319 



GEODESY. 



GEODESY. 



350 



In 1819, M. Struve, who was then director of the observatory of 

 Dorpat, while engaged in the survey of Livonia, suggested to the 

 university of Dorpat the desirableness of measuring the arc of the 

 meridian included between the island of Hugland in the Gulf of 

 Finland, and the town of Jacobetadt in the province of Courland. 

 The sanction of the emperor having been obtained for the project, 

 the operations were commenced, and were finally completed in the 

 year 1827. The terrestrial angles were measured with Reichen- 

 bach's Universal Instrument. The latitudes of the stations were 

 determined by observations with a transit adjusted in the prime 

 vertical. The arc measured 3 35' 5", and passed very nearly through 

 the meridian of the observatory at Dorpat In the same year in which 

 M. Struve brought to a close the operations connected with this arc, 

 General Tenner also completed the measurement of the arc of the 

 meridian included between Bristen in Courland, and Belin iu the 

 province of Grodno. The amplitude of this arc wa found to be 

 4 32'. As Belin, the northern station of this arc, was distant only 

 4' 47" from Jacobstadt, the southern station of the Livoniaii arc, it 

 became desirable to connect trigonometrically the two arcs together. 

 This was effected in 1827-8, by M. Struve and General Tenner, inde- 

 pendently of each other, and the results upon being transmitted sepa- 

 rately in sealed letters to Bessel, were found to exhibit a most satis- 

 factory accordance. The amplitude of the entire arc thus measured 

 between Hogland and Belin amounted to 8 2* 28''. (Struve, 

 ' Beschriebung der Breitengrad messung in den Ostseeprovinzen Russ- 

 lands,' *c. Dorpat, 1831.) 



In 1845, the Russian arc was extended northwards as far as Tornea, 

 the southern extremity of the Lapland arc. It thereby received an 

 accession of length amounting to 5 26'. M. Struve had for his prin- 

 cipal coadjutor on this occasion, M. Wolstedt, who was subsequently 

 appointed director of the Observatory of Helsingfor*. While the arc- 

 was being prolonged towards the north, General Tenner was engaged 

 in extending it southwards, until it reached the northern frontier of 

 the province of Bessarabia. By this operation its length received a 

 further increase of 3" 17' 47". The entire arc now extended from 

 Tomea in kt. 65 50' 34" to Souprounkontsi in lat. 48 45' 1". It 

 consequently possessed an amplitude of 17 J 5' 33". In 1849 it was 

 extended southwards through the entire province of Bessarabia to 

 Ismail on the Danube. The amplitude of the entire arc now amounted 

 to 20' 31'. 



Under the auspice* of the Swedish government the Russian arc of 

 the meridian has been extended to the Arctic Ocean. The Norwegian 

 portion of the arc was executed by M. Hansteen, of Chriatiania, and 

 the Swedish portion by M. Selander, Director of the Observatory of 

 Stockholm. The Swedish arc extends from Tornea iu lat. 65 51', to 

 Atjick in lat. 68 54'. Its amplitude therefore amounts to 3 3'. The 

 Norwegian arc extends from Atjick to Fuglenaes, in lat. 70 40', and 

 consequently embraces an amplitude of 1 46'. The two arcs together 

 measure 4 4'J'. 



The Ruseo-Scandinavian arc of the meridian uow extends hum 

 Ismail on the Danube, lat. 45 20' 20'8", to Fuglenaes on the Arctic 

 Ocean, lat. 70 40' 11""3. Ita amplitude amounts to 25 20 1 8'"5; and 

 it is consequently the largest arc of the meridian which has been 

 hitherto measured on the earth's surface. (Struve, ' Expose" historique 

 dee travaux executes jusqu'a la fin de I'lumce 1851, pour la mesure 

 du Mi ridien entre Fuglenaes, 70 40', et Ismail, 45 20', &c. ; ' 

 St. Petersbourg, 1852.) 



Two arcs of meridian have been measured in Hanover and Denmark, 

 which, though of comparatively small extent, are very valuable by 

 reason of the skilful manner in which the operations were conducted, 

 and the great probable accuracy of the results. The first was ol'taiued 

 by connecting the two observatories of Gbttingen and Altona, which 

 are situated nearly in the same meridian, by means of a chain of 

 les proceeding from a base which was measured by Gauss in 

 1820. From the same base another chain of triangles was carried 

 through Denmark, by means of which the geodetical distance between 

 the ]>anillels of Lauenburg (in Hanover) and Lysabbel (in the island of 

 Alsen) was computed. The celestial arc was determined by Schu- 

 macher with Bradley's zenith sector, sent from the observatory at 

 iwich for the purpose. (Gauss, 'Bestimmung des Breitensunter- 

 schiedes zwischen deu Sternwarten von Gottingen und Altona, &c.'; 

 Bessel, ' Antron. Nachrichten,' No. 333.) 



An arc, of which the amplitude is 1 30' 28", was also measured 

 hi Prussia, by Bessel, between 1831 and 1838. The immediate object 

 of this undertaking was to connect the Russian triangulation with a 

 chain of triangles which had been meisured in the western part of 

 ;i, extending through Hesse, Thuringia, and Brandenburg, to 

 Silefia, and connecting the Dutch (and thereby also the French and 

 English) triangles with those of Bavaria and Austria. In this operation 

 Bessel included the measure of an arc of the meridian of Konigsberg. 

