Joseph de Mendoza y Ríos and the Philosophy of Precision: Scientific Rationality, Instrumentation, and the Problem of Longitude

Calculating longitude as precisely as possible is important for navigation and requires resolving issues in relation to position and measurement while the ship is moving. The names of Euler, Bezout, Laplace, and other distinguished mathematicians are linked to studies on this problem. It can be said that in past times, these theoretical and practical problems were as important as they are today. Now cutting-edge technologies and computers are used. The determination of longitude (Throughout this paper, “latitude” and “longitude” referring to the ship’s position are understood as geographical coordinates. When discussing the position of celestial bodies, the corresponding celestial reference system (mainly ecliptic coordinates) is explicitly indicated.) by astronomical means is mathematically a seemingly simple problem of spherical trigonometry. However, its effective resolution required theoretical developments and the design of special instruments for observation and calculation. Within the group of mathematicians who were interested in these problems at the turn of the eighteenth to the nineteenth century, the figure of Joseph de Mendoza y Ríos stands out. This article is concerned with the achievements of this mathematician from Seville who contributed substantially to the solution of the problem of calculating longitude for which he received one of the great prizes awarded by the Board of Longitude in London. His contributions in this area were manifold and cover a broad spectrum of the problems of nautical astronomy. All these elements: design of instruments to capture astronomical information, development of an analytical method, formulation of an approximate calculation procedure, and preparation of auxiliary (supportive) calculation instruments allowing skipping stages in the transition from observation to position data. Mendoza y Ríos In this work, the authors explain the mathematical calculations of determining longitude by means of lunar distances that are due to Joseph de Mendoza y Ríos.