Sextant: A Voyage Guided by the Stars and the Men Who Mapped the World’s Oceans. David Barrie

mathematicians and astronomers across Europe were also trying hard to develop a method of determining the time by the ‘lunar-distance method’. The theory underlying the use of ‘lunars’ was that the angular distance between the moon and the sun (planets and certain stars could also be used, with some loss of accuracy) changed so rapidly and predictably that it could be used like a celestial clock – a clock that told the same time anywhere in the world, though it was, of course, not always visible. But the complicated behaviour of the moon – powerfully influenced as it is by the gravity both of the sun and of the earth – made it much harder to predict its celestial coordinates with accuracy than those of the other heavenly bodies.

      Although Newton had dazzled the world with the laws of motion that allowed the paths of the sun and its planets to be predicted with hitherto unimaginable precision, the moon had defeated him. But though his lunar tables were not good enough for the purposes of determining longitude, Edmond Halley (1656–1742) recognized that the errors in them recurred regularly every eighteen years and eleven days – in accordance with a well-known cycle of eclipses. This discovery enabled him to develop a rule for correcting the tables, which was later improved by the French astronomer Pierre-Charles Le Monnier (1715–99). There were still imperfections, but in 1750 another Frenchman, Alexis Claude de Clairaut (1713–65), published a new theory of the moon’s motion in response to a competition launched by the St Petersburg Academy in Russia. Though the predictions that accompanied it were incomplete, this represented a major step forward. The great Swiss mathematician Leonhard Euler (1707–83), building on Clairaut’s work, published his own theory of lunar motion in 1753, and it was this that enabled a young, self-taught German astronomer called Tobias Mayer (1723–62) to achieve a major breakthrough.¹ The effort to find an astronomical solution to the longitude problem was thus a model of scientific internationalism.

      Appointed Professor of Mathematics at the University of Göttingen in 1751, Mayer closely analysed the available observational data and, with the help of Euler, prepared new tables of the moon’s motions that proved far more accurate than any previously available. His work first was already under discussion in England as early as 1754. In 1755 the Astronomer Royal, Dr James Bradley, reported to the Board on his examination of Mayer’s tables:

      In more than 230 comparisons which I have already made I did not find any difference so great as 1½' between the observed longitude of the Moon and that which I computed by the tables … it seems probable that, during this interval of time, the tables generally gave the Moon’s place true within one minute of a degree.

      A more general comparison may perhaps discover larger errors; but those which I have hitherto met with being so small, that even the biggest could occasion an error of but little more than half a degree of longitude, it may be hoped that the tables of the Moon’s motions are exact enough for the purpose of finding at sea the longitude of a ship, provided that the observations that are necessary to be made on shipboard can be taken with sufficient exactness.²

      With Mayer’s tables it seemed possible that a practical, astronomical method of determining the time accurately on board ship might at last be within reach. To make this lunar-distance method work successfully, however, a very accurate device for measuring angular distances was essential. The standard Hadley quadrant could measure angles only up to 90 degrees, and since the angular separation of the sun and moon often exceeded that amount a larger instrument would plainly be helpful. Mayer himself had proposed the use of a circular device – the ‘reflecting circle’ – but when Captain John Campbell of the Royal Navy was testing Mayer’s tables at sea in 1757 he found it inconvenient to use. Campbell then came up with the simple idea of enlarging Hadley’s quadrant, and so commissioned a leading instrument-maker, John Bird, to make the very first sextant.³