LECT. LECTURE XII. Shewing how to calculate the mean time of any New or Full Moon, or Eclipse, from the creation of the world to the year of CHRIST 5800. In the following tables, the mean lunation is about a 20th part of a second of time longer than its measure as now printed in the third edition of my Astronomy; which makes a difference of an hour and 30 minutes in 8000 years.-But this is not material, when only the mean times are required. PRECEPTS. To find the mean time of any New or Full Moon in any given year and month after the Christian Æra. 1. If the given year be found iv the third column of the Table of the moon's mean motion from the sun, under the title Years before and after CHRIST; write out that year, with the mean motions belonging to it, and thereto join the given month with its mean motions. But, if the given year be not in the table, take out the next lesser one to it that you find, in the same column; and thereto add as many complete years, as will make up the given year: then, join the given month, and all the respective mean motions. a 2. Collect these mean motions into one sum of signs, degrees, minutes, and seconds ; remembering, that 60 seconds (") make a minute, 60 minutes (") a degree, 30 degrees (o) a sign, and 12 signs (“) a circle. When the signs exceed 12, or 24, or 36 (which are whole circles) reject them, and set down only the remainder; which together with the odd degrees, minutes, and seconds LECT, already set down, must be reckoned the whole sum of the collection. XII. 3. Subtract the result, or sum of this collection, from 12 signs; and write down the remainder. Then, look in the table, under Days, for the next less mean motions to this remainder, and subtract them from it, writing down their remainder. This done, look in the table under hours (marked H) for the next less mean motions to this last remainder, and subtract them from it, writing down their remainder. Then look in the table under minutes (marked M) for the next less mean motions to this remainder, and subtract them from it, writing down their remainder. Lastly, look in the table under seconds (marked S) for the next less mean motions to this remainder, either greater or less; and against it you have the seconds answering thereto. 4. And these times collected, will give the mean time of the required new moon; which will he right in common years, and also in January and February in leapyears but always one day too late in leap-years after February. LROT EXAMPLE I. Required the time of new moon in Seplember, 1764 ? (a year not inserted in the table.) The sum of these mean motions is 1 12 0 24 Which, being subtracted from a circle, or 12 0 0 0 Leaves remaining 10 17 59 36 Next less mean motion for 26 d. subtract 10 16 57 34 . . These times, being collected, would shew the mean time of the required new moon in September 1764, to be on the 26th day, at 2 hours 2 min. 12 sec. past noon. But, as it is in a leap-year, and after February, the time is one day too late. So, the true mean time is September the 25th. at 2 min. 12 sec. past II in the after noon. N. B. The tables always begin the day at noon, and reckon thence forward, to the noon of the day following. LECT XII. To find the mean time of full moon in any given year and month after the Christian Era. Having collected the moon's mean motion from the sun for the beginning of the given year and month, and subtracted their sum from 12 signs (as in the former example) add 6 signs to the remainder, and then proceed in all respects as above. EXAMPLE II. Required the mean time of full Moon in September, 1764? So, the mean time, according to the tables, is the 11th XU. noon. of September, at 7 hours 40 minutes 8 seconds past LECT. One day too late, being after February in a leap-year. And thus may the mean time of any new or full moon be found, in any year after the Christian Æra. To find the mean time of new or full moon in any given year and month before the Christian Æra. If the given year before the year of CHRIST 1. be found in the third column of the table, under the title Years before and after CHRIST, write it out, together with the given month, and join the mean motions. But, if the given year be not in the table, take out the next greater one to it that you find ; which being still farther back than the given year, add as many complete years to it as will bring the time forward to the given year; then join the month, and proceed in all respects as above. EXAMPLE III. Required the mean time of new moon in May, the year before Christ, 585? The next greater year in the table is 600; which being 15 years before the given year, add the mean motion for 15 years to those of 600, together with those for the beginning of May. Moon from sun. |