The Measure of All Things

by Ken Alder

  This time they were right. Everything was now reversed. Instead of the Academy of Sciences sponsoring a meridian expedition to define the metric system, the creation of a metric system had become the main justification for the state-funding of science. On August 1, 1793, one week before the dissolution of the Academy of Sciences, a new law codified the metric system as we know it today and gave the French people one year to prepare themselves for its obligatory use. Of course, the meridian expedition would not be completed by then, as everyone recognized. Hence, the law established a “provisional” meter which state administrators and commercial enterprises might use while they waited for the meridian survey’s “definitive” results. The value for this provisional meter had been coaxed out of the Academy under some duress.

  Even before Delambre and Méchain had set out, Borda had privately estimated that the meter would come out to about 443.5 lignes in the old Paris units. (A ligne was one-twelfth of a pouce (inch), so that a pied (foot) contained 144 lignes.) It was a quick back-of-the-envelope calculation based on what everyone already knew about the size and shape of the earth. In public, however, Borda said nothing. To announce this estimate might have undercut the efforts to measure the meridian properly.

  Several state agencies were impatient to know this value, however. The plan for a new national map, which would enable the government to accurately tax every piece of landed property in France, had been stalled because the surveyors were expecting to use the new standard of length. Nor could the Treasury decimalize the currency without some sense of the weight of the new silver coins. In January 1793 the Finance Committee begged the Commission of Weights of Measures to make a serious estimate of the likely length of the meter. To oblige them, Borda, Lagrange, and Laplace, three of the most illustrious mathematical physicists of all time, did so in three easy steps. They assumed that the length of a 1 degree of arc at 45 degrees of north latitude was average for the entire quarter meridian; they took the value for this distance from Cassini III’s survey of 1740; then they multiplied this number by 90 (for the 90 degrees of the quarter meridian) and divided by 10 million. Their guesstimate came to 443.44 lignes. Nothing could be simpler.

  Yet only when the Academy was threatened with dissolution later that year did the Commission cough up this value. By then, control of the nation’s legislature had been seized by the Jacobin party, who had vested executive power in the hands of a Committee of Public Safety. This Committee included not only political radicals like Robespierre and Saint-Just, but also military engineers like Lazare Carnot and Prieur de la Côte-d’Or, whose task it was to direct the war effort and organize the production of war matériel. The law of August 1, 1793, was intended to implement the metric system as soon as possible, using this provisional meter as the standard. Not long thereafter, Lalande wrote to Delambre to tell him there was little point now in pressing on with the mission. “The new measures are being adopted for commerce independent of the new measure of the earth; so there’s little need for you to push yourself too hard to bring your results in now.”

  Delambre spent that week in his hometown of Amiens, conducting his observations from the second story of the cathedral’s spire, the loftiest in France. The interior of the spire was encumbered with heavy carpentry and massive bells. The steeple also inclined slightly to the west, which slightly skewed his observations. Below, the red-brick town appeared calm, and no one was without bread—although food riots had disturbed the city the previous month, and bakers were again running low on provisions. On September 9, shortly after Delambre left town, officials arrested sixty-four priests who refused to swear allegiance to the state.

  Though he rarely went home or commented on politics, Delambre had joined an Amiens political society in 1791, one cofounded by his brother-in-law. The Société des Amis de la Constitution preached moderation, despite its motto: Vivre libre ou mourir (“Live free or die”). Delambre shared the Society’s principled moderation. Amid the passion, he dared suggest to his hometown newspaper that both democrats and aristocrats repudiate their extremist factions and discuss their differences at a nightly educative assembly. “To be reasonable,” he urged, “one must be without passion.” This modest proposal was blasted by another local citizen, Gracchus Babeuf, the radical politician who would one day be called the world’s first Communist. Delambre, he sneered, had failed to understand that “a man without passion is incapable of noble enterprises; great deeds are beyond his reach; he is without energy and hence contemptible.” Delambre’s response was to emphasize the modesty of his proposal, and to express the hope that his opponent, by venting his bilious tirade, had at least improved his health. This was as close to political commentary as Delambre would get in thirty years of service to a half-dozen régimes: the Ancien Régime monarchy, the constitutional monarchy, the Republic, the Directory, Napoleon’s Empire, and finally the Restoration monarchy. Throughout his decades of public service he maintained a careful ambiguity about his political views.

