Tobias Mayer's Contributions to Observational Astronomy

Delambre J. , Histoire de l'astronomie au XVIIIième siècle (Paris, 1827), 429.

Grant Robert , History of physical astronomy (London, 1852), 208.

The original Latin edition Elementa matheseos universae (2 vols, Halle, 1715–17), was the norm on which the first four German editions were based. In the fifth German edition, of which vols ii-iv were published in Halle (1737) and vol. i in Frankfurt and Leipzig (1738), the arrangement of the content differs in that the section on analysis is reserved until the end.

Mayer T. , Mathematischer Atlas (Augsburg, 1745), Tab. XXIII.

Ibid., Tab. XXII.

Sandler Christian , “Die homännischen Erben”, Zeitschrift für Wissenschaftliche Geographie, vii (1890), 333–50 and 418–48.

Forbes E. G. , “Nuremberg's astronomical heritage”, Journal of the British Astronomical Association, lxxxi (1971), 391–3.

Forbes E. G. , “Das Eimmartische Observatorium zu Nürnberg”, Sterne und Weltraum, ix (1970), 311–15.

Ruge Sophus , “Aus der Sturm- und Drang-Periode der Geographie”, Zeitschrift für Wissenschaftliche Geographie, v (1885), 249–60. Cf. p. 250.

This map, drawn by Mayer in 1748, was published under the title “Vorstellung der in der Nacht zwischen den 8. und 9. Aug. 1748 vorfallenden partialen Mond Finsternis…” in Doppelmaier's J. G. Atlas coelestis (Nuremberg, 1752).

The German title of this collection of ephemerides, etc. is: “Historisch und geographischer Calendar … unter Genemhaltung der von Sr. Königl. Maj. in Preussen in Dero Residenz Berlin gestifteten Academie der Wissenschaften”.

Riccioli G. B. , Almagestum novum astronomiam veterem … (Bologna, 1651), Figs 1–6; and in Hevelius J. , Selenographia (Danzig, 1647).

“Beschreibung eines neuen Mikrometers. Durch Tob. Mayer”, to be found on pp. 1–11; and “Abhandlung über die Umwälzung des Monds um seine Axe/und die scheinbare Bewegung der Mondsflecken”, pp. 52–183.

A description of Mayer's observing techniques, based on that contained in his treatise on the lunar libration (cf. ref. 13 above), is given in Forbes E. G. , “Tobias Mayer's Mondkarten”, Sterne und Weltraum, viii (1969), 36–39.

These results, for some 89 lunar markings, were first published posthumously by Georg Christoph Lichtenberg (see ref. 45) under the title “Observationes de Tabulae Selenographica”. Prior to this time, however, Johann Heinrich Lambert had followed Mayer's method (see ref. 13) to determine the selenographic coordinates of almost three times as many features on the Moon's surface and listed his own results for 66 of the most prominent lunar markings in the Astronomisches Jahrbuch für das Jahr 1776 (Berlin, 1774), 151–2.

Encyclopaedia britannica (seventh edn, Edinburgh, 1842), xiv, 335.

de Lalande J. , Astronomie (third edn, Paris, 1792), iii, 317–32.

Gauss C. F. , Theoria motus corporum coelestium in sectionibus conicis solem ambientium (Hamburg, 1809).

“Astronomische Beobachtung der grossen Sonnenfinsterniss J. J. 1748. den 25. Julius zu Nürnberg in dem Homannischen Hause angestellet. Mit nöthigen Anmerkungen”, Kosmographische Nachrichten u Sammlungen auf d. J. 1748 (Nürnberg, 1750), 11–40.

This correspondence, which is still unpublished, comprises four letters by Mayer and seven by Delisle dated between 21 August 1748 and 27 January 1751. Nine of these are preserved at the Paris Observatory among Ms B1 4–6 (tomes IX-XI), while the remaining two are contained among Mayer's papers in the Göttingen University library under Cod. Ms. Tob. Mayer 15₂, Bl. 12, 14.

Mayer had already made a study of Wurzelbau's data in his “Untersuchungen über die Geographische Länge und Breite der Stadt Nürnberg” (1747), in Forbes E. G. (ed.), The unpublished writings of Tobias Mayer, i (Göttingen, 1972), 33–43, and concluded that his estimate of 49°28′07” had to be reduced by 27”, to 49°27′40”. The results of his redetermination, published in “Latitudo Geographica Urbis Norimbergae”, Commentarii Societatis Regiae Scientiarum Göttingensis, i (1752), 373–8, indicated that the reduced value was still 23” too high; and that the latitude of the Eimmart Observatory (or castle) should be only 49°27′17”. The latitude of the Homann Buildings, from which Mayer's own observations were made, was still smaller: Namely, 49°27′10”.

