#Horizontal sextant angles.# The location of a position by the three-point problem, using sextant angles, is much more exact than by bearings, but is less used because not so well known and also because additional instruments are required and the conditions are not always favorable. It is so valuable a method, however, that it should be used, when necessary, on every well-equipped vessel. A single horizontal angle taken with a sextant between objects, as two lighthouses, defines the position of the vessel as somewhere on the circumference of a circle passing through the two objects and the vessel. A protractor laid on the chart with two of its arms set at the observed angle and passing through the two objects, will permit of locating two or more points of this circle on the chart. This furnishes a line of position which may be combined with other information to locate the vessel. With a compass bearing of one of the objects the position may be plotted directly from the single angle. Two sextant angles measured at the same instant between three objects furnish one of the most accurate means of locating the position of a vessel, this being the same method that is ordinarily used in hydrographic surveying, known as the three-point problem. (Fig. 44.) The two angles are conveniently set off on a three-arm protractor, which is shifted on the chart until the three arms touch the three points, when the position of the center is plotted. A third angle to a fourth point furnishes a valuable check in case of doubt. Two angles may also be taken to four objects without any common point, and in this case portions of the two circles of position are plotted and their intersection will be the ship's position. The value of this method depends largely on the selection of favorably located objects, and it is quite important that the principles of the three-point problem be understood. If the ship is on or near the circumference of a circle which passes through the three objects the position will be very weak, and the same is true if the distance between any two of the objects is small as compared with the distance from them to the vessel. A useful general rule is that the position will be strong if the middle one of the three objects is the nearest to the vessel, provided that no two of the objects are close together in comparison with the distance to the vessel.