The Girth of the Earth

Forty years, ten countries, one line

Friedrich Georg Wilhelm von Struve spent forty years measuring the circumference of the earth, finishing in 1855. His answer was off by 1,679 metres — about 0.004%.

He fathered eighteen children by two wives. (You live in the abundance of 2026 inner Sydney and wonder how you could possibly have children. You are a eunuch.)

The Struves were a freak of heredity — five generations of working astronomers, rivaled only by the great astronomers of the Herschel dynasty (William, who found Uranus; his sister Caroline, who found eight comets; his son John, who mapped the southern skies from the Cape; his grandson Alexander who carried the family into meteor spectroscopy). Friedrich, twenty-three years old in 1816 and based at the Imperial Observatory at Dorpat in Russian Estonia, decided he would measure his planet. To the inch.

The first man to measure the circumference of the earth did it with a shadow and a well, in 240 BC. Eratosthenes of Cyrene was chief librarian at Alexandria — appointed by Ptolemy III to keep the largest collection of scrolls in the world. Critics, recorded centuries later in the Suda, nicknamed him Beta because he was perennially second-best: at poetry, mathematics, astronomy, music theory, geography, philology. He had heard about a well at Syene — modern Aswan, six hundred miles up the Nile — where, on the longest day of the year, at noon, the sun struck the water at the bottom of the shaft directly.

The implication, to Eratosthenes, was geometric. If the sun stood directly above Syene at that moment, a vertical stick anywhere else on Earth would, at the same moment, cast a shadow that betrayed the curvature of the ground between the two points. He drove a gnomon — the vertical rod of a sundial — into the soil at Alexandria, waited for noon on the solstice, and measured the angle of its shadow: seven point two degrees, exactly one fiftieth of a circle. The distance from Syene to Alexandria was, by the count of the bematists — professional pacers in Ptolemaic employ, trained from boyhood to walk in unvarying strides across desert and floodplain — five thousand stadia. Multiply by fifty. Two hundred and fifty thousand stadia for the whole circumference of the planet. Nobody today is entirely sure which stadion he was using; the Greeks had several. Depending on the conversion, his figure falls somewhere between thirty-nine and forty-six thousand kilometres — off by, at worst, a few percent; at best, a fraction of one.

Struve endeavoured for greater precision. He would mark a single line of longitude — a meridian — running 1,600 miles from the Arctic coast of Norway down to the Black Sea, conveniently passing through his home in Dorpat. He began on his own front doorstep. He scratched a small letter X into the marble step of his observatory and worked outward from there.

He would use triangulation. Measure one side and two angles, and the rest of the triangle reveals itself. Pick a distant hill or steeple. Sight to it from one end of a known baseline. Move to the other end. Sight again. Three angles, summing to 180 degrees by Euclidean fiat — and now the two remaining sides could be deduced.

What that looked like in practice was hauling heavy brass-and-glass instruments — German theodolites, twelve-foot zenith sectors, quadrants that took two men to lift — through swamp and forest and snowstorm, across rivers and lakes and the wind-blasted ice of the Scandinavian north. Where there was no convenient hill or church spire to sight from, the surveyors built their own wooden towers and dragged the gear up with rope and pulley. To take one reading across the Gulf of Finland, they scaled the spire of an old church, built a platform among the bats, and watched for the answering flash of a heliograph — a mirror that signalled by catching the sun — mounted on a tower they had themselves erected on the opposite shore.

In total: 258 main triangles. Ten baselines for cross-checking, laid out with chains of brass that resisted the swelling of summer heat and the contraction of winter cold. Forty years of it.

The work proceeded in fits and starts, dependent on the moods of the imperial treasury. The breakthrough came in the late 1830s when Tsar Nicholas I — by training an engineer, never having expected to inherit the throne — became enchanted with the project. He built Struve a new observatory at Pulkovo, south of the Winter Palace, and shipped in a thirty-inch refracting telescope from Cambridge, Massachusetts. With the imperial coffers flowing, the arc advanced. The line was at last completed, Hammerfest to the Black Sea, in the summer of 1855.

Each of Struve’s stations had been fixed by drilling deep into bedrock, pouring molten lead into the cavity, sinking a steel bolt through the cooling metal, and capping the assembly with a brass plate — foundations that now lie scattered across ten countries, from Norway to Ukraine. In 2005 UNESCO declared what was left a World Heritage Site. By that point only thirty-four of the original points could still be located. The rest had been ground down by frost and vandals, or pried up by hunters who melted the lead into buckshot.

Struve measured a quarter meridian of 10,002,174 metres, deducing a planetary circumference of 40,008,696 metres. NASA’s modern satellite figure is 40,007,017. Struve had been off by 1,679 metres. Eratosthenes, working with a stick and a shadow in Alexandria two thousand years earlier, had been off by 1.4 million.