Advertisement

Archive for History of Exact Sciences

, Volume 46, Issue 3, pp 253–283 | Cite as

C. F. Gauss and geodetic observations

  • Oscar Sheynin
Article

Keywords

Geodetic Observation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

C. F. Gauss: Works

  1. C. F. Gauss (1809)Theoria motus ... German transl.: Aus der Theorie der Bewegung der Himmelkörperetc. InGauss (1887, pp. 92–117).Google Scholar
  2. C. F. Gauss (1816) Bestimmung der Genauigkeit der Beobachtungen.Ibid., pp. 109–117.Google Scholar
  3. C. F. Gauss (1823) Theoria combinationis ... German transl.: Theorie der den kleinsten Fehlern unterworfenen Combination der Beobachtungen.Ibid., pp. 1–53.Google Scholar
  4. C. F. Gauss (1826) Selbstanzeige ofGauss (1828).Ibid., pp. 200–204.Google Scholar
  5. C. F. Gauss (1828) Supplementum theoriae combinationis ... German transl.: Theorie der ... Combinationetc. ..., Ergänzung.Ibid., pp. 54–91.Google Scholar
  6. : (1845) Anwendung der Wahrscheinlichkeitsrechnung auf die Bestimmung der Bilanz für Witwenkassen. [2.] Nachlass.Werke, Bd.4. Göttingen, 1880, pp. 125–157.Google Scholar
  7. C. F. Gauss (1887)Abhandlungen zur Methode der kleinsten Quadrate. Hrsg.,A. Börsch &P. Simon. Berlin.Google Scholar
  8. C. F. Gauss (1900)Werke, Bd.8. Göttingen — Leipzig.Google Scholar
  9. C. F. Gauss (1903)Werke, Bd.9. Göttingen — Leipzig.Google Scholar
  10. C. F. Gauss (1975)Werke. Ergänzungsreihe, Bd.1. Hildesheim.Google Scholar

C. F. Gauss: Correspondence

  1. C. F. Gauss [Gauss, Bessel] (1880),Briefwechsel zwischen Gauss und Bessel. Leipzig. Reprinted asGauss (1975). Quotations in my text are from this reprint.Google Scholar
  2. C. F. Gauss Peters, C. A. F. (Hrsg.) (1860–1865),Briefwechsel zwischen Gauss und Schumacher, Bde1–6. Altona.Google Scholar
  3. C. F. Gauss Schäfer, G. (Hrsg.) (1927),Briefwechsel zwischen Gauss und Gerling. Berlin.Google Scholar
  4. Schilling, C. (1900–1909),W. Olbers. Sein Leben und sein Werk. Bd.2, Abt. 1–2, this beingBriefwechsel zwischen Gauss und Olbers. Berlin.Google Scholar

