In 1819, French physicist and astronomer François Jean Dominique Arago (1786–1853) used a newly developed polarimeter (Fig. 7.1) to observe the tail of a brilliant comet that appeared in late June. Ten years earlier, Etienne Malus (1775–1812) discovered that light can be polarized by reflection. He was observing the reflected rays of the sun through a birefringent crystal (Iceland Spar) and found that when he rotated the crystal, the two images of the sun became darker or brighter. Arago observed the same effect when the light of the comet’s tail was seen through the polariscope. He observed Capella (which was at the same altitude as the comet) with the same arrangement of telescope-polariscope, but polarization did not happen. Thus, the terrestrial atmosphere was not involved in the observed effect. Capella was a self-luminous object and its light did not show polarization, but the light of the comet (or a part of it) should be reflected light:
We must conclude from these observations that the cometary light was not entirely composed of rays having the properties of direct light, there being light which was reflected specularly or polarized, that is, coming from the sun. It can not be stated with absolute certainty that comets shine only with borrowed light, for bodies, in becoming self-luminous, do not, on that account, lose the power of reflecting foreign light.
Arago’s discovery was the first interpretation of cometary light before the application of spectroscopy in astronomy. It was so significant that a generation later Alexander von Humboldt (1769–1859) mentioned it as “the most important and decisive observations that we possess on the nature and the light of comets.” After centuries of cometary observations scientists were able to judge confidently the nature of a comets’ light or at least about a part of it.
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References
François Jean Dominique Arago, “Quelques nouveaux details sur la passage de la comète découverte dans le mois de Juillet 1819, devant le disque du soleil”, Annales de chimie et de physique, série 2, 13 (1820), 104–110; Also in François Arago, Oeuvres complètes (Paris: 1859), Tom 11, pp. 509–524. The translation is quoted from: Alexander von Humboldt, Cosmos: A Sketch of the Physical Description of the Universe, translated from the German by E. C. Otté, 2 vols. (New York: Harper, 1850), vol. 1., p. 105.
Humboldt, Cosmos, p. 105.
Humboldt believed in a kind of internal process in the planets or comets which might produce light or affect the light they reflect from the sun. He says: “These beautiful experiments still leave it undecided whether, in addition to this reflected solar light comets may not have light of their own. Even in the case of the planets, as, for instance, in Venus, an evolution of independent light seem very probable. The variable intensity of light in comets can not always be explained by the position of their orbits and their distances from the Sun. it would seem to indicate, in some individuals, the existence of an inherent process of condensation, and an increased or diminished capacity of reflecting borrowed light”. Ibid., pp. 105–106. Laplace also believed that the sun and stars are encompassed in a layer of self-luminous fluid. See below.
William Herschel, “Astronomical Observations relating to the Construction of the Heavens, arranged for the Purpose of a critical Examination, the Result of which appears to throw some new Light upon the Organization of the celestial Bodies”, Philosophical Transactions 101 (1811), 333. Like many other natural philosophers in the eighteenth century, Herschel believed in the fundamental role of the active principles – light, electricity, fire and fermentation – in the construction and function of nature. Herschel in his numerous publications considered the nature of the self-luminous nebulae, the structure of the sun, and the action of the sun’s rays on matter. During his studies of the sun’s rays Herschel discovered the infrared radiation, which was an invisible active emission. For Herschel’s theory of light and matter see: Simon Schaffer, “The Great Laboratories of the Universe: William Herschel on Matter Theory and Planetary Life”, Journal for the History of Astronomy 11 (1980), 81–111.
Idem., “On Nebulous Stars, properly so called”, Philosophical Transactions 81 (1791), 83–84. It is interesting that Herschel does not mentions cometary tails in this analogy.
Ibid., pp. 87–88.
In his famous paper about the construction of the heavens he defines the nebulous matter: “ By nebulous matter I mean to denote that substance, or rather those substances which give out light, whatsoever may be their nature, or of whatever different powers they may be possessed”. See Herschel, “Astronomical Observations relating to the Construction of the Heavens”, p. 277.
Herschel, “Astronomical Observations relating to the Construction of the Heavens”, p. 292.
Ibid., pp. 299–305.
Ibid., p. 306.
William Herschel, “Observations of a Comet, made with a View to investigate its Magnitude and Nature of its Illumination. To which is added, an Account of a new Irregularity lately perceived in the apparent Figure of the Planet Saturn”, Philosophical Transactions 98 (1808), 156–157. Herschel also points out that the light of this comet had much greater resemblance to the light of stars than to the mild reflection of the solar rays from the moon.
Ibid., p. 158.
Ibid., pp. 138–140.
