Longitude: The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time - Dava Sobel (2005)

Chapter 9. Hands on Heaven’s Clock

The moving Moon went up the sky,

And no where did abide:

Softly she was going up,

And a star or two beside.

—SAMUEL TAYLOR COLERIDGE, “The Rime of the Ancient Mariner”

The moving moon, full, gibbous, or crescent-shaped, shone at last for the navigators of the eighteenth century like a luminous hand on the clock of heaven. The broad expanse of sky served as dial for this celestial clock, while the sun, the planets, and the stars painted the numbers on its face.

A seaman could not read the clock of heaven with a quick glance but only with complex observing instruments, with combinations of sightings taken together and repeated as many as seven times in a row for accuracy’s sake, and with logarithm tables compiled far in advance by human computers for the convenience of sailors on long voyages. It took about four hours to calculate the time from the heavenly dial— when the weather was clear, that is. If clouds appeared, the clock hid behind them.

The clock of heaven formed John Harrison’s chief competition for the longitude prize; the lunar distance method for finding longitude, based on measuring the motions of the moon, constituted the only reasonable alternative to Harrison’s timekeepers. By a grand confluence, Harrison produced his sea clocks at precisely the same period when scientists finally amassed the theories, instruments, and information needed to make use of the clock of heaven.

In longitude determination, a realm of endeavor where nothing had worked for centuries, suddenly two rival approaches of apparently equal merit ran neck and neck. Perfection of the two methods blazed parallel trails of development down the decades from the 1730s to the 1760s. Harrison, ever the loner, pursued his own quiet course through a maze of clockwork machinery, while his opponents, the professors of astronomy and mathematics, promised the moon to merchants, mariners, and Parliament.

In 1731, the year after Harrison wrote out the recipe for H-1 in words and pictures, two inventors—one English, one American—independently created the long-sought instrument upon which the lunar distance method depended. Annals of the history of science give equal credit to John Hadley, the country squire who first demonstrated this instrument to the Royal Society, and Thomas Godfrey, the indigent Philadelphia glazier who was struck, almost simultaneously, by the same inspiration. (Later it was discovered that Sir Isaac Newton had also drawn plans for a nearly identical device, but the description got lost until long after Newton’s death in a mountain of paperwork left with Edmond Halley. Halley himself, as well as Robert Hooke before him, had sketched out similar designs for the same purpose.)

Most British sailors called the instrument Hadley’s (not Godfrey’s) quadrant, quite understandably. Some dubbed it an octant, because its curved scale formed the eighth part of a circle; others preferred the name reflecting quadrant, pointing out that the machine’s mirrors doubled its capacity. By any name, the instrument soon helped sailors find their latitude and longitude.

Older instruments, from the astrolabe to the cross-staff to the backstaff, had been used for centuries to determine latitude and local time by gauging the height of the sun or a given star above the horizon. But now, thanks to a trick done with paired mirrors, the new reflecting quadrant allowed direct measurement of the elevations of two celestial bodies, as well as the distances between them. Even if the ship pitched and rolled, the objects in the navigator’s sights retained their relative positions vis-à-vis one another. As a bonus, Hadley’s quadrant boasted its own built-in artificial horizon that proved a lifesaver when the real horizon disappeared in darkness or fog. The quadrant quickly evolved into an even more accurate device, called a sextant, which incorporated a telescope and a wider measuring arc. These additions permitted the precise determination of the ever-changing, telltale distances between the moon and the sun during daylight hours, or between the moon and stars after dark.

With detailed star charts and a trusty instrument, a good navigator could now stand on the deck of his ship and measure the lunar distances. (Actually, many of the more careful navigators sat, the better to steady themselves, and the real sticklers lay down flat on their backs.) Next he consulted a table that listed the angular distances between the moon and numerous celestial objects for various hours of the day, as they would be observed from London or Paris. (As their name implies, angular distances are expressed in degrees of arc; they describe the size of the angle created by two lines of sight, running from the observer’s eye to the pair of objects in question.) He then compared the time when he saw the moon thirty degrees away from the star Regulus, say, in the heart of Leo the Lion, with the time that particular position had been predicted for the home port. If, for example, this navigator’s observation occurred at one o’clock in the morning, local time, when the tables called for the same configuration over London at 4 A.M., then the ship’s time was three hours earlier—and the ship itself, therefore, at longitude forty-five degrees west of London.

