Coming of Age in the Milky Way

by Timothy Ferris

  Two ways of obtaining distance data were available. One, micrometry, was theoretically crude but practically accessible. The other, triangulation, was perfect in theory but difficult to accomplish in practice.

  Micrometry consisted of using a micrometer—an eyepiece equipped with an adjustable knife blade—to measure the apparent diameter of a planet as seen through a telescope. The astronomer then estimated the distance of a planet by comparing its apparent diameter with what he guessed to be its actual diameter. Obviously, the result could be no better than the guess as to the planet’s diameter. A few astronomers guessed very well indeed: Christian Huygens in 1659 assumed that the diameter of Mars was about 60 percent that of the earth (the correct figure is 53 percent), then measured the apparent size of the disk of Mars through a telescope and calculated a value for the astronomical unit of one hundred million miles. This came astonishingly close to the truth—the mean distance separating the earth from the sun is ninety-three million miles—but it depended entirely upon the accuracy of Huygens’s hunch about the size of Mars, and that, as Huygens himself was the first to concede, was “a slippery basis” upon which to base so important a result.1 The issue was not who made the luckiest guess, but who could obtain observational data that would establish the value of the astronomical unit to everyone’s satisfaction. This micrometry alone could not do.

  Triangulation, called parallax (from the Greek parallaxis, for the value of an angle), was the sounder method. If a planet were observed simultaneously by two observers stationed thousands of miles apart—one in France, say, and the other in Mexico—its position against the background stars would appear to be slightly altered for the astronomer in Mexico as compared to the one in France, owing to their different perspectives on it. If both this angle and the baseline distance separating the two astronomers could be measured, the distance to the planet could be calculated through the straightforward application of euclidean geometry.

  That triangulation was theoretically sound had been appreciated since ancient times. The difficulty lay in execution. First, one had to know the exact distance between two widely separated observers; this required reasonably accurate intercontinental maps. Second, the observations had to be carried out at the same time, to avoid errors introduced by the motions of the planets and by the rotation of the earth on its axis; this required accurate clocks and a way of synchronizing them. Third, the position of the planet against the stars had to be plotted precisely, because any triangle drawn between a planet and two points on Earth is going to be a very long, thin triangle indeed. Still, the thing could be done, given sufficient exactitude in the measurement of terrestrial space and time.

  The parallax of Mars was first obtained by simultaneously observing the planet’s apparent location from two widely separated places on Earth. The difference in perspective made it possible to measure the value of angle X, which yields the distance from Earth to Mars. The angle, however, is small: Were the earth the size depicted in this illustration, Mars would be five hundred feet away.

  The parallax of stars can best be measured by using as a baseline not the earth but the earth’s orbit around the sun. Even with so large a baseline, however, angle X is extremely small: Were the earth’s orbit the size here depicted, the nearest star would be more than two miles away.

  Fortunately for science, rapid progress was being made in both cartography and chronometry. The agency responsible, however, was less the pursuit of pure knowledge than the accumulation of the booty of empire. The wealth of the world flowed into eighteenth-century Europe in ships: From their holds came the Indian rosewood of the dining tables where Newton and Halley were entertained, the African gold inlay on the plates, the turkey with corn they were served as the main course, the chocolate for dessert, and the tobacco they smoked afterward. But blue-water navigation was as hazardous as it was inexact, and sailors who ventured far beyond the sight of land were forever groping their way in the unknown—they were “at sea,” as we still say today—with results that ranged from delay to disaster. Many a cargo of silver, sugar, or hardwood had been conveyed across the Atlantic or Indian oceans only to be dashed against the rocks of Land’s End or the Cape of Good Hope. The situation had improved little in the century that had passed since the geographer Richard Hakluyt wrote of navigators that “no kind of men in any profession in the commonwealth pass their years in so great and continual hazard of life. … Of so many, so few grow to gray hairs.”2 The definitive catastrophe came in 1707, when Sir Cloudesley Shovell, four ships of his fleet, and fully two thousand of his men were lost on the rocks of the Scilly Islands of southwest England, this on a night when his navigators had reckoned that the fleet was in safe waters hundreds of miles to the west. Clearly, something had to be done.

