The Longitude rewards refer to the system of inducement prizes offered by the British government for a simple and practical method for the precise determination of a ship's longitude at sea. The rewards, established through an Act of Parliament (the Longitude Act) in 1714, were administered by the Board of Longitude.
This was by no means the first reward to be offered to solve this problem. Philip II of Spain offered one in 1567, Philip III in 1598 offered 6,000 ducats and a pension, whilst the States General of the Netherlands offered 10,000 florins shortly after. However, these large sums were never won, though several people were awarded smaller amounts for significant achievements.
The Longitude Problem
The measurement of longitude was a problem that came into sharp focus as people began making transoceanic voyages. Determining latitude was relatively easy in that it could be found from the altitude of the sun at noon with the aid of a table giving the sun's declination for the day. For longitude, early ocean navigators had to rely on dead reckoning, based on calculations of the vessel's heading and speed for a given time (much of which was based on intuition on the part of the master and/or navigator). This was inaccurate on long voyages out of sight of land, and these voyages sometimes ended in tragedy. An accurate determination of longitude was also necessary to determine the proper "magnetic declination", that is, the difference between indicated magnetic north and true north, which can differ by up to 10 degrees in the important trade latitudes of the Atlantic and Indian Oceans. Finding an adequate solution to determining longitude at sea was therefore of paramount importance.
For details on many of the other efforts towards determining the longitude, see History of longitude.
The need for better navigational accuracy for increasingly longer oceanic voyages had been an issue explored by many European nations for centuries before the passing of the Longitude Act in England in 1714. Monarchies in Portugal, Spain, and the Netherlands offered financial incentives for solutions to the problem of longitude as early as 1598. 
Addressing the problem of longitude fell, primarily, into three categories: terrestrial, celestial, and mechanical.  This included detailed atlases, lunar charts, and timekeeping mechanisms at sea. It is postulated by scholars that the economic gains and political power to be had in oceanic exploration, and not scientific and technological curiosity, is what resulted in the swift passing of the Longitude Act of 1714 and the largest and most famous reward, the Longitude Prize being offered. 
Establishing the Rewards
In the early 1700s, a series of very public and very tragic maritime disasters occurred, including the wrecking of a squadron of naval vessels on the Scilly Islands in 1707.  Around the same time, mathematician Thomas Axe decreed in his will that a £1,000 prize be awarded for promising research into finding “true longitude” and that annual sums be paid to scholars involved in making corrected world maps. 
In 1713, when the Whiston-Ditton longitude proposal was presented at the opening of the session of Parliament, a general understanding of the longitude problem prompted the formation of a parliamentary committee and the swift passing of the Longitude Act on July 8, 1714.  Within this act, is detailed three rewards based on levels of accuracy, which are the same accuracy requirements used for the Axe prize, set by Whiston and Ditton in their petition, and recommended by Sir Isaac Newton and Edmund Halley to the parliamentary committee. 
- £20,000 – highest reward offered for being able to determine a ship’s longitude within ½ degree, requiring sustained accuracy within two seconds in any twenty-four period maintained under the conditions of an ocean voyage
- £15,000 – second highest reward offered requiring accuracy within 2/3 degree
- £10,000 – lowest reward offered requiring accuracy within 1 degree, which is a span of 60 nautical miles
In addition, rewards were on offer for those who could produce a method that worked within 80 geographical miles of the coast (where ships would be in most danger), and for those with promising ideas who needed financial help to bring them to trial.
Proposed methods would be tested by sailing through the ocean, from Britain to any port in West Indies (about six weeks) without losing its longitude beyond the limits listed above. The parliamentary committee also established the Board of Longitude. This panel of adjudicators would review proposed solutions and were also given authority to grant up to £2,000 in advances for promising projects that did not entirely fulfill the terms of the prize levels, but that were still found worthy of encouragement.  The exact terms of the requirements for the prizes would later be contended by several recipients, including John Harrison. Ultimately, the £20,000 reward was not awarded to anyone, though John Harrison came closest with a series of payments totaling £23,065.  The Board of Longitude remained in existence for more than 100 years. When it was officially disbanded in 1828, an excess of £100,000 had been disbursed. 
