Newton’s theory of tail formation can be regarded as the Achilles’ heel of his theory of comets. The process that Newton introduced for tail formation was based on the function of the rarified and receding particles of the ether, which carried along the particles of cometary atmosphere. This assumption, as illustrated in chapter four and five of the present work, was unable to answer some challenging questions proposed even by Newton’s disciples. These questions can be classified into three groups based on (1) the role of different agents in the formation of a tail; (2) the interaction of the ethereal particles and the particles of the comet’s atmosphere; and (3) the interaction of the cometary atmosphere and the atmosphere of the sun.
In the first category, the questions were related to the basic factors responsible for triggering tail formation. Since some comets with perihelia around the orbit of Venus produced tails long before and after their closest approaches to the sun, it was a dilemma why the inner planets – including the earth – did not produce tails. In other words, it was a key question whether the amount of heat a comet received or the quality of its atmosphere was the main agent in the formation of a tail.
The second group of questions considered some sophisticated problems regarding the nature and function of the ethereal particles. Defined as the most subtle corpuscles in the cosmos, the ethereal particles had to carry along the atmospheric particles of a comet that undoubtedly were heavier and bigger. The insufficiency of the theory became more evident when it was found that the process had to be performed in a situation where the comet’s head was moving at a speed of a few thousands of miles per minute. Thus, the heating and rarifying of the ethereal particles were taking place in such a manner that they could move away the cometary particles with a speed more than the orbital speed of the comet and continue to recede for millions of miles. Furthermore, it was not known why Newton did not assign a role for the sun’s rays to act on the highly rarified particles of cometary tails.
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References
Ephraim Chambers, “Zodiacal Light”, Cyclopædia, or an Universal Dictionary of Arts and Sciences, 5 vols. (London: 1778–1788), vol. 4, p. 1394.
For a summary of major theories about the aurora in the eighteenth century see: J. Morton Briggs, Jr., “Aurora and Enlightenment, Eighteenth-Century Explanations of the Aurora Borealis”, Isis 58 (1967), 491–503.
Maraldi, “Observations d’une Lumiere Horisontale”, Memoires de l’Académie royale des Sciences, 1717, p. 30. Maraldi published two articles about his observations of the aurora of 11 April 1716 and 15 December 1716 (he did not describe the aurora of March 1716). His theory is stated in his second article. See: Briggs, “Aurora”, p. 493.
Edmund Halley, “An Account of the Late Surprising Appearance of the Lights Seen in the Air, on the Sixth of March Last; With an Attempt to Explain the Principal Phaenomena thereof; As It Was Laid before the Royal Society by Edmund Halley, J. V. D. Savilian Professor of Geom. Oxon, and Reg. Soc. Secr.”, Philosophical Transactions of Royal Society of London 29 (1714–1716), 406–428, esp. pp. 423–428.
Halley points out this resemblance: “Nor do we find any thing like it [aurora] in what wee see of the Celestial Bodies, unless it be the Effluvia projected out of the Bodies of Comets to a vast Hight”. See Ibid., p. 427.
Chambers, Cyclopedia…, 4th ed., vol. 4, p. 1394.
Jean-Jacques d’Ortous de Mairan, Traité Physique et Historique de l’Aurore Boréale (Paris: 1733), pp. 10–30, 86–94, 142–145, 219–228. For a brief description see: Briggs, “Aurora”, pp. 494–498.
Ibid., p. 272.
Ibid., p. 273–274.
Ibid., p. 279.
E. Schofield, “Rowning, John”, in Charles C. Gillispie (ed.), Dictionary of Scientific Biography, 15 vols. (New York: Charles Scribner’s Sons, 1972), vol. 11, pp. 579–580.
John Rowning, A Compendious System of Natural Philosophy: With Notes Containing the Mathematical Demonstration, and Some Occasional Remarks. In Four Parts (London: Printed for Sam Harding, 1744), pp. 98–99.
Ibid., p. 105.
James Bradley, “A Letter from the Reverend Mr. James Bradley, Savilian Professor of Astronomy at Oxford, and F.R.S. to Dr. Edmund Halley Astronom. Reg. &c. Giving an Account of a New Discovered Motion of the Fix’d Stars”, Philosophical Transactions 35 (1727–1728), 646.
Rowning, A Compendious System, pp. 108–112.
