system are accompanied by one or more such bodies, which revolve around their primary, as a secondary planet. The earth has one moon; Mars two; Jupiter five (the fifth is seldom seen); Saturn eight, and also meteoric rings; Uranus four, and Neptune one or

more.

"Comets are luminous bodies whose very eccentric paths lie around the sun.

“Fixed stars are distinguished from the planets inasmuch as their relative positions in the heavens remain the same from year to year. Unlike the planets, which shine by reflected light of the sun, the fixed stars shine by their own light the same as our sun, and are supposed to be the centers of other solar systems. The only fixed stars used in navigation are those of the first and second magnitude. The distances of a few of the fixed stars have been determined; of these distances, none are less than 200,000 times the distance of the earth from the sun. In other words, light travels at the rate of 186,000 miles a second, and it takes eight minutes for the light to come to the earth from the sun; to come from the nearest fixed star oc (centauri, a southern star) it would take three years.

The celestial bodies used for navigation purposes and from which data are derived from the Nautical Almanac and Sextant, are the Sun, Moon, Mars, Venus, Jupiter, Saturn and the fixed stars of first and second magnitude. In this book the sun only will be considered, but the student should understand that the stars are used in practically the same manner as the sun, and if he can use the sun he can also use the stars. There is a feeling current among seamen that there is something mysterious about stars, and that it requires a college education to successfully study them; this is not so. For stellar work in navigation, if one is to study by himself, Lecky's "Wrinkles in Practical Navigation is doubtless the best book.

Nautical Astronomy. To a person on the surface of the earth the heavens appear like a huge hollow sphere the center of which is the center of the earth. This idea of a large, hollow sphere is more apparent when one is at sea. Only one-half of this sphere is visible to a person on the earth's surface. If a plumb line were drawn through the person and extended far enough in both direc

tions, it would pass through the center of the earth and in the other direction to the surface of the supposed hollow sphere.

Now a surface or plane perpendicular to the plumb line and extending on all sides to meet the concave celestial surface, would divide the hollow sphere into two parts; this plane is called the Rational Horizon. In Fig. 15 let circle E represent the earth and the large circle H Z' H', etc., the above-mentioned hollow sphere, or celestial concave, as it is called; let P be the north and T the south pole; T P is then the axis of the earth. P' or T P prolonged

H

R

A

M

S

N

T

E

N
Fig. 15.

Q

H

until it cuts the celestial concave is the elevated pole, so called. Let Z be the position of an observer standing upon the surface of the earth; then, as already defined, H H' is the rational horizon, the circle Q'Q' at right angles to the axis T P P' is the equator on the earth, the celestial equator being QQ. Hereafter all circles mentioned will be on the celestial concave and not on the earth, although the corresponding circles on the earth, if one cares to consider them, are similar in every respect. For instance, the latitude of a point in the celestial concave is the same as the latitude of a point similarly situated upon the earth. Take point Z on the earth (Fig. 15), and Z' the similar point in the celestial concave, or zenith point; they both have the same latitude and longitude, because their location is given in degrees, etc., and there are just as many degrees in the arc Q Z' as there are in arc Q' Z. As QQ is the equator, the latitude of Z is the arc Q'Z or Q Z'expressed in degrees, minutes and seconds, as defined on page 5. The circle H Z'H' N is the observer's meridian. Let S be the position of the sun in the heavens at any given time; let P' S R M be another meridian passing through the sun's position and making the angle o with the observer's meridian; furthermore, let circle Z'S AN be a great circle, also passing through the sun's position

S and the zenith Z', making the angle a with the observer's meridian. Angle o is called the hour angle and the angle a the sun's azimuth. Angle o is generally expressed in hours, minutes and seconds, and is the apparent time of the observer at Z on the earth (see explanation of time, page 44). Reference to Fig. 16 in connection with Fig. 15 may make these definitions clearer.

N

Fig. 16 is a view of the celestial concave looking from Z, the observer's position on earth, up to the zenith directly overhead; the same letters are used and refer in both figures (Figs. 15 and 16) to the same points. R S is the sun's declination, or its distance north or south of the equator in degrees, etc. A S is the true altitude of the sun, or its distance above the rational horizon; QZ' is the latitude of Z or Z'; the longitude has already been de- H fined. S P' is the sun's polar distance, S Z' the sun's zenith distance and Z'P' the colatitude of the observer's position at Z. Z'N in Fig. 15

and Z' N', Fig. 16, is the

prime vertical or vertical circle

passing through the east or west points.

Fig. 16

P

H'

The student should learn and know what the following terms mean; their use will appear later. They are all essential in the work of navigation, declination, altitude, zenith distance, polar distance, celestial meridian, azimuth, hour angle, colatitude, etc.

Declination is the distance of the sun or any celestial body from the equator, given in the Nautical Almanac (see page 50), for every day in the year.

Altitude is the distance of any celestial body above the horizon, and is measured by a sextant.

Zenith distance is 90° minus the altitude.

Polar distance is 90° minus the declination.

Hour Angle. At three o'clock, for example (or to be more

correct, three hours apparent time), the sun's hour angle is three hours; that is, it takes three hours from the time the sun crosses the meridian (which it does at noon) until it reaches the position where its hour angle is three hours.

Colatitude is 90° minus the latitude.

Azimuth of a body is the angle at the zenith between the observer's meridian and the circle of altitude as per Fig. 15; when on the prime vertical the azimuth of a body is 90°. Amplitude is the arc of the horizon between the point where

the sun rises or sets and the east or west point; it is the complement of the azimuth.

The Sextant. This instrument, shown by Fig. 17, is used for measuring angles between two points by bringing the reflected image of one of the points to coincide with the other as seen directly. The frame of the sextant is usually made of brass or gun metal. C is the index glass, D the horizon glass, half of

which is silvered. A is the arc, and is divided into degrees, which are generally subdivided to ten minutes; the movable arm B carries at K a vernier by which still finer readings may be had; the verniers are generally divided so that the angle may be read to twenty seconds. G is a telescope which screws into a ring which holds it; N is an inverting telescope which is often used in place of G; H is an eyepiece without lenses, and also screws into the telescope ring; M is a colored eyepiece which goes with the telescope; E and F are colored screens, used when the sun is bright; O is a wooden handle by which the instrument is held.

The principle on which the sextant works is this: If a ray of light suffers two successive reflections in the same plane by two plane mirrors, the angle between the first and last direction of the ray is twice the angle of the mirrors. D is set parallel to C X, and mirror C turns with arm B. The angle between S C and S' G is twice the angle between the two mirrors D and C; then if the angle X'C X is 60°, the divisions on the scale A in the same length of arc X X' will be 120°. The use of the sextant is as follows: We wish to find the angle between two points S and S'.