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The Problem of Reflection in Eighteenth-Century Projectile Theories of Light

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Abstract

This paper explores the mechanical models elaborated by projectile theorists throughout the eighteenth century to explain the reflection of light. Influenced by Isaac Newton’s Opticks, these projectile theorists proposed that repulsion was the cause of reflection. My purpose is to show that their models were not unified and lacked a deeper understanding of the origin of repulsive powers. This analysis illustrates how a simple optical phenomenon was not easy for eighteenth-century theorists to explain, even when the projectile theory of light was prominent among natural philosophers.

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Fig. 1

Source: Newton, Principia (ref. 5), 624

Fig. 2

Source: Newton, Principia (ref. 5), 624; Cheyne, Principles (ref. 13), 75

Fig. 3

Source: Desaguliers, “Optical experiments” (ref. 14)

Fig. 4

Source: Desaguliers, “Optical experiments” (ref. 14)

Fig. 5

Source: Desaguliers, “Optical experiments” (ref. 14)

Fig. 6
Fig. 7

Source: Rowning, Compendious (1737) (ref. 23), plate 1

Fig. 8

Source: Worster, Compendious (ref. 28), 227

Fig. 9

Source: Worster, Compendious (ref. 28), 225

Fig. 10

Source: Worster, Compendious (ref. 28), 228

Fig. 11

Source: Smith, Opticks (ref. 31), plate for p. 73

Fig. 12

Source: Porterfield, Treatise (ref. 33), plate 2

Fig. 13

Source: Emerson, Elements (ref. 35), plate 2

Fig. 14

Source: Boscovich, Theory (ref. 38), 342

Fig. 15

Source: Herschel, Scientific Papers (ref. 40), plate D

Fig. 16

Source: Herschel, Scientific Papers (ref. 40), lxxiv

Fig. 17

Source: Melvill, “Observations” (ref. 44), tab. 3

Fig. 18

Source: Melvill, “Observations” (ref. 44), tab. 3

Fig. 19

Source: Melvill, “Observations” (ref. 44), tab. 3

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Notes

  1. Cantor’s book (see ref. 4, 206–2) lists several projectile theorists who published works in the eighteenth and nineteenth centuries. From that list, I selected those who published books or papers on optics from the publication of Newton’s Opticks in 1704 to 1800. Of course, some of them are not discussed in this paper, since I could not find in their works any mention to mechanical models that treated reflection of light.

  2. The lowercase m is not shown in Cheyne’s figure.

  3. There is no surviving biographical account of Worster.

References

  1. Alan E. Shapiro, “Newton’s Optics and Atomism,” in The Cambridge Companion to Newton, ed. I. Bernard Cohen and George E. Smith, 227–55 (Cambridge: Cambridge University Press, 2002), 227.

  2. For a list of subjects Newton discussed in the “Queries,” see Derek Gjertsen, The Newton Handbook (London: Routledge & Kegan Paul, 1986), 519–20.

  3. For an overview of the reception of Newtonian doctrines in Europe, see Helmut Pulte and Scott Mandelbrote, eds., The Reception of Isaac Newton in Europe, vol. 1 (London: Bloomsbury, 2019).

  4. An early analysis of these mechanical models was made by Geoffrey Cantor, Optics after Newton: Theories of Light in Britain and Ireland, 1704–1840 (Manchester: Manchester University Press 1983), 32–42

  5. Isaac Newton, The Principia: Mathematical Principles of Natural Philosophy, trans. I. Bernard Cohen and Anne Whitman (Berkeley: University of California Press, 1999), 622.

  6. For a detailed analysis of book 2, including on its various problematic parts, see Alan E. Shapiro, Fits, Passions and Paroxysms (Cambridge: Cambridge University Press, 1993).

  7. Isaac Newton, Opticks (Mineola: Dover, 1952), 262.

  8. Newton, Opticks (ref. 7), 263, 266, 269.

  9. Newton, Opticks (ref. 7), 395.

  10. Newton, Opticks (ref. 7), 281.

  11. Between 1675 and 1676, Newton presented two papers to the Royal Society of London on colored rings in thin films and colors of bodies. In one of them, known today as “Hypothesis of Light,” Newton discussed a model based on the vibrations of ethereal particles caused by the impinging of light on bodies. These vibrations originated optical phenomena such as the rings in thin films. When he wrote Opticks, he replaced this model for the theory of fits and only briefly mentioned the former. See Shapiro, Fits (ref. 6), 72–89.

