2

  The Size of All the Earth

  Unbounded freedom ruled the wandering scene

  Nor fence of ownership crept in between

  To hide the prospect of the following eye

  Its only bondage was the circling sky

  —JOHN CLARE, “THE MORES” (1837)

  Finding one of the survey marker points for what is now called the Struve Geodetic Arc in central Latvia turned out to be a little less easy than I imagined. The rented car was old, its driver a little unfamiliar with the territory, it was raining, and we managed to get a flat tire. But by great good fortune there was a farm nearby and a couple of Britons who raised alpacas on it, and they had the necessary tools and a jack. After we had bolted on the spare wheel and been fed on strawberries and tea—and had petted the alpacas, perhaps not an everyday occurrence in contemporary Latvia—the rain eased somewhat, and then we were off again into the woods. Eventually we came across a green metal notice by the dirt road on which we were traveling, and behind it was a footpath that led up a hill to a clearing.

  The sign identified this otherwise sparsely inhabited and unremarkable spot in the woods as lying in the parish of Sausneja, on the far outskirts of the town of Ergli, in that middle part of Latvia once known as Livonia. This was a part of the Baltic countryside that had been battled over for centuries by, in particular, the armies of Germany, Poland, Russia, and Sweden. Locally all had been peaceful for some recent years—although painful memories of the Nazi occupation and the fifty years of Soviet rule that followed were still fresh.

  There is constant local fretting today that the Russians might well soon return, laying claim to lands that some in Moscow and St. Petersburg have long believed still rightly belong as a crucial Baltic component of their empire. The average Latvian is thus only too well aware that the farmland that makes up most of his country has been all too frequently demanded by others, has been fought over and requisitioned by outsiders, and is still claimed by foreign rivals who see the dwindling presence of the two million Latvians—whose distinctive language, culture, and music have survived centuries of tussling and threatened eradication—as a mere inconvenience. The historical fate of land worldwide could easily be illustrated by the situation of Latvia’s sixteen million acres: they have been variously bought, sold, owned, seized, fought over, confiscated, and ultimately parceled out to private owners, a melancholy parable of territorial ambitions and desires. And yet right here, in the middle of this Baltic nowhere, is something belonging to all the world.

  On the footpath leading up into the woods the grass was slippery from the showers, and clouds of mosquitoes frothed languidly under the dripping branches. After a quarter of a mile, at the low summit from which through the thinning trees we had a fine view of the meadows, small lakes, and rivers below, there was what I had hoped for: a three-foot obelisk standing guard beside a flattish alien stone that was half-buried in the ground, almost invisible among the grasses. The stone—granodiorite by the look of it and probably brought in from the hills up near the Estonian border—had a large X crudely incised on its weathered surface. It was a marker, said a plaque on the obelisk, that had been placed there in 1821. It was one of two surviving relics in Latvia of what since 2005 has been designated a United Nations World Heritage Site, as illustrating one of the first and most important attempts to establish with great accuracy the size and shape of Planet Earth.

  It was the Greek librarian-scholar-astronomer Eratosthenes who famously first computed the circumference of our planet, some 2200 years ago. He did so by comparing the angle at which the sun’s noontime rays fell onto the water wells in Alexandria, his Egyptian hometown, on the same day that they fell vertically on, and thus illuminated the very bottom of similar wells in Aswan, some 524 miles upriver along the Nile. The shafts of sunlight in Alexandria were slightly off vertical, and Eratosthenes suspected that this was entirely due to the curvature of the Earth, if indeed the Earth was the enormous ball-shaped planet that many since Pythagoras, Plato, and Aristotle had suspected it to be. He measured the angular difference at 7 degrees—about one-fiftieth of the 360 degrees of the sphere. It followed, he reasoned, that if 524 miles was a fiftieth of the total, then the circumference of the sphere would be some 24,000 miles, nearly 39,000 kilometers—not too far from the roughly 40,007 kilometers that satellites, lasers, and GPS devices declare it to be today. For this hugely significant and pioneering realization, Eratosthenes of Cyrene, equipped only with a fine and logical mind, a protractor, a set square, and a plumb line, now occupies a deservedly permanent place in history.

  But fast-forward two thousand years, and to the more rigidly scientific minds of the early nineteenth century. A number of scientists of the time—notably many of them French, with names like Picard, Bouguer, La Condamine, Delambre—grappled with the knotty problem of ascertaining the Earth’s size and shape: Was it a sphere or a spheroid, oblate or prolate? Was it flattened at the poles, broadened at the equator? Their attempts mainly involved as precise as possible measurements of short stretches of the planet’s meridians, a few miles long—and the results were good, but not convincingly so. There had been some moderate success, for example, with surveys conducted in the late eighteenth century in Peru and Lapland, but the equipment available was comparatively crude, the lengths of the meridians unsatisfactorily short, the results unconvincing.