Other Authors

  1. Airy, G. B. ([1861] 1879),On the algebraical and numerical theory of errors of observations etc. London.Google Scholar
  2. Barnett, V. &Lewis, T. ([1978] 1984),Outliers in statistical data. Chichester a.o.Google Scholar
  3. Bernoulli, D. (1770–1771), Mensura sortis ad fortuitam successionem rerum naturaliter contingentium applicata (Bernoulli 1982, pp. 326–360).Google Scholar
  4. Bernoulli, D. (1778), Dijudicatio ... Engl. transl.: The most probable choiceetc. SeeKendall (1961)Google Scholar
  5. Bernoulli, D. (1780), Specimen philosophicum de compensationibus horologicisetc. (Bernoulli 1982, pp. 376–390).Google Scholar
  6. Bernoulli, D. (1982),Werke, Bd.2. Hrsg.,B. L. van der Waerden. Basel.Google Scholar
  7. Bertrand, J. (1888),Calcul des probabilités. Paris. Reprints: 1889, 1907, 1970, 1972.Google Scholar
  8. Bervi, N. V. (1899), Determining the most probable value of the observed object apart from Gauss's postulate.Bulleten Imp. Moskovskoe obshchestvo liubitelei estestvosnania, antropologii i etnografii, Otdelenie fisicheskikh nauk, vol.10, No. 1, 41–45 (in Russian).Google Scholar
  9. Bessel, F. W. (1816), Untersuchungen über die Bahn des Olbersschen Kometen.Abh. Preuss. Akad. [Berlin], math. Kl, 1812–1813, 119–160.Google Scholar
  10. Bessel, F. W. (1820), Beschreibung des auf des Königsberger Sternwarte.Astron. Jahrb. für 1823, 161–168. Berlin.Google Scholar
  11. Bessel, F. W. (1826), Methode die Thermometer zu berichtigen.Abhandlungen, Bd.3. Leipzig, 1876, pp. 226–233.Google Scholar
  12. Bessel, F. W. (1838),Gradmessung in Ostpreussen. Berlin.Google Scholar
  13. Breen, H. (1849), Correction of Lindenau's elements of the orbit of Venus.Monthly Notices Roy. Astron. Soc., vol.9, 49–51.Google Scholar
  14. Campbell, N. R. (1928),An account of the principles of measurement and calculation. London. a.o.Google Scholar
  15. Chebyshev, P. L. (1936),Theory of probability. Lectures read in 1879–1880 as written down byA. M. Liapunov. Ed.,A. N. Krylov. Moscow — Leningrad. (In Russian.)Google Scholar
  16. Clarke, A. R. (1880),Geodesy. Oxford.Google Scholar
  17. Colclough, A. R. (1987), Two theories of experimental error.J. Res. Nat. Bureau Stand. vol.92, No. 3, 167–185.Google Scholar
  18. Cournot, A. A. ([1843] 1984),Exposition de la théorie des chances et des probabilités Ed.,B. Bru.. Paris.Google Scholar
  19. Cramér, H. (1946),Mathematical methods of statistics. Princeton.Google Scholar
  20. Czuber, E. (1891),Theorie der Beobachtungsfehler. Leipzig.Google Scholar
  21. Dale, A. I. (1991), T. Bayes's work on infinite series.Hist. math., vol.18, 312–327.Google Scholar
  22. Delambre, J. B. J. (1810),Rapport historique sur les progrès des sciences mathématiques depuis 1789 et sur leur état actuel. Paris. Reprint: Amsterdam, 1966.Google Scholar
  23. Delambre, J. B. J. (1814a), Analyse des travaux de la Classe des sci. math. et phys. de l'Institut, pendant l'année 1811.Mém. cl. math. et phys. Inst. Imp. de France année 1811, pt. 2, first paging, i–lxxviii. Paris.Google Scholar
  24. Delambre, J. B. J. (1814b),Astronomie théorique et pratique, t.2. Paris.Google Scholar
  25. Delambre, J. B. J. (1912),Grandeur et figure de la terre. Paris.Google Scholar
  26. DeMoivre, A. (1756),Doctrine of chances. Third ed. London.Google Scholar
  27. DeMorgan, A. (1845), Theory of probabilities. InEnc. Metropolitana. Pure sciences, vol.2, pp. 393–490. London.Google Scholar
