The Mapmaker's Wife (5 page)

The Cartesian vortices. The circle in the center of each vortex represents a sun.

From René Descartes
, Principles of Philosophy
(1644). Edgar Fahs Smith Collection, University of Pennsylvania Library

Across the English Channel, Sir Isaac Newton was in partial agreement with Descartes: He too believed that science should search for a mechanical explanation of the universe. However, his inquiries and mathematical brilliance led him to a different model, one that followed Kepler’s notion of “attraction at a distance.” By his twenty-fourth birthday, in 1666, Newton had deduced a mathematical formula for gravity. The attraction between two bodies, he concluded, is directly proportional to the product of their masses and indirectly proportional to the square of the distance between their centers. Thus the tug of gravity at the earth’s surface is sixty-four times stronger than it is at a place eight times further from the earth’s center. However, when Newton applied his theory to the moon’s movements, the numbers did not quite add up. At that time, English sea charts—whose authors were apparently unaware of the arc measurements made by Snell and Norwood fifty years earlier—stated that one degree of latitude was only sixty miles, and if that were so, the earth was too small to exert a sufficient gravitational pull to keep the moon in its orbit. This led the baffled Newton, a historian later wrote,
“to entertain a notion that together with the force of gravity there might be a mixture of that force which the moon would have if it was carried along in a vortex.” In other words, perhaps Descartes was partly right.

Newton’s doubts about his theory of gravity disappeared in 1682 after he came upon Picard’s updated estimate for the size of the earth. Once he plugged in 24,714 miles for the earth’s circumference, his formula for gravity worked almost perfectly.
“How these Attractions (between bodies) may be perform’d, I do not here consider,” he wrote in his masterpiece,
Principia
. “What I call Attraction may be perform’d by impulse, or by some other means unknown to me. I use that Word here to signify only in general any force by which bodies tend towards one another, whatsoever be the Cause.”

In
Principia
, Newton specifically attacked Descartes’s vortex theory, pointing the French to their own experiments as proof that Descartes was wrong. The fact that Richer’s pendulum clock beat slower in Cayenne was evidence that gravitational pull at the equator
was less than it was in Paris, which in turn was evidence that the earth bulged at the equator—the clock was further away from the earth’s center. And the reason the earth bulged at the equator was because it rotated on its axis, which created a stronger centrifugal force at the equator than at the poles.
^*
The same physics, Newton argued, had turned Jupiter into a similar oblate shape. In Book III of
Principia
, Newton summed up his challenge to French beliefs, proclaiming—as Proposition 18, Theorem 16—that
“the axes of the planets are less than the diameters drawn perpendicular to the axes.” By his calculation, this ratio of axis to diameter should be 229 to 230.

At first, Newton’s work did not cause much of a stir in France. England and France were constantly at war during this period, which diminished the exchange of scientific information, and the Newtonian ideas that did filter into Paris had to compete with a variety of other ponderings on the earth’s shape. In 1691, Samuel Eisenschmidt, a famous astronomer from Strasbourg, concluded in his
Treatise of the Figure of the Earth
that the earth was a
“spheroid prolonged toward the poles,” similar to what the French believed. Thomas Burnet, an Englishman, published his
Sacred Theory of the Earth
shortly afterward, and he agreed with Eisenschmidt. Such differing theories subsequently served as a catalyst for the academy’s measurement of a meridian throughout the whole of France, but that lengthy effort—as Cassini happily reported in 1718—proved that Newton was wrong.

Nor were the academy members swayed by the supporting bits of evidence that Newton had called upon. The fact that Jupiter was flattened at the poles was not seen as particularly relevant. The physics that governed the “supralunar” world—the heavens beyond the moon—were not believed to be the same as those that
governed the sublunar world of the earth and its orbiting satellite. This distinction between supralunar and sublunar realms went all the way back to the Greeks. The academy members also had an explanation for Richer’s pendulum experiment. Differences in temperature that led metal to shrink or expand were thought to be at fault. Either that, or poor work on Richer’s part:
“It is suspected that this resulted from some error in the observations,” Cassini sniffed. Even more telling, Newton was at a loss to offer a mechanical explanation for how this force of gravity might work. The Cartesians had developed a rational, understandable explanation for the universe: a fluidlike ether that
pushed
on orbiting planets. All Newton had come up with was a mathematical formula, one that seemed to require the invisible hand of God, reaching across vast regions. The idea of attraction at such distances, Huygens wrote in a letter to Newton, was
“absurd.”

