PRINCIPLES AND PROBLEMS PREPARATORY TO THE APPLICATION OF THE INSTRUMENTS TO PRACTICAL By practical astronomy, is understood the knowledge of observing the celestial bodies, with respect to their position and time of the year, and of deducing from these observations certain conclusions, useful in calculating the time when any proposed proposition of these bodies shall happen. OF THE TERRESTRIAL LATITUDE. "I he latitude of any place is equal to the elevation of the pole of the equator above that place. The distance between the zenith and the horizon, and that between the pole, is equal, for each of them are 90 degrees. If, therefore, we take zenith from the pole, away the distance of the which is common to both, the remainder, that is, the elevation of the pole; or latitude of the place, is equal to the distance from the zenith to the equator. The distance from the.zenith to the pole is equal to the complement of the latitude to 90 degrees. The inclination of the equator to the horizon, is also equal to the complement of the latitude to 90 degrees.* *In plate 3, fig. 5, P represents the pole, EQ the equator, HO the horizon, PH the elevation of the pole, Z the zenith, HZO, or the visible part of the heavens, contains twice 90, or 180 degrees; All those stars that are not further from the pole than the latitude, are called circumpolar stars. If the greatest and less altitudes of a circumpolar star be determined by observation, half the sum gives you the latitude of the place. The complement of the meridian altitude of a star is its zenith distance; and this is called north or south, according as the star is north or south at the time of observation. In The latitude of a place is equal to a star's meridian zenith distance added to the declination, if the star passes between the zenith and the equator. all other cases, the latitude is the difference between the meridian zenith distance and the declination of the star. The greatest declination of the sun, is equal to the inclination of the ecliptic to the equator. it being 90 degrees from Z to H, and 90 degrees from Z to 0: but it is also 90 from the pole P to E the equator. If you take away PE, there remains 90 degrees for the other two arcs. In other words, the elevation of the pole and the clevation of the equator are together equal to 90 degrees; i. e. in technical terms, the elevation of the pole is the complement of the elevation of the equator to 90 degrees. Hence one being known and subtracted from 90, gives the other. Hence also it is clear, that the elevation of the equator is equal to the distance of the pole from the zenith, both being equal to the distance of the pole from 90 degrees. Hence also the distance of the equator from the zenith is equal to the elevation of the pole, or latitude of the place; for HZ is equal to 90, and PE is equal to 90; take away PZ, common to both, and the remainders, PH, ZE must be equal. The inclination of the equator to the ecliptic is equal to half the difference between the sun's meridian altitudes on the longest and shortest days. The latitude of the place and the zenith distance of a star being given, to find the declination of the star. 1. When the latitude of the place and zenith distance are of different kinds, that is, one north and the other south, their difference is the declination ; but it is of the same name with the latitude, when that is the greater of the two; otherwise it is of the contrary kind. 2. When the latitude and zenith distance are of the same kind, that is, both north or both south, their sum is the declination, and it is of the same kind with the latitude. OF CELESTIAL LONGITUDE, LATITUDE, &c. It has been already observed, that in order to measure and estimate the motion of the sun and stars, it was necessary to fix on some point in the heavens, to which their motions might be referred. The vernal equinoctial point is that point from which astronomers reckon what is called longitude in the celestial sphere. The ecliptic is divided into twelve signs, of 30 degrees each, with whose names and characters you are acquainted. Astronomers begin at the first point of Aries, and reckon from west to east. Celestial longitude is, therefore, the number of degrees on the ecliptic contained between the first point of Aries and any celestial object, or between the first point of Aries and a circle passing through the object perpendicular to the ecliptic. Thus if y C, plate 15, fig. 8, represents the ecliptic, and r the first point of Aries, and any star be at S on the ecliptic, or at s on a circle psS, perpendicular to the ecliptic, then will the arch YS be the longitude of the stars s, S. The latitude of a celestial object is its distance from the ecliptic, reckoned on a circle perpendicular thereto. Thus a star at s, plate 15, fig. 8, will have for latitude the arc Ss; but placed at S on the ecliptic, it will have no latitude. As the diurnal motion is in the direction of the equator, astronomers, to facilitate both observation and calculation, found it necessary to determine the situation of celestial bodies with respect to this circle, which is effected by determining their right ascension and declination. Right ascension and declination are, with respect to the equator, what longitude and latitude are, with respect to the ecliptic. Thus if represent the equator, and the first Y point of Aries, then will Y E be the right ascension of a star situated at E on the equator, or at e in a circle e perpendicular thereto; the star at E will have no declination, but that at e is measured by the arch eE. Y G G GENERAL OBSERVATIONS. To fix your attention with greater certainty to the objects of research, it may be proper to observe, that as practical astronomy consists in determining the position of celestial objects for a given instant, it may be reduced to three things: 1. The knowledge of the obliquity of the ecliptic. 2. The measure of time. 3. The right ascensions and declinations of the stars, &c. OF THE OBLIQUITY OF THE ECLIPTIC. The obliquity of the ecliptic is a very important element of astronomy, because it enters into the calculation of all spheric triangles where the ecliptic and equator are concerned. The obliquity of the ecliptic being equal to the sun's greatest declination, i.e. when in the tropics, the obliquity may be ascertained by observing the meridian height of the sun's centre on one of the solstitial days; and this quantity taken from the height of the equator, at the place of observation, gives the declination of the tropic. Or, more accurately, observe the sun's meridian altitude in each tropic: this will give their distance, half of which is the distance of each tropic from the equator, |