Gauss, Meyerstein and Hanoverian Metrology

Summary

The growing need for standardized units of measure led to major metrological reforms in the mid-nineteenth century. This paper focusses on their implementation in the Kingdom of Hanover and the involvement of C.F. Gauss. His papers reveal how much the success of his precision measurements hinged on the skill of his mechanic M. Meyerstein. A discussion of the regional weights and measures and the standardization procedure is followed by a description of various precision balances and the weighing methods employed as well as a review of the problems posed by reliable length calibration. The success of the enterprise rested not only on intellectual prestige and ministerial clout but also on the hands-on skill of the mechanical practitioner.

I would like to thank the archivists and curators in the collections mentioned in the annotation for their helpful advice and permission to quote from the unpublished sources. Kathryn Olesko has provided me with many helpful hints on various Meyerstein-related documents in odd corners of the Göttingen archives; she and an anonymous referee for Annals of Science have also pointed out some contextual issues which have been incorporated as best as possible in this final version. The former curator of the Göttingen physical instruments collection, Gustav Beuermann, and the curator of the Museum der Göttinger Chemie, Günther Beer, were both very helpful in granting me access to various Meyerstein instruments in their collections and sharing their extensive knowledge about their intricate handling. My wife Ann M. Hentschel has done a marvellous job with the translation into English of the primary sources quoted in this paper and general proofreading.

Notes

¹The underlying laws are published in Sammlung der Gesetze, Verordnungen und Ausschreiben für das Königreich Hannover vom Jahre 1836 (Hannover: Kius, 1836), part 1, 117–25 and 159–72. Please note the differing British and German spellings of Hanover vs. Hannover in the various sources cited. The German Elector of Hanover succeeded the Stuarts on the British throne, starting with George I in 1714 and ending with William IV (born in 1765) who reigned from 1830 until his death in 1837. Victoria became Queen of Britain, and her uncle, the Duke of Cumberland, ascended the Hanoverian throne following Salic law, stipulating male succession.

²On the foregoing see ibid. (note 1), 118–19. Old definitions and conversions of the Hanoverian weights and measures are provided, for instance, in Harald Witthöft, Umrisse einer historischen Metrologie zum Nutzen der wirtschafts- und sozialgeschichtlichen Forschung. Maß und Gewicht in Stadt und Land Lüneberg, im Hanseraum und im Kurfürstentum/Königreich Hannover vom 13. bis zum 19. Jahrhundert, 2 vols (Göttingen, 1979), 60ff., 145f., 709–13, 715f.; Louis Haase, Hannoversche Gesetzgebung über Maß und Gewicht (Hannover, 1854), 1–18; Christian and Friedrich Noback, Münz- Maass- und Gewichtsbuch, 1st ed. (Leipzig, 1858), 270f. Witthöft, idem, also provides further socio-historic and economic context and some primary documents.

³The laws (note 1) list the locations of the verification offices (on pages 122 and 162) outline their daily business, (166f), and specify standardization fees, (168ff). The Prussian Regulation on Measures and Weights of 1816 evidently guided the wording of this law, which also engaged a ‘Commission of Experts’ and required that a copy be deposited at the Mathematical Class of the Berlin Academy of Sciences, ‘to safeguard the mathematically precise accuracy for all time to come’. See Joachim Albert Eytelwein, ‘Über die Prüfung der Normal-Maaße und Gewichte für den königlich-preußischen Staat und ihre Vergleichung mit den französischen Maaßen und Gewichten’, Abhandlungen der mathematischen Klasse der kgl. Akademie der Wissenschaften, Berlin, für das Jahr 1825 (Berlin, 1828), 1–21; as well as, e.g., Harald Witthöft, ‘Längenmaß und Genauigkeit 1660 bis 1870 als Problem der deutschen historischen Metrologie’, Technikgeschichte, 57 (1990), 189–219 (196f.); furthermore, on precision as a normative value of scientific and general cultural practices: The Values of Precision, edited by Norton Wise (Princeton, 1995); Kathryn Olesko, ‘Der praktische Gauss’, in ‘Wie der Blitz einschlägt, hat sich das Räthsel gelöst’ (Göttingen, 2005), 236–58.

⁹The new Hanoverian Himten of 1¼ cubic feet (Hanoverian measure) corresponded to 31.152 lt or 2160 in³ (Zoll) or 66 ½ Pfund distilled water at 15° Réaumur; see Witthöft (note 2), 146ff., 715f.

