The debate over the size and shape of the earth, which erupted in full force in the 1720s, resonated in particular with the French public. As the members of the French Academy of Sciences proudly wrote, this question had a long history and was so elemental that the intellectual progress of human civilization could be charted by following the steps that societies had made in solving it.
SCHOLARS IN ancient Greece and other early civilizations believed that the earth was flat, which is how it appears to the untutored eye. The idea that the earth might be a sphere, freely floating in space, was first advanced in the sixth century B.C. by the Greek philosopher Pythagoras. Aristotle subsequently provided evidence for this notion. The height of the sun, he noted, changed as one traveled north or south. And that could only be so, he pointed out, if one were traveling along a curve that altered one’s line of sight. He estimated that the earth’s circumference was 400,000 stades (about 40,000 miles).
Around 235 B.C., the Greek scholar Eratosthenes, who was head of the royal library in Alexandria, came up with a clever idea for actually calculating the earth’s size. He had heard that there was a well in the town of Syene where the sun cast no shadow at noon on the summer solstice. That meant that the sun must be directly overhead at that moment. Alexandria was thought to be located directly north of Syene, and in Alexandria, at noon on the summer solstice, the sun cast a shadow equal to one-fiftieth of a circle (7.2 degrees). The distance between the two cities was thus one-fiftieth of the earth’s circumference. Eratosthenes estimated the cities to be 5,000 stades apart—camel caravans traveling 100 stades a day took fifty days to travel from one city to the other—and thus he concluded that the earth’s circumference was 250,000 stades.
His was obviously a rough calculation. He could not be certain that Alexandria was located directly north of Syene, and his estimate of the distance between the two cities was little better than a guess. However, Eratosthenes had come up with a sound theoretical method for determining the earth’s size. First, measure the distance between two points along a north-south line, which is known as a meridian.* Next, measure the angle to the sun from each of the two points, which reveals how far apart those two points are in degrees. That is all the data needed to determine the earth’s size. Posidonius applied these principles in the first century B.C. and concluded that the earth’s circumference was 240,000 stades, a figure that the Greek geographer Strabo later revised to 180,000 stades (about 18,000 miles).
Ptolemy’s map of the world.
By permission of the British Library.
During the second century B.C., the Greek astronomer Hipparchus conceived of a method for mapping the earth. A globe could be divided into 360 degrees along its breadth and length, creating a grid of latitude and longitude lines. Lines of latitude would encircle the globe parallel to the equator, while lines of longitude would encircle the globe through the poles. Every place on earth could be located at the intersection of two lines. While Hipparchus’s idea was wonderfully elegant, it had its practical limitations. Angular measurements of the sun’s apparent position in the sky—how high it was above the horizon at a specific time and date—could be used to determine the latitude, or north-south position, of any point on the globe. Figuring out longitude was much more difficult. Hipparchus understood how, in theory, it could be done. The Greeks believed that the sun revolved around the earth once every twenty-four hours. Thus, the sun, in its westward march across the sky, crossed fifteen degrees of longitude every hour, or one degree every four minutes. To measure longitude, then, it would be necessary to compare time in two places at once. If the sun in one city was reaching its highest point in the sky at the same time that, in a city to the west, it was still four minutes shy of that position, then those two cities were located one degree of longitude apart. But how could such simultaneous measurements be made in the absence of an accurate portable clock? The Greeks kept time with sundials and hourglasses filled with sand, neither of which measured time with sufficient precision.
Even so, the principles for mapping cities and landmasses on a spherical globe were now understood, and in the second century A.D. Claudius Ptolemy used them to create a world atlas. He relied on the reports of travelers to locate cities by latitude and a guessed-at longitude; to plot distances, he used Strabo’s revised estimate of Posidonius’s calculations of the earth’s circumference. His decision to trust Strabo rather than Posidonius was a fateful one: Many centuries later, it would dramatically alter world history.