 A base of 935 tpises was measured with great precision. The angles 

 were observed with a theodolite of 15 inches diameter, and the latitudes 

 at the two extremities (Truntz and Memel) determined, as in Struve's 

 method, with a transit-instrument adjusted in the prime vertical. 

 The details are given by Bessel in a work which should be in the 

 hands of every one concerned with geodetical operations of the highest 

 order. (Bewel, ' Gradmessung in Ost-Preusaen und ihro Verbindung 

 mit Preusaischen und Hussiachen Dreieckskettcn, Berlin/ 1838.) 



The anomalous natxtre of the result deduced by Laeaille, from his 

 measurement of an arc of the meridian at the Cape of Good Hope, 

 lias been already alluded to. It is gratifying to learn that Mr. 

 Maclear, by remeasuring and extending Lacaille's arc, has succeeded 

 in completely removing the difficulty arising from this cause, and has 

 obtained results which exhibit a moat satisfactory accordance with the 

 theory of gravitation. It is understood that the details of Mr. Maclear's 

 labours will shortly be published. The amplitude of the arc measured 

 by him amounts to 4 11' 45' '538. The following table exhibits a 

 comparison between the observed latitudes at the various stations of 

 the arc, and the corresponding latitudes calculated from Airy's elements 

 of the earth's figure. 



Station. 



North End of arc 

 Kamies .Sector Berg . 

 Ileercnlogcracnts Berg 

 Royal Observatory . 

 Zwart Kop . . . 

 Cape Point 



Obserwd Lat. 



29 -U'l?' 



30 21 29 



31 58 9 



33 66 3 



34 13 32 



li ; 

 lo 

 11 

 10 

 II 



34 21 C -26 



Cal. Lat. Diff. 



29"44'17"-35 + 0"'31 



SO 21 20 -73 + 8 -37 



31 58 9-64 -J3 



83 56 3 -20 .... 



34 1333 -80 1 -67 



34 21 6-80 -54 



Mr. Maclear remarks that the disturbing effect produced by the 

 attraction of the immense Bushman Table Land, the mean elevation of 

 which above the level of the sea exceeds 3000 feet, is sufficient to 

 account for the deflection observed at Kamies Berg. 



AVe shall conclude this historical sketch of geodetieal operations 

 with a brief statement of the results deduced by Mr. Airy from the 

 measurement of the arc of longitude comprised between the Royal 

 Observatory, Greenwich, and Feaghmain, a station of the Ordnance 

 Survey, situate in the island of Valentia, on the west coast of Ireland. 

 The plan proposed by Mr. Airy, was to ascertain the difference of lon- 

 gitude of the two stations by the triangulations of the Ordnance 

 Survey, assuming the elements of the earth's figure as previously 

 determined by him, and to compare the result with the difference of 

 longitude derived from the transportation of chronometers. The 

 operations connected with this object were carried into etfect in the 

 year 1844. The following are the final results, the intermediate stations 

 of Liverpool and Kingston (Dublin), through which the chronometers 

 passed, being also included in the investigation. 



in. s. 



Geodetic arc of longitude from Greenwich to Liverpool . 12 0-35 

 Curonometric arc 12 0-0} 



Cbronomctric arc smaller 



Geodetic arc from Greenwich to Kingston' 

 Chronometric ore .... 



Chrouometric arc smaller 



0-30 



24 31-48 

 24 31-20 



0-23 



Geodetic arc from Greenwich to Feaghmain 



Chronometric arc 



.4123-07 

 41 23-23 



Chronometric arc larger 



Geodetic arc from Liverpool to Kingston 

 Chronometric are .... 



Chronometric arc larger 



0-16 



0-02 



Geodetic arc from Kingston tu Fcagbm.dll . . . . 1651-59 

 Chronometric arc 1052-03 



Chronomctric arc larger 



0-41 



By means of the different surveys to which we have now alluded 

 the greater part of Europe has been covered with chains of triangles, 

 whereby not only the geographical positions of all the principal places 

 and remarkable objects have been determined by actual measurement, 

 but all the measured arcs of meridian and parallel, and all the prin- 

 cipal observatories have been trigonometrically connected with each 

 other. The comparison of the astronomical and geodetical positions of 

 so many connected points is, perhaps, even better calculated to lead to 

 an accurate knowledge of the local configuration of this quarter of the 

 globe than the measurement of isolated degrees. 



We proceed now to give a general view of the methods of con- 

 ducting a trigonometrical survey, and computing the results of the 

 observations. 



measurement of the Sate. The foundation of every trigonometrical 

 survey ia the measurement of a ground-line, or base, in terms of which 

 all the distances are to be computed. This is an operation which ia 

 attended with considerable difficulty, and requires to be executed with 

 the most minute precision ; for any error with which the result may 

 be affected is multiplied in the sides of the triangles in the ratio of 

 their length to the length of the base ; and all other distances con- 

 cluded from the survey are affected in the same proportion. An error 

 in the base amounting only to an inch in the mile would vitiate the 

 determination of the earth's diameter to the extent of 110 yards. 



The general method of proceeding may be thus described : A pieco 

 of ground must be selected as free from obstructions and as nearly 

 level as possible. The terminal points must be defined by permanent 

 marks ; for example, by a fine dot, or the intersection of two straight 