²¹The Parisian platinum kilogram standard was deposited in Paris on that date; see, e.g., Hans R. Jenemann in: Genauigkeit und Präzision in der Geschichte der Wissenschaften und des Alltags, edited by Dieter Hoffmann and Harald Witthöft (Braunschweig, 1996 = PTB-Texte, vol 4), 183–211, and references therein. When Carl August Steinheil made a new kilogram standard for Bavaria in 1837, he chose to make it out of transparent quartz crystal, as this surface neither oxidizes nor is otherwise transformed over time: see Meyer-Stoll (note 6), 21ff.

²²Biographical information on Gauss’ pupil, the astronomer Heinrich Christian Schumacher, is available, for instance, in Lutz Brandt, ‘Heinrich Christian Schumacher zum Gedächtnis’, Gauss-Gesellschaft—Mitteilungen, 14 (1977), 75–93 and Hans Weil, Carl Philipp Heinrich Pistor, Begründer der optisch-mechanischen Kunst in Berlin. Versuch einer Biographie, 3rd ed. (Berlin, 2000), sec. 28. See F. Arago's obituary on the Parisian instrument maker, Henri-Prudent Gambey (1787–1847), in his Notices biographiques, vol 3. Schumacher minutely compares this copy (B) against kilogram A of the Parisian archives; see Heinrich C. Schumacher, ‘Vergleichung des Kilogramm von Platina, welches Etatsrath Schumacher aufbewahrt, mit dem gesetzlichen Kilogramme der Archive’, Schumachers Jahrbuch (Stuttgart and Tübingen, 1836), 237–50.

²³Repsold's work on weight standards are generally discussed by Koch (note 6); in the biography, see esp. 181–88. Gauss adds in his report of 1841, ‘I had Repsold in Hamburg make 2 half-kilograms (C) of brass, which prior to dispatch had been most scrupulously compared against B by Conference Councillor Schumacher. He conveyed to me the extensive recordings of all the weighings that occupied him from 11 August–6 October’.

²⁴The standard Prussian pound (D) had been manufactured by the Berlin instrument maker, Carl Philipp Heinrich Pistor (1778–1847); see the report by Eytelwein (note 3) in the proceedings of the Berlin Academy of Sciences. On Pistor, see Weil (note 22) and Koch's biography of Repsold (note 6).

²⁵Gauss comments about this weight in his report, ‘Pound E, which I had arranged for Senior Mining Councillor Schaffrinsky to produce in Berlin was carefully compared against D by the latter and Professor Encke prior to dispatch on two days (1836 March 21 and 23), and was found to be 1/2 milligram heavier on the balance, the recordings have been communicated to me in extenso’. G.S. Schaffrinsky (c.1765–1843) was a member of the Prussian ‘Commission of Experts’ responsible for verifying the sample measures. The other members were Privy Senior Building Councillor Johann Albert Eytelwein (1765–1849), the professor of physics at Berlin Paul Erman (1764–1851), Privy Senior Building Councillor August Leopold Crelle (1780–1855), and Privy Postal Councillor Pistor. See Eytelwein (note 3) as well as, e.g., Witthöft (note 3).

⁴On Meyerstein's Jewish family background, training, life, and work, see Klaus Hentschel, Gaussens unsichtbare Hand: Der Universitäts-Mechanicus und Maschinen-Inspector Moritz Meyerstein. Ein Instrumentenbauer im 19. Jahrhundert (Göttingen, 2005 = Abhandlungen der Göttinger Akademie der Wissenschaften, 3rd ser, vol 52). Gauss’ work in metrology has not yet been adequately covered in any of the scientific biographies written about him, e.g. Guy Waldo Dunnington, C.F. Gauss, Titan of Science, 1st ed. (New York, 1955); and only a few of his pertinent texts quoted below in extenso have been included in his collected works (Werke), issued by the Göttingen Academy of Sciences in eleven volumes between 1870 and 1929. Please note that this paper adopts the British spelling of Gauß throughout.

⁵See Gauss papers, at the Staats- & Universitätsbibliothek Göttingen, Department of Manuscripts and Rare Prints (in the following abbreviated as SUB), Physik 27, sheet 4 on the composition of the commission, sheets 2–3 for a calendar on Gauss’ correspondence (no mention of Meyerstein in it) as well as sheet 3 verso for an inventory. K.F. Müller studied for two years 1818–1820 at Gött ingen then returned to the military, first in the artillery batallion at Stade, and was subsequently promoted in the Hanoverian general staff to captain (1828), battery chief (1838), major (1842), and major general (1856). From 1829, on he was also teaching at the Hanover Artillery and Engineering School as well as at the General Staff Academy; see Wilhelm Rothert, Im alten Königreich Hannover 1814–1866 (Hannover, 1914 = Allgemeine Hannoversche Biographie, vol 2), 560f.

