Isaac Newton's Historia Cometarum and the Quest for Elliptical Orbits

Seneca Lucius Annaeus , Quaestiones naturales, transl. by Corcoran Thomas H. (Cambridge, MA, 1972), Bk 7.3.1, 231–3.

Ruffner J. A. , “The curved and the straight: Cometary theory from Kepler to Hevelius”, Journal for the history of astronomy, ii (1970), 178–94.

Flamsteed to Towneley, 11 May 1677, The correspondence of John Flamsteed the first Royal Astronomer , ed. by Forbes E. G. (3 vols, Bristol and Philadelphia, 1995–2002; hereafter: Flamsteed correspondence), i, 552–4.

Hooke Robert , Cometa (London, 1678), in Gunther R. T. (ed.), Early science in Oxford (15 vols, London, 1967–68), viii, 209–71, pp. 251 seq.

Understand that apparent length provides at best a rough indication of the true length depending on perspective and other factors.

Flamsteed's copy of Gallet's observations mixed old and new style dates as if they were all old style. They would have been included in his letter of 12 February 1680/1 sent to James Crompton for Newton. The full letter was lost or discarded, with an abstract added to a blank page of Flamsteed's 7 March 1680/1 letter. The correspondence of Isaac Newton , ed. by Turnbull H. W. (7 vols, Cambridge, 1959–77; hereafter: Correspondence), ii, 336, 343, 348–9. Other material was entered in Newton's Waste Book, see ref. 10. Flamsteed tried to blame Newton for the confusion. The same misrepresentation was in the copy sent to Towneley, 7 February 1680/1, Flamsteed correspondence, i, 756. Flamsteed also indicated that Gallet's observations were made at Rome, rather than at Avignon.

Cambridge University Library (CUL) Add Ms 3965.11, f. 153. Reel 4 in the Chadwick-Healy microfilm edition of Sir Isaac Newton manuscripts and papers available at many institutions or through interlibrary loan. Some scholars will have access to digital scans of documents in CUL Add Ms 3965 through the RLG Cultural Materials Project available at a few subscribing libraries. The document used initial data from Flamsteed, later corrected in his letter of 12 February 1680/1. When plotted, the calculated parameters map a straight line.

Flamsteed to Crompton for Newton, 15 December 1680/1; Flamsteed to Crompton, 3 January 1680/1, Correspondence, ii, 315–17, 319–20.

CUL Add Ms 3965.14, 614r. Reel 5. The list is consistent with what could have been compiled from Giovanni Battista Riccioli, Almagestum novum (2 parts, Bologna, 1651), ii, 2–20. The memorable listings followed an account by an anonymous observer for 15 December 1680/1 cited in a letter of 28 February 1680/1 and preceded a list of his observations, one of which (for 11 January 1680/1) was revised in a letter of 16 April 1681. By that time he largely discounted the rest as insufficiently accurate. Correspondence, ii, 346, 365–6.

The theory would have been part of Flamsteed's letter of 12 February 1680/1 but not deemed worth saving. See ref. 6. The details are known from Flamsteed's letter to Halley, 17 February 1680/1 and Newton's response of 28 February 1680/1. Correspondence, ii, 336–47. The letter of 12 February also included the first full set of observations from Greenwich and a partial set from Paris. These observations were preserved in Newton's Waste Book along with a corrected copy of Gallet's observations, and further observations of the November comet made by Tho[mas] Hill at Canterbury and Marco Antonio Cellio at Rome (from Flamsteed's letter of 7 March). CUL Add Ms 4004, f. 98v. Newton copied the “former” set of Greenwich observations from Flamsteed's letter of 12 February in preference to the revised set of 7 March. This former set originally listed the longitude for 10 January as Aries 20°49½′ altered sometime after the 16 April letter to 20°41½′ in closer agreement with revised set. See Correspondence, ii, 354, 365.

Flamsteed to Towneley, 22 March 1689/1, Flamsteed correspondence , i, 781. See also The Gresham lectures of John Flamsteed, ed. by Forbes E. G. (London, 1975), 30, 105–17.

Newton to Flamsteed, 28 February 1680/1, Correspondence, ii, 346.

