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Title: The Study of Astronomy - adapted to the capacities of youth
Author: Stedman, John Gabriel
Language: English
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*** Start of this LibraryBlog Digital Book "The Study of Astronomy - adapted to the capacities of youth" ***
[Illustration: _Plate I._
The COPERNICAN or SOLAR SYSTEM.
_The comparative Distances of the Planets from the Sun_
_T. Conder Sculp^t._]
THE
STUDY OF ASTRONOMY,
ADAPTED TO THE
CAPACITIES OF YOUTH:
_IN TWELVE FAMILIAR DIALOGUES_,
BETWEEN
A TUTOR AND HIS PUPIL:
Explaining the General PHÆNOMENA of the HEAVENLY
BODIES, the THEORY of the TIDES, &c.
_ILLUSTRATED WITH COPPER-PLATES._
BY JOHN STEDMAN.
_LONDON_:
PRINTED FOR C. DILLY, IN THE POULTRY.
M.DCC.XCVI.
------------------------------------------------------------------------
ERRATA.
Page 20. line 8. _for_ he _read_ the.
—— 22. — 6. ⎫
⎪
—— 23. — 2. ⎪ — disk — disc.
⎬
—— 42. — last ⎪
⎪
—— 79. — 5. ⎭
—— 74. — 6. — it axis — its axis.
—— 78. — 19. _dele_ Mercury.
------------------------------------------------------------------------
PREFACE.
It has long been a matter of surprize to those who are interested in the
education of youth, that, among the numerous publications intended for
their improvement, so few attempts have been made to facilitate the
study of Astronomy.
Many excellent treatises have been written on this important and useful
science; but if it be considered that they abound with technical terms,
unintelligible to juvenile minds, it cannot be expected that they should
derive any great advantage from the perusal of them.
To remove these difficulties, the Author has endeavoured, whenever he
had occasion to use them, to give such illustrations as to leave no
doubt on the young student’s mind respecting their true meaning.
The subject appeared to him to be best calculated for dialogues, which
are certainly more agreeable as well as more perspicuous to young
persons, than the discouraging formality of a treatise. And it is
presumed the language will be found natural and easy.
In the order he has chosen, he has been careful not to introduce any
thing new, till the former part, on which it depends, has been clearly
explained.
On the whole, it has been his aim to render it as concise and plain as
the nature of the subject will admit; and he flatters himself, that at a
time when the sciences are so universally studied, the introduction now
offered to the public will not be unacceptable.
------------------------------------------------------------------------
CONTENTS.
DIALOGUE I. p. 1.
Introduction. Definition. The sun and planets. A
globe defined. Sun’s distance and magnitude.
Planets, what; their names, periods, and
distances from the sun; their magnitudes,
compared with the earth; called inferior and
superior, why. Comets; derivation of the name.
Solar system; why so called.
DIALOGUE II. p. 10.
Different systems explained. Planets appear like
stars; they shine by reflection; how known
from stars; they never twinkle, why. Stars
shine with their own native light; their
inconceivable distance; are suns, the centers
of other systems. Plurality of worlds.
DIALOGUE III. p. 20.
The earth has the appearance of a star to Venus.
Remote objects appear at equal distances from
us. Our earth is a moon to the moon. The orb
of the moon visible soon after the change; her
disc and bulk compared with the earth; her
mean distance. Sun’s disc compared with hers.
Our sun a star, if seen from a planet of
another system. Stars as far from each other
as the nearest is to us. Stars distinguished
by their apparent magnitude. The Milky Way
innumerable stars. Number of stars visible at
one time to the naked eye.
DIALOGUE IV. p. 29.
Stars divided into constellations; necessary for
ascertaining the situation of the planets, and
of the stars with each other. Planets motion
regular if seen from the sun; irregular as
seen from the earth, the motion being
sometimes direct, sometimes retrograde; at
others they appear stationary. Superior and
inferior conjunction, and opposition, what.
Venus has the different phases of the moon.
Planets, how distinguished from each other.
DIALOGUE V. p. 39.
Ecliptic, what. Inclination of the orbits of the
planets. Nodes of the planets, what. A plane,
what. Planets move in unbounded space. Mercury
and Venus seen on the sun’s disc. Number of
signs in the zodiac. Zodiac, what. A degree,
what. Names of the signs. Number of degrees in
each sign. Sun’s place in the ecliptic. Table
of signs, their characters, &c. To find the
sun’s place in the ecliptic for any day in the
year.
DIALOGUE VI. p. 50.
The orbits of the planets are not true circles,
but somewhat elliptical. Perihelion, aphelion,
and mean distance, what. Attraction, what.
Laws of attraction. Attraction of gravitation,
its effects. Simple motion rectilineal.
Attractive or centripetal, and projectile or
centrifugal forces, what.
DIALOGUE VII. p. 61.
Bodies moving in circles have a tendency to fly
off. Planets kept in their orbits by the joint
action of the centripetal and centrifugal
forces; they describe equal areas in equal
times. Orbits of the comets very elliptical.
The earth in its perihelion in December.
Equation of time. Center of gravity, what; sun
and planets move round it. Sun the center of
the system.
DIALOGUE VIII. p. 73.
The earth revolves on its axis. Cause of day and
night. The motion of the earth so uniform as
not to be perceived. The apparent motion of
the sun caused by the earth’s motion on its
axis. An objection to the earth’s motion
answered. The sun and some of the planets
revolve on their axes. Atmosphere, what; cause
of twilight. Horizon, what; the sun and moon
appear largest near the horizon, why; they
appear above the horizon when below it; caused
by refraction; proved by experiment.
DIALOGUE IX. p. 87.
Inclination of the earth’s axis. An angle, what.
The poles, what. Equinoctial, what. Earth’s
parallelism described. The axis of the earth
points to the same parts of the heavens.
Equator, ecliptic, polar circles, and
meridians, explained. Difference of time
between places lying under different
meridians. Longitude, what. How to reduce
longitude to time, and time to longitude.
Latitude, what.
DIALOGUE X. p. 101.
The seasons. Vernal and autumnal equinoxes. Days
and nights always equal, if the axis of the
earth were perpendicular to the plane of its
orbit. Seasons occasioned by the inclination
of the earth’s axis. Seasons continued. Days
and nights equal at all times under the
equator. The sun above the horizon of the
poles six months; and six months below them
alternately, so that they have but one day and
one night in the year; the longest day under
the polar circles is twenty-four hours. The
sun rises on different points of the compass
at different seasons of the year. Twilight in
the polar regions of long duration. We are
nearest the sun in winter, yet it is our
coldest season, why. The earth divided into
zones; proved to be globular, but is not a
true sphere.
DIALOGUE XI. p. 120.
The moon. Her diameter, synodical and periodical
revolutions. Her phases. Has always the same
side to the earth, and makes a revolution on
her axis every lunation. Has mountains and
valleys, but no seas nor atmosphere; yet may
be inhabited. Her real and apparent motion
described. Eclipses. Of the sun; total and
partial eclipses. Digit, what. Eclipse of the
moon. Penumbra, what. Central and total
eclipse. Why we have not an eclipse at every
full and change of the moon. She does not
always rise with the sun at change; nor when
he sets at full. She is visible when totally
eclipsed.
DIALOGUE XII. p. 136.
Tides. Occasioned by the attraction of the sun
and moon, and their centrifugal forces;
exemplified by an experiment. Spring and neap
tides. Tides not highest directly under and
opposite the moon, but after she has passed
the meridian. They are later and later every
day. Rule for finding the proportional
magnitudes of the planets compared with the
earth; or the proportion that one globe bears
to another. A cube number, what. Table of
roots, squares, and cubes; an example. Rule
for finding the mean distances of the planets
from the sun. Dr. Turner’s rule for extracting
the cube root; an example to explain the rule.
Example to find the mean distance of Mercury
from the sun. Table of diameters, &c.
Conclusion.
------------------------------------------------------------------------
DIALOGUE I.
TUTOR.
Well, Sir! I suppose this early visit is in consequence of my promise,
and your anxiety to become an astronomer.
PUPIL. It is, Sir.—And as astronomy is a science of which I have a very
imperfect idea, I must beg of you to explain it to me.
TUTOR. That I shall do with pleasure. But you surely cannot wholly
forget what I have formerly told you. However, as I mean to treat the
subject as if you had no previous knowledge of it, you will have an
opportunity from what you can recollect, to make such remarks, and ask
such questions, as may appear most material to you.
PUPIL. I thank you, Sir, it is just what I wish.
TUTOR. By astronomy then is meant a knowledge of the heavenly bodies,
the sun, moon, planets, comets, and stars, respecting their nature,
magnitudes, distances, motions, &c.
PUPIL. I fear I shall find it a difficult study.
TUTOR. Have patience.——
“The wise and prudent conquer difficulties,
“By daring to attempt them. Sloth and folly
“Shiver and shrink at sight of toil and danger,
“And make the impossibility they fear.”
PUPIL. This gives me encouragement, and, if you will have patience with
me, I will endeavour to profit by your instructions.——Pray, Sir, what is
the sun?
TUTOR. The sun, the source of light and heat, has been considered a
globe of fire, round which seven other spherical bodies revolve at
different distances from him, and in different periods of time, from
west by south to east. These are the planets[1].
[Footnote 1: From _Planeta_, roving or wandering.]
PUPIL. Any round ball is a globe, is it not?
TUTOR. A sphere or globe is defined a round solid body, every part of
whose surface is equally distant from a point within called its center;
and a line drawn from one side through the center to the opposite side,
is called its diameter.
PUPIL. You say the sun has been considered a globe of fire. Is he not
now thought to be so?
TUTOR. [2]Doctor Herschell, from some late observations, is of a
different opinion.—But what think you of his magnitude?
[Footnote 2: See his letter read at the Royal Society, December
18th, 1794.]
PUPIL. I really cannot conjecture.—This I know, that when I saw him
through the fog the other day, he appeared about the size of a common
plate.
TUTOR. You must not always judge by appearances. You will find that
there is a material difference between his real and apparent magnitude,
which I think you will be convinced of when I tell you, that he is no
less than 95 millions of miles from our earth.
PUPIL. Ninety-five millions of miles! You astonish me.
TUTOR. You will, I dare say, be no less surprized at being told, that he
is more than a million of times as large as our earth.
PUPIL. It is almost incredible! And what are the planets?
TUTOR. The planets are opaque, that is dark bodies, which receive their
light from the sun; and, as I told you, revolve about him. The first, or
that nearest the sun, is called Mercury, the next Venus, then the Earth,
Mars, Jupiter, Saturn, and Georgian, or the Georgium Sidus.[3] These are
called primary planets.
[Footnote 3: Their characters are,
Sun, Merc. Venus, Earth, Mars, Jup. Saturn, Georgian,
☉ ☿ ♀ ♁ ♂ ♃ ♄ ♅ .]
PUPIL. Are there then any others?
TUTOR. Yes. There are fourteen others, which move round their respective
primaries as their centers, and with them round the sun, and are called
secondaries, satellites or moons.
PUPIL. Have all the primaries secondaries?
TUTOR. Only four of them have moons. The earth, I need not tell you, has
one; Jupiter has four; Saturn seven, besides a stupendous ring which
surrounds his body; and Georgian two.
PUPIL. In what time, and at what distances, from the sun, do the planets
perform their periodical revolutions?
TUTOR. _Mercury_ revolves about the sun in 88 days, at the distance of
36 millions of miles.
_Venus_, at the distance of 68 millions of miles, completes her
revolution in 224 days.
_Earth_, on which we live, at the distance of 95 millions of miles,
performs its period in one year.[4]
[Footnote 4: The motion of the earth in its orbit is at the rate of
68 thousand miles an hour.]
_Mars_, at the distance of 145 millions of miles, in little less than
two of our years.
_Jupiter_, at the distance of 494 millions of miles, in near 12 years.
_Saturn_, at the distance of 906 millions of miles, in about 30 years.
_Georgian_, discovered a few years since by Dr. Herschell, performs its
period at the distance of 1812 millions of miles, in about 83 years.[5]
[Footnote 5: As the distances of the planets, when marked in miles,
are a burthen to the memory, astronomers often express their mean
distances in a shorter way, by supposing the distance of the earth
from the sun to be divided into ten parts. Mercury may then be
estimated at four of such parts from the sun, Venus at seven, the
Earth at ten, Mars at fifteen, Jupiter at fifty-two such parts,
Saturn at ninety-five, and Georgian 190 parts. See Plate I. Fig. 1.
These are calculated by multiplying the respective distances of the
planets by 10, and dividing by 95, the mean distance of the earth
from the sun; and may be set off by any scale of equal parts.]
PUPIL. What proportion does the earth bear in magnitude to the other
planets?
TUTOR. The earth is fourteen times as large as Mercury, very little
larger than Venus, and three times as large as Mars. But Jupiter is more
than fourteen hundred times as large as the earth; Saturn above a
thousand times as large, exclusive of his ring; and Georgian eighty-two
times as large.
PUPIL. Have you any thing else, Sir, to remark concerning the planets?
TUTOR. There are several other things I intend to make you acquainted
with, namely, their nature, appearances, motions, &c. At present I shall
only say, that Mercury and Venus are called [6]inferior planets, their
orbits or paths described in going round the sun, being within that of
the earth; and the other four, whose orbits are without the earth’s
orbit, [7]superior planets.
[Footnote 6: Perhaps with more propriety _interior_ or _inward_.]
[Footnote 7: _Exterior_ or _outward_.]
PUPIL. There is one thing more I wish to know, if——
TUTOR. I suppose you were going to say if not too much trouble; that is
quite unnecessary, as you well know that where I see a desire to learn,
teaching is to me a pleasure.—What is it?
PUPIL. That you will be so kind as to inform me what the comets are, and
if they have any motion?
TUTOR. The knowledge we have of comets is very imperfect, as they afford
few observations on which to ground conjecture. They are generally
supposed to be planetary bodies, forming a part of our system: for, like
the planets, they revolve about the sun, but in different directions,
and in extremely long elliptic curves, being sometimes near the sun, at
others staying far beyond the orbit of the outermost planet; whereas the
orbits of the planets are nearly circular. The period of one, which
appeared in 1680, is computed to be 575 years.
PUPIL. Whence do they derive their name?
TUTOR. From _Cometa_, a _hairy star_, because they appear with long
tails, somewhat resembling hair: some, however, have been seen without
this appendage, as well defined and round as planets.
PUPIL. You say _our_ system: what am I to understand by it?
TUTOR. The word system, in an astronomical sense, means a number of
bodies moving round one common center or point: and, because the planets
and comets revolve about the sun, it is called the _Solar System_ (Plate
I. fig. 2.); and we say _our_ system, as the earth is one of the
planets. Other systems have been invented for solving the appearances
and motions of the heavenly bodies, a description of which I shall leave
till I next see you.
------------------------------------------------------------------------
DIALOGUE II.
PUPIL.
I am afraid, Sir, I am come before you are prepared for me: but the very
great pleasure I received yesterday, induced me to be with you as early
as possible.
