white” (ibid., p. 129). For this reason, Bechler has concluded that “it might well have been wholly thought-experiment” (Bechler, “‘A Less Agreeable Matter:’ The Disagreeable Case of Newton and Achromatic Refraction”, p. 114). On the basis of CUL Add. Ms. 3970, ff. 411r–412r, Alan E. Shapiro has tempered Bechler’s claim that Newton never performed this experiment (Shapiro, “Newton’s ‘Achromatic’ Dispersion Law: Theoretical Background and Experimental Evidence”, pp. 113–114, p. 97). However, he grants that the outcome of Newton’s experiment was contrary to the later published version, that the refractive indexes Newton used “were not experimentally derived, but calculated ones taken from the refraction rules” (ibid., pp. 105, 107, cf. p. 114), and that Newton had falsified his earlier claim (id., “Skating on the Edge: Newton’s Investigations of Chromatic Dispersion and Achromatic Prisms and Lenses”, p. 119).

  100. 100.

    Shapiro, ed., The Optical Papers of Isaac Newton, I, pp. 87/89, cf. p. 439.

  101. 101.

    For the references see footnote 95.

  102. 102.

    Ibid., I, p. 291, cf. Propositions 1, 4, 5, 10 on pp. 293–294; Newton, The Opticks, Proposition II, Book I, Part I, p. 26, Proposition III, Book I, Part I, p. 63, Proposition V, Book I, Part II, p. 134. Newton’s acceptance of Huygens’ criticism also lead him to accept two kinds of white: a natural and an artificial white. For further discussion see Shapiro, “The Evolving Structure of Newton’s Theory of White Light and Color”, pp. 223–225.

  103. 103.

    In Proposition VIII of Part III of Book II of The Opticks, Newton wrote: “The Rays of Light, whether they be very small Bodies projected, or only Motion or Force propagated, are moved in right Lines; and whenever a Ray of Light is by any Obstacle turned out of its rectilinear way, it will never return into the same rectilinear way, unless perhaps by very great accident.” (Newton, The Opticks, p. 268; cf. Newton’s annotation in CUL Adv.b.39.3, p. 70).

  104. 104.

    Newton, The Opticks, Book III, Part I, pp. 317–339.

  105. 105.

    Shapiro, “Twenty-Nine Years in the Making: Newton’s Opticks”.

  106. 106.

    For detailed treatments see: Shapiro, “Newton’s Experimental Investigation of Diffraction for the Opticks: A Preliminary Study”; id., “Newton’s Experiments on Diffraction”; and, Nauenberg, “Comparison of Newton’s Diffraction Measurements with the Theory of Fresnel”.

  107. 107.

    Reconstructions of Newton’s experiments are furthermore to be found in Stuewer, “A Critical Analysis of Newton’s Work on Diffraction” and, more recently, in Silverman and Strange, “The Newton Two-Knife Experiment: Intricacies of Wedge Diffraction”.

  108. 108.

    Newton, The Opticks, pp. 329–330.

  109. 109.

    Ibid., pp. 331–332.

  110. 110.

    Ibid., p. 332.

  111. 111.

    Shapiro, “Newton’s Experiments on Diffraction”, p. 66. For a reconstruction of Newton’s rectilinear model of diffraction, see: ibid., pp. 54–63.

  112. 112.

    Newton, The Opticks, p. 339; CUL Add. Ms. 3970, f. 338v. This has lead Ronchi to make the rather exaggerated statement that “no one could have worked better than Newton, not to build, but rather to demolish, the corpuscular theory” (Ronchi, The Nature of Light, A Historical Survey, p. 191).

  113. 113.

