soundings with great accuracy. Soundings may thus be made along any number of known lines, and a comparison of the depths found on different lines, at or near their points of intersection, will show with what degree of accuracy the work has been done.

Sounding-lines should be made of strong cord, and divided into feet or fathoms, by different colored rags or other marks. The lead is shaped like the frustum of a cone, with the base B, hollowed out, to hold some grease. The land or mud of the bottom adheres to the grease, and thus shows the nature of the bottom, which should be entered in the field-book, and laid down upon the map. As the cord is liable to change its length, it should be compared from time to time with some standard. In tide-waters, the exact time of each sounding is to be noticed, and an assistant should note the height of the tide at regular intervals, upon a tide-guage. The tide-guage is permanently placed at some convenient point of the harbor, and its 0 point is referred by means of a spirit-level, to some fixed bench-mark, on a level with mean low-water mark, to which all the soundings must be reduced.

B

49. Having plotted the work done with the theodolite, as also the outline of the harbor traced with the compass, it remains to delineate the bottom of the harbor; and this is done by means of horizontal curves, which have already been used to represent broken or undulating ground.

Let the plane of reference be taken through low-water mark, or to coincide with the surface of the water at low tide. The accuracy with which the bottom of the harbor is to be delineated, will guide us in fixing the distance between the horizontal planes of section.

The first horizontal plane should be passed at a distance below the shallowest point that has been sounded, equal to the number of feet fixed upon for the distance.

intersects the bottom of the harbor determined as in Book III. Sec. II. And similarly, for the other horizontal planes of section.

Having thus delineated the bottom of the harbor, and noted on the map the distance of each intersecting plane below the plane of reference, let such lines be drawn as will indicate the channels, shoals, sunken rocks, and direc tion of the current.

In the example given in plate. 6, soundings have been made in three directions from the sand-bar in the harbor, and also from the rocky shore across to the light-house.

BOOK V.

OF NAVIGATION.

SECTION I.

DEFINITIONS.

1. WE have given, in the preceding parts of this work, various applications of Plane Trigonometry. We propose, in this Book to explain the best methods of determining the place of a ship at sea. This application of Trigonometry constitutes the science and art of Navigation.

2. There are two methods of determining the place of a ship at sea.

1st. When a ship departs on her voyage, if we note her courses and the distance sailed, we may, at any time, by means of Plane Trigonometry, determine her place, very nearly. ·

2d. By means of observations on the heavenly bodies, and the aid of Spherical Trigonometry, we may determine with great accuracy, the place of the ship. This method is called Nautical Astronomy.

The first part of Navigation, viz., the cases which can be solved without the aid of observations on the heavenly bodies, will be alone treated of.

3. The earth is nearly spherical. For the purposes of Navigation it may be considered as perfectly so. It revolves round one of its diameters, called the axis, in about twenty-four hours.

4. The great circle, whose poles are the extremities of

are called the poles of the earth-one is called the north pole, and the other the south pole.

5. The circumference of every great circle which passes through the poles, cuts the equator at right angles, and is a meridian circle. Every place on the surface of the earth has its own meridian; but for the purposes of Geography and Navigation, all the meridians are reckoned from a particular meridian, which is called the first meridian. The English have fixed on the meridian of the Greenwich Observatory, for the first meridian.

6. The longitude of any place is the arc of the equator, intercepted between the meridian of that place and the first meridian, and is east or west, according as the place lies east or west of the first meridian.

7. The difference of longitude of two places is the arc of the equator included between their meridians; this arc is equal to the difference of longitudes when they are of the same name, and to the sum of the longitudes, when they are of different names.

8. The latitude of a place is its distance from the equator, measured on the meridian of the place, and is north or south according as the place lies north or south of the equator.

9. The small circles drawn parallel to the equator, are called parallels of latitude. The arc of any meridian intercepted between the parallels passing through any two places, measures the difference of latitude of those places; this difference is found by subtracting the less latitude from the greater, when the latitudes are of the same name, and by adding them when they are of different names.

10. The sensible horizon of any place is an imaginary plane, supposed to touch the earth at that place, and to be extended indefinitely.

A plane passing through the centre of the earth, and parallel to the sensible horizon, is called the rational horizon.

The north and south line, is the intersection of the plane of the meridian circle with the sensible horizon, and the line which is drawn perpendicular to this, is called the

11. The course of a ship, at any point, is the angle which her track or keel makes with the meridian. So long as the course is unchanged, the ship would sail in a straight line, if the meridians were truly parallel; but as the meridians bend constantly toward the pole, the direction of her path is continually changing, and she moves in a curve called the rhumb line. The course of a ship is indicated by the mari ner's compass.

needle corresponds to the diameter NS. The diameter EW, at right angles to NS, is intended to indicate the east and west points. The points of the compass are thus read: beginning at the north point, and going east, we say, north and by east, north north east, north east and by north, north east; and so on, round the compass, as indicated by the letters.

The card being permitted to turn freely on the pin, on which it is poised, as a centre, the line NS will always indicate the true magnetic meridian, but this, as we have seen in (Bk. II., Sec. 7-14), is not the true meridian, and hence, the variation must always be allowed for.

On the interior of the compass box, in which the card swings, are two marks a and b, which lie in a line passing