OF THE HARVEST MOON. The moon rises about three quarters of an hour later on any day than on the day preceding; but in places of considerable latitude, there is a remarkable difference about the time of harvest, when, at the season of full moon, it rises for several nights together, only about 17 minutes later on one day than on the day preceding. By thus succeeding the sun before twilight is ended, the moon prolongs the light, to the great benefit of those who are engaged in gathering the fruits of the earth; and hence the full moon at this season is called the harvest moon. The full moon nearest the vernal equinox rises with the greatest difference of time, viz. an hour and a quarter later each day than on the former.-Problem XXIX. explains, by the globe, the phenomenon of the harvest moon; and Problem XXX. the equation of time. PROBLEM XXIV. To assign the Orbit of the Moon its proper situation in the Heavens for any given time. 1. Find the moon's ascending node in White's Ephemeris: the descending node will be 180° distant from that. At the distance of 90° from these nodes, reckoning each way, count 54" to the north of the ecliptic on one side, and 51 to the south on the other side. 2. Fasten a silk line round the globe, to cut the ecliptic at the nodes, and to pass over these two points, made at the distance of 51° on each side of the ecliptic; and this will represent the moon's orbit for the given day. EXAMPLES. 1. Represent the moon's orbit for Oct. 25th, 1828. The moon's ascending node is 15° 56′ in Libra, and the descending node will be 15° 56′ in Aries:-make the silk line cut the ecliptic in these two points; and at the distance of 90° from these points, let it be 51° to the north of the ecliptic on one side, and 51° to the south on the other side, and it will represent the orbit for that day. 2. Point out the moon's orbit for the present month. PROBLEM XXV. To find the Moon's Diurnal Motion in the Ecliptic for any given Day. Find the moon's longitude for the given day, on the right-hand page of White's Ephemeris; subtract from this its longitude on the preceding day; or subtract this from the longitude of the succeeding day; and the difference will be the quantity of diurnal motion sought. EXAMPLE. Required the moon's diurnal motion Oct. 25, 1828. II 32° 52′ ୪ 19 32 Answ. 13 20 From the moon's diurnal motion may be found its longitude for any hour, by the rule of three; thus, As 24 hours is to the quantity of daily motion, so is the number of hours to the quantity of motion in that time; for example, Required the moon's longitude for Oct. 25th, 1828, at 9 p.m. As 24: 13° 20' :: 9: 5°, the motion in 9 hours. The moon's longitude at noon will be П 2° 52′; to this add 5° 0, and its longitude, at 9 o'clock p.m. will be п 7° 52′. PROBLEM XXVI. To mark upon the Globe the Moon's place in the Heavens for any given Day and Hour. Find its longitude for the given hour by the last problem, and its latitude for the given day at noon from White's Ephemeris; put a small patch, with the moon's astronomical character marked upon it, on this place, and it will represent the moon. The moon's declination, right ascension, altitude, azimuth, &c., may be found in the same way as the declination, &c. of the sun or stars, but not with equal accuracy, on account of the moon's motion. EXAMPLES.-1. Required the moon's place for November 28th, 1828, at 8 hrs. p.m. The moon's longitude at 8 will be a 28° 38', and its latitude at noon, given in the Ephemeris, 3o 57′ S. 2. Required the moon's declination for the present day at midnight, and its altitude and azimuth at Newcastle, if it be above the horizon there at that time. PROBLEM XXVII. To find the Time of the Moon's Rising, Southing, and Setting, for any Latitude and given Day of the Year. From the Ephemeris, find the moon's latitude and longitude for the given day, and put on a patch to represent its place; then its rising, southing, and setting may be found the same way as the rising, &c., of the stars. EXAMPLES. 1. Find the moon's rising and southing on December 25th, 1828, at London. Answ. South 2 hrs. 56 min. a.m. Rises 8 hrs. 34 min. p.m. 2. Required the moon's rising, southing, and setting, at Newcastle, on December 28th, this year. PROBLEM XXVIII. To find the Time of the Year when the Sun or Moon will be liable to be Eclipsed. 1. Compare the sun's longitude, at the time of new moon, with the place of the moon's nodes: and if it be within 18", there may be an eclipse of the sun. 2. Compare the same at the time of full moon; and if it is within 12°, there may be an eclipse of the moon. EXAMPLES.-1. Was the sun eclipsed in April, 1828 ? Answ. New moon happened on the 14th; the place of the moon's node on that day was 26° 15', the sun's longitude was 24° 29′; hence the moon was within 2o of its node, and an eclipse took place. 2. Was the moon eclipsed in December, 1838? Ans. Full moon happened on the 30th: the moon's nodes on that day were 29o 21', and ₪ 29' 21'; the sun's longitude my 8o 25': hence the moon was 99° 4′ from its nearest node, and consequently no eclipse took place. 3. Find, by the globe, what eclipses of the sun or moon will happen this year. PROBLEM XXIX. To explain the Phenomena of Harvest Moon. Elevate the globe for any northern latitude, suppose for Newcastle. In September, when the sun is in the beginning of Libra, the moon, at full, must be in or near the beginning of Aries and as the mean motion of the moon is 13o in a day, put a patch on the first point of Aries, and another 13° beyond it on the ecliptic: this last will point out the moon's place the first night after full. Its place on the second, third, &c., night may be found by putting more patches at the distance of 13o from each other. Bring the first patch to the horizon, and observe the hour turn the globe till the second patch come to the horizon, and the index will show that it rises only 17 minutes later than the former. Thus 17 m. is the difference of the moon's rising on two successive nights. The other patches will come to the horizon, in little more than that time, after each other; which shows that the difference of the moon's rising several nights successively is little more than 17 m. each night. The difference of the moon's rising for a week will not be 2 hrs. The small angle which that part of the moon's orbit makes with the horizon is the reason of its rising at that season, for several evenings, with so small a difference of time. That part of the moon's orbit near Libra makes the greatest angle with the horizon; and the full moon that happens in Libra rises with the greatest difference of time. This may be seen by placing patches on the globe, from the first of Libra, to represent the moon's place for several successive nights, when it will be seen that the difference of rising in two evenings will be 1 hour 17 minutes. That point of the ecliptic which rises at the least angle with the horizon, sets at the greatest; and therefore when there is the least difference in the time of rising, there will be found to be the greatest in the time of setting. EXAMPLES. Required the difference in the times of the harvest. moon's rising for seven days successively, at 1. St. Petersburg, 2. Edinburgh, 3. London, 4. Gibraltar. PROBLEM XXX. To explain by the Globe the Equation of Time. Mean, or equal time is measured by a clock, that is supposed to go without variation, and to measure exactly 24 hours from noon to noon. Apparent time is that time as measured by a good sun-dial. The sun's motion being in the ecliptic, and not in the equator, and equal portions of the ecliptic passing over the meridian in unequal times, causes a difference between equal and apparent time: the adjustment of this difference is called the equation of time. To show this upon the globe, make pencil marks all round the equator and ecliptic, at equal distances, (suppose 15°) from each other, beginning with Aries. |