Perhaps there is nothing more useful in simple coast-sailing and entering harbors than to know how to find one's exact position upon the chart, at a moment's notice, by means of taking what is called cross-bearings. Nothing is necessary for this purpose, but a pair of parallel-rulers, a compass, and a sight of any two well-defined objects in view, that may be known upon the chart by their general relative positions, such as lighthouses, lightships, buoys, churches, headlands, &c.
The parallel-rulers are two rulers attached by means of two brass swivels, so that they can be moved over the surface of a chart in any parallel direction to that from which they are first started; and are used to define direction upon any part of the chart. For instance, being placed upon the printed compass upon the chart, say upon the line of N.W. and S.E., they can be moved about the chart, carrying this same direction N.W. and S.E., to any other part of the chart. The two objects decided upon to be taken should be in such a direction as to form somewhat nearly a right angle with the yacht to obtain the most perfect results. All depends upon the aptitude with which the observer can line the object to be observed, i.e., its bearing by compass.
The writer knows of nothing so important and useful as this simple method of knowing just where one is at any moment, and thus be enabled to know just how to steer to avoid all dangers. These sights, or cross-bearings, can be taken every ten minutes with ease in fine weather, and the position of the yacht exactly defined.
Example I. (see diagram, Fig. 1).—Bring the compass in its box on deck (it should be of large size, so as to guide the eye; and small pocket-compasses are useless for this purpose), and, standing behind it, line with the eye with great care the bearing of the north lighthouse by the compass, this we will suppose to be N.W. by N.; mark this upon a slip of paper, and then move the person so as to see the south lighthouse in the same way across the face of the compass, which is always between the observer and the object to be observed; and line the bearing of this lighthouse by compass, in the same manner, which we will suppose to be S.W. With these two results marked upon paper, refer to the chart, and place the parallel-rulers upon the printed compass, designed upon the chart, upon the line of N.W. by W. and S.E. by S. (its opposite), and move them by means of the pivots till one part of them rests upon north lighthouse; then draw a line of indefinite length upon the chart. Take up the rulers, and in the same manner place them upon the printed compass on the chart, on the line of S.W. and N.E., and carry them forward, keeping this angle, till some part rests upon south lighthouse; then draw a line which will at some point intersect the former line, which, if the bearings have been correctly taken, will be the exact position of the yacht at the time of the observation.
It will be shown too, by experiment, that considerable variation of the bearings, when the angle is large, may be made, without changing very much the position of the yacht, proving how valuable this process is for practical use, as a considerable error in the bearings will still enable one to know almost exactly the position of the yacht; whilst a good observation will give it exact.
Example II. (see diagram Fig. 2).—Placing the compass in front of the observer, it is found that the lighthouse bears W. by compass, and that the lightship bears S. W. by S. With these two bearings we consult the chart, and lay off the two lines by means of the parallel-rulers; and, if the chart gives the distance in miles of the lightship from the lighthouse, then, by means of a common rule of equal parts, we shall be able to measure the distance of the yacht from the lighthouse or from the lightship. At the foot of most charts, however, will be found a scale of miles, and, having once ascertained the exact position of the yacht by means of cross-bearings, it will be very easy, with a pair of dividers, to find its distance in miles from any desired object within view, or designed upon the chart, and, by the use of the parallel-rulers, the course, by compass, that should be sailed to reach any desired point.
It is often useful to know how many geographical or nautical miles, which measure at the equator 6,086.4 feet in length, are contained in a degree of longitude at different latitudes; that is to say, a degree of longitude east or west of 89° N. latitude is only 1.05 nautical mile in length; and yet, in another sense, this 1.05 is 60 miles, or one degree in length: hence the following table:—