Longitude and Time

Our trusty friend the Watch.

The ships that did not know where they were

On the night of 22 October 1707 — the English calendar still kept the old style — a squadron of the Royal Navy was returning from the Mediterranean under the command of Sir Cloudesley Shovell, one of the most celebrated admirals in the realm. For days it had been sailing in fog and foul weather, and the pilots, gathered in council, had reckoned the fleet’s position out to sea, in safe waters, west of Brittany. They were instead on the Scillies, the scatter of rocks that closes off the south-west of England. Four ships of the line dashed themselves to pieces there in the dark in the course of a single night; the dead were, by the severest estimates, nearly two thousand, the admiral among them.

It was not the first disaster of its kind nor the last, but it was the one the realm could not ignore: the greatest naval power in the world had lost a whole fleet not to the enemy, not to the storm, but for not knowing where it was [Sobel 1995].

The ignorance had a precise structure, and it is worth looking at closely, for it is one of the finest asymmetries in the history of science. One half of the position, latitude, had been known since antiquity: it is enough to measure how high the sun stands at noon, or the pole star at night, and the sky tells you to which ring of the Earth you belong. The other half, longitude, does not let itself be read in the sky by any simple means, because the Earth turns: the noon sun at London is identical to the noon sun in the Azores, only it arrives later. In that “later,” however, lies the whole solution. The planet completes a turn in twenty-four hours, and so rotates fifteen degrees every hour: if you know, in the same instant, the local time of the point where you are — and the sun gives you that — and the time of the port from which you set out, the difference between the two gives you your longitude: one exact hour of discrepancy, fifteen degrees; four minutes, one degree. Longitude is not a place: it is a clock running behind. The problem of position at sea thus reduced to a problem of horology — knowing what time it is at home while you are on the other side of the world — and for the seventeenth century this was as much as to say it was insoluble: the best clocks on land, the masterpieces of Huygens included, became scrap iron at sea, dazed by the rolling, the salt, and the swings of temperature that expand metals and unstring springs.

The consequences were not only shipwrecks. Unable to know their longitude, captains sailed “by latitude”: they ran down to the right ring and then ran along it, straight west or east, on routes everyone knew — pirates and privateers first of all. Crossings stretched by weeks, and the extra weeks were paid in scurvy, the disease of slowness, which killed more sailors than all the battles of the century. Unknown longitude was a universal tax on commerce and on war: every ship paid it, on every voyage, in time, in men, and in lost cargoes. For this reason the problem, apparently technical, was in truth the strategic question of the age; and for this reason, in the summer of 1714, the English Parliament did what governments do when they cannot solve a problem but know what it costs: they put a prize on it.

A prize for the impossible

The Longitude Act of 1714 was not a new idea: the Spain of Philip II and then Holland had already put up prizes for longitude, and Galileo in person had negotiated with both his own solution — the eclipses of the satellites of Jupiter, a celestial clock perfectly regular and visible from the whole planet. The idea was splendid and worked very well: on land. It remade the cartography of Europe, shortened France by a few degrees (Louis XIV complained, so it is said, of having lost more territory to his astronomers than to his enemies — the anecdote is too fine to be guaranteed, and is to be taken as such), but at sea it was useless: no one has ever held Jupiter in a telescope from the deck of a rolling ship.

The English initiative began from below, as befits a nation of shipowners: a petition of captains, merchants, and officers of London reached Parliament in the spring of 1714, and the committee charged with examining it summoned as consultants the two most authoritative men available, Newton and Halley. Newton’s deposition is a small classic of technological assessment: he listed the four conceivable methods — the clock, the satellites of Jupiter, the lunar distances, and what we would now call perfected dead reckoning — and for each indicated the defect that kept it from the sea, noting of the clock that “by reason of the motion of the Ship, the Variation of Heat and Cold, Wet and Dry, such a Watch hath not yet been made”: not impossible, mark it, only not yet made — the exact formula that separates scepticism from prophecy. As for the immediate spark, it was the loudest proposal of the year: Whiston and Ditton, two mathematicians, suggested anchoring lightships along the oceanic routes, charged with firing luminous shells at midnight visible and audible for scores of miles — an idea hydraulically impracticable (the oceans are deep) but which nonetheless forced everyone to discuss the problem, and Parliament to legislate. The prize raised the stakes to an unprecedented level: twenty thousand pounds — several million today — to whoever furnished a method for determining longitude within half a degree at the end of a voyage to the West Indies; lesser prizes for lesser precisions. To judge, a college of admirals, professors, and members of Parliament was instituted, the Board of Longitude: it would cross the century as the longest-lived technical-scientific committee in English history, and as the target of all the curses of this chapter [Sobel 1995].

