##
**The snare of simplicity: the Newton-Flamsteed correspondence revisited.**
*(English)*
Zbl 1281.01007

Newton’s fitting of the motion of comets into the same theory of motion as the planets was a major step towards his principle of universal gravitation. This paper presents a closer look at the first stages of this step than have been presented before, namely the period around Newton’s correspondence with England’s Astronomer Royal, John Flamsteed, concerning the latter’s observations and theory of a comet of 1680. The author’s reconstruction of Newton’s work on comets during this time reveals the extent to which Newton’s private work coincided with the more public communications he made, mainly with Flamsteed.

A brief indication is given of how comets were generally regarded by the mid-17th century as moving in straight, or nearly straight, lines. The 1680 comet, mainly visible from southern Europe, was briefly observed by Newton and marked the beginning of his first serious interest in the subject since observations he made of comets in 1664 and 1665. Observations made in November indicating motion towards the sun and in December away from it, caused most observers to regard it as actually two comets. Flamsteed alone regarded it as one and looked to Newton for help in corroborating his explanation of the motion. Without committing himself, Newton provided in reply possible critiques of Flamsteed’s theory involving magnetic attraction between sun and comet, as Newton meanwhile worked on his own to calculate the actual paths of what he too took as two comets initially.

Newton began his observations using a 3-foot telescope but soon switched to a 7-foot telescope with an added micrometer for making precise measurements as the comet receded from view. Combining his observations with those provided by Flamsteed he based his initial calculations on the comet’s positions for several days in December 1680. The extant documentation contains only summaries and not the full worksheets or finished products and thus may only be taken to indicate the direction of Newton’s work, as the author indicates, and not his conclusions. In calculating the actual, as opposed to apparent, path, Newton would have used the calculation methods described in his Lucasian lectures for the academic year 1676–77 for solving the problem of determining the position of a comet from three observations of its course assuming it travels uniformly in a straight line. Additional observational data came to him from Germany, apparently in March or April 1681. An unpublished manuscript contains Newton’s calculations for converting his micrometer readings to position coordinates but it took several years before Newton apparently settled on an appropriate correction factor. The length and position of the comet’s tail was taken as an important factor in determining its true motion and Newton’s data on this appears in the Principia. The present paper carefully details Newton’s effort, recorded in his notes, to formulate a “harmonic law of tails” which was later abandoned. At one point in his discussion with Flamsteed, Newton suggested that it could be argued, on behalf of Flamsteed’s theory, that the comet’s path was affected by the sun’s supposed magnetism to move towards the sun and then recede from it by means of a centrifugal force. Though this suggestion of a parabolic approximation has been taken by some commentators as the earliest indication that Newton was considering comets as coming under his law of gravitation, the author points out that the proposed mechanism in its details is quite different from the gravitational one developed by Newton in 1684. Furthermore, Newton proceeded in the same discussion to aspects of the topic under the assumption of uniform motion in a nearly straight line.

Though the “snare of simplicity” and “the Platonic archetypes” are given as hints of a possible reason for Newton’s “predilection for straightness” in his search for the path, the idea is not developed here. The author makes it clear, however, that such adherence caused Newton to disregard much of the data that he had collected by the time he left the work in 1681. All in all this paper illustrates how much there is to be discovered in Newton’s rough notes that help to tell the story behind the Principia.

A brief indication is given of how comets were generally regarded by the mid-17th century as moving in straight, or nearly straight, lines. The 1680 comet, mainly visible from southern Europe, was briefly observed by Newton and marked the beginning of his first serious interest in the subject since observations he made of comets in 1664 and 1665. Observations made in November indicating motion towards the sun and in December away from it, caused most observers to regard it as actually two comets. Flamsteed alone regarded it as one and looked to Newton for help in corroborating his explanation of the motion. Without committing himself, Newton provided in reply possible critiques of Flamsteed’s theory involving magnetic attraction between sun and comet, as Newton meanwhile worked on his own to calculate the actual paths of what he too took as two comets initially.

