The Nautical Almanac and the lunar-distance method in the mariner's hands
An annual volume of precomputed lunar distances, issued by the British Board of Longitude from 1767 onward, leaving the seaman on board only the sextant observation and a short correction. The lunar distance was taken with the sextant, but then the arithmetic began: the angle had to be cleared of refraction and parallax and compared with the tabulated place of the Moon, and that meant hours of computing on a rocking table.
The English Astronomer Royal Nevil Maskelyne turned the task around: the computing should be done in advance and ashore. The first issue, compiled for the year 1767, gave precomputed distances of the Moon from the Sun and from selected stars for every three hours of Greenwich time.
The idea of precomputed tables came from France: the astronomer Nicolas Louis de Lacaille had placed such tables in the Connaissance des Temps for 1761. The British almanac was paid for and published by the Board of Longitude; it was computed by a scattered workforce of hired calculators that included women. From this point the lunar method stopped being a possibility on paper and became ordinary shipboard practice, running alongside the chronometer for a long time.
Why this date
exact: the first issue was compiled for the year 1767 and printed in London in 1766. The axis value is 1767, the year the almanac was compiled for, because that is the year from which it works at sea. The imprint of the first issue is given from a bibliographical reference and was not checked against the title page itself.
What it grew from
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The Longitude Act of 1714 and the Board of Longitude
prerequisite for · Confidence: high
The Nautical Almanac was not a private publication: it was paid for and published by the Board of Longitude, under the supervision of the astronomer royal, Maskelyne. Without a state body willing to pay year after year for the computing work, annual precomputed tables do not exist.
Dispute: The hard dependence applies to this particular publication, not to the idea of precomputation. The same passage in Higgitt shows that the Frenchman Lacaille printed precomputed tables in the Connaissance des Temps for 1761 with no British Board at all, and that the British almanac was 'inspired' by them. So without the Board of Longitude there would have been no Nautical Almanac as such, but precomputed lunar distances already existed in Europe.
Link sources
- Rebekah Higgitt, «Longitude», Encyclopedia of the History of Science, vol. 4, issue 1 (April 2021) (2021) Verified 20 Sep 2026
These were published in official ephemerides, Connaissances des Temps in 1761 and inspired the British Nautical Almanac, paid for and published by the Board of Longitude from 1767 under the supervision of the astronomer royal, Nevil Maskelyne.
- Seb Falk, «Ships, Clocks & Stars: The Quest for Longitude», Science Museum Group Journal, Autumn 2014 (2014) Verified 5 Oct 2026
But from then on they met with increasing regularity and bureaucratisation, initially to discuss possible solutions and later, after Harrison's designs were successfully copied and economised and after astronomical work had brought about the Nautical Almanac that greatly simplified the computation of lunar distances, to support methodological refinements and improvements in the production and maintenance of instruments.
"Verified" means that on that day the quotation was found at the address given, word for word. No date means we have not been able to open the source yet, not that the quotation is wrong.
- Rebekah Higgitt, «Longitude», Encyclopedia of the History of Science, vol. 4, issue 1 (April 2021) (2021) Verified 20 Sep 2026
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The double-reflecting octant
prerequisite for · Confidence: high
A lunar distance is the angle between the Moon and a star, which has to be taken from a rocking deck to within minutes of arc. Hadley's double reflection yields exactly such a measurement, and Campbell's sextant, grown out of the octant with its arc of 120 degrees, was made to the requirements of this method. Tables are useless without an instrument able to deliver an observed angle of the needed accuracy.
Dispute: The historians put it more mildly than a hard dependence requires: Falk says 'particularly useful', Higgitt 'greatly facilitated'. None of those quoted asserts strict physical impossibility outright, and the link is called a hard one on the substance of the accuracy requirement rather than on the letter of the quotations. What argues for it is the chronology: the lunar-distance method itself was described in print by Werner in 1514, more than two centuries before the octant, and through all that time it did not work at sea.
Link sources
- Seb Falk, «Ships, Clocks & Stars: The Quest for Longitude», Science Museum Group Journal, Autumn 2014 (2014) Verified 20 Sep 2026
Hadley's octant and the sextants that later incorporated Hadley's innovations were particularly useful for the precise measurements required in the lunar-distance method, and in any case it is hardly surprising that the NMM curators chose to place them on the right hand side of the gallery, where they help Mayer's maps and Maskelyne's tables to stand a chance of attracting attention away from Harrison's shiny clocks.
- Rebekah Higgitt, «Longitude», Encyclopedia of the History of Science, vol. 4, issue 1 (April 2021) (2021) Verified 20 Sep 2026
Timekeepers were tested alongside the lunar-distance method, supported by predictive tables and newly developed double-reflection observing instruments – octants, sextants and circles – that greatly facilitated ship-board observations by using mirrors to align objects and produce a reading of their angular distance.