The bounty attracted all sorts, and the list of absurd proposals is a genre to itself: the most famous proposed distributing aboard ships the “powder of sympathy,” a magical remedy which, applied not to the wound but to the weapon that had inflicted it, would make the injured dog taken aboard start at a distance — one had only to stab in London, every day at noon, the dog’s bandage, and the yelp would give the time of Greenwich aboard. Whether it was a serious proposal or a satire of the serious ones, historians still dispute; that it circulated tells how far beyond reach the problem seemed. The sensible roads, in fact, were only two, and they had been known to all since the sixteenth century. Either one built a clock able to carry the time of home across the ocean; or one used the one clock already installed above the ocean, the sky itself — not Jupiter, too difficult, but the Moon, which moves across the ground of the fixed stars by one of its own widths every hour, a slow hand on a dial of constellations. The method of “lunar distances,” however, required two things that did not exist in 1714: tables of the lunar motion precise enough not to spoil everything, and an instrument for measuring angles from the deck of a ship. It is no accident that the Royal Observatory at Greenwich had been founded, as early as 1675, with the explicit mandate of putting order in the sky “for the perfecting of the art of navigation”: the observatory had been born as the technical office of the longitude problem, and the thing, as we shall see, would have consequences down to today — it is by this thread that the time of the whole world would come to be called “Greenwich.”

While Harrison filed his gears, the lunar method too was filling its two gaps, and by hands no less memorable. The instrument arrived in 1731 with Hadley’s octant, father of the sextant: two mirrors that bring the heavenly body to rest on the horizon within the same eyepiece, so that the rolling moves both targets together and the angle stays legible even from a deck that pitches — the first measure of precision ever made possible on an unstable platform. The tables came from Germany: Tobias Mayer, an astronomer of Göttingen, tamed the motion of the Moon — the most capricious problem in celestial mechanics, on which Newton and Euler had blunted their pens — into tables accurate enough, and sent them to the Board. They worked: and the Board, which the myth paints as a congregation of persecutors, paid them too — three thousand pounds to Mayer’s widow, who had died in the meantime, and three hundred to Euler for the underlying theorems. The prize for longitude, never “won” in full by anyone, was in fact distributed in instalments over half a century to whoever had moved the problem along: clockmakers, astronomers, astronomers’ widows. As a research-funding agency, the Board worked far better than as a jury.

It is worth fixing at once the point that the myth of longitude tends to blur: the clock and the Moon were not a good idea and a bad one, they were two good ideas with complementary defects. The clock, had it existed, would have been simple to use but impossible to verify at sea: if it breaks down or drifts, it lies, and it lies with the same face with which it tells the truth. The lunars were laborious but do not break down: the sky has no springs. How laborious, the scene as it really was makes clear: three observers on deck in the same instant — one taking with the sextant the distance between the Moon’s limb and a star of the zodiac, the other two the altitudes of the two bodies above the horizon — then down to the cabin, to “clear” the observed distance of the effects of refraction and parallax with pages of trigonometry, and at last the comparison with the tables to read, in that corrected distance, the time of Greenwich the Moon was marking on the dial of the stars. A trained officer, before the almanac of which we shall speak, took four hours over it; a clumsy one took a wrong course. A century later, the well-equipped ships would use both: the chronometer for daily use, the Moon to check the chronometer. But to get there someone first had to build the impossible clock; and here the story becomes the story of one man alone, because for forty years he truly was alone.