Roger Long, after mentioning theories of tail formation, including Rowning’s, criticizes him regarding the size of comet’s atmosphere he adopted in his theory: “the greatest objection to it [Rowning’s theory] is the immense largeness of the atmospheres that must now be supposed, to account for the length of the tails of some comets, which have been said to measure above 200 semidiameters of our earth”. See: Long, Astronomy, p. 555.
Schofield, “Rowning, John”, pp. 579–580.
Long, Astronomy, p. 555.
Leonhard Euler, “Recherches Physiques Sur la Cause de la Queüe des Cometes, de la Lumiere Boreale, et de la Lumiere Zodiacale”, Histoire de l’Académie Royale des Sciences et des Belles Lettres de Berlin, 1746, p. 117. A similar idea was stated by Mairan. According to him, since the sun’s rays barely penetrate the denser parts of a coma, only the particles at the outmost parts of it can be pushed by the solar rays. As a result, the tail “former un Cone, ou Cylindre creux”. Thus, an observer at the night side of a comet will see the tail as a surrounding illuminated wall. See Mairan, Traité, pp. 276–277.
Euler, “Recherches Physiques”, p. 119.
Euler does not acknowledge the Newtonian corpuscular theory of light but adopts a wave theory. However, he admits that light rays exert pressure on small particles, such as dust. He also refers to experiments done by burning mirrors to show the effect. See Ibid., p. 121.
Ibid., pp. 122–125.
Ibid., p. 120.
Ibid., pp. 126–127.
Ibid., pp. 128–129.
Curtis Wilson, “The problems of perturbation analytically treated: Euler, Clairaut, d’Alembert” in Taton and Wilson, eds., The General History of Astronomy, vol. 2B, p. 91. For a detailed account of development of Euler’s ideas about action-at-a-distance see: Curtis Wilson, “Euler on action-at-a-distance and fundamental equations in continuum mechanics”, in P.M. Harman, Alan E. Shapiro (eds.), Investigation of Difficult Things: Essays on Newton and the History of the exact Sciences in Honour of D.T. Whiteside (Cambridge: Cambridge University Press, 1992), pp. 399–420.
Euler by proving the formula e ix = cos x + i sin x (where i is the complex number, i 2 = −1) connected the trigonometric and exponential functions. This innovation laid down a calculus-based approach to trigonometry which was essential in the development of the analysis of orbital elements in perturbed orbits. See: Ibid., pp. 89–107, Wilson, “Euler on action-at-a-distance”, pp. 399; Katz, A History of Mathematics, pp. 554–558; Curtis Wilson, “Astronomy and Cosmology”, in Roy Porter (ed.), The Cambridge History of Science, Volume 4: Eighteenth-Century Science (Cambridge: Cambridge University Press, 2003), pp. 328–353, especially pp. 334–337.
For the history of the Cartesian System after the emergence of Newtonian physics see: Aiton, The Vortex Theory, 152–193, 209–256, especially pp. 244–256.
Simon Schaffer, “The Phoenix of Nature: Fire and Evolutionary Cosmology in Wright and Kant”, Journal for the History of Astronomy 9 (1978), pp. 180–200, especially pp. 189–192.
Ibid., p. 190.
Allgemeine Naturgeschichte und Theorie Des Himmels oder Versuch von der Verfassung und dem mechanischen Ursprungedes ganzen Weltgebäudes, nach Newtonischen Grundsätzen abgehandelt (Leipzig: 1755). For English translation see: Immanuel Kant, Universal Natural History and Theory of Heavens; or an Essay on the Constitution and Mechanical Origin of the Whole Universe Treated According to Newton’s Principles, trans. W. Hastie (Glasgow: 1900). Also: Kant’s Cosmogony, as in His Essay on the Retardation of the Rotation of the Earth and His Natural History and Theory of the Heavens, trans. W. Hastie, revised and edited with an introduction and appendix by Willy Ley (New York: Greenwood, 1968). All quotations from Kant’s Cosmogony in this section are from the latter work.
For Wright’s theory of the Milky Way and its influence on Kant see: Schaffer, “The Phoenix of Nature”, pp. 180–200.
Kant, Cosmogony, pp. 38–39.
Ibid., p. 47.
Ibid., p. 55.
Ibid., p. 55. Kant’s prediction came true in his lifetime: Uranus was discovered in 1781 by William Herschel.
