Mayer’s Lunar Tables Enable Mariners to Determine Longitude at Sea

Johann Mayer compiled and disseminated tables of astronomical distances, supplemented with mathematical formulas and instructions, to guide navigators to determine longitude at sea. These lunar tables helped sea travelers avoid dangerous areas, reduced the occurrence of shipwrecks and disappearances, and enhanced trade, exploration, and military expeditions.

Summary of Event

Eighteenth century sea travelers Navigation;and longitude[longitude] lacked an accurate method for measuring longitude while aboard vessels until Johann Tobias Mayer compiled astronomical information in the 1750’s that enabled navigators to compute east and west locations from the prime meridian. Prime meridian Prior to the mid-eighteenth century, sailors had used the length of time required to pass between two landmarks to report possible longitudes. Navigators often relied on instinct to supplement meager information. Sea conditions introduced such factors as wave turbulence, which rendered mariners’ calculations more complex than land-based longitudinal measurements. Without land references in the middle of oceans, crews simply had no reliable method to determine longitudes at sea. It was relatively simple, on the other hand, to determine latitude Latitude at sea by measuring the angle of the Sun at noon. If they were to report locations and hazards to other sea travelers, though, navigators needed precise determinations of both latitude and longitude. [kw]Mayer’s Lunar Tables Enable Mariners to Determine Longitude at Sea (1752-Mar., 1756)
[kw]Sea, Mayer’s Lunar Tables Enable Mariners to Determine Longitude at (1752-Mar., 1756)
[kw]Longitude at Sea, Mayer’s Lunar Tables Enable Mariners to Determine (1752-Mar., 1756)
[kw]Mariners to Determine Longitude at Sea, Mayer’s Lunar Tables Enable (1752-Mar., 1756)
[kw]Enable Mariners to Determine Longitude at Sea, Mayer’s Lunar Tables (1752-Mar., 1756)
[kw]Tables Enable Mariners to Determine Longitude at Sea, Mayer’s Lunar (1752-Mar., 1756)
[kw]Lunar Tables Enable Mariners to Determine Longitude at Sea, Mayer’s (1752-Mar., 1756)
Longitude at sea
Lunar tables
[g]Germany;1752-Mar., 1756: Mayer’s Lunar Tables Enable Mariners to Determine Longitude at Sea[1350]
[c]Science and technology;1752-Mar., 1756: Mayer’s Lunar Tables Enable Mariners to Determine Longitude at Sea[1350]
[c]Astronomy;1752-Mar., 1756: Mayer’s Lunar Tables Enable Mariners to Determine Longitude at Sea[1350]
[c]Transportation;1752-Mar., 1756: Mayer’s Lunar Tables Enable Mariners to Determine Longitude at Sea[1350]
Mayer, Johann Tobias
Euler, Leonhard
Maskelyne, Nevil
Bradley, James
Harrison, John

Renaissance scientists, including Galileo, made many suggestions that later proved relevant to Mayer’s work. Astronomical and temporal information were constants in longitude investigations. In 1514, Johann Werner hypothesized that one could determine longitudes based on distances between the Moon Moon (of Earth) and stars. By 1675, English king Charles II had established the Royal Observatory at Greenwich Royal Observatory, Greenwich, England and the position of astronomer royal. The astronomer royal was charged with cataloging astronomical information based on Greenwich time and the prime meridian, located at the observatory, in order to achieve better navigational techniques.

Shipwrecks motivated Spanish and Dutch rulers and the British parliament to offer incentives, including financial rewards, to anyone who could develop a reliable instrument or method to determine longitudes at sea. These governments wanted naval voyages and merchant trade to proceed safely, uninterrupted by the collisions or disappearances that could result from a lack of longitudinal information. On October 22, 1707, Rear Admiral Cloudsley Shovel Shovel, Cloudsley and his crews on four warships crashed Shipwrecks on the rocky coast of the Scilly Islands, near southwestern England. Confused by fog and lacking longitude details, they did not realize they were close to land.

