The Body as Measure

Let there be one measure of wine throughout our kingdom, and one measure of ale, and one measure of corn, namely the London quarter […]. And let it be with weights as with measures.

The arm on the door

On a market day in the fourteenth century, in some Italian town, buying a length of cloth was an exercise in trust. The draper would unroll it across the counter and measure it by the arm, with the gesture we still use to estimate the length of a rope: one end pinched between the fingers, the fabric drawn taut to the shoulder, and again. But men’s arms are not equal, and the buyer knew it well. For this reason the arm that truly counted was not made of flesh: it was an iron bar fixed beside the door of the town hall, or a groove carved into the stone of the cathedral, against which anyone could lay his purchase and check. In many Italian towns those walled-in standards can still be seen — at Assisi, for example, on the flank of the communal palace — long narrow slots in the façade, polished by centuries of verification, beside which one sometimes finds the outlines of the regulation brick and roof tile.

Around the stone standard there grew an entire apparatus of guarantee. The guilds stamped their cloth with lead seals certifying measure and quality at the source, so that the goods travelled with their credentials sewn into them; sworn brokers stood as third parties between foreign sellers and local buyers; the market magistracies kept registers, levied fines, and burned false measures in the square. And when commerce crossed borders, the merchant law had its conflict rule, simple and universally understood: the measure of the place where the contract is concluded prevails. At the great fairs — in Champagne, at Geneva, at Lyon — the foreigner bought and sold in the units of the fair, not his own, and it was precisely that certainty that made possible the meeting of merchants from half a continent.

The public standard was the stone answer to a problem that runs through this entire history: a measure is worth only as much as the trust of those who accept it. Within the walls, that trust was guaranteed by the commune, the guilds, custom.

But one had only to pass the town gate for the compact to change. Florence’s arm was not Siena’s, nor Pisa’s; Genoa’s hundredweight was not Venice’s; and the same name — pound, ounce, bushel, modius — denoted different quantities from one valley to the next.

The professional merchant lived with this fragmentation as the sailor lives with the tides. Around 1340 Francesco Balducci Pegolotti, an agent of the Florentine company of the Bardi, compiled a practical guide for his colleagues — we know it as the Pratica della mercatura — which is in large part an immense ready-reckoner of conversions: how much the cantar of Acre yields in pounds of Florence, how the cane of Provence squares with the Tuscan arm, marketplace by marketplace, commodity by commodity, from the Hanseatic towns to Tana on the Sea of Azov, gateway to the silk road. Alongside the equivalences, Pegolotti notes the tares, the customs of weighing, the gratuities owed to the public weighers: everything a factor needed to know in order not to be robbed legally. To know how to trade meant, before anything else, to know other men’s measures; and that knowledge cost years of apprenticeship, mistakes paid out of one’s own pocket, archives of letters between branches. The accounting of fragmentation was a profession within the profession.

To us, accustomed to a world in which a metre is a metre everywhere, all this looks like chaos. But that is a retrospective judgement, and an ungenerous one. To those who inhabited it, that world was ordered: every measure had its guarantor, its stone standard, its tribunal. It was a local order, negotiated, made to measure — the phrase is apt — for the life it had to serve. To understand the logic of that order, and to understand why at a certain point it ceased to suffice, is the right way to begin this history: because the metric system was not born out of nothing against ignorance, but out of a long conflict within a world that measured a great deal, and in its own way measured superbly.

The pharaoh’s rod

Long before the medieval markets, measure was born as an affair of state. The Egyptian word meh niswt, “royal cubit,” says it all in the name: the fundamental unit of pharaonic Egypt — the distance from the elbow to the tip of the middle finger, about fifty-two centimetres — belonged to the sovereign, not to anatomy. The arm was an idea; the standard was an object of state. Several survive: rods of wood or stone divided into seven palms of four fingers each, often covered with religious inscriptions, like the cubit that belonged to the architect Kha, now in the Egyptian Museum of Turin. The detail of the seven palms deserves attention: the “common” cubit, anyone’s forearm, counted six; the royal cubit added a seventh, and that very excess over anatomy declared that the legal unit no longer coincided with anyone’s body — not even the pharaoh’s. The most solemn standards were of dark granite, made to last as long as the temples that kept them [Crease 2011].