Ibid., pp. 71–75. Kant criticizes Newton’s idea that the Creator situated denser planets closer to the sun because they can endure more of its heat. He argues that in this case the surface material of the earth should be much denser for the reason that the sun has no effect on the interior parts of the planet. Kant also states that “Newton was afraid that if the earth were plunged in the rays of the sun, as near as Mercury, it would burn like a comet, and that its matter would not have sufficient fire-resisting power not to be dissipated by such heat”. (Ibid., p. 74; the original text is: “Newton befürchtete, wenn die Erde bis zu der Nähe des Mercurs in den Strahlen der Sonne versenkt würde, so dürfte sie wie ein Komet brennen und ihre Materie nicht genugsame Feuerbeständigkeit haben, um durch diese Hitze nicht zerstreuet zu werden”. See Kant, Allgemeine Naturgeschichte und Theorie Des Himmels oder Versuch von der Verfassung und dem mechanischen Ursprungedes ganzen Weltgebäudes, nach Newtonischen Grundsätzen abgehandelt (Leipzig: 1755, p. 41, emphasis is mine). However, in the Principia, where Newton compares the heat that Mercury and the earth obtain from the sun, he does not state that comets burn: “If the earth were located […] in the orbit of Mercury, it would immediately go off in a vapor”, (Newton, Principia, p. 814). In the major post-Newtonian cometary works the idea of the burning of comets was held by Voltaire (see chapter five, above), however, Kant does not mention the source of this idea.
Ibid., pp. 86–89. One of the conclusions of this reasoning is that the direction of revolution of the planets and comets must be the same. Kant points out this issue and states that the retrograde comets may have seen due to an optical illusion. Ibid., p. 88.
Ibid., pp. 89–90.
Ibid., p. 90.
Ibid., pp. 101–102. For Kant’s evolutionary cosmology see: Schaffer, “The Phoenix of Nature”, especially pp. 189–193; Schechner, Comets, Popular Culture, pp. 203–205.
Ibid., pp. 117–119. Kant explains that a close approach of a comet or cooling down of the region where the ring was located caused the condensation of the vapor and its precipitation.
For the history of Kant’s book on cosmogony see the introduction of Willy Ley in Ibid., pp. vii–xx.
For a general history of electricity in the seventeenth and eighteenth centuries see: J. L. Heilbron, Electricity in the 17 th and 18 th Centuries (Berkeley: University of California Press, 1979); Roderick Weir Home, Electricity and Experimental Physics in Eighteenth-Century Europe (Brookfield: Variorum, 1992); Edward Tatnall Canby, A History of Electricity (New York: Hawthorn Books, 1968); Herbert W. Meyer, A History of Electricity and Magnetism (Cambridge: MIT Press, 1971); Roderick Weir Home, “Mechanics and Experimental Physics”, in Roy Porter (ed.), The Cambridge History of Science, Volume 4, pp. 354–374, especially pp. 363–374; Jonathan Shectman, Groundbreaking Scientific Experiments, Inventions and Discoveries of the 18 th Century (Westport, CT: Greenwood Press, 2003), pp. 80–91, 95–103.
Hauksbee published several papers explaining his experiments with different materials in the spinning glass globe. For his report of experiment with evacuated globes see: Fra. Hauksbee, “An Account of an Experiment Made before the Royal Society at Gresham College, Together with a Repetition of the Same, Touching the Production of a Considerable Light upon a Slight Attrition of the Hands on a Glass Globe Exhausted of Its Air: With Other Remarkable Occurrences”, Philosophical Transactions, 25 (1706–1707), 2277–2282. It has to be noted that this experiment had its roots in Jean Picard’s accidental discovery that a shaken mercury barometer was glowing in the dark (1676). See: Shectman, Groundbreaking Scientific Experiments, p. 84.
Home, “Mechanics and Experimental Physics”, pp. 368–369.
Heilbron, Electricity in the 17 th and 18 th Centuries, p. 83.
Ibid., p. 82. As we know from modern physics, the intensity of glow in a vacuum tube (or the passage of electricity in it) is related to the pressure of air in the tube or the glass globe.
