238 27 25 65

19 15 0 S.

TABLE X.

The Longitudes, Latitudes, and Magnitudes, of the most remarkable fixed Stars that the Moon can Eclipse, or make a near Appulse to; exactly rectified to the Begin ning of the Year 1800.

11 21 342

14 44 331

9 44 N.

537 N

17 4 480

13 11 S.

8 18 3

1 48 7 N.

27 12 7 4 1

56 N.

E

3 0 235 45

30 S.

5 40 02 35

37 S.

તા

γ

22 20 324 94 41 N.

0 23 56 1 2 18 N

1 51 13 1 39 52 N. 5 0 36 4 0 23 S. 6.58 21 4 32 175. 8 40 56 52151 28 28 266 56 48 5 0 25 212 22 24 N 3 31 54 2 5 31 5 733 11 3 55 225 9 35 40 3 24 55

12 2 25 5 2335

12 11 590 53 36N) 13 27 441 28 7M 1 15 18 4 36 46 NĮ 17 24 234 57. 5. 18 59 16 2 S2 ES 20 44 28 2 33 5. 25 55 40 2 347 S 0 28 524 N 847 60 21

14 20.58

M

2 30 250 50 34 S.
5 18 436 46 12 S.

σ

a

7 8.53 2 2 28 N. 3

т

4

4

AAN

33333++++

σ

T

β

EXPLANATION

OF THE

TABLE S.

TABLE I. contains the sun's longitude for the noon of every day in the year 1802: this year was chosen, because it is the second from leap year, and will, therefore, correspond more nearly to the sun's real longitude for each day of a series of a few years, than a table would which contained the longitudes for every day on the year before or after leap year. If tables of the sun's longitude for four years had been given, they would not answer for any great length of time, because the sum of four years, one of which is a bissextile, does not exactly equal four sidereal years. This table, however, though not perfect, may be useful; for, from the longitudes here given, the sun's right ascension may be deduced sufficiently exact to find the culminating of any star, by subtracting its R. A. from that of the sun; and by these means the star may be known. The longitude for any intermediate time between the noons of two given days may be readily found by proportion; thus, to find the sun's longitude on May 3d, 1802, at 4 o'clock, P.M.:

Long. May 4, noon 8 13° 53′ 43′′ | As24h: 1° 46'6" Long. May 3, noon 8 12 17 37 :: 4h: 17′ 41′′

Difference for 1 day 1 46 6

Hence 12° 17′ 37′′ + 17′ 41′′ = 12° 35′ 18′′ of 8, sun's longitude at the given hour.

TABLE II., which contains the sun's declination to each degree of his longitude, will be very useful in conjunction with the former. Each of the 2d, 3d, and 4th columns contains the declinations corresponding to every degree of four signs of the sun's longitude; thus, the 2d column shews the declination answering to each degree of aries and libra, by reckoning from the top of the page to the bottom, and the declination to each degree of virgo and pisces, estimating from the bottom to the top: it will also be seen, that the declinations in this column, corresponding to the different points of aries and virgo, are wh, and those answering to the several points of libra and pisces, soul. The method of finding the declination for any given time may be shewn by an example; thus, to determine the declination on May 3d, 1802, at 4" P.M.: the longitude we have found to be 12° 35′ 18′′ of 8, and the declination agreeing to 13° of 8 is 15° 45′ 30′′ N. the dec. to 12° of 15° 27′ 13′′, their difference 18′ 17′′; then 60': 18′ 17′′ :: 35 18" : 10′ 13′′; wherefore 15° 27′ 13′′ + 10′ 13′′

15° 37′ 26" north, the declination sought. When the place is not on the meridian of Greenwich, the declination may be found by adding to, or subtracting from, the given time, the time corresponding to the difference of longitude (according to the kind of longitude and declination), and then proceeding as above. Where the differences are not tolerably uniform, and when great accuracy is required, recourse must be had to the method of interpolation.

TABLE III., containing the sun's right ascensions, requires no explanation; the R. A.'s for any given time may be determined in the same way as the declinations if they are wanted in degrees, &c. they may be found by multiplying the tabular R. A.'s by 15.

TABLE IV. contains the sun's semidiameter and hourly motion for every ten degrees of mean anomaly; they may be readily found for any intermediate degrees by proportion. From the table it appears that the semidiameter of the sun, when it is greatest. in perigee, is 16′ 19′′,and when least in apogee, 1 5′ 47′′", their difference being 32"; the difference between the greatest hourly motion, when the sun is in perigee, and the least, when he is in apogee, is 10". The use of this table is greatest in the calculation of eclipses; it may be exemplified, by finding the sun's apparent semidiameter and hourly motion, on Aug. 27, 1802, when there will be a solar eclipse, partly visible at Greenwich. The place of the sun's apogee is nearly 9° of cancer, which answers to the 2d of July Tab. I); this day is 56 days before the day of the eclipse: the mean anomaly may be found sufficiently near, by saying, as 365: 350°:: 56d: 55° = 25° to this we, by p oportion, find 15′ 53 the corresponding semidiameter, and 2' 25" the hourly motion.

TABLE V. exhibits the sun's mean parallar for each 5° of apparent altitude: in cases of great accuracy, the parallax for any intermediate altitude may be determined by proportional differences, as in the other tables. The parallax must be added to the apparent altitude, to give the true altitude.

TABLE VI. of the epuction of time, shews that equation for every degree of the sun's longitude, and will answer tolerably nearly for the days when the sun has those longitudes. The equations with the sign are to be added to the apparent time, to have