  The problem had to do with the determination of longitude. It had long been possible for a ship’s navigator to find his latitude—his location in a north-south direction—by measuring the altitude above the horizon of the pole star or of the sun at noon. The instrument employed for this purpose was the astrolabe (from the Greek for “to take a star”), a disk made of copper or tin, five to seven inches in diameter, fitted with a movable sighting arm. At local noon on any clear day aboard a ship of the line, three officers could be seen helping to shoot the sun—one holding the astrolabe steady, another sighting it, and a third reading the elevation—while deckhands stood by to catch the navigator when he fell or to retrieve the astrolabe if it were dropped and went scuttling across the rolling deck. The efficiency of the astrolabe had been improving, through the endeavors of Newton, Halley, John Hadley, Thomas Godfrey, and others, who made the instrument less cumbersome by reducing it first to a quarter of a circle (the “quadrant”), then to a sixth (the “sextant”), by employing mirrors to fold its optics so that the observer could see sun and horizon superimposed, and by adding filters and a telescope for greater accuracy. But, although these improvements helped navigators refine their calculations of latitude, they did not help them determine their longitude—their position in the east-west direction. Here the question was as much one of time as of space.

  As the earth turns, the stars troop across the sky at a rate of fifteen degrees per hour. This means that if you know the time, the sky will tell you where you are. But knowledge of the exact time was just what navigators of Newton’s day lacked. On land, time was kept by pendulum clocks, but pendulums do not work at sea; the rolling of the boat wrecks their performance. A typical ship’s clock in the early eighteenth century was accurate to no better than five or ten minutes per day, which translated into a miscalculation of fully five hundred miles in longitude after only ten days at sea. It was just such an error that had dashed Cloudesley Shovell’s fleet on the rocks of the Scilly Islands.

  The problem of determining longitude at sea had defied resolution for so long that many regarded it as unsolvable. The mathematician in Cervantes’s The Dog’s Dialog muses crazily that he has “spent twenty-two years searching for the fixed point”— el punto fijo, the correct longitude—“and here it leaves me, and there I have it, and when it seems I really have it and it cannot possibly escape me, then, when I am not looking, I find myself so far away again that I am astonished. The same thing happens with squaring the circle.”3 Sebastian Cabot on his deathbed claimed that God had revealed the answer to him, but added, alas, that He had also sworn him to secrecy.

  Still, the longitude problem was obviously imperative, and more than a few inventors took it on, encouraged by the large cash prizes proffered by the governments of seafaring states like Spain, Portugal, Venice, Holland, and England. The richest of these was a prize of twenty thousand pounds, offered by the British Board of Longitude to anyone who could devise a practicable method of determining longitude on a transatlantic crossing to within one-half a degree, which equals sixty-three nautical miles at the latitude of London. John Harrison, an uneducated carpenter turned clock-maker, pursued the prize for much of his working life. He constructed a succession o
f “watches” (the term, meaning a portable clock, comes from the shipboard practice of dividing up the day into six watches of four hours each) of increasingly subtle and rugged design, checking them for accuracy by observing the disappearance of designated stars behind a neighbor’s chimney each night. His masterpiece, a marine chronometer that took him nineteen years to complete, was transported to Port Royal, Jamaica, aboard H.M.S. Deptford in 1761–1762, was there tested against sightings of the sun, and was found to have lost only 5.1 seconds in eighty days—a performance that many of today’s timepieces could not match. Nonetheless, it took Harrison years of lobbying to collect a portion of the prize, and he never got it all; twenty thousand pounds was a lot of money.