  For the results to be entirely satisfactory to the geodesists’ community it would require the measurement of one very long meridian line, hundreds of miles worth, and with exceptionally accurate instruments to make the measurements and perform the calculations. It took the chutzpah of a Russian, and the foresight of two imperial tsars, ruling at the very height of their empire’s global standing, to confront the problem head-on, to disdain the work of the ancient Greeks, and to dismiss what those in the Russian capital regarded as the halfhearted shillyshallying of the French measuring platoons and of those who had similarly tried in South America and the Scandinavian Arctic.

  One of the preeminent astronomers of the time, living in what was then the Russian possession of Estonia, was Friedrich Wilhelm Georg von Struve, of a family who—rivaled, perhaps, only by the Herschels*—uncannily produced five generations of highly competent astronomers. It was Struve who decided that, for the glory of his empire, it would fall to him to measure the world properly, and to do so with the greatest of precision. And since to do so required the measurement of the exact length of one of the planet’s meridians, or lines of longitude, he would do so along a track conveniently close to where he lived in Estonia, some 25 degrees east of Greenwich. (It is probably needless to say that only the measurement of longitude-line meridians will give the size of the world, since all those meridians pass entirely around the world. By contrast only one line of latitude—the equator—girdles the entire planet; the others—such as the Tropics of Cancer and Capricorn, or the Arctic Circle, are very much shorter, and encompass only fractions of the planetary sphere.)

  The task took Struve fully forty years. The Struve Geodetic Arc, by which he is now internationally memorialized, is one of the greatest—but also one of the least remembered—of the scientific achievements of the age. The traces of its progress are to be found passing through ten countries now, from the near Arctic north in Norway down to the warmth of the Black Sea west of Odessa in Ukraine. And passing, as it happens, through the alpaca-rich Latvian hamlet where the X is marked on an almost hidden piece of stone.

  A series of small markers, running in a line from Norway to the Black Sea, show where Friedrich von Struve measured the meridian to determine the exact size of the Earth.

  Struve was a young and exceptionally energetic man* when he formally began the survey at his observatory in the Imperial University in what was then the city of Dorpat—now Tartu—in Russian Estonia. His idea was to chart the exact length of his meridian running for about 1600 miles—and from this both derive the size and shape of the planet and by doing so enable the making of ever more accurate maps—a growing necessity since the private ownership and distribution of land was becoming ever more commonplace.

  He decided he would begin his survey beside the marble front doorstep of the yellow-and-white painted Dorpat Great Observatory, of which he was director—and which, thanks to the generosity and scientific curiosity of the Tsar Alexander I, he was busily stocking with a formidable and most necessary collection of telescopes and surveying equipment.

  One summer’s day in 1816, Struve and his fellow astronomers hauled out of the observatory basement the key elements of this stupendous accumulated arsenal of measuring devices—in prime position an enormous German-made theodolite (one of Struve’s surveyors had seven theodolites and would choose the one that best suited the reading he wanted to take), a twelve-foot-long telescope known as a zenith sector, a giant brass quadrant, and a set of precisely made surveyor’s chains. With infinite care and exactness and working with a team of Dorpat students, Struve used these and a variety of tripods and drills and tower-building equipment to measure first a long baseline between the observatory and a local hill, and from which he would then begin his historic triangulation.

  As its name implies, triangulation has everything to do, and with elegant simplicity, with the realities of the geometry of triangles. With the idea that if you can know the exact length of one of a triangle’s sides, and carefully measure the three angles of the figure, then the lengths of the other two sides can be calculated with dispatch. This unadorned fact of plain geometry has enabled the measuring, planning, and making of just about everything concerned with large tracts of raw and unimproved land—from the building of the Pyramids of Giza to the accurate placement of the Iron Curtain—and to the measuring of the size of the world.

  So, once Herr Struve had carved his letter X into his observatory doorstep, he performed two specific acts. First—by employing a sextant and a chronometer—he determined the latitude and longitude of his initial position. Next he created a baseline that originated from the center point of the X. By using either finely calibrated wooden or metal bars, or more usually special chains—Gunter’s chains most probably, each one 66 feet long and with 100 links, made of a brass that was little affected by changing temperature and would neither stretch nor shrink—he then determined the length of this baseline, with accuracy to the smallest possible fraction of an inch.

  He would next erect his Munich-made Reichenbach theodolite over one end of this line—with the instrument’s tripod center point poised exactly over the baseline’s measured end point—and using the graduated graticule of his theodolite telescope he would peer out across the landscape and select a prominent distant point, a hill or a steeple or a tree—and mark a notional second line all the way to that. He would then lug his theodolite and quadrant and zenith sector—or have his staff help him do so, since these instruments were formidably unwieldy and heavy things, enormous confections of brass and glass and wheels and gears and all mounted on metal-bound ash tripods—to the other end of the baseline: the doorstep end, where the triangle was begun. And from the new mounting point on top of the baseline’s exact origination point, just above the scribed letter X, he would peer through the lens and draw a third line to the self-same point (the hill, steeple, or tree), which he had seen from the line’s other end.