Ibid., pp. 142–143.
William Herschel, “Observations of the second Comet, with Remarks on its Construction”, Philosophical Transactions 102 (1812), p. 234. The brightness of an image seen through the ocular of a telescope or the relative light transmitting capacity of a telescope (which is also the twilight factor) is equal to d2 (D/M)2, where d is the diameter of the exit pupil, D is the diameter of the objective, and M is magnification. Thus, when all conditions are the same, using a higher magnification yields dimmer images at the ocular. See: J. B. Sidgwick, Amateur Astronomer’s Handbook (New York: Dover, 1971), pp. 29–31.
Ibid., p. 235.
Ibid., pp. 236–237. For William Herschel’s cosmology see: Michael Hoskin, William Herschel and the Construction of the Heavens (New York: Norton, 1964); Idem, “The English Background to the Cosmology of Wright and Herschel”, in Wolfgang Yougrau, Allen D. Breck (eds.), Cosmology, History and Theology (NewYork: Plenum, 1977), pp. 291–321; Idem, “William Herschel’s early investigations of nebulae: A reassessment”, Journal for the History of Astronomy 10 (1979), 165–176; Schaffer, “The Great Laboratories of the Universe”, pp. 81–111; Idem, “Herschel in Bedlam: Natural History and Stellar Astronomy”, British Journal for the History of Science 13 (1980), 211–239; Idem, “The nebular hypothesis and the science of progress”, in J. R. Moore, ed. History, Humanity and Evolution (Cambridge: Cambridge University Press, 1989), pp. 131–164; Bernard Lovell, “Herschel’s Work on the Structure of the Universe”, Notes and Records of the Royal Society of London 33 (1978), 57–75; Stephen G. Brush, Nebulous Earth, The Origin of the Solar System and the Core of the Earth from Laplace to Jeffreys (Cambridge: Cambridge University Press, 1996), pp. 29–36.
The Essai…originally published as the “Introduction” to the second edition of Laplace’s Théorie analytique des probabilités (Paris: 1812). See Charles C. Gillispie, R. Fox, I. Grattan-Guinness, “Laplace, Pierre-Simon, Marquis de”, in Charles C. Gillispie (ed.), Dictionary of Scientific Biography, 15 vols. (New York: Charles Scribner’s Sons, 1972), vol. 15, p. 388. Laplace wrote the Essai… and Exposition when he was appointed professor at the new École Normale after the French Revolution in 1789. There, he was asked to deliver lectures on celestial mechanics and probability theory without using mathematics. See Brush, Nebulous Earth, p. 20.
Six editions of Exposition du système du monde were published from 1796 to 1835. One of the subjects that underwent changes was the theory of comets, which will be considered below.
Pierre Simon Marquis de Laplace, A Philosophical Essay on Probabilities, trans. E. T. Bell (New York: Dover, 1951), p. 97.
Laplace also in different editions of the Exposition has calculated the probability of a chance causation of the solar system. In its third edition (1808) which appeared after the discovery of the first four asteroids (Ceres in 1801, Pallas in 1802, Juno in 1804 and Vesta in 1807) Laplace stated that it is more than four thousand billion against one that the arrangement of the solar system is the effect of chance. In a paper written in 1773 (before the discovery of two satellites for Saturn, the planet Uranus, its satellites, and asteroids) Laplace made his calculations for only six planets and ten satellites which were the moon, four satellites of Jupiter and five of Saturn. He used Daniel Bernoulli’s formula in which the chance that n bodies all moved in the same one of two directions is 2−n+1 and found the probability to be 2−15 or 1/32, 768 that at least one of the motions of the planets, satellites (and the ring of Saturn) had been determined by chance. See: Brush, Nebulous Earth, p. 21; Stanley L. Jaki, “The five forms of Laplace’s cosmogony”, American Journal of Physics 44 (1976), 4–5.
Ibid., p. 98.
Ibid., pp. 99–101. We will return to Laplace’s nebular theory when discussing his Exposition du système du monde.
Ibid., 102. Kant also uses a similar analogy to illustrate the stars outside of the plane of the Milky Way: “Those suns which are least closely related to this plane […] so to speak, [are] the comets among the suns. See Kant, Cosmogony, p. 47.
Ibid. pp. 103–104. This idea that comets are strangers to the solar system appeared in the fourth edition of the Exposition (1813). Before that Laplace assumed comets to originate from the same nebula that condensed to form the solar system. See below.