What all this seriousness was for, the Nile explains. The Egyptian economy depended on the annual flood, and the flood was measured: the nilometer translated the river’s level into cubits and fractions, and on that reading hung the harvest forecast and the year’s tax. After each flood, when the silt had erased the boundaries of the fields, teams of surveyors — the “rope-stretchers,” as the Greeks would later call them — redrew the parcels with cords knotted at regular intervals. Herodotus relates that from this very accounting of the inundated land geometry was born, which still carries in its name the measuring of the earth. The tradition is probably too fine to be wholly true, but it captures a fact: in Egypt to measure was to administer, and exactness was a bureaucratic virtue before it was an intellectual one.

When it had to, that machine could be extraordinarily precise. The four sides of the Great Pyramid of Giza, about two hundred and thirty metres long, differ among themselves by a few centimetres: a uniformity that presupposes reliable standards, repeatable procedures, and systematic control of deviations [Crease 2011]. It was not love of exactness in the abstract: it was applied theology. The monument had to be perfect because the order it embodied — cosmic and political at once — admitted no blemish.

Mesopotamia, which was Egypt’s rival and mirror, built an even more systematic edifice. The kingdoms of the twin rivers counted in base sixty — the talent of sixty minas, the mina of sixty shekels — and that choice, passing through Babylonian astronomy, still governs us every time we divide the hour into sixty minutes and the circle into three hundred and sixty degrees: it is the oldest standard in unbroken force in human history. The weight-standards were polished stones, often in the shape of a sleeping duck, the neck folded back over the body, inscribed with the value and sometimes with the name of the guaranteeing sovereign; the statues of Gudea, lord of Lagash at the end of the third millennium, portray him seated with the plan of a temple on his knees and a graduated rule — the oldest ruler we know, carved as an attribute of sovereignty beside the sceptre. Further east, in the cities of the Indus valley, archaeologists have found sets of cubic weights of polished chert proceeding in regular ratios — one, two, four, eight, sixteen — nearly identical from one site to another across a territory as vast as half of Europe, and fired bricks that everywhere respect the same proportions: of that civilization we cannot read the script, but we read its metrology perfectly well, and it is already a form of state [Crease 2011]. The India of the historical kingdoms would later codify the matter with a thoroughness worthy of a manual: the Arthashastra, the great treatise of government, provides for a superintendent of weights and measures, the state manufacture of standards, and periodic verifications at a fixed fee. And where the centralized state was lacking, the same function found other flesh to inhabit: in the gold-bearing West Africa, Akan merchants weighed the precious dust with sets of brass weights cast by the lost-wax method — animals, proverbs, miniature scenes — consistent from one generation to the next, the portable guarantee of a corporation rather than of a king. The grammar is everywhere the same; only the keeper changes.

Where there is measure there is fraud, and where there is fraud there is law: this too begins at once. Among the provisions of the Code of Hammurabi, in the eighteenth century before Christ, stands the sentence of drowning for the alewife who collects her silver by a heavier weight; the Book of Deuteronomy forbids keeping in one’s bag “two weights, a large and a small,” and the prophets count the false measure among the abominations. It is worth noting the register: the incorrect measure is not an error, it is a sin. For millennia metrology dwells in the vocabulary of justice, not of technique — and the standards stand in the temples, beside the gods who guarantee their sanctity.

No image expresses this kinship better than the balance, which is at once the oldest instrument of precision and the oldest moral metaphor. In the Egyptian judgement of the dead, painted for fifteen hundred years on papyri and tomb walls, the heart of the deceased is set on one pan and on the other stands the feather of Maat, the goddess of right order: Anubis checks the pointer, Thoth records the result. It is a weighing performed by the book — the last judgement as a metrological assay — and from there the balance has never left our imagination of justice: it is held by Themis and her heirs on the pediments of courthouses, held by the archangel of judgement in the cathedrals. The real instrument, meanwhile, went its way: to the symmetrical two-pan balance, as old as the cities, Rome added the steelyard with unequal arms — quicker, more portable, and far easier to rig, since a dishonest counterweight is all it takes; the statutes of every age devote to stamped counterweights and steelyard inspections the same anxious care. Weighing is the gesture in which measure and justice coincide down to the very language: even today we “weigh” our faults, our arguments, our words.

