279
Calculation of the true Heliocentric Place of Venus at the approximate Time of her true Conjunction.
Epoch of 2’ s place, 1800..... ...
Mean place of 2 j Aphelion of " 2
Long, of 2’s &>
s . o » »
4 25 9 1
1 17 5 51
7 20 42 44
1 24 7
2 40
1
S. O'"
10 R 36 12
0 10 32
19
s. 0
2 14 52 8
u 6 43
12
( 13 years| 144 day's
Her motion in. . ...-( 21 hours
40 minutesL 14", 027
Mean place of 2 at proposed time.
Elliptic equation of her orbit.. .......
2 4 24 24
— 42 50,7
10 8 47 3
2 4 24 24
2 14 59 3
2 3 41 33,3
<j> in her orbit . . ..
2 3 41 33,3
+ I 9,2
2 3 42 42,5
3 25 37 21
V____ f
11 18 42 30,3
V ^_— J
True place of 2 in ecliptic .
2’s mean Anom.
2 from Q
Calculation of the true Heliocentric Place of Venus, one Hour after the approximate Time of her Conjunction, in order to determine
1613, May 24d. 21h. 40m. 14"027.
Mean motion of 5 in one hour.
Mean place of ? at proposed time.
Elliptic equation of orbit of $...
True place of 2 in her orbit.
Reduction to the ecliptic...
True place of 2 in ecliptic.....
Mean place of 2
Aphelion of 2
Long, of Q, of 2
s. o '
2 4 24 24
4 0,3
S. 0 '
10 8 47 3
2 4 28 24,3
S. » '
2 14 59 3
2 3 45 34,9
2 4 28 24,3
— 42 49,4
3 25 41 21,3
11 18 46 31,9
' V
2’s mean Anom.
2 from Q
2 3 45 34,9
+ 1 9
2 3 46 43,9
From the above calculations for the approximate time of theconjunction, the true time of the phenomenon may be found inthe following manner: subtract two signs 3° 42' 42"5, the true he-liocentric place of 2 in the ecliptic on May 24, 1813, at21h.-40m. 14”,027, from two signs 3° 42' 43"5, the true place of © atthe same time ; the remainder 1" is the true distance of 2 from■an opposition to the ©, as seen from the Sun . Again, subtracttwo signs, 3° 42' 42,”5, the true ecliptic heliocentric place of 2 atthe approximate time of her conjunction, from 2S. 3M6' 43”,9,her true place one hour after ; the remainder, 4' 1”,4, is her truehorary motion in the ecliptic. Also, 2' 23",01, IheQ's true ho-rary motion, subtracted from 4' l',4, the true horary motion of 2 ,leaves 1'37",49 for the relative horary motion' of © and 2 hiecliptic. And 1’ 37",49 : 60 minutes of time:: 1", the true dis-tance of 2 from her conjunction at the calculated lime, : 36”,927,the quantity that the approximate differs from the true time of thesuperior conjunction. These seconds being added to May 24d.2lh 40m. 14”,027, because the planet is not yet arrived at herconjunction, give May 24d. 21 h. 40m. 50”,954 for the mean timeof the phenomenon at Paris, and is as exact as the tables whencethese calculations have been made. If 9' 20" be subtracted fromMav 24d. 21h. 40m. 50”,954, the remainder May 24d. 21h. 31m.30”,954, will be the meantime of the conjunction at Greenwich.The equation of the mean to true time, -f- 3' 28",4 applied to May£4d. 21h. 31m. 30",954, gives May 24d. 21b. 34m. 59",354. forthe apparent time of the superior conjunction at Greenwich.Q. K. F.
(83.) As to the conjunctions, oppositions, direct and retrogrademotions, &c. of the superior planets, they depend. on the combi-nations of their motions, with that ot the Earth ; and aremore frequent in Saturn than in Jupiter, and in Jupiter than inMars , but most frequent of all in U erschel ; because the slowerthe motion of the planet is, the sooner the Earth will overtake it,so as to have it again in any given situation. 1 bus, suppose Saturn
to be in conjunction with the Sun in 9° of <y, if he were to standstill for one year, then he would again be in conjunction in 9° ofbut as he goes on slow!)', according to the order of the signs, about12° annually, the Earth must go through almost 13° more than anentire revolution ; so that there will be almost a year and 13 days,between any conjunction between the Sun and Saturn , and theconjunction immediately following. As Jupiter moves in his or-bit with greater velocity than Saturn, the Earth must have a pro-portionably larger space added to the year; and as Mars movesswifter still, the time betwixt any two of his conjunctions mustbe still longer. The time when a superior planet will return intoany given situation, may be found by the methods already laiddown for the inferior planets; and the true conjunctions, &c. may'be found in the superior planets as in the inferior.
(80.) An idea of several of these particulars may be obtainedfrom an inspection of Fig. 1. Plate XXI1. Let the Earth be at G ;then if Venus be at II, she is in her inferior conjunction, and herapparent place is with the Sun among the stars at L, yet, becauseshe is not in the node, she will not exactly coincide with the Sun atL, but will appear a little lower than the ecliptic, that is, she willhave south latitude ; had II been the node she would have beenin the ecliptic or had no latitude ; had H been above the plane ofthe ecliptic, her latitude would have been north, or she wouldhave been seen above the point L. If we suppose Venus at Q,she is in her superior conjunction, and, when situated as in thefigure, her latitude is north. In the present instance she is notseen on the sun’s disk when at Id, or hid behind him at Q ; but,should Venus be at B when the Earth is at D, she .will appear topass over the surface of the Sun like a black spot. The Earth beingat G, if we suppose V enus at T, she will be at her greatest elonga-tion, and will appear at M about 46 or 47 degrees from L, the placeof the Sun , her latitude being south. That she will appear at M,in the line SM from the Sun , parallel to the line GT in which she isseen, is evident from the great distance of the stars, ai which dis-5’ tauc#