TUTOR. I am glad to see you, and happy to find you are so well pleased
with your difficult study. It will, I assure you, give you more exalted
ideas of the Deity than any that I know of. The Psalmist was undoubtedly
of this opinion when he said, The Heavens declare the glory of God, and
the Firmament sheweth his handy work.
PUPIL. I will no longer call it a difficult, but a pleasing study, and
feel myself ashamed at having used the expression. I shall now beg you
to explain to me the different systems.
TUTOR. The system I have been describing to you was known and taught by
Pythagoras, a Greek philosopher, who flourished about 500 years before
Christ, as he found it impossible, in any other way, to give a
consistent account of the heavenly motions.
This system, however, was so extremely opposite to all the prejudices of
sense and opinion, that it never made any great progress, nor was ever
widely spread in the ancient world.
Ptolemy, an Egyptian philosopher, who flourished 130 years after Christ,
supposed that the earth was fixed in the center, and that the sun and
the rest of the heavenly bodies moved round it in twenty-four hours, or
one natural day, as this seemed to correspond with the sensible
appearances of the cœlestial motions. This system was maintained from
the time of Ptolemy to the revival of learning in the sixteenth century.
At length, Copernicus, a native of Poland, a bold and original genius,
adopted the Pythagorean system, and published it to the world in the
year 1530. This doctrine had been so long in obscurity, that the
restorer of it was considered as the inventor.
Europe, however, was still immersed in ignorance; and the general ideas
of the world were not able to keep pace with those of a refined
philosophy. This occasioned Copernicus to have few abettors, but many
opponents. Tycho Brahe, in particular, a noble Dane, sensible of the
defects of the Ptolemaic system, but unwilling to acknowledge the motion
of the earth, endeavoured, about 1586, to establish a new system of his
own; but, as this proved to be still more absurd than that of Ptolemy,
it was soon exploded, and gave way to the [8]Copernican or true Solar
System.
[Footnote 8: See Plate I. fig. 2.]
PUPIL. I confess, I should have thought with Ptolemy, that the earth was
in the center, and that the sun moved round it.
TUTOR. You must at present content yourself with knowing that it is not
so; and it shall be my business to prove it.
PUPIL. May I beg the favour of the information you intended respecting
the planets?
TUTOR. I will grant it with pleasure. The planets are spherical bodies,
which appear like stars, but are not luminous; that is, they have no
light in themselves; though they give us light; for they shine by
reflecting the light of the sun.
PUPIL. You say, Sir, that they appear like stars; if so, how am I to
know them from stars?
TUTOR. Very easily: for the stars, or as they are more properly called
fixed stars, always keep the same situation with respect to each other;
whereas the planets, as they move round the sun, must be continually
changing their places among the fixed stars, and with one another.
PUPIL. Is there any other method of distinguishing them besides what you
have mentioned?
TUTOR. Yes. The planets never twinkle like the fixed stars, and are seen
earliest in the evening and latest in the morning.
PUPIL. How is the twinkling of the stars in a clear night accounted for?
TUTOR. It arises from the continual agitation of the air or atmosphere
through which we view them; the particles of air being always in motion,
will cause a twinkling in any distant luminous body, which shines with a
strong light.
PUPIL. Then, I suppose, the planets not being luminous, is the reason
why they do not twinkle.
TUTOR. Most certainly. The feeble light with which they shine is not
sufficient to cause such an appearance.
PUPIL. Have the stars then light in themselves?
TUTOR. They undoubtedly shine with their own native light, or we should
not see even the nearest of them: the distance being so immensely great,
that if a cannon-ball were to travel from it to the sun, with the same
velocity with which it left the cannon, it would be more than 1 million,
868 thousand years, before it reached it.[9]
[Footnote 9: The distance of Syrius is 18,717,442,690,526 miles. A
cannon-ball going at the rate of 1143 miles an hour, would only
reach the sun in about 1,868,307 years, 88 days.
Adams’s Lectures, vol. 4. page 44.]
PUPIL. This is wonderful indeed! what then are they supposed to be?
TUTOR. Suns.
PUPIL. Suns! the fixed stars suns!
TUTOR. Yes, suns.
“One sun by day, by night ten thousand shine.”
And what will increase your astonishment, each of them is the center of
a system of planets, which move round him.[10]
[Footnote 10: Dr. Herschell says, that in some clusters of stars he
has observed, they appear too close together to admit any planets to
revolve about them.]
“Observe how system into system runs.”
“What other planets circle other suns.”
PUPIL. I am almost lost.—I used to think they were designed to give us
light.
TUTOR. This is a vulgar error.—They were doubtless created for a much
nobler purpose, since thousands of them are invisible to us without the
help of a telescope; and we receive more light from the moon than from
all the stars together.
PUPIL. How do you know they are suns? Is their being luminous a proof of
their being so?
TUTOR. No. But we know that the sun shines with his own light on all the
planets belonging to our system; and from what I have told you, have the
greatest reason to believe that the stars shine with their own light: we
therefore from analogy conclude, that they are so many suns conveying
light and heat to other worlds[11].
[Footnote 11: Dr. Herschell thinks it probable that the sun and
fixed stars may be inhabited.]
PUPIL. Are there then other worlds besides this we live in?
TUTOR. Consider.—Has not the earth we inhabit a moon to enlighten it?
PUPIL. Yes, Sir.
TUTOR. And have I not told you that Jupiter, Saturn, and Georgian, have
also moons?
PUPIL. This I well remember.
TUTOR. For what purpose then do you suppose those orbs were designed?
PUPIL. Indeed, I cannot tell.
TUTOR. You surely cannot imagine that they were intended for our use,
since we knew nothing of them till after the invention of telescopes.
PUPIL. That is what I think no one can suppose.
TUTOR. And do not all the planets enjoy the benefit of the sun in common
with us?
PUPIL. Undoubtedly.
TUTOR. Well, then; of what use would the light and heat be which is
conveyed to them from the sun; or the light which they receive from
their moons if there are no inhabitants?
PUPIL. I know of none.
TUTOR. Can you then have any doubt about their being inhabited?
PUPIL. No, Sir.—But you say that the stars are suns, each of which is
the center of a system of planets or worlds.
TUTOR. If you are satisfied that the planets belonging to our system are
inhabited, and that the fixed stars are suns, the centers of other
systems, what reasonable objection can you have to all the planets in
the universe being so?
PUPIL. It is what I cannot comprehend.
TUTOR. It may be so.—But is not the same Almighty Power, who does
nothing in vain, as capable of making ten thousand worlds if he pleased,
as well as one?
PUPIL. I will not presume to dispute his power; but are we not told that
all mankind descended from Adam?
TUTOR. Yes; Moses wrote concerning this earth, he has not made us
acquainted with the inhabitants of the other planets: for aught we know
they might descend from other Adams.—To-morrow evening, I hope to see
you again.
------------------------------------------------------------------------
DIALOGUE III.
PUPIL.
I recollect, Sir, you mentioned last night, that the planets appear like
stars. Our earth is a planet; how can it have the appearance of a star?
TUTOR. If you were on the planet Venus, the earth would have as much the
appearance of a star as Venus has to us.
PUPIL. But Venus appears amongst the fixed stars.
TUTOR. Yes. And so would the earth appear from Venus.
PUPIL. How can it be?
TUTOR. Because, in whatever part of the universe we are, we appear to be
in the center of a concave, that is hollow, sphere, where remote objects
appear at equal distances from us: so that, whether we are on the planet
Venus or on the earth, in this particular the effect will be the same.
PUPIL. Then the light _we_ receive from the sun is by reflection
conveyed to the other planets.
TUTOR. No doubt of it. And our earth appears as a moon to the
inhabitants of the moon, and undergoes the various changes of that
planet.
PUPIL. Have you any proof of this, Sir?
TUTOR. Nothing can be clearer; for, on a fine evening, soon after the
change of the moon, when the earth appears nearly as a full moon to the
moon, and we see a faint streak of light, the whole body of the moon is
visible to us.
PUPIL. I remember to have seen it.
TUTOR. You do?—The earth then will appear there thirteen times as large
as the moon does to us; of course it must reflect a strong light on the
body of the moon, and it is by that light we see that part of the moon
which is turned from the sun.
PUPIL. Is the earth, then, only thirteen times as big as the moon?
TUTOR. In solidity it is about fifty times as large; but its disc or
face is only thirteen times.
PUPIL. What is the moon’s distance from the earth?
TUTOR. 240 thousand miles, which is about 400 times less than that of
the sun.
PUPIL. And yet she appears as far distant as the sun.
TUTOR. You are now, I hope, convinced of what I said relative to distant
objects.
PUPIL. I am, Sir: and I suppose the reason of the moon’s appearing as
large as the sun, is because she is so much nearer to us.
TUTOR. It is so.—For, at a total eclipse of the sun, which happens when
the moon is in a right line between the sun and the earth, the sun is
obscured from our sight, although his disc is 160 thousand times as
large as that of the moon. In like manner would the moon, when at full,
be hid by placing your cricket-ball in a line between your eye and her,
yet, you know, the ball is not so large as the moon; but being nearer
the eye, it is apparently so.
PUPIL. This is very clear. But——
TUTOR. I conjecture you were going to ask me to explain the nature of
eclipses.
PUPIL. That was certainly my intention, Sir.
TUTOR. There are other things you must be made acquainted with before
you will be able to comprehend it, and which I will endeavour to make
you understand before we enter on the subject.
PUPIL. Whenever you please, Sir.
TUTOR. You have taken a view of the earth from the planet Venus.—Suppose
I transport you to one of the planets belonging to another system; what
description do you think you should give of it?
PUPIL. I must consider. What I now call a star would be a sun. The
planets of that system I should see as I now do those belonging to ours:
our sun would be a star; and the earth, with all the other planets,
would be invisible.
TUTOR. Very well, Sir. Can you then find it difficult to conceive that
all the stars are as far from each other in unbounded space as our sun
is from the nearest star?
PUPIL. It is hard to conceive: but when I consider that wherever I am,
every remote object appears at an equal distance from me, the difficulty
vanishes.
TUTOR. That you might form some idea of the immense distance of the
fixed stars, you must recollect, I mentioned the time a cannon-ball
would be in reaching the nearest of them.
PUPIL. I do, Sir. More than 1,868,000 years.
TUTOR. You have an excellent memory. I suppose then you know the
distance of the earth from the sun?
PUPIL. Yes, Sir. I wrote it down; and, it made so strong an impression
on my memory, that I believe I shall never forget it.—95 millions of
miles.
TUTOR. Now, suppose the earth to be in that part of its orbit which is
nearest to the star, it would be 95 millions of miles nearer to it than
the sun is.
PUPIL. Certainly.
TUTOR. And, in the opposite side of its orbit, as much farther from the
star.
PUPIL. Without doubt.
TUTOR. Then you find that the earth is 190 millions of miles nearer to
the star at one time of the year than it is at another; and yet the
magnitude of the star does not appear the least altered, nor is its
distance affected by it.
PUPIL. A proof of its amazing distance.—I was going to ask a silly
question.
TUTOR. What is it? perhaps not so simple as you may imagine.
PUPIL. Whether the most conspicuous stars are not supposed to be the
nearest to us?
TUTOR. Undoubtedly.—And are called stars of the first magnitude; the
next in splendor, stars of the second magnitude; and so on to the sixth
magnitude; and those beyond, which are not visible to the naked eye, are
called telescopic stars.
PUPIL. The distance of the telescopic stars must be great indeed, beyond
all conception.
TUTOR. You judge rightly; and their numbers are beyond all computation.
Doctor Herschell says, he has not a doubt but that the broad circle in
the heavens, called the Milky Way, is a most extensive stratum of stars,
he having discovered in it many thousands. Besides, some stars appear to
him double, others treble, &c. not that they are really so, but are
stars at different distances from us, which appear nearly in a right
line.
“As in the milky-way a shining white
“O’erflows the heav’ns with one continued light,
“That not a single star can shew his rays,
“Whilst jointly all promote the common blaze.”
PUPIL. I have heard of numbering the stars; but that, I find, is
impossible.
TUTOR. If you mean that immense host of stars I have been describing, it
is impossible; but, though in a clear winter’s night, without moonshine,
they seem to be innumerable, which is owing to their strong sparkling,
and our looking at them in a confused manner; yet when the whole
firmament is divided as it has been done by the ancients, the number
that can be seen at a time, by the naked eye, is not above a thousand.
PUPIL. Pray, Sir, how did the ancients divide the firmament?
TUTOR. I would willingly answer your question; but, as I find I shall
not have time to give you that information I wish, I shall postpone it
till I see you to-morrow evening.
------------------------------------------------------------------------
DIALOGUE IV.
TUTOR.
The ancients, in reducing astronomy to a science, combined the fixed
stars into constellations, allowing several stars to make one
constellation: and, for the better distinguishing and observing them,
they reduced the constellations to the forms of animals, or to the
images of some known things, by which means they were enabled to signify
to others any particular star they meant to notice. Job mentions two of
the constellations, namely, Orion and Pleiades, which shews the study of
astronomy to be very ancient.
PUPIL. Pray, Sir, how may I know them?
TUTOR. By studying the use of the cælestial globe, on which they are
drawn.
PUPIL. Will you be kind enough to instruct me, Sir?
TUTOR. At some future time I probably may: at present you are not
prepared for it.
PUPIL. I am satisfied.—Have you any thing more to remark of the
constellations, Sir?
TUTOR. Yes. The situation of the planets, as they are continually
changing their places, could not be pointed out without first dividing
the stars into constellations: hence, necessity was the mother of
invention.
PUPIL. And I think a very ingenious one.—If I may be allowed a
comparison, I will suppose the different kingdoms of the world on my
dissected map, to represent so many constellations; then, if I hear of
London, I know it is in England; if of Paris, in France; of Lisbon, in
Portugal; and so on. These I would compare with stars of the first
magnitude, being the chief cities of their respective kingdoms; inferior
cities, stars of the second magnitude; principal towns of the third, &c.
TUTOR. A very apt comparison indeed. Now if you hear of a traveller
setting off from London to Dover, thence to Calais, Paris, Bern, and so
on to Rome, you know that he must go through part of England, Flanders,
France, Switzerland, and Italy, passing many towns and villages on his
way.
PUPIL. That is very evident.
TUTOR. Very well, then; in like manner would the planets, if seen from
the sun, be traced from star to star, from constellation to
constellation, through their whole periods.
PUPIL. It is not possible to view them from the sun, surely, is it?
TUTOR. No, certainly.
PUPIL. Why then do you say if seen from the sun?
TUTOR. Because it is there only their motions can appear uniform; as
seen from the earth they apparently move very irregularly.—Suppose you
were in the center of a circular course; and, whilst a horse was going
round, you kept your eye on him: cannot you conceive that you should see
him run round the course in a regular manner, moving the whole time the
same way?
PUPIL. It is not at all difficult to conceive.
TUTOR. Again. Imagine yourself placed at a considerable distance on the
outside of the course, where you could see the horse the whole time he
was going round, would he appear to move as uniformly as before?
PUPIL. Certainly not: on the opposite side of the course his motion
would be the same as when I stood in the center of it; when he was
approaching me, I should scarcely see him move; in that part of the
course next to me he would move in a direction contrary to what he did
at first; and again when going from me, his motion would be scarcely
visible.
