Lectures in Navigation

by Ernest Gallaudet Draper

Select two objects marked on the chart, so far apart that each will bear about 45° off your bow but in opposite directions. These bearings will be secured in the best way by the use of your pelorus. Correct each bearing for Variation and Deviation so that it will be a true bearing. Then with the parallel rulers carry the bearing of one object from the chart compass card until you can intersect the object itself and draw a line through it. Do exactly the same with the other object. Where the two lines intersect, will be the position of the ship at the time the bearings were taken.

Now supposing you wish to find the latitude and longitude of that position of the ship. For the latitude, measure the distance of the place from the nearest parallel with the dividers. Take the dividers to the latitude scale at the side of the chart and put one point of them on the same parallel. Where the other point touches on the latitude scale, will be the latitude desired. For the longitude, do exactly the same thing, but use a meridian of longitude instead of a parallel of latitude and read from the longitude scale at the top or bottom of the chart instead of from the side.

2. Bearing and distance of a known object, the height of which is known.

Take a bearing of, say, a lighthouse the height of which is known. The height of all lighthouses on the Atlantic Coast can be found in a book published by the U.S. Dept. of Commerce. Correct the bearing, as mentioned in case No. 1. Now read the angle of the height of that light by using your sextant. Do this by putting the vernier 0 on the arc 0, sliding the limb slowly forward until the top of the lighthouse in the reflected horizon just touches the bottom of the lighthouse in the true horizon. With this angle and the known height of the light, enter Table 33 in Bowditch. At the left of the Table will be found the distance off in knots. This method can be used with any fairly perpendicular object, the height of which is known and which is not more than 5 knots away, as Table 33 is not made out for greater distances.

3. Two bearings of the same object, separated by an interval of time and

with a run during that interval.

Take a compass bearing of some prominent object when it is either 2, 3 or 4 points off the bow. Take another bearing of the same object when it is either 4, 6 or 8 points off the bow. The distance run by the ship between the two bearings will be her distance from the observed object at the second bearing. "The distance run is the distance off."
A diagram will show clearly just why this is so:

The ship at A finds the light bearing NNW 2 points off her bow. At B, when the light bears NW and 4 points off, the log registers the distance from A to B 9 miles. 9 miles, then, will be the distance from the light itself when the ship is at B. The mathematical reason for this is that the distance run is one side of an isosceles triangle. Such triangles have their two sides of equal length. For that reason, the distance run is the distance off. Now the same fact holds true in running from B, which is 4 points off the bow, to C, which is 8 points off the bow, or directly abeam. The log shows the distance run between B and C is 6.3 miles. Hence, the ship is 6.3 miles from the light when directly abeam of it. This last 4 and 8 point bearing is what is known as the "bow and beam" bearing, and is the standard method used in coastwise navigation. Any one of these methods is of great value in fixing your position with relation to the land, when you are about to go to sea.