the diagonal?
8. (Pg. 73) What portion of a year is represented by the three diagonals
in the figure?
9. (Pg. 73) How will what you have learned respecting motion in a curve,
apply to the earth's motion?
10. (Pg. 73) In what form are you directed to cut a piece of card to aid
in illustrating the two forces acting upon the earth?
11. (Pg. 73) How must you apply it to this purpose? (fig. 2. plate 6.)
12. (Pg. 73) If these two forces did not exactly balance each other,
what would result?
13. (Pg. 73) Does the earth revolve in a circular orbit?
14. (Pg. 73) What results from its motion in an ellipsis?
15. (Pg. 74) What is represented by the lines A C, A B, in fig. 3. plate
6?
16. (Pg. 74) Were the projectile force to carry the earth from B to D,
(fig. 3.) what would result?
17. (Pg. 74) When it has arrived at E, what angle will be formed by the
lines representing the two forces?
18. (Pg. 74) What effect will the accelerated motion then produce?
19. (Pg. 75) What is the form of the earth's orbit, and what
circumstances produce this form?
20. (Pg. 75) What is the consequence as regards the regularity of the
earth's motion?
21. (Pg. 75) What law governs as regards the spaces passed over, and how
is this explained by fig. 4. plate 6?
22. (Pg. 75) What is meant by _perihelion_, and by _aphelion_?
23. (Pg. 75) What is the difference of the distance of the earth from
the sun, in these two points?
24. (Pg. 76) At what season of the year is it nearest to, and at what
furthest from the sun?
25. (Pg. 76) What is the mean distance of the earth from the sun?
26. (Pg. 76) Why is but little effect produced, as regards temperature,
by the change of distance?
27. (Pg. 76) Has it any influence on the sun's apparent size?
28. (Pg. 76) Are the summer and winter, half years, of the same length;
what is their difference, and what is the cause?
29. (Pg. 76) What are the planets?
30. (Pg. 77) What circumstances render it probable that they are
habitable globes?
31. (Pg. 77) What is believed respecting the fixed stars?
32. (Pg. 77) What discoveries have been made in the moon?
33. (Pg. 77) What prevents our seeing the planets, if there are any,
which revolve round the fixed stars?
34. (Pg. 77) What prevents our seeing the stars and planets in the
day-time?
35. (Pg. 78) What other motions have the earth and planets, besides that
in their orbits?
36. (Pg. 78) What is the imaginary line called, round which they
revolve?
37. (Pg. 78) How does this occasion night and day?
38. (Pg. 78) In what direction does the earth turn upon its axis, and
what apparent motion of the sun, moon, and stars is thereby produced?
39. (Pg. 79) What must be the appearance of the earth to an inhabitant
of one of the planets?
40. (Pg. 79) What the appearance of the sun to the inhabitants of
planets in other systems?
41. (Pg. 79) What the appearance of the earth to an inhabitant of the
moon?
CONVERSATION VII.
OF THE PLANETS.
OF THE SATELLITES OR MOONS. GRAVITY DIMINISHES AS THE SQUARE OF THE
DISTANCE. OF THE SOLAR SYSTEM. OF COMETS. CONSTELLATIONS, SIGNS OF THE
ZODIAC. OF COPERNICUS, NEWTON, &c.
MRS. B.
The planets are distinguished into primary and secondary. Those which
revolve immediately about the sun are called primary. Many of these are
attended in their course by smaller planets, which, revolve round them:
these are called secondary planets, satellites, or moons. Such is our
moon which accompanies the earth, and is carried with it round the sun.
_Emily._ How then can you reconcile the motion of the secondary planets
to the laws of gravitation; for the sun is much larger than any of the
primary planets; and is not the power of gravity proportional to the
quantity of matter?
_Caroline._ Perhaps the sun, though much larger, may be less dense than
the planets. Fire you know, is very light, and it may contain but little
matter, though of great magnitude.
_Mrs. B._ We do not know of what kind of matter the sun is made; but we
may be certain, that since it is the general centre of attraction of our
system of planets, it must be the body which contains the greatest
quantity of matter in that system.