    The title of Section XIV is “The motion of minimally small bodies that are acted on by centripetal forces tending toward each of the individual parts of some great body” [De motu corporum minimorum, quæ viribus centripetis ad singulas magni alicujus corporis partes tendentibus agantur] (Newton, The Principia, p. 622). In Proposition XCIV Newton stipulated these conditions: “If two homogeneous mediums are separated from each other by a space terminated on the two sides by parallel planes, and a body passing through this space is attracted or impelled perpendicularly toward either medium [corpus in transitu per hoc spatium attrahatur vel impellatur perpendiculariter versus medium alterutrum] and is not acted on or impeded by any other force, and the attraction at equal distances from each plane (taken on the same side of that place) is the same everywhere; then I say that the sine of the angle of incidence onto either plane will be to the sine of the angle of emergence from the other plane in a given ratio.” (Newton, The Principia, p. 622). In Proposition XCV, Newton established that under the same conditions as in Proposition CXIV, “the velocity of the body before incidence is to its velocity after emergence as the sine of the angle of emergence to the sine of the angle of incidence” (ibid., p. 623). For further details on Newton’s proofs for the sine law of refraction, see Dijksterhuis, Lenses and Waves, pp. 196–200 and Bechler, “Newton’s Search for a Mechanistic Model of Colour Dispersion”, pp. 14–17.

  114. 114.

    Newton, The Principia, p. 625. Descartes’ discussion of the law of refraction can be found in La Dioptrique (Descartes, Œuvres de Descartes, VI, pp. 93–105, esp. pp. 101–102).

  115. 115.

    Newton, The Principia, p. 626 [italics added].

  116. 116.

    This detail is significant, for Newton considers those cases in which the incident ray is nearly parallel to the plane RS, so that the perpendicular velocity of the incident ray is infinitely little. See the following footnote.

  117. 117.

    The proposition to which Newton refers is in Newton, The Opticks, pp. 79–80 [italics added]: “If any Motion or moving thing whatsoever be incident with any Velocity on any broad and thin space terminated on both sides by two parallel Planes, and in its Passage through that space be urged perpendicularly towards the farther Plane is of given Quantities; the perpendicular velocity of that Motion of Thing, as its emerging out of that space, shall be always equal to the square Root of the sum of the square of the perpendicular velocity of that Motion or Thing as its Incidence on that space; and of the square of the perpendicular velocity which that Motion or Thing would have at its Emergence, if at its Incidence its perpendicular velocity was infinitely little.”

  118. 118.

    In other words, Newton showed that \(\frac{{A{D^{\textrm{2}}}}}{{E{F^{\textrm{2}}}}} \times C{F^2} = C{D^2} + \left(\frac{{M{C^{\textrm{2}}}}}{{N{G^{\textrm{2}}}}} \times C{G^2}\right)\). Since \(A{D^{\textrm{2}}} = M{C^{\textrm{2}}} - C{D^{\textrm{2}}}\), we can add these to both sides of the equality sign, so that: \(A{D^{\textrm{2}}} + \left(\frac{{A{D^{\textrm{2}}}}}{{E{F^{\textrm{2}}}}} \times C{F^{\textrm{2}}}\right) = M{C^{\textrm{2}}} - C{D^{\textrm{2}}} + C{D^{\textrm{2}}} + \left(\frac{{M{C^{\textrm{2}}}}}{{N{G^{\textrm{2}}}}} \times C{G^2}\right)\). Thus we obtain: \(\frac{{\left(E{F^{\textrm{2}}} \times A{D^{\textrm{2}}}\right) + \left(A{D^{\textrm{2}}} \times C{F^{\textrm{2}}}\right)}}{{E{F^2}}} = \frac{{\left(N{G^{\textrm{2}}} \times M{C^{\textrm{2}}}\right) + \left(M{C^{\textrm{2}}} \times C{G^{\textrm{2}}}\right)}}{{N{G^{\textrm{2}}}}}\), from which \(\frac{{A{D^{\textrm{2}}}}}{{E{F^{\textrm{2}}}}} \times \left(E{F^2} + C{F^2}\right) = \frac{{M{C^{\textrm{2}}}}}{{N{G^{\textrm{2}}}}} \times \left(N{G^2} + C{G^2}\right)\) follows. However, from what is given its follows that \(\left(E{F^2} + C{F^2}\right) = \left(N{G^2} + C{G^2}\right)\), so that \(\frac{{A{D^{\textrm{2}}}}}{{E{F^{\textrm{2}}}}} = \frac{{M{C^{\textrm{2}}}}}{{N{G^{\textrm{2}}}}}\) and therefore \(\frac{{AD}}{{EF}} = \frac{{MC}}{{NG}}\) obtains. Furthermore, from what is given, AD represents the sine of the incident ray (= sin(R i )) and EF represents the sine of the emerging ray (= sin(R e )), so that \(\frac{{\sin (Ri)}}{{\sin ({\mathop{Re}\nolimits} )}} = \frac{{MC}}{{NG}}\).

