1/4 
through that centre, and inclined in a certain 
direction to its orbit. Afterwards, they 
change more and more into ellipses, during 
one quarter of the planet’s annual revolution ; 
and all the superior conjunctions are then 
made above the planet’s centre, and the infe- 
rior conjunctions below it : during a second 
quarter of the planet’s revolution, these ellip- 
ses become narrower, the satellites are nearer 
the centre in their conjunctions, and at the 
end of a second quarter of the revolution, all 
the ellipses are again become right lines with 
equal inclination, but in a contrary direction. 
In the third quarter of the revolution, they 
are formed anew into ellipses, the superior 
conjunctions are made below the centre, and 
the inferior ones above ; lastly, in the fourth 
•quarter of the revolution, when the planet is 
returning to the same point of its orbit, these 
•ellipses again decrease in breadth, and all 
return to the first state. 4. The times of 
the superior and inferior conjunctions of the 
satellites being compared, their intervals are 
nearly equal to their semirevolution. 
Since, then, the satellites uniformly de- 
scribe orbits nearly circular or elliptical, with 
their respective primary at their centre or 
focus, they are probably moved by a force of 
the same nature with that which moves their 
planets round the Sun ; that is, they revolve 
about their primaries in consequence of a cen- 
tral force, and of a constant impulsive force : 
if so (which indeed observations render cer- 
tain), they must follow Kepler’s two rules 
namely, 1. The satellites must describe 
areas of their orbits proportional to the 
times; 2. Their mean distances from the 
centres of their respective primaries, must be 
as the cube-roots of the squares of the 
times 7 of their revolutions. 
The time of a synodic revolution of a satel- 
lite may be found in the following manner : 
Observe, when the primary planet is in op- 
position, the passage of a satellite over its 
body ; and mark the time when it is half-way 
•between the two opposite edges of the planet’s 
<lisc, for then it will be nearly in conjunction 
with the centre of the planet, and also in 
conjunction with the Sun. After a long space 
of time, observe again when the primary pla- 
net is in opposition, and the secondary in 
conjunction with its centre ; and divide the 
intervening space of time between the two 
observations, by the number of conjunctions 
of the Sun in that space, the quotient is the 
time of a synodic revolution. Or, the same 
thing may be found by means of the eclipses 
of the satellite : Observe when the satellite 
enters the shadow of its primary, called its 
immersion ; or when it comes out of the 
shadow, called its emersion ; and after a very 
long interval of time, when an eclipse hap- 
pens as nearly as possible in the same situa- 
tion both with respect to the node and to the 
place of the primary planet, again mark the 
time of the emersion or immersion (which- 
ever was used in the former observation) ; 
and from the interval of these times, and the 
number of eclipses in that interval, the mean 
time of a synodic revolution will be obtained 
by division. 
' ‘To determine the time of a periodic revolu- 
tion, it must be considered, that in the return 
of a satellite to its mean conjunction, it de- 
scribes a revolution in its orbit, together with 
the main angle m, described by the primary 
planet in that time.: hence this analogy, As 
ASTRONOMY. 
360° + m : 360 : : time of a synodic revolu- 
tion : the time of a periodic revolution. 
The distauce of a satellite from its primary 
may be easily found by means of its greatest 
elongation, as seen from the earth, in the fol- 
lowing manner *. let S (fig. 9) represent the 
Sun, E the Earth, P any planet, one of its sa- 
tellites at A, and the angle of elongation PEA 
a maximum ; then the distances P E and 
E S are known from the theory ot the planet, 
and the time of observation ; and since the 
angle P E A is known in the right-angled tri- 
angle A E P, also the side P E, the side A P 
is readily obtained. After the same manner, 
when the earth and planetare in any other situa- 
tions, e, p, and the satellite at a at its greatest 
elongation, find e p by the theory of the earth 
and planet, and the given time, whence from 
the angle of elongation pea, determine the 
distance p a. Make a series of such observa- 
tions at all suitable opportunities, and calcu- 
late ap or A P from each of them ; for thus 
we may ascertain the greatest and least dis- 
tance of the satellite from its primary, and 
half the difference of these will give the ec- 
centricity of the orbit. These elements, if 
not determined accurately, may be corrected 
by subsequent observations. 
