ASTRONOMY. 
same velocity from observations on the fixed 
stars. Hence also it appears, that in deter- 
mining the time of an eclipse of a satellite as 
seen from the earth, an allowance must be 
made, corresponding with the different dis- 
tances of the earth and planet ; this allow- 
ance is called the equation ot light. 
The satellites of Jupiter, Saturn, and Her* 
schel, are subject to changes in their orbits, 
with respect to the situation of the apsides 
and nodes, the inclination of their orbits, their 
excentricity, &c. similar to those of the moon, 
and from similar causes. But in many in- 
stances they prevail to a greater degree, in 
consequence of the disturbing forces of the 
satellites upon each other; hence, therefore, 
a frequent revision of the tables is necessary. 
The satellites of Jupiter, being situated 
nearer to the earth than those of any other 
planet, and being of very considerable im- 
portance in astronomy and navigation, have 
been more regularly and carefully observed 
than the other satellites ; in consequence of 
which the elements of their orbits are deter- 
mined with greater precision than those of the 
other satellites. The chief of these elements, 
as given by M. de Lalande, are exhibited in 
the following table. 
SATELLITES OF JUPITER. 
S 
o ° o o , 
| <D 00 CM 00 j£ 
o ^ 'O 'sO ^ ^ 
^ cr co co cn Od 
^ ° 
o Q* 0 * 0 * 0 * 
rC <£> 
r— < 
-d </5 
g 
a -r . £ 00 
44 
£ > o oi ci 
Cl IS r-l 
« co co w cs 
CM 
^vo g 
6 ^ 
5 ‘O G CD 
a ^ id a 
« CO 01 N 02 
>obooao 
CD to CD CO 05 •cf 
HTjin'c on 
—i CO CD CM W CM 
CD 5 _ 
00 co « 25 
. cm n 
Ci »C 0-1 CM O 
V CM -1 
bpn 
6 
I- oc ^ 
Cd CM 
SC CO N N 
^ CO CO CO Cd C 1 ! 
to *0 
CO co 
cj ^ 
G G) 
I> CO 
B 
00 cc cc ^ ^ 
I CO CO CO CO cot 
Of Eclipses. 
The eclipses of the Sun and Moon are 
phenomena that command the attention even 
of the vulgar ; who have always retained a su- 
perstitious veneration for the science of astro- 
nomy, chiefly on account of the means it af- 
fords of foretelling events of this nature. And 
though in reality the knowledge required in 
calculating an eclipse does not essentially differ 
from that employed in determining the time 
of the rising and setting of the Sun or Moon, 
yet there is no doubt that a more particular 
attention to this subject will be acceptable to 
the reader. 
As the shadows of the Moon and Earth are 
the causes of eclipses, it will be necessary 
first to determine the figure of those shadows. 
Because the Sun, the Earth, and the Moon 
are spherical bodies, it follows that the sha- 
dows of the two latter must be either' conical 
or cylindrical ; that is to say (lag. 12), if the 
Sun I K be less than the Earth C D, the shadow 
of the latter will be part of a cone, whose sec- 
tion is terminated by the lines C E, D F, and 
whose base is indefinitely distant : or, if the 
Suit A B be equal to the Earth C D, the shadow 
will be a cylinder between the lines C G, D H, 
whose base is indefinitely distant. In either 
case the shadows of the Earth must occasion- 
ally fall upon and eclipse the superior planets, 
when in opposition to the Sun. But this never 
happens ; and therefore the Sun is neither less 
than, nor equal to, the Earth, but greater. 
We know moreover, from the Sun’s parallax, 
that it is much greater than the Earth ; because 
the Sun’s diameter seen from the Earth is 
about 32 minutes, whereas the Earth’s diame- 
ter seen from the Sun is only about 17 
seconds, a quantity that may be regarded as 
insensible or inconsiderable in many obser- 
vations. And since the Sun exceeds the 
Earth in so high a proportion, it must of ne- 
cessity be yet greater with regard to the 
Moon, because this last is less than the Earth. 
Let A B (fig. 13) represent the Sun greater 
than the Earth C D. The rays of light A C, 
B D, passing from the extreme edges of the 
Sun, and in contact with the Earth on the 
same side, will afterwards meet or cross in 
the point K. No part of the Sun’s light will 
appear within the cone C K D ; which is there- 
fore the shadow in which an observer, being 
placed, would be totally deprived of the Sun. 