You must recollect, that the force of attraction is not only
proportional to the quantity of matter, but to the degree of proximity
of the attractive body: this power is weakened by being diffused, and
diminishes as the distance increases.
_Emily._ Then if a planet was to lose one-half of its quantity of
matter, it would lose one half of its attractive power; and the same
effect would be produced by removing it to twice its former distance
from the sun; that I understand.
_Mrs. B._ Not so perfectly as you imagine. You are correct as respects
the diminution in size, because the attractive force is in the same
proportion as the quantity of matter; but were you to remove a planet to
double its former distance, it would retain but one-fourth part of its
gravitating force; for attraction decreases not in proportion to the
simple increase of the distance, but as the squares of the distances
increase.
_Caroline._ I do not exactly comprehend what is meant by the squares, in
this case, although I know very well what is in general intended by a
square.
_Mrs. B._ By the square of a number we mean the product of a number,
multiplied by itself; thus two, multiplied by two, is four, which is
therefore the square of two; in like manner the square of three, is
nine, because three multiplied by three, gives that product.
_Emily._ Then if one planet is three times more distant from the sun
than another, it will be attracted with but one-ninth part of the force;
and if at four times the distance, with but one-sixteenth, sixteen being
the square of four?
_Mrs. B._ You are correct; the rule is, that _the attractive force is in
the inverse proportion of the square of the distance_. And it is easily
demonstrated by the mathematics, that the same is the case with every
power that emanates from a centre; as for example, the light from the
sun, or from any other luminous body, decreases in its intensity at the
same rate.
_Caroline._ Then the more distant planets, move much slower in their
orbits; for their projectile force must be proportioned to that of
attraction? But I do not see how this accounts for the motion of the
secondary, round the primary planets, in preference to moving round the
sun?
_Emily._ Is it not because the vicinity of the primary planets, renders
their attraction stronger than that of the sun?
_Mrs. B._ Exactly so. But since the attraction between bodies is
mutual, the primary planets are also attracted by the satellites which
revolve round them. The moon attracts the earth, as well as the earth
the moon; but as the latter is the smaller body, her attraction is
proportionally less; therefore, neither the earth revolves round the
moon, nor the moon round the earth; but they both revolve round a point,
which is their common centre of gravity, and which is as much nearer to
the earth than to the moon, as the gravity of the former exceeds that of
the latter.
_Emily._ Yes, I recollect your saying, that if two bodies were fastened
together by a wire or bar, their common centre of gravity would be in
the middle of the bar, provided the bodies were of equal weight; and if
they differed in weight, it would be nearer the larger body. If then,
the earth and moon had no projectile force which prevented their mutual
attraction from bringing them together, they would meet at their common
centre of gravity.
_Caroline._ The earth then has a great variety of motion, it revolves
round the sun, round its own axis, and round the point towards which the
moon attracts it.
_Mrs. B._ Just so; and this is the case with every planet which is
attended by satellites. The complicated effect of this variety of
motions, produces certain irregularities, which, however, it is not
necessary to notice at present, excepting to observe that they
eventually correct each other, so that no permanent derangement exists.
The planets act on the sun, in the same manner as they are themselves
acted on by their satellites; for attraction, you must remember, is
always mutual; but the gravity of the planets (even when taken
collectively) is so trifling compared with that of the sun, that were
they all placed on the same side of that luminary, they would not cause
him to move so much as one-half of his diameter towards them, and the
common centre of gravity, would still remain within the body of the sun.
The planets do not, therefore, revolve round the centre of the sun, but
round a point at a small distance from its centre, about which the sun
also revolves.
_Emily._ I thought the sun had no motion?
_Mrs. B._ You were mistaken; for besides that round the common centre of
gravity, which I have just mentioned, which is indeed very
inconsiderable, he revolves on his axis in about 25 days; this motion is
ascertained by observing certain spots which disappear, and reappear
regularly at stated times.
[Illustration: PLATE VII.]
_Caroline._ A planet has frequently been pointed out to me in the
heavens; but I could not perceive that its motion differed from that of
the fixed stars, which only appear to move.
