After the expedition – results, reception, significance and verifying measurements
It is easy to imagine that Maupertuis and his expedition returned to Paris feeling pleased with themselves. They had taken their measurements, which confirmed that the Earth was flattened at the poles, as they had previously assumed. But the reception was not all positive. Maupertuis’s measurements were only finally confirmed by a Finnish verifying measurement in the 1920s.
The Cassinis bend after three years
The expedition returned to Paris a year and four months after their departure, on 20 August 1737. Just over a week later, Maupertuis presented the result at the Académie des sciences.
Empirical research by the Maupertuis expedition showed that the Earth had flattened toward its poles.
The result was not accepted in Paris without questioning. The result of the measurements undermined established scientific practices and called into question the tradition of Cassini’s astronomical and geodetic work in particular.
The Maupertuis expedition was criticised for being known as enthusiastic supporters of Newton. The strong bias raised doubts about the validity of the measurement results.
It was only at a session of the Académie des sciences in 1740 that Cassini de Thury announced that new verifying measurements made in France proved the measurements made by the Lapland expedition to be correct.
The measurement results were in the right direction
Maupertuis published La Figure de la Terre in 1738 as a research report spiced by an adventurous travelogue.
In his foreword, Maupertuis justified his expedition’s research first and foremost in terms of improving the accuracy of navigation.
He also highlighted other benefits of the study: knowing the exact shape of the Earth helps to determine the parallax of the Moon and the water level – in short, the parallax of the Moon is the angle at which the ray of the Earth appears when viewed from the Moon. Knowing the exact parallax of the Moon was significant for astronomy.
According to the expedition’s measurements, the longitude of the meridian arc was 57,437 toises (fathoms) at the Arctic Circle, compared to 57,060 toises (fathoms) in Paris. In metres, the figures rounded to one decimal place were 111,944.7 and 111,209.9 metres. The difference in the measure of the degree of the meridian was about 735 metres, according to Maupertuis’ degree measurement.
Newton predicted the Earth’s lithification ratio to be 1:230. According to the Maupertuis expedition, it was 1:179. The current exact value is 1:298,257223563 (WGS84, World Geodetic System 1984). In kilometres, this is about 43 kilometres.
The diameter of the Earth, measured from pole to pole, is about 43 kilometres shorter than the equivalent diameter at the equator. The diameter of the Earth at the equator is 12,756.3 kilometres. The diameter from pole to pole is 12,713.6 kilometres.
Although the difference sounds small, it once caused errors, especially in nautical charts.
The results of the Maupertuis expedition were therefore not entirely accurate and were later refined. The error was just under 400 metres, or about 13 seconds of arc.
The Peruvian expedition did not return from its expedition until ten years after its departure, in 1745. However, they had sent back measurements from their expedition, which confirmed the results of the northern expedition as being in the right direction.
Immediate effects
The visit of French natural scientists had a major impact on the development of Swedish science.
Anders Celsius’, who was the Professor of Astronomy at the University of Uppsala, encounter with Maupertuis and other French mathematicians and astronomers was important, especially in terms of his career. On Celsius’ initiative, a modern astronomical observatory was built in Uppsala in 1741.
In Finland, the Land Surveying Commission was established after the visit of the degree-measuring expedition in 1748. The Commission’s aim was to draw up maps of every parish in Finland. This was the first baseline survey of Finland.
Several editions of the travel books written by Maupertuis and Outhier were printed and translated into various languages. They disseminated information and images of Lapland to the Central European reading public.
In addition to correct information, the works spread a stereotypical and exoticising image of the indigenous people of the North. The Sámi were described in the works as strangely behaving savages.
Maupertuis’s texts on Niemivaara and the Tengeliönjoki river in particular began to take on a life of their own in poetry.
The names of the measurement points were once used as keywords in the French Encyclopedia (Diderot and d’Alembert). Thus a number of hills in the Torne Valley became part of European scientific history.
Around the time of the French Revolution, the system of units of measurement was reformed. At that time, a new basic unit, the metre, was introduced. It was one tenth of a millionth of the length of the meridian arc between the North Pole and the equator.
To determine the exact length of the meridian arc, the results of geodetic expeditions were needed.
Swedish degree measuring on the trail of Maupertuis
Maupertuis and Celsius planned new measurements on Lake Vättern in central Sweden. However, the plan did not materialise.
After the first measurements in Peru and the Torne Valley, similar large-scale degree measurements were taken all over the world. The measurements confirmed and refined the result obtained by the Maupertuis expedition.