⁶Not all of the aforementioned metrologists have been studied adequately. See, e.g., Kathryn Olesko, ‘The meaning of precision: The exact sensibility in early nineteenth-century Germany’, in Wise (note 3), 103–34 about Prussia in general (esp. 121ff.), as well as Kasimir Lawrynowicz's biography, Friedrich Wilhelm Bessel 1784–1846 (Basel, 1995), 252–64. For commented transcriptions of Repsold's correspondance, see Der Briefwechsel von Johann Georg Repsold mit Carl Friedrich Gauss und Heinrich Christian Schumacher, edited by Jürgen Koch (Hamburg, 2000). Other biographies are: Jürgen Koch, Der Hamburger Spritzenmeister und Mechaniker Johann Georg Repsold (1770–1830), ein Beispiel für die Feinmechanik im norddeutschen Raum zu Beginn des 19. Jahrhunderts (Norderstedt, 2001), Cornelia Meyer-Stoll, ‘Die Regulierung der bayerischen Landesmaße’, Akademie Aktuell (Munich, March 2005), 20–25 on Steinheil and Bavaria, as well as the papers by Alder, Schaffer, and Gooday in Wise (note 3) on metrologists in France and Britain, respectively.

⁷See SUB, Gauss papers, Physik 26, Maß und Gewichtsregulierung. Correspondence with Hanoverians. Ministry of the Interior, G. Hoppenstedt to Gauss, 29 Aug. 1836, sheets 2–3. See also Gauss’ own collection of various pertinent laws idem, Physik 24.

⁸See SUB, Gauss papers, Physik 26, Maß und Gewichtsregulierung. Correspondence with Hanoverians. Ministry of the Interior, G. Hoppenstedt to Gauss, 29 Aug. 1836, sheets 2–3. See also Gauss’ own collection of various pertinent laws idem., Physik 26, sheet 5, head of the Royal Ministry of the Interior of Hanover and Great Britain G. Hoppenstedt to Gauss. For exact transcriptions of the German original documents quoted here, including more detailed document descriptions, see my comprehensive biographical study, Hentschel (note 4).

¹⁰After completing his studies in law at Celle, Stade and Oldenburg, von der Wisch worked until his retirement in December 1848 as councillor of justice. See Rothert (note 5) S. 593.

¹¹SUB, Gauss papers, Physik 26, sheet 7, letter to Gauss postmarked 9 November. Two tables in Gauss’ hand are on the verso headed ‘testing the Troughton yard’ and ‘schedule for testing Meyerstein's scale’.

¹²See the letter of 3 January 1837, ibid., sheet 11, ‘that the mechanic assigned the manufacture be recommended to accelerate in every way practicable’.

¹³See the letter of 3 January 1837, ibid., sheet 11, ‘that the mechanic assigned the manufacture be recommended to accelerate in every way practicable’., Physik 34, folder: Maß- und Gewichtsregulierung, Kosten der Waagen, Gewichte und Hohlmaße, sheet 5. See also the bill dated 15 July 1837 (sheet 3) presented below, also comprising eight hollow measures besides templets and mahogany boxes.

¹⁴On the Hanoverian triangulation, see, e.g., Gauss’ Werke 8 (1903), Olesko (note 3), pp. 247–50 and further references given therein. The following letter to Gauss is preserved in SUB (note 4) vol. Gauss papers, Physik 26, sheets 9–10.

¹⁵On the Hanoverian triangulation, see, e.g., Gauss’ Werke 8 (1903), Olesko (note 3), pp. 247–50 and further references given therein. The following letter to Gauss is preserved in SUB (note 4) vol. Gauss papers., Physik 34, sheet 3, transcription. Sheet 4 is another transcription (by Gauss).

¹⁶The administrative jurist Hoppenstedt studied jurisprudence at Göttingen and served successfully as maire adjoint in Hanover from 1810, later also serving as municipal director. In 1817, he was a government councillor, and from 1824 privy cabinet councillor at the Ministry of the Interior. His particular responsibility concerned appointments at the University of Göttingen, in which he proved to be extremely gifted. See Rothert (note 5), 544f., Waldemar Röhrbein, ‘Hoppenstedt, Georg’, in Neue Deutsche Biographie, 9 (1972), 620–21 and Wolfgang Huge, ‘Gewerbeförderung und Handwerkerfortbildung im Königreich Hannover. Zum pädagogischen Wirken des Gewerbevereins für das Königreich Hannover (1828–1866)’, Technikgeschichte 57 (1990), 211–34 (214–17) on Hoppenstedt's role in the founding of the trade association.

¹⁷SUB, Gauss papers, Physik 26, sheet 15, to Gauss.

¹⁸SUB, Gauss papers, Physik 26, sheet 15, to Gauss., sheet 18.

