The Great Debate II: Longitude
The story of longitude
M.V.N. Murthy
The Institute of Mathematical Sciences, Chennai 

Conflicts in science can be fascinating and have occurred often enough. The history of longitude is a record of an effort to discover means of determining longitude over several centuries. This history is not without conflict. It was ultimately settled after a huge controversy which involved astronomers and technologists. The technologists, who were dismissed as mere mechanics, ultimately won the day and the prize. This is the story of Longitude.
Consequences of ignorance
"In 1592, for example, a squadron of six English men-of-war coasted off the Azores, lying in ambush for Spanish traders heading back from the Caribbean. The Madre de Deus, an enormous Portuguese galleon returning from India, sailed into their web. Despite her thirty-two brass guns, the Madre de Deus lost the brief battle, and Portugal lost a princely cargo. Under the ship's hatches lay chests of gold and silver coins, pearls, diamonds, amber, musk, tapestries, calico, and ebony. The spices had to be counted by the tons ...The Madre de Deus proved herself a prize worth half a million pounds sterling--or approximately half the net value of the entire English Exchequer at that date". Quote from Dava Sobel in the book "Longitude".
Before the advent of 18th century, the global ignorance of longitude wreaked economic havoc on a grand scale. Before an accurate method of determining longitude was discovered, the ships were confined to a few narrow shipping lanes. Forced to navigate by latitude alone, the shipping lanes were crowded by whaling ships, merchant ships, war ships and pirate ships. Safe passage was never assured and the ships fell prey to one another.
The Prize
Until the middle of the 18th century, determining the position of ships at sea was a huge problem. Great explorers like Vasco Da Gama, Ferdinand Magellan and Francis Drake achieved a lot but largely through good luck and chance. There were huge risks of shipwrecks, supplies running out because of wrong calculations of duration of travel, etc. This was especially true for countries that were heavily involved in maritime trade.
The situation came to a boiling point in 1707 when nearly four warships were lost and many sailors died, close to the shipping centres of England.
This event catapulted the longitude question into the forefront of national and international affairs of the time. The Longitude Act was framed in 1714 by the Parliament in England. The Board of Longitude promised a prize of 20,000 pounds sterling for a solution of the longitude problem! The prize was to be awarded to the first person to demonstrate a practical method of determining the longitude of a ship at sea with an accuracy of half a degree.
The Catch
The key to knowing how far a ship is from the home port is simple in theory. As is already clear, the problem was far more serious to navigators than to those who move on the land. The latitude and longitude together measure how far around the world one is from the home port. See the box for more details.
There are 360 degrees of latitude and 360 degrees of longitude. Earth is divided into 24 time zones (the number of hours in a day). So every 15 (=360/24) degree change in longitude amounts to one hour. So, an English sailor in the middle of the sea can find out the local time where he is, by looking at the position of the Sun. He must somehow know what is the local time in England. Then a comparison of the local time with the time in England will immediately indicate the longitude of the place with reference to England (or any other home base).
Where the problem lies
This is simple in theory but how does one know the local time at home when a ship is in mid sea? The reality in the 18th century and earlier was that no one had ever made a clock that could remain accurate in a ship that is rolling over the waves and suffering large changes in temperature.
Astronomers and their Solution
Astronomers approached the problem of longitude by appealing to the heavens, literally. At that time, the orbits of the four brightest satellites of Jupiter were known. Galileo in 1612 proposed that their positions could be used as a universal clock which then would lead to the determination of the longitude at any place.
However such a method had practical difficulties, like observing the moons of Jupiter from the decks of a moving ship! In 1683, Edmund Halley used telescopic observations on the relative motion of the moon with respect to fixed stars as a means of measuring time. Though not very successful at the time it lead to the lunar distance method.
Astronomical Observatories
Quickly this was brought to the attention of the powers-that-be. Soon observatories were built in Paris, London, Berlin and other places for the express purpose of determining longitude using heavenly intervention. This of course also led to other important discoveries that formulated our current view of the universe.
The observatories helped in measuring the positions of stars with high precision as also a working method for mapping the moon's motion relative to stars and the Sun. Tobias Mayer and Euler produced a set of tables predicting the position of the moon more accurately than ever before. Mayer was a German cartographer and astronomer while the Swiss Mathematician Euler contributed several elegant equations regarding the relative motion of the Sun, the Earth and the moon.
Popularity of the lunar distance method
James Bradley, the Astronomer Royal at Greenwich, compared Mayer's projections with actual observations taken at the observatory. The agreement was excellent! This excited the aStronomer Nevil Maskelyne who contributed much using his own experiments at sea to improve the lunar distance method.
With the help of these tables, the longitude could be determined to within half a degree. These tables were published in the form of an almanac every year. When Mayer died of infection in 1762 the board awarded 3000 pounds in recognition of his work to his family and another 300 pounds to Euler for his founding equations.
Problems with the method
Admirals in the Navy and the members of the Board of Longitude started openly endorsing the lunar distance method in spite of its practical difficulties. The navigator had to measure the altitudes of various heavenly bodies and their angular distances so as to use the tables. They also had to make corrections forthe refraction effects due to nearness of the horizon, parallax problems etc.
