American Scientist Magazine; Sept-Oct 2002


Finding Out the Longitude



 by J. Donald Fernie


The Colledge will the whole world measure,

Which most impossible conclude,

And Navigators make a pleasure

By finding out the longitude.

Every [sailor] shall then with ease

Sayle any ships to th' Antipodes.

—Anonymous, circa 1661


Modern astronomers, like most research scientists today, are resigned to spending a significant fraction of their working hours writing grant applications and pleading with government agencies for the funding of ever-more-expensive research facilities. Could it have ever been the other way around? Was there ever a time when governments of their own accord established major observatories and then set about staffing them with top-notch scientists wherever these might be found? There was! It was the 17th century.


Needless to say, the governments were not acting out of any sudden urge to understand the universe. The driving power was utterly pragmatic—someone somehow had to find out how a ship at sea could determine its longitude. As things stood by the mid-1600s, navigators could readily find their latitude—that is, how far north or south they were—but were never sure how far east or west they might be. The result was that all too often they sailed their ship in one direction when they should have gone in quite another. The resulting shipwrecks led to the loss of thousands of lives and cargoes worth fortunes.


Even as late as 1707 there occurred the famous episode of Admiral Sir Cloudesley Shovel (I love that name), whose fleet ran through totally overcast skies and violently stormy weather while returning to England from Gibraltar. After 12 days of such weather, no one was certain where they were. The fleet's navigators conferred and concluded they were well west of the French island of Ouessant—'Ushant' in British terminology—which lies off Brittany and marks the southern entrance to the English Channel. It was said that an ordinary seaman on the Admiral's flagship publicly disagreed with this conclusion and was promptly hanged from the yardarm for his insubordination. The fleet then turned eastward, hoping, presumably, to sight the island and so enter the Channel. Instead, during the night they ran headlong into the Scilly Isles just off the southwest tip of England. Four ships and two thousand men were lost, including the Admiral. Virtually every writer on the subject of longitude cites this story as an example of how urgent the need for a way of determining longitude had become. Ironically, however, if you examine a map, you find that to have run into the Scilly Isles this way, they must indeed have been well west of Ouessant in terms of longitude. The error, though, was one of latitude! They were actually about 1.5 degrees north of where they thought they were. In any case, ships at sea sailing for 12 completely overcast days would have had no way of knowing either their latitude or longitude with any certainty, right up to the mid-20th century, when electronic aids like Loran became available in some parts of the world.


This crisis in sea travel became ever more urgent as world exploration and trading developed, so that a Royal Observatory in Paris in 1667 and another in Greenwich in 1675 were established, largely in the hope that they would lead to an astronomical solution to the longitude problem. (There was considerable contrast in the way the two observatories came about. The French lavished funds on theirs, but the royal warrant authorizing the building of the Greenwich observatory announced that "the paying of such materials and workmen as shall be used and employed therein, [shall come] out of such monies as shall come to your hands [from the sale of] old and decayed [gun-]powder. " Also, the choice of Greenwich as a site was at least partly influenced by the fact that an old, disused building there would provide many of the necessary building materials, and some wood, iron and lead would come from a gatehouse demolished in the Tower of London. Moreover, the astronomer appointed to the new observatory was poorly paid and had to provide all necessary instruments, including telescopes, himself.)


Why was longitude determination such a difficult problem compared with finding latitude? A very basic answer is that latitude is measured north or south and so is independent of the earth's east-west rotation, whereas longitude's determination by celestial means is affected by that rotation. Latitude can be found, in principle, from angular measures alone—say the angle of the midday sun above the horizon—but longitude requires knowledge of time. Thus if a mariner had a clock keeping Greenwich time and found that it read 2 p.m. when the sun was at its maximum angle above the horizon—the local noon—he would know that his longitude was two hours west of Greenwich. The whole problem lay in finding a clock that would keep time with sufficient accuracy over the long voyages of the 17th and 18th centuries. The best timekeepers of the age were pendulum clocks, but these were useless on the heaving deck of a small ship, whereas spring-wound clocks were relatively crude and hopelessly inaccurate for voyages over many weeks or months.


There had been hopes that the variation of the compass—the angle between the directions of magnetic north and true north—might do the trick, since it was known to vary with position on the earth. Could longitude be calibrated in terms of the variation and perhaps latitude? By 1701 Edmond Halley had dashed these hopes, showing that in the western North Atlantic, for instance, the isogonic lines (of constant variation) run almost east-west and so are independent of longitude.



Thus the turn to astronomy. Were there natural phenomena in the sky whose happenings might be predicted with precision well ahead of time, so that the observation of those happenings could then provide the Greenwich time for correcting an onboard clock? Indeed there were! Lunar and solar eclipses, for instance. And Galileo had for years touted the idea of using the bright satellites of Jupiter, which, as they revolve about the planet, undergo a variety of eclipses, transits and occultations as seen from the earth. There was also the moon itself; in the course of its monthly orbit about the earth, it is seen moving against a background of stars, and if its changing position in this pattern is predictable, then observations of its position will tell the time. This scheme became known as the method of lunar distances, referring to the angle between the moon and various bright stars as a function of time.