Indeed, if one wanted to know the shape of the earth, and one had to choose between the concrete measurements of the French and the obscure mathematics of an Englishman, how could anyone doubt which presented a stronger case?
“It is obvious,” Fontenelle declared, “that the current measurements, which are the refinement of Cassini’s work, must be preferred to the result of geometrical theories based on a very small number of very simple assumptions, which are isolated from all the complications of physics and reality.” Even the great Belgian mathematician, Johann Bernoulli, complained that Newton’s theories relating to the shape of the earth were little better than
“gibberish.” “I tried to understand it,” he wrote in a letter to one of his students. “I read and reread what he had to say concerning the subject, but I could not understand a thing. All I found was obscurity and impenetrability.”

Yet Newtonian physics would not go away. In 1713, France, England, and Holland signed the Treaty of Utrecht, which brought an end to the War of the Spanish Succession and ushered in a thirty-year period of peace that encouraged the sharing of scientific ideas throughout Europe. Huguenots living in England helped
speed this intellectual exchange. More than 200,000 French Protestants had fled France following a 1685 edict that deemed Protestantism heretical, and they busily published works in French that were designed to open up Catholic France to outside influences. In 1725, John Theophilus Desaguliers, a Huguenot refugee and experimental physicist, took up the Newtonian cause by publishing a blistering critique of Cassini’s measurements in the
Philosophical Transactions
of the Royal Society of London. He dismissed Cassini’s work as so sloppily done that it could not possibly raise questions about the elegant theories of Newton. Debate over the shape of the earth and Newtonian physics had moved to center stage in European science. It was the first topic discussed at the inaugural meeting of the Russian Academy of Sciences in 1725, and the argument there turned so vitriolic that in 1729 the minutes of the academy had to be expunged, lest the members be embarrassed by a record of their outbursts.

Dissension began to surface within the French Academy as well. The revolt against Cartesian doctrine was led by a young mathematician with a sharp tongue, Pierre-Louis Moreau de Maupertuis. He had visited London in the spring of 1728 and had returned convinced that Cartesian cosmology, with its swirling particles pushing the planets along, was not just wrong but
dumb
. The twice-weekly meetings of the French Academy of Sciences were ordinarily quite civil affairs, but Maupertuis, as one historian wrote,
“badgered, intimidated, cajoled, coerced, and ridiculed the Cartesians in the Academy,” gleefully attacking their mathematics as being tedious and incomprehensible. Although Maupertuis may have wounded the sensibilities of many, a number of the younger members were drawn to his side, including Alexis-Claude Clairaut, a child prodigy in math who had been elected to the academy at age eighteen. Maupertuis elaborated on Newtonian physics in a 1732 paper, “Discours sur les différentes figures des astres,” and Clairaut followed with papers criticizing Cassini’s measurements. It all led an infuriated Fontenelle to cry out in protest. Why did Maupertuis and his band of rebels want to
“justify the English at the expense of
the French?” he complained.
“Who would have ever thought it necessary to pray to Heaven to preserve Frenchmen from a too favorable bias for an incomprehensible system, they who love clarity so dearly, and for a System originating in a foreign land, they who have been charged with loving only that which is their own?”

There was much at stake for Fontenelle, Cassini, and the rest of the academy’s older members. Their life’s work and the reputation of French science were at risk. The academy had long embraced Cartesian physics, all the way back to the mid-1600s when Descartes’s writings were officially banned as heretical, and it was only now—in 1733—that the Jesuits were finally beginning to teach Descartes’s doctrine. The academy had made measurement of the earth’s size and shape a priority since it had first opened its doors, and it had spent a half-century on that effort, which had come to an apparently successful conclusion in 1718. The triumphs of the past would fall apart if Newton were right.