Newton began his observations using a 3-foot telescope but soon switched to a 7-foot telescope with an added micrometer for making precise measurements as the comet receded from view. Combining his observations with those provided by Flamsteed he based his initial calculations on the comet’s positions for several days in December 1680. The extant documentation contains only summaries and not the full worksheets or finished products and thus may only be taken to indicate the direction of Newton’s work, as the author indicates, and not his conclusions. In calculating the actual, as opposed to apparent, path, Newton would have used the calculation methods described in his Lucasian lectures for the academic year 1676–77 for solving the problem of determining the position of a comet from three observations of its course assuming it travels uniformly in a straight line. Additional observational data came to him from Germany, apparently in March or April 1681. An unpublished manuscript contains Newton’s calculations for converting his micrometer readings to position coordinates but it took several years before Newton apparently settled on an appropriate correction factor. The length and position of the comet’s tail was taken as an important factor in determining its true motion and Newton’s data on this appears in the Principia. The present paper carefully details Newton’s effort, recorded in his notes, to formulate a “harmonic law of tails” which was later abandoned. At one point in his discussion with Flamsteed, Newton suggested that it could be argued, on behalf of Flamsteed’s theory, that the comet’s path was affected by the sun’s supposed magnetism to move towards the sun and then recede from it by means of a centrifugal force. Though this suggestion of a parabolic approximation has been taken by some commentators as the earliest indication that Newton was considering comets as coming under his law of gravitation, the author points out that the proposed mechanism in its details is quite different from the gravitational one developed by Newton in 1684. Furthermore, Newton proceeded in the same discussion to aspects of the topic under the assumption of uniform motion in a nearly straight line.

Though the “snare of simplicity” and “the Platonic archetypes” are given as hints of a possible reason for Newton’s “predilection for straightness” in his search for the path, the idea is not developed here. The author makes it clear, however, that such adherence caused Newton to disregard much of the data that he had collected by the time he left the work in 1681. All in all this paper illustrates how much there is to be discovered in Newton’s rough notes that help to tell the story behind the Principia.

Reviewer: Albert C. Lewis (Austin)

### MSC:

01A45 | History of mathematics in the 17th century |

70-03 | History of mechanics of particles and systems |

PDF
BibTeX
XML
Cite

\textit{J. A. Ruffner}, Arch. Hist. Exact Sci. 67, No. 4, 415--455 (2013; Zbl 1281.01007)

Full Text:
DOI

### References:

[1] | Unpublished Newton manuscripts in Cambridge University Library (CUL) with estimated dates. |

[2] | MS Add. 3958.1, ff. 9–13 (1667). |

[3] | MS Add. 3965.5, f. 22v (Jan 1684/5). |

[4] | MS Add. 3965.11, f. 153r (Jan 1680/1); ff. 154r–155v (Mar 1680/1); ff. 172r–173v (1685); ff. 175r–176v (1685). |

[5] | MS Add. 3965.14, f. 554r (1684–85); f. 554v (February 1680/1?); f. 598 (Jan–Mar 1680/1); ff. 613r–614v (Mar 1680/1, 1685?); ff. 615r–616v (Feb-Mar 1680/1 with additions possibly as late as the 1720s.). |

[6] | MS Add. 3990 (1685). |

[7] | MS Add. 4004, ff., 97r, 98r–105r, largely Mar-Apr 1680/1 with additions in 1682, 1684 and 1685. |

[8] | Published Works. |

[9] | Bayer, Johannes. 1603. Uranometria omnium asterismorum contineis schemata with Explicatio characterum aeneis urnometriae imaginum. Ulm: J. Gorlini. Available at www.lindahall/bayer). |

[10] | Bertolini Meli, Domenico. 1993. Equivalence and priority, Newton versus Leibniz. Oxford: Clarendon Press. · Zbl 0792.01008 |

[11] | Birch, Thomas. 1756–1757. The History of the Royal Society of London for improving of natural knowledge. 4 vols. London, reprinted. 1968. New York: Johnson ReprintCorp. |

[12] | Brahe, Tycho. 1648. Opera omnia sive astronomiae instauratae progymnasmata in duas partes. Francofurti: I. G. Schönwetter. |

