[Footnote 1: By the aid of the accompanying figure, the work called a triangulation may be understood. Let A B be the arc. Measure the base A C very carefully from the extremity A to the first station C. Take other stations, D, E, F, G, H, I, &c., on alternate sides of the meridian, and observe the angles of the triangles, A C D, C D E, D E F, E F G, &c. Then in the triangle A C D, the angles and the side A C being known, the side C D may be found. Likewise in the triangle C D E, C D and the angles being known, the side D E may be found; and so on through all the triangles. Now determine the direction of the meridian in the ordinary way, and observe the angle M A C which it makes with the base A C. Then in the triangle A C M, because A C and the adjacent angles are known. A M, C M, and the angle A C M, may be found, and A M is the first portion of the arc. Then in the triangle D M N, since the side D M = C D - C M, and the adjacent angles are known, the sides M N, D N, and the angle M N D may be found, and M N is the next portion of the arc. Again, in the triangle N E P, because E N = D E - D N, and the adjacent angles are known, N P, the third portion of the arc, may be found. By proceeding thus through all the triangles, piece by piece, the whole length of the arc A D may be determined.] After some discussion, it was decided that the southern extremity of the base would serve for a starting-point. It was the twenty-fourth meridian east from Greenwich, and extended over seven degrees of latitude, from 20° to 27°, without any apparent natural obstacle. Towards the north it certainly crossed the eastern end of Lake Ngami, but Arago had met with greater difficulties than this when he applied his geodesy to connect the coast of Spain with the Balearic Islands. It was accordingly decided that meridian 24° should be measured, since, if it were afterwards prolonged into Europe, a northern arc of the same meridian might be measured on Russian territory. [Illustration: The Astronomers at Work.] The astronomers proceeded at once to choose a station which should form the vertex of the first triangle. This was a solitary tree to the right of the meridian, standing on a mound about ten miles away. It was distinctly visible from each extremity of the base, and its slender top facilitated the taking of its bearings. The angle made by the tree with the south-east extremity of the base was first observed, with the help of one of Borda's repeating circles. The two telescopes were adjusted so that their axes were exactly in the plane of the circle, in such a way that their position represented the angular distance between the tree and the north-west extremity of the base. This admirably-constructed instrument corrects nearly all the errors of observation, and indeed, if the repetitions are numerous, the errors tend to counterbalance and correct each other.