Tobias Mayer's Contributions to the Development of Lunar Theory

The most reliable and comprehensive source of information regarding this early phase of Mayer's life is: Eberhardt Paul , “Urkundliche Beiträge zu der Jugendgeschichte des Astronomen Johann Tobias Mayer”, Literarische Beiträge des Staatsanzeigers (Stuttgart, 1908), 117–187. This article was reprinted, with several minor amendments, in Aus Alt Esslingen (Esslingen, 1924), 207–224.

Franz J. M. , Homännischer Bericht von Verfertigung grosser Weltkugeln (Nuremberg, 1746).

These are entitled: “Sammlungen verschiedener fremden und eignen Beobachtungen von Länge und Breite …” and “Collectanea geographica et mathematica” (Cod. MS. T. Mayer 10 and 15₁₁ respectively, in the “Handschriftenabteilung” of the Göttingen University library). This quotation constitutes the opening paragraph of a section entitled “Untersuchungen über die geographische Länge and Breite der Stadt Nürnberg”, in Cod. MS. T. Mayer 15₁₁ (loc. cit. (n. 3)). Errors in the original are reproduced in the transcription.

“Vorstellung der in der Nacht zwischen den 8. und 9. Aug. 1748 vorfallenden partialen Mond Finsternis …” (1748), published as Tab. XXI in Doppelmaier's J. G. Atlas coelestis (Nuremberg, 1752).

These aims are defined in § 40, pp. 43–5 of Franz J. M. , Homannische Vorschläge von den nöthigen Verbesserungen der Weltbeschreibungswissenschaft und einer disfals bey der Hommanischen Handlung zu errichtenden neuen Academie (Nuremberg, 1747).

“Beschreibung eines neuen Mikrometers. Durch Tob. Mayer”, Kosmographische Sammlungen auf d. J. 1748 (Nuremberg, 1750), 1–11.

“Beobachtungen einiger Zusammenkunften des Monds mit Fixsternen/im Jahr 1747 und 1748 zu Nürnberg in dem Homännischen Hause angestellet. Von Tob. Mayer”, ibid., 41–51.

“Tobias Mayers Beweis dass der Mond keinen Luftkreis habe”, ibid., 397–419.

“Abhandlung über die Umwälzung des Monds um seine Axe/und die scheinbare Bewegung der Mondsflecken. Worinnen der Grund einer verbesserten Mondsbeschreibung aus neuen Beobachtungen geleget wird. Von Tob. Mayer”, ibid., 52–183.

Bericht von den Mondskugeln welche bey der Kosmographischen Gesellschaft in Nürnberg … verfertiget werden. The authorship of this 24-page pamphlet, which was published in Nuremberg in 1750, is usually ascribed to Mayer; but it may have been written by Franz himself.

Erd- und Himmelsgloben, ihre Geschichte und Konstruction. nach dem Italienischen Matteo Fiorinis frei bearbeitet von Sigmund Günther mit 9 Textfiguren (Leipzig, 1895), 129, 130.

A copy of the unpublished letter from Gerhardt Adolph von Munchhausen (in Hanover) to Tobias Mayer, Mathematician in Nuremberg, 26 November 1750, is preserved in the Personalakte Tobias Mayer Nummer 4/Vb 18, Dekanate u. Universität Archiv, Göttingen.

Thirty-one letters between Mayer and Euler during the years 1751–55 have been published by Kopelevich Y. K. in Istoriko-Astronomijezke Issledowanje , v (1959), 279–427; and jointly with the writer in ibid., x (1969), 285–310.

This is evident not only in the correspondence itself, but from several earlier remarks which Mayer made. For example, in § 12, p. 28 of his treatise “Astronomische Beobachtung der grossen Sonnenfinsterniss J. J. 1748 den 25. Julius/zu Nürnberg in dem Homannischen Hause angestellet. Mit nöthigen Anmerkungen”, (op. cit. (n. 8), 11–40), he remarks: “Ich habe am sichersten zu gehen geglaubt, wenn ich hierinnen Herrn Eulern folgte. Dieser grose Mann hat in den Mondstafeln, die unter seinen opusculis befindlich sind, so wohl den Lauf des Monds überhaupt, als auch besonders die Weite desselben von der Erde für jede Zeit, unstreitig viel umständlicher zu bestimmen gelehret, als noch von irgend jemanden anders geschehen ist….”