The distances of a satellite from the centre 
of its primary may also be found, by measur- 
ing with a micrometer, at the time of the sa- 
tellite’s greatest elongation, its distance from 
the centre of the planet, also the semidiameter 
of the planet : for then the distance is known 
in terms of that semidiameter. Or, if the 
planet and satellite cannot at once be brought 
into the field of view of a telescope (which 
mav sometimes happen), the distance of the 
satellite may be measured, at its greatest 
elongation, by observing the time of the pas- 
sage of the planet’s disc over a wire adjusted 
as an hour circle in the field of a telescope ; 
and comparing it with the interval between 
the passage of the planet’s centre, and that of 
the satellite. To give this method the greatest 
degree of accuracy, the observations should 
be repeated so long as the interval from the 
passages of the planet to that of the satellite 
continues increasing ; for when it begins to 
decrease, the satellite will have passed its 
greatest elongation. The methods given in 
this article, may also be applied to the deter- 
mination of the distances when in the apsides, 
the excentricity, and the greatest equation, 
by means of a long series of observations. 
* Or, when the periodic times of all the sa- 
tellites of a planet are known, and the mean 
distance of one of them ; the mean distances 
of the others may be found from the propor- 
tion between the squares of the periodic 
times, and the cubes of the distances. And, 
on the contrary, if the relative distances of all 
the satellites from their primary be known, 
and the periodic time of one of them, the 
periodic times of the others may be found by 
the same proportion. 
The eclipses of the satellites are of consi- 
derable importance to astronomy and geo- 
graphy ; it therefore becomes requisite to ex- 
plain them. To this end, let S (fig. 10) be 
the Sun ; E e the orbit of the Earth ; P the 
place of the planet ; v s o the orbit of a satel- 
lite ; then, it is evident, that whenever the 
satellite, in its orbit, passes through the sha- 
dow of the primary, its light is obscured, and 
it becomes eclipsed. The duration of the 
eclipse will depend upon the obliquity of the 
satellite’s orbit to that of the planet, and the 
distance of the satellite from the node : foi j 
(fig. 11) a less proportion in n of the inclined 
orbit will pass through the shadow O I m n, 
than if tiie orbit coincided with O N ; and j 
in the nodes the satellite is both in its own 
orbit, and that of the planet, and n m be- 1 
comes equal to O I. Now (fig. 10), when 1 
the earth is at E before the opposition ot the I 
planet, the spectator will see the immersion at I 
i, and in some particular instances, the emer- I 
sion at o also: when the earth is at e after j 
opposition, an observer will see the emersion j 
at o ; but whether he sees the immersion, 1 
will depend upon the position of the earth J 
with respect to the plane of the planet’s or- J 
bit. When the earth is at E, the conjunction 
of the satellite happens later at the earth j 
than at the Sun ; but when it is at e, the con- J 
junction occurs later at the Sun than at the j 
earth. If the earth be at e, and the satellite 
at v, it cannot be seen by an observer at e, 
because the body of the planet intervenes ; j 
this is not an eclipse, but an occultation. In J 
order to find the diameter of the planet’s 
shadow at the distance of any 7 of the satellites, . 
let the time of an eclipse (that is, the time 
occupied from the immersion to the emer- 
sion) be observed wfiien the satellite is in one of 
its nodes ; for then the satellite passes through 
the centre of the shadow, and the eclipse is 
called central : then use this analogy, As the 
time of a synodic revolution ot the satellite : 
the duration of the eclipse : : 360° : the dia-i 
meter of the shadow, in degrees of the satel- 
lite’s orbit. But should it so happen that 
both the immersion and emersion cannot be 
seen when the satellites are in the nodes, 
which is always the case with the first and! 
second of Jupiter's satellites, then it is usual to 
compare the immersions some days before 
the opposition of the planet, with the emer- 
sions some days after ; and hence, knowing 
how many 7 synodic revolutions have been made 
in the intervening time, the time of the trail* 
sit through the shadow, and consequently the 
corresponding measure in degrees, becomej 
known. 
The eclipses of the satellites afford us a 
manifest proof of the velocity of light. For, if! 
the motion of light were infinite, or if it came 
to us from immense distances in an instant, itj 
is evident we should see the commencement! 
of an eclipse of a satellite at the same moment, 
whatever distance we might be from it ; but, 
on the contrary, if light move progressively, 
then it is equally evident, that the farther we 
are from a planet, the later it will be befori 
we perceive the beginning ot an eclipse ot one 
of its satellites, because the light will occupy 
a longer time in travelling to us. M. Roemei 
was the first who deduced, from actual ob- 
servations, the real velocity of light : he found' 
(and it has since been confirmed by repeatea 
experiments) that when the earth is exactly 
between Jupiter and the Sun, his satellites 
are seen eclipsed about 8^ minutes sooned 
than they would be according to the tables a 
but that when the earth is at its greatest dis-j 
tance from Jupiter, these eclipses happen 
about 84 minutes later than the tables predied 
them. Hence it follows that light takes ud 
about 16^ minutes of time in passing oyer thd 
diameter of the earth’s orbit, which is, at j 
mean, 190 millions of miles ; this is very nearly 
at the astonishing rate of 200,000 miles in a 
second. Dr. Bradley found very nearly ttu 