_Mrs. B._ The great distance of the planets, renders their apparent
motion so slow, that the eye is not sensible of their progress in their
orbits, unless we watch them for some considerable length of time: but
if you notice the nearness of a planet to any particular fixed star, you
may in a few nights perceive that it has changed its distance from it,
whilst the stars themselves always retain their relative situations. The
most accurate idea I can give you of the situation and motion of the
planets in their orbits, will be by the examination of this diagram,
(plate 7. fig. 1.) representing the solar system, in which you will find
every planet, with its orbit delineated.
_Emily._ But the orbits here are all circular, and you said that they
were elliptical. The planets appear too, to be moving round the centre
of the sun; whilst you told us that they moved round a point at a little
distance from thence.
_Mrs. B._ The orbits of the planets are so nearly circular, and the
common centre of gravity of the solar system, so near the centre of the
sun, that these deviations are too small to be represented. The
dimensions of the planets, in their proportion to each other, you will
find delineated in fig. 2.
Mercury is the planet nearest the sun; his orbit is consequently
contained within ours; his vicinity to the sun, prevents our frequently
seeing him, so that very accurate observations cannot be made upon
Mercury. He performs his revolution round the sun in about 87 days,
which is consequently the length of his year. The time of his rotation
on his axis is not known; his distance from the sun is computed to be 37
millions of miles, and his diameter 3180 miles. The heat of this planet
is supposed to be so great, that water cannot exist there but in a state
of vapour, and that even quicksilver would be made to boil.
_Caroline._ Oh, what a dreadful climate!
_Mrs. B._ Though we could not live there, it may be perfectly adapted to
other beings, destined to inhabit it; or he who created it may have so
modified the heat, by provisions of which we are ignorant, as to make it
habitable even by ourselves.
Venus, the next in the order of planets, is 68 millions of miles from
the sun: she revolves about her axis in 23 hours and 21 minutes, and
goes round the sun in 244 days, 17 hours. The orbit of Venus is also
within ours; during nearly one-half of her course in it, we see her
before sun-rise, and she is then called the morning star; in the other
part of her orbit she rises later than the sun.
_Caroline._ In that case we cannot see her, for she must rise in the day
time?
_Mrs. B._ True; but when she rises later than the sun, she also sets
later; so that we perceive her approaching the horizon after sun-set:
she is then called Hesperus, or the evening star. Do you recollect those
beautiful lines of Milton?
Now came still evening on, and twilight gray
Had in her sober livery all things clad;
Silence accompanied; for beast and bird,
They to their grassy couch, these to their nests
Were slunk, all but the wakeful nightingale;
She all night long her amorous descant sung;
Silence was pleas'd; now glowed the firmament
With living sapphires. Hesperus that led
The starry host, rode brightest, till the moon
Rising in clouded majesty, at length
Apparent queen unveil'd her peerless light,
And o'er the dark her silver mantle threw.
The planet next to Venus is the Earth, of which we shall soon speak at
full length. At present I shall only observe that we are 95 millions of
miles distant from the sun, that we perform our annual revolution in 365
days 5 hours and 49 minutes; and are attended in our course by a single
moon.
Next follows Mars. He can never come between us and the sun, like
Mercury and Venus; his motion is, however, very perceptible, as he may
be traced to different situations in the heavens; his distance from the
sun is 144 millions of miles; he turns round his axis in 24 hours and 39
minutes; and he performs his annual revolution, in about 687 of our
days: his diameter is 4120 miles. Then follow four very small planets,
Juno, Ceres, Pallas and Vesta, which have been recently discovered, but
whose dimensions, and distances from the sun, have not been very
accurately ascertained. They are generally called asteroids.
Jupiter is next in order: this is the largest of all the planets. He is
about 490 millions of miles from the sun, and completes his annual
period in nearly 12 of our years. He turns round his axis in about ten
hours. He is above 1200 times as big as our earth; his diameter is
86,000 miles. The respective proportions of the planets cannot,
therefore, you see, be conveniently delineated in a diagram. He is
attended by four moons.
The next planet is Saturn, whose distance from the sun, is about 900
millions of miles; his diurnal rotation is performed in 10 hours and a
quarter: his annual revolution is nearly 30 of our years. His diameter
is 79,000 miles. This planet is surrounded by a luminous ring, the
nature of which, astronomers are much at a loss to conjecture: he has
seven moons. Lastly, we observe the planet Herschel, discovered by Dr.
