SECTION 9. GEODESY. In order to identify the existing old monuments, as well as to obtain the necessary elements for locating the new monuments on the lines forming the boundary, the following geodetic operations were executed: I. Tracing the parallels according to the method of tangents and offsets. II. Tracing the meridian section by simple alignment, its direction having been previously verified. III. Tracing the azimuth lines, either by straight lines connecting consecutive existing old monuments directly, or by the aid of auxiliary lines starting at one of these monuments and passing as closely as possible to the next monument. IV. Triangulation made in the vicinity of the initial monument on the Rio Grande by the United States section to refer the initial monument to its astronomical observatory, and the reference of the longitude of the initial monument to the astronomical station at Juarez made by the Mexican section by flash signals at night. V. Triangulation made in Nogales by the United States section and repeated by the Mexican section to refer Monument No. 127, at the west end of the line on parallel 31° 20′, to the astronomical observatory occupied successively by both sections of the commission. VI. Triangulation made in the vicinity of Yuma, Ariz., by the United States section, and repeated by the Mexican section, to refer Monuments No. 204 and No. 207 to the astronomical observatory at Yuma, Ariz., occupied successively by both sections of the commission. All the preceding operations were executed independently and at different epochs by the two sections of the commission, the results being compared as soon as practicable after reduction. On parallels 31° 47' and 31° 20' new monuments intervening between two consecutive existing old monuments were located upon a curved line joining the latter, the curvature of this line being as nearly that of the corresponding parallel as possible. On the meridian section and on the azimuth lines the new monuments were located upon the straight lines joining consecutive existing old monuments. In tracing straight lines, as well as in triangulation, heliotropes were generally used for distant signals. In the following tables are given the lines run by the two sections, respectively, and the measured offsets to existing monuments from those lines on parallels 31° 47' and 31° 20′, and on the azimuth lines: * A check tangent was run from United States astronomical station No. 2 between Monuments Nos. 15 and 21, giving offsets of 4.14 and 29.30 meters, respectively. Offsets to above points on parallel 31° 47′ are all measured to the north. Meridian section. The line traced by both sections on the meridian section of the boundary was the straight line joining Monuments Nos. 40, 46, and 53, which had been found to lie exactly in the meridian. |