244 THE POPULAR SCIENCE MONTHLY. 



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 di- 

 rection at the beginning of the eighteenth century, and the distance 

 between Dunkerque and Perpignan, the northern and southern ex- 

 tremities 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 tri- 

 angles 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 meas- 

 ured 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. 