Compare Newton's point of agreement with Flamsteed's view “that ye atmosphere about ye head [of a comet] shines also the suns light, though perhaps not altogether by it” (ibid.) with one aspect of Hooke's analysis, “the light of the Comet did not depend wholly from the Sun beams”, Cometa (ref. 4), 261. But see also Newton's notes “ex Hookii Cometa edito ann 1678” (“from Hooke's Cometa published in 1678”). CUL Add Ms 4004, ff. 103r–104r. Reel 14. Judged on the basis of the immediately surrounding material, these notes were made in March 1680/1 when Newton began to compile information on comets from a variety of sources. When he first read the work is at issue.

CUL Add Ms 4004, f. 101r.

Newton to Flamsteed, 16 April 1681, Correspondence, ii, 364.

Correspondence, ii, 366.

Westfall R. S. , Never at rest: A biography of Isaac Newton (Cambridge, 1980), 353. The title comes from Jewish National and University Library, Yah. Ms. Var 1 Newton Ms 16.2. Reel 39. Hereafter: Yahuda Ms.

Schaffer Simon , “Comets and idols: Newton's cosmology and political theology”, in Theerman P. Seef A. F. (eds), Action and reaction (Cranbury, NJ, 1993), 183–231, p. 220. From an unused preface for the third edition. The mathematical papers of Isaac Newton, ed. by Whiteside D. T. (8 vols, Cambridge, 1967–81; hereafter: Mathematical papers), vii, 495. See also Nicholas Fatio de Duillier to Christiaan Huygens, 29 February 1691, Correspondence, iii, 193.

Yahuda Ms 17.2, ff. 18r–19r. Reel 39. Two paragraphs on f. 20r are repeated in “Philosophical origins”, Yahuda Ms 16.2, f. 1. Westfall indicates the basic argument of Yahuda Ms 16.2 is sketched in Yahuda Ms 17.2, f. 14. He dates the material to late 1683 or early 1684, Never at rest (ref. 17), 351–2, n. 55. See also Iliffe R. , “Is he like other men?”, in Maclean G. (ed.), Culture and society in the Stuart Restoration (Cambridge, 1995), 159–176, see pp. 164–70, esp. notes 19, 21, 23, 24, 28.

CUL Add Ms 4004, f. 101v. The added sentence is at f. 99r. Reel 14. Some scholars think Newton learned these details at a meeting in 1682 when Halley returned from the Continent. I am unaware of any independent evidence for such a meeting.

CUL Add Ms 3965.7, ff. 55–62. Reel 4. Mathematical papers , vi, 59. Herivel John , The background to Newton's Principia (London, 1965), 257–92, p. 285.

CUL Add Ms 3965.7, ff. 40–54. Reel 4. Herivel, op. cit. (ref. 21), 301.

Ibid., 302.

Newton to Flamsteed, 12 January 1684/5, Correspondence, ii, 413.

Newton's request is lost. The contents are known from Flamsteed's response of 27 December 1684. Correspondence, ii, 403–6.

Newton to Aston, 24 February 1684/5, Correspondence, ii, 415.

CUL Add Ms 3990. Reel 12. Published posthumously as A treatise of the system of the world. Translated into English (London, 1728; 2nd edn, 1731; reprinted 1969). Also Sir Isaac Newton's Mathematical principles of natural philosophy and his System of the world , transl. by Motte Andrew Cajori Florian (Berkeley, 1930, etc.; hereafter: Newton's system, Cajori edn), 549–626. Section numbers follow those in this edition. A more faithful critical translation is needed.

Newton's system, Cajori edn, Section l, 549–50.

Early drafts of DMCII, Sections 57, 58, 63, and 64 are found in CUL Add Ms 3965.11, ff. 175–76. Reel 4.

CUL Add Ms 3965.11, ff. 172r–173v. Reel 4.

Hevelius Johannes , Cometographia (Gdansk, 1668); Descriptio cometae anno aerae Christ. M.DC.LVX. exorti… (Gdansk, 1666); Mercurius in sole visus Gedani (Gdansk, 1662); Annus climactericus (Gdansk, 1685).

Riccioli , Almagestum novum (ref. 9).