  12. Newton, Opticks (ref. 7), 372–73.

  13. George Cheyne, Philosophical Principles of Religion: Natural and Revealed (London: George Strahan, 1715), 81.

  14. John T. Desaguliers, “II. Optical experiments made in the beginning of August 1728, before the President and several members of the Royal Society, and other gentlemen of several nations, upon occasion of Signior Rizzetti’s opticks, with an account of the said book,” Philosophical Transactions of the Royal Society of London 35 (1728), 596–629.

  15. On this matter, see Massimo Mazzotti, “Newton in Italy,” in Pulte and Mandelbrote, eds., Reception (ref. 3), 159–78. In his letter, Desaguliers seemed quite upset with the “arrogant manner” in which Rizzetti had insulted Newton, claiming that the Italian could have learned the truthfulness of the experiments from his previous reproductions to French philosophers in 1715 and other materials.

  16. Desaguliers, “Optical experiments” (ref. 14), 617–18.

  17. Desaguliers, “Optical experiments” (ref. 14), 624, 628.

  18. Willem Jacob ’sGravesande, Mathematical Elements of Natural Philosophy, trans. John T. Desaguliers, vol. 2, 6th ed. (London: W. Innys et al., 1747). The original version was in Latin, published in 1720 (vol. 1) and 1721 (vol. 2).

  19. ’sGravesande, Mathematical Elements (ref. 18), 201, 203.

  20. ’sGravesande, Mathematical Elements (ref. 18), 204. Emphasis by ’sGravesande.

  21. Benjamin Martin, New Elements of Optics (London: Printed for the Author, 1759), 57. See figure 6 in plate 3. In other books, Martin also did not advance a discussion on the cause of reflection based on a repulsive power. I have analyzed the following works: Philosophical Grammar (5th ed., 1755), New and Compendious System of Optics (1740), A Course of Lectures in Natural and Experimental Philosophy (1743), An Essay on Electricity and its supplement (both of 1746), Philosophia Britannica (1747), A Panegyric on the Newtonian Philosophy (2nd ed., 1754), A Plain and Familiar Introduction to the Newtonian Philosophy (2nd ed., 1754), New Elements of Optics (1759), and Optical Essays (1765).

  22. Andrew Baxter, Matho (London: A. Millar, 1745), 215; Robert Blair, “Experiments and observations on the unequal refrangibility of light,” Transactions of the Royal Society of Edinburgh 3, no. 2 (1794), 3–76, on 74; Richard Helsham, A Course of Lectures in Natural Philosophy, 4th ed. (London: J. Nourse, 1767), 336; Joseph Harris, A Treatise of Optics (London: B. White, 1775), 4; Charles Hutton, A Mathematical and Philosophical Dictionary. Vol. 2. (London: J. Johnson, 1795), 344; William Enfield, Institutes of Natural Philosophy, Theoretical and Experimental (London: J. Johnson, 1785), 161; Henry Brougham, “Experiments and observations on the inflection, reflection, and colours of light,” Philosophical Transactions of the Royal Society of London 86 (1796), 227–77, on 235.

  23. The publication of this book was very erratic, with other editions and volumes being published almost at the same time. See Robert Schofield, Mechanism and Materialism: British Natural Philosophy in the Age of Reason (Princeton: Princeton University Press, 1970), 35. I have used the first edition for part 3 (Optics)—John Rowning, A Compendious System of Natural Philosophy, pt. 3 (London: Sam Harding, 1737)—and the second volume of the second edition for the continuation of part 3—A Compendious System of Natural Philosophy, vol. 2 (London: Sam Harding, 1753).

  24. Rowning, Compendious (1737) (ref. 23), 8.

  25. Rowning, Compendious (1753) (ref. 23), 158.

  26. Rowning, Compendious (1753) (ref. 23), 160, 162.

  27. Rowning, Compendious (1753) (ref. 23), 167.

  28. Benjamin Worster, A Compendious and Methodical Account of the Principles of Natural Philosophy, 2nd ed. (London: Stephen Austen, 1730).

