PART V. APPLICATION OF SPHERICAL TRIGONOMETRY TO NAUTICAL ASTRONOMY. 103. NAVIGATION, as we have seen, is the determination of the place of a ship at sea, that is to say her latitude and longitude, by the dead reckoning." The dead reckoning proceeds upon the hypothesis that the ship's course and the distance she sails are accurately known; and if this were really the case, her true place might be found by the methods given in Part III. But this is impossible. 1. From the difficulty of steering exactly upon the intended course. 2. From the uncertainty of lee-way. 3. From errors of the log, occasioned by the heaving of the sea, unknown currents, and the rudeness of the instrument itself. The "dead reckoning" is, however, indispensable in determining the ship's place during cloudy weather, and is useful at all times for detecting the existence and velocity of currents. The main reliance must be upon astronomical observations, and the method of determining a ship's place by means of these constitutes the science of nautical astronomy, DEFINITIONS. 104. For the purpose of measuring the angular distances of the heavenly bodies from each other, and from the horizon, it is convenient to suppose them all situated as they really appear to an observer on the earth, viz., in a spherical concave surrounding the earth, and concentric with it. This imaginary concave, which the student may suppose identical with the blue vault of the sky, is called the celestial sphere. The position of a point on the celestial sphere, like the position of a point on the terrestrial sphere, is fixed by its latitude and longitude. On the celestial sphere the circle of longitude is the ecliptic; and secondaries passing, therefore, through the poles of the ecliptic, are the circles of celestial latitude; the point from which longitude is measured is the vernal equinoctial point. Commencing at this point, the ecliptic is divided into twelve parts called signs; a sign is, therefore, 30°. The twelve signs are named, and symbolically expressed, as follows: 4. Cancer. 7. Libra. 1. r Aries. 10. vs Capricornus. Aquarius. 11. 8. m Scorpio. The vernal equinoctial point is called the first point of Aries. The longitude is measured from this point in one direction, viz., in the order of the signs, or from w. to E. Parallels of latitude on the terrestrial sphere correspond to parallels of declination on the celestial. Of these, the two which touch the ecliptic in the first points of Cancer and Capricorn, are called the tropics of Cancer and of Capricorn. These first points of Cancer and Capricorn* are respectively called the summer and winter solstice; because for a day or two before and after the sun enters them he appears to be stationary, and the days to be of equal length, so slowly does his declination at those times change, for his motion is obviously very nearly parallel to the equator. The declination circle, through the solstitial points, is called the solstitial colure, and that through the equinoctial points the equinoctial colure. Secondaries to the equator, we have said (Art. 79), are called declination or hour circles. The declination of a heavenly body is its distance from the equator in degrees, minutes, and seconds, measured on the declination or hour circle. which passes through the body. The right ascension of a heavenly body is the number of degrees and fractions of a degree measured on the equator, between the vernal equinox or first of Aries, and the circle of declination which passes through the body. Another definition of right ascension is the angle at the pole of the equator or of the earth, comprehended between the hour or declination circle through the vernal equinox, and the hour circle through the heavenly body. Right ascension is now commonly expressed in hours, minutes, and * At the first of these points the sun, which up to the time of its arrival there had been moving north, begins to move backwards towards the south; at the second from going south he begins to climb upwards towards the north, whence it appears that the points in question are named in allusion to the habits of the animals after which they are called. |