Letters on Astronomy - in which the Elements of the Science are Familiarly - Explained in Connection with Biographical Sketches of the

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Title: Letters on Astronomy - in which the Elements of the Science are Familiarly - Explained in Connection with Biographical Sketches of the - Most Eminent Astronomers
Author: Olmsted, Denison, 1791-1859
Language: English
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*** Start of this LibraryBlog Digital Book "Letters on Astronomy - in which the Elements of the Science are Familiarly - Explained in Connection with Biographical Sketches of the - Most Eminent Astronomers" ***

[Illustration PATH OF BIELA'S COMET.]

LETTERS

ASTRONOMY,

IN WHICH THE

ELEMENTS OF THE SCIENCE

ARE

FAMILIARLY EXPLAINED IN CONNECTION WITH BIOGRAPHICAL SKETCHES OF THE
MOST EMINENT ASTRONOMERS.

WITH NUMEROUS ENGRAVINGS.

BY DENISON OLMSTED, LL.D.,

PROFESSOR OF NATURAL PHILOSOPHY AND ASTRONOMY IN YALE COLLEGE

Revised Edition.

INCLUDING THE LATEST DISCOVERIES.

NEW YORK: HARPER & BROTHERS, PUBLISHERS, 329 & 331 PEARL STREET,
FRANKLIN SQUARE.

1855.

Entered according to Act of Congress, in the year 1840, by

MARSH, CAPEN, LYON, AND WEBB,

in the Clerk's Office of the District Court of Massachusetts.

TO THE

REVISED EDITION.

SINCE the first publication of these Letters, in 1840, the work has
passed through numerous editions, and received many tokens of public
favor, both as a class-book for schools and as a reading-book for the
family circle. The valuable discoveries made in the science within a few
years have suggested an additional Letter, which is accordingly annexed
to the series in the present revised form, giving a brief but
comprehensive notice of all the leading contributions with which
Astronomy has of late been enriched.

The form of _Letters_ was chosen on account of the greater freedom it
admits, both of matter and of style, than a dress more purely
scientific. Thus the technical portion of the work, it was hoped, might
be relieved, and the whole rendered attractive to the youthful reader of
either sex by interspersing sketches of the master-builders who, in
successive ages, have reared the great temple of Astronomy, composing,
as they do, some of the most remarkable and interesting specimens of the
human race.

The work was addressed to a female friend (now no more), who was a
distinguished ornament of her sex, and whose superior intellect and
refined taste required that the work should be free from every thing
superficial in matter or negligent in style; and it was deemed by the
writer no ordinary privilege that, in the composition of the work, an
image at once so exalted and so pure was continually present to his
mental vision.

YALE COLLEGE, _January_, 1853.

CONTENTS.

PREFACE, 3

LETTER I.

Introductory Observations, 9

LETTER II.

Doctrine of the Sphere, 16

LETTER III.

Astronomical Instruments.--Telescope, 29

LETTER IV.

Telescope continued, 36

LETTER V.

Observatories, 42

LETTER VI.

Time and the Calendar, 59

LETTER VII.

Figure of the Earth, 69

LETTER VIII.

Diurnal Revolution, 81

LETTER IX.

Parallax and Refraction, 89

LETTER X.

The Sun, 101

LETTER XI.

Annual Revolution.--Seasons, 111

LETTER XII.

Laws of Motion, 126

LETTER XIII.

Terrestrial Gravity, 134

LETTER XIV.

Sir Isaac Newton.--Universal Gravitation.--Figure
of the Earth's Orbit.--Precession of the Equinoxes, 143

LETTER XV.

The Moon, 157

LETTER XVI.

The Moon.--Phases.--Harvest Moon.--Librations, 172

LETTER XVII.

Moon's Orbit.--Her Irregularities, 180

LETTER XVIII.

Eclipses, 195

LETTER XIX.

Longitude.--Tides, 208

LETTER XX.

Planets.--Mercury and Venus, 225

LETTER XXI.

Superior Planets: Mars, Jupiter, Saturn, and Uranus, 243

LETTER XXII.

Copernicus.--Galileo, 254

LETTER XXIII.

Saturn.--Uranus.--Asteroids, 274

LETTER XXIV.

The Planetary Motions.--Kepler's Laws.--Kepler, 291

LETTER XXV.

Comets, 312

LETTER XXVI.

Comets, 334

LETTER XXVII.

Meteoric Showers, 346

LETTER XXVIII.

Fixed Stars, 365

LETTER XXIX.

Fixed Stars, 383

LETTER XXX.

System of the World, 392

LETTER XXXI.

Natural Theology, 406

LETTER XXXII.

Recent Discoveries, 414

Index, 423

LETTERS ON ASTRONOMY.

LETTER 1.

INTRODUCTORY OBSERVATIONS.

"Ye sacred Muses, with whose beauty fired,
My soul is ravished, and my brain inspired,
Whose priest I am, whose holy fillets wear;
Would you your poet's first petition hear,
Give me the ways of wandering stars to know,
The depths of heaven above, and earth below;
Teach me the various labors of the moon,
And whence proceed th' eclipses of the sun;
Why flowing tides prevail upon the main,
And in what dark recess they shrink again;
What shakes the solid earth, what cause delays
The Summer nights, and shortens Winter days."
_Dryden's Virgil_

TO MRS. C---- M----.

DEAR MADAM,--In the conversation we recently held on the study of
Astronomy, you expressed a strong desire to become better acquainted
with this noble science, but said you had always been repelled by the
air of severity which it exhibits, arrayed as it is in so many technical
terms, and such abstruse mathematical processes: or, if you had taken up
some smaller treatise, with the hope of avoiding these perplexities, you
had always found it so meager and superficial, as to afford you very
little satisfaction. You asked, if a work might not be prepared, which
would convey to the general reader some clear and adequate knowledge of
the great discoveries in astronomy, and yet require for its perusal no
greater preparation, than may be presumed of every well-educated English
scholar of either sex.

You were pleased to add the request, that I would write such a work,--a
work which should combine, with a luminous exposition of the leading
truths of the science, some account of the interesting historical facts
with which it is said the records of astronomical discovery abound.
Having, moreover, heard much of the grand discoveries which, within the
last fifty years, have been made among the _fixed stars_, you expressed
a strong desire to learn more respecting these sublime researches.
Finally, you desired to see the argument for the existence and natural
attributes of the Deity, as furnished by astronomy, more fully and
clearly exhibited, than is done in any work which you have hitherto
perused. In the preparation of the proposed treatise, you urged me to
supply, either in the text or in notes, every _elementary principle_
which would be essential to a perfect understanding of the work; for
although, while at school, you had paid some attention to geometry and
natural philosophy, yet so much time had since elapsed, that your memory
required to be refreshed on the most simple principles of these
elementary studies, and you preferred that I should consider you as
altogether unacquainted with them.

Although, to satisfy a mind, so cultivated and inquisitive as yours, may
require a greater variety of powers and attainments than I possess, yet,
as you were pleased to urge me to the trial, I have resolved to make the
attempt, and will see how far I may be able to lead you into the
interior of this beautiful temple, without obliging you to force your
way through the "jargon of the schools."

Astronomy, however, is a very difficult or a comparatively easy study,
according to the view we take of it. The investigation of the great laws
which govern the motions of the heavenly bodies has commanded the
highest efforts of the human mind; but profound truths, which it
required the mightiest efforts of the intellect to disclose, are often,
when once discovered, simple in their complexion, and may be expressed
in very simple terms. Thus, the creation of that element, on whose
mysterious agency depend all the forms of beauty and loveliness, is
enunciated in these few monosyllables, "And God said, let there be
light, and there was light;" and the doctrine of universal gravitation,
which is the key that unlocks the mysteries of the universe, is simply
this,--that every portion of matter in the universe tends towards every
other. The three great laws of motion, also, are, when stated, so plain,
that they seem hardly to assert any thing but what we knew before. That
all bodies, if at rest, will continue so, as is declared by the first
law of motion, until some force moves them; or, if in motion, will
continue so, until some force stops them, appears so much a matter of
course, that we can at first hardly see any good reason why it should be
dignified with the title of the first great law of motion; and yet it
contains a truth which it required profound sagacity to discover and
expound.

It is, therefore, a pleasing consideration to those who have not either
the leisure of the ability to follow the astronomer through the
intricate and laborious processes, which conducted him to his great
discoveries, that they may fully avail themselves of the _results_ of
this vast toil, and easily understand truths which it required ages of
the severest labor to unfold. The descriptive parts of astronomy, or
what may be called the natural history of the heavens, is still more
easily understood than the laws of the celestial motions. The
revelations of the telescope, and the wonders it has disclosed in the
sun, in the moon, in the planets, and especially in the fixed stars, are
facts not difficult to be understood, although they may affect the mind
with astonishment.

The great practical purpose of astronomy to the world is, enabling us
safely to navigate the ocean. There are indeed many other benefits which
it confers on man; but this is the most important. If, however, you ask,
what advantages the study of astronomy promises, as a branch of
education, I answer, that few subjects promise to the mind so much
profit and entertainment. It is agreed by writers on the human mind,
that the intellectual powers are enlarged and strengthened by the
habitual contemplation of great objects, while they are contracted and
weakened by being constantly employed upon little or trifling subjects.
The former elevate, the latter depress, the mind, to their own level.
Now, every thing in astronomy is great. The magnitudes, distances, and
motions, of the heavenly bodies; the amplitude of the firmament itself;
and the magnificence of the orbs with which it is lighted, supply
exhaustless materials for contemplation, and stimulate the mind to its
noblest efforts. The emotion felt by the astronomer is not that sudden
excitement or ecstasy, which wears out life, but it is a continued glow
of exalted feeling, which gives the sensation of breathing in a purer
atmosphere than others enjoy. We should at first imagine, that a study
which calls upon its votaries for the severest efforts of the human
intellect, which demands the undivided toil of years, and which robs the
night of its accustomed hours of repose, would abridge the period of
life; but it is a singular fact, that distinguished astronomers, as a
class, have been remarkable for longevity. I know not how to account for
this fact, unless we suppose that the study of astronomy itself has
something inherent in it, which sustains its votaries by a peculiar
aliment.

It is the privilege of the student of this department of Nature, that
his cabinet is already collected, and is ever before him; and he is
exempted from the toil of collecting his materials of study and
illustration, by traversing land and sea, or by penetrating into the
depths of the earth. Nor are they in their nature frail and perishable.
No sooner is the veil of clouds removed, that occasionally conceals the
firmament by night, than his specimens are displayed to view, bright and
changeless. The renewed pleasure which he feels, at every new survey of
the constellations, grows into an affection for objects which have so
often ministered to his happiness. His imagination aids him in giving
them a personification, like that which the ancients gave to the
constellations; (as is evident from the names which they have
transmitted to us;) and he walks abroad, beneath the evening canopy,
with the conscious satisfaction and delight of being in the presence of
old friends. This emotion becomes stronger when he wanders far from
home. Other objects of his attachment desert him; the face of society
changes; the earth presents new features; but the same sun illumines the
day, the same moon adorns the night, and the same bright stars still
attend him.

When, moreover, the student of the heavens can command the aid of
telescopes, of higher and higher powers, new acquaintances are made
every evening. The sight of each new member of the starry train, that
the telescope successively reveals to him, inspires a peculiar emotion
of pleasure; and he at length finds himself, whenever he sweeps his
telescope over the firmament, greeted by smiles, unperceived and unknown
to his fellow-mortals. The same personification is given to these
objects as to the constellations, and he seems to himself, at times,
when he has penetrated into the remotest depths of ether, to enjoy the
high prerogative of holding converse with the celestials.

It is no small encouragement, to one who wishes to acquire a knowledge
of the heavens, that the subject is embarrassed with far less that is
technical than most other branches of natural history. Having first
learned a few definitions, and the principal circles into which, for
convenience, the sphere is divided, and receiving the great laws of
astronomy on the authority of the eminent persons who have investigated
them, you will find few hard terms, or technical distinctions, to repel
or perplex you; and you will, I hope, find that nothing but an
intelligent mind and fixed attention are requisite for perusing the
Letters which I propose to address to you. I shall indeed be greatly
disappointed, if the perusal does not inspire you with some portion of
that pleasure, which I have described as enjoyed by the astronomer
himself.

The dignity of the study of the heavenly bodies, and its suitableness to
the most refined and cultivated mind, has been recognised in all ages.
Virgil celebrates it in the beautiful strains with which I have headed
this Letter, and similar sentiments have ever been cherished by the
greatest minds.

As, in the course of these Letters, I propose to trace an outline of the
history of astronomy, from the earliest ages to the present time, you
may think this the most suitable place for introducing it; but the
successive discoveries in the science cannot be fully understood and
appreciated, until after an acquaintance has been formed with the
science itself. We must therefore reserve the details of this subject
for a future opportunity; but it may be stated, here, that astronomy was
cultivated the earliest of all the sciences; that great attention was
paid to it by several very ancient nations, as the Egyptians and
Chaldeans, and the people of India and China, before it took its rise in
Greece. More than six hundred years before the Christian era, however,
it began to be studied in this latter country. Thales and Pythagoras
were particularly distinguished for their devotion to this science; and
the celebrated school of Alexandria, in Egypt, which took its rise about
three hundred years before the Christian era, and flourished for several
hundred years, numbered among its disciples a succession of eminent
astronomers, among whom were Hipparchus, Eratosthenes, and Ptolemy. The
last of these composed a great work on astronomy, called the 'Almagest,'
in which is transmitted to us an account of all that was known of the
science by the Alexandrian school. The 'Almagest' was the principal
text-book in astronomy, for many centuries afterwards, and comparatively
few improvements were made until the age of Copernicus. Copernicus was
born at Thorn, in Prussia, in 1473. Previous to his time, the doctrine
was held, that the earth is at rest in the centre of the universe, and
that the sun, moon, and stars, revolve about it, every day, from east to
west; in short, that the _apparent_ motions of the heavenly bodies are
the same with their _real_ motions. But Copernicus expounded what is now
known to be the true theory of the celestial motions, in which the sun
is placed in the centre of the solar system, and the earth and all the
planets are made to revolve around him, from west to east, while the
apparent diurnal motion of the heavenly bodies, from east to west, is
explained by the revolution of the earth on its axis, in the same time,
from west to east; a motion of which we are unconscious, and which we
erroneously ascribe to external objects, as we imagine the shore is
receding from us, when we are unconscious of the motion of the ship that
carries us from it.

Although many of the appearances, presented by the motions of the
heavenly bodies, may be explained on the former erroneous hypothesis,
yet, like other hypotheses founded in error, it was continually leading
its votaries into difficulties, and blinding their minds to the
perception of truth. They had advanced nearly as far as it was
practicable to go in the wrong road; and the great and sublime
discoveries of modern times are owing, in no small degree, to the fact,
that, since the days of Copernicus, astronomers have been pursuing the
plain and simple path of truth, instead of threading their way through
the mazes of error.

Near the close of the sixteenth century, Tycho Brahe, a native of
Sweden, but a resident of Denmark, carried astronomical observations
(which constitute the basis of all that is valuable in astronomy) to a
far greater degree of perfection than had ever been done before. Kepler,
a native of Germany, one of the greatest geniuses the world has ever
seen, was contemporary with Tycho Brahe, and was associated with him in
a part of his labors. Galileo, an Italian astronomer of great eminence,
flourished only a little later than Tycho Brahe. He invented the
telescope, and, both by his discoveries and reasonings, contributed
greatly to establish the true system of the world. Soon after the
commencement of the seventeenth century, (1620,) Lord Bacon, a
celebrated English philosopher, pointed out the true method of
conducting all inquiries into the phenomena of Nature, and introduced
the _inductive method of philosophizing_. According to the inductive
method, we are to begin our inquiries into the causes of any events by
first examining and classifying all the _facts_ that relate to it, and,
from the comparison of these, to deduce our conclusions.

But the greatest single discovery, that has ever been made in astronomy,
was the law of universal gravitation, a discovery made by Sir Isaac
Newton, in the latter part of the seventeenth century. The discovery of
this law made us acquainted with the hidden forces that move the great
machinery of the universe. It furnished the key which unlocks the inner
temple of Nature; and from this time we may regard astronomy as fixed on
a sure and immovable basis. I shall hereafter endeavor to explain to you
the leading principles of universal gravitation, when we come to the
proper place for inquiring into the causes of the celestial motions, as
exemplified in the motion of the earth around the sun.

LETTER II.

DOCTRINE OF THE SPHERE.

"All are but parts of one stupendous whole,
Whose body Nature is, and God the soul."--_Pope._

LET us now consider what astronomy is, and into what great divisions it
is distributed; and then we will take a cursory view of the doctrine of
the sphere. This subject will probably be less interesting to you than
many that are to follow; but still, permit me to urge upon you the
necessity of studying it with attention, and reflecting upon each
definition, until you fully understand it; for, unless you fully and
clearly comprehend the circles of the sphere, and the use that is made
of them in astronomy, a mist will hang over every subsequent portion of
the science. I beg you, therefore, to pause upon every paragraph of this
Letter; and if there is any point in the whole which you cannot clearly
understand, I would advise you to mark it, and to recur to it
repeatedly; and, if you finally cannot obtain a clear idea of it
yourself, I would recommend to you to apply for aid to some of your
friends, who may be able to assist you.

_Astronomy is that science which treats of the heavenly bodies._ More
particularly, its object is to teach what is known respecting the sun,
moon, planets, comets, and fixed stars; and also to explain the methods
by which this knowledge is acquired. Astronomy is sometimes divided into
descriptive, physical, and practical. Descriptive astronomy respects
_facts_; physical astronomy, _causes_; practical astronomy, the _means
of investigating the facts_, whether by instruments or by calculation.
It is the province of descriptive astronomy to observe, classify, and
record, all the phenomena of the heavenly bodies, whether pertaining to
those bodies individually, or resulting from their motions and mutual
relations. It is the part of physical astronomy to explain the causes of
these phenomena, by investigating the general laws on which they depend;
especially, by tracing out all the consequences of the law of universal
gravitation. Practical astronomy lends its aid to both the other
departments.

The definitions of the different lines, points, and circles, which are
used in astronomy, and the propositions founded upon them, compose the
_doctrine of the sphere_. Before these definitions are given, I must
recall to your recollection a few particulars respecting the method of
measuring angles. (See Fig. 1, page 18.)

A line drawn from the centre to the circumference of a circle is called
a _radius_, as C D, C B, or C K.

Any part of the circumference of a circle is called an _arc_, as A B, or
B D.

An angle is measured by an arc included between two radii. Thus, in
Fig. 1, the angle contained between the two radii, C A and C B, that is,
the angle A C B, is measured by the arc A B. Every circle, it will be
recollected, is divided into three hundred and sixty equal parts, called
degrees; and any arc, as A B, contains a certain number of degrees,
according to its length. Thus, if the arc A B contains forty degrees,
then the opposite angle A C B is said to be an angle of forty degrees,
and to be measured by A B. But this arc is the same part of the smaller
circle that E F is of the greater. The arc A B, therefore, contains the
same number of degrees as the arc E F, and either may be taken as the
measure of the angle A C B. As the whole circle contains three hundred
and sixty degrees, it is evident, that the quarter of a circle, or
_quadrant_, contains ninety degrees, and that the semicircle A B D G
contains one hundred and eighty degrees.

[Illustration Fig. 1.]

The _complement_ of an arc, or angle, is what it wants of ninety
degrees. Thus, since A D is an arc of ninety degrees, B D is the
complement of A B, and A B is the complement of B D. If A B denotes a
certain number of degrees of latitude, B D will be the complement of the
latitude, or the colatitude, as it is commonly written.

The _supplement_ of an arc, or angle, is what it wants of one hundred
and eighty degrees. Thus, B A is the supplement of G D B, and G D B is
the supplement of B A. If B A were twenty degrees of longitude, G D B,
its supplement, would be one hundred and sixty degrees. An angle is said
to be _subtended_ by the side which is opposite to it. Thus, in the
triangle A C K, the angle at C is subtended by the side A K, the angle
at A by C K, and the angle at K by C A. In like manner, a side is said
to be subtended by an angle, as A K by the angle at C.

Let us now proceed with the doctrine of the sphere.

A section of a sphere, by a plane cutting it in any manner, is a circle.
_Great circles_ are those which pass through the centre of the sphere,
and divide it into two equal hemispheres. _Small circles_ are such as do
not pass through the centre, but divide the sphere into two unequal
parts. The _axis_ of a circle is a straight line passing through its
centre at right angles to its plane. The _pole_ of a great circle is the
point on the sphere where its axis cuts through the sphere. Every great
circle has two poles, each of which is every where ninety degrees from
the great circle. All great circles of the sphere cut each other in two
points diametrically opposite, and consequently their points of section
are one hundred and eighty degrees apart. A great circle, which passes
through the pole of another great circle, cuts the latter at right
angles. The great circle which passes through the pole of another great
circle, and is at right angles to it, is called a _secondary_ to that
circle. The angle made by two great circles on the surface of the sphere
is measured by an arc of another great circle, of which the angular
point is the pole, being the arc of that great circle intercepted
between those two circles.

In order to fix the position of any place, either on the surface of the
earth or in the heavens, both the earth and the heavens are conceived to
be divided into separate portions, by circles, which are imagined to cut
through them, in various ways. The earth thus intersected is called the
_terrestrial_, and the heavens the _celestial_, sphere. We must bear in
mind, that these circles have no existence in Nature, but are mere
landmarks, artificially contrived for convenience of reference. On
account of the immense distances of the heavenly bodies, they appear to
us, wherever we are placed, to be fixed in the same concave surface, or
celestial vault. The great circles of the globe, extended every way to
meet the concave sphere of the heavens, become circles of the celestial
sphere.

The _horizon_ is the great circle which divides the earth into upper and
lower hemispheres, and separates the visible heavens from the invisible.
This is the _rational_ horizon. The _sensible_ horizon is a circle
touching the earth at the place of the spectator, and is bounded by the
line in which the earth and skies seem to meet. The sensible horizon is
parallel to the rational, but is distant from it by the semidiameter of
the earth, or nearly four thousand miles. Still, so vast is the distance
of the starry sphere, that both these planes appear to cut the sphere in
the same line; so that we see the same hemisphere of stars that we
should see, if the upper half of the earth were removed, and we stood on
the rational horizon.

The poles of the horizon are the zenith and nadir. The _zenith_ is the
point directly over our heads; and the _nadir_, that directly under our
feet. The plumb-line (such as is formed by suspending a bullet by a
string) is in the axis of the horizon, and consequently directed towards
its poles. Every place on the surface of the earth has its own horizon;
and the traveller has a new horizon at every step, always extending
ninety degrees from him, in all directions.

_Vertical circles_ are those which pass through the poles of the
horizon, (the zenith and nadir,) perpendicular to it.

The _meridian_ is that vertical circle which passes through the north
and south points.

The _prime vertical_ is that vertical circle which passes through the
east and west points.

The _altitude_ of a body is its elevation above the horizon, measured on
a vertical circle.

The _azimuth_ of a body is its distance, measured on the horizon, from
the meridian to a vertical circle passing through that body.

The _amplitude_ of a body is its distance, on the horizon, from the
prime vertical to a vertical circle passing through the body.

Azimuth is reckoned ninety degrees from either the north or south point;
and amplitude ninety degrees from either the east or west point. Azimuth
and amplitude are mutually complements of each other, for one makes up
what the other wants of ninety degrees. When a point is _on_ the
horizon, it is only necessary to count the number of degrees of the
horizon between that point and the meridian, in order to find its
azimuth; but if the point is _above_ the horizon, then its azimuth is
estimated by passing a vertical circle through it, and reckoning the
azimuth from the point where this circle cuts the horizon.

The _zenith distance_ of a body is measured on a vertical circle passing
through that body. It is the complement of the altitude.

The _axis of the earth_ is the diameter on which the earth is conceived
to turn in its diurnal revolution. The same line, continued until it
meets the starry concave, constitutes the _axis of the celestial
sphere_.

The _poles of the earth_ are the extremities of the earth's axis: the
_poles of the heavens_, the extremities of the celestial axis.

The _equator_ is a great circle cutting the axis of the earth at right
angles. Hence, the axis of the earth is the axis of the equator, and its
poles are the poles of the equator. The intersection of the plane of the
equator with the surface of the earth constitutes the _terrestrial_, and
its intersection with the concave sphere of the heavens, the
_celestial_, equator. The latter, by way of distinction, is sometimes
denominated the _equinoctial_.

The secondaries to the equator,--that is, the great circles passing
through the poles of the equator,--are called _meridians_, because that
secondary which passes through the zenith of any place is the meridian
of that place, and is at right angles both to the equator and the
horizon, passing, as it does, through the poles of both. These
secondaries are also called _hour circles_ because the arcs of the
equator intercepted between them are used as measures of time.

The _latitude_ of a place on the earth is its distance from the equator
north or south. The _polar distance_, or angular distance from the
nearest pole, is the complement of the latitude.

The _longitude_ of a place is its distance from some standard meridian,
either east or west, measured on the equator. The meridian, usually
taken as the standard, is that of the Observatory of Greenwich, in
London. If a place is directly _on_ the equator, we have only to
inquire, how many degrees of the equator there are between that place
and the point where the meridian of Greenwich cuts the equator. If the
place is north or south of the equator, then its longitude is the arc of
the equator intercepted between the meridian which passes through the
place and the meridian of Greenwich.

The _ecliptic_ is a great circle, in which the earth performs its annual
revolutions around the sun. It passes through the centre of the earth
and the centre of the sun. It is found, by observation, that the earth
does not lie with its axis at right angles to the plane of the ecliptic,
so as to make the equator coincide with it, but that it is turned about
twenty-three and a half degrees out of a perpendicular direction, making
an angle with the plane itself of sixty-six and a half degrees. The
equator, therefore, must be turned the same distance out of a
coincidence with the ecliptic, the two circles making an angle with each
other of twenty-three and a half degrees. It is particularly important
that we should form correct ideas of the ecliptic, and of its relations
to the equator, since to these two circles a great number of
astronomical measurements and phenomena are referred.

The _equinoctial points_, or _equinoxes_, are the intersections of the
ecliptic and equator. The time when the sun crosses the equator, in
going northward, is called the _vernal_, and in returning southward, the
_autumnal_, equinox. The vernal equinox occurs about the twenty-first of
March, and the autumnal, about the twenty-second of September.

The _solstitial points_ are the two points of the ecliptic most distant
from the equator. The times when the sun comes to them are called
_solstices_. The Summer solstice occurs about the twenty-second of June,
and the Winter solstice about the twenty-second of December. The
ecliptic is divided into twelve equal parts, of thirty degrees each,
called _signs_, which, beginning at the vernal equinox, succeed each
other, in the following order:

1. Aries, [Zodiac: Aries]
2. Taurus, [Zodiac: Taurus]
3. Gemini, [Zodiac: Gemini]
4. Cancer, [Zodiac: Cancer]
5. Leo, [Zodiac: Leo]
6. Virgo, [Zodiac: Virgo]
7. Libra, [Zodiac: Libra]
8. Scorpio, [Zodiac: Scorpio]
9. Sagittarius, [Zodiac: Sagittarius]
10. Capricornus, [Zodiac: Capricornus]
11. Aquarius, [Zodiac: Aquarius]
12. Pisces. [Zodiac: Pisces]

The mode of reckoning on the ecliptic is by signs, degrees, minutes, and
seconds. The sign is denoted either by its name or its number. Thus, one
hundred degrees may be expressed either as the tenth degree of Cancer,
or as 3s 10°. It will be found an advantage to repeat the signs in their
proper order, until they are well fixed in the memory, and to be able to
recognise each sign by its appropriate character.

Of the various meridians, two are distinguished by the name of
_colures_. The _equinoctial colure_ is the meridian which passes through
the equinoctial points. From this meridian, right ascension and
celestial longitude are reckoned, as longitude on the earth is reckoned
from the meridian of Greenwich. The _solstitial colure_ is the meridian
which passes through the solstitial points.

The position of a celestial body is referred to the equator by its right
ascension and declination. _Right ascension_ is the angular distance
from the vernal equinox measured on the equator. If a star is situated
_on_ the equator, then its right ascension is the number of degrees of
the equator between the star and the vernal equinox. But if the star is
north or south of the equator, then its right ascension is the number of
degrees of the equator, intercepted between the vernal equinox and that
secondary to the equator which passes through the star. _Declination_ is
the distance of a body from the equator measured on a secondary to the
latter. Therefore, right ascension and declination correspond to
terrestrial longitude and latitude,--right ascension being reckoned from
the equinoctial colure, in the same manner as longitude is reckoned from
the meridian of Greenwich. On the other hand, celestial longitude and
latitude are referred, not to the equator, but to the ecliptic.
_Celestial longitude_ is the distance of a body from the vernal equinox
measured on the ecliptic. _Celestial latitude_ is the distance from the
ecliptic measured on a secondary to the latter. Or, more briefly,
longitude is distance _on_ the ecliptic: latitude, distance _from_ the
ecliptic. The _north polar distance_ of a star is the complement of its
declination.

_Parallels of latitude_ are small circles parallel to the equator. They
constantly diminish in size, as we go from the equator to the pole. The
_tropics_ are the parallels of latitude which pass through the
solstices. The northern tropic is called the tropic of Cancer; the
southern, the tropic of Capricorn. The _polar circles_ are the parallels
of latitude that pass through the poles of the ecliptic, at the distance
of twenty-three and a half degrees from the poles of the earth.

The _elevation of the pole_ of the heavens above the horizon of any
place is always equal to the latitude of the place. Thus, in forty
degrees of north latitude we see the north star forty degrees above the
northern horizon; whereas, if we should travel southward, its elevation
would grow less and less, until we reached the equator, where it would
appear _in_ the horizon. Or, if we should travel northwards, the north
star would rise continually higher and higher, until, if we could reach
the pole of the earth, that star would appear directly over head. The
_elevation of the equator_ above the horizon of any place is equal to
the complement of the latitude. Thus, at the latitude of forty degrees
north, the equator is elevated fifty degrees above the southern horizon.

The earth is divided into five zones. That portion of the earth which
lies between the tropics is called the _torrid zone_; that between the
tropics and the polar circles, the _temperate zones_; and that between
the polar circles and the poles, the _frigid zones_.

The _zodiac_ is the part of the celestial sphere which lies about eight
degrees on each side of the ecliptic. This portion of the heavens is
thus marked off by itself, because all the planets move within it.

After endeavoring to form, from the definitions, as clear an idea as we
can of the various circles of the sphere, we may next resort to an
artificial globe, and see how they are severally represented there. I do
not advise to _begin_ learning the definitions from the globe; the mind
is more improved, and a power of conceiving clearly how things are in
Nature is more effectually acquired, by referring every thing, at first,
to the grand sphere of Nature itself, and afterwards resorting to
artificial representations to aid our conceptions. We can get but a very
imperfect idea of a man from a profile cut in paper, unless we know the
original. If we are acquainted with the individual, the profile will
assist us to recall his appearance more distinctly than we can do
without it. In like manner, orreries, globes, and other artificial aids,
will be found very useful, in assisting us to form distinct conceptions
of the relations existing between the different circles of the sphere,
and of the arrangements of the heavenly bodies; but, unless we have
already acquired some correct ideas of these things, by contemplating
them as they are in Nature, artificial globes, and especially orreries,
will be apt to mislead us.

I trust you will be able to obtain the use of a globe,[1] to aid you in
the study of the foregoing definitions, or doctrine of the sphere; but
if not, I would recommend the following easy device. To represent the
earth, select a large _apple_, (a melon, when in season, will be found
still better.) The eye and the stem of the apple will indicate the
position of the two poles of the earth. Applying the thumb and finger of
the left hand to the poles, and holding the apple so that the poles may
be in a north and south line, turn this globe from west to east, and its
motion will correspond to the diurnal movement of the earth. Pass a wire
or a knitting needle through the poles, and it will represent the _axis_
of the sphere. A circle cut around the apple, half way between the
poles, will be the _equator_; and several other circles cut between the
equator and the poles, parallel to the equator, will represent
_parallels of latitude_; of which, two, drawn twenty-three and a half
degrees from the equator, will be the _tropics_, and two others, at the
same distance from the poles, will be the _polar circles_. A great
circle cut through the poles, in a north and south direction, will form
the _meridian_, and several other great circles drawn through the poles,
and of course perpendicularly to the equator, will be secondaries to the
equator, constituting meridians, or _hour circles_. A great circle cut
through the centre of the earth, from one tropic to the other, would
represent the _plane_ of the ecliptic; and consequently a line cut round
the apple where such a section meets the surface, will be the
terrestrial _ecliptic_. The points where this circle meets the tropics
indicate the position of the _solstices_; and its intersection with the
equator, that of the _equinoctial points_.

The _horizon_ is best represented by a circular piece of pasteboard, cut
so as to fit closely to the apple, being movable upon it. When this
horizon is passed through the poles, it becomes the horizon of the
equator; when it is so placed as to coincide with the earth's equator,
it becomes the horizon of the poles; and in every other situation it
represents the horizon of a place on the globe ninety degrees every way
from it. Suppose we are in latitude forty degrees; then let us place our
movable paper parallel to our own horizon, and elevate the pole forty
degrees above it, as near as we can judge by the eye. If we cut a circle
around the apple, passing through its highest part, and through the east
and west points, it will represent the _prime vertical_.

Simple as the foregoing device is, if you will take the trouble to
construct one for yourself, it will lead you to more correct views of
the doctrine of the sphere, than you would be apt to obtain from the
most expensive artificial globes, although there are many other useful
purposes which such globes serve, for which the apple would be
inadequate. When you have thus made a sphere for yourself, or, with an
artificial globe before you, if you have access to one, proceed to point
out on it the various arcs of azimuth and altitude, right ascension and
declination, terrestrial and celestial latitude and longitude,--these
last being referred to the equator on the earth, and to the ecliptic in
the heavens.

When the circles of the sphere are well learned, we may advantageously
employ projections of them in various illustrations. By the _projection
of the sphere_ is meant a representation of all its parts on a plane.
The plane itself is called the plane of projection. Let us take any
circular ring, as a wire bent into a circle, and hold it in different
positions before the eye. If we hold it parallel to the face, with the
whole breadth opposite to the eye, we see it as an entire circle. If we
turn it a little sideways, it appears oval, or as an ellipse; and, as we
continue to turn it more and more round, the ellipse grows narrower and
narrower, until, when the edge is presented to the eye, we see nothing
but a line. Now imagine the ring to be near a perpendicular wall, and
the eye to be removed at such a distance from it, as not to distinguish
any interval between the ring and the wall; then the several figures
under which the ring is seen will appear to be inscribed on the wall,
and we shall see the ring as a circle, when perpendicular to a straight
line joining the centre of the ring and the eye, or as an ellipse, when
oblique to this line, or as a straight line, when its edge is towards
us.

[Illustration: Fig. 2.]

It is in this manner that the circles of the sphere are projected, as
represented in the following diagram, Fig. 2. Here, various circles are
represented as projected on the meridian, which is supposed to be
situated directly before the eye, at some distance from it. The horizon
H O, being perpendicular to the meridian, is seen edgewise, and
consequently is projected into a straight line. The same is the case
with the prime vertical Z N, with the equator E Q, and the several small
circles parallel to the equator, which represent the two tropics and the
two polar circles. In fact, all circles whatsoever, which are
perpendicular to the plane of projection, will be represented by
straight lines. But every circle which is perpendicular to the horizon,
except the prime vertical, being seen obliquely, as Z M N, will be
projected into an ellipse, one half only of which is seen,--the other
half being on the other side of the plane of projection. In the same
manner, P R P, an hour circle, is represented by an ellipse on the plane
of projection.

FOOTNOTE:

[1] A small pair of globes, that will answer every purpose required by
the readers of these Letters, may be had of the publishers of this Work,
at a price not exceeding ten dollars; or half that sum for a celestial
globe, which will serve alone for studying astronomy.

LETTER III.

ASTRONOMICAL INSTRUMENTS.----TELESCOPE.

"Here truths sublime, and sacred science charm,
Creative arts new faculties supply,
Mechanic powers give more than giant's arm,
And piercing optics more than eagle's eye;
Eyes that explore creation's wondrous laws,
And teach us to adore the great Designing Cause."--_Beattie_.

If, as I trust, you have gained a clear and familiar knowledge of the
circles and divisions of the sphere, and of the mode of estimating the
position of a heavenly body by its azimuth and altitude, or by its right
ascension and declination, or by its longitude and latitude, you will
now enter with advantage upon an account of those _instruments_, by
means of which our knowledge of astronomy has been greatly promoted and
perfected.

The most ancient astronomers employed no instruments of observation, but
acquired their knowledge of the heavenly bodies by long-continued and
most attentive inspection with the naked eye. Instruments for measuring
angles were first used in the Alexandrian school, about three hundred
years before the Christian era.

Wherever we are situated on the earth, we appear to be in the centre of
a vast sphere, on the concave surface of which all celestial objects are
inscribed. If we take any two points on the surface of the sphere, as
two stars, for example, and imagine straight lines to be drawn to them
from the eye, the angle included between these lines will be measured by
the arc of the sky contained between the two points. Thus, if D B H,
Fig. 3, page 30, represents the concave surface of the sphere, A, B, two
points on it, as two stars, and C A, C B, straight lines drawn from the
spectator to those points, then the angular distance between them is
measured by the arc A B, or the angle A C B. But this angle may be
measured on a much smaller circle, having the same centre, as G F K,
since the arc E F will have the same number of degrees as the arc A B.
The simplest mode of taking an angle between two stars is by means of an
arm opening at a joint like the blade of a penknife, the end of the arm
moving like C E upon the graduated circle K F G. In fact, an instrument
constructed on this principle, resembling a carpenter's rule with a
folding joint, with a semicircle attached, constituted the first rude
apparatus for measuring the angular distance between two points on the
celestial sphere. Thus the sun's elevation above the horizon might be
ascertained, by placing one arm of the rule on a level with the horizon,
and bringing the edge of the other into a line with the sun's centre.

[Illustration Fig. 3.]

The common surveyor's compass affords a simple example of angular
measurement. Here, the needle lies in a north and south line, while the
circular rim of the compass, when the instrument is level, corresponds
to the horizon. Hence the compass shows the azimuth of an object, or how
many degrees it lies east or west of the meridian.

It is obvious, that the larger the graduated circle is, the more
minutely its limb may be divided. If the circle is one foot in diameter,
each degree will occupy one tenth of an inch. If the circle is twenty
feet in diameter, a degree will occupy the space of two inches, and
could be easily divided into minutes, since each minute would cover a
space one thirtieth of an inch. Refined astronomical circles are now
divided with very great skill and accuracy, the spaces between the
divisions being, when read off, magnified by a microscope; but in former
times, astronomers had no mode of measuring small angles but by
employing very large circles. But the telescope and microscope enable us
at present to measure celestial arcs much more accurately than was done
by the older astronomers. In the best instruments, the measurements
extend to a single second of space, or one thirty-six hundredth part of
a degree,--a space, on a circle twelve feet in diameter, no greater than
one fifty-seven hundredth part of an inch. To divide, or _graduate_,
astronomical instruments, to such a degree of nicety, requires the
highest efforts of mechanical skill. Indeed, the whole art of
instrument-making is regarded as the most difficult and refined of all
the mechanical arts; and a few eminent artists, who have produced
instruments of peculiar power and accuracy, take rank with astronomers
of the highest celebrity.

I will endeavor to make you acquainted with several of the principal
instruments employed in astronomical observations, but especially with
the telescope, which is the most important and interesting of them all.
I think I shall consult your wishes, as well as your improvement, by
giving you a clear insight into the principles of this prince of
instruments, and by reciting a few particulars, at least, respecting its
invention and subsequent history.

The _Telescope_, as its name implies, is an instrument employed for
viewing distant objects.[2] It aids the eye in two ways; first, by
enlarging the visual angle under which objects are seen, and, secondly,
by collecting and conveying to the eye a much larger amount of the light
that emanates from the object, than would enter the naked pupil. A
complete knowledge of the telescope cannot be acquired, without an
acquaintance with the science of optics; but one unacquainted with that
science may obtain some idea of the leading principles of this noble
instrument. Its main principle is as follows: _By means of the
telescope, we first form an image of a distant object,--as the moon, for
example,--and then magnify that image by a microscope._

[Illustration Fig. 4.]

Let us first see how the image is formed. This may be done either by a
convex lens, or by a concave mirror. A convex lens is a flat piece of
glass, having its two faces convex, or spherical, as is seen in a common
sun-glass, or a pair of spectacles. Every one who has seen a sun-glass,
knows, that, when held towards the sun, it collects the solar rays into
a small bright circle in the focus. This is in fact a small _image_ of
the sun. In the same manner, the image of any distant object, as a star,
may be formed, as is represented in the following diagram. Let A B C D,
Fig. 4, represent the tube of the telescope. At the front end, or at the
end which is directed towards the object, (which we will suppose to be
the moon,) is inserted a convex lens, L, which receives the rays of
light from the moon, and collects them into the focus at _a_, forming an
image of the moon. This image is viewed by a magnifier attached to the
end B C. The lens, L, is called the _object-glass_, and the microscope
in B C, the _eyeglass_. We apply a microscope to this image just as we
would to any object; and, by greatly enlarging its dimensions, we may
render its various parts far more distinct than they would otherwise be;
while, at the same time, the lens collects and conveys to the eye a much
greater quantity of light than would proceed directly from the body
under examination. A very few rays of light only, from a distant object,
as a star, can enter the eye directly; but a lens one foot in diameter
will collect a beam of light of the same dimensions, and convey it to
the eye. By these means, many obscure celestial objects become
distinctly visible, which would otherwise be either too minute, or not
sufficiently luminous, to be seen by us.

But the image may also be formed by means of a _concave mirror_, which,
as well as the concave lens, has the property of collecting the rays of
light which proceed from any luminous body, and of forming an image of
that body. The image formed by a concave mirror is magnified by a
microscope, in the same manner as when formed by the concave lens. When
the lens is used to form an image, the instrument is called a
_refracting telescope_; when a concave mirror is used, it is called a
_reflecting telescope_.

The office of the object-glass is simply _to collect_ the light, and to
form an _image_ of the object, but not to magnify it: the magnifying
power is wholly in the eyeglass. Hence the principle of the telescope is
as follows: _By means of the object-glass_, (in the refracting
telescope,) _or by the concave mirror_, (in the reflecting telescope,)
_we form an image of the object_, _and magnify that image by a
microscope_.

The invention of this noble instrument is generally ascribed to the
great philosopher of Florence, Galileo. He had heard that a spectacle
maker of Holland had accidentally hit upon a discovery, by which distant
objects might be brought apparently nearer; and, without further
information, he pursued the inquiry, in order to ascertain what forms
and combinations of glasses would produce such a result. By a very
philosophical process of reasoning, he was led to the discovery of that
peculiar form of the telescope which bears his name.

Although the telescopes made by Galileo were no larger than a common
spyglass of the kind now used on board of ships, yet, as they gave new
views of the heavenly bodies, revealing the mountains and valleys of
the moon, the satellites of Jupiter, and multitudes of stars which are
invisible to the naked eye, it was regarded with infinite delight and
astonishment.

_Reflecting_ telescopes were first constructed by Sir Isaac Newton,
although the use of a concave reflector, instead of an object-glass, to
form the image, had been previously suggested by Gregory, an eminent
Scotch astronomer. The first telescope made by Newton was only six
inches long. Its reflector, too, was only a little more than an inch.
Notwithstanding its small dimensions, it performed so well, as to
encourage further efforts; and this illustrious philosopher afterwards
constructed much larger instruments, one of which, made with his own
hands, was presented to the Royal Society of London, and is now
carefully preserved in their library.

Newton was induced to undertake the construction of reflecting
telescopes, from the belief that refracting telescopes were necessarily
limited to a very small size, with only moderate illuminating powers,
whereas the dimensions and powers of the former admitted of being
indefinitely increased. Considerable _magnifying_ powers might, indeed,
be obtained from refractors, by making them very long; but the
_brightness_ with which telescopic objects are seen, depends greatly on
the dimensions of the beam of light which is collected by the
object-glass, or by the mirror, and conveyed to the eye; and therefore,
small object-glasses cannot have a very high illuminating power. Now,
the experiments of Newton on colors led him to believe, that it would be
impossible to employ large lenses in the construction of telescopes,
since such glasses would give to the images, they formed, the colors of
the rainbow. But later opticians have found means of correcting these
imperfections, so that we are now able to use object-glasses a foot or
more in diameter, which give very clear and bright images. Such
instruments are called _achromatic_ telescopes,--a name implying the
absence of prismatic or rainbow colors in the image. It is, however, far
more difficult to construct large achromatic than large reflecting
telescopes. Very large pieces of glass can seldom be found, that are
sufficiently pure for the purpose; since every inequality in the glass,
such as waves, tears, threads, and the like, spoils it for optical
purposes, as it distorts the light, and produces nothing but confused
images.

