Department of
Science & Technology Studies
University College London

Nicholas Kollerstrom's
Newton on the Moon
Bibliography 

Primary sources, unpublished

• Joseph-Nicolas Delisle, Tables du Soleil & de la Lune suivant la theorie de Newton dans la 2nd Edition de ses Principles, calcul_es en 1716 Observatoire de Paris Archives, MSS A2.9, No.23.
• Joseph-Nicholas Delisle correspondence, Paris Observatory MSS B1.
• John Flamsteed, Lunar Tables, 36 pages at CUL, RGO1/50H, notebook dated 1702-1714.
• Edmond Halley, Astronomical Notebook, fair manuscript copy 518 pp., in Royal Astronomical Society Library.
• Jeremiah Horrox, Philosophical Exercises, The Second Part, ULC, RGO 1.68B.
• Journal Book of the Royal Society, XII, 1720-26 (pp. 10-12, 12 May 1720 report of exchange between Newton and Halley).
• Isaac Newton, Theory of the Moon Royal Society MS 247, ff. 15/16, copy by David Gregory, 4 sides written on two pages, dated 27 Feb then 25 Mar 1700; original at ULC, Add.3966,10.
• Isaac Newton, manuscripts on Comparison of the calculated place of the Moon with Observation, (c.1694-1724, but not in chronological sequence), ULC Add. 3966,15.

Primary sources, published

• Francis Baily, An Account of the Revd. John Flamsteed, The first astronomer-Royal, compiled from his own manuscripts, and other authentic documents, never before published 1835, reprinted (Holland) 1966.
• Francis Baily, Supplement to the Account of the Revd. John Flamsteed, 1837, facsimile reprinted (Holland) 1966.
• I.Bernard Cohen, Isaac Newton's Theory of the Moon's Motion (1702), With a bibiliographical and historical introduction, Folkestone,1975.
• La Connoissance des Temps Paris 1686 (for Equation of Time).
• The Correspondence of Sir Isaac Newton and Professor Cotes, Ed. Joseph Edleston, 1850, facsimile reprint 1969.
• William Crabtree's letter to Gascoigne of July 21, 1642, on Horrox theory, see Horrox Opera, below.
• Joseph-Nicholas DeLisle, Lettres sur les Tables Astronomiques de M.Halley, Journal des Scavans, Paris Dec. 1749, pp.848-858, and March 1750, pp.150-163. The second letter (which claimed DeLisle was the first to prepare tables from TMM) is in the Archives of the Paris Observatoire. The first is quoted by Baily (1835, p.705).
• John Flamsteed De Inaequalitate Dierum solarium Dissertatio Astronomica London 1673 published as a supplement to Jeremiah Horrocks Opera Posthuma 1673, pp.441-464.
• John Flamsteed, "Doctrine of the Sphere", in Sir Jonas Moore's A New Systeme of the Mathematics, 1681, Vol.1, part VI, pp.1-75.
• The Gresham Lectures of John Flamsteed, E. Forbes Ed., 1975.