AS THE ROMAN EMPIRE fell in the fifth century A.D. and Christianity took hold, Ptolemy’s map and much of the knowledge underlying it was lost to Europe. Early Christian writers warned of the dangers of being too curious and scoffed at the notion that the earth was a sphere. In the sixth century, a monk in Alexandria, Cosmas Indicopleustes, drew the first Christian map. He took his inspiration from Saint Paul’s declaration that the Tabernacle, a tent used as a portable house of worship, was a model of the world. His drawing showed the earth to be a conelike mountain inside a rectangular box that looked like a trunk. Other Christian maps of the Middle Ages depicted an earth in the shape of Christ’s body (the rivers of the world were his veins), or as a flat disc with Jerusalem at the center. Such maps were often illustrated with scenes from the Bible and ancient fables, which many people took to be literally true. The medieval world was one in which dolphins leapt over the mainsails of ships, flying crocodiles had breath so foul it could kill, and African ants were as big as mastiffs. Travelers to foreign lands were likely to encounter horse-footed men, men with only one leg but a foot large enough to be used as a parasol, and men with drooping ears that covered their bodies, eliminating the need for clothing.
A medieval Christian map with Jerusalem at the center of the world.
By permission of the British Library.
The arrival of the compass in Mediterranean lands in the twelfth century brought about the demise of Christian flat-earth beliefs. This navigational device triggered an explosion in maritime exploration, and soon European sailors were drawing up sea charts with compass lines, maps that fit not at all with the medieval ones drawn to reflect religious teachings. In 1472, a printing of Ptolemy’s map appeared in Europe, putting longitude and latitude lines back onto the world’s atlas.
Based on maps like this one by Henricus Martellus in 1488, it seemed feasible to reach Asia by sailing west from Europe.
By permission of the British Library.
Europe’s rediscovery of Ptolemy’s work raised an intriguing question: Would it be possible to sail west from Europe and reach the Far East, with its lucrative spice and silk trade, in a reasonable time? Ptolemy, relying on Strabo, had pegged the earth’s circumference at around 18,000 miles, and fifteenth-century maps did not differ greatly from that figure. If that were true, Christopher Columbus reasoned, then it should be only 2,400 nautical miles from the Canary Islands to Japan. When he struck land at about that distance, he naturally assumed the islands were near the Asian continent.
Once it became clear that Columbus had stumbled upon a New World, the question of the earth’s size became of paramount importance. The world was clearly bigger than anyone had thought, but how much bigger? All of the European powers were sending out trading ships to distant lands and the best cartographers of the day were scrambling to draw new maps, and yet the earth’s size was not even roughly known. “Plato, Aristotle, and the old philosophers made progress, and Ptolemy added a great deal more,” wrote Jean Fernel, physician to the king of France. “Yet, were one of them to return today, he would find geography changed beyond recognition. A new globe has been given to us by the navigators of our time.” In 1525, Fernel attempted to measure its size, reviving a scientific quest that had been neglected for more than 1,500 years. To measure one degree of latitude, Fernel traveled in his coach from Paris to Amiens and used the wheels of his coach as an odometer. He counted 17,024 revolutions of the wheel during the journey and then multiplied this number by the wheel’s
circumference to determine the distance between the two cities, which were roughly located on a north-south meridian. After using a quadrant to determine the latitude of each city, he concluded that a degree of arc was sixty-three miles.*
The limitations of his method were evident. The road he traveled went up and down hills and certainly did not follow a perfectly straight line. A few years later, a Dutch mathematician, Gemma Frisius, proposed a more scientific method for measuring land distances—triangulation. His idea took advantage of the powers of trigonometry. An initial baseline of several miles could be measured; this line would serve as the first side of the first triangle. The angles from the baseline’s two endpoints to a distant third point could then be determined. After these measurements, the surveyors would know both the length of one side of the triangle and all of its angles, and with that information in hand, they could mathematically calculate the lengths of the triangle’s other two sides. By repeating this process a number of times, longer distances could be measured with a fair degree of precision.*
Nearly a century later, the Dutch astronomer Willebrord Snell finally put Frisius’s idea to work. In 1615, he marked off thirty-three interconnecting triangles across the frozen meadows separating Alkmaar from Bergen op Zoom, a distance of eighty miles. He then found that these two points were 1.19 degrees apart in latitude, and thus he concluded that one degree of arc was sixty-seven miles. Soon a London mathematician, Richard Norwood, improved on Snell’s effort by using a surveyor’s chain to measure the baseline more precisely (the critical first step in the triangulation process). In 1635, he reported that a degree of arc was 69.5 miles. Next, an Italian group weighed in with a finding that suggested Norwood’s calculation was too small—the earth’s circumference was larger still by another 10 percent. The science of geodesy—the study of the earth’s size and shape—was coming into its own as a recognized discipline, even if scientists were not coming up with quite the same answers.