[13] | Buchwald, Jed Z., and Mordechai Feingold. 2013. Newton and the origin of civilization. Princeton and Oxford: Princeton University Press. · Zbl 1267.01022 |

[14] | Cassini, Giovanni D. 1681. Observations sur la comete qui a paru au mois de decembre 1680 et en janvier 1681. Paris, E. Michallet, reprinted 1681 as Abrege des observations & des reflexions sur la comete qui a paru au mois de decembre 1680, & au mois de janvier, fevier & mars de cette annee 1681. Paris: E. Michallet. |

[15] | Christianson, Gale. 1984. In the presence of the Creator. New York: Free Press. |

[16] | Cosgrave, Denis. 2001. Apollo’s eye: a cartographic genealogy of the earth in the western imagination. Baltimore: John Hopkins University Press. |

[17] | Descartes, Rene. 1983. Principles of philosophy, trans. V. R Miller and R. P. Miller, Dordrecht: Kluwer Academic Press. |

[18] | Dobbs, Betty Jo T. 1988. Newton’s rejection of the mechanical ether: empirical difficulties and guiding assumptions. In Scrutinizing science, ed. A. Donovan, et al. Dordrecht: Kluwer Academic Publishers. |

[19] | Flamsteed, John. 1712. Historiæ coelestis libri duo. London: J. Matthews. |

[20] | Flamsteed, John. 1995–2002. The Correspondence of John Flamsteed. The first Astronomer Royal, ed. Eric G. Forbes et al. 3 vols. Philadelphia: Institute of Physics Press. · Zbl 0989.01533 |

[21] | Forbes, Eric G. 1975. The Gresham Lectures of John Flamsteed. London: Mansell. |

[22] | Forbes, Eric G. 1990. The Comet of 1680–81. In Standing on the shoulders of giants, ed. N.J. Thrower, 312–323. Berkeley: University of California Press. |

[23] | Gassendi, Pierre. 1658. Syntagma philosophiae, Liber V, De cometis & novis sideris, in Opera Omnia, 6 vols. Lugduni: L. Anisson and J. B. Devenet. |

[24] | Hall, A. Rupert. 1992. Isaac Newton, adventurer in thought. Oxford: Blackwell. · Zbl 0976.01014 |

[25] | Harrison, John. 1978. The Library of Isaac Newton. Cambridge: Cambridge University Press. |

[26] | Heidarzadeh, Tofigh. 2008. A History of physical theories of comets, from Aristotle to Whipple. Dordrecht: Springer. |

[27] | Hellman, C.D. 1944. The comet of 1677: its place in the history of astronomy. Columbia University Press. New York: AMS Press. |

[28] | Hevelius, Johannes. 1665. Prodromus cometicus quo historia cometae anno 1664 exorti cursum. Gedani: S. Reiniger. |

[29] | Hevelius, Johannes. 1666. Descriptio cometae anno aerae M.DC.LXV ... cui addita est Mantissa cometici observationes omnes prior cometae MDCLXIV. Gedani: S. Reiniger. |

[30] | Hevelius, Johannes. 1668. Cometographia, totam naturam cometarum. Gedani: S. Reiniger. |

[31] | Hevelius, Johannes. 1679. Machinae coelistis pars posterior. Gedani: S. Reiniger. |

[32] | Hevelius, Johannes. 1685. Annus climactericus. Gedani: D. F. Rheti. |

[33] | Hevelius, Johannes. 1690. Prodromus astronomiæ. Gedani: J. Z. Stolli. |

[34] | Hooke, Robert. 1678. Cometa, or remarks about comets, lectures and collections. London: J. Martyn. |

[35] | Hooke, Robert. 1705. The Postumous works of Robert Hooke, ed. Richard Waller. London: S. Smith and B. Walford. |

[36] | Horrox, Jeremiah. 1678. Opera posthuma (new edition). London: M. Pitt. |

[37] | Hughes, D.W. 1988. The Principia and comets. Notes and Records of the Royal Society of London 42: 53–74. · Zbl 0641.01006 |