¹⁹On the following see ibid., sheets 49–52 for an undated draft in Gauss’ hand, as well as Physik 29, sheets 5–15 for a certified transcription of the submitted final, dated 27 January 1841. The full German text can be found in supplement vol. 11,1 (1927) to Gauss’ Werke (note 4), 7–15.

²⁰On the following see ibid., sheets 49–52 for an undated draft in Gauss’ hand, as well as Physik 29, sheets 5–15 for a certified transcription of the submitted final, dated 27 January 1841. The full German text can be found in supplement vol. 11,1 (1927) to Gauss’ Werke (note 4), 7–15., Physik 26, sheet 51 or the almost verbatim version in Physik 29, sheets 9–10. Compare the Inventarium der Kommission über Maße und Gewichte in Physik 27, sheet 3 verso, which lists, ‘(3) set Pruss[ian] weights from lb downwards, (4) set Pruss. med. weights, (5) set Pruss. gem weights, (6) individual gem weights, (7) Kohnbaum's set, (8) pound E (Enke), (9) two half kg by Repsold, (10) balance by Repsold, [. . .] (13) large balance’. Concerning the other points on the list, see note 77.

²⁶SUB, Gauss papers, Physik 26, sheet 50 verso (original emphasis). Gauss does not mention that Kater already used this fine adjustment procedure for the standard British pound; see Henry Kater, ‘An account of the construction and adjustment of the new standards of weights and measures of the United Kingdom of Great Britain and Ireland’, Philosophical Transactions of the Royal Society of London, 116 (1826), 1–52 (13ff., 26), also available as separatum (London, 1826). On Kater, see note 82 below.

²⁷SUB, Gauss papers, Physik 26, sheet 50 verso (original emphasis). Gauss does not mention that Kater already used this fine adjustment procedure for the standard British pound; see Henry Kater, ‘An account of the construction and adjustment of the new standards of weights and measures of the United Kingdom of Great Britain and Ireland’, Philosophical Transactions of the Royal Society of London, 116 (1826), 1–52 (13ff., 26), also available as separatum (London, 1826). On Kater, see note 82 below., quoted from the draft version, omitting the few struck words, sheets 49–50.

²⁸SUB, Gauss papers, Physik 26, sheet 50 verso (original emphasis). Gauss does not mention that Kater already used this fine adjustment procedure for the standard British pound; see Henry Kater, ‘An account of the construction and adjustment of the new standards of weights and measures of the United Kingdom of Great Britain and Ireland’, Philosophical Transactions of the Royal Society of London, 116 (1826), 1–52 (13ff., 26), also available as separatum (London, 1826). On Kater, see note 82 below., quoted from the draft version, omitting the few struck words., sheets 50–51 (original emphasis). Compare the empirical determinations of the buoyancy of air in Wilhelm Felgentraeger, Feine Waagen, Wägungen und Gewichte (Berlin, 1932), 249ff.: rev. ed. of: Theorie, Konstruktion und Gebrauch der feineren Hebelwaagen (Leipzig, 1907). This point is already raised in Schumacher (note 22), 239ff. He could not, however, perform this weighing of the Parisian kilogram (A) under water, ‘owing to its legal importance’. Instead, he was forced to determine its density from measurements of the height and diameter of the original cylinder and figure out indirectly the disturbing effects of air buoyancy on the weighings in order to obtain its weight in vacuum. This reduction of metrological measurements to vacuum conditions had been pioneered by Bessel in his second pendulum investigation of 1828, which, however, aimed at determining standards of length, not weight.

²⁹See, e.g., Gauss’ remarks on a letter addressed to him dated 7 September 1836, ‘46.919 [;] 70.378 Meyersteinian milligrams’, followed by measurements of length (idem, sheet 5 recto, left margin).

³⁰Gauss and Bessel had applied such statistical analysis outside the context of pure mathematics, primarily to determine errors in measurement series in astronomy and physics. See, e.g., volume 4 of Gauss’ works (note 4), Dunnington (note 4), 19–21 and O.B. Sheynin, ‘C.F. Gauss and the theory of errors’, Archive for History of Exact Sciences, 20 (1978), 21–72.

³¹The various steps of Gauss’ precision weighing procedure are specified in Felgentraeger (note 28), 263ff., see esp. 175ff. on the exchange mechanisms. See also Gauss’ notes in Physik 26, sheet 57 on his weighing method and the procedures to test the balances. The following quote is the closing paragraph of the draft report, sheet 52.

³²See, e.g., A.M. Basedow and H.R. Jenemann, ‘Waage und Wägung’, in Quantitative organische Elementaranalyse, edited by Friedrich Ehrenberger (Weinheim, 1991), 79–107 (82).

³³SUB, Gauss papers, Physik 34, sheet 1 (the amount for the stamps was subsequently added). Cf. the payment instructions to the royal general bursar in the amount of 700 Reichsthaler (no. 2117), idem, sheet 2.

