F.G.W. Struve ja Liivimaa triangulatsioon


{ A.Torim Geodeet 6(30) 2002 31-34 }


F.G.W. Struve and the Triangulation of Livonia


A. Torim


Tartu Astrophysical Observatory, Tõravere, Tartumaa, EE2444 Estonia


W. Struve esimeseks suuremaks geodeetiliseks tööks oli Liivimaa astronoomilis-trigonomeetriline mõõdistamine (1816-1819), mis pani aluse kõigile tema järgnevatele töödele. Töö toimus Liivimaa Üldkasuliku ja Ökonoomilise Sotsieteedi ülesandel, kavatsusega välja anda Liivimaa topograafiline kaart, mis pidi tuginema mõisa- ja riigimaade plaanidele. Selleks oli vaja geodeetilist alusvõrku, mida tollal Liivimaal veel polnud. Sotsieteet pöördus Tartu Ülikooli poole ja sõlmitud lepingu kohaselt pidi W. Struve rajama geodeetilise alusvõrgu ja kaardi koostama C.G.Rücker. Töö teostamisekse kasutas Struve Troughtoni 10-tollist sekstanti. Liivimaa triangulatsioon hõlmas Põhja-Lätit Daugava jõest kuni 59. laiuskraadini Kesk-Eestis. Kubermangu ida- ja lõunapoolne osa kaeti kolmnurkade võrguga. Kinnise maastiku tõttu rajati piki Riia lahe rannikut Riiast Pärnuni astronoomiliste punktide ahel, mis koosnes 14 põhipunktist. Kubermangu ida-ja lõunaosa trigonomeetriline võrk koosnes 292 punktist, milleks kasutati põhiliselt kohalikke ehitusi. Triangulatsioon jagati täpsuse järgi kolme järku. Triangulatsioonivõrk orienteeriti Tartu Tähetornist Äksi kirikule mõõdetud asimuudi järgi ning tugines 13.34 km pikkusele baasijoonele, mis mõõdeti 1919. aasta talvel Võrtsjärve jääl. Üldse määrati Liivimaa mõõdistamisel 325 punkti koordinaadid. Tööde käigus määrati trigonomeetrilise nivelleerimisega ka 280 punkti kõrgused merepinnast. Liivimaa triangulatsiooni rajamise käigus tehtud ulatuslike geodeetiliste tööde puuduseks oli suhteliselt väike täpsus ja asjaolu, et W. Struve ei kindlustanud triangulatsioonipunkte tsentritega, mistõttu need varsti hävisid.




The quick development of astro-geodetical works at Tartu (Dorpat) University at the beginning of the 19th century is inseparable from the name of Wilhelm Struve. In the history of science W.Struve is known above all as an astronomer. But the share of geodesy in his publications is significant - among 129 works 48 were devoted to geodesy. His main works in the field of geodesy (Struve, 1831; Struve, 1844; Struve, 1849; Struve, 1860) will always be remembered in the history of astro-geodetical works.


W. Struve's first greater astro-geodetical work was the astronomical-trigonometrical survey of Livonia, which laid the ground to all his subsequent works and already showed his abilities as a scientist and geodesist. The work was done on the order of the Livonian Society of Public Utility and Economy (Livlandische Gemeinnützige und Ökonomische Societät), which intended to issue a topographic map of Livland, that was to be grounded on the reduced and corrected maps of estates and state lands. A basic network was not yet existing in Livonia at that time. The Society applied to Dorpat University for technical help and made a contract with W. Struve to set up the geodetic network. The map was to be drawn up by the surveyor of Livonian Nobility Carl Gottlieb Rücker (1778-1856). Although W. Struve carried out his fieldwork with the help of students in the 1816-1819 summer holidays, the mapping dragged on and came out on six sheets only in 1839. The province called Livonia covered the northern part of Latvia down to the river Düna, and the southern and central parts of Estonia. Livonian latitudes ranged from 56° 32' to 59° stretching from the Livonian Bay and the Gulf of Pernau to the Lake Peipus covering 4°08' in longitude. W.Struve had to cover a territory for about 44,000 km2 with the geodetic network. Since no topographical survey maps were available, it was not easy for the 23-year-old Struve to plan his work. The closed landscapes of Livonia, lack of equipment and shortage of time forced W. Struve to choose the astronomical-trigonometrical survey technique where he could use instruments of the Dorpat Observatory. Some equipment he designed himself. For the measuring of horizontal angles, azimuths and latitudes, a Troughton's 10-inch mirror sextant was used and the measurements were checked with a Baumann's repeated circle.