The achromatic telescope (that is, the refracting telescope, having such
an object-glass as to give a colorless image) was invented by Dollond, a
distinguished English artist, about the year 1757. He had in his
possession a quantity of glass of a remarkably fine quality, which
enabled him to carry his invention at once to a high degree of
perfection. It has ever since been, with the manufacturers of
telescopes, a matter of the greatest difficulty to find pieces of glass,
of a suitable quality for object-glasses, more than two or three inches
in diameter. Hence, large achromatic telescopes are very expensive,
being valued in proportion to the _cubes_ of their diameters; that is,
if a telescope whose aperture (as the breadth of the object-glass is
technically called) is two inches, cost one hundred dollars, one whose
aperture is eight inches would cost six thousand four hundred dollars.

Since it is so much easier to make large reflecting than large
refracting telescopes, you may ask, why the latter are ever attempted,
and why reflectors are not exclusively employed? I answer, that the
achromatic telescope, when large and well constructed, is a more perfect
and more durable instrument than the reflecting telescope. Much more of
the light that falls on the mirror is absorbed than is lost in passing
through the object-glass of a refractor; and hence the larger achromatic
telescopes afford a stronger light than the reflecting, unless the
latter are made of an enormous and unwieldy size. Moreover, the mirror
is very liable to tarnish, and will never retain its full lustre for
many years together; and it is no easy matter to restore the lustre,
when once impaired.

In my next Letter, I will give you an account of some of the most
celebrated telescopes that have ever been constructed, and point out the
method of using this excellent instrument, so as to obtain with it the
finest views of the heavenly bodies.

FOOTNOTE:

[2] From two Greek words, =têle=, (_tele_,) _far_, and =schopeô=,
(_skopeo_,) _to see_.

LETTER IV

TELESCOPE CONTINUED.

----"the broad circumference
Hung on his shoulders like the moon, whose orb
Through _optic glass_ the Tuscan artist views
At evening, from the top of Fesolé
Or in Valdarno, to descry new lands,
Rivers or mountains, in her spotted globe."--_Milton._

The two most celebrated telescopes, hitherto made, are Herschel's
_forty-feet reflector_, and the _great Dorpat refractor_. Herschel was a
Hanoverian by birth, but settled in England in the younger part of his
life. As early as 1774, he began to make telescopes for his own use;
and, during his life, he made more than four hundred, of various sizes
and powers. Under the patronage of George the Third, he completed, in
1789, his great telescope, having a tube of iron, forty feet long, and a
speculum, forty-nine and a half inches or more than four feet in
diameter. Let us endeavor to form a just conception of this gigantic
instrument, which we can do only by dwelling on its dimensions, and
comparing them with those of other objects with which we are familiar,
as the length or height of a house, and the breadth of a hogshead or
cistern, of known dimensions. The reflector alone weighed nearly a ton.
So large and ponderous an instrument must require a vast deal of
machinery to work it, and to keep it steady; and, accordingly, the
framework surrounding it was formed of heavy timbers, and resembled the
frame of a large building. When one of the largest of the fixed stars,
as Sirius, is entering the field of this telescope, its approach is
announced by a bright dawn, like that which precedes the rising sun; and
when the star itself enters the field, the light is insupportable to the
naked eye. The planets are expanded into brilliant luminaries, like the
moon; and innumerable multitudes of stars are scattered like glittering
dust over the celestial vault.

The great Dorpat telescope is of more recent construction. It was made
by Fraunhofer, a German optician of the greatest eminence, at Munich, in
Bavaria, and takes its name from its being attached to the observatory
at Dorpat, in Russia. It is of much smaller dimensions than the great
telescope of Herschel. Its object-glass is nine and a half inches in
diameter, and its length, fourteen feet. Although the price of this
instrument was nearly five thousand dollars, yet it is said that this
sum barely covered the actual expenses. It weighs five thousand pounds,
and yet is turned with the finger. In facility of management, it has
greatly the advantage of Herschel's telescope. Moreover, the sky of
England is so much of the time unfavorable for astronomical observation,
that _one hundred_ good hours (or those in which the higher powers can
be used) are all that can be obtained in a whole year. On this account,
and on account of the difficulty of shifting the position of the
instrument, Herschel estimated that it would take about six hundred
years to obtain with it even a momentary glimpse of every part of the
heavens. This remark shows that such great telescopes are unsuited to
the common purposes of astronomical observation. Indeed, most of
Herschel's discoveries were made with his small telescopes; and
although, for certain rare purposes, powers were applied which magnified
seven thousand times, yet, in most of his observations, powers
magnifying only two or three hundred times were employed. The highest
power of the Dorpat telescope is only seven hundred, and yet the
director of this instrument, Professor Struve, is of the opinion, that
it is nearly or quite equal in quality, all things considered, to
Herschel's forty-feet reflector.

It is not generally understood in what way greatness of size in a
telescope increases its powers; and it conveys but an imperfect idea of
the excellence of a telescope, to tell how much it magnifies. In the
same instrument, an increase of magnifying power is always attended with
a diminution of the light and of the field of view. Hence, the lower
powers generally afford the most agreeable views, because they give the
clearest light, and take in the largest space. The several circumstances
which influence the qualities of a telescope are, illuminating power,
distinctness, field of view, and magnifying power. Large mirrors and
large object-glasses are superior to smaller ones, because they collect
a larger beam of light, and transmit it to the eye. Stars which are
invisible to the naked eye are rendered visible by the telescope,
because this instrument collects and conveys to the eye a large beam of
the few rays which emanate from the stars; whereas a beam of these rays
of only the diameter of the pupil of the eye, would afford too little
light for distinct vision. In this particular, large telescopes have
great advantages over small ones. The great mirror of Herschel's
forty-feet reflector collects and conveys to the eye a beam more than
four feet in diameter. The Dorpat telescope also transmits to the eye a
beam nine and one half inches in diameter. This seems small, in
comparison with the reflector; but much less of the light is lost on
passing through the glass than is absorbed by the mirror, and the mirror
is very liable to be clouded or tarnished; so that there is not so great
a difference in the two instruments, in regard to illuminating power, as
might be supposed from the difference of size.

_Distinctness of view_ is all-important to the performance of an
instrument. The object may be sufficiently bright, yet, if the image is
distorted, or ill-defined, the illumination is of little consequence.
This property depends mainly on the skill with which all the
imperfections of figure and color in the glass or mirror are corrected,
and can exist in perfection only when the image is rendered completely
achromatic, and when all the rays that proceed from each point in the
object are collected into corresponding points of the image,
unaccompanied by any other rays. Distinctness is very much affected by
the _steadiness_ of the instrument. Every one knows how indistinct a
page becomes, when a book is passed rapidly backwards and forwards
before the eyes, and how difficult it is to read in a carriage in rapid
motion on a rough road.

_Field of view_ is another important consideration. The finest
instruments exhibit the moon, for example, not only bright and distinct,
in all its parts, but they take in the whole disk at once; whereas, the
inferior instruments, when the higher powers, especially, are applied,
permit us to see only a small part of the moon at once.

I hope, my friend, that, when you have perused these Letters, or rather,
while you are perusing them, you will have frequent opportunities of
looking through a good telescope. I even anticipate that you will
acquire such a taste for viewing the heavenly bodies with the aid of a
good glass, that you will deem a telescope a most suitable appendage to
your library, and as certainly not less an ornament to it than the more
expensive statues with which some people of fortune adorn theirs. I will
therefore, before concluding this letter, offer you a few _directions
for using the telescope_.

Some states of weather, even when the sky is clear, are far more
favorable for astronomical observation than others. After sudden changes
of temperature in the atmosphere, the medium is usually very unsteady.
If the sun shines out warm after a cloudy season, the ground first
becomes heated, and the air that is nearest to it is expanded, and
rises, while the colder air descends, and thus ascending and descending
currents of air, mingling together, create a confused and wavy medium.
The same cause operates when a current of hot air rises from a chimney;
and hence the state of the atmosphere in cities and large towns is very
unfavorable to the astronomer, on this account, as well as on account
of the smoky condition in which it is usually found. After a long season
of dry weather, also, the air becomes smoky, and unfit for observation.
Indeed, foggy, misty, or smoky, air is so prevalent in some countries,
that only a very few times in the whole year can be found, which are
entirely suited to observation, especially with the higher powers; for
we must recollect, that these inequalities and imperfections are
magnified by telescopes, as well as the objects themselves. Thus, as I
have already mentioned, not more than one hundred good hours in a year
could be obtained for observation with Herschel's great telescope. By
_good_ hours, Herschel means that the sky must be very clear, the moon
absent, no twilight, no haziness, no violent wind, and no sudden change
of temperature. As a general fact, the warmer climates enjoy a much
finer sky for the astronomer than the colder, having many more clear
evenings, a short twilight, and less change of temperature. The watery
vapor of the atmosphere, also, is more perfectly dissolved in hot than
in cold air, and the more water air contains, provided it is in a state
of perfect solution, the clearer it is.

A _certain preparation of the observer himself_ is also requisite for
the nicest observations with the telescope. He must be free from all
agitation, and the eye must not recently have been exposed to a strong
light, which contracts the pupil of the eye. Indeed, for delicate
observations, the observer should remain for some time beforehand in a
dark room, to let the pupil of the eye dilate. By this means, it will be
enabled to admit a larger number of the rays of light. In ascending the
stairs of an observatory, visitors frequently get out of breath, and
having perhaps recently emerged from a strongly-lighted apartment, the
eye is not in a favorable state for observation. Under these
disadvantages, they take a hasty look into the telescope, and it is no
wonder that disappointment usually follows.

Want of steadiness is a great difficulty attending the use of the
highest magnifiers; for the motions of the instrument are magnified as
well as the object. Hence, in the structure of observatories, the
greatest pains is requisite, to avoid all tremor, and to give to the
instruments all possible steadiness; and the same care is to be
exercised by observers. In the more refined observations, only one or
two persons ought to be near the instrument.

In general, _low powers_ afford better views of the heavenly bodies than
very high magnifiers. It may be thought absurd, to recommend the use of
low powers, in respect to large instruments especially, since it is
commonly supposed that the advantage of large instruments is, that they
will bear high magnifying powers. But this is not their only, nor even
their principal, advantage. A good light and large field are qualities,
for most purposes, more important than great magnifying power; and it
must be borne in mind, that, as we increase the magnifying power in a
given instrument, we diminish both the illumination and the field of
view. Still, different objects require different magnifying powers; and
a telescope is usually furnished with several varieties of powers, one
of which is best fitted for viewing the moon, another for Jupiter, and a
still higher power for Saturn. Comets require only the lowest
magnifiers; for here, our object is to command as much light, and as
large a field, as possible, while it avails little to increase the
dimensions of the object. On the other hand, for certain double stars,
(stars which appear single to the naked eye, but double to the
telescope,) we require very high magnifiers, in order to separate these
minute objects so far from each other, that the interval can be
distinctly seen. Whenever we exhibit celestial objects to inexperienced
observers, it is useful to precede the view with good _drawings_ of the
objects, accompanied by an explanation of what each appearance,
exhibited in the telescope, indicates. The novice is told, that
mountains and valleys can be seen in the moon by the aid of the
telescope; but, on looking, he sees a confused mass of light and shade,
and nothing which looks to him like either mountains or valleys. Had his
attention been previously directed to a plain drawing of the moon, and
each particular appearance interpreted to him, he would then have looked
through the telescope with intelligence and satisfaction.

LETTER V.

OBSERVATORIES.

"We, though from heaven remote, to heaven will move,
With strength of mind, and tread the abyss above;
And penetrate, with an interior light,
Those upper depths which Nature hid from sight.
Pleased we will be, to walk along the sphere
Of shining stars, and travel with the year."--_Ovid._

An observatory is a structure fitted up expressly for astronomical
observations, and furnished with suitable instruments for that purpose.

The two most celebrated observatories, hitherto built, are that of Tycho
Brahe, and that of Greenwich, near London. The observatory of Tycho
Brahe, Fig. 5, was constructed at the expense of the King of Denmark, in
a style of royal magnificence, and cost no less than two hundred
thousand crowns. It was situated on the island of Huenna, at the
entrance of the Baltic, and was called Uraniburg, or the palace of the
skies.

Before I give you an account of Tycho's observatory, I will recite a few
particulars respecting this great astronomer himself.

Tycho Brahe was of Swedish descent, and of noble family; but having
received his education at the University of Copenhagen, and spent a
large part of his life in Denmark, he is usually considered as a Dane,
and quoted as a Danish astronomer. He was born in the year 1546. When he
was about fourteen years old, there happened a great eclipse of the sun,
which awakened in him a high interest, especially when he saw how
[Illustration Fig. 5.] accurately all the circumstances of it answered
to the prediction with which he had been before made acquainted. He was
immediately seized with an irresistible passion to acquire a knowledge
of the science which could so successfully lift the veil of futurity.
His friends had destined him for the profession of law, and, from the
superior talents of which he gave early promise, and with the advantage
of powerful family connexions, they had marked out for him a
distinguished career in public life. They therefore endeavored to
discourage him from pursuing a path which they deemed so much less
glorious than that, and vainly sought, by various means, to extinguish
the zeal for astronomy which was kindled in his youthful bosom.
Despising all the attractions of a court, he contracted an alliance with
a peasant girl, and, in the peaceful retirement of domestic life,
desired no happier lot than to peruse the grand volume which the
nocturnal heavens displayed to his enthusiastic imagination. He soon
established his fame as one of the greatest astronomers of the age, and
monarchs did homage to his genius. The King of Denmark became his
munificent patron, and James the First, King of England, when he went to
Denmark to complete his marriage with a Danish Princess, passed eight
days with Tycho in his observatory, and, at his departure, addressed to
the astronomer a Latin ode, accompanied with a magnificent present. He
gave him also his royal license to print his works in England, and added
to it the following complimentary letter: "Nor am I acquainted with
these things on the relation of others, or from a mere perusal of your
works, but I have seen them with my own eyes, and heard them with my own
ears, in your residence at Uraniburg, during the various learned and
agreeable conversations which I there held with you, which even now
affect my mind to such a degree, that it is difficult to decide, whether
I recollect them with greater pleasure or admiration." Admiring
disciples also crowded to this sanctuary of the sciences, to acquire a
knowledge of the heavens.

The observatory consisted of a main building, which was square, each
side being sixty feet, and of large wings in the form of round towers.
The whole was executed in a style of great magnificence, and Tycho, who
was a nobleman by descent, gratified his taste for splendor and
ornament, by giving to every part of the structure an air of the most
finished elegance. Nor were the instruments with which it was furnished
less magnificent than the buildings. They were vastly larger than had
before been employed in the survey of the heavens, and many of them were
adorned with costly ornaments. The cut on page 46, Fig. 6, represents
one of Tycho's large and splendid instruments, (an astronomical
quadrant,) on one side of which was figured a representation of the
astronomer and his assistants, in the midst of their instruments, and
intently engaged in making and recording observations. It conveys to us
a striking idea of the magnificence of his arrangements, and of the
extent of his operations.

Here Tycho sat in state, clad in the robes of nobility, and supported
throughout his establishment the etiquette due to his rank. His
observations were more numerous than all that had ever been made before,
and they were carried to a degree of accuracy that is astonishing, when
we consider that they were made without the use of the telescope, which
was not yet invented.

Tycho carried on his observations at Uraniburg for about twenty years,
during which time he accumulated an immense store of accurate and
valuable _facts_, which afforded the groundwork of the discovery of the
great laws of the solar system established by Kepler, of whom I shall
tell you more hereafter.

But the high marks of distinction which Tycho enjoyed, not only from his
own Sovereign, but also from foreign potentates, provoked the envy of
the courtiers of his royal patron. They did not indeed venture to make
their attacks upon him while his generous patron was living; but the
King was no sooner dead, and succeeded by a young monarch, who did not
feel the same [Illustration Fig. 6.] interest in protecting and
encouraging this great ornament of the kingdom, than his envious foes
carried into execution their long-meditated plot for his ruin. They
represented to the young King, that the treasury was exhausted, and that
it was necessary to retrench a number of pensions, which had been
granted for useless purposes, and in particular that of Tycho, which,
they maintained, ought to be conferred upon some person capable of
rendering greater services to the state. By these means, they succeeded
in depriving him of his support, and he was compelled to retreat under
the hospitable mansion of a friend in Germany. Here he became known to
the Emperor, who invited him to Prague, where, with an ample stipend, he
resumed his labors. But, though surrounded with affectionate friends and
admiring disciples, he was still an exile in a foreign land. Although
his country had been base in its ingratitude, it was yet the land which
he loved; the scene of his earliest affection; the theatre of his
scientific glory. These feelings continually preyed upon his mind, and
his unsettled spirit was ever hovering among his native mountains. In
this condition he was attacked by a disease of the most painful kind,
and, though its agonizing paroxysms had lengthened intermissions, yet he
saw that death was approaching. He implored his pupils to persevere in
their scientific labors; he conversed with Kepler on some of the
profoundest points of astronomy; and with these secular occupations he
mingled frequent acts of piety and devotion. In this happy condition he
expired, without pain, at the age of fifty-five.[3]

The observatory at Greenwich was not built until a hundred years after
that of Tycho Brahe, namely, in 1676. The great interests of the British
nation, which are involved in navigation, constituted the ruling motive
with the government to lend their aid in erecting and maintaining this
observatory.

The site of the observatory at Greenwich is on a commanding eminence
facing the River Thames, five miles east of the central parts of London.
Being part of a royal park, the neighboring grounds are in no danger of
being occupied by buildings, so as to obstruct the view. It is also in
full view of the shipping on the Thames; and, according to a standing
regulation of the observatory, at the instant of one o'clock, every day,
a huge ball is dropped from over the house, as a signal to the
commanders of vessels for regulating their chronometers.

The buildings comprise a series of rooms, of sufficient number and
extent to accommodate the different instruments, the inmates of the
establishment, and the library; and on the top is a celebrated camera
obscura, exhibiting a most distinct and perfect picture of the grand and
unrivalled scenery which this eminence commands.

This establishment, by the accuracy and extent of its observations, has
contributed more than all other institutions to perfect the science of
astronomy.

To preside over and direct this great institution, a man of the highest
eminence in the science is appointed by the government, with the title
of _Astronomer Royal_. He is paid an ample salary, with the
understanding that he is to devote himself exclusively to the business
of the observatory. The astronomers royal of the Greenwich observatory,
from the time of its first establishment, in 1676, to the present time,
have constituted a series of the proudest names of which British science
can boast. A more detailed sketch of their interesting history will be
given towards the close of these Letters.

Six assistants, besides inferior laborers, are constantly in attendance;
and the business of making and recording observations is conducted with
the utmost system and order.

The great objects to be attained in the construction of an observatory
are, a commanding and unobstructed view of the heavens; freedom from
causes that affect the transparency and uniform state of the
atmosphere, such as fires, smoke, or marshy grounds; mechanical
facilities for the management of instruments, and, especially, every
precaution that is necessary to secure perfect steadiness. This last
consideration is one of the greatest importance, particularly in the use
of very large magnifiers; for we must recollect, that any motion in the
instrument is magnified by the full power of the glass, and gives a
proportional unsteadiness to the object. A situation is therefore
selected as remote as possible from public roads, (for even the passing
of carriages would give a tremulous motion to the ground, which would be
sensible in large instruments,) and structures of solid masonry are
commenced deep enough in the ground to be unaffected by frost, and built
up to the height required, without any connexion with the other parts of
the building. Many observatories are furnished with a movable dome for a
roof, capable of revolving on rollers, so that instruments penetrating
through the roof may be easily brought to bear upon any point at or near
the zenith.

You will not perhaps desire me to go into a minute description of all
the various instruments that are used in a well-constructed observatory.
Nor is this necessary, since a very large proportion of all astronomical
observations are taken on the meridian, by means of the transit
instrument and clock. When a body, in its diurnal revolution, comes to
the meridian, it is at its highest point above the horizon, and is then
least affected by refraction and parallax. This, then, is the most
favorable position for taking observations upon it. Moreover, it is
peculiarly easy to take observations on a body when in this situation.
Hence the transit instrument and clock are the most important members of
an astronomical observatory. You will, therefore, expect me to give you
some account of these instruments.

[Illustration Fig. 7.]

The _transit instrument_ is a telescope which is fixed permanently in
the meridian, and moves only in that plane. The accompanying diagram,
Fig. 7, represents a side view of a portable transit instrument,
exhibiting the telescope supported on a firm horizontal axis, on which
it turns in the plane of the meridian, from the south point of the
horizon through the zenith to the north point. It can therefore be so
directed as to observe the passage of a star across the meridian at any
altitude. The accompanying graduated circle enables the observer to set
the instrument at any required altitude, corresponding to the known
altitude at which the body to be observed crosses the meridian. Or it
may be used to measure the altitude of a body, or its zenith distance,
at the time of its meridian passage. Near the circle may be seen a
spirit-level, which serves to show when the axis is exactly on a level
with the horizon. The framework is made of solid metal, (usually brass,)
every thing being arranged with reference to keeping the instrument
perfectly steady. It stands on screws, which not only afford a steady
support, but are useful for adjusting the instrument to a perfect
level. The transit instrument is sometimes fixed immovably to a solid
foundation, as a pillar of stone, which is built up from a depth in the
ground below the reach of frost. When enclosed in a building, as in an
observatory, the stone pillar is carried up separate from the walls and
floors of the building, so as to be entirely free from the agitations to
which they are liable.

The use of the transit instrument is to show the precise instant when a
heavenly body is on the meridian, or to measure the time it occupies in
crossing the meridian. The _astronomical clock_ is the constant
companion of the transit instrument. This clock is so regulated as to
keep exact pace with the stars, and of course with the revolution of the
earth on its axis; that is, it is regulated to _sidereal_ time. It
measures the progress of a star, indicating an hour for every fifteen
degrees, and twenty-four hours for the whole period of the revolution of
the star. Sidereal time commences when the vernal equinox is on the
meridian, just as solar time commences when the sun is on the meridian.
Hence the hour by the sidereal clock has no correspondence with the hour
of the day, but simply indicates how long it is since the equinoctial
point crossed the meridian. For example, the clock of an observatory
points to three hours and twenty minutes; this may be in the morning, at
noon, or any other time of the day,--for it merely shows that it is
three hours and twenty minutes since the equinox was on the meridian.
Hence, when a star is on the meridian, the clock itself shows its right
ascension, which you will recollect is the angular distance measured on
the equinoctial, from the point of intersection of the ecliptic and
equinoctial, called the vernal equinox, reckoning fifteen degrees for
every hour, and a proportional number of degrees and minutes for a less
period. I have before remarked, that a very large portion of all
astronomical observations are taken when the bodies are on the meridian,
by means of the transit instrument and clock.

Having now described these instruments, I will next explain the manner
of using them for different observations. Any thing becomes a measure of
time, which divides duration equally. The equinoctial, therefore, is
peculiarly adapted to this purpose, since, in the daily revolution of
the heavens, equal portions of the equinoctial pass under the meridian
in equal times. The only difficulty is, to ascertain the amount of these
portions for given intervals. Now, the clock shows us exactly this
amount; for, when regulated to sidereal time, (as it easily may be,) the
hour-hand keeps exact pace with the equator, revolving once on the
dial-plate of the clock while the equator turns once by the revolution
of the earth. The same is true, also, of all the small circles of
diurnal revolution; they all turn exactly at the same rate as the
equinoctial, and a star situated any where between the equator and the
pole will move in its diurnal circle along with the clock, in the same
manner as though it were in the equinoctial. Hence, if we note the
interval of time between the passage of any two stars, as shown by the
clock, we have a measure of the number of degrees by which they are
distant from each other in right ascension. Hence we see how easy it is
to take arcs of right ascension: the transit instrument shows us when a
body is on the meridian; the clock indicates how long it is since the
vernal equinox passed it, which is the right ascension itself; or it
tells us the difference of right ascension between any two bodies,
simply by indicating the difference in time between their periods of
passing the meridian. Again, it is easy to take the _declination_ of a
body when on the meridian. By declination, you will recollect, is meant
the distance of a heavenly body from the equinoctial; the same, indeed,
as latitude on the earth. When a star is passing the meridian, if, on
the instant of crossing the meridian wire of the telescope, we take its
distance from the north pole, (which may readily be done, because the
position of the pole is always known, being equal to the latitude of the
place,) and subtract this distance from ninety degrees, the remainder
will be the distance from the equator, which is the declination. You
will ask, why we take this indirect method of finding the declination?
Why we do not rather take the distance of the star from the equinoctial,
at once? I answer, that it is easy to point an instrument to the north
pole, and to ascertain its exact position, and of course to measure any
distance from it on the meridian, while, as there is nothing to mark the
exact situation of the equinoctial, it is not so easy to take direct
measurements from it. When we have thus determined the situation of a
heavenly body, with respect to two great circles at right angles with
each other, as in the present case, the distance of a body from the
equator and from the equinoctial colure, or that meridian which passes
though the vernal equinox, we know its relative position in the heavens;
and when we have thus determined the relative positions of all the
stars, we may lay them down on a map or a globe, exactly as we do places
on the earth, by means of their latitude and longitude.

The foregoing is only a _specimen_ of the various uses of the transit
instrument, in finding the relative places of the heavenly bodies.
Another use of this excellent instrument is, to regulate our clocks and
watches. By an observation with the transit instrument, we find when the
sun's centre is on the meridian. This is the exact time of _apparent_
noon. But watches and clocks usually keep _mean_ time, and therefore, in
order to set our timepiece by the transit instrument, we must apply to
the apparent time of noon the equation of time, as will be explained in
my next Letter.

A _noon-mark_ may easily be made by the aid of the transit instrument. A
window sill is frequently selected as a suitable place for the mark,
advantage being taken of the shadow projected upon it by the
perpendicular casing of the window. Let an assistant stand, with a rule
laid on the line of shadow, and with a knife ready to make the mark, the
instant when the observer at the transit instrument announces that the
centre of the sun is on the meridian. By a concerted signal, as the
stroke of a bell, the inhabitants of a town may all fix a noon-mark from
the same observation. If the signal be given on one of the days when
apparent time and mean time become equal to each other, as on the
twenty-fourth of December, no equation of time is required.

As a noon-mark is convenient for regulating timepieces, I will point out
a method of making one, which may be practised without the aid of the
telescope. Upon a smooth, level plane, freely exposed to the sun, with a
pair of compasses describe a circle. In the centre, where the leg of the
compasses stood, erect a perpendicular wire of such a length, that the
termination of its shadow shall fall upon the circumference of the
circle at some hour before noon, as about ten o'clock. Make a small dot
at the point where the end of the shadow falls upon the circle, and do
the same where it falls upon it again in the afternoon. Take a point
half-way between these two points, and from it draw a line to the
centre, and it will be a true meridian line. The direction of this line
would be the same, whether it were made in the Summer or in the Winter;
but it is expedient to draw it about the fifteenth of June, for then the
shadow alters its length most rapidly, and the moment of its crossing
the wire will be more definite, than in the Winter. At this time of
year, also, the sun and clock agree, or are together, as will be more
fully explained in my next Letter; whereas, at other times of the year,
the time of noon, as indicated by a common clock, would not agree with
that indicated by the sun. If the upper end of the wire is flattened,
and a small hole is made in it, through which the sun may shine, the
instant when this bright spot falls upon the circle will be better
defined than the termination of the shadow.

Another important instrument of the observatory is the _mural circle_.
It is a graduated circle, usually of very large size, fixed permanently
in the plane of the meridian, and attached firmly to a perpendicular
wall; and on its centre is a telescope, which revolves along with it,
and is easily brought to bear on any object in any point in the
meridian. It is made of large size, sometimes twenty feet in diameter,
in order that very small angles may be measured on its limb; for it is
obvious that a small angle, as one second, will be a larger space on the
limb of an instrument, in proportion as the instrument itself is larger.
The vertical circle usually connected with the transit instrument, as in
Fig. 7, may indeed be employed for the same purposes as the mural
circle, namely, to measure arcs of the meridian, as meridian altitudes,
zenith distances, north polar distances, and declinations; but as that
circle must necessarily be small, and therefore incapable of measuring
very minute angles, the mural circle is particularly useful in measuring
these important arcs. It is very difficult to keep so large an
instrument perfectly steady; and therefore it is attached to a massive
wall of solid masonry, and is hence called a _mural_ circle, from a
Latin word, (_murus_,) which signifies a wall.

The diagram, Fig. 8, page 56, represents a mural circle fixed to its
wall, and ready for observations. It will be seen, that every expedient
is employed to give the instrument firmness of parts and steadiness of
position. The circle is of solid metal, usually of brass, and it is
strengthened by numerous radii, which keep it from warping or bending;
and these are made in the form of hollow cones, because that is the
figure which unites in the highest degree lightness and strength. On the
rim of the instrument, at A, you may observe a microscope. This is
attached to a micrometer,--a delicate piece of apparatus, used for
reading the minute subdivisions of angles; for, after dividing the limb
of the instrument as minutely as possible, it will then be necessary to
magnify those divisions with the microscope, and subdivide each of these
parts with the micrometer. Thus, if we have a mural circle twenty feet
in diameter, and of course nearly sixty-three feet in circumference,
since there are twenty-one thousand and six hundred minutes in the
whole circle, we shall find, by calculation, that one minute would
occupy, on the limb of such an instrument, only about one thirtieth of
an inch, and a second, only one eighteen hundredth of an inch. We could
not, therefore, hope to carry the actual divisions to a greater degree
of minuteness than minutes; but each of these spaces may again be
subdivided into seconds by the micrometer.

[Illustration Fig. 8.]

From these statements, you will acquire some faint idea of the extreme
difficulty of making perfect astronomical instruments, especially where
they are intended to measure such minute angles as one second. Indeed,
the art of constructing astronomical instruments is one which requires
such refined mechanical genius,--so superior a mind to devise, and so
delicate a hand to execute,--that the most celebrated instrument-makers
take rank with the most distinguished astronomers; supplying, as they
do, the means by which only the latter are enabled to make these great
discoveries. Astronomers have sometimes made their own telescopes; but
they have seldom, if ever, possessed the refined manual skill which is
requisite for graduating delicate instruments.

The _sextant_ is also one of the most valuable instruments for taking
celestial arcs, or the distance between any two points on the celestial
sphere, being applicable to a much greater number of purposes than the
instruments already described. It is particularly valuable for measuring
celestial arcs at sea, because it is not, like most astronomical
instruments, affected by the motion of the ship. The principle of the
sextant may be briefly described, as follows: it gives the angular
distance between any two bodies on the celestial sphere, by reflecting
the image of one of the bodies so as to coincide with the other body, as
seen directly. The arc through which the reflector is turned, to bring
the reflected body to coincide with the other body, becomes a measure of
the angular distance between them. By keeping this principle in view,
you will be able to understand the use of the several parts of the
instrument, as they are exhibited in the diagram, Fig. 9, page 58.

It is, you observe, of a triangular shape, and it is made strong and
firm by metallic cross-bars. It has two reflectors, I and H, called,
respectively, the index glass and the horizon glass, both of which are
firmly fixed perpendicular to the plane of the instrument. The index
glass is attached to the movable arm, ID, and turns as this is moved
along the graduated limb, EF. This arm also carries a _vernier_, at D, a
contrivance which, like the micrometer, enables us to take off minute
parts of the spaces into which the limb is divided. The horizon glass,
H, consists of two parts; the upper part being transparent or open, so
that the eye, looking through the telescope, T, can see through it a
distant body, as a star at S, while the lower part is a reflector.

[Illustration Fig. 9.]

Suppose it were required to measure the angular distance between the
moon and a certain star,--the moon being at M, and the star at S. The
instrument is held firmly in the hand, so that the eye, looking through
the telescope, sees the star, S, through the transparent part of the
horizon glass. Then the movable arm, ID, is moved from F towards E,
until the image of M is reflected down to S, when the number of degrees
and parts of a degree reckoned on the limb, from F to the index at D,
will show the angular distance between the two bodies.

FOOTNOTE:

[3] Brewster's Life of Newton

LETTER VI.

TIME AND THE CALENDAR.

"From old Eternity's mysterious orb
Was Time cut off, and cast beneath the skies."--_Young._

HAVING hitherto been conversant only with the many fine and sentimental
things which the poets have sung respecting Old Time, perhaps you will
find some difficulty in bringing down your mind to the calmer
consideration of what time really is, and according to what different
standards it is measured for different purposes. You will not, however,
I think, find the subject even in our matter-of-fact and unpoetical way
of treating it, altogether uninteresting. What, then, is time? _Time is
a measured portion of indefinite duration._ It consists of equal
portions cut off from eternity, as a line on the surface of the earth is
separated from its contiguous portions that constitute a great circle of
the sphere, by applying to it a two-foot scale; or as a few yards of
cloth are measured off from a piece of unknown or indefinite extent.

Any thing, or any event which takes place at equal intervals, may become
a measure of time. Thus, the pulsations of the wrist, the flowing of a
given quantity of sand from one vessel to another, as in the hourglass,
the beating of a pendulum, and the revolution of a star, have been
severally employed as measures of time. But the great standard of time
is the period of the revolution of the earth on its axis, which, by the
most exact observations, is found to be always the same. I have
anticipated a little of this subject, in giving an account of the
transit instrument and clock, but I propose, in this letter, to enter
into it more at large.

The time of the earth's revolution on its axis, as already explained, is
called a sidereal day, and is determined by the revolution of a star in
the heavens. This interval is divided into twenty-four _sidereal_
hours. Observations taken on numerous stars, in different ages of the
world, show that they all perform their diurnal revolution in the same
time, and that their motion, during any part of the revolution, is
always uniform. Here, then, we have an exact measure of time, probably
more exact than any thing which can be devised by art. _Solar time_ is
reckoned by the apparent revolution of the sun from the meridian round
to the meridian again. Were the sun stationary in the heavens, like a
fixed star, the time of its apparent revolution would be equal to the
revolution of the earth on its axis, and the solar and the sidereal days
would be equal. But, since the sun passes from west to east, through
three hundred and sixty degrees, in three hundred and sixty-five and one
fourth days, it moves eastward nearly one degree a day. While,
therefore, the earth is turning round on its axis, the sun is moving in
the same direction, so that, when we have come round under the same
celestial meridian from which we started, we do not find the sun there,
but he has moved eastward nearly a degree, and the earth must perform so
much more than one complete revolution, before we come under the sun
again. Now, since we move, in the diurnal revolution, fifteen degrees in
sixty minutes, we must pass over one degree in four minutes. It takes,
therefore, four minutes for us to _catch up_ with the sun, after we have
made one complete revolution. Hence the solar day is about four minutes
longer than the sidereal; and if we were to reckon the sidereal day
twenty-four hours, we should reckon the solar day twenty-four hours four
minutes. To suit the purposes of society at large, however, it is found
more convenient to reckon the solar days twenty-four hours, and throw
the fraction into the sidereal day. Then,

24h. 4m. : 24h. :: 24h. : 23h. 56m. 4s.

That is, when we reduce twenty-four hours and four minutes to
twenty-four hours, the same proportion will require that we reduce the
sidereal day from twenty-four hours to twenty-three hours fifty-six
minutes four seconds; or, in other words, a sidereal day is such a part
of a solar day. The solar days, however, do not always differ from the
sidereal by precisely the same fraction, since they are not constantly
of the same length. Time, as measured by the sun, is called _apparent
time_, and a clock so regulated as always to keep exactly with the sun,
is said to keep apparent time. _Mean time_ is time reckoned by the
_average_ length of all the solar days throughout the year. This is the
period which constitutes the _civil_ day of twenty-four hours, beginning
when the sun is on the lower meridian, namely, at twelve o'clock at
night, and counted by twelve hours from the lower to the upper meridian,
and from the upper to the lower. The _astronomical_ day is the apparent
solar day counted through the whole twenty-four hours, (instead of by
periods of twelve hours each, as in the civil day,) and begins at noon.
Thus it is now the tenth of June, at nine o'clock, A.M., according to
civil time; but we have not yet reached the tenth of June by
astronomical time, nor shall we, until noon to-day; consequently, it is
now June ninth, twenty-first hour of astronomical time. Astronomers,
since so many of their observations are taken on the meridian, are
always supposed to look towards the south. Geographers, having formerly
been conversant only with the northern hemisphere, are always understood
to be looking towards the north. Hence, left and right, when applied to
the astronomer, mean east and west, respectively; but to the geographer
the right is east, and the left, west.

Clocks are usually regulated so as to indicate mean solar time; yet, as
this is an artificial period not marked off, like the sidereal day, by
any natural event, it is necessary to know how much is to be added to,
or subtracted from, the apparent solar time, in order to give the
corresponding mean time. The interval, by which apparent time differs
from mean time, is called the _equation of time_. If one clock is so
constructed as to keep exactly with the sun, going faster or slower,
according as the lengths of the solar days vary, and another clock is
regulated to mean time, then the difference of the two clocks, at any
period, would be the equation of time for that moment. If the apparent
clock were _faster_ than the mean, then the equation of time must be
subtracted; but if the apparent clock were slower than the mean, then
the equation of time must be added, to give the mean time. The two
clocks would differ most about the third of November, when the apparent
time is sixteen and one fourth minutes greater than the mean. But since
apparent time is sometimes greater and sometimes less than mean time,
the two must obviously be sometimes equal to each other. This is, in
fact, the case four times a year, namely, April fifteenth, June
fifteenth, September first, and December twenty-fourth.

Astronomical clocks are made of the best workmanship, with every
advantage that can promote their regularity. Although they are brought
to an astonishing degree of accuracy, yet they are not as regular in
their movements as the stars are, and their accuracy requires to be
frequently tested. The transit instrument itself, when once accurately
placed in the meridian, affords the means of testing the correctness of
the clock, since one revolution of a star, from the meridian to the
meridian again, ought to correspond exactly to twenty-four hours by the
clock, and to continue the same, from day to day; and the right
ascensions of various stars, as they cross the meridian, ought to be
such by the clock, as they are given in the tables, where they are
stated according to the accurate determinations of astronomers. Or, by
taking the difference of any two stars, on successive days, it will be
seen whether the going of the clock is uniform for that part of the day;
and by taking the right ascensions of different pairs of stars, we may
learn the rate of the clock at various parts of the day. We thus learn,
not only whether the clock accurately measures the length of the
sidereal day, but also whether it goes uniformly from hour to hour.

Although astronomical clocks have been brought to a great degree of
perfection, so as hardly to vary a second for many months, yet none are
absolutely perfect, and most are so far from it, as to require to be
corrected by means of the transit instrument, every few days. Indeed,
for the nicest observations, it is usual not to attempt to bring the
clock to a state of absolute correctness, but, after bringing it as near
to such a state as can conveniently be done, to ascertain how much it
gains or loses in a day; that is, to ascertain the _rate_ of its going,
and to make allowance accordingly.

Having considered the manner in which the smaller divisions of time are
measured, let us now take a hasty glance at the larger periods which
compose the calendar.

As a _day_ is the period of the revolution of the earth on its axis, so
a _year_ is the period of the revolution of the earth around the sun.
This time, which constitutes the _astronomical year_, has been
ascertained with great exactness, and found to be three hundred and
sixty-five days five hours forty-eight minutes and fifty-one seconds.
The most ancient nations determined the number of days in the year by
means of the _stylus_, a perpendicular rod which casts its shadow on a
smooth plane bearing a meridian line. The time when the shadow was
shortest, would indicate the day of the Summer solstice; and the number
of days which elapsed, until the shadow returned to the same length
again, would show the number of days in the year. This was found to be
three hundred and sixty-five whole days, and accordingly, this period
was adopted for the civil year. Such a difference, however, between the
civil and astronomical years, at length threw all dates into confusion.
For if, at first, the Summer solstice happened on the twenty-first of
June, at the end of four years, the sun would not have reached the
solstice until the twenty-second of June; that is, it would have been
behind its time. At the end of the next four years, the solstice would
fall on the twenty-third; and in process of time, it would fall
successively on every day of the year. The same would be true of any
other fixed date.

Julius Cæsar, who was distinguished alike for the variety and extent of
his knowledge, and his skill in arms, first attempted to make the
calendar conform to the motions of the sun.

"Amidst the hurry of tumultuous war,
The stars, the gods, the heavens, were still his care."

Aided by Sosigenes, an Egyptian astronomer, he made the first correction
of the calendar, by introducing an additional day every fourth year,
making February to consist of twenty-nine instead of twenty-eight days,
and of course the whole year to consist of three hundred and sixty-six
days. This fourth year was denominated _Bissextile_, because the sixth
day before the Kalends of March was reckoned twice. It is also called
Leap Year.

The Julian year was introduced into all the civilized nations that
submitted to the Roman power, and continued in general use until the
year 1582. But the true correction was not six hours, but five hours
forty-nine minutes; hence the addition was too great by eleven minutes.
This small fraction would amount in one hundred years to three fourths
of a day, and in one thousand years to more than seven days. From the
year 325 to the year 1582, it had, in fact, amounted to more than ten
days; for it was known that, in 325, the vernal equinox fell on the
twenty-first of March, whereas, in 1582, it fell on the eleventh. It was
ordered by the Council of Nice, a celebrated ecclesiastical council,
held in the year 325, that Easter should be celebrated upon the first
Sunday after the first full moon, next following the vernal equinox; and
as certain other festivals of the Romish Church were appointed at
particular seasons of the year, confusion would result from such a want
of constancy between any fixed date and a particular season of the year.
Suppose, for example, a festival accompanied by numerous religious
ceremonies, was decreed by the Church to be held at the time when the
sun crossed the equator in the Spring, (an event hailed with great joy,
as the harbinger of the return of Summer,) and that, in the year 325,
March twenty-first was designated as the time for holding the festival,
since, at that period, it was on the twenty-first of March when the sun
reached the equinox; the next year, the sun would reach the equinox a
little sooner than the twenty-first of March, only eleven minutes,
indeed, but still amounting in twelve hundred years to ten days; that
is, in 1582, the sun reached the equinox on the eleventh of March. If,
therefore, they should continue to observe the twenty-first as a
religious festival in honor of this event, they would commit the
absurdity of celebrating it ten days after it had passed by. Pope
Gregory the Thirteenth, who was then at the head of the Roman See, was a
man of science, and undertook to reform the calendar, so that fixed
dates would always correspond to the same seasons of the year. He first
decreed, that the year should be brought forward ten days, by reckoning
the fifth of October the fifteenth; and, in order to prevent the
calendar from falling into confusion afterwards, he prescribed the
following rule: _Every year whose number is not divisible by four,
without a remainder, consists of three hundred and sixty-five days;
every year which is so divisible, but is not divisible by one hundred,
of three hundred and sixty-six; every year divisible by one hundred, but
not by four hundred, again, of three hundred and sixty-five; and every
year divisible by four hundred, of three hundred and sixty-six._

Thus the year 1838, not being divisible by four, contains three hundred
and sixty-five days, while 1836 and 1840 are leap years. Yet, to make
every fourth year consist of three hundred and sixty-six days would
increase it too much, by about three fourths of a day in a century;
therefore every hundredth year has only three hundred and sixty-five
days. Thus 1800, although divisible by four, was not a leap year, but a
common year. But we have allowed a _whole_ day in a hundred years,
whereas we ought to have allowed only _three fourths_ of a day. Hence,
in four hundred years, we should allow a day too much, and therefore, we
let the four hundredth remain a leap year. This rule involves an error
of less than a day in four thousand two hundred and thirty-seven years.

The Pope, who, you will recollect, at that age assumed authority over
all secular princes, issued his decree to the reigning sovereigns of
Christendom, commanding the observance of the calendar as reformed by
him. The decree met with great opposition among the Protestant States,
as they recognised in it a new exercise of ecclesiastical tyranny; and
some of them, when they received it, made it expressly understood, that
their acquiescence should not be construed as a submission to the Papal
authority.

In 1752, the Gregorian year, or _New Style_, was established in Great
Britain by act of Parliament; and the dates of all deeds, and other
legal papers, were to be made according to it. As above a century had
then passed since the first introduction of the new style, eleven days
were suppressed, the third of September being called the fourteenth. By
the same act, the beginning of the year was changed from March
twenty-fifth to January first. A few persons born previously to 1752
have come down to our day, and we frequently see inscriptions on
tombstones of those whose time of birth is recorded in old style. In
order to make this correspond to our present mode of reckoning, we must
add eleven days to the date. Thus the same event would be June twelfth
of old style, or June twenty-third of new style; and if an event
occurred between January first and March twenty-fifth, the date of the
year would be advanced one, since February 1st, 1740, O.S. would be
February 1st, 1741, N.S. Thus, General Washington was born February
11th, 1731, O.S., or February 22d, 1732, N.S. If we inquire how any
present event may be made to correspond in date to the old style, we
must subtract twelve days, and put the year back one, if the event lies
between January first and March twenty-fifth. Thus, June tenth, N.S.
corresponds to May twenty-ninth, O.S.; and March 20th, 1840, to March
8th, 1839. France, being a Roman Catholic country, adopted the new style
soon after it was decreed by the Pope; but Protestant countries, as we
have seen, were much slower in adopting it; and Russia, and the Greek
Church generally, still adhere to the old style. In order, therefore, to
make the Russian dates correspond to ours, we must add to them twelve
days.