• John Flamsteed, Historia Coelestis Britannica, 1725, Vols II and III.
• The Preface to John Flamsteed's Historia Coelestis Britannica Ed. Alan Chapman, Greenwich Maritime Monograph, 1982.
• David Gregory, Astronomiae Physicae at Geometricae Elementa 1702, with 'Lunae Theoria Newtoniana' on pp. 332-336; reprinted 1726; translated as The Elements of Physical and Geometrical Astronomy 1715, 2nd Edition 1726, 2 vols, with TMM on pp563-571; facsimile reprint (Sources of Science, no.119) NY & London, Johnson Reprint 1972.
• Edmond Halley, Catalogus Stellarum Australium ('Quaedam lunaris theoria emendationem spedantia' p.12), 1679.
• Edmond Halley Ed., Historia Coelestis Libri Duo, 'by John Flamsteed' 1712.
• The Three Voyages of Edmond Halley in the "Paramore", 1698-1701, Norman J.Thrower Ed., 1981.
• J.Horrox, Opera Posthuma 1673, epilogue by Flamsteed p.491, edited by John Wallis (esp. J.Horrox letter to W.Crabtree December 20th 1638, for 'germ of new theory': Wallis erroneously printed the year as 1628).
• Tobias Mayer, Novae Tabulae Solis et Lunae, G_ttingen Commentarii, 1753.
• Newton's Principia, Motte translation (1729) of 3rd Edition (1725), F. Cajori edn., Vol II, University of California Press, 1962.
• Isaac Newton, 'Philosophiae Naturalis Principia Mathematica' 2nd Edn. 1713.
• W.Hodgson, Theory of Jupiter's Satellites, Introduction (on LeMonnier publishing Flamsteed's tables), 1750.
• The Correspondence of Isaac Newton, Volume IV 1694-1709, J.F.Scott Ed., Cambridge, 1967.
• R.Stephenson, Newton's Lunar Theory Exhibited Analytically, Cambridge 1834.
• Thomas Streete, Astronomia Carolina, a new theorie of Coelestial Motions, 1661; An Appendix to Astronomia Carolina, 1674; Latin translation by Morino, with added Tabulas Rudolphinas Johann Baptista Morino, N_renberg 1705; 2rd Edn. (posthumous) ed. Halley, with Halley's 1680s sextant observations and 'a proposal how to find the Longitude'; 3rd edition, 1716.
• Thomas Streete, The Description and Use of the Planetary Systeme together with Easie Tables 1674. A reply to Flamsteed's allegation of plagiarism over the Horroxian theory is appended.
• William Whiston, Praelectiones astronomicae Cantabrigae in scholios publicis habitae... 1707, containing 'Tabulae plurimae astronomicae Flamstedianae correctae;' TMM plus commentary pp.309-327, with date Dec.6, 1703; trans. Astronomical Lectures, Read in the Publick Schools at Cambridge 1715, 2nd Edition Corrected 1728, with TMM on pp.345-368; Facsimile Reprint (Sources of Science, no. 122) N.Y & London 1972. (N.B. Whiston's Praelectiones Physico-Mathematicae of 1710 has no TMM or astronomical tables).

