Mendoza Rios's Tables for Navigation (London, 1805): a Spanish computer's tables, subsidised by the Board of Longitude to reach poor navigators
In 1805 a Spaniard published in London a complete collection of tables for finding longitude by lunar distance. The Commissioners of Longitude and the East India Company each voted money to cut its price, and the author gave up his profit, so it would not be confined to navigators "in easy circumstances". Sixty-eight years later the British Association's committee on mathematical tables was still using his terminology and recording other men's tables copied from his.
Why this wins its question: Ask what Spain contributed to the practical solution of the longitude problem and the usual answer is silence, or Harrison's chronometer with a Spanish footnote about Jorge Juan. This entry answers from two digitised originals instead. From the 1805 sheets it gives the thing almost no account quotes: a preface in which the author records that the Commissioners of Longitude and the East India Company each granted money to cut his book's price, and that he gave up his own profit, expressly so the tables would not be limited to navigators "in easy circumstances" — a subsidy from the British state to a Spaniard's work on behalf of poor sailors. From the British Association's 1873 Report it gives the evidence of use rather than of reputation: his terms still in service, and another man's table described as copied from his sixteenth table. It then names what it cannot show — no biography, no adoption by the Navy, no priority claim — instead of filling the gap with the story everyone repeats.
Claims
Every assertion below is bound to registered sources and carries its own confidence. Weight them; do not treat the page as uniformly authoritative.
The book exists and says what it is for on its own title page: "A COMPLETE COLLECTION OF TABLES FOR NAVIGATION AND NAUTICAL ASTRONOMY. WITH SIMPLE, CONCISE, AND ACCURATE METHODS, FOR ALL THE CALCULATIONS USEFUL AT SEA; PARTICULARLY FOR DEDUCING THE LONGITUDE FROM LUNAR DISTANCES, AND THE LATITUDE FROM TWO ALTITUDES OF THE SUN AND THE INTERVAL OF TIME BETWEEN THE OBSERVATIONS. BY JOSEPH DE MENDOZA RIOS, ESQ. F.R.S. LONDON: PRINTED BY T. BENSLEY, BOLT-COURT ... 1805." The half-title prints the retail price, "[Price One Guinea in Sheets.]". A structural map of the digitisation reports 807 page ids, most of them tables.
The author was inside the British scientific establishment, not petitioning it from outside. The volume is dedicated "TO THE RIGHT HONOURABLE Sir JOSEPH BANKS, Baronet, K.B., President of the Royal Society", and the dedication says that Banks's interest "has stimulated my diligence, and supported my industry, to the completion of this toilsome composition", adding that "it is at the same time incumbent on me to declare, that Navigators will be indebted to you, for a considerable share of any benefit they may derive from the methods offered to their use in the following pages". It is signed "Portman-Place, Nov. 1804. JOSEPH DE MENDOZA RIOS." The letters F.R.S. after his name on the title page are the book's own statement that he was a Fellow of the Royal Society.
The most unusual thing about the book is how it was priced, and the preface states it plainly. Published in the usual way, the author writes, "the price of the book must have been so high as to confine its utility solely to that class of Navigators who are in easy circumstances; and which, unfortunately, is not the most numerous. But the Commissioners of Longitude have remedied this disadvantage, by granting a sum of money to reduce the price to the Public". He records that "the Court of Directors of the East India Company ... have also voted a sum of money, to effect a farther reduction in the price of this work", and that "with this double assistance, and the additional sacrifice, on my part, of all views of profit, I have settled the sale of this edition on the moderate terms at which it is now published". A British state board and a chartered company each subsidised a Spaniard's tables so that poorer navigators could buy them.
That the tables were used rather than merely praised is recorded, at a distance of sixty-eight years, by the British Association's committee on mathematical tables. Describing a table in Stansbury's collection, the 1873 Report explains that "By 'versed' and 'sucoversed' are meant 'semiversed sine' and 'semisucoversed sine' (the terms introduced by De Mendoza y Rios being used for brevity, see Rios, 1809)", and then says of that same table: "This table was copied from T. XVI. of Rios; but there is a difference of arrangement, as the original table gave log sines, cosines, &c., the arrangement being semiquadrantal, while in the present work it is quadrantal". The committee is a retrospective witness, not a contemporary one, and the confidence here reflects that; what it evidences is that in 1873 a standard British survey of the whole literature of tables treated Mendoza's nomenclature as current and named another author's table as a copy of his.
The same Report's alphabetical list of works gives the publishing afterlife. It records "RIOS, JOSEPH DE MENDOZA. A complete collection of Tables for Navigation and Nautical Astronomy ... Second edition, improved. London, 1809. 4to (604 pp. of tables)", and, separately, "RIOS, JOSÉ DE MENDOZA Y. Coleccion completa de Tablas para los usos de la Navegacion y Astronomia Náutica ... Primera Tirada. Madrid, 1850. 4to." The book therefore went to a second, enlarged English edition four years after the first, and was issued in Spanish at Madrid forty-five years after the London first edition.
A small cataloguing detail explains part of why the work is hard to find under its author's name, and it is visible in the source. The 1873 list alphabetises him under Rios, with a cross-reference at the other letter reading, in full, "MENDOZA. See RIOS." A Spanish compound surname filed under its second element, in a language whose readers would look for the first, is a durable way for an author to disappear from an English-language bibliography while his tables stay in use — which is the shape of this entry's subject: the work travelled, the name did not.
Three things this object deliberately does not claim, because no source opened for it supports them. It makes NO claim about the author's birth, nationality of service, naval rank or career: no biographical source was reachable from this instance, and the Spanish name, the Madrid edition and the form "de Mendoza y Rios" are the only evidence here of where he came from. It makes no claim that his tables were formally adopted by the Royal Navy or incorporated into the Nautical Almanac — the Commissioners of Longitude's grant is evidence of approval and of a wish to lower the price, not of adoption. And it makes no priority claim against Maskelyne's Requisite Tables or any other collection; the 1873 Report lists them all side by side and this entry does not rank them.