TUTOR. This I think will give you a tolerable idea of the irregular
motion of the inferior planets, as seen from the earth. When farthest
from us their motion is said to be direct; when nearest to us
retrograde, because they appear to be moving back again; and, when
approaching, or going from us, we say they are stationary; because, if
then observed in a line with any particular star, they will continue so
for a considerable time: now these appearances could not happen if they
moved round the earth.
PUPIL. Nothing can be plainer: for if the earth were in the center we
should always see them move the same way.
TUTOR. When the planet is nearest to us, that is in a line between us
and the sun, we say it is in its inferior conjunction; when farthest
from us, and the sun is between us and the planet, in its superior
conjunction. But the superior planets have alternately a conjunction and
an opposition.
PUPIL. A conjunction, I suppose, when the sun is between the earth and
the planet, and an opposition when the earth is between the sun and the
planet; that is, when the planet is nearest to us, and appears to be
opposite to the sun?
TUTOR. You are right.—Therefore, when in conjunction it rises and sets,
nearly with the sun; but in opposition, it rises nearly when the sun
sets, and sets when he rises.
PUPIL. Why do you say nearly, Sir?
TUTOR. Because it cannot be exactly, but when the sun, earth, and planet
are in a _right_ line, which seldom happens.
PUPIL. How do you account for this, Sir?
TUTOR. At present I fear you will not be able to comprehend what I wish
to explain, as I must use a term you are unacquainted with. The reason
is, that the planets are very seldom in or near their nodes at their
conjunctions or oppositions.
PUPIL. I do not indeed understand what you mean by the word _nodes_.
TUTOR. It will be explained to you in due time, and I shall conclude
this evening with a few more remarks relative to the appearance of the
planets.
PUPIL. Any thing you please, Sir.
TUTOR. You know that the planets, being opaque bodies, receive their
light from the sun; and that only that part which is turned to the sun
can be enlightened by him, whilst the opposite side must remain in
darkness.
PUPIL. This is self-evident: if I hold my ball to the candle it will
have the same effect.
TUTOR. Tell me then how you think they will appear as seen from the
earth.
PUPIL. If, when you shewed me Venus, she had not appeared perfectly
round, I should say that, both before and after her superior conjunction
I should see her nearly with a full face; when stationary, only half
enlightened, like the moon at first quarter; because, an equal portion
of the dark and bright parts will be turned towards us; the bright part
will be decreasing till her inferior conjunction, when the dark side
will be turned towards us, and consequently invisible; the light will
then increase; and, when she is again stationary, she will appear like
the moon at last quarter.
TUTOR. When seen through a telescope she has the different appearances
you have mentioned; and when I next see you I will shew you that both
Venus and Mercury may sometimes be seen when in their inferior
conjunctions; the superior planets always appear with nearly a full
face.
PUPIL. How are the planets distinguished from each other?
TUTOR. _Mercury_, from his vicinity to the sun, is seldom seen, being
lost in the splendor of the solar brightness. When seen, he emits a very
bright white light.
_Venus_, known by the names of the morning and evening star, is the
brightest, and to appearance, the largest of all the planets; her light
is of a white colour, and so considerable, that in a dusky place she
projects a sensible shade. She is visible only for three or four hours
in the morning or evening, according as she is before or after the sun.
_Mars_ is the least bright of all the planets. He appears of a dusky
reddish hue, and much larger at some periods than at others, according
as he is nearer to, or farther from us.
_Jupiter_ is distinguished by his peculiar magnitude and light. To the
naked eye he appears almost as large as Venus, but not altogether so
bright.
_Saturn_ shines but with a pale feeble light, less bright than Jupiter,
though less ruddy than Mars.
_The Georgium Sidus_ cannot be readily perceived without the assistance
of a telescope.
------------------------------------------------------------------------
DIALOGUE V.
TUTOR.
Before I proceed to explain what I promised you, it is necessary you
should be informed that the earth as seen from the sun, in its
periodical revolutions, will describe a circle among the stars which
astronomers call the _ecliptic_, and sometimes _the sun’s annual path_,
because the sun, as seen from the earth, always appears in that line.
PUPIL. Do not all the planets move in the ecliptic?
TUTOR. No.—On account of the obliquity of their orbits, they are, in
every revolution, one half of their periods above the ecliptic, and the
other half below it.
PUPIL. I think I comprehend your meaning; but shall be obliged to you,
Sir, if you can make it clearer to me.
TUTOR. I have here a little design, (Plate II. Fig. 1.) which will
answer our purpose: where S represents the sun; ABCD, the orbit of the
earth; and EFGH, the orbit of one of the inferior planets, suppose
Venus.
[Illustration: _Plate II._
_T. Conder Sculp^t._]
PUPIL. Now I understand it perfectly: the half EHG rises above, and the
other half EFG sinks below it, from the points EG, which I perceive are
in a line with the orbit of the earth. But pray, Sir, have you any name
for that dotted line?
TUTOR. Yes, it is called the _line_ of the nodes; and the points EG the
_nodes_ of the planet: the latter is called the ascending node, because,
when the planet is in G, it is ascending or rising above the orbit of
the earth; or, which is the same thing, above the ecliptic: and when in
E, it is descending or sinking below it, whence _it_ is called the
descending node. But you must remember that the orbits of all the
planets do not cross or intersect the ecliptic in the same points; but
that their nodes or intersections are at different parts of it.
PUPIL. How can the orbit of the earth and the ecliptic be the same?
TUTOR. They are very different; but being in the same plane, if the
orbit of any planet inclines to one it must incline equally to the
other.
PUPIL. You will, I fear, Sir, think me very stupid: but I must beg of
you to inform me what you mean by a plane?
TUTOR. Any flat surface is a plane. You may therefore suppose the edge
of a round tea-table to represent the ecliptic, and a circle within it,
drawn from the center of the table, the orbit of the earth: will they
not be both in the same plane?
PUPIL. Certainly.
TUTOR. You must not imagine, when I am speaking to you of the plane of
the ecliptic, or plane of the earth’s orbit, that it is a visible flat
surface, or, in speaking of the orbits of the planets, I mean solid
rings.—No. The planets perform their revolutions with the utmost
regularity, in unbounded space; and, like a bird thro’ the air, leave no
track behind them.
PUPIL. How then are they retained in their orbits?
TUTOR. The question, I confess, is natural, and is what I expected; but
I must of necessity postpone it to another opportunity; and shall now
fulfil the promise I made of shewing you in what manner the inferior
planets may be seen when in their inferior conjunctions. Cast your eye
again on the little design I gave you, and consider, if Venus were in
her ascending node at G, when the earth is at _b_; or, in her descending
node, at E, when the earth is at _a_, what the effect would be.
PUPIL. She would be in a line with the sun.
TUTOR. And, on the sun’s disc, she would appear a dark round spot,
passing over it. These appearances, which are called transits, happen
very seldom: because she is very seldom in or near her nodes at her
inferior conjunctions. There was one in June 1761, one in June 1769; and
the next will be in the year 1874. And as Mercury is seen in the same
manner, it is a proof that their orbits must be within that of the
earth.
PUPIL. I thank you, Sir, and shall be obliged to you to inform me how
many constellations the earth pastes over in every revolution?
TUTOR. Twelve, which correspond with the months of the year, and are
called the twelve signs of the zodiac.
PUPIL. What is the zodiac?
TUTOR. That part of the heavens which contains the twelve signs, and
which you may conceive to be a zone or belt extending eight degrees on
each side the ecliptic, in which the planets constantly revolve: so that
no planet is ever seen more than eight degrees either north or south,
that is above or below the ecliptic.
PUPIL. What am I to understand by a degree?
TUTOR. All circles, whether great or small, are supposed to be divided
into 360 equal parts, called degrees, and each degree into 60 equal
parts, called minutes: therefore, if I speak of a circle in the heavens,
the circumference of the earth, or any other circle, by a degree is
meant the 360th part of that circle; and a minute the 60th part of a
degree.
PUPIL. What are the names of the twelve signs?
TUTOR. The first is called Aries, which you know signifies a Ram;
Taurus, the Bull; Gemini, the Twins; Cancer, the Crab; Leo, the Lion;
Virgo, the Virgin; Libra, the Balance; Scorpio, the Scorpion;
Sagittarius, the Archer; Capricorn, the Goat; Aquarius, the
Water-bearer; and Pisces, the Fishes.
PUPIL. Do you wish me to commit these to memory, Sir?
TUTOR. It is very requisite; but as I know you are fond of verse, you
shall hear what Doctor Watts says—
The Ram, the Bull, the heav’nly Twins,
And next the Crab the Lion shines,
The Virgin, and the Scales:
The Scorpion, Archer, and Sea-goat,
The Man that holds the Water-pot,
And Fish with glitt’ring tails.
PUPIL. I like it much, as it will assist my memory.
TUTOR. As the twelve signs correspond with the months of the year, the
earth must pass over nearly one degree every day, one sign every month,
and in twelve months complete a whole circle, or 360 degrees; therefore
every sign must contain 30 degrees, because 30 multiplied by 12 is equal
to 360.
PUPIL. It must be so.
TUTOR. You must remember, that when the earth is in any sign, as seen
from the sun, the sun will be in the opposite sign, as seen from the
earth: for instance, if the earth be in Aries, the sun will be in Libra;
if in Taurus, the sun will be in Scorpio, &c. therefore, as by the
earth’s annual motion, the sun _appears_ to move, we always speak of the
sun’s, not the earth’s place, in the ecliptic.—You do not seem to
understand me?
PUPIL. Not perfectly, Sir.
TUTOR. Take this orange, and put it in the middle of the round table
before us, and place an apple on the opposite side next the window: the
orange may represent the sun, the apple the earth, and the window the
sign Aries. Now go round the table to the apple; look at the orange, and
tell me to what part of the room the eye will be directed.
PUPIL. To the part opposite to the window, Sir.
TUTOR. If then you suppose the door, which is opposite to the window, to
be the sign Libra, the sun will be in Libra when the earth is in
Aries—will it not?
PUPIL. It is very plain.
TUTOR. I shall now give you a table of the signs, their characters, the
corresponding months, and the days of the month the sun enters each
sign, by means of which, if you reckon a degree for a day, you may find
the sun’s place, nearly, for any day in the year.
PUPIL. This will give me much pleasure, and I shall be happy to have it.
THE TABLE.
NORTHERN SIGNS.
Aries, Taurus, Gemini, Cancer, Leo, Virgo.
♈ ♉ ♊ ♋ ♌ ♍
March, April, May, June, July, Aug.
20, 20, 21, 21, 23, 23.
SOUTHERN SIGNS.
Libra, Scorpio, Sagittarius, Capricorn, Aqua. Pisces.
♎ ♏ ♐ ♑ ♒ ♓
Sept. October, November, Decem. Jan. Feb.
23, 23, 21, 21, 20, 18.
PUPIL. Why do you write northern and southern signs, Sir?
TUTOR. Because they are situated north and south of a circle in the
heavens, called the equinoctial, which circle crosses the ecliptic in
the points Aries and Libra, and extends 23-1/2 degrees on each side of
it; and which I shall have occasion to mention to you another time.
PUPIL. When you think proper, Sir, I shall be glad to have it explained
to me.
TUTOR. Look at your table, and tell me what sign and what degree the sun
is in the 30th of March, and 20th of October.
PUPIL. The sun enters Aries the 20th of March, of course he must be 10
degrees in that sign the 30th; and, as he does not enter Scorpio till
the 23d of October, he must want three degrees of completing the sign
Libra; he must therefore, on the 20th of October, be in 27 degrees of
Libra.
TUTOR. Very well.—Do you learn the table, as you will have a farther use
for it.
------------------------------------------------------------------------
DIALOGUE VI.
PUPIL.
Since I was last with you, Sir, I have been thinking of what you then
told me, that the planets perform their revolutions in open space: I
have not the least idea how this can be; if convenient, I shall be happy
to have it explained.
TUTOR. It will be necessary first to inform you, that the orbits or
paths described by the revolution of the planets round the sun, are not
true circles (as Plate II. fig. 2.) but somewhat elliptical, that is,
longer one way than the other, as fig. 3.
PUPIL. This is exceedingly plain.
TUTOR. In a circle, the periphery or circumference is equally distant
from a point within called its center, as A; but an ellipsis has two
points called the focuses or foci, as B C. In one of these, called its
lower focus, is the sun: so that you see in every revolution of the
planet it must be nearer to the sun in one part of its orbit, than it is
in another.
PUPIL. I see it clearly.
TUTOR. Now let S (Plate II. fig. 4.) represent the sun, A B C D a planet
in different parts of its orbit; when it is nearest to the sun, as at A
it is said to be in its _perihelion_; when at B its _aphelion_; but when
at C or D its middle or mean distance, because the distance S C or S D
is the middle between A S the least and B S the greatest distance; and
half the distance between the two focuses is called the _eccentricity_
of its orbit, as S E or E F.
PUPIL. This I will endeavour to understand; but I find it will take me
some time to be perfected in it.
TUTOR. You may study it at your leisure, as it will not prevent our
proceeding to the thing proposed, namely, the laws which govern the
motion of the planets, or ATTRACTION OF GRAVITATION.
PUPIL. By attraction I think you mean that property in bodies whereby
they have a tendency to approach each other. I remember you told me that
the magnet I had the other day attracted the needle.
TUTOR. Yes. And you may recollect that when I took a feather suspended
by a thread, and put it near the conductor of the electrical machine, it
was strongly attracted by it, and adhered to it as long as the machine
was kept in motion.
PUPIL. I remember it well. But what am I to understand by attraction of
gravitation?
TUTOR. The sun, being the largest body, _attracts_ the earth and all the
other planets, they _gravitate_ or have a tendency to approach the sun;
the earth being larger than the moon _attracts_ her, and she
_gravitates_ towards the earth; the planets are attracted by and
gravitate towards each other; a stone when thrown from the earth, by its
attraction and the gravitating power or weight of the stone, is brought
to the earth again; the waters in the ocean gravitate towards the center
of the earth; and it is by this power we stand on all parts of the earth
with our feet pointing to the center.
PUPIL. This information affords me great pleasure.
TUTOR. Having mentioned attraction of magnetism, electricity, and
gravitation, it may not be amiss to inform you of another kind, called
_attraction of cohesion_.
PUPIL. Any thing which tends to my improvement, I shall be obliged to
you to communicate.
TUTOR. By attraction of cohesion is meant that property in bodies which
connects or firmly unites the different particles of matter of which the
body is composed.
PUPIL. Pray, Sir, inform me what you mean by the _laws_ of attraction?
TUTOR. You are to understand, 1st. That _attraction decreases as the
squares of the distances between the centers of the attracting bodies
increase_.
PUPIL. I must beg you, Sir, to explain to me the meaning of the squares
of the distances.
TUTOR. Any number multiplied into itself is a square number, thus 1 is
the square of 1; 4 is the square of 2; 9 is the square of 3, and so on,
because 1 multiplied into itself is 1; 2 by 2 is 4; 3 by 3 is 9, &c. Now
suppose, that when the planet is at B (Plate II. fig. 4.) it is twice as
far from the sun as it is at A: how much more will it be attracted by
the sun at A than at B?