It may seem to you very remarkable, that so much pains should have been
bestowed upon this subject; but without a correct and uniform standard
of time, the dates of deeds, commissions, and all legal papers; of fasts
and festivals, appointed by ecclesiastical authority; the returns of
seasons, and the records of history,--must all fall into inextricable
confusion. To change the observance of certain religious feasts, which
have been long fixed to particular days, is looked upon as an impious
innovation; and though the times of the events, upon which these
ceremonies depend, are utterly unknown, it is still insisted upon by
certain classes in England, that the Glastenbury thorn blooms on
Christmas day.

Although the ancient Grecian calendar was extremely defective, yet the
common people were entirely averse to its reformation. Their
superstitious adherence to these errors was satirized by Aristophanes,
in his comedy of the Clouds. An actor, who had just come from Athens,
recounts that he met with Diana, or the moon, and found her extremely
incensed, that they did not regulate her course better. She complained,
that the order of Nature was changed, and every thing turned topsyturvy.
The gods no longer knew what belonged to them; but, after paying their
visits on certain feast-days, and expecting to meet with good cheer, as
usual, they were under the disagreeable necessity of returning back to
heaven without their suppers.

Among the Greeks, and other ancient nations, the length of the year was
generally regulated by the course of the moon. This planet, on account
of the different appearances which she exhibits at her full, change,
and quarters, was considered by them as best adapted of any of the
celestial bodies for this purpose. As one lunation, or revolution of the
moon around the earth, was found to be completed in about twenty-nine
and one half days, and twelve of these periods being supposed equal to
one revolution of the sun, their months were made to consist of
twenty-nine and thirty days alternately, and their year of three hundred
and fifty-four days. But this disagreed with the annual revolution of
the sun, which must evidently govern the seasons of the year, more than
eleven days. The irregularities, which such a mode of reckoning would
occasion, must have been too obvious not to have been observed. For,
supposing it to have been settled, at any particular time, that the
beginning of the year should be in the Spring; in about sixteen years
afterwards, the beginning would have been in Autumn; and in thirty-three
or thirty-four years, it would have gone backwards through all the
seasons, to Spring again. This defect they attempted to rectify, by
introducing a number of days, at certain times, into the calendar, as
occasion required, and putting the beginning of the year forwards, in
order to make it agree with the course of the sun. But as these
additions, or _intercalations_, as they were called, were generally
consigned to the care of the priests, who, from motives of interest or
superstition, frequently omitted them, the year was made long or short
at pleasure.

The _week_ is another division of time, of the highest antiquity, which,
in almost all countries, has been made to consist of seven days; a
period supposed by some to have been traditionally derived from the
creation of the world; while others imagine it to have been regulated by
the phases of the moon. The names, Saturday, Sunday, and Monday, are
obviously derived from Saturn, the Sun, and the Moon; while Tuesday,
Wednesday, Thursday, and Friday, are the days of Tuisco, Woden, Thor,
and Friga, which are Saxon names for Mars, Mercury, Jupiter, and
Venus.[4]

The common year begins and ends on the same day of the week; but leap
year ends one day later than it began. Fifty-two weeks contain three
hundred and sixty-four days; if, therefore, the year begins on Tuesday,
for example, we should complete fifty-two weeks on Monday, leaving one
day, (Tuesday,) to complete the year, and the following year would begin
on Wednesday. Hence, any day of the month is one day later in the week,
than the corresponding day of the preceding year. Thus, if the sixteenth
of November, 1838, falls on Friday, the sixteenth of November, 1837,
fell on Thursday, and will fall, in 1839, on Saturday. But if leap year
begins on Sunday, it ends on Monday, and the following year begins on
Tuesday; while any given day of the month is two days later in the week
than the corresponding date of the preceding year.

FOOTNOTE:

[4] Bonnycastle's Astronomy.

LETTER VII.

FIGURE OF THE EARTH.

"He took the golden compasses, prepared
In God's eternal store, to circumscribe
This universe, and all created things;
One foot he centred, and the other turned
Round through the vast profundity obscure,
And said, 'Thus far extend, thus far thy bounds,
This be thy just circumference, O World!'"--_Milton._

IN the earliest ages, the earth was regarded as one continued plane;
but, at a comparatively remote period, as five hundred years before the
Christian era, astronomers began to entertain the opinion that the earth
is round. We are able now to adduce various arguments which severally
prove this truth. First, when a ship is coming in from sea, we first
observe only the very highest parts of the ship, while the lower
portions come successively into view. Were the earth a continued plane,
the lower parts of the ship would be visible as soon as the higher, as
is evident from Fig. 10, page 70.

[Illustration Fig. 10.]

[Illustration Fig. 11.]

Since light comes to the eye in straight lines, by which objects become
visible, it is evident, that no reason exists why the parts of the ship
near the water should not be seen as soon as the upper parts. But if the
earth be a sphere, then the line of sight would pass above the deck of
the ship, as is represented in Fig. 11; and as the ship drew nearer to
land, the lower parts would successively rise above this line and come
into view exactly in the manner known to observation. Secondly, in a
lunar eclipse, which is occasioned by the moon's passing through the
earth's shadow, the figure of the shadow is seen to be spherical, which
could not be the case unless the earth itself were round. Thirdly,
navigators, by steering continually in one direction, as east or west,
have in fact come round to the point from which they started, and thus
confirmed the fact of the earth's rotundity beyond all question. One may
also reach a given place on the earth, by taking directly opposite
courses. Thus, he may reach Canton in China, by a westerly route around
Cape Horn, or by an easterly route around the Cape of Good Hope. All
these arguments severally prove that the earth is round.

But I propose, in this Letter, to give you some account of the unwearied
labors which have been performed to ascertain the _exact_ figure of the
earth; for although the earth is properly described in general language
as round, yet it is not an exact sphere. Were it so, all its diameters
would be equal; but it is known that a diameter drawn through the
equator exceeds one drawn from pole to pole, giving to the earth the
form of a _spheroid_,--a figure resembling an orange, where the ends are
flattened a little and the central parts are swelled out.

Although it would be a matter of very rational curiosity, to investigate
the precise shape of the planet on which Heaven has fixed our abode, yet
the immense pains which has been bestowed on this subject has not all
arisen from mere curiosity. No accurate measurements can be taken of the
distances and magnitudes of the heavenly bodies, nor any exact
determinations made of their motions, without a knowledge of the exact
figure of the earth; and hence is derived a powerful motive for
ascertaining this element with all possible precision.

The first satisfactory evidence that was obtained of the exact figure of
the earth was derived from reasoning on the effects of the earth's
_centrifugal force_, occasioned by its rapid revolution on its own axis.
When water is whirled in a pail, we see it recede from the centre and
accumulate upon the sides of the vessel; and when a millstone is whirled
rapidly, since the portions of the stone furthest from the centre
revolve much more rapidly than those near to it, their greater tendency
to recede sometimes makes them fly off with a violent explosion. A case,
which comes still nearer to that of the earth, is exhibited by a mass of
clay revolving on a potter's wheel, as seen in the process of making
earthen vessels. The mass swells out in the middle, in consequence of
the centrifugal force exerted upon it by a rapid motion. Now, in the
diurnal revolution, the equatorial parts of the earth move at the rate
of about one thousand miles per hour, while the poles do not move at
all; and since, as we take points at successive distances from the
equator towards the pole, the rate at which these points move grows
constantly less and less; and since, in revolving bodies, the
centrifugal force is proportioned to the velocity, consequently, those
parts which move with the greatest rapidity will be more affected by
this force than those which move more slowly. Hence, the equatorial
regions must be higher from the centre than the polar regions; for, were
not this the case, the waters on the surface of the earth would be
thrown towards the equator, and be piled up there, just as water is
accumulated on the sides of a pail when made to revolve rapidly.

Huyghens, an eminent astronomer of Holland, who investigated the laws of
centrifugal forces, was the first to infer that such must be the actual
shape of the earth; but to Sir Isaac Newton we owe the full developement
of this doctrine. By combining the reasoning derived from the known laws
of the centrifugal force with arguments derived from the principles of
universal gravitation, he concluded that the distance through the earth,
in the direction of the equator, is greater than that in the direction
of the poles. He estimated the difference to be about thirty-four miles.

But it was soon afterwards determined by the astronomers of France, to
ascertain the figure of the earth by actual measurements, specially
instituted for that purpose. Let us see how this could be effected. If
we set out at the equator and travel towards the pole, it is easy to see
when we have advanced one degree of latitude, for this will be indicated
by the rising of the north star, which appears in the horizon when the
spectator stands on the equator, but rises in the same proportion as he
recedes from the equator, until, on reaching the pole, the north star
would be seen directly over head. Now, were the earth a perfect sphere,
the meridian of the earth would be a perfect circle, and the distance
between any two places, differing one degree in latitude, would be
exactly equal to the distance between any other two places, differing in
latitude to the same amount. But if the earth be a spheroid, flattened
at the poles, then a line encompassing the earth from north to south,
constituting the terrestrial meridian, would not be a perfect circle,
but an ellipse or oval, having its longer diameter through the equator,
and its shorter through the poles. The part of this curve included
between two radii, drawn from the centre of the earth to the celestial
meridian, at angles one degree asunder, would be greater in the polar
than in the equatorial region; that is, the degrees of the meridian
would lengthen towards the poles.

The French astronomers, therefore, undertook to ascertain by actual
measurements of arcs of the meridian, in different latitudes, whether
the degrees of the meridian are of uniform length, or, if not, in what
manner they differ from each other. After several indecisive
measurements of an arc of the meridian in France, it was determined to
effect simultaneous measurements of arcs of the meridian near the
equator, and as near as possible to the north pole, presuming that if
degrees of the meridian, in different latitudes, are really of different
lengths, they will differ most in points most distant from each other.
Accordingly, in 1735, the French Academy, aided by the government, sent
out two expeditions, one to Peru and the other to Lapland. Three
distinguished mathematicians, Bouguer, La Condamine, and Godin, were
despatched to the former place, and four others, Maupertius, Camus,
Clairault, and Lemonier, were sent to the part of Swedish Lapland which
lies at the head of the Gulf of Tornea, the northern arm of the Baltic.
This commission completed its operations several years sooner than the
other, which met with greater difficulties in the way of their
enterprise. Still, the northern detachment had great obstacles to
contend with, arising particularly from the extreme length and severity
of their Winters. The measurements, however, were conducted with care
and skill, and the result, when compared with that obtained for the
length of a degree in France, plainly indicated, by its greater amount,
a compression of the earth towards the poles.

Mean-while, Bouguer and his party were prosecuting a similar work in
Peru, under extraordinary difficulties. These were caused, partly by the
localities, and partly by the ill-will and indolence of the inhabitants.
The place selected for their operations was in an elevated valley
between two principal chains of the Andes. The lowest point of their arc
was at an elevation of a mile and a half above the level of the sea;
and, in some instances, the heights of two neighboring signals differed
more than a mile. Encamped upon lofty mountains, they had to struggle
against storms, cold, and privations of every description, while the
invincible indifference of the Indians, they were forced to employ, was
not to be shaken by the fear of punishment or the hope of reward. Yet,
by patience and ingenuity, they overcame all obstacles, and executed
with great accuracy one of the most important operations, of this
nature, ever undertaken. To accomplish this, however, took them nine
years; of which, three were occupied in determining the latitudes
alone.[5]

I have recited the foregoing facts, in order to give you some idea of
the unwearied pains which astronomers have taken to ascertain the exact
figure of the earth. You will find, indeed, that all their labors are
characterized by the same love of accuracy. Years of toilsome watchings,
and incredible labor of computation, have been undergone, for the sake
of arriving only a few seconds nearer to the truth.

The length of a degree of the meridian, as measured in Peru, was less
than that before determined in France, and of course less than that of
Lapland; so that the spheroidal figure of the earth appeared now to be
ascertained by actual measurement. Still, these measures were too few in
number, and covered too small a portion of the whole quadrant from the
equator to the pole, to enable astronomers to ascertain the exact law of
curvature of the meridian, and therefore similar measurements have since
been prosecuted with great zeal by different nations, particularly by
the French and English. In 1764, two English mathematicians of great
eminence, Mason and Dixon, undertook the measurement of an arc in
Pennsylvania, extending more than one hundred miles.

[Illustration Fig. 12.]

[Illustration Fig. 13.]

These operations are carried on by what is called a system of
_triangulation_. Without some knowledge of trigonometry, you will not be
able fully to understand this process; but, as it is in its nature
somewhat curious, and is applied to various other geographical
measurements, as well as to the determination of arcs of the meridian, I
am desirous that you should understand its general principles. Let us
reflect, then, that it must be a matter of the greatest difficulty, to
execute with exactness the measurement of a line of any great length in
one continued direction on the earth's surface. Even if we select a
level and open country, more or less inequalities of surface will occur;
rivers must be crossed, morasses must be traversed, thickets must be
penetrated, and innumerable other obstacles must be surmounted; and
finally, every time we apply an artificial measure, as a rod, for
example, we obtain a result not absolutely perfect. Each error may
indeed be very small, but small errors, often repeated, may produce a
formidable aggregate. Now, one unacquainted with trigonometry can easily
understand the fact, that, when we know certain parts of a triangle, we
can find the other parts by calculation; as, in the rule of three in
arithmetic, we can obtain the fourth term of a proportion, from having
the first three terms given. Thus, in the triangle A B C, Fig. 12, if we
know the side A B, and the angles at A and B, we can find by
computation, the other sides, A C and B C, and the remaining angle at C.
Suppose, then, that in measuring an arc of the meridian through any
country, the line were to pass directly through A B, but the ground was
so obstructed between A and B, that we could not possibly carry our
measurement through it. We might then measure another line, as A C,
which was accessible, and with a compass take the bearing of B from the
points A and C, by which means we should learn the value of the angles
at A and C. From these data we might calculate, by the rules of
trigonometry, the exact length of the line A B. Perhaps the ground might
be so situated, that we could not reach the point B, by any route;
still, if it could be seen from A and C, it would be all we should want.
Thus, in conducting a trigonometrical survey of any country, conspicuous
signals are placed on elevated points, and the bearings of these are
taken from the extremities of a known line, called the base, and thus
the relative situation of various places is accurately determined. Were
we to undertake to run an exact north and south line through any
country, as New England, we should select, near one extremity, a spot of
ground favorable for actual measurement, as a level, unobstructed plain;
we should provide a measure whose length in feet and inches was
determined with the greatest possible precision, and should apply it
with the utmost care. We should thus obtain a _base line_. From the
extremities of this line, we should take (with some appropriate
instrument) the bearing of some signal at a greater or less distance,
and thus we should obtain one side and two angles of a triangle, from
which we could find, by the rules of trigonometry, either of the unknown
sides. Taking this as a new base, we might take the bearing of another
signal, still further on our way, and thus proceed to run the required
north and south line, without actually measuring any thing more than the
first, or base line. Thus, in Fig. 13, we wish to measure the distance
between the two points A and O, which are both on the same meridian, as
is known by their having the same longitude; but, on account of various
obstacles, it would be found very inconvenient to measure this line
directly, with a rod or chain, and even if we could do it, we could not
by this method obtain nearly so accurate a result, as we could by a
series of triangles, where, after the base line was measured, we should
have nothing else to measure except angles, which can be determined, by
observation, to a greater degree of exactness, than lines. We therefore,
in the first place, measure the base line, A B, with the utmost
precision. Then, taking the bearing of some signal at C from A and B, we
obtain the means of calculating the side B C, as has been already
explained. Taking B C as a new base, we proceed, in like manner, to
determine successively the sides C D, D E, and E F, and also A C, and C
E. Although A C is not in the direction of the meridian, but
considerably to the east of it, yet it is easy to find the corresponding
distance on the meridian, A M; and in the same manner we can find the
portions of the meridian M N and N O, corresponding respectively to C E
and E F. Adding these several parts of the meridian together, we obtain
the length of the arc from A to O, in miles; and by observations on the
north star, at each extremity of the arc, namely, at A and at O, we
could determine the difference of latitude between these two points.
Suppose, for example, that the distance between A and O is exactly five
degrees, and that the length of the intervening line is three hundred
and forty-seven miles; then, dividing the latter by the former number,
we find the length of a degree to be sixty-nine miles and four tenths.
To take, however, a few of the results actually obtained, they are as
follows:

Places of observation. Latitude. Length of a deg.
in miles.
Peru, 00° 00' 00" 68.732
Pennsylvania, 39 12 00 68.896
France, 46 12 00 69.054
England, 51 29 54-1/2 69.146
Sweden, 66 20 10 69.292

This comparison shows, that the length of a degree gradually increases,
as we proceed from the equator towards the pole. Combining the results
of various estimates, the dimensions of the terrestrial spheroid are
found to be as follows:

Equatorial diameter, 7925.648 miles.
Polar diameter, 7899.170 "
Average diameter, 7912.409 "

The difference between the greatest and the least is about twenty-six
and one half miles, which is about one two hundred and ninety-ninth part
of the greatest. This fraction is denominated the _ellipticity_ of the
earth,--being the excess of the equatorial over the polar diameter.

The operations, undertaken for the purpose of determining the figure of
the earth, have been conducted with the most refined exactness. At any
stage of the process, the length of the last side, as obtained by
calculation, may be actually measured in the same manner as the base
from which the series of triangles commenced. When thus measured, it is
called the _base of verification_. In some surveys, the base of
verification, when taken at a distance of four hundred miles from the
starting point, has not differed more than one foot from the same line,
as determined by calculation.

Another method of arriving at the exact figure of the earth is, by
observations with the _pendulum_. If a pendulum, like that of a clock,
be suspended, and the number of its vibrations per hour be counted, they
will be found to be different in different latitudes. A pendulum that
vibrates thirty-six hundred times per hour, at the equator, will vibrate
thirty-six hundred and five and two thirds times, at London, and a still
greater number of times nearer the north pole. Now, the vibrations of
the pendulum are produced by the force of gravity. Hence their
comparative number at different places is a measure of the relative
forces of gravity at those places. But when we know the relative forces
of gravity at different places, we know their relative distances from
the centre of the earth; because the nearer a place is to the centre of
the earth, the greater is the force of gravity. Suppose, for example, we
should count the number of vibrations of a pendulum at the equator, and
then carry it to the north pole, and count the number of vibrations made
there in the same time,--we should be able, from these two observations,
to estimate the relative forces of gravity at these two points; and,
having the relative forces of gravity, we can thence deduce their
relative distances from the centre of the earth, and thus obtain the
polar and equatorial diameters. Observations of this kind have been
taken with the greatest accuracy, in many places on the surface of the
earth, at various distances from each other, and they lead to the same
conclusions respecting the figure of the earth, as those derived from
measuring arcs of the meridian. It is pleasing thus to see a great
truth, and one apparently beyond the pale of human investigation,
reached by two routes entirely independent of each other. Nor, indeed,
are these the only proofs which have been discovered of the spheroidal
figure of the earth. In consequence of the accumulation of matter above
the equatorial regions of the earth, a body weighs less there than
towards the poles, being further removed from the centre of the earth.
The same accumulation of matter, by the force of attraction which it
exerts, causes slight inequalities in the motions of the moon; and since
the amount of these becomes a measure of the force which produces them,
astronomers are able, from these inequalities, to calculate the exact
quantity of the matter thus accumulated, and hence to determine the
figure of the earth. The result is not essentially different from that
obtained by the other methods. Finally, the shape of the earth's shadow
is altered, by its spheroidal figure,--a circumstance which affects the
time and duration of a lunar eclipse. All these different and
independent phenomena afford a pleasing example of the harmony of truth.
The known effects of the centrifugal force upon a body revolving on its
axis, like the earth, lead us to infer that the earth is of a spheroidal
figure; but if this be the fact, the pendulum ought to vibrate faster
near the pole than at the equator, because it would there be nearer the
centre of the earth. On trial, such is found to be the case. If, again,
there be such an accumulation of matter about the equatorial regions,
its effects ought to be visible in the motions of the moon, which it
would influence by its gravity; and there, also, its effects are traced.
At length, we apply our measures to the surface of the earth itself, and
find the same fact, which had thus been searched out among the hidden
things of Nature, here palpably exhibited before our eyes. Finally, on
estimating from these different sources, what the exact amount of the
compression at the poles must be, all bring out nearly one and the same
result. This truth, so harmonious in itself, takes along with it, and
establishes, a thousand other truths on which it rests.

FOOTNOTE:

[5] Library of Useful Knowledge: History of Astronomy, page 95.

LETTER VIII.

DIURNAL REVOLUTIONS.

"To some she taught the fabric of the sphere,
The changeful moon, the circuit of the stars,
The golden zones of heaven."--_Akenside._

WITH the elementary knowledge already acquired, you will now be able to
enter with pleasure and profit on the various interesting phenomena
dependent on the revolution of the earth on its axis and around the sun.
The apparent diurnal revolution of the heavenly bodies, from east to
west, is owing to the actual revolution of the earth on its own axis,
from west to east. If we conceive of a radius of the earth's equator
extended until it meets the concave sphere of the heavens, then, as the
earth revolves, the extremity of this line would trace out a curve on
the face of the sky; namely, the celestial equator. In curves parallel
to this, called the _circles of diurnal revolution_, the heavenly bodies
actually _appear_ to move, every star having its own peculiar circle.
After you have first rendered familiar the real motion of the earth from
west to east, you may then, without danger of misapprehension, adopt the
common language, that all the heavenly bodies revolve around the earth
once a day, from east to west, in circles parallel to the equator and to
each other.

I must remind you, that the time occupied by a star, in passing from any
point in the meridian until it comes round to the same point again, is
called a _sidereal day_, and measures the period of the earth's
revolution on its axis. If we watch the returns of the same star from
day to day, we shall find the intervals exactly equal to each other;
that is, _the sidereal days are all equal_. Whatever star we select for
the observation, the same result will be obtained. The stars, therefore,
always keep the same relative position, and have a common movement
round the earth,--a consequence that naturally flows from the hypothesis
that their _apparent_ motion is all produced by a single _real_ motion;
namely, that of the earth. The sun, moon, and planets, as well as the
fixed stars, revolve in like manner; but their returns to the meridian
are not, like those of the fixed stars, at exactly equal intervals.

The _appearances_ of the diurnal motions of the heavenly bodies are
different in different parts of the earth,--since every place has its
own horizon, and different horizons are variously inclined to each
other. Nothing in astronomy is more apt to mislead us, than the
obstinate habit of considering the horizon as a fixed and immutable
plane, and of referring every thing to it. We should contemplate the
earth as a huge globe, occupying a small portion of space, and encircled
on all sides, at an immense distance, by the starry sphere. We should
free our minds from their habitual proneness to consider one part of
space as naturally _up_ and another _down_, and view ourselves as
subject to a force (gravity) which binds us to the earth as truly as
though we were fastened to it by some invisible cords or wires, as the
needle attaches itself to all sides of a spherical loadstone. We should
dwell on this point, until it appears to us as truly up, in the
direction B B, C C, D D, when one is at B, C, D, respectively, as in the
direction A A, when he is at A, Fig. 14.

Let us now suppose the spectator viewing the diurnal revolutions from
several different positions on the earth. On the _equator_, his horizon
would pass through both poles; for the horizon cuts the celestial vault
at ninety degrees in every direction from the zenith of the spectator;
but the pole is likewise ninety degrees from his zenith, when he stands
on the equator; and consequently, the pole must be in the horizon. Here,
also, the celestial equator would coincide with the prime vertical,
being a great circle passing through the east and west points. Since all
the diurnal circles are parallel to the equator, consequently, they
would all, like the equator be perpendicular to the horizon. Such a
view of the heavenly bodies is called a right sphere, which may be thus
defined: _a right sphere is one in which all the daily revolutions of
the stars are in circles perpendicular to the horizon_.

[Illustration Fig. 14.]

A right sphere is seen only at the equator. Any star situated in the
celestial equator would appear to rise directly in the east, at midnight
to be in the zenith of the spectator, and to set directly in the west.
In proportion as stars are at a greater distance from the equator
towards the pole, they describe smaller and smaller circles, until, near
the pole, their motion is hardly perceptible.

If the spectator advances one degree from the equator towards the north
pole, his horizon reaches one degree beyond the pole of the earth, and
cuts the starry sphere one degree below the pole of the heavens, or
below the north star, if that be taken as the place of the pole. As he
moves onward towards the pole, his horizon continually reaches further
and further beyond it, until, when he comes to the pole of the earth,
and under the pole of the heavens, his horizon reaches on all sides to
the equator, and coincides with it. Moreover, since all the circles of
daily motion are parallel to the equator, they become, to the spectator
at the pole, parallel to the horizon. Or, _a parallel sphere is that in
which all the circles of daily motion are parallel to the horizon_.

To render this view of the heavens familiar, I would advise you to
follow round in mind a number of separate stars, in their diurnal
revolution, one near the horizon, one a few degrees above it, and a
third near the zenith. To one who stood upon the north pole, the stars
of the northern hemisphere would all be perpetually in view when not
obscured by clouds, or lost in the sun's light, and none of those of the
southern hemisphere would ever be seen. The sun would be constantly
above the horizon for six months in the year, and the remaining six
continually out of sight. That is, at the pole, the days and nights are
each six months long. The appearances at the south pole are similar to
those at the north.

A perfect parallel sphere can never be seen, except at one of the
poles,--a point which has never been actually reached by man; yet the
British discovery ships penetrated within a few degrees of the north
pole, and of course enjoyed the view of a sphere nearly parallel.

As the circles of daily motion are parallel to the horizon of the pole,
and perpendicular to that of the equator, so at all places between the
two, the diurnal motions are oblique to the horizon. This aspect of the
heavens constitutes an oblique sphere, which is thus defined: _an
oblique sphere is that in which the circles of daily motion are oblique
to the horizon_.

Suppose, for example, that the spectator is at the latitude of fifty
degrees. His horizon reaches fifty degrees beyond the pole of the earth,
and gives the same apparent elevation to the pole of the heavens. It
cuts the equator and all the circles of daily motion, at an angle of
forty degrees,--being always equal to what the altitude of the pole
lacks of ninety degrees: that is, it is always equal to the co-altitude
of the pole. Thus, let H O, Fig. 15, represent the horizon, E Q the
equator, and P P´ the axis of the earth. Also, _l l, m m, n n_,
parallels of latitude. Then the horizon of a spectator at Z, in latitude
fifty degrees, reaches to fifty degrees beyond the pole; and the angle E
C H, which the equator makes with the horizon, is forty degrees,--the
complement of the latitude. As we advance still further north, the
elevation of the diurnal circle above the horizon grows less and less,
and consequently, the motions of the heavenly bodies more and more
oblique to the horizon, until finally, at the pole, where the latitude
is ninety degrees, the angle of elevation of the equator vanishes, and
the horizon and the equator coincide with each other, as before stated.

[Illustration Fig. 15.]

_The circle of perpetual apparition is the boundary of that space around
the elevated pole, where the stars never set._ Its distance from the
pole is equal to the latitude of the place. For, since the altitude of
the pole is equal to the latitude, a star, whose polar distance is just
equal to the latitude, will, when at its lowest point, only just reach
the horizon; and all the stars nearer the pole than this will evidently
not descend so far as the horizon. Thus _m m_, Fig. 15, is the circle of
perpetual apparition, between which and the north pole, the stars never
set, and its distance from the pole, O P, is evidently equal to the
elevation of the pole, and of course to the latitude.

In the opposite hemisphere, a similar part of the sphere adjacent to the
depressed pole never rises. Hence, _the circle of perpetual occultation
is the boundary of that space around the depressed pole, within which
the stars never rise._

Thus _m´ m´_, Fig. 15, is the circle of perpetual occultation, between
which and the south pole, the stars never rise.

In an oblique sphere, the horizon cuts the circles of daily motion
unequally. Towards the elevated pole, more than half the circle is above
the horizon, and a greater and greater portion, as the distance from the
equator is increased, until finally, within the circle of perpetual
apparition, the whole circle is above the horizon. Just the opposite
takes place in the hemisphere next the depressed pole. Accordingly, when
the sun is in the equator, as the equator and horizon, like all other
great circles of the sphere, bisect each other, the days and nights are
equal all over the globe. But when the sun is north of the equator, the
days become longer than the nights, but shorter, when the sun is south
of the equator. Moreover, the higher the latitude, the greater is the
inequality in the lengths of the days and nights. By examining Fig. 15,
you will easily see how each of these cases must hold good.

Most of the appearances of the diurnal revolution can be explained,
either on the supposition that the celestial sphere actually turns
around the earth once in twenty-four hours, or that this motion of the
heavens is merely apparent, arising from the revolution of the earth on
its axis, in the opposite direction,--a motion of which we are
insensible, as we sometimes lose the consciousness of our own motion in
a ship or steam-boat, and observe all external objects to be receding
from us, with a common motion. Proofs, entirely conclusive and
satisfactory, establish the fact, that it is the earth, and not the
celestial sphere, that turns; but these proofs are drawn from various
sources, and one is not prepared to appreciate their value, or even to
understand some of them, until he has made considerable proficiency in
the study of astronomy, and become familiar with a great variety of
astronomical phenomena. To such a period we will therefore postpone the
discussion of the earth's rotation on its axis.

While we retain the same place on the earth, the diurnal revolution
occasions no change in our horizon, but our horizon goes round, as well
as ourselves. Let us first take our station on the equator, at sunrise;
our horizon now passes through both the poles and through the sun, which
we are to conceive of as at a great distance from the earth, and
therefore as cut, not by the terrestrial, but by the celestial, horizon.
As the earth turns, the horizon dips more and more below the sun, at the
rate of fifteen degrees for every hour; and, as in the case of the polar
star, the sun appears to rise at the same rate. In six hours, therefore,
it is depressed ninety degrees below the sun, bringing us directly under
the sun, which, for our present purpose, we may consider as having all
the while maintained the same fixed position in space. The earth
continues to turn, and in six hours more, it completely reverses the
position of our horizon, so that the western part of the horizon, which
at sunrise was diametrically opposite to the sun, now cuts the sun, and
soon afterwards it rises above the level of the sun, and the sun sets.
During the next twelve hours, the sun continues on the invisible side of
the sphere, until the horizon returns to the position from which it set
out, and a new day begins.

Let us next contemplate the similar phenomena at the _poles_. Here the
horizon, coinciding, as it does, with the equator, would cut the sun
through its centre and the sun would appear to revolve along the surface
of the sea, one half above and the other half below the horizon. This
supposes the sun in its annual revolution to be at one of the equinoxes.
When the sun is north of the equator, it revolves continually round in a
circle, which, during a single revolution, appears parallel to the
equator, and it is constantly day; and when the sun is south of the
equator, it is, for the same reason, continual night.

When we have gained a clear idea of the appearances of the diurnal
revolutions, as exhibited to a spectator at the equator and at the pole,
that is, in a right and in a parallel sphere, there will be little
difficulty in imagining how they must be in the intermediate latitudes,
which have an oblique sphere.

The appearances of the sun and stars, presented to the inhabitants of
different countries, are such as correspond to the sphere in which they
live. Thus, in the fervid climates of India, Africa, and South America,
the sun mounts up to the highest regions of the heavens, and descends
directly downwards, suddenly plunging beneath the horizon. His rays,
darting almost vertically upon the heads of the inhabitants, strike with
a force unknown to the people of the colder climates; while in places
remote from the equator, as in the north of Europe, the sun, in Summer,
rises very far in the north, takes a long circuit towards the south, and
sets as far northward in the west as the point where it rose on the
other side of the meridian. As we go still further north, to the
northern parts of Norway and Sweden, for example, to the confines of the
frigid zone, the Summer's sun just grazes the northern horizon, and at
noon appears only twenty-three and one half degrees above the southern.
On the other hand, in mid-winter, in the north of Europe, as at St.
Petersburgh, the day dwindles almost to nothing,--lasting only while the
sun describes a very short arc in the extreme south. In some parts of
Siberia and Iceland, the only day consists of a little glimmering of the
sun on the verge of the southern horizon, at noon.

LETTER IX.

PARALLAX AND REFRACTION.

"Go, wondrous creature! mount where science guides,
Go measure earth, weigh air, and state the tides;
Instruct the planets in what orbs to run,
Correct old Time, and regulate the sun."--_Pope._

I THINK you must have felt some astonishment, that astronomers are able
to calculate the exact distances and magnitudes of the sun, moon, and
planets. We should, at the first thought, imagine that such knowledge as
this must be beyond the reach of the human faculties, and we might be
inclined to suspect that astronomers practise some deception in this
matter, for the purpose of exciting the admiration of the unlearned. I
will therefore, in the present Letter, endeavor to give you some clear
and correct views respecting the manner in which astronomers acquire
this knowledge.

In our childhood, we all probably adopt the notion that the sky is a
real dome of definite surface, in which the heavenly bodies are fixed.
When any objects are beyond a certain distance from the eye, we lose all
power of distinguishing, by our sight alone, between different
distances, and cannot tell whether a given object is one million or a
thousand millions of miles off. Although the bodies seen in the sky are
in fact at distances extremely various,--some, as the clouds, only a few
miles off; others, as the moon, but a few thousand miles; and others, as
the fixed stars, innumerable millions of miles from us,--yet, as our eye
cannot distinguish these different distances, we acquire the habit of
referring all objects beyond a moderate height to one and the same
surface, namely, an imaginary spherical surface, denominated the
celestial vault. Thus, the various objects represented in the diagram on
next page, though differing very much in shape and diameter, would all
be _projected_ upon the sky alike, and compose a part, indeed, of the
imaginary vault itself. The place which each object occupies is
determined by lines drawn from the eye of the spectator through the
extremities of the body, to meet the imaginary concave sphere. Thus, to
a spectator at O, Fig 16, the several lines A B, C D, and E F, would all
be projected into arches on the face of the sky, and be seen as parts of
the sky itself, as represented by the lines A´ B´, C´ D´, and E´ F´. And
were a body actually to move in the several directions indicated by
these lines, they would appear to the spectator to describe portions of
the celestial vault. Thus, even when moving through the crooked line,
from _a_ to _b_, a body would appear to be moving along the face of the
sky, and of course in a regular curve line, from _c_ to _d_.

[Illustration Fig. 16.]

But, although all objects, beyond a certain moderate height, are
projected on the imaginary surface of the sky, yet different spectators
will project the same object on _different parts_ of the sky. Thus, a
spectator at A, Fig. 17, would see a body, C, at M, while a spectator at
B would see the same body at N. This change of place in a body, as seen
from different points, is called parallax, which is thus defined:
_parallax is the apparent change of place which bodies undergo by being
viewed from different points_. [Illustration Fig. 17.]

The arc M N is called the _parallactic arc_, and the angle A C B, the
_parallactic angle_.

It is plain, from the figure, that near objects are much more affected
by parallax than distant ones. Thus, the body C, Fig. 17, makes a much
greater parallax than the more distant body D,--the former being
measured by the arc M N, and the latter by the arc O P. We may easily
imagine bodies to be so distant, that they would appear projected at
very nearly the same point of the heavens, when viewed from places very
remote from each other. Indeed, the fixed stars, as we shall see more
fully hereafter, are so distant, that spectators, a hundred millions of
miles apart, see each star in one and the same place in the heavens.

It is by means of parallax, that astronomers find the distances and
magnitudes of the heavenly bodies. In order fully to understand this
subject, one requires to know something of trigonometry, which science
enables us to find certain unknown parts of a triangle from certain
other parts which are known. Although you may not be acquainted with the
principles of trigonometry, yet you will readily understand, from your
knowledge of arithmetic, that from certain things given in a problem
others may be found. Every triangle has of course three sides and three
angles; and, if we know two of the angles and one of the sides, we can
find all the other parts, namely, the remaining angle and the two
unknown sides. Thus, in the triangle A B C, Fig. 18, if we know the
length of the side A B, and how many degrees each of the angles A B C
and B C A contains, we can find the length of the side B C, or of the
side A C, and the remaining angle at A. Now, let us apply these
principles to the measurements of some of the heavenly bodies.

[Illustration Fig. 18.]

[Illustration Fig. 19.]

In Fig. 19, let A represent the earth, C H the horizon, and H Z a
quadrant of a great circle of the heavens, extending from the horizon to
the zenith; and let E, F, G, O, be successive positions of the moon, at
different elevations, from the horizon to the meridian. Now, a spectator
on the surface of the earth, at A, would refer the moon, when at E, to
_h_, on the face of the sky, whereas, if seen from the centre of the
earth, it would appear at H. So, when the moon was at F, a spectator at
A would see it at _p_, while, if seen from the centre, it would have
appeared at P. The parallactic arcs, H _h_, P _p_, R _r_, grow
continually smaller and smaller, as a body is situated higher above the
horizon; and when the body is in the zenith, then the parallax vanishes
altogether, for at O the moon would be seen at Z, whether viewed from A
or C.

Since, then, a heavenly body is liable to be referred to different
points on the celestial vault, when seen from different parts of the
earth, and thus some confusion be occasioned in the determination of
points on the celestial sphere, astronomers have agreed to consider the
true place of a celestial object to be that where it would appear, if
seen from the centre of the earth; and the doctrine of parallax teaches
how to reduce observations made at any place on the surface of the
earth, to such as they would be, if made from the centre.

When the moon, or any heavenly body, is seen in the horizon, as at E,
the change of place is called the horizontal parallax. Thus, the angle A
E C, measures the horizontal parallax of the moon. Were a spectator to
view the earth from the centre of the moon, he would see the
semidiameter of the earth under this same angle; hence, _the horizontal
parallax of any body is the angle subtended by the semidiameter of the
earth, as seen from the body_. Please to remember this fact.

It is evident from the figure, that the effect of parallax upon the
place of a celestial body is to _depress_ it. Thus, in consequence of
parallax, E is depressed by the arc H _h_; F, by the arc P _p_; G, by
the arc R _r_; while O sustains no change. Hence, in all calculations
respecting the altitude of the sun, moon, or planets, the amount of
parallax is to be added: the stars, as we shall see hereafter, have no
sensible parallax.

It is now very easy to see how, when the parallax of a body is known, we
may find its distance from the centre of the earth. Thus, in the
triangle A C E, Fig. 19, the side A C is known, being the semidiameter
of the earth; the angle C A E, being a right angle, is also known; and
the parallactic angle, A E C, is found from observation; and it is a
well-known principle of trigonometry, that when we have any two angles
of a triangle, we may find the remaining angle by subtracting the sum of
these two from one hundred and eighty degrees. Consequently, in the
triangle A E C, we know all the angles and one side, namely, the side A
C; hence, we have the means of finding the side C E, which is the
distance from the centre of the earth to the centre of the moon.

[Illustration Fig. 20.]

When the distance of a heavenly body is known, and we can measure, with
instruments, its angular breadth, we can easily determine its
_magnitude_. Thus, if we have the distance of the moon, E S, Fig. 20,
and half the breadth of its disk S C, (which is measured by the angle S
E C,) we can find the length of the line, S C, in miles. Twice this line
is the diameter of the body; and when we know the diameter of a sphere,
we can, by well-known rules, find the contents of the surface, and its
solidity.

You will perhaps be curious to know, _how the moon's horizontal parallax
is found_; for it must have been previously ascertained, before we could
apply this method to finding the distance of the moon from the earth.
Suppose that two astronomers take their stations on the same meridian,
but one south of the equator, as at the Cape of Good Hope, and another
north of the equator, as at Berlin, in Prussia, which two places lie
nearly on the same meridian. The observers would severally refer the
moon to different points on the face of the sky,--the southern observer
carrying it further north, and the northern observer further south,
than its true place, as seen from the centre of the earth. This will be
plain from the diagram, Fig. 21. If A and B represent the positions of
the spectators, M the moon, and C D an arc of the sky, then it is
evident, that C D would be the parallactic arc.

[Illustration Fig. 21.]

These observations furnish materials for calculating, by the aid of
trigonometry, the moon's horizontal parallax, and we have before seen
how, when we know the parallax of a heavenly body, we can find both its
distance from the earth and its magnitude.

Beside the change of place which these heavenly bodies undergo, in
consequence of parallax, there is another, of an opposite kind, arising
from the effect of the atmosphere, called _refraction_. Refraction
elevates the apparent place of a body, while parallax depresses it. It
affects alike the most distant as well as nearer bodies.

In order to understand the nature of refraction, we must consider, that
an object always appears in the direction in which the _last_ ray of
light comes to the eye. If the light which comes from a star were bent
into fifty directions before it reached the eye, the star would
nevertheless appear in the line described by the ray nearest the eye.
The operation of this principle is seen when an oar, or any stick, is
thrust into water. As the rays of light by which the oar is seen have
their direction changed as they pass out of water into air, the apparent
direction in which the body is seen is changed in the same degree,
giving it a bent appearance,--the part below the water having apparently
a different direction from the part above. Thus, in Fig. 22, page 96, if
S _a x_ be the oar, S _a b_ will be the bent appearance, as affected by
refraction. The transparent substance through which any ray of light
passes is called a _medium_. It is a general fact in optics, that, when
light passes out of a rarer into a denser medium, as out of air into
water, or out of space into air, it is turned _towards_ a perpendicular
to the surface of the medium; and when it passes out of a denser into a
rarer medium, as out of water into air, it is turned _from_ the
perpendicular. In the above case, the light, passing out of space into
air, is turned towards the radius of the earth, this being perpendicular
to the surface of the atmosphere; and it is turned more and more towards
that radius the nearer it approaches to the earth, because the density
of the air rapidly increases near the earth.

[Illustration Fig. 22.]

Let us now conceive of the atmosphere as made up of a great number of
parallel strata, as A A, B B, C C, and D D, increasing rapidly in
density (as is known to be the fact) in approaching near to the surface
of the earth. Let S be a star, from which a ray of light, S _a_, enters
the atmosphere at _a_, where, being much turned towards the radius of
the convex surface, it would change its direction into the line _a b_,
and again into _b c_, and _c_ O, reaching the eye at O. Now, since an
object always appears in the direction in which the light finally
strikes the eye, the star would be seen in the direction O _c_, and,
consequently, the star would apparently change its place, by
refraction, from S to S´, being elevated out of its true position.
Moreover, since, on account of the continual increase of density in
descending through the atmosphere, the light would be continually turned
out of its course more and more, it would therefore move, not in the
polygon represented in the figure, but in a corresponding curve line,
whose curvature is rapidly increased near the surface of the earth.

When a body is in the zenith, since a ray of light from it enters the
atmosphere at right angles to the refracting medium, it suffers no
refraction. Consequently, the position of the heavenly bodies, when in
the zenith, is not changed by refraction, while, near the horizon, where
a ray of light strikes the medium very obliquely, and traverses the
atmosphere through its densest part, the refraction is greatest. The
whole amount of refraction, when a body is in the horizon, is
thirty-four minutes; while, at only an elevation of one degree, the
refraction is but twenty-four minutes; and at forty-five degrees, it is
scarcely a single minute. Hence it is always important to make our
observations on the heavenly bodies when they are at as great an
elevation as possible above the horizon, being then less affected by
refraction than at lower altitudes.

Since the whole amount of refraction near the horizon exceeds
thirty-three minutes, and the diameters of the sun and moon are
severally less than this, these luminaries are in view both before they
have actually risen and after they have set.

The rapid increase of refraction near the horizon is strikingly evinced
by the _oval_ figure which the sun assumes when near the horizon, and
which is seen to the greatest advantage when light clouds enable us to
view the solar disk. Were all parts of the sun equally raised by
refraction, there would be no change of figure; but, since the lower
side is more refracted than the upper, the effect is to shorten the
vertical diameter, and thus to give the disk an oval form. This effect
is particularly remarkable when the sun, at his rising or setting, is
observed from the top of a mountain, or at an elevation near the
seashore; for in such situations, the rays of light make a greater angle
than ordinary with a perpendicular to the refracting medium, and the
amount of refraction is proportionally greater. In some cases of this
kind, the shortening of the vertical diameter of the sun has been
observed to amount to six minutes, or about one fifth of the whole.

The apparent enlargement of the sun and moon, when near the horizon,
arises from an optical illusion. These bodies, in fact, are not seen
under so great an angle when in the horizon as when on the meridian, for
they are nearer to us in the latter case than in the former. The
distance of the sun, indeed, is so great, that it makes very little
difference in his apparent diameter whether he is viewed in the horizon
or on the meridian; but with the moon, the case is otherwise; its
angular diameter, when measured with instruments, is perceptibly larger
when at its culmination, or highest elevation above the horizon. Why,
then, do the sun and moon appear so much larger when near the horizon?
It is owing to a habit of the mind, by which we judge of the magnitudes
of distant objects, not merely by the angle they subtend at the eye, but
also by our impressions respecting their distance, allowing, under a
given angle, a greater magnitude as we imagine the distance of a body to
be greater. Now, on account of the numerous objects usually in sight
between us and the sun, when he is near the horizon, he appears much
further removed from us than when on the meridian; and we unconsciously
assign to him a proportionally greater magnitude. If we view the sun, in
the two positions, through a smoked glass, no such difference of size is
observed; for here no objects are seen but the sun himself.