The daunting problem of determining longitude, which had been at the top of every king’s wish list since the New World had been discovered, was also coming close to being solved. The Greeks had realized that determining longitude would require comparing local times at two different places at the same moment, and in 1616, Italian astronomer Galileo Galelei came up with a proposal for doing just that. Jupiter’s satellites, he discovered, could be used as a celestial timepiece. Galileo, who had been training a telescope on Jupiter every night for six years, had painstakingly composed tables charting the orbits of its four moons, which would rhythmically disappear on one side of the planet and then reappear on the other. Because this movement could be predicted from his charts, the eclipse of the moons could serve as a celestial signal that would enable observers in two different places to check local times at precisely the same instant. Galileo’s tables could provide the local time at his laboratory for an observed eclipse, and observers elsewhere could calculate how far east or west they were of Galileo’s laboratory based on the difference in their local time from Galileo’s. Every four minutes of difference in local time would equal one degree of difference in longitude.
Galileo’s idea was not immediately recognized for the brilliant solution that it was. In 1598, King Philip III of Spain had offered a huge reward to the “discoverer of longitude,” a prize that had drawn a flood of crank ideas, causing Galileo’s proposal, sent to the Spanish monarch in 1616, to initially fall on deaf ears. By that time, the king and his court had lost faith that the problem was ever going to be solved. In 1632, a frustrated Galileo brought his idea to the Dutch, who took another decade to fully embrace it. But even then, there remained a secondary problem that needed to be solved before his method could be put to good use: How could observers accurately determine local times at night, when the moons of Jupiter would be visible? Local time could be set by close observation of the sun, but even the best mechanical watches of the early sixteenth century lost or gained fifteen minutes every twenty-four hours. In 1657, Dutch mathematician Christiaan Huygens developed the needed timepiece—a pendulum clock. His wondrous invention relied on gravity to beat out time, each swing of the pendulum precisely ticking off one second.
Nearly 2,000 years after Eratosthenes had first sought to measure the earth, the stage was set for cartography to be transformed from an art into a science, a challenge that King Louis XIV of France, in 1666, agreed to take on.
THE FRENCH ACADEMY OF SCIENCES, which held its first meeting on December 22, 1666, was the brainchild of Jean-Baptiste Colbert, the king’s minister of finance. He convinced Louis XIV that gathering scientists together into an academy and providing them with salaries and funds for their experiments would bring both glory and commercial benefits to the Crown. The academy could be expected to produce improvements in mapmaking and navigation that would give France an advantage in trading and warfare.
Christiaan Huygens’s diagram of his pendulum clock.
By permission of the British Library.
With the king’s blessing, Colbert extended his recruitment efforts beyond France. In an age when European monarchs were constantly waging war, fighting over distant territories and trade routes, Colbert boldly made the French Academy of Sciences an international group, recruiting astronomers, mathematicians, and geographers from Germany, Italy, and Holland. He hired Huygens, a Dutchman, to help direct it and gave him a princely salary of 6,000 livres. He plucked Italian astronomer Gian Domenico Cassini, whose fame rested on his study of Jupiter’s moons, away from the University of Bologna with a similarly rich offer. Cassini moved his family into a grand observatory that the academy was building outside Paris, an arrangement that so pleased him he changed his name to Jean-Dominique Cassini in honor of his adopted country.