PUPIL. You say, Sir, that the distance is twice as great at B as at A?
TUTOR. I do.
PUPIL. Then as the square of the distance 2 is 4, the decrease of
attraction at B, the planet at A will be attracted with four times the
force it would be at B.—Am I right, Sir?
TUTOR. Perfectly so. And if the distance at B were three times as great
as at A, it would be attracted with a force nine times as great.
PUPIL. I perceive it must be so.
TUTOR. I shall now give you the 2d law, namely, That _bodies attract one
another with forces proportionable to the quantities of matter they
contain_.
PUPIL. Do all bodies of the same magnitude contain equal quantities of
matter?
TUTOR. No, certainly: For a ball of cork may be as large as one of lead,
and yet not contain the same quantity of matter, because it is more
porous, and not so compact or dense a body as the lead; neither will a
ball of lead of the same magnitude as one of gold contain an equal
quantity of matter.—So the sun, though a million of times as big as the
earth, contains a quantity of matter only 200,000 as great, therefore
attracts the earth with a force 200,000 as great as the earth attracts
him.
PUPIL. I think this is clear.
TUTOR. We will now suppose that in the river are two boats of equal
bulk, at the distance of twenty yards from each other, and that a man in
one boat pulls a rope which is fastened to the other, what effect will
be produced, or where do you think the boats will meet?
PUPIL. Had you not told me that bodies attract one another with forces
which are proportioned to the quantities of matter they contain, I
should say the boat to which the rope is fastened would come to that in
which the man stands: but as I imagine you mean to apply this to
attraction, by the above rule, they will meet at a point which is half
way between them.
TUTOR. If one boat were three times the bulk of the other, how then?
PUPIL. The lightest would move three times as far as the heaviest, or 15
yards whilst the heaviest moved only 5.
TUTOR. Upon my word you reason philosophically. In both cases you are
perfectly right.
PUPIL. As the sun is so immense a body that his quantity of matter is so
much greater than the planets, I am at a loss to know why they are not
by the power of attraction drawn to him.
TUTOR. And so they would if the attractive power were not counteracted
by another of equal force.
PUPIL. Did you not say, Sir, that the planets are kept in their orbits
by attraction?
TUTOR. I did. But you find that by attraction _only_ the sun would draw
all the planets to himself.
PUPIL. That is evident. But I wish to know what this counteracting power
you speak of is?
TUTOR. I will tell you presently.—You must remember that _simple_ motion
is naturally rectilineal, that is, all bodies, if there were nothing to
prevent them, would move in strait lines.
PUPIL. Then as the planetary motion is circular, it cannot be simple?
TUTOR. No. It is a _compound_ of the two forces I have been mentioning:
the one is called the attractive or centripetal force; the other, the
projectile or centrifugal force.
PUPIL. The former I clearly comprehend, but not the latter. I can
conceive, that if two bodies approach each other by attraction they must
move in a right line.
TUTOR. If you shoot a marble on a smooth piece of ice, in what direction
will it run?
PUPIL. Strait forward.
TUTOR. This is a projectile force.—Could you, do you think, shoot it in
any other direction?
PUPIL. No, Sir.
TUTOR. Then is not this motion also rectilineal?
PUPIL. It is.
TUTOR. When you strike a ball with your cricket-bat, or throw a stone
with your hand, is it not projected or thrown forward by the force of
the bat or hand?
PUPIL. Certainly.
TUTOR. And does it not move in a strait line?
PUPIL. At first it appears to do so; but afterwards it inclines towards
and falls to the earth.
TUTOR. Cannot you account for this?
PUPIL. I suppose it must be drawn to the earth by attraction.
TUTOR. You are right. The attraction of the earth, and the resistance of
the atmosphere or air through which it moves, retards its progress, or
it would continue moving in a strait line, with a velocity equal to that
which was at first impressed upon it. In like manner the beneficent
Creator of the Universe impressed a force on all the planets which
should be equal to that of the attractive power of the sun, that one
might not overcome the other.
PUPIL. This wants explaining.
TUTOR. I would willingly gratify you, but as I have much more to say on
the subject, I fear it will be too great a burthen on your memory; it
will therefore be better to postpone it.
PUPIL. As you please, Sir.
------------------------------------------------------------------------
DIALOGUE VII.
TUTOR.
Having at our last meeting explained to you the nature of the attractive
and projectile forces, I shall proceed to shew you that it is by the
joint action or combination of these two forces that the planets are
retained in their orbits.
PUPIL. I am all anxiety, as I wish to be informed how, or in what manner
they can act against each other, to produce that effect.
TUTOR. Answer me a few questions, and you will soon know.
PUPIL. As many as you please, Sir.
TUTOR. If you whirl a stone in a sling, what will be its motion?
PUPIL. Circular.
TUTOR. Is you let it suddenly slip out of the sling, will it continue
its circular motion?
PUPIL. No, Sir, but fly off in a strait line.
TUTOR. This line you must remember is what mathematicians call the
tangent of a circle, as A _a_, B _b_, &c. (Plate II. fig. 5.) for all
bodies moving in a circle have a natural tendency to fly off in that
direction. Thus a body at A will tend towards _a_; at B towards _b_, and
so on; but the central force acting against it preserves its circular
motion.
PUPIL. By the central force here you mean the action of the hand, do you
not?
TUTOR. Yes. For, as soon as the stone is released and that power is
lost, it assumes its natural, that is, its rectilineal motion.—Again. If
you are left at liberty, cannot you run strait forward?
PUPIL. Yes, Sir.
TUTOR. Now, suppose one of your companions were to fasten a rope round
your body, and at the extent of it were to stand still and hold it
tight, with a force equal to that with which you run, could you, do you
think, move in a strait line, that is, in a tangent of a circle?
PUPIL. No, Sir. I must run in a circle.
TUTOR. Why?
PUPIL. Because, whilst the rope is extended I am prevented running in
any other direction.
TUTOR. Just so it is with the planets: the attractive or centripetal
force of the sun being equal to that of the projectile or centrifugal
force of the planets, they are by attraction prevented moving on in a
strait line, and, as it were, drawn towards the sun; and by the
projectile force from being overcome by attraction. They must therefore
revolve in circular orbits.
PUPIL. What I have so long wished is now accomplished. I understand it
perfectly.
TUTOR. What I have now explained relates not only to the primary planets
which have the sun for their center of motion; but, you must remember
that the secondary planets are governed by the same laws, in revolving
about their respective primaries; for, as by the attractive power of the
sun combined with the projectile force of the primary planets they are
retained in their orbits; so also the action of the primaries upon their
respective secondaries together with their projectile force, will
preserve them in their orbits.
PUPIL. Pray, Sir, what have you else to observe?
TUTOR. Have I not told you that the orbits of the planets are not true
circles, but a little elliptical?
PUPIL. Yes, Sir; and I shall be glad to know the reason of it.
TUTOR. If the attractive power of the sun were uniformly the same in
every part of their orbits they would be true circles, and the planets
would pass over _equal_ portions of their orbits in _equal_ times; that
is, they would move from B to C, (Plate II. fig. 5.) in the same time as
from A to B, &c.
PUPIL. That is clear, but as their orbits are elliptical, when the
planets are farthest from the sun, the velocity with which they move
must be lessened as the attraction is decreased.
TUTOR. And they must consequently pass over _unequal_ parts of their
orbits in _equal_ portions of time. And, as _a double velocity will
balance a quadruple or fourfold power of gravity or attraction_, it
follows, that as the centripetal force is four times as great at A as at
B (Plate II. fig. 4.) the centrifugal force will be twice as great, and
would carry a planet from A to _a_ in the same time it would from B to
_b_, and in its orbit from A to _c_ as soon as from B to _d_, and
thereby describe the area, or space contained between the letters A S
_c_, in the same time as the area or space B S _d_. For according to the
laws of the planetary motions, in their periodical revolutions, _they
always describe equal areas in equal times_.
PUPIL. The orbits of the comets being very elliptical, the irregularity
of their motions must be exceedingly great.
TUTOR. Great, indeed!—One of them passed so near the sun as to acquire a
heat which Sir Isaac Newton computed to be two thousand times hotter
than red hot iron.[12]
[Footnote 12: Dr. Herschel is of opinion, that bodies near the sun
do not acquire so great a degree of heat as has been generally
imagined.]
PUPIL. Astonishing! If they pass so near the sun, the centripetal force
must act powerfully on the body of the comet.
TUTOR. And that force, you know, must be equalled by the projectile
force; so you find they move when near the sun with amazing
celerity.—But when arrived at their aphelion, where the influence of the
sun is weak, what a transition!
PUPIL. Wonderful, indeed!—Their motion is excessively slow, and the sun
must appear little more than a fixed star. Surely they cannot be
inhabited, can they?
TUTOR. We cannot speak positively; but, as they differ so much from the
planets, which we have reason to suppose are so, it is imagined they are
designed for some purpose unknown to us.
PUPIL. When is the earth in its perihelion?
TUTOR. In December; and our summer half year is longer than the winter
half, by about eight days.
PUPIL. I suppose this is occasioned by the inequality of the earth’s
annual motion.
TUTOR. It is; and this inequality is the cause of the difference of time
between the sun and a well regulated clock; the latter keeps equal time,
whilst the former is constantly varying.
PUPIL. I have often seen in the almanack clock fast, clock slow, but did
not know the meaning of it: I imagine it is that the clock should be so
much faster or slower than the time by the sun as is there mentioned.
TUTOR. It is: but there are tables calculated to shew the difference of
time for every day in the year; so that if you know the exact times of
the day by the sun, and have one of these tables, you will see what the
time should be by the clock, to a second, which is not shewn in a common
almanack.
PUPIL. In speaking of the annual or yearly motion of the earth, you have
no where mentioned the cause of the seasons; will it be agreeable to do
it now, Sir?
TUTOR. The vicissitudes of the seasons, the cause of day and night, &c.
shall be the subject of future lessons: we shall find sufficient to
employ us at present.
PUPIL. I think you told me just now that the earth is nearest the sun in
December; that is our winter; this seems a little mysterious.
TUTOR. It may appear so to you now, by-and-by you will be of a different
opinion. I shall explain this matter to you with that of the seasons,
&c.
PUPIL. I fear I have interrupted you.—As you said you had sufficient
employment for us, I shall be glad to know what it is.
TUTOR. Hitherto I have spoken of the sun’s being fixed, and that the
planets revolve about him as a center. Instead of which the sun and
planets move round one common center, called the center of gravity.
PUPIL. What is this center of gravity?
TUTOR. Have you never seen a person raise a heavy weight by means of a
long pole or leaver, which it was not in his power to lift without it?
PUPIL. Yes, Sir, and it excited my astonishment.
TUTOR. Now, suppose the weight to see raised to be 10 Cwt. and the prop
on which the leaver rested 1 foot from the body to be raised; and the
person at the other end of the leaver 10 feet from the prop; with what
weight must he press to raise the 10 Cwt.?
PUPIL. I think that very easy; for, as he is ten times as far from the
prop as the weight is, a pressure of 1 Cwt. which is one-tenth of the
weight to be raised will do it.
TUTOR. To be sure; and yet you say you were astonished when you saw it!
Every thing we do not understand at first appears difficult.—To apply
this to our present purpose. You see that a weight of 1 Cwt. at 10 feet
from a prop, will balance another of 10 Cwt. at one foot from it. Now,
instead of a prop let the two weights be nicely poised on a center,
round which they may freely turn; the heaviest would move in a circle,
whose radius, or distance from the center would be one foot, whilst the
lightest would move in one 10 feet from the center in the same time.
PUPIL. Is the center round which they move the center of gravity?
TUTOR. It is; and round an imaginary point as a center the sun and
planets move, always preserving an equilibrium. If the earth were the
only attendant on the sun, as his quantity of matter is 200,000 times as
great as that of the earth, he would revolve in a circle a 200,000th
part of the earth’s distance from him, in the same time as the earth is
making one revolution in its orbit, or in one year; but, as the planets
in their orbits must vary in their positions, the center of gravity
cannot be always at the same distance from the sun.
PUPIL. If it were, the balance could not be preserved.
TUTOR. Clearly so. But you must know that the quantity of matter in the
sun so far exceeds that of all the planets together, that even if they
were all in a line on one side of him he would never be more than his
own diameter distant from his center of gravity; therefore, astronomers
consider the sun as the center of the system, and express themselves
accordingly.
PUPIL. As you told me the secondary planets are governed by the same
laws as the primaries, I imagine they also with their primaries move
round a center of gravity.
TUTOR. They do so.—The earth and moon, Jupiter with his satellites,
Saturn and his attendants, revolve about their respective centers;
these, with the sun and the rest of the planetary system, make their
circuits round their center; every system in the universe is supposed to
revolve in like manner; and all these together to move round one _common
center_.—How are we lost in contemplating the omniscience of the Deity!
How difficult to conceive so many millions of bodies of dead matter
constantly in motion, so nicely balanced and governed by such unerring
laws!—Well may we say with the Psalmist, “Lord! how manifold are thy
works, in wisdom hast thou made them all.”
------------------------------------------------------------------------
DIALOGUE VIII.
TUTOR.
I shall now, agreeably to my promise, explain to you the cause of day
and night, and then proceed with the vicissitudes of the seasons.
PUPIL. That is what I much wish to know; and had you not told me that
the earth moved round the sun every year, I should have found no
difficulty in accounting for the succession of day and night, since the
sun appears to rise and set every day.
TUTOR. That is true; but I think I must have convinced you that so
immense a body as the sun cannot revolve about the earth; as well may
you suppose that in roasting a bird it is necessary that the fire should
move round it.
PUPIL. That I think would be very absurd, as it is much easier for the
bird on the spit to turn to the fire, than for the fire to go round the
bird.
TUTOR. You are certainly right, and if the earth revolve on its axis
every twenty-four hours, will not the different parts of it be
alternately turned to the sun, as the bird on the spit is to the fire?
PUPIL. I do not clearly comprehend what you mean by the axis of the
earth; for, as it moves in open space and has no support, it can have
nothing to resemble the spit on which it turns.
TUTOR. Certainly not. By the earth’s axis is meant an imaginary line
passing through its center, on which it is supposed to turn; as your
ball if rolled on the ground would revolve on an axis whilst it was
moving forward.
PUPIL. I can now answer your question in the affirmative: and, as our
year consists of 365 days, I imagine the earth must make as many
revolutions on its axis whilst it is going once round the sun.
TUTOR. Undoubtedly: and as only one half of a spherical body can at any
time be enlightened by a luminous body, that part of the earth only
which is turned to the sun, can receive the benefit of his enlivening
rays, when it will be day; whilst the opposite part will be involved in
darkness, and it will be night.
PUPIL. I perceive it must be so. But, if the earth move in the manner
you describe, I cannot conceive how it is that we are not sensible of
its motion.
TUTOR. If the motion of the earth were irregular it would be
perceptible; but as it meets with no obstruction the motion must be so
uniform as not to be perceived.
PUPIL. Had I recollected this, I need not have given you this
trouble.—But I am continually meeting with fresh difficulties.
