After taking a latitude at noon and obtaining a position, a course and distance to a position nearer the destination is usually required. A course and distance from an estimated noon position may be worked prior to noon and then corrected at noon by the observed latitude and morning position line, by means of a plotting chart, giving reliable results quickly and accurately.

In Fig. 1, BA and CA represent the course and distance from B to A and C to A respectively. BD and EC are arcs of concentric circles with centre A; and AC = AE and AB = AD.

If BD and CD are small in comparison with AB, arcs BD and EC may be considered straight lines and the figure BECD a rectangle. If the rectangle can be solved, the distance AC can be deduced from AB, i.e. AC = AB - DC or AC = AB + DC if C lies the other side of BD.