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Latitude by two altitudes of the Sun – Douwes’ and Riddle's methods

Published online by Cambridge University Press:  12 February 2024

Ana Filipa Queirós ,
António Costa Canas  and
Teresa Sousa Open the ORCID record for Teresa Sousa [Opens in a new window]
Ana Filipa Queirós
Affiliation:
Escola Naval, Base Naval de Lisboa – Alfeite, 2801-001 Almada, Portugal
António Costa Canas
Affiliation:
Escola Naval, Base Naval de Lisboa – Alfeite, 2801-001 Almada, Portugal CINAV, Escola Naval, Instituto Universitário Militar, Base Naval de Lisboa – Alfeite, 2810-001 Almada, Portugal CH-ULisboa, Universidade de Lisboa, 1600-214 Lisboa, Portugal
Teresa Sousa*
Affiliation:
Escola Naval, Base Naval de Lisboa – Alfeite, 2801-001 Almada, Portugal CINAV, Escola Naval, Instituto Universitário Militar, Base Naval de Lisboa – Alfeite, 2810-001 Almada, Portugal Center for Mathematics and Applications (NovaMath), FCT NOVA, 2829-516 Caparica, Portugal
*
*Corresponding author: Teresa Sousa; Email: teresa.maria.sousa@marinha.pt
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Abstract

In approximately 1740, Cornelis Douwes presented an algorithmic method to determine the latitude when it is impossible to observe the Sun at the meridian passage. To apply Douwes’ method, it is necessary to know two altitudes of the Sun, the time elapsed between observations, the Sun's declination at the time when the greater altitude was observed and the latitude by account. Douwes’ method, originally written in Dutch, was translated and published in English by Richard Harrison in 1759. This translation made possible the dissemination of this method throughout Europe. In 1821, James Ivory proposed a new method that was independent of the latitude by account. This method was improved by Edward Riddle in 1822. Riddle's proposal was widely disseminated throughout Europe during the 19th century. In this work, our objective is to study the reliability of these two methods. For that purpose, we will apply the algorithmic methods of Douwes and Riddle to determine the latitude using real observations made during the years 2021 and 2022. The results obtained will then be compared with the GPS (Global Positioning System) latitude to assess the reliability of each method.

Keywords

Cornelis DouwesEdward Riddlelatitude calculation methods
Type
Research Article
Information
The Journal of Navigation , First View , pp. 1 - 14
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Copyright
Copyright © The Author(s), 2024. Published by Cambridge University Press on behalf of The Royal Institute of Navigation

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References

Bowditch, N. (1837). The New American Practical Navigator. Being an Epitome of Navigation. New York: E. & G. W. Blunt.Google Scholar
Douwes, C. (1754). Verhandeling om buiten den Middag op Zee de waare Middags-Breedte te vinden, Haarlem.Google Scholar
Douwes, C. (1760). Zeemans-Tafelen en Voorbeelden. Amsterdam: Joannes van Keulen en Zoonen.Google Scholar
Estancel, V. (1658). Tiphys Lvsitano ov Regimento Navtico Novo, Évora.Google Scholar
Harrison, R. (1759). A New Set of Logarithmic Solar Tables.Google Scholar
Ivory, J. (1821). On the problem in Nautical Astronomy for finding the latitude by means of two observations of the Sun's altitude and the time elapsed between them. The Philosophical Magazine and Journal, LVIII, 81–90.CrossRefGoogle Scholar
Leitão, J. (1865). Guia Náutica ou Tratado Prático de Navegação. Lisboa: Sociedade Typographica Franco Portuguesa.Google Scholar
Norie, J. (1828). A New and Complete Epitome of Practical Navigation. 9th ed. London: J. W. Norie & Co.Google Scholar
Norie, J. (1835a). A New and Complete Epitome of Practical Navigation. 11th ed. London: Lords of Commissioners of the Admiralty.Google Scholar
Norie, J. (1835b). A Complete Epitome of Practical Navigation. 18th ed. London: Lords of Commissioners of the Admiralty.Google Scholar
Nunes, P. (1537). Tratado da Sphera Astronomici Introdvctorii de Spaera Epitome. Lisboa: Germão Galharde.Google Scholar
Nunes, P. (2002). Tratado da Sphera Astronomici Introdvctorii de Spaera Epitome. Lisboa: Fundação Calouste Gulbenkian.Google Scholar
(1855). Report of the council to the thirty-fifth annual general meeting of the society. Monthly Notices of the Royal Astronomical Society, 15(4), 101–144. https://doi.org/10.1093/mnras/15.4.101CrossRefGoogle Scholar
Riddle, E. (1822). Suggestions for simplifying Mr. Ivory's solution of double altitude problem. Philosophical Magazine and Journal, LX, 167–170.CrossRefGoogle Scholar
Robertson, J. (1772). The elements of navigation; containing the theory and practice. With the necessary tables. To which is added, A treatise of marine fortification. 3rd ed., Vol. 2, Printed by J. Nourse, London.Google Scholar
(2020). The Nautical Almanac for the Year 2021. Tauton: The UK Hydrographic Office.Google Scholar
(2021). The Nautical Almanac for the Year 2022. Tauton: The UK Hydrographic Office.Google Scholar