  119. 119.

    Newton, The Opticks, pp. 80–81. See furthermore: Sabra, Theories of Light: from Descartes to Newton, pp. 305–308 and Bechler, “Newton’s Search for a Mechanistic Model of Colour Dispersion”, pp. 27–31. Newton’s proof remained unchanged in all editions. It is worth quoting Whiteside’s comment: “In this over-complicated restatement of the simple Cartesian emission model Newton thoroughly obscures the basic point that the sine-law of refraction – here produced much like a deus ex machina – derives from the invariance of the horizontal component of the speed of the light “ray” in its passage through the optical interface at which it receives its downwards impulse or refractive force, and his introduction of an undemonstrated rule for the increase in “orbital” speed thereby engendered serves only further to confuse it.” (Whiteside, ed., The Mathematical Papers of Isaac Newton, VI, pp. 430–431, footnote 28).

  120. 120.

    Newton, The Opticks, pp. 81–82 [italics added].

  121. 121.

    Zev Bechler has furthermore shown that Newton’s model presupposed that rays AC and MC have equal velocity and that the constancy of the sine law depends on the velocity of the incident ray (Bechler, “Newton’s Search for a Mechanistic Model of Colour Dispersion”, pp. 27–31). In the proof of the sine law in The Opticks, Newton entirely obscured the physical meaning of the constancy of \(\displaystyle\frac{{MC}}{{NG}}\).

  122. 122.

    Shapiro, Fits, Passions, and Paroxysms, p. 50, cf. pp. 65, 76. On Newton’s rings, see Newton, The Opticks, pp. 193–244 [= Parts I and II of Book II] and Shapiro, Fits, Passions, and Paroxysms, pp. 79–89; on the colours of thick plates, see Newton, The Opticks, pp. 289–315 [= Part IV of Book II] and Shapiro, Fits, Passions, and Paroxysms, pp. 150–181. In Part IV of Book II Newton extended the model he used in his treatment of the colours of thin plates to the colours of thick plates (Newton, The Opticks, Observations 7–9, Book II, Part IV, pp. 297–307; Shapiro, Fits, Passions, and Paroxysms, Chapter 3).

  123. 123.

    Cohen, ed., Isaac Newton’s Papers and Letters on Natural Philosophy, pp. 188–189; Newton Correspondence, I, pp. 373–374.

  124. 124.

    Newton, The Opticks, pp. 281–288. In Part III, Book II of The Opticks Newton introduced the following definition: “The returns of the disposition of any Ray to be reflected I will call its Fits of easy Reflection, and those of its disposition to be transmitted its Fits of easy Transmission, and the space it passes between every return and the next return, the Interval of its Fits.” (ibid., p. 281). For further discussion, see Shapiro, Fits, Passions, and Paroxysms, Chapter 4.

  125. 125.

    Newton, The Opticks, pp. 289–315; Shapiro, Fits, Passions, and Paroxysms, pp. 150–179.

  126. 126.