That the single measure is a political programme, for that matter, was first understood by the first man to unify a state of continental dimensions. When in 221 before Christ Qin Shi Huang completed the conquest of the Chinese kingdoms, among his first decrees as emperor were the unification of weights, of measures of capacity, of coinage, of writing, and even of the gauge of cart axles, so that the ruts of the imperial roads might be passable by every vehicle of the empire. The bronze standards bore the edict engraved upon them; officials distributed and verified them. Two millennia before the French Revolution, the uniform measure was already what it would become again: the tangible sign that a territory obeys a single law.

The Greece of the cities never had a common measure — as it never had a common state — and this too is instructive: each polis kept its own foot, and the differences can still be read in the stones of the temples. The stadion, which by definition made six hundred feet, thus changed length from sanctuary to sanctuary, and that of Olympia — which legend wished measured against the feet of Heracles himself — did not coincide with that of Delphi nor with that of Athens. What Greece invented was not the universal unit, but the public control of the unit: at Athens a college of magistrates drawn by lot, the metronomoi, watched over the market’s weights and measures, and sets of official standards in bronze and stone, inscribed as public, have come back from the excavations of the agora. Measure as a civic function, subject to rotation and accountability like any other magistracy: within fragmentation, an idea destined to endure.

Rome turned this tradition into infrastructure. The Roman foot — a little under thirty centimetres — generated the double pace, and a thousand paces made the mile we still call by that name; the iugerum ruled the land of the colonies into squares; the aediles policed the markets, and in the municipalities a stone table with standard cavities — one can still be visited at Pompeii, beside the forum — allowed the measures of capacity to be checked at a glance, while imperial bronze standards for liquids and for weight served as reference for the provinces. The roads, the cadastres, the aqueducts, the legions: all presupposed units shared from Britain to Syria. It was the first European experiment in metrology on a continental scale, and it lasted as long as the empire. When the scale of economic life turned local again, so did the measures: not out of barbarism, but because measure always follows the dimension of the world it has to serve.

Half the Roman world, meanwhile, had passed to Islam, and there the control of measure found one of its most enduring forms. In the Muslim cities the markets were watched over by the muhtasib, magistrate of the hisba — the Qur’anic obligation to promote the right and forbid the unlawful — armed with standards and manuals: the surviving treatises of hisba teach, with notable technical refinement, how to recognize off-centre balances, weights hollowed out and refilled with lead, double-bottomed bushels. From Cordova to Cairo to Baghdad, for nearly a thousand years, it was the same figure under the same name: proof that the problem — and the solution — belonged to no single civilization.

When the empire fell, its metrological dream went on tormenting whoever took up its crown in the West. Charlemagne, crowned heir of the Caesars, ordered in his capitularies that all should have “equal and just measures and just and equal weights,” in the cities as in the monasteries; tradition later attached to his name the weight-standard that France would keep until the Revolution, the so-called pile de Charlemagne. But the edict presupposes the apparatus, and the Carolingian apparatus dissolved with the dynasty: the feudal fragmentation of measures, the one we met at the market, is precisely the child of that shipwreck — every lord who acquired a piece of sovereignty acquired with it the bushel that went with it.

The medieval kings never ceased to dream of the lost uniformity. In England a twelfth-century chronicle relates that Henry I, exasperated by the variety of arms, imposed as the measure of the realm the yard, the distance from the tip of his nose to the thumb of his outstretched arm: the anecdote is almost certainly a legend born at court, but it is an instructive legend, because it shows where the origin of legitimate measure was still being sought — in the body of the sovereign, the one body that could claim to stand for all. The clause of Magna Carta quoted at the head of this chapter — one measure of wine, of ale, of corn for the whole realm — is of 1215, and the English sovereigns repeated it, almost word for word, for centuries: a sign that it was easier to carve than to enforce. Something, however, took root in England earlier than elsewhere: the standards of the realm kept at the Treasury, and that “Winchester bushel” which tradition traced back to King Edgar and which the late-medieval statutes fixed as the reference for the grain trade — an imperfect but comparatively early uniformity, which partly explains why England of all places would later look with detachment upon the metric revolution of others. The premodern state had neither the inspectors nor the roads nor the registers to impose its own standard on every market in the territory. Measure remained, in fact, a local question. And locality, as we are about to see, had its reasons.