  28. Dixon, W. J. (1962), Rejection of observations. In:Contributions to order statistics. EdsA. E. Sarhan &B. G. Greenberg. New York — London, pp. 299–342.Google Scholar
  29. Dorsey, N. E. &C. Eisenhart (1969), On absolute measurements. (Ku 1969, pp. 49–55).Google Scholar
  30. Dreyer, J. L. E. (1890),Tycho Brahe. Edinburgh.Google Scholar
  31. Eisenhart, C. (1963), Realistic evaluation of the precision and accuracy of instrument calibration. (Ku 1969, pp. 21–47).Google Scholar
  32. Eisenhart, C. (1968), Expression of the uncertainties of final results. (Ku 1969, pp. 69–72).Google Scholar
  33. Eisenhart, C. (1978), Gauss. In:Intern. Enc. of Statistics, vol.1, pp. 378–386. Eds.W. H. Kruskal &Judith M. Tanur. New York — London.Google Scholar
  34. Encke, J. F. (1832), Über die Bergründung der Methode der kleinsten Quadrate.Abh. Kgl. Akad. Wiss. zu Berlin, Math. Kl., 1831, pp. 73–78.Google Scholar
  35. Encke, J. F. (1834–1836), Über die Methode der kleinsten Quadrate.Ges. math. und astron. Abh., Bd.2, pp. 1–200. Berlin, 1888.Google Scholar
  36. Erman, Ad. (Hrsg.) (1852),Briefwechsel zwischen Olbers und Bessel, Bde1–2. Leipzig.Google Scholar
  37. Forbes, E. G. (1978), The astronomical work of C. F. Gauss.Hist. Math., vol.5, No. 2, 167–181.Google Scholar
  38. Fourier, J. B. J. (1824), Règle usuelle pour la recherche des résultats moyensetc. Bull. sci. math., astron., phys. et chim. this beingBull. Universelle des sci., premier sect., t.2, 88–89. A supplement written byDeflers (pp. 89–90) contains a pertinent numerical example.Deflers also states thatFourier read his note at theSociété philomatique le 3 juill., dernier.Google Scholar
  39. Fourier, J. B. J. (1826), Mémoire sur les résultats moyensetc. (Fourier 1890, pp. 525–545).Google Scholar
  40. Fourier, J. B. J. (1829), Second mémoire sur les résultats moyensetc. (Fourier 1890, pp. 551–590).Google Scholar
  41. Fourier, J. B. J. (1890),Oeuvres, t.2. Paris.Google Scholar
  42. Galloway, T. (1839),A treatise on probability. Edinburgh.Google Scholar
  43. Gerling, Ch. L. (1839),Beiträge zur Geographie Kurhessens etc. Cassel.Google Scholar
  44. Gerling, Ch. L. (1843),Die Ausgleichungsrechnung etc. Hamburg — Gotha.Google Scholar
  45. Giacomo, P. (1981), News from the BIPM.Metrologia, vol.17, 69–74.Google Scholar
  46. Glaisher, J. W. L. (1872), On the law of facility of errors of observationsetc. Mem. Roy. Astron. Soc., vol.39, 75–124.Google Scholar
  47. Gleissberg, W. (1964), Zur Begründung des Auftretens zufälliger Beobachtungsfehler.Sterne, Bd.40, No. 5–6, 105–108.Google Scholar
  48. Gnedenko, B. V. &O. B. Sheynin ([1978] 1992), The theory of probability. In:Mathematics of the nineteenth century, pp. 211–282. Eds,A. N. Kolmogorov &A. P. Yushkevich. Basel a.o. Transl. from Russian.Google Scholar
  49. Hansen [P. A.], (1831), Über die Anwendung der Wahrscheinlichkeitsrechnung auf geodätische Vermessungenetc. Astron. Nachr., Bd.9, No. 202, 189–204.Google Scholar
  50. Harter, H. L. (1977, date of preface),A chronological annotated bibliography on order statistics, vol.1. No place. Publ. by the US Air Force and several of its sub-units.Google Scholar
  51. Hauber, C. Fr. (1832), Theorie der mittleren Werthe.Z. f. Phys. Math., Bd.10, 425–457.Google Scholar
  52. Helmert, F. R. (1872),Die Ausgleichungsrechnung etc. Leipzig.Google Scholar