William Watson, “An Account of the Phenomena of Electricity in Vacuo, with Some Observations Thereupon”, Philosophical Transactions, 47 (1751–1752), 366–367. In electricity, Watson’s fame rests on his theory of charge conservation which states that bodies normally have equal density of electrical fluid or ether. However, if the density of the electric fluid is unequal in different bodies, the fluid will flow and will be seen as an electric discharge. In other words, his theory says that electricity can not be created or destroyed but only can be transferred from one object to another. See: Idem, “A Sequel to the Experiments and Observations Tending to Illustrate the Nature and Properties of Electricity”, Philosophical Transactions 44 (1746–1747), 704–749, especially p. 742.
Franklin, Benjamin, Experiments and Observations on Electricity. Made at Philadelphia in America (London, 1751), pp. 51–55.
Ibid., pp. 45–46.
Ibid., p. 46.
John Canton, “Electrical Experiments, with an Attempt to Account for Their Several Phenomena; Together with Some Observations on Thunder-Clouds”, Philosophical Transactions, 48 (1753–1754), 357–358. Canton, in a letter to the president of the Royal Society, shows how electricity became a focus of interest after Franklin’s demonstration of the electric origin of the lightning: “My Lord, as electricity, since the discovery of it in the clouds and atmosphere, is become an interesting subject to mankind; your lordship will not be displeased with any new experiments or observations, that lead to a farther acquaintance with its nature and properties”. See: John Canton, “A Letter to the Right Honourable the Earl of Macclesfield, President of the Royal Society, concerning some new electrical Experiments”, Philosophical Transactions, 48 (1753–1754), 780.
George Matthias Bose (1710–1761), Joseph Priestley (1733–1804) and Giambatista Beccaria (1716–1781) were among those who envisaged a relation between electrical phenomena and the aurora borealis. Priestley says that Beccaria “thinks that the Aurora Borealis may be this electric matter performing its circulation, in such a state of the atmosphere as renders it visible, or approaching nearer to the earth than usual”; and “Signior Beccaria adds, that when the Aurora Borealis has extended lower than usual into the atmosphere, various sounds, as of rumbling, and hissing, have been heared”. See Priestley, The History and Present State of Electricity, vol. 1, pp. 410, 436. Priestley himself takes for granted that the aurora had an electric origin: “That the Aurora Borealis is an electrical phenomenon was, I believe never disputed, from the time that lightening was proven to be one”. Ibid., p. 436. See also Schechner, Comets, Popular Culture, pp. 181–187.
Franklin did not have a well-defined theory of a universal ether. In one of his last papers, he assumed, like Newton, that the ether was a medium where the light-producing vibrations were formed. His ideas about the fluid of heat, electric matter and subtle fluid producing light are discussed in: Cohen, Franklin and Newton, pp. 320–343, especially pp. 340–343.
Franklin, Experiments, pp. 51–52.
Joseph Priestley, The History and Present State of Electricity, with Original Experiments, 3rd ed., 2 vols. (London: 1775), vol. 2, p. 162.
For different models of the ether in the eighteenth century see: Cantor and Hodge, “Introduction”, pp. 29–31.
Hugh Hamilton, Philosophical Essays on the following Subjects. I. On the Ascent of Vapours, the Formation of Clouds, Rain and Dew, and on several other Phœnomena of Air and Waters. II. Observations and Conjectures on the Nature of the Aurora Borealis, and the Tails of Comets. III. On the Principles of Mechanicks, 2nd ed. (London: 1767), pp. 90–91. It is interesting that Hamilton not only fails to mention the observation of the white glow around the eclipsed sun (the solar corona which was assumed to be the solar atmosphere by his contemporaries), but also is silent about all theories which had been developed to explain the zodiacal light, in all of them the existence of a solar atmosphere (with various extensions) was admitted. Accepting a solar atmosphere would create a major difficulty in Hamilton’s theory regarding the possible attraction or repulsion between the solar atmosphere and cometary tails. Although Hamilton does not discuss this specific subject, it seems that by admitting a solar atmosphere he would not be able to explain the shape and orientation of cometary tails in the vicinity of the sun.
Ibid., p. 92. Hamilton’s description of Newton’s theory is confusing. He only discusses the tail formation when a comet approaches too close to the sun to enter its so-called atmosphere.
Ibid., pp. 95–97.
Ibid., pp. 100–102.
Ibid., p. 105.
Ibid., p. 113.