The justice of the bushel

The first reason is the simplest: anthropometric measures are convenient. The foot, the palm, the thumb, the arm, the pace, the fathom: the instrument is always with you, the estimate is immediate, and for most everyday uses the approximation suffices. When more than a single body was needed, the community knew how to manage with elegance. A manual of practical geometry printed in 1535 by Jakob Köbel prescribes the method for establishing the “right and lawful” rod: let sixteen men be stopped as they leave Sunday mass, just as they come, tall and short; let their left feet be set in a row, toe against heel; the total length is the rod, and its sixteenth part is the lawful foot. It is statistical sampling avant la lettre — the average that smooths the extremes — and at the same time a rite: the measure issues from the assembled community, and for that reason binds everyone.

The arithmetic of these measures, too, which today seems a caprice, had its logic. The foot divides into twelve inches, the pound into twelve ounces, the shilling into twelve pence; other units proceed by sixteen, by twenty, by sixty. These are numbers chosen by people who did their sums in their heads and divided constantly: twelve splits exactly among two, three, four, and six partners; sixteen halves four times running; ten, which divides only by two and by five, is from the market’s point of view a mediocre number. Base ten would win later, when written and then printed calculation got the better of mental reckoning, and the decimal arithmetic of the Indo-Arabic numerals made every conversion a mere matter of decimal points. The numbers of measures, too, in short, tell who used them and how.

The second reason runs deeper: many ancient measures describe not abstract space but labour and yield. Land was not counted in units of area: it was counted in days — how much a yoke of oxen ploughs in one — or in bushels of seed, how much grain it takes to sow it. These are units a modern surveyor regards with horror, because the “day” of a stony field on a slope is smaller than that of a field on the plain. But that is precisely the point: the bushel of sowing incorporates the quality of the land, the day’s work incorporates the toil, and for the peasant who must live by it or pay rent on it those are the facts that matter. Witold Kula, the historian who devoted to this world the book that remains its best map, speaks of “representative” measures: each unit represents a concrete relation among men, land, and labour, and is understood only within that relation [Kula 1986].

There is finally a third property, which moderns easily miss: the ancient measure is negotiable, and negotiability is a social valve. The bushel can be filled level or heaped; the hand can press the grain or leave it loose; to the cut of cloth one can add “good measure,” the extra finger of abundance that signals fair dealing. None of this was left to chance: the town statutes regulated every gesture of weighing as a laboratory protocol is regulated today — who was to wield the strickle, the round-sectioned stick with which the heap of the bushel is struck off, with what motion to pass it, whether the grain was to be poured from rest or from a height, even on which side the buyer was to stand. To different commodities, moreover, different measures were due even for the same magnitude: in many marketplaces the unit of length for silk was not that for wool, nor that for common linen, because the value of the goods justified different fineness of guarantee [Kula 1986]. Around these gestures there had even grown a trade: in the larger towns the right to measure grain, salt, coal belonged to corporations of sworn measurers, public experts who took an oath, answered with their own patrimony, and handed the office down, and whose mere presence served as guarantee, as a certifying signature does today [Kula 1986]. It was a baroque metrology, certainly; but every one of its complications answered a real conflict that men had learned to forestall.

In a world without precision scales, codified generosity was the most practical way of staying on the right side of the law and of reputation. The same elastic logic governed bread: in many towns the price of the loaf stayed fixed by law — a penny is a penny — and it was its weight that rose and fell with the price of grain. The measure was adjusted, not the number: for a society in which small coin was rigid and literacy rare, it was the most transparent solution, not the least honest.

But every valve can be turned both ways, and here the history of measures shows its hard side. In the feudal world to measure belonged to the same family of rights as to mill and to bake: as the peasant was bound to the lord’s mill and to his oven, so was he bound to his bushel, for a fee, and the right of measure was leased, inherited, sold like any other rent. The bushel — the physical standard, the object of wood hooped with iron — thus stood as a rule in the lord’s hands, and it was with that bushel that the peasant paid the tithe and the rent. Kula has documented, in Polish and French archives, a drift as silent as it was systematic: the seigneurial bushel growing from generation to generation, the heaped measure exacted at collection and the level measure granted at sale, the “new measures” introduced in fact and defended in court [Kula 1986]. The peasants protested, appealed, sometimes rose in revolt; the courts filled with expert reports on bushels and minas; and the demand that runs through centuries of rural uprisings is not the abolition of measures, but the “just measure” — the old one, the grandfather’s, the one from before the abuse. He who controls the standard controls the value of everything poured into it: the struggle for measure was, for centuries, class struggle waged in units of volume.