  53. Henke, R. (1894),Über die Methode der kleinsten Quadrate. Leipzig. Zweite unveränderte Aufl. Erste Aufl.: 1868.Google Scholar
  54. Heyde, C. C. &E. Seneta (1977),I. J. Bienaymé. New York a.o.Google Scholar
  55. Huygens, C. ([1669] 1895), Correspondance.Oeuvr. compl., t.6, pp. 531–532. La Haye.Google Scholar
  56. Ivory, J. (1825–1826), On the method of least squares.Lond., Edinb. Dublin Philos. Mag. & J., vol.65, 1–10, 81–88, 161–168; vol.68, 161–165.Google Scholar
  57. Jordan, W. (Hrsg.) (1882),Höhere Geodäsie und Topographie des Deutschen Reiches. Stuttgart.Google Scholar
  58. Kapteyn, J. C. (1912), Definition of the correlation-coefficient.Monthly Notices Roy. Astron. Soc., vol.72, No. 6, 518–525.Google Scholar
  59. Kendall, M. G. (1961), Daniel Bernoulli on maximum likelihood. Incorporates Engl. transl, ofBernoulli (1778).Biometrika, vol.48, 1–18. (E. S. Pearson &M. G. Kendall 1970, pp. 155–172).Google Scholar
  60. Kendall, Sir Maurice &R. L. Plackett (Eds) (1977),Studies in the history of statistics and probability, vol.2. London.Google Scholar
  61. Knobloch, E. (1985), Zu Grundlagenproblematik der Fehlertheorie. In:Festschrift für Helmuth Gericke. Hrsg.M. Folkerts et al. Stuttgart, 561–590.Google Scholar
  62. Kolmogorov, A. N. (1946), On the substantiation of the method of least squares.Uspekhi math. nauk, vol.1, No. 1, 57–70 (in Russian).Google Scholar
  63. Kornfeld, M. (1955), On the theory of errors.Doklady Akademii Nauk SSSR, vol.103, No. 2, 213–214 (in Russian).Google Scholar
  64. Kotz, S. &N. L. Johnson (Eds) (1982–1988),Encyclopedia of statistical sciences, vols1–9. New York a.o.Google Scholar
  65. Kruskal, W. H. (1960), Some remarks on wild observations. (Ku 1969, pp. 346–348).Google Scholar
  66. Ku, H. H. (1967), Statistical concepts in metrology. (Ku 1969, pp. 296–330).Google Scholar
  67. Ku, H. H. (Ed.) (1969),Precision measurement and calibration. Selected Nat. Bureau of Standards papers on statistical concepts and procedures. NBS Sp. Publ. 300, vol1. Washington.Google Scholar
  68. Lancaster, H. O. (1972), Development of the notion of statistical dependence. (Kendall &Plackett 1977, pp. 293–308).Google Scholar
  69. Laplace, P. S. ([1814] 1820),Essai philosophique sur les probabilités. The edition of 1820 was reprinted inLaplace'sOeuvr. compl., t.7, No. 1. Paris, 1886, with separate paging. In my text, I refer to theOeuvr. compl. Google Scholar
  70. Lehmann, E. L. (1959),Testing statistical hypotheses. New York — London.Google Scholar
  71. Lévy, P. (1925),Calcul des probabilités. Paris.Google Scholar
  72. Liapunov, A. M. (1975), On Gauss's formula for estimating the measure of precision of observations.Istoriko-mathematicheskie issledovania, vol.20, 319–328, in Russian. Posth. publ. with my comments.Google Scholar
  73. Merriman, M. (1877), List of writings relating to the method of least squaresetc. Trans. Connecticut Acad. Arts Sci., vol.4, pt. 1, 151–232.Google Scholar
  74. Newcomb, S. (1886), A generalized theory of the combination of observationsetc. Amer. J. Math., vol.8, 343–366.Google Scholar
  75. Pearson, E. S. &M. G. Kendall (Eds) (1970),Studies in the history of statistics and probability, vol.1. London.Google Scholar
  76. Pearson, K. (1920), Note on the history of correlation.Biometrika, vol.13. (Pearson &Kendall 1970, pp. 185–205).Google Scholar
