39* ASTRO 
the oppofition on December 31, 1783, for an epoch to 
which the other obfervations were to be reduced. Th? 
interval between this and the preceding oppofition was 
36gd. ijh. 49'. 28"; from this oppofition he counted back 
the fame interval of time ; and in like manner he counted 
forwards from the epoch two equal intervals ; thus he got 
four equal intervals of time, to w hich times he found the 
places of the planet upon its orbit; and, upon comparing 
their differences, he difcovered that they had irregularities 
not confident w ith the motion of a body in an ellipfe ; 
thefe, therefore, mud have arifen from fome inaccuracies 
in the obfervations; and as, upon account of the fmall in¬ 
tervals of the places, fuch errors would be the caufe of 
great errors in the elements of the orbit, it was neceflary 
to correct thefe inaccuracies, fo as to give the differences 
fuch a law, as near as podible, that they ought to have. 
The next confideration was, upon what principle this 
correction was to be made ; and this was, by finding, as 
nearly as podible, about what part of the ellipfe the pla¬ 
net was in at the time of the above obfervations, and then 
by obferving in fimilar parts of the ellipfes defcribed by 
the other planets, w,hat law the fird and fecond diderences 
of the angles defcribed in equal times obferve. The pla¬ 
ces of the planet in the ecliptic at five points of time be¬ 
ing known, its place at any other point of time may be 
very accurately found by interpolation. Now, on March 
6, 1782, at 6h. 14'. 56". mean time (at which time the pla¬ 
net was dationary), its apparent longitude upon the eclip¬ 
tic was obferved to be 2f. 28°. 49'. 27"; the heliocentric 
longitude was alfo found by interpolation; hence the dif- 
tance of the planet from the Sun came out 18-9053, the 
Earth’s diftance being unity. By interpolating the place 
of the planet for March, 7d. 6h. 14'. 56". it was found to 
have moved 43’4365" in twenty-four hours ; but a planet 
revolving about the Sun in a circle whofe radius is 18 9053, 
will have its diurnal motion =43• 1647". Now, the angu¬ 
lar velocity of a body in an ellipfe is to the angular velocity 
in a circle at the fame didance, in the fubduplicate ratio of 
half the latus rectum to the didance; hence the planet’s dif¬ 
tance from the Sun was lefs than half the latus redhim. Al¬ 
fo, by a like procefs for April 1781 it appears, that at that 
time the angular motion of the planet exceeded, by a very 
little, the angular motion of a body in a circle at the fame 
didance; therefore its didance from its perihelion could 
be but a very little lefs than ninety degrees. We find, 
moreover, that the angular velocity of the planet about 
the Sun was continually accelerated at the time of the 
above obfervations, and therefore the planet was approach¬ 
ing its perihelion. Now, by examining the Tables of the 
planet’s motions in fimilar fituations, it appears that, in 
equal intervals of time, the fird differences decreafe very 
(lowly, and the fecond differences increafe very dowly. 
Mr. Robifon therefore gave to the fird differences a very 
fmall diminution, and to the lecond differences a very 
fulfil increafe, and this correction was made without al¬ 
tering any of the longitudes more than 3''; for the fird 
-obfervation had its longitude diininifhed 1", the fecond 
and third increafed 2-5'', and the fourth and fifth diminidi- 
ed by 3"; and this mud be allowed to be w ithin the limits 
of probability. 1 lie elements deduced arc as follow : 
Mean didance 
Eccentricity 
(Periodic times 
Mean anomaly 
Long, of aphelion 1 for epoch Dec. 31, f 11 23 -9 51 
Long, of the node J 1783, / 2 12 46 14 
Inclination of the orbit - - o 46 25 
Equation of the centre ... 5 26 56-6 
Thefe elements, fays Mr. Robinfon, are as accurate as 
the obfervations on which they are founded can give them ; 
and, in 17S8, agree very well with the obfervations, the 
diderences being as often as much in defect as in cxcefs; 
but, as the obfervations were made lb near together, it 
cannot be expected that this agreement will lad for a ioog 
19-08247 
0-9006 
S3-35? 