  The astronomers and geographers, however, did not have to wait as long as did the mariners to improve their measurements of earthly space and time. Maps were constantly improving: Although pendulum clocks were not yet reliable at sea, they could be synchronized on land, by observing transits and eclipses of the satellites of Jupiter. (The Dutch had awarded Galileo a gold chain for proposing this ingenious idea, though they could not make it work on board ship, since any telescopic magnification sufficient to resolve Jupiter’s moons also magnified the rocking of the boat too much for the planet to be kept in view.) In France, cartographers led by Giovanni Cassini and Jean Picard employed Galileo’s method to cage the continent in a cat’s cradle of surveyor’s triangles, producing an accurate map that enabled Picard to determine the circumference of the earth to within 126 miles of the correct value.*

  Equipped with better maps and clocks, astronomers tried to triangulate the neighboring planets Mars and Venus. In 1672, an international expedition led by the young French astronomer Jean Richer sailed to Cayenne, on the South American seacoast three hundred miles north of the equator. There he observed Mars during its closest approach to Earth at the same time that his colleagues, their clocks synchronized to Richer’s, sighted Mars from their post at the French Academy. Cassini sorted through the data and derived a value for the astronomical unit of eighty-seven million miles. This approximated the correct figure of ninety-three million miles, but given the many residual inaccuracies of the instruments and techniques of the time, Cassini’s like Huygens’s earlier estimate necessarily was regarded as but an educated guess.

  Venus comes closer to Earth than does Mars, and so should be still more accessible to triangulation, but when closest it is lost in the glare of the sun. Twice in a long while, however, in pairs of events separated by just over a century, Venus passes directly in front of the sun. During these transits, as they are called, the planet appears as a black circle silhouetted against the blazing solar disk. Edmond Halley, who had observed a transit of Mercury during his expedition to St. Helena, realized that the distance to Venus might be determined by timing, from widely separated stations, exactly when the planet appeared and disappeared from the face of the sun. The edge of the sun would serve as a clearly defined backdrop, the planet as a kind of surveyor’s stake out in space.

  Halley knew that he would not live to observe a transit of Venus. There had been a pair of transits in 1631 and 1639, a generation before he was born; the next pair were due in 1761 and 1769, by which time he would have been over a hundred years old.* (Halley must have been getting used to this sort of thing; he didn’t live to see the return of Halley’s Comet, either.) And so it was with the insistence of a man striving to project his words beyond the grave that Halley, in a paper published in 1716 “which,” he wrote, “I prophecy will be immortal,” outlined the procedure for the benefit of astronomers yet unborn:

  We therefore recommend again and again, to the curious investigators of the stars to whom, when our lives are over, these observations are entrusted, that they, mindful of our advice, apply themselves to the undertaking of these observations vigorously. And for them we desire and pray for all good luck, especially that they not be deprived of this coveted spectacle by the unfortunate obscuration of cloudy heavens, and that the immensities of the celestial spheres, compelled to more precise boundaries, may at last yield to their glory and eternal fame.4

  Previous observations of transits had been rare and rather haphazard. Pierre Gassendi in Paris managed to observe a transit of Mercury in 1631 that Kepler had predicted; he stamped on the floor to alert his young assistant to measure the altitude of the sun, but the boy, growing impatient after three days of waiting for the great event, had wandered off. Gassendi’s solitary published observation was useless for triangulation, though it did reveal that the disk of Mercury was much smaller than had been thought: “I could hardly be persuaded that it was Mercury, so much was I preoccupied by the expectation of a greater size,”5 Gassendi wrote. This supported the contention of Galileo that the solar system was considerably larger than had been estimated by Ptolemy and the other geocentrists.

