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ley 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 equinoctial points to be 0.4.2016 along the equator, and 0.1849 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' 71.5, we will have 1 :d :: 8' 7".5 : 487.5 xd, the time employed by light to come from the planet to the earth.

4871.5 X dm Again, 24h : 487",5xd :: m :

the aberration : 24

457".5 X dm which,when m is expressed in minutes, becomes =

Hence

1440 the log of the aberration in seconds=constart 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 object in right ascension be 2° 86', the object being direct, and its distance from the earth .825, the mean distance of the Sun being 1. Required the aberration a right ascension ? Constant logarithm

9.5296 Distance object

.825

9 9164 Geoc. diurn, mot. in right asc. 2° 36 = 156' 2.1931

Aberration in right ascension 431.56 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 Ixix. 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

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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 antes cedentia, 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 theobliquity 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, expressed 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 de. clination 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, 22 December 1804? Geocentric longitude 9' 14° 36', in time

18h 58' .4 Equation to geo. long. Table Lxx. Part 1.

.

+ 5.0 Geocentric longitude in time corrected

19 3.+ To which, from Part 11. the equation is -0.44,

which multiplied by the lat. 2° 12' S.=-2.2, the

product is .968 = 1.0 nearly And.968 mult. by 1.0, the number from Part 11. is to .

1.0

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TABLE LXXI.

Difference between the Meridian Altitude of an Object, and its

Altitude onc 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 36

Product
Observed altitude

176".4 = 3'nearly

76 48

Meridian altitude
Zenith distance
Declinati on

79 51 20 9N. 10 4 N.

Latitude

30 13 N. 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 letween

the Noon 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. I.

TABLE I.

TABLE II.

TO CONVERT TIME TO LONGITUDE.

TO REDUCE LONGITUDE TO TIME.

M S

D M

D M

Hours. Deg.

Deg. H. Min.

T

S

S

1

1

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31 32 33 34 35 36 37 38 39 40

7

38

9 10

10 11 12 13 14 15 16 17 18 19 20

M D M S M S T S T 1 0 15 2 0 30

0 45

1 0 5 1.15 6 1 30 7

1 45 8 2 0 9 2 15 10 2 30

2 45 12 3 () 13 3 15 14 3 30 15 3 45 16 4 0 17 4 15 18 4 30 19 4 45 20 5 0 21 5 15 22 5 30 23 5 45 24 6 0 25 6 15 26 6 30 27 6 45 28 7 0 29 7 15 30 7 30

39 40 41 42 43 44 45 46 47 48 49 50

165 180 195 210 225 240 255 270 285 300 315 330 345 360

DM MS ST 7 45 8 0 8 15 8 30 8 45 9 0 9 15 9 30 9 45 10 0 10 15 10 30 10 45 11 0 11 15 11 30 11 45 12 0 12 15 12 30 12 45 13 0 13 15 13 30 13 45 14 0 14 15 14 30 '14 45 15 0

12 13 14 15 16

HM MS ST 0 4 e 8 012 016 ( 20 0 24 0 28 0 32 0 36 ( 40 044 0 48 0 52 ( 56 1 0 I 4 18 1 12 1 16 | 20 1 24 1 28 1 32 1 36 | 40 I 44 1 48 1 52 1 56 2 0

70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260

HM MS ST 2 4 2 8 2 12 2 16 2 20 2 24 2 28 2 32 2 36 2 40 % 44 2 48 2 52 2 56 3 0 3.4 3 8 3 12 3 16 3 20 3 24 3 28 3 32 3 36 3 40 3 44 3 48 3 52 3 56 4 0

41 42 43 44 45 46 47 48 49 50

4 40
5 20

0
6 40
7 20
8 0
8 40
9 20
10 0
10 40
11 20
12 0
12 40
13 20
14 0
14 40
15 20
16 0
16 40
17 20
18 0
18 40
19 20
20 0
20 40
21 20
22 0
22 40
23 20
24 0

