The Hunt for Vulcan

by Thomas Levenson

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  Another way of thinking about that transformation came with what Laplace did next. His monumental Celestial Mechanics fills five volumes—1,500 pages of dense analysis and calculation—and seeks to demonstrate that Newtonian universal gravitation, the mutual attraction of all objects in the sky on each other, could “when subjected to rigorous calculations, [yield] a complete explanation of all celestial phenomena and means of perfecting the tables and theories of the motion of heavenly objects.”

  By the end of his expansive calculation Laplace confirmed (to his own satisfaction) that he’d done it: the dynamics of the solar system—by implication, of the entire universe—were governed by the law of gravitation as Newton had first stated it. As his discovery of the roughly nine-hundred-year cycle of Saturn and Jupiter’s motion had suggested, he now concluded that the solar system as a whole was stable, its motion conformable to itself on every time scale thus far examined. Such stability lent support to his third conclusion: the solar system—and by extension, the universe as a whole—was subject to what was formally called “determinism.” Every event, everything that can be seen or measured or otherwise observed, was the outcome of some specific process or cause that could have generated only that outcome.

  That claim contains an obvious implication—one that leapt out at Laplace’s contemporaries. As the anecdote goes, Napoleon took a moment during the brief peace of 1802 to engage in a bit of intellectual banter. He entertained a few savants—Sir William Herschel himself, the distinguished physicist Count Rumford, his minister of the interior—a chemist by profession—Jean-Antoine Chaptal, and Laplace. After exchanging politenesses with Herschel, the First Consul next turned to Laplace, who had just published the third volume of Celestial Mechanics. Released from matters of state, Napoleon delighted in putting awkward questions to his guests, and so he told his mathematical friend that he had read Newton, and saw that his great book had mentioned God often. But “I have perused yours, but failed to find his name even once.” Why is that, he asked?

  In the grand tradition of this story, Laplace is reported to have replied, “I have no need of that hypothesis.”

  That sounds almost too perfect, but in an age of conversation as bloodless duel, it’s not impossible that Laplace could have come up with such a perfect riposte on the spot. But even if the dialogue has been “improved,” still, something along those lines passed between the two men. Herschel noted in his diary that Napoleon had asked “who is the author of all this” and that Laplace “wished to shew that a chain of natural causes would account for the construction and preservation of the system.”

  The deeper controversy concerns what Laplace really meant. Did he truly deny God’s existence? Or was he saying something slightly more modest, that gods were irrelevant to the day-to-day management of reality? Such an underemployed deity could exist, and might even safely be regarded as an ultimate first cause, the source of the universe at the beginning of time. But after that, Laplace seems to have been saying, the divine need play no role in that universe’s unfolding history. Newton had long since recognized that the mathematical principles of natural philosophy might tend a susceptible mind that way, but he denied the possibility. Rather, he saw in his studies of nature the chance to track down his God within creation; nature as it conformed to His will would reveal to an adept (like Newton) the hand of the deity in action. The uncertainties that he couldn’t resolve in celestial mechanics only reinforced the idea that an all-powerful being still had a job to do to keep the entire system on track.

  By the time Laplace finished solving the equations of motion for the solar system, though, his update to Newton’s system appeared to run just fine on its own. In analyses spanning centuries, the planets needed no help to return to their courses. A “chain of natural causes” could account for Saturn’s wavering orbit; for the motions of Jupiter’s moons; for the demonstration of the long-term stability of all the planets’ trajectories; even (speculatively) for the origin of the solar system as a whole. Laplace’s God had indeed ceased to be a necessary actor; divine action becomes a “hypothesis”—and a superfluous one at that, not worth a moment’s attention. As the historian Roger Hahn puts it, “Nowhere in his writings, either public or private, does Laplace deny God’s existence. He merely ignores it.”

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  That’s a fair gloss on Laplace’s view, but it’s incomplete. Stripped to its essence, Laplace’s career becomes a lifelong meditation on the question of cause and effect. Might it be possible to imagine that the tools of Newtonian science could yield perfect knowledge, a grasp of the full chain of events that led to any observable set of circumstances? Yes, he said, it is:

  We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.

  That “intellect” is now sometimes called Laplace’s demon. It is a mighty creature, to be sure, especially if you take its powers to the limit of Laplace’s imagination. He wrote this description of his demon in 1814, the year Napoleon’s empire shattered. Men, even or perhaps especially on a battlefield, are matter in motion. The intelligence that could trace the chain of cause and effect that carries each bullet to its halt, each soldier to his fate, could surely capture (“in a single formula”) the collapse of the entire imperial cause.

  And, as Laplace surely knew, Celestial Mechanics could be read as a kind of demonic text, offering a set of tools with which its readers could discover “the future just like the past” of the solar system. Such science doesn’t merely describe, of course. The immediate successors to Newton’s revolutionary generation used the interplay between meticulous observation and the mathematization of nature to generate both a formal account of what had already been measured, and what such measurements might suggest about what was yet to be observed. God-like knowledge was there—to be approached, if never fully attained.