See Pierre Simon Laplace, “Mémoire sur l’inclinaison moyenne des orbites des comètes, sur la figure de la terre, et sur les fonctions”, in Laplace, Oeuvres complètes de Laplace, 14 vols. (Paris: Paris: Gauthier-Villars, 1878–1912), vol. 8, pp. 279–321; Pierre Simon Laplace, Théorie analytique des probabilités (Paris: Courcier, 1812), pp. 253–261.
Gillispie, et al, “Laplace”, pp. 290–292.
For a history of orbit calculations of Lexell’s comet see: Alexander-Guy Pingré, Cométographie, ou Traité historique et Théorique de Comètes, 2 vol. (Paris: 1783–1784), vol. 2, pp. 106–107; David Milne, Essay on Comets (Edinburgh: 1828), pp. 100–109;Yeomans, Comets, pp. 157–160; Gary W. Kronk, Cometography, A Catalog of Comets, vol. 1: Ancient – 1799 (Cambridge: Cambridge University Press), pp. 447–451.
Since Lexell’s comet had not been observed before, to verify its calculated period and orbital elements the French National Institute offered a prize for the most complete investigation of the comet’s orbital characteristics. The winner was Johann Karl Burckhard (1773–1825), German mathematician and astronomer, whose research yielded almost the same results as those of Lexell. See Milne, Essay on Comets, pp. 100–101; Pierre Simon Laplace, Celestial Mechanics, trans. Nathaniel Bowditch, 4 vols. (New York: Chelsea, 1966), vol. 4, pp. 429.
Laplace, Celestial Mechanics, vol. 4, p. 436. Nevil Maskelyne (1732–1811) was the fifth Astronomer Royal, who published the first volume of the Nautical Almanac in 1766. Maskelyne carried on for almost half a century the tradition of precise observation which Bradley established at the Greenwich Observatory. See: Berry, A Short History of Astronomy, pp. 273–274; Hoskin, Illustrated History, pp. 180; a complete history of Maskelyne’s life and works is in Derek Howse, Nevil Maskelyne, The Seaman’s Astronomer (Cambridge: Cambridge University Press, 1989).
Ibid., p. 437(Laplace’s Italics). Laplace even before publishing the fourth volume of the Celestial Mechanics (where he estimated cometary masses) believed that only a direct collision of a comet with the earth produces destructive effects. In the second edition of the Exposition (1799) he states: “They [comets] pass so rapidly by us, that the effects of their attraction are not to be apprehended. It is only by striking the earth that they can produce any disastrous effect. But this circumstance, though possible, is so little probable in the course of a century […] that no reasonable apprehension can be entertained of such an event”. See: Laplace, The System of the World, 2nd ed., trans. J. Pond, 2 vols. (London: 1809), vol. 2, p. 63.
It has to be noted that Laplace calculated the mass of the moon with a higher accuracy. While Newton estimated the moon’s mass to be 1/40 of the earth’s mass, Laplace using different methods, estimated it at between 1/50 to 1/74, but declared the ratio 1/68.5 as the most likely value. See: Ibid, vol. 3, pp. 336–339.
Laplace, The System of the World, trans. Henry H. Harte, 2 vols. (Dublin: 1830), vol. 1, p. 79. Also in Laplace, Exposition, in Oeuvres completes, vol. 6, 57. Laplace’s idea about the role of comets in the history of the earth changed during the time he was developing his cosmogony. In the last edition of the Exposition he maintained that cometary impacts can only produce local revolutions. To trace the changing ideas of Laplace on cometary impacts see: Schechner, Comets, Popular Culture, pp. 208–214; for a review of the history of geological ideas in the second half of the eighteenth century in which the extraterrestrial considerations are marginalized see: Kenneth L. Taylor, “Earth and Heaven, 1750–1800: Enlightenment Ideas about the Relevance to Geology of Extraterrestrial Operations and Events”, Earth Sciences History 17 (1998), 84–91.
Ibid., p. 205.
A collision between a comet and a planet may happen if (1) the radius vector of the comet is exactly equal to the planet’s distance from the sun; (2) the comet located exactly in the plane of the planet’s orbit and (3) the longitude of its ascending or descending node is equal to the heliocentric longitude of the planet. It is very improbable that two objects in the vastness of the space fulfill all of these requirements exactly. See Milne, Essay on Comets, pp. 115–116. The French mathematician Dionis du Séjour (1734–1794), in a treatise entitled Essai sur les comètes en général; et particulièrement sur celles qui peuvent approcher de l’orbite de la terre (1775), studied the probability of impact of a comet on the earth and showed that from all comets with orbital elements that were ascertained none could pass the earth closer than about twice the moon’s distance, and none of them ever passed the earth closer than nine times the moon’s distance. See: Denison Olmsted, Letters on Astronomy (New York: 1853), p. 344.