Ibid., pp. 114–115. Hamilton first points out that a comet, like the moon, to keep its one side towards the sun should be an oblong spheroid.
Ibid., pp. 123–126.
Ibid., p. 128. Hamilton also refers to experiments done by John Woodward (1665–1728) which showed something from air or the earth, aside from water, is needed for the nourishment of the planets. For Woodward’s results see: John Woodward, “Some Thoughts and Experiments Concerning Vegetation”, Philosophical Transactions 21 (1699), 193–227.
Ibid.
Hamilton in his description of the aurora seen in March 1716 says that the electric matter rose so high that it was seen from Ireland to Poland and western Russia, or extended at least over 30 degrees of longitude and from the 50th latitude over almost all the north of Europe. According to Hamilton, an imaginary spectator placed at a considerable distance from the earth would see the aurora as a train of light, like a cometary tail, extended from the north pole of the earth. Ibid., pp. 99–100.
Ibid., pp. 129–130. Hamilton refers to Newton’s conclusion about the nature of cometary tails in proposition 41 of book 3 of the Principia: “Further, I suspect that that spirit which is the smallest but most subtle and most excellent part of our air, and which is required for the life of all things, comes chiefly from comets”. See: Newton, Principia, p. 926.
Cohen, Franklin and Newton, p. 287.
Although Hamilton mentions that the curvature of a tail is not due to any resisting matter in space and it only appears because of rapid motion of comet’s head relative to the extremities of the tail, he attributes the brightness of the leading part of a tail to a condensation in fore parts of a tail due to a slight resistance of subtle ether. See Hamilton, Philosophical Essays, pp. 120–131.
This brief survey only covers those writings in English which discuss the physics of comets.
Encyclopaedia Britannica: or, a Dictionary of Arts and Sciences, Compiled upon a New Plan in which The different Sciences and Arts are digested into distinct Treatises or Systems, And the various Technical Terms, etc., are explained as they occur in the order of the Alphabet, 3 vols. (Edinburgh: Printed for A. Bell and C. Macfarquhar and sold by C. Macfarquhar, 1771), vol. 1, pp. 444–445. Comets are defined under the general entry of ‘Astronomy’.
Encyclopaedia Britannica,…, 2nd ed,. 10 vols. (Edinburgh: Printed for J. Balfour, 1778–1783), vol. 2, pp. 761–769.
Encyclopaedia Britannica,…, 3nd ed,. 10 vols. (Edinburgh: 1797), vol. 2, pp. 445–470.
Ephraim Chambers, Cyclopædia, or an Universal Dictionary of Arts and Sciences, 5 vols. (London: 1778–1788), vol. 1, pp. 905–906.
Charles Burney, An Essay Towards a History of the Principal Comets that have Appeared since the Year 1742. Including a particular Detail of the Return of the famous Comet of 1682 in 1759, according to the Calculation and Prediction of Dr. Halley. … With Remarks and Reflections upon the Present Comet. To which is prefixed, a Letter upon Comets, Addressed to the Late M. de Maupertuis written in the year 1742 (London: 1769), pp. 81–85.
Thomas Vivian, Cosmology, An Enquiry into the Cause of what is called Gravitation or Attraction, in which the Motions of the Heavenly Bodies, … are deduced … (Bath: 1791), pp. 103–106.
Samuel Vince, A Complete System of Astronomy (Cambridge: 1797), pp. 444–446.
Margaret Bryan, A Compendious System of Astronomy, in a Course of Familiar Lectures, in which the Principles of that Science are clearly elucidated, so as to be intelligible to those who have not studied the Mathematics… (London: 1799), p. 126.
Charles Hutton, An Astronomical Dictionary Compiled from Hutton’s Mathematical and Philosophical Dictionary, to which is prefixed an introduction Containing a brief history of Astronomy, and a familiar illustration of its elementary principles by Nathan S. Read (New-Haven:1817), pp. 45–48.
James Ferguson, Ferguson’s Astronomy, Explained upon Sir Isaac Newton’s Principles, with notes and supplementary chapters by David Brewster, 2 vols. (Philadelphia: Printer by and for Abraham Small, 1817), vol. 1, pp. 354.
William Phillips, Eight Familiar Lectures on Astronomy (New York: James Eastburn, 1818), p. 84.