  29. Worster, Compendious (ref. 28), 226.

  30. Worster, Compendious (ref. 28), 227, 229.

  31. Robert Smith, A Compleat System of Opticks, vol. 1. (Cambridge: Printed for the Author, 1738).

  32. Smith, Opticks (ref. 31), 90, 93.

  33. William Porterfield, A Treatise on the Eye, vol. 1. (London: A. Miller, 1759).

  34. Porterfield, Treatise (ref. 33), 301–2.

  35. William Emerson, The Elements of Optics (London: J. Nourse, 1768).

  36. Emerson, Elements (ref. 35), 52.

  37. There are numberless materials regarding Boscovich’s works and ideas. To this analysis, the most useful were Richard Olson, “The Reception of Boscovich’s Ideas in Scotland,” Isis 60, no. 1 (1969), 91–103; and Luca Guzzardi, “Ruggiero Boscovich and ‘The Forces Existing in Nature,’” Science in Context 30, no. 4 (2017), 385–422.

  38. I have consulted the English version of the book. See Roger Boscovich, A Theory of Natural Philosophy (Chicago: Open Court Publishing Company, 1922).

  39. Boscovich, Theory (ref. 38), 345n.

  40. These papers were published in William Herschel, The Scientific Papers of Sir William Herschel, vol. 1 (London: Royal Society & Royal Astronomical Society, 1912).

  41. Herschel, Scientific Papers (ref. 40), lxx–lxxi.

  42. Oliver Goldsmith, A Survey of Experimental Philosophy, vol. 2 (London: T. Carnan/F. Newbery, London, 1776). The book was written in 1765 and published posthumously.

  43. Goldsmith, Survey (ref. 42), 377.

  44. Thomas Melvill, “Observations on Light and Colours,” Essays and Observations, Physical and Literary, vol. 2. (Edinburgh: G. Hamilton & J. Balfour, 1756).

  45. Melvill, “Observations” (ref. 44), 25. Emphasis by Melvill.

  46. Melvill, “Observations” (ref. 44), 25–26.

  47. Melvill, “Observations” (ref. 44), 30. Melvill was not the first to mention this particular idea. Worster also thought that a repulsive power caused small needles to “swim upon the water,” but he did not advance the idea as Melvill did. See Worster, Compendious (ref. 28), 25.

  48. Melvill, “Observations” (ref. 44), 26, 29.

  49. Melvill, “Observations” (ref. 44), 31.

  50. Joseph Priestley, The History and Present State of Discoveries Relating to Vision, Light and Colours, 2 vols. (London: J. Johnson, 1772).

  51. For a comprehensive analysis of this book, see Breno Arsioli Moura, “Newtonian Optics and the Historiography of Light in the 18th Century: A Critical Analysis of Joseph Priestley’s The History of Optics,” Transversal—International Journal for the Historiography of Science 5 (2018): 157–70.

  52. Priestley, History (ref. 50), 771.

  53. Herschel, Scientific Papers (ref. 40), lxx.

  54. John Rowning, A Compendious System of Natural Philosophy, vol. 1 (London: Sam Harding, 1753), ix.

  55. John Robison, “Light,” in Encyclopædia Britannica, vol. 13 (Edinburgh: A. Bell & C. Macfarquhar, 1797), 305.

  56. George Gregory, The Economy of Nature, vol. 1. (London: J. Johnson, 1798), 30, 184.

  57. Gibbes Jordan, New Observations Concerning the Colours of Thin Transparent Bodies (London: T. Cadell & W. Davies, 1800), 94–95.

  58. Throughout the eighteenth century, the projectile theory of light faced many other problems. See Cantor, Optics (ref. 4), 50–90, for a deep investigation of these problems.

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Acknowledgements

I would like to acknowledge two Brazilian research agencies for the financial support: Sao Paulo Research Foundation (FAPESP, Grant nº 2014/04366-2) and Brazilian National Council for Scientific and Technological Development (CNPq, Grant nº 400118/2016-5).

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Breno Arsioli Moura is Assistant Professor of History of Science and Physics Teaching at Federal University of ABC, Brazil. His main research interests are in history of optics and eighteenth-century natural philosophy.

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Arsioli Moura, B. The Problem of Reflection in Eighteenth-Century Projectile Theories of Light. Phys. Perspect. 22, 191–214 (2020). https://doi.org/10.1007/s00016-020-00266-w

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