Mayer to Euler, 4 July 1751; Kopelevich , op. cit. (n. 15), 281.

Euler L. , “Recherches sur les irregularités du mouvement de Jupiter et de Saturne”, Recuell des pièces qui ont remporté les prix de l'Académie royale des Sciences, depuis leur fondation, vii (1769), 1–84. The prize was awarded to Euler for this treatise in 1748, and it was published one year later.

This was based upon the Saros cycle of eclipses: viz. 223 lunations = 18 years 11&frac1/3; days (approximately). See Halley Edmond , Tabulae astronomicae; accedunt de usu tabularum praecepta (London, 1749), section entitled “De lunae computo corrigendo”.

Mayer T. , “In parallaxin lunae eiusdemque a terra distantiam inquisitio”, Commentarii Societatis Regiae Scientiarum Gottingensis, i (1752), 379–384.

Histoire de l'Academie royale des Sciences de Paris. Année MDCCXLIII (1746): Mémoires, 17–32.

Clairaut A. C. , “Du système du monde dans les principes de la gravitation universelle”, ibid., Année MDCCXLV (1749); Mémoires, 329–390. Also “De l'orbite de la Lune en ne negligeant pas les quarres des quantites de même ordre que les forces perturbatrices”, ibid., Année MDCCXLVIII (1752); Mémoires, 421–440.

These were published posthumously in Flamsteed's three-volume Historia coelestis Britannica (London, 1725).

Halley Edmond , Philosophical transactions, xix (1695), 174. Mayer initially estimated the amount of the Moon's secular acceleration to be 7” per century, but later increased this figure to 9”.

Mayer's reasoning, which reveals the depth of his insight into problems of this nature, is outlined in his letter to Euler of 22 August 1753. See Kopelevich , op. cit. (n. 15), Letter 13, 361–364.

Op. cit. (n. 18).

Nevertheless, Euler re-introduces the concept of a resisting aetherial fluid in his solution of the problem of the secular acceleration of the Moon's mean motion for which he shared the Paris Academy prize with Joseph Louis de Lagrange in 1772. P.S. de Laplace explicitly rejects Euler's hypothesis in a memoir submitted to that Academy in the following year.

Loc. cit. (n. 20), ii (1753), 383–430.

Kopelevich Y. K. , “The Petersburg Astronomy Contest in 1751”, Astronomicheskii Zhurnal, xlii (1965), 845–853; English translation in Soviet Astronomy—AJ, ix (1966), 653–660.

In the preface to his own Théorie de la lune (Paris, 1754), d'Alembert refers in a contemptuous way to Mayer's tables and does not accept their author's claim for their accuracy. He also minimises Euler's own contributions to the lunar theory.

The justification for this statement can be obtained from a comparison of the relevant remarks in Kopelevich, op. cit. (n. 15), Letter 10, 348 (also, note 2) and op. cit. 18, Letter 3 (10^a), 306 (also, note 3).

See Dunthorne Richard , “On the motion of the Moon”, Philosophical transactions , xliv (1746/47), 412–420 (published in 1747); and “On the acceleration of the Moon”, ibid., xlvi (1749/50), 162–172 (published in 1752).

A catalogue of lunar eclipses giving details of 64 eclipses between 5 July 1610 and 17 April 1753 (arranged in order of their respective Saros cycles) and the 139 lunar positions observed by Bradley between 11 September 1743 and 11 April 1745, are appended to Mayer's “Tabularium Lunarium in commentt. S.R. Tom. II contentarum usus in investiganda longitudine maris”, loc. cit. (n. 20), iii (1754), 375–384; cf. 385–396. Many more details of lunar eclipses up to the year 1678 are also contained in an unpublished quarto manuscript entitled “Historia eclipsium ab anno 1610, quo telescopio observationes fieri coeperunt”, Cod. Ms. T. Mayer 15₄₈ (loc. cit. (n. 3)).

“Observationes Astronomicae A. 1753 Gottingae habitae”, loc. cit. (n. 20), iii (1754), 449–454; also, op. cit. (n. 9).

Mayer discusses the method outlined in the foregoing paragraph, in his letter to Euler of 6 March 1754. See Kopelevich, op. cit. (n. 15), 385–390.

“Observationes astronomicae quadrante murali habitae in observatorio Gottingensi” (read on 6 November 1756), in Lichtenberg Christoph Georg , Opera inedita Tobiae Mayeri I (Göttingen, 1775), 11–20.