[38] | Huygens, Christiaan. 1888–1950. Oeurves complètes, 22 vols. La Haye: M. Nijhoff. · JFM 38.0714.02 |

[39] | Iliffe, Rob. 1995. Is he like other men? The meaning of the Principia Mathematica, and the author as idol. In Culture and society in the Stuart Restoration, ed. G. MacLean, 159–176. Cambridge: Cambridge University Press. |

[40] | Jervis, Jane L. 1985. Cometary theory in fifteenth-century Europe. Dordrecht: Kluwer. |

[41] | Kepler, Johannes. 1619. De cometis libelli tres. Augustae Vindelicorum: A. Apergerum. |

[42] | Kepler, Johannes. 1627. Tabulæ Rudolphinæ. Ulmæ: J. Saurii. |

[43] | Knox, Robert. 1681. An Historical relation of the land of Ceylon in the East-Indies. London, reprinted, 1995, New Delhi: Navrang Booksellers & Publishers. |

[44] | Kollerstrom, N. 1999. The Path of Halley’s comet, and Newton’s late apprehension of the law of gravity. Annals of Science 56: 331–356. · Zbl 0973.01008 |

[45] | Lachièze-Rey, Marc, and Jean-Pierre Luminet. 2001. Celestial Treasury. Cambridge: Cambridge University Press. |

[46] | Lubieniecki, Stanislaw. 1666–1668. Theatrum cometicum, 3 vols in 2. Amstelodami: D. Baccanude, reprinted. 1681, Lugduni Batavarum: P. Vander Meersche. |

[47] | McGuire, J.E., and Martin Tamny. 1983. Certain philosophical questions: Newton’s Trinity Notebook. Cambridge: Cambridge University Press. |

[48] | Mercator, Gerhard. 1551. Celestial Globe, images at lib.harvard.edu. |

[49] | Mercator, Nicolaus. 1676. Institutionum astronomicarum libri duo. London: G. Godbid. |

[50] | Nauenberg, Michael. 1994. Newton’s early computational method for dynamics. Archive for History of Exact Sciences 46: 221–252. · Zbl 0801.01005 |

[51] | Newton, Isaac. 1686. Philosophiae naturalis principia mathematica. London: J. Streater. · Zbl 0732.01044 |

[52] | Newton, Isaac. 1728. A Treatise of the system of the world. London: F. Fayram. · Zbl 0242.01010 |

[53] | Newton, Isaac. 1959–1977. The Correspondence of Isaac Newton, ed. H. W. Turnbull, et al. 7 vols. Cambridge: Cambridge University Press. |

[54] | Newton, Isaac. 1960. Sir Isaac Newton’s Principles of Natural Philosophy and his System of the World, trans. A. Motte and revised by Florian Cajori. Berkeley: University of California Press. |

[55] | Newton, Isaac. 1967–1981. The Mathematical papers of Isaac Newton, ed. Derek T. Whiteside, 8 vols. Cambridge: Cambridge University Press. |

[56] | Newton, Isaac. 1972. Isaac Newton’s Philosophiae naturalis principia mathematica. The third edition (1726) with variant readings assembled by Alexandre Koyré, I. B. Cohen, & Anne Whitman, 2 vols. Cambridge: at the University Press. |

[57] | Newton, Isaac. 1999. The Principia, mathematical principles of natural philosophy, a new translation by I. Bernard Cohen and Anne Whitman. Berkeley: University of California Press. · Zbl 0961.01034 |

[58] | Pingré, [Alexandre Guy]. 1783–1784. Cometographie ou traité historique et théorique des comètes. 2 vols. Paris, Imprimerie Royale. |

[59] | Plot, Robert. 1677. The Natural history of Oxford-shire. Oxford: S. Millers. |

[60] | Ponthaeus, J. D. 1681. Cometicae observationes habitae ab Academia Physico-mathematica Romana anno 1680 et 1681. Rome: Academia Physico-matematica. |