His title was the nominal one of Professor of Economy, from which Johann Friedrich Penther had just retired. The duties specified in G. A. von Münchhausen's letter of appointment, dated 26 November 1750, were the teaching of practical mathematics, and research.

Klingenstierna S. , “Methodus nova eclipses solares computandi in breves regulas redacta”, Acta S.R. Scient. Upsaliensis 1742 (Stockholm, 1748), 107–28.

de La Caille Abbé N. L. , “Sur le calcul des projections en général, et en particulier sur le Calcul des Projections propres aux Eclipses du Soleil & aux Occultations des Étoiles fixes par la Lune”, Histoire de l'Académie royale des Sciences de Paris. Année MDCCXLIV (1748), 191–238.

After he was successful in his attempt to improve the lunar theory, Mayer returned to this theme and delivered a lecture on 3 September 1757 to the Göttingen Scientific Society entitled “Methodus facilis et accurata computandi eclipses solares in dato loco conspicuas”. This was published posthumously by Lichtenberg in his edition of Mayer's Opera inedita (ref. 45), and translated into English by Forbes (op. cit. (ref. 45), 71–80). A slightly improved version of the analysis of it given in the introduction to the latter work (ibid., 24–39) may be found in Forbes E. G. ' “Tobias Mayer's method for calculating the circumstances of a solar eclipse”, Annals of science, xxviii (1972), 177–89.

Mayer adapted the formulae used by Euler in his “Recherches sur les irregularités du mouvement de Jupiter et Saturne” (1749), to the theory of the Moon's motion. This prize-winning essay was later included in the Paris Academy's Recueil des pièces qui ont remportés les prix de l'Académie des Sciences, depuis leur fondation, vii (1769), 1–84.

Published in Commentarii Societatis Regiae Scientiarum Göttingensis, ii (1753), 159–82.

These are tabulated in his letter to Euler of 6 January 1752, published in Forbes Eric G. (ed.), The Euler-Mayer correspondence (1751–1755) (London, 1971), 48.

Newton Isaac , Principia mathematica (second edn, London, 1713), Prop. XXIX, Prob. X.

Published in Histoire de l'Académie 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, 329–90.

Clairaut A. C. , “De l'orbite de la Lune en ne négligeant pas les quarrés des quantités de même ordre que les forces perturbatrices”, ibid., Année MDCCXLVIII (1752), 421–40.

Kopelevich Y. K. , “The Petersburg astronomy contest in 1751”, Soviet Astronomy—AJ, ix (1966), 653.

Commentarii Societatis Regiae Scientiarum Gottingensis, ii (1753), 383–430.

le Rond D'Alembert J. , Recherches sur différent points importants du système du monde (Paris, 1754), refers contemptuously to Mayer's tables (see ref. 34 above).

Euler to Mayer; Berlin, 26 February 1754, in Forbes E. G. (ed.), op. cit. (ref. 28), 79.

The story of the Board of Longitude's involvement with Mayer, John Harrison, and other claimants for this prize is recounted in the author's National Maritime Museum monograph The birth of navigational science (London, 1974).

Mayer T. , “Tabularium lunarium in commentt. S. R. Tom. II contentarum usus in investiganda longitudine maris”, Commentarii Societatis Regiae Scientiarum Gottingensis, iii (1754), 375–96.

A report on Mayer's “methodus longitudinum promota” appeared in the Göttingische Anzeigen von gelehrten Sachen for 19 October 1754, 125 Stück, pp. 1073–6; but it was first published posthumously in Maskelyne Nevil (ed.), Tabulae motuum solis et lunae novae et correctae; auctore Tobia Mayer (London, 1770).

A diagram of Mayer's own instrument also appears in Maskelyne's edition of Mayer's Tabulae. A discussion of its principles and later modifications by others to the original design is given by J. F. Benzenberg in the lengthy introduction to his Erstlinge von Tobias Mayer (Düsseldorf, 1812).