  His duty lay to his mission and on that basis he was determined to proceed. He could manage without Lefrançais, so long as Bellet remained with him. The young instrument-maker had proved himself an excellent observer and a cheerful companion. He accompanied Delambre at every step of the mission, and would do so until its final triangle. Delambre paid him a 500-livre bonus out of the savings from Lefrançais’ salary. And now that the Academy was abolished, he himself could collect a daily wage as a Commissioner for Weights and Measures. It came to the princely sum of 10 francs a day, roughly the salary of a competent artisan.

  In early October Delambre at last connected the new season’s chain of triangles with the Paris chain of the previous year. This meant that he had now formed a continual lattice of triangles from Dunkerque through the Ile-de-France, about one-third of the distance to his rendezvous in Rodez. In late October he passed to the south of the capital to pick up where he had left off the previous winter.

  Working in the Orléans forest just north of the Loire River, Delambre was caught up in the political tensions he had so far evaded that year. The church tower at Cour-Dieu which had served as Cassini III’s signal in 1740 was completely hemmed in by trees, and no plausible substitute could be found amid the rolling terrain of tall oaks in the old royal forests, a favorite hunting spot of the Bourbon kings. Delambre’s only option was to construct an observation tower on a low hill called Châtillon. Where nature offered no elevated view, and belfries were unavailable, the geodeser had to build from scratch.

  The construction of this sixty-four-foot wooden tower took over a month and attracted unwanted attention. The citizens of the surrounding hamlets wondered about the strange doings in the former royal forest. “They reported seeing three or four hundred brigands building scaffolds and piercing holes in church towers . . . , undoubtedly in preparation for a counterrevolutionary uprising.” This would have been amusing but for the fact that the local citizens had called for six hundred soldiers to attack the site. Fortunately, when the time came they vented their anger elsewhere. On December 27, just as the tower was nearing completion, the local popular society unanimously voted instead to destroy a nearby stone obelisk erected in honor of the 1740 survey by Cassini as an “odious sign of extinct despotism in the guise of a stone pyramid called the meridian and built by the one-time lords as a sign of their greatness.” The obelisk was torn down to be used for paving stones at the same time that the eminent jurist Malesherbes, on whose land the obelisk stood, was executed for acting as the king’s lead counsel in his final (futile) defense.

  On New Year’s Eve, Delambre and Bellet climbed their high tower platform at Châtillon for the first time and began to hoist their precious circle into position with ropes and pulleys. The observation deck had been boxed in to provide shelter from storms and snow. Unfortunately, this protection also gave the wind a broader surface area to push against. The circle had just arrived safely when a tremendous gust shook the tower, forcing the observers to scramble back to ea
rth, a fifteen-minute ordeal because the circle had to be lowered with care. The next day, the wind was calmer and they remounted the tower. But the cold was painful, the day short, and their observations of poor quality.

  Yet when the devastating blow came two days later, it emanated from neither the local citizenry, nor the weather, but from the supreme power in the land. On January 4, 1794, Delambre received a letter from the Commission of Weights and Measures notifying him that by order of the Committee of Public Safety he had been purged from the meridian survey along with several of his colleagues. The letter informed him that he was to hand over all his field notes, calculations, and instruments so that a successor might take his place “should the meridian survey continue.”

  Whatever this meant for the future of the mission, to quit there would have negated the months of labor that had gone into building the Châtillon tower. If a winter storm toppled the tower, all the surrounding triangles would have to be redone. At a minimum, the survey ought to terminate at fixed stations—such as the church towers along the Loire at Châteauneuf and Orléans—so that his successor, should one ever be appointed, might start his labors from a secure foundation. Moreover, Delambre estimated that he would need at least three months to put his notebooks in order and complete his calculations. He wrote to the Commission, begging for a chance to implement this plan, while setting furiously to work to carry it out before they refused.

