GEODESY (from Gk. yeaakuala, geOdaisia, art of mensuration, from Tfj, ge', earth + &kw, daiein, to divide). The science of the earth, its size, shape, and figure. The operations of the geodesist are primarily a mere extension of ordinary surveying (q.v.), so as to cover a greater extent of territory, and to increase the precision of observations. Furthermore, the geodesist makes use of astronomical methods to determine the latitudes and longitudes of various important points in his survey, in order that maps and charts may be provided with their necessary reference lines. We may, therefore, define the objects of a geodetic survey thus: to determine accurately the relative posi tions of widely separated points on the earth's surface and the directions and lengths of the lines joining them, and to determine astronomically the absolute positions of widely separated points on the earth's surface. In the first case, the work simply supplies a skeleton of exact dis tances and directions on which to base a more detailed survey of the intervening country, as described under Topographic Surveying (see SUR VEYING) ; in the second, the results furnish the data for computing the shape and size of the earth, in addition to their use in making more detailed surveys. In both cases the points deter mined form the vertices of a series of triangles joining all points of the system. One or more lines in this system of triangles and all of the angles are very carefully measured, and the lengths of all the other lines in the system are computed. The azimuths of certain lines are also determined, and, if desired, the latitudes and longitudes of all the points in the system and the lengths and azimuths of all the connecting lines. The work as a whole is denominated triangulation.
Triangulation systems are of all degrees of magnitude up to the large primary systems cov ering entire continents, the single lines in which are sometimes over 100 miles long. In making a triangulation survey, the first task is to select and measure a base line. This base should be located on nearly level ground, and its situation should be selected with special reference to the location of the triangles of the system. It is
measured with extreme care by means of steel tapes and metal bars, careful allowances being made for temperature, sag, pull, etc., and the measurement being repeated several times to eliminate error. By these means it is common practice to reduce the error to film 1 in 100,000 to 1 in 1,000,000; measurements have been made in which the probable error was reduced to 1 in 2,000,000. In primary triangulation the length of base line employed is usually from three to ten miles; it is from two to three miles long for secondary triangulation, and from one-half to one mile long in testing triangulation. The base line, as a b in the figure, having been measured, a point c is selected upon some distant elevation which is visible from both its ends, and here a `station' is erected which consists of a pole or target mounted on a tower to serve as an object on which to 'sight.' A theodolite is then set up first at a and then at b, and the angles at these points are measured by sighting on the station at c. From a, a sight is also secured on d, enabling the angle c a d to be measured. The theodolite is then removed to c, back sights are secured on a and b, and fore sights on d, f, and e. Movement of the instrument is then made to d, e, f, etc., in succession and the angles 'measured. The first triangle a b c, after the instrumental readings have been completed at each apex, is a triangle in which one side, the base line a b, and all the angles are known. From these known data the lengths of the two remaining sides a c and b c are easily calculated. The side a c being cal culated gives the length of one side of the second triangle a c d, of which the angles are determined by instrumental readings at the apices a, c, and d. Calculation gives the length of the side d c, which is also one side of the third triangle. By repe titions of the same process triangles IV to XI, inclusive, are calculated. Generally after the system of triangles has covered a distance, as from a to m, of from 200 to 600 miles, a second base line, as A: m, is measured a-nd the survey is checked up by its means.