Voltaire was soon to discover just how touchy the country was on the subject. He had lived in England from 1726 to 1729, exiled from Paris for his usual needling of all things French, and there he had become an ardent disciple of Newton. He had written a series of letters on English society and Newtonian physics, which were published in England to good reviews. However, when a French version of his writings, titled
Lettres philosophiques
, appeared in Paris in 1734, authorities ordered that the book,
“being scandalous, and offensive to religion, good morals and the respect owed to the State, should be burned by the executioner, at the foot of the great stairway.” Pamphlets appeared charging Voltaire with defamation and degradation of his own people, a warrant was issued for his arrest, and he was forced to flee to Cirey in Champagne, where he holed up in the chateau of a beautiful woman, Madame Gabrielle-Émilie du Châtelet.
“Apparently a poor Frenchman is not allowed to express his belief in the proven existence of a gravitational force, or of a vacuum in space, or that the earth is flat at the poles, and that Descartes’ theory is absurd,” he bitterly complained in a letter to Maupertuis. Cassini and the other old fogies in the academy, he
added, had
“this senseless and ridiculous phantom, the vortices, haunting their erudite heads.”

The rancorous debate swept up everyone in the academy. As one eighteenth-century scholar wrote, it occupied the minds of the
“most eminent geniuses of Europe.” Pierre Bouguer, a mathematician who was the same age as Maupertuis, tried to carve out a middle ground by synthesizing Cartesian and Newtonian views. The earth, he argued,
“cannot have any determinate shape, but instead it alternatively takes different shapes, representing extremes.” His model, which relied on fluid mechanics, provided an explanation for why one set of observations would find an elongated earth and another a flattened one: The earth was constantly changing shapes. Meanwhile, Cassini once again measured a degree of latitude near Paris, and once again he came up with results indicating that the earth was a prolate spheroid. The Cartesians in the academy also had the pleasure of awarding a prize in 1734 to Bernoulli for an essay in which he devised a set of mathematical equations showing that swirling whirlpools would indeed cause the earth to be elongated at the poles. Bernoulli, whose reputation for brilliance was second to none in Europe, further pleased the older members of the academy by praising Cassini’s measurements as
“inconceivably exact” and dismissing the criticisms of Maupertuis, whom he had once tutored, as
“sectarian” and “indiscreet.”

Bernoulli’s essay gave Cartesian cosmology a theoretical weight it had previously lacked. The academy’s Cartesians could now point to both mathematical theory and experimental evidence to support their worldview. But so too could the Newtonians. They had Newton’s law of gravity, his work on centrifugal forces, and Richer’s experiment in Cayenne with the pendulum clocks. Great minds were lined up on both sides, and both sides realized, as Maupertuis declared in 1733, that a decisive experiment was needed to get at the
“facts of the matter.” In December of that year, the astronomer Louis Godin, a senior member of the French Academy, proposed one that everyone agreed would resolve the issue. The academy would send an expedition to the equator to measure a
degree of arc. The difference between the degree of an arc there and one in France should be of a magnitude that would supersede any imprecision in the measurement itself. Was the earth, as the Newtonians would have it, shaped like a squashed orange? Or was it, as the Cartesians believed, prolonged at the poles and pulled in at the equator, its appearance—as some in the academy liked to quip—like that of a “pot-bellied man wearing a tight belt?”

The great scientific question of the day had been neatly defined. A team of ten French scientists would soon be on its way to the Viceroyalty of Peru, to the high Andean town of Quito. And there, it so happened, lived a young Catholic girl, Isabel Gramesón, who, in 1734, had just turned six years old.

*
A meridian is any imaginary north-south line encircling the globe and passing through the poles.

*
He determined that a degree was sixty-eight Italian miles, which was roughly equivalent to sixty-three English miles.

*
In this process, a side from the first triangle—its length having been mathematically calculated—serves as a side of the second one. As a result, only the first baseline in the grid needs to be physically measured. All of the other distances can be determined mathematically based on the angles of the triangles.