  77. Pearson, K. (1978),The history of statistics in the 17th & 18th centuries. Posth. publ. byE. S. Pearson. London.Google Scholar
  78. Poincaré, H. (1896)Calcul des probabilités. Paris.Google Scholar
  79. Poisson, S. D. (1833), Discours prononcé aux funérailles de M. Legendre.J. reine und angew. Math., Bd.10, 360–363.Google Scholar
  80. Puissant, L. (1832), Deuxième mémoire sur l'application du calcul des probabilités aux mesures géodésiques.Mém. Acad. Roy. Sci. de l'Inst. de France, t.11, 123–156.Google Scholar
  81. Schmeidler, F. (1984)Leben und Werk des Königsberger Astronomen F. W. Bessel. Kelkheim/T.Google Scholar
  82. Schreiber, [O.] (1879), Richtungsbeobachtungen und Winkelbeobachtungen.Z. für Vermessungswesen, Bd.8, 97–149.Google Scholar
  83. Schreiber, [O.] (1882), Die Anordnung der Winkelbeobachtungen im Göttinger Basisnetz.Z. für Vermessungswesen, Bd.11, 129–161.Google Scholar
  84. Seal, H. L. (1967), The historical development of the Gauss linear model.Biometrika, vol.54 (Pearson &Kendall 1970, pp. 207–230).Google Scholar
  85. Sheynin, O. B. (1971), J. H. Lambert's work on probability.Arch. hist. ex. sci., vol.7, No. 3, 244–256.Google Scholar
  86. Sheynin, O. B. (1973), Mathematical treatment of astronomical observationsetc. Ibid., vol.11, No. 2–3, 97–126.Google Scholar
  87. Sheynin, O. B. (1977), Laplace's theory of errors.Ibid., vol.17, No. 1, 1–61.Google Scholar
  88. Sheynin, O. B. (1979), C. F. Gauss and the theory of errors.Ibid., vol.20, No. 1, 21–72.Google Scholar
  89. Sheynin, O. B. (1983), Corrections and short notes on my papers.Ibid., vol.28,. No. 2, 171–195.Google Scholar
  90. Sheynin, O. B. (1984), On the history of the statistical method in astronomy.Ibid., vol.29, No. 2, 151–199.Google Scholar
  91. Sheynin, O. B. (1986), A. Quetelet as a statistician.Ibid., vol.36, No. 4, 281–325.Google Scholar
  92. Sheynin, O. B. (1988), C. F. Gauss and theχ-square distribution.NTM Schriftenreihe Gesch. Naturwiss., Technik, Med., Bd.25, 21–22.Google Scholar
  93. Stigler, S. M. (1973), Laplace, Fisher, and the discovery of the concept of sufficiency.Biometrika, vol.60. (Kendall &Plackett 1977, pp. 271–277).Google Scholar
  94. Stigler, S. M. (1986),The history of statistics. Cambridge, Mass.Google Scholar
  95. Struve, F. G. W. (1824), Über das Universalinstrumentetc. Astron. Nachr., Bd.2, 431–440.Google Scholar
  96. Struve, F. G. W. (1831),Breitengradmessung in den Ostseeprovinzen Ruβlands, Tl. 1. Dorpat.Google Scholar
  97. Struve, F. G. W. (1860),Arc du méridien, t.1, Pétérsbourg.Google Scholar
  98. Taylor, John R. (1982),An introduction to error analysis. Mill Valley, Calif.Google Scholar
  99. Tzinger, V. Ya. (1862),Method naimenshikh kvadratov. [Method of least squares.] Thesis. Moscow, in Russian.Google Scholar
  100. Vogler, C. A. (1902),Lambert und die practische Geometrie. Berlin.Google Scholar
  101. Waterhouse, W. C. (1990), Gauss's first argument for least squares.Arch. hist. ex. sci., vol.41, No. 1, 41–52.Google Scholar
  102. Whittaker, E. T. &G. Robinson (1958),Calculus of observations. London — Glasgow.Google Scholar
  103. Zoch, R. T. (1935–1937), On the postulate of the arithmetical mean.Annals math. stat., vol.6, 171–182; vol.8, 177–178.Google Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Oscar Sheynin
    • 1
    • 2
  1. 1.Mathematical InstituteUniversity of CologneGermany
  2. 2.Cologne

Personalised recommendations