The two thousand casualties caused by that crash became a catalyst for intensified efforts to find longitude. The British parliament approved the Longitude Act Longitude Act (1714) of 1714, specifying a £20,000 prize overseen by a Board of Longitude for the first practicable method of finding longitude that could be successfully tested on a voyage between Great Britain and the West Indies. The winning technique had to be consistently accurate in its determinations of longitude, within one-half degree, during the entire trip.

The British Admiralty preferred what astronomers called the lunar distance method, Lunar distance method (navigation) which combined astronomical data with time and nautical measurement factors to determine longitude. Mathematical prodigy Mayer decided to work on the longitude problem, even though he had no sea navigation experience, believing the lunar distance method had the greatest potential for success. He realized that navigators using the lunar distance method to figure longitudes needed correct star locations and reliable predictions of future lunar and solar movements during specified time periods. Mayer joined the Cosmographical Society, built a telescope to observe lunar motion and eclipses of the Earth and stars, and mapped the lunar surface, hypothesizing that the Moon lacked an atmosphere.

To collect precise measurements, Mayer designed a repeating circle, Repeating circle (astronomy) because he considered John Hadley’s reflecting quadrant, introduced in 1731, to be limited and inaccurate when measuring distances between stars and the Moon. Mayer’s circle could measure angles greater than 90°. Mayer skillfully made and evaluated his observations and documented astronomical information, including lunar, solar, and stellar locations and motions. He used this information to project the future positions of celestial bodies. He considered how the atmosphere and temperatures affected astronomical measurements. He began corresponding with Swiss mathematician Leonhard Euler and used Euler’s equations to complement his data. By 1752, the Royal Society of Göttingen Royal Society of Göttingen, Germany printed Mayer’s lunar tables in its Transactions. Already teaching mathematics at Georg August Academy in Göttingen, Mayer accepted directorship of the school’s observatory in 1754.

In 1755, Mayer submitted a revised copy of his lunar tables to English admiral Lord Anson, Anson, Lord first lord of the Admiralty, who gave them to the Board of Longitude in March, 1756. Astronomer royal James Bradley studied Mayer’s data and declared that it was consistent with the information he had compiled at the Greenwich Observatory. From 1757 to 1759, Captain John Campbell tested Mayer’s tables at sea, using Mayer’s repeating circle instead of a quadrant, but the Seven Years’ War hindered effective evaluation of Mayer’s data.

Nevil Maskelyne next tested Mayer’s tables during a 1761-1762 voyage to St. Helena and proclaimed Mayer’s tables accurate. Mayer continued making observations to enhance his lunar tables. Before he died, Mayer provided more precise tables for sea tests. Mayer’s widow submitted her husband’s refined tables to the Board of Longitude. Maskelyne tried them on his trips to the Barbados in 1763 and 1764. He published Mayer’s tables in the British Mariner’s Guide (1763), British Mariner’s Guide (Maskelyne) showing sailors how to apply the tables to measure longitude from ships.

In February, 1765, Maskelyne became the fifth astronomer royal, acquiring a seat on the Board of Longitude. He supported rewarding Mayer’s heirs for his lunar tables. Several British East India Company captains told the board about their successes with Mayer’s tables but commented that longitude equations were difficult to calculate. Maskelyne suggested the board approve publishing an annual almanac with Mayer’s final tables and simplified trigonometric information to ease computation. A parliamentary act granted money for the Nautical Almanac. Nautical Almanac Praising Mayer’s lunar tables, the board awarded Mayer’s widow £3,000 and Euler £300. Maskelyne edited Mayer’s Tabulae motuum solis et lunae novae et correctae
Tabulae motuum solis et lunae novae et correctae (Mayer) (1770; new and correct table of the motion of the Sun and the Moon). The commissioners of longitude issued a revised edition the next decade. Mayer’s memoirs and star catalog also appeared posthumously.