And there was a measure that the central power manipulated on its own account, on the scale of a realm: money. We forget it because today money seems to us a world apart, but almost all the great monetary units in history were born as units of weight — the talent and the shekel, the pound that still lives in the Italian lira, the French livre, and the pound sterling, which originally was exactly this: a pound of silver of “sterling” alloy. As long as money is metal weighed and struck, the minting is a metrological certification: the sovereign who impresses his face upon it swears to the weight and the fineness of the blank. And precisely for this reason debasement — reducing the fine while keeping the name — is the subtlest of metrological frauds: the lord’s bushel on a national scale, with the aggravation that the forger is the guarantor himself. Subjects who clipped coins with shears ended on the gallows; princes who clipped the alloy by edict were called reformers of the coinage. Here too the eighteenth century inherited an ancient lesson: he who judges the measure cannot be he who profits by it. It is no accident that the watch over the English Mint, in the years of the great recoinage, was entrusted to the most unsuspectable of keepers — Isaac Newton, who hunted counterfeiters with the same rigour with which he had weighed the heavens.

The same logic governed the measure that seems to us the most natural of all: that of time. For almost all of history, the hour was not a fixed duration but a fraction: the twelfth part of the daylight, long in summer and short in winter, sounded by the bells that called to work, to market, to prayer. Time, too, that is, was a “representative” measure: it measured the day as lived, not an abstract flow equal to itself. Equal hours arrived only with the mechanical clock of the fourteenth-century bell-towers, and they were a small silent revolution: for the first time a machine, not the sun nor labour, dictated the partition of life. What happens when that machine becomes precise enough to govern not only the city but navigation, the railways, and at last the whole planet, we shall see two chapters on; here it is enough to note that time entered the modern age by the same door as the other measures — ceasing to represent life in order to begin regulating it.

It is worth pausing on the vocabulary, because it says something essential. The premodern measure is “just” or “false,” “good” or “short”: moral and juridical categories. It is never “exact,” because exactness is not yet an available category: exact with respect to what? There is no universal reference against which to err; there is only the local compact, and he who breaks it commits not an error but a wrong. The idea that a measure might be objectively mistaken — mistaken even if all the contracting parties agree — requires a conceptual invention that is not yet there: the single standard, external to all the parties. Keep this threshold in mind: all the rest of the book recounts how it was crossed, and at what cost.

Man, the measure of all things

“Man is the measure of all things,” tradition had Protagoras say, and for once a philosophical maxim is to be taken literally: for most of human history, things were measured literally with man — with his arm, his foot, his day’s labour. The body, moreover, was not only the instrument of measures: it was also their norm. Vitruvius, in the treatise that would educate architecture for two thousand years, derives the units — the finger, the palm, the foot, the cubit — from the proportions of the well-formed man, and observes that a body laid out with arms and legs spread inscribes itself in the circle and the square: when Leonardo drew that observation, he made of it the most celebrated image of humanism. Within that drawing is a theory of measure: the unit is right if it stands to the building as the palm stands to the man, and to measure the world means to recognize in it the proportions of the body. All the history that follows — the metre taken from the Earth, the second taken from the atom — can be read as the long leave-taking from this idea: the exit of measure from the body. But the letter conceals the more serious lesson, which this chapter has tried to set in order: measuring has never been a mere technical gesture. To measure is to institute a convention, and to keep it alive.

A measure, in the end, is a promise between strangers. The iron arm walled in beside the palace door says: you and I, who do not know and do not trust each other, both accept this third term, and before it we are equal. The whole apparatus we have met — the pharaoh’s granite, the temple, the statute, the rite of the sixteen feet on the church steps — serves to make that promise credible and durable. A contemporary economist would say that the public standard lowers transaction costs: every verification spared, every lawsuit avoided, every expert report rendered superfluous is wealth that stays within the exchange instead of dissipating in suspicion. It is a correct translation, provided it does not make us forget the original: before being efficiency, the shared measure is a fact of peace. The societies we have crossed knew it so well that they entrusted their standards to the gods.

