In the same way we carry the direction N.E. from the compass design to the beacon B, and draw the line from B indicated by the rule. The point C where these lines cut represents the position of the vessel, and the distance between C and the beacons or the shore can be measured with the dividers by referring to the graduated meridian on the side of the chart as a scale.
Fig. 48.
While a vessel is sailing along the shore her distance from it can be calculated as follows: We select any prominent point on the shore, as the tree A in ([Fig. 48]. We take its bearing, which we find to be N.W. From A we draw the line A B in a N.W. magnetic direction by the compass design. Our vessel’s course is N. by W. From any point B on the line A B we draw a line B C in a N. by W. direction. When we have sailed a certain distance, say five miles by the log, we take another bearing of the tree and find it is now N.E. of us. From A we draw a line corresponding to this last bearing, which cuts the line C B at C. Taking C B a distance of five miles as our scale, we can measure the distance between the vessel’s position C and the tree A. A chart is not needed for the above method of calculating one’s distance. A sheet of paper with a compass design sketched on it is all that is necessary.
The following is a very easy method of calculating the distance of an object that one is passing, and requires no chart or diagram. Take a bearing of the object, and observe the angle this bearing makes with the vessel’s course; also note the time. As the vessel sails on, this angle will increase until at last it is doubled. The vessel’s distance from the object will then equal the distance she has travelled since the first bearings were taken. ([Fig. 49] will make this method clear. A is the object on shore, C and B the position of the vessel when the bearings were taken. A C D is the angle formed by the course E D and the first bearings. When this angle is doubled, as at A B D, the line B C will equal the line A B.
Fig. 49.
If one is sailing parallel to a coast, the following is a rapid method of ascertaining one’s distance from the shore. Note the time when an object on shore is exactly at right angles to the vessel’s course. When one has brought the object at an angle of 45° to the vessel’s course—looking aft—calculate the distance travelled since the time was noted. The distance from the shore will be the same. Thus, in ([Fig. 50], the vessel’s direction when she is at B is at right angles to the bearings of A the object on shore. When the vessel has arrived at C, the angle A C B has a value of 45°. It follows that C D, the distance from the shore, equals C B, the distance travelled.