If G be the point on the geodetic corresponding to F on that one of the plane curves which contains the normal at Cadiz (by "corresponding" we mean that F and G are on a meridian) then G is to the north of F; at a quarter of the whole distance from Cadiz GF is 458 ft., at half the distance it is 637 ft., and at three-quarters it is 473 ft. The azimuth of the geodetic at Cadiz differs 20" from that of the vertical plane, which is the astronomical azimuth. The azimuth of a geodetic line cannot be observed, so that the line does not enter of necessity into practical geodesy, although many formulae connected with its use are of great simplicity and elegance. The geodetic line has always held a more important place in the science of geodesy among the mathematicians of France, Germany and Russia than has been assigned to it in the operations of the English and Indian triangulations. Although the observed angles of a triangulation are not geodetic angles, yet in the calculation of the distance and reciprocal bearings of two points which are far apart, and are connected by a long chain of triangles, we may fall upon the geodetic line in this manner:-- If A, Z be the points, then to start the calculation from A, we obtain by some preliminary calculation the approximate azimuth of Z, or the angle made by the direction of Z with the side AB or AC of the first triangle. Let P1 be the point where this line intersects BC; then, to find P2, where the line cuts the next triangle side CD, we make the angle BP1P2 such that BP1P2 + BP1A = 180 deg. This fixes P2, and P3 is fixed by a repetition of the same process; so for P4, P5 .... Now it is clear that the points P1, P2, P3 so computed are those which would be actually fixed by an observer with a theodolite, proceeding in the following manner. Having set the instrument up at A, and turned the telescope in the direction of the computed bearing, an assistant places a mark P1 on the line BC, adjusting it till bisected by the cross-hairs of the telescope at A. The theodolite is then placed over P1, and the telescope turned to A; the horizontal circle is then moved through 180 deg. The assistant then places a mark P2 on the line CD, so as to be bisected by the telescope, which is then moved to P2, and in the same manner P3 is fixed. Now it is clear that the series of points P1, P2, P3 approaches to the geodetic line, for the plane of any two consecutive elements P_(n-1) P_n, P_n P_(n+1) contains the normal at P_n.