6 Conjunction when planets are in the same point of the ecliptic. * Sextile when 2 Signs dist. ▲ Trine when 4 Signs dist. Quartile when 3 Signs dist. 8 Opposition when 6 Signs dist. The conjunction and opposition are called the syzygies, and the quartile aspects the quadratures; these terms are applied chiefly to the moon. (H) The horizon is a great circle which separates the visible half of the heavens from the invisible. This horizon is distinguished by the sensible and rational horizon, when applied to the earth. The sensible horizon is the boundary of the spectator's view at sea or land; and a plane parallel to this circle, passing through the earth's centre, is called the rational horizon. (I) The cardinal points are the east, west, north and south, points of the horizon. The mariner's compass, which is divided into 32 points, each 11°.15', (F. 74.) is a representation of the horizon. (K) The Zenith is a point in the celestial sphere directly over the head of the spectator, being the elevated pole of the horizon. (L) The Nadir is a point in the celestial sphere directly under the feet of the spectator, and is diametrically opposite to the zenith; being the depressed pole of the horizon. (M) Azimuth, or vertical circles, are great circles passing through the zenith and nadir. They cut the horizon at right angles. The altitudes of the heavenly bodies are measured on these circles. (N) The prime vertical is that azimuth circle which passes through the east and west points in the horizon. (0) Meridians are great circles passing through the poles of the world, and cutting the equinoctial at right angles. They are also called hour circles; and upon the terrestrial sphere, circles of longitude. (P) Circles of celestial longitude are great circles passing through the poles of the ecliptic, and cutting it at right angles. (Q) The latitude of any object in the heavens, is an arc of a circle of longitude contained between the centre of that object and the ecliptic. (R) The latitude of any place on the earth, is the elevation of the pole above the horizon, and the complement of the latitude, is the distance of the pole from the zenith. Or the latitude is the distance of the zenith of the place from the equinoctial, on the celestial sphere. (S) The declination of any celestial object, is an arc of a meridian contained between the centre of that object and the equinoctial. (T) Parallels of declination are small circles parallel to the equinoctial. (U) The altitude of any object in the heavens, is an arc of an azimuth or vertical circle, contained between the centre of the object and the horizon. (W) Parallels of altitude are small circles parallel to the horizon. (X) Parallels of celestial latitude are small circles parallel to the ecliptic. (Y) The tropics are small circles parallel to the equinoctial, at 23°.28' from it, and touch the ecliptic in the points of cancer and capricorn; they are the limits of the sun's progress to the north and south of the equinoctial. (Z) The zenith distance of any celestial object is the arc of a vertical circle, contained between the centre of that object and the zenith, being the complement of the altitude. (A) The polar distance of any object in the heavens, is an arc of a meridian contained between the centre of that object and the pole of the equinoctial. (B) The amplitude of any celestial object is an arc of the horizon, contained between the centre of the object when rising or setting, and the east or west point of the horizon. (C) The azimuth of any object in the heavens, is an arc of the horizon, contained between an azimuth or vertical circle, (passing through the object,) and the north or south point of the horizon. (D) The right ascension of an object, is the distance between the point aries and a meridian passing through the object, reckoned on the equinoctial. It is so called, because, in a right sphere, this meridian will coincide with the horizon when the object is rising. Or, we may define it to be the angle at the pole, formed between a meridian passing through aries, and a meridian passing through the object. (E) The oblique ascension of an object, is the distance of the equinoctial point aries from the horizon when the object is rising. Or, it is that degree of the equinoctial which rises with the object in an oblique sphere. (F) The oblique descension is the distance of the point aries from the horizon when the object is setting. Or, it is that degree of the equinoctial which sets with the object in an oblique sphere. (G) The ascensional, or descensional difference, is the dif ference between the right and oblique ascension or descension, and with respect to the sun, it is the time he rises before six, when his declination is of the same name as the latitude, or sets before six, when the declination and latitude have contrary names. (H) The equinoctial colure is a great circle passing through the pole and the equinoctial points aries and libra. (I) The solstitial colure is a great circle passing through the pole and the points and v; called solstitial points, because when the sun is near these points he seems to have nearly the same altitude at noon, for several days, and therefore apparently stops or stands still. (K) The arctic circle is a parallel of declination at the distance of 23°.28' from the north pole, or 66°.32′ from the equinoctial. It is generally called the north polar circle. (L) The antarctic circle, called likewise the south polar circle, is the same distance from the south pole as the arctic circle is from the north pole. (M) Apparent noon, the time when the sun comes to the meridian, or 12 o'clock, as shewn by a sun-dial. (N) True, or mean noon, twelve o'clock as shewn by a well regulated chronometer, so adjusted as to go 24 hours in a mean solar day.