On 12 May 1735 a ship, the Portefaix, set sail from the port of Rochefort on the Atlantic coast of France. Its destination was the West Indies, and its normal crew was accompanied by three members of the French Académie Royale des Sciences, an instrument maker, an engineer/cartographer, a draftsman/artist, two doctors, two assistants and a considerable quantity of equipment. This group would meet up with two Spanish naval officers in the West Indies before sailing on to Panama, where they would cross the isthmus, take another ship to the Peruvian coast, and then proceed by river and mountain roads to the equatorial city of Quito (now the capital of Ecuador). The aim of this Franco–Spanish mission was to measure, on the ground, the length of a degree of latitude, in order to decide once and for all whether the Earth was flattened at its poles (as predicted by Newton) or elongated like a rugby ball (as had been deduced from the theory of Descartes).

As the complexity of the journey indicates, this was never going to be easy, yet the potential rewards were huge. Controversy over the shape of the Earth had raged in the Académie for years, with strong positions being taken by both sides. Not only was the Earth’s shape a crucial distinction between Newtonian and Cartesian theories of gravity, ocean navigation also depended on knowing it, and experimental data obtained from measurements along the meridian in France were inconclusive. It had become clear that measurements must be made where the differences between the two theories would be greatest – namely, near the poles and near the equator. Hence, the Académie launched two geodesic missions, one to Lapland and one to Peru, each accompanied by its own standard of length. Known as the toise du Perou and the toise du Nord, the two standards were made of iron and had been constructed to be as close as possible in length. They would be compared again when they returned from Peru and Lapland to ensure that the two missions’ measurements were comparable.

This is how matters stand near the beginning of the narrative in Larrie Ferreiro’s Measure of the Earth, which takes as its subject matter both the Peruvian geodesic mission and the historical circumstances in which it took place. Ferreiro’s introduction sets the context of the story very well, as he describes not only the background to the scientific arguments, but also the political and national rivalries surrounding the mounting of such a mission. Some of the most important rivalries were, in fact, those that developed between the expedition’s participants as they jockeyed for position in the Académie. Competition between the main players is a theme that runs through the whole story – right up to the disputes about the publication of the results.

The Academicians who set off for Peru were Louis Godin, an astronomer and initially leader of the mission; Pierre Bouguer, an astronomer, mathematician and hydrographer who soon took over from Godin as leader; and Charles Marie de la Condamine, a scientist and adventurer whose name is now the one most associated with the expedition. Having arrived in Quito in May 1736, a year after setting sail, they immediately began laying out and measuring the length of a 10 km baseline that stretched along an east–west line near the equator.

This was a necessary first step for their overall plan, which was to lay out on the ground a set of 30 linked triangles stretching south for 300 km, representing about three degrees of latitude. The summits of the double column of volcanoes stretching due south from Quito would provide vantage points for triangulation. Once the baseline was complete, the next step was to measure the angle between each end of it and the first volcano. From these two angles and the length of the baseline, the researchers could calculate the lengths of the other two sides of this first triangle, and hence the position of the first volcano summit relative to the baseline. Using one of these other sides as a new baseline, they would repeat the operation with another volcano further south, until they had covered the full mountain range. The distance from the original baseline to the farthest summit could thus be calculated as a multiple of the length of the original baseline. The final operation was to determine the difference in latitude represented by this distance. This they did by measuring, from each end of the chain of triangles, the altitude of a particular star. Dividing the length of the chain by the difference in latitude would tell them the length of a degree of latitude.

They completed their baseline in October 1736, which might seem like fairly good progress, considering that they had only arrived in Quito that spring. However, according to the original schedule, by that time they should have already been halfway down the volcanic chain. Indeed, the entire mission was supposed to take only three years. In the event, the final star sightings were completed and the final result calculated only in January 1743, nearly four years late – and the scientists still had to get home.

One reason for the delay was that the scientists had severely underestimated both the difficulty of working at high altitude (Quito is 2800 m above sea level) and the vagaries of the weather, which meant that they sometimes waited months for a clear sight of a distant reference point. Worse, the local population was suspicious and hostile. Word had got around that the researchers were a band of adventurers intent on finding and stealing gold, so the arms they had brought to protect themselves from wild animals were more often used instead to protect themselves from local people. The ever-present bureaucracy also made life difficult for them, especially when the newly elected captain general of the region initially refused expedition members’ entreaties to cash letters of credit.

The final, and perhaps most severe, source of delay was that the senior members of the expedition quickly fell out among themselves. Even before they left France, it was clear that Godin had no idea how to treat his men, and he disputed endlessly with Bouguer and Condamine regarding the plans for the expedition. Soon after their arrival in Quito, his role was taken over by Bouguer. However, this was just the beginning of a series of rivalries, all of which Ferreiro recounts in great detail, basing his account on the many letters and reports that survive. There is a fascinating story here, and I particularly liked the wealth of additional information and comment in the extensive notes at the end, which are much more than simply bibliographic references.

The final extraordinary part of the story concerns the scientists’ journeys home. The French side of the expedition had been financed by the Académie, so the three Academicians all got back relatively quickly: Bouguer in 1744, La Condamine six months later and Godin, who carried the famous toise, in 1751. It transpired, however, that no arrangements had been made to bring home junior members of the expedition. As a result, they were essentially abandoned in Peru. Two never managed to get home at all, dying in South America many years later. Meanwhile, Godin’s young cousin, who was one of the assistants, spent 15 years waiting at the mouth of the Amazon because the Portuguese authorities refused to give him permission to travel up the river. The authorities would not even let him send a message to his wife, who had been stranded 1000 km upstream after becoming pregnant. She eventually managed to make her own way down (after all her children had died), and was finally reunited with her husband. They sailed back to France more than 30 years after the Portefaix had left Rochefort.

That the Geodesic Mission to Peru eventually succeeded in everything it set out to do, despite many difficulties, was a tremendous achievement for all concerned. The result, which confirmed the information obtained (with much less difficulty) by the Lapland mission, showed that Newton was right: the Earth is an oblate spheroid flattened at the poles. But perhaps more importantly, according to Ferreiro, theirs was the first truly international scientific project. Those of us who participate in modern international collaborations must be grateful that, even with airport delays, our journeys around the world take days rather than years, and family members do not end up stranded in the jungle!

• 2011 Basic Books £15.99/$28.00hb 376pp