sidered very great. This fact was so keenly felt that the work done in France was extended both in a southward and in a northward direction at the beginning of the eighteenth century, and the distance between Dunkerque and Perpignan, the northern and southern extremities of France, was obtained by triangulation.
What is geodetical triangulation? If two sides and one angle, or one side and two angles, or three sides of a triangle, are known, the remaining parts of the triangle can be calculated by means of well-known formulas. It is on this property of triangles that geodetical or trigonometrical triangulation is based. Supposing the exact distance between two cities situated from one hundred to five hundred miles from each other has to be measured, it is not necessary to tramp the whole distance with a surveyor's chain or other measuring instrument. Such measurement would be too tedious, besides being incorrect, and could not be made in a straight line, even supposing that the ground between the two cities were all level, and that no obstacles intervened to render such straight-line measurement altogether impossible. But this difficulty can be obviated and the exact distance ascertained by means of triangulation. A number of intermediate points are taken, situated so that each three of them form a triangle in which the angles are not too small to be measured. The two ends of the line whose length has to be calculated are also used as points. A series of triangles is thus obtained, the sides of which are of course imaginary, between the points chosen. These points are called stations. The whole system of stations, and of the imaginary lines between these, is what is known as a triangular or trigonometrical net, because when drawn on paper all the lines between the various stations form a sort of net. If the actual distance between two of the stations of the net is known, and if the angles between any two lines of the net are measured by means of special instruments, all the distances between the various stations can be calculated, and thus the distances between any two stations, whether terminal or intermediate, can be ascertained.
However simple this work may seem in appearance, the difficulties to be encountered in its execution, and the probabilities of errors to be avoided, are so many that special scientific skill and thorough ability and training are required in those who have to undertake the practical execution of the work. Like much other scientific work, it has to be a work of love rather than a matter of duty on the part of the executors on whose observations the accuracy of the result necessarily depends. Dangerous ascents and solitary life on the top of high mountains, with no other society than that of the few assistants who accompany him, are common occurrences for the geodete. Not less dangerous to him is the ignorance and greed of the mountaineers, who, seeing his bright, well-kept instruments, imagine that they are made of gold, and often do not stop at any means to get possession of what they consider will make their fortune.