The most comprehensive discussion of Mayer's and his widow's involvement with the British Admiralty concerning this matter, containing references to the relevant manuscript sources consulted and to the author's previous writings on the subject, is Forbes Eric G. , “Tobias Mayer's claim for the longitude prize: A study in 18th century Anglo-German relations”, Journal of navigation, xxviii (1975), 77–90.

Mayer T. , “Nova methodus perficiendi instrumenta geometrica et novum instrumentum goniometricum”, Commentarii Societatis Regiae Scientiarum Gottingensis, ii (1753), 325–36.

Forbes E. G. , “Tobias Mayer's new astrolabe (1759): Its principles and construction”, Annals of science, xxvii (1971), 109–16.

Forbes E. G. , “The foundation of the first Göttingen Observatory: A study in politics and personalities”, Journal for the history of astronomy, v (1974), 22–29; also “Tobias Mayer und die Gründung der ersten Sternwarte zu Göttingen”, Sterne und Weltraum, xiii (1974), 191–6.

The foregoing description of Mayer's investigation of his mural quadrant is based on his “Observationes astronomicae quadrante murali habitae in observatorio Gottingensi” (1756), published posthumously in Georg Christoph Lichtenberg, Opera inedita Tobiae Mayeri, i (Göttingen, 1775), 11–20; of which an English translation is given in Forbes Eric G. , Tobias Mayer's Opera inedita (London, 1971), 62–70.

Forbes , Tobias Mayer's Opera inedita, 67.

A description of Mayer's early researches on this theme is contained in a pamphlet of this title published in Göttingen soon after his arrival there in 1751.

Mayer's subsequent work on astronomical refraction is a dominant theme in his initial exchange of letters with Euler. See Forbes , op. cit. (ref. 28).

Published in Histoire de l'Académie royale des Sciences de Paris. Année MDCCXXXIX (1741); Mémoires, 407–23.

Mayer to Euler; Göttingen, 6 January 1752. See Forbes , op. cit. (ref. 28), 50, where, however, an error of transcription was incurred by subsuming the last term of the formula under the square root symbol.

Euler to Mayer; Berlin, 18 March 1752. Ibid., 50–55.

Mayer to Euler; Göttingen, September/December 1752. Ibid., 58–59.

Bruhns C. , Die astronomische Strahlenbrechung in ihrer historischen Entwicklung (Leipzig, 1861).

Ibid., 51–60. The values for the coefficients, which are derived empirically, do not correspond exactly to those in the formula quoted above, but rather to those in the published version (see ref. 56) derived in the manner outlined in the following paragraph.

Halley E. , “Some Remarks on the Allowances to be made in Astronomical Observations for the Refraction of the Air…. With an accurate Table of Refractions”, Philosophical transactions of the Royal Society, xxxi (no. 368 for May-August 1721), 169–72.

Maskelyne (ed.), op. cit. (ref. 39), 64.

A description of this instrument is given by Lichtenberg (op. cit. (ref. 45)) in his commentary on Mayer's “De variationibus thermometri accuratius definiendis” (1755). English translations of that tract and commentary are in Forbes, op. cit. (ref. 45), 53–61 and 113–19 respectively.

An assessment of the theoretical insights and practical significance of this important aspect of Mayer's astronomical researches, based largely upon the information contained in the Euler-Mayer correspondence, has already been published in Forbes Eric G. , “Tobias Mayer's contributions to the development of lunar theory”, Journal for the history of astronomy, i (1970), 144–54. To avoid duplication, and to keep the length of this article to within reasonable bounds, it is not being dealt with here.

Mayer's “Theoria motus Martis ex principio attractionis Newtonianae deductae” (1756), and its English translation, are contained in Forbes (ed.), op. cit. (ref. 21), 153–9.

“A more accurate definition of the variations of a thermometer”, in Forbes , op. cit. (ref. 45), 53–61.

See “Temperature”, Encyclopaedia britannica (seventh edn, Edinburgh, 1842), xvii, 543. Predictions for the more northerly latitudes were too high.

Bouguer , La figure de la terre, 1 actually makes a statement to the effect that the mean temperature drops from 24°R to 0°R from low-lying places to an altitude of about 2400 toises, and adopts the linear decrease of temperature with altitude as a working hypothesis in reducing his observations.

Delambre J. , Histoire de l'astronomie au dix-huitième siècle (Paris, 1827), 447.