Mercator Nicolas , Institutionum astronomicarum libri duo (London, 1675).

Kepler Johannes , Tabulae Rudolphinae (Ulm, 1627), in Gesammelte Werke, ed. by Caspar Max Hammer Franz (Munich, 1937–), x, 104–42; Wing Vincent , Astronomia Britannica (London, 1669), tables, 70, passim.

Cometae observationes cometae habitae ab Academia Physicomathematica Romana anno 1680 et 1681 (Rome, 1681), ed. by Ponteo Giuseppe . This book was probably first seen by Newton in 1685.

Hevelius , Cometographia , Bk 12, 719–913. Lubienski Stanislaw , Theatrum cometarum pars posterior (Amsterdam, 1666) might have been a supplemental source but I find no specific trace of its use at this time.

Riccioli , Almagestum novum (ref. 9), i, 226.

Descartes René , The principles of philosophy, transl. by Miller V. R. Miller R. P. (Dordrecht, 1983), sections 128, 157.

There was confusion whether four or better three different comets appeared in 1618. Newton followed Riccioli and Hevelius in considering this comet to be the fourth. No period has been established for it. Kronk Gary W. , Cometography: A catalog of comets (4 vols, Cambridge, 1999–2008), i, 338–41.

Newton's System, Cajori edn (ref. 27), 576.

Newton Isaac , Philosophiae naturalis principia mathematica (London, 1687; hereafter: Principia (1687)), 420; The Principia, a new translation by I. Bernard Cohen and Anne Whitman (Berkeley, 1999; hereafter: Principia (1999)), 819.

Principia (1687), 474; (1999), 888–90.

Lucasian Lecture 9, 1676, problem 16, CUL Dd 9.68, f. 200; Mathematical papers, v, 210–13. Similar methods were used by Kepler and others. Variations were used in DMCII, lemmas 3, 4, and 5 for interpolation. Newton's System, Cajori edn (ref. 27), 623–4.

CUL Add Ms 4004, f. 98v. See ref. 10. He sought Flamsteed's latest revisions as he prepared to construct an actual orbit in September 1685. Correspondence, ii, 419.

CUL Add Ms 4004, f. 101r. Reel 14.

Ibid.

McGuire J. E. Tamny Martin , Certain philosophical questions: Newton's Trinity notebook (Cambridge, 1983), 412–13. The dates for this comet are new style.

Kepler Johannes , De cometis libelli tres (Augsberg, 1619–20) in Gesammelte Werke (ref. 34), iv, 196.

Ibid., 195, 200–1. Kepler's account mixed his observations with those of Cysatus and several other astronomers, making it difficult to determine which were which. I have followed Riccioli's tabulations, Almagestum novum (ref. 9), ii, 20–1.

Kepler , op. cit. (ref 48), iv, 194.

Hevelius , Cometographia (ref. 31), 627.

Aristotle , Meteorologica , transl. by Lee H. P. D. (Cambridge, MA, 1952), Bk 1.6, 343b, 44–7.

Siculus Diodorus , Historical library, transl. by Sherman C. L. (Cambridge, MA, 1971), Bk 15.2, 88–91.

Hevelius , Cometographia (ref. 31), 796–7, 904.

CUL Add Ms 3965.14, f. 613v. Reel 5.

Isaac Newton's Philosophiae naturalis principia mathematica: The third edition (1726) with variant readings , assembled by Koyré Alexandre Cohen I. B. Whitman Anne (2 vols, Cambridge, 1972; hereafter: Principia, Koyre/Cohen), ii, 747.

The Gemini sign is followed by a 2 and what seems to be a 6 although the loop still evident may be a smaller than usual 0 rather than the bottom part of a 6. Notice what happens if a bold 5 is inscribed over a 6.

Hevelius , Cometographia (ref. 31), 827, 905.

Newton , Principia (1687), 476; (1999), 890.

Newton's System, Cajori edn (ref. 27), 625.

Mercator , Institutionum astronomicarum (ref. 33). Newton's copy is in the library of Trinity College, Cambridge, NQ 10.152. The holograph annotations are on page 213.