³⁴Eytelwein (note 3) had only aimed at ±1 mg for the Prussian Urpfund in 1825; Schumacher (note 22) reached 0.01 mg. The following is from SUB, Gauss papers, Physik 26, sheets 22–23, to Gauss, received 5 Apr.

³⁵Various magistrates and bailiffs posed initial resistance to these customs weights; they were only officially introduced as the new standard on 1 July 1858. See Anonymous, ‘Ueber die vorgeschlagene Einführung des Zollpfundes als Handelsgewicht im deutschen Zollvereine’. Mittheilungen des Gewerbe-Vereins für das Königreich Hannover (1855), 170–76; Witthöft (note 2), 694.

³⁶On Weber, who had been appointed in 1831 with Gauss’ strong support, see, e.g., Eduard Riecke, Wilhelm Weber—Rede gehalten in der öffentlichen Sitzung der Akademie der Wissenschaften (Göttingen: Dieterich, 1892); Heinrich Weber, Wilhelm Weber—eine Lebensskizze (Breslau, 1893); Karl-Heinrich Wiederkehr, Wilhelm Eduard Weber—Erforscher der Wellenbewegung und der Elektrizität 1804–1891 (Stuttgart, 1967).

³⁷SUB, Gauss papers, Physik 26, sheets 76–77; handwritten draft dated 1 March 1854. Crossed out passages are omitted here.

³⁸SUB, Gauss papers, Physik 26, sheets 76–77; handwritten draft dated 1 March 1854. Crossed out passages are omitted here., sheet 77, including a few editorial clarifications by me. Repsold's balance is discussed in Koch's correspondence edition (note 6).

³⁹On the following see ibid., sheet 57, ‘Prüfung der großen Waage des chemischen Laboratorii, auf ihre Empfindlichkeit und die Uebereinstimmung ihrer Angaben’. This description of the procedure for checking the sensitivity of the balance includes the records of thirteen trials in three series (twice each with one mg discrepancy, once without), signed by Dr Heeren. See furthermore Felgentraeger (note 28), 9ff. and 254ff. on this weighing method and the following figure for a photograph of this balance, preserved at the Museum der Göttingern Chemie.

⁴¹In a document dated 10 July 1854, this order for a 1/32 Zollpfund was changed to 1/30, A.F. Wedemeyer to Privy Court Councillor Gauss in Göttingen, ibid., sheet 34.

⁴²Article 36 of the ‘Proclamation by the Royal Ministers of the Interior, regarding the implementation of the law on measures and weights’ (see note 1 on page 1 above) reads (on p. 165), [Par. 1,]

To maintain the required equivalence, the sample measures and weights for all verification offices should henceforth be verified by the Verification Office at Hanover and be specially designated as sample measures. [Par. 2,] For this purpose, the Verification Office at Hanover should be supplied with a special stamp and sample measures and weights, which are to be used solely for the calibration of sample measures and weights of verification offices, but which are to be carefully stored together with the stamp at the Magistrate's. [Par. 3,] We retain the right soon and from time to time to order a new comparison of these sample measures and weights against the originals deposited with Us, which latter are to be verified by a special commission and stored together with the records thereto under seal of the Ministry.

⁴⁰SUB, Gauss papers, Physik 26, sheets 28–29, to Gauss.

⁴³The king appointed this administrative civil servant as interior minister on 21 November 1853. Wedemeyer had previously been working in the War Ministry until 1850. He stayed in office until 29 July 1855: Rothert (note 5), 591.

⁴⁴See A.F. Wedemeyer's letter to Gauss dated 10 July 1854, SUB, Gauss papers, Physik 26, sheet 36.

⁴⁵The contemporary theory and practice of precision balances are described in Moritz Rühlmann, Allgemeine Maschinenlehre, vol. 1 (Braunschweig, 1862), 129–53. Two sales lists of Meyerstein's instruments are reproduced in facsimile in the appendix Hentschel (note 4).

⁴⁶See Hans R. Jenemann, Die Waage des Chemikers (Frankfurt, 1979), 39, for an illustration of a similar balance for Berzelius from 1835.

⁴⁷On the following, see William H. Brock, The Fontana History of Chemistry (London, 1992), 151ff. Peter Lundgren also discusses Lavoisier's reception in Sweden, in: Bildungschancen und soziale Mobilität in der städtischen Gesellschaft des 19. Jahrhunderts (Göttingen, 1988). Lavoisier's laboratory was equipped with a precision balance by the ‘adjusteur de la Monnaie’ Chemin as well as by Mégnié and Nicolas Fortin; see Bernadette Bensaude-Vincent, ‘La balance, un univers de mesure’, Actualité chimique, no 2 (1994), 36–39, and Bruno Jacomy's articles, ‘Une visite au laboratoire de Lavoisier’, Actualité chimique, no. 2 (1994), 52–54 and ‘Le laboratoire de Lavoisier’, Musée des Arts et Métiers—La Revue, no. 6 (March 1994), 17–22. Fortin's balance from 1788 could bear loads of up to 10 kg, then indicating a precision of about 20 mg. The one by Mégnié allowed a direct reading of M±5 mg for a load of 600 g.