See: Morton L. Schagrin, “Early Observations and Calculations of Light Pressure”, American Journal of Physics 42 (1974), pp. 927–929; Home, “Mechanics and Experimental Physics”, pp. 363–366. For a review of theories of light in the eighteenth century, see: Casper Hakfoort, Optics in the Age of Euler: Conceptions of the Nature of Light, 1700–1795 (Cambridge: Cambridge University Press, 1995); Geoffrey Cantor, Optics after Newton: Theories of Light in Britain and Ireland, 1704–1840 (Manchester: Manchester University Press, 1983); Eugene Frankel, “Corpuscular Optics and the Wave Theory of Light: The Science and Politics of a Revolution in Physics”, Social Studies of Science 6 (1976), 141–184.
Schagrin, “Early Observations and Calculations of Light Pressure”, pp. 931–932; Idem, “Experiments on the Pressure of Light in the 18th Century”, Akten des Internationalen Leibniz-Kongresses…, Band II (1974), pp. 217–239.
Ibid., pp. 933–935. According to Martin, a candle emits 4.1 × 1044 particles and each particle has a mass of less than 10−6 of a grain (one grain = 0.0648 g). The average space between the particles of light was calculated to be in the order of magnitude of 10−16 of the size of a hair. For John Michell’s innovative ideas on light see: Simon Schaffer, “John Michell and Black Holes”, Journal for the History of Astronomy 10 (1979), 42–43.
Ibid., p. 934. Franklin first stated his doubts in a letter to Cadwallader Colden in 1752 and read to the Royal society in 1756.
Gerald Holton, Physics, the Human Adventure: From Copernicus to Einstein and Beyond (New Brunswick: Rutgers University Press, 2001), pp. 234–235; Lissa Roberts, “A Word and the World: The Significance of Naming the Calorimeter”, Isis 82 (1991), pp. 198–222.
Bruce R. Wheaton, “Heat and Thermodynamics”, in W. F. Bynum, E. J. Browne, Roy Porter, eds. Dictionary of the History of Science (Princeton: Princeton University Press, 1981), pp. 179–182. For a review of chemical physics of heat developed by Lavoisier and Laplace see: Charles Coulston Gillispie, “Laplace, Pierre-Simon, Marquis de”, in Charles Coulston Gillispie, ed., Dictionary of Scientific Biography, 16 vols. (New York:Charles Scribner’s Son, 1972), vol. 15, pp. 312–316.
In Young’s double slit experiment, a monochromatic light is passing from two very narrow parallel slits which are cut into a non-transparent sheet. On a screen located at a distance to the slits a pattern of alternating light and dark regions appears. This effect can only be interpreted by a wave theory of light: the interference of waves propagating from the two slit create constructive interference when they reinforce, and cause destructive interference when the waves cancel. Poisson based on Fresnel’s wave theory theoretically concluded that it was necessary for a bright spot to appear at the center of the shadow of a circular opaque obstacle. He expected that this unreasonable prediction would disprove Fresnel’s wave theory, but Fresnel (and then Dominique Arago) showed that there was such a bright spot at the center of the shadow. This effect also could be explained by the constructive interference of the diffracted light from the edge of the circular obstacle. See Holton, Physics, pp. 347–348.
Holton, Physics, p. 349. There are a great number of publications about the early nineteenth century debates on the nature of light. A comprehensive technical history can be found in Jed Z. Buchwald, The Rise of the Wave Theory of Light (Chicago: Chicago University Press, 1989); the impact of theories of light on the theories of the ether is discussed in Idem, “Optics and the Theory of the Punctiform Ether”, Archive for the History of Exact Sciences 21(1979), pp. 245–278; for a history of optics in the eighteenth century, with an emphasis of Euler’s work see: Caspar Hakfoort, Optics in the Age of Euler, Conceptions of the nature of light, 1700–1795 (Cambridge: Cambridge University Press, 1995), especially pp. 27–72; an analysis of debates on theories of light in the eighteenth and nineteenth centuries is in Peter Achinstein, “Hypotheses, Probability, and Waves”, British Journal for the Philosophy of Science 41(1990), pp. 117–147; Idem, Particles and Waves: Historical Essays in the Philosophy of Science (New York; Oxford University Press, 1991); an analysis of Achinstein’s work is in Chris Eliasmith, Paul Thagard, “Waves, Particles, and Explanatory Coherence”, British Journal for the Philosophy of Science 48 (1997), pp. 1–19; for a review of light theories in the first half of the nineteenth century see Xiang Chen, Peter Barker, “Cognitive appraisal and power: David Brewster, Henry Brougham, and the tactics of the emission-undulatory controversy during the early 1850s”, Studies in the History and Philosophy of Science 23(1992) pp. 75–101; and Xiang Chen, “The Debate on the Polarity of Light, during the Optical Revolution”, Archive for the History of Exact Sciences (50) 1997, pp. 359–393.
