Arc measurements and Earth parameters

The basic principle of arc measurement to determine the size of the Earth was originally thought up by Eratosthenes of Cyrene (276 – 194 BC). His calculation of the diameter of the Earth based on the length of shadows was quite accurate for his era and this method was in use until the era of satellite geodesy. During the 17th century it became clear that the true shape of the Earth is not a perfect sphere; but it was unknown if the sphere is elongated or flattened at the poles. As an accurate length measurement was very difficult at this time, no distinct statement could be made.
The initialisation of the triangulation gave essential improvement in man’s ability to measure the figure of the Earth. If the length of a side of a triangle is known and the adjacent angles to the third edge are measured it is possible to determine the exact location of this point. To transmit this method now on longer distances, adjoining triangles are attached forming of a line, which finally builds the arc of a meridian measurement. Astronomical measurements allow calculating the exact latitude and longitude of the position. To get the length transmitted on long distances, baselines with the length of 2-12 km are measured by joining iron bars with calibrated length.
In the years of 1730-1740, the French Academy of Sciences sent out two expeditions to southern Lapland and to Peru. Famous names like Bouguer, Maupertuis, Celsius and La Condamine participated in these arc measurements. To get the best results for the parameter of oblateness it was necessary to measure the length of 1° on the Earth’s surface once near the poles and once near the equator to get the largest possible difference. Whilst the South American crew was fighting against the significant influence of the Andes on their plumbs (from which Bouguer followed his theories of the vertical deflection), the work of Maupertuis resulted in disagreeing values in comparison with other arcs. Only years later, the Lapland arc was re-measured by order of the Swedish Royal Academy but again errors on the observations resulted in a bad value for the oblateness.
In the years 1802-1843, William Lambton and George Everest made a comparable arc measuring in India with the length of 21° from Cape Comorin north to the Himalayas.
After the defeat of Napoleon and the Vienna Conference, many countries did not trust the peace and used the time to prepare for new possible wars. Tsar Alexander I. was willing to provide large amounts of money to support science and particularly survey to improve the mapping systems. This built the foundation for the initial measurements by Tenner and Struve.

Most Significant Contributors of the Struve Geodetic Arc

Friedrich Georg Wilhelm Struve was born in Altona, Denmark (now part of Germany) in 1793 and died 1864 in Pulkovo, Russia. After moving to the Russian Empire and studying a few semesters of Philosophy, he changed to Astronomy and Mathematics at the University of Dorpat (now Tartu) in Estonia, where he later became professor and director of the Dorpat Observatory. Among his duties in the Arc Measurement, he was continuing his astronomical studies. Even though he was known as Vassily Jakovlevich in Russia, he always used his first name Wilhelm or the initials F.G.W. in his publications. He married twice and had 18 children. His son Otto Wilhelm, his grandsons Karl Hermann and Ludwig and his great-grandsons Georg and Otto all became famous astronomers publishing important studies about the precession of the Earth, double star systems and the movement of the moons of Saturn.
Lt. Gen. Carl F. de Tenner was born in 1783 near Narva, Russia (now Estonia) and died 1859 in Warsaw. In the war campaigns against the army of Napoleon he was a General of Infantry of the Russian Imperial General Staff. He acquired his knowledge in survey manly in self-education, similar to Struve. He began his triangulation work in 1816 along the meridian of Vilnius (Lithuania) at 25° 25’ east, so it was actually him who started the measurement of the Struve Arc.


A few years before the beginning of the measurements of the Struve Arc, important improvements in the accuracy of chronometers were achieved which are necessary to measure the longitude with the required precision. This helped much to achieve the good accuracy of the results as the astronomic measurements could be determined much better than earlier. To get the principle of the triangulation realised on the Earth’s surface, hills or mountains are used to get optimal eye-sight between the stations. As the included countries are not mainly characterised by large mountain ranges but rather thick forests, wooden towers were built to elevate the surveyors above the treetops5. Far visible triangles served as marks for the sighting with the instruments. In the whole chain, only two buildings, namely the Alatornio Church (Tornea, Finland) and the Dorpat Observatory (Tartu, Estonia) were used.
As Struve and Tenner did not start their measurements together, different instruments and techniques were used. Struve used a theodolite from Reichenbach of Munich while Tenner had seven instruments in use by Baumann, Troughton, Reichenbach and Ertel. Of the ten measured baselines, seven were measured by Struve and his instruments and three by Tenner. Both used iron bars with different designs, usages and lengths6. Large differences can also be seen in the usage of the point marks. In the first part of the triangulation measured by Struve (see below), marks were mainly engraved on wood, which did not survive until the present investigations. In the Scandinavian areas, the points were marked on solid rock by drilling a hole, filling it with lead and sometimes with a brass plate on the top. Most of the plates have been removed since then and the lead was probably removed by hunters to made shots out of it. Tenner on the other hand often built stone structures in cross-form with a square centre stone, which holds the drilled holes. Those marks have been found up to a metre below the ground level, which makes them harder to locate nowadays.