Herschel, by whom it was named the Georgium Sidus, and which is attended
by six moons.
_Caroline._ How charming it must be in the distant planets, to see
several moons shining at the same time; I think I should like to be an
inhabitant of Jupiter or Saturn.
_Mrs. B._ Not long I believe. Consider what extreme cold must prevail in
a planet, situated as Saturn is, at nearly ten times the distance at
which we are from the sun. Then his numerous moons are far from making
so splendid an appearance as ours; for they can reflect only the light
which they receive from the sun; and both light, and heat, decrease in
the same ratio or proportion to the distances, as gravity. Can you tell
me now how much more light we enjoy than Saturn?
_Caroline._ The square of ten is a hundred; therefore, Saturn has a
hundred times less--or to answer your question exactly, we have a
hundred times more light and heat, than Saturn--this certainly does not
increase my wish to become one of the poor wretches who inhabit that
planet.
_Mrs. B._ May not the inhabitants of Mercury, with equal plausibility,
pity us for the insupportable coldness of our situation; and those of
Jupiter and Saturn for our intolerable heat? The Almighty power which
created these planets, and placed them in their several orbits, has no
doubt peopled them with beings, whose bodies are adapted to the various
temperatures and elements, in which they are situated. If we judge from
the analogy of our own earth, or from that of the great and universal
beneficence of Providence, we must conclude this to be the case.
_Caroline._ Are not comets, in some respects similar to planets?
_Mrs. B._ Yes, they are; for by the reappearance of some of them, at
stated times, they are known to revolve round the sun; but in orbits so
extremely eccentric, that they disappear for a great number of years. If
they are inhabited, it must be by a species of beings very different,
not only from the inhabitants of this, but from those of any of the
other planets, as they must experience the greatest vicissitudes of heat
and cold; one part of their orbit being so near the sun, that their
heat, when there, is computed to be greater than that of red-hot iron;
in this part of its orbit, the comet emits a luminous vapour, called the
tail, which it gradually loses as it recedes from the sun; and the comet
itself totally disappears from our sight, in the more distant parts of
its orbit, which extends considerably beyond that of the furthest
planet.
The number of comets belonging to our system cannot be ascertained, as
some of them are several centuries before they make their reappearance.
The number that are known by their regular reappearance is, I believe,
only three, although their whole number is very considerable.
_Emily._ Pray, Mrs. B., what are the constellations?
_Mrs. B._ They are the fixed stars; which the ancients, in order to
recognise them, formed into groups, and gave the names of the figures,
which you find delineated on the celestial globe. In order to show their
proper situations in the heavens, they should be painted on the internal
surface of a hollow sphere, from the centre of which you should view
them; you would then behold them as they appear to be situated in the
heavens. The twelve constellations, called the signs of the zodiac, are
those which are so situated, that the earth, in its annual revolution,
passes directly between them, and the sun. Their names are Aries,
Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius,
Capricornus, Aquarius, Pisces; the whole occupying a complete circle, or
broad belt, in the heavens, called the zodiac. (plate 8. fig. 1.) Hence,
a right line drawn from the earth, and passing through the sun, would
reach one of these constellations, and the sun is said to be in that
constellation at which the line terminates: thus, when the earth is at
A, the sun would appear to be in the constellation or sign Aries; when
the earth is at B, the sun would appear in Cancer; when the earth was at
C, the sun would be in Libra; and when the earth was at D, the sun would
be in Capricorn. You are aware that it is the real motion of the earth
in its orbit, which gives to the sun this apparent motion through the
signs. This circle, in which the sun thus appears to move, and which
passes through the middle of the zodiac, is called the ecliptic.
_Caroline._ But many of the stars in these constellations appear beyond
the zodiac.
[Illustration: PLATE VIII.]
_Mrs. B._ We have no means of ascertaining the distance of the fixed
stars. When, therefore, they are said to be in the zodiac, it is merely
implied that they are situated in that direction, and that they shine
upon us through that portion of the heavens, which we call the zodiac.
_Emily._ But are not those large bright stars, which are called stars of
the first magnitude, nearer to us, than those small ones which we can
scarcely discern?
