The Great Debate II: Longitude M.V.N. Murthy The Institute of Mathematical Sciences, Chennai " 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 in to 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", Dava Sobel in the book "Longitude". Introduction: 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. 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 not without conflicts. 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. The Latitude and Longitude: The most natural way of defining the position of any object on a surface, flat or curved, is to define an appropriate coordinate system with an origin which serves as a reference relative to which all other points are marked by two coordinates, just we do it on a graph paper with grids. A sphere, as is well known is generated by rotating a half-circle by 360 degrees. Thus the position of a point on a sphere can be uniquely specified by two angles, the angle on the half circle and amount by which it should be rotated in order to reach the precise point on the sphere. Since the Earth is a sphere to a very good approximation, any position on Earth may be denoted by two angles, namely the latitude (angle in the half circle) and longitude (the angle by which the half circle is rotated). This is actually an ancient method and was proposed by Eratosthenes from Greece in 3rd century BC for the first time. By 150 AD, astronomer Ptolemy had already plotted these lines on the maps of the World. Thus on any map of the Earth (flat projection of the spherical earth), the latitudes appear as horizontal lines but are actually circular and the longitudes appear as curved lines joining the north and the south poles thus forming a grid like pattern. The equator that divides the Earth into Northern and Southern hemispheres is a natural choice for fixing the zero latitude where as the poles correspond to 90 deg. north and 90 deg. south latitudes. Determination of the latitude of any place is relatively easy as it can be found by the altitude of the Sun at noon. The easiest but approximate method, at any place, is to measure the angle of the Sun at noon when the Sun is directly over the equator (21 March or 21 September corresponding to spring and autumn equinoxes). It is approximate because small corrections have to be made for Earth not being a precise sphere but is actually an ellipsoid. But this is easily done. At night one can use the inclination of the pole star to determine the latitude (in the northern hemisphere). Measuring the latitude at any other time of the year is also not very difficult since the north-south movement of the Sun over the whole year is well known and correcting for the position of the Sun is easily done. This was well known to the sailors even in mid sea and they could calculate the latitude easily. However, the accurate determination of position on the globe, crucial for navigational purposes, required not just the latitude but also the longitude. Unlike the zero degree latitude which is fixed in a natural way by dividing the globe into northern and southern hemispheres, the zero degree longitude has no ready reference. In principle it can be any where, the greek astronomer Ptolemy was free to put it along the longitude line running through Canary islands off the northwest coast of Africa. Over centuries the zero line moved through many places before it settled down at last on a line passing through Greenwich near London. The prime meridian, as it is called now, passes through the Royal Observatory at Greenwich. The intersection of the prime meridian with the equatorial latitude thus provides the origin of the coordinate system that describes the whole globe. The Prize: Until the middle of 18th century determination of the position of ships at sea was huge problem for navigators. If great explorers like Vasco Da Gama, Ferdinand Magellan to Francis Drake got to where they were going it was through good luck and chance. There were huge risks of shipwrecks, supplies running out because of wrong calculations of duration of travel, etc., especially for countries that were heavily involved in maritime trade. It came to a boiling point in 1707 when nearly four warships were lost, many sailors died, close to the shipping centers 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 which promised a prize of 20,000 pound sterling for a solution of the longitude problem to be administered by the Board of Longitude. 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 of the great circle. 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 longitude measures how far around the world one is from the home port along with a knowledge of the latitude. Earth is divided into 24 time zones and every 15 degree change in longitude amounts a difference of one hour. Thus a comparison of the local time (found by knowing the position of the Sun) with the local time at the home port will immediately indicate the longitude of the place with reference to the home base. This is simple in theory but how does one know the local time at home port when a ship is in mid sea? The reality in 18th century and before 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. The Astronomers: Astronomers approached the problem of longitude challenge by appealing to the heavens, literally. Galileo in 1612 proposed that with an accurate knowledge of the orbits of the four brightest satellites of Jupiter, one could use their positions as a universal clock which then would lead to the determination of the longitude. 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. 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 lead to other important discoveries that formulated our view of the universe. The observatories helped in measuring the positions of stars with high precision as also a working method for mapping moon's motion relative to stars and the Sun. The German cartographer and astronomer Tobias Mayer, with help from Swiss Mathematician Euler who contributed several elegant equations regarding the relative motion of the Sun, the Earth and Moon to help Mayers calculations, produced a set tables predicting the position of the Moon more accurately than ever before. James Bradley, who had succeeded Halley as Astronomer Royal at Greenwich, compared Mayer's projections with actual observations taken at the observatory. The agreement was excellent and excited the Astronomer Nevil Maskelyne who contributed much using his own experiments at sea to improve the lunar distance method. The longitude, with the help of these tables, could be determined to within half a degree. Maskelyne proposed annual publication of lunar distance predictions as a nautical almanac every year. Investigators from all over the world got involved and the tables became better and better. When Mayer died of infection in 1762 the board awarded pound 3000 in recognition of his work to his family and another pound 300 to Euler for his founding equations. 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, he had to battle the refraction effects due to nearness of the horizon, the parallax problems. 