Editions of TMM, Eighteenth-Century

• David Gregory, Astronomiae Physicae (Latin) 1702
• Elements of ... Astronomy (English) 1715, 1726
• A New and most Accurate Theory of the Moon's Motion; Whereby all her Irregularities may be solved, and her Place truly calculated to Two Minutes. Written by That Incomparable Mathematican Mr. Isaac Newton (English pamphlet, no name) 1702
• Harris's Lexicon Technicum under heading 'Moon' (English) 1704, 1708, 1716, 1725, 1736
• Miscellanea Curiosa 1 pp.270-281 (English) 1705, 1708, 1726
• William Whiston, Praelectiones Astronomicae (Latin) 1707
• Astronomical Lectures 1715, 1728; 1782 (English)
• Samuel Horsley Ed., Opera of Newton (Latin) 1782.

Primary-source Astronomy Textbooks

• C.Brent, The Compendious Astronomer, Containing New and Correct Tables ('The Tables of the Moon are disposed according to sir Isaac Newton's Theory'), 1741.
• Angelo Capello, Astrosophiae Numerica Supplementum... Exactissimae Luminarum Tabulae juxta hypotheses ac mensuras celeb. Geometrae Isaacci Newtoni, Venice, 1737.
• Jacques Cassini, Tables Astronomiques, Paris 1740.
• Richard Dunthorne, Practical Astronomy of the Moon: or, new Tables... Exactly constructed from Sir Isaac Newton's Theory, as published by Dr Gregory in his Astronomy, London & Oxford, 1739 (copy at ULC).
• Leonhard Euler, Theoria Motus Lunae exhibens omnes eius inaequalitates, St Petersburg 1753.
• Nicasius Grammaticus, Tabulae Lunares ex Theoria et Mensuris Geometrae Celeberrimi domini Isaaci Newtoni, Ingolstadt, 1726.
• Nicholas Greenwood, Astronomia Anglicana 1689.
• Edmond Halley, Tabulae Astronomicae, accedunt de usu tabularum preacepta, London 1749; trans: Astronomical Tables with Precepts both in English & Latin for comparing the places of the Sun, Moon etc., 1752.
• Peter Horrebov, Nova Theoria Lunae was published in 'Biblioteca Novissima' Magdebourg 1718, according to Delisle.
• Charles Leadbetter, Uranoscopia, or the Contemplation of the Heavens... Also, an Explanation and Demonstration of the Keplarian and Flamsteedian Methods of Computing the Times and Principal appearances of Solar Eclipses, 1735.
• Charles Leadbetter, A Complete System of Astronomy, 2nd edition 1742, 2 vols.
• Tobias Mayer, Theoriae Lunae juxta Systema Newtonianum, 1767.
• Tobias Mayer, Tabulae Motuum Solis et Lunae, 1770 (contains letters of Bradley, and review of Halley's method).
• Nicholas Mercator, Institutionum Astronomicarum, Libri Duo cum Tabulis Tychonianis, 1676.
• Pierre Le Monnier, Institutions Astronomiques, ou leçons elementaires d'astronomie, Paris 1746.
• John Newton, Astronomia Britannicae, 1657.
• G.B.Riccioli, Astronomia Reformata tomi duo Bononia (Bologna) 1665.
• Jeremy Shakerly, Tabulae Britannicae 1653.
• Van Lansberge, Theoriae Motuum Coelestum, in Opera Omnia, Zelandiae 1663.
• Vincent Wing, Urania Practica, with divers rules and tables of extraordinary use in navigation, 1649.
• Vincent Wing, Harmonicon Coeleste, conteining an absolute and entire Piece of Astronomie, 1651.
• Vincent Wing, Astronomia Britannica 1669.
• Robert Wright, New & Correct Tables of the lunar motions, according to the Newtonian Theory, Manchester 1732.

Primary-source Articles
     (a) Philosophical Transactions:

• "Extract of two Letters, written by Mr Flamsteed..." (contra Streete), 9 (1675), pp.219-221.
• "Mr Flamsteed's letter of July 24, 1676...concerning Mr Horroxes lunar Systeme" 10 (1675), pp.368-377.
• "A Letter from Mr Flamsteed...", 13 (1683) Section 154, pp.404-8.
• "An Account of the Moon's Eclipse, February 2, 1710 observed at Streatham near London, and compared with the Calculation, by the Rev. Mr H. Cressener, FRAS" 27 (1710-12), pp.16-19.
• E.Halley, "A Proposal of a Method for Finding Longitude at Sea within a Degree, or Twenty Leagues", 37 (1731/2), pp.185-95.
• "A Letter from Mr Richard Dunthorne...concerning the Moon's Motion", 44 (1747), pp.412-420, read on 5th February.

     (b) Others:

• Review of TMM in: Histoire des Ouvrages des Savans, January-March 1703, pp.121-23.
• A.C Clairaut, "De l'Orbite de la Lune dans le syst_me Newtonian", Histoire de l'Academie Royale des Sciences, 173, Paris (1743, Pub. 1746) pp123-129.
• "Mayer's new Tables of the Sun and Moon", Gentleman's Magazine, August 1754 London XXIV pp.374-376, no name; extract quoted in Forbes 1980, pp.143-146, citing author as John Bevis.
• John Harris' Lexicon Technicum of 1704, section entitled "Moon". (reprint of TMM with comments, and quotes from Flamsteed).
• Edmond Halley, Foreword to Miscellanea Curiosa 1708 (on accuracy of TMM).

