ASTRONOMY, and OBLIQUITY.
In order to determine the relative situation of differ ent places upon the surface uf the earth, it is necessary to have some fixed or arbitrary points from which their distance is to be reckoned. The equator, or equi noctial line, which is equidistant from the two poles of the earth, has been naturally employed as one of the points of reference; the distance of any place from the equator, counted upon a meridian or hour circle passing throug,h the poles, being called its lo'itude. As there is no fixed point in the equator from which the distance of the place is to be reckoned in an opposite direction, astronomers have assumed the meridian, or hour circle, which passes through the capital of their country, as the beginning of their scale, and have called the dis tance of any place in degrees from that meridian its lon gitude; the meridian from which the reckoning is made being called the first meridian. Thus the English rec kon the longitude from the meridian of Greenwich, and the French from the meridian of Paris.
In determining the latitude of a place, let us suppose that C, PLATE XXXIX. Fig. 9. is the earth, A any place on its surface, HII its horizon, which will be at right angles to the radius AC, .tE.E the equator, NS the earth's axis pointing to the north pole P. Join CP, AP, and produce C/E to T. Then, since RCT is a right angled triangle, it is divided into two similar triangles by the perpendicular CA. (Playfair's Euclid, Book vi. Prop. 8.) And therefore the angle ARC is equal to the angle ACIE, the distance of the place from the equator, or its latitude. But ARC is equal to the vertical angle PRH ; and since, on account of the great distance of the fixed stars, the earth's semidiameter AC does not sub tend a sensible angle at P, the angle APC is insensi ble, and we shall have the angle PRH, which is equal to the latitude of the place A, equal to the angle PAH, or the height of the pole above the horizon of the place A. If, therefore, there was a star exactly in the pole P, the latitude of the place might always be found by taking its height above the horizon. As the star called the Pole star is not exactly in the pole, we may obtain the height of the pole by measuring the alti tude of any circumpolar star, when it is on the meridian above and below the pole ; for in this case half the sum of the two altitudes, properly corrected by refraction, will be the latitude of the place. Thus, if MAH be the altitude of the circumpolar star when below the pole, and NAH its altitude when on the meridian above the pole, then PAH, the real latitude of the place, is evident ly an arithmetical mean between these two altitudes.
As the pole is 90° distant from the equator, and as the distance of the pole from the horizon is equal to the lati tude of the place, the distance of the equator from the horizon must obviously be equal to the colatitude of the place, or the latitude of the place subtracted from 90° ; for these three distances make up two right angles. By determining, therefore, the height of the equator above the horizon, and subtracting this height from 90°, we shall obtain the latitude of the place. The height of the equator may be obtained, by taking the meridian altitude of the sun at any time, and subtracting from it the sun's declination, if the sun is north of the equator, or adding the sun's declination if the sun is south of the equator. The difference of these numbers, or their sum, will be the height of the equator, or the colatitude of the place. The same result may be obtained, by em ploying the meridian altitude of any of the planets or fixed stars whose declinations are known, allowance be ing made for the effects of refraction and parallax.
When the sun comes to the meridian of any place, it is noon or 12 o'clock at that place ; and therefore, since the equator is divided into 360', and since the earth turns round in 24 hours, 15° of the equator will correspond to 1 hour of time ; and when it is noon at any one place, it will be 1 o'clock at all places 15° eastward of it, and 11 o'clock at all places 15° west of it. If any celestial phenomenon, therefore, should occur, such as an eclipse of the moon, an eclipse of Jupiter's satellites, &c. which is not affected by the distance of the place from the equator, the difference of the longitude of all the places at which it is observed will be discovered. 11' the moon enters into the earth's shadow at 6 o'clock in the evening at London, and at hall past 6 o'clock at another place, then this place is evidently half an hour to the cast of London, or q degrees, 15 degrees of longitude being equal to one hour of time. The longitude may also be found by means of a chronometer or time-piece, ad justed to the time at any given meridian. Wherever this chronometer is taken, it will show the time of the place where it was adjusted, and the difference between the time thus shown, and the time deduced from a celestial observation, or a well regulated time piece, at any other place, will be the difference of their longitude in time. An account of the chronometers which are used for this purpose, will be found under the article CHRONO METER ; and the various methods of finding the longi tude both at land and at sea, will be given under the word LONGITUDE.