  Their sealed response arrived a few days later in the hands of the engineer Gaspard Prony, Delambre’s former colleague in the former Academy and, as it turned out, his replacement on the Commission. Yet Prony always found an excuse not to hand over their answer. Instead, he assisted Delambre with his observations at Châtillon, and even accompanied him to Orléans to finish the triangles on the banks of the Loire. The crucifix that had once stood at the top of the Orléans cathedral spire—and that would have made an ideal signal, like the crosshairs on a telescopic sight—had recently been replaced with a misshapen cast-iron Liberty bonnet. The cathedral, now known as the Temple of Reason, had just that week witnessed an even greater sacrilege. La belle Rosalie, a young prostitute who worked the rue Soufflet, had been costumed as a goddess, with a pike in one hand and a Revolutionary red cap on her head, so that she might be paraded through town on a tremendous chariot bedecked with tricolor flags and pulled by twelve white horses led by six young men in togas. All the town’s citizenry had followed, wearing Roman attire. At one point, the float had to squeeze under a low portal and the goddess was heard to shout, “Hey, you bastards! Hey, buggers! Stop, you fuckers, I’m falling off!” before she hopped down into the crowd so as to clamber back up on the other side.

  In a year and a half of labor, Delambre had covered nearly half his assigned itinerary from Dunkerque to Rodez, surveying a two-hundred-mile arc from the North Sea coast to the banks of the Loire. In doing so he had zigzagged more than twelve times that distance, or some twenty-four hundred miles on the hard roads of France. On January 22, 1794, he made a final note in his expedition logbook: “It began to rain and there was no time to redo the angles.” Later that day, Prony handed over the Commission’s response, now three weeks overdue. The cover letter read:

  Citizen,

  The Commission of Weights and Measures has sent one of its members to bring you the decree of the Committee of Public Safety regarding your request, and to invite you to conclude your operations in such a way as to ensure that your temporary signals become unnecessary. It further enjoins you to complete the transcription of your calculations and observations as you suggest.

  Lagrange, President of the Commission of Weights and Measures

  In ambiguous language, his friends on the Commission had honored Delambre’s request, allowing him to keep his expedition logbooks for the time being. The enclosed order in the hand of Prieur de la Côte-d’Or was written on the imposing stationery of the Committee of Public Safety. It was dated December 23, 1793, now a full month past:

  The Committee of Public Safety, considering how important it is for the improvement of public morale that government officials delegate their powers and functions solely to men known to be trustworthy for their Republican virtues and their abhorrence of kings . . . decrees that from this day forth Borda, Lavoisier, Laplace, Coulomb, Brisson, and Delambre cease to be members of the Commission of Weights and Measures, and that they immediately hand over to the remaining commissioners all their instruments, calculations, notebooks, with a full inventory of the same. And furthermore, that the remaining members of the Commission . . . apply Revolutionary enthusiasm to bring the new weights and measures into use among all citizens.

  C.-A. Prieur, B. Barère, Carnot, R. Lindet, Billaud-Varenne

  The next day Delambre packed his equipment to return to Paris. “Even though, for the life of me, I cannot understand why I have been recalled, I will return without complaint to those occupations from which I was regrettably torn away.” On his way he had one personal matter to attend to. His patron, Geoffroy d’Assy, was being sought by the Revolutionary police. Delambre needed to stop at the d’Assy country residence in Bruyères-le-Châtel, where d’Assy was living in retreat.

  The Revolution had entered the phase known as the Terror, when the Jacobin state declared an emergency military draft, imposed wage and price controls, and enforced its decrees with imprisonment and execution. The world’s first war of mass mobilization was being fought. On the frontiers of France, a coalition of Prussians, Austrians, English, and Spaniards was ranged against the Republic. From within, the Republic was being undermined by defiant aristocrats, reactionary peasants, grain-hoarding merchants, and recalcitrant priests. Lavoisier had been arrested earlier that month along with the rest of the financiers of the “tax farm” that had once collected so many odious and unfair levies on the king’s behalf. And just as Delambre arrived at the d’Assy residence, his patron was likewise hauled off to the Luxembourg prison.