TUTOR. You have only to mention what they are, and I shall take a
pleasure in removing them.
PUPIL. I thank you, Sir; and shall be obliged to you to inform me, how
the motion of the earth can cause the sun to appear to move?
TUTOR. When in a carriage which went smoothly on the road, or in a boat
whose motion was scarcely perceptible on the water, did you never fix
your attention on the objects you passed?
PUPIL. Yes, often, Sir.
TUTOR. And had you not known that you really moved, and that the trees,
&c. were immoveable in the ground, what then would have been your
opinion?
PUPIL. That the trees, &c. moved in a direction contrary to that in
which I was moving.
TUTOR. Is not this sufficient to convince you that the apparent motion
of the sun may be occasioned by the revolution of the earth on its axis?
PUPIL. It is:—But if so large a body as the earth make a revolution on
its axis in 24 hours, it must move with great velocity.
TUTOR. It does so; and the inhabitants of London by this motion are
carried at the rate of 560 miles an hour[13].
[Footnote 13: The hourly motion under the equator is 900 miles.]
PUPIL. What an astonishing rapidity!
TUTOR. Now, the sun with the rest of the heavenly bodies must move round
the earth, or the earth must revolve on its axis in 24 hours, to cause
that appearance.
PUPIL. That is plain.
TUTOR. Well then, great as you may suppose the velocity of the earth on
its axis to be, if the sun move round the earth his hourly motion will
be nearly 25 millions of miles; and beyond conception would be that of
the fixed stars. Which now do you think is most probable, that the sun
and stars should move round the earth, or that they, by the simple
motion of the earth, should appear to be in motion?
PUPIL. The latter, to be sure, Sir.—I have one difficulty remaining,
which is this; if a lark rise from a field near London and remain in the
air a quarter of an hour, if the earth move at the rate of 560 miles an
hour, it will go 140 miles whilst the lark is suspended, and yet it
continues over the field,—how can this be?
TUTOR. This objection to the motion of the earth has been made by those
who were older and who thought themselves wiser too than yourself. They
either did not know or did not consider, that the atmosphere which
surrounds the earth is a part of itself, and gravitates towards it, and
therefore partakes of the earth’s motion and carries the lark along with
it. Besides, as the Sun, Venus, Mars, and Jupiter are known to revolve
on their axes, we have reason to suppose that the other planets,
together with the earth, must have the same motion[14].
[Footnote 14: Dr. Herschell says that several of the fixed stars
revolve on their axes.]
PUPIL. How is it known that they do revolve on their axes; and in what
time do they perform their revolutions?
TUTOR. By the assistance of telescopes dark spots have been seen on the
disc of the sun, by the motion of which it is found that he revolves on
his axis in 25-1/4 days; Venus performs her diurnal revolution in about
23 ho. 21 min.; Mars goes round his axis in 24 ho. 39 min.; and Jupiter
in 9 ho. 56 min.; as to the rest, no spot or any fixed point has been
discovered to ascertain the length of their day; Mercury being too near
the sun, and Saturn and the Georgium Sidus too remote for our
observations.
PUPIL. I can no longer doubt of the earth’s motion: and, if it will not
be improper, a description of the atmosphere will give me pleasure.
TUTOR. That I can have no objection to. The atmosphere is a thin,
invisible fluid, most dense or heavy near the earth, but grows gradually
rarer or lighter the higher we ascend, so much so, that at the tops of
some high mountains it is difficult to breathe. It serves not only to
suspend the clouds, furnish us with wind and rain, and answer the common
purposes of breathing, but is also the cause of the morning and evening
twilight, and of all the glory and brightness of the firmament.
PUPIL. How, pray?
TUTOR. If there were no atmosphere, the sun would yield no light but
when our eyes were directed towards him; and the heavens would appear
dark and as full of stars as on a dark winter’s night; but the
atmosphere being strongly illuminated by the sun, reflects the light
back upon us, and makes the whole heavens to shine so strongly, that the
faint light of the stars is obscured, and they are rendered invisible.
PUPIL. I find then the atmosphere is of more use than I imagined. But
how is it the cause of the twilight?
TUTOR. The atmosphere is about 45 miles above the surface of the earth,
therefore the sun’s rays falling upon the higher parts of it before
rising, by reflection causes a faint light, which increases till he
appears above the horizon; and in the evening it decreases after he
sets, till he is 18 degrees below the horizon, where the morning
twilight begins, and the evening twilight ends.
PUPIL. By the horizon, I think you mean that distant boundary of our
sight where the heavens and the earth seem to join all around us, as it
appears from an eminence.
TUTOR. The very same. ’Tis that imaginary circle which intercepts from
our view the sun, moon, and stars each night; and when, by the rotation
of the earth, they appear to descend below it, we say they are set; as
on the contrary, each morning, when they appear above it, we say they
rise.
“To find the spacious line, cast round thine eyes,
“And where the earth’s high surface joins the skies,
“Where stars first set, and first begin to shine,
“There draw the fancy’d image of this line.”
PUPIL. A very pleasing description, indeed.
TUTOR. You will remember that this is called the _rational horizon_; but
that which respects land and water is called the _sensible horizon_. The
former divides the heavens into two equal parts, and is 90 degrees
distant from a point directly over our heads, called the _zenith_, and
the opposite point of the heavens directly under our feet, called the
_nadir_.—But I must resume the subject of the atmosphere.
PUPIL. Had I not thought you had finished your description of the
atmosphere, I should not have presumed to interrupt you.
TUTOR. What I have told you respecting the horizon is necessary for you
to be acquainted with; therefore, the suspension is immaterial.—You
must, I make no doubt, have observed the sun and moon at rising and
setting to appear larger than when higher above the horizon.
PUPIL. I have, frequently, Sir.
TUTOR. And cannot you tell the reason of it?
PUPIL. No, Sir.
TUTOR. The reason is this: In viewing them, when near the horizon, you
see them through a thicker medium than when they are higher, that is,
you see them through a greater quantity of the atmosphere; and you not
only see them larger, but really above the horizon whilst they are
actually below it.
PUPIL. How do you account for this, Sir?
TUTOR. Light, like material bodies, if it meet with no obstruction, will
move in right lines; now, the rays of the sun in coming to the earth
must pass through a great quantity of the atmosphere, which being a
fluid, refracts or bends the rays of light, by which refraction it is
that we are favoured with the sight of the sun 3-1/4 minutes every
morning before he rises above the horizon, and every evening after he
sinks below it, which in one year amounts to more than 40 hours. This
refraction is greatest near the horizon, and ends in the zenith.
PUPIL. Pray, Sir, can you make this clearer by an experiment?
TUTOR. I have just thought of one. Take a bason filled with water, and a
strait stick or piece of wire; put it perpendicularly into the water,
that is, that it lean neither way, and there will be no refraction;
incline it a little towards the edge of the bason and it will appear a
little bent at the surface of the water; incline it still more, and the
refraction will be greater.
PUPIL. I have often seen this appearance when I have put my stick into
water, but did not before know the cause.
TUTOR. You may try one more experiment. Pour the water out of the bason,
and set the bason on the floor; put a guinea into it, and let it
represent the sun.—Why do you smile?
PUPIL. Because I have not the sun’s representative to try the experiment
with.
TUTOR. Well, well, put a shilling into the bason and call it the moon,
and it will answer the same purpose:—Walk backward till you just lose
sight of it, then the right line from your eye continued over the edge
of the bason must pass beyond the money at the bottom of it.
PUPIL. That is evident.
TUTOR. Keep your position, and desire some friend to pour the water
gently into the bason so as not to remove the money, and you will
clearly distinguish it. Now, if you call the edge of the bason the
horizon, the water the atmosphere, and the shilling the moon, is it not
clear that you will see it above the horizon, when it is really below
it?
PUPIL. I think so, Sir.
TUTOR. Well, try the experiment, and let me know the result when I next
see you.
------------------------------------------------------------------------
DIALOGUE IX.
TUTOR.
I presume, Sir, you have made the experiment I recommended to you.
PUPIL. I have, Sir; and am so well convinced of what you told me, that
nothing farther need be said on the subject.
TUTOR. As that is the case, I shall proceed.—I dare say you do not
forget what the plane of the ecliptic is.
PUPIL. I do not, Sir; but have a perfect recollection of it.
TUTOR. Now, remember, that the axis of the earth is not upright or
perpendicular to the plane of the ecliptic, but inclines to, or leans
towards it, 23-1/2 degrees, and makes an angle with it of 66-1/2
degrees.
PUPIL. An angle signifies a corner; but that cannot be the meaning here.
TUTOR. That is what is generally understood by an angle: but, in
geometry, it means the meeting of any two lines which incline to one
another, in a certain point. Now, if you conceive the axis of the earth
to be one line, and the plane of the ecliptic the other, the point where
they meet or cross each other will form an angle.
PUPIL. I think I understand it; but how can it contain 23-1/2 or 66-1/2
degrees?
TUTOR. You know what a degree is.
PUPIL. If I remember right it is the 360th part of a circle.
TUTOR. It is so: and the measure of an angle is an arc or part of the
circumference of a circle, whose angular point is the center: and so
many 360th parts as any arc contains, so many degrees the measure of the
angle is said to be; thus, Z C P (Plate III. fig. 1.) makes an angle of
23-1/2 degrees, because the arc Z P contains 23-1/2 360th parts of the
whole circle. Then if A B represent the plane of the ecliptic, and N C S
the axis of the earth, as D N contains the same number of degrees as Z
P, will not its inclination from a perpendicular be 23-1/2 degrees?
[Illustration: _Plate III._
_T. Conder Sculp^t._]
PUPIL. Nothing can be plainer.
TUTOR. For the same reason, as P B contains 66-1/2 parts of the whole
circle, the axis of the earth makes an angle of 66-1/2 degrees with the
plane of the ecliptic. And, if you add 23-1/2 to 66-1/2 the sum will be
90, which is the measure Z B, or the fourth part of the circle, and
makes what is called a right angle, at the point or center C.
PUPIL. It is very clear:—but what do the other letters refer to?
TUTOR. The extremities of the earth’s axis are called the poles, N the
north, and S the south pole, and P the north-pole star, to which, and to
the opposite part of the heavens, the axis always points. These
extremities in the heavens appear motionless, whilst all other parts
seem in a continual state of revolution: the circle of motion appears to
increase with the distance from the apparently motionless points to that
circle in the heavens which is at an equal distance between them, called
the equinoctial, represented by the letters Æ Q; and is the same I
promised some time ago to explain to you.
PUPIL. I recollect it: and as the line A B represents the plane of the
ecliptic, I suppose the line Æ Q is the plane of the equinoctial, which
I see crosses it as you then told me.
TUTOR. You are right: and it makes an angle with it of 23-1/2 degrees.
It is called the equinoctial, because when the sun appears there, that
is, in Aries or Libra, the days and nights are equal in all parts of the
world, which I shall shew you in due time; and shall now explain to you
what I have just mentioned, that the axis of the earth always points to
the same parts of the heavens. I am apprehensive you will think it
strange that this should be the case, and the axis keep parallel to
itself.
PUPIL. What am I to understand by the axis being parallel to itself?
TUTOR. Two lines are said to be parallel when they do not incline to but
keep at equal distances from each other; so that if they were infinitely
continued, they would never meet. Now, if you can conceive a line drawn
parallel to the earth’s axis in any part of its orbit, it will be
parallel to it in every other part of it. A little drawing I have by me,
(Plate III. fig 2.) where the earth is represented in four different
parts of its orbit, I think will make this plain to you.
PUPIL. I comprehend your meaning clearly. But, as the orbit of the earth
is 190 millions of miles in diameter, I have not the least conception
how it can incline to the same points. Had you not told me to the
contrary, I should have thought it must move round them in every
revolution of the earth about the sun.
TUTOR. That such a motion would be perceptible is evident, if the fixed
stars were near the earth; but, compared with their distance, 190
millions of miles is but a mere point: therefore, the axis always
inclines to the same points of the heavens.
PUPIL. This is a greater proof of the inconceivable distance of the
stars than what you mentioned before, and I thought that very
astonishing:
Wonders on wonders constantly arise,
Whene’er we view the earth, or sea, or skies.
TUTOR. It is very true. And the more we search, the more we have cause
to admire the works of the Almighty.
PUPIL. Pray, Sir, what is the next thing you propose?
TUTOR. To make you acquainted with the other circles you see in the
figure (Plate III. fig. 1.) as it is very necessary you should know
them.
PUPIL. Will you be kind enough to tell me their names, Sir, and I will
endeavour to remember them?
TUTOR. That line which divides the globe into two equal parts, called
the northern and southern hemispheres, which answers to the equinoctial
in the heavens, and is equally distant from the two poles, is called the
_equator_; the other which crosses it, as I before told you, is the
_ecliptic_; the smaller circle, north of the equator, is the _tropic of
Cancer_; that south of it, the _tropic of Capricorn_; the circles next
the poles are called the _polar circles_; or that next the north pole,
the _arctic circle_, and that next the south pole, the _antarctic
circle_; each of which is 23-1/2 degrees distant from its respective
pole, as are the tropics from the equator.
PUPIL. You have not mentioned the lines which cross the other circles,
and terminate in the poles; what are they called?
TUTOR. They are called _meridians_, because when any of them, as the
earth revolves on its axis, is opposite to the sun, it is mid-day or
noon along that line. Twenty-four of these lines are usually drawn on
the globe to correspond with the twenty-four hours of the day; but you
are not to suppose there are no more than twenty-four; for every place
that lies ever so little east or west of another place has a different
meridian.—To make this clearer to you, we will suppose the upper 12
(Plate III. fig. 1.) to be opposite the sun, it will of course be noon
along that line; the next meridian marked 1, being 15 degrees east, will
have passed the meridian 1 hour, consequently it will there be one in
the afternoon, and so on, according to the order of the figures, till
you come to the lower 12, which being the part of the earth turned
directly from the sun, it will be midnight on that meridian; on the next
meridian, as you proceed round, it will be one in the morning, the next
two, and so on till you arrive at the upper twelve, where you set off.
So you see there must be a continual succession of day and night. This
difference of time between places lying under different meridians is
what is called longitude.
PUPIL. I think I have heard of a Mr. Harrison, who made a time-keeper
for determining the longitude. Shall I trespass at all if I beg a little
farther information on this subject?
TUTOR. It is my wish at all times to satisfy your curiosity, when I can
do it with propriety. I shall therefore comply with your request.—Mr.
Harrison’s time-keeper, and those made since by other artists, are so
constructed, that the heat and cold of different climates will not
affect them; for, all metals are more or less expanded by heat, and
contracted by cold; for which reason it is, that a clock or watch made
in the usual way will not keep equal time. Now, all that is required of
these time-keepers to ascertain the longitude is this: Suppose a captain
of a vessel sailing from London to the West Indies, we will say
Kingston, in Jamaica. On his passage thither he makes an observation,
and finds the sun on the meridian, or that it is twelve o’clock in that
situation, when by his time-keeper it is two in the afternoon in London,
whence he concludes he is 30 degrees west of London.
PUPIL. I must beg you to explain this to me, as I do not understand why
two hours of time should be equal to 30 degrees of longitude.