- Steven Wepster, «Precomputed lunar distances», (Universiteit Utrecht) Verified 20 Sep 2026
his measuring device was brushed aside in favour of the sextant, which is a development of Hadley's octant, conceived by Capt. Campbell, meeting the requirements of high accuracy and large angles set by the lunar distance method.
"Verified" means that on that day the quotation was found at the address given, word for word. No date means we have not been able to open the source yet, not that the quotation is wrong.
- Seb Falk, «Ships, Clocks & Stars: The Quest for Longitude», Science Museum Group Journal, Autumn 2014 (2014) Verified 20 Sep 2026
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The lunar tables of Tobias Mayer
prerequisite for · Confidence: high
The almanac is numbers recast into a form the mariner can use, and those numbers were Mayer's: every lunar position in the first ten issues, for the years 1767 to 1776, was computed from Mayer's tables of 1762.
Dispute: The fact itself is not in dispute, but the division of labour deserves to be stated exactly: Mayer supplied the numbers, while what made the method usable at sea was not the quality of the tables but the removal of the computing to the shore. Wepster states plainly that the Board found Mayer's method itself impractical because of the amount of calculation, so the almanac is not a continuation of the tables but a different move made on their basis.
Link sources
- Steven Wepster, «Precomputed lunar distances», (Universiteit Utrecht) Verified 20 Sep 2026
In the first ten almanacs, for the years 1767-1776, all lunar positions were computed from Mayer's 1762 tables.
- Steven Wepster, «Precomputed lunar distances», (Universiteit Utrecht) Verified 20 Sep 2026
And Mayer's method was not practical because it entailed too much work, in the form of many hours of calculations.
- «Tobias Mayer», MacTutor History of Mathematics Archive, University of St Andrews Verified 20 Sep 2026
The Tables of the Moon had been brought by the late Professor Mayer of Göttingen to a sufficient exactness to determine the Longitude at Sea to within a Degree, as appeared by the Trials of several Persons who made use of them.
- Rebekah Higgitt, «Longitude», Encyclopedia of the History of Science, vol. 4, issue 1 (April 2021) (2021) Verified 20 Sep 2026
One went to the widow of Tobias Mayer, whose application of Leonhard Euler's mathematical techniques to lunar observations had allowed him to produce greatly improved lunar tables.
"Verified" means that on that day the quotation was found at the address given, word for word. No date means we have not been able to open the source yet, not that the quotation is wrong.
- Steven Wepster, «Precomputed lunar distances», (Universiteit Utrecht) Verified 20 Sep 2026
What grew out of it
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Babbage's Analytical Engine: a design that stayed on paper
influenced · Confidence: medium
Errors in printed tables, above all those from which the Nautical Almanac was computed, were the practical stimulus for Babbage's calculating engines: the Difference Engine was conceived in 1820–1821 while preparing ancillary tables for the Almanac at the Astronomical Society, and the Analytical Engine of 1834 grew out of the same project.
Dispute: The stimulus from tables led to the Difference Engine, whereas this link concerns the Analytical Engine: according to Grier, Babbage conceived it in 1834 as a more general machine while the Difference Engine was still unfinished. The Computer History Museum stresses that tabular errors were not his only motive: he also saw his engines as a new technology of mathematics.
Link sources
- Grier D. A. «Babbage, Charles», Complete Dictionary of Scientific Biography (New DSB, via Encyclopedia.com) (2008) Verified 20 Sep 2026
In 1820 he became a founding member of the Astronomical Society, a group of businessmen who were interested in revising the Royal Nautical Almanac, the annual volume that was used by navigators and surveyors.
- Grier D. A. «Babbage, Charles», Complete Dictionary of Scientific Biography (New DSB, via Encyclopedia.com) (2008) Verified 20 Sep 2026
In preparing some ancillary tables for the Almanac, Babbage conceived of a machine that might assist with the calculation.
- [Lardner D.] «Babbage's Calculating Engine», Edinburgh Review 59, no. 120 (1834) Verified 20 Sep 2026
If proof were wanted to establish incontrovertibly the utter impracticability of precluding numerical errors in works of this nature, we should find it in this succession of error upon error, produced, in spite of the universally acknowledged accuracy and assiduity of the persons at present employed in the construction and management of the Nautical Almanac. It is only by the mechanical fabrication of tables that such errors can be rendered impossible.
- Computer History Museum, «The Babbage Engine: Overview» Verified 20 Sep 2026
His work on the engines led him from mechanized arithmetic to the entirely new realm of automatic computation. Tabular errors provided a practical stimulus. But this was not his only motive. He also saw his engines as a new technology of mathematics.
"Verified" means that on that day the quotation was found at the address given, word for word. No date means we have not been able to open the source yet, not that the quotation is wrong.