[61] | Ptolemy, Claudius. 1998. Ptolemy’s Almagest, trans. G. J. Toomer. Princeton: Princeton University Press. |

[62] | Riccioli, Giovanni. B. 1651. Almagestum novum astronomiam veterem novamque complectens, 2 parts. Bononiae: Victorii Benatii. |

[63] | Ruffner, J.A. 1971. The curved and the straight: cometary theory from Kepler to Hevelius. Journal for the History of Astronomy 2: 178–194. |

[64] | Ruffner, J.A. 2000. Newton’s propositions on comets: steps in transition, 1681–1684. Archive for History of Exact Sciences 54: 259–77. |

[65] | Ruffner, J.A. 2010. Isaac Newton’s Historia cometarum and the quest for elliptical orbits. Journal History of Astronomy 41: 425–51. |

[66] | Ruffner, J.A. 2012. Newton’s De gravitatione: a review and reassessment. Archive for History of Exact Sciences 66: 241–264. |

[67] | Schaffer, Simon. 1987. Newton’s comets and the transformation of astrology. In Astrology, Science and Society, ed. P. Curry, 219–243. Woodbridge: Boydell Press. |

[68] | Schaffer, Simon. 1993. Comets and idols: Newton’s cosmology and political theology. In Action and Reaction, ed. P. Theerman, and A.F. Seef, 183–231. Cranbury, NJ: Associated University Presses. |

[69] | Schechner, Sara J. 1997. Comets, popular culture, and the birth of modern cosmology. Princeton: Princeton University Press. |

[70] | Snell, Willebrord. 1619. Descriptio cometa, qui anno 1618 mense Novembri primùm effulsit, [with] Christoph Rothman, Mathematici descriptio accuati cometae anni 1585. Lugduni Batavorum: Elzevir. |

[71] | Streete, Thomas. 1661. Astronomia carolina. London: L. Lloyd. |

[72] | Wallis, Helen M. 1978. Geographie is better than divinitie: maps, globes, and geography in the days of Samuel Pepys. In The Compleat plattmaker, ed. N. Thrower, 1–43. Berkeley: University of California Press. |

[73] | Ward, Seth. 1653. Idea trigonometriae demonstratae (In usum Juventutis Oxoiensis.) Item praelectio De cometis et Inquisitio in Bullialdi Astronomiae Philolaicae Fundamenta. Oxoniae: Lichfield. |

[74] | Westfall, Richard S. 1971. Force in Newton’s physics: the science of mechanics in the seventeenth century. London: Macdonald. · Zbl 0242.01009 |

[75] | Westfall, Richard S. 1980. Never at rest a biography of Isaac Newton. Cambridge: Cambridge University press. · Zbl 0532.01023 |

[76] | Westman, Robert S. 2011. The Copernican question: prognostication, skepticism, and celestial order. Berkeley: University of California press. |

[77] | Whiteside, D.T. 1964. Newton’s early thoughts on planetary motion: a fresh look. British Journal for the History of Science 2: 117–28. · Zbl 0138.24904 |

[78] | Whiteside, D.T. 1970. Before the Principia: the maturing of Newton’s thoughts on dynamical astronomy, 1664–1684. Journal for the History of Astronomy 1: 5–19. |

[79] | Whitfield, Peter. 1995. The Mapping of the heavens. San Francisco in association with the British Library: Pomegranate Artbooks. |

[80] | Wilson, Curtis. 1969. From Kepler’s laws, so-called to universal gravitation: empirical factors. Archive for History of Exact Science 6: 89–170. · Zbl 0191.27901 |

[81] | Wilson, Curtis. 1989. The Newtonian achievement in astronomy. In The General History of Astronomy, Volume 2, Planetary astronomy from the renaissance to the rise of astrophysics, Part A: Tycho Brahe to Newton, ed. R. Taton, and C. Wilson, 233–274. Cambridge: Cambridge University Press. · Zbl 0734.01001 |

[82] | Wing, Vincent. 1651. Harmonicon coeleste. London: R. Leybourn. |

[83] | Wing, Vincent. 1669. Astronomia britannica. London: J. Macock. |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.