ASTRONOMY. 
393 
fition in feveral fucccffive oppofitions of the planet; but Earth; and confequently the planet will appear in conjunc- 
no eclipfes have yet happened fince the difcovery of thefe tion with the Sun. But, as the orbit of the Earth is be- 
fatellites, and it would be waiting a long time to put in tween the Sun and the orbit of the fuperior planet, it is 
practice the other method. Dr. Herfchel, therefore, took polfible for the Earth to be betw een the Sun and the pla- 
their fituations whenever he could ascertain them with 
lome degree of precilion, and then reduced them by com¬ 
putation to fuch fituations as w-ere neceffary for his purpofe. 
In computing the periodic times, he has taken the fynodic 
revolution, as the pofitions of their orbits, at the times 
when their fituations were taken, were not fufficiently 
known to get a very accurate fiderial revolution. The 
mean of feveral refults gave the fynodic revolution of the 
firfi fatellite 8d. 17!!. x'. 19*3". and of the fecond 13d. 1 ih. 
3'. I's". The refults, he obferves, of which thefe are a 
mean, do not much ditfer among themfelves, and there¬ 
fore the mean is probably tolerably accurate. The epochs 
from which their fituations may at any time be computed 
are, for the firfi, October 19, 1787, at 19I1. 11'. 28". and, 
for the fecond, at 17I1. 22'. 40". at which times they were 
76° 43' north, following the planet. 
The next thing to be determined, in the elements of 
thefe fatellites, was their difiances from the planet; to ob¬ 
tain which, he found one difiance by obfervation, and then 
the other from the periodic times. Now, in attempting to 
difcover the difiance of the fecond, the orbit was feemingly 
elliptical. On March 18, 1787, at Sh. 2'. 50". he found 
the elongation to be 46'46'', this being the greateft of all 
the meafures he had taken. Hence, at the mean difiance 
of the Georgian from the Earth, this elongation will be 
44-23". Admitting, therefore, for the prefent, fays Dr. 
Herfchel, that the fatellite moves in a circular orbit, we 
may take 44-23" for the true difiance, without much er¬ 
ror ; hence, as the fquares of the periodic times are as the 
cubes of the difiances, the difiance of the firfi fatellite 
comes out 33-09". The fynodic revolutions were here 
ufed inftead of the fiderial, which will make but a fmall 
error. 
The laft thing to be done was to determine the inclina¬ 
tion of the orbits, and places of their nodes. And here a 
difficulty prefented itfelf, which could not be got over at 
the time of his firfi obfervation; for it could not then be 
determined which part of the orbit was inclined to the 
Earth, and which from it. On the two different fuppofi- 
tions, therefore, Dr. Herfchel has computed the inclina¬ 
tions of the orbits, and the places of the nodes, and found 
them as follows : The orbit of the fecond fatellite is in¬ 
clined to the ecliptic 99 0 43' 53-3", or 8t° 6' 4-4" ; itsaf- 
cending node upon the ecliptic is in 3I’. 18 0 . or 81 '. 6°. and, 
when the planet comes to the afcending node of this fa¬ 
tellite, which will happen about the year 1799, or 1818, 
the northern half of the orbit will be turned towards the 
eafi or wefi at the time of its meridian pafiage. M. de 
Lambre makes the afcending node in 5L 21°. or Sf. 9 0 . 
from Dr. Herfchel’s obfervations. The (ituation of the 
orbit of the firfi fatellite does not materially differ from 
that of the fecond. The light of the fatellites is extreme¬ 
ly faint; the fecond is the brighteft, but the difference is 
fmall. The fatellites are probably not lefs than thole of 
Jupiter. There will be eclipfes of thefe fatellites about 
the year 1799, or 1818, when they will appear to afcend 
through the ffiadow of the planet, in a direction almoft 
perpendicular to the ecliptic. 
Of the Phenomena peculiar to the Superior Planets. 
We have feen that the greatefi elongation of the inferior 
planets is lefs than ninety degrees, or a quarter of a cir¬ 
cle ; fo that they are never far from the Sun, but confiantly 
attend it. But the fuperior planets do not always attend the 
Sun, as the inferior ones do; they are indeed fometimes in 
conjunftion with it, but then they are fometimes in oppo- 
fition to, or 180 degrees from, it. Let S, in the annexed 
figure, be the Sun, ABDC the orbit of any fuperior pla¬ 
net, Mars, for infiance; and EFG, the Earth’s orbit. If 
the Earth be at E, the Sun at S, and the planet at D, the 
Sun and the planet will be both on the fame fide of the 
Vol. II. No. 78. 
net, and confequently for the planet and the Sun to be on 
oppofite (ides of the Earth, or the planet to be in oppofi- 
tion; thus, if, when the Earth is at E, Mars be at A, he is 
then in oppolition to the Sun. A fuperior planet is in qua¬ 
drature with the Sun, when its geocentric place is ninety 
degrees from the geocentric place of the Sun. If the 
Earth be at E, and Mars at B or C, he is in quadrature 
with the Sun; tor the lines AE, EB, form a right angle, 
as do alio the lines EA, EC. 
As the Earth goes round the Sun in lefs time, and in a 
lefs orbit, than any of the fuperior planets, it will not be 
amifs to luppofe a fuperior planet to fiand ftill in fome part 
of its orbit, while the Earth goes once round the Sun ia 
her’s, and confider the appearances the planets would then 
have, which are thefe: 1. While the Earth is in her mod 
diftant femicircle, the apparent motion of the planet would 
be direcl. 2. While the Earth is in her neareft femicircle, 
the planet would be retrograde. 3. While the Earth is 
near the points of contact of a line drawn front the planet, 
fo as to be a tangent to the Earth’s orbit, the planet would 
be fationary. 
To illuftrate this, let ABCDEFHG, in the following 
figure, be the orbit of the Earth; S, the Sun; PQVO, 
the orbit of Mars; LMNRT, an arc of the ecliptic. Let 
us now fuppofe the planet Mars to continue at P, while 
the Earth goes round in her orbit, according to the order 
of the letters ABC, &c. ABCDEFHG mav be conli- 
dered as fo many ftations, from whence an inhabitant of 
the Earth would view Mars at different times of the year ; 
and if ftraight lines be drawn, from each of thefe ftations, 
5 H through 