Mayer’s astronomical measurements and lunar tables contributed to the development of dependable techniques for navigators to identify their longitude at sea. Determining one’s position at sea made it possible reliably to travel to specific ports, meet other vessels, avoid known hazards, and track and confront enemy fleets. By refining information about lunar movement and positions, Mayer sped the transition from an era of navigation by instinct and educated guesses to one of navigation based on precise and reliable astronomical computations. Indeed, Mayer’s tables were precise to within a half degree, because he had carefully analyzed and honed his observations of the Moon, Sun, and stars. In addition to adopting his tables, many navigators considered Mayer’s repeating circle useful. Instrument makers produced and sold the circle, improving upon its initial materials and design.

At the same time that Mayer compiled his lunar tables, carpenter and clockmaker John Harrison aspired to solve the longitude problem. He devised several chronometers, Chronometers which passed trials, but the Board of Longitude hesitated to award Harrison its prize because he was not an astronomer. The Longitude Act of 1765 included restrictions aimed against Harrison, but he persisted. Explorer James Cook Cook, James consulted chronometers to figure longitudes during his 1769 New Zealand journey. He considered Harrison’s timing device convenient to use, especially when weather interfered with lunar methods. By 1773, King George III had convinced Parliament to designate Harrison their longitude prize’s winner.

In the late eighteenth century, chronometers became commercially available. Merchants mostly used the expensive devices, while many sailors continued to rely on lunar distance methods until they could afford chronometers. Navies initially retained lunar techniques for military purposes. Able to calculate accurate longitudes consistently, sailors navigated with more confidence. Because chronometer use became widespread, the Longitude Act of 1828 repealed the Board of Longitude. Inspired by eighteenth century precedents, modern navigators look skyward to satellite technology tracking exact longitudes as they travel by water, land, and air.

Further Reading

  • Andrewes, William J. H., ed. The Quest for Longitude. Cambridge, Mass.: Collection of Historical Scientific Instruments, Harvard University, 1996. Proceedings of a November 1993 longitude symposium held at Harvard University that comprehensively explored the history of longitude research and navigation strategies. Includes an illustration of Mayer’s portrait.
  • Forbes, Eric G. The Birth of Scientific Navigation: The Solving in the Eighteenth Century of the Problem of Finding Longitude at Sea. London: National Maritime Museum, 1974. The editor of volumes of Mayer’s writings and correspondence with Euler tells how Mayer influenced navigation and interacted with his peers, the Board of Longitude, and the British Admiralty.
  • Howse, Derek. Greenwich Time and the Longitude. London: Philip Wilson, 1997. Describes how humans have determined longitude since ancient times, emphasizing eighteenth century developments, including Mayer’s innovative tables to improve navigation. Illustrations, maps, bibliography.
  • ________. Nevil Maskelyne: The Seaman’s Astronomer. Foreword by Sir Francis Graham-Smith. New York: Cambridge University Press, 1989. Examines Mayer’s and Maskelyne’s professional relationship as they sought to achieve accurate longitude measurement methods. Glossary, appendices, illustrations.
  • Sobel, Dava. Longitude: The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time. New York: Walker, 1995. Focuses on John Harrison’s efforts but also discusses Mayer’s lunar tables and the attempts of others to win Parliament’s prize.
  • Williams, J. E. D. From Sails to Satellites: The Origin and Development of Navigational Science. New York: Oxford University Press, 1992. Places Mayer’s development of his repeating circle and lunar tables in context with tools and methods used by navigators prior to and after the eighteenth century.

Astronomy Wars in England

Halley Predicts the Return of a Comet

Quest for Longitude

Flamsteed’s Star Catalog Marks the Transition to Modern Astronomy

Bradley Discovers the Nutation of Earth’s Axis

Euler Develops the Concept of Function

Büsching Publishes A New System of Geography

Seven Years’ War

Herschel Begins Building His Reflecting Telescope

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