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. However on some days or nights heavenly intervention in the form of clouds and rain would play the spoil sport. Nevertheless, the work of Mayer along with Euler caught the attention of the Board of Longitude for evaluation and consideration for the longitude prize. The Clockmaker--John Harrison: 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 devise! It was preposterous-- ranged against the might of the scientific community Harrison had to endure the many unpleasant trials before establishing his method as the most natural, simple and practical one. John Harrison was a mechanical genius who pioneered the science of portable precision time keeping devises now-a-days called Chronometers. These are simply very accurate and rugged clocks. Even Isaac Newton in his time feared that this was impossible but Harrison invented a clock that would keep the time from the home port accurately in any remote corner of the world providing a ready reference to determine the longitude of the place once the local time is accurately known. You only needed a pair of eyes. The concept of using clocks for recording time was old and was there before Harrison. For example the pendulum clocks were used on land with some success to determine the longitude. Christian Huygens, who made important contributions to optics, had made one such accurate clock. However, the pendulum clocks of 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 used to expand or contract 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. Harrison was born in 1693. He had no formal education but learnt carpentry from his father. He built his first clock entirely made up of wood in 1713 (which is preserved even today). Working with his younger brother he built a pendulum clock with the pendulum rod made of alternate wires of brass and steel which eliminated the problem of pendulum's length increasing in warmer weather, thus slowing the clock. This had an accuracy of 1 second in a month better than any clock found in London. Early on Harrison realised that he would have to devise portable clocks of high accuracy which could withstand the ships unruly movements as well as temperature variations of more than 30-40 degrees Celsius in order to solve the Longitude problem. 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 Harrison's precision wooden clocks driven by springs and could run for one day at a time. Unlike pendulum clocks, H1 was mounted in such way that it ran independent of the direction of gravity. Harrison did not lay claim to the longitude prize at this stage, instead he asked for financial assistance to make better versions. He built a second variation H2 around 1740, but realised that the design had faults. The balance was not good enough to with stand the motion of a ship. He worked on his third version H3 until 1759 bringing in new concepts in to clock making like . bimetallic strip, to compensate the balance spring for the effects of changes in temperature, . caged roller bearing, in order to make it almost friction less requiring almost no lubrication. These are inventions which found application in variety of other machines. In spite of these innovations, H3 still did not make it to the accuracy required by the Board of Longitude to award the prize. It is also not clear why Harrison took such a long time to come up with H3 though he appeared to be working almost entirely on its design. Well before H3 design was complete, Harrison realised that an entirely new design would be required to solve the longitude problem-- it had to be a pocket watch. No one in 1750's would have thought that a pocket watch could have the needed accuracy. He requested support for making two such watches "one of such size as may be worn in the pocket and the other bigger..." The fourth time keeper made by Harrison, H4, was just 13cm in diameter weighing about 1.45kg, looked like a big pocket watch. Harrison was ready for staking his claim to the Longitude prize and the trials began soon enough. Harrison's son William set sail for the West Indies on 18 January 1761 for the trial but had to wait for a long time in between and finally arrived in Jamaica on 19 January 1762. The watch had lost only five seconds after 81 days at sea. The total error when H4 returned to London was just under two minutes. The accuracy was better than that required by the Board of Longitude. At this stage the Longitude prize should have obviously gone to Harrison as his watch had done all that the Longitude Act demanded, but it was not to be. There was some consolation for Harrison, however, as 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: Every success of Harrison was distrusted by the scientific elite who backed the astronomical lunar distance method to the hilt. Harrison had to compete with the now Astronomer Royal Nevil Maskelyne who was not only involved in perfecting the lunar distance method but also one of the commissioners on the Board of Longitude charged with awarding the longitude prize. The contest rules were changed whenever he saw it fit to favour the chances of astronomers over the likes of Harrison and other "mechanics". The Board members first demanded that Harrison disclose the workings of H4 to a specially appointed committee implying that the accuracy of H4 was a fluke. They demanded that copies of the watch should be made and tested. Finally even after these rather ridiculous conditions were satisfied, they only awarded half the prize, that is pound 10,000. Harrison initially refused to accept these proposals, but finally acceded to all the demands and received the first half of the longitude prize. In order to get the second half of the prize, Harrison had to make at least two more watches himself while the original was taken away for testing at the Royal observatory, and have them tested. Harrison now in seventies (tired and worn out after all the trials and tribulations), with help from his son William, worked on the fifth time keeper H5 while making copies was assigned to one Larcum Kendall. H5 and the copies of H4 by Kendall were completed in 1769 and inspected in early 1770 by the same panel that examined H4. The Board again changed rules and demanded that the copies of H4 be made by Harrison alone though the copies made by Kendall were just as good. 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. The Board of Longitude, however, still refused recognise the results of this trial. Harrison as a last resort petitioned the Parliament and was finally awarded the second half of the Longitude Prize in 1773--after forty years of struggling against political intrigue, insults from academics. For Harrison this was more important since it was finally recognised that he had solved the longitude problem. The final denouement was the voyage of Captain Cook to 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. However, through several improvements the chronometers were made small and affordable and were used by vast majority of navigators. With three marine chronometers to serve as checks as well as keep times from different zones lunar distance method was obsolete. The end came when wireless telegraph time signals were used in conjunction with marine chronometers for navigation in the 20th century. Ironically until 1905 navigators had to learn the lunar table method as it was required to obtain certain licenses whether they used it or not. The trials and tribulations of clock makers and astronomers seems distant now with modern solutions which give the navigators 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 few meters any where on the globe. However, 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. In 1920 during his research for the book, The Marine Chronometer, its History and Development, Lt. Cdr. Rupert Gould discovered the great time keepers made by Harrison. They were found in the stores of the Royal Observatory at Greenwich in complete neglect. He got permission to restore them- a project that occupied the rest of his life. Every stage of the restoration work was recorded by Gould in 18 meticulously detaied note books. The restored clocks are now important exhibits in the Royal Observatory. Though famous in his time, Harrison's life had been consigned to history until Rupert Gould retold his extraordinary story in 1923 through his book. 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