While it was possible to cover the southern and eastern parts of Livonia with a network of triangles, the western territories posed more problems since they were relatively lower and mostly covered with forests. Therefore a chain of astronomical points was fixed along the coastline of Livonian Bay from Riga to Pernau.


Geodetic network in the Southern and Eastern Livonia


The trigonometrical network in southern and eastern parts of the province consisted of 292 points. Mostly local buildings (churches, manor houses, windmills etc.) were used and only 63 geodetic signals and marks were built. These marks and signals were not affixed with centres and they vanished soon. The triangulation network was divided into three categories according to the accuracy.



Fig.1. Base-line measurement on the lake Wirzjärw-See


Of 90 triangles of the first order (64 points), only for 53 W. Struve managed to measure all three angles. For the other 37 triangles only two angles were measured. In the triangles of the second order with 40 new points mostly two angles were measured. The points (187 new points) of the triangles of the third order were determined with the cuts from the higher degree points. The average length of the sides of the triangles was 25 km (the longest being 60 km) and their shapes varied widely. From the data given in his diary we can conclude that W. Struve had failed to establish a solid and uniform system for measuring the angles. The average mean square errors of the triangles of the first degree were 15". The triangulation network was orientated according to the azimuth drawn from Dorpat Observatory to the church of Äksi (Ex), and was measured with the order Baumann's repeating circle.


The triangulation network was constructed on the 13.34 km baseline measured in the winter 1819 on the ice of lake Võrtsjärv (Wirzjärw-See) near the villages of Rannaküla and Uniküla. For these measurements W. Struve designed a measure consisting of five wooden rods (à 1 toise = 1.949 m) connected with pin joints, with a total length of 9.75 m. The terminal rods had a silvered scale and two identical sets were used for the measurements. The base was measured only once and in one direction. During the measuring the base was divided into two parts, on which two bordering triangles were found from measuring of angles (Fig.1). W. Struve did not reduce the length of the baseline to the sea-level, unlike he did later with the arc measurements. Struve estimated the measuring accuracy of the base line to be 1:40,000 of the total length. With the help of the two connection triangles the length of the base was forwarded to the starting line of the triangulation between the churches of Tarvastu (Tarwast) and Rannu (Randen). The length of the starting line was 18,52 km with the error of 1:28,000 of the total length.


For the astronomical source of the geodetic network Struve chose the first order points of Dorpat Observatory and Riga Cathedral, whose astronomical coordinates (latitude φ and longitude λ) he measured himself. For astronomical observations either a bigger or a smaller sextant, Baumann's artifical horizon, and Arnold's pocket chronometer was used.


The chain of astronomical points from Riga to Pernau


Because of closed landscapes in the western parts of Livonia, W. Struve could not develop the triangulation network and therefore from Riga to Pernau (Pärnu-Jaagupi) a chain of astronomical points was established. The most interesting thing is the method he used for founding this chain (traverse) and later improved by W. Struve himself which became a prototype for modern parallactic polygonometrics. The chain from Riga to Pernau consists of 14 main points, where the azimuths and also partly geographical latitudes were measured. Separate small triangulation networks were formed from the starting and ending points of the chain: near Riga the system consisted of eight triangles and near Pernau of 24 triangles (15 points) of the 2nd degree.




Fig.2. Triangulation network near Pernau


The base-line for the Riga triangulation was measured with a steel chain along the ice of the river Düna at the end of the winter 1818. The 2.16 km long base-line for Pernau triangulation was measured along the smooth costal meadow between Audru and Valgeranna (Fig. 2). For the measurements the used steel chain was controlled repeatedly before and after the measurements on the wooden floor of the church of Audru. Small bases were also measured in the centre of the four triangles of the chain. The angles in the points of triangulation were measured with a sextant similarily to the points on the continuous network of inland.