The carpenter who stopped time

John Harrison was a Yorkshire carpenter transplanted to Lincolnshire, the son of a joiner, an amateur organist, a fierce reader of everything that came his way on mechanics. He had no clockmaker’s shop nor apprenticeship behind him: his first clocks he built, literally, of wood — oak and boxwood, with gears shaped along the grain so they would not split — and they still run. As an unknown provincial he had already solved, for his bell-tower pendulums, two problems that tormented the professionals of London: thermal expansion, mastered with the “gridiron” pendulum in which rods of brass and steel lengthen in opposite directions and cancel each other out, and friction, almost abolished with an escapement of his own invention, called the “grasshopper” for the way the teeth alight and leap away, so gentle as to need no oil — and the oils of the eighteenth century were the leading cause of death of clocks. The escapement is the point where a clock lives or dies: Harrison had already left his mark there before touching the sea [Landes 1983].

In 1730 he brought to London the design of a marine clock. And here the myth of the craftsman thwarted by the academy meets its first problem, for the academy received him with open arms: Edmond Halley, Astronomer Royal and member of the Board, heard him, encouraged him, and directed him to George Graham, the most authoritative clockmaker in England — who, after a day’s conversation, lent him money out of his own pocket, without interest or security. The first marine clock, H1, was thus born in five years of labour: a machine of gleaming brass over thirty kilograms, with two great linked balances oscillating in opposition, immune to rolling by construction. Tried on the Lisbon route in 1736, on the return it corrected the pilot’s reckoning by some sixty miles: the Board, impressed, did what no myth records — it funded Harrison, with the first of a long series of grants that would sustain his work for decades. The relationship between the carpenter and the Board began as a research contract, not as a war; the war would come, but later, and for reasons more interesting than contempt [Sobel 1995].

There followed thirty years that are told in three abbreviations. H2, more robust, was never tried at sea — there was the war with Spain, and the Admiralty did not want to make a gift of the prodigy to a privateer — and it was Harrison himself who condemned it, finding in it a flaw of conception in the balances. H3, begun in 1740, held him prisoner for nineteen years: a machine of hundreds of parts in which he invented, among other things, the bimetallic strip — the strip of brass and steel welded together that curves with heat and straightens the balance, today inside every thermostat on the planet — and the caged-roller bearings that are the ancestors of ball bearings. It never satisfied him: H3 was a masterpiece that did not reach its own bar. The turn came from where no one, not even he, expected it: from a pocket watch. For years Harrison had believed, with everyone, that only a large slow machine could be stable; then a portable timepiece built to his design by a London colleague opened his eyes to the contrary. A small but fast oscillator, high in frequency and high in energy, crosses the sea’s perturbations as a spinning top crosses the bumps: it does not suffer them, it skims over them. H4, finished in 1759, is a silver disc thirteen centimetres across, a kilo and a half of mechanism with rubies and diamonds at the points of friction: the object that closes a problem two centuries old, and which Harrison, at sixty-six, called simply “my Watch” [Landes 1983].

The trial and the war of attrition

The official trials were two, both toward the Caribbean. In 1761–62 H4 sailed to Jamaica in the hands of William Harrison, son and operative arm of the old man: on arrival, its accumulated error was measured in a handful of seconds — a position within the requirements of the maximum prize, and beyond. The Board did not pay: the regulations were badly written, the verification of the arrival longitude debatable, and above all a single stroke does not distinguish merit from luck — a clock that drifts may, by chance, drift toward the truth. The objection was quibbling in manner and sensible in substance, and it is the heart of the whole affair: how does one certify a single object? The second trial, toward Barbados in 1764, was secured by astronomers at both ends: H4 arrived with an error of about ten miles, three times within the requirements of the twenty thousand pounds. At that point the problem was no longer whether the clock worked, but what the prize was meant to buy: a miraculous object or a method for making others? [Sobel 1995]

