Longitude was a much harder nut to crack. In principle, all one needs is an accurate clock, set to Greenwich time. When the Sun "passes the meridian" at noon, we only need to check the clock: if Greenwich time is 3 p.m., we know that 3 hours ago it was noon at Greenwich and we are therefore at longitude 15° x 3 = 45 degrees west.

    However, accurate clocks require a fairly sophisticated technology. Pendulum clocks can keep time quite accurately on firm land, but the pitching and rolling of a ship makes them quite unsuitable for sea duty.

    Non-pendulum clocks--e.g. wristwatches, before they became electronic--use a balance wheel, a small flywheel rotating back and forth through a small angle. A flat spiral spring is wrapped around its axis and it always brings the wheel back to its original position. The period of each back-and-forth oscillation is then only determined by the strength of the spring and the mass of the wheel, and it can replace the swing of the pendulum in controlling the motion of the clock's hands.

    Gravity plays no role here, and motions of the ship also have very little effect; as discussed in a later section, a vaguely similar method was used in 1973 for "weighing" astronauts in the weightless environment of a space station. For navigation, however, such a clock must be very accurate, which is not easy to achieve: friction must be minimal, and so must changes in the dimensions of the balance wheel and properties of the spring due to changing temperature and other factors.

    In the 17th and 18th century, when the navies of Britain, Spain, France and Holland all tried to dominate the seas, the "problem of longitude" assumed great strategic importance and occupied some of the best scientific minds. In 1714 Britain announced a prize of 20,000 pounds--a huge sum in those days--for a reliable solution, and John Harrison, a British clockmaker, spent decades trying to achieve it. His first two "chronometers," of 1735 and 1739, though accurate, were bulky and delicate pieces of machinery; they have been restored and are ticking away on public display, at the Royal Astronomical Observatory in Greenwich. Only his 4th instrument, tested in 1761, proved satisfactory, and it took some additional years before he received his prize.

  In September 1917, Wood and some colleagues embarked for Europe aboard the steamship Adriatic, to help US allies use science in fighting World War I. To hinder German submarines from intercepting the ship, it location was kept secret from everybody, including its passengers.

  What follows are Wood's own notes, reproduced in "Doctor Wood" by William Seabrook (1940). The book is out of print, but remains worth reading (if you can find it) for its great store of stories, of which this one is a fair sample.

  "We sailed on night after night, the weather growing colder and colder, and the North Star climbing towards the zenith. One afternoon it occured to Colpitts [one of the traveling scientists] that it was the night of the autumnal equinox, on which both longitude and latitude can be calculated from the elevation of the North Star and the time of sunset [6 hours after noon]. I made a quadrant out of two sticks of wood and a protractor. By sighting one stick on the horizon and the other on the star, I determined its elevation, given which Colpitts, who had timed the sunset, worked out our position in a few minutes. This news spread rapidly, throwing the ship's officers into a frenzy, as all information regarding the course we were sailing was a dead secret. Next morning we discovered the ships' officers had set all of the clocks available to passengers three-quarters of an hour ahead, to confuse and baffle the scientists aboard."

    Tales of Navigation #2 :     Nansen

  In 1893 the Norwegian explorer Fridtjof Nansen set out towards the north pole (located in the ice-covered Arctic Ocean) in a specially strengthened ship, the "Fram." Having studied the currents of the Arctic Ocean, Nansen allowed "Fram" to be frozen into the polar ice, with which it slowly drifted across the water. Nearly two years, later, realizing that the course of "Fram" fell short of the pole, Nansen (who had prepared for this possibility) left the ship with his colleague Johansen and attempted to reach the pole by sleds over the ice. About 400 miles short of the pole they had to turn back: they wintered on a desolate island, in a hut they built of stones and walrus hides, and the following spring they headed for the islands of Svalbard (Spitzbergen).

      They had been in the icy wilderness for more than a year, completely out of touch, but they always knew exactly where they were, because each man carried a spring-powered chronometer. Then disaster struck--in a moment of distraction, both forgot to rewind their chronometers and allowed them to run down. Suddenly, they were lost! Based on their last recorded positions, they made a guess and reset their timepieces, but the rest of their journey was clouded by uncertainty. Luckily, they did not have much further to go, and as chance had it, they encountered a British Arctic expedition which took them home. "Fram" broke free from the edge of the ice at about the same time; it is now on public display in Oslo.