horizon, and to keep him in view for some 
minutes after he is really set below it. _ The 
effect of this refraction is about six minutes 
every day at a mean rate. 
From the same cause, the heavenly bodies 
appear higher than they really are, so that to 
bring the apparent altitudes to the true ones, 
the quantity of refraction must be subtracted. 
The higher they rise the less are the rays 
refracted, and when the heavenly bodies are 
in the. zenith, they suffer no refraction, ac- 
cording to the principles of optics hereafter 
to be demonstrated. Tables of refractions 
have been calculated by various astronomers, 
as sir I. Newton, Mr. Thomas Simpson, Dr. 
Bradley, Mr. Mayer, &c. The following 
specimen is taken from Dr. Bradley’s table, 
which is esteemed the most correct, and 
chiefly used by astronomers. For the 
method of calculating these tables, see Mr. 
Simpson’s Dissert, p. 46, 4to. Gregory’s 
Astron. Vol. I. Pa. 66, and Vince’s Astron. 
Vol. I. 4to. ch. 7. 
MEAN ASTRONOMICAL REFRACTIONS 
IN ALTITUDE. 
App 
Alt. 
Refrac- 
tion. 
A PP 
Alt. 
Refrac- 
tion. 
App 
Alt. 
Refrac- 
tion. 
0° 
33' 
O'' 
22° 
2' 
20" 
44° 
0' 
59" 
1 
24 
29 
23 
2 
14 
45 
0 
57 
2 
18 
35 
24 
2 
7 
48 
0 
51 
3 
14 
36 
25 
2 
2 
50 
0 
48 
4 
11 
51 
26 
1 
56 
52 
0 
44 
5 
9 
54 
27 
1 
51 
55 
0 
40 
6 
8 
28 
28 
1 
47 
58 
0 
35 
7 
7 
20 
29 
1 
42 
60 
0 
S3 
8 
6 
29 
30 
1 
38 
62 
0 
30 
9 
5 
48 
31 
1 
35 
65 
0 
26 
10 
5 
15 
32 
1 
31 
68 
0 
23 
11 
4 
47 
33 
1 
28 
70 
0 
21 
12 
4 
23 
34 
1 
24 
72 
0 
18 
13 
4 
3 
35 
1 
21 
75 
0 
15 
14 
3 
45 
36 
1 
18 
78 
0 
12 
15 
3 
30 
37 
1 
16 
80 
0 
10 
16 
3 
17 
38 
I 
13 
82 
0 
8 
17 
3 
4 
39 
1 
10 
85 
0 
5 
18 
2 
54 
40 
1 
8 
88 
0 
2 
19 
2 
45 
41 
1 
5 
89 
0 
1 
20 
2 
35 
42 
1 
3 
90 
0 
3 
21 
2 
27 
43 
1 
1 
Dr. Keill, in his Lectures on Astronomy, 
observes, that it is entirely owing to the at- 
mosphere that the heavens appear bright in 
the day time. For without it, only that part 
of the heavens would be luminous in which 
the sun is placed ; and if we could live with- 
out air, and should turn our backs to the sun, 
the whole heavens would appear as dark as 
in the night. In this case also we should 
have no twilight, but a sudden transition from 
the brightest sun-shine to dark night immedi- 
ately upon the setting of the sun ; which 
would be extremely inconvenient, if not 
fatal to the eyes of mortals. See Keill’s 
Astron. Lect. xx. 
The twilight is longest in a parallel sphere, 
and shortest in a right sphere : and in an 
oblique sphere, the nearer the sphere ap- 
proaches to parallel, the longer is the twilight. 
In a parallel sphere, the twilight will con- 
tinue till the sun’s declination toward the de- 
pressed pole is 1 8° : but in this sphere his 
declination is never more than 23% degrees ; 
whence the twilight will only cease, whilst 
the sun’s decimation is increasing from 18° 
to 23% degrees, and decreasing again till in 
ASTRONOMY. 
its decrease it becomes 18 degrees. The 
twilight is here caused by the annual motion 
of the earth. In a right sphere, the sun ap- 
pears to be carried, by the daily motion of 
the earth, in circles perpendicular to the 
horizon ; whence it is carried directly down- 
wards by the whole daily motion, and will 
arrive at 18 degrees below the horizon the 
soonest possible: whereas, in an oblique 
sphere, its path is oblique to the plane ot 
the horizon, and therefore will be longer 
before it has descended 18 degrees below the 
horizon : and the difference of the time of 
twilight will increase with the degree of ob- 
liquity. As the sun sets more obliquely at 
some parts of the year than others, the twi- 
light varies in its duration. 
Of the Seasons. It is the annual motion 
of the earth round the sun, which occasions 
the diversity of seasons. To understand 
this, it must be remembered, that the axis 
of the earth is inclined to the plane of its 
orbit about 23 % degrees, and it keeps always 
parallel to itself ; that is, it is always directed 
to the same point of the heavens. 
