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object b is the angle contained between the direction a b and the meridian x y.

30. Cross-bearings is a term applied to bearings taken of two objects from the same place. Thus, the bearings of a and b, Fig. 6, taken by an observer at o, are cross-bearings. The lines of direction of these bearings will naturally intersect or cross each other at the place of the observer.

31. Sea horizon is that apparent boundary of the visible heavens. It may also

FIG. 6 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. 7, if the large circle abc

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, south, east, and west; north and south, east and west being diametrically opposite each other, as indicated by

the figure. The length Fig. 7

of the radius of this circle, or the sea horizon's distance from the observer, is varied, depending entirely on the height of the observer's eye above the surface of the sea,

32. The following will give the student an idea of the sea horizon's distance, expressed in nautical miles, corresponding to certain heights of the eye:

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Thus, an object seen on the sea horizon on a clear day, the height of the eye being for instance 20 feet, is about 5 miles away.

33. The tropics are the latitude parallels corresponding to latitude 23° 27.5' north or south. The tropic of Cancer

cd', Fig. 8, is in north latitude and the tropic of Capricorn rol in south latitude. The zone

bounded by the tropics is I called the torrid zone.

34. The Arctic and Antarctic circles are the latitude parallels corresponding to latitude 66° 32' north and south, respectively. The zones

enclosed by these circles FIG, 8

a Pa' and n P' n' are called the frigid zones, or Arctic and Antarctic regions.

The portions of the earth included between the torrid and the frigid zones are termed the temperate zones, distinguished respectively as the north and south temperate zones.

35. Determination of a Position on the Earth's Surface.-From the foregoing explanations and definitions the student will readily realize 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 finds his latitude he knows how far north or south he is from the equator; and by obtaining his longitude, he knows the distance of his ship east or west from the first meridian. Then, by consulting his chart he is at once able to mark upon it the exact position of his vessel.

We will now proceed to describe the instruments used at sea by means of which these important functions—latitude and longitude-are determined in that branch of the science defined as navigation by dead reckoning.

THE COMPASS

ERRORS AND ADJUSTMENTS 36. Brief History of the Compass.-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 navigate a vessel. The mariner's compass 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 increasing utility to mankind. To whom we are indebted for the discovery of the magnetic needle and its directing power, or for its application as an aid to travelers on land and water, we do not know. It is generally believed, however, that the compass was known in China about 2,630 years before the Christian era. The first record of its use 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 that they showed the Chinese how to use it in navigation.

Doctor Gilbert, of Colchester, England, in his “De Magnet," published in 1600, stated that the compass was brought to Italy from China by Marco Polo, in the year 1295, or thereabouts. But there is evidence of its having been used in France about the year 1150, in Syria during the same period, and in Scandinavia previous to 1266. The Norwegian historian, Asa Frode, in an account of the discovery of Iceland, says that in the year 868, when Folke Wilgerdson, a renowned viking, was about to set sail on a voyage of discovery, he took with him three ravens to serve as guides, because in those times seamen had no leiderstein in the northern countries. In Icelandic, leid means “leader,” and stein, stone ''; consequently, leiderstein signifies “leading stone,” or “guiding stone."

In all probability, this account was written about the end of the 11th century, Asa Frode being born in 1060. There is strong evidence, therefore, that the mariner's compass became known in Northern Europe between the years 868 and 1100. It did not become generally known throughout Europe, however, until during the 13th century.

In ancient treatises on navigation, the east point is treated as the principal compass point. At present the Chinese use the south, and all other nations the north point as the principal point on the compass card.

37. 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 AC

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, FIG. 9

may be brief. It consists of one or several magnetic needles attached to the underside of a circular card of some semitransparent substance, such

RRHURATONTA

as mica. This card a b, Fig. 9, being suspended on a conical brass socket c, called the cap, with a hard stone, usually ruby or agate, in its center, is delicately balanced on a central pivot p, around which it is free to move in a horizontal plane. It is usually enclosed in a small metallic box or bowl that is so hung, in gimbals, as to preserve its horizontal position, notwithstanding the rolling or pitching of the ship. This

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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.

38. Divisions of the Compass Card.—The compass card is divided at its circumference into 360°, and also into 32 divisions of 11° 15' each, called points, the latter being

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