Ibid., vol. 2, p. 49.
Bruno Morando, “Laplace”, in R. Taton, C. Wilson, eds. The General History of Astronomy, vol. 2B, p. 144.
Humboldt calls it as an ‘immortal work” which France possesses (Humboldt, Cosmos, p. 48), and François Arago classes it “among the beautiful monuments of the French language” (Morando, “Laplace’”, p. 144); also see: Jaki, “The five forms of Laplace’s cosmogony”, p. 4; Berry, A Short History of Astronomy, p. 306.
Jaki, “The five forms of Laplace’s cosmogony”, pp. 4–11; R. Stolzle, “Die Entwicklungsgeschichte der Nebularhypothese von Laplace, Ein Beitrag zur Geschichte der Naturphilosophie”, in Geburtstag Georg Freiherrn von Hertling, Abhandlungen aus dem Gebiete der Philosophie und ihrer Geschichte: eine Festgabe zum 70 (Freiburg: Herder, 1913), 349–369; Charles Allen Whitney, The Discovery of Our Galaxy (NewYork: Knopf, 1971), pp. 133–154; B. J. Levin, “Laplace, Bessel, and the Icy Model of Cometary Nuclei”, The Astronomy Quarterly 5 (1985), 113–118; Brush, Nebulous Earth, pp. 20–23; Schechner, Comets, Popular Culture, pp. 208–214.
Levin, “Laplace, Bessel”, pp. 114, 117.
This chapter – of Comets – which is chapter X of book one in the first three editions and chapter XII in the last three, remained intact in all editions.
This is the chapter where Laplace introduces his theory of cometary nuclei in the third and the fourth editions but omits it in the fifth and the sixth editions. Due to revisions in different editions of the Exposition, the chapter numbers are varied. The chapter (of the figures…) is numbered VI in the first, second and third editions, but is number V in the other editions. See: Laplace, Exposition du système du monde, 1st ed., 2 vols. (Paris: 1796), vol. 1, pp. 165–172; Idem, Exposition…, 2nd ed (Paris: 1799), p. 119–124; Idem, Exposition…, 4th ed (Paris: 1813), p. 127–134; Idem, Exposition…, 5th ed, 2 vols. (Paris: 1824), vol.1, pp. 225–236; Idem, Exposition…, 6th ed., in Laplace, Oevres complètes de Laplace, 14 vols. (Paris: 1878–1912), vol. 6, pp. 135–141.
Laplace in other publications also discusses the structure of comets; however, his description in book two of the Exposition is more complet. For example see: Laplace, “Sur les comètes”, read in 1813, reprinted in Laplace, Oeuvres complètes de Laplace, 14 vols. (Paris: 1878–1912), vol. 13, pp. 88–97; Idem, A Philosophical Essay, p. 99.
In 1783 Laplace and Lavoisier published their studies on the nature of heat and introduced the famous ice calorimeter they had devised to measure any change in the amount of heat during the change of state. Their treatise entitled Mémoire sur la chaleur, in four parts, discusses the nature of heat, the determination of specific heats of various substances, theory of physical chemistry, and finally methods of study of combustion and respiration. See Gillispie, et al, “Laplace”, pp. 312–316; Roberts, “A Word and the World”, pp. 199–222; Henry Guerlac, “Chemistry as a Branch of Physics: Laplace’s Collaboration with Lavoisier”, Historical Studies in the Physical Sciences, 7 (1985), 193–276.
Laplace, The System of the World (1830), p. 200.
Laplace also omitted three chapters of book four of the Exposition in the fifth edition, in order to develop their contents in a separate treatise concerning the phenomena dependant on molecular action. Since he did not prepare the treatise, the deleted chapters were restored in the sixth edition which appeared after Laplace’s death. See: Levin, “Laplace, Bessel, and the Icy Model”, p. 114. It is not known why Laplace deleted the passage regarding the change of state of comets from the fifth edition.
The omission of this passage was pointed out for the first time by B. J. Levin. He emphasized that “in both French editions of Laplace’s collected works and in all translations into other languages, the text of the Exposition du système du monde is given according to the sixth Paris edition, and therefore the excluded passage on comets remained practically lost to astronomy” (Levin, “Laplace, Bessel, and the Icy Model”, p. 115). Obviously, he did not have access to Henry Harte’s English translation of the Exposition which was published in 1830 and contained the whole omitted passage. Levin’s unawareness of this translation caused him to ask a French speaking astrophysicist (Armand H. Delsemme) to translate the omitted passage. However, Harte’s translation itself is a mystery: it is a translation of the fifth edition of the Exposition, but it contains the omitted passage without any explanation of the translator. Harte added several explanatory notes to his translation but neither in those notes nor in the introduction does he give a clue about the original text he chose for translation. The original text could not be the fourth edition (1813) because it contains Laplace’s discussion of the observation of Enke’s comet in 1818 and 1819.