21 22 23 24

51 52 53 54 55 56 57 58 59 60

18 19 20 21 22 23 24 25 26 27 28 29 30

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Dist. of Ht. of the eye above the sea, in feet. land in 5 | 10 | 15 | 20 25 30 35 40 sea miles. Dip Dip Dip Dip Dip Dip Dip Dip miles, ten i

1 0 1 28 56 85 113 141 170 198 226) 0 2 141 28 42

56 71 85/99,113 3 9 19 381 47 56 66 75 0 4 7 14 21 28 351 42 49 57 0 5 6 111 171 221 28 341 391 45 0

91 14 19 23 28 33 38 0 7

8 12 161 20 247 28 32 0 8

7 11 14 18 21 25 28

6 9 13 16/ 191 22 25 1

11 14 17 201 23 1

9 12 14 16 19 1 3

8/ 101 11 141 15 1 2

7 8 10 12 13 2 2 3 6 8 10

12) 3

7

9 101 3 4 5 6 7 8 8

3 4 5 6 6 n
4

3 4 4 5 6 7
5
2

4 4 5
6

21 3 41 4 5) Dist.

Dip. in minutes.

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280

9.5

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0 0

32.9 0 5 32.0

10 31.2 U 15 30.4 0 20 29.7 0 25 28.9 0 30 28.2 0 35 27.5 0 40 26.8 0 45

26.2 050 25.5 0 55 24.9 1 0 24.3 1 10 23.2 1 20 22.1 1 30 21.1 1 40 20.2 1 50 19.3 2 0 18.4 2 20 16.9 2 40 15.6 3 0 14.4 3 20 13.4 3 40 12.5 4 0 11.7 4 30 10.6 5 0 9.7 5.30 9.0 6 0 8.3 6 30 7.7 70 7.2

6.3

5.6 10 5.1 11 4.6 12 4.2 13 3.9 14 3.6 15 8.3 16

3.1 18

2.8 20 2.4 22 2.2 24 2.0 26

1.8 28 1.6 30 1.5 32

1.4 34

1.3 36

1.2 38

1.1 40

1.0 45 0.8 50 0.7 55 0.6 60

0.5 65 0.4 70 0.3 80 0,1 90

0.0 Alt. Corr.

1 0 0]33 0 5 0 9 54 10 05 15 20 02 3532 2011 30 67 24 0 532 10 5 5 9 46 10 105 1020 102 3432 401 29 68 23 0 1031 921 5 1019 38|10 2015 5120 20 2 32133 01 28

69 22 0 15 30 35 5 15 9 30 10 30 5 0 20 3012 31133 2011 26 70 21 0 2029 50 5 2019 2310 401+ 56 20 40/2 29 133 401 25 71 19 0 25/29 61 5 25 9 15 10 504 51 20 50 2 2834 01 24 72 18 030128 23 5 3019 811 04 47121 02 27 34 20/1 2S 73 17 035/27 411 5 35|9111 1014 4321 1012 26134 40/1 22 74 16 0 40/27 01 5 40 8 5411 2014 39/21 2012 25/35 01 21 75 15 O 45/26 20 5 45 8 47 11 304 34 21 3012 24/35 2011 20 76 14 0 50125 42 5 508 41 11 404 31 21 40 2 23 35 40 1 19 77 13 0 55125 5 $ 55 8 34 11 50/4 27/21 502 21 36 01 18 78 12 1 024 2916 0 8 28 12 04 23 28 02 2036 301 17 79 11 1 5 23 54 6 58 21 12 1014 20122 10 2 19 37 oll 16 80 10 1 10/23 20 6 10 8 15 12 2014 10/22 2012 18 37 30 1 14 81 1 15 22 47 6 158 9 12 30 4 1322 302 1738 011 13 82 1 20 22 15 6 2018 3 12 4014 9 22 40 2 16 38 3011 11 83 7 1 25 21 44 6 257 57 12 504 622 502 15139 01 10 84 1 3021 15 6 307 51 13 04 323 0 2 14 39 30 1 9 85 5 1 35 20 461 6 35 7 45 13 104 0/23 1012 13:40 Oli 8 86 1 40120 18 6 407 40 13 20 3 57123 202 12 40 301 7