    See: Mandelbaum, Philosophy, Science, and Sense Perception and McGuire, “Atoms and the ‘Analogy of Nature’”. “Transduction” is also referred to as “transdiction.” I prefer “transduction” because of the analogy with other forms of ampliative reasoning such as induction and abduction.

  127. 127.

    See Section 2.1 in Chapter 2.

  128. 128.

    Hooke, A Discourse of Comets in: Hooke, The Posthumous Works of Robert Hooke, p. 165.

  129. 129.

    Boyle, Excellency of Mechanical Hypothesis (ca. 1674), in: Boyle, The Works of Robert Boyle, VIII, p. 108, cf. p. 16.

  130. 130.

    Descartes, René Descartes: Principles of Philosophy, p. 285. For the original, see Descartes, Œuvres de Descartes, VIII, Pars quarta, § CCIII, pp. 325–326: “At insensilibus corporum particulis determinatas figuras & magnitudines & motus assigno, tanquam si eas vidissem, & tamen fateor esse insensiles; atque ideò quærent fortasse nonnuli, unde ergo quales sint agnoscam. Quibus respondeo: me primò quidem, ex simplicissimis & maximè notis principiis, quorum cognitio mentibus nostris à naturâ indita est, generaliter considerâsse, quænam præcipuæ differentiæ inter magnitudines & figuras & situs corporum, ob solam exiguitatem suam, insensilium esse possent, & quinam sensiles effectus ex variis eorum concursibus sequerentur. Ac deinde, cùm similes aliquos effectus in rebus sensibilibus animadverti, eas ex simili talium corporum concursu ortas existimâsse; praesertim cùm nullus alius ipsas explicandi modus excogitari posse videbatur.”

  131. 131.

    Cf.: “At quamvis fortè hoc pacto intelligatur quomodo res omnes naturales fieri potuerint, non tamen ideò concludi debet, ipsas revera sic factas esse.” (ibid., Pars quarta, § CCIV, p. 327).

  132. 132.

    Descartes, René Descartes: Principles of Philosophy, p. 286. For the original, see Descartes, Œuvres de Descartes, VIII, Pars quarta, § CCIII, p. 327: “Nam quemadmodum ab eodem artifice duo horologia fieri possunt, quæ, quamvis horas æquè bene indicent, & extrinsecus omnino similia sint, intus tames ex valde dissimili rotularum compage constant: ita non dubium est, quin summus rerum opifex omnia illa, quæ videmus, pluribus diversis modis potuerit efficere.”

  133. 133.

    Ibid., Pars quarta, § CCV, p. 327. Descartes’ explanation of refraction in Les Météores (1637) is a notable example of transduction in his work (Descartes, Œuvres de Descartes, VI, Discours VIII, pp. 331–333). For a thorough discussion, see Buchwald, “Descartes’ Experimental Journey Past the Prism and through the Invisible World”, pp. 8–21.

  134. 134.

    Newton, The Principia, p. 943.

  135. 135.

    Translation of: “↓A phænomenis Philosophia naturalis incipit↓. In his tractandis Philosophia experimentalis consistit. Ab hac Philosophia ↓experimentali ad rerum↓ ad causas efficientes & finales, & ↓ab his omnibus ad naturam rerum insensibilium & ultimo↓ ad Philosophiam hypotheticam transeundum est:]” (CUL Add. Ms. 3965, f. 422r [additions and corrections to the second edition of the Principia]).

  136. 136.