The commission to construct these timekeepers had been given to Kampe by Professor U. von Segner as the person responsible for supervising the constructing and equipping of the Göttingen Observatory (see Forbes , op. cit. (ref. 44)). They appear to have been completed to his satisfaction before the end of 1752. Kampe's onerous town-council duties prevented him from keeping another contract to construct a 3ft radius quadrant for that observatory, which Mayer himself was obliged to finish for him.

See Baily F. , “Mayer's Catalogue of Stars, corrected and enlarged; together with a comparison of the places of the greater part of them, with those given by Bradley; and a reference to every observation of every Star”, Memoirs of the Royal Astronomical Society, iv (1831), 391–445.

This formula is contained in Mayer's “Observationes astronomicae …” eventually published in the Opera inedita (see ref. 45).

van Biesbroeck G. , “The astronomical works of Olaus Roemer”, Journal of the Royal Astronomical Society of Canada, vii (1913), 342–58.

Strömgren E. , “Om Ole Rømers Meridianobservationer Til Bestemmelse af Fikstjerners Rektascensioner samt om Formeln til Saadanne Observationers Korrigering for Fejl i Meridian-Instrumentets Opstillung”, Nordisk Astronomisk Tidsskrift Ny Raekke, xvii (1936), 17–26.

Cod. Ms. Tob. Mayer 15₃₈.

Horrebow Peter , Operum mathematico-physicorum (3 vols, Copenhagen, 1741), iii, 167–208.

Eibe T. and Meyer K. , Ole Rømers Adversaria (Copenhagen, 1910).

Mayer announced his correction formula for meridian transits of stars in a lecture to the Göttingen Scientific Society on 18 November 1756: It was, however, first published posthumously by Lichtenberg (op. cit. (ref. 45)) in 1775.

This was based on Baily , op. cit. (ref. 65).

“Fixarum zodiacalium catalogus novus ex observationibus Gottingensibus ad initium anni 1756 constructus”, in Lichtenberg , op. cit. (ref. 45), 49–74; translated into English by Forbes , op. cit. (ref. 45), 92–112.

The deteriorating conditions of life in Göttingen following the first occupation by French troops in July 1757, and the detrimental effects that these had on Mayer's astronomical work, are fully described in chap. 4 of the author's recent biography Tobias Mayer (1723–62); Pioneer of enlightened science in Germany (Vandenhoeck and Ruprecht, Göttingen, 1980).

This quote is from loc. cit. (ref. 74). See Forbes , op. cit. (ref. 45), 93.

Justification for this statement is given in my analysis of that method in the introduction to op. cit. (ref. 45), 41–43.

These were published posthumously by Maskelyne (ed.), op. cit. (ref. 39).

This method, which was popular with both astronomers and navigators, normally involved observing the Sun's altitude several hours before mid-day and at the time after mid-day when the Sun had sunk back to the same altitude. The mean of the two times noted on a reliable clock gave the local apparent noon, when the Sun was on the observer's meridian. Mayer had simply to compare this time with that of the Sun's transit across his mural quadrant in order to determine the inclination of the latter to the meridian plane.

Mayer T. , “Observationes astronomicae A.1753 Gottingae habitae”, Commentarii Societatis Regiae Scientiarum Gottingensis, iii (1754), 441–54.

Mayer to La Caille; Göttingen, 8 January 1758—an extract preserved in the Depôt de la Marine, Paris, Ms 2 JJ 66, tome XIV, no. 14 (my translation). The entire known correspondence between these two astronomers consists of fourteen letters between 4 August 1757 and 28 June 1761: Nine are to be found in the Göttingen University Library under Cod. Ms. Philos. 159: “Briefe von und an J. Tobias Mayer”, pp. 11/12–25 and 40; four are at the Depôt de la Marine under Ms JJ 66, tome XIV, nos. 14, 96 and Ms JJ 67, tome XV, nos. 15, 66; and one (Mayer to La Caille, 15 April 1758) appears to be missing.

The exchange of views between Mayer and La Caille, summarized in this paragraph, is based upon the contents of the correspondence preserved in the two repositories cited in ref. 81 above.

de La Caille N. L. , “Recherches sur les Réfractions Astronomiques, et sur la Hauteur du Pole à Paris. Avec une nouvelle Table de Réfractions”, Histoire de l'Académie royale des Sciences de Paris. Année MDCCLV (1761); Mémoires, 547–93.