Secondary Sources

• William Andrewes, Ed., The Quest for Longitude, 1996 Harvard University Press (The Proceedings of the 1993 symposium held at Harvard).
• Armitage, Edmond Halley, 1966.Jean S. Bailly, Histoire de l'Astronomie
• Moderne, II (1779), pp.508-10 (on Horrox), III (1782), p.150.
• D.Brewster, Memoirs of the life, Writings, and Discoveries of Sir Isaac Newton, 2 vols Edinburgh, 1855 (reprinted Johnson Reprints 1965).
• D.Castillejo, The Expanding Force in Newton's Cosmos, Madrid 1978.
• Allan Chapman, Three North-Country Astronomers Manchester 1982.
• Allan Chapman, Dividing the Circle, the development of critical angular measurements in astronomy 1500-1850 New York & London, 1990.
• I. Bernard Cohen, The Newtonian Revolution, 1980.
• Charles H. Cotter, A History of Nautical Astronomy 1968.
• Jean Le Ronde d'Alembert, Recherches sur diff_rens points importans du Systeme du monde Vol.1, Ch.22, & Vol.3 on history; Paris 1754-6, facsimile reprint Brussels 1966.
• Jean Baptiste Delambre, Histoire de l'Astronomie au Dix-huiti_me Si_cle Paris 1827, pp.29 (apogee & node equations), 282 (Halley's use of Saros).
• J.L.E.Dreyer, A History of Astronomy from Thales to Kepler, New York 1906, 1953.
• Eric Forbes, Greenwich Observatory Volume I, "Origins and Early History 1675-1835", 1975.
• Eric Forbes, Thobias Meyer (1723-62) Pioneer of Enlightened Science in Germany, Gottingen 1980.
• Alfred Gautier Essai historique sur le problème des Trois Corps, Paris 1817.
• Owen Gingerich and Barbara Welther, Planetary, Lunar and Solar Positions AD 1650-1805, Harvard 1983; see Preface, "The Accuracy of Historical Ephimerides", pp.i-xxiii.
• Owen Gingerich, The Eye of Heaven: Ptolemy, Copernicus and Kepler, New York 1993.
• B. Heckart, Edmond Halley 1984.
• Derek Howse, Greenwich Time and the Discovery of Longitude 1980.
• Derek Howse, "Newton, Halley and the Royal Observatory", in Standing on the Shoulders of giants, Ch. 2, N.J. Thrower Ed., 1990.
• Derek Howse, "The Lunar-distance Method of Measuring Longitude", in The Quest for Longitude, Harvard 1997.
• Derek Howse, "Longitude-finding by Astronomy" Companion Encyclopaedia of the History and Philosophy of the Mathematical Sciences, I.Grattan-Guinness Ed., 1994, II, pp.1134-8.
• John Kelly, Practical Astronomy during the Seventeenth Century: Almanack- makers in America and England, Harvard Dissertations in the History of Science, New York 1991.
• Louis T.More, Isaac Newton: A Biography, NY & London 1934, facsimile reprinted New York, 1962.
• Otto Neugebauer, The Exact Sciences in Antiquity, Brown University Press, printed in Denmark, 1957 (Halley's use of term 'Saros', p.142).
• Otto Neugebauer, History of Ancient Mathematical Astronomy Vol. I, Springer-Verlag Berlin & New York, 1975.
• John North, The Fontana history of Astronomy and Cosmology 1994.
• Bruce Stephenson, Kepler's Physical Astronomy Springer-Verlag Berlin & New York, 1987.
• E. Taylor, The Haven-Finding Art 1956.
• Norman J. Thrower, Ed., Standing on the Shoulders of Giants, A Longer View of Newton and Halley, Berkeley & Oxford, 1990.
• Richard Westfall, Never at Rest, A Biography of Isaac Newton, Cambridge 1980.
• William Whewell, History of the Inductive Sciences, from the earliest to the present times, 1837, I p.457 (Horrox), II, pp.178-186, 214-222, 302-304.
• Derek T.Whiteside, The Mathematical Papers of Isaac Newton, IV (1674-1684), p.665 for treatment of upper-focus and mean anomaly; VI pp.509,519 for Horroxian theory; VII (1691-1695), pp.xxiv, xxv, and xxviii, CUP 1967.
• Curtis Wilson, Astronomy from Kepler to Newton, Variorum Reprints, 1987.
• Curtis Wilson & Rene Taton Ed., The General History of Astronomy, Volume 2 Planetary astronomy from the Renaissance to the rise of astrophysics, Cambridge 1989. Part A: Tycho Brahe to Newton, Chapters 10 and 12: "Predictive Astronomy in the century after Kepler" and "The Newtonian achievement in astronomy."