But there will be a partial shadow or penum- 
bra between those rays AD M, B C L, that 
pass from the extreme edges of the Sun, and 
touch the opposite extremes of the Earth ; 
that is to say, an observer between the lines 
C Land D M,. but without the dark cone, 
C K D, will see only a part of the Sun, the 
rest being hidden by the interposition of the 
Earth: the quantity of the Sun thus obscured 
will be greater, and the penumbra darker, the 
nearer the observer is placed to the coneCK D. 
Lastly, if the observer be situated beyond the 
vertex of the dark shadow K, between the 
lines K N, K O, formed by the continuation 
of the extreme rays, he will behold the ex- 
terior parts of the Sun forming a lucid ring, 
environing the Earth on all sides. 
The angle C K D, at the vertex of the 
Earth’s shadow, is (by Euclid I. 32) equal to 
the difference between the diameter of the 
Sun seen from the Earth, or angle AC B, and 
the diameter of the Earth seen from the Sun, 
or angle C B D, Or, if the earth’s apparent 
1/3 
diameter from the Sun be rejected as inconsi- 
derable, the angle of the shadow will be equal 
to the Sun’s apparent diameter. 
The angle C I D, at the vertex of the pe- 
numbra, is equal to the sum of the diameter of 
the Sun seen from the Earth, or angle A C B, 
and the diameter of the Earth seen from the 
Sun, or angle CAD: or, it the Earth’s appa- 
rent diameter from the Sun be rejected as 
inconsiderable, the angle of the penumbra is 
equal to the Sun’s apparent diameter. Every 
thing that has been here shewn respecting the 
shadows of the Earth, is true in l.ke circum- 
stances of the Moon. 
To apply these observations to the facts, let 
A B (lig. 14) represent the Sun, C D the 
Earth, and I K or L the Moon in its orbit 
K M N ; let the Moon be at 1 K, between 
the Sun and the Earth ; its total shadow may 
then entirely deprive a part ot the Earth at 0 
of the Sun’s light, and its penumbra will cause 
a partial eclipse of the Sun to the inhabitants, 
between G and H. Again, suppose the Moon 
to be at L, and it will itself be eclipsed by the 
interposition of the Earth, between it and the 
Sun. In lunar eclipses, the Earth’s penumbra 
is not attended to, because its effects in ob- 
scuring the Moon cannot be observed with, 
precision by a spectator placed on the Earth. 
Eclipses can only happen when the Moon 
is near one of the nodes of its orbit. Let ABM 
(fig. 15) represent the Sun, viewed from the 
Earth ; C D a portion of the ecliptic, or Sun’s 
apparent path ; and E F a part of the orbit of 
the Moon, which planet is represented at 
different times by the circles G, H, I. It is 
evident, that the eclipse or obscuration of the 
Sun entirely depends on the position of the 
node N, and the angle of inclination F N D. 
If the angle of inclination remain unaltered 
while the node N is very remote from the 
centre K of the Sun, the points K and L may- 
be farther apart than to permit any occulta- 
tion or apparent contact; and it is clear, that 
an enlargement of the angle F N D may pro- 
duce the same effect: on the contrary, an 
approach or coincidence of N with K, or a di- 
minution of the angle F N K, may cause an 
eclipse, the quantity of obscuration in which 
will be so much greater, as these circum- 
stances are more prevalent. 
The Sun’s place Iv in the ecliptic being 
known from tables, together with the inclina-- 
nation of the Moon’s orbit, the place ot the 
node, and of the Moon itself, and likewise the* 
apparent diameters of the luminaries respec- 
tively, it will be easy to find the velocity of 
the Moon in elongation, and consequently 
the beginning, middle,.end, quantity of obscu- 
ration, and other requisites, concerning the 
eclipse. If the computation be made from 
the tabular places of the heavenly bodies, ther 
result will give the eclipse as seen from the 
centre of the Earth; because, in all tables 
where the Earth is spoken of, that centre is 
meant, except otherwise mentioned. But it 
is required to determine the particulars of the 
eclipse for a given place on the Earth’s surface,, 
and this includes the consideration of paral- 
lax. The Sun’s parallax Vicing very minute 
may in this, and most other cases, be reject- 
ed: but the Moon’s parallax is so great, that 
it is at least of as much consequence as any 
other element whatever. For, on this ac- 
count, the Moon’s apparent path, as seem 
from the surface of the Earth, is so different; 
from that which it would have when beheld 