The Longitude Act offered a very large incentive for solutions to the longitude problem. Some later recipients of rewards, such as Euler and Mayer, made clear publicly that that the money was not the incentive, but instead the important improvements to navigation and cartography. Other recipients, such as Kendall and Harrison had to appeal to the Board of Longitude and other governmental officials for adequate compensation for their work. Still others submitted radical and impractical theories, some of which can be seen in a collection at Harvard’s Houghton Library.  Schemes and ideas for improvements to instruments and astronomy, both practical and impractical, can be seen among the digitised archives of the Board of Longitude.
Though the Board of Longitude did not award £20,000 at one time, they did offer sums to various individuals in recognition of their work for improvements in instrumentation or in published atlases and star charts.
List of awardees by amount
- John Harrison - £23,065 awarded overall after many years of contention with the Board as discussed in detail in the next section.
- Thomas Mudge - £500 advance in 1777 for developing his marine timekeeper and a £3,000 award approved by a special committee in 1793 in recognition for his accomplishments. 
- Tobias Mayer - £3,000 awarded to his widow for lunar distance tables, which were published in The National Almanac in 1766 and used by James Cook in his voyages 
- Charles Mason - £1,317 awarded for various contributions and improvements on Mayer’s lunar tables. 
- Larcum Kendall - £800 total for his copy of and improvements and simplifications of Harrison’s sea watch (£500 for K1 – Kendall’s copy of Harrison’s H4, £200 for modified K2, and £100 for last modification model K3). 
- Jesse Ramsden - £615 awarded for his engine-divided sextant with the requirement that he share his methods and the design with other instrument makers. 
- Thomas Mudge - £500 advance in 1777 for developing his marine chronometer and a £3,000 award approved by a special committee in 1793 in recognition for his accomplishments. 
- John Arnold - £300 awarded in increments to improve his timekeeping design and experiments, though the accuracy required for the prize was never met. 
- Leonhard Euler - £300 awarded for contributions to the lunar distance method in aid of Mayer.
A full list of rewards made by the Commissioners and Board of Longitude was drawn up by Derek Howse, in an Appendix to his article on the finances of the Board of Longitude.
Only two women are know to have submitted proposals to the Longitude Commissioners, Elizabeth Johnson and Jane Squire. Incoming submissions can be found among the correspondence of the digitised papers of the Board of Longitude.
John Harrison’s contested reward
The winner of the most reward money under the Longitude Act is John Harrison for sea timekeepers, including his H4 sea watch. Harrison was 21 years old when the Longitude Act was passed. He spent the next 45 years perfecting the design of his timekeepers. He first received a reward from the Commissioners of Longitude in 1737 and did not receive his final payment until he was 80. 
Harrison was first awarded £250 in 1737, in order to improve on his promising H1 sea clock, leading to the construction of H2. £2,000 was rewarded over the span of 1741-1755 for continued construction and completion of H2 and H3.From 1760-1765, Harrison received £2,865 for various expenses related to the construction, ocean trials, and eventual award for the performance of his sea watch H.4.  Despite the performance of the H4 exceeding the accuracy requirement of the highest reward possible in the original Longitude Act, Harrison was rewarded £7,500 (that is, £10,000 minus payments he had received in 1762 and 1764) once he had revealed the method of making his device, and was told that he must show that his single machine could be replicated before the final £10,000 could be paid. 
Harrison made one rather than the requested two further copies of H4, and he and his family members eventually appealed to King George III after petitions for further rewards were not answered by the Board of Longitude.  A reward of £8,750 was granted by Parliament in 1773 for a total payment of £23,065 spanning thirty-six years. 