* (0) The equation of time at noon, is the interval between the true and apparent noon. (P) A sidereal year is the interval of time from the sun's leaving any fixed star till he returns to it again, and consists of 365d. 6h. 9m. 12sec. of mean solar time. (Q) A tropical or solar year is the interval of time from * A mean solar day is a period not marked out by any observable phenomena, but an artificial interval of time. The time elapsed from the sun's leaving the meridian on any day till it returns to the same meridian the next day is called a true solar day, and is subject to a continual variation, arising from the obliquity of the ecliptic, and the unequal motion of the earth in its orbit, A clock or chronometer, therefore, which measures time by equal motion, cannot be so adjusted as to keep time exactly with the sun, or always to shew 12 o'clock when the sun is on the meridian; to correct these irregularities, the year is divided into as many imaginary days, each of 24 hours in length, as there are real days in the year measured by the sun's return to the meridian; one of these imaginary days is called a mean solar day, and a clock adjusted so as to go 24 hours in one of these days, is said to be regulated to mean solar time. The year thus consists of as many mean solar days as true solar days; the clock being just as much before the sun, on some days of the year, as the sun is before the clock on others. The difference is given in page II. of the Nautical Almanac for every day in the year. The time shewn by the clock is called true or mean time, and the time shewn by the sun is called apparent time. If a clock be adjusted to go 24 hours, from the passage of any fixed star over the meridian till it returns to it again, its rate of going at any time may be determined by comparing it with the transit of that fixed star. A clock thus regulated is said to be adjusted to sidereal time. Here nature affords a standard exceeding in exactness any imitation that can be produced by art, there is no irregularity in the earth's diurnal motion, its diurnal revolution on its axis being uniformly performed in 24 hours of sidereal time=23h. 56m. 4sec. of mean solar time. the sun's leaving one tropic, or equinox, till he returns to it again, and consists of 365d. 5h. 48m. 48 sec. of mean solar time. (R) Nonagesimal degree of the ecliptic, is that point which is the most elevated above the horizon; and is measured by the angle which the ecliptic makes with the horizon at any elevation of the pole; or, it is the distance between the zenith, and the pole of the ecliptic. This angle is frequently used in the calculation of solar eclipses. (S) The medium Cæli, or mid-heaven, is that point of the ecliptic which culminates, or is on the meridian at any given time. (T) The Crepusculum, or twilight, is that faint light which we perceive before the sun rises, and after he sets. It is produced by the rays of light being refracted in their passage through the earth's atmosphere, and reflected from the different particles thereof. (U) A constellation is a collection of stars on the surface of the celestial sphere, circumscribed by the outlines of some assumed figure, as a ram, a dragon, a bear, &c. This division is necessary, in order to direct a person to any part of the heavens, where any particular star is situated. (W) The diurnal and nocturnal arcs. In all places of the earth, except the two poles, the horizon cuts the equinoctial into two equal parts. In all places situated on the equator, the horizon cuts all the parallels of declination into two equal parts, and here the sun and all the stars are 12 hours above the horizon, and 12 hours below. In places between the equator and the elevated pole, the parallels of declination are unequally divided; the greater arc being above the horizon, and the less arc below. In all places between the equator and the depressed pole, the parallels of declination are unequally divided; the greater arc being below the horizon, and the less arc above. In all cases, the arcs which are above the horizon are called diurnal arcs, and those below, nocturnal arcs. Or, the parallel, which the sun, moon, or stars, describe from their rising to setting, is called the diurnal arc; and that parallel which each of them describes, from the setting to the rising, is called the nocturnal arc. II. Introductory Astronomical Problems.* PROBLEM I. (X) To turn degrees, or parts of the equator into time. These are the same as in the former editions, being extracted from the general examples, and from the notes upon them. Those which depend upon the Nautical Almanac have been recalculated and adapted to the year 1822. RULE. Multiply the number of degrees by 4, and the product will be the corresponding time. NOTE. Seconds multiplied by 4 produce thirds of time. EXAMPLE. Turn 25°.15'.16" of the equator into time. 25°. 15'. 16". 4 Answer. 1h. 41′. 1′′. 4′′. Also, 77°.2.10" of longitude=5b.8.8".40"" of time, and 124°.16'.30" of the equator=8h.17.6" of time. PROBLEM II. (Y) To turn time into degrees. RULE. Multiply the hours by 60, and add the odd minutes, if any, to the product, one-fourth of which will be degrees; multiply the remainder by 60, and add the odd seconds, if any, to the product, one-fourth of which will be minutes, &c. EXAMPLE. Find the number of degrees, &c. corresponding to 1,41′. 1".4". 41′. 1′′. 4′′′′. 1b. 60 Also, 3h.4'.28" of time=46°.7' of longitude, and 8.17.6" of time 124°.16.30" of longitude. PROBLEM III. (Z) Given the time under any known meridian to find the corresponding time at Greenwich.* * Since the earth makes one revolution on its axis from west to cast in 24 hours, the sun must apparently make one revolution round the earth from east to west in |