Articles

• J.C.Adams, "On Newton's Solution of Kepler's Problem" Monthly Notices of the Royal Astronomical Society, 43 (1882) pp.43-9.
• Francis Baily, "Some Account of the Astronomical Observations made by Dr Edmund Halley, at the Royal Observatory at Greenwich" Memoirs of the Royal Astronomical Society, VIII (1835), pp.169-190.
• I. Bernard Cohen, "Kepler's Century" Vistas in Astronomy 18 (1975) pp.3-36.
• Allan Chapman, "Jeremiah Horrocks...  ", Quarterly Journal of the Royal Astronomical Society, ...
• Alan Cook, "Halley and the Saros" Quarterly Journal of the Royal Astronomical Society, 37 (1996) pp.349-353.
• S.B.Gaythorpe, "On Horrocks's Treatment of the Evection and the Equation of the Centre" Monthly Notices of the Royal Astronomical Society, LXXXV (1925), pp.858-865.
• S.B.Gaythorpe, "Jeremiah Horrocks and his 'New Theory of the Moon'" Journal of the British Astronomical Association, 67, (1957), pp.134-44.
• Owen Gingerich and B.Welther, "Note on Flamsteed's Lunar Tables" British Journal for the History of Science, 7 (1974), pp.257-8.
• John Greenberg, "Degrees of Longitude and the Earth's Shape: The Diffusion of a Scientific Idea in Paris in the 1730s" (section 3, "Delisle's lost Chance") Annals of Science, 41 (1984) pp.151-158.
• Derek Howse, "The Astronomers Royal and the Problem of Longitude" Antiquarian Horology Autumn 1993, pp.43-52.
• Niels Jorgenson, "On the Moon's Elliptic Inequality, Evection and Variation and Horrox's 'New Theory of the Moon'" Centaurus, 18 (1974) pp.316-18.
• N.Kollerstrom, "Newton's Lunar Mass Error" Journal of the British Astronomica Association, 95 (1985), pp.151-3.
• N.Kollerstrom, "Newton's two 'Moon-tests'" British Journal for History of Science, 24 (1991), pp.369-72.
• N.Kollerstrom, "The Edmond Halley 'Bull's Eye' Enigma" Journal of the British Astronomical Association, 100 (1990) p.7.
• N.Kollerstrom,  "The Hollow World of Edmond Halley",  Journal of the History of Astronomy, .1992....
• N.Kollerstrom and B.Yallop, "Flamsteed's Lunar Data 1692-5, sent to Newton" Journal for the History of Astronomy XXVI (1995) 237-246.
• N.Kollerstrom, "A Reintroduction of Epicycles: Newton's lunar Theory and Halley's Saros Correction" Quarterly Journal of the Royal Astronomical Society, 36 (1995) pp.357-368.
• D.H.Sadler, "Lunar Distances and the Nautical Almanac" Vistas in Astronomy, 20 (1976) pp.113-121.
• F.R.Stephenson and L.V.Morrisson, "Long-Term Changes in the Rotation of the Earth: 700BC to AD 1980" Phil. Trans. Ser. A, 313 (1984), pp.47-70.
• F.R.Stephenson, "Long-Term fluctuations in the Earth's Rotation: 700 BC - AD 1990" Phil. Trans. Ser. A, 351 (1995) pp.165-202.
• Victor Thoren, "Kepler's Second Law in England" British Journal for History of Science, 7 (1974), pp.243-256.
• Frederick Tolles, "Philadelphia's First Scientist, James Logan" Isis XLVII (1956), pp.20-30.
• Craig Waff, "Newton and the Motion of the Moon, an Essay Review" Centaurus, 21 (1977), pp.64-75.
• Richard Westfall, "Newton and the Fudge Factor" Science CLXXIX (Feb 1973) pp.751-58.
• "Newton and Flamsteed. Remarks on an article in No. CIX Quarterly Review: by the Rev. William Whewell", Philosophical Magasine VIII (1836) pp.139-147 (anonymous book review), reprinted in Royal Society "Tract 46" pp.3-19.
• Derek. T. Whiteside, "Newton's Lunar Theory, From High Hope to Disenchantment" Vistas in Astronomy, 19 (1976), pp.317-28.
• Curtis Wilson, "Horrox, Harmonies and the Exactitude of Kepler's Third Law" Science and History: Studies in Honour of Edward Rosen, Studia Copernicana, 16, Wroclaw (1978), pp.235-59.
• Curtis Wilson, "On the Origin of Horrocks's Lunar Theory" Journal for History of Astronomy xviii (1987), pp.77- 94.
• Curtis Wilson, "The Perturbation of Solar Tables from Lacaille to Delambre: the Rapprochement of Observation and Theory" Archive for History of Exact Sciences 22 (1980), Part I pp.53-188, Part II pp.189-304.
• Curtis Wilson, "The Great Inequality of Jupiter and Saturn: from Kepler to Laplace" Archive for History of the Exact Sciences, 33 (1985), pp.15- 290 (p.16, Flamsteed's accuracy).
• Curtis Wilson, "Newton on the Moon's Variation and Apsidal Motion" (in preparation)
• Edwin Wolf, "The Romance of James Logan's Books" William and Mary Quarterly XIII (1956), pp.342-353.

