fey and Maskelyne. The results, as given by the French astronomers, differ a little therefrom; for, according to M. de la Lande, the mean annual precession of the equinoxes in longitude is 50".25 in the present century; and by the late calculations of M. de la Place, the combined action of the planets makes the annual advance of the equinoc tial points to be 0.2016 along the equator, and 0.1949 along the ecliptic. Agreeable to these elements, M. de. Lambre has given very full tables of the precession in right ascension and declination, in the Connaissance des Tems for 1792.

TABLE LXIX.

Aberration of the Planets in Longitude.

Since the aberration of a planet or comet is equal to its geocentric motion during the interval of time employed by light to move from the planet to the earth; if, therefore, the distance of the planet from the earth, and its geocentric motion in any proposed time, as a day, be given, the aberration may be found. For let d denote the above distance, m the diurnal geocentric motion of the planet; then, the mean distance of the Sun from the earth being assumed equal to 1, and the time employed by light to come that distance 8′ 7.5, we will have 1: d:: 8' 7.5 487".5xd, the time employed by light to come from the planet to the earth.

487".5 Xdm

the aberration:

24

Hence

which, when m is expressed in minutes, becomes

487".5×dm

1440

the log of the aberration in seconds constant log 9.5296, + log. of the distance of the planet from the earth,+log. of the diurnal motion of the planet in minutes, thus:

Let the diurnal geocentric motion of an be 2° 36', the object being direct, and its .825, the mean distance of the Sun being 1. in right ascension?

Constant logarithm

Distance object

.825

object in right ascension distance from the earth Required the aberration

9.5296

99164

Geoc. diurn. mot. in right asc. 2° 36 =156' 2.1931

Aberration in right ascension

43".56

1.6391

In like manner, the aberration in longitude, latitude, or declination, may be found. The aberration of the Moon in longitude does not amount to half a second.

Table LXIX. contains the aberration of the planets in longitude, in which all the orbits except that of Mercury are supposed to be circular. It was given by M. de la Lande in the second volume of his edition of Dr. Halley's Tables, printed at Paris in 1759, page 166, and again in the third volume of the third edition of his Astronomy, page 119.

When

When the longitude or latitude, the right ascension or declination, of a planet is increasing, the aberration is subtractive from the mean place to obtain the apparent; but when the planet is moving in antecedentia, or contrary to the order of the signs, and when it is ap. proaching the ecliptic or equinoctial, the aberration is additive: hence, when the planet's motion is direct, the aberration is negative; and when retrograde, the aberration is positive; and when the planet is stationary, the aberration is 0.

TABLE LXX.

For computing the Right Ascension of a Planet in Time.

The right ascensions of the planets are not given in the Nautical Almanac. The right ascension, however, may be computed from the given geocentric longitude and latitude, and the obliquity of the ecliptic, by Prop. 11. page 42, or more readily by Table LXX. which was computed by M. de Lambre.

Reduce the geocentric longitude of the planet to time; to which apply the equation from Part 1. answering to the given longitude, ex· pressed in signs and degrees, and the aggregate will be the longitude in time corrected.

Now multiply the equation from Part 11. answering to the longitude in time corrected, by the latitude of the star, the sign of the latitude being + when N. and if S; and the product, when the signs of the factors are like, is to be added to the longitude in time corrected, but subtracted therefrom when the signs are unlike. Again, multiply the product by the equation from Part 111. corresponding to the declination of the object, and the last product being added to the former quantity, will be the right ascension of the object in time.

EXAMPLE.

Required the right ascension of Mercury in time, 22d December 1804

Geocentric longitude 9° 14° 36', in time
Equation to geo. long. Table LXX. Part 1.

18h 58' .4

+

5.0

Geocentric longitude in time corrected To which, from Part II. the equation is which multiplied by the lat. 2° 12′ S. product is .968 = 1.0 nearly

19

3.4

0.44,

2°.2, the

And .968 mult. by 1.0, the number from Part 111. is

Right ascension of Mercury in time

Sun's right ascension

Apparent time of Mercury's passage over the meridian

1

2.1

++

TABLE LXXI.

Difference between the Meridian Altitude of an Object, and its Altitude one Minute before or after the Time of its Passage over the Meridian.

Since the difference between the meridian altitude of an object, and its altitude a few minutes before, or after, is nearly proportional to the square of the time from its transit; the meridian altitude, therefore, of an object, may be found from the altitude observed a few minutes before or after its passage over the meridian, by adding to the observed altitude, the product of the number from the table answering to the given latitude and declination, by the square of the interval of time between the time of the observation and that of its transit, thus:

Let the latitude be about 30, N. declination 10° 4' N. and the latitude observed 6' after the passage of the object over the meridian 79° 48'. To find the meridian altitude?

The number fr. Tab. LXX. to given lat. and dec. is 5′′.9
The given interval is 6', the square of which is

Product

Observed altitude

36

Meridian altitude

Zenith distance

Declinati on

Latitude

When the Sun comes near the zenith, the above assumption of the difference of altitude being proportional to the square of the time, is not strictly accurate.

TABLE LXXII.

For computing the final Effect of Parallax on the Distance between the Moon and the Sun or a Fixed Star.

This table contains the third correction of distance, according to Methods vi. and VII. pages 159161, of Vol. 1.

6.3

2 35 16 4

7 356 49 15

03 30 25
103 28 25 10 2

02

245 300 56

U°

9

146 00 55

5.6

2 40 15 45

7 406 45 15

20 3

2 45 15 27

7 45 6 41 15

2 50 15 97506 37 15

2 55 14 52 7 556 3315

06 29 16

26 25 202
00 53
30 3 24 25 301 5947
40 3 21 25 401 5847 300 52
00 51
50 3 19 25 501 5748
03 1726
514 20 8 56 25 16 10 3 15 26 101 5549
4 8 10 6 22 16 203 12 26 201 55 49
3 10 14
3 15 13 49 8 156 1816 30 3 10 26 301 5450
3 20 13 34 8 20 6 15 16 40 3 8 26 401 53 50
3 25 13 20 8 25 6 1116 503 626 501 5251
817
3 30 13 6 8 306
03 427 01 5151
3 35 12 53 8 356 517 103 327 151 50 52
117 203 127 301 49 52
59 27 451 4853
8 505 55 17 402 57 28 01 4753 300 42
55 52 17 50 2 55 28 15 1 4654
05 48 18 02 54 28 301 4555
55 45 18 10 2 52 28 451 44 56
105 42 18 20 2 51 29 01 42
9 15 5 39 18 302 4929 201 41

45

0.8

4 2011

8

9 20 5 36 18 402 47 29 401 40

50

0.7

4 25 10 58

9 25 5 34 18
9 305 31 19
9 35 5 28 19

9 405 25 19

50 2 4630 01 38 02 44 30 201 37 10 2 43 30 40 1 36 20 2 4131 01 35 9 455 23 19 302 40 31 201 33

4 50 10 11 9 505 20 19 402 38 31 401 32
4 55 10 29 555 18 19 502 37 32 01 31
Alt. Refr. Alt. Refr. Alt. Refr. Alt. Refr.

1

0

Refr.