When the base-line has been established and measured, and its terminals have been so marked with permanent material as to be practically indestructible, the base has to be developed—that is, a complete set of observations has to be made for the purpose of connecting the base with the stations of the net. The base being, as a rule, much shorter than the sides of the triangles of the actual net, it can not be connected directly with these large sides, as the triangles thus formed would have very small angles. A special net of triangles, the sides of which grow larger by degrees until they reach the large sides of the actual net, is established. This small net is given the form of a polygon for the purpose of increasing the accuracy. Longer bases are sometimes divided into two halves, and, besides the two terminals, a central station is established in the middle of the base, and thus three base stations are obtained instead of two. All the angular observations at the base stations, and at those which may be called stations of development, are made in the same number and with the same accuracy as in those of the net proper. They are all considered as first-class stations.
All geodetical points at which angular observations are made can be divided into four classes. In the first class are included all the base stations, the developing stations, and the actual stations of the geodetical net. The second class includes those stations which are of secondary importance geodetically, and which do not belong to the net proper. The observations at these stations are not so exhaustive as in first-class stations, although they are used also for controlling the observations of the others. Third- and fourth-class stations have more importance as topographical points, as they are used by the topographical operators as starting-points when mapping out the country. For scientific purposes, only the data collected at first-class stations are used, all others being rejected.
For ordinary topographical purposes, the number of angular observations at each station is not so large as when these have to be used for scientific purposes.
Except for the measurement of bases, geodetical triangulation consists almost exclusively in angular observations. In fact, it can be called essentially a measurement by angles, the work to be done, and on which many years may be spent before even a small net can be called complete, being an uninterrupted series of measurements of angles. Very delicate instruments are used in these measurements. The best part of an observer's outfit consists of a good theodolite. Although simple in principle, the theodolite is a very complicated instrument, and a good deal of practice is necessary to enable an observer to become efficient in handling this delicate machine. It consists chiefly in a good field-glass, which can be turned in every direction, so as to enable the observer to see the exact spots in the distance which are the stations of the net, and of a circle on which a scale, carefully divided, enables the observer to read the angle between
