Two successive bearings of a single object, as, for instance, a lighthouse, noting the distance run in the interval, afford a convenient and much used means of locating the position with respect to that object. Such bearings are drawn on the chart in reversed direction from the object. The distance run between the bearings, as read by the log and corrected for current if practicable, is scaled off with dividers and the course of the vessel is set off with parallel ruler; the latter is then moved across the two plotted directions until the distance intercepted between them equals that scaled with the dividers, and the edge of the ruler then represents the track of the vessel. (Fig. 42.) If the angle from the bow, or from the course of the vessel, for the second bearing is double that for the first bearing, the distance from the object at the second bearing is equal to that run by the vessel in the interval, and the use of this simple relation is designated as "doubling the angle on the bow." If the angles between the course and the object are respectively 45° and 90° when the two bearings are taken on an object on the shore, the distance that the ship passes offshore when the object is abeam is equal to the distance run between the two bearings; this is a much used navigational device, known as the "bow and beam bearing" or the "four-point bearing." There is an advantage, however, in using bearings at two and four points (or 22.5° and 45°), as these give the probable distance that the object will be passed before it is abeam. #Ranges.# A valuable line of position is obtained by noting when two well-situated objects are in range, that is, one back of the other in the line of sight from the vessel, as, for instance, a church spire appearing behind a lighthouse or a rock in line with a prominent point. Such ranges are of course entirely free from compass errors, and should be noted whenever there is favorable opportunity. The value of the range in plotting will increase with the distance between the objects, and if the two are close in proportion to the distance to the vessel the direction will be weak owing to the uncertainty in drawing a direction through close points. Artificial ranges are often erected as aids to navigation, usually to indicate the course to be followed in passing through a channel. Ranges afford a valuable guide in avoiding dangers, as for example an inspection of the chart may show that if a certain lighthouse is kept in line with or open from an islet a dangerous shoal will be given a good berth; on coasts not well buoyed such danger ranges are sometimes marked on the charts. (Fig. 43.) [Illustration: DANGER BEARING FIG. 41.] [Illustration: POSITION BY SUCCESSIVE BEARINGS TWO AND FOUR POINT BEARINGS FIG. 42.] [Illustration: RANGE TO AVOID DANGER FIG. 43.]