ephemerides the moon's place is only shewn at the beginning of each day, or XII o'clock at noon, it becomes necessary to supply, by a table, this deficiency, and assign thereby her place for any intermediate time. In the nautical ephemeris, published under the authority of the Board of Longitude, we have the moon's place for noon and midnight, with rules for accurately obtaining any intermediate time; but as this ephemeris may not always be at hand, we shall insert, from Mr. Martin's Treatise on the Globes, a table for finding the hourly motion of the moon. In order, however, to use this table, it will be necessary, first, to find the quantity of the moon's diurnal motion in the ecliptic for any given day; for the quantity of the moon's diurnal motion varies from about 11 deg. 46 min. the least, to 15 deg. 16 min. when greatest. The following tables are calculated from the least of 11 deg. 46 min. to the greatest of 15 deg. 16 min. every column increasing 10 minutes; upon the top of the column is the quantity of the diurnal motion, and on the side of the table are the 24 hours; by which means it will be easy to find what part of the diurnal motion of the moon answers to any given number of hours. Thus, suppose the diurnal motion to be 12° 32', look on the top column for the number nearest to it, which you will find to be 12° 36', in the sixth column; and under it, against 9 hours, you will find 4 deg. 43 min. which is her motion in the ecliptic in the space of 9 hours for that day. The quantity of the diurnal motion for any day is found by taking the difference between it and the preceding day. Thus, let the diurnal motion for the 11th of May, 1787, be required. TABLES FOR FINDING THE HOURLY MOTION OF THE MOON, AND THEREBY HER TRUE PLACE AT ANY TIME OF THE DAY. TABLE I. HOURS. 11 46 11 56 12 6 12 16 12 26 12 36 12 46 12 56 13 6 13 16 13 26 d. m.d. md. m. d. m. d. m. d. m.d. m. d. m. d. md. m. d. m. HOURS. A TABLE II. 13 30 13 40 13 50 14 6 14 16 14 26 14 36 14 46 14 56 15 6 15 16 d. md. md. m. d. m. d. m. d. m. d. m. d. m. d. md. m. d. m. 16 9 4 9 11 9 17 9 21 9 12 9 37 9 44 9 51 9 57 10 4 10 11 17 9 38 9 45 9 52 9 59 10 20 10 13 10 20 10 28 10 33 10 42 10 49 18 10 12 10 19 10 27 10 34 10 42 10 49 10 57 11 4 11 12 11 19 11 27 19 10 4610 54 11 5 11 10 11 18 11 26 11 34 11 41 11 49 11 57 12 5 20 11 29 11 38 11 37 11 24 11 12 2.12 10 12 18 12 27 12 35 12 42 21 11 58 12 3 12 11 12 2012 8 9 12 38 12 40 12 55 13 4 13 13 13 21 22 12 28 12 37 12 46 12 55 13 5 13 14 13 23 13 33 13 41 13 50 13 50 23 13 2 13 12 13 21 13 31 13 43 13 59 13 59 14 9 14 10 14 28 14 38 24 13 36 13 46 13 5614 6 14 16 14 36 14 36 14 46 14 56 15 6 15 16 The moon's path may be represented on the globe in a very pleasing manner, by tying a silken line over the surface of the globe exactly on the ecliptic; then, finding by an ephemeris the place of the nodes for the given time, confine the silk at these two points, and at 90 degrees distance from them elevate the line about 5 deg. from the ecliptic, and depress it as much on the other, and it will then represent the lunar orbit for that day. PROBLEM XLI. To find the moon's place in the ecliptic for any given hour of the day. You should be provided with an ephemeris,* that will give the moon's latitude and place in the ecliptic: first, note her place in the ecliptic upon the globe, and then counting so many degrees amongst the parallels in the zodiac, either above or below the ecliptic, as her latitude is north or south upon the given day, and that will be the point which represents the true place of the moon for that time, to which apply the artificial sun, or a small patch. Thus, on the 11th of May, 1787, she was at noon in 2 deg. 35 min. of Pisces, and her latitude was 4 deg. 18 min.; but, as her diurnal motion for that day is 12, 48 in nine hours, she will have passed over 4 deg. 47 min. which, added to her place at noon, gives 7 h. 22 min. for her place on the 11th of May, at nine at night. *The Nautical Almanack is the best English ephemeris. White's Ephemeris is a very useful manual. EDIT. |