_Mrs. B._ It may be so; or the difference of size and brilliancy of the
stars may proceed from their difference of dimensions; this is a point
which astronomers are not enabled to determine. Considering them as
suns, I see no reason why different suns should not vary in dimensions,
as well as the planets belonging to them.
_Emily._ What a wonderful and beautiful system this is, and how
astonishing to think that every fixed star may probably be attended by a
similar train of planets!
_Caroline._ You will accuse me of being very incredulous, but I cannot
help still entertaining some doubts, and fearing that there is more
beauty than truth in this system. It certainly may be so; but there does
not appear to me to be sufficient evidence to prove it. It seems so
plain and obvious that the earth is motionless, and that the sun and
stars revolve round it;--your solar system, you must allow, is directly
in opposition to the evidence of our senses.
_Mrs. B._ Our senses so often mislead us, that we should not place
implicit reliance upon them.
_Caroline._ On what then can we rely, for do we not receive all our
ideas through the medium of our senses?
_Mrs. B._ It is true that they are our primary source of knowledge; but
the mind has the power of reflecting, judging, and deciding upon the
ideas received by the organs of sense. This faculty, which we call
reason, has frequently proved to us, that our senses are liable to err.
If you have ever sailed on the water, with a very steady breeze, you
must have seen the houses, trees, and every object on the shore move,
while you were sailing.
_Caroline._ I remember thinking so, when I was very young; but I now
know that their motion is only apparent. It is true that my reason, in
this case, corrects the error of my sight.
_Mrs. B._ It teaches you, that the apparent motion of the objects on
shore, proceeds from your being yourself moving, and that you are not
sensible of your own motion, because you meet with no resistance. It is
only when some obstacle impedes our motion, that we are conscious of
moving; and if you were to close your eyes when you were sailing on
calm water, with a steady wind, you would not perceive that you moved,
for you could not feel it, and you could see it only by observing the
change of place of the objects on shore. So it is with the motion of the
earth: every thing on its surface, and the air that surrounds it,
accompanies it in its revolution; it meets with no resistance:
therefore, like the crew of a vessel sailing with a fair wind, in a calm
sea, we are insensible of our motion.
_Caroline._ But the principal reason why the crew of a vessel in a calm
sea do not perceive their motion, is, because they move exceedingly
slow, while the earth, you say, revolves with great velocity.
_Mrs. B._ It is not because they move slowly, but because they move
steadily, and meet with no irregular resistances, that the crew of a
vessel do not perceive their motion; for they would be equally
insensible to it, with the strongest wind, provided it were steady, that
they sailed with it, and that it did not agitate the water; but this
last condition, you know, is not possible, for the wind will always
produce waves which offer more or less resistance to the vessel, and
then the motion becomes sensible, because it is unequal.
_Caroline._ But, granting this, the crew of a vessel have a proof of
their motion, which the inhabitants of the earth cannot have,--the
apparent motion of the objects on shore, or their having passed from one
place to another.
_Mrs. B._ Have we not a similar proof of the earth's motion, in the
apparent motion of the sun and stars? Imagine the earth to be sailing
round its axis, and successively passing by every star, which, like the
objects on land, we suppose to be moving instead of ourselves. I have
heard it observed by an aerial traveller in a balloon, that the earth
appears to sink beneath the balloon, instead of the balloon rising above
the earth.
It is a law which we discover throughout nature, and worthy of its great
Author, that all its purposes are accomplished by the most simple means;
and what reason have we to suppose this law infringed, in order that we
may remain at rest, while the sun and stars move round us; their regular
motions, which are explained by the laws of attraction, on the first
supposition, would be unintelligible on the last, and the order and
harmony of the universe be destroyed. Think what an immense circuit the
sun and stars would make daily, were their apparent motions, real. We
know many of them, to be bodies more considerable than our earth; for
our eyes vainly endeavour to persuade us, that they are little
brilliants sparkling in the heavens; while science teaches us that they
are immense spheres, whose apparent dimensions are diminished by
distance. Why then should these enormous globes daily traverse such a
prodigious space, merely to prevent the necessity of our earth's
revolving on its axis?