    Hypothesis III goes as follows: “Hypoth. III. Qualitates corporum quæ intendi et remitti nequeunt quæque corporibus omnibus competunt in quibus experimenta instituere licet sunt qualitates corporum universorum. Idem intelligendum est de qualitatibus corporum omnium ejusdem generis[.] Fundamentum ↓esse↓ videtur Philosophiæ totius. [This passage explains what Newton had in mind when, in the published text to Rule III, he wrote somewhat out of the blue “And this is the foundation of all natural philosophy.” (Newton, The Principia, p. 796).] Neque enim aliter ↓qualitates ↓corporum↓ insensibilium↓ a qualitatibus sensibilium [illegible word] qualitates sensibilium derivare licet.” (CUL 3965, f. 266r, cf. f. 267r [additions and corrections to the first edition of the Principia; italics added]). See further: McGuire, “Atoms and the ‘Analogy of Nature’”; Cohen, Introduction to Newton’s Principia, pp. 184–187; and, Shapiro, Fits, Passions, and Paroxysms, p. 45.

  137. 137.

    This material is on CUL Add. Ms. 3970, ff. 337r–338v and ff. 342r–346r [ca. 1700–1704].

  138. 138.

    CUL Add. Ms. 3970, f. 388r–v [late 1680s–early 1690s; italics added].

  139. 139.

    Such analogy was invoked by Newton in his 1675 An Hypothesis explaining y e properties of Light (Newton, Correspondence, I, pp. 374, 376; Cohen, ed., Isaac Newton’s Papers and Letters on Natural Philosophy, pp. 188, 192).

  140. 140.

    Cf. the scholium to Proposition XCVI in Book I of the Principia already referred to in the previous section.

  141. 141.

    Shapiro, Fits, Passions, and Paroxysms, pp. 45, 125, 134.

  142. 142.

    Translation of: “De solis sensibilibus et eorum partibus hic agitur propterea quod argumentum Inductionis in ijs solis locum habeat. Reliqua quæ non sentituntur sed per hypothesin tamen a nonnulis corpora nominantur, in Metaphysica et Philosophia hypothetica rectius tractanda sunt.” (CUL Add. Ms. 3965, f. 422r [ca. 1715]). A full transcription of this definition is given in the appendix to his chapter.

  143. 143.

    See Section 2.2 in Chapter 2.

  144. 144.

    Newton, The Opticks, p. 245 [underscore added]; cf. Proposition II, Book II, Part III, p. 248ff. and Proposition I, Book II, Part III, p. 251ff. Newton had dealt with the colours of thin plates in Parts I–II of Book III.

  145. 145.

    Newton, The Opticks, Book II, Part III, pp. 245–288; Shapiro, Fits, Passions, and Paroxysms, pp. 113, 118.

  146. 146.

    Newton, The Opticks, p. 245 [italics added].

  147. 147.

    Ibid., pp. 268–269 [italics added]; cf. CUL Add. Ms. 3970, f. 479r.

  148. 148.

    CUL Adv.b.39.3, p. 70. On Newton’s hierarchical hypothesis see furthermore: Figala, “Newton as an Alchemist”; id., “Die exakten Alchemie von Isaac Newton”, pp. 162–173; Gregory, “The Newtonian Hierarchic System of Particles”; Kubbinga, “Newton’s Theory of Matter”; Thackray, Atoms and Powers – an Essay on Newtonian Matter-Theory and the Development of Chemistry; and, Shapiro, “Newton’s Optics and Atomism”, esp. pp. 245–249. At the end of Proposition VII in Part III of Book I, Newton had spelled out the implication of his hierarchical account of the structure of matter: “However it will add much to our Satisfaction, if those Corpuscles can be discover’d with Microscopes; which if we shall at length attain to, I fear it will be the utmost improvement of this Sense. For it seems impossible to see the more secret and noble Works of Nature within the Corpuscles by reason of their transparency.” (Newton, The Opticks, p. 262 [italics added]).

  149. 149.

    Huygens’ tackle on the problem of transduction was by reducing the propagation of light to a problem of velocity (Dijksterhuis, Lenses and Waves, p. 192).

  150. 150.

    See Section 2.4.5 in Chapter 2 and Section 3.4.5 in Chapter 3.

  151. 151.

    Cf. Janiak, Newton as Philosopher, p. 108.

  152. 152.