+f. 
years 
32'. 51" 
N O M Y. 
time. The dar No. 964, obferved by Mayer in 1756, is’ 
not now to be found; and, by computing the place of this 
planet for the time of his obfervation, Mr. Robifon found 
the planet to be only 3'52" wedward of the dar, and i” 
northward, from which he fufpeCted that it might have 
been this planet which Mayer obferved. It will appear, 
however, that this was not the cafe. It was alfo conjec¬ 
tured by fome adronomers, that the dar No. 34, Tauri, of 
the Britifh catalogue, was the new planet; but Mr. Ro¬ 
bifon thinks this conjecture by no means to be admitted, 
as it cannot be made to agree with the elements. Mr. 
Robifon has computed Tables of this planet’s motion, and 
obferves, that the deviations from obfervations made near 
the vernal dations are in defeat, whild thofe near the au¬ 
tumnal flations are in excefs. Hence it may be prefumed, 
that the mean didance and periodic time are fomevvhat too 
fmall, and the aphelion too forward. This he did not per¬ 
ceive till after he had computed his Tables; and, he ob¬ 
ferves, the talk was too tedious to make the computations 
anew. He therefore pubiifhes them, not in the perfuafion 
that they are perfect, hut becaufe they are more confident 
with obfervations than thofe of M. de la Place, and Oriani, 
the only ones which lie had then feen. 
M. de la Lande, in the Hidoire de 1 ’Academic Royafe 
des Sciences, 1787, has corrected thefe eleinents, after de¬ 
termining tw-o didances from the Sun, the angle, and the 
time between. The refults given by him are as follow; 
Mean longitude in 1784 
3d 14 0 . 49'. 
14' 
Aphelion 
11 16 19 
30 
Equation 
5 26 
47 
Secular motion 
2 Q 11 
11 
Mean didance 
Tropical revolution 
Sidereal revolution 
19-2033 
3 °t >37 \ dayg 
30737/ ; 
Thefe elements are formed from taking into confidera¬ 
tion the didurbing forces of Jupiter and Saturn, w hich 
M. de la Lande found necedary; for ot-hrarwife the didan¬ 
ces would be reprefented very well, when the longitude 
varied conliderably. Thefe elements give the place of the 
planet different from the place of the dar obferved by 
Mayer in 1756 by 11', from which we may conclude that 
that dar was not the Georgian planet. 
To correct the place of the node, M. de la Lande found 
the heliocentric longitudes on September 28, 1781, and 
March 8, 1788, to be 2f. 29 0 . 51'. 24". and 3d 28°. 48L 
49". and latitudes 13' 38" and 33' 20-3". But the precef- 
fion of the equinoxes being 5' 24" in the interval, it mud 
be fubtrafled from the difference of the longitudes to get 
the true motion in longitude, which was therefore 28° 52' 
1"; and the lad latitude was diminidied 3" for the fame 
reafon, but augmented 1" on account of the motion of the 
node; hence the place of the node at the beginning of 1781 
was if. i2°. 44'. 12", and the inclination 46' 20". M. de 
la Grange makes the annual motion in longitude of the 
aphelion to be 53-42"; and that of the node to be 12-5". 
But, if the denfity of Venus be fuch as is fuppofed by 
La Lande, the annual motion of the nodes will be20" 40"'. 
Of the Satellites of the Georgian Planet. 
On January 11, 1787, as Dr. Herfchel was obferving 
the Georgian planet, he perceived, near its difk, fome very 
fmall dars, whofe places he noted. The next evening, 
upon examining them, he found that two of them were 
miffing. Sufpedfing therefore that they might be fatel- 
lites, which had difappearwl i.11 confequence of having 
changed their fituation, he continued his obfervations, and 
In the courfe of a month difcovered them to be fatellites, 
as he had at fird conjectured. Of this difeovery he gave 
an account in the Phil. Tranf. for 1787. The next year he 
publifhed a farther account of this difeovery, containing 
their periodic times, didances, and petitions of their orbits, 
fo far as he was able then to afeertain them. The mod 
convenient method of determining the periodic time of a 
iittelhte, is either from its eclipfes, or fr®m taking its po- 
fitioa 