With all these inputs, initially the calculation would take hours, but with time it was improved and the time required was reduced to about 30 minutes when the process became usable. Even then, on some days or nights heavenly intervention in the form of clouds and rain would play spoil-sport. And of course, on a travelling ship, the calculation had to be done at least once a day!
Nevertheless, the work of Mayer along with Euler caught the attention of the Board of Longitude for evaluation and consideration for the longitude prize.
Clock-makers and their Solution
That however was not going to be easy; the English clock-maker John Harrison offered the navigating people a little ticking device to lay claim to the prize. The user did not have to know any mathematics or astronomy to use it--they just had to 'watch' the device!
No-one could believe it. At that time, it appeared to every one that computing longitude was a difficult mathematical exercise. How could one clock replace all those complicated observations and calculations?! It was preposterous---ranged against the might of the scientific community Harrison had to endure many unpleasant trials before establishing that his method was the most natural, simple and practical one.
John Harrison
Born in 1693, John Harrison was a mechanical genius. He pioneered the science of portable clocks: precision time-keeping devices now-a-days called chronometers. These are simply very accurate and rugged clocks. Even Isaac Newton in his time had feared that this would be impossible.
Harrison invented a clock that would keep the time accurately. Once set to the home time, it would keep showing that time in any remote corner of the world. This is exactly what was needed as a ready reference to determine the longitude of the far-away place (once the local time was accurately known). You only needed a pair of eyes!
The innovations
The concept of using clocks for recording time was old and was there before Harrison. For example pendulum clocks existed. Christian Huygens, who made important contributions to optics, had made one such accurate clock. However, the pendulum clocks of the 18th century could not be used on chopping and rolling seas with confidence.
So Harrison did away with the pendulum and constructed a series of friction-free clocks that required little cleaning or lubrication. Temperature variation was another problem when moving from Europe to the tropics. The metals of which the clock-parts were made used to expand or contract with heat or cold thus affecting the accuracy of the clock's time keeping.
Harrison combined different metallic components in such a way that when one component expanded or contracted, there was a counteracting component that kept the clock rate constant. The clock he built had an accuracy of 1 second in a month, better than any clock found in London then.
In all he constructed more than four different types of clocks over a long period from 1730-1759. The first one known as H1 was essentially a portable version of his precision wooden clocks. While H2 had a design fault, H3 was a big improvement although still not accurate enough for the Board of Longitude to award him the prize.
Soon Harrison realised that an entirely new design would be required to solve the longitude problem-- it had to be a pocket watch. His design H4 was just 13cm in diameter weighing about 1.45kg, looked like a big pocket watch and performed to the accuracy required. Even then, there was stiff resistance from the atronomers who preferred the lunar tables. It took Harrison a life-time before his work was finally recognised and the prize was awarded.
In the mean-while, the Royal Society (a prestigious scientific body in England) awarded Harrison the highest medal of honour, the Copley medal, in 1749. The recepients later include Benjamin Franklin, Henry Cavendish, Joseph Priestley, Earnest Rutherford and Albert Einstein. There was also an offer of Fellowship of the Royal Society (FRS) which Harrison declined.
The final denounment
Harrison was asked to make more watches to prove that the high accuracy of H4 was not an accident! He planned to make two more. He was now in his seventies (tired and worn out after all the trials and tribulations)a. He took help from his son William when working on the fifth time keeper H5. He also asked Larcum Kendall to make a copy of H4.
The Board of Longitude, wrongly influenced by the Astronomer Royal Nevil Maskelyne, once again denied Harrison's claim.
Harrison gave up his efforts to convince the board and made an appeal to King George III through his private astronomer. He along with his son got an audience after which the King remarked " ...these people have been cruelly wronged...". H5 was then put on trial by the King himself in 1772 and performed extremely well.
After intervention by the Parliament, Harrison was finally awarded the full Longitude Prize in 1773--after forty years of struggling against political intrigue and insults from academics.
The final denouement was the voyage of Captain Cook to the Antarctic, returning after a voyage of three years in 1775, through trying conditions, entirely aided by the copy of H4. Harrison died a year after Cook's return in 1776. He was 83.
Though the trials proved the utility of the marine chronometers, they remained expensive and the lunar distance method continued to be used till about 1850. Lunar distance tables were published regularly and last Almanac was published in 1912.
The end came when wireless telegraph time signals were used in conjunction with marine chronometers for navigation in the 20th century.
The trials and tribulations of clock makers and astronomers seems distant now with modern solutions which give the navigators a number of choices to determine accurate positional information using radars and GPS, the satellite navigation system. Using these the position can now be fixed accurate to within a few meters any where on the globe.
The technological spin-offs from the efforts of clock makers, dubbed mere mechanics at that time, is huge. Similarly, the accurate star maps prepared by the astronomers, using the observations in the several observatories constructed for the purpose, expanded the understanding of the universe. The threads of longitude thus ran much deeper and farther than just mapping the globe.
References:
1. Dava Sobel, "Longitude: The story of a lone genius who solved the greatest scientific problem of his time. " A dramatic account of the scientific quest, The Longitude Problem.
2. Jonathan Betts, "John Harrison and Lt. Cdr Rupert T. Gould" e-book.
3. Wikipedia-- History of longitude, http://en.wikipedia.org/wiki/History_of_longitude