    Newton, The Principia, p. 404.

  153. 153.

    Smith, “The Newtonian Style in Book II of the Principia”, p. 266.

  154. 154.

    In Section VII Newton considered three types of fluids: rarified, elastic, and continuous ones. A rarified fluid consists of small bodies which are spread out evenly. An elastic fluid is basically a rarified fluid endowed with additional repulsive forces, or as Newton called them “centrifugal forces,” between the impinging bodies and the moving body. Newton’s results for these two types of non-continuous fluids are provided in Propositions XXXII–XXXV (Newton, The Principia, pp. 724–733). A continuous fluid is a fluid in which the particles are in contact (for Newton’s results, see Propositions XXXVI–XL in: ibid., pp. 733–750). See Gauld, “Newton’s Investigations of the Resistance to Moving Bodies in Continuous Fluids and the Nature of ‘Frontier Science’” for discussion of some of the propositions from Section VII.

  155. 155.

    Newton, The Principia, pp. 697–698.

  156. 156.

    Ibid., p. 699.

  157. 157.

    See Howe, “Newton on Electricity and The Aether”. It should be noted that Home’s study is based on material from or related to The Opticks.

  158. 158.

    In his manuscript De natura acidorum (March 1691/2), Newton had shown the predominance of attraction during certain chemical processes (Newton, Correspondence, III, pp. 205–214).

  159. 159.

    See especially Newton’s manuscript De vita et morte vegetabili (CUL Add. Ms. 3970, ff. 237r–238v; transcribed in Mamiani and Trucco, “Newton E I Fenomeni della Vita”, pp. 78–79). According to Mamiani and Trucco, this piece was composed in the same period as the General Scholium.

  160. 160.

    See especially Newton’s unpublished manuscript, De motu et sensatione animalium which was also related to the composition of the General Scholium (CUL Add. Ms. 3970, f. 236r, transcribed in Mamiani and Trucco, “Newton E I Fenomeni della Vita”, pp. 78–79). See also Wes Wallace’s interesting study “The vibrating nerve impulse in Newton, Willis and Gassendi”.

  161. 161.

    Hall and Hall, eds., Unpublished Scientific Papers of Isaac Newton, pp. 333, 350–351, 355–359; Mamiani and Trucco, “Newton E I Fenomeni della Vita”, pp. 69–96, 78–87 [for transcriptions of CUL Add. Ms. 3970, f. 236r, f. 237r–v, f. 238v–r, f. 240r–v]. Cf. Newton, The Principia, pp. 287–292, 943–944 and Newton, The Opticks, p. 340 [Query 8], pp. 353–354 [Query 25], pp. 375–400 [Query 31].

  162. 162.

    Hall and Hall, eds., Unpublished Scientific Papers of Isaac Newton, p. 187.

  163. 163.

    Newton, The Principia, pp. 943–944.

  164. 164.

    In the left margin of the concluding paragraph of the General Scholium on CUL Adv.b.39.2, p. 484, Newton added the words “electrici & elastici,” which were to be inserted after “Spiritus.” In a draft version of the final paragraph of the General Scholium on CUL Add. Ms. 3965, f. 152r-v, Newton wrote “spiritus electricus.”

  165. 165.

    Hall and Hall, eds., Unpublished Scientific Papers of Isaac Newton, p. 303.

  166. 166.

    Ibid., p. 304.

  167. 167.

    Ibid., p. 306.

  168. 168.

    Cf. Newton, The Opticks, p. 397 and McGuire and Rattansi, “Newton and the ‘Pipes of Pan’”, p. 125.

  169. 169.

    Cf. Newton, The Principia, pp. 411, 588–589.

  170. 170.

    Hall and Hall, eds., Unpublished Scientific Papers of Isaac Newton, p. 307.

  171. 171.

    Ibid., p. 333 [italics added], cf. p. 321.

  172. 172.