- Grier D. A. «Babbage, Charles», Complete Dictionary of Scientific Biography (New DSB, via Encyclopedia.com) (2008) Verified 20 Sep 2026
Other links
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The longitude problem and the marine chronometer (John Harrison's H4)
parallel to · Confidence: high
Two independent solutions to one problem, brought to completion in the same years and by the same institution. The chronometer carries prime-meridian time with it, the lunar method reads that time off the sky, and the Board of Longitude judged both to be workable.
Dispute: Historians disagree not about whether there were two solutions but about what to call their relationship. Higgitt writes: 'Some histories suggest the story of longitude is one of competition between astronomical and timekeeper methods', and immediately: 'Newer scholarship has instead emphasized complementarity', adding that 'Ultimately, where precision was needed or if there was any uncertainly, timekeepers and astronomical methods were used together', because a timekeeper required observations of local time and lunar observations required a watch. So parallel here is to be read as 'two independent lines solving one problem', not as 'rivals of which one survived'. The edge should not reproduce the popular scheme of Harrison against the astronomers: Higgitt states plainly that 'No one method or individual definitively "solved" the problem of longitude'.
Link sources
- Seb Falk, «Ships, Clocks & Stars: The Quest for Longitude», Science Museum Group Journal, Autumn 2014 (2014) Verified 20 Sep 2026
The exhibition presents each of these methods alongside their original proponents, explaining them succinctly before narrowing them down to the two eventual front runners: the timekeepers and the lunar-distance method.
- Seb Falk, «Ships, Clocks & Stars: The Quest for Longitude», Science Museum Group Journal, Autumn 2014 (2014) Verified 20 Sep 2026
Of course, even once the Board had agreed that both the chronometric and lunar-distance methods had been proved workable, the considerable task of development still lay ahead.
- Rebekah Higgitt, «Longitude», Encyclopedia of the History of Science, vol. 4, issue 1 (April 2021) (2021) Verified 20 Sep 2026
In the 18th century, both the lunar-distance and timekeeper methods were rewarded, promoted and developed.
"Verified" means that on that day the quotation was found at the address given, word for word. No date means we have not been able to open the source yet, not that the quotation is wrong.
- Seb Falk, «Ships, Clocks & Stars: The Quest for Longitude», Science Museum Group Journal, Autumn 2014 (2014) Verified 20 Sep 2026
The sentence about lunar distances in the inaugural issue comes from the Wikipedia article. A verbatim quotation is needed from the work it cites: «Explanatory Supplement to the Astronomical Ephemeris», 1961, section 7D.
Node sources
- Wikipedia, «The Nautical Almanac» Verified 5 Oct 2026
The main distinctive feature of the inaugural issue for 1767 was the tabulation of lunar distances as a tool to facilitate the determination of longitude at sea from observations of the Moon.
- Steven Wepster, «Precomputed lunar distances», (Universiteit Utrecht) Verified 5 Oct 2026
His plan was to take as much as possible of the dreadful calculations ashore, away from the mariner.
- Steven Wepster, «Precomputed lunar distances», (Universiteit Utrecht) Verified 5 Oct 2026
Maskelyne's plan materialised in the publication of the Nautical Almanac, containing (among other data) pre-computed lunar distances for three-hourly intervals.
- Rebekah Higgitt, «Longitude», Encyclopedia of the History of Science, vol. 4, issue 1 (April 2021) (2021) Verified 5 Oct 2026
It was a French astronomer, Nicolas Louis de Lacaille, who first produced pre-computed tables and a method to facilitate the lunar-distance method. These were published in official ephemerides, Connaissances des Temps in 1761 and inspired the British Nautical Almanac, paid for and published by the Board of Longitude from 1767 under the supervision of the astronomer royal, Nevil Maskelyne.
- Seb Falk, «Ships, Clocks & Stars: The Quest for Longitude», Science Museum Group Journal, Autumn 2014 (2014) Verified 5 Oct 2026
On the astronomical side, the exhibition explores the work of the cottage industry that evolved to produce the Nautical Almanac, with teams of observers and human computers notably including some women.
- Seb Falk, «Ships, Clocks & Stars: The Quest for Longitude», Science Museum Group Journal, Autumn 2014 (2014) Verified 5 Oct 2026
after astronomical work had brought about the Nautical Almanac that greatly simplified the computation of lunar distances
"Verified" means that on that day the quotation was found at the address given, word for word. No date means we have not been able to open the source yet, not that the quotation is wrong.
Further reading
Not evidence: these carry no quotation and support nothing we wrote. They are books and scans to read next.
- «The Nautical Almanac and Astronomical Ephemeris, for the Year 1767», London: J. Nourse & Mess. Mount and Page, 1766 (1766)