⁴⁸Rühlmann (note 45), 135 offers various examples of sensitivity coefficients, from the smallest weight perceptible to the balance up to the maximum load, ranging between 1/64,000 and 1/20 million (the latter for a Bianchi balance from 1855).

⁴⁹Jenemann (note 46), 41.

⁵⁰Beam designs and their various shapes are discussed in Felgentraeger (note 28), 41–71.

⁵¹For details on the design, material, and production of knife edges and bearing plates, see ibid., pp. 73–88.

⁵²I am grateful to Dr Beer at the Museum der Göttinger Chemie for explaining to me the practical handling of this balance. For more general instructions, see also Rühlmann (note 45), 132f. Detailed instructions on the adjustment and use of a balance of almost identical design are also available at the archive of the Chemical Heritage Foundation in Philadelphia. They had been provided with a balance Charles Frederick Chandler had purchased in Berlin from the instrument maker, August Oertling. The instrument itself is also among their holdings. (On Oertling, see note 70.)

⁵³See, e.g., Jenemann (note 46), 41ff. In this context, L. Ambronn, ‘Beitrag zur Geschichte der Feinmechanik’, Beiträge zur Geschichte von Technik und Industrie, 9 (1919), 1–40 (33), also mentions ‘the workshop of M. Meyerstein in Göttingen enjoying considerable repute under Gauss and Weber’.

⁵⁴Meyerstein was probably not yet aware that even brass undergoes various crystallization changes as a consequence of being worked and polished, likewise causing changes in length of a balance beam. For this reason, Sartorius, the fine instrument manufacturers at Göttingen, placed all its newly cut balance parts in storage for a longer period of time, resulting in delays in fine adjustment and delivery. I thank Dr Jost Lemmerich for this information.

⁵⁵See Koch (2000, note 6), 61; Gauss’ comment in a letter to Adolf und Georg Repsold from 23 September 1836 that, owing to Meyerstein's absence, he had performed a single weighing experiment allows the conclusion that his mechanic was crucially involved in such weighings.

⁵⁶Letter dated 4 February 1837, Gauss (1927, note 19), 31, where Gauss also alludes to a new testing procedure of his.

⁵⁷See Göttingische gelehrte Anzeigen, 13 March 1837, reprinted in Gauss’ works (note 4), vol. 5, 511–13. On experimental checking of knife-edge positions, see also Felgentraeger (note 28), 99, 241f.

⁵⁸Cf. the Ministry's letter to Gauss referenced in note 11 above, and the transcription of Meyerstein's bill above including a fibre balance (referenced in note 33). See also Olesko (note 6), 119f.

⁵⁹See Moritz Meyerstein, Verzeichniss astronomischer und physikalischer Instrumente (Göttingen, 1845), 4, section on physics, nos 9–13, reprinted in facsimile in Hentschel (note 4), appendix I, 271–81; as well as Moritz Meyerstein, ‘Preisverzeichniss der astronomischen und physikalischen Werkstätte von M. Meyerstein, Universitäts- Instrumenten- und Maschinen-Inspector in Göttingen’, Astronomische Nachrichten, 53 (1860), nos 1265–67, cols 263–72, 301–4 (col 268), nos 14–21 indicating some slightly raised prices, from 20 RTh for the large individual weights and sets from 1 mg to 1 g; reprinted in facsimile in Hentschel (note 4), appendix I, 283–88. See also Noback (note 2), 271 on the definition and subdivisioning of the Hanoverian pound. Koch (2001, note 6), 176–87 describes comparable work by Johann Repsold on the Hamburg standard and series of weights, Meyer-Stoll (note 6) on Bavaria, and Olesko (note 6), 121–25 on Bessel's and Theodor Baumann's work for Prussia.

⁶⁰Meyerstein (1845, note 59), section on weights and measures. See also Wilhelm Weber, ‘Ueber drei neue Methoden der Konstruktion von Waagen’. Göttinger gelehrte Anzeigen, 22 (1837), 209–22, reprinted in Weber's Gesammelte Werke, vol. 1 (1892), 489–96 and pl. XII (490f.); and Hans R. Jenemann, ‘Die Göttinger Präzisionsmechanik und die Fertigung feiner Waagen’, Göttinger Jahrbuch, 36 (1988), 181–201 (193–95). One of these rarer instruments is among the historical collection of the 1st Institute of Physics at the University of Göttingen (item H 145). See the list of items by Meyerstein, Hentschel (note 4), appendix 2, 289ff.

