Having in the last chapter described the various instruments which enable a mariner to direct his course, we will now give some further explanations of the method of employing the chart and compass.

Cross Bearings.—When a vessel is in sight of land, her position can be calculated with exactness by several methods.

First. By cross bearings of two known objects. If two well-known landmarks are visible on shore, we observe how each of them bears by our compass. We then refer to the chart, lay down these bearings with the parallel rule, and the point where the lines cut will represent the vessel’s position.

For instance (see (Fig. 47), the beacon A is found to be N.W. of us, the beacon B N.E. of us. We lay our parallel rule on the magnetic compass design on the chart so that its edge passes through N.W. and also through the centre of the compass. We then slide the rule to the beacon A on the chart—preserving the direction—and draw with a pencil the line from A indicated by the edge of the rule.

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.

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.

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.

An azimuth compass is one specially adapted for taking bearings. Its card is more carefully divided than that of the steering compass, and it is fitted with sight vanes.

However, bearings sufficiently accurate for practical purposes can be taken with the ordinary compass. Hold a piece of string across the centre of the compass, and, looking along it, direct it towards the object whose bearing is required, as if taking an aim with a gun. The direction of the string will then indicate the bearing on the compass card beneath.

In taking cross bearings endeavour to obtain a difference between them of as near 90° as possible; for if the difference be small, as, for example, 10°, or large, as 150°, a small error in the bearing will cause a great error in the calculation of the vessel’s position.

If, when directing one’s course out of sight of land, as, for instance, from Yarmouth to the mouth of the Elbe, head winds are met with, and it becomes necessary to tack, it is an advantage as a general rule to sail on that tack on which the vessel looks up best for her port, and not to go about until she has brought herself to a position on which the other tack is the most favourable, and so on. The ship thus constantly keeps her port in the wind’s eye, and any change in the direction of the wind can be taken advantage of. But if a vessel stands on, till the tack be a losing one in order that she may fetch her destination on the next tack, a change in the wind may put her dead to leeward of her port and she will have lost ground by the ill-judged tactics.

When tacking out of sight of land, the direction and length of each successive board can be pricked out on the chart by using the dividers and parallel rule in the manner already described, and the position of the vessel at any time will thus be known.

Before land is lost sight of, what is termed a departure is taken from the last well-known object on the shore. Its bearing is taken by compass, its distance by log is estimated, and the time is noted. A departure can also be taken by cross bearings.

It is from the departure that the voyage is reckoned out.

In determining the course and position of a vessel at sea, allowance must be made for leeway and for the set of the tide. The leeway is greater when the sea is rough and when the sails are reefed. The amount of leeway can be roughly estimated by looking over a vessel’s stern at her wake, which will not be in the same line as her keel, but at an angle to it.

Having measured this angle, apply it to the left when the vessel is on the starboard tack, to the right when she is on the port tack.

If the strength and direction of a current are known, its effect upon the vessel’s course and distance made must be allowed for.

If the set of the current is in the same direction as the ship’s direction—either with her or opposed to her—her course is unaffected, but her rate of motion over the ground is increased or lessened by as many knots an hour as the current is flowing. The rate of current must therefore be added to or deducted from the distance logged. The log, of course, only indicates the vessel’s speed through the water, and does not register the current.

If the current is across a vessel’s direction, it will influence both her course and rate of sailing.

In order to find the course that should be steered so as to make good a required course in a cross current we proceed as follows. In either of the two Figs. 51 and 52, let A be the position of the vessel, B the port we desire to make, and let the arrow represent the direction of the current. With the dividers take from the scale at the side of the chart the number of miles the current runs per hour, and lay down this distance A C in the direction of the arrow. Then take from the scale the number of miles the vessel is going per hour, and with this distance as radius, and C as the centre, describe a circle.

The line joining C and D—the point where the circle and the line A B cut—represents the direction in which the vessel must be steered so as to keep on the line A B. Draw A E parallel and equal to C D. Then if the vessel be steered from A towards E, and travel the distance A E through the water she will in reality have made the distance A D in the direction of her port. In the two figures the alteration of the vessel’s course is about the same, but as the current is contrary in (Fig. 51, A D, the distance made, is much less than A E, the distance sailed, whereas in (Fig. 52 the current is favourable and therefore the distance made is greater than the distance sailed.

In current sailing, every advantage must be taken of the tide, and it is often possible to fetch a port dead to windward on one tack by what is termed underbowing the tide.

For instance, if we are bound for a port due north of us, and the wind is also due north, while we have a current running to the eastward, we can, by putting our vessel on the tack that directs her to the westward of north, that is, in this case the starboard tack, bring the tide on the lee bow so that the result of our north-west course and the easterly current is that our vessel travels due north.

Hence it is very necessary, while tacking across the sea, to know exactly when the tide will turn, so that we can put the vessel about to the best advantage.

If we are crossing a broad stretch of water such as the North Sea, with the wind free, and are likely to be in more than one tide, we can usually with advantage steer a course straight for our port, without paying much attention to the currents, as the effects of the ebb and flood will cancel each other, and we will be able to make a good land-fall.

The rise, rate, and direction of the tide at springs and neaps are generally given on the chart. If the hour of high water for the particular day and place are known, the speed of the current and the height above low water can be roughly calculated from the following data. Unless the conformation of the coast produces a variation from the general rule, the tide rises from low to high water in six hours and a quarter and falls from high to low water in the same time. The rise and fall are not uniform. During the first and last hours of flood the rise is smallest. During the second hour it greatly increases. At the fourth hour the tide has reached its maximum rate, and from then the rate of rising diminishes in the same proportion until high water. The same, rule applies to the ebb tide.

Fig. 53 represents the range of the tide in the open sea, which we have divided into sixteen equal parts. It has been found that the tide will rise one division in the first hour, three in the second hour, four in the third hour, four in the fourth hour, three in the fifth hour, and one in the last sixth hour and a quarter.

We have already explained that the time of high water at any particular spot at the full and change of the moon is indicated on the chart—thus, for instance, H.W. at F. and C. 6 h. 10 m., which signifies high water at full and change of the moon at six hours ten minutes. If we have no tide tables at hand, we can roughly calculate the time of high water for the day by adding forty-eight minutes for every day that has passed since the last full or new moon to the time at full and change given on the chart.

But a more accurate method is to refer to the Admiralty tide tables, or, what will answer the purpose equally well, to Pearson’s Nautical Almanac, a little book which we strongly recommend to the yachtsman. Here he will find daily tide tables, morning and afternoon, for London and other principal English ports, together with the height of the rise in feet.

Besides these, there is an extensive lists of ports and positions on the coast of England and Europe with their Tidal Constants. The constant for a given place is the number of hours and minutes that are to be added to or subtracted from the time of high water at the standard port or port of reference in order to obtain the time of high water at the given place.

For instance, supposing London to be the standard port, as it is in Pearson’s Almanac, and we require to know the hour of high water at Portland Breakwater on a given day. We first refer to the table of constants, and find + 5 h. 3 m. to be the constant of Portland Breakwater. We then turn to the London tide table, and find the time of high water for the day—morning or afternoon, as the case may be. We add five hours and three minutes to this, and the result will be the required time. Had the sign before the constant been-instead of + we should have subtracted and not added.

If we require the high water at a port where the tidal constant is not given in the tables, but where high water at full and change is given on the chart, find the high water at full and change of some port—London, for example, whose constant is in the tables. Subtract the lesser of these two times from the greater, the remainder will be the constant of our port—additive if the full and change at the port be greater than that of London, subtractive if it be less.