  By these somewhat cumbersome means he would have plotted himself a triangle. By doing this, he would also have drawn himself three angles—all of which would, by the ineluctable magic of Euclidean truth—add up to 180 degrees. By precisely measuring the three angles, once again with his theodolite, Struve would then be able to calculate the exact length of the other two sides of the triangle. They would be as accurately measured as the baseline—but this time not with chains, but with calculated mathematical deduction.

  This, then, is the basic magic of triangulation: that from measuring the exact length of just one line and then afterward drawing two more and measuring the resulting trinity of angles, the length of the two other lines—which would hitherto be unmeasured distances between places—could be worked out. Geometry was all: the notion of having to chain every line—through jungle, across mountains, or up slippery wet grass slopes in Latvia—was now entirely unnecessary. Simple mathematics—and formidably precise instruments fashioned with finely chased brass, lubricated bearings, well anchored and highly stable footings, and impeccably polished and perfectly shaped lenses were key—produced elegant and accurate answers, time and time again.

  It was slow and ponderous work. In total, the surveyors in these hinterlands of the Russian empire found it necessary to construct 258 main triangles, and for checking purposes to measure ten baselines—using varieties of chains and metal and wooden bars that, it was claimed at the time, could give an accuracy of length as great as one part per million. The men had to haul their immense instruments over swamps and lakes and rushing rivers, through forests and snowstorms and, in the wilds of the Scandinavian north, across brutally gale-swept ice fields.

  To make one set of triangles across the Gulf of Finland the men had to clamber up the inside the tiny spire of an ancient church, then build a platform among the bat-infested rafters, aim their brassbound telescope across the body of water, and peer through the sea fret for the pinpoint of flashing light from a heliograph that had been set up on a tower they had specially erected on the far side. Tower building was indeed a major part of the survey work: so often there was no available hill or steeple or lighthouse, and so a rickety wooden tower had to be constructed and the equipment hauled up it with ropes and systems of pulleys—the construction having the added benefit of allowing the triangulators to see above the tree line, for the spruce and Scotch pine of the northern forests tended to block the view.

  The project proceeded in fits and starts, its progress depending largely on the generosity of the St. Petersburg treasury on Nevsky Prospekt. It received a great fillip in the late 1830s, when Nicholas I, having assumed the role of tsar following the death of his brother Alexander, felt sufficiently in control of his empire* to demand the building of a new observatory in Pulkovo, just south of the Winter Palace. Tsar Nicholas, who never anticipated he would rise to the throne, was an engineer by trade, was fascinated by machinery of all kinds. Struve, now famous and honored by astronomical societies around the world, would be invited over from Dorpat to be the director of the new Pulkovo Observatory; he would be allowed to buy the best and the biggest astronomical devices then known—including a then legendary 30-inch refracting telescope built for him by the firm of Alvan Clark and Sons, close by Harvard College in Cambridge, Massachusetts.

  And sufficient money would now be pumped into the meridian project to complete it. As it duly was, in the summer of 1855. The line was at last fully measured, Hammerfest to the Black Sea; and from its length could be deduced the length of a quarter meridian, pole to equator. It had never before been done, and it produced metrics of an accuracy never before known.

  And thus the planet, it was calculated, now had a Great Circle of a carefully derived size and shape. Each quarter meridian, Struve’s teams declared in a massive tract that he published that summer, was worked out as being exactly 10,002,174 meters long. Its circumference was thus four times that, or 40,008,696 meters.

  It was staggeringly accurate. By comparison: the latest figure put out by NASA, based on satellite measurements, shows the planet coming in at 40,007,017 meters round. Eratosthenes, two thousand years before, had calculated the circumference as being, in today’s units, 38,624,000 meters. Herr Struve’s globe was larger than both, but not by much.

  With the world’s size now so carefully worked out—and a clutch of the world’s senior surveyors met in Paris in 1883, to begin the measuring of another nearby meridian that would head even farther south, all the way from Cairo, through the jungles of east Africa to the Cape of Good Hope, to make the calculations more perfect still—the team left for other work. The physical evidence of their art would remain, however. The actual reference points of the scores of huge European triangles, so precisely made—with long holes drilled into rocks, molten lead poured inside, steel bolts fixed into place as the lead cooled, brass plates secured on top, all to produce impeccably accurate foundations for the instrument—were left to suffer in the cold and heat of Finnish winters and Ukrainian summers. Weather, vandals, hunters (who liked to steal the lead to make into buckshot), and fast-growing vegetation gnawed away at the relics of the arc’s completeness. By the time, in 2005, when the United Nations decided that what remained of the Struve Arc be made a World Heritage Site—alongside the Grand Canyon, the Pyramids, Westminster Abbey, and the Sydney Opera House—only thirty-four of the original points could be found. The U.N. officials duly saw to it that monuments to Struve should be built all along the line, with big marble memorial columns at the two termini, in Hammerfest up in the Arctic north and the village of Staro-Nekrasivka down on the Black Sea coast. Ten countries—Norway, Sweden, Finland, Russia, Estonia, Latvia, Lithuania, Belarus, Moldova, and Ukraine—now play host to Herr Struve’s monumental achievement.