Parliament, with the Act of 1765, chose the second answer and translated it into conditions: half the prize on delivery and on explanation — Harrison had to take H4 apart piece by piece before a commission of experts, surrendering in an afternoon the secrets of a lifetime — and the other half when the design had proved reproducible by other hands. The demand was institutionally impeccable and humanly cruel, and the old man lived it as an expropriation. The rest of the decade was a war of attrition: the clockmaker Larcum Kendall received the commission to copy H4 and drew from it K1, a replica so perfect that Harrison himself praised its workmanship; Harrison, by now nearly eighty, built with his son H5, the second exemplar required; and when the Board went on demanding trials, he went over everyone’s head to the king. George III, who dabbled in science in earnest, had H5 tried in his private observatory for ten weeks and, by the account handed down in the family, promised: “By God, Harrison, I will see you righted.” In 1773 Parliament voted the old man a sum equal to the balance of the prize — as a sovereign recognition, however, not as a winning: formally, the twenty thousand pounds of the Longitude Act were never “won” by anyone, and the Board went on for another half century funding tables, instruments, and expeditions. There is indeed a reckoning the myth never makes, and it is worth making: adding up the forty years of grants, the partial prizes, and the final balance, Harrison received from the public purse more than the twenty thousand pounds of the proclamation. The system that exasperated him had also maintained him, funded him, and at last paid him: it is not the Board’s absolution, for the Board was often pedantic and sometimes mean, but it is the difference — which this book will meet again — between a story of heroes and villains and a story of institutions grappling with a new problem: how does one buy, with everyone’s money, a thing that does not yet exist? Harrison died three years later, at eighty-three, rich, embittered, and immortal [Sobel 1995].

In this story the modern public has learned to see a villain, and he bears the name of Nevil Maskelyne: astronomer, clergyman, from 1765 Astronomer Royal and so an ex-officio member of the Board, and champion of the rival method. The portrait demands justice as much as the affair itself. Maskelyne was no envious courtier: he was the most serious professional of the lunar method, the man who turned the lunar distances from an acrobatics for mathematicians into a procedure for naval officers. His Nautical Almanac, published from 1767 and then every year, offered the positions of the Moon pre-calculated for every three hours: the shipboard calculation crashed from four hours to half an hour, and the sextant — the other child of the century — did the rest. Behind the almanac there was an invisible factory that deserves a line, for it is metrology applied to people: a network of home computers scattered across England — schoolmasters, curates, the odd mathematician’s widow — to whom Maskelyne sent the ephemerides to compute, always in independent pairs ignorant of one another’s existence, with a third “comparer” paid to find the divergences. Two blind calculations and a comparison: it is the same logic as the three chronometers aboard and the repeated measures, applied to mental labour — human error treated, a century early, as a variable to be designed for. Maskelyne had structural conflicts of interest, certainly: in 1766 he held H4 under trial at Greenwich for nearly a year and published a report of it severe to the point of ungenerousness — the clock, tried under conditions Harrison judged captious, came out unreliable — and the old man answered him with a vitriolic pamphlet, opening a war in print that delighted the booksellers. But his underlying thesis was correct: a method for the world’s navy cannot depend on a single piece issued from the hands of a genius, and until the chronometers became an industry, the lunars were the only public solution — reproducible by anyone with a sextant, an almanac, and patience. The true story is not the duel between a hero and a bureaucrat: it is the conflict, genuinely difficult, between the excellence of a prototype and the requirements of a standard. The reader of the previous chapters recognizes the theme: a measure, to exist at all, must be able to dwell in many hands.

The hour goes to sea

The reconciliation was made, as often, by markets and trades. Kendall had shown that H4 could be copied, but a copy cost as much as a small ship; the next generation of London clockmakers — John Arnold and Thomas Earnshaw above all, rivals at white heat — redesigned the chronometer for production: simpler and more robust escapements, standardized compensation balances, repeatable parts. In a generation the price fell by an order of magnitude, and “chronometer” ceased to be a proper name and became an inventory item. Nineteenth-century maritime practice settled on a wisdom that would deserve a treatise: serious ships carried three chronometers. Not one, because a single clock that errs you cannot detect; not two, because two clocks in disagreement leave you in doubt; three, because the majority unmasks the traitor. It is the first appearance, in the form of wood and brass, of a principle we shall find at the heart of modern metrology: trust never dwells in a single instrument, it dwells in the organized comparison among instruments [Landes 1983].

Around the chronometer there grew also a discipline, made of daily gestures and of a subtle idea. The gestures: wind every morning at the same hour, never two windings, a register of temperatures, and the object suspended on gimbals in its box, untouchable as a tabernacle. The idea, which is the true intellectual legacy of chronometry, lies in the “rate”: no one cares whether the chronometer is exact — no mechanical clock is — what matters is that it err always in the same way. A chronometer that gains a steady two seconds a day is a perfect instrument: one notes the rate at departure and corrects with a multiplication; one that swings unpredictably between plus and minus one is useless. The distinction between the constant error, which is measured and subtracted, and the capricious error, which can only be suffered, is the backbone of the theory the sixth chapter will see born; the captains were already practising it, with the rate-book, half a century before it had a name. And the observatories institutionalized it: Greenwich took to organizing annual trials in which factory chronometers competed for months inside ovens and ice-boxes, classed by the stability of their rate, and the trial certificate became a price on the list. The state no longer bought miracles from a lone genius: it bought certified regularity from an industry — the Board’s problem, solved by administrative means.