_Twilight_ is another phenomenon depending on the agency of the earth's
atmosphere. It is that illumination of the sky which takes place just
before sunrise and which continues after sunset. It is owing partly to
refraction, and partly to reflection, but mostly to the latter. While
the sun is within eighteen degrees of the horizon, before it rises or
after it sets, some portion of its light is conveyed to us, by means of
numerous reflections from the atmosphere. At the equator, where the
circles of daily motion are perpendicular to the horizon, the sun
descends through eighteen degrees in an hour and twelve minutes. The
light of day, therefore, declines rapidly, and as rapidly advances after
daybreak in the morning. At the pole, a constant twilight is enjoyed
while the sun is within eighteen degrees of the horizon, occupying
nearly two thirds of the half year when the direct light of the sun is
withdrawn, so that the progress from continual day to constant night is
exceedingly gradual. To an inhabitant of an oblique sphere, the twilight
is longer in proportion as the place is nearer the elevated pole.

Were it not for the power the atmosphere has of dispersing the solar
light, and scattering it in various directions, no objects would be
visible to us out of direct sunshine; every shadow of a passing cloud
would involve us in midnight darkness; the stars would be visible all
day; and every apartment into which the sun had not direct admission
would be involved in the obscurity of night. This scattering action of
the atmosphere on the solar light is greatly increased by the
irregularity of temperature caused by the sun, which throws the
atmosphere into a constant state of undulation; and by thus bringing
together masses of air of different temperatures, produces partial
reflections and refractions at their common boundaries, by which means
much light is turned aside from a direct course, and diverted to the
purposes of general illumination.[6] In the upper regions of the
atmosphere, as on the tops of very high mountains, where the air is too
much rarefied to reflect much light, the sky assumes a black appearance,
and stars become visible in the day time.

Although the atmosphere is usually so transparent, that it is invisible
to us, yet we as truly move and live in a fluid as fishes that swim in
the sea. Considered in comparison with the whole earth, the atmosphere
is to be regarded as a thin layer investing the surface, like a film of
water covering the surface of an orange. Its actual height, however, is
over a hundred miles, though we cannot assign its precise boundaries.
Being perfectly elastic, the lower portions, bearing as they do, the
weight of all the mass above them, are greatly compressed, while the
upper portions having little to oppose the natural tendency of air to
expand, diffuse themselves widely. The consequence is, that the
atmosphere undergoes a rapid diminution of density, as we ascend from
the earth, and soon becomes exceedingly rare. At so moderate a height as
seven miles, it is four times rarer than at the surface, and continues
to grow rare in the same proportion, namely, being four times less for
every seven miles of ascent. It is only, therefore, within a few miles
of the earth, that the atmosphere is sufficiently dense to sustain
clouds and vapors, which seldom rise so high as eight miles, and are
usually much nearer to the earth than this. So rare does the air become
on the top of Mount Chimborazo, in South America, that it is incompetent
to support most of the birds that fly near the level of the sea. The
condor, a bird which has remarkably long wings, and a light body, is the
only bird seen towering above this lofty summit. The transparency of the
atmosphere,--a quality so essential to fine views of the starry
heavens,--is much increased by containing a large proportion of water,
provided it is perfectly dissolved, or in a state of invisible vapor. A
country at once hot and humid, like some portions of the torrid zone,
presents a much brighter and more beautiful view of the moon and stars,
than is seen in cold climates. Before a copious rain, especially in hot
weather, when the atmosphere is unusually humid, we sometimes observe
the sky to be remarkably resplendent, even in our own latitude.
Accordingly, this unusual clearness of the sky, when the stars shine
with unwonted brilliancy, is regarded as a sign of approaching rain; and
when, after the rain is apparently over, the air is remarkably
transparent, and distant objects on the earth are seen with uncommon
distinctness, while the sky exhibits an unusually deep azure, we may
conclude that the serenity is only temporary, and that the rain will
probably soon return.

FOOTNOTE:

[6] Sir J. Herschel.

LETTER X.

THE SUN.

"Great source of day! best image here below
Of thy Creator, ever pouring wide,
From world to world, the vital ocean round,
On Nature write, with every beam, His praise."--_Thomson._

THE subjects which have occupied the preceding Letters are by no means
the most interesting parts of our science. They constitute, indeed,
little more than an introduction to our main subject, but comprise such
matters as are very necessary to be clearly understood, before one is
prepared to enter with profit and delight upon the more sublime and
interesting field which now opens before us.

We will begin our survey of the heavenly bodies with the SUN, which
first claims our homage, as the natural monarch of the skies. The moon
will next occupy our attention; then the other bodies which compose the
solar system, namely, the planets and comets; and, finally, we shall
leave behind this little province in the great empire of Nature, and
wing a bolder flight to the fixed stars.

The _distance_ of the sun from the earth is about ninety-five millions
of miles. It may perhaps seem incredible to you, that astronomers should
be able to determine this fact with any degree of certainty. Some,
indeed, not so well informed as yourself, have looked upon the
marvellous things that are told respecting the distances, magnitudes,
and velocities, of the heavenly bodies, as attempts of astronomers to
impose on the credulity of the world at large; but the certainty and
exactness with which the predictions of astronomers are fulfilled, as an
eclipse, for example, ought to inspire full confidence in their
statements. I can assure you, my dear friend, that the evidence on which
these statements are founded is perfectly satisfactory to those whose
attainments in the sciences qualify them to understand them; and, so far
are astronomers from wishing to impose on the unlearned, by announcing
such wonderful discoveries as they have made among the heavenly bodies,
no class of men have ever shown a stricter regard and zeal than they for
the exact truth, wherever it is attainable.

Ninety-five millions of miles is indeed a vast distance. No human mind
is adequate to comprehend it fully; but the nearest approaches we can
make towards it are gained by successive efforts of the mind to conceive
of great distances, beginning with such as are clearly within our grasp.
Let us, then, first take so small a distance as that of the breadth of
the Atlantic ocean, and follow, in mind, a ship, as she leaves the port
of New York, and, after twenty days' steady sail, reaches Liverpool.
Having formed the best idea we are able of this distance, we may then
reflect, that it would take a ship, moving constantly at the rate of ten
miles per hour, more than a thousand years to reach the sun.

The diameter of the sun is towards a million of miles; or, more exactly,
it is eight hundred and eighty-five thousand miles. One hundred and
twelve bodies as large as the earth, lying side by side, would be
required to reach across the solar disk; and our ship, sailing at the
same rate as before, would be ten years in passing over the same space.
Immense as is the sun, we can readily understand why it appears no
larger than it does, when we reflect, that its distance is still more
vast. Even large objects on the earth, when seen on a distant eminence,
or over a wide expanse of water, dwindle almost to a point. Could we
approach nearer and nearer to the sun, it would constantly expand its
volume, until finally it would fill the whole vault of heaven. We could,
however, approach but little nearer to the sun without being consumed by
the intensity of his heat. Whenever we come nearer to any fire, the heat
rapidly increases, being four times as great at half the distance, and
one hundred times as great at one tenth the distance. This fact is
expressed by saying, that the heat increases as the square of the
distance decreases. Our globe is situated at such a distance from the
sun, as exactly suits the animal and vegetable kingdoms. Were it either
much nearer or much more remote, they could not exist, constituted as
they are. The intensity of the solar light also follows the same law.
Consequently, were we nearer to the sun than we are, its blaze would be
insufferable; or, were we much further off, the light would be too dim
to serve all the purposes of vision.

The sun is one million four hundred thousand times as large as the
earth; but its matter is not more than about one fourth as dense as that
of the earth, being only a little heavier than water, while the average
density of the earth is more than five times that of water. Still, on
account of the immense magnitude of the sun, its entire quantity of
matter is three hundred and fifty thousand times as great as that of the
earth. Now, the force of gravity in a body is greater, in proportion as
its quantity of matter is greater. Consequently, we might suppose, that
the weight of a body (weight being nothing else than the measure of the
force of gravity) would be increased in the same proportion; or, that a
body, which weighs only one pound at the surface of the earth, would
weigh three hundred and fifty thousand pounds at the sun. But we must
consider, that the attraction exerted by any body is the same as though
all the matter were concentrated in the centre. Thus, the attraction
exerted by the earth and by the sun is the same as though the entire
matter of each body were in its centre. Hence, on account of the vast
dimensions of the sun, its surface is one hundred and twelve times
further from its centre than the surface of the earth is from its
centre; and, since the force of gravity diminishes as the square of the
distance increases, that of the sun, exerted on bodies at its surface,
is (so far as this cause operates) the square of one hundred and twelve,
or twelve thousand five hundred and forty-four times less than that of
the earth. If, therefore, we increase the weight of a body three hundred
and fifty-four thousand times, in consequence of the greater amount of
matter in the sun, and diminish it twelve thousand five hundred and
forty-four times, in consequence of the force acting at a greater
distance from the body, we shall find that the body would weigh about
twenty-eight times more on the sun than on the earth. Hence, a man
weighing three hundred pounds would, if conveyed to the surface of the
sun, weigh eight thousand four hundred pounds, or nearly three tons and
three quarters. A limb of our bodies, weighing forty pounds, would
require to lift it a force of one thousand one hundred and twenty
pounds, which would be beyond the ordinary power of the muscles. At the
surface of the earth, a body falls from rest by the force of gravity, in
one second, sixteen and one twelfth feet; but at the surface of the sun,
a body would, in the same time, fall through four hundred and
forty-eight and seven tenths feet.

The sun turns on his own axis once in a little more than twenty-five
days. This fact is known by observing certain dark places seen by the
telescope on the sun's disk, called _solar spots_. These are very
variable in size and number. Sometimes, the sun's disk, when viewed with
a telescope, is quite free from spots, while at other times we may see a
dozen or more distinct clusters, each containing a great number of
spots, some large and some very minute. Occasionally, a single spot is
so large as to be visible to the naked eye, especially when the sun is
near the horizon, and the glare of his light is taken off. One measured
by Dr. Herschel was no less than fifty thousand miles in diameter. A
solar spot usually consists of two parts, the _nucleus_ and the _umbra_.
The nucleus is black, of a very irregular shape, and is subject to great
and sudden changes, both in form and size. Spots have sometimes seemed
to burst asunder, and to project fragments in different directions. The
umbra is a wide margin, of lighter shade, and is often of greater extent
than the nucleus. The spots are usually confined to a zone extending
across the central regions of the sun, not exceeding sixty degrees in
breadth. Fig. 23 exhibits the appearance of the solar spots. As these
spots have all a common motion from day to day, across the sun's disk;
as they go off at one limb, and, after a certain interval, sometimes
come on again on the opposite limb, it is inferred that this apparent
motion is imparted to them by an actual revolution of the sun on his own
axis. We know that the spots must be in contact, or very nearly so, at
least, with the body of the sun, and cannot be bodies revolving around
it, which are projected on the solar disk when they are between us and
the sun; for, in that case, they would not be so long in view as out of
view, as will be evident from inspecting the following diagram. Let S,
Fig. 24, page 106, represent the sun, and _b_ a body revolving round it
in the orbit _a b c_; and let E represent the earth, where, of course,
the spectator is situated. The body would be seen projected on the sun
only while passing from _b_ to _c_, while, throughout the remainder of
its orbit, it would be out of view, whereas no such inequality exists in
respect to the two periods.

[Illustration Fig. 23.]

[Illustration Fig. 24.]

If you ask, what is the _cause_ of the solar spots, I can only tell you
what different astronomers have supposed respecting them. They attracted
the notice of Galileo soon after the invention of the telescope, and he
formed an hypothesis respecting their nature. Supposing the sun to
consist of a solid body embosomed in a sea of liquid fire, he believed
that the spots are composed of black cinders, formed in the interior of
the sun by volcanic action, which rise and float on the surface of the
fiery sea. The chief objections to this hypothesis are, first, the _vast
extent_ of some of the spots, covering, as they do, two thousand
millions of square miles, or more,--a space which it is incredible
should be filled by lava in so short a time as that in which the spots
are sometimes formed; and, secondly, the _sudden disappearance_ which
the spots sometimes undergo, a fact which can hardly be accounted for by
supposing, as Galileo did, that such a vast accumulation of matter all
at once sunk beneath the fiery flood. Moreover, we have many reasons for
believing that the spots are _depressions_ below the general surface.

La Lande, an eminent French astronomer of the last century, held that
the sun is a solid, opaque body, having its exterior diversified with
high mountains and deep valleys, and covered all over with a burning sea
of liquid matter. The spots he supposed to be produced by the flux and
reflux of this fiery sea, retreating occasionally from the mountains,
and exposing to view a portion of the dark body of the sun. But it is
inconsistent with the nature of fluids, that a liquid, like the sea
supposed, should depart so far from its equilibrium and remain so long
fixed, as to lay bare the immense spaces occupied by some of the solar
spots.

Dr. Herschel's views respecting the nature and constitution of the sun,
embracing an explanation of the solar spots, have, of late years, been
very generally received by the astronomical world. This great
astronomer, after attentively viewing the surface of the sun, for a long
time, with his large telescopes, came to the following conclusions
respecting the nature of this luminary. He supposes the sun to be a
planetary body like our earth, diversified with mountains and valleys,
to which, on account of the magnitude of the sun, he assigns a
prodigious extent, some of the mountains being six hundred miles high,
and the valleys proportionally deep. He employs in his explanation no
volcanic fires, but supposes two separate regions of dense clouds
floating in the solar atmosphere, at different distances from the sun.
The exterior stratum of clouds he considers as the depository of the
sun's light and heat, while the inferior stratum serves as an awning or
screen to the body of the sun itself, which thus becomes fitted to be
the residence of animals. The proofs offered in support of this
hypothesis are chiefly the following: first, that the appearances, as
presented to the telescope, are such as accord better with the idea that
the fluctuations arise from the motions of clouds, than that they are
owing to the agitations of a liquid, which could not depart far enough
from its general level to enable us to see its waves at so great a
distance, where a line forty miles in length would subtend an angle at
the eye of only the tenth part of a second; secondly, that, since clouds
are easily dispersed to any extent, the great dimensions which the solar
spots occasionally exhibit are more consistent with this than with any
other hypothesis; and, finally, that a lower stratum of clouds, similar
to those of our atmosphere, was frequently seen by the Doctor, far below
the luminous clouds which are the fountains of light and heat.

Such are the views of one who had, it must be acknowledged, great
powers of observation, and means of observation in higher perfection
than have ever been enjoyed by any other individual; but, with all
deference to such authority, I am compelled to think that the hypothesis
is encumbered with very serious objections. Clouds analogous to those of
our atmosphere (and the Doctor expressly asserts that his lower stratum
of clouds are analogous to ours, and reasons respecting the upper
stratum according to the same analogy) cannot exist in hot air; they are
tenants only of cold regions. How can they be supposed to exist in the
immediate vicinity of a fire so intense, that they are even dissipated
by it at the distance of ninety-five millions of miles? Much less can
they be supposed to be the depositories of such devouring fire, when any
thing in the form of clouds, floating in our atmosphere, is at once
scattered and dissolved by the accession of only a few degrees of heat.
Nothing, moreover, can be imagined more unfavorable for radiating heat
to such a distance, than the light, inconstant matter of which clouds
are composed, floating loosely in the solar atmosphere. There is a
logical difficulty in the case: it is ascribing to things properties
which they are not known to possess; nay, more, which they are known not
to possess. From variations of light and shade in objects seen at
moderate distances on the earth, we are often deceived in regard to
their appearances; and we must distrust the power of an astronomer to
decide upon the nature of matter seen at the distance of ninety-five
millions of miles.

I think, therefore, we must confess our ignorance of the nature and
constitution of the sun; nor can we, as astronomers, obtain much more
satisfactory knowledge respecting it than the common apprehension,
namely, that it is an immense globe of fire. We have not yet learned
what causes are in operation to maintain its undecaying fires; but our
confidence in the Divine wisdom and goodness leads us to believe, that
those causes are such as will preserve those fires from extinction, and
at a nearly uniform degree of intensity. Any material change in this
respect would jeopardize the safety of the animal and vegetable
kingdoms, which could not exist without the enlivening influence of the
solar heat, nor, indeed, were that heat any more or less intense than it
is at present.

If we inquire whether the surface of the sun is in a state of actual
combustion, like burning fuel, or merely in a state of intense ignition,
like a stone heated to redness in a furnace, we shall find it most
reasonable to conclude that it is in a state of ignition. If the body of
the sun were composed of combustible matter and were actually on fire,
the material of the sun would be continually wasting away, while the
products of combustion would fill all the vast surrounding regions, and
obscure the solar light. But solid bodies may attain a very intense
state of ignition, and glow with the most fervent heat, while none of
their material is consumed, and no clouds or fumes rise to obscure their
brightness, or to impede their further emission of heat. An ignited
surface, moreover, is far better adapted than flame to the radiation of
heat. Flame, when made to act in contact with the surfaces of solid
bodies, heats them rapidly and powerfully; but it sends forth, or
_radiates_, very little heat, compared with solid matter in a high state
of ignition. These various considerations render it highly probable to
my mind, that the body of the sun is not in a state of actual
combustion, but merely in a state of high ignition.

The solar beam consists of a mixture of several different sorts of rays.
First, there are the _calorific_ rays, which afford heat, and are
entirely distinct from those which afford light, and may be separated
from them. Secondly, there are the _colorific_ rays, which give light,
consisting of rays of seven distinct colors, namely, violet, indigo,
blue, green, yellow, orange, red. These, when separated, as they may be
by a glass prism, compose the _prismatic spectrum_. They appear also in
the rainbow. When united again, in due proportions, they constitute
white light, as seen in the light of the sun. Thirdly, there are found
in the solar beam a class of rays which afford neither heat nor light,
but which produce chemical changes in certain bodies exposed to their
influence, and hence are called _chemical_ rays. Fourthly, there is
still another class, called _magnetizing_ rays, because they are capable
of imparting magnetic properties to steel. These different sorts of rays
are sent forth from the sun, to the remotest regions of the planetary
worlds, invigorating all things by their life-giving influence, and
dispelling the darkness that naturally fills all space.

But it was not alone to give heat and light, that the sun was placed in
the firmament. By his power of attraction, also, he serves as the great
regulator of the planetary motions, bending them continually from the
straight line in which they tend to move, and compelling them to
circulate around him, each at nearly a uniform distance, and all in
perfect harmony. I will hereafter explain to you the manner in which the
gravity of the sun thus acts, to control the planetary motions. For the
present, let us content ourselves with reflecting upon the wonderful
force which the sun must put forth, in order to bend out of their
courses, into circular orbits, such a number of planets, some of which
are more than a thousand times as large as the earth. Were a ship of war
under full sail, and it should be required to turn her aside from her
course by a rope attached to her bow, we can easily imagine that it
would take a great force to do it, especially were it required that the
force should remain stationary and the ship be so constantly diverted
from her course, as to be made to go round the force as round a centre.
Somewhat similar to this is the action which the sun exerts on each of
the planets by some invisible influence, called gravitation. The bodies
which he thus turns out of their course, and bends into a circular orbit
around himself, are, however, many millions of times as ponderous as the
ship, and are moving many thousand times as swiftly.

LETTER XI.

ANNUAL REVOLUTION.--SEASONS

"These, as they change, Almighty Father, these
Are but the varied God. The rolling year
Is full of Thee."--_Thomson._

WE have seen that the apparent revolution of the heavenly bodies, from
east to west, every twenty-four hours, is owing to a real revolution of
the earth on its own axis, in the opposite direction. This motion is
very easily understood, resembling, as it does, the spinning of a top.
We must, however, conceive of the top as turning without any visible
support, and not as resting in the usual manner on a plane. The annual
motion of the earth around the sun, which gives rise to an apparent
motion of the sun around the earth once a year, and occasions the change
of seasons, is somewhat more difficult to understand; and it may cost
you some reflection, before you will settle all the points respecting
the changes of the seasons clearly in your mind. We sometimes see these
two motions exemplified in a top. When, as the string is pulled, the top
is thrown forwards on the floor, we may see it move forward (sometimes
in a circle) at the same time that it spins on its axis. Let a candle be
placed on a table, to represent the sun, and let these two motions be
imagined to be given to a top around it, and we shall have a case
somewhat resembling the actual motions of the earth around the sun.

When bodies are at such a distance from each other as the earth and the
sun, a spectator on either would project the other body upon the concave
sphere of the heavens, always seeing it on the opposite side of a great
circle one hundred and eighty degrees from himself.

Recollect that the path in which the earth moves round the sun is
called the ecliptic. We are not to conceive of this, or of any other
celestial circle, as having any real, palpable existence, any more than
the path of a bird through the sky. You will perhaps think it quite
superfluous for me to remind you of this; but, from the habit of seeing
the orbits of the heavenly bodies represented in diagrams and orreries,
by palpable lines and circles, we are apt inadvertently to acquire the
notion, that the orbits of the planets, and other representations of the
artificial sphere, have a real, palpable existence in Nature; whereas,
they denote the places where mere geometrical or imaginary lines run.
You might have expected to see an orrery, exhibiting a view of the sun
and planets, with their various motions, particularly described in my
Letter on astronomical instruments and apparatus. I must acknowledge,
that I entertain a very low opinion of the utility of even the best
orreries, and I cannot recommend them as auxiliaries in the study of
astronomy. The numerous appendages usually connected with them, some to
support them in a proper position, and some to communicate to them the
requisite motions, enter into the ideas which the learner forms
respecting the machinery of the heavens; and it costs much labor
afterwards to divest the mind of such erroneous impressions. Astronomy
can be exhibited much more clearly and beautifully to the mental eye
than to the visual organ. It is much easier to conceive of the sun
existing in boundless space, and of the earth as moving around him at a
great distance, the mind having nothing in view but simply these two
bodies, than it is, in an orrery, to contemplate the motion of a ball
representing the earth, carried by a complicated apparatus of wheels
around another ball, supported by a cylinder or wire, to represent the
sun. I would advise you, whenever it is practicable, to think how things
are in Nature, rather than how they are represented by art. The
machinery of the heavens is much simpler than that of an orrery.

In endeavoring to obtain a clear idea of the revolution of the earth
around the sun, imagine to yourself a plane (a geometrical plane, having
merely length and breadth, but no thickness) passing through the centres
of the sun and the earth, and extended far beyond the earth till it
reaches the firmament of stars. Although, indeed, no such dome actually
exists as that under which we figure to ourselves the vault of the sky,
yet, as the fixed stars appear to be set in such a dome, we may imagine
that the circles of the sphere, when indefinitely enlarged, finally
reach such an imaginary vault. All that is essential is, that we should
imagine this to exist far beyond the bounds of the solar system, the
various bodies that compose the latter being situated close around the
sun, at the centre.

Along the line where this great circle meets the starry vault, are
situated a series of constellations,--Aries, Taurus, Gemini, &c.,--which
occupy successively this portion of the heavens. When bodies are at such
a distance from each other as the sun and the earth, I have said that a
spectator on either would project the other body upon the concave sphere
of the heavens, always seeing it on the opposite side of a great circle
one hundred and eighty degrees from himself. The place of a body, when
viewed from any point, is denoted by the position it occupies among the
stars. Thus, in the diagram, Fig. 25, page 114, when the earth arrives
at E, it is said to be in Aries, because, if viewed from the sun, it
would be projected on that part of the heavens; and, for the same
reason, to a spectator at E, the sun would be in Libra. When the earth
shifts its position from Aries to Taurus, as we are unconscious of our
own motion, the sun it is that appears to move from Libra to Scorpio, in
the opposite part of the heavens. Hence, as we go forward, in the order
of the signs, on one side of the ecliptic, the sun seems to be moving
forward at the same rate on the opposite side of the same great circle;
and therefore, although we are unconscious of our own motion, we can
read it, from day to day, in the motions of the sun. If we could see
the stars at the same time with the sun, we could actually observe, from
day to day, the sun's progress through them, as we observe the progress
of the moon at night; only the sun's rate of motion would be nearly
fourteen times slower than that of the moon. Although we do not see the
stars when the sun is present, we can observe that it makes daily
progress eastward, as is apparent from the constellations of the zodiac
occupying, successively, the western sky immediately after sunset,
proving that either all the stars have a common motion westward,
independent of their diurnal motion, or that the sun has a motion past
them from west to east. We shall see, hereafter, abundant evidence to
prove, that this change in the relative position of the sun and stars,
is owing to a change in the apparent place of the sun, and not to any
change in the stars.

[Illustration Fig. 25.]

To form a clear idea of the two motions of the earth, imagine yourself
standing on a circular platform which turns slowly round its centre.
While you are carried slowly round the entire of the circuit of the
heavens, along with the platform, you may turn round upon your heel the
same way three hundred and sixty-five times. The former is analogous to
our annual motion with the earth around the sun; the latter, to our
diurnal revolution in common with the earth around its own axis.

Although the apparent revolution of the sun is in a direction opposite
to the real motion of the earth, as regards absolute space, yet both are
nevertheless from west to east, since these terms do not refer to any
directions in absolute space, but to the order in which certain
constellations (the constellations of the Zodiac) succeed one another.
The earth itself, on opposite sides of its orbit, does in fact move
towards directly opposite points of space; but it is all the while
pursuing its course in the order of the signs. In the same manner,
although the earth turns on its axis from west to east, yet any place on
the surface of the earth is moving in a direction in space exactly
opposite to its direction twelve hours before. If the sun left a visible
trace on the face of the sky, the ecliptic would of course be distinctly
marked on the celestial sphere, as it is on an artificial globe; and
were the equator delineated in a similar manner, we should then see, at
a glance, the relative position of these two circles,--the points where
they intersect one another, constituting the equinoxes; the points where
they are at the greatest distance asunder, that is, the solstices; and
various other particulars, which, for want of such visible traces, we
are now obliged to search for by indirect and circuitous methods. It
will aid you, to have constantly before your mental vision an imaginary
delineation of these two important circles on the face of the sky.

The equator makes an angle with the ecliptic of twenty-three degrees and
twenty-eight minutes. This is called the obliquity of the ecliptic. As
the sun and earth are both always in the ecliptic, and as the motion of
the earth in one part of it makes the sun appear to move in the
opposite part, at the same rate, the sun apparently descends, in Winter,
twenty-three degrees and twenty-eight minutes to the south of the
equator, and ascends, in Summer, the same number of degrees north of it.
We must keep in mind, that the celestial equator and celestial ecliptic
are here understood, and we may imagine them to be two great circles
delineated on the face of the sky. On comparing observations made at
different periods, for more than two thousand years, it is found, that
the obliquity of the ecliptic is not constant, but that it undergoes a
slight diminution, from age to age, amounting to fifty-two seconds in a
century, or about half a second annually. We might apprehend that, by
successive approaches to each other, the equator and ecliptic would
finally coincide; but astronomers have discovered, by a most profound
investigation, based on the principles of universal gravitation, that
this irregularity is confined within certain narrow limits; and that the
obliquity, after diminishing for some thousands of years, will then
increase for a similar period, and will thus vibrate forever about a
mean value.

As the earth traverses every part of her orbit in the course of a year,
she will be once at each solstice, and once at each equinox. The best
way of obtaining a correct idea of her two motions is, to conceive of
her as standing still for a single day, at some point in her orbit,
until she has turned once on her axis, then moving about a degree, and
halting again, until another diurnal revolution is completed. Let us
suppose the earth at the Autumnal equinox, the sun, of course, being at
the Vernal equinox,--for we must always think of these two bodies as
diametrically opposite to each other. Suppose the earth to stand still
in its orbit for twenty-four hours. The revolution of the earth on its
axis, from west to east, will make the sun appear to describe a great
circle of the heavens from east to west, coinciding with the equator. At
the end of this period, suppose the sun to move northward one degree,
and to remain there for twenty-four hours; in which time, the
revolution of the earth, will make the sun appear to describe another
circle, from east to west, parallel to the equator, but one degree north
of it. Thus, we may conceive of the sun as moving one degree north,
every day, for about three months, when it will reach the point of the
ecliptic furthest from the equator, which point is called the _tropic_,
from a Greek word, signifying _to turn_; because, after the sun has
passed this point, his motion in his orbit carries him continually
towards the equator, and therefore he seems to turn about. The same
point is also called the _solstice_, from a Latin word, signifying to
_stand still_; since, when the sun has reached its greatest northern or
southern limit, while its declination is at the point where it ceases to
increase, but begins to decrease, there the sun seems for a short time
stationary, with regard to the equator, appearing for several days to
describe the same parallel of latitude.

When the sun is at the northern tropic, which happens about the
twenty-first of June, his elevation above the southern horizon at noon
is the greatest in the year; and when he is at the southern tropic,
about the twenty-first of December, his elevation at noon is the least
in the year. The difference between these two meridian altitudes will
give the whole distance from one tropic to the other, and consequently,
twice the distance from each tropic to the equator. By this means, we
find how far the tropic is from the equator, and that gives us the angle
which the equator and ecliptic make with each other; for the greatest
distance between any two great circles on the sphere is always equal to
the angle which they make with each other. Thus, the ancient astronomers
were able to determine the obliquity of the ecliptic with a great degree
of accuracy. It was easy to find the situation of the zenith, because
the direction of a plumb-line shows us where that is; and it was easy to
find the distances from the zenith where the sun was at the greatest and
least distances; respectively. The difference of these two arcs is the
angular distance from one tropic to the other; and half this arc is the
distance of either tropic from the equator, and of course, equal to the
obliquity of the ecliptic. All this will be very easily understood from
the annexed diagram, Fig. 26. Let Z be the zenith of a spectator
situated at C; Z _n_ the least, and Z _s_ the greatest distance of the
sun from the zenith. From Z _s_ subtract Z _n_, and then _s n_, the
difference, divided by two, will give the obliquity of the ecliptic.

[Illustration Fig. 26.]

The motion of the earth in its orbit is nearly seventy times as great as
its greatest motion around its axis. In its revolution around the sun,
the earth moves no less than one million six hundred and forty thousand
miles per day, sixty-eight thousand miles per hour, eleven hundred miles
per minute, and nearly nineteen miles every second; a velocity nearly
sixty times as great as the greatest velocity of a cannon ball. Places
on the earth turn with very different degrees of velocity in different
latitudes. Those near the equator are carried round on the circumference
of a large circle; those towards the poles, on the circumference of a
small circle; while one standing on the pole itself would not turn at
all. Those who live on the equator are carried about one thousand miles
an hour. In our latitude, (forty-one degrees and eighteen minutes,) the
diurnal velocity is about seven hundred and fifty miles per hour. It
would seem, at first view, quite incredible, that we should be whirled
round at so rapid a rate, and yet be entirely insensible of any motion;
and much more, that we could be going so swiftly through space, in our
circuit around the sun, while all things, when unaffected by local
causes, appear to be in such a state of quiescence. Yet we have the most
unquestionable evidence of the fact; nor is it difficult to account for
it, in consistency with the general state of repose among bodies on the
earth, when we reflect that their relative motions, with respect to each
other, are not in the least disturbed by any motions which they may have
in common. When we are on board a steam-boat, we move about in the same
manner when the boat is in rapid motion, as when it is lying still; and
such would be the case, if it moved steadily a hundred times faster than
it does. Were the earth, however, suddenly to stop its diurnal
revolution, all movable bodies on its surface would be thrown off in
tangents to the surface with velocities proportional to that of their
diurnal motion; and were the earth suddenly to halt in its orbit, we
should be hurled forward into space with inconceivable rapidity.

I will next endeavor to explain to you the phenomena of the _Seasons_.
These depend on two causes; first, the inclination of the earth's axis
to the plane of its orbit; and, secondly, to the circumstance, that the
axis always remains parallel to itself. Imagine to yourself a candle
placed in the centre of a ring, to represent the sun in the centre of
the earth's orbit, and an apple with a knittingneedle running through it
in the direction of the stem. Run a knife around the central part of the
apple, to mark the situation of the equator. The circumference of the
ring represents the earth's orbit in the plane of the ecliptic. Place
the apple so that the equator shall coincide with the wire; then the
axis will lie directly across the plane of the ecliptic; that is, at
right angles to it. Let the apple be carried quite round the ring,
constantly preserving the axis parallel to itself, and the equator all
the while coinciding with the wire that represents the orbit. Now, since
the sun enlightens half the globe at once, so the candle, which here
represents the sun, will shine on the half of the apple that is turned
towards it; and the circle which divides the enlightened from the
unenlightened side of the apple, called the _terminator_, will pass
through both the poles. If the apple be turned slowly round on its axis,
the terminator will successively pass over all places on the earth,
giving the appearance of sunrise to places at which it arrives, and of
sunset to places from which it departs. If, therefore, the equator had
coincided with the ecliptic, as would have been the case, had the
earth's axis been perpendicular to the plane of its orbit, the diurnal
motion of the sun would always have been in the equator, and the days
and nights would have been equal all over the globe. To the inhabitants
of the equatorial parts of the earth, the sun would always have appeared
to move in the prime vertical, rising directly in the east, passing
through the zenith at noon, and setting in the west. In the polar
regions, the sun would always have appeared to revolve in the horizon;
while, at any place between the equator and the pole, the course of the
sun would have been oblique to the horizon, but always oblique in the
same degree. There would have been nothing of those agreeable
vicissitudes of the seasons which we now enjoy; but some regions of the
earth would have been crowned with perpetual spring, others would have
been scorched with the unremitting fervor of a vertical sun, while
extensive regions towards either pole would have been consigned to
everlasting frost and sterility.

To understand, then, clearly, the causes of the change of seasons, use
the same apparatus as before; but, instead of placing the axis of the
earth at right angles to the plane of its orbit, turn it out of a
perpendicular position a little, (twenty-three degrees and twenty-eight
minutes,) then the equator will be turned just the same number of
degrees out of a coincidence with the ecliptic. Let the apple be carried
around the ring, always holding the axis inclined at the same angle to
the plane of the ring, and always parallel to itself. You will find that
there will be two points in the circuit where the plane of the equator,
that you had marked around the centre of the apple, will pass through
the centre of the sun; these will be the points where the celestial
equator and the ecliptic cut one another, or the equinoxes. When the
earth is at either of these points, the sun shines on both poles alike;
and, if we conceive of the earth, while in this situation, as turning
once round on its axis, the apparent diurnal motion of the sun will be
the same as it would be, were the earth's axis perpendicular to the
plane of the equator. For that day, the sun would revolve in the
equator, and the days and nights would be equal all over the globe. If
the apple were carried round in the manner supposed, then, at the
distance of ninety degrees from the equinoxes, the same pole would be
turned from the sun on one side, just as much as it was turned towards
him on the other. In the former case, the sun's light would fall short
of the pole twenty-three and one half degrees, and in the other case, it
would reach beyond it the same number of degrees. I would recommend to
you to obtain as clear an idea as you can of the cause of the change of
seasons, by thinking over the foregoing illustration. You may then clear
up any remaining difficulties, by studying the diagram, Fig. 27, on page
122.

[Illustration Fig. 27.]

Let A B C D represent the earth's place in different parts of its orbit,
having the sun in the centre. Let A, C, be the positions of the earth at
the equinoxes, and B, D, its positions at the tropics,--the axis _n s_
being always parallel to itself. It is difficult to represent things of
this kind correctly, all on the same plane; but you will readily see,
that the figure of the earth, here, answers to the apple in the former
illustration; that the hemisphere towards _n_ is above, and that towards
_s_ is below, the plane of the paper. When the earth is at A and C, the
Vernal and Autumnal equinoxes, the sun, you will perceive, shines on
both the poles _n_ and _s_; and, if you conceive of the globe, while in
this position, as turned round on its axis, as it is in the diurnal
revolution, you will readily understand, that the sun would describe the
celestial equator. This may not at first appear so obvious, by
inspecting the figure; but if you consider the point _n_ as raised above
the plane of the paper, and the point _s_ as depressed below it, you
will readily see how the plane of the equator would pass through the
centre of the sun. Again, at B, when the earth is at the southern
tropic, the sun shines twenty-three and a half degrees beyond the north
pole, _n_, and falls the same distance short of the south pole, _s_. The
case is exactly reversed when the earth is at the northern tropic, and
the sun at the southern. While the earth is at one of the tropics, at B,
for example, let us conceive of it as turning on its axis, and we shall
readily see, that all that part of the earth which lies within the north
polar circle will enjoy continual day, while that within the south polar
circle will have continual night; and that all other places will have
their days longer as they are nearer to the enlightened pole, and
shorter as they are nearer to the unenlightened pole. This figure
likewise shows the successive positions of the earth, at different
periods of the year, with respect to the signs, and what months
correspond to particular signs. Thus, the earth enters Libra, and the
sun Aries, on the twenty-first of March, and on the twenty-first of
June, the earth is just entering Capricorn, and the sun, Cancer. You
will call to mind what is meant by this phraseology,--that by saying the
earth enters Libra, we mean that a spectator placed on the sun would see
the earth in that part of the celestial ecliptic, which is occupied by
the sign Libra; and that a spectator on the earth sees the sun at the
same time projected on the opposite part of the heavens, occupied by the
sign Cancer.

Had the axis of the earth been perpendicular to the plane of the
ecliptic, then the sun would always have appeared to move in the
equator, the days would every where have been equal to the nights, and
there could have been no change of seasons. On the other hand, had the
inclination of the ecliptic to the equator been much greater than it is,
the vicissitudes of the seasons would have been proportionally greater,
than at present. Suppose, for instance, the equator had been at right
angles to the ecliptic, in which case, the poles of the earth would have
been situated in the ecliptic itself; then, in different parts of the
earth, the appearances would have been as follows: To a spectator on the
_equator_, (where all the circles of diurnal revolution are
perpendicular to the horizon,) the sun, as he left the vernal equinox,
would every day perform his diurnal revolution in a smaller and smaller
circle, until he reached the north pole, when he would halt for a
moment, and then wheel about and return to the equator, in a reverse
order. The progress of the sun through the southern signs, to the south
pole, would be similar to that already described. Such would be the
appearances to an inhabitant of the equatorial regions. To a spectator
living in an _oblique_ sphere, in our own latitude, for example, the
sun, while north of the equator, would advance continually northward,
making his diurnal circuit in parallels further and further distant from
the equator, until he reached the circle of perpetual apparition; after
which, he would climb, by a spiral course, to the north star, and then
as rapidly return to the equator. By a similar progress southward, the
sun would at length pass the circle of perpetual occultation, and for
some time (which would be longer or shorter, according to the latitude
of the place of observation) there would be continual night. To a
spectator on the _pole_ of the earth and under the pole of the heaven,
during the long day of six months, the sun would wind its way to a point
directly over head, pouring down upon the earth beneath not merely the
heat of the torrid zone, but the heat of a torrid noon, accumulating
without intermission.

The great vicissitudes of heat and cold, which would attend these
several movements of the sun, would be wholly incompatible with the
existence of either the animal or the vegetable kingdom, and all
terrestrial Nature would be doomed to perpetual sterility and
desolation. The happy provision which the Creator has made against such
extreme vicissitudes, by confining the changes of the seasons within
such narrow bounds, conspires with many other express arrangements in
the economy of Nature, to secure the safety and comfort of the human
race.

Perhaps you have never reflected upon all the reasons, why the several
changes of position, with respect to the horizon, which the sun
undergoes in the course of the year, occasion such a difference in the
amount of heat received from him. Two causes contribute to increase the
heat of Summer and the cold of Winter. The higher the sun ascends above
the horizon, the more directly his rays fall upon the earth; and their
heating power is rapidly augmented, as they approach a perpendicular
direction. When the sun is nearly over head, his rays strike us with far
greater force than when they meet us obliquely; and the earth absorbs a
far greater number of those rays of heat which strike it
perpendicularly, than of those which meet it in a slanting direction.
When the sun is near the horizon, his rays merely glance along the
ground, and many of them, before they reach it, are absorbed and
dispersed in passing through the atmosphere. Those who have felt only
the oblique solar rays, as they fall upon objects in the high latitudes,
have a very inadequate idea of the power of a vertical, noonday sun, as
felt in the region of the equator.

The increased length of the day in Summer is another cause of the heat
of this season of the year. This cause more sensibly affects places far
removed from the equator, because at such places the days are longer and
the nights shorter than in the torrid zone. By the operation of this
cause, the solar heat accumulates there so much, during the longest days
of Summer, that the temperature rises to a higher degree than is often
known in the torrid climates.

But the temperature of a place is influenced very much by several other
causes, as well as by the force and duration of the sun's heat. First,
the _elevation_ of a country above the level of the sea has a great
influence upon its climate. Elevated districts of country, even in the
torrid zone, often enjoy the most agreeable climate in the world. The
cold of the upper regions of the atmosphere modifies and tempers the
solar heat, so as to give a most delightful softness, while the
uniformity of temperature excludes those sudden and excessive changes
which are often experienced in less favored climes. In ascending certain
high mountains situated within the torrid zone, the traveller passes, in
a short time, through every variety of climate, from the most oppressive
and sultry heat, to the soft and balmy air of Spring, which again is
succeeded by the cooler breezes of Autumn, and then by the severest
frosts of Winter. A corresponding difference is seen in the products of
the vegetable kingdom. While Winter reigns on the summit of the
mountain, its central regions may be encircled with the verdure of
Spring, and its base with the flowers and fruits of Summer. Secondly,
the proximity of the _ocean_ also has a great effect to equalize the
temperature of a place. As the ocean changes its temperature during the
year much less than the land, it becomes a source of warmth to
contiguous countries in Winter, and a fountain of cool breezes in
Summer. Thirdly, the relative _humidity_ or _dryness_ of the atmosphere
of a place is of great importance, in regard to its effects on the
animal system. A dry air of ninety degrees is not so insupportable as a
humid air of eighty degrees; and it may be asserted as a general
principle, that a hot and humid atmosphere is unhealthy, although a hot
air, when dry, may be very salubrious. In a warm atmosphere which is
dry, the evaporation of moisture from the surface of the body is rapid,
and its cooling influence affords a most striking relief to an intense
heat without; but when the surrounding atmosphere is already filled with
moisture, no such evaporation takes place from the surface of the skin,
and no such refreshing effects are experienced from this cause. Moisture
collects on the skin; a sultry, oppressive sensation is felt; and chills
and fevers are usually in the train.

LETTER XII.

LAWS OF MOTION.

"What though in solemn silence, all
Move round this dark, terrestrial ball!
In reason's ear they all rejoice,
And utter forth a glorious voice;
For ever singing, as they shine,
'The hand that made us is divine.'"--_Addison._

HOWEVER incredible it may seem, no fact is more certain, than that the
earth is constantly on the wing, flying around the sun with a velocity
so prodigious, that, for every breath we draw, we advance on our way
forty or fifty miles. If, when passing across the waters in a
steam-boat, we can wake, after a night's repose, and find ourselves
conducted on our voyage a hundred miles, we exult in the triumphs of
art, which could have moved so ponderous a body as a steam-ship over
such a space in so short a time, and so quietly, too, as not to disturb
our slumbers; but, with a motion vastly more quiet and uniform, we have,
in the same interval, been carried along with the earth in its orbit
more than half a million of miles. In the case of the steam-ship,
however perfect the machinery may be, we still, in our waking hours at
least, are made sensible of the action of the forces by which the motion
is maintained,--as the roaring of the fire, the beating of the piston,
and the dashing of the paddle-wheels; but in the more perfect machinery
which carries the earth forward on her grander voyage, no sound is
heard, nor the least intimation afforded of the stupendous forces by
which this motion is achieved. To the pious observer of Nature it might
seem sufficient, without any inquiry into second causes, to ascribe the
motions of the spheres to the direct agency of the Supreme Being. If,
however, we can succeed in finding the secret springs and cords, by
which the motions of the heavenly bodies are immediately produced and
controlled, it will detract nothing from our just admiration of the
Great First Cause of all things. We may therefore now enter upon the
inquiry into the nature or laws of the forces by which the earth is made
to revolve on her axis and in her orbit; and having learned what it is,
that causes and maintains the motions of the earth, you will then
acquire, at the same time, a knowledge of all the celestial machinery.
The subject will involve an explanation of the laws of motion, and of
the principles of universal gravitation.

It was once supposed, that we could never reason respecting the laws
that govern the heavenly bodies from what we observe in bodies around
us, but that motion is one thing on the earth and quite another thing in
the skies; and hence, that it is impossible for us, by any inquiries
into the laws of terrestrial Nature, to ascertain how things take place
among the heavenly bodies. Galileo and Newton, however, proceeded on the
contrary supposition, that Nature is uniform in all her works; that the
same Almighty arm rules over all; and that He works by the same fixed
laws through all parts of His boundless realm. The certainty with which
all the predictions of astronomers, made on these suppositions, are
fulfilled, attests the soundness of the hypothesis. Accordingly, those
laws, which all experience, endlessly multiplied and varied, proves to
be the laws of terrestrial motion, are held to be the laws that govern
also the motions of the most distant planets and stars, and to prevail
throughout the universe of matter. Let us, then, briefly review these
great laws of motion, which are three in number. The FIRST LAW is as
follows: _every body perseveres in a state of rest, or of uniform motion
in a straight line, unless compelled by some force to change its state_.
By _force_ is meant any thing which produces motion.