In 1799 and between 1801 and 1803, Jöns Svanberg (1771–1851), Swedish astronomer, mathematician and professor at Uppsala University, repeated Maupertuis’s measurements on behalf of the Royal Swedish Academy of Sciences.
Svanberg had lived in Tornio during his youth. The interpreter of Maupertuis’s astrometric degree-measuring expedition, Anders Hellant of Tornio, had inspired him to take up astronomy.
Svanberg’s measurements extended the Maupertuis chain of triangles at both ends. In the new measurement, the meridian arc was 469.7 metres shorter than that of the Maupertuis expedition.
Svanberg was criticised for not having repeated Maupertuis’s measurement as it stood. This meant that errors could not be located.
The Struve chain of survey triangulations was a major project lasting 40 years
More than a hundred years after Maupertuis’ expedition, the same hills of the Torne Valley were traversed by surveyors of the Struve Geodetic Arc.
The Russian astronomer Friedrich Georg Wilhelm von Struve (1793–1864) led a huge degree-measuring project to establish a chain of triangles from Hammerfest in northern Norway to the Black Sea. The total length of the triangulation network was 2,820 kilometres.
In the north, the Struve chain was surveyed between 1842 and 1852. Swedish and Norwegian collaborators were responsible for the measurements north of Tornio.
Seven of the Maupertuis measurement points were also used in the Struve triangulation: Kittisvaara, Pullinki, Niemivaara, Iso-Horila (aka Horilankero), Aavasaksa, Huitaperi and Kaakamavaara.
In Tornio, the newer and taller tower of the Church of Alatornio was used instead of Church of Tornio.
Additionally, the Struve chain in the Torne Valley included a new measurement point at Perävaara in Karunki, Sweden, about 25 kilometres north of Haparanda.
Finnish verifying measurement solved the Maupertuis measurement result
The final solution to Maupertuis’ degree measurement was given by a study published in 1928 by Yrjö Leinberg (1896–1974) and Victor Ölander (1897–1973).
Leinberg took astronomical measurements at the end points of the chain of triangles in Tornio and Pello, and Ölander took gravimetric measurements.
The errors in the degree measuring were due to a variety of reasons, but the most significant errors came from astronomical observations. Although the zenith sector made by George Graham was a high-quality instrument, reading its measurements accurately was a challenge. The one-second difference in length meant a deviation of about 30 metres.
All the different sources of error had the same effect: they increased the length. The overall deviation was 12,62 seconds.
The error was so large that if it had been in the other direction, Maupertuis would not have been able to prove that the Earth was flattened at its poles.
With his verifying measurements, Leinberg also proved that the triangulation made by the Maupertuis expedition was correct.
Sources:
Iliffe, Rob. “‘Aplatisseur du monde et de Cassini’: Maupertuis, Precision Measurement, and the Shape of the Earth in the 1730s”. History of Science, Vol. 31, s. 335–375. 1993.
Kukkamäki, T. J. Geodeettinen laitos 1918–1968. Suomen geodeettisen laitoksen julkaisuja, N:o 65 a. Helsinki, 1968.
Lundholm, Kjell. “Matkailijoita Tornionlaaksossa”. Tornionlaakson historia II. 1600-luvulta vuoteen 1809. Eds. Olof Hederyd et al. Tornionlaakson kuntien historiakirjatoimikunta. Jyväskylä, 1993.
National Land Survey: https://www.maanmittauslaitos.fi/struvenketju
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Pekonen, Osmo. “Johdanto: Maan muotoa mittaamassa”. Maan muoto ynnä muita kirjoituksia Lapista. Ed. Osmo Pekonen. Väyläkirjat, 2019.
Tobé, Erik. Anders Celsius och den franska gradmätningen i Tornedalen 1736–1737. Acta Universitatis Upsaliensis, 2003.
Tobé, Erik. Fransysk visit i Tornedalen 1736–1737. Om en gradmätningsexpedition och dess nyckelpersoner. Tornedalica, Luleå, 1986.
Weinz, Erik. “Personer och händelser kring gradmätningen i Tornedalen 1736–1737. Några anteckningar som förord.” Ed. Erik Weinz. Tornedalica Nr 23. Kalix, 1977.
Wikipedia: https://sv.wikipedia.org/wiki/Jöns_Svanberg
Weinz, Erik. “Personer och händelser kring gradmätningen i Tornedalen 1736–1737. Några anteckningar som förord.” Ed. Erik Weinz. Tornedalica Nr 23. Kalix, 1977.