  Later that winter, a storm felled the Châtillon tower.

  CHAPTER FOUR

  The Castle of Mont-Jouy

  There is almost nothing right or wrong which does not alter with a change in clime. A shift of three degrees of latitude is enough to overthrow all jurisprudence. One’s location on the meridian decides the truth, that or a change in territorial possession. Fundamental laws alter. What is right changes with the times. Strange justice that is bounded by a river or a mountain! The truth on this side of the Pyrénées, error on the other.

  —BLAISE PASCAL, Pensées

  Cut off by war on the far side of the Pyrénées, Méchain knew little of these developments. For nine months he heard no news from France. The most recent letter was dated March 1793, from before his accident at the water-pumping station. For two months after that injury he convalesced in bed, until the summer sun lured him out of his dark room onto the terrace of the Fontana de Oro. The summer solstice was approaching, and Méchain insisted that he be carried out, not in search of a solar cure, but in search of solar knowledge. He was borne out into the dazzling Mediterranean summer and propped up on pillows under the repeating circle. The salt breeze breathed across the paving stones. The noonday heat silenced the town. Just out of sight, the sea sloshed against the quays. The fashionable crowd on the Rambla had retreated indoors. Only mad dogs, Englishmen, and solar astronomers go out in Barcelona’s noonday sun in summer.

  Tranchot had prepared the instrument for him. For four thousand years stargazers had sought to define one of astronomy’s most fundamental constants: the obliquity of the ecliptic, or in other words, the angle of the earth’s tilt relative to the plane of its orbit around the sun. With the Borda circle to hand, and the summer solstice upon them, Méchain had an ideal opportunity to make the definitive measurement of this constant.

  This was painful work under the best of circumstances, but Méchain insisted that he alone take the readings. While Tranchot held the smoked lens to the astronomer’s eye, Méchain tracked the sun until it reached its maximum altitude
. Then Tranchot rotated the Borda circle for him, while Méchain fine-tuned the position of the scope. Working together, they managed to take a few preliminary readings before the heat of the sun began to distort the circle’s brass gauge. Méchain was having difficulty fine-tuning the scope with his left hand. For a man recovering from a shattered chest—for a right-handed man with a dangling right arm—the effort was too much. They were forced to break off. A relapse followed. For twenty years he had labored in the dark bureaus of naval cartography to map a Mediterranean coast he had never seen. Now its light suffused his mind, even when his eyes were shut.

  Salvà was worried and proposed a medicinal cure at the thermal springs of Caldas. Chastened, Méchain took his advice. The hot baths and showers were comforting. But six months after his accident, his right arm still hung limp at his side. The doctors told him he might never recover its use. “Time has done more than art,” he would conclude a few years later when his arm had regained its strength.

  By the time he returned from the spa—still impaired, if somewhat more capable—Spain was on the verge of a military victory that would make her mistress of both slopes of the Pyrénées, unifying Catalonia for the first time in 150 years. France may have declared war first, but Spain struck first. In May, General Ricardos, the supreme Spanish commander, ordered his main body of 40,000 troops through the saddle west of the Bellegarde fortress where Hannibal had attacked two thousand years before, while three columns of 3,500 of Ricardos’ soldiers spilled through the high inland passes that Méchain and Tranchot had triangulated the previous summer. Overpowering the French garrison at La Garde, they marched down the Tech valley to join the main body of troops occupying the plains of Roussillon. Had they pressed their advantage then, the Spaniards might well have conquered Perpignan. Instead they paused to fortify the heights, set siege to Bellegarde, and surround the city. All April, May, and June, within sight of the panicked citizens of Perpignan, they bombarded Bellegarde from nearby Puig Camellas, reducing the mighty fortress to rubble. When the brave French garrison finally surrendered, one thousand prisoners were marched to Barcelona, to be incarcerated in the Mont-Jouy castle where Méchain had conducted his celestial observations the year before. The captives were lodged in a cellar and guarded by cannon charged with shrapnel “in order to avoid insolence from so evil a people.”