CALIFORNIA

CHAPTER I.

DEFINITIONS RELATING TO NAVIGATION.

1. That science, generally termed Navigation, which affords the knowledge necessary to conduct a ship from point to point upon the earth, enabling the mariner to determine, with a sufficient degree of accuracy, the position of his vessel at any time, is properly divided into two branches: Navigation and Nautical Astronomy.

2. Navigation, in its limited sense, is that branch which treats of the determination of the position of the ship by reference to the earth, or to objects thereon. It comprises (a) Piloting, in which the position is ascertained from visible objects upon the earth, or from soundings of the depth of the sea, and (b) Dead Reckoning, in which the position at any moment is deduced from the direction and amount of a vessel's progress from a known point of departure.

3. Nautical Astronomy is that branch of the science which treats of the determination of the vessel's place by the aid of celestial objects-the sun, moon, planets,

or stars.

4. Navigation and Nautical Astronomy have been respectively termed GeoNavigation and Celo-Navigation, to indicate the processes upon which they depend. 5. As the method of piloting can not be employed excepting near land or in moderate depths of water, the navigator at sea must fix his position either by dead reckoning or by observation of celestial objects; the latter method is more exact, but as it is not always available, the former must often be depended upon.

6. THE EARTH.-The Earth is an oblate spheroid, being a nearly spherical body slightly flattened at the poles; its longer or equatorial axis measures about 7,927 statute miles, and its E shorter axis, around which it rotates, about 7,900 statute miles.

The Earth (assumed for purposes of illustration to be a sphere) is represented in figure 1. The Axis of Rotation, usually spoken of simply as the Axis, is PP'.

The Poles are the points, P and P', in which the axis intersects the surface, and are designated, respectively, as the North Pole and the South Pole.

N

P

G.

N

P'

מן

T'

T

n

Η Σ

W

M

M'

FIG. 1.

The Equator is the great circle EQMW, formed by the intersection with the earth's surface of a plane perpendicular to the axis; the equator is equidistant from the poles, every point upon it being 90° from each pole.

Meridians are the great circles PQP', PMP', PM'P', formed by the intersection with the earth's surface of planes secondary to the equator (that is, passing through its poles and therefore perpendicular to its plane).

Parallels of Latitude are small circles NTn, N'n'T', formed by the intersection with the earth's surface of planes passed parallel to the equator.

The Latitude of a place on the surface of the earth is the arc of the meridian intercepted between the equator and that place. Latitude is reckoned North and South, from the equator as an origin, through 90° to the poles; thus, the latitude of the point T is MT, north, and of the point T', M'T', north. The Difference of Latitude between any two places is the arc of a meridian intercepted between their parallels of latitude, and is called North or South, according to direction; thus, the difference of latitude between T and T' is Tn' or T'n, north from T or south from T'.

The Longitude of a place on the surface of the earth is the arc of the equator intercepted between its meridian and that of some place from which the longitude is

reckoned. Longitude is measured East or West through 180° from the meridian of a designated place, such meridian being termed the Prime Meridian; the prime meridian used by most nations, including the United States, is that of Greenwich, England. If, in the figure, the prime meridian be PGQP', then the longitude of the point T is QM, east, and of T', QM', east. The Difference of Longitude between any two places is the arc of the equator intercepted between their meridians, and is called East or West, according to direction; thus, the difference of longitude between T and T' is MM', east from M or west from M'. The Departure is the linear distance, measured on a parallel of latitude, between two meridians; unlike the various quantities previously defined, departure is reckoned in miles; the departure between two meridians varies with the parallel of latitude upon which it is measured; thus, the departure between the meridians of T and T' is the number of miles corresponding to the distance Tn in the latitude of T, or to n'T' in the latitude of T'.

The curved line which joins any two places on the earth's surface, cutting all the meridians at the same angle, is called the Rhumb Line, Loxodromic Curve, or Equiangular Spiral. In the figure this line is represented by TrT'. The constant angle which this line makes with the meridians is called the Course; and the length of the line between any two places is called the Distance between those places.

The mile employed by navigators is the Nautical or Sea Mile. This unit is defined in the United States of America as being 6,080.27 feet in length and equal to one-sixtieth part of a degree of a great circle of a sphere whose surface is equal in area to the area of the surface of the earth.

The nautical mile is not exactly the same in all countries, but, from the navigator's standpoint, the various lengths adopted do not differ materially.

Since latitude has been capable of easier and more accurate determination than longitude, it might naturally be expected that there exists an intimate relation between the nautical mile and the minute of latitude (or the length of that portion of a meridian which, if the earth were a perfect sphere, would subtend the angle of 1' at the center); but because the earth is not a perfect sphere, the length of that portion of a meridian that subtends an angle of 1' at the center of the earth varies slightly in length from the Equator to the poles, and consequently the relation between the nautical mile and the minute of latitude is not exactly invariable. The average length of one minute of curvature of the meridian is 1,852.201 meters, or 6,076.82 feet; and, accordingly, in France, Germany, and Austria, the nautical mile is taken to be 1,852 meters.

For purposes of navigation the nautical mile is assumed to be equal to a minute of latitude in all parts of the world; and, hence, when a vessel changes her position to the north or south by 1 nautical mile, it may always be considered that the latitude has changed 1'. Owing to the fact that the meridians converge toward the poles, the difference of longitude produced by a change of position of 1 mile to the east or west will vary with the latitude; thus, a departure of 1 mile will equal a difference of longitude of 1' at the Equator, but of more than 1' at any higher latitude, being in fact equal to 1'.1 of longitude in latitude 30° and to 2' of longitude in latitude 60°.

In England the nautical mile, corresponding to the Admiralty knot, is regarded as having a length of 6,080 feet.

The statute mile of 5,280 feet, which is employed in land measurements, is commonly used in navigating river and lake vessels. This is notably the case on the Great Lakes of America, but with the recognition of the advantages to be gained by the practice of nautical astronomy in the navigation of these vessels, the use of the nautical mile is extending.

The Great Circle Track or Course between any two places is the route between those places along the circumference of the great circle which joins them. In the figure this line is represented by TT'. From the properties of a great circle (which is a circle upon the earth's surface formed by the intersection of a plane passed through its center) the distance between two points measured on a great circle track is shorter than the distance upon any other line which joins them. Except when the two points are on the same meridian or when both lie upon the equator, the great circle track will always differ from the rhumb line, and the great circle track will intersect