The traverse between Riga and Pernau ran closely along the meridian. Its length was 186 km. The distances between the main points of the line were calculated on the base-line or derived from the differences of geographical latitudes and azimuths of the adjacent points. The length of the lines between the points amounted from 3 to 34 km. Altogether the coordinates of 33 points were determined in this region. The network for the western part of Livonia remained "hanging" for the geodetic purposes, being connected with inlands triangulation network with only one point (Riga Cathedral), that considerably diminished the accuracy of its orientation.


Altogether W. Struve determined the coordinates of 325 points during his survey of Livonia. The origin of the plane rectangular co-ordinates was determined conventionally and for that the intersection point of the central meridian of Livonia (near the town of Valmiera) and the southern-most point of the triangulation (the tower of Krustpils (Kreutzburg) castle) were used.


Determination of altitudes of the points


During the triangulation of Livonia the elevations from the sea level of ca 280 points were determined with trigonometrical levelling, that was based on the sea level of the Livonian Bay in the mouth of Düna. Vertical angles were measured with a new height measurer, the so-called "horizontal sector" (objective  Ø 5 cm, f=48 cm, magnification 30x), constructed by W. Struve and built in the workshop of Dorpat University. This enabled him to measure small vertical angles (± 10°) with the accuracy of ± 4". As the biggest drawback of his instrument, W. Struve considered the fact that the sighting axis of the telescope was not congruent with the geometrical axis. Unfortunately W. Struve did not measure the vertical angles on all the network points, as he did with the arc measurement.


The measuring data of trigonometrical levelling of Livonia together with the works done during the arc measurements enabled W. Struve to calculate the refraction coefficient of the Earth atmosphere (k=0.2137), which is only slightly different of the result by Gauss (k=0.3106). The average mean square errors were rather large and they depended on the distances between the points (5-50 km), extending from 0.19 to 7.60 meters.


W. Struve considered the work he had begun as one stage of the mapping of Livonia. For an eventual improvement of the results he wanted to re-measure a part of the triangulation network, but the existing equipment did not guarantee the needed accuracy.




Geodetical network for the mapping of Livonia was a big and serious task for young and inexperienced Struve. Unforeseen difficulties cooled down his initial enthusiasm. In addition to the chain of triangles of favourable shape along the Dorpat meridian, a group of geometrically unfavourable triangles with long sides and small angles was formed. Because of large forests and bogs, vast territories were left without geodetic points. The building of high geodetic signals was not feasible. Therefore on the coast of Baltic Sea a chain of astronomical points was formed, which was connected with the inland triangulation network through only one point. The measuring equipment proved to be inadequate for such a vast task. Besides, Struve was pressed for time with his field works because he could use for that only the months of his summer leave from the University.


As Struve did not fix his triangulation points with permanent centres, many of them were destroyed even before the map of Livonia came out in its final form. Among the triangulation points preserved on the territory of Estonia, we can mention in addition to Tartu Observatory some churches (St.Elisabeth church in Pernau, churches of Paistu, Pilistvere, Torma, Rannu,

Tarvastu, Mihkli). As a whole, the triangulation of Livonia was, to quote Struve's own words, "an eloquent example of how an enterprise involving considerable labour can be carried out in a short period of time, with limited equipment and at low cost".




1. Struve W. 1831, Beschreibung  der Breitengradmessung in den Ostseeprovinzen Russlands.

2 Theile, nebst Kupfertafeln. Dorpat.


2. Struve W. 1844, Resultate der in den Jahren 1816 bis 1819 ausgeführten astronomisch – trigonometrischen Vermessung  Livlands. St.-Petersburg.


3. Struve W. 1849,  Beschreibung der zur Ermittelung des Höhenunterschiedes zwischen dem Schwarzen und dem Caspischen Meere... St.-Petersburg.


4. Struve W. 1860, Are du méridien de 25°20' entre le Danube et la Mer Glaciale. St.Pétersbourg.