Convention, however, does not mean arbitrariness, and the distinction is the heart of the whole matter. That the foot is worth twelve inches is a choice; but once chosen, it must hold up to the test of the world: grain settles in the bushel, iron expands in the heat, wet rope shortens, and a convention that ignores these facts dies of lawsuits. For this reason metrological conventions have never been pure decisions: they are decisions selected by use, surviving because they worked better than the alternatives. The history this book recounts can be read entirely in this way — a long selection of ever more robust conventions, from those that held up a market to those that hold up a planet — and the reader will do well to carry the question with him from the start: when we say that a measure is “true,” what exactly are we saying? The technical content of metrology will change beyond recognition in the course of this history; its social substance will not. Even when the standards are beams of light and constants of nature, voted by a show of hands in a congress hall, they will remain promises between strangers: only, on a planetary scale. Whoever finds the arm on the door naïve will discover, upon reaching the last chapter, that he never abandoned that gesture: he merely refined it.

There is finally a weakness that no authority can heal, because it dwells in matter itself: the standard is an object, and objects grow old. The reference toise of all France was an iron bar walled in 1668 to a pillar of the Grand Châtelet, the court of Paris, with two studs between which the fathoms to be verified had to fit exactly. It stood in the open, exposed to knocks, to rust, and to millions of verifications; when, a century later, it was compared with better-kept standards, it proved deformed, and in 1766 it had to be declared void and replaced. The paradox is exquisite: by definition the standard cannot err, so for a century it had been the whole of France, if anything, that had “lengthened” with respect to its own iron. Whoever laughs at this quibble will have to think again seven chapters on, when the very same paradox — a cylinder of metal kept with every care, and yet at odds with its own copies — will force the planet to refound the unit of mass.

If the old order was so coherent, why did it die? Not of ignorance, but of others’ success: in the seventeenth and eighteenth centuries three forces, grown slowly, broke its scale. The first is long-distance commerce. Pegolotti’s ready-reckoner was already the symptom of a world in which every conversion is a cost, a risk, and an occasion for dispute; with the oceanic routes, the joint-stock companies, marine insurance, and bill-of-exchange credit that world did not cease to widen, and every contract concluded at a distance — on goods the buyer would not see for months — multiplied the dead weight of metrological uncertainty. The second is the modern state: to tax, to conscript, to provision, and to administer a national territory requires addable numbers. The great eighteenth-century cadastres, which claimed to survey and class every parcel of a duchy or a kingdom, stumbled systematically into the thicket of local units; an intendant cannot govern with six hundred different bushels, nor can a ministry of war reckon an army’s rations in measures that change at every stage of the march. The third force, the newest of all, is experimental science. An experiment is worth something only if a distant colleague can repeat it, and to repeat it he must be able to remake its measures: when Torricelli’s barometric experiments bounced from Florence to Paris to Clermont, every replication had to begin by translating Florentine inches into Parisian ones. The Royal Society and the Académie already corresponded across borders; their magnitudes did not. And a community that was founding its own authority on reproducibility could not long tolerate that reproducibility should stop at the customs house.

It was in scientific circles that the idea took shape that would dominate the following century: if no local standard can bind the whole world, let the standard be taken from nature, which belongs to no one. To measure the Earth, in itself, was an ancient enterprise: Eratosthenes had estimated its circumference in the third century before Christ by comparing the noon shadows at Syene and Alexandria, and in the ninth century the caliph al-Ma’mun had sent his astronomers onto a Mesopotamian plain to measure with pace and rod the length of a degree of meridian — science as an affair of state, once again. But it is one thing to measure the Earth with one’s own units, and another to reverse the relation and make the Earth the unit: this inversion, simple and vertiginous, is the invention of the seventeenth century. The proposals came early and already surprisingly complete. In 1670 Gabriel Mouton, a parish vicar of Lyon, suggested deriving the unit of length from the terrestrial meridian — a minute of arc, to be subdivided by powers of ten — and pointed to the pendulum as the practical instrument for keeping and reproducing it: in a single pamphlet, the anchoring to the Earth and the decimal division, that is, the programme of the metric system a hundred and twenty years early. The most beloved candidate, however, remained the pendulum itself: the length of the pendulum that beats the second — a little less than what we now call a metre — seemed a constant offered by the heavens. Many proposed it, in many variants: John Wilkins set it at the centre of his project for a universal language in 1668, where the universal measure was to accompany the universal vocabulary; Jean Picard, who in 1670 had remeasured an arc of meridian between Paris and Amiens with unprecedented precision, suggested calling its standard version the “astronomical radius”; Christiaan Huygens, who had written the mathematical theory of the pendulum, derived from it his “horary foot.” For a decade it seemed settled: the unit would issue from a clock. Then, in 1672, the astronomer Jean Richer took to Cayenne, near the equator, a pendulum regulated in Paris, and found that there it ran slow: to make it beat true again he had to shorten it by a couple of millimetres. Gravity, then, changes from place to place; the most beloved “natural” standard depended on latitude. Newton would make of that trifle an argument for the flattened shape of the Earth; for the metrologists it was a sentence. Questioned with sufficient precision, nature had given the first of a long series of inconvenient answers: not even I am as uniform as you hope. It was a warning, and no one took it fully to heart: the Earth that was not regular enough for the pendulum would not be regular enough for the meridian either. But that, in 1791, remained to be discovered.