“Methodus facilis et accurata computandi eclipses solares in dato loco conspicuas” (read on 3 September 1757), ibid., 21–30.

“De novo fixarum zodiacalium catalogo commentatio” (read on 5 April 1759), ibid., 43–48; followed by “Fixarum zodiacalium catalogus novus ex observationibus Gottingensibus ad initium Anni 1756 constructus”, ibid., 49–74.

“De motu fixarum proprio commentatio” (read on 12 January 1760), ibid., 75–81.

“De variationibus thermometri accuratius definiendis” (read on 13 September 1755), ibid., 1–10.

“De affinitate colorum commentatio” (read at a public lecture on 18 November 1758), ibid., 31–42.

Lichtenberg nowhere specifies the reasons for his selection of the treatises in question. This conclusion has been based on a study of his published correspondence and, more particularly, on a statement cited by Hahn Paul , Georg Christoph Lichtenberg und die exakten Wissenschaften (Göttingen, 1927), 23.

Forbes Eric G. , “Tobias Mayer's lunar tables”, Annals of science, xxii (1966), 105–116.

Op. cit. (n. 33).

Euler to Mayer ; Berlin, 11 June 1754. See Kopelevich , op. cit. (n. 15), 393–395.

Tabulae motuum solis et lunae novae et correctae; auctore Tobia Mayer: Quibus accedit methodus longitudinum promota, eodem auctore (London, 1770). This posthumous publication, which was edited by Maskelyne Nevil and published both in Latin and in English, also contains an appendix to this method composed by Mayer at a later date.

This is the instrument known as Mayer's Repeating Circle, the first printed diagram of which is to be found in ibid., Tab. II.

“Nova methodus perficiendi instrumenta geometrica et novum instrumentum goniometricum”, loc. cit. (n. 20), ii (1753), 325–336.

“Experimenta circa visus aciem”, ibid., iv (1755), 120–135.

An abstract of this lecture to the Gottingen Scientific Society is contained in the Göttingische Anzeigen von gelehrten Sachen, (1754), 125 St., 1073–6.

Op. cit. (n. 45), 395.

Four encouraging letters were sent from Best to Michaelis on 13 September, 8 October, 5 and 19 November 1754, and their contents were undoubtedly disclosed to Mayer. The originals are preserved in the Göttingen University library under Cod. Ms. Michaelis 320, pp. 555–569.

This is stated explicitly in an unpublished letter from Best to Sturm P. , London 15 February 1757, preserved among “Briefe von und an J. Tobias Mayer”, Cod. Ms. philos. 159, pp. 1, 2 (loc. cit. (n. 3)).

The vital part played by Michaelis in furthering Mayer's claim is amply evident in 35 letters between himself and Best dating between 1754 and 1756 (loc. cit. (n. 52), 535–671) and in an even larger batch of correspondence relating to the same theme and period preserved in the Staatsarchiv Hannover (Hannover Des. 92 xxxiv No. II, 4, a¹). Details concerning several further documents in The Records Room of the Royal Greenwich Observatory are given in op. cit. (n. 43).

Forbes Eric G. , “The Origin and Development of the Marine Chronometer”, Annals of science, xxii (1966), 1–25.

This is stated by Mayer's widow (Maria Victoria) in her letter of 27 June 1765 to the Lords of the Admiralty, published in op. cit. (n. 43), 108–9.

At the important meeting of the Board of Longitude on 9 February 1765, when resolutions were passed concerning the awards to be paid to both Harrison and Mayer, Maskelyne had arranged for four ships' officers to be called in to testify independently that the method of lunars was indeed generally reliable to within this limit.

Act 5 George III, c. 20.

Op. cit. (n. 46).

This is clearly stated by Maskelyne in his preface to The nautical almanac for 1767. Mayer's own tables were superseded a decade later by others compiled by Mason Charles , embodying essentially the same theoretical principles but based upon the more reliable and extensive observational data that were steadily being amassed at the Royal Observatory, Greenwich.

Nockholds G. W. Mrs. , née Susanna Fisher, “Early Timekeepers at Sea. The story of the general adoption of the chronometer between 1770 and 1820”, Journal of antiquarianhorology, iv (1963), 110–113 and 148–152.

History of physical astronomy … (London, 1852), 208.