TUTOR. You must consider, that as the earth makes a complete revolution
on its axis in 24 hours, it must pass over 360 degrees in that time:
now, if you divide 360 by 24, the quotient 15, will be the number of
degrees passed over in one hour; 30 degrees will be equal to two hours,
&c. The difference of time between London and his situation is two
hours, consequently the difference of longitude must be 30 degrees: and,
it must be west, because the sun had passed the meridian of London; for,
as the earth revolves from west by south to east, one place which lies
east of another must come first to the meridian or opposite to the sun.
Therefore, when longitude is reckoned from London, if the place lie east
of that meridian the time will be before; if west, after London.
PUPIL. I see it clearly; and as 60 minutes make an hour, if I divide it
by 15, the quotient 4 will be the minutes answering to one degree.
TUTOR. You are right: and for the same reason, 4 seconds of time are
equal to one minute of longitude, which you know is the 60th part of a
degree.—Our captain when arrived at Kingston, finds the difference of
time between it and London 5 ho. 6 min. 32 sec. Can you tell me the
longitude of Kingston?
PUPIL. If I bring the hours and minutes to minutes, and divide by 4, the
quotient I think will be degrees, will it not?
TUTOR. It will: and the seconds of time divided by 4, will be minutes of
longitude. Now try if you can do it.
PUPIL. Five hours 6 minutes, multiplied by 60 will be 306 minutes, this
divided by 4, will give 76 degrees and 2 over, which 2 is half a degree,
or 30 minutes: and 32 seconds of time divided by 4, will be 8 minutes of
longitude, the sum of which is 76 degrees 38 minutes for the longitude
of Kingston.
TUTOR. Very well.—I have just now thought of another method of reducing
time to longitude, and longitude to time, which you may probably find
easier. However, when you are in possession of both, you may use which
you please.
PUPIL. That which is easiest must, I think, be best.
TUTOR. I will give it you, and let me have your opinion of it.
To reduce time to longitude.
Multiply the hours, minutes, and seconds of time by 15, or
rather by the factors as they are called, namely 3 and 5,
carrying one for every 60 in the minutes and seconds, and
setting down the remainder, thus:
ho. min. sec.
5 6 32 difference of
3 time.
────────────────
15 19 36
5
────────────────
Degrees 76 38 0 longitude.
════════════════
Divide the degrees and minutes of longitude by 5 and 3 and the
quotient will be the difference of time.
PUPIL. I give this the preference.
TUTOR. As longitude is seldom mentioned without being accompanied with
latitude, that you may not be ignorant of its meaning when you meet with
it, I shall just tell you that it is the distance of any place from the
equator, reckoned in degrees and minutes on the meridian, and is either
north or south as the place lies north or south of the equator. The
latitude of any place is equal to the elevation of the pole above the
horizon. The latitude of the heavenly bodies is reckoned from the
ecliptic, and terminates in the arctic and antarctic circles: and their
longitude begins at the point Aries.
PUPIL. What is the measure of a degree?
TUTOR. A degree of latitude is 60 geographical, or 69-1/2 English miles:
and a degree of longitude on the equator is equal to it, because the
equator as well as the meridians divides the globe into two equal parts.
But a degree of longitude decreases as you approach the poles: for at
the poles the meridians meet in a point, consequently a degree there can
have no dimension. To-morrow I will shew you the cause of the seasons.
------------------------------------------------------------------------
DIALOGUE X.
PUPIL.
I think, Sir, when you left me last night you told me our next business
would be to explain the nature of the seasons?
TUTOR. I did so, and am persuaded you will find no great difficulty in
comprehending it.—Cast your eye on the little drawing I gave you, (Plate
III. fig. 2.) where the earth is represented as situated at the four
quarters of the year, namely, Spring, Summer, Autumn, and Winter.—But
before we proceed to an explanation it will be necessary to remark,
that, in the little scheme the eye is supposed to be elevated above the
plane of the earth’s orbit, and that we see it very obliquely. The orbit
by this means appears very elliptical; and, the enlightened hemisphere,
or that half of the earth which is turned to the sun in the spring, and
the darkened hemisphere, or that turned from him in the autumn, are
there represented.
PUPIL. This I understand.
TUTOR. Well then, we will begin with the spring.—In this situation of
the earth the equator is exactly opposed to the sun: and, as he always
enlightens a hemisphere, or half of its surface, his rays will reach to
both the poles: whence, from the diurnal revolution of the earth, the
day and night are equal all over the globe.
PUPIL. This I remember you told me happened when the sun was in Aries
and Libra. The sun is now entering Aries: and, as we are in the rays of
the sun one half of the diurnal revolution, and in the shadow of the
earth, or dark, the other half, the day and night must be equal.
TUTOR. Certainly. And as the sun enters Aries in the equinoctial, it is
then called the _Vernal_, that is, _Spring Equinox_. When the sun enters
the opposite sign Libra, the same effects are produced, and it is then
called the _Autumnal Equinox_.
PUPIL. You have passed on from Spring to Autumn.
TUTOR. I have so.—We will now return, and trace the earth in its orbit
from spring to summer.—You have already seen that the north and south
poles are both enlightened, and that the day and night are equal at the
equinoxes. If the axis of the earth were perpendicular to the plane of
the earth’s orbit, this would constantly be the case, and we should have
no diversity of seasons: for, the sun being over the equator, the poles
must be perpetually enlightened, and of course we should have equal day
and night at all times of the year.
PUPIL. That is plain. I suppose then that it is to the inclination of
the earth’s axis we are indebted for the increase and decrease of days.
TUTOR. It is occasioned by the inclination of the earth’s axis and its
preserving its parallelism, which I explained to you last evening.—As
the sun is now in the first point of Aries, the earth you know must be
in the beginning of Libra, it being the opposite sign.—Now fix your
attention on the scheme, and imagine the earth to be advancing in its
orbit through Libra, Scorpio, and Sagittarius: and at the first degree
of Capricorn give me your opinion of the earth’s position.
PUPIL. The north pole is turned to the sun, the south pole from him, and
the tropic of Cancer is opposite to him.
TUTOR. How many degrees are the tropics from the equator, or, in other
words, what is the inclination of the earth’s axis?
PUPIL. Twenty-three degrees and a half.
TUTOR. And so far are the rays of the sun cast beyond the north pole,
and fall short of the south pole: so that the whole of the arctic circle
is enlightened, and the antarctic circle involved in darkness.
PUPIL. What conclusion am I to draw from this?
TUTOR. That in the northern half of the globe it is the longest day, or
summer, and in the southern half the shortest, or winter, whilst under
the equator the days and nights are equal.
PUPIL. I used to think that when it was winter or summer here it was so
in every part of the world.
TUTOR. You now find your mistake. For as the earth is making its
progress from Libra, the north pole is approaching the sun, and the
south pole receding from him: consequently the length of the day is
increasing in the northern hemisphere and decreasing in the
southern.—The sun has now been three months above the horizon of the
north pole, and the same time below that of the south pole, and in three
months more, when the earth arrives at Aries, the scene will be
reversed: the sun will be over the equator, both poles will be again
enlightened, and the day and night will be equal in every part of the
globe. The sun will now be rising to the south and setting to the north
pole. This is our Autumn.
PUPIL. And as the earth is advancing towards winter, the south pole will
be turning to the sun, and the north pole from him, whence I conclude
that when the earth is in Cancer it must be summer, south of the
equator, when it is our winter.
TUTOR. Most assuredly. For you see that the sun is over the tropic of
Capricorn, which you know is as much south of the equator as the tropic
of Cancer is north of it, where the sun was in our summer. The antarctic
circle is now enlightened, and the arctic obscured in shade; but, under
the equator there is neither increase nor decrease, the days and nights
being each twelve hours.
PUPIL. It is now our winter, the sun has been three months above the
horizon of the south pole, and will continue so till the vernal equinox,
when he will again rise to the north pole, and so on in regular
succession.
TUTOR. It must be plain then to you that there can be but one day and
one night at each of the poles, reckoning the time the sun is above or
below their respective horizons; under the arctic and antarctic circles,
the longest day is twenty-four hours, and in the shortest the sun is
just visible in the horizon at noon. The longest day decreases in length
the nearer we approach the equator, where I before observed there is no
variation, because the circle bounding light and darkness, in every
position of the earth, divides the equator into two equal parts; and, it
must be observed, that the longest day and longest night are equal to
each other in every part of the globe.
PUPIL. If the longest day under the arctic circle be just twenty-four
hours, the sun must rise in the north.
TUTOR. He does so, makes a complete circle and sets in the [15]north
again. From the arctic circle to the equator, he rises north of the east
and sets north of the west: at the equator he rises due east and sets
due west, thence southward to the antarctic circle, he rises south of
the east, and sets south of the west: and under the antarctic circle, as
I observed just now, he is visible in the horizon in the south at noon.
[Footnote 15: Here it must be observed that there will be a little
variation from sun-rising to sun-setting, as the earth is advancing
in its orbit.]
PUPIL. We usually say, the sun rises in the east and sets in the west.
TUTOR. At the equinoxes it must be so in all parts of the globe, the
poles excepted: in every other situation, except under the equator,
there is a continual change. What I have now told you, respecting the
northern hemisphere, will be reversed at our shortest day: that is, in
the northern hemisphere the sun will rise south of the east and set
south of the west; and, in the southern hemisphere the contrary, the sun
will be in the horizon, at noon, under the arctic circle, and the day
will be twenty-four hours under the antarctic circle.
PUPIL. Pray Sir, are the regions within the polar circles inhabited? If
they are, their situation, in winter, must, I think, be dreadful.
TUTOR. It is foreign to my present purpose to speak of the inhabitants
of the earth, as that more properly belongs to Geography. Thus much
however I shall tell you, that, although it must be very cold and
dreary, they are not so long deprived of light as you may imagine; for,
even under the poles, when the sun is hidden from them, they are but a
short time in total darkness, for, you must recollect, that the twilight
continues till the sun is eighteen degrees below the horizon; and the
sun’s greatest depression, you know, can be but twenty three degrees and
a half, equal to the inclination of the earth’s axis. Besides this, the
moon is above the horizon of the poles a fortnight together; being half
her period north, and the other half south, of the equator; and, as the
moon at full is in the sign opposite to the sun, the tropical full moons
must be twenty-four hours above the horizon at the polar circles.
PUPIL. This description is very pleasing, as I had no idea of their
being favoured with so much light in the absence of the sun: and, I
find, as the sun is longer above the horizon in summer than in winter,
the moon, on the contrary, continues longer with us in winter, when we
most need her assistance, than she does in summer.
TUTOR. As you seem to understand what I have been explaining, I shall
shew you, that the reason why it is hottest when we are farthest from
the sun is, that in winter when we are nearest to him the days are
shorter, his rays sail very obliquely on us, and are more dispersed than
they are in summer, when he not only remains longer above the horizon,
but being higher, his rays fall more direct on us, by which means the
earth becomes so much heated that it has not time in the short nights to
get cold again.—When the earth is nearest the sun it is summer in the
southern hemisphere, therefore it is reasonable to suppose that the heat
there must far exceed ours in the same latitude; but to counteract this
their summer is shorter by eight days than ours: and it is well known
that it is much colder near the poles in the southern than in the
northern hemisphere: but this is accounted for from there being more
land to retain the heat in the latter than in the former.
PUPIL. My doubts on this head being now removed, I must beg you to give
me such other information as you may think proper.
TUTOR. As there are different degrees of heat and cold, the earth has
been divided into five zones, namely, one torrid, two temperate, and two
frigid zones.
PUPIL. How are they distinguished?
TUTOR. The torrid zone is all that space surrounding the globe contained
between the tropics, having the equator running through the middle of
it. It is so called on account of its excessive heat, for, twice every
year the sun is vertical to the inhabitants, that is, he shines directly
on their heads, and casts no shadow, but under their feet, at noon.
PUPIL. We find it sometimes extremely hot here in our summer; surely, in
the torrid zone it must be almost insupportable?
TUTOR. They are inured to it from their infancy.—But we are departing
from our subject.—The temperate zones are comprehended between the
tropics and polar circles, that between the tropic of Cancer and the
arctic circle is called the north temperate zone, and that between the
tropic of Capricorn and the antarctic circle the south temperate zone.
PUPIL. I suppose they are called temperate because the heat is not so
intense as in the torrid zone?
TUTOR. True. Neither is the cold so severe as in the frigid zones, which
are those regions comprized within the polar circles, and are
denominated north and south, as they are contiguous to the north or
south poles.
PUPIL. Why are they called frigid?
TUTOR. They are called frigid or frozen zones, because near the poles
there are perpetual fields of ice, the heat of the sun, even in summer,
being insufficient to dissolve it.—Now try if you can tell me the
breadth of each zone in degrees.
PUPIL. The torrid zone being twenty-three degrees and a half on each
side the equator must be forty-seven degrees, which must also be the
breadth of the frigid zones, as the polar circles are distant
twenty-three degrees and a half from the poles, which are their centers.
And, as from the equator to either pole is ninety degrees, from the
equator to the tropics twenty-three and a half, and from the polar
circle to the pole twenty-three and a half, if the sum of these, that
is, forty-seven, be taken from ninety, the remainder, forty-three, will
be the breadth of each of the temperate zones.
TUTOR. Very well.
PUPIL. From what you have told me I have no doubt but that the earth is
globular, but I have no proof of it: I must therefore beg your
assistance.
TUTOR. That it cannot be an extended plane, as some have imagined, is
very evident; for, if it were, the angle made with that plane and the
north pole star would be always equal, for reasons I have before given
you: neither can it be cylindrical, that is like a garden roller, as
others have supposed.—If a person travel northward the pole star becomes
more elevated, and if he could penetrate to the north pole of the earth
the star would be in the zenith, or directly over his head: on the
contrary, if he travel southward, it is more and more depressed till he
arrives at the equator, where the star is in the horizon; as he proceeds
it disappears, and other stars rise to his view, invisible to us. Here
then you see it must be circular northward and southward.
PUPIL. I am convinced it must be so.
TUTOR. And it is as certain that it is so east and west: for, navigators
have often sailed round it steering the same course: that is, if they
sail an easterly or westerly course at setting off, by continuing the
same course they will return to the port whence they departed. This you
know they could not do if it were not round, any more than an insect
could, by crossing a round table, arrive at the place it set out from;
but, by going round the edge it would be still going forward and come
again to the point it had left.
PUPIL. It is very evident.
TUTOR. Again. In every direction, if a ship be seen at a distance, the
first things observed are the top-mast and rigging, whilst the hull or
body of the ship is hidden behind the convexity, that is roundness of
the water, just as you would see a man coming over a hill, you would
first see his head, he would be rising more and more to your view till
he arrived at the top, where he would be full in sight.
PUPIL. I am at a loss to account for the convexity of the water. How can
its surface be round?
TUTOR. Have you never observed the drops of water falling from the eaves
of a house?
PUPIL. Often, Sir.
TUTOR. Of what shape were they?
PUPIL. Globular.—But what is the cause of their being so?
TUTOR. Attraction.—For as every particle of water which composes the
drop tends to the same center, every part of the surface must be
equidistant from the center, it must therefore be spherical. In like
manner if you separate quicksilver, each portion will form itself into a
globe.