Stages of the Measurement

The measurement of a meridian arc with the length of more than 25° was not initially the aim of neither Struve nor Tenner. On the contrary they were in charge of different triangulation works in the same area around Livonia (later divided into Estonia and Latvia) and they did not know each other until 1828. This resulted in several phases of the arc measurement.

  • First Phase (1816-1831) – Central West Russia: As mentioned above, it was Colonel Tenner who started the trigonometric survey in the western provinces of the Russian Empire. By the end of phase one he had measured an arc of 4.5° between the latitudes 25°-27° from Bristen to Belin. Struve started his measurements in 1822 from Jacobstadt to the north and crossed half of the Gulf of Finland up to a little island with the station Hogland (now Gogland, Z). The triangle side over the Gulf had a length of more than 80 km which is the longest triangle side of the whole arc. In the last years of this stage Struve and Tenner met for the first time and decided to connect their stations Jacobstadt and Bristen which are located only 32km apart. After matching their different unit systems – Struve used the old French Toise (6 feet, about 1.949m) and Tenner used the Russian Sajène (7 feet, about 2.134m) – they had triangulated an arc of the length of 8°2.5’, tied to three baselines and five astronomical azimuths.
  • Second Phase (1830-1844) – First Extensions: With the financial support from the Russian Tsar Nicholas I, Struve extended the arc to the north through autonomous Finland to connect it in Tornio (now Tornea) with the ancient Lapland Arc, measured by Maupertius. At the same time, Tenner continued his work to the south through the Ukraine to the Dnestre (now Dniester) river.
  • Third Phase (1844-1851) – Sweden, Norway and Bessarabia: To measure the most northern part, political agreements had to be made as Sweden and Norway were administratively separated but both reigned by King Karl XIV. Johann and King Oskar I. later. Responsible for the Swedish part was the astronomer Nils Haqvin Selander; the Norwegian measurements were undertaken by Christoper Hansteen, director of the Christiania Observatory. The measurements ended in Fuglenaes (Lat. 70°40’11.2”), a small town near Hammerfest at the Arctic Sea. Tenner meanwhile continued his work through the area of Bessarabia (now Moldova) and finished it in Staro-Nekrassowka (Lat. 45°20’02.8”), Ukraine.
  • Fourth Phase (1852-1855) – Completion: In the last years of the project, some additional measurements were made and to mark the most northern and southern stations, monuments were established in Fuglenaes and Staro-Nekrassowka. Because of the small size of the northernmost station, Hammerfest is often named instead of Fuglenaes.


Within 39 years, a meridian arc with the length of 25° 20’ 08.29” and the total number of 258 principal triangles, 265 basic points, 10 baselines and 13 astronomical stations was measured.
After completing the arc measurements, Struve published the results in two volumes of “Arc du Méridien de 25° 20’ entre le Danube et la Mer Glaciale mésure depuis 1816 jusqu’en 1855” [Struve, 1860] together with maps. Due to his failing health Struve was not able to publish his third volume containing a full account of the astronomic measurements, final results, evaluation of several arc measurements and the derivation of Earth parameters. Through the astronomical stations, the whole arc can be divided into 12 segments which can be used separately to compute the length of 1°. These values clearly indicated an oblate shape of the Earth. Struve computed a provisional result of the oblateness parameter f of 1:294.73 in combination with values of Bessel and Everest. Compared to modern results, this value has an overall accuracy of 1/200’000 over the 2820km length of the arc which is consistent with 5mm per km. The measurement of this arc was used later in several calculations of the Earth parameters by Bessel, Clarke, Krassowsky and many others.
After the completion of the measurements, Struve went back to his work at the Pulkovo Observatory (near Saint Petersburg) where all the descriptions of the work and other documents have been archived. During the World War II the Observatory became a target of the German air attacks and was totally destroyed. Fortunately the main instruments and large parts of the library could be saved.
The work carried out had not only earned respect because of the accuracy achieved. The cooperation of several monarchs, astronomers, military surveyors and instrument manufacturers for such a large scientific project after the time of the French Revolution and the Napoleonic War is remarkable and was an ideal example for later investigation campaigns. It also helped the newly established unit “metre” to spread into scientific and popular usage. In several countries, the stations of the Struve Arc have later been used in national networks and some of them are still important today.

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