The South African
Military History Society

Die Suid-Afrikaanse Krygshistoriese Vereniging

The Longitude Problem

By Gil Jacobs

Position on the surface of the Earth can be specified using a two-dimensional co-ordinate system. The co-ordinates are longitude and latitude and they are sufficient to specify a position uniquely.

In the eighteenth century navigators already knew how to determine latitude, but could only guess at their longitude using "dead reckoning", and the further they travelled, the less useful a dead reckoning position became.

A navigator needs to know two things to determine longitude:-

The local time could be obtained from noon observations of the Sun with a sextant. The instant when the Sun is at its highest altitude above the horizon is the time of local noon.

The problem was simple to state - how can one know the time at Greenwich when one is many thousands of miles away after a period of several months?

The problem of finding the longitude was taken very seriously, so seriously that in 1714 the English parliament offered a very substantial reward for finding a solution to this problem.
The reward was:-

(20,000 was a fortune in the early eighteenth century!)

The body of persons who would decide who the winner became known as "The Board of Longitude".

An accurate and reliable clock would solve the problem. Unfortunately, such clocks did not exist at the time. Clocks were lubricated with vegetable oil which soon became rancid. The clock then had to be stopped and cleaned. Pendulum clocks would not keep good time at sea because of the ship's motion.

Sir Isaac Newton did not believe that it would be possible to develop a clock which could keep time accurately enough on a ship at sea.

As the Moon moves in its orbit around the Earth it is seen to move against the background of the stars. Why not use the Moon as a clock? This was the solution proposed by the astronomers.

In order to use this method it would be necessary to predict the Moon's position accurately - to within one arcsecond. [Note:- One arcminute is a sixtieth of a degree. One arcsecond is a sixtieth of an arcminute.]

Unfortunately the Moon's motion is very complicated as it is affected by the gravitational pull of the Sun and the planets.

The Royal Observatory in Greenwich was established in 1675 for the sole purpose of solving the longitude problem. The first Astronomer Royal, John Flamsteed, proved that the rotation of the Earth was constant enough for the determination of longitude. He also made an accurate catalogue of star positions.

The second Astronomer Royal, Edmond Halley, spent 18 years studying the Moon's motion.

Tobias Meyer published a lunar theory based on Euler's work which enabled longitude to be determined to an accuracy of one degree. In 1762 he improved the accuracy to 16 arcminutes.

The double reflecting quadrant was invented by Hadley in 1731 and could measure angles with an error less than 2 arcminutes.
The sextant was invented in 1757 and could measure angles with an error less than one arcminute.

The scene was set for the introduction of what was known as the "Lunar Distance" method. The fifth Astronomer Royal, Neville Maskelyne, introduced the Nautical Almanac which was first published in 1767, and has been published every year since then. These almanacs contained tables showing the lunar distances of seven bright stars and the Sun for every three hours. This was continued until 1905.

The Lunar Distance method was cumbersome and difficult, but once astronomers had prepared calculation tables a longitude could be calculated in half an hour.

John Harrison (1693-1776) was a carpenter who could make accurate clocks. He solved the lubrication problem by making the working parts out of an oily wood, lignum vitae, making the clocks self-lubricating. He also invented:-

He could make pendulum clocks that were more than accurate enough to solve the longitude problem, but how was such a clock to maintain its accuracy on a ship which was always pitching, rolling and yawing?

From 1735 to 1759 Harrison made three clocks known as H1, H2 and H3. H1 was taken to sea and performed very well. Lieut. - Commander Rupert Gould, who restored Harrison's clocks in the early part of the twentieth century, believed that H2 would have qualified for the 10,000 prize.

H2 and H3 were not taken to sea - Harrison was not satisfied with the performance of H2, and H3 was outperformed by H4. Harrison was awarded the Copley medal by the Royal Society in 1749.

Harrison completed H4 in 1760. H4 was radically different from the other clocks. H4 looks like a very big pocket watch. Harrison had decided that the best solution to the problem of a ship's motion was a very fast-moving balance wheel.

In 1761 H4 was taken on a voyage to Jamaica. The ship departed on the 18tn November and Jamaica was reached on the 21st January. H4 was then five seconds slow which corresponds to an error in longitude of 1.25 arcminutes - after more than nine weeks! Its accuracy was much better than the requirement for the longitude prize, but the Board of Longitude insisted on another trial. The clock was taken to Barbados in 1764, when it again performed excellently, but the Board of Longitude was still not satisfied! H4 was accompanied on these voyages by Harrison's son William - Harrison himself was now too old for a sea voyage.

Kendall made an almost exact copy of H4 known as K1. K1 was used by Captain Cook on his second voyage and proved once again that a chronometer could be used to determine longitude. Cook called K1 "Our faithful guide through all vicissitudes of climates".

As the Board of Longitude seemed determined not to give Harrison his just reward, an appeal was made to King George III. Harrison and his son were granted an audience. "By God, Harrison, I'll see you righted!", the King said.

The Board of Longitude had by now taken possession of all Harrison's clocks, so he made a fifth clock which became known as H5. This clock was tested under the personal supervision of George III and its error was only 4.5 seconds after ten weeks.

As a result of the King's intervention, parliament awarded Harrison most of the balance of the prize money due to him three years before he died.

Harrison's method of finding longitude was adopted by more and more navigators as chronometers became less expensive. The cumbersome lunar distance method then became obsolete.

Main lecture delivered to the Johannesburg branch of the SA Military History Society on 12th June, 2014

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