“I say, Old Boy, do you smoke?” a brazen sun asked of the moon in an old English newspaper cartoon portraying the lunar distance method. “No, you brute,” the skittish moon replied. “Keep your distance!”

Hadley’s quadrant capitalized on the work of astronomers, who had cemented the positions of the fixed stars on the celestial clock dial. John Flamsteed alone personally donated some forty man-years to the monumental effort of mapping the heavens. As the first astronomer royal, Flamsteed conducted 30,000 individual observations, all dutifully recorded and confirmed with telescopes he built himself or bought at his own expense. Flamsteed’s finished star catalog tripled the number of entries in the sky atlas Tycho Brahe had compiled at Uraniborg in Denmark, and improved the precision of the census by several orders of magnitude.

Limited as he was to the skies over Greenwich, Flamsteed was glad to see the flamboyant Edmond Halley take off for the South Atlantic in 1676, right after the founding of the Royal Observatory. Halley set up a mini-Greenwich on the island of St. Helena. It was the right place but the wrong atmosphere, and Halley counted only 341 new stars through the haze. Nevertheless, this achievement earned him a flattering reputation as “the southern Tycho.”

During his own tenure as astronomer royal, from 1720 to 1742, Halley studiously tracked the moon. The mapping of the heavens, after all, was merely a prelude to the more challenging problem of charting the moon’s course through the fields of stars.

The moon follows an irregular elliptical orbit around the Earth, so that the moon’s distance from the Earth and relation to the background stars is in constant flux. What’s more, since the moon’s orbital motion varies cyclically over an eighteen-year period, eighteen years’ worth of data constitute the bare minimum groundwork for any meaningful predictions of the moon’s position.

Halley not only observed the moon day and night, to reveal the intricacies of her motions, he also pored through ancient eclipse records for clues about her past. Any and all data regarding lunar orbital motions might be grist for creating the tables navigators needed. Halley concluded from these sources that the moon’s rate of revolution about the Earth was accelerating over time. (Today, scientists assert that the moon is not speeding up; rather, the Earth’s rotation is slowing down, braked by tidal friction, but Halley was correct in noting a relative change.)

Even before he became astronomer royal, Halley had made predictions regarding the return of the comet that immortalized his name. He also showed, in 1718, that three of the brightest stars had changed their positions in the heavens over the two millennia since Greek and Chinese astronomers had plotted their whereabouts. Just within the century-plus since Tycho’s maps, Halley found that these three stars had shifted slightly. Nevertheless, Halley assured sailors that this “proper motion” of the stars, though it stands as one of his greatest discoveries, was only barely perceptible over eons, and would not mar the utility of the clock of heaven.

At the age of eighty-three, while he was still hale and hearty, Halley tried to pass the torch as astronomer royal to his heir apparent, James Bradley, but the king (George II) wouldn’t hear of it. Bradley had to wait to take office until after Halley died, nearly two years later, just a couple of weeks past New Year’s Day in January 1742. The inauguration of the new astronomer royal presaged a drastic reversal of fortune for John Harrison, whom Halley had always admired. Bradley, despite his 1735 endorsement of the sea clock, felt little affinity for anything outside astronomy.

Bradley had distinguished himself early in his career by trying to gauge the distance to the stars. Although he failed to find the actual size of this gap, his efforts with a telescope twenty-four feet long provided the first hard evidence that the Earth really did move through space. As a result of this same failed attempt to measure stellar distances, Bradley arrived at a new, true value for the speed of light, improving on Ole Roemer’s earlier estimate. He also determined the shockingly large diameter of Jupiter, and detected tiny deviations in the tilt of the Earth’s axis, which he correctly blamed on the pull of the moon.

Once ensconced at Greenwich, Astronomer Royal Bradley, like Flamsteed and Halley before him, took the perfection of navigation as his primary mission. He out-Flamsteeded Flamsteed with his precision maps of the heavens—and his modest refusal of a raise in pay when it was offered to him.

The Paris Observatory, meanwhile, redoubled the efforts at Greenwich. Picking up where Halley had left off years earlier, French astronomer Nicolas Louis de Lacaille headed for the Cape of Good Hope in 1750. There he cataloged nearly two thousand southern stars over Africa. Lacaille left his brand on the skies of the nether hemisphere by defining several new constellations, and naming them after the great beasts of his own contemporary pantheon— Telescopium, Microscopium, Sextans (the Sextant), and Horologium (the Clock).