The academy made drawing an accurate map of France its first priority. To begin this task, the academy asked French astronomer Jean Picard to newly determine the earth’s circumference. Picard used varnished wooden rods to carefully stake out a seven-mile baseline between Paris and Fontainebleau, and he employed a quadrant equipped with two telescopes to lay out a precise grid of thirteen triangles from Paris to Amiens. He utilized both solar and celestial observations to determine the latitudes of the endpoints on his north-south meridian, and after two years of painstaking labor, he reported that a degree of arc was 57,060 toises (a French unit of measurement), or 69.1 miles.
Galileo’s idea of using Jupiter’s moons as a celestial timepiece to determine the longitude of various places could now be put to the test. This effort was led by Cassini, and after nearly a decade of work, the academy unveiled a startling new map of France. Some cities had moved more than 100 miles, and the country’s coastline had shifted 1.5 degrees closer to Paris. Along its southern border, the coastline had jumped thirty-five miles to the north. France had noticeably shrunk, prompting King Louis XIV, upon being shown the map on May 1, 1682, to lament that the academy’s work “has cost me a major portion of my realm.”
Jean Picard’s measurement of a degree of latitude.
By permission of the British Library.
First France, then the world. Data began pouring into the Paris observatory from astronomers throughout Europe, who utilized Cassini’s tables of Jupiter’s moons and newly made pendulum clocks to make their observations. Jesuit missionaries fanning out to the Far East were outfitted with instruments and trained by the academy so that they too could send in longitude and latitude data. Cassini turned all this information into a huge world map, twenty-four feet in diameter, that mesmerized those who saw it. The boundaries between European kingdoms had been redrawn, the Mediterranean coastline had a new shape, and the distant continent of Asia was snapping into focus.
The Paris Observatory.
By permission of the British Library.
At the turn of the century, Cassini and his son Jacques initiated yet another grand project, one that involved building on Picard’s earlier triangulation work. Picard had measured a distance along a north-south meridian in the vicini
ty of Paris. The Cassinis decided that they would extend this triangulation across all of France. By doing so, they would further refine the academy’s measurement of the earth’s circumference, and they would also be able to address a nagging question about the earth’s shape: Was it a perfect sphere?
Ever since Galileo’s time, astronomers focusing their telescopes on Jupiter had noticed that it was flattened at the poles. That observation led to speculation that perhaps the earth was similarly shaped, and then reports began coming into the academy about the strange behavior of the pendulum clock at diverse locations. In 1672, the academy had sent Jean Richer to Cayenne, on the northern coast of South America, where he had found that a pendulum clock that was accurate in Paris lost two minutes, twenty-eight seconds each day. In order to make the clock keep accurate time in Cayenne, Richer had needed to shorten the pendulum by one-twelfth of an inch. Although gravity was not yet understood, Richer’s experiment indicated that its force was not equal at all points on the globe, suggesting that something was indeed amiss with the earth’s shape. And if the earth was not a perfect sphere, then the length of one degree of latitude—as one moved north or south along a meridian line—should change ever so slightly.
The Cassinis began their work in the south of France, where they found a degree of arc to be 57,097 toises (69.2 miles). This was thirty-seven toises—237 feet—longer than Picard’s arc in Paris. Although far from conclusive, “the success of this work gave us room to conjecture that the degrees of the meridian increase as they approach the equator; whence it results that the earth is prolonged toward the poles,” Jacques Cassini wrote. Over the next eighteen years, the academy extended its triangulation across eight degrees of latitude, a distance of more than 550 miles. This work proceeded fitfully, interrupted by the War of the Spanish Succession and Jean Cassini’s death in 1712, but it produced data consistent with the first observations made in the south. A degree of arc in the north of France was only 56,960 toises, nearly 140 toises shorter than an arc in the southern part of the country. Each degree of latitude apparently increased by fifteen toises or so as one moved toward the equator, and the conclusion to be drawn from this was clear. The earth, Jacques Cassini flatly declared in a 1718 presentation to the academy, was a “prolate spheroid”—elongated at the poles and cinched in at the equator.*
The Mapmaker's Wife: A True Tale of Love, Murder, and Survival in the Amazon Page 2