The foregoing law has been fully established by experiment, and is
conformable to all experience. It embraces several particulars. First, a
body, when at rest, remains so, unless some force puts it in motion; and
hence it is inferred, when a body is found in motion, that some force
must have been applied to it sufficient to have caused its motion. Thus,
the fact, that the earth is in motion around the sun and around its own
axis, is to be accounted for by assigning to each of these motions a
force adequate, both in quantity and direction, to produce these
motions, respectively.

Secondly, when a body is once in motion, it will continue to move for
ever, unless something stops it. When a ball is struck on the surface of
the earth, the friction of the earth and the resistance of the air soon
stop its motion; when struck on smooth ice, it will go much further
before it comes to a state of rest, because the ice opposes much less
resistance than the ground; and, were there no impediment to its
motion, it would, when once set in motion, continue to move without
end. The heavenly bodies are actually in this condition: they continue
to move, not because any new forces are applied to them; but, having
been once set in motion, they continue in motion because there is
nothing to stop them. This property in bodies to persevere in the state
they are actually in,--if at rest, to remain at rest, or, if in motion,
to continue in motion,--is called _inertia_. The inertia of a body
(which is measured by the force required to overcome it) is proportioned
to the quantity of matter it contains. A steam-boat manifests its
inertia, on first starting it, by the enormous expenditure of force
required to bring it to a given rate of motion; and it again manifests
its inertia, when in rapid motion, by the great difficulty of stopping
it. The heavenly bodies, having been once put in motion, and meeting
with nothing to stop them, move on by their own inertia. A top affords a
beautiful illustration of inertia, continuing, as it does, to spin after
the moving force is withdrawn.

Thirdly, the motion to which a body naturally tends is _uniform_; that
is, the body moves just as far the second minute as it did the first,
and as far the third as the second; and passes over equal spaces in
equal times. I do not assert that the motion of all moving bodies is _in
fact_ uniform, but that such is their _tendency_. If it is otherwise
than uniform, there is some cause operating to disturb the uniformity to
which it is naturally prone.

Fourthly, a body in motion will move in a _straight line_, unless
diverted out of that line by some external force; and the body will
resume its straight-forward motion, whenever the force that turns it
aside is withdrawn. Every body that is revolving in an orbit, like the
moon around the earth, or the earth around the sun, _tends_ to move in a
straight line which is a tangent[7] to its orbit. Thus, if A B C, Fig.
28, represents the orbit of the moon around the earth, were it not for
the constant action of some force that draws her towards the earth, she
would move off in a straight line. If the force that carries her towards
the earth were suspended at A, she would immediately desert the circular
motion, and proceed in the direction A D. In the same manner, a boy
whirls a stone around his head in a sling, and then letting go one of
the strings, and releasing the force that binds it to the circle, it
flies off in a straight line which is a tangent to that part of the
circle where it was released. This tendency which a body revolving in an
orbit exhibits, to recede from the centre and to fly off in a tangent,
is called the _centrifugal force_. We see it manifested when a pail of
water is whirled. The water rises on the sides of the vessel, leaving a
hollow in the central parts. We see an example of the effects of
centrifugal action, when a horse turns swiftly round a corner, and the
rider is thrown outwards; also, when a wheel passes rapidly through a
small collection of water, and portions of the water are thrown off from
the top of the wheel in straight lines which are tangents to the wheel.

[Illustration Fig. 28.]

The centrifugal force is increased as the velocity is increased. Thus,
the parts of a millstone most remote from the centre sometimes acquire a
centrifugal force so much greater than the central parts, which move
much slower, that the stone is divided, and the exterior portions are
projected with great violence. In like manner, as the equatorial parts
of the earth, in the diurnal revolution, revolve much faster than the
parts towards the poles, so the centrifugal force is felt most at the
equator, and becomes strikingly manifest by the diminished weight of
bodies, since it acts in opposition to the force of gravity.

Although the foregoing law of motion, when first presented to the mind,
appears to convey no new truth, but only to enunciate in a formal manner
what we knew before; yet a just understanding of this law, in all its
bearings, leads us to a clear comprehension of no small share of all the
phenomena of motion. The second and third laws may be explained in fewer
terms.

The SECOND LAW of motion is as follows: _motion is proportioned to the
force impressed, and in the direction of that force_.

The meaning of this law is, that every force that is applied to a body
produces its full effect, proportioned to its intensity, either in
causing or in preventing motion. Let there be ever so many blows applied
at once to a ball, each will produce its own effect in its own
direction, and the ball will move off, not indeed in the zigzag, complex
lines corresponding to the directions of the several forces, but in a
single line expressing the united effect of all. If you place a ball at
the corner of a table, and give it an impulse, at the same instant, with
the thumb and finger of each hand, one impelling it in the direction of
one side of the table, and the other in the direction of the other side,
the ball will move diagonally across the table. If the blows be exactly
proportioned each to the length of the side of the table on which it is
directed, the ball will run exactly from corner to corner, and in the
same time that it would have passed over each side by the blow given in
the direction of that side. This principle is expressed by saying, that
a body impelled by two forces, acting respectively in the directions of
the two sides of a parallelogram, and proportioned in intensity to the
lengths of the sides, will describe the diagonal of the parallelogram in
the same time in which it would have described the sides by the forces
acting separately.

The converse of this proposition is also true, namely, that any single
motion may be considered as the _resultant_ of two others,--the motion
itself being represented by the diagonal, while the two _components_ are
represented by the sides, of a parallelogram. This reduction of a motion
to the individual motions that produce it, is called the _resolution of
motion_, or the _resolution of forces_. Nor can a given motion be
resolved into _two_ components, merely. These, again, may be resolved
into others, varying indefinitely, in direction and intensity, from all
which the given motion may be considered as having resulted. This
composition and resolution of motion or forces is often of great use, in
inquiries into the motions of the heavenly bodies. The composition often
enables us to substitute a single force for a great number of others,
whose individual operations would be too complicated to be followed. By
this means, the investigation is greatly simplified. On the other hand,
it is frequently very convenient to resolve a given motion into two or
more others, some of which may be thrown out of the account, as not
influencing the particular point which we are inquiring about, while
others are far more easily understood and managed than the single force
would have been. It is characteristic of great minds, to simplify these
inquiries. They gain an insight into complicated and difficult subjects,
not so much by any extraordinary faculty of seeing in the dark, as by
the power of removing from the object all incidental causes of
obscurity, until it shines in its own clear and simple light.

If every force, when applied to a body, produces its full and legitimate
effect, how many other forces soever may act upon it, impelling it
different ways, then it must follow, that the smallest force ought to
move the largest body; and such is in fact the case. A snap of a finger
upon a seventy-four under full sail, if applied in the direction of its
motion, would actually increase its speed, although the effect might be
too small to be visible. Still it is something, and may be truly
expressed by a fraction. Thus, suppose a globe, weighing a million of
pounds, were suspended from the ceiling by a string, and we should apply
to it the snap of a finger,--it is granted that the motion would be
quite insensible. Let us then divide the body into a million equal
parts, each weighing one pound; then the same impulse, applied to each
one separately, would produce a sensible effect, moving it, say one
inch. It will be found, on trial, that the same impulse given to a mass
of two pounds will move it half an inch; and hence it is inferred, that,
if applied to a mass weighing a million of pounds, it would move it the
millionth part of an inch.

It is one of the curious results of the second law of motion, that an
unlimited number of motions may exist together in the same body. Thus,
at the same moment, we may be walking around a post in the cabin of a
steam-boat, accompanying the boat in its passage around an island,
revolving with the earth on its axis, flying through space in our annual
circuit around the sun, and possibly wheeling, along with the sun and
his whole retinue of planets, around some centre in common with the
starry worlds.

The THIRD LAW of motion is this: _action and reaction are equal, and in
contrary directions_.

Whenever I give a blow, the body struck exerts an equal force on the
striking body. If I strike the water with an oar, the water communicates
an equal impulse to the oar, which, being communicated to the boat,
drives it forward in the opposite direction. If a magnet attracts a
piece of iron, the iron attracts the magnet just as much, in the
opposite direction; and, in short, every portion of matter in the
universe attracts and is attracted by every other, equally, in an
opposite direction. This brings us to the doctrine of universal
gravitation, which is the very key that unlocks all the secrets of the
skies. This will form the subject of my next Letter.

FOOTNOTE:

[7] A tangent is a straight line touching a circle, as A D, in Fig. 28

LETTER XIII.

TERRESTRIAL GRAVITY.

"To Him no high, no low, no great, no small,
He fills, He bounds, connects, and equals all."--_Pope._

WE discover in Nature a tendency of every portion of matter towards
every other. This tendency is called _gravitation_. In obedience to this
power, a stone falls to the ground, and a planet revolves around the
sun. We may contemplate this subject as it relates either to phenomena
that take place near the surface of the earth, or in the celestial
regions. The former, _gravity_, is exemplified by falling bodies; the
latter, _universal gravitation_, by the motions of the heavenly bodies.
The laws of terrestrial gravity were first investigated by Galileo;
those of universal gravitation, by Sir Isaac Newton. Terrestrial gravity
is only an individual example of universal gravitation; being the
tendency of bodies towards the centre of the earth. We are so much
accustomed, from our earliest years, to see bodies fall to the earth,
that we imagine bodies must of necessity fall "downwards;" but when we
reflect that the earth is round, and that bodies fall towards the centre
on all sides of it, and that of course bodies on opposite sides of the
earth fall in precisely opposite directions, and towards each other, we
perceive that there must be some force acting to produce this effect;
nor is it enough to say, as the ancients did, that bodies "naturally"
fall to the earth. Every motion implies some force which produces it;
and the fact that bodies fall towards the earth, on all sides of it,
leads us to infer that that force, whatever it is, resides in the earth
itself. We therefore call it _attraction_. We do not, however, say what
attraction _is_, but what it _does_. We must bear in mind, also, that,
according to the third law of motion, this attraction is mutual; that
when a stone falls towards the earth, it exerts the same force on the
earth that the earth exerts on the stone; but the motion of the earth
towards the stone is as much less than that of the stone towards the
earth, as its quantity of matter is greater; and therefore its motion is
quite insensible.

But although we are compelled to acknowledge the _existence_ of such a
force as gravity, causing a tendency in all bodies towards each other,
yet we know nothing of its _nature_, nor can we conceive by what medium
bodies at such a distance as the moon and the earth exercise this
influence on each other. Still, we may trace the modes in which this
force acts; that is, its _laws_; for the laws of Nature are nothing else
than the modes in which the powers of Nature act.

We owe chiefly to the great Galileo the first investigation of the laws
of terrestrial gravity, as exemplified in falling bodies; and I will
avail myself of this opportunity to make you better acquainted with one
of the most interesting of men and greatest of philosophers.

Galileo was born at Pisa, in Italy, in the year 1564. He was the son of
a Florentine nobleman, and was destined by his father for the medical
profession, and to this his earlier studies were devoted. But a fondness
and a genius for mechanical inventions had developed itself, at a very
early age, in the construction of his toys, and a love of drawing; and
as he grew older, a passion for mathematics, and for experimental
research, predominated over his zeal for the study of medicine, and he
fortunately abandoned that for the more congenial pursuits of natural
philosophy and astronomy. In the twenty-fifth year of his age, he was
appointed, by the Grand Duke of Tuscany, professor of mathematics in the
University of Pisa. At that period, there prevailed in all the schools a
most extraordinary reverence for the writings of Aristotle, the
preceptor of Alexander the Great,--a philosopher who flourished in
Greece, about three hundred years before the Christian era. Aristotle,
by his great genius and learning, gained a wonderful ascendency over the
minds of men, and became the oracle of the whole reading world for
twenty centuries. It was held, on the one hand, that all truths worth
knowing were contained in the writings of Aristotle; and, on the other,
that an assertion which contradicted any thing in Aristotle could not be
true. But Galileo had a greatness of mind which soared above the
prejudices of the age in which he lived, and dared to interrogate Nature
by the two great and only successful methods of discovering her
secrets,--experiment and observation. Galileo was indeed the first
philosopher that ever fully employed experiments as the means of
learning the laws of Nature, by imitating on a small what she performs
on a great scale, and thus detecting her modes of operation. Archimedes,
the great Sicilian philosopher, had in ancient times introduced
mathematical or geometrical reasoning into natural philosophy; but it
was reserved for Galileo to unite the advantages of both mathematical
and experimental reasonings in the study of Nature,--both sure and the
only sure guides to truth, in this department of knowledge, at least.
Experiment and observation furnish materials upon which geometry builds
her reasonings, and from which she derives many truths that either lie
for ever hidden from the eye of observation, or which it would require
ages to unfold.

This method, of interrogating Nature by experiment and observation, was
matured into a system by Lord Bacon, a celebrated English philosopher,
early in the seventeenth century,--indeed, during the life of Galileo.
Previous to that time, the inquirers into Nature did not open their eyes
to see how the facts really _are_; but, by metaphysical processes, in
imitation of Aristotle, determined how they _ought to be_, and hastily
concluded that they were so. Thus, they did not study into the laws of
motion, by observing how motion actually takes place, under various
circumstances, but first, in their closets, constructed a definition of
motion, and thence inferred all its properties. The system of reasoning
respecting the phenomena of Nature, introduced by Lord Bacon, was this:
in the first place, to examine all the facts of the case, and then from
these to determine the laws of Nature. To derive general conclusions
from the comparison of a great number of individual instances
constitutes the peculiarity of the Baconian philosophy. It is called the
_inductive_ system, because its conclusions were built on the induction,
or comparison, of a great many single facts. Previous to the time of
Lord Bacon, hardly any insight had been gained into the causes of
natural phenomena, and hardly one of the laws of Nature had been clearly
established, because all the inquirers into Nature were upon a wrong
road, groping their way through the labyrinth of error. Bacon pointed
out to them the true path, and held before them the torch-light of
experiment and observation, under whose guidance all successful students
of Nature have since walked, and by whose illumination they have gained
so wonderful an insight into the mysteries of the natural world.

It is a remarkable fact, that two such characters as Bacon and Galileo
should appear on the stage at the same time, who, without any
communication with each other, or perhaps without any personal knowledge
of each other's existence, should have each developed the true method of
investigating the laws of Nature. Galileo practised what Bacon only
taught; and some, therefore, with much reason, consider Galileo as a
greater philosopher than Bacon. "Bacon," says Hume, "pointed out, at a
great distance, the road to philosophy; Galileo both pointed it out to
others, and made, himself, considerable advances in it. The Englishman
was ignorant of geometry; the Florentine revived that science, excelled
in it, and was the first who applied it, together with experiment, to
natural philosophy. The former rejected, with the most positive disdain,
the system of Copernicus; the latter fortified it with new proofs,
derived both from reason and the senses."

When we reflect that geometry is a science built upon self-evident
truths, and that all its conclusions are the result of pure
demonstration, and can admit of no controversy; when we further reflect,
that experimental evidence rests on the testimony of the senses, and we
infer a thing to be true because we actually see it to be so; it shows
us the extreme bigotry, the darkness visible, that beclouded the human
intellect, when it not only refused to admit conclusions first
established by pure geometrical reasoning, and afterwards confirmed by
experiments exhibited in the light of day, but instituted the most cruel
persecutions against the great philosopher who first proclaimed these
truths. Galileo was hated and persecuted by two distinct bodies of men,
both possessing great influence in their respective spheres,--the one
consisting of the learned doctors of philosophy, who did nothing more,
from age to age, than reiterate the doctrines of Aristotle, and were
consequently alarmed at the promulgation of principles subversive of
those doctrines; the other consisting of the Romish priesthood,
comprising the terrible Inquisition, who denounced the truths taught by
Galileo, as inconsistent with certain declarations of the Holy
Scriptures. We shall see, as we advance, what a fearful warfare he had
to wage against these combined powers of darkness.

Aristotle had asserted, that, if two different weights of the same
material were let fall from the same height, the heavier one would reach
the ground sooner than the other, in proportion as it was more weighty.
For example: if a ten-pound leaden weight and a one-pound were let fall
from a given height at the same instant, the former would reach the
ground ten times as soon as the latter. No one thought of making the
trial, but it was deemed sufficient that Aristotle had said so; and
accordingly this assertion had long been received as an axiom in the
science of motion. Galileo ventured to appeal from the authority of
Aristotle to that of his own senses, and maintained, that both weights
would fall in the same time. The learned doctors ridiculed the idea.
Galileo tried the experiment in their presence, by letting fall, at the
same instant, large and small weights from the top of the celebrated
leaning tower of Pisa. Yet, with the sound of the two weights clicking
upon the pavement at the same moment, they still maintained that the
ten-pound weight would reach the ground in one tenth part of the time of
the other, because they could quote the chapter and verse of Aristotle
where the fact was asserted. Wearied and disgusted with the malice and
folly of these Aristotelian philosophers, Galileo, at the age of
twenty-eight, resigned his situation in the university of Pisa, and
removed to Padua, in the university of which place he was elected
professor of mathematics. Up to this period, Galileo had devoted himself
chiefly to the studies of the laws of motion, and the other branches of
mechanical philosophy. Soon afterwards, he began to publish his
writings, in rapid succession, and became at once among the most
conspicuous of his age,--a rank which he afterwards well sustained and
greatly exalted, by the invention of the telescope, and by his numerous
astronomical discoveries. I will reserve an account of these great
achievements until we come to that part of astronomy to which they were
more immediately related, and proceed, now, to explain to you the
leading principles of _terrestrial gravity_, as exemplified in falling
bodies.

First, _all bodies near the earth's surface fall in straight lines
towards the centre of the earth_. We are not to infer from this fact,
that there resides at the centre any peculiar force, as a great
loadstone, for example, which attracts bodies towards itself; but bodies
fall towards the centre of the sphere, because the combined attractions
of all the particles of matter in the earth, each exerting its proper
force upon the body, would carry it towards the centre. This may be
easily illustrated by a diagram. Let B, Fig. 29, page 140, be the
centre of the earth, and A a body without it. Every portion of matter in
the earth exerts some force on A, to draw it down to the earth. But
since there is just as much matter on one side of the line A B, as on
the other side, each half exerts an equal force to draw the body towards
itself; therefore it falls in the direction of the diagonal between the
two forces. Thus, if we compare the effects of any two particles of
matter at equal distances from the line A B, but on opposite sides of
it, as _a_, _b_, while the force of the particle at _a_ would tend to
draw A in the direction of A _a_, that of _b_ would draw it in the
direction of A _b_, and it would fall in the line A B, half way between
the two. The same would hold true of any other two corresponding
particles of matter on different sides of the earth, in respect to a
body situated in any place without it.

[Illustration Fig. 29.]

Secondly, _all bodies fall towards the earth, from the same height, with
equal velocities_. A musket-ball, and the finest particle of down, if
let fall from a certain height towards the earth, tend to descend
towards it at the same rate, and would proceed with equal speed, were it
not for the resistance of the air, which retards the down more than it
does the ball, and finally stops it. If, however, the air be removed out
of the way, as it may be by means of the air-pump, the two bodies keep
side by side in falling from the greatest height at which we can try the
experiment.

Thirdly, _bodies, in falling towards the earth, have their rate of
motion continually accelerated_. Suppose we let fall a musket-ball from
the top of a high tower, and watch its progress, disregarding the
resistance of the air: the first second, it will pass over sixteen feet
and one inch, but its speed will be constantly increased, being all the
while urged onward by the same force, and retaining all that it has
already acquired; so that the longer it is in falling, the swifter its
motion becomes. Consequently, when bodies fall from a great height, they
acquire an immense velocity before they reach the earth. Thus, a man
falling from a balloon, or from the mast-head of a ship, is broken in
pieces; and those meteoric stones, which sometimes fall from the sky,
bury themselves deep in the earth. On measuring the spaces through which
a body falls, it is found, that it will fall four times as far in two
seconds as in one, and one hundred times as far in ten seconds as in
one; and universally, the space described by a falling body is
proportioned to the time multiplied into itself; that is, to the square
of the time.

Fourthly, _gravity is proportioned to the quantity of matter_. A body
which has twice as much matter as another exerts a force of attraction
twice as great, and also receives twice as much from the same body as it
would do, if it were only just as heavy as that body. Thus the earth,
containing, as it does, forty times as much matter as the moon, exerts
upon the moon forty times as much force as it would do, were its mass
the same with that of the moon; but it is also capable of _receiving_
forty times as much gravity from the moon as it would do, were its mass
the same as the moon's; so that the power of attracting and that of
being attracted are reciprocal; and it is therefore correct to say, that
the moon attracts the earth _just as much_ as the earth attracts the
moon; and the same may be said of any two bodies, however different in
quantity of matter.

Fifthly, _gravity, when acting at a distance from the earth, is not as
intense as it is near the earth_. At such a distance as we are
accustomed to ascend above the general level of the earth, no great
difference is observed. On the tops of high mountains, we find bodies
falling towards the earth, with nearly the same speed as they do from
the smallest elevations. It is found, nevertheless, that there is a real
difference; so that, in fact, the weight of a body (which is nothing
more than the measure of its force of gravity) is not quite so great on
the tops of high mountains as at the general level of the sea. Thus, a
thousand pounds' weight, on the top of a mountain half a mile high,
would weigh a quarter of a pound less than at the level of the sea; and
if elevated four thousand miles above the earth,--that is, _twice_ as
far from the centre of the earth as the surface is from the centre,--it
would weigh only one fourth as much as before; if _three times_ as far,
it would weigh only one ninth as much. So that the force of gravity
decreases, as we recede from the earth, in the same proportion as the
square of the distance increases. This fact is generalized by saying,
that _the force of gravity, at different distances from the earth, is
inversely as the square of the distance_.

Were a body to fall from a great distance,--suppose a thousand times
that of the radius of the earth,--the force of gravity being one million
times less than that at the surface of the earth, the motion of the body
would be exceedingly slow, carrying it over only the sixth part of an
inch in a day. It would be a long time, therefore, in making any
sensible approaches towards the earth; but at length, as it drew near to
the earth it would acquire a very great velocity, and would finally rush
towards it with prodigious violence. Falling so far, and being
continually accelerated on the way, we might suppose that it would at
length attain a velocity infinitely great; but it can be demonstrated,
that, if a body were to fall from an infinite distance, attracted to the
earth only by gravity, it could never acquire a velocity greater than
about seven miles per second. This, however, is a speed inconceivably
great, being about eighteen times the greatest velocity that can be
given to a cannon-ball, and more than twenty-five thousand miles per
hour.

But the phenomena of falling bodies must have long been observed, and
their laws had been fully investigated by Galileo and others, before the
cause of their falling was understood, or any such principle as
gravity, inherent in the earth and in all bodies, was applied to them.
The developement of this great principle was the work of Sir Isaac
Newton; and I will give you, in my next Letter, some particulars
respecting the life and discoveries of this wonderful man.

LETTER XIV.

SIR ISAAC NEWTON.--UNIVERSAL GRAVITATION.--FIGURE OF THE EARTH'S
ORBIT.--PRECESSION OF THE EQUINOXES.

"The heavens are all his own; from the wild rule
Of whirling vortices, and circling spheres,
To their first great simplicity restored.
The schools astonished stood; but found it vain
To combat long with demonstration clear,
And, unawakened, dream beneath the blaze
Of truth. At once their pleasing visions fled,
With the light shadows of the morning mixed,
When Newton rose, our philosophic sun."--_Thomson's Elegy._

SIR ISAAC NEWTON was born in Lincolnshire, England, in 1642, just one
year after the death of Galileo. His father died before he was born, and
he was a helpless infant, of a diminutive size, and so feeble a frame,
that his attendants hardly expected his life for a single hour. The
family dwelling was of humble architecture, situated in a retired but
beautiful valley, and was surrounded by a small farm, which afforded but
a scanty living to the widowed mother and her precious charge. The cut
on page 144, Fig 30, represents the modest mansion, and the emblems of
rustic life that first met the eyes of this pride of the British nation,
and ornament of human nature. It will probably be found, that genius has
oftener emanated from the cottage than from the palace.

[Illustration Fig. 30.]

The boyhood of Newton was distinguished chiefly for his ingenious
mechanical contrivances. Among other pieces of mechanism, he constructed
a windmill so curious and complete in its workmanship, as to excite
universal admiration. After carrying it a while by the force of the
wind, he resolved to substitute animal power, and for this purpose he
inclosed in it a mouse, which he called the miller, and which kept the
mill a-going by acting on a tread-wheel. The power of the mouse was
brought into action by unavailing attempts to reach a portion of corn
placed above the wheel. A water-clock, a four-wheeled carriage propelled
by the rider himself, and kites of superior workmanship, were among the
productions of the mechanical genius of this gifted boy. At a little
later period, he began to turn his attention to the motions of the
heavenly bodies, and constructed several sun-dials on the walls of the
house where he lived. All this was before he had reached his fifteenth
year. At this age, he was sent by his mother, in company with an old
family servant, to a neighboring market-town, to dispose of products of
their farm, and to buy articles of merchandise for their family use; but
the young philosopher left all these negotiations to his worthy partner,
occupying himself, mean-while, with a collection of old books, which he
had found in a garret. At other times, he stopped on the road, and took
shelter with his book under a hedge, until the servant returned. They
endeavored to educate him as a farmer; but the perusal of a book, the
construction of a water-mill, or some other mechanical or scientific
amusement, absorbed all his thoughts, when the sheep were going astray,
and the cattle were devouring or treading down the corn. One of his
uncles having found him one day under a hedge, with a book in his hand,
and entirely absorbed in meditation, took it from him, and found that it
was a mathematical problem which so engrossed his attention. His
friends, therefore, wisely resolved to favor the bent of his genius, and
removed him from the farm to the school, to prepare for the university.
In the eighteenth year of his age, Newton was admitted into Trinity
College, Cambridge. He made rapid and extraordinary advances in the
mathematics, and soon afforded unequivocal presages of that greatness
which afterwards placed him at the head of the human intellect. In 1669,
at the age of twenty-seven, he became professor of mathematics at
Cambridge, a post which he occupied for many years afterwards. During
the four or five years previous to this he had, in fact, made most of
those great discoveries which have immortalized his name. We are at
present chiefly interested in one of these, namely, that of _universal
gravitation_; and let us see by what steps he was conducted to this
greatest of scientific discoveries.

In the year 1666, when Newton was about twenty-four years of age, the
plague was prevailing at Cambridge, and he retired into the country. One
day, while he sat in a garden, musing on the phenomena of Nature around
him, an apple chanced to fall to the ground. Reflecting on the
mysterious power that makes all bodies near the earth fall towards its
centre, and considering that this power remains unimpaired at
considerable heights above the earth, as on the tops of trees and
mountains, he asked himself,--"May not the same force extend its
influence to a great distance from the earth, even as far as the moon?
Indeed, may not this be the very reason, why the moon is drawn away
continually from the straight line in which every body tends to move,
and is thus made to circulate around the earth?" You will recollect that
it was mentioned, in my Letter which contained an account of the first
law of motion, that if a body is put in motion by any force, it will
always move forward in a straight line, unless some other force compels
it to turn aside from such a direction; and that, when we see a body
moving in a curve, as a circular orbit, we are authorized to conclude
that there is some force existing within the circle, which continually
draws the body away from the direction in which it tends to move.
Accordingly, it was a very natural suggestion, to one so well acquainted
with the laws of motion as Newton, that the moon should constantly bend
towards the earth, from a tendency to fall towards it, as any other
heavy body would do, if carried to such a distance from the earth.
Newton had already proved, that if such a power as gravity extends from
the earth to distant bodies, it must decrease, as the square of the
distance from the centre of the earth increases; that is, at double the
distance, it would be four times less; at ten times the distance, one
hundred times less; and so on. Now, it was known that the moon is about
sixty times as far from the centre of the earth as the surface of the
earth is from the centre, and consequently, the force of attraction at
the moon must be the square of sixty, or thirty-six hundred times less
than it is at the earth; so that a body at the distance of the moon
would fall towards the earth very slowly, only one thirty-six hundredth
part as far in a given time, as at the earth. Does the moon actually
fall towards the earth at this rate; or, what is the same thing, does
she depart at this rate continually from the straight line in which she
tends to move, and in which she would move, if no external force
diverted her from it? On making the calculation, such was found to be
the fact. Hence gravity, and no other force than gravity, acts upon the
moon, and compels her to revolve around the earth. By reasonings equally
conclusive, it was afterwards proved, that a similar force compels all
the planets to circulate around the sun; and now, we may ascend from the
contemplation of this force, as we have seen it exemplified in falling
bodies, to that of a universal power whose influence extends to all the
material creation. It is in this sense that we recognise the principle
of universal gravitation, the law of which may be thus enunciated; _all
bodies in the universe, whether great or small, attract each other, with
forces proportioned to their respective quantities of matter, and
inversely as the squares of their distances from each other_.

This law asserts, first, that attraction reigns throughout the material
world, affecting alike the smallest particle of matter and the greatest
body; secondly, that it acts upon every mass of matter, precisely in
proportion to its quantity; and, thirdly, that its intensity is
diminished as the square of the distance is increased.

Observation has fully confirmed the prevalence of this law throughout
the solar system; and recent discoveries among the fixed stars, to be
more fully detailed hereafter, indicate that the same law prevails
there. The law of universal gravitation is therefore held to be the
grand principle which governs all the celestial motions. Not only is it
consistent with all the observed motions of the heavenly bodies, even
the most irregular of those motions, but, when followed out into all its
consequences, it would be competent to assert that such irregularities
must take place, even if they had never been observed.

Newton first published the doctrine of universal gravitation in the
'Principia,' in 1687. The name implies that the work contains the
fundamental principles of natural philosophy and astronomy. Being
founded upon the immutable basis of mathematics, its conclusions must of
course be true and unalterable, and thenceforth we may regard the great
laws of the universe as traced to their remotest principle. The greatest
astronomers and mathematicians have since occupied themselves in
following out the plan which Newton began, by applying the principles of
universal gravitation to all the subordinate as well as to the grand
movements of the spheres. This great labor has been especially achieved
by La Place, a French mathematician of the highest eminence, in his
profound work, the 'Mecanique Celeste.' Of this work, our distinguished
countryman, Dr. Bowditch, has given a magnificent translation, and
accompanied it with a commentary, which both illustrates the original,
and adds a great amount of matter hardly less profound than that.

[Illustration Fig. 31.]

We have thus far taken the earth's orbit around the sun as a great
circle, such being its projection on the sphere constituting the
celestial ecliptic. The real path of the earth around the sun is
learned, as I before explained to you, by the apparent path of the sun
around the earth once a year. Now, when a body revolves about the earth
at a great distance from us, as is the case with the sun and moon, we
cannot certainly infer that it moves in a circle because it appears to
describe a circle on the face of the sky, for such might be the
appearance of its orbit, were it ever so irregular a curve. Thus, if E,
Fig. 31, represents the earth, and ACB, the irregular path of a body
revolving about it, since we should refer the body continually to some
place on the celestial sphere, XYZ, determined by lines drawn from the
eye to the concave sphere through the body, the body, while moving from
A to B through C, would appear to move from X to Z, through Y. Hence, we
must determine from other circumstances than the actual appearance, what
is the true figure of the orbit.

[Illustration Fig. 32.]

Were the earth's path a circle, having the sun in the centre, the sun
would always appear to be at the same distance from us; that is, the
radius of the orbit, or _radius vector_, (the name given to a line drawn
from the centre of the sun to the orbit of any planet,) would always be
of the same length. But the earth's distance from the sun is constantly
varying, which shows that its orbit is not a circle. We learn the true
figure of the orbit, by ascertaining the _relative distances_ of the
earth from the sun, at various periods of the year. These distances all
being laid down in a diagram, according to their respective lengths, the
extremities, on being connected, give us our first idea of the shape of
the orbit, which appears of an oval form, and at least resembles an
ellipse; and, on further trial, we find that it has the properties of an
ellipse. Thus, let E, Fig. 32, be the place of the earth, and _a_, _b_,
_c_, &c., successive positions of the sun; the _relative_ lengths of the
lines E _a_, E _b_, &c., being known, on connecting the points _a_,
_b_, _c_, &c., the resulting figure indicates the true figure of the
earth's orbit.

These relative distances are found in two different ways; first, _by
changes in the sun's apparent diameter_, and, secondly, _by variations
in his angular velocity_. The same object appears to us smaller in
proportion as it is more distant; and if we see a heavenly body varying
in size, at different times, we infer that it is at different distances
from us; that when largest, it is nearest to us, and when smallest,
furthest off. Now, when the sun's diameter is accurately measured by
instruments, it is found to vary from day to day; being, when greatest,
more than thirty-two minutes and a half, and when smallest, only
thirty-one minutes and a half,--differing, in all, about seventy-five
seconds. When the diameter is greatest, which happens in January, we
know that the sun is nearest to us; and when the diameter is least,
which occurs in July, we infer that the sun is at the greatest distance
from us. The point where the earth, or any planet, in its revolution, is
nearest the sun, is called its _perihelion_; the point where it is
furthest from the sun, its _aphelion_. Suppose, then, that, about the
first of January, when the diameter of the sun is greatest, we draw a
line, E _a_, Fig. 32, to represent it, and afterwards, every ten days,
draw other lines, E _b_, E _c_, &c.; increasing in the same ratio as the
apparent diameters of the sun decrease. These lines must be drawn at
such a distance from each other, that the triangles, E _a b_, E _b c_,
&c., shall be all equal to each other, for a reason that will be
explained hereafter. On connecting the extremities of these lines, we
shall obtain the figure of the earth's orbit.

Similar conclusions may be drawn from observations on the sun's _angular
velocity_. A body appears to move most rapidly when nearest to us.
Indeed, the apparent velocity increases rapidly, as it approaches us,
and as rapidly diminishes, when it recedes from us. If it comes twice as
near as before, it appears to move not merely twice as swiftly, but four
times as swiftly; if it comes ten times nearer, its apparent velocity
is one hundred times as great as before. We say, therefore, that the
velocity varies inversely as the square of the distance; for, as the
distance is diminished ten times, the velocity is increased the square
of ten; that is, one hundred times. Now, by noting the time it takes the
sun, from day to day, to cross the central wire of the
transit-instrument, we learn the comparative velocities with which it
moves at different times; and from these we derive the comparative
distances of the sun at the corresponding times; and laying down these
relative distances in a diagram, as before, we get our first notions of
the actual figure of the earth's orbit, or the path which it describes
in its annual revolution around the sun.

Having now learned the fact, that the earth moves around the sun, not in
a circular but in an elliptical orbit, you will desire to know by what
forces it is impelled, to make it describe this figure, with such
uniformity and constancy, from age to age. It is commonly said, that
gravity causes the earth and the planets to circulate around the sun;
and it is true that it is gravity which turns them aside from the
straight line in which, by the first law of motion, they tend to move,
and thus causes them to revolve around the sun. But what force is that
which gave to them this original impulse, and impressed upon them such a
tendency to move forward in a straight line? The name _projectile_ force
is given to it, because it is the same _as though_ the earth were
originally projected into space, when first created; and therefore its
motion is the result of two forces, the projectile force, which would
cause it to move forward in a straight line which is a tangent to its
orbit, and gravitation, which bends it towards the sun. But before you
can clearly understand the nature of this motion, and the action of the
two forces that produce it, I must explain to you a few elementary
principles upon which this and all the other planetary motions depend.

You have already learned, that when a body is acted on by two forces, in
different directions, it moves in the direction of neither, but in some
direction between them. If I throw a stone horizontally, the attraction
of the earth will continually draw it downward, out of the line of
direction in which it was thrown, and make it descend to the earth in a
curve. The particular form of the curve will depend on the velocity with
which it is thrown. It will always _begin_ to move in the line of
direction in which it is projected; but it will soon be turned from that
line towards the earth. It will, however, continue nearer to the line of
projection in proportion as the velocity of projection is greater. Thus,
let A C, Fig. 33, be perpendicular to the horizon, and A B parallel to
it, and let a stone be thrown from A, in the direction of A B. It will,
in every case, commence its motion in the line A B, which will therefore
be a tangent to the curve it describes; but, if it is thrown with a
small velocity, it will soon depart from the tangent, describing the
line A D; with a greater velocity, it will describe a curve nearer the
tangent, as A E; and with a still greater velocity, it will describe the
curve A F.

[Illustration Fig. 33.]

As an example of a body revolving in an orbit under the influence of two
forces, suppose a body placed at any point, P, Fig. 34, above the
surface of the earth, and let P A be the direction of the earth's
centre; that is, a line perpendicular to the horizon. If the body were
allowed to move, without receiving any impulse, it would descend to the
earth in the direction P A with an accelerated motion. But suppose that,
at the moment of its departure from P, it receives a blow in the
direction P B, which would carry it to B in the time the body would fall
from P to A; then, under the influence of both forces, it would descend
along the curve P D. If a stronger blow were given to it in the
direction P B, it would describe a larger curve, P E; or, finally, if
the impulse were sufficiently strong, it would circulate quite around
the earth, and return again to P, describing the circle P F G. With a
velocity of projection still greater, it would describe an ellipse, P I
K; and if the velocity be increased to a certain degree, the figure
becomes a parabola, L P M,--a curve which never returns into itself.

[Illustration Fig. 34.]

In Fig. 35, page 154, suppose the planet to have passed the point C, at
the aphelion, with so small a velocity, that the attraction of the sun
bends its path very much, and causes it immediately to begin to approach
towards the sun. The sun's attraction will increase its velocity, as it
moves through D, E, and F, for the sun's attractive force on the planet,
when at D, is acting in the direction D S; and, on account of the small
angle made between D E and D S, the force acting in the line D S helps
the planet forward in the path D E, and thus increases its velocity. In
like manner, the velocity of the planet will be continually increasing
as it passes through D, E, and F; and though the attractive force, on
account of the planet's nearness, is so much increased, and tends,
therefore, to make the orbit more curved, yet the velocity is also so
much increased, that the orbit is not more curved than before; for the
same increase of velocity, occasioned by the planet's approach to the
sun, produces a greater increase of centrifugal force, which carries it
off again. We may see, also, the reason why, when the planet has reached
the most distant parts of its orbit, it does not entirely fly off, and
never return to the sun; for, when the planet passes along H, K, A, the
sun's attraction retards the planet, just as gravity retards a ball
rolled up hill; and when it has reached C, its velocity is very small,
and the attraction to the centre of force causes a great deflection from
the tangent, sufficient to give its orbit a great curvature, and the
planet wheels about, returns to the sun, and goes over the same orbit
again. As the planet recedes from the sun, its centrifugal force
diminishes faster than the force of gravity, so that the latter finally
preponderates.

[Illustration Fig. 35.]

I shall conclude what I have to say at present, respecting the motion of
the earth around the sun, by adding a few words respecting the
precession of the equinoxes.

The _precession of the equinoxes_ is a slow but continual shifting of
the equinoctial points, from east to west. Suppose that we mark the
exact place in the heavens where, during the present year, the sun
crosses the equator, and that this point is close to a certain star;
next year, the sun will cross the equator a little way westward of that
star, and so every year, a little further westward, until, in a long
course of ages, the place of the equinox will occupy successively every
part of the ecliptic, until we come round to the same star again. As,
therefore, the sun revolving from west to east, in his apparent orbit,
comes round to the point where it left the equinox, it meets the equinox
before it reaches that point. The appearance is as though the equinox
_goes forward_ to meet the sun, and hence the phenomenon is called the
_precession_ of the equinoxes; and the fact is expressed by saying, that
the equinoxes retrograde on the ecliptic, until the line of the
equinoxes (a straight line drawn from one equinox to the other) makes a
complete revolution, from east to west. This is of course a retrograde
motion, since it is contrary to the order of the signs. The equator is
conceived as _sliding_ westward on the ecliptic, always preserving the
same inclination to it, as a ring, placed at a small angle with another
of nearly the same size which remains fixed, may be slid quite around
it, giving a corresponding motion to the two points of intersection. It
must be observed, however, that this mode of conceiving of the
precession of the equinoxes is purely imaginary, and is employed merely
for the convenience of representation.

The amount of precession annually is fifty seconds and one tenth;
whence, since there are thirty-six hundred seconds in a degree, and
three hundred and sixty degrees in the whole circumference of the
ecliptic, and consequently one million two hundred and ninety-six
thousand seconds, this sum, divided by fifty seconds and one tenth,
gives twenty-five thousand eight hundred and sixty-eight years for the
period of a complete revolution of the equinoxes.

Suppose we now fix to the centre of each of the two rings, before
mentioned, a wire representing its axis, one corresponding to the axis
of the ecliptic, the other to that of the equator, the extremity of each
being the pole of its circle. As the ring denoting the equator turns
round on the ecliptic, which, with its axis, remains fixed, it is easy
to conceive that the axis of the equator revolves around that of the
ecliptic, and the pole of the equator around the pole of the ecliptic,
and constantly at a distance equal to the inclination of the two
circles. To transfer our conceptions to the celestial sphere, we may
easily see that the axis of the diurnal sphere (that of the earth
produced) would not have its pole constantly in the same place among the
stars, but that this pole would perform a slow revolution around the
pole of the ecliptic, from east to west, completing the circuit in about
twenty-six thousand years. Hence the star which we now call the
pole-star has not always enjoyed that distinction, nor will it always
enjoy it, hereafter. When the earliest catalogues of the stars were
made, this star was twelve degrees from the pole. It is now one degree
twenty-four minutes, and will approach still nearer; or, to speak more
accurately, the pole will come still nearer to this star, after which it
will leave it, and successively pass by others. In about thirteen
thousand years, the bright star Lyra (which lies near the circle in
which the pole of the equator revolves about the pole of the ecliptic,
on the side opposite to the present pole-star) will be within five
degrees of the pole, and will constitute the pole-star. As Lyra now
passes near our zenith, you might suppose that the change of position of
the pole among the stars would be attended with a change of altitude of
the north pole above the horizon. This mistaken idea is one of the many
misapprehensions which result from the habit of considering the horizon
as a fixed circle in space. However the pole might shift its position in
space, we should still be at the same distance from it, and our horizon
would always reach the same distance beyond it.

The time occupied by the sun, in passing from the equinoctial point
round to the same point again, is called the _tropical year_. As the sun
does not perform a complete revolution in this interval, but falls short
of it fifty seconds and one tenth, the tropical year is shorter than the
sidereal by twenty minutes and twenty seconds, in mean solar time, this
being the time of describing an arc of fifty seconds and one tenth, in
the annual revolution.

The changes produced by the precession of the equinoxes, in the apparent
places of the circumpolar stars, have led to some interesting results in
_chronology_. In consequence of the retrograde motion of the equinoctial
points, the _signs_ of the ecliptic do not correspond, at present, to
the _constellations_ which bear the same names, but lie about one sign,
or thirty degrees, westward of them. Thus, that division of the ecliptic
which is called the sign Taurus lies in the constellation Aries, and the
sign Gemini, in the constellation Taurus. Undoubtedly, however, when the
ecliptic was thus first divided, and the divisions named, the several
constellations lay in the respective divisions which bear their names.

LETTER XV.

THE MOON.

"Soon as the evening shades prevail
The Moon takes up the wondrous tale,
And nightly to the listening earth
Repeats the story of her birth."--_Addison._

HAVING now learned so much of astronomy as relates to the earth and the
sun, and the mutual relations which exist between them, you are prepared
to enter with advantage upon the survey of the other bodies that compose
the solar system. This being done, we shall then have still before us
the boundless range of the fixed stars.

The moon, which next claims our notice, has been studied by astronomers
with greater attention than any other of the heavenly bodies, since her
comparative nearness to the earth brings her peculiarly within the range
of our telescopes, and her periodical changes and very irregular
motions, afford curious subjects, both for observation and speculation.
The mild light of the moon also invites our gaze, while her varying
aspects serve barbarous tribes, especially, for a kind of dial-plate
inscribed on the face of the sky, for weeks, and months, and times, and
seasons.

The moon is distant from the earth about two hundred and forty thousand
miles; or, more exactly, two hundred and thirty-eight thousand five
hundred and forty-five miles. Her angular or apparent diameter is about
half a degree, and her real diameter, two thousand one hundred and sixty
miles. She is a companion, or satellite, to the earth, revolving around
it every month, and accompanying us in our annual revolution around the
sun. Although her nearness to us makes her appear as a large and
conspicuous object in the heavens, yet, in comparison with most of the
other celestial bodies, she is in fact very small, being only one
forty-ninth part as large as the earth, and only about one seventy
millionth part as large as the sun.

The moon shines by light borrowed from the sun, being itself an opaque
body, like the earth. When the disk, or any portion of it, is
illuminated, we can plainly discern, even with the naked eye, varieties
of light and shade, indicating inequalities of surface which we imagine
to be land and water. I believe it is the common impression, that the
darker portions are land and the lighter portions water; but if either
part is water, it must be the darker regions. A smooth polished surface,
like water, would reflect the sun's light like a mirror. It would, like
a convex mirror, form a diminished image of the sun, but would not
itself appear luminous like an uneven surface, which multiplies the
light by numerous reflections within itself. Thus, from this cause, high
broken mountainous districts appear more luminous than extensive plains.