PUPIL. All this is very clear. And, for the same reason, the water in
the ocean must be convex; for, I remember you told me that it gravitated
towards the center of the earth.
TUTOR. Once more.—I think you must have seen an eclipse of the moon.
PUPIL. I have, Sir.
TUTOR. Of what figure was the darkened part?
PUPIL. Circular.
TUTOR. Take this ball, and hold it before the candle between your finger
and thumb, so that the shadow may be thrown on the wall, and in all
positions you will find it circular.
PUPIL. It is so.
TUTOR. Apply this crown piece in the same manner, with the flat side to
the candle.
PUPIL. It is a circle.
TUTOR. Turn it a little obliquely.
PUPIL. It is now an ellipsis.
TUTOR. Now turn the edge to the candle.
PUPIL. The shadow is a strait line.
TUTOR. You now see that no other body than that of a globe can in all
positions cast a circular shadow.
PUPIL. I do, Sir.
TUTOR. The darkness on the disc of the moon at the time of an eclipse is
the shadow of the earth, which in all situations is circular; the earth,
therefore, which casts the shadow, must be a globe.
PUPIL. It must be so.—But——
TUTOR. The earth is mountainous.—It is so: but remember that the highest
mountain bears no greater proportion to the bulk of the earth than the
small irregularities on the peel of an orange bears to that fruit: that
objection therefore is soon removed. And yet it is not a true sphere.
PUPIL. What then?
TUTOR. A spheroid, that is, it is a little flattened at the poles, and
is in shape not unlike an orange or a turnip. This you will not be
surprized at when I tell you that the equatorial parts are about four
thousand miles from the center of motion.
PUPIL. I suppose then you infer that as the centrifugal force is greater
the farther it is removed from the center, that the parts near the poles
have a tendency to fly off towards the equator.
TUTOR. I do. And as we have finished this part of our subject, I shall
take leave of you.
------------------------------------------------------------------------
DIALOGUE XI.
TUTOR.
I now propose giving you a description of the moon, and I doubt not it
will afford you some degree of pleasure.
PUPIL. Indeed it will, as I know little more than that she is a
secondary planet or satellite, revolving round the earth, and with it
round the sun.
TUTOR. You know her mean distance from the earth.
PUPIL. I did not recollect that: 240 thousand miles.
TUTOR. Right. Her diameter is about 2161 miles, and her bulk about a
fiftieth part of the earth’s. Her axis is almost perpendicular to the
plane of the ecliptic, consequently she can have no diversity of
seasons.
PUPIL. What is her period?
TUTOR. The time she takes to revolve from one point of the heavens to
the same again is called her _siderial_ or _periodical revolution_, and
is performed in 27 days, 7 hours, 43 minutes; but _synodical
revolution_, or the time taken up to revolve from the sun to the same
apparent situation with respect to the sun again, or from change to
change, is 29 days, 12 hours, and 44 minutes.
PUPIL. I do not clearly comprehend it.
TUTOR. If the earth had no annual motion, the period of the moon would
be uniformly 27 days, 7 hours, 43 minutes; but you are to consider that
whilst the moon is revolving round the earth, the earth is advancing in
its orbit, and of course she must be so much longer in completing her
synodical revolution as the difference of time between that and her
siderial revolution. This I will make clear to you in a few
minutes.—What is the situation of the hour-hand and minute-hand of a
watch at twelve o’clock?
PUPIL. They will be in conjunction.
TUTOR. And will they be in conjunction at one?
PUPIL. No, Sir.
TUTOR. Yet the minute-hand has made a complete revolution: but before
they can be in conjunction again the minute-hand must move forward till
it overtakes the hour-hand.
PUPIL. I now understand it, and must beg you to explain to me the
different phases of the moon.
TUTOR. Take this ivory ball, and suspend it by the string with your hand
between your eye and the candle. Let the candle represent the sun, the
ball the moon, and your head the earth. In this situation, as the candle
enlightens only one half of the ball, the part turned from you will be
enlightened, and the part turned to you will be dark. This will be a
representation of the moon at change, and as no part of her enlightened
hemisphere is turned to the earth, she can reflect no light upon it, and
consequently is invisible to us. She now rises and sets nearly with the
sun.—Turn yourself a little to the left, and you will observe a streak
of light like what is called the new moon.
PUPIL. I see it clearly.
TUTOR. Move round one quarter.
PUPIL. One half of the side next me is now enlightened.
TUTOR. You may conceive it to be the moon at first quarter.—Go on, and
you will see the light increase till the ball is opposite to the candle,
when the side next you will be wholly illumined, and will give you a
just idea of the moon at full, which now rises about the time of
sun-setting, being opposite to the sun: and, the farther she advances in
her orbit the later she rises.
PUPIL. It is plain it must be so. She rises with the sun at change,
being then in conjunction: and as she revolves in her orbit the same way
as the earth does on its axis, the earth will have farther to revolve
each day before it can see the moon. At the full she is in opposition,
and of course rises when the sun sets: and so continues to rise later
and later, till the change again.
TUTOR. You imagine that the moon rises exactly with the sun when she is
at change; and when he sets, at full. I will presently convince you of
your mistake; and would have you now proceed with your ball. Place it
again opposite to the candle, and as you turn round you will find the
light gradually decrease as it before increased, that the side that was
before enlightened is now dark, and the dark side light. When you have
gone three quarters round, one half of the side next you will be
enlightened, and will resemble the moon at last quarter. As you go on
the darkened part will increase, till you arrive at the place you set
off from, where the light is quite obscured.
PUPIL. I have now completed the circuit, and am much delighted with it,
as by this simple contrivance I can perceive the various changes of the
moon, and that the western side is enlightened from the change to the
full, and the eastern side from the full to the change.
TUTOR. I find then it has fully answered the purpose intended.
PUPIL. Indeed it has. But if you will give me leave I will use the ball
again.
TUTOR. By all means.
PUPIL. I perceive, as I move round, that the same side of the ball is
turned towards me whilst every part is turned to the candle. Is it so
with the moon?
TUTOR. It is: and as every part of the moon is turned to the sun, she
makes one revolution on her axis whilst she makes one in her orbit.
PUPIL. This is very singular. If the same side of the moon be always
turned to the earth, the opposite side of course can never see it.
TUTOR. And they must likewise be deprived of the earth as a moon.
PUPIL. True. But how is it known that the same side of the moon is
always opposed to the earth?
TUTOR. The moon, like our earth, consists of mountains and valleys,
which, when seen through a good telescope, are very beautiful. The
mountainous parts appear as lucid spots and bright streaks of light: and
as the same spots, &c. are constantly turned to the earth, she must keep
the same side to the earth.
PUPIL. It is very clear. Are there no seas?
TUTOR. It was formerly imagined that the dark parts were seas, but later
observations prove that they are hollow places or caverns, which do not
reflect the light of the sun. Besides, if there were seas there would
consequently be exhalations, and if exhalations, clouds and vapours, and
an atmosphere to support them. That there are no clouds is evident,
because when our atmosphere is clear, and the moon above our horizon in
the night-time, all her parts appear constantly with the same clear,
serene, and calm aspect.
PUPIL. Has the moon then no atmosphere?
TUTOR. If she has it is imperceptible to us: for, when she approaches
any star, we cannot discover with our best telescopes any change of
colour or diminution of lustre in the star till the instant it is lost
behind her: whence it is clear, that she can have no such gross medium
as our atmosphere to surround her.
PUPIL. May we not then doubt whether she be inhabited or not, as without
air we cannot breathe?
TUTOR. The same Almighty Being who created us and gave us air to
breathe, may have provided a different way for their existence. It does
not hold good that, because we could not live there, she is not
inhabited. Fish will live a considerable time in water under an
exhausted receiver: and, I have heard of a toad being found in a block
of marble. Your doubt therefore, I think, ought not to be admitted.
PUPIL. I am satisfied. And must now beg to be informed how I may observe
the moon’s motion.
TUTOR. Her real motion round the earth, may be easily known by remarking
when she is near any particular star. Thus, suppose you see her west,
that is to the right of it, she will be approaching, then in conjunction
with, and afterwards pass it towards the east. Her apparent motion is
that of rising and setting, which is occasioned by the rotation of the
earth on its axis.
PUPIL. I remember not long since, when you shewed me Jupiter, that the
moon was west of him: the next evening I saw her almost appear to touch
him, and soon after at a great distance from him easterly. I now see
that her real motion is from west by south to east, and her apparent
motion from east by south to west.
TUTOR. If you have no objection, I will now explain the cause of
eclipses.
PUPIL. So far from it, that it will give me the greatest pleasure.
TUTOR. Take your ivory ball, suspend it as before, in a right line
between your eye and the candle.—Can you see the candle?
PUPIL. No, Sir.
TUTOR. For what reason.
PUPIL. Because the ball prevents the light coming to me.
TUTOR. This then represents an eclipse of the sun, which can never
happen but when the moon is between the sun and the earth, which must be
at the change: for, as light passes in a right line, the sun is hidden
to that part of the earth which is under the moon, and therefore he must
be eclipsed. If the whole of the sun be obscured by the body of the
moon, the eclipse is total: if only a part be darkened, it is a partial
eclipse; and so many twelfth parts of the sun’s diameter, as the moon
covers, so many digits are said to be eclipsed.
PUPIL. May not the word digit be applied to the moon as well as the sun?
TUTOR. It may: for it means a twelfth part of the diameter of either the
sun, or the moon.
PUPIL. As you have now shewn me the cause of an eclipse of the sun, I am
anxious to have that of the moon explained.
TUTOR. We must again have recourse to your little ball.—Turn yourself
round till it is opposite to the candle in a line with your head, and
you will see that no light can be thrown on it from the candle, because
your head is between them. In like manner the rays of the sun are
prevented falling on the moon, by the interposition of the earth: she
must therefore be eclipsed.
PUPIL. I see it clearly. And as an eclipse of the sun happens when the
moon is at change, that of the moon must be when she is at full; for, it
is then only the earth’s shadow can fall on the moon, the earth being at
no other time between the sun and her.
TUTOR. The diameter of the shadow is about three times that of the moon,
and consequently the moon must be totally eclipsed whilst she continues
in it. On the contrary, the shadow of the moon at an eclipse of the sun,
covers so small a part of the earth’s surface, that the sun is totally
or centrally eclipsed to but a small part of it; and its duration is
very short. But a faint or partial shadow surrounds this darkened shade,
in which the sun is more or less eclipsed, as the place is nearer to or
farther from its center; this partial shadow is called the _penumbra_. I
have prepared for you a little drawing, representing an eclipse both of
the sun and moon, which I think will enable you better to understand
what I have been explaining. (Plate IV. Fig. 1 and 2.) In the former,
_p. p._ is the penumbra.
[Illustration: _Plate IV._
_T. Conder Sculp^t._]
PUPIL. In what does a central differ from a total eclipse?
TUTOR. An eclipse of the sun may be central, and not total; for, those
who are under the point of the dark shadow, will see the edge of the sun
like a fine luminous ring, all around the dark body of the moon when the
sun is eclipsed at the moon’s greatest distance from the earth; but when
she is nearest the earth at an eclipse of the sun, the eclipse is total.
When the penumbra first touches the earth, the general eclipse begins;
when it leaves the earth, the general eclipse ends. An eclipse of the
moon always begins on the moon’s eastern side, and goes off on her
western side; but an eclipse of the sun begins on the sun’s western
side, and goes off on his eastern side. When the moon is eclipsed in
either of her nodes, the eclipse is both central and total.
PUPIL. Pray, what is the reason we have not an eclipse at every full and
change of the moon?
TUTOR. For the same reason that Mercury and Venus are not seen to pass
over she sun’s disc at every inferior conjunction.
PUPIL. Is the orbit of the moon then inclined to the plane of the
ecliptic?
TUTOR. It is: and no eclipse of the sun can happen but when the moon is
within 17 degrees of either of her nodes: neither can there be one of
the moon, unless she be within 12 degrees. At all other new moons she
passeth either above or below the sun, as seen from the earth: and at
all other full moons above or below the earth’s shadow, according as she
is north or south of the ecliptic. You now see that the moon must
sometimes rise before and sometimes after the sun at change, and before
or after he sets at full.
PUPIL. I do, Sir, and am much obliged to you for this pleasing account
of the moon, and of eclipses: and if you have any thing farther to
observe, it will afford me additional pleasure.
TUTOR. You may, at some time or other, have an opportunity of seeing a
total eclipse of the moon; it will therefore be necessary to prepare you
for a phænomenon which otherwise you might be much surprized at, and
that is, that after the moon is immersed in the earth’s shadow, she is
still visible.
PUPIL. This is a phænomenon that I am not able to account for; for, the
moon being an opaque body, she cannot shine by her own light[16], and
the rays of the sun are prevented falling on her by the interposition of
the earth, she cannot therefore shine by reflection.
[Footnote 16: Dr. Herschell supposes the moon and the rest of the
planets may have some inherent light: the side of the planet Venus,
turned from the sun, having been seen, as we see the moon soon after
the change.]
TUTOR. It is by reflection that we see her; for the rays of the sun
which fall upon our atmosphere are refracted or bent into the earth’s
shadow, and so falling upon the moon are reflected back to us. If we had
no atmosphere, she would be totally dark, and of course invisible to us.
PUPIL. What is her appearance?
TUTOR. It is that of a dusky colour, somewhat like tarnished copper.—I
have one thing more to remark before we quit this subject, which is,
that the moon’s nodes have a retrograde or backward motion, in a
direction contrary to the earth’s annual motion, and go through all the
signs and degrees of the ecliptic in little less than nineteen years,
when there will be a regular period of eclipses, or return of the same
eclipses for many ages.
PUPIL. Pray, Sir, what do you propose for our next subject?
TUTOR. The ebbing and flowing of the sea, or cause of the tides.
------------------------------------------------------------------------
DIALOGUE XII.
TUTOR.
In order to explain the cause of the tides, I have since I saw you last
prepared a little drawing for you, (Plate IV. fig. 3.) where S
represents the sun, M the moon at change, E the center of the earth, and
A B C D its surface, covered with water. It is obvious, from the
principles of gravitation, that if the earth were at rest the water in
the ocean would be truly spherical, if its figure were not altered by
the action of some other power. But, daily experience proves that it is
continually agitated.
PUPIL. What is the cause of this agitation?
TUTOR. The attraction of the sun and moon, particularly the latter: for,
as she is so much nearer the earth than the sun, she attracts with a
much greater force than he does, and consequently raises the water much
higher, which, being a fluid, loses as it were its gravitating power,
and yields to their superior force.
PUPIL. What proportion does the attractive power of the sun bear to that
of the moon?
TUTOR. As three to ten. So when the moon is at change, the sun and moon
being in conjunction, or on the same side of the earth, the action of
both bodies is on the surface of the water, the moon raising it ten
parts,[17] and the sun three, the sum of which is thirteen parts,
represented by B _b_. Now it is evident, that if thirteen parts be added
by the attractive power of those bodies, the same number of parts must
be drawn off from some other part, as A _a_, C _c_. It will now be
high-water under the moon at _b_, and its opposite side _d_, and
low-water at _a_ and _c_.