In this fashion, astronomers built one of the three pillars supporting the lunar distance method: They established the positions of the stars and studied the motion of the moon. Inventors had put up another pillar by giving sailors the means to measure the critical distances between the moon and the sun or other stars. All that remained for the refinement of the method were the detailed lunar tables that could translate the instrument readings into longitude positions. The creation of these lunar ephemerides turned out to be the hardest part of the problem. The complexities of the moon’s orbit thwarted progress in predicting lunar-solar and lunar-stellar distances.

Thus Bradley received with great interest the set of lunar tables compiled by a German mapmaker, Tobias Mayer, who claimed to have provided this missing link. Mayer thought he could lay claim to the longitude prize, too, which inspired him to send his idea, along with a new circular observing instrument, to Lord Anson of the English Admiralty, a member of the Board of Longitude. (This same George Anson, now first lord of the Admiralty, had commanded the Centurion on her dismal tour of the South Pacific between Cape Horn and Juan Fernandez Island in 1741.) Admiral Lord Anson turned the tables over to Bradley for evaluation.

Mayer, the mapmaker, worked in Göttingen, nailing down precise coordinates for the productions of the Homann Cartographic Bureau. He used, among his many tools, the eclipses of the moon and lunar occultations of the stars (that is, the predicted disappearance of certain stars as the moon moved in front of them). Although he focused on land maps, Mayer had to rely on the moon for fixing positions in time and space, just as a sailor would. And in the course of meeting his own needs for predicting the lunar positions, he grasped an advance that applied directly to the longitude problem; he created the first set of lunar tables for the moon’s location at twelve-hour intervals. He drew invaluable help in this enterprise from his four-year correspondence with the Swiss mathematician Leonhard Euler, who had reduced the relative movements of the sun, the Earth, and the moon to a series of elegant equations.

Bradley compared Mayer’s projections with hundreds of observations he took himself at Greenwich. The match excited him, because Mayer never missed an angular distance by more than 1.5 minutes of arc. This accuracy could mean finding longitude to within half a degree—and that was the magic number for the top prize stated in the Longitude Act. In 1757, the same year the manuscript tables came into his hands, Bradley arranged to have them tested at sea by Captain John Campbell aboard the Essex. The testing continued on subsequent voyages off the coast of Brittany, despite the Seven Years War, and the lunar distance method swelled with new promise. After the thirty-nine-year-old Mayer died of an infection in 1762, the board awarded his widow £3,000 in recognition of the work he had done. Another £300 went to Euler, for his founding theorems.

Thus the lunar distance method was propagated by individual investigators scattered all across the globe, each one doing his small part on a project of immense proportions. No wonder the technique assumed an air of planet-wide importance.

Even the difficulty of taking lunar distances, or lunars, as they came to be called, augmented their respectability. In addition to the need for measuring the altitudes of the various heavenly bodies and the angular distances between them, a navigator had to factor in the objects’ nearness to the horizon, where the steep refraction of light would put their apparent positions considerably above their actual positions. The navigator also battled the problem of lunar parallax, since the tables were formulated for an observer at the center of the Earth, while a ship rides the waves at about sea level, and the sailor on the quarterdeck might stand a good twenty feet higher than that. Such factors required rectifying by the appropriate calculations. Clearly, a man who mastered the mathematical manipulation of all this arcane information, while still keeping his sea legs, could justly congratulate himself.

The admirals and astronomers on the Board of Longitude openly endorsed the heroic lunar distance method, even in its formative stages, as the logical outgrowth of their own life experience with sea and sky. By the late 1750s the technique finally looked practicable, thanks to the cumulative efforts of the many contributors to this large-scale international enterprise.

In comparison, John Harrison offered the world a little ticking thing in a box. Preposterous!

Worse, this device of Harrison’s had all the complexity of the longitude problem already hardwired into its works. The user didn’t have to master math or astronomy or gain experience to make it go. Something unseemly attended the sea clock, in the eyes of scientists and celestial navigators. Something facile. Something flukish. In an earlier era, Harrison might have been accused of witchcraft for proposing such a magic-box solution. As it was, Harrison stood alone against the vested navigational interests of the scientific establishment. He became entrenched in this position by virtue of his own high standards and the high degree of skepticism expressed by his opponents. Instead of the accolades he might have expected for his achievements, he was to be subjected to many unpleasant trials that began after the completion of his masterpiece, the fourth timekeeper, H-4, in 1759.