⁶¹Jenemann (note 60), 195–97; Weber (1892, note 60), 494f.; Philipp Carl, ‘Die Wage’, Carl's Repertorium für Experimental-Physik, 1 (1866), 7–41, pl. I–VII (30ff., pl. VI); Rühlmann (note 45), 133f.

⁶²See, e.g., Witthöft (note 3) or Georg Wilhelm Muncke, ‘Maß’, in Johann Samuel Traugott Gehler's Physikalisches Wörterbuch revised by Gmelin, Littrow, Muncke, Pfaff, vol. 6, part 1 (1836), 1218–391 (1222ff.); Karl Karmarsch, ‘Über Maß und Gewicht’, Mittheilungen des Gewerbe-Vereins für das Königreich Hannover, new ser. (1856) no. 1, cols 38–51, 101–16, 141–46 (cols 40ff., 105ff.); Herbert Arthur Klein, The Science of Measurement. A Historical Survey (New York, 1974), chaps 4–5 for older, frequently anthropomorphic measures of length.

⁶³On the latter, see Hentschel (note 4), 173ff.

⁷⁰Johann August Daniel Oertling (1803–1866), a former apprentice of Pistor, established his own workshop in Berlin in 1826 that specialized in astronomical and physical instruments.

⁷³See also the following note.

⁶⁴Universitätsarchiv Göttingen (henceforth abbreviated as UAG) Kur., 4 V h 16, sheets 7–10, quoted from sheets 7 and 9, received 20 December 1832.

⁶⁵The model for Meyerstein's comparator was an analogous instrument built by Edward Troughton (1753–1836) in London; for the calibration of the British standard length, see Edward Troughton, ‘An account of a method of dividing astronomical and other instruments by ocular inspection, in which the usual tools of graduating are not employed’, Philosophical Transactions of the Royal Society of London, 99 (1809), 105–45, pls II–IV (esp. 136–40 on linear divisioning and a comparator); and Gloria Clifton, Directory of British Scientific Instrument Makers 1550–1851 (London, 1996), 281f. Pistor performed corresponding work on the Prussian standard; see Eytelwein (note 3), 2f.

⁶⁶140 Rheinländischer Gulden (Rhenish guilder) were worth a little under 94 Reichsthaler.

⁶⁷UAG Kur., 4 V h 16, sheets 13–14, 20 May 1833. J. von Utzschneider's bill dated 10 May 1833 is also preserved (idem, sheet 14b).

⁶⁸See Moses Kaern, ‘Das erdmagnetische Observatorium in der Scheune. Messungen mit dem originalgetreuen Nachbau eines Magnetometers von Gauss und Weber’, Gauss-Gesellschaft—Mitteilungen 39 (2002), 23–52 (36f., 43).

⁶⁹UAG Kur., 4 V h 16, sheets 18–20, received 8 February 1834.

⁷¹UAG Kur., 4 V h 16, sheets 22–23, Universitäts-Kuratorium to Weber, 25 February 1834, ‘that one iron prism of 4-foot length be purchased for the sum of twenty thaler, Prussian curr.,—to which disbursement the University Cashier is authorized as of today's date’.

⁷²UAG Kur., 4 V h 16, sheets 22–23, Universitäts-Kuratorium to Weber, 25 February 1834, ‘that one iron prism of 4-foot length be purchased for the sum of twenty thaler, Prussian curr.,—to which disbursement the University Cashier is authorized as of today's date’., sheet 57.

⁷⁴On the budgetary issue see, e.g., Weber's report ‘on the current state of the Physical Cabinet’ dated 20 October 1837, UAG Kur., 4 V h 16, sheets 50–54, here sheets 53f.,

I hope that this humble report will contribute toward grounds for the conviction that firstly the expansion of the physical sciences in our time makes two things indispensable for a university of the sciences, namely, good course apparatus and finer apparatus for higher scientific education; furthermore, after so little has been applied to either for a long time, suddenly the much remaining to be done is become ever more urgent; finally, that in our times the high place due our university can only be assured by the disposition of an annual fund as in the chemical sciences.

A pencilled note to the left of this paragraph specifies, ‘Budget for t[he] chemical laboratory is [roughly] 700 r. JM’.

⁷⁵I am grateful to Prof. Gustav Beuermann for his detailed explanation of the nicely preserved length comparator, a part of the historical instruments collection of the 1st Institute of Physics, University of Göttingen.

⁷⁸George Dollond (1774–1852), a mechanic and optician in London, was a fellow of the Royal Society (since 1820) and member of the Royal Astronomical Society.

