place, as the table directs, will give the approximate time of high water in the afternoon.

Then, take the interval between the reduced time of the phase and the approximate time of high water; find the corresponding equation; which applied as before to the syzigy time of water will give the time of the afternoon high water. If the time of the morning high water is required, increase the last interval by twelve hours, if the given day fall before the phase; or diminish it by twelve hours, when it falls after that phase. And the equation to this time applied to the syzigy time, gives the morning time of high water.

The method commonly used at sea to find the distance sailed over in a given time, is by means of a log-line and half-minute glass. The interval between each knot made upon that line, called the log line, ought to be fifty feet in order to adapt it to a glass which runs thirty seconds. But though the line and glass be at any time perfectly adjusted to each other; yet as the line shrinks after having been wetted, and as the weather has a considerable effect upon the glass, it is, therefore, necessary to examine them from time to time, and the distance given by them must be corrected accordingly. For doing this, and finding the true distance sailed over, rules are laid down.

Problem 1. The distance sailed by the log, and the seconds run by the glass being given, to find the true distance, the line being supposed right,

Rule. Multiply the distance given by the

log, by thirty; and divide the product by the seconds run by the glass; the quotient will be the true distance:

Problem 2. Given the distance sailed by the log, and the measured interval between two adjacent knots on the line; to find the true distance, the glass running exactly thirty seconds,

Rule. Multiply twice the distance sailed, by the measured length of a knot; point off two figures to the right, and the remainder will be the true distance.

Problem 3. Given the length of a knot, the number of seconds run by the glass, in half a minute; and the distance sailed by the log; to find the true distance.

Rule. Multiply the distance sailed by the log, by six times the measured length of a knot, and divide the product by the seconds run by the glass; the quotient, pointing off one figure to the right, will be the true distance.

PLANE SAILING.

Plane sailing is the art of navigating a ship upon principles deduced from the notion of the earth's being an extended plane. Upon this supposition the meridians are regarded as parallel right lines. The parallels of latitude are at right angles to the meridians; the lengths of the degrees on the meridians, the equator, and the parallels of latitude, are every where equal, and the degrees of longitude are reckoned on the parallels of latitude as well as on the equator. In plane sailing, four circumstances are prin

cipally concerned; namely, course, distance, difference of latitude, and departure.

The course is the angle contained between the meridian and the line described by the ship; and is usually expressed in points of the

compass.

The distance, is the number of miles a ship has sailed on a direct course, in a given time.

Difference of latitude is the portion of a meridian contained between the parallels of latitude sailed from and come to; and is reckoned either north or south, according as the course is in the northern, or the southern hemisphere.

The departure, is the distance of the ship from the meridian of the place she left reckoned on a parallel of latitude. In this sailing, the departure and difference of longitude are esteemed equal.

TRAVERSE SAILING.

If a ship sail upon two or more courses in a given time, the irregular track she describes is called a traverse; and to resolve a traverse, is the method of reducing these several courses, and the distances run, into a single course and distance. The method chiefly used for this purpose, is called inspection, and is performed by means of a table; in which are arranged, in separate columns, the courses, the distances, differences of latitude, and departure.

PARALLEL SAILING.

The figure of the earth being spherical, the meridians gradually approach one another, and

meet at the poles. The meridian distance, answering to the same difference of longitude, will, therefore, be variable with the latitude of the parallel upon which it is reckoned; and the same difference of longitude will not answer to a given meridian distance, when reckoned upon different parallels.

Parallel sailing, is the method of finding the distance between two places lying in the same parallel, whose longitudes are known: or to find the difference of longitude answering to a given distance run in an east or west direction. This sailing is particularly useful in making low, or small islands.

MIDDLE LATITUDE SAILING.

The earth being a sphere, the meridians meet at the poles; and since a rhumb line makes equal angles with every meridian, the line which a ship describes is, therefore, that kind of curve called a spiral. To resolve and reduce this is taught by middle latitude sailing,

MERCATOR'S SAILING.

The difference of longitude made upon an oblique rhumb cannot be exactly determined by using the middle latitude sailing. In mercator's sailing, the difference of longitude is very easily found, and the several problems of sailing resolved with the utmost accuracy, by the aid of a chart, or equivalent tables, in which the meridians are straight lines parallel to one another; and the degrees of latitude, which, at the equator, are equal to those of longitude,

increase with the distance of the parallel from the equator. The parts of the meridian, thus increased, are called meridianal parts.

CURRENT SAILING.

The preceding methods of navigation, are founded upon the assumption that the water has no motion. And these may answer tolerably well in those parts, where the ebbings and flowings are regular, as then the effect of the tide will be nearly counterbalanced. But in places where there is a constant current, or setting of the sea towards the same point, an allowance for the change of the ship's place, arising from its influence, must be made. The method of resolving those problems, in which, the effect of a current or heave of the sea is taken into consideration, is called, current sailing.

Oblique sailing is the application of oblique angled plane triangles to the solution of problems at sea. This branch of navigation is peculiarly useful in coasting, and in the surveying

of shores and harbours.

Windward sailing is, when a ship, is obliged by a contrary wind, to sail on different tacks in order to gain her intended port, and the object of this part of the science of navigation is to find the proper course, and distance to be run on each tack. For the accomplishment of this, there are several problems and operations.

QUESTIONS.

What is navigation? Among what nations of antiquity was navigation most cultivated? Among what modern nations has navigation been most cultivated? What is na