  Laplace died in 1827, seventy-eight years old. His analyses of the mechanics of heavenly bodies were already undergoing revision. Just as his own mathematical advances over Newton led him to a more comprehensive account of the solar system, so new methods enabled his successors to build increasingly precise models of planetary motion driven by universal gravitation. One man took pride of place in this ongoing transformation: Urbain-Jean-Joseph Le Verrier, who would fulfill his predecessor’s vision of cosmic order with a discovery that seemed to his contemporaries the most perfect display imaginable of the power of Newtonian science.

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  * To find out how strongly the earth attracts the moon, for example, all you would have to do is plug in the numbers: the mass of the earth (almost 6 × 1024 kilograms, if you’re wondering) times the mass of the moon (7.35 × 1022 kilograms, or roughly 80 times less than that of Earth) multiplied by the gravitational constant—6.67384 × 10-11 N m2/kg-2 (N is the symbol for newtons, units of force)—and divided by the square of the distance between the center of the earth and the center of the moon (384,403 kilometers—which is an approximation, as the moon’s orbit is not perfectly circular). Do all the multiplication and division and you get your answer: the force of gravity exerted between the earth and the moon is about 1.99 × 1020N.

  “THAT STAR IS NOT ON THE MAP”

  In the 1830s (and still) number 63 Quai d’Orsay turned an attractive face toward the river. In the guidebooks already being read by that novel nineteenth-century species, the tourist, number 63 is described as a “handsome house”—one, the writers warned, that concealed a much more plebeian reality. Visitors—by appointment only, no more than two at a time, welcome only on Thur
sdays—would be ushered into a courtyard, and then on to the rooms where workers, mostly women, took bales of raw tobacco through every stage needed to produce the finished stuff of habit: hand-rolled cigars, spun strands of chew that became “the solace of the Havre marin,” gentlemen’s snuff. Most of the campus was turned over to laborers serving the machines—choppers, oscillating funnels, snuff mills, rollers, sifters, cutters, and more. By the latter half of the nineteenth century, the works at the Quai d’Orsay would turn out more than 5,600 tons of finished tobacco per year, and was, according to the ubiquitous Baedeker, “worthy of a visit”—though indulging one’s curiosity carried a price: “the pungent smell of the tobacco saturates the clothes and is not easily got rid of.”

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  A spectacle, certainly, and as an early palace of industry clearly worthy of the guidebooks (themselves novelties). By any stretch of the imagination, though, the Manufacture des Tabacs was an odd place to look for someone who would become the most celebrated mathematical astronomer of his day—but not everyone follows a straight course to the person they might become. Thus it was that in 1833 a young man, freshly minted as a graduate of the celebrated École polytechnique, could be found every working day at the Quai d’Orsay, reporting for duty at the research arm of the factory, France’s École des Tabacs.

  No one ever doubted that Urbain-Jean-Joseph Le Verrier had potential: he had been a star student in secondary school, winner of second prize in a national mathematics competition, eighth in his class at the polytechnique. But his early career offered no hints to what would follow. Funneled into the tobacco engineering section in university, he was more or less shunted directly toward the Quai d’Orsay and the task of solving French big tobacco’s problems.

  It’s not clear whether Le Verrier actively enjoyed the life of a tobacco engineer—or merely tolerated it. Nothing in his later career remotely suggests he was a born chemist. But he was consistent: if given a task, he got down to it. Never mind all that early training in abstract mathematics; if required, he could be as practical as the next man, and so turned himself into a student of the combustion of phosphorus. That was useful research—tobacco monopolists care about matches. But whether or not he relished his job, he certainly got out as soon as he could. A position back at the École polytechnique opened up in 1836 for a répétiteur—assistant—to the professor of chemistry. Le Verrier applied, and as an until-then almost uniformly successful prodigy, had every hope…until the post went to someone else.

  Le Verrier would prove to be a man who catalogued slights, tallied enemies, and held his grudges close. But he never accepted a check as a measure of his true worth. A second assistantship became available, this time in astronomy. He applied for that too. Never mind his seven years among the tobacco plants; Le Verrier seems to have believed that he could simply ramp up his math chops to the standard required at the highest level of French quantitative science. As he wrote to his father, “I must not only accept but seek out opportunities to extend my knowledge. […] I have already ascended many ranks, why should I not continue to rise further?” Thus it was that Le Verrier came into orbit around the great body of work left by that giant of French astronomy, Pierre-Simon Laplace.

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  Laplace had gone to his grave in 1827 convinced that he had solved the core of his great problem. To a pretty good approximation, he was correct. He had shown that the solar system as a whole could be rendered intelligible, its motions accounted for by Newtonian gravitation as expressed within mathematical models—“theories” of the planets. Properly employed, those models could describe the motions of the physical system explicitly, accurately, and indefinitely into the future. If there was some work left to do, new methods to be explored, more observations to be considered, discoveries within the system (like the newly discovered “minor planets”—asteroids—and comets), the basic picture seemed sound.

