Crafty navigators in the 15th and 16th centuries noted that as the moon circles the earth it changes its position at a constant rate relative to the sun and the stars. If the angle between the centre of the moon and a star or the centre of the sun could be measured, they reckoned they could calculate the time of the observation and then work out their longitude. They were right, but could not measure the angles involved accurately, and if they had been able to do so, they still lacked the data to do their sums.
Gathering this information was hard work. From 1689 to 1704 John Flamsteed, Britain's first Astronomer Royal, compiled tables for lunar distances. In 1756, Tobias
Mayer, keen to claim the British government's prize for finding longitude, sent his tables to the Board of Longitude. These were tested in 1761 on a voyage to St Helena. Longitude could always be found to within a degree but the report generously described the calculations for finding longitude by lunar distances as laborious.
There were a couple of problems preventing the adoption of lunar distances. Quadrants, the forerunners of today's sextants, only measure angles up to 90o. Lunar distances sometimes exceed this and in 1759 Captain John Campbell RN asked London instrument maker, John Bird, to make him a quadrant whose arc was one sixth of a circle (see Figure 17.1). So, the familiar sextant covering 120o of arc was born. Even so, the method did not gain popularity until the Nautical Almanac came out in 1767.
On his first Pacific voyage, James Cook sailed with a nautical almanac containing lunar distances. In his hands the results gave errors between 25-40'. This was as good as it got and Cook must have been delighted when Harrison finally produced his chronometer.
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