278

ASTRONOMY.

Calculation of 2 ’•? true Heliocentric Longitude, six Hours after the Time of her mean superior Conjunction, in order to determine

her true Motion in six Hours.

Mean Longitude of 2 at the Time of her mean Conjunction. .

Her mean Motion in six Hours... . .

Mean place of 2 at proposed Time.

Mean Long. 2

Aphelion of 2

Long, of 2’s SJ

s. 0 ' "Is. o > »

1 29 39 1,3 10 8 47 3

24 2,01 0 0

s. 0 ' "

2 14 59 3

0 0

2 0 3 3,3 10 8 47 3 '

— 44 14,5 j 2 0 3 3,3

2 14 59 3

1 29 18 4S,8

1 29 18 48,8

1 35

1 29 20 23,8

3 21 16 0,3

V--/

11 14 19 45,8

\- y -- 1

£ ’s mean Anom.

2’s dist. from £3

From the preceding operations the approximate time of thetrue superior conjunction of 2 maybe readily ascertained in thefollowing manner: From the true place of the bun at the meansuperior conjunction, 2 Signs 0° 51' 44",2, subtract the true longi-tude of 2 at the same time, 1 Sign 28° 56' 16"; the remainder,1° 55' 28",2, is the true distance of 2 from an opposition to theEarth , as seen from the Sun. Again, 1 Sign 28° 56' 16", the trueplace of 2 at her mean superior conjunction, subtracted from1 Sign 29° 20' 23",8, her true place six hours afterwards, gives24' 7",8 for her true motion in the ecliptic in six hours. Also,14 24",36, Q’s true motion in six hours, subtracted from24' 7",8, 2’ s true ecliptic motion in the same time, gives9' 43",44, the relative ecliptic motion of © and 2 > n slx hours,as seen from the Sun. And 9' 43”,44, the relative motion of ©and 2 hi six hours, is to six hours, or 360 minutes of time, as1°. 55' 28",2, the true heliocentric distance of 2 from her supe-rior conjunction, to 2 days, 23h. 14m. 54",42 ; which quantity-being added to May 2ld. 22h. 25m. 19",12, the mean time ofthe mean superior conjunction of Venus , gives May 24d. 21h.40m. 14',027, the mean time of the true conjunction at Paris .If 9m. 20s. the quantity in time that Paris is to the east of the RoyalObservatory at Greenwich , be subtracted from May 24d. 21h.

40m. 14",027, the remainder, May 24, at 21h. 30m. 54",027, willbe the mean lime of the phenomenon at Greenwich very nearly.The reason why this last proportion will not give the time of theconjunction exactly, arises from the supposition of the relativemotion of O and 2 being constantly the same every six hours thatelapses between the mean and true conjunction. But this suppo-sition is by no means true ; for on account of the eccentricity ofthe orbits of the Sun and Venus , the quantity of the elliptic equa-tion is constantly changing ; so that in no two consecutive secondsof time can their relative motion be precisely the same, except inthe very rare instance of the greatest equation happening in themiddle of the second, or in any other extreme case of a similarnature. But the first approximation is sufficiently exact for allcommon purposes, as it will never vary from the truth more thana very few minutes. To obtain it more exactly the Sen and pla-net’s true place in the ecliptic must be calculated for the approxi-mate time of the true conjunction ; and also their relative eclipticmotion in a small portion of time immediately preceding or suc-ceeding the conjunction ; as e. g. in one hour. The followingcalculations are made in order to obtain the time of the true con-junction more accurately :

Calculation of the ©’* true Place on May 24, 1813, at 21 h. 40»t. 14”,027, mean time at Paris , or at 21 h. 30 m. 54",027»

Greenwich Time.

TCnorh of mean place. 1813..

O’s mean Long.

s. » '

9 9 45 12,1

4 21 55 59,5

51 44,8

1 38,6

,6

* l Mav 24.

iiis mean motion for-j w Min ^.:.

i. 14”,027.

Q’s mean place at proposed time...*.

2 2 34 35,6

+ 1 8 32,1

Q’s mean place equated....

2 3 43 7,7

- 5,0

- .8,4

- 0,5

+ 3,2

- 0,2

- 12,0

1,3

~ * r ]).

i 6 .

CVs true place.......

2 3 42 43,5

Q’s Apogee.

42

31

24,5

937

876

30

9 42 55,5

2 34 35,6

10 22 51 40,1

n

453

36!

2572471

720

185

Nut.

967

25

606

21

843 j816 505 {905 |992 |627

O’s mean Anomaly.

The Sun’s mean Anomaly gives 2' 23",91 forhis horary motion.

First equation of true to mean time, (Arg. O’smean Anomaly,) -f- 4' 34", 1 ; second equation,(Arg. O’s true place,) — 8' 3",4; third equation,(sum of all the little equations of Q except thenutation, converted into time,) — 0",8 ; fourthequation, (Arg. present obliquity of the eclip-tic, 23° 27' 44",5,)— 0", 1 : sum, or true equa-tion of time, — 3' 28",4. The equation ofmean to true time is consequently -(- 3' 28 ,4.

Calculation