  There were, though, more anomalies than the edifice of Celestial Mechanics acknowledged. Some of the theories of the planets were proving a bit less settled than Laplace had believed, and some, like Mercury’s, were obviously inadequate, unable to predict the planet’s behavior with remotely acceptable precision. Despite such problems (or possibilities), no researcher had yet returned to the whole of Laplace’s program. Several astronomers in France and elsewhere worked on individual questions in planetary dynamics, but none were trying to resolve the system as a whole, to go from a theory of any given planet to one of the solar system, top to bottom.

  Enter Le Verrier, of whom one of his colleagues would later say, “Laplace’s inheritance was unclaimed; and he boldly took possession of it.” Over his first two years at the polytechnique, Le Verrier surveyed the whole field of solar system dynamics, beginning to suspect that seemingly minor gravitational interactions might matter more than his predecessors had believed—that over time they produce effects that would be noticeable. He seized the opportunity, setting himself as his first major project the goal of recalculating at higher mathematical resolution the motions of the four inner planets—Mercury, Venus, Earth, and Mars. It took him just two years, a phenomenal pace given that he had started from zero as a mathematical astronomer.

  Le Verrier presented his results to the French Academy of Sciences in 1839. He came to one striking conclusion: when you take one more term into consideration than prior calculations had attempted, it becomes impossible to say for certain whether or not the orbit of the inner planets would remain stable over the very long haul. Neither he nor anyone else knew how to find a complete solution to the equations that could confirm whether Mercury, Venus, Mars—and Earth—would remain forever on their present tracks.

  Crucially, Le Verrier was already showing himself willing to tangle with the acknowledged master of celestial mechanics. Laplace had concluded from his studies of Jupiter and Saturn that the stability of the solar system was proved; here was a young man just two years into the field suggesting otherwise.

  It was a fine first effort—good enough to garner attention from the men who could advance his career past an assistantship. At the same time, it was, as Le Verrier knew, still preliminary work, nothing more than recasting an old calculation. But it managed to hook him on celestial mechanics as a life project—and for his next major task, he set himself a problem that no prior researcher had been able to solve: Mercury.

  If the planets were a family, Mercury would be the sneaky little sibling: it might be up to something, but it was so good at slipping past any attempt to pin it down it was hard to be sure. But that was no longer quite as true, as Le Verrier’s gift for finding a ripe problem showed itself. Over the preceding decade, advances in instruments and technique made it possible to follow Mercury with a previously unattainable accuracy. He gave credit where it was due: “In recent times, from 1836 to 1842,” Le Verrier reported to the Académie, “two hundred useable observations of Mercury have been carried out” at the Paris Observatory. With these and other records, he was able to construct a better picture of the way Venus influenced Mercury’s orbit as the two planets moved from one configuration to another. That, in turn, led him to a new estimate of Mercury’s mass, with his answer falling within a few percentage points of the modern value.

  These were satisfying outcomes—filling in some of the more elusive details of one corner of the solar system. But Le Verrier really wanted a complete account of Mercury, a system of equations encompassing the full range of gravitational tugs that affect its orbit, which can be used to identify planetary positions past and future. Observations constrain such models: any solution to a model’s equations has to at least reproduce what observers already know about a planet’s orbit. More data meant more constraint, and hence a more accurate set of predictions about where the planet would go next. Those predictions, the “table” of the planet, are the test of any planetary theory.

  The final exam for Le Verrier’s first version of such a theory for Mercury came in 1845, its next scheduled transit of the sun, best viewed
from the United States. Transits are ideal reality checks for such work: mid-nineteenth-century chronometers were accurate enough to note the instant Mercury’s disk would cross the edge of the sun. On May 8, 1845, astronomers in Cincinnati, Ohio, watched as the clock ticked off to the moment Le Verrier had predicted for the start of the event. The astronomer at the eyepiece of the telescope trained on the sun saw “the dark break which the black body of the planet made on the bright disk of the sun.” He called out “Now!” and checked his timepiece. Against Le Verrier’s prediction, Mercury was sixteen seconds late.

  Mercury in transit across the face of the sun in 2006

  This was an impressive result—better by far than any previous published table for Mercury, back to the one prepared by Edmond Halley himself. But it wasn’t good enough. That sixteen-second error, small as it seemed, still meant that Le Verrier had missed something that kept the real Mercury out of sync with his abstract, theoretical planet. Le Verrier had planned to publish his calculation following the transit. Instead, he pulled the manuscript and let the problem lie for a time. Mercury would have to wait quite a while, as it turned out, for almost immediately he found himself conscripted into a confrontation with what was fast becoming the biggest embarrassment within the allegedly settled “System of the World.”

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  Uranus was the troublemaker, and had been for decades. After Herschel’s serendipitous discovery of the “new” planet, astronomers swiftly realized that others had seen it before, thinking it a star. In 1690, John Flamsteed, the first Astronomer Royal and Newton’s sometime-collaborator, sometime-antagonist, placed it on one of his sky maps as the star 34 Tauri. Dozens of other missed-chance observations turned up in observers’ records, until in 1821, one of Laplace’s students at the Bureau, Alexis Bouvard, combined those historical sightings with the systematic searches that had followed Herschel’s news to create a new table for Uranus, one supposed to confirm that it obeyed the same Newtonian laws that governed its planetary kin.