Jed Z. Buchwald, “Waves, Philosophers and Historians”, Proceedings of the Biennial Meeting of the Philosophy of Science association, 2 vols. (Chicago: Chicago University Press, 1992), vol. 2, p. 206.
Thomas S. Kuhn, The Structure of Scientific Revolutions, 3rd ed. (Chicago: The University of Chicago Press, 1996), p. 13.
The underlying social factors in development of astronomy were not only different in England and France, but also the diverse approaches of the British and the Continental mathematicians to analysis and mechanics brought about different levels of advancement in the calculus-related parts of mathematics. For the differences between the Newtonian calculus and that of Leibniz (which was maintained by the Continental mathematicians) see: Katz, A History of Mathematics, pp. 503–531; Boyer, A History of Mathematics, pp. 391–414; D. T. Whiteside, “Patterns of Mathematical Thought in the Late Seventeenth Century”, Archive for the History of Exact Sciences 1 (1961), pp. 173–388; Curtis Wilson, “The problem of perturbation analytically treated: Euler, Clairaut, d’Alembert”, in R. Taton and C. Wilson (eds.), The General History of Astronomy, vol. 2B, pp. 89–94;Craig Fraser, “Mathematics”, in Roy Porter (ed.), The Cambridge History of Science, Volume 4: Eighteenth-Century Science (Cambridge: Cambridge University Press, 2003), pp. 305–327; For a history of mathematics in Britain in the eighteenth century see Niccolò Guicciardini, The Development of Newtonian Calculus in Britain, 1700–1800 (Cambridge: Cambridge University Press, 1989); For a social history of science in France during the second half of the seventeenth century see: Roger Hahn, The Anatomy of a Scientific Institution, The Paris Academy of Sciences, 1666–1803 (Berkeley: University of California Press, 1971).
Curtis Wilson, “The problem of perturbation analytically treated”, pp. 89–107; Pannekoek, A History of Astronomy, pp. 299–303.
Regarding the uncertainties in the planetary masses, the perturbative effects of the undiscovered planets, and the problems in the method of approximation, Clairaut’s calculations had a fairly small error. See Yeomans, Comets, pp. 111–139; Pannekoek, A History of Astronomy, pp. 302–303; Curtis Wilson, “Clairaut’s Calculation of the Eighteenth-Century Return of Halley’s Comet”, Journal for the History of Astronomy 24 (1993), 1–15; Craig B. Waff, “Predicting the mid-eighteenth-century return of Halley’s Comet”, in R. Taton and C. Wilson, eds., The General History of Astronomy, vol. 2B, pp. 69–82; Peter Broughton, “The First Predicted Return of Comet Halley”, Journal for the History of Astronomy 16 (1985), 123–133; For a history of return of Halley’s comet in 1759 see: Simon Schaffer, “ Halley, Delisle, and the Making of the Comet”, in Norman J. W. Thrower, eds., Standing on the Shoulders of Giants, pp. 254–298; Craig B. Waff, “The First International Halley Watch: Guiding the Worldwide Search for Comet Halley, 1755–1759”, Ibid., pp. 373–411; Idem, Comet Halley’s First Expected Return: English Public Apprehensions, 1755–1758”, Journal for the History of Astronomy 17 (1986), 1–37; Ruth Wallis, “The Glory of Gravity–Halley’s Comet 1759”, Annals of Science 41 (1984), 279–286; Phillip Stewart, “Science and superstition: Comets and the French public in the eighteenth century”, American Journal of Physics 54 (1986), 16–24.
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(2008). Non-Newtonian Theories of Comets. In: A History of Physical Theories of Comets, From Aristotle to Whipple. Archimedes: New Studies In The History And Philosophy Of Science And Technology, vol 19. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-8323-5_6
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