[Footnote 17: By part here I do not mean any specific measure.]
PUPIL. That the attraction of the sun and moon must occasion a swelling
of the waters on the side next them, I can readily conceive, and that
this swell must cause a falling off at the sides: but that the tide
should rise as high on the side opposite to the sun and moon, in a
direction contrary to their attraction, is what I am not able to account
for.
TUTOR. This difficulty will be removed when you consider that all bodies
moving in circles have a constant tendency to fly off from their
centers. Now, as the earth and moon move round their center of gravity,
that part of the earth which is at any time opposite to the moon will
have a greater centrifugal force than the side next her, and at the
earth’s center the centrifugal force exactly balances the attractive
force: therefore, as much water is thrown off by the centrifugal force
on the side opposite to the moon, as is raised on the side next her by
her attraction. Hence, it is plain, that at D, fig. 3, the centrifugal
force must be greater than at the center E, and at E than B, because the
part D is farther from the center of motion than the part B. On the
contrary, the part B being nearer the moon than the center E, the
attracting power must there be strongest, and weakest at D. And, as the
two opposing powers balance each other at the earth’s center, the tides
will rise as high on that side from the moon, by the excess of the
centrifugal force, as they rise on the side next her by the excess of
her attraction.
PUPIL. In this explanation you have mentioned nothing of the sun.
TUTOR. From what I have already said it must be plain to you that if
there were no moon the sun by his attraction would raise a small tide on
the side next him; and, it is as evident that the tides opposite would
be raised as high by the centrifugal force: for the sun and earth, as
well as the earth and moon, move round their center of gravity. This may
be exemplified by an easy experiment. Take a flexible hoop, suppose of
thin brass, tie a string to it and whirl it round your head, and it will
assume an elliptical shape; the tightness of the string drawing out the
side next to your hand, and the centrifugal force throwing off the
other.
PUPIL. This I clearly comprehend.
TUTOR. I shall now refer you to the next figure, (fig. 4.) where F
represents the moon at full: the sun and moon are in opposition, and yet
the tide is as high on each side as in the former case. I wish you to
shew me the cause.
PUPIL. I will use my endeavour to do it, Sir.
TUTOR. Then I doubt not you will accomplish it.
PUPIL. When the moon is at full, ten parts of water are raised from that
side of the earth next her, by her attraction; and, as the side which is
next her is opposite to the sun, three parts must be thrown off by his
centrifugal force, the sum of which will be thirteen parts next the
moon.—From the side opposite to the moon, and under the sun, ten parts
are thrown off by her centrifugal force, and three raised by his
attraction, making thirteen, the same as before.
TUTOR. I could not have done it better. These are called _Spring Tides_.
But when the moon is in her quarters, the action of the sun and moon are
in opposition to each other; that is, they act in contrary directions
(see fig. 5.) The moon of herself would raise the water ten parts under
her, and throw off ten parts by her centrifugal force on the opposite
side; but, the sun being then in a line with the low-water, his action
keeps the tides from falling so low there, and consequently from rising
so high under and opposite to her. His power, therefore, on the
low-water being three parts, leaves only seven parts for the high water,
under and oppose the moon. These are called _Neap Tides_.
PUPIL. This is very plain.
TUTOR. You would naturally suppose that the tides ought to be highest
directly under and opposite to the moon: that is, when the moon is due
north and south. But we find, that in open seas, where the water flows
freely, the moon is generally past the north and south meridian when it
is high-water. For, if the moon’s attraction were to cease when she was
past the meridian, the motion of ascent communicated to the water before
that time would make it continue to rise for some time after: as the
heat of the day is greater at three o’clock in the afternoon than it is
at twelve; and it is hotter in July and August than in June, when the
sun is highest and the days are longest.
PUPIL. These are convincing reasons. And, pray what time after the moon
has passed the meridian, is it high-water?
TUTOR. If the earth were entirely covered with water, so that the tides
might regularly follow the moon, she would always be three hours past
the meridian of any given place when the tide was at the highest at that
place. But, as the earth is not covered with water, the tides do not
always answer to the same distance of the moon from the meridian at the
same places, because the regular course of the tides is much interrupted
by the different capes and corners of the land running out into the
oceans and seas in different directions, and also by their running
through shoals and channels. But, at whatever distance the moon is from
the meridian on any given day, at any place, when the tide is at its
height there, it will be so again the next day, much about the time when
the moon is at the like distance from the meridian again.
PUPIL. Are not the tides later every day than they were the preceding
day?
TUTOR. Yes; and the reason is obvious: for, whilst the earth is
revolving on its axis in twenty-four hours, the moon will be advancing
in her orbit; therefore the earth must turn as much more than round its
axis before the same place which was under her can come to the same
place again with respect to her, as she has advanced in her orbit during
that interval of time, which is 50 minutes. This being divided by 4,
gives 12-1/2 minutes; so that it will be 6 hours 12-1/2 minutes from
high to low-water, and the same time from low to high-water: or 12 hours
25 minutes from high-water to high-water again.
PUPIL. This I understand perfectly well.
TUTOR. I have now finished my description of the tides, and having a
little time to spare, if you wish to know how to find the proportionate
magnitude of the planets with that of the earth, and to calculate their
distances from the sun, I will employ it that way.
PUPIL. At our first conference I remember you shewed me the proportion
that the other planets bear to the earth, with their periods and
distances from the sun; but to have it in my power to make the
calculations myself, will certainly give me great pleasure.
TUTOR. To find what proportion any planet bears to the earth; or, that
one globe bears to another, you must observe that, _all spheres or
globes are in proportion to one another as the cubes of their
diameters_. So that you have nothing more to do than to cube the
diameter of each, and divide the greatest by the least number, and the
quotient will shew you the proportion that one bears to the other.
PUPIL. The operation appears very simple; but, as I do not know what a
cube number is, I cannot perform it.
TUTOR. You cannot forget what a square number is.
PUPIL. The product of any number multiplied into itself is a square
number, as 4 is the square of 2.
TUTOR. Any square number multiplied by its root, or first power, will be
a cube number. Thus 4 multiplied by 2 will be 8, which is the cube of 2;
9 is the square or second power, and 27 the cube or third power of 3,
&c. This you will perhaps better understand by
A TABLE OF
Roots. 1. 2. 3. 4. 5. 6. 7. 8. 9.
Squares. 1. 4. 9. 16. 25. 36. 49. 64. 81.
Cubes. 1. 8. 27. 64. 125. 216. 343. 512. 729.
PUPIL. I do, Sir; and am now prepared for an example.
TUTOR. The diameter of the sun is 893552 miles, of the earth 7920 miles;
how much does the sun exceed the earth in magnitude?
PUPIL. The cube of 893522, the sun’s diameter, is 713371492260872648;
and of 7920, the earth’s, 496793088000. And 713371492260872648 divided
by 496793088000 is equal to 1435952, and so many times is the bulk of
the sun greater than that of the earth.
TUTOR. This one example may suffice, as I intend by and by to give you a
table of diameters, &c.; you may then calculate the rest at your
leisure.
PUPIL. I shall now, Sir, be glad to have the other explained.
TUTOR. The periods of the planets, or the times they take to complete
their revolutions in their orbits, are exactly known; and the mean
distance of the earth from the sun has been also ascertained. Here,
then, we have the periods of all, and the mean distance of one, to find
the distances of the rest; which may be found by attending to the
following proportion:
As the square of the period of any one planet,
Is to the cube of its mean distance from the sun;
So is the square of the period of any other planet,
To the cube of its mean distance.
The cube root of this quotient will be the distance sought.
PUPIL. Here again I find myself at a loss, as I have not learnt to
extract the cube root.
TUTOR. I will give you [18]Doctor Turner’s rule, which I think will
answer your purpose.
[Footnote 18: Young Geometrician’s Companion.]
“First, having set down the given number, or resolvend, make a dot over
the unit figure, and so on over every third figure (towards the left
hand in whole numbers, but towards the right hand in decimals); and so
many dots as there are, so many figures will be in the root.
Next, seek the nearest cube to the first period; place its root in the
quotient, and its cube set under the first period. Subtract it
therefrom; and to the remainder bring down one figure only of the next
period, which will be a dividend.
Then, square the figure put in the quotient, and multiply it by 3, for a
divisor. Seek how often this divisor may be had in the dividend, and set
the figure in the quotient, which will be the second place in the root.
Now, cube the figures in the root, and subtract it from the two first
periods of the resolvend; and to the remainder bring down the first
figure of the next period, for a new dividend. Square the figures in the
quotient, and multiply it by 3, for a new divisor; then proceed in all
respects as before, till the whole is finished.”
The following example will, I trust, make it clear to you.
EXAMPLE.
It is required to find the cube root of 15625.
. .
15625 (25
8
─────
12) 76
15625
─────
.....
═════
Point every third figure, and the first period will be 15; the nearest
cube to which, in the table I gave you just now, you will find to be 8,
and its root 2; the 8 you must place under the 15, and the 2 in the
quotient: take 8 from 15 and 7 will remain, to which bring down 6, the
first figure of the next period, and you have 76 for a dividend. The
figure put in the quotient is 2, the square of which is 4, which
multiplied by 3 is 12, for a divisor. Now 12 in 76 will be 5 times; cube
25, and you will have 15625, which, subtract from the resolvend, and
nothing will remain; which shews that the resolvend is a cube number,
and 25 its root.
PUPIL. You say 12 in 76 is 5 times; I should have said 6 times.
TUTOR. In common division it would be so; but as the cube of 26 would be
greater than the resolvend from which you are to subtract it, it can go
but 5 times.
PUPIL. Now, Sir, I think I have a sufficient knowledge of the rule to
solve a problem.
TUTOR. The earth’s period is 365 days, and its mean distance from the
sun 95 millions of miles; the period of Mercury is 88 days—what is his
mean distance?
PUPIL. As the distance of the earth is given, I must make the square of
365 the first term, the cube of 95 the second, and the square of 88 the
third term of the proportion.
TUTOR. Certainly.—Take your slate, or a piece of paper, prepare your
numbers, and make your proportion.
PUPIL. I find the square of 365 = 133225; of 88 = 7744; and the cube of
95 = 857375.
Then 133225 : 857375 :: 7744 to a fourth term.
I now multiply the second and third terms together, and divide the
product by the first, the quotient 49836 is the cube of the mean
distance of Mercury from the sun in millions of miles, and the fourth
term sought.
TUTOR. So far you are right. Now extract the root.
. .
49836 (36 3 36
27 3 36
─── ── ─────
27) 228 Sq. of 3 = 9 216
46656 Mul. by 3 108
───── ── ─────
3180 Divisor 27 1296
═════ ══ 36
─────
7776
3888
─────
Cube of 36 = 46656
═════
PUPIL. The root I find to be 36, which is the mean distance of Mercury
from the sun, in millions of miles.
TUTOR. You now see, that although 27 in 228 will go 8 times, yet here it
will go but 6 times; and, as there is a remainder, it shews you that the
resolvend is not a cube number.
PUPIL. I see it clearly.
TUTOR. You now seem perfect in the rule; I shall therefore not trouble
you with any more examples, but shall give you the table I promised you.
┌─────────────────────────────────────────────────────────────────────┐
│ TABLE. │
├──────────┬──────────┬───────────────┬───────────────┬───────────────┤
│ Names │Diameters,│ Magnitude, │ Periods, │ Mean Distance │
│ of the │in English│ compared │ in │ from the Sun, │
│ PLANETS. │ Miles. │with the Earth.│Years and Days.│ in Mil. of │
│ │ │ │ │ Miles. │
├──────────┼──────────┼───────────────┼───────────────┼───────────────┤
│Sun │ [A]893522│ 1435952 │ —— │ —— │
│ │ │ │ │ │
│Mercury │ 3261│ 1/14 │ 0 —— 88 │ 36 │
│ │ │ │ │ │
│Venus │ 7699│ 5/49 │ 0 —— 224 │ 68 │
│ │ │ │ │ │
│Earth │ 7920│ 1 │ 1 or 365 │ 95 │
│ │ │ │ │ │
│Moon │ 2161│ 1/49 │ —— │ —— │
│ │ │ │ │ │
│Mars │ 5312│ 1/3 │ 1 and 322 │ 145 │
│ │ │ │ │ │
│Jupiter │ 90255│ 1479 │ 11 —— 314 │ 494 │
│ │ │ │ │ │
│Saturn │ 80012│ 1031 │ 29 —— 167 │ 906 │
│ │ │ │ │ │
│Georgian │ 34217│ 82 │ 83 —— 121 │ 1812 │
└──────────┴──────────┴───────────────┴───────────────┴───────────────┘
[Footnote A: The Diameters were taken from Adams’s Lectures, Vol. IV.
p. 39.]
PUPIL. I shall take the first opportunity of calculating the rest, in
which I am certain I shall have great satisfaction.
* * * * *
TUTOR. I have now conducted you through the elementary parts of
astronomy, have given you a general view of the system of the world, and
prepared you to pursue the study with profit and pleasure.—In your
future researches, the more accurate you are, the more you will discover
of regularity, symmetry, and order in the constitution of the frame of
nature.
“Hail, Sov’reign Goodness! all-productive Mind!
“On all thy works thyself inscrib’d we find;
“How various all, how variously endow’d,
“How great their number, and each part how good!
“How perfect then must the Great Parent shine, ⎫
“Who, with one act of energy divine, ⎬
“Laid the vast plan, and finish’d the design!” ⎭
THE END.
------------------------------------------------------------------------
Directions to the Bookbinder.
Plate I. _to face the_ Title.
———— II. —— _page_ 40.
———— III. —— —— 88.
———— IV. —— —— 131.
------------------------------------------------------------------------
Transcriber’s note:
All instances of ‘disk’ changed to ‘disc’
Errata, instance of ‘disk’ on page 79 added, “—— 79. — 5. ⎭”
Page 11, ‘Years’ changed to ‘years,’ “130 years after Christ”
Page 20, ‘h e’ changed to ‘the,’ “would have as much the appearance”
Page 24, ‘cannon ball’ changed to ‘cannon-ball,’ “the time a cannon-ball
would”
Page 63, comma changed to full stop after ‘TUTOR,’ “TUTOR. Why?”
Page 65, ‘a’ changed to ‘_a_,’ “carry a planet from A to _a_”
Page 74, ‘itaxis’ changed to ‘its axis,’ “if the earth revolve on its
axis every”
Page 78, ‘Mercury’ struck after ‘Sun,’ “Sun, Venus, Mars, and Jupiter
are known to revolve on their axes”
Page 93, ‘cancer’ changed to ‘Cancer,’ “is the _tropic of cancer_; that”
Page 93, ‘capricorn’ changed to ‘Capricorn,’ “the _tropic of capricorn_”
Page 115, ‘othes’ changed to ‘other,’ “and other stars rise to his”
Page 115, ‘bnt’ changed to ‘but,’ “out from; but, by going round”
Page 116, ‘it’s’ changed to ‘its,’ “How can its surface be round”
Page 128, full stop inserted after ‘eclipses,’ “explain the cause of
eclipses.”
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