The most famous trial, meanwhile, had been signed by the greatest navigator of the century — and it is an instructive trial precisely because it was no act of faith. On his first voyage Cook had sailed without a chronometer, taking lunars with Maskelyne’s almanac; on the second, between 1772 and 1775, he carried K1 from the Antarctic to the tropics together with the lunars, using the sky to weigh the clock and the clock to lighten the sky. He came back converted: in the log K1 is “our trusty friend,” the “never failing guide.” Cook’s route — three years of unknown oceans charted with a precision that stayed in use for a century — was the field demonstration that closed the discussion in the only honest way, by making the rivals work in pairs: from then on the question was no longer whether the chronometer, but how many and at what price. There remained the serving of the clock, for a chronometer is only as good as the time you put into it: the ports equipped themselves to give it. From 1833, on the roof of the Greenwich observatory, a black ball rises and falls every day, at one o’clock precisely, visible from all the Thames: the captains regulated their chronometers on that drop, and the ball — which still drops — is the first public time signal in history, the direct ancestor of the six pips of the radio. Exact time was becoming a service.

It was the telegraph, in the mid-nineteenth century, that closed for good the terrestrial side of longitude. Two observatories linked by a wire can exchange signals and compare their clocks to a tenth of a second: the relative longitudes of the continents, pursued for centuries with eclipses and chronometers in suitcases, became routine measures, and when in 1866 the transatlantic cable entered stable service, America too knew at last, to a hundred metres, where it was with respect to Greenwich. There is an elegant symmetry in this passage: the problem of longitude had been born as a problem of transporting time, and it died at the moment time ceased to travel by ship and began to travel at the speed of light. But that very wire, stitching the observatories together, was about to stitch something else: the hours of the living.

The hour of the world

As long as one travelled on horseback, every city lived serenely in its own noon: Bristol is ten minutes west of London, and ten minutes after London its sun culminates — what else should an honest clock mark? It was the railway that made the obvious intolerable. A train crosses in a few hours a dozen local noons; a timetable written in twelve local hours is a riddle, and two trains on the same line with two different hours are an appointment with disaster. The English companies cut the knot with the sword: from 1840 the Great Western adopted for all its stations the time of London — Greenwich time — and within a decade nearly all the railways of the realm followed it. “Railway time” overrode the bell-towers: in the provincial towns the public clocks took to marking two truths, and for some decades England lived in a double accounting of time that today seems a hallucination.

Only in 1880 did Parliament sanction what the railways had already done: the legal time of the island would be that of Greenwich. The sun, for the law, had ceased to give the hour [Landes 1983].

The United States, four time zones wide, lived the problem multiplied: scores of competing “railway times,” stations with three dials, connections missed for ambiguity of noon. The solution was imposed, once again, by the companies, without waiting for Congress: on 18 November 1883 — the “day of the two noons,” because east of each new time boundary the clocks went back and noon struck twice — the North American railways divided the continent into time zones of exactly one hour, anchored to standard meridians. The idea of extending the system to the whole planet already had its apostle, the Canadian railway engineer Sandford Fleming, and found its seat the following year: in October 1884 twenty-five countries gathered at Washington, at the invitation of the American government, to choose the zero meridian of the world. France proposed a “neutral” meridian; the Atlantic islands evoked to that end convinced no one; and the final count was merciless: Greenwich was chosen as prime meridian with a single vote against, because — the decisive argument — about two-thirds of the world’s tonnage already sailed on charts that counted from Greenwich, in homage to a century of the Nautical Almanac. The conference also recommended the universal day and the time zones; France, wounded, officially kept the time of Paris until 1911, when it aligned itself with Greenwich by a law that defined French legal time as “Paris mean time, retarded by nine minutes and twenty-one seconds” — Greenwich time pronounced without naming it, a masterpiece of horary diplomacy. The rest of Europe fell into line by degrees and by railway: Italy, which since 1866 had lived on the time of Rome, passed in 1893 to the time of Central Europe — the zone that governs us still — to make peace with the international train timetables. Thus the mandate of 1675 was fulfilled by the longest road: the observatory founded to give the hour to mariners ended by giving it to the planet — not because an empire had imposed it by force, but because an infrastructure of charts, almanacs, and habits had made it the world’s default. Standards, a lesson we shall meet again, are won more with catalogues than with cannon.