    On CUL Add. Ms. 3965, f. 5v, Newton wrote that it follows from observation that all bodies are hard, mobile and impenetrable, even insensible ones (“etiam insensibiles”).

  173. 173.

    Hall and Hall, eds., Unpublished Scientific Papers of Isaac Newton, pp. 333–336, cf. pp. 321–323.

  174. 174.

    Ibid., pp. 336–340, cf. pp. 324–327.

  175. 175.

    On CUL Add. Ms. 3965, f. 266r, Newton wrote: “Datur spiritus infinitus et omnepræsens in quo materia secundum leges mathematicas movetur.”

  176. 176.

    Hall and Hall, eds., Unpublished Scientific Papers of Isaac Newton, pp. 340–341 [italics added].

  177. 177.

    Ibid., p. 345.

  178. 178.

    Westfall, Never at Rest, pp. 744–748.

  179. 179.

    Ibid., pp. 684–686; Dobbs, The Janus Faces of Genius, p. 222; Newton, The Principia, p. 281; Guerlac, “Newton’s Optical Aether, His Draft of a Porposed Addition to his Opticks”; and, Hawes, “Newton’s Revival of the Aether Hypothesis and the Explanation of Gravitational Attraction”.

  180. 180.

    Cohen, Introduction to Newton’s Principia, pp. 240–241. See Westfall, Never at Rest, p. 745, footnote 149 for a list of possibly similar drafts. Of course, Newton was not for the first time asserting his belief in such a spirit (cf. his second optical paper (1675) in Cohen, ed., Isaac Newton’s Papers and Letters on Natural Philosophy, pp. 179–184). There he noted that these spirits were installed “at first by the immediate hand of the Creator; and ever since by the power of nature” (ibid., p. 180).

  181. 181.

    Newton, The Principia, p. 944.

  182. 182.

    Hall and Hall, eds., Unpublished Scientific Papers of Isaac Newton, p. 354.

  183. 183.

    Ibid.

  184. 184.

    And not “orange juice” as Westfall notes (Westfall, Never at Rest, p. 746).

  185. 185.

    Hall and Hall, eds., Unpublished Scientific Papers of Isaac Newton, p. 345.

  186. 186.

    Ibid.

  187. 187.

    This was Newton’s earlier explanation of the rising of water between glass plates (Westfall, Never at Rest, p. 746).

  188. 188.

    Hall and Hall, eds., Unpublished Scientific Papers of Isaac Newton, p. 455.

  189. 189.

    Newton, The Principia, pp. 287–292, 289. CUL Add. Ms. 3965, f. 351r–v is but irrelevantly different from the folios Cohen has transcribed. Related material is on CUL Add. Ms. 9597.2.18.92, f. 2r.

  190. 190.

    Hall and Hall, eds., Unpublished Scientific Papers of Isaac Newton, pp. 288–290.

  191. 191.

    Ibid., p. 283.

  192. 192.

    Ibid., p. 287 [italics added].

  193. 193.

    Ibid., p. 289 [italics added].

  194. 194.

    The reader can understand Newton’s dissatisfaction by comparing the values obtained when multiplying the inclination (which stood as a measure for the attractive force of the glass) with the square of the corresponding distance.

  195. 195.

    Hall and Hall, eds., Unpublished Scientific Papers of Isaac Newton, p. 289. In CUL Add. Ms 3968, f. 586 [draft material pertaining to Newton’s review of the Principia in Acta Eruditorum], Newton noted that “He [Newton] has told his friends that there are sufficient Phaenomena to ground an inquiry upon but not yet sufficient to determine the laws of attraction.” (Cohen’s translation in Newton, The Principia, p. 282).

  196. 196.

