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will intersect all meridians at the same angle. Thus, in Fig. 5 (a), if the ship sails from a to b, the line ab, representing her course, or track, will intersect all meridians at the same angle; in other words, the angles Pab, Pa' b, Pa' b, etc. are all equal. Since the meridians all converge toward the pole, it is evident that this line, called the rhumb line, in its continuity is an unending spiral (see Fig. 5 (6)] always approaching the pole but never actually reaching it. The reason for this is that the pole, bearing due north, cannot be reached on any other course than due north.
29. Thė distance between two places, or the distance run by the ship on any course, is the length of the rhumb line joining the two places, expressed in nautical or statute miles. It is sometimes termed the “ nautical distance” to distinguish it from the “shortest distance” on a greatcircle track.
30. The departure is the distance made good by the ship due east or due west, or the distance between any two places measured on one of their parallels. The departure is usually expressed in miles.
In order to more fully explain the foregoing terms the student is referred to Fig. 6. There, if a ship sails from a to b, the line a, b is the distance, and if the lines x y and z v represent meridians running north and south, ac is the difference of latitude, the angle at a the course, and the distance cb the departure.
31. The bearing of an object or place is the angle that the direction of the object or place makes with the meridian, and is the same as the course toward it. Thus, in Fig. 6, if an observer is standing at a, the bearing of the object b is
the angle y ab contained between the direction a b and the meridian x y.
32. Cross-bearings is a term applied to bearings taken of two objects from the same place. Thus, the bearings of
a and b, Fig. 7, taken by an observer at 0, are crossbearings. The lines of direction of these bearings will naturally intersect, or cross, each other at the place of the observer.
33. The sea horizon is the apparent boundary of the visible heavens. It may also be defined as a small circle drawn on the surface
of the earth, the center of which is the observer's eye. Thus, in Fig. 8, if the large circle a bc represents the earth and an observer is stationed at 0, the small circle NESW is the visible, or sea, horizon. Its principal points, called the “horizon points,” are four, viz., north, east, south, and west; north and south, east and west being diametrically opposite each other, as indicated in the figure. The length of the radius of this circle, or, in other words the sea horizon's distance from the observer, is varied, depending on the height of the observer's eye above the surface of the sea.
The following table will give the student an idea of the sea horizon's distance expressed in both nautical and statute miles:
Thus, an object seen on the horizon on a clear day, the height of the eye being, for instance, 20 feet, is 5.13 nautical, or 5.91 statute, miles away.
34. Determination of a Position on the Earth's Surface. – From the foregoing explanations and definitions, the student will readily understand that any point, or place, on the surface of the earth is determined when its latitude and longitude are known. Hence, the principal object of navigation is the determination of these quantities. When the navigator, by one method or another (hereafter to be described), finds his latitude, he knows how many degrees, minutes, etc. he is north or south of the equator, and by obtaining his longitude he knows how many degrees, minutes, etc. he is east or west of the first, or Greenwich, meridian. Then, by consulting his chart, he will at once be able to mark upon it the exact position of his vessel.
Before explaining the methods used in determining the position of a ship at sea, we will describe the principal instruments used by a navigator, and by means of which courses, distances, and the depth of water are measured and recorded. In doing so, particular attention will be paid to the compass, its errors and adjustment-a subject of great importance to all navigators.
ERRORS AND ADJUSTMENTS
35. Among the several instruments used by a navigator, the compass is unquestionably the most important, as without its aid it would be nearly impossible to conduct the navigation of a vessel. This instrument is undoubtedly one of the greatest and most useful inventions ever made, not only because of its definiteness as a discovery, but because of its continual and unceasing utility to mankind.
To whom we are indebted for the discovery of the magnetic needle and its directing power, or for its practical application as an aid to travelers on both land and water, we do not know. It is, however, generally believed that the compass was known in China about 2,630 years before the Christian era. The first record of its employment on land was in the year 2634 B. C. The Chinese first used it for maritime purposes about 300 A. D., although the Japanese claim to have shown them how to apply it for navigational purposes. There is evidence that the mariner's compass was known in northern Europe between the years 868 and 1100 A. D. It did not become generally known throughout Europe, however, until during the 13th century.
In ancient treatises on navigation, the cast point is treated as the principal compass point. At present, the Chinese use the south, and all other nations the north, as the principal point on the compass card.
36. General Description of the Compass. – The general principle of the compass may be expressed as follows: A bar of magnetized steel, apart from disturbing forces, having a free horizontal motion on a pivot, points in a definite direction, or to that point known as the magnetic pole.
Nowadays, the compass in one form or another is familiar to all; its description, therefore, may be quite brief. consists of one or several magnetic needles attached to the
under side of a circular card of some semitransparent substance, such as mica. This card a b, Fig. 9, being suspended on a conical brass socket c, called the cap, with a hard stone, such as ruby or agate in its center, is delicately balanced on a central pivot Þ, around which it is free to move in a
PL horizontal plane. It is usually enclosed in small metallic box, or bowl, that is so hung in gimbals as to preserve its horizontal position, notwithstanding the rolling and pitching of the ship. This bowl is again placed in the top of a strong case of wood or bronze, called the binnacle, which is firmly secured to the deck of the ship.
37. Divisions of the Compass Card. – The card to which the magnetic needle, or needles, is secured is called the compass card; it is divided at its circumference into 360° and also into 32 divisions of 11° 15' each, called points, the latter being subdivided into half points and quarter points, as shown in Fig. 10. The four principal points are named after the principal horizon points-north, east, south, and westand are usually termed the cardinal points, while the points midway between the cardinals are called the intercardinal, or quadrantal, points. Every point has a name, and these the student should learn, so as to be able to repeat them in regular order from north around by way of east and back to north, and vice versa. This procedure, generally known as “boxing the compass,” will, with the aid of Fig. 10, be comparatively easy.
38. Commencing from the north point at the top of the card and going around to the right, or in the direction in which the hands of a watch move, the names of the points are as follows: North, north-by-cast, north-northeast, northeast-by-north, northeast, northeast-by-east, east-northeast, east-bynorth. East, east-by-south, east-southeast, southeast-by-east,