by Dava Sobel
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 long
itude 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.
10.
The Diamond
Time keeper
The cabinet is formed of gold
And pearl and crystal shining bright,
And within it opens into a world
And a little lovely moony night.
—WILLIAM BLAKE, “The Crystal Cabinet”
Rome wasn’t built in a day, they say. Even a small part of Rome, the Sistine Chapel, took eight years to construct, plus another eleven years to decorate, with o Michelangelo sprawled atop his scaffolding from 1508 to 1512, frescoing scenes from the Old Testament on the ceiling. Fourteen years passed from the conception to the completion of the Statue of Liberty. The carving of the Mount Rushmore Monument likewise spanned a period of fourteen years. The Suez and Panama Canals each took about ten years to excavate, and it was arguably ten years from the decision to put a man on the moon to the successful landing of the Apollo lunar module.
It took John Harrison nineteen years to build H-3.
Historians and biographers cannot explain why Harrison—who turned out a turret clock in two years flat when he had scant experience to guide him, and who made two revolutionary sea clocks within nine years—should have lingered so long in the workshop with H-3. No one suggests that the workaholic Harrison dallied or became distracted. Indeed, there is evidence that he did nothing but work on H-3, almost to the detriment of his health and family, since the project kept him from pursuing most other gainful employment. Although he took on a few mundane clockmaking jobs to make ends meet, his recorded income during this period seems to have come entirely from the Board of Longitude, which granted him several extensions on his deadline and five payments of £500 each.
The Royal Society, which had been founded in the previous century as a prestigious scientific discussion group, rallied behind Harrison all through these trying years. His friend George Graham and other admiring members of the society insisted that Harrison leave his workbench long enough to accept the Copley Gold Medal on November 30, 1749. (Later recipients of the Copley Medal include Benjamin Franklin, Henry Cavendish, Joseph Priestley, Captain James Cook, Ernest Rutherford, and Albert Einstein.)
Harrison’s Royal Society supporters eventually followed the medal, which was the highest tribute they could confer, with an offer of Fellowship in the Society. This would have put the prestigious initials F.R.S. after his name. But Harrison declined. He asked that the membership be given to his son William instead. As Harrison must have known, Fellowship in the Royal Society is earned by scientific achievement; it cannot ordinarily be transferred, even to one’s next of kin, in the manner of a property deed. Nevertheless, William was duly elected to membership in his own right in 1765.
This sole surviving son of John Harrison took up his father’s cause. Though a child when the work on the sea clocks began, William passed through his teens and twenties in the company of H-3. He continued working faithfully with his father on the longitude timekeepers until he was forty-five years old, shepherding them through their trials and supporting the elder Harrison through his tribulations with the Board of Longitude.
As for the challenge of H-3, which contains 753 separate parts, the Harrisons seem to have taken it in stride. They never cursed the instrument or rued its long rule over their lives. In a retrospective review of his career milestones, John Harrison wrote of H-3 with gratitude for the hard lessons it taught him: “[H]ad it not been through some transactions I had with my third machine . . . and as to be so very weighty or so highly useful a matter or discovery and as never to be known or discovered without it . . . and worth all the money and time it cost viz my curious third machine.”
One of the innovations Harrison introduc
ed in H-3 can still be found today inside thermostats and other temperature-control devices. It is called, rather unpoetically, a bi-metallic strip. Like the gridiron pendulum, only better, the bi-metallic strip compensates immediately and automatically for any changes in temperature that could affect the clock’s going rate. Although Harrison had done away with the pendulum in his first two sea clocks, he had maintained gridirons in their works, combining brass and steel rods mounted near the balances to render the clocks immune to temperature changes. Now, with H-3, he produced this simplified, streamlined strip—of fine sheet brass and steel riveted together—to accomplish the same end.
A novel antifriction device that Harrison developed for H-3 also survives to the present day—in the caged ball bearings that smooth the operation of almost every machine with moving parts now in use.
H-3, the leanest of the sea clocks, weighs only sixty pounds—fifteen pounds less than H-1 and twenty-six pounds lighter than H-2. In place of the dumbbell-shaped bar balances with their five-pound brass balls at either end, H-3 runs on two large, circular balances, mounted one above the other, linked by metal ribbons, and controlled by a single spiral spring.
Harrison had been aiming for compactness, mindful of the cramped quarters in a captain’s cabin. He never considered trying to make a longitude watch to fit in the captain’s pocket, because everyone knew that a watch could not possibly achieve the same accuracy as a clock. H-3, svelte in its dimensions of two feet high and one foot wide, had gone about as far as a sea clock could go toward diminution when Harrison completed the bulk of the work on it in 1757. Although he still wasn’t altogether thrilled with its performance, Harrison deemed H-3 small enough to meet the definition of shipshape.