A word on the mean time that was winning: noon too, like everything in this book, had been tamed. The true sun is a poor clock — it speeds up and slows down with the seasons, by reason of the elliptical orbit and the tilt of the axis — and the astronomers had long since replaced it with a mathematical average of itself. The time of the zones is therefore twice artificial: the time of a sun that does not exist, counted from a meridian where almost no one lives. The reader of the first chapter, the one of the unequal hours long in summer and short in winter, can measure here the whole parabola: in five centuries time had passed from representing the day as lived to regulating it from an office in London.

Coordinated time

There remains the last question, the deepest, and it was a mathematician who put it in the right way. Henri Poincaré spent years inside the French time-machine — at the Bureau des Longitudes, among telegraph cables, geodesists, and synchronization protocols — and in 1898, in an essay entitled The Measure of Time, he laid bare what everyone did and no one said: when we assert that two distant events are simultaneous, we are not observing a fact, we are applying a procedure. The telegraphers who synchronized Paris with the provinces — and then with Dakar, with Quito, with Indochina — sent a signal, received the reply, and divided by two the time of the round trip: the simultaneity that came out was not discovered, it was constructed, with a correction for the travel of the signal. The “true” time, universal, flowing equal for all above our heads, appears in none of these operations; only coordinated time appears, fabricated from clocks, wires, and conventions of calculation. A few years later, a young examiner at the Bern patent office — across whose desk passed, for a living, the patents for the synchronization of the electric clocks of the Swiss stations — took that procedure and promoted it to a definition: in the relativity of 1905 simultaneity is the protocol of synchronization with light signals, and from that taking-seriously of the convention there follow, with the logic of a theorem, all the marvels and scandals of relativistic time. It is not a case of philosophy overhearing technique: it is the technique of measure — telegraphs, longitudes, station clocks — that becomes philosophy, and then physics [Galison 2003].

Here the conceptual graft of the chapter lets itself be said in three words: to coordinate is to define. The first chapter showed that to measure is to institute a convention between strangers; time carries this truth to its extreme degree, because of time there is not even the illusion of a standard one could wall into a wall — there is only the agreement, kept instant by instant, among clocks that speak to one another. Exact time is a network, not a thing: so was the Greenwich ball, so were the radio signals that from 1910 the Eiffel Tower — redeemed from uselessness precisely by the time service — rained upon the chronometers of half the world, so is the Bureau International de l’Heure born shortly after to arbitrate among the observatories, direct ancestor of the institutes that today assemble the legal time of the planet. When the reader reaches the eighth chapter, where clocks that err by one second in an age of the universe compare themselves by optical fibre and satellite, he will recognize the same architecture: more precision, identical philosophy.

And Harrison? His direct legacy is in the pocket of anyone reading these lines. The global positioning system is, to the letter, Harrison’s solution promoted to cosmic infrastructure: a constellation of atomic clocks in orbit that transmit exact time, and a receiver which, comparing the delays of the signals, calculates its own position — longitude included, naturally — as the navigator compared the chronometer with the sun. Every difference measured in nanoseconds is worth, on the ground, about thirty centimetres; and the clocks in orbit must be corrected every day for the effects of relativity, which at those altitudes and speeds shift time by tens of microseconds — enough, neglected, to accumulate kilometres of error in the course of a day. The chain is vertiginous but straight: from the carpenter who wanted to carry the time of Greenwich to Jamaica, to the telegraph that carried it into the continents, to the radio that carried it into homes, to the satellites that carry it into every telephone — always the same problem, knowing what time it is elsewhere, and always the same answer, building trust among distant clocks. Time, meanwhile, had become a matter too serious to leave to one nation alone: and indeed, in the very decades when the world was giving itself a common hour, it was giving itself — for the first time in history — also a common office of measures. It is a treaty signed in Paris in 1875, and it is the story of the next chapter.