Mayer did, however, manage to make some micrometric measurements of Venus's transit which were reported in the Göttingische Anzeigen von gelehrten Sachen for 20 June 1761, 8 Stück, pp. 57–58.

Op. cit. (ref. 74).

Mayer T. , Astronomical observations, made at Göttingen, from 1756 to 1761 (London, 1826), published by Order of the Commissioners of Longitude.

Cod. Ms. Philos. 45c: “Astron. Beobb. T. Mayer” (1756).

The facts referred to in this paragraph were extracted from Lindenau B. and Bohnenberger J. F. (eds), “Ueber den von Tobias Mayer im Jahr 1756 beobachteten Planeten Uranus. Von Hrn. Oberhofmeister Freiherrn von Zach”, Zeitschrift für Astronomie und verwandte Wissenschaft, iii (1817), 3–22.

See op. cit. (ref. 86), “Advertisement”.

Op. cit. (ref. 45).

Op. cit. (ref. 57).

Op. cit. (ref. 65).

Auwers A. , Tobias Mayer's Sternverzeichniss, nach den Beobachtungen auf der Göttinger Sternwarte in den Jahren 1756 bis 1760 (Leipzig, 1894).

Halley E. , “Considerations on the Change of the Latitudes of some of the principal fixt Stars”, Philosophical transactions of the Royal Society, xxx (1718), 736–8.

Cassini J. , “Du Mouvement apparent des Étoiles fixes en Longitude”, Histoire de l'Académie royale des Sciences de Paris. Année MDCCXXXVII (1740); Mémoires, 273–87.

Mayer found these in Horrebow , op. cit. (ref. 70). They were later published independently by Galle J. G. , O. Roemeri triduum observationum astronomicarum a. 1706 institutarum (Berlin, 1845).

Cited in ref. 70.

See Baily F. , “La Caille's catalogue of 398 principal stars …”, Memoirs of the Royal Astronomical Society, v (1833), 93–124.

Mayer T. , “De motu fixarum proprio commentatio” (1760), in Lichtenberg , op. cit. (ref. 45), 75–81.

Forbes , op. cit. (ref. 45), 112.

Herschel W. , “On the proper Motion of the Sun and Solar System; with an Account of several Changes that have Happened among the Fixed Stars since the Time of Mr. Flamstead”, Philosophical transactions of the Royal Society, lxxiii (1783), 274–83.

The proper motions of these stars were taken from Galle , op. cit. (ref. 96); and the figures for two of them (β and ∊ Cygni) extrapolated linearly to refer to a 50-year rather than a 44-year interval, in order that they should be directly comparable with those of the other ten stars.

Op. cit. (ref. 99).

Op. cit. (ref. 101), 283.

Herschel W. , “On the direction and velocity of the motion of the Sun, and solar system”, Philosophical transations of the Royal Society, xcv (1805), 233–56; and “On the quantity and the velocity of the solar motion”, ibid., xcvi (1806), 205–37.

Prévost P. , “Mémoire sur le mouvement progressif du centre de gravité de tout le Système solaire”, Nouveaux Mémoires de l'Académie royale des Sciences et Belles-Lettres. Année MDCCLXXXI (Berlin, 1783), 418–21; “Mémoire sur l'origine des vitesses projectiles, contenant quelques recherches sur le mouvement du Système solaire”, ibid., 422–62 and 472.

E.g., Prévost P. and Maurice F. , “Über die eigene Bewegung einiger Sterne, zwischen 1756 und 1797”, Astronomisches Jahrbuch für das Jahr 1805… (Berlin, 1802); Bessel F. W. , Fundamenta astronomiae pro anno MDCCLV (Königsberg, 1818), 308–13; and Bailey F. , “On the proper motion of the fixed stars”, Memoirs of the Royal Astronomical Society, v (1833), 147–70.

Poisson D. , “Mémoire sur le mouvement de la lune autour de la terre”, Mémoires de l'Académie royale des Sciences de l'Institut de France, xiii (1835), 209–335.

de Laplace P. S. , “Sur l'équation séculaire de la lune”, Histoire de l'Académie royale des Sciences de Paris. Année MXCCLXXVI (1788), 235–64.

Forbes E. G. , “The foundation and early development of the Nautical almanac”, Journal of the Institute of Navigation, xviii (1965), 391–401. See also op. cit. (refs 37 and 41).

Details of how this was achieved are given in Forbes, op. cit. (ref. 58).

See op. cit. (ref. 2), above.