In popular culture
- Rupert T. Gould's 1923 "The Marine Chronometer" (ISBN 0907462057) is a thorough reference work on the Marine Chronometer. It covers the chronometer's history from the earliest attempts to measure longitude while including detailed discussions and illustrations of the various mechanisms and their inventors.
- Dava Sobel's 1996 bestseller Longitude (ISBN 0-14-025879-5) recounts Harrison's story. A film adaptation of Longitude was released by Granada Productions and A&E in 2000, starring Michael Gambon as Harrison and Jeremy Irons as Rupert Gould.
- The Island of the Day Before, by Umberto Eco
- Gulliver’s Travels, by Jonathan Swift
In the formation of popular societies
- National Association of Watch and Clock Collectors (NAWCC)
- The Longitude Symposium
- History of longitude
- Nevil Maskelyne
- Lunar distance
- John Harrison
- Larcum Kendall
- James Cook
- Longitude Prize 2014, modern prize for achievements in science, in the spirit of but not directly related to the longitude prize
- O'Connor, J J; Robertson, E F (1997). "Longitude and the Académie Royale". MacTutor History of Mathematics.
- Bell, A.E. (1950). The Life of Christian Huygens. Edward Arnold, London. p. 35.
- Latitude can also be determined in the Northern Hemisphere from the angle above the horizon of Polaris, the northern pole star. However, since Polaris is not precisely at the pole, it can only estimate the latitude unless the precise time is known or many measurements are made over time. While many measurements can be made on land, this makes it impractical for determining latitude at sea.
- Andrewes, William J.H. (1996). "Introduction". The Quest for Longitude: The Proceedings of the Longitude Symposium: 1-10.
- Knowles, Jeremy R (1996). "Opening Address at the Longitude Symposium". The Quest for Longitude: The Proceedings of the Longitude Symposium: 11-12.
- Stimson, Alan (1996). "The Longitude Problem: The Navigator's Story". The Quest for Longitude: The Proceedings of the Longitude Symposium: 71-84.
- Turner, A.J. (1996). "In the Wake of the Act, but Mainly Before". The Quest for Longitude: The Proceedings of the Longitude Symposium: 115-132.
- Sobel, Dana (1995). The Illustrated Longitude. New York: Walker and Company.
- Andrewes, William J.H. (1996). "Even Newton Could Be Wrong: The Story of Harrison’s First Three Sea Clocks". The Quest for Longitude: The Proceedings of the Longitude Symposium: 189-234.
- Howse, Derek. "Britain's Board of Longitude: The Finances" (PDF). Mariner's Mirror (1998). Retrieved 30 April 2015.
- Gingerich, Owen (1996). "Cranks and opportunists: "Nutty" solutions to the longitude problem". The Quest for Longitude: The Proceedings of the Longitude Symposium: 134-148.
- "Papers of the Board of Longitude". Cambridge Digital Library. Retrieved 30 April 2015.
- Betts, Jonathan (1996). "Arnold and Earnshaw: The Practicable Solution". The Quest for Longitude: The Proceedings of the Longitude Symposium: 311-330.
- Bruyns, W.F.J. Morzer (1996). "Navigation". The Quest for Longitude: The Proceedings of the Longitudinal Symposium.
- Sobel, Dava (1995). Longitude: The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time. New York: Walker and Company.
- Howse, Derek. "Britain’s Board of Longitude: The Finances, 1714-1828" (PDF). Mariner's Mirror (1998). Retrieved 30 April 2015.
- "Papers of the Board of Longitude". Cambridge Digital Library. Retrieved 30 April 2015.
- Quill, Humphrey (1966). John Harrison: The Man who found Longitude. London: John Baker Publishers.
- Dunn, Richard; Higgitt, Rebekah (2014). Finding longitude: how clocks and stars helped solve the longitude problem. Glasgow: Collins. ISBN 9780007525867.