The obliquity of the ecliptic is not perma- 
nent, but is perpetually diminishing, by the 
ecliptic approaching nearer to a parallelism 
with the equator, at the rate of about half 
a second in a year, or from 50 seconds to 
55 seconds in a hundred years. The incli- 
nation at this time is rather less than 23 de- 
grees, 28 minutes. The diminution of the 
obliquity of the ecliptic to the equator is 
owing to the action of the planets upon the 
earth, especially the planets Venus and Ju- 
piter. The obliquity of the ecliptic is found 
by observing with great accuracy the me- 
ridian altitude of the sun’s centre, on the 
days of the summer and winter solstice : then 
the difference of the two, will be the distance 
between the tropics ; the half of which is 
the obliquity sought. 
Let Fig. 6, Plate Astronomy, represent the 
earth in different parts of its elliptic orbit. 
In the spring, the circle which separates 
the light from the dark side of the globe, 
called the terminator, passes through the 
poles as appears in the position A. r l he 
earth then, in its diurnal rotation about its 
axis, has every part of its surface as long in 
light as in shade; therefore the days are 
equal to the nights all over the world, the 
sun being at that time vertical to the equa- 
torial parts of the earth. 
As the earth proceeds in its orbit, and 
comes into the position B, the sun becomes 
vertical to those parts of the earth under the 
tropic, and the inhabitants of the northern 
hemisphere will enjoy summer, on account 
of the solar rays falling more perpendicu- 
larly upon them; they will also have their 
days longer than their nights, in proportion 
as they are more distant from the equator ; 
and those within the polar circle, as will be 
perceived by the figure, will have constant 
day-light. At the same time, the .inhabit- 
ants of the southern hemisphere have win- 
ter, their days being shorter than their 
nights, in proportion as they are farther from 
the equator ; and the inhabitants of the polar 
regions will have constant night. 
The earth then continues its course to the 
position C, when the terminator again passes 
through the poles, and the days and nights 
are equal. 
After this, the earth advances to the 
Y 2 
171 
position D, at which time the inhabitants of 
the northern hemisphere have winter, and 
their days are shorter than their nights. 
The positions B and D, are the solstitial 
points ; and A and C, the equinoctial points; 
they are not equidistant from each other, 
because the sun is not in the centre, but in 
the focus of the ellipsis. In summer, when 
the earth is at B, the sun is farther from it 
than in the winter, when the earth is at D ; 
and in fact, tire diameter of the sun^ appears 
longer in winter than in summer. The dif- 
ference of heat is not owing to the sun’s being 
nearer to us, or more remote, but to the de- 
gree of obliquity with which its rays strike 
any part of the earth. 
Of the Moon. The moon is, next to the 
sun, the most remarkable of the celestial 
objects. Its form is spherical, like that of 
the earth, round which it revolves, and by 
which it is carried round the sun. Its orbit 
is also elliptical, having the earth in one of 
the foci of the ellipsis. ’The moon always 
keeps the same side towards the earth, shew- 
ing only at one time a little more of one side, 
and at another time a little more of the 
other. Hence as the moon revolves about 
its axis, its periodical time must be equal to 
that of its revolution in its orbit round the 
earth. This is found to be the case with 
the fifth satellite of Saturn as it regards its 
primary. And though the year is ot the 
same absolute length, both to the earth and 
moon, yet the number of days in each is 
very different : the former having 365| na- 
tural days in its year, but the latter has 
only about 12%, every day and night in the 
moon being as long as 29 a on the earth. 
The face of the moon, as seen through a 
telescope, appears diversified with hills and 
valleys. This is proved by viewing her at 
any other time than when she is full ; for 
then there is no regular line bounding light 
and darkness; but the edge or border of the 
moon appears jagged ; and even in the dark 
part near the borders of the lucid surface, 
there are seen some small spaces enlightened 
by the sun’s beams. 
Besides, it is moreover evident, that the 
spots in the moon taken for mountains and 
valleys, are really such from their shadows. 
For in all situations of the moon, the ele- 
vated parts are constantly found to cast a 
triangular shadow in a direction from the 
sun; and the cavities are always dark on the 
side next to the sun, and illuminated on the 
opposite side. Hence astronomers are en- 
abled to find the height of the lunar moun- 
tains. Dr. Iveill, in his Astronomical Lec- 
tures, has calculated the height of St. Cathe- 
rine’s hill to be nine miles. Since, how- 
ever, the loftiest mountains upon the earth 
are but about three miles in height, it ha* 
been long considered as very improbable 
that those of a planet so much inferior in 
size to the earth should exceed in such vast 
proportion the highest of our mountains. 
By the observations of Dr. Herschel, 
made in November, 1779, and the four fol- 
lowing months, we learn, that the altitude 
of the lunar mountains has been very much 
exaggerated. His observations were made 
with great caution, by means of a New- 
tonian reflector, six feet eight inches long, 
and with a magnifying power of 222 times, 
determined by experiment ; and the method 
which he made use of to ascertain the alti- 
