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 mariner's compass.

12. The mariner's compass consists of a circular card, whose circumference is divided into thirty-two equal parts called points; each point being subdivided into four parts, called quarter points.

To the under side of this card a

slender bar of mag

netized steel, called

a needle, is permanently attached.

The direction of the

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

placed that this line shall be parallel to the keel of the ship. Consequently, if b be placed towards the bow of the vessel, the point which it marks on the card will show the compass course, for the line NS is always on the magnetic meridian, and EW is east and west. The course is generally read to quarter points, and as a quadrant contains eight points, each point is equal to 90° ÷ 8 = 11° 15'; and a quarter point = 11° 15'÷ 4 = 2° 48′ 45′′. The table of Rhumbs, after the Traverse Table, shows the degrees in each course, to quarter points.

13. A ship's rate of sailing is determined by means of an instrument, called the log, and an attached line called the log line. The log is a piece of wood in the form of a sector of a circle, the rim of which is loaded with lead, so that when it is heaved into the sea it assumes a vertical position. The log line is so attached as to hold the log square against the water, that it may not be drawn along after the ship as the line unwinds from the reel, by the ship's forward motion.

The time in which the log line unwinds from the reel, is noted by a sand-glass, through which the sand passes in half a minute; that is, in the one hundred and twentieth part of an hour.

For convenience, the log line is divided into equal parts, marked by knots, and each part is equal to the one hundred and twentieth part of a nautical or geographical mile*.

Now, since half a minute is the one hundred and twentieth part of an hour, and each knot indicates the one hundred and twentieth part of a mile, it follows that the number of knots reeled off while the half minute glass runs out, will indicate the rate of the ship's sailing per hour.

* A geographical mile is one minute, or one-sixtieth of a degree, measured on the equator. Taking the diameter at 7916 English miles, the geographical mile will be about 6079 feet; that is, one-sixth greater than the English mile, which

SECTION II.

OF PLANE SAILING.

14. Let the diagram EPQ represent a portion of the earth's surface, P the pole, and EQ the equator. Let AB be any rhumb line, or track described by a ship in sailing from A to B.

B

d

Conceive the path of the ship to be divided into very small parts, and through the points of division draw meridians, and also the parallels of latitude b'b, c'c, d'd, e'e, and B'B: a series of triangles will thus be formed, but so small that each may be considered as a plane triangle.

In these triangles, the sum of the bases

Ab' + bc' + cd' + de' + ef = AB',

which is equal to the difference of latitude between the points A and B. Also,

b'b + cc + d'd + e'e+fB = BB',

which is equal to the distance that the ship has departed from the meridian AB'P, and is called the departure in sailing from A to B.

Therefore, the distance sailed, the dif ference of latitude made, and the departure, may be represented by the hypothenuse, the base and perpendicular of a rightangled triangle, of which the angle opposite the departure is the course.

When any of the four parts abovenamed are given, the other two can be determined. This method of determining

B'

the place of a ship reduces all the elements to the parts