CUL Add. Ms 3965.11, ff. 175r–176v. Reel 5. Another source for Section 64 was Extracta ex Hevelii anno climacterico. CUL Add Ms 3965.14, ff. 581r–582r. Reel 5. Hevelius , Annus climactericus (ref. 31). A deletion in Section 64 (CUL Add Ms 3990, f. 41) indicates the use of Ponteo's edition of the Roman observations of 1680 and 1681 (ref. 35) A set of Ponteo's November observations is in CUL Add Ms 4004, f. 98r.

CUL Add Ms 3965.11, f. 176v.

CUL Add Ms 3965.14, f. 613v. Ruffner J. A. , “Newton's propositions on comets: Steps in transition, 1681–84”, Archive for history of exact sciences, liv (2000), 259–77.

For a different interpretation, see Schechner Sara J. , Comets, popular culture, and the birth of modern cosmology (Princeton, 1997), especially p. 142. The passages were taken from Hevelius who in turn quoted from older accounts. Cometographia (ref. 31), 797, 822, 827, 836, 844–5, 876–77, 880–1, 883. A passage about Justin was more likely from Riccioli, Almagestum novum (ref. 9), ii, 4. See also Iliffe's discussion of Newton's antagonism to astrological signs, “Other men” (ref. 19), 168–9.

Newton's System, Cajori edn (ref. 27), 606.

For a detailed discussion of Newton's views about tails as finally represented in Principia, third edition, see Heidarzadeh Tofigh , A history of physical theories of comets, from Aristotle to Whipple (Dordrecht, 2008), 96–101, 111–17.

See Whiteside's calculus-based derivation, Mathematical papers, vi, 484–5.

Newton's System , Cajori edition (ref. 27), 618–19. The times cited for perihelion distances of 122, 350, and 390 parts (a.u. = 1000) were said to be 30, 33½, and 34 days, respectively. In fact his Table I attributed these transit times to perihelion distances half those values. For a method of calculating intermediate values, see Mathematical papers, vi, 484, n. 10.

Newton's System, Cajori edition (ref. 27), 625.

Principia (1687), 480; (1999), 895.

Principia (1687), 498; (1999), 918.

Principia (1687), 506; (1999), 926.

Principia (1687), 480; (1999), 895.

Principia (1687), 508–9; (1999), 928–9.

Halley Edmond , “Astronomiae cometicae synopsis”, Philosophical transactions , xxiv (1705), 1882–99, pp. 1886, 1897; idem, A synopsis of the astronomy of comets, in Whiston William , Sir Isaac Newton's mathematick philosophy more easily demonstrated (London, 1716, reprinted 1972; hereafter: Whiston/Halley), 409–44, pp. 414, 439. A full discussion of the different editions of Halley's “Synopsis” is David W. Hughes, “Edmond Halley: His interest in comets”, in Thrower N. J. (ed.), Standing on the shoulders of giants (Berkeley, 1990), 324–72.

Whiston/Halley (ref. 76), 439. It is not clear why Halley did not include the comet of 1380 prominently listed by both Hevelius and Lubieniecki.

Ibid., 440.

Principia (1999), 936.

Principia, 937.

Principia (1687), 420; (1999), 819. In 1695, responding to a query by Halley, he suggested the influence of Jupiter or Saturn might increase or decrease a comet's period by a day up to a year or more. Correspondence, iii, 181.

Cooke Alan , Edmond Halley: Charting the heavens and the seas (Oxford, 1998), 214.

Gregory's David memoranda of March 1702/3. Correspondence, iii, 402–3.

Newton Isaac , Philosophiae naturalis principia mathematica, editio secunda (Cambridge, 1713), 464–5; Principia, Koyre/Cohen (ref. 56), 733.

Whiston/Halley (ref. 76), 441. Newton had noted similarities between the comets of 1680 and 1106 but Hevelius did not list the comet of 531 and dated the comet of 44 b.c. associated with the death of Julius Caesar as 41 b.c. Halley's source could have been Lubieniecki, op. cit. (ref. 31).

Principia (1999), 911. The table is on page 912. The result is also highlighted in the Preface, p. 400.

Schaffer Simon , “Halley, Delisle, and the making of the comet”, in Thrower (ed.), op. cit. (ref. 76), 254–98.