Determining longitude was one of the most pressing scientific challenges of the late 18th century, mobilising efforts across nations to improve maritime navigation and ensure safer and more efficient voyages. In Portugal, the establishment of the Royal Maritime, Military, and Geographical Society (SRMMG) in 1798, under the leadership of D. Rodrigo de Sousa Coutinho, signalled an ambitious attempt to modernise nautical science and restore the nation's maritime prestige. Among the works presented to the SRMMG, a notable contribution came from José Monteiro da Rocha, then director of the Royal Astronomical Observatory of the University of Coimbra, with his ‘Taboada Náutica’ for the calculation of longitudes, introduced in 1799.
This communication examines the works on longitude presented to the SRMMG, focusing on Monteiro da Rocha’s contributions and the methods he proposed for longitude determination. It investigates the interplay between Portuguese scientific practices and other maritime powers, such as France and England, situating these efforts within the broader context of global longitude debates and advancements. By adopting a comparative framework, the study evaluates how Portuguese approaches aligned with or diverged from contemporaneous developments in other nations. Beyond highlighting the role of the SRMMG, this analysis provides fresh perspectives on the connections between science and power, illustrating their impact on territorial management and maritime dominance during the transition from the Long Enlightenment to the Age of Empires.

The interest of the novo-Hispanics in mathematics was divided between its teaching, the practices of measurement and astronomical observation and, particularly, the geographical location of both the latitude and longitude of Mexico City and California, among other points. Here I ask myself about the practices oriented to the geographic determination of two crucial points at that time, Mexico City and California. To this end, I will discuss the practices of repair, care and acquisition of astronomical measuring instruments and then focus on how they communicated their results among their contemporaries.

This was expressed in the exploration of the territory, with it, the analysis of mining exploitation and the issues that directly affected the “functioning” of the colony, such as the drainage of the Valley of Mexico. This exploration will allow us to contribute to the history of measurement and scientific instruments.

Determining the position of a ship at sea with ‘precision’ has been a challenge for mathematicians, astronomers, cosmographers and navigators. The controversies over the most accurate methods for determining longitude involved debates about the best instruments used, especially in the case of astronomical observations. Although the invention of the marine chronometer developed by John Harrison (1693-1776) in the mid-18th century gradually sparked innovation, its use was not widespread until the first decades of the 19th century. At this time, the debate about the best methods and instruments for determining the longitude of ships intensified among hydrographers, astronomers and pilots of various nationalities.
For this communication, we will highlight the proposals of the portuguese mathematician and lensman of the Royal Marine Academy Guards, José Maria Dantas Pereira, published in his memoir entitled “Memória sobre os instrumentos de reflexão”. The drawings - as well as the instruments - help to demonstrate the arguments used by mathematicians and designers. The use of the category ‘paper instruments’ gains relevance in this analysis as the descriptions and ways of using the artefacts are loaded with discussions that go beyond technical aspects and provide us with interesting elements to understand the debates.