But there were problems with all these schemes. Lunar and solar eclipses were too rare to be of general use to a mariner, although they were the principal means of establishing the longitudes of remote ports and inhabited places generally, especially if the results from a number of eclipses over the years were averaged. The use of Jupiter's satellites, although fine in principle, had so many practical difficulties that the method never was acceptable to mariners. To mention just two problems: It was next to impossible to hold a telescope steady enough on the heaving deck of a small ship to time the eclipses accurately. Also, Jupiter is in the daylight sky for months at a time, during which periods the method is simply inapplicable. As for the moon moving against a background pattern of stars, well, although it too is in the daylight sky for part of each month, its angular distance from the sun could then be used. But the moon's apparent motion is so complicated (largely because it is so near the earth that higher-order dynamical effects become discernible), that for many years predictions of its position versus time were not accurate enough. There was the further drawback that because of the moon's proximity to the earth, its position among the stars when observed even at the same instant from different localities is different because of a parallax effect. Thus the calculations involved in finding one's longitude this way were laborious and liable to error in the hands of the average mariner.


The Board of Longitude


Even decades after the founding of the royal observatories, the astronomers were not making much progress on the longitude problem, and meanwhile lives and valuable cargoes continued to be lost to shipwreck. Several maritime nations offered considerable rewards to anyone who could solve the problem adequately. In 1714 Britain offered a prize of £20,000 to anyone who could convince a panel of experts, known as the Board of Longitude, of a method that would determine longitude to within half a degree after a trans-Atlantic voyage. A sum of that magnitude, worth millions of dollars in today's terms, was, of course, a clarion call to every crackpot everywhere.


Very soon the Board of Longitude needed a secretary to hand out stereotypical answers to stereotypical proposals. Some applicants simply had no idea what the longitude problem was about. Thus Dr. Woeman wrote, "acquainting the Board that he can express p and the ratio of 1 to -2 in integrals, and that this comprehends the discovery of the Longitude." Others had some inkling of the problem but proposed hopelessly naive solutions. Mr. Owen Straton, for instance, had to be informed that a sundial would not win the prize. Only slightly better on the scale of naivete was Mr. Haldanby's offering, which noted that sailing northwest near the equator meant that having increased your latitude by 1 degree, you had also moved 1 degree westward in longitude, and that he could provide a table that would apply to other latitudes and directions. The difficulties introduced by ocean currents seem not to have occurred to him.



A proposal that received a good deal of attention beyond the Board was that of Whiston and Ditton. William Whiston had succeeded Isaac Newton as Lucasian Professor at the University of Cambridge, and so his opinions on scientific matters carried some weight. The Whiston-Ditton scheme envisioned small ships being anchored at intervals of a few hundred miles across an ocean, it being "known" that the North Atlantic was nowhere more than 300 fathoms deep. Each ship would have a powerful gun that would fire a shell 6,440 feet vertically upward at midnight each night. At the apex of its ascent, the shell would explode with a brilliant flash and monstrous boom that could be seen and later heard as much as a hundred miles away. This would allow other ships to locate themselves relative to the anchored ship, whose longitude would have been established by, say, lunar eclipses. Problems of staffing and provisioning such ships, keeping enemy ships and pirates at bay, and so forth, were waved away. A competitor noted that this proposal was "a very whimsical Notion, looking very Ridiculous in Mr Ditton and Mr Whiston; the first of which Gentlemen I do not know, but as for the other, People says he is a little beside himself, or rather, if he has any such Thing as Brains, they are really crackt."


But the pi¸ce de rˇsistance of all such schemes was the one based on "the powder of sympathy." Its author was anonymous and very likely wrote satirically (since anonymous inventors are not usually awarded major prizes). The method hinged on a medicinal powder that when applied to a wound would cause the wounded person to start up, possibly with a cry. Nothing unusual there, but the author claimed to have found that if the powder was applied not to the wound itself but to a bandage that had previously been on the wound, the effect was the same. Thus it was proposed that each ship carry a wounded dog, and that a bandage from the wound be left at Greenwich, where at precisely noon each day it would be dipped into a solution of the powder of sympathy. The dog, wherever in the world its ship was at that moment, would then obligingly yelp and the mariner could then note the local time and so find his longitude.


As the years went by, the preferred methods of finding longitude narrowed to two: improvements to the method of lunar distances and improvements in the marine chronometer. Lunar distances continued in use well into the 19th century, but in the end it was the chronometer that won out, and in our own time, of course, radio signals and now the Global Positioning System have reduced the problem to triviality.


© J. Donald Fernie




Andrewes, W. J. H., ed. 1996. The Quest for Longitude. Cambridge, Mass.: Harvard University Press.

Brown, L. A. 1949. The Story of Maps. Boston: Little, Brown & Co.

Forbes, E. G. 1975. Greenwich Observatory, Vol. 1. London: Taylor and Francis.

Howse, D. 1980. Greenwich Time and the Discovery of the Longitude. Oxford, England: Oxford University Press.


Some material added by Daniel.


Here is a picture of the first truly accurate marine chronometer (also known as a clock on a boat).


This is HarrisonÕs H-1.