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.

1

11 46 11 56 12 6 12 16 12 26 12 36 12 46 12 56 13 6 13 16 13 26 m.d. m.d.

d. m. d.

m.d.

m.

1

0 31 12

1 33
24

1 281 20 131 132 158 159 2123 5227 229 231 234 62572593134 7326329332335 8355 359 4246

d. m. d. m. d.

m.d. m d. m. d. m.

TABLE II.

1 HOURS.

1234567

13 30 13 40 13 50 14 614 16 14 26 14 36 14 46 14 5615 615 16 md. m.d. m.

d.

md.md. m.d. m.d. m. d.

m.d. m. d. m.d.

036 036 037 037 038 0 38 112 113 114 115 115 116 149 151 151 155 154 226228 230 231 233 3537393 11 339 341 345 346 39 415 418 421 424 47

1031034 035 036 036
1819 116 110 111
142 142 146 146 147 148
216 28 219 221 222 224
250 252 254 256 25830
6324 326 329 331334339
7358 414 4 4 7 4 10 4 10
8432 435 439 442
9565 10 5 13

445

5 17

10 5 40 542 548 552

421
557

11 6 14

12 6 48

13 722

449

ن

452 455 4595255 525 528 5 32 5 06 5 40 5 43 6165696 13 6 17 6 22

920 926 932

6 19 623 628 632 637 641 6 46 653 650 7378713 728 723 727 733 738 744 749 7 54 14 7 56 8088813 819 825 881 837 15 8 30 836 842 849 855 16 9 4 911 917 921 912 17 938 945 952 9 59 10 20 18 10 12 10 19 10 27 10 34 10 42 19 10 46 10 54 11 5 11 10 11 18 20 11 29 11 38 11 37 11 24 11 8 21 11 58 12 3 12 11 12 20 12 22 12 28 12 37 12 46 12 55 13 5 23 13 213 12 13 21 13 31 13 43 24 13 36 13 46 13 56 14 6 14 16

1

9

91 97914 937944 951 9 57 10 4 10 11 10 13 10 20 10 28 10 33 10 42 10 49 10 49 10 57 11 4 11 12 11 19 11 27 11 26 11 34 11 41 11 49 11 57 12 5 12 2 12 10 12 18 12 27 12 35 12 42 12 38 12 40 12 55 13 4 13 13 13 21 13 14 13 23 13 33 13 41 13 50 13 30 13 59 13 59 149 14 10 14 28 14 38 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.