    In CUL Add. Ms. 3970, f. 240r, Newton wrote: “Et (attractiones elect) quemadmodum attractio gravitatis ad majores Planetarum (Cometarum) & maris nostri motus explicandos sufficit: sic vires electricae et magneticae (ad motus minores alios omnes particularum corporum motus exp[l]icando sufficere videntur) ad explicandas actiones et motus particularum (inter se) corporis cujuscumque inter se sufficere videntur.” (Mamiani and Trucco, “Newton E I Fenomeni della Vita”, p. 86).

  197. 197.

    Hall and Hall, eds., Unpublished Scientific Papers of Isaac Newton, pp. 290–292. Again there is much correspondence with material from Query 31.

  198. 198.

    Ibid., p. 333.

  199. 199.

    Newton, The Opticks, pp. 2–3.

  200. 200.

    Ibid., p. 3

  201. 201.

    Ibid., p. 4.

  202. 202.

    Ibid.

  203. 203.

    Ibid., p. 5.

  204. 204.

    Ibid.

  205. 205.

    Ibid.

  206. 206.

    Ibid.

  207. 207.

    See Section 2.4.4 in Chapter 2.

  208. 208.

    Cf. Schuster, “‘Waterworlds’: Descartes’ Vortices and their Crafting as Explanations of Gravity”, p. 37. A lot of additional historical work remains to be done on the status of the mixed sciences and relation to physico-mathematics in the early modern period. For the early modern period, see Dear, Discipline and Experience, esp. Chapter 6. On the mixed sciences, Laird, The Scientiae Mediae in Medieval Commentaries on Aristotle’s Posterior Analytics remains central. A useful overview of the “mixed sciences” is provided in Brown, “The Evolution of the Term ‘Mixed Mathematics’”. In his Discipline and Experience, Peter Dear explains that the emergence of physico-mathematics is to be considered as a answer to some characteristic tensions within the mixed sciences, which in order to establish themselves as rigorous associated themselves with mathematical demonstrations, but to a lesser extent with physical explanations (Dear, Discipline and Experience, pp. 163, 168, 170).

  209. 209.

    Dijksterhuis, “Once Snell Breaks Down”, p. 185.

  210. 210.

    See Section 4.5 in this chapter.

  211. 211.

    Newton, Correspondence, II, p. 104.

  212. 212.

    Cf. Shapiro, “Newton’s ‘Achromatic’ Dispersion Law”, pp. 123, 128.

  213. 213.

    Ronchi, The Nature of Light, pp. 162–163; Westfall, “The Development of Newton’s Theory of Color”, p. 357 and CUL Add. Ms. 3996, f. 72v, cf. CUL Add. Ms. 3970, f. 291r.

  214. 214.

    Cf. “If refraction be performed by attraction of the rays, the sines of incidence must be to the sines of refraction in a given proportion as we shewed in or Principles of Philosophy; & this Rule is true by experience.” (CUL Add. Ms. 3970, f. 289r).

  215. 215.

    Cf. Shapiro who notes on Newton’s periodic ethereal vibrations: “Newton, […], was trapped by his own methodology, which compelled him to suppress his physical model and thereby rob his theory of much of its intelligibility” (Shapiro, “Huygens” Traité de la Lumière and Newton’s Opticks”, p. 224).

  216. 216.

    Crossed-out sentence on CUL Add. Ms. 3968, f. 586v [ca. 1714].

  217. 217.

    Cf. CUL Add. Ms. 3965, f. 504r. In Newton’s final list of corrections for the second edition of the Principia these definitions were crossed out and did not make it into print. CUL Add. Ms. 3965, f. 437v seems to contain a previous version of this definition.

  218. 218.

    Cf. CUL Add. Ms. 3965, f. 430r, f. 544r; cf. CUL 9597.2.18.97, [ff. 1r–2r].

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    Steffen Ducheyne

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Ducheyne, S. (2012). Facing the Limits of Deductions from Phenomena: Newton’s Quest for a Mathematical-Demonstrative Optics. In: “The main Business of natural Philosophy”. Archimedes, vol 29. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2126-5_4

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