Laplace, The System of the World, trans. H. Harte, pp. 200–203.
Holton, Physics, pp. fo234–239; Douglas McKie, Niels H. de V. Heathcote, The Discovery of Specific and Latent Heats (London: Edward Arnold, 1935), pp. 222–249; R. J. Morris, “Lavoisier and the Caloric Theory”, British Journal of the History of Science 6 (1972), 1–38; Luis M. R. Saraiva, “Laplace, Lavoisier and the Quantification of Heat”, Physis 34 (1997), 99–137. Laplace met Rumford (and William Herschel) in 1802. All three scientists visited Napoleon Bonaparte when he was the First Consul. See: Whitney, The Discovery of Our Galaxy, pp. 123–124.
Friedrich Wilhelm Bessel (1784–1846) in a paper published in 1836 suggested that the nucleus of a comet is not a solid body like the earth or the moon. He theorized that the matter of cometary nuclei must change to a vapor state easily. Inspired by Laplace’s theory Bessel wrote: “The fact volatility shows first on the surface side right under the sun, and its action is stronger, and extended to an always larger fraction of the surface, by a closer proximity of the sun and by a longer duration, fits well with the observations. The fact that the vaporization and its latent heat must be protected from destruction, has been, if I am not mistaken, noticed first by Laplace”. According to Levin Bessel apparently read the above-mentioned passage in the third or the fourth edition of the Exposition, and unable to find it in the later editions expressed his uncertainty in referring the idea to Laplace. See Levin, “Laplace, Bessel, and the Icy Model”, p. 114.
Laplace, The System of the World (1830), pp. 203–205.
Ibid., pp. 206–207.
Laplace’s nebular hypothesis has been the subject of several studies. Here we mainly concentrate on the situation of comets in this hypothesis. For Laplace’s cosmology and its evolution see: Jaki, “The five forms of Laplace’s cosmogony”, pp. 4–11; Brush, Nebulous Earth, pp. 20–29; Roger Hahn, “Laplace and the vanishing role of God in the physical universe”, in Harry Woolf (ed.), The Analytic Spirit: Essays in the History of Science in Honor of Henry Guerlac (Ithaca: Cornell University Press, 1981), pp. 85–95, Ronald L. Numbers, Creation by Natural Law, Laplace’s Nebular Hypothesis in American Thought (Seattle: University of Washington Press, 1977), pp. 3–13, 124–132; Jacques Merleau-Ponty, “Laplace As a Cosmologist”, in Wolfgang Yourgrau, Allen D. Breck, eds., Cosmology, History, and Theology (New York: Plenum Press, 1977), pp. 283–291.
Laplace, Exposition, 1st ed., vol. 2, p. 302; Idem, The System of the World, 2nd ed, pp. 363–364.
Laplace, Exposition, 4th ed., p. 436. Laplace did not give any clue about the stellar systems and the average distance between the stars.
Laplace, The Philosophical Essay, p. 102.
Laplace, The System of the World (1830), vol. 2, p. 136.
For the eighteenth century developments on the perturbation theory see: Jeff A. Suzuki, “A History of the Stability Problem in Celestial Mechanics, from Newton to Laplace”, PhD. diss., Boston University, 1996. Suzuki elaborates technically the main problems and developments in the perturbation theory and shows the critical role of Lagrange and his superiority to Laplace in some fields. Also see: Berry, A Short History of Astronomy, pp. 289–321; Morando, “Laplace”, 131–142; Curtis Wilson, “The problems of perturbation analytically treated”, pp. 89–107; Idem, “Perturbation and Solar Tables from Lacaille to Delambre: the Rapprochment of Observation and Theory, Part I”, Archive for the History of Exact Sciences 22 (1980), 189–296; Gillispie, et al, “Laplace”, pp. 322–333; Florin Diacu, Philip Holms, Celestial Encounters, The Origin of Chaos and Stability (Princeton: Princeton University Press, 1996), pp. 127–157.
Milne, Essay on Comets, p. 109.
Ibid., p. 120.
H. N. Robinson, A Treatise of Astronomy, Descriptive, Theoretical and Physical (New York: 1857), p. 54.
Ibid., p. 160, quoted from Ezra Otis Kendall, Uranography, or, A Description of Heavens (Philadelphia: 1845).
Olmsted, Letters on Astronomy, pp. 345–346.
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(2008). Comets in the Laplacian Cosmos. 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_7
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