Even a single Sumner line, however, furnishes valuable information, as it may be combined with other sources of information to obtain an approximation to the position. The vessel must be somewhere on this line, and this gives a good check on the position by dead reckoning, or an intersection may be obtained with a line or bearing of a distant land object, or a line of soundings may be compared on the chart with the Sumner line.
If an observation is taken when the observed heavenly body is bearing abeam, it is evident that the resulting Sumner line will be the direction of the course of the vessel, and this fact may be useful in shaping the course when nearing the land or a danger.
Dead reckoning. When impossible to obtain the position by any other means, it is computed or plotted from the last determined position, using the courses and distances run as shown by compass and log and allowing for effect of current and wind. Because of uncertainties in all these elements, positions so obtained may be from five to twenty miles in error in a two-hundred-mile run, depending of course to some extent on the speed of the vessel.
Compass bearings. A compass bearing of a single object, as a lighthouse or a tangent to a point of land, laid down on the chart, shows that the vessel is somewhere on that line, and when combined with other information, as with a Sumner line or the course by dead reckoning or the distance by a vertical angle, will give a position whose correctness of course depends on the accuracy of the data used. Bearings of two objects not in the same direction give two lines on the chart whose intersection is the position. This will be very weak if the angle of intersection is acute, and will become stronger as it approaches a right angle. A bearing of a third object should be taken when practicable, as it affords a valuable check in that the three lines should intersect in the same point; if they do not do so when plotted the error is either in the observations, or the compass, or the plotting, or the chart. ([Fig. 40]). All compass bearings are of course dependent upon the accuracy of the compass and the knowledge of its errors due to the local magnetic effect of the ship, and also upon the correctness with which the magnetic variation from true north is known. Bearings of near objects should therefore always be preferred, and those of distant objects considered as giving only approximate positions. An error of one degree in the bearing of an object 30 miles away will deflect the plotted line about one-half mile. Because of the facility with which they may be taken compass bearings are much used for inshore navigation, but in point of reliability they are inferior to some of the other methods.
A single or "danger" bearing of an object is often a valuable guide in avoiding a danger. For example, a reef may lie to the westward of a line drawn South 10° East from a lighthouse; in approaching a vessel will pass safely to the eastward of the reef if the lighthouse is not allowed to bear any to the northward of North 10° West. ([Fig. 41.])
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.])
DANGER BEARING
FIG. 41.