87 3 1 45 19 51 64517 35 13 30 3 54 23 302 1141 015 88 2 I 50/19 25 6 5017 3013 403 51 23 4012 10:41 3011 4 89 1 1 55 19 0 6 55 7 25 13 503 48 23 5012 9/42 01 3 90 2 0 18 351 7 017 20:14 03 4512+ 012

8 +2 30 1 2 2 5 18 11 57 15 14 10 3 432 1012

743 01 1 TABLE VII. 2 10117 481 1017 11/14 20 3 40124 2012 643 301 0 PARALLAX OF 2 15 17 26 7 15 7 6 14 303 38124 302 544 (0 59 THE SUN IN 2 20 17 4 2017 2114 4013 35/24 402 444 300 58 ALTITUDE. 2 2516 441 y 2516 5714 50/3 33 24 50 2 3/45 00 57) Alt. Par. 2 30 16 23 7 306 53 15 03 30 25 0 2 2 45 300 56 00 ght 2 35 16 4 3516 49115 103 28 25 10/2 1 46 00 55 3 9 2 40115 45 7 406 45 15 2013 26/25 20/2 0 46 30/0 54

9 2 43 15 271 456 41 15 30/3 24 25 30 1 59 47 0 0 53

9 2 50/15 91 T p 506 37 15 403 21 25 401 58/47 300 52 12 9 2 55 14 52 ñ 556 33 15 503 1925 501 57 48 0 0 51 15 8 3 0 14 3618 06 29 16 0 3 17 26 01 56 48 30 0.50 18 3 5 14 20 8 516 25 16 10 3 15 26 101 55 49 00 49 21 3 10114 4 8 10 6 22 16 20 3 12126 201 55 49 300 49 24 8 3 15 13 491 8 1516 18 16 30 3 10 26 30 1 54 50 00 48 27

8 3 20 13 34) 8 2016 15/16 40/3 8/26 40 1 53/50 300 47 30 8 3 25 13 201 8 256 11/16 5013 6126 501 52 51 olo 46 33 7 3 30 13 6 8 3016 8 17 013 4/27 01 51 51 30/0 45 36 7 3 35 12 531 8 3516 517 10/3 3 27 1511 50/52 00 44 39 7 3 40/12 401 8 40 6 1117 2013 1/27 30/1 49 52 300 44 42 6 3 45 12 27) 8 455 58 17 30/2 59/27 45 1 48/53 0 0 43 45 3 50 12 151 8 505 5517 40/2 57/28 01 47 53 300 42 48 6 3 55 12 3 8 555 52 17 5012 55 28 15 1 46 54 00 41 51 5 4 011 51 9 05 48/18 012 54/28 30|| 45/55 olo 40 54 5 4 511 401 9 55 45|18 10 2 52128 451 44156 00 38 57 5 4 10/11 29 9 10 5 42 18 2012 51129 0|1 42 57 10 37 60 4 15 11 181 9 15 5 39 18 30/2 49/29 20/1 41 58 0 35 63 4 4 20/11 8 9 2015 36 18 40/2 47129 401 40 59 0 34 66 4 4 25 10 58 9 25 5 34 18 50 2 46/30 01 38 60 10 33 69 3 4 30 10 481 9 30 5 31 19 0/2 44 30 201 37 61 TO 32 72 3 4 35 10 391 9 35 5 28 19 10 2 43|30 401 36 62 0 30 75 2 * 40/10 29 9 405 2519 20/2 41 31 01 35 63 10 29 78 2 4 45/10 201 9 45 5 23 19 30/2 40131 2011 33 64 0 28 81 1 4 5010 u 9 505 20 19 4012 38|31 40 1 32 650 26 84 1 4 55 10 2 9 55/5 18/19 5012 37 32 01 31 66 0 25 90 0 Alt. (Refr. Alt. Refr. Alt. (Refr. Alt. Refr. Alt. \Refr. Alt. Refr.

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