One king, one law, one measure

The French eighteenth century thus inherited a double discontent. Above, the men of the Enlightenment saw in the thicket of measures a scandal of reason and a brake on commerce: hundreds of names of units circulated in the realm, and since the same name changed value from one parish to the next, the effective values ran into the tens of thousands [Kula 1986]. Below, the peasants carried on their centuries-old war against the lord’s bushel. The monarchy, it must be said, had tried: projects of unification had circulated throughout the century, and in 1775 the reforming minister Turgot had gone so far as to charge Condorcet with preparing a reform founded on the seconds pendulum, measured at the latitude of forty-five degrees. But every attempt foundered on the same reef: the local measures were rights, and rights were property — of cities, of corporations, of lords. To touch the bushel meant to touch the rent of him who owned it; Turgot fallen, his pendulum fell with him. To unify the measures of France one had first to abolish the privileges of France, and for that no minister would do: it took the night of the fourth of August. The two angers, that of the philosophers and that of the peasants, did not resemble each other, but they converged on the same target, and in 1789 they were set down in writing together. In the cahiers de doléances — the notebooks of grievances drawn up by every community for the Estates General — the demand to unify weights and measures is among the most frequent of the whole realm, condensed into a formula that sounds like a slogan: one king, one law, one weight, and one measure [Kula 1986]. It is worth weighing that phrase: the people did not ask for science, they asked for justice — the definitive end of the bushel that grows in the master’s hands. Science, for its part, asked for a universal standard. The Revolution found itself in the rare position of being able to promise both with a single act.

The opportunity took shape between 1790 and 1791, when Talleyrand brought before the National Assembly the project prepared in the circles of the Académie, where Condorcet, Lagrange, Laplace, and Borda sat. And for a moment the dream was wider than France: Talleyrand proposed that the new unit be born of a collaboration between the Académie and the Royal Society, on the pendulum at forty-five degrees; in London, in the same weeks, Sir John Riggs Miller was urging upon the Commons the reform of English measures, and in New York the secretary of state Thomas Jefferson was presenting to Congress a plan of decimal unification likewise founded on the pendulum. Three revolutions of measure, coordinated, in the same year: the opportunity would never present itself again. It evaporated for the usual reasons — the mistrust between London and Paris, the elections that swept away Riggs Miller, a distracted Congress — and each went his own way; the Anglo-Saxons, by inertia, kept the old. Whoever wonders why an Atlantic of inches still separates two systems of measure finds the exact fork here, in the years 1790–91.

Left alone, France raised the stakes. The principle was the one matured in the previous century: the new measure would belong to no body and no king, but to the Earth itself, “for all times, for all peoples,” in the formula tradition attributes to Condorcet. There remained the piece of nature to be chosen. The seconds pendulum, already wounded by Richer’s discovery, was set aside; the more ambitious and more French proposal prevailed: the metre would be the ten-millionth part of the quarter of the terrestrial meridian, from the North Pole to the equator, and to fix it the arc of meridian that crosses France from Dunkirk to Barcelona would be remeasured with precision never seen. The Assembly approved in March 1791.

On paper it was a triumph of geometric reason. In practice, it meant sending men with quadrants and telescopes to triangulate half of western Europe while France slid into war and Terror: bell-tower by bell-tower, summit by summit, amid expired passports, suspicious committees, and crowds convinced that those strange signals on the towers were messages to the enemy. The Académie chose for the enterprise two astronomers of the first rank, Jean-Baptiste Delambre and Pierre Méchain. What happened to them — and what one of the two carried to his grave — is the story of the next chapter.