Triangulation

Triangulation is the process of dividing any portion of the earth's surface into triangles, from the measurement of which maps may be constructed, The first step in the process is to choose a suitable horizontal line, called the base-line (q.v.), and to measure it very accurately, a length of about five miles being generally a convenient distance to work with, if the peculiarities of the district will allow the possibility of such a line being obtained. From the ends of this base-line a certain point is observed, the angles between the base-line and the lines joining its ends with the chosen point being measured by a theodolite (q.v.); the distance of this point is then obtained by calculation. Working in this way, any fixed pair of points can be taken as a new base-line, and so a number of triangles can be built up. In ordinary topographical survey it is usual to select convenient points - such as the peaks of mountains - very far apart, so that large triangles are obtained. these, are called primary triangles, and are subdivided into any number of smaller or secondary triangles. The side of a primary triangle may be only a few miles in length, or may exceed 100 miles. When very distant points are to be observed, they are often marked by strong limelight in dull weather, or by some arrangement for reflecting solar rays in sunny lands. The selection of convenient spots in triangulation is not always a very simple matter. Angles as near sixty degrees as possible are the best to measure, greater errors creeping in where calculations are made from very acute angles; the nature of the country, however, often interferes to prevent the possibility of this arrangement, and familiarity with the district in question is the only guide to the selection of the most suitable stations. To prevent the multiplication of errors new base-lines are chosen every now and then, their lengths calculated by continuous triangulation from the old base-line, and then actually measured. If the two results agree, the intermediate survey, is accepted as accurate. It must be remembered that the surface of the earth is curved, so that the aid of spherical trigonometry must be invoked in the calculations. This will perhaps be better appreciated by considering the case where the survey of one country is connected with that of another across the sea - as in the triangulation necessary to connect the survey of England with that of Ireland, and of the Continent - the curvature of a watery surface being more apparent than that of a land covered with irregularities. An important piece of triangulation is that necessary in measuring an arc of the meridian for the determination of the length of a degree of latitude at any place. In this case only a few triangles are necessary, but astronomical observations are made - usually on the sun or the pole-star at certain definite times - in order to fix the position of the meridian itself. [ORDNANCE SURVEY.]