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

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.