  As for Venus, its transit on December 6–7, 1631, was visible only from the New World and appears to have been viewed by not a single human being, and the transit of November 24, 1639, was observed by but two people, the English astronomer and clergyman Jeremiah Horrocks and his friend William Crabtree. Alarmingly for Horrocks, who was a clergyman, the transit occurred on a Sunday, when he was obliged to preach two sermons. He rushed home from church, peered through his telescope at 3:15 P.M., and saw Venus, “the object of my most sanguine wishes … just wholly entered upon the Sun’s disk.”6 Venus, like Mercury, looked smaller than had been predicted—Kepler thought Venus would cover one quarter of the sun, an enormous overestimate—and so to behold its tiny apparent size helped improve human appreciation of interplanetary distances. But Horrocks had no way to measure the apparent diameter of the disk precisely, and, since he was but one observer, he could not have triangulated Venus even if he had possessed an accurate clock. Crabtree, for his part, was so overwhelmed by the sight of an entire world dwarfed by the sun that he made no coherent notes at all, prompting Horrocks to protest that “we astronomers have a certain … disposition [to be] distractedly delighted with light and trifling circumstances.”7

  But the world had changed by the time the transits of Venus of 1761 and 1769 came due. Astronomy had become an organized science, conducted by professionals, sponsored by scientific societies, and supported by government funds. Now at last, it was felt, science had the resources to sound the dimensions of the solar system. Halley’s implorations were remembered, and the transits were scrutinized by scores of observers equipped with micrometers, accurate clocks, and brass telescopes mounted on hardwood tripods at sites as far away as Siberia, South Africa, Mexico, and the South Pacific.

  And, to an extent, the transit observers succeeded, though not without suffering sufficient tribulations to remind them that while the motions of the planets may be sublime the affairs of this world are marbled with chaos. The astronomer Charles Mason and the surveyor Jeremiah Dixon, later of the Mason-Dixon Line, were attacked by a French frigate while making their way to Africa (this was during the Seven Years’ War) with a loss of eleven dead and thirty-seven wounded; they reached Cape Town under military escort and observed the 1761 transit, only to find that they differed by many seconds in their estimate of the time when Venus had entered and left the disk of the sun. William Wales timed the transit from Hudson Bay, Canada, after enduring mosquitoes, horseflies, and a winter sufficiently severe that, as he noted with empirical exactitude, a half-pint of brandy left unattended iced over in only five minutes. Jean-Baptiste Chappe d’Auteroche, dispatched by the French Academy into the depths of Russia, raced across the frozen Volga and through Siberian forests in horse-drawn sleds, arrived at Tobolsk six days prior to the transit, posted guards to repel angry mobs who blamed him for causing spring floods by interfering with the sun, and managed to observe the transit. He died eight years later in Baja California after timing the 1769 transit, of an epidemic that spared but one member of his party, who dutifully returned his data to Paris. Alexandre-Gui Pingré was rained out for most of the transit in Madagascar, lost his s
hip to the British and was returned to Lisbon under British guns; a humanist as well as a scientist, he took comfort in the ship’s rations of spirits: “Liquor,” he wrote, “gives us the necessary strength for determining the distance of … the sun.”8

  Least fortunate of all was Guillaume le Gentil, who sailed from France on March 26, 1760, planning to observe the transit the following year from the east coast of India. Monsoons blew his ship off course, and transit day found him becalmed in the middle of the Indian Ocean, unable to make any useful observations. Determined to redeem the expedition by observing the second transit, Le Gentil booked passage to India, built an observatory atop an obsolete powder magazine in Pondicherry, and waited. The sky remained marvelously clear throughout May, only to cloud over on June 4, the morning of the transit, then clear again as soon as the transit was over. Wrote Le Gentil:

  I was more than two weeks in a singular dejection and almost did not have the courage to take up my pen to continue my journal; and several times it fell from my hands, when the moment came to report to France the fate of my operations…. This is the fate which often awaits astronomers. I had gone more than ten thousand leagues; it seemed that I had crossed such a great expanse of seas, exiling myself from my native land, only to be the spectator of a fatal cloud which came to place itself before the sun at the precise moment of my observation, to carry off from me the fruits of my pains and of my fatigues.9