Lunar Theory

• The Astronomical Almanac 1994, Washington (for DT values).
• John C.Adams, Lectures on the Lunar Theory Cambridge 1900.
• D.Brower and G.Clemence, Methods of Celestial Mechanics 1961 Ch.12 (for node equation).
• Ernest Brown, An Introductory Treatise on the Lunar Theory, Cambridge 1896, 1960.
• Michelle Chapront-Touz_ and Jean Chapront, "ELP 2000-85: a semi-analytical lunar ephemeris adequate for historical times" Astronomy and Astrophysics, 190 (1988), pp.340-352.
• Michelle Chapront-Touz_ & Jean Chapront, Lunar Tables and Programs from 4000BC to AD 8000, Richmond, Virginia, 1992.
• Peter Duffett-Smith, Astronomy with your personal computer, Cambridge 1985 (includes computer programme).
• Explanatory Supplement to The Astronomical Ephemeris, HMSO, 1961; reprinted 1984, new edition 1992 by Willmann-Bell, Richmond, Virginia, US.
• Hugh Godfray, An Elementary Treatise on The Lunar Theory, 1871.
• D.W.Hughes, B.D.Yallop & C.Y.Hohenkerk, "The Equation of Time" Monthly notices of the Royal Astronomical Society, 238 (1989) pp.1529-1535.
• Improved Lunar Ephemeris 1952-1959 by the Nautical Almanac Offices of the USA and UK Washington, 1954; for improvement to ILE (ref. j=2) see: "Explanation, Moon", The Astronomical Ephemeris, Washington & London 1972, p.539.
• J.Meeus, Astronomical Formulae for Calculators Richmond, Virginia, US 1985, 3rd Edn.
• J.Meeus, Astronomical Tables of the Sun,Moon and Planets, Richmond, Virginia, 1983.
• J.Meeus, Astronomical Algorithms, Richmond, Virginia, US, 1991.
• A.E.Roy, Orbital Motion 1978.
• Royal Greenwich Observatory, NAO Technical Note No 48, Approximate Lunar Co-ordinates 1979 B. Emerson (gives modern equations).
• W.M.Smart, Textbook on Spherical Astronomy Cambridge 1977 6th Edition.
• Harold Spencer Jones, General Astronomy 1961 4th Edn., esp. pp.123-130 on lunar theory.
• Richard Stevenson, Newton's Lunar Theory Exhibited Analytically 1934, Cambridge.
• R.Woodhouse, An Elementary Treatise on Astronomy, 1812, Vol.II.

The contents of this page remain the copyrighted, intellectual property of Nicholas Kollerstrom.  Details. rev: May 1998