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Direct Methods of Sight Reduction: An Historical Review

Published online by Cambridge University Press:  23 November 2009

Extract

In general terms the principal problem in astronomical navigation is the solving of a spherical triangle - the PZX-triangle. The fundamental formula of spherical trigonometry for finding an angle given the three sides of a spherical triangle is the cosine formula. By transposition this formula can be used for finding a side given the opposite angle and the other two sides. Because the cosine formula is not suitable for use with logarithms numerous formulae have been derived from it with the aim of simplifying logarithmic computation. The term ‘direct method’ applies to a method the basis of which is generally the cosine formula or any of its derivatives although some direct methods are based on Napier's Rules for right-angled spherical triangles.

Type
Research Article
Copyright
Copyright © The Royal Institute of Navigation 1982

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References

1 Sadler, D. H. (1948). Tables for the Reduction of Astronomical Sights. This Journal, 1, 298Google Scholar.

2 Sumner, T. H. (1843). A New and Accurate Method for Finding the Bearing of the Land. … BostonGoogle Scholar.

3 Marcq Saint-Hilaire, A. (1875). Calcul du point observé Revue Maritime et Coloniale, 31, 341, 714.Google Scholar

4 Maskelyne, N. (1767). Tables Requisite to be used with the Nautical Ephemerisjor Finding Latitude and Longitude at Sea. Published by Order of the Commissioners of Longitude. [Second Edition, 1781; Third and Last Edition, 1802]Google Scholar

5 Norie, J. W. published his A New and Complete Epitome of Practical Navigation….to which is added a New and Correct Set of Tables in 1802Google Scholar. The work was dedicated to ‘The Honourable The Court of Directors of the United Company of Merchants of England trading in the East Indies’. In the 4th edition (published in 18 14) Norie claimed that his Nautical Tables ‘have been very generally adopted by the Officers of the Navy and in the Honourable East India Company's Service, and have received the approbation of navigators in general’.

6 Borda, J. C. de (1787). Description et Usage du Cercle de Reflexion. ParisGoogle Scholar.

7 Inman, James (17761859) was Professor of the Royal Naval College at Portsmouth. The first edition of his Navigation and Nautical Astronomy for the Use of British SeamenGoogle Scholar was published in 1821. In 1829 he published his Nautical Tables designed for the Use of British Seamen. Successive editions of the tables appeared right down to 1940.

8 Thomson, D. (1823). Lunar and Horary Tables. Edinburgh.Google Scholar

6 Raper, H. (1840). The Practice of Navigation and Nautical Astronomy. LondonGoogle Scholar. This work earned for its author a Gold Medal of the Royal Geographical Society. Lieut. Henry Raper (1799–1859) retired from active service in 1825, from which time he devoted himself to nautical science. He served repeatedly on the councils of the Royal Geographical and Royal Astronomical Societies, and for many years was Secretary of the Royal Astronomical Society.

10 See Cotter, C. H. (1973). Henry Raper's Spherical Traverse Table. This Journal, 26, 240.Google Scholar

11 Ibid. p. 242.

12 Mackay, A. (1793). The Theory and Practice of Finding the Longitude… in two volumes. LondonGoogle Scholar.

13 Goodwin, H. B. (1899). The simplification of formulae in Nautical Astronomy. Nautical Magazine, Glasgow, 83.Google Scholar

14 Goodwin, H. B. (1910). The Haversine in Nautical Astronomy. Nautical Magazine Glasgow, 83,Google Scholar

15 Davis, P. L. H. (1910). Requisite Tables. London.Google Scholar

16 Grambow, J. B. (1940). Historical note on the latest improvements in navigation. Hydrographic Review, Monaco, 17.Google Scholar

17 Douwes, C. (1747). Verhandling om buiten den Middag op zee de waare middags Breedte te vinden. Haarlem.Google Scholar

18 Peaux, R. (1912). Zeevaartkundige Tafelen. Rotterdam.Google Scholar

19 de Matta, J. N. (1906). Taboa Polytelica. Lisbon.Google Scholar

20 See Cotter, C. H. (1973) Martelli's Tables. This Journal, 26, 485Google Scholar.

21 Johnson, A. C. (1875). On Finding Latitude and Longitude in Cloudy Weather. LondonGoogle Scholar.

22 Guyou, E. (1884). Tables de poches, donnant lc point Observe et les Droites de Hauteur. ParisGoogle Scholar.

23 Guyou, E. (1888). Calcul du point Observé à l'aide de la Table des Latitudes croissantes. Annale Hydrographique. Paris.Google Scholar

24 See Cotter, C. H. (1976). Nautical Astronomy and the Mercator principle. This Journal, 29, 14.Google Scholar

25 Rust, A. (1918). Practical Tables for Navigators and Aviators. Philadelphia.Google Scholar

26 Goodwin, H. B. (1921). The Alpha, Beta, Gamma Navigation Tables. London.Google Scholar

27 Soule, C. C. and Dreisonstok, J. Y. (1932). Manuscript Tables for Altitude and Azimuth. Annapolis.Google Scholar

28 Weems, P. V. H. (1944). The Secant Time Sight. Annapolis.Google Scholar

29 See Cotter, C. H. (1973). Aquino's Short-Method Tables. This Journal, 26, 152.Google Scholar

30 Aquino, R. de (1912).Google Scholar‘The New Altitude Tables.’ Given in The ‘Newest’ Navigation Altitude and Azimuth Tables. 2nd Edition. LondonGoogle Scholar and Rio de Janeiro.

31 Aquino, R. de (1937). An All Log Tangent · Log Secant Navigation Table. US Naval Institute Proceedings. May 1937. Annapolis.Google Scholar

32 Purey-Cust, H. E. (1928). Sumner's Method. London.Google Scholar

33 Aquino, R. de (1933). A NavegaÇao Hodierna com Logaritmos de 1633. Rcvista Maritima Brasileira. Oct.-Nov. 1933. Rio de JaneiroGoogle Scholar

34 Sadler, D.H. (1972). Gaussian logarithms and navigation. This Journal, 25, 252.Google Scholar

35 Braga, R. R. (1924). Taboas de Alturas paro o Calculo da Recta Marcq-St-Hilaire. Paris.Google Scholar

36 Soeken, B. (1914). Höohentafeln. Hamburg.Google Scholar

37 Teege, H. (1919). Vierstcllige logarithmische Tafel zur Berechnung dcr Hohc eines Gestirns. BerlinGoogle Scholar.

38 Canić, C. (1923). Tavole Nautichc. Catlaro.Google Scholar

39 It is hoped that a note on these methods, under the title ‘Delambre's Analogies and Kindred Solutions for Altitude or Zenith Distance‘ will be published shortly.

40 Yonemura's tables were included in Ogura, S. (1920). New Altitude and Azimuth Tables. Tokyo.Google Scholar

41 Hugon, P. (1947). Nouvelles tables pour le calcul de la droite de hauteur à partir du pointe estime. ParisGoogle Scholar.

42 Comrie, L. J. See, for example, the ‘Preface and Explanation’ in Chambers' Shorter Six-Figure Mathematical Tables (London, 1961)Google Scholar; also ‘Preface and Explanation’ in Hughes' Tables for Sea and Air Navigation (London, 1938)Google Scholar.

43 The address was published in 1962. Burton, S. M. (1962). The gestation and birth of my nautical tables. This Journal, 15, 460.Google Scholar

44 Captain H. S. Blackburne, a teacher of navigation in London, and later Principal Examiner of Masters and Mates for the Government of New Zealand, was the author of several works on nautical astronomy, including inspection tables first published in 1914.