The measurement of the base occupied thirty-eight days, from the 6th of March to the 13th of April, and without loss of time the chiefs decided to begin the triangles. The first operation was to find the southern extremity of the arc, and the same being done at the northern extremity, the difference would give the number of degrees measured.
Measuring the Arc of the Meridian.
On the 14th they began to find their latitude. Emery and Zorn had already on the preceding nights taken the altitude of numerous stars, and their work was so accurate that the greatest error was not more than 2", and even this was probably owing to the refraction caused by the changes in the atmospheric strata. The latitude thus carefully sought was found to be 27.951789°. They then found the longitude, and marked the spot on an excellent large scale map of South Africa, which showed the most recent geographical discoveries, and also the routes of travellers and naturalists, such as Livingstone, Anderson, Magyar, Baldwin, Burchell, and Lichtenstein. They then had to choose on what meridian they would measure their arc. The longer this arc is the less influence have the errors in the determination of latitude. The arc from Dunkirk to Formentera, on the meridian of Paris, was exactly 9° 56´. They had to choose their meridian with great circumspection. Any natural obstacles, such as mountains or large tracts of water, would seriously impede their operations; but happily, this part of Africa seemed well suited to their purpose, since the risings in the ground were inconsiderable, and the few water-courses easily traversed. Only dangers, and not obstacles, need check their labours.
This district is occupied by the Kalahari desert, a vast region extending from the Orange River to Lake Ngami, from lat. 20° S. to lat. 29°. In width, it extends from the Atlantic on the west as far as long. 25° E. Dr. Livingstone followed its extreme eastern boundary when he travelled as far as Lake Ngami and the Zambesi Falls. Properly speaking, it does not deserve the name of desert. It is not like the sands of Sahara, which are devoid of vegetation, and almost impassable on account of their aridity. The Kalahari produces many plants; its soil is covered with abundant grass; it contains dense groves and forests; animals abound, wild game and beasts of prey; and it is inhabited and traversed by sedentary and wandering tribes of Bushmen and Bakalaharis. But the true obstacle to its exploration is the dearth of water which prevails through the greater part of the year, when the rivers are dried up. However, at this time, just at the end of the rainy season, they could depend upon considerable reservoirs of stagnant water, preserved in pools and rivulets. Such were the particulars given by Mokoum. He had often visited the Kalahari, sometimes on his own account as a hunter, and sometimes as a guide to some geographical exploration.
It had now to be actually considered whether the meridian should be taken from one of the extremities of the base, thus avoiding a series of auxiliary triangles[1].
[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.
