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before six, when the declination and latitude have contrary IlalileS. (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 g2 and wy; 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.” (O) 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 startill 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, can not 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. Asec, of mean solar time.

the sun's leaving one tropic, or equinox, till he returns to it again, and consists of 365d. 5h. 48m, 48sec. 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 Caeli, 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 pro

duct will be the corresponding time.

NoTE. Seconds multiplied by 4 produce thirds of time.

Minutes multiplied by 4 produce seconds of time.
Degrees multiplied by 4 produce minutes of time.

EXAMPLE.

Turn 25°.15'.16" of the equator into time.
25°. 15. 16".
4.

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Also, 77°.2.10" of longitude-5".8".8”.40” of time, and

124°.16.30" of the equator=8*.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.

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Also, 3h.4.28% of time=46°.7% of longitude, and 8h.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 east in 24 hours, the sun must apparently make one revolution round the carth from east to west in

RULE. Turn the longitude of the place under the known meridian into time (X. 265.): add this time to the time at the given place if the longitude be west, or subtract it if east, and the sum or remainder will be the time at Greenwich. If the sum exceed 24 hours, subtract 24 hours from it, the remainder will shew the time at Greenwich on the following day: if the longitude, when turned into time, cannot be subtracted from the time at the given place, add 24 hours to the time at the given place before you subtract, the remainder will shew the time on the preceding day.

EXAMPLE I, Find the time at Greenwich, on the 12th of August, when it is 7.h.25 at a place in longitude 97°.45' west. Time at the given place 7.h.25° Long, 97°.45, in time - - = 6.31 W. Time at Greenwich - - 13 . 56, or 56 minutes past 1 in the morning on the 13th of August.*

EXAMPLE II. Find the time at Greenwich, on the 1st of May, when it is 22b.40 at a place in longitude 160° W. Time at the given place 22".40'. Long. 160°, in time = 10.40 W.

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Find the time at Greenwich, on the 8th of April, when it is 16.26 at a place in longitude 98°.45' East.

the same time. Now, the longitudes of all places on the earth are reckoned on the equator, which is divided into 360 degrees, and the whole of it passes the sun in 24 hours; it follows that every 15° of motion is one hour in time, every degree 4 minutes, &c. (as in Prob. I. and II.) Hence, a place one degree eastward of Greenwich will have noon, and every hour of the day, four minutes sooner than at Greenwich; and a place one degree westward of Greenwich will have noon, and every hour of the day, four minutes later. * The astronomical day begins at noon, and is counted forward to 24 hours, or the succeeding noon, when the next day begins, being 12 hours later than the civil day, which commences at the preceding midnight; thus August 12th, at 13h.56'

astronomical time, is August 13th at 1h.56' in the morning, according to civil reckoning.

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Find the time at Greenwich, on the 4th of June, when it is 5h. 26 at a place in longitude 120° East. Time at the given place + 24h. =29*.26' Long. 120°, in time - - - - = 8.- E. Time at Greenwich - - - - 21 26, on the 3d of June.

PRACTICAL ExAMPLES.

1. What Greenwich time answers to noon at a place in 60° East longitude?

Answer. 20 hours, on the preceding day.

2. What Greenwich time answers to noon at a place in longitude 60° West?

Answer. 4 hours.

3. Find the time at Greenwich when it is 195.42 at a place in 28°.30' E. longitude.

Answer. 17b.48'.

PROBLEM IV.

(A) Given the time at Greenwich to find the corresponding time under any known meridian. RULE. Turn the longitude of the place under the known meridian into time (X. 265.): add this time to the time at Greenwich if the longitude be east, or subtract it if west, and the sum or remainder will be the time under the known meridian. If the sum exceed 24 hours, subtract 24 hours from it, the remainder will shew the time at the given meridian on the Jollowing day: if the longitude, when turned into time, cannot be subtracted from the given time at Greenwich, add 24 hours to the time at Greenwich before you subtract, the remainder will shew the time on the preceding day.

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