⁷⁶UAG Kur., 4 V h 16, sheet 58, bill dated 20 October 1837. For the telescope, he also charged 64 Rth and for the beam compass 60 Rth.

⁷⁷See SUB, Gauss papers, Physik 27, Geschäftsführung der commission über Maße und Gewichte, sheet 3 verso, ‘Inventory, (No. 1) yard by Dollond […] (No. 11) cast-iron comparator stand, (12) measuring rod of 640 mm, […] (14) apparatus for the marking of measures of length’. (Other inventory items are listed in note 20 above.)

⁷⁹See the second note (**) to Meyerstein's bill dated 15 July 1837, transcribed above in the first section. The first item on list A of instruments built by Meyerstein still a part of this collection, reads, ‘Length measure of 640 mm length with 60 cm in millimeter divisions on brass as well as two attachable reading guides with vernier, in hinged wooden box, 1836’. Hentschel (note 4), appendix 2, 293. Both length measures are depicted in colour in Hermann Schreiber, Historische Gegenstände und Instrumente im Institut für Geophysik der Universität Göttingen (Göttingen, 2000), 42. The other length measures illustrated there from the instruments collection of the Göttingen Geophysics Institute are of a younger date.

⁸⁰The standard was made available by the Kaiserliche Normal-Eichungskommission; see Karl Schering, ‘Beobachtungen im magnetischen Observatorium. I. Bestimmung der Horizontalintensität’, Nachrichten der königlichen Gesellschaft der Wissenschaften zu Göttingen (1881) 133–76 (138f.) and plate.

⁸¹Schumacher's Jahrbuch from 1836 (note 22), 235 quotes a thermal expansion coefficient for brass that alters a length of 1 at 0°C to 1.001920 at 100°C (according to Stampfer), whereas Lavoisier and Laplace had determined 1.001878.

⁸²Henry Kater, for instance, conducted temperature corrections of −0.001740 in; see his ‘An account of the comparison of various British Standards of linear measure’, Philosophical Transactions of the Royal Society of London, 111 (1821), 75–94. His other articles, ‘Construction of a copy of the Imperial Yard’, Philosophical Transactions of the Royal Society of London, 121 (1831), 345–48; and ‘An Account of the Standards Prepared for the Russian Government, (London, 1832), the latter of which was inaccessible to me, describe the procedures used to copy calibrated standards. Kater participated in the surveys of India, returning to England for health reasons, where he served as brigade-major in Ipswich and devoted himself mainly to metrology. This research earned him membership in the Royal Society of London in 1815 and the Copley gold medal in 1817; see H. Mannes Chichester, ‘Kater, Henry’, Dictionary of National Biography, 30 (1892), 240–41.

⁸³The law cited in note 1 above specifies on p. 118 in particular, 1 yard = 36 inches, 1 foot = 12 (English) inches. The above definition thus makes 11.5 English inches = 12 Hanoverian inches = 29.209 centimetres.

⁸⁴On the foregoing, see SUB, Gauss papers, Physik 31.

⁸⁶See Kater (note 26) for a detailed description of the procedure used in manufacturing the copies of the standard yard for the Exchequer in Westminster, Guildhall, London, Edinburgh, and Dublin. The original standard yard by Bird, deposited at Westminster in 1760, had been destroyed in the fire of 1834. Henry Kater, ‘On the error in standards of linear measure, arising from the thickness of the bar on which they are traced’, Philosophical Transactions of the Royal Society of London, 120 (1830), 359–81 (378f.) mentions Dollond's copy from 1828 and length comparisons against other measuring rods.

⁸⁷Kater had shown that a slight bending of just 0.01 in of unsuitably thin measuring rods could already lead to reading errors on the scale in order of magnitude 0.0001 to 0.0006 in; Kater (1830, note 86), 374ff. The solution he suggested, which was adopted by others as well, was to inlay the finely calibrated scale in a heavier supporting bar. Both of Meyerstein's measuring rods at Göttingen have this two-element design.

⁸⁵On the foregoing, see SUB, Gauss papers., Physik 29, sheets 1–4; copy certified by Chancellery Councillor Bening dated 13 April 1841. This document was included in the supplement volume of Gauss’ collected works (note 19), 3–6, but to the best of my knowledge has hitherto neither been translated into English nor been situated within the context of Gauss’ measurement practices.

⁸⁸UAG Kur., 4 V h 16, sheet 66, W. Weber's application to the Royal Cabinet with a ‘most obedient request by Professor Listing concerning new acquisitions for the Physical Cabinet of Göttingen’, dated 29 June 1847 (orig. emphasis).

⁸⁹See the summary by Norton Wise in Wise (note 3), 358 on ‘networks of trust’.