[Illustration Figures 36, 37. TELESCOPIC VIEWS OF THE MOON.]

By the aid of the telescope, we may see undoubted indications of
mountains and valleys. Indeed, with a good glass, we can discover the
most decisive evidence that the surface of the moon is exceedingly
varied,--one part ascending in lofty peaks, another clustering in
huge mountain groups, or long ranges, and another bearing all the marks
of deep caverns or valleys. You will not, indeed, at the first sight of
the moon through a telescope, recognise all these different objects. If
you look at the moon when half her disk is enlightened, (which is the
best time for seeing her varieties of surface,) you will, at the first
glance, observe a motley appearance, particularly along the line called
the _terminator_, which separates the enlightened from the unenlightened
part of the disk. (Fig. 37.) On one side of the terminator, within the
dark part of the disk, you will see illuminated points, and short,
crooked lines, like rude characters marked with chalk on a black ground.
On the other side of the terminator you will see a succession of little
circular groups, appearing like numerous bubbles of oil on the surface
of water. The further you carry your eye from the terminator, on the
same side of it, the more indistinctly formed these bubbles appear,
until towards the edge of the moon they assume quite a different aspect.

Some persons, when they look into a telescope for the first time, having
heard that mountains and valleys are to be seen, and discovering nothing
but these unmeaning figures, break off in disappointment, and have their
faith in these things rather diminished than increased. I would advise
you, therefore, before you take even your first view of the moon through
a telescope, to form as clear an idea as you can, how mountains, and
valleys, and caverns, situated at such a distance from the eye, ought to
look, and by what marks they may be recognised. Seize, if possible, the
most favorable period, (about the time of the first quarter,) and
previously learn from drawings and explanations, how to interpret every
thing you see.

What, then, ought to be the respective appearances of mountains,
valleys, and deep craters, or caverns, in the moon? The sun shines on
the moon in the same way as it shines on the earth; and let, us reflect,
then, upon the manner in which it strikes similar objects here. One
half the globe is constantly enlightened; and, by the revolution of the
earth on its axis, the terminator, or the line which separates the
enlightened from the unenlightened part of the earth, travels along from
east to west, over different places, as we see the moon's terminator
travel over her disk from new to full moon; although, in the case of the
earth, the motion is more rapid, and depends on a different cause. In
the morning, the sun's light first strikes upon the tops of the
mountains, and, if they are very high, they may be brightly illuminated
while it is yet night in the valleys below. By degrees, as the sun
rises, the circle of illumination travels down the mountain, until at
length it reaches the bottom of the valleys; and these in turn enjoy the
full light of day. Again, a mountain casts a shadow opposite to the sun,
which is very long when the sun first rises, and shortens continually as
the sun ascends, its length at a given time, however, being proportioned
to the height of the mountain; so that, if the shadow be still very long
when the sun is far above the horizon, we infer that the mountain is
very lofty. We may, moreover, form some judgment of the shape of a
mountain, by observing that of its shadow.

Now, the moon is so distant that we could not easily distinguish places
simply by their elevations, since they would be projected into the same
imaginary plane which constitutes the apparent disk of the moon; but the
foregoing considerations would enable us to infer their existence. Thus,
when you view the moon at any time within her first quarter, but better
near the end of that period, you will observe, on the side of the
terminator within the dark part of the disk, the tops of mountains which
the light of the sun is just striking, as the morning sun strikes the
tops of mountains on the earth. These you will recognise by those white
specks and little crooked lines, before mentioned, as is represented in
Fig. 37. These bright points and lines you will see altering their
figure, every hour, as they come more and more into the sun's light;
and, mean-while, other bright points, very minute at first, will start
into view, which also in turn grow larger as the terminator approaches
them, until they fall into the enlightened part of the disk. As they
fall further and further within this part, you will have additional
proofs that they are mountains, from the shadows which they cast on the
plain, always in a direction opposite to the sun. The mountain itself
may entirely disappear, or become confounded with the other enlightened
portions of the surface; but its position and its shape may still be
recognised by the dark line which it projects on the plane. This line
will correspond in shape to that of the mountain, presenting at one time
a long serpentine stripe of black, denoting that the mountain is a
continued range; at another time exhibiting a conical figure tapering to
a point, or a series of such sharp points; or a serrated, uneven
termination, indicating, in each case respectively, a conical mountain,
or a group of peaks, or a range with lofty cliffs. All these appearances
will indeed be seen in miniature; but a little familiarity with them
will enable you to give them, in imagination, their proper dimensions,
as you give to the pictures of known animals their due sizes, although
drawn on a scale far below that of real life.

In the next place, let us see how valleys and deep craters in the moon
might be expected to appear. We could not expect to see depressions any
more than elevations, since both would alike be projected on the same
imaginary disk. But we may recognise such depressions, from the manner
in which the light of the sun shines into them. When we hold a china
tea-cup at some distance from a candle, in the night, the candle being
elevated but little above the level of the top of the cup, a luminous
crescent will be formed on the side of the cup opposite to the candle,
while the side next to the candle will be covered by a deep shadow. As
we gradually elevate the candle, the crescent enlarges and travels down
the side of the cup, until finally the whole interior becomes
illuminated. We observe similar appearances in the moon, which we
recognise as deep depressions. They are those circular spots near the
terminator before spoken of, which look like bubbles of oil floating on
water. They are nothing else than circular craters or deep valleys. When
they are so situated that the light of the sun is just beginning to
shine into them, you may see, as in the tea-cup, a luminous crescent
around the side furthest from the sun, while a deep black shadow is cast
on the side next to the sun. As the cavity is turned more and more
towards the light, the crescent enlarges, until at length the whole
interior is illuminated. If the tea-cup be placed on a table, and a
candle be held at some distance from it, nearly on a level with the top,
but a little above it, the cup itself will cast a shadow on the table,
like any other elevated object. In like manner, many of these circular
spots on the moon cast deep shadows behind them, indicating that the
tops of the craters are elevated far above the general level of the
moon. The regularity of some of these circular spots is very remarkable.
The circle, in some instances, appears as well formed as could be
described by a pair of compasses, while in the centre there not
unfrequently is seen a conical mountain casting its pointed shadow on
the bottom of the crater. I hope you will enjoy repeated opportunities
to view the moon through a telescope. Allow me to recommend to you, not
to rest satisfied with a hasty or even with a single view, but to verify
the preceding remarks by repeated and careful inspection of the lunar
disk, at different ages of the moon.

The various places on the moon's disk have received appropriate names.
The dusky regions being formerly supposed to be seas, were named
accordingly; and other remarkable places have each two names, one
derived from some well-known spot on the earth, and the other from some
distinguished personage. Thus, the same bright spot on the surface of
the moon is called _Mount Sinai_ or _Tycho_, and another, _Mount Etna_
or _Copernicus_. The names of individuals, however, are more used than
the others. The diagram, Fig. 36, (see page 159,) represents rudely, the
telescopic appearance of the full moon. The reality is far more
beautiful. A few of the most remarkable points have the following names
corresponding to the numbers and letters on the map.

1. Tycho, 6. Eratosthenes,
2. Kepler, 7. Plato,
3. Copernicus, 8. Archimedes,
4. Aristarchus, 9. Eudoxus,
5. Helicon, 10. Aristotle.

A. Mare Humorum, _Sea of Humors_,
B. Mare Nubium, _Sea of Clouds_,
C. Mare Imbrium, _Sea of Rains_,
D. Mare Nectaris, _Sea of Nectar_,
E. Mare Tranquillitatis, _Sea of Tranquillity_,
F. Mare Serenitatis, _Sea of Serenity_,
G. Mare Fecunditatis, _Sea of Plenty_,
H. Mare Crisium, _Crisian Sea_.

The heights of the lunar mountains, and the depths of the valleys, can
be estimated with a considerable degree of accuracy. Some of the
mountains are as high as five miles, and the valleys, in some instances,
are four miles deep. Hence it is inferred, that the surface of the moon
is more broken and irregular than that of the earth, its mountains being
higher and its valleys deeper, in proportion to its magnitude, than
those of the earth.

The varieties of surface in the moon, as seen by the aid of large
telescopes, have been well described by Dr. Dick, in his 'Celestial
Scenery,' and I cannot give you a better idea of them, than to add a few
extracts from his work. The lunar mountains in general exhibit an
arrangement and an aspect very different from the mountain scenery of
our globe. They may be arranged under the four following varieties:

First, _insulated mountains_, which rise from plains nearly level,
shaped like a sugar loaf, which may be supposed to present an appearance
somewhat similar to Mount Etna, or the Peak of Teneriffe. The shadows
of these mountains, in certain phases of the moon, are as distinctly
perceived as the shadow of an upright staff, when placed opposite to the
sun; and these heights can be calculated from the length of their
shadows. Some of these mountains being elevated in the midst of
extensive plains, would present to a spectator on their summits
magnificent views of the surrounding regions.

Secondly, _mountain ranges_, extending in length two or three hundred
miles. These ranges bear a distant resemblance to our Alps, Apennines,
and Andes; but they are much less in extent. Some of them appear very
rugged and precipitous; and the highest ranges are in some places more
than four miles in perpendicular altitude. In some instances, they are
nearly in a straight line from northeast to southwest, as in the range
called the _Apennines_; in other cases, they assume the form of a
semicircle, or crescent.

Thirdly, _circular ranges_, which appear on almost every part of the
moon's surface, particularly in its southern regions. This is one grand
peculiarity of the lunar ranges, to which we have nothing similar on the
earth. A plain, and sometimes a large cavity, is surrounded with a
circular ridge of mountains, which encompasses it like a mighty rampart.
These annular ridges and plains are of all dimensions, from a mile to
forty or fifty miles in diameter, and are to be seen in great numbers
over every region of the moon's surface; they are most conspicuous,
however, near the upper and lower limbs, about the time of the half
moon.

The mountains which form these circular ridges are of different
elevations, from one fifth of a mile to three miles and a half, and
their shadows cover one half of the plain at the base. These plains are
sometimes on a level with the general surface of the moon, and in other
cases they are sunk a mile or more below the level of the ground which
surrounds the exterior circle of the mountains.

Fourthly, _central mountains_, or those which are placed in the middle
of circular plains. In many of the plains and cavities surrounded by
circular ranges of mountains there stands a single insulated mountain,
which rises from the centre of the plain, and whose shadow sometimes
extends, in the form of a pyramid, half across the plain to the opposite
ridges. These central mountains are generally from half a mile to a mile
and a half in perpendicular altitude. In some instances, they have two,
and sometimes three, different tops, whose shadows can be easily
distinguished from each other. Sometimes they are situated towards one
side of the plain, or cavity; but in the great majority of instances
their position is nearly or exactly central. The lengths of their bases
vary from five to about fifteen or sixteen miles.

The _lunar caverns_ form a very peculiar and prominent feature of the
moon's surface, and are to be seen throughout almost every region, but
are most numerous in the southwest part of the moon. Nearly a hundred of
them, great and small, may be distinguished in that quarter. They are
all nearly of a circular shape, and appear like a very shallow egg-cup.
The smaller cavities appear, within, almost like a hollow cone, with the
sides tapering towards the centre; but the larger ones have, for the
most part, flat bottoms, from the centre of which there frequently rises
a small, steep, conical hill, which gives them a resemblance to the
circular ridges and central mountains before described. In some
instances, their margins are level with the general surface of the moon;
but, in most cases, they are encircled with a high annular ridge of
mountains, marked with lofty peaks. Some of the larger of these cavities
contain smaller cavities of the same kind and form, particularly in
their sides. The mountainous ridges which surround these cavities
reflect the greatest quantity of light; and hence that region of the
moon in which they abound appears brighter than any other. From their
lying in every possible direction, they appear, at and near the time of
full moon, like a number of brilliant streaks, or radiations. These
radiations appear to converge towards a large brilliant spot,
surrounded by a faint shade, near the lower part of the moon, which is
named Tycho,--a spot easily distinguished even by a small telescope. The
spots named Kepler and Copernicus are each composed of a central spot
with luminous radiations.[8]

The broken surface and apparent geological structure of the moon has
suggested the opinion, that the moon has been subject to powerful
_volcanic_ action. This opinion receives support from certain actual
appearances of volcanic fires, which have at different times been
observed. In a total eclipse of the sun, the moon comes directly between
us and that luminary, and presents her dark side towards us under
circumstances very favorable for observation. At such times, several
astronomers, at different periods, have noticed bright spots, which they
took to be volcanoes. It must evidently require a large fire to be
visible at all, at such a distance; and even a burning spark, or point
but just visible in a large telescope, might be in fact a volcano raging
like Etna or Vesuvius. Still, as fires might be supposed to exist in the
moon from different causes, we should require some marks peculiar to
volcanic fires, to assure us that such was their origin in a given case.
Dr. Herschel examined this point with great attention, and with better
means of observation than any of his predecessors enjoyed, and fully
embraced the opinion that what he saw were volcanoes. In April, 1787, he
records his observations as follows: "I perceive three volcanoes in
different places in the dark part of the moon. Two of them are already
nearly extinct, or otherwise in a state of going to break out; the third
shows an eruption of fire or luminous matter." On the next night, he
says: "The volcano burns with greater violence than last night; its
diameter cannot be less than three seconds; and hence the shining or
burning matter must be above three miles in diameter. The appearance
resembles a small piece of burning charcoal, when it is covered with a
very thin coat of white ashes; and it has a degree of brightness about
as strong as that with which such a coal would be seen to glow in faint
daylight." That these were really volcanic fires, he considered further
evident from the fact, that where a fire, supposed to have been
volcanic, had been burning, there was seen, after its extinction, an
accumulation of matter, such as would arise from the production of a
great quantity of lava, sufficient to form a mountain.

It is probable that the moon has an _atmosphere_, although it is
difficult to obtain perfectly satisfactory evidence of its existence;
for granting the existence of an atmosphere bearing the same proportion
to that planet as our atmosphere bears to the earth, its dimensions and
its density would be so small, that we could detect its presence only by
the most refined observations. As our twilight is owing to the agency of
our atmosphere, so, could we discern any appearance of twilight in the
moon, we should regard that fact as indicating that she is surrounded by
an atmosphere. Or, when the moon covers the sun in a solar eclipse,
could we see around her circumference a faint luminous ring, indicating
that the sunlight shone through an aerial medium, we might likewise
infer the existence of such a medium. Such a faint ring of light has
sometimes, as is supposed, been observed. Schroeter, a German
astronomer, distinguished for the acuteness of his vision and his powers
of observation in general, was very confident of having obtained, from
different sources, clear evidence of a lunar atmosphere. He concluded,
that the inferior or more dense part of the moon's atmosphere is not
more than fifteen hundred feet high, and that the entire height, at
least to the limit where it would be too rare to produce any of the
phenomena which are relied on as proofs of its existence, is not more
than a mile.

It has been a question, much agitated among astronomers, whether there
is _water_ in the moon. Analogy strongly inclines us to reply in the
affirmative. But the analogy between the earth and the moon, as derived
from all the particulars in which we can compare the two bodies, is too
feeble to warrant such a conclusion, and we must have recourse to other
evidence, before we can decide the point. In the first place, then,
there is no positive evidence in favor of the existence of water in the
moon. Those extensive level regions, before spoken of, and denominated
seas in the geography of this planet, have no other signs of being
water, except that they are level and dark. But both these particulars
would characterize an earthly plain, like the deserts of Arabia and
Africa. In the second place, were those dark regions composed of water,
the terminator would be entirely smooth where it passed over these
oceans or seas. It is indeed indented by few inequalities, compared with
those which it exhibits where it passes over the mountainous regions;
but still, the inequalities are too considerable to permit the
conclusion, that these level spots are such perfect levels as water
would form. They do not appear to be more perfect levels than many plain
countries on the globe. The deep caverns, moreover, seen in those dusky
spots which were supposed to be seas, are unfavorable to the supposition
that those regions are covered by water. In the third place, the face of
the moon, when illuminated by the sun and not obscured by the state of
our own atmosphere, is always serene, and therefore free from clouds.
Clouds are objects of great extent; they frequently intercept light,
like solid bodies; and did they exist about the moon, we should
certainly see them, and should lose sight of certain parts of the lunar
disk which they covered. But neither position is true; we neither see
any clouds about the moon, with our best telescopes, nor do we, by the
intervention of clouds, ever lose sight of any portion of the moon when
our own atmosphere is clear. But the want of clouds in the lunar
atmosphere almost necessarily implies the absence of water in the moon.
This planet is at the same distance from the sun as our own, and has, in
this respect, an equal opportunity to feel the influence of his rays.
Its days are also twenty-seven times as long as ours, a circumstance
which would augment the solar heat. When the pressure of the atmosphere
is diminished on the surface of water, its tendency to pass into the
state of vapor is increased. Were the whole pressure of the atmosphere
removed from the surface of a lake, in a Summer's day, when the
temperature was no higher than seventy-two degrees, the water would
begin to boil. Now it is well ascertained, that if there be any
atmosphere about the moon, it is much lighter than ours, and presses on
the surface of that body with a proportionally small force. This
circumstance, therefore, would conspire with the other causes mentioned,
to convert all the water of the moon into vapor, if we could suppose it
to have existed at any given time.

But those, who are anxious to furnish the moon and other planets with
all the accommodations which they find in our own, have a subterfuge in
readiness, to which they invariably resort in all cases like the
foregoing. "There may be," say they, "some means, unknown to us,
provided for retaining water on the surface of the moon, and for
preventing its being wasted by evaporation: perhaps it remains unaltered
in quantity, imparting to the lunar regions perpetual verdure and
fertility." To this I reply, that the bare possibility of a thing is but
slight evidence of its reality; nor is such a condition possible, except
by miracle. If they grant that the laws of Nature are the same in the
moon as in the earth, then, according to the foregoing reasoning, there
cannot be water in the moon; but if they say that the laws of Nature are
not the same there as here, then we cannot reason at all respecting
them. One who resorts to a subterfuge of this kind ruins his own cause.
He argues the existence of water in the moon, from the analogy of that
planet to this. But if the laws of Nature are not the same there as
here, what becomes of his analogy? A liquid substance which would not
evaporate by such a degree of solar heat as falls on the moon, which
would not evaporate the faster, in consequence of the diminished
atmospheric pressure which prevails there, could not be water, for it
would not have the properties of water, and things are known by their
properties. Whenever we desert the cardinal principle of the Newtonian
philosophy,--that the laws of Nature are uniform throughout all her
realms,--we wander in a labyrinth; all analogies are made void; all
physical reasonings cease; and imaginary possibilities or direct
miracles take the place of legitimate natural causes.

On the supposition that the moon is inhabited, the question has often
been raised, whether we may hope that our telescopes will ever be so
much improved, and our other means of observation so much augmented,
that we shall be able to discover either the lunar inhabitants or any of
their works.

The improbability of our ever identifying _artificial structures_ in the
moon may be inferred from the fact, that a space a mile in diameter is
the least space that could be distinctly seen. Extensive works of art,
as large cities, or the clearing up of large tracts of country for
settlement or tillage, might indeed afford some varieties of surface;
but they would be merely varieties of light and shade, and the
individual objects that occasioned them would probably never be
recognised by their distinctive characters. Thus, a building equal to
the great pyramid of Egypt, which covers a space less than the fifth of
a mile in diameter, would not be distinguished by its figure; indeed, it
would be a mere point. Still less is it probable that we shall ever
discover any inhabitants in the moon. Were we to view the moon with a
telescope that magnifies ten thousand times, it would bring the moon
apparently ten thousand times nearer, and present it to the eye like a
body twenty-four miles off. But even this is a distance too great for us
to see the works of man with distinctness. Moreover, from the nature of
the telescope itself, we can never hope to apply a magnifying power so
high as that here supposed. As I explained to you, when speaking of the
telescope, whenever we increase the magnifying power of this instrument
we diminish its field of view, so that with very high magnifiers we can
see nothing but a point, such as a fixed star. We at the same time,
also, magnify the vapors and smoke of the atmosphere, and all the
imperfections of the medium, which greatly obscures the object, and
prevents our seeing it distinctly. Hence it is generally most
satisfactory to view the moon with low powers, which afford a large
field of view and give a clear light. With Clark's telescope, belonging
to Yale College, we seldom gain any thing by applying to the moon a
higher power than one hundred and eighty, although the instrument admits
of magnifiers as high as four hundred and fifty.

Some writers, however, suppose that possibly we may trace indications of
lunar inhabitants in their works, and that they may in like manner
recognise the existence of the inhabitants of our planet. An author, who
has reflected much on subjects of this kind, reasons as follows: "A
navigator who approaches within a certain distance of a small island,
although he perceives no human being upon it, can judge with certainty
that it is inhabited, if he perceives human habitations, villages,
corn-fields, or other traces of cultivation. In like manner, if we could
perceive changes or operations in the moon, which could be traced to the
agency of intelligent beings, we should then obtain satisfactory
evidence that such beings exist on that planet; and it is thought
possible that such operations may be traced. A telescope which magnifies
twelve hundred times will enable us to perceive, as a visible point on
the surface of the moon, an object whose diameter is only about three
hundred feet. Such an object is not larger than many of our public
edifices; and therefore, were any such edifices rearing in the moon, or
were a town or city extending its boundaries, or were operations of this
description carrying on, in a district where no such edifices had
previously been erected, such objects and operations might probably be
detected by a minute inspection. Were a multitude of living creatures
moving from place to place, in a body, or were they even encamping in an
extensive plain, like a large army, or like a tribe of Arabs in the
desert, and afterwards removing, it is possible such changes might be
traced by the difference of shade or color, which such movements would
produce. In order to detect such minute objects and operations, it would
be requisite that the surface of the moon should be distributed among at
least a hundred astronomers, each having a spot or two allotted to him,
as the object of his more particular investigation, and that the
observations be continued for a period of at least thirty or forty
years, during which time certain changes would probably be perceived,
arising either from physical causes, or from the operations of living
agents."[9]

FOOTNOTE:

[8] Dick's 'Celestial Scenery,' Chapter IV

LETTER XVI.

THE MOON.--PHASES.--HARVEST MOON.--LIBRATIONS.

"First to the neighboring Moon this mighty key
Of nature he applied. Behold! it turned
The secret wards, it opened wide the course
And various aspects of the queen of night:
Whether she wanes into a scanty orb,
Or, waxing broad, with her pale shadowy light,
In a soft deluge overflows the sky."--_Thomson's Elegy._

LET us now inquire into the revolutions of the moon around the earth,
and the various changes she undergoes every month, called her _phases_,
which depend on the different positions she assumes, with respect to the
earth and the sun, in the course of her revolution.

The moon revolves about the earth from west to east. Her apparent orbit,
as traced out on the face of the sky, is a great circle; but this fact
would not certainly prove that the orbit is really a circle, since, if
it were an ellipse, or even a more irregular curve, the projection of
it on the face of the sky would be a circle, as explained to you before.
(See page 148.) The moon is comparatively so near to the earth, that her
apparent movements are very rapid, so that, by attentively watching her
progress in a clear night, we may see her move from star to star,
changing her place perceptibly, every few hours. The interval during
which she goes through the entire circuit of the heavens, from any star
until she comes round to the same star again, is called a _sidereal
month_, and consists of about twenty-seven and one fourth days. The time
which intervenes between one new moon and another is called a _synodical
month_, and consists of nearly twenty-nine and a half days. A new moon
occurs when the sun and moon meet in the same part of the heavens; but
the sun as well as the moon is apparently travelling eastward, and
nearly at the rate of one degree a day, and consequently, during the
twenty-seven days while the moon has been going round the earth, the sun
has been going forward about the same number of degrees in the same
direction. Hence, when the moon comes round to the part of the heavens
where she passed the sun last, she does not find him there, but must go
on more than two days, before she comes up with him again.

The moon does not pursue precisely the same track around the earth as
the sun does, in his apparent annual motion, though she never deviates
far from that track. The inclination of her orbit to the ecliptic is
only about five degrees, and of course the moon is never seen further
from the ecliptic than about that distance, and she is commonly much
nearer to the ecliptic than five degrees. We may therefore see nearly
what is the situation of the ecliptic in our evening sky at any
particular time of year, just by watching the path which the moon
pursues, from night to night, from new to full moon.

The two points where the moon's orbit crosses the ecliptic are called
her _nodes_. They are the intersections of the lunar and solar orbits,
as the equinoxes are the intersections of the equinoctial and ecliptic,
and, like the latter, are one hundred and eighty degrees apart.

The changes of the moon, commonly called her _phases_, arise from
different portions of her illuminated side being turned towards the
earth at different times. When the moon is first seen after the setting
sun, her form is that of a bright crescent, on the side of the disk next
to the sun, while the other portions of the disk shine with a feeble
light, reflected to the moon from the earth. Every night, we observe the
moon to be further and further eastward of the sun, until, when she has
reached an elongation from the sun of ninety degrees, half her visible
disk is enlightened, and she is said to be in her _first quarter_. The
terminator, or line which separates the illuminated from the dark part
of the moon, is convex towards the sun from the new to the first
quarter, and the moon is said to be _horned_. The extremities of the
crescent are called _cusps_. At the first quarter, the terminator
becomes a straight line, coinciding with the diameter of the disk; but
after passing this point, the terminator becomes concave towards the
sun, bounding that side of the moon by an elliptical curve, when the
moon is said to be _gibbous_. When the moon arrives at the distance of
one hundred and eighty degrees from the sun, the entire circle is
illuminated, and the moon is _full_. She is then _in opposition_ to the
sun, rising about the time the sun sets. For a week after the full, the
moon appears gibbous again, until, having arrived within ninety degrees
of the sun, she resumes the same form as at the first quarter, being
then at her _third quarter_. From this time until new moon, she exhibits
again the form of a crescent before the rising sun, until, approaching
her _conjunction_ with the sun, her narrow thread of light is lost in
the solar blaze; and finally, at the moment of passing the sun, the dark
side is wholly turned towards us, and for some time we lose sight of the
moon.

By inspecting Fig. 38, (where T represents the earth, A, B, C, &c., the
moon in her orbit, and _a_, _b_, _c_, &c., her phases, as seen in the
heavens,) we shall easily see how all these changes occur.

[Illustration Fig. 38.]

You have doubtless observed, that the moon appears much further in the
south at one time than at another, when of the same age. This is owing
to the fact that the ecliptic, and of course the moon's path, which is
always very near it, is differently situated with respect to the
_horizon_, at a given time of night, at different seasons of the year.
This you will see at once, by turning to an artificial globe, and
observing how the ecliptic stands with respect to the horizon, at
different periods of the revolution. Thus, if we place the two
equinoctial points in the eastern and western horizon, Libra being in
the west, it will represent the position of the ecliptic at sunset in
the month of September, when the sun is crossing the equator; and at
that season of the year, the moon's path through our evening sky, one
evening after another, from new to full, will be nearly along the same
route, crossing the meridian nearly at right angles. But if we place the
Winter solstice, or first degree of Capricorn, in the western horizon,
and the first degree of Cancer in the eastern, then the position of the
ecliptic will be very oblique to the meridian, the Winter solstice being
very far in the southwest, and the Summer solstice very far in the
northeast; and the course of the moon from new to full will be nearly
along this track. Keeping these things in mind, we may easily see why
the moon runs sometimes high and sometimes low. Recollect, also, that
the new moon is always in the same part of the heavens with the sun, and
that the full moon is in the opposite part of the heavens from the sun.
Now, when the sun is at the Winter solstice, it sets far in the
southwest, and accordingly the new moon runs very low; but the full
moon, being in the opposite tropic, which rises far in the northeast,
runs very high, as is known to be the case in mid-winter. But now take
the position of the ecliptic in mid-summer. Then, at sunset, the tropic
of Cancer is in the northwest, and the tropic of Capricorn in the
southeast; consequently, the new moons run high and the full moons low.

It is a natural consequence of this arrangement, to render the moon's
light the most beneficial to us, by giving it to us in greatest
abundance, when we have least of the sun's light, and giving it to us
most sparingly, when the sun's light is greatest. Thus, during the long
nights of Winter, the full moon runs high, and continues a very long
time above the horizon; while in mid-summer, the full moon runs low, and
is above the horizon for a much shorter period. This arrangement
operates very favorably to the inhabitants of the polar regions. At the
season when the sun is absent, and they have constant night, then the
moon, during the second and third quarters, embracing the season of full
moon, is continually above the horizon, compensating in no small degree
for the absence of the sun; while, during the Summer months, when the
sun is constantly above the horizon, and the light of the moon is not
needed, then she is above the horizon during the first and last
quarters, when her light is least, affording at that time her greatest
light to the inhabitants of the other hemisphere, from whom the sun is
withdrawn.

About the time of the Autumnal equinox, the moon, when near her full,
rises about sunset a number of nights in succession. This occasions a
remarkable number of brilliant moonlight evenings; and as this is, in
England, the period of harvest, the phenomenon is called the _harvest
moon_. Its return is celebrated, particularly among the peasantry, by
festive dances, and kept as a festival, called the _harvest home_,--an
occasion often alluded to by the British poets. Thus Henry Kirke White:

"Moon of harvest, herald mild
Of plenty, rustic labor's child,
Hail, O hail! I greet thy beam,
As soft it trembles o'er the stream,
And gilds the straw-thatch'd hamlet wide,
Where innocence and peace reside;
'Tis thou that glad'st with joy the rustic throng,
Promptest the tripping dance, th' exhilarating song."

To understand the reason of the harvest moon, we will, as before,
consider the moon's orbit as coinciding with the ecliptic, because we
may then take the ecliptic, as it is drawn on the artificial globe, to
represent that orbit. We will also bear in mind, (what has been fully
illustrated under the last head,) that, since the ecliptic cuts the
meridian obliquely, while all the circles of diurnal revolution cut it
perpendicularly, different portions of the ecliptic will cut the horizon
at different angles. Thus, when the equinoxes are in the horizon, the
ecliptic makes a very small angle with the horizon; whereas, when the
solstitial points are in the horizon, the same angle is far greater. In
the former case, a body moving eastward in the ecliptic, and being at
the eastern horizon at sunset, would descend but a little way below the
horizon in moving over many degrees of the ecliptic. Now, this is just
the case of the moon at the time of the harvest home, about the time of
the Autumnal equinox. The sun being then in Libra, and the moon, when
full, being of course opposite to the sun, or in Aries; and moving
eastward, in or near the ecliptic, at the rate of about thirteen degrees
per day, would descend but a small distance below the horizon for five
or six days in succession; that is for two or three days before, and the
same number of days after, the full; and would consequently rise during
all these evenings nearly at the same time, namely, a little before, or
a little after, sunset, so as to afford a remarkable succession of fine
moonlight evenings.

The moon _turns on her axis_ in the same time in which she revolves
around the earth. This is known by the moon's always keeping nearly the
same face towards us, as is indicated by the telescope, which could not
happen unless her revolution on her axis kept pace with her motion in
her orbit. Take an apple, to represent the moon; stick a knittingneedle
through it, in the direction of the stem, to represent the axis, in
which case the two eyes of the apple will aptly represent the poles.
Through the poles cut a line around the apple, dividing it into two
hemispheres, and mark them, so as to be readily distinguished from each
other. Now place a candle on the table, to represent the earth, and
holding the apple by the knittingneedle, carry it round the candle, and
you will see that, unless you make the apple turn round on the axis as
you carry it about the candle, it will present different sides towards
the candle; and that, in order to make it always present the same side,
it will be necessary to make it revolve exactly once on its axis, while
it is going round the circle,--the revolution on its axis always keeping
exact pace with the motion in its orbit. The same thing will be
observed, if you walk around a tree, always keeping your face towards
the tree. If you have your face towards the tree when you set out, and
walk round without turning, when you have reached the opposite side of
the tree, your back will be towards it, and you will find that, in order
to keep your face constantly towards the tree, it will be necessary to
turn yourself round on your heel at the same rate as you go forward.

Since, however, the motion of the moon on its axis is uniform, while the
motion in its orbit is unequal, the moon does in fact reveal to us a
little sometimes of one side and sometimes of the other. Thus if, while
carrying the apple round the candle, you carry it forward a little
faster than the rate at which it turns on its axis, a portion of the
hemisphere usually out of sight is brought into view on one side; or if
the apple is moved forward slower than it is turned on its axis, a
portion of the same hemisphere comes into view on the other side. These
appearances are called the moon's _librations in longitude_. The moon
has also a _libration in latitude_;--so called, because in one part of
her revolution more of the region around one of the poles comes into
view, and, in another part of the revolution, more of the region around
the other pole, which gives the appearance of a tilting motion to the
moon's axis. This is owing to the fact, that the moon's axis is inclined
to the plane of her orbit. If, in the experiment with the apple, you
hold the knittingneedle parallel to the candle, (in which case the axis
will be perpendicular to the plane of revolution,) the candle will shine
upon both poles during the whole circuit, and an eye situated where the
candle is would constantly see both poles; but now incline the needle
towards the plane of revolution, and carry it round, always keeping it
parallel to itself, and you will observe that the two poles will be
alternately in and out of sight.

The moon exhibits another appearance of this kind, called her _diurnal
libration_, depending on the daily rotation of the spectator. She turns
the same face towards the _centre_ of the earth only, whereas we view
her from the surface. When she is on the meridian, we view her disk
nearly as though we viewed it from the centre of the earth, and hence,
in this situation, it is subject to little change; but when she is near
the horizon, our circle of vision takes in more of the upper limb than
would be presented to a spectator at the centre of the earth. Hence,
from this cause, we see a portion of one limb while the moon is rising,
which is gradually lost sight of, and we see a portion of the opposite
limb, as the moon declines to the west. You will remark that neither of
the foregoing changes implies any actual motion in the moon, but that
each arises from a change of position in the spectator. Since the
succession of day and night depends on the revolution of a planet on its
own axis, and it takes the moon twenty-nine and a half days to perform
this revolution, so that the sun shall go from the meridian of any place
and return to the same meridian again, of course the lunar day occupies
this long period. So protracted an exposure to the sun's rays,
especially in the equatorial regions of the moon, must occasion an
excessive accumulation of heat; and so long an absence of the sun must
occasion a corresponding degree of cold. A spectator on the side of the
moon which is opposite to us would never see the earth, but one on the
side next to us would see the earth constantly in his firmament,
undergoing a gradual succession of changes, corresponding to those which
the moon exhibits to the earth, but in the reverse order. Thus, when it
is full moon to us, the earth, as seen from the moon, is then in
conjunction with the sun, and of course presents her dark side to the
moon.

Soon after this, an inhabitant of the moon would see a crescent,
resembling our new moon, which would in like manner increase and go
through all the changes, from new to full, and from full to new, as we
see them in the moon. There are, however, in the two cases, several
striking points of difference. In the first place, instead of
twenty-nine and a half days, all these changes occur in one lunar day
and night. During the first and last quarters, the changes would occur
in the day-time; but during the second and third quarters, during the
night. By this arrangement, the lunarians would enjoy the greatest
possible benefit from the light afforded by the earth, since in the half
of her revolution where she appears to them as full, she would be
present while the sun was absent, and would afford her least light while
the sun was present. In the second place, the earth would appear
thirteen times as large to a spectator on the moon as the moon appears
to us, and would afford nearly the same proportion of light, so that
their long nights must be continually cheered by an extraordinary degree
of light derived from this source; and if the full moon is hailed by our
poets as "refulgent lamp of night,"[10] with how much more reason might
a lunarian exult thus, in view of the splendid orb that adorns his
nocturnal sky! In the third place, the earth, as viewed from any
particular place on the moon, would occupy invariably the same part of
the heavens. For while the rotation of the moon on her axis from west to
east would appear to make the earth (as the moon does to us) revolve
from east to west, the corresponding progress of the moon in her orbit
would make the earth appear to revolve from west to east; and as these
two motions are equal, their united effect would be to keep the moon
apparently stationary in the sky. Thus, a spectator at E, Fig. 38, page
175, in the middle of the disk that is turned towards the earth, would
have the earth constantly on his meridian, and at E, the conjunction of
the earth and sun would occur at mid-day; but when the moon arrived at
G, the same place would be on the margin of the circle of illumination,
and will have the sun in the horizon; but the earth would still be on
his meridian and in quadrature. In like manner, a place situated on the
margin of the circle of illumination, when the moon is at E, would have
the earth in the horizon; and the same place would always see the earth
in the horizon, except the slight variations that would occur from the
librations of the moon. In the fourth place, the earth would present to
a spectator on the moon none of that uniformity of aspect which the moon
presents to us, but would exhibit an appearance exceedingly diversified.
The comparatively rapid rotation of the earth, repeated fifteen times
during a lunar night, would present, in rapid succession, a view of our
seas, oceans, continents, and mountains, all diversified by our clouds,
storms, and volcanoes.

FOOTNOTES:

[9] Dick's 'Celestial Scenery.'

[10]

"As when the moon, refulgent lamp of night,
O'er heaven's clear azure sheds her sacred light,
When not a breath disturbs the deep serene,
And not a cloud o'ercasts the solemn scene,
Around her throne the vivid planets roll,
And stars unnumbered gild the glowing pole;
O'er the dark trees a yellower verdure shed,
And tip with silver every mountain's head;
Then shine the vales, the rocks in prospect rise,
A flood of glory bursts from all the skies;
The conscious swains, rejoicing in the sight,
Eye the blue vault, and bless the useful light."

_Pope's Homer._

LETTER XVII.

MOON'S ORBIT.--HER IRREGULARITIES.

"Some say the zodiac constellations
Have long since left their antique stations,
Above a sign, and prove the same
In Taurus now, once in the Ram;
That in twelve hundred years and odd,
The sun has left his ancient road,
And nearer to the earth is come,
'Bove fifty thousand miles from home."--_Hudibras._

WE have thus far contemplated the revolution of the moon around the
earth as though the earth were at rest. But in order to have just ideas
respecting the moon's motions, we must recollect that the moon likewise
revolves along with the earth around the sun. It is sometimes said that
the earth _carries_ the moon along with her, in her annual revolution.
This language may convey an erroneous idea; for the moon, as well as the
earth, revolves around the sun under the influence of two forces, which
are independent of the earth, and would continue her motion around the
sun, were the earth removed out of the way. Indeed, the moon is
attracted towards the sun two and one fifth times more than towards the
earth, and would abandon the earth, were not the latter also carried
along with her by the same forces. So far as the sun acts equally on
both bodies, the motion with respect to each other would not be
disturbed. Because the gravity of the moon towards the sun is found to
be greater, at the conjunction, than her gravity towards the earth, some
have apprehended that, if the doctrine of universal gravitation is true,
the moon ought necessarily to abandon the earth. In order to understand
the reason why it does not do thus, we must reflect, that, when a body
is revolving in its orbit under the influence of the projectile force
and gravity, whatever diminishes the force of gravity, while that of
projection remains the same, causes the body to approach nearer to the
tangent of her orbit, and of course to recede from the centre; and
whatever increases the amount of gravity, carries the body towards the
centre. Thus, in Fig. 33, page 152, if, with a certain force of
projection acting in the direction A B, and of attraction, in the
direction A C, the attraction which caused a body to move in the line A
D were diminished, it would move nearer to the tangent, as in A E, or A
F. Now, when the moon is in conjunction, her gravity towards the earth
acts in opposition to that towards the sun, (see Fig. 38, page 175,)
while her velocity remains too great to carry her with what force
remains, in a circle about the sun, and she therefore recedes from the
sun, and commences her revolution around the earth. On arriving at the
opposition, the gravity of the earth conspires with that of the sun, and
the moon's projectile force being less than that required to make her
revolve in a circular orbit, when attracted towards the sun by the sum
of these forces, she accordingly begins to approach the sun, and
descends again to the conjunction.

The attraction of the sun, however, being every where greater than that
of the earth, the actual path of the moon around the sun is every where
concave towards the latter. Still, the elliptical path of the moon
around the earth is to be conceived of, in the same way as though both
bodies were at rest with respect to the sun. Thus, while a steam-boat is
passing _swiftly_ around an island, and a man is walking _slowly_ around
a post in the cabin, the line which he describes in space between the
forward motion of the boat and his circular motion around the post, may
be every where concave towards the island, while his path around the
post will still be the same as though both were at rest. A nail in the
rim of a coach-wheel will turn around the axis of the wheel, when the
coach has a forward motion, in the same manner as when the coach is at
rest, although the line actually described by the nail will be the
resultant of both motions, and very different from either.

We have hitherto regarded the moon as describing a great circle on the
face of the sky, such being the visible orbit, as seen by projection.
But, on a more exact investigation, it is found that her orbit is not a
circle, and that her motions are subject to very numerous
irregularities. These will be best understood in connexion with the
causes on which they depend. The law of universal gravitation has been
applied with wonderful success to their developement, and its results
have conspired with those of long-continued observation, to furnish the
means of ascertaining with great exactness the place of the moon in the
heavens, at any given instant of time, past or future, and thus to
enable astronomers to determine longitudes, to calculate eclipses, and
to solve other problems of the highest interest. The whole number of
irregularities to which the moon is subject is not less than sixty, but
the greater part are so small as to be hardly deserving of attention;
but as many as thirty require to be estimated and allowed for, before we
can ascertain the exact place of the moon at any given time. You will be
able to understand something of the cause of these irregularities, if
you first gain a distinct idea of the mutual actions of the sun, the
moon, and the earth. The irregularities in the moon's motions are due
chiefly to the disturbing influence of the sun, which operates in two
ways; first, by acting unequally on the earth and moon; and secondly, by
acting obliquely on the moon, on account of the inclination of her orbit
to the ecliptic. If the sun acted equally on the earth and moon, and
always in parallel lines, this action would serve only to restrain them
in their annual motions around the sun, and would not affect their
actions on each other, or their motions about their common centre of
gravity. In that case, if they were allowed to fall towards the sun,
they would fall equally, and their respective situations would not be
affected by their descending equally towards it. But, because the moon
is nearer the sun in one half of her orbit than the earth is, and in the
other half of her orbit is at a greater distance than the earth from the
sun, while the power of gravity is always greater at a less distance; it
follows, that in one half of her orbit the moon is more attracted than
the earth towards the sun, and, in the other half, less attracted than
the earth.

To see the effects of this process, let us suppose that the projectile
motions of the earth and moon were destroyed, and that they were allowed
to fall freely towards the sun. (See Fig. 38, page 175.) If the moon was
in conjunction with the sun, or in that part of her orbit which is
nearest to him, the moon would be more attracted than the earth, and
fall with greater velocity towards the sun; so that the distance of the
moon from the earth would be increased by the fall. If the moon was in
opposition, or in the part of her orbit which is furthest from the sun,
she would be less attracted than the earth by the sun, and would fall
with a less velocity, and be left behind; so that the distance of the
moon from the earth would be increased in this case, also. If the moon
was in one of the quarters, then the earth and the moon being both
attracted towards the centre of the sun, they would both descend
directly towards that centre, and, by approaching it, they would
necessarily at the same time approach each other, and in this case their
distance from each other would be diminished. Now, whenever the action
of the sun would increase their distance, if they were allowed to fall
towards the sun, then the sun's action, by endeavoring to separate them,
diminishes their gravity to each other; whenever the sun's action would
diminish the distance, then it increases their mutual gravitation.
Hence, in the conjunction and opposition, their gravity towards each
other is diminished by the action of the sun, while in the quadratures
it is increased. But it must be remembered, that it is not the total
action of the sun on them that disturbs their motions, but only that
part of it which tends at one time to separate them, and at another time
to bring them nearer together. The other and far greater part has no
other effect than to retain them in their annual course around the sun.

The cause of the lunar irregularities was first investigated by Sir
Isaac Newton, in conformity with his doctrine of universal gravitation,
and the explanation was first published in the 'Principia;' but, as it
was given in a mathematical dress, there were at that age very few
persons capable of reading or understanding it. Several eminent
individuals, therefore, undertook to give a popular explanation of these
difficult points. Among Newton's contemporaries, the best commentator
was M'Laurin, a Scottish astronomer, who published a large work entitled
'M'Laurin's Account of Sir Isaac Newton's Discoveries.' No writer of his
own day, and, in my opinion, no later commentator, has equalled
M'Laurin, in reducing to common apprehension the leading principles of
the doctrine of gravitation, and the explanation it affords of the
motions of the heavenly bodies. To this writer I am indebted for the
preceding easy explanation of the irregularities of the moon's motions,
as well as for several other illustrations of the same sublime doctrine.

The figure of the moon's orbit is an ellipse. We have before seen, that
the earth's orbit around the sun is of the same figure; and we shall
hereafter see this to be true of all the planetary orbits. The path of
the earth, however, departs very little from a circle; that of the moon
differs materially from a circle, being considerably longer one way than
the other. Were the orbit a circle having the earth in the centre, then
the radius vector, or line drawn from the centre of the moon to the
centre of the earth, would always be of the same length; but it is found
that the length of the radius vector is only fifty-six times the radius
of the earth when the moon is nearest to us, while it is sixty-four
times that radius when the moon is furthest from us. The point in the
moon's orbit nearest the earth is called her _perigee_; the point
furthest from the earth, her _apogee_. We always know when the moon is
at one of these points, by her apparent diameter or apparent velocity;
for, when at the perigee, her diameter is greater than at any time, and
her motion most rapid; and, on the other hand, her diameter is least,
and her motion slowest, when she is at her apogee.

