While the radius of curvature of this arc is obviously not uniform (being, in the mean, about 600 metres greater in the northern than in the southern part), the Russo-Scandinavian meridian arc (from 45° to 70°), on the other hand, is very uniformly curved, and gives, with an ellipticity of 1/299.15, a = 6378455 metres; this arc gives the plausible value 1/298.6 for the ellipticity. But in the case of this arc the orographical circumstances are more favourable.
The west-European and the Russo-Scandinavian meridians indicate another anomaly of the geoid. They were connected at the Central Bureau by means of east-to-west triangle chains (principally by the arc of parallel measurements in lat. 52°); it was shown that, if one proceeds from the west-European meridian arcs, the differences between the astronomical and geodetic latitudes of the Russo-Scandinavian arc become some 4″ greater.
The central European meridian, which passes through Germany and the countries adjacent on the north and south, is under review at Potsdam (see the publications of the Kgl. Preuss. Geod. Inst., Lotabweichungen, Nos. 1-3). Particular notice must be made of the Vienna meridian, now carried southwards to Malta. The Italian triangulation is now complete, and has been joined with the neighbouring countries on the north, and with Tunis on the south.
The United States Coast and Geodetic Survey has published an account of the transcontinental triangulation and measurement of an arc of the parallel of 39°, which extends from Cape May (New Jersey), on the Atlantic coast, to Point Arena (California), on the Pacific coast, and embraces 48° 46′ of longitude, with a linear development of about 4225 km. (2625 miles). The triangulation depends upon ten base-lines, with an aggregate length of 86 km. the longest exceeding 17 km. in length, which have been measured with the utmost care. In crossing the Rocky Mountains, many of its sides exceed 100 miles in length, and there is one side reaching to a length of 294 km., or 183 miles; the altitude of many of the stations is also considerable, reaching to 4300 metres, or 14,108 ft., in the case of Pike’s Peak, and to 14,421 ft. at Elbert Peak, Colo. All geometrical conditions subsisting in the triangulation are satisfied by adjustment, inclusive of the required accord of the base-lines, so that the same length for any given line is found, no matter from what line one may start.
Over or near the arc were distributed 109 latitude stations, occupied with zenith telescopes; 73 azimuth stations; and 29 telegraphically determined longitudes. It has thus been possible to study in a very complete manner the deviations of the vertical, which in the mountainous regions sometimes amount to 25 seconds, and even to 29 seconds.
With the ellipticity 1/299.15, = 6377897 ± 65 metres (prob. error); in this calculation, however, some exceedingly perturbed stations are excluded; for the employed stations the mean perturbation in longitude is ± 4.9″ (zenith-deflection east-to-west ± 3.8″).
The computations relative to another arc, the “eastern oblique arc of the United States,” are also finished. It extends from Calais (Maine) in the north-east, to the Gulf of Mexico, and terminates at New Orleans (Louisiana), in the south. Its length is 2612 km. (1623 miles), the difference of latitude 15° 1′, and of longitude 22° 47′. In the main, the triangulation follows the Appalachian chain of mountains, bifurcating once, so as to leave an oval space between the two branches. It includes among its stations Mount Washington (1920 metres) and Mount Mitchell (2038 metres). It depends upon six base-lines, and the adjustment is effected in the same manner as for the arc of the parallel. The astronomical data have been afforded by 71 latitude stations, 17 longitude stations, and 56 azimuth stations, distributed over the whole extent of the arc. The resulting dimensions of an osculating spheroid were found to be
With the ellipticity 1/399.15, = 6378041 metres ± 80 (prob. er.).
During the years 1903-1906 the United States Coast and Geodetic Survey, under the direction of O. H. Tittmann and the special management of John F. Hayford, executed a calculation of the best ellipsoid of rotation for the United States. There were 507 astronomical determinations employed, all the stations being connected through the net-work of triangles. The observed latitudes, longitude and azimuths were improved by the attractions of the earth’s crust on the hypothesis of isostasis for three depths of the surface of 114, 121 and 162 km., where the isostasis is complete. The land-masses, within the distance of 4126 km., were taken into consideration. In the derivation of an ellipsoid of rotation, the first case proved itself the most favourable, and there resulted:—
The most favourable value for the depth of the isostatic surface is approximately 114 km.
The measurement of a great meridian arc, in long. 98° W., has been commenced; it has a range of latitude of 23°, and will extend over 50° when produced southwards and northwards by Mexico and Canada. It may afterwards be connected with the arc of Quito. A new measurement of the meridian arc of Quito was executed in the years 1901-1906 by the Service géographique of France under the direction of the Académie des Sciences, the ground having been previously reconnoitred in 1899. The new arc has an amplitude in latitude of 5° 53′ 33″, and stretches from Tulcan (lat. 0° 48′ 25″) on the borders of Columbia and Ecuador, through Columbia to Payta (lat. - 5° 5′ 8″) in Peru. The end-points, at which the chain of triangles has a slight north-easterly trend, show a longitude difference of 3°. Of the 74 triangle points, 64 were latitude stations; 6 azimuths and 8 longitude-differences were measured, three base-lines were laid down, and gravity was determined from six points, in order to maintain indications over the general deformation of the geoid in that region. Computations of the attraction of the mountains on the plumb-line are also being considered. The work has been much delayed by the hardships and difficulties encountered. It was conducted by Lieut.-Colonel Robert Bourgeois, assisted by eleven officers and twenty-four soldiers of the geodetic branch of the Service géographique. Of these officers mention may be made of Commandant E. Maurain, who retired in 1904 after suffering great hardships; Commandant L. Massenet, who died in 1905; and Captains I. Lacombe, A. Lallemand, and Lieut. Georges Perrier (son of General Perrier). It is conceivable that the chain of triangles in longitude 98° in North America may be united with that of Ecuador and Peru: a continuous chain over the whole of America is certainly but a question of time. During the years 1899-1902 the measurement of an arc of meridian was made in the extreme north, in Spitzbergen, between the latitudes 76° 38′ and 80° 50′, according to the project of P. G. Rosén. The southern part was determined by the Russians—O. Bäcklund, Captain D. D. Sergieffsky, F. N. Tschernychev, A. Hansky and others—during 1899-1901, with the aid of 1 base-line, 15 trigonometrical, 11 latitude and 5 gravity stations. The northern part, which has one side in common with the southern part, has been determined by Swedes (Professors Rosén, father and son, E. Jäderin, T. Rubin and others), who utilized 1 base-line, 9 azimuth measurements, 18 trigonometrical, 17 latitude and 5 gravity stations. The party worked under excessive difficulties, which were accentuated by the arctic climate. Consequently, in the first year, little headway was made.
- O. and A. Börsch, “Verbindung d. russ.-skandinav. mit der franz.-engl. Breitengradmessung” (Verhandlungen der 9. Allgem. Conf. d. I. E. in Paris, 1889, Ann. xi.).
- U.S. Coast and Geodetic Survey; H. S. Pritchett, superintendent. The Transcontinental Triangulation and the American Arc of the Parallel, by C. A. Schott (Washington, 1900).
- U.S. Coast and Geodetic Survey; O. H. Tittmann, superintendent. The Eastern Oblique Arc of the United States, by C. A. Schott (1902).
- Missions scientifiques pour la mesure d’un arc de méridien au Spitzberg entreprises en 1899-1902 sous les auspices des gouvernements russe et suédois. Mission russe (St Pétersbourg, 1904); Mission suédoise (Stockholm, 1904).