1752 - Accurate Lunar Tables

Tobias Mayer, a German astronomer aged 29, publishes Tabulæ motuum Solis et Lunæ novæ et correctæ, that are tables of the relative position of the Moon, in the transactions of the Königliche Gesellschaft der Wissenschaften zu Göttingen.

These tables are so accurate – a few minutes of arc – as to finally enable application of the method of lunar distances to determine time with an uncertainty limited to a few minutes at worst. This paves the way to determining longitude at sea with precision. This is a tour de force achieved by an isolated scholar.

Moreover Mayer is an autodidact in mathematics, which may surprise as he was elected last year at the chair of economy and mathematics of the renowned university of Göttingen. He has become famous for his study of the Moon libration delivered in 1750.

¤ What is libration? It mainly but not solely stems from the tilt of lunar rotation axis to lunar orbital axis. It results in a fluctuation of the lunar hemisphere visible from the Earth. The moon overall shows six tenths of its surface over time if it shows only a half of it at once.

This is only an aspect of moon strangeness. It also displays irregularities in its motion, if we may name irregularities what we do not understand. It even raised doubts about the completion of Newton's law of gravitation. But Alexis Claude Clairaut, 39, has just found an approximate solution of the three-body problem which permits to reconcile lunar motion with Newton's theory up to the third order. He has published his Théorie de la Lune accordingly. Leonhard Euler, 45, in connection with Mayer, is working on the same issue.

¤ The Moon is not the only celestial body which seemed to violate Newton's law of gravitation. Mercury also displays 'irregularities' as the precession of its orbit. There is no explanation for the time being.

It seems that Mayer's decisive contribution to the precision of lunar tables stems from his invention of a new instrument, the reflecting circle, a parent to octant.

As for the determination of longitude through the lunar distance method, it was suggested by Johannes Werner (†1522) in the complement to his translation of Claudius Ptolemy’s Geography, that is In Hoc Opere Haec Continentur Nova Translatio Primi Libri Geographicae Cl Ptolomaei (1514), and developed by Peter Apian (†1552) in his Cosmographicus Liber (1524).

__________

LINKS WITH PREVIOUS CHRONICLES

1714 - The Longitude Act

1731 - Appearance of the Octant

__________

IN RETROSPECT FROM TODAY

NOTE A - About the tables.

Mayer will send revised and even more accurate tables – their precision rises to one minute of arc – to London in 1755, likely to the Board of Longitude. These tables will be used by Astronomer Nevil Maskelyne to promote, then demonstrate in 1761, calculation of time through an observation of lunar position. Mayer’s tables will be improved by Charles Mason (†1786) who was awarded £1317 by the Board of Longitude. We do not know the equation used by the Board to assess so precisely Mason's reward. The corrected tables will be published posthumously in 1787.

NOTE B - About their usage in the determination of longitude.

Werner and Apian were almost forgotten in 1752. Mayer therefore writes Tabularium Lunarium Usus in Investiganda Longitudine Maris (1753) to explain their usage to the scholars of Göttingen. It will be re-published in 1770 in London, still in latin.

NOTE C - About the reward for longitude accuracy improvement.

Mayer certainly expected to receive the £20,000 reward from the Board of Longitude, which would objectively have been fair after a trial. Alas he is to decease too early from typhus in 1762. Before dying, he pushes his widow to get to London where she is awarded £3,000. This is the widow's mite to the widow, if we may say so. The impact on navigation accuracy is crucial.

NOTE D - About practical usage of the lunar distance method.

Louis-Antoine de Bougainville, 40 years in 1769, will use it to work out time so longitude during his voyage around the world (1766-69). James Cook, one year older than Bougainville, will do the same in his first voyage around the world (1768-71) and will use both a marine chronometer as well as the lunar-distance method during the second and the third of his circumnavigations (1772-75 & 76-79).

Integration of the method in the Nautical Almanac by Maskelyne in 1767 and in the Connoissance des Temps by Lalande in 1774 will make calculation much easier. As a consequence the lunar- distance method comes out as well-proven and established amongst the seafarers from the 1770s.

NOTE E - On further improvements.

In the 1780s Jean-Charles de Borda, around 50 years old, will improve the reflecting circle and will also achieve a reduction of the lunar-distance method, quite important to develop precise navigation and the number of persons able to use it as the chronometer remains highly expensive up to the 1820-30s so only affordable to happy few navigators.

Astronomers Richard Dunthorne and Israel Lyons, Maskelyne's assistants, proposed their own improvements in the 1770s. It is worth noticing that Dunthorne had understood aspects of lunar irregularities as early as 1746, before Clairaut and Euler, likely at the same time as Mayer.

__________

SUGGESTED BIBLIOGRAPHY

Eva Germaine Rimington Taylor – The Haven-Finding Art, A History of Navigation from Odysseus to Captain Cook – London, 1958