the two bearings, until the distance run in the dividers between the times of taking the bearings agree with each bearing; one leg of the dividers will show the position of the ship when the first bearing was taken, the other leg her position at the time of last bearing. 4.—The distance from a light of known elevation can also be easily ascertained by referring to the table showing the distance of the visible horizon from various elevations. Example:-The eye of an observer is elevated 20 feet above the sea, and a light known to be elevated 155 feet has just appeared above the horizon; required the distance. 5. Again, the distance from a lighthouse, ship, or other object of known elevation above the sea, or from some other base line, can be easily ascertained with a sextant as follows:-Multiply the height or elevation of the object in feet by 565 and divide by the minutes of angle which it subtends, as shown on the arc of the sextant; the result will be the distance in miles. Example :Cape Wrath Light above high water = 400 feet × 565 = 226 Angle at the eye of an observer 1° 53' x 60' = 113 2 miles. HOW TO MAKE USE OF THE DANGER ANGLE. The danger angle can only be applied when two well defined promontories or landmarks, whose relative bearings from a known danger have been accurately determined, can be observed from the immediate vicinity of the danger. Example :-Suppose D to represent a well known danger, covered at all states of the tide; A and B two well defined landmarks. It is required to pass outside of the danger D at a distance of not less than half a mile. Describe a circle with a radius of half a mile about D, and in that part of its circumference most remote from A and B, take any point C; join AB, BC, CA, and about the triangle ABC describe the circle ABEC. The angle ACB is equal to the angle AEB, or to any other angle in the same segment, and is consequently the angle which if placed on a sextant and kept on, will keep the ship on some part of the circumference of the circle ABEC. Should the angle shown on the sextant increase beyond what it ought to be by the chart, the ship will be inside the circle of danger, and vice versa. DIURNAL RISE AND FALL OF THE TIDES. The alternate rise and fall of the tide is due to the attractive influences of the sun and moon, which draw or lift up the waters of the ocean toward themselves. Since the force of gravity increases as the square of the distance diminishes, it is evident that the waters on the part of the earth which is nearest the moon will feel in a greater degree the power of her attraction, and be raised accordingly; while those waters further removed from her influence will be less raised: but as the force of attraction acts in straight lines, the waters on the part of the earth which is most remote from the moon will be raised as well as those immediately facing her hence the spheroidal form assumed by the ocean. Again, if a line be drawn from the centre of the moon through the centre of the earth, the two points where it cuts the spheroid will be those of high water; and all points equally distant or 90 degrees from each will be those of low water, according to the progress of the tide-wave. Although the sun is so much larger than the moon, the latter on account of her nearness to the earth has the most powerful effect upon the tides, her influence being nearly three times as great as that of the sun. It is when the sun and moon unite their influences, which they do at new and full moon, that the tides rise highest, and are called SPRING-TIDES. When the moon is in her quarters, her action is directly opposed to that of the sun and consequently the tides are then lowest, and are called NEAP TIDES. As the moon crosses the meridian of a place every 24 hours, 50 minutes, 30 seconds, the sea in that space of time ebbs twice and flows twice all over the world; therefore, in the open sea the tide requires nearly six hours and a quarter to rise from low water to high water, and the same time to fall from high to low water. The Range of the tide is the difference between the levels of high and low water. The rise or fall of the tide per hour assumes very nearly the following proportions In the first hour about of the range. In the third hour about In the fourth hour about 16 of the range. of the range. of the range. In the fifth hour about is of the range. 6 In the sixth hour about 1 of the range. 16 Thus, at about two hours from low water, the tide has risen one-fourth of its range; at three hours, or half tide, it has risen one-half of its range; and at four hours, it has risen three-fourths of its range. Now, as any of the above quantities taken from a sounding will only reduce it to the low water of the tide for that day (which may happen to be a neap-tide, while the depths marked on the chart are given for low water at ordinary springs), it becomes necessary to apply a further correction before a cast of the lead taken at any state of the tide on any day besides full and change will admit of direct comparison with the depths marked on the chart. This correction is extremely simple, and easy of application, and only necessitates the use of the Admiralty Tide Tables, which contain the requisite data and examples for the reduction of soundings under all circumstances. HOW TO FIND THE TIME OF HIGH WATER. The Tide Tables for the British and Irish Ports, published by order of the Lords Commissioners of the Admiralty, contain the morning and afternoon tides for twenty-four of the principal home ports, and tidal constants for various British, Irish, and European ports, which, being applied according to the sign + or to the times or heights belonging to the standard port to which each of them is referred, will afford a ready means of determining approximately the height as well as the time of high water at each of those several places; in addition to which they have the time of high water on full and change days at the principal places on the globe, arranged according to the apparent progress of the tide-wave, as well as alphabetically, with the rise of the tide at springs and neaps. When the above tide tables are not at hand, nor any other tables available, the time of high water can be found approximately by either of the two following methods. I. To the time of high water at full and change, as given in the Sailing Directions and Nautical Almanac, or shown by Roman numerals on the chart, add 49 minutes for every day that has elapsed since full and change, the sum being the P.M. tide for the given day. II. To the time of high water at full and change add the time of the Moon's Meridian Passage corrected for longitude (see page IV. of each month in the Nautical Almanac and corresponding Explanation), the sum being the P.M. tide for the given day. HOW TO ALLOW FOR THE SET AND DRIFT B Current for one hour Course to Steer. True Course. Distance Ship will Log in one hour. Let A represent the ship's place on the chart and D her destination, join AD, then the line AD is the course required to be made good. From A draw a line AB in the direction in which the current sets and equal to the distance it runs in one hour, then take in the dividers the distance the ship will log in one hour, and place one leg of the dividers at B, letting the other leg take the D |