Time to solve longitude: The lunar distance method

06 Oct 2014

If you don’t have an accurate clock to tell the time with, you can use a celestial one-like the moon.

We saw last week that the simplest solution to the problem of longitude was one of time difference. You can determine how far east or west you are of a given location if you know the difference between local time (determined by the sun) and time in that location. If you don’t have an accurate clock to tell the time with, you can use a celestial one-like the moon. That is the foundation of the lunar distance method. The moon is a bit like the hands on the clock, moving against the stars, which are the numbers on the dial. To make the lunar distance method work, two things are needed. The first is an instrument for making observations and marking angles. This emerged in the 1730s, around the same time Harrison began working on his first sea clocks. Both John Hadley in Britain and Thomas Godfrey in America were simultaneously working on an instrument to make observations of the heavens easier: the octant.   The octant was incredibly successful among mariners, and by the 1750s it was becoming the standard navigation instrument at sea. The second thing is accurate charts and tables of the position of the moon and the stars. However, the motion of the moon is very complicated, following a pattern that repeats  only once in every 18 years-even Isaac Newton hadn’t been able to figure this out. To employ this method, very precise observations of the movement of the moon relative to that of the stars were needed, over a prolonged period of time. In the 1750s, a German map maker called Tobias Mayer set to work on this problem, and he produced much improved Lunar Tables to help mariners find their longitude at sea. Tobias Mayer has been largely lost in the footnotes of history, despite there even being a museum dedicated to him. Leonhard Euler, once described Mayer as ‘undoubtedly the greatest astronomer in Europe’ and with good reason. It was Mayer’s work that made the lunar distance method possible. Mayer’s main interest was actually land mapping, for which the accurate determination of longitudes was crucial, and in the 1750s, while at the University of Göttingen, Mayer created new lunar and solar tables to improve this work. He also came up with a design for a repeating circle, an instrument for making accurate observations, but it was only after much encouragement that he sent his ideas to the Board of Longitude, since he doubted that the Board would reward a foreigner (that said, Britain and Hanover did share a king at the time). The Astronomer Royal, James Bradley, checked the tables, however, and found them to be very accurate, while sea trials showed that Mayer’s ideas could be used to find longitude at sea (and also led to the development of the sextant). Nevil Maskelyne became a lifelong advocate of the lunar distance method after using Mayer’s tables on his voyages to St Helena in 1761 and Barbados in 1763. As a result, the Board eventually awarded Mayer, or rather his widow, £3,000 in recognition of his work. A surprising footnote to this, according to his biographer, is that Mayer had never even seen the sea. However, even with Mayer’s tables, the lunar distance method was not without problems. Maskeleyne worked out that to use Mayer's tables require around 3 to 4 hours of calculations. Maskelyne's British mariner's guide was an explanation of how to use lunar distance at sea and was his first attempt to make life easier for the ordinary mariner. The astronomical data and computations upon which the abbreviated version of the lunar-distance method was based, still needed to be precise enough and widely available for years in advance to be of widespread use – which increasingly came to pass from about the 1760s onwards as Maskelyne published the Nautical Almanacs and associated Tables. However, weather could still pose a problem to observations, calculations still took some time to complete, and older mariners were sometimes reluctant to learn the skills necessary to use the lunar-distance method. In fact, astronomical navigation is still used today and all ships still have a sextant and a nautical almanac…as I found out on my most recent holiday, which you can read about here: Navigation Vacation