The moon's nodes constantly shift their positions in the ecliptic, from
east to west, at the rate of about nineteen and a half degrees every
year, returning to the same points once in eighteen and a half years. In
order to understand what is meant by this backward motion of the nodes,
you must have very distinctly in mind the meaning of the terms
themselves; and if, at any time, you should be at a loss about the
signification of any word that is used in expressing an astronomical
proposition, I would advise you to turn back to the previous definition
of that term, and revive its meaning clearly in the mind, before you
proceed any further. In the present case, you will recollect that the
moon's nodes are the two points where her orbit cuts the plane of the
ecliptic. Suppose the great circle of the ecliptic marked out on the
face of the sky in a distinct line, and let us observe, at any given
time, the exact moment when the moon crosses this line, which we will
suppose to be close to a certain star; then, on its next return to that
part of the heavens, we shall find that it crosses the ecliptic sensibly
to the westward of that star, and so on, further and further to the
westward, every time it crosses the ecliptic at either node. This fact
is expressed by saying that _the nodes retrograde on the ecliptic_;
since any motion from east to west, being contrary to the order of the
signs, is called retrograde. The line which joins these two points, or
the line of the nodes, is also said to have a retrograde motion, or to
revolve from east to west once in eighteen and a half years.

The _line of the apsides_ of the moon's orbit revolves from west to
east, through her whole course, in about nine years. You will recollect
that the apsides of an elliptical orbit are the two extremities of the
longer axis of the ellipse; corresponding to the perihelion and aphelion
of bodies revolving about the sun, or to the perigee and apogee of a
body revolving about the earth. If, in any revolution of the moon, we
should accurately mark the place in the heavens where the moon is
nearest the earth, (which may be known by the moon's apparent diameter
being then greatest,) we should find that, at the next revolution, it
would come to its perigee a little further eastward than before, and so
on, at every revolution, until, after nine years, it would come to its
perigee nearly at the same point as at first. This fact is expressed by
saying, that the perigee, and of course the apogee, revolves, and that
the line which joins these two points, or the line of the apsides, also
revolves.

These are only a few of the irregularities that attend the motions of
the moon. These and a few others were first discovered by actual
observation and have been long known; but a far greater number of lunar
irregularities have been made known by following out all the
consequences of the law of universal gravitation.

The moon may be regarded as a body endeavoring to make its way around
the earth, but as subject to be continually impeded, or diverted from
its main course, by the action of the sun and of the earth; sometimes
acting in concert and sometimes in opposition to each other. Now, by
exactly estimating the amount of these respective forces, and
ascertaining their resultant or combined effect, in any given case, the
direction and velocity of the moon's motion may be accurately
determined. But to do this has required the highest powers of the human
mind, aided by all the wonderful resources of mathematics. Yet, so
consistent is truth with itself, that, where some minute inequality in
the moon's motions is developed at the end of a long and intricate
mathematical process, it invariably happens, that, on pointing the
telescope to the moon, and watching its progress through the skies, we
may actually see her commit the same irregularities, unless (as is the
case with many of them) they are too minute to be matters of
observation, being beyond the powers of our vision, even when aided by
the best telescopes. But the truth of the law of gravitation, and of the
results it gives, when followed out by a chain of mathematical
reasoning, is fully confirmed, even in these minutest matters, by the
fact that the moon's place in the heavens, when thus determined, always
corresponds, with wonderful exactness, to the place which she is
actually observed to occupy at that time.

The mind, that was first able to elicit from the operations of Nature
the law of universal gravitation, and afterwards to apply it to the
complete explanation of all the irregular wanderings of the moon, must
have given evidence of intellectual powers far elevated above those of
the majority of the human race. We need not wonder, therefore, that such
homage is now paid to the genius of Newton,--an admiration which has
been continually increasing, as new discoveries have been made by
tracing out new consequences of the law of universal gravitation.

The chief object of astronomical _tables_ is to give the amount of all
the irregularities that attend the motions of the heavenly bodies, by
estimating the separate value of each, under all the different
circumstances in which a body can be placed. Thus, with respect to the
moon, before we can determine accurately the distance of the moon from
the vernal equinox, that is, her longitude at any given moment, we must
be able to make exact allowances for all her irregularities which would
affect her longitude. These are in all no less than sixty, though most
of them are so exceedingly minute, that it is not common to take into
the account more than twenty-eight or thirty. The values of these are
all given in the lunar tables; and in finding the moon's place, at any
given time, we proceed as follows: We first find what her place would be
on the supposition that she moves uniformly in a circle. This gives her
_mean_ place. We next apply the various corrections for her irregular
motions; that is, we apply the _equations_, subtracting some and adding
others, and thus we find her _true_ place.

The astronomical tables have been carried to such an astonishing degree
of accuracy, that it is said, by the highest authority, that an
astronomer could now predict, for a thousand years to come, the precise
moment of the passage of any one of the stars over the meridian wire of
the telescope of his transit-instrument, with such a degree of accuracy,
that the error would not be so great as to remove the object through an
angular space corresponding to the semidiameter of the finest wire that
could be made; and a body which, by the tables, ought to appear in the
transit-instrument in the middle of that wire, would in no case be
removed to its outer edge. The astronomer, the mathematician, and the
artist, have united their powers to produce this great result. The
astronomer has collected the data, by long-continued and most accurate
observations on the actual motions of the heavenly bodies, from night to
night, and from year to year; the mathematician has taken these data,
and applied to them the boundless resources of geometry and the
calculus; and, finally, the instrument-maker has furnished the means,
not only of verifying these conclusions, but of discovering new truths,
as the foundation of future reasonings.

Since the points where the moon crosses the ecliptic, or the moon's
nodes, constantly shift their positions about nineteen and a half
degrees to the westward, every year, the sun, in his annual progress in
the ecliptic, will go from the node round to the same node again in less
time than a year, since the node goes to meet him nineteen and a half
degrees to the west of the point where they met before. It would have
taken the sun about nineteen days to have passed over this arc; and
consequently, the interval between two successive conjunctions between
the sun and the moon's node is about nineteen days shorter than the
solar year of three hundred and sixty-five days; that is, it is about
three hundred and forty-six days; or, more exactly, it is 346.619851
days. The time from one new moon to another is 29.5305887 days. Now,
nineteen of the former periods are almost exactly equal to two hundred
and twenty-three of the latter:

For 346.619851 × 19=6585.78 days=18 y. 10 d.
And 29.5305887 × 223=6585.32 " = " " " "

Hence, if the sun and moon were to leave the moon's node together, after
the sun had been round to the same node nineteen times, the moon would
have made very nearly two hundred and twenty-three conjunctions with the
sun. If, therefore, she was in conjunction with the sun at the beginning
of this period, she would be in conjunction again at the end of it; and
all things relating to the sun, the moon, and the node, would be
restored to the same relative situation as before, and the sun and moon
would start again, to repeat the same phenomena, arising out of these
relations, as occurred in the preceding period, and in the same order.
Now, when the sun and moon meet at the moon's node, an eclipse of the
sun happens; and during the entire period of eighteen and a half years
eclipses will happen, nearly in the same manner as they did at
corresponding times in the preceding period. Thus, if there was a great
eclipse of the sun on the fifth year of one of these periods, a similar
eclipse (usually differing somewhat in magnitude) might be expected on
the fifth year of the next period. Hence this period, consisting of
about eighteen years and ten days, under the name of the _Saros_, was
used by the Chaldeans, and other ancient nations, in predicting
eclipses. It was probably by this means that Thales, a Grecian
astronomer who flourished six hundred years before the Christian era,
predicted an eclipse of the sun. Herodotus, the old historian of Greece,
relates that the day was suddenly changed into night, and that Thales of
Miletus had foretold that a great eclipse was to happen _this year_. It
was therefore, at that age, considered as a distinguished feat to
predict even the year in which an eclipse was to happen. This eclipse is
memorable in ancient history, from its having terminated the war between
the Lydians and the Medes, both parties being smitten with such
indications of the wrath of the gods.

The _Metonic Cycle_ has sometimes been confounded with the Saros, but it
is not the same with it, nor was the period used, like the Saros, for
foretelling eclipses, but for ascertaining the _age_ of the moon at any
given period. It consisted of nineteen tropical years, during which time
there are exactly two hundred and thirty-five new moons; so that, at the
end of this period, the new moons will recur at seasons of the year
corresponding exactly to those of the preceding cycle. If, for example,
a new moon fell at the time of the vernal equinox, in one cycle,
nineteen years afterwards it would occur again at the same equinox; or,
if it had happened ten days after the equinox, in one cycle, it would
also happen ten days after the equinox, nineteen years afterwards. By
registering, therefore, the exact days of any cycle at which the new or
full moons occurred, such a calendar would show on what days these
events would occur in any other cycle; and, since the regulation of
games, feasts, and fasts, has been made very extensively, both in
ancient and modern times, according to new or full moons, such a
calendar becomes very convenient for finding the day on which the new or
full moon required takes place. Suppose, for example, it were decreed
that a festival should be held on the day of the first full moon after
the Vernal equinox. Then, to find on what day that would happen, in any
given year, we have only to see what year it is of the lunar cycle; for
the day will be the same as it was in the corresponding year of the
calendar which records all the full moons of the cycle for each year,
and the respective days on which they happen.

The Athenians adopted the metonic cycle four hundred and thirty-three
years before the Christian era, for the regulation of their calendars,
and had it inscribed in letters of gold on the walls of the temple of
Minerva. Hence the term _golden number_, still found in our almanacs,
which denotes the year of the lunar cycle. Thus, fourteen was the golden
number for 1837, being the fourteenth year of the lunar cycle.

The inequalities of the moon's motions are divided into periodical and
secular. _Periodical_ inequalities are those which are completed in
comparatively short periods. _Secular_ inequalities are those which are
completed only in very long periods, such as centuries or ages. Hence
the corresponding terms _periodical equations_ and _secular equations_.
As an example of a secular inequality, we may mention the acceleration
of the _moon's mean motion_. It is discovered that the moon actually
revolves around the earth in a less period now than she did in ancient
times. The difference, however, is exceedingly small, being only about
ten seconds in a century. In a lunar eclipse, the moon's longitude
differs from that of the sun, at the middle of the eclipse, by exactly
one hundred and eighty degrees; and since the sun's longitude at any
given time of the year is known, if we can learn the day and hour when
an eclipse occurred at any period of the world, we of course know the
longitude of the sun and moon at that period. Now, in the year 721,
before the Christian era, Ptolemy records a lunar eclipse to have
happened, and to have been observed by the Chaldeans. The moon's
longitude, therefore, for that time, is known; and as we know the mean
motions of the moon, at present, starting from that epoch, and
computing, as may easily be done, the place which the moon ought to
occupy at present, at any given time, she is found to be actually nearly
a degree and a half in advance of that place. Moreover, the same
conclusion is derived from a comparison of the Chaldean observations
with those made by an Arabian astronomer of the tenth century.

This phenomenon at first led astronomers to apprehend that the moon
encountered a resisting medium, which, by destroying at every revolution
a small portion of her projectile force, would have the effect to bring
her nearer and nearer to the earth, and thus to augment her velocity.
But, in 1786, La Place demonstrated that this acceleration is one of the
legitimate effects of the sun's disturbing force, and is so connected
with changes in the eccentricity of the earth's orbit, that the moon
will continue to be accelerated while that eccentricity diminishes; but
when the eccentricity has reached its minimum, or lowest point, (as it
will do, after many ages,) and begins to increase, then the moon's
motions will begin to be retarded, and thus her mean motions will
oscillate for ever about a mean value.

LETTER XVIII.

ECLIPSES.

----"As when the sun, new risen,
Looks through the horizontal misty air,
Shorn of his beams, or from behind the moon,
In dim eclipse, disastrous twilight sheds
On half the nations, and with fear of change
Perplexes monarchs: darkened so, yet shone,
Above them all, the Archangel."--_Milton._

HAVING now learned various particulars respecting the earth, the sun,
and the moon, you are prepared to understand the explanation of solar
and lunar eclipses, which have in all ages excited a high degree of
interest. Indeed, what is more admirable, than that astronomers should
be able to tell us, years beforehand, the exact instant of the
commencement and termination of an eclipse, and describe all the
attendant circumstances with the greatest fidelity. You have doubtless,
my dear friend, participated in this admiration, and felt a strong
desire to learn how it is that astronomers are able to look so far into
futurity. I will endeavor, in this Letter, to explain to you the leading
principles of the calculation of eclipses, with as much plainness as
possible.

An _eclipse of the moon_ happens when the moon, in its revolution around
the earth, falls into the earth's shadow. An _eclipse of the sun_
happens when the moon, coming between the earth and the sun, covers
either a part or the whole of the solar disk.

The earth and the moon being both opaque, globular bodies, exposed to
the sun's light, they cast shadows opposite to the sun, like any other
bodies on which the sun shines. Were the sun of the same size with the
earth and the moon, then the lines drawn touching the surface of the sun
and the surface of the earth or moon (which lines form the boundaries of
the shadow) would be parallel to each other, and the shadow would be a
cylinder infinite in length; and were the sun less than the earth or
the moon, the shadow would be an increasing cone, its narrower end
resting on the earth; but as the sun is vastly greater than either of
these bodies, the shadow of each is a cone whose base rests on the body
itself, and which comes to a point, or vertex, at a certain distance
behind the body. These several cases are represented in the following
diagrams, Figs. 39, 40, 41.

[Illustration Figs. 39, 40, 41.]

It is found, by calculation, that the length of the moon's shadow, on an
average, is just about sufficient to reach to the earth; but the moon is
sometimes further from the earth than at others, and when she is nearer
than usual, the shadow reaches considerably beyond the surface of the
earth. Also, the moon, as well as the earth, is at different distances
from the sun at different times, and its shadow is longest when it is
furthest from the sun. Now, when both these circumstances conspire, that
is, when the moon is in her perigee and along with the earth in her
aphelion, her shadow extends nearly fifteen thousand miles beyond the
centre of the earth, and covers a space on the surface one hundred and
seventy miles broad. The earth's shadow is nearly a million of miles in
length, and consequently more than three and a half times as long as the
distance of the earth from the moon; and it is also, at the distance of
the moon, three times as broad as the moon itself.

An eclipse of the sun can take place only at new moon, when the sun and
moon meet in the same part of the heavens, for then only can the moon
come between us and the sun; and an eclipse of the moon can occur only
when the sun and moon are in opposite parts of the heavens, or at full
moon; for then only can the moon fall into the shadow of the earth.

[Illustration Fig. 42.]

The nature of eclipses will be clearly understood from the following
representation. The diagram, Fig. 42, exhibits the relative position of
the sun, the earth, and the moon, both in a solar and in a lunar
eclipse. Here, the moon is first represented, while revolving round the
earth, as passing between the earth and the sun, and casting its shadow
on the earth. As the moon is here supposed to be at her average distance
from the earth, the shadow but just reaches the earth's surface. Were
the moon (as is sometimes the case) nearer the earth her shadow would
not terminate in a point, as is represented in the figure, but at a
greater or less distance nearer the base of the cone, so as to cover a
considerable space, which, as I have already mentioned, sometimes
extends to one hundred and seventy miles in breadth, but is commonly
much less than this. On the other side of the earth, the moon is
represented as traversing the earth's shadow, as is the case in a lunar
eclipse. As the moon is sometimes nearer the earth and sometimes further
off, it is evident that it will traverse the shadow at a broader or a
narrower part, accordingly. The figure, however, represents the moon as
passing the shadow further from the earth than is ever actually the
case, since the distance from the earth is never so much as one third of
the whole length of the shadow.

It is evident from the figure, that if a spectator were situated where
the moon's shadow strikes the earth, the moon would cut off from him the
view of the sun, or the sun would be totally eclipsed. Or, if he were
within a certain distance of the shadow on either side, the moon would
be partly between him and the sun, and would intercept from him more or
less of the sun's light, according as he was nearer to the shadow or
further from it. If he were at _c_ or _d_, he would just see the moon
entering upon the sun's disk; if he were nearer the shadow than either
of these points, he would have a portion of this light cut off from his
view, and more, in proportion as he drew nearer the shadow; and the
moment he entered the shadow, he would lose sight of the sun. To all
places between _a_ or _b_ and the shadow, the sun would cast a partial
shadow of the moon, growing deeper and deeper, as it approached the true
shadow. This partial shadow is called the moon's _penumbra_. In like
manner, as the moon approaches the earth's shadow, in a lunar eclipse,
as soon as she arrives at _a_, the earth begins to intercept from her a
portion of the sun's light, or she falls in the earth's penumbra. She
continues to lose more and more of the sun's light, as she draws near to
the shadow, and hence her disk becomes gradually obscured, until it
enters the shadow, when the sun's light is entirely lost.

As the sun and earth are both situated in the plane of the ecliptic, if
the moon also revolved around the earth in this plane, we should have a
solar eclipse at every new moon, and a lunar eclipse at every full moon;
for, in the former case, the moon would come directly between us and
the sun, and in the latter case, the earth would come directly between
the sun and the moon. But the moon is inclined to the ecliptic about
five degrees, and the centre of the moon may be all this distance from
the centre of the sun at new moon, and the same distance from the centre
of the earth's shadow at full moon. It is true, the moon extends across
her path, one half her breadth lying on each side of it, and the sun
likewise reaches from the ecliptic a distance equal to half his breadth.
But these luminaries together make but little more than a degree, and
consequently, their two semidiameters would occupy only about half a
degree of the five degrees from one orbit to the other where they are
furthest apart. Also, the earth's shadow, where the moon crosses it,
extends from the ecliptic less than three fourths of a degree, so that
the semidiameter of the moon and of the earth's shadow would together
reach but little way across the space that may, in certain cases,
separate the two luminaries from each other when they are in opposition.
Thus, suppose we could take hold of the circle in the figure that
represents the moon's orbit, (Fig. 42, page 197,) and lift the moon up
five degrees above the plane of the paper, it is evident that the moon,
as seen from the earth, would appear in the heavens five degrees above
the sun, and of course would cut off none of his light; and it is also
plain that the moon, at the full, would pass the shadow of the earth
five degrees below it, and would suffer no eclipse. But in the course of
the sun's apparent revolution round the earth once a year he is
successively in every part of the ecliptic; consequently, the
conjunctions and oppositions of the sun and moon may occur at any part
of the ecliptic, and of course at the two points where the moon's orbit
crosses the ecliptic,--that is, at the nodes; for the sun must
necessarily come to each of these nodes once a year. If, then, the moon
overtakes the sun just as she is crossing his path, she will hide more
or less of his disk from us. Since, also, the earth's shadow is always
directly opposite to the sun, if the sun is at one of the nodes, the
shadow must extend in the direction of the other node, so as to lie
directly across the moon's path; and if the moon overtakes it there, she
will pass through it, and be eclipsed. Thus, in Fig. 43, let BN
represent the sun's path, and AN, the moon's,--N being the place of the
node; then it is evident, that if the two luminaries at new moon be so
far from the node, that the distances between their centres is greater
than their semidiameters, no eclipse can happen; but if that distance is
less than this sum, as at E, F, then an eclipse will take place; but if
the position be as at C, D, the two bodies will just touch one another.
If A denotes the earth's shadow, instead of the sun, the same
illustration will apply to an eclipse of the moon.

[Illustration Fig. 43.]

Since bodies are defined to be in conjunction when they are in the
_same_ part of the heavens, and to be in opposition when they are in
_opposite_ parts of the heavens, it may not appear how the sun and moon
can be in conjunction, as at A and B, when they are still at some
distance from each other. But it must be recollected that bodies are in
conjunction when they have the same longitude, in which case they are
situated in the same great circle perpendicular to the ecliptic,--that
is, in the same secondary to the ecliptic. One of these bodies may be
much further from the ecliptic than the other; still, if the same
secondary to the ecliptic passes through them both, they will be in
conjunction or opposition.

In a total eclipse of the moon, its disk is still visible, shining with
a dull, red light. This light cannot be derived directly from the sun,
since the view of the sun is completely hidden from the moon; nor by
reflection from the earth, since the illuminated side of the earth is
wholly turned from the moon; but it is owing to refraction from the
earth's atmosphere, by which a few scattered rays of the sun are bent
round into the earth's shadow and conveyed to the moon, sufficient in
number to afford the feeble light in question.

It is impossible fully to understand the _method of calculating
eclipses_, without a knowledge of trigonometry; still it is not
difficult to form some general notion of the process. It may be readily
conceived that, by long-continued observations on the sun and moon, the
laws of their revolution may be so well understood, that the exact
places which they will occupy in the heavens at any future times may be
foreseen and laid down in tables of the sun and moon's motions; that we
may thus ascertain, by inspecting the tables, the instant when these two
bodies will be together in the heavens, or be in conjunction, and when
they will be one hundred and eighty degrees apart, or in opposition.
Moreover, since the exact place of the moon's node among the stars at
any particular time is known to astronomers, it cannot be difficult to
determine when the new or full moon occurs in the same part of the
heavens as that where the node is projected, as seen from the earth. In
short, as astronomers can easily determine what will be the relative
position of the sun, the moon, and the moon's nodes, for any given time,
they can tell when these luminaries will meet so near the node as to
produce an eclipse of the sun, or when they will be in opposition so
near the node as to produce an eclipse of the moon.

A little reflection will enable you to form a clear idea of the
situation of the sun, the moon, and the earth, at the time of a solar
eclipse. First, suppose the conjunction to take place at the node; that
is, imagine the moon to come _directly_ between the earth and the sun,
as she will of course do, if she comes between the earth and the sun the
moment she is crossing the ecliptic; for then the three bodies will all
lie in one and the same straight line. But when the moon is in the
ecliptic, her shadow, or at least the axis, or central line, of the
shadow, must coincide with the line that joins the centres of the sun
and earth, and reach along the plane of the ecliptic towards the earth.
The moon's shadow, at her average distance from the earth, is just about
long enough to reach the surface of the earth; but when the moon, at the
new, is in her apogee, or at her greatest distance from the earth, the
shadow is not long enough to reach the earth. On the contrary, when the
moon is nearer to us than her average distance, her shadow is long
enough to reach beyond the earth, extending, when the moon is in her
perigee, more than fourteen thousand miles beyond the centre of the
earth. Now, as during the eclipse the moon moves nearly in the plane of
the ecliptic, her shadow which accompanies her must also move nearly in
the same plane, and must therefore traverse the earth across its central
regions, along the terrestrial ecliptic, since this is nothing more than
the intersection of the plane of the celestial ecliptic with the earth's
surface. The motion of the earth, too, on its axis, in the same
direction, will carry a place along with the shadow, though with a less
velocity by more than one half; so that the actual velocity of the
shadow, in respect to places over which it passes on the earth, will
only equal the difference between its own rate and that of the places,
as they are carried forward in the diurnal revolution.

We have thus far supposed that the moon comes to her conjunction
precisely at the node, or at the moment when she is crossing the
ecliptic. But, secondly, suppose she is on the north side of the
ecliptic at the time of conjunction, and moving towards her descending
node, and that the conjunction takes place as far from the node as an
eclipse can happen. The shadow will not fall in the plane of the
ecliptic, but a little northward of it, so as just to graze the earth
near the pole of the ecliptic. The nearer the conjunction comes to the
node, the further the shadow will fall from the polar towards the
equatorial regions.

In a solar eclipse, the shadow of the moon travels over a portion of the
earth, as the shadow of a small cloud, seen from an eminence in a clear
day, rides along over hills and plains. Let us imagine ourselves
standing on the moon; then we shall see the earth partially eclipsed by
the moon's shadow, in the same manner as we now see the moon eclipsed by
the shadow of the earth; and we might calculate the various
circumstances of the eclipse,--its commencement, duration, and
quantity,--in the same manner as we calculate these elements in an
eclipse of the moon, as seen from the earth. But although the general
characters of a solar eclipse might be investigated on these principles,
so far as respects the earth at large, yet, as the appearances of the
same eclipse of the sun are very different at different places on the
earth's surface, it is necessary to calculate its peculiar aspects for
each place separately, a circumstance which makes the calculation of a
solar eclipse much more complicated and tedious than that of an eclipse
of the moon. The moon, when she enters the shadow of the earth, is
deprived of the light of the part immersed, and the effect upon its
appearance is the same as though that part were painted black, in which
case it would be black alike to all places where the moon was above the
horizon. But it not so with a solar eclipse. We do not see this by the
shadow cast on the earth, as we should do, if we stood on the moon, but
by the interposition of the moon between us and the sun; and the sun may
be hidden from one observer, while he is in full view of another only a
few miles distant. Thus, a small insulated cloud sailing in a clear sky
will, for a few moments, hide the sun from us, and from a certain space
near us, while all the region around is illuminated. But although the
analogy between the motions of the shadow of a small cloud and of the
moon in a solar eclipse holds good in many particulars, yet the velocity
of the lunar shadow is far greater than that of the cloud, being no less
than two thousand two hundred and eighty miles per hour.

The moon's shadow can never cover a space on the earth more than one
hundred and seventy miles broad, and the space actually covered commonly
falls much short of that. The portion of the earth's surface ever
covered by the moon's penumbra is about four thousand three hundred and
ninety-three miles.

The apparent diameter of the moon varies materially at different times,
being greatest when the moon is nearest to us, and least when she is
furthest off; while the sun's apparent dimensions remain nearly the
same. When the moon is at her average distance from the earth, she is
just about large enough to cover the sun's disk; consequently, if, in a
central eclipse of the sun, the moon is at her mean distance, she covers
the sun but for an instant, producing only a momentary eclipse. If she
is nearer than her average distance, then the eclipse may continue total
some time, though never more than eight minutes, and seldom so long as
that; but if she is further off than usual, or towards her apogee, then
she is not large enough to cover the whole solar disk, but we see a ring
of the sun encircling the moon, constituting an _annular eclipse_, as
seen in Fig. 44. Even the elevation of the moon above the horizon will
sometimes sensibly affect the dimensions of the eclipse. You will
recollect that the moon is nearer to us when on the meridian than when
in the horizon by nearly four thousand miles, or by nearly the radius of
the earth; and consequently, her apparent diameter is largest when on
the meridian. The difference is so considerable, that the same eclipse
will appear total to a spectator who views it near his meridian, while,
at the same moment, it appears annular to one who has the moon near his
horizon. An annular eclipse may last, at most, twelve minutes and
twenty-four seconds.

[Illustration Fig. 44.]

Eclipses of the sun are more frequent than those of the moon. Yet lunar
eclipses being visible to every part of the terrestrial hemisphere
opposite to the sun, while those of the sun are visible only to a small
portion of the hemisphere on which the moon's shadow falls, it happens
that, for any particular place on the earth, lunar eclipses are more
frequently visible than solar. In any year, the number of eclipses of
both luminaries cannot be less than two nor more than seven: the most
usual number is four, and it is very rare to have more than six. A total
eclipse of the moon frequently happens at the next full moon after an
eclipse of the sun. For since, in a solar eclipse, the sun is at or near
one of the moon's nodes,--that is, is projected to the place in the sky
where the moon crosses the ecliptic,--the earth's shadow, which is of
course directly opposite to the sun, must be at or near the other node,
and may not have passed too far from the node before the moon comes
round to the opposition and overtakes it. In total eclipses of the sun,
there has sometimes been observed a remarkable radiation of light from
the margin of the sun, which is thought to be owing to the zodiacal
light, which is of such dimensions as to extend far beyond the solar
orb. A striking appearance of this kind was exhibited in the total
eclipse of the sun which occurred in June, 1806.

A total eclipse of the sun is one of the most sublime and impressive
phenomena of Nature. Among barbarous tribes it is ever contemplated with
fear and astonishment, and as strongly indicative of the displeasure of
the gods. Two ancient nations, the Lydians and Medes, alluded to before,
who were engaged in a bloody war, about six hundred years before Christ,
were smitten with such awe, on the appearance of a total eclipse of the
sun, just on the eve of a battle, that they threw down their arms, and
made peace. When Columbus first discovered America, and was in danger of
hostility from the Natives, he awed them into submission by telling them
that the sun would be darkened on a certain day, in token of the anger
of the gods at them, for their treatment of him.

Among cultivated nations, a total eclipse of the sun is recognised, from
the exactness with which the time of occurrence and the various
appearances answer to the prediction, as affording one of the proudest
triumphs of astronomy. By astronomers themselves, it is of course viewed
with the highest interest, not only as verifying their calculations, but
as contributing to establish, beyond all doubt, the certainty of those
grand laws, the truth of which is involved in the result. I had the good
fortune to witness the total eclipse of the sun of June, 1806, which was
one of the most remarkable on record. To the wondering gaze of childhood
it presented a spectacle that can never be forgotten. A bright and
beautiful morning inspired universal joy, for the sky was entirely
cloudless. Every one was busily occupied in preparing smoked glass, in
readiness for the great sight, which was to be first seen about ten
o'clock. A thrill of mingled wonder and delight struck every mind when,
at the appointed moment, a little black indentation appeared on the limb
of the sun. This gradually expanded, covering more and more of the solar
disk, until an increasing gloom was spread over the face of Nature; and
when the sun was wholly lost, near mid-day, a feeling of horror pervaded
almost every beholder. The darkness was wholly unlike that of twilight
or night. A thick curtain, very different from clouds, hung upon the
face of the sky, producing a strange and indescribably gloomy
appearance, which was reflected from all things on the earth, in hues
equally strange and unnatural. Some of the planets, and the largest of
the fixed stars, shone out through the gloom, yet with their usual
brightness. The temperature of the air rapidly declined, and so sudden a
chill came over the earth, that many persons caught severe colds from
their exposure. Even the animal tribes exhibited tokens of fear and
agitation. Birds, especially, fluttered and flew swiftly about, and
domestic fowls went to rest.

Indeed, the word _eclipse_ is derived from a Greek word, (= ekleipsis=,
_ekleipsis_,) which signifies to fail, to faint or swoon away; since the
moon, at the period of her greatest brightness, falling into the shadow
of the earth, was imagined by the ancients to sicken and swoon, as if
she were going to die. By some very ancient nations she was supposed, at
such times, to be in pain; and, in order to relieve her fancied
distress, they lifted torches high in the atmosphere, blew horns and
trumpets, beat upon brazen vessels, and even, after the eclipse was
over, they offered sacrifices to the moon. The opinion also extensively
prevailed, that it was in the power of witches, by their spells and
charms, not only to darken the moon, but to bring her down from her
orbit, and to compel her to shed her baleful influences upon the earth.
In solar eclipses, also, especially when total, the sun was supposed to
turn away his face in abhorrence of some atrocious crime, that either
had been perpetrated or was about to be perpetrated, and to threaten
mankind with everlasting night, and the destruction of the world. To
such superstitions Milton alludes, in the passage which I have taken for
the motto of this Letter.

The Chinese, who, from a very high period of antiquity, have been great
observers of eclipses, although they did not take much notice of those
of the moon, regarded eclipses of the sun in general as unfortunate, but
especially such as occurred on the first day of the year. These were
thought to forebode the greatest calamities to the emperor, who on such
occasions did not receive the usual compliments of the season. When,
from the predictions of their astronomers, an eclipse of the sun was
expected, they made great preparation at court for observing it; and as
soon as it commenced, a blind man beat a drum, a great concourse
assembled, and the mandarins, or nobility, appeared in state.

LETTER XIX.

LONGITUDE.--TIDES.

"First in his east, the glorious lamp was seen,
Regent of day, and all the horizon round
Invested with bright rays, jocund to run
His _longitude_ through heaven's high road; the gray
Dawn and the Pleiades before him danced,
Shedding sweet influence."--_Milton._

THE ancients studied astronomy chiefly as subsidiary to astrology, with
the vain hope of thus penetrating the veil of futurity, and reading
their destinies among the stars. The moderns, on the other hand, have in
view, as the great practical object of this study, the perfecting of the
art of navigation. When we reflect on the vast interests embarked on the
ocean, both of property and life, and upon the immense benefits that
accrue to society from a safe and speedy intercourse between the
different nations of the earth, we cannot but see that whatever tends to
enable the mariner to find his way on the pathless ocean, and to secure
him against its multiplied dangers, must confer a signal benefit on
society.

In ancient times, to venture out of sight of land was deemed an act of
extreme audacity; and Horace, the Roman poet, pronounces him who first
ventured to trust his frail bark to the stormy ocean, endued with a
heart of oak, and girt with triple folds of brass. But now, the
navigator who fully avails himself of all the resources of science, and
especially of astronomy, may launch fearlessly on the deep, and almost
bid defiance to rocks and tempests. By enabling the navigator to find
his place on the ocean with almost absolute precision, however he may
have been driven about by the winds, and however long he may have been
out of sight of land, astronomers must be held as great benefactors to
all who commit either their lives or their fortunes to the sea. Nor
have they secured to the art of navigation such benefits without
incredible study and toil, in watching the motions of the heavenly
bodies, in investigating the laws by which their movements are governed,
and in reducing all their discoveries to a form easily available to the
navigator, so that, by some simple observation on one or two of the
heavenly bodies, with instruments which the astronomer has invented, and
prepared for his use, and by looking out a few numbers in tables which
have been compiled for him, with immense labor, he may ascertain the
exact place he occupies on the surface of the globe, thousands of miles
from land.

The situation of any place is known by its latitude and longitude. As
charts of every ocean and sea are furnished to the sailor, in which are
laid down the latitudes and longitudes of every point of land, whether
on the shores of islands or the main, he has, therefore, only to
ascertain his latitude and longitude at any particular place on the
ocean, in order to find where he is, with respect to the nearest point
of land, although this may be, and may always have been, entirely out of
sight to him.

To determine the _latitude_ of a place is comparatively an easy matter,
whenever we can see either the sun or the stars. The distance of the sun
from the zenith, when on the meridian, on a given day of the year,
(which distance we may easily take with the sextant,) enables us, with
the aid of the tables, to find the latitude of the place; or, by taking
the altitude of the north star, we at once obtain the latitude.

The _longitude_ of a place may be found by any method, by which we may
ascertain how much its time of day differs from that of Greenwich at the
same moment. A place that lies eastward of another comes to the meridian
an hour earlier for every fifteen degrees of longitude, and of course
has the hour of the day so much in advance of the other, so that it
counts one o'clock when the other place counts twelve. On the other
hand, a place lying westward of another comes to the meridian later by
one hour for every fifteen degrees, so that it counts only eleven
o'clock when the other place counts twelve. Keeping these principles in
view, it is easy to see that a comparison of the difference of time
between two places at the same moment, allowing fifteen degrees for an
hour, sixty minutes for every four minutes of time, and sixty seconds
for every four seconds of time, affords us an accurate mode of finding
the difference of longitude between the two places. This comparison may
be made by means of a chronometer, or from solar or lunar eclipses, or
by what is called the lunar method of finding the longitude.

_Chronometers_ are distinguished from clocks, by being regulated by
means of a balance-wheel instead of a pendulum. A watch, therefore,
comes under the general definition of a chronometer; but the name is
more commonly applied to larger timepieces, too large to be carried
about the person, and constructed with the greatest possible accuracy,
with special reference to finding the longitude. Suppose, then, we are
furnished with a chronometer set to Greenwich time. We arrive at New
York, for example, and compare it with the time there. We find it is
five hours in advance of the New-York time, indicating five o'clock,
P.M., when it is noon at New York. Hence we find that the longitude of
New York is 5×15=75 degrees.[11] The time at New York, or any individual
place, can be known by observations with the transit-instrument, which
gives us the precise moment when the sun is on the meridian.

It would not be necessary to resort to Greenwich, for the purpose of
setting our chronometer to Greenwich time, as it might be set at any
place whose longitude is known, having been previously determined. Thus,
if we know that the longitude of a certain place is exactly sixty
degrees east of Greenwich, we have only to set our chronometer four
hours behind the time at that place, and it will be regulated to
Greenwich time. Hence it is a matter of the greatest importance to
navigation, that the longitude of numerous ports, in different parts of
the earth, should be accurately determined, so that when a ship arrives
at any such port, it may have the means of setting or verifying its
chronometer.

This method of taking the longitude seems so easy, that you will perhaps
ask, why it is not sufficient for all purposes, and accordingly, why it
does not supersede the move complicated and laborious methods? why every
sailor does not provide himself with a chronometer, instead of finding
his longitude at sea by tedious and oft-repeated calculations, as he is
in the habit of doing? I answer, it is only in a few extraordinary cases
that chronometers have been constructed of such accuracy as to afford
results as exact as those obtained by the other methods, to be described
shortly; and instruments of such perfection are too expensive for
general use among sailors. Indeed, the more common chronometers cost too
much to come within the means of a great majority of sea-faring men.
Moreover, by being transported from place to place, chronometers are
liable to change their _rate_. By the rate of any timepiece is meant its
deviation from perfect accuracy. Thus, if a clock should gain one second
per day, one day with another, and we should find it impossible to bring
it nearer to the truth, we may reckon this as its rate, and allow for it
in our estimate of the time of any particular observation. If the error
was not uniform, but sometimes greater and sometimes less than one
second per day, then the amount of such deviation is called its
"variation from its mean rate." I introduce these minute statements,
(which are more precise than I usually deem necessary,) to show you to
what an astonishing degree of accuracy chronometers have in some
instances been brought. They have been carried from London to Baffin's
Bay, and brought back, after a three years' voyage, and found to have
varied from their mean rate, during the whole time, only a second or
two, while the extreme variation of several chronometers, tried at the
Royal Observatory at Greenwich, never exceeded a second and a half.
Could chronometers always be depended on to such a degree of accuracy as
this, we should hardly desire any thing better for determining the
longitude of different places on the earth. A recent determination of
the longitude of the City Hall in New York, by means of three
chronometers, sent out from London expressly for that purpose, did not
differ from the longitude as found by a solar eclipse (which is one of
the best methods) but a second and a quarter.

_Eclipses of the sun and moon_ furnish the means of ascertaining the
longitude of a place, because the entrance of the moon into the earth's
shadow in a lunar eclipse, and the entrance of the moon upon the disk of
the sun in a solar eclipse, are severally examples of one of those
instantaneous occurrences in the heavens, which afford the means of
comparing the times of different places, and of thus determining their
differences of longitude. Thus, if the commencement of a lunar eclipse
was seen at one place an hour sooner than at another, the two places
would be fifteen degrees apart, in longitude; and if the longitude of
one of the places was known, that of the other would become known also.
The exact instant of the moon's entering into the shadow of the earth,
however, cannot be determined with very great precision, since the moon,
in passing through the earth's penumbra, loses its light gradually, so
that the moment when it leaves the penumbra and enters into the shadow
cannot be very accurately defined. The first contact of the moon with
the sun's disk, in a solar eclipse, or the moment of leaving it,--that
is, the beginning and end of the eclipse,--are instants that can be
determined with much precision, and accordingly they are much relied on
for an accurate determination of the longitude. But, on account of the
complicated and laborious nature of the calculation of the longitude
from an eclipse of the sun, (since the beginning and end are not seen at
different places, at the same moment,) this method of finding the
longitude is not adapted to common use, nor available at sea. It is
useful, however, for determining the longitude of fixed observatories.
The _lunar method of finding the longitude_ is the most refined and
accurate of all the modes practised at sea. The motion of the moon
through the heavens is so rapid, that she perceptibly alters her
distance from any star every minute; consequently, the moment when that
distance is a certain number of degrees and minutes is one of those
instantaneous events, which may be taken advantage of for comparing the
times of different places, and thus determining their difference of
longitude. Now, in a work called the 'Nautical Almanac,' printed in
London, annually, for the use of navigators, the distance of the moon
from the sun by day, or from known fixed stars by night, for every day
and night in the year, is calculated beforehand. If, therefore, a sailor
wishes to ascertain his longitude, he may take with his sextant the
distance of the moon from one of these stars at any time,--suppose nine
o'clock, at night,--and then turn to the 'Nautical Almanac,' and see
_what time it was at Greenwich_ when the distance between the moon and
that star was the same. Let it be twelve o'clock, or three hours in
advance of his time: his longitude, of course, is forty-five degrees
west.

This method requires more skill and accuracy than are possessed by the
majority of seafaring men; but, when practised with the requisite degree
of skill, its results are very satisfactory. Captain Basil Hall, one of
the most scientific commanders in the British navy, relates the
following incident, to show the excellence of this method. He sailed
from San Blas, on the west coast of Mexico, and, after a voyage of eight
thousand miles, occupying eighty-nine days, arrived off Rio de Janeiro,
having, in this interval, passed through the Pacific Ocean, rounded Cape
Horn, and crossed the South Atlantic, without making any land, or even
seeing a single sail, with the exception of an American whaler off Cape
Horn. When within a week's sail of Rio, he set seriously about
determining, by lunar observations, the precise line of the ship's
course, and its situation at a determinate moment; and having
ascertained this within from five to ten miles, ran the rest of the way
by those more ready and compendious methods, known to navigators, which
can be safely employed for short trips between one known point and
another, but which cannot be trusted in long voyages, where the moon is
the only sure guide. They steered towards Rio Janeiro for some days
after taking the lunars, and, having arrived within fifteen or twenty
miles of the coast, they hove to, at four in the morning, till the day
should break, and then bore up, proceeding cautiously, on account of a
thick fog which enveloped them. As this cleared away, they had the
satisfaction of seeing the great Sugar-Loaf Rock, which stands on one
side of the harbor's mouth, so nearly right ahead, that they had not to
alter their course above a point, in order to hit the entrance of the
harbor. This was the first land they had seen for three months, after
crossing so many seas, and being set backwards and forwards by
innumerable currents and foul winds. The effect on all on board was
electric; and the admiration of the sailors was unbounded. Indeed, what
could be more admirable than that a man on the deck of a vessel, by
measuring the distance between the moon and a star, with a little
instrument which he held in his hand, could determine his exact place on
the earth's surface in the midst of a vast ocean, after having traversed
it in all directions, for three months, crossing his track many times,
and all the while out of sight of land?

The lunar method of finding the longitude could never have been
susceptible of sufficient accuracy, had not the motions of the moon,
with all their irregularities, been studied and investigated by the most
laborious and profound researches. Hence Newton, while wrapt in those
meditations which, to superficial minds, would perhaps have appeared
rather curious than useful, inasmuch as they respected distant bodies of
the universe which seemed to have little connexion with the affairs of
this world, was laboring night and day for the benefit of the sailor and
the merchant. He was guiding the vessel of the one, and securing the
merchandise of the other; and thus he contributed a large share to
promote the happiness of his fellow-men, not only in exalting the powers
of the human intellect, but also in preserving the lives and fortunes of
those engaged in navigation and commerce. Principles in science are
rules in art; and the philosopher who is engaged in the investigation of
these principles, although his pursuits may be thought less practically
useful than those of the artisan who carries out those principles into
real life, yet, without the knowledge of the principles, the rules would
have never been known. Studies, therefore, the most abstruse, are, when
viewed as furnishing rules to act, often productive of the highest
practical utility.

Since the _tides_ are occasioned by the influence of the sun and moon, I
will conclude this Letter with a few remarks on this curious phenomenon.
By the tides are meant the alternate rising and falling of the waters of
the ocean. Its greatest and least elevations are called _high and low
water_; its rising and falling are called _flood and ebb_; and the
extraordinary high and low tides that occur twice every month are called
_spring and neap tides_. It is high or low tide on opposite sides of the
globe at the same time. If, for example, we have high water at noon, it
is also high water to those who live on the meridian below us, where it
is midnight. In like manner, low water occurs simultaneously on opposite
sides of the meridian. The average amount of the tides for the whole
globe is about two and a half feet; but their actual height at different
places is very various, sometimes being scarcely perceptible, and
sometimes rising to sixty or seventy feet. At the same place, also, the
phenomena of the tides are very different at different times. In the Bay
of Fundy, where the tide rises seventy feet, it comes in a mighty wave,
seen thirty miles off, and roaring with a loud noise. At the mouth of
the Severn, in England, the flood comes up in one head about ten feet
high, bringing certain destruction to any small craft that has been
unfortunately left by the ebbing waters on the flats and as it passes
the mouth of the Avon, it sends up that small river a vast body of
water, rising, at Bristol, forty or fifty feet.

Tides are caused by the unequal attractions of the sun and moon upon
different parts of the earth. Suppose the projectile force by which the
earth is carried forward in her orbit to be suspended, and the earth to
fall towards one of these bodies,--the moon, for example,--in
consequence of their mutual attraction. Then, if all parts of the earth
fell equally towards the moon, no derangement of its different parts
would result, any more than of the particles of a drop of water, in its
descent to the ground. But if one part fell faster than another, the
different portions would evidently be separated from each other. Now,
this is precisely what takes place with respect to the earth, in its
fall towards the moon. The portions of the earth in the hemisphere next
to the moon, on account of being nearer to the centre of attraction,
fall faster than those in the opposite hemisphere, and consequently
leave them behind. The solid earth, on account of its cohesion, cannot
obey this impulse, since all its different portions constitute one mass,
which is acted on in the same manner as though it were all collected in
the centre; but the waters on the surface, moving freely under this
impulse, endeavor to desert the solid mass and fall towards the moon.
For a similar reason, the waters in the opposite hemisphere, falling
less towards the moon than the solid earth does, are left behind, or
appear to rise.

[Illustration Fig. 46.]

But if the moon draws the waters of the earth into an oval form towards
herself, raising them simultaneously on the opposite sides of the earth,
they must obviously be drawn away from the intermediate parts of the
earth, where it must at the same time be low water. Thus, in Fig. 46,
the moon, M, raises the waters beneath itself at Z and N, at which
places it is high water, but at the same time depresses the waters at H
and R, at which places it is low water. Hence, the interval between the
high and low tide, on successive days, is about fifty minutes,
corresponding to the progress of the moon in her orbit from west to
east, which causes her to come to the meridian about fifty minutes later
every day. There occurs, however, an intermediate tide, when the moon is
on the lower meridian, so that the interval between two high tides is
about twelve hours, and twenty-five minutes.

Were it not for the impediments which prevent the force from producing
its full effects, we might expect to see the great tide-wave, as the
elevated crest is called, always directly beneath the moon, attending it
regularly around the globe. But the inertia of the waters prevents their
instantly obeying the moon's attraction, and the friction of the waters
on the bottom of the ocean still further retards its progress. It is
not, therefore, until several hours (differing at different places)
after the moon has passed the meridian of a place, that it is high tide
at that place.

The _sun_ has an action similar to that of the moon, but only _one
third_ as great. On account of the great mass of the sun, compared with
that of the moon, we might suppose that his action in raising the tides
would be greater than the moon's; but the nearness of the moon to the
earth more than compensates for the sun's greater quantity of matter.
As, however, wrong views are frequently entertained on this subject, let
us endeavor to form a correct idea of the advantage which the moon
derives from her proximity. It is not that her actual amount of
attraction is thus rendered greater than that of the sun; but it is that
her attraction for the _different parts_ of the earth is very unequal,
while that of the sun is nearly uniform. It is the _inequality_ of this
action, and not the absolute force, that produces the tides. The sun
being ninety-five millions of miles from the earth, while the diameter
of the earth is only one twelve thousandth part of this distance, the
effects of the sun's attraction will be nearly the same on all parts of
the earth, and therefore will not, as was explained of the moon, tend to
separate the waters from the earth on the nearest side, or the earth
from the waters on the remotest side, but in a degree proportionally
smaller. But the diameter of the earth is one thirtieth the distance of
the moon, and therefore the moon acts with considerably greater power on
one part of the earth than on another.

As the sun and moon both contribute to produce the tides, and as they
sometimes act together and sometimes in opposition to each other, so
corresponding variations occur in the height of the tide. The _spring
tides_, or those which rise to an unusual height twice a month, are
produced by the sun and moon's acting together; and the _neap tides_, or
those which are unusually low twice a month, are produced by the sun and
moon's acting in opposition to each other. The spring tides occur at the
syzygies: the neap tides at the quadratures. At the time of new moon,
the sun and moon both being on the same side of the earth, and acting
upon it in the same line, their actions conspire, and the sun may be
considered as adding so much to the force of the moon. We have already
seen how the moon contributes to raise a tide on the opposite side of
the earth. But the sun, as well as the moon, raises its own tide-wave,
which at new moon coincides with the lunar tide-wave. This will be plain
on inspecting the diagram, Fig. 47, on page 220, where S represents the
sun, C, the moon in conjunction, O, the moon in opposition, and Z, N,
the tide-wave. Since the sun and moon severally raise a tide-wave, and
the two here coincide, it is evident that a peculiarly high tide must
occur when the two bodies are in conjunction, or at new moon. At full
moon, also, the two luminaries conspire in the same way to raise the
tide; for we must recollect that each body contributes to raise a tide
on the opposite side. Thus, when the sun is at S and the moon at O, the
sun draws the waters on the side next to it away from the earth, and
the moon draws the earth away from the waters on that side; their united
actions, therefore, conspire, and an unusually high tide is the result.
On the side next to O, the two forces likewise conspire: for while the
moon draws the waters away from the earth, the sun draws the earth away
from the waters. In both cases an unusually low tide is produced; for
the more the water is elevated at Z and N, the more it will be depressed
at H and R, the places of low tide.

[Illustration Fig. 47.]

Twice a month, also, namely, at the quadratures of the moon, the tides
neither rise so high nor fall so low as at other times, because then the
sun and moon act against each other. Thus, in Fig. 48, while F tends to
raise the water at Z, S tends to depress it, and consequently the high
tide is less than usual. Again, while F tends to depress the water at R,
S tends to elevate it, and therefore the low tide is less than usual.
Hence the difference between high and low water is only half as great at
neap as at spring tide. In the diagrams, the elevation and depression of
the waters is represented, for the sake of illustration, as far greater
than it really is; for you must recollect that the average height of the
tides for the whole globe is only about two and a half feet, a quantity
so small, in comparison with the diameter of the earth, that were the
due proportions preserved in the figures, the effect would be wholly
insensible.

[Illustration Fig. 48.]

The variations of distance in the sun are not great enough to influence
the tides very materially, but the variations in the moon's distances
have a striking effect. The tides which happen, when the moon is in
perigee, are considerably greater than when she is in apogee; and if she
happens to be in perigee at the time of the syzygies, the spring tides
are unusually high.

The motion of the tide-wave is not a _progressive_ motion, but a mere
undulation, and is to be carefully distinguished from the currents to
which it gives rise. If the ocean completely covered the earth, the sun
and moon being in the equator, the tide-wave would travel at the same
rate as the earth revolves on its axis. Indeed, the correct way of
conceiving of the tide-wave, is to consider the moon at rest, and the
earth, in its rotation from west to east, as bringing successive
portions of water under the moon, which portions being elevated
successively, at the same rate as the earth revolves on its axis, have a
relative motion westward, at the same rate.

The tides of rivers, narrow bays, and shores far from the main body of
the ocean, are not produced in those places by the direct action of the
sun and moon, but are subordinate waves propagated from the great
tide-wave, and are called _derivative_ tides, while those raised
directly by the sun and moon are called _primitive_ tides.

[Illustration Fig. 49.]

The velocity with which the tide moves will depend on various
circumstances, but principally on the depth, and probably on the
regularity, of the channel. If the depth is nearly uniform the tides
will be regular; but if some parts of the channel are deep while others
are shallow, the waters will be detained by the greater friction of the
shallow places, and the tides will be irregular. The direction, also, of
the derivative tide may be totally different from that of the primitive.
Thus, in Fig. 49, if the great tide-wave, moving from east to west, is
represented by the lines 1, 2, 3, 4, the derivative tide, which is
propagated up a river or bay, will be represented by the lines 3, 4, 5,
6, 7. Advancing faster in the channel than next the bank, the tides will
lag behind towards the shores, and the tide-wave will take the form of
curves, as represented in the diagram.

On account of the retarding influence of shoals, and an uneven, indented
coast, the tide-wave travels more slowly along the shores of an island
than in the neighboring sea, assuming convex figures at a little
distance from the island, and on opposite sides of it. These convex
lines sometimes meet, and become blended in such a way, as to create
singular anomalies in a sea much broken by islands, as well as on coasts
indented with numerous bays and rivers. Peculiar phenomena are also
produced, when the tide flows in at opposite extremities of a reef or
island, as into the two opposite ends of Long-Island Sound. In certain
cases, a tide-wave is forced into a narrow arm of the sea, and produces
very remarkable tides. The tides of the Bay of Fundy (the highest in the
world) are ascribed to this cause. The tides on the coast of North
America are derived from the great tide-wave of the South Atlantic,
which runs steadily northward along the coast to the mouth of the Bay of
Fundy, where it meets the northern tide-wave flowing in the opposite
direction. This accumulated wave being forced into the narrow space
occupied by the Bay, produces the remarkable tide of that place.

The largest lakes and inland seas have no perceptible tides. This is
asserted by all writers respecting the Caspian and Euxine; and the same
is found to be true of the largest of the North-American lakes, Lake
Superior. Although these several tracts of water appear large, when
taken by themselves, yet they occupy but small portions of the surface
of the globe, as will appear evident from the delineation of them on the
artificial globe. Now, we must recollect that the primitive tides are
produced by the _unequal_ action of the sun and moon upon the different
parts of the earth; and that it is only at points whose distance from
each other bears a considerable ratio to the whole distance of the sun
or moon, that the inequality of action becomes manifest. The space
required to make the effect sensible is larger than either of these
tracts of water. It is obvious, also, that they have no opportunity to
be subject to a derivative tide.

Although all must admit that the tides have _some connexion_ with the
sun and the moon, yet there are so many seeming anomalies, which at
first appear irreconcilable with the theory of gravitation, that some
are unwilling to admit the explanation given by this theory. Thus, the
height of the tide is so various, that at some places on the earth there
is scarcely any tide at all, while at other places it rises to seventy
feet. The time of occurrence is also at many places wholly unconformable
to the motions of the moon, as is required by the theory, being low
water where it should be high water; or, instead of appearing just
beneath the moon, as the theory would lead us to expect, following it at
the distance of six, ten, or even fifteen, hours; and finally, the moon
sometimes appears to have no part at all in producing the tide, but it
happens uniformly at noon and midnight, (as is said to be the case at
the Society Islands,) and therefore seems wholly dependent on the sun.

Notwithstanding these seeming inconsistencies with the law of universal
gravitation, to which the explanation of the tides is referred, the
correspondence of the tides to the motions of the sun and moon, in
obedience to the law of attraction, is in general such as to warrant the
application of that law to them, while in a great majority of the cases
which appear to be exceptions to the operation of that law, local causes
and impediments have been discovered, which modified or overruled the
uniform operation of the law of gravitation. Thus it does not disprove
the reality of the existence of a force which carries bodies near the
surface of the earth towards its centre, that we see them sometimes
compelled, by the operation of local causes, to move in the opposite
direction. A ball shot from a cannon is still subject to the law of
gravitation, although, for a certain time, in obedience to the impulse
given it, it may proceed in a line contrary to that in which gravity
alone would carry it. The fact that water may be made to run up hill
does not disprove the fact that it usually runs down hill by the force
of gravity, or that it is still subject to this force, although, from
the action of modifying or superior forces, it may be proceeding in a
direction contrary to that given by gravity. Indeed, those who have
studied the doctrine of the tides most profoundly consider them as
affording a striking and palpable exhibition of the truth of the
doctrine of universal gravitation.

FOOTNOTE:

[11] The exact longitude of the City Hall, in the city of New York, is
4h. 56m. 33.5s.

LETTER XX.

PLANETS.--MERCURY AND VENUS.

"First, Mercury, amidst full tides of light,
Rolls next the sun, through his small circle bright;
Our earth would blaze beneath so fierce a ray,
And all its marble mountains melt away.
Fair Venus next fulfils her larger round,
With softer beams, and milder glory crowned;
Friend to mankind, she glitters from afar,
Now the bright evening, now the morning, star."--_Baker._

THERE is no study in which more is to be hoped for from a lucid
arrangement, than in the study of astronomy. Some subjects involved in
this study appear very difficult and perplexing to the learner, before
he has fully learned the doctrine of the sphere, and gained a certain
familiarity with astronomical doctrines, which would seem very easy to
him after he had made such attainments. Such an order ought to be
observed, as shall bring out the facts and doctrines of the science just
in the place where the mind of the learner is prepared to receive them.
Some writers on astronomy introduce their readers at once to the most
perplexing part of the whole subject,--the planetary motions. I have
thought a different course advisable, and have therefore commenced these
Letters with an account of those bodies which are most familiarly known
to us, the earth, the sun, and the moon. In connexion with the earth, we
are able to acquire a good knowledge of the artificial divisions and
points of reference that are established on the earth and in the
heavens, constituting the doctrine of the sphere. You thus became
familiar with many terms and definitions which are used in astronomy.
These ought to be always very clearly borne in mind; and if you now meet
with any term, the definition of which you have either partially or
wholly forgotten, let me strongly recommend to you, to turn back and
review it, until it becomes as familiar to you as household words.
Indeed, you will find it much to your advantage to go back frequently,
and reiterate the earlier parts of the subject, before you advance to
subjects of a more intricate nature. If this process should appear to
you a little tedious, still you will find yourself fully compensated by
the clear light in which all the succeeding subjects will appear. This
clear and distinct perception of the ground we have been over shows us
just where we are on our journey, and helps us to find the remainder of
the way with far greater ease than we could otherwise do. I do not,
however, propose by any devices to relieve you from the trouble of
thinking. Those who are not willing to incur this trouble can never
learn much of astronomy.

In introducing you to the planets, (which next claim our attention,) I
will, in the first place, endeavor to convey to you some clear views of
these bodies individually, and afterwards help you to form as correct a
notion as possible of their motions and mutual relations.

The name _planet_ is derived from a Greek word, (= planêtês=,
_planetes_,) which signifies a _wanderer_, and is applied to this class
of bodies, because they shift their positions in the heavens, whereas
the fixed stars constantly maintain the same places with respect to each
other. The planets known from a high antiquity are, Mercury, Venus,
Earth, Mars, Jupiter, and Saturn. To these, in 1781, was added Uranus,
(or _Herschel_, as it is sometimes called, from the name of its
discoverer;) and, as late as the commencement of the present century,
four more were added, namely, Ceres, Pallas, Juno, and Vesta. These
bodies are designated by the following characters:

1. Mercury, [Planet: Mercury]
2. Venus, [Planet: Venus]
3. Earth, [Planet: Earth]
4. Mars, [Planet: Mars]
5. Vesta, [Planet: Vesta]
6. Juno, [Planet: Juno]
7. Ceres, [Planet: Ceres]
8. Pallas, [Planet: Pallas]
9. Jupiter, [Planet: Jupiter]
10. Saturn, [Planet: Saturn]
11. Uranus, [Planet: Uranus]

The foregoing are called the _primary_ planets. Several of these have
one or more attendants, or satellites, which revolve around them as they
revolve around the sun. The Earth has one satellite, namely, the Moon;
Jupiter has four; Saturn, seven; and Uranus, six. These bodies are also
planets, but, in distinction from the others, they are called
_secondary_ planets. Hence, the whole number of planets are twenty-nine,
namely, eleven primary, and eighteen secondary, planets.

You need never look for a planet either very far in the north or very
far in the south, since they are always near the ecliptic. Mercury,
which deviates furthest from that great circle, never is seen more than
seven degrees from it; and you will hardly ever see one of the planets
so far from it as this, but they all pursue nearly the same great route
through the skies, in their revolutions around the sun. The new planets,
however, make wider excursions from the plane of the ecliptic,
amounting, in the case of Pallas, to thirty-four and a half degrees.

Mercury and Venus are called _inferior_ planets, because they have their
orbits nearer to the sun than that of the earth; while all the others,
being more distant from the sun than the earth, are called _superior_
planets. The planets present great diversities among themselves, in
respect to distance from the sun, magnitude, time of revolution, and
density. They differ, also, in regard to satellites, of which, as we
have seen, three have respectively four, six, and seven, while more than
half have none at all. It will aid the memory, and render our view of
the planetary system more clear and comprehensive, if we classify, as
far as possible, the various particulars comprehended under the
foregoing heads. As you have had an opportunity, in preceding Letters,
of learning something respecting the means which astronomers have of
ascertaining the distances and magnitudes of these bodies, you will not
doubt that they are really as great as they are represented; but when
you attempt to conceive of spaces so vast, you will find the mind wholly
inadequate to the task. It is indeed but a comparatively small space
that we can fully comprehend at one grasp. Still, by continual and
repeated efforts, we may, from time to time, somewhat enlarge the
boundaries of our mental vision. Let us begin with some known and
familiar space, as the distance between two places we are accustomed to
traverse. Suppose this to be one hundred miles. Taking this as our
measure, let us apply it to some greater distance, as that across the
Atlantic Ocean,--say three thousand miles. From this step we may advance
to some faint conception of the diameter of the earth; and taking that
as a new measure, we may apply it to such greater spaces as the distance
of the planets from the sun. I hope you will make trial of this method
on the following comparative statements respecting the planets.

_Distances from the Sun, in miles._

1. Mercury, 37,000,000
2. Venus, 68,000,000
3. Earth, 95,000,000
4. Mars, 142,000,000
5. Vesta, 225,000,000
6. Juno, }
7. Ceres, } 261,000,000
8. Pallas, }
9. Jupiter, 485,000,000
10. Saturn, 890,000,000
11. Uranus, or Herschel, 1800,000,000

The _dimensions_ of the planetary system are seen from this table to be
vast, comprehending a circular space thirty-six hundred millions of
miles in diameter. A rail-way car, travelling constantly at the rate of
twenty miles an hour, would require more than twenty thousand years to
cross the orbit of Uranus.

_Magnitudes._

Diam. in miles.
1. Mercury, 3140
2. Venus, 7700
3. Earth, 7912
4. Mars, 4200
5. Ceres, 160
6. Jupiter, 89,000
7. Saturn, 79,000
8. Uranus, 35,000

We remark here a great diversity in regard to magnitude,--a diversity
which does not appear to be subject to any definite law. While Venus, an
inferior planet, is nine tenths as large as the earth, Mars, a superior
planet, is only one seventh, while Jupiter is twelve hundred and
eighty-one times as large. Although several of the planets, when nearest
to us, appear brilliant and large, when compared with most of the fixed
stars, yet the angle which they subtend is very small,--that of Venus,
the greatest of all, never exceeding about one minute, which is less
than one thirtieth the apparent diameter of the sun or moon. Jupiter,
also, by his superior brightness, sometimes makes a striking figure
among the stars; yet his greatest apparent diameter is less than one
fortieth that of the sun.

_Periodic Times_.

Mercury revolves around the sun in nearly 3 months.
Venus, " " " " 7-1/2 "
Earth, " " " " 1 year.
Mars, " " " " 2 years.
Ceres, " " " " 4-2/3 "
Jupiter, " " " " 12 "
Saturn, " " " " 29 "
Uranus, " " " " 84 "

From this view, it appears that the planets nearest the sun move most
rapidly. Thus, Mercury performs nearly three hundred and fifty
revolutions while Uranus performs one. The apparent progress of the most
distant planets around the sun is exceedingly slow. Uranus advances only
a little more than four degrees in a whole year; so that we find this
planet occupying the same sign, and of course remaining nearly in the
same part of the heavens, for several years in succession.

After this comparative view of the planets in general, let us now look
at them individually; and first, of the inferior planets, Mercury and
Venus.

MERCURY and VENUS, having their orbits so far within that of the earth,
appear to us as attendants upon the sun. Mercury never appears further
from the sun than twenty-nine degrees, and seldom so far; and Venus,
never more than about forty-seven degrees. Both planets, therefore,
appear either in the west soon after sunset, or in the east a little
before sunrise. In high latitudes, where the twilight is long, Mercury
can seldom be seen with the naked eye, and then only when its angular
distance from the sun is greatest. Copernicus, the great Prussian
astronomer, (who first distinctly established the order of the solar
system, as at present received,) lamented, on his death-bed, that he had
never been able to obtain a sight of Mercury; and Delambre, a
distinguished astronomer of France, saw it but twice. In our latitude,
however, we may see this planet for several evenings and mornings, if we
will watch the time (as usually given in the almanac) when it is at its
greatest elongations from the sun. It will not, however, remain long for
our gaze, but will soon run back to the sun. The reason of this will be
readily understood from the following diagram, Fig. 50. Let S represent
the sun, E, the earth, and M, N, Mercury at its greatest elongations
from the sun, and O Z P, a portion of the sky. Then, since we refer all
distant bodies to the same concave sphere of the heavens, it is evident
that we should see the sun at Z, and Mercury at O, when at its greatest
eastern elongation, and at P, when at its greatest western elongation;
and while passing from M to N through Q, it would appear to describe the
arc O P; and while passing from N to M through R, it would appear to run
back across the sun on the same arc. It is further evident that it would
be visible only when at or near one of its greatest elongations; being
at all other times so near the sun as to be lost in his light.

[Illustration Fig. 50.]

A planet is said to be in _conjunction_ with the sun when it is seen in
the same part of the heavens with the sun. Mercury and Venus have each
two conjunctions, the inferior and the superior conjunction. The
_inferior conjunction_ is its position when in conjunction on the same
side of the sun with the earth, as at Q, in the figure; the _superior
conjunction_ is its position when on the side of the sun most distant
from the earth, as at R.

The time which a planet occupies in making one entire circuit of the
heavens, from any star, until it comes round to the same star again, is
called its _sidereal revolution_. The period occupied by a planet
between two successive conjunctions with the earth is called its
_synodical revolution_. Both the planet and the earth being in motion,
the time of the synodical revolution of Mercury or Venus exceeds that of
the sidereal; for when the planet comes round to the place where it
before overtook the earth, it does not find the earth at that point, but
far in advance of it. Thus, let Mercury come into inferior conjunction
with the earth at C, Fig. 51. In about eighty-eight days, the planet
will come round to the same point again; but, mean-while, the earth has
moved forward through the arc E E´, and will continue to move while the
planet is moving more rapidly to overtake her; the case being analogous
to that of the hour and minute hand of a clock.

[Illustration Fig. 51.]

The synodical period of Mercury is one hundred and sixteen days, and
that of Venus five hundred and eighty-four days. The former is increased
twenty-eight days, and the latter, three hundred and sixty days, by the
motion of the earth; so that Venus, after being in conjunction with the
earth, goes more than twice round the sun before she comes into
conjunction again. For, since the earth is likewise in motion, and moves
more than half as fast as Venus, by the time the latter has gone round
and returned to the place where the two bodies were together, the earth
is more than half way round, and continues moving, so that it will be a
long time before Venus comes up with it.

The motion of an inferior planet is _direct_ in passing through its
superior conjunction, and _retrograde_ in passing through its inferior
conjunction. You will recollect that the motion of a heavenly body is
said to be direct when it is in the order of the signs from west to
east, and retrograde when it is contrary to the order of the signs, or
from east to west. Now Venus, while going from B through D to A, (Fig.
51,) moves from west to east, and would appear to traverse the celestial
vault B´ S´ A´, from right to left; but in passing from A through C to
B, her course would be retrograde, returning on the same arc from left
to right. If the earth were at rest, therefore, (and the sun, of course,
at rest,) the inferior planets would appear to oscillate backwards and
forwards across the sun. But it must be recollected that the earth is
moving in the same direction with the planet, as respects the signs, but
with a slower motion. This modifies the motions of the planet,
accelerating it in the superior, and retarding it in the inferior,
conjunction. Thus, in Fig. 51, Venus, while moving through B D A, would
seem to move in the heavens from B´ to A´, were the earth at rest; but,
mean-while, the earth changes its position from E to E´, on which
account the planet is not seen at A´, but at A´´, being accelerated by
the arc A´ A´´, in consequence of the earth's motion. On the other hand,
when the planet is passing through its inferior conjunction A C B, it
appears to move backwards in the heavens from A´ to B´, if the earth is
at rest, but from A´ to B´´, if the earth has in the mean time moved
from E to E´, being retarded by the arc B´ B´´. Although the motions of
the earth have the effect to accelerate the planet in the superior
conjunction, and to retard it in the inferior, yet, on account of the
greater distance, the apparent motion of the planet is much slower in
the superior than in the inferior conjunction, Venus being the whole
breadth of her orbit, or one hundred and thirty-six millions of miles
further from us when at her greatest, than when at her least, distance,
as is evident from Fig. 51. When passing from the superior to the
inferior conjunction, or from the inferior to the superior, through the
greatest elongations, the inferior planets are _stationary_. Thus, (Fig.
51,) when the planet is at A, the earth being at E, as the planet's
motion is directly towards the spectator, he would constantly project it
at the same point in the heavens, namely, A´; consequently, it would
appear to stand still. Or, when at its greatest elongation on the other
side, at B, as its motion would be directly from the spectator, it would
be seen constantly at B´. If the earth were at rest, the stationary
points would be at the greatest elongations, as at A and B; but the
earth itself is moving nearly at right angles to the planet's motion,
which makes the planet appear to move in the opposite direction. Its
direct motion will therefore continue longer on the one side, and its
retrograde motion longer on the other side, than would be the case, were
it not for the motion of the earth. Mercury, whose greatest angular
distance from the sun is nearly twenty-nine degrees, is stationary at an
elongation of from fifteen to twenty degrees; and Venus, at about
twenty-nine degrees, although her greatest elongation is about
forty-seven degrees.

Mercury and Venus exhibit to the telescope _phases_ similar to those of
the moon. When on the side of their inferior conjunction, as from B to C
through D, Fig. 52, less than half their enlightened disk is turned
towards us, and they appear horned, like the moon in her first and last
quarters; and when on the side of the superior conjunction, as from C to
B through A, more than half the enlightened disk is turned towards us,
and they appear gibbous. At the moment of superior conjunction, the
whole enlightened orb of the planet is turned towards the earth, and the
appearance would be that of the full moon; but the planet is too near
the sun to be commonly visible.

[Illustration Fig. 52.]

We should at first thought expect, that each of these planets would be
largest and brightest near their inferior conjunction, being then so
much nearer to us than at other times; but we must recollect that, when
in this situation, only a small part of the enlightened disk is turned
toward us. Still, the period of greatest brilliancy cannot be when most
of the illuminated side is turned towards us, for then, being at the
superior conjunction, its light will be diminished, both by its great
distance, and by its being so near the sun as to be partially lost in
the twilight. Hence, when Venus is a little within her place of greatest
elongation, about forty degrees from the sun, although less than half
her disk is enlightened, yet, being comparatively near to us, and
shining at a considerable altitude after the evening or before the
morning twilight, she then appears in greatest splendor, and presents an
object admired for its beauty in all ages. Thus Milton,

"Fairest of stars, last in the train of night,
If better thou belong not to the dawn,
Sure pledge of day that crown'st the smiling morn
With thy bright circlet."

Mercury and Venus both _revolve on their axes_ in nearly the same time
with the earth. The diurnal period of Mercury is a little greater, and
that of Venus a little less, than twenty-four hours. These revolutions
have been determined by means of some spot or mark seen by the
telescope, as the revolution of the sun on his axis is ascertained by
means of his spots. Mercury owes most of its peculiarities to its
proximity to the sun. Its light and heat, derived from the sun, are
estimated to be neatly seven times as great as on the earth, and the
apparent magnitude of the sun to a spectator on Mercury would be seven
times greater than to us. Hence the sun would present to an inhabitant
of that planet, with eyes like ours, an object of insufferable
brightness; and all objects on the surface would be arrayed in a light
more glorious than we can well imagine. (See Fig. 53.) The average heat
on the greater portion of this planet would exceed that of boiling
water, and therefore be incompatible with the existence both of an
animal and a vegetable kingdom constituted like ours.

The motion of Mercury, in his revolution round the sun, is swifter than
that of any other planet, being more than one hundred thousand miles
every hour; whereas that of the earth is less than seventy thousand.
Eighteen hundred miles every minute,--crossing the Atlantic ocean in
less than two minutes,--this is a velocity of which we can form but a
very inadequate conception, although, as we shall see hereafter, it is
far less than comets sometimes exhibit.

Venus is regarded as the most beautiful of the planets, and is well
known as the _morning and evening star_. The most ancient nations,
indeed, did not recognise the morning and evening star as one and the
same body, but supposed they were different planets, and accordingly
gave them different names, calling the morning star Lucifer, and the
evening star Hesperus. At her period of greatest splendor, Venus casts a
shadow, and is sometimes visible in broad daylight. Her light is then
estimated as equal to that of twenty stars of the first magnitude. In
the equatorial regions of the earth, where the twilight is short, and
Venus, at her greatest elongation, appears very high above the
horizon, her splendors are said to be far more conspicuous than in
our latitude.

[Illustration Fig. 53. APPARENT MAGNITUDES OF THE SUN, AS SEEN FROM THE
DIFFERENT PLANETS.]

[Illustration Figures 54, 55, 56. VENUS AND MARS.]

Every eight years, Venus forms her conjunction with the sun in the same
part of the heavens. Whatever appearances, therefore, arise from her
position with respect to the earth and the sun, they are repeated every
eight years, in nearly the same form.

Thus, every eight years, Venus is remarkably conspicuous, so as to be
visible in the day-time, being then most favorably situated, on several
accounts; namely, being nearest the earth, and at the point in her orbit
where she gives her greatest brilliancy, that is, a little within the
place of greatest elongation. This is the period for obtaining fine
telescopic views of Venus, when she is seen with spots on her disk. Thus
two figures of the annexed diagram (Fig. 54) represent Venus as seen
near her inferior conjunction, and at the period of maximum brilliancy.
The former situation is favorable for viewing her inequalities of
surface, as indicated by the roughness of the line which separates the
enlightened from the unenlightened part, (the _terminator_.) According
to Schroeter, a German astronomer, Venus has mountains twenty-two miles
high. Her mountains, however, are much more difficult to be seen than
those of the moon.

The sun would appear, as seen from Venus, twice as large as on the
earth, and its light and heat would be augmented in the same proportion.
(See Fig. 53.) In many respects, however, the phenomena of this planet
are similar to those of our own; and the general likeness between Venus
and the earth, in regard to dimensions, revolutions, and seasons, is
greater than exists between any other two bodies of the system.

I will only add to the present Letter a few words on the _transits_ of
the inferior planets.

The transit of Mercury or Venus is its passage across the sun's disk, as
the moon passes over it in a solar eclipse. The planet is seen projected
on the sun's disk in a small, black, round spot, moving slowly over the
face of the sun. As the transit takes place only when the planet is in
inferior conjunction, at which time her motion is retrograde, it is
always from left to right; and, on account of its motion being retarded
by the motion of the earth, (as was explained by Fig. 51, page 232,) it
remains sometimes a long time on the solar disk. Mercury, when it makes
its transit across the sun's centre, may remain on the sun from five to
seven hours.

You may ask, why we do not observe this appearance every time one of the
inferior planets comes into inferior conjunction, for then, of course,
it passes between us and the sun. It must, indeed, at this time, cross
the meridian at the same time with the sun; but, because its orbit is
inclined to that of the sun, it may cross it (and generally does) a
little above or a little below the sun. It is only when the conjunction
takes place at or very near the point where the two orbits cross one
another, that is, near the _node_, that a transit can occur. Thus, if
the orbit of Mercury, N M R, Fig. 50, (page 231,) were in the same plane
with the earth's orbit, (and of course with the sun's apparent orbit,)
then, when the planet was at Q, in its inferior conjunction, the earth
being at E, it would always be projected on the sun's disk at Z, on the
concave sphere of the heavens, and a transit would happen at every
inferior conjunction. But now let us take hold of the point R, and lift
the circle which represents the orbit of Mercury upwards seven degrees,
letting it turn upon the diameter _d b_; then, we may easily see that a
spectator at E would project the planet higher in the heavens than the
sun; and such would always be the case, except when the conjunction
takes place at the node. Then the point of intersection of the two
orbits being in one and the same plane, both bodies would be referred to
the same point on the celestial sphere. As the sun, in his apparent
revolution around the earth every year, passes through every point in
the ecliptic, of course he must every year be at each of the points
where the orbit of Mercury or Venus crosses the ecliptic, that is, at
each of the nodes of one of these planets;[12] and as these nodes are on
opposite sides of the ecliptic, consequently, the sun will pass through
them at opposite seasons of the year, as in January and July, February
and August. Now, should Mercury or Venus happen to come between us and
the sun, just as the sun is passing one of the planet's nodes, a transit
would happen. Hence the transits of Mercury take place in May and
November, and those of Venus, in June and December.

Transits of Mercury occur more frequently than those of Venus. The
periodic times of Mercury and the earth are so adjusted to each other,
that Mercury performs nearly twenty-nine revolutions while the earth
performs seven. If, therefore, the two bodies meet at the node in any
given year, seven years afterwards they will meet nearly at the same
node, and a transit may take place, accordingly, at intervals of seven
years. But fifty-four revolutions of Mercury correspond still nearer to
thirteen revolutions of the earth; and therefore a transit is still more
probable after intervals of thirteen years. At intervals of thirty-three
years, transits of Mercury are exceedingly probable, because in that
time Mercury makes almost exactly one hundred and thirty-seven
revolutions. Intermediate transits, however, may occur at the other
node. Thus, transits of Mercury happened at the ascending node in 1815,
and 1822, at intervals of seven years; and at the descending node in
1832, which will return in 1845, after thirteen years.

Transits of Venus are events of very unfrequent occurrence. Eight
revolutions of the earth are completed in nearly the same time as
thirteen revolutions of Venus; and hence two transits of Venus may occur
after an interval of eight years, as was the case at the last return of
the phenomenon, one transit having occurred in 1761, and another in
1769. But if a transit does not happen after eight years, it will not
happen at the same node, until an interval of two hundred and
thirty-five years: but intermediate transits may occur at the other
node. The next transit of Venus will take place in 1874, being two
hundred and thirty-five years after the first that was ever _observed_,
which occurred in 1639. This was seen, for the first time by mortal
eyes, by two youthful English astronomers, Horrox and Crabtree. Horrox
was a young man of extraordinary promise, and indicated early talents
for practical astronomy, which augured the highest eminence; but he died
in the twenty-third year of his age. He was only twenty when the transit
appeared, and he had made the calculations and observations, by which he
was enabled to anticipate its arrival several years before. At the
approach of the desired time for observing the transit, he received the
sun's image through a telescope in a dark room upon a white piece of
paper, and after waiting many hours with great impatience, (as his
calculation did not lead him to a knowledge of the precise time of the
occurrence,) at last, on the twenty-fourth of November, 1639, old style,
at three and a quarter hours past twelve, just as he returned from
church, he had the pleasure to find a large round spot near the limb of
the sun's image. It moved slowly across the sun's disk, but had not
entirely left it when the sun set.

The great interest attached by astronomers to a transit of Venus arises
from its furnishing the most accurate means in our power of determining
the _sun's horizontal parallax_,--an element of great importance, since
it leads us to a knowledge of the distance of the earth from the sun,
which again affords the means of estimating the distances of all the
other planets, and possibly, of the fixed stars. Hence, in 1769, great
efforts were made throughout the civilized world, under the patronage of
different governments, to observe this phenomenon under circumstances
the most favorable for determining the parallax of the sun.

The common methods of finding the parallax of a heavenly body cannot be
relied on to a greater degree of accuracy than four seconds. In the case
of the moon, whose greatest parallax amounts to about one degree, this
deviation from absolute accuracy is not very material; but it amounts to
nearly half the entire parallax of the sun.

If the sun and Venus were equally distant from us, they would be equally
affected by parallax, as viewed by spectators in different parts of the
earth, and hence their _relative_ situation would not be altered by it;
but since Venus, at the inferior conjunction, is only about one third as
far off as the sun, her parallax is proportionally greater, and
therefore spectators at distant points will see Venus projected on
different parts of the solar disk, as the planet traverses the disk.
Astronomers avail themselves of this circumstance to ascertain the sun's
horizontal parallax, which they are enabled to do by comparing it with
that of Venus, in a manner which, without a knowledge of trigonometry,
you will not fully understand. In order to make the difference in the
apparent places of Venus on the sun's disk as great as possible, very
distant places are selected for observation. Thus, in the transits of
1761 and 1769, several of the European governments fitted out expensive
expeditions to parts of the earth remote from each other. For this
purpose, the celebrated Captain Cook, in 1769, went to the South Pacific
Ocean, and observed the transit at the island of Otaheite, while others
went to Lapland, for the same purpose, and others still, to many other
parts of the globe. Thus, suppose two observers took their stations on
opposite sides of the earth, as at A, and B, Fig. 57, page 242; at A,
the planet V would be seen on the sun's disk at _a_, while at B, it
would be seen at _b_.

The appearance of Venus on the sun's disk being that of a well-defined
black spot, and the exactness with which the moment of external or
internal contact may be determined, are circumstances favorable to the
exactness of the result; and astronomers repose so much confidence in
the estimation of the sun's horizontal parallax, as derived from
observations on the transit of 1769, that this important element is
thought to be ascertained within one tenth of a second. The general
result of all these observations gives the sun's horizontal parallax
eight seconds and six tenths,--a result which shows at once that the sun
must be a great way off, since the semidiameter of the earth, a line
nearly four thousand miles in length, would appear at the sun under an
angle less than one four hundredth of a degree. During the transits of
Venus over the sun's disk, in 1761 and 1769, a sort of penumbral light
was observed around the planet, by several astronomers, which was
thought to indicate an _atmosphere_. This appearance was particularly
observable while the planet was coming on or going off the solar disk.
The total immersion and emersion were not instantaneous; but as two
drops of water, when about to separate, form a ligament between them, so
there was a dark shade stretched out between Venus and the sun; and when
the ligament broke, the planet seemed to have got about an eighth part
of her diameter from the limb of the sun. The various accounts of the
two transits abound with remarks like these, which indicate the
existence of an atmosphere about Venus of nearly the density and extent
of the earth's atmosphere. Similar proofs of the existence of an
atmosphere around this planet are derived from appearances of twilight.

[Illustration Fig. 57.]

The elder astronomers imagined that they had discovered a _satellite_
accompanying Venus in her transit. If Venus had in reality any
satellite, the fact would be obvious at her transits, as, in some of
them at least, it is probable that the satellite would be projected near
the primary on the sun's disk; but later astronomers have searched in
vain for any appearances of the kind, and the inference is, that former
astronomers were deceived by some optical illusion.

FOOTNOTE:

[12] You will recollect that the sun is said to be at the node, when the
places of the node and the sun are both projected, by a spectator on the
earth, upon the same part of the heavens.

LETTER XXI.

SUPERIOR PLANETS: MARS, JUPITER, SATURN, AND URANUS.

"With what an awful, world-revolving power,
Were first the unwieldy planets launched along
The illimitable void! There to remain
Amidst the flux of many thousand years,
That oft has swept the toiling race of men,
And all their labored monuments, away."--_Thomson._

MERCURY AND VENUS, as we have seen, are always observed near the sun,
and from this circumstance, as well as from the changes of magnitude and
form which they undergo, we know that they have their orbits within that
of the earth, and hence we call them _inferior_ planets. On the other
hand, Mars, Jupiter, Saturn, and Uranus, exhibit such appearances, at
different times, as show that they revolve around the sun at a greater
distance than the earth, and hence we denominate them _superior_
planets. We know that they never come between us and the sun, because
they never undergo those changes which Mercury and Venus, as well as the
moon, sustain, in consequence of their coming into such a position.
They, however, wander to the greatest angular distance from the sun,
being sometimes seen one hundred and eighty degrees from him, so as to
rise when the sun sets. All these different appearances must naturally
result from their orbits' being exterior to that of the earth, as will
be evident from the following representation. Let E, Fig. 58, page 244,
be the earth, and M, one of the superior planets, Mars, for example,
each body being seen in its path around the sun. At M, the planet would
be in opposition to the sun, like the moon at the full; at Q and Q´, it
would be seen ninety degrees off, or in quadrature; and at M´, in
conjunction. We know, however, that this must be a superior and not an
inferior conjunction, for the illuminated disk is still turned towards
us; whereas, if it came between us and the sun, like Mercury, or Venus,
in its inferior conjunction, its dark side would be presented to us.

[Illustration Fig. 58.]

The superior planets do not exhibit to the telescope different phases,
but, with a single exception, they always present the side that is
turned towards the earth fully enlightened. This is owing to their great
distance from the earth; for were the spectator to stand upon the sun,
he would of course always have the illuminated side of each of the
planets turned towards him; but so distant are all the superior planets,
except Mars, that they are viewed by us very nearly, in the same manner
as they would be if we actually stood on the sun. Mars, however, is
sufficiently near to appear somewhat gibbous when at or near one of its
quadratures. Thus, when the planet is at Q, it is plain that, of the
hemisphere that is turned towards the earth, a small part is
unilluminated.

Mars is a small planet, his diameter being only about half that of the
earth, or four thousand two hundred miles. He also, at times, comes
nearer to the earth than any other planet, except Venus. His _mean_
distance from the sun is one hundred and forty-two millions of miles;
but his orbit is so elliptical, that his distance varies much in
different parts of his revolution. Mars is always very near the
ecliptic, never varying from it more than two degrees. He is
distinguished from all the planets by his deep red color, and fiery
aspect; but his brightness and apparent magnitude vary much, at
different times, being sometimes nearer to us than at others by the
whole diameter of the earth's orbit; that is, by about one hundred and
ninety millions of miles. When Mars is on the same side of the sun with
the earth, or at his opposition, he comes within forty-seven millions of
miles of the earth, and, rising about the time the sun sets, surprises
us by his magnitude and splendor; but when he passes to the other side
of the sun, to his superior conjunction, he dwindles to the appearance
of a small star, being then two hundred and thirty-seven millions of
miles from us. Thus, let M, Fig, 58, represent Mars in opposition, and
M´, in the superior conjunction, while E represents the earth. It is
obvious that, in the former situation, the planet must be nearer to the
earth than in the latter, by the whole diameter of the earth's orbit.
When viewed with a powerful telescope, the surface of Mars appears
diversified with numerous varieties of light and shade. The region
around the poles is marked by white spots, (see Fig. 56, page 237,)
which vary their appearances with the changes of seasons in the planet.
Hence Dr. Herschel conjectured that they were owing to ice and snow,
which alternately accumulate and melt away, according as it is Winter or
Summer, in that region. They are greatest and most conspicuous when that
part of the planet has just emerged from a long Winter, and they
gradually waste away, as they are exposed to the solar heat. Fig. 56,
represents the planet, as exhibited, under the most favorable
circumstances, to a powerful telescope, at the time when its gibbous
form is strikingly obvious. It has been common to ascribe the ruddy
light of Mars to an extensive and dense atmosphere, which was said to be
distinctly indicated by the gradual diminution of light observed in a
star, as it approaches very near to the planet, in undergoing an
occultation; but more recent observations afford no such evidence of an
atmosphere.

By observations on the spots, we learn that Mars revolves on his axis in
very nearly the same time with the earth, (twenty-four hours thirty-nine
minutes twenty-one seconds and three tenths,) and that the inclination
of his axis to that of his orbit is also nearly the same, being thirty
degrees eighteen minutes ten seconds and eight tenths. Hence the changes
of day and night must be nearly the same there as here, and the seasons
also very similar to ours. Since, however, the distance of Mars from the
sun is one hundred and forty-two while that of the earth is only
ninety-five millions of miles, the sun will appear more than twice as
small on that planet as on ours, (see Fig. 53, page 236,) and its light
and heat will be diminished in the same proportion. Only the equatorial
regions, therefore, will be suitable for the existence of animals and
vegetables.

The earth will be seen from Mars as an inferior planet, always near the
sun, presenting appearances similar, in many respects, to those which
Venus presents to us. It will be to that planet the evening and morning
star, sung by their poets (if poets they have) with a like enthusiasm.
The moon will attend the earth as a little star, being never seen
further from her side than about the diameter under which we view the
moon. To the telescope, the earth will exhibit phases similar to those
of Venus; and, finally, she will, at long intervals, make her transits
over the solar disk. Mean-while, Venus will stand to Mars in a relation
similar to that of Mercury [Illustration Figures 59, 60. JUPITER AND
SATURN.] to us, revealing herself only when at the periods of her
greatest elongation, and at all other times hiding herself within the
solar blaze. Mercury will never be visible to an inhabitant of Mars.

Jupiter is distinguished from all the other planets by his great
_magnitude_. His diameter is eighty-nine thousand miles, and his volume
one thousand two hundred and eighty times that of the earth. His figure
is strikingly spheroidal, the equatorial being more than six thousand
miles longer than the polar diameter. Such a figure might naturally be
expected from the rapidity of his diurnal rotation, which is
accomplished in about ten hours. A place on the equator of Jupiter must
turn twenty-seven times as fast as on the terrestrial equator. The
distance of Jupiter from the sun is nearly four hundred and ninety
millions of miles, and his revolution around the sun occupies nearly
twelve years. Every thing appertaining to Jupiter is on a grand scale. A
world in itself, equal in dimensions to twelve hundred and eighty of
ours; the whole firmament rolling round it in the short space of ten
hours, a movement so rapid that the eye could probably perceive the
heavenly bodies to change their places every moment; its year dragging
out a length of more than four thousand days, and more than ten thousand
of its own days, while its nocturnal skies are lighted up with four
brilliant moons;--these are some of the peculiarities which characterize
this magnificent planet.

The view of Jupiter through a good telescope is one of the most splendid
and interesting spectacles in astronomy. The disk expands into a large
and bright orb, like the full moon; the spheroidal figure which theory
assigns to revolving spheres, especially to those which turn with great
velocity, is here palpably exhibited to the eye; across the disk,
arranged in parallel stripes, are discerned several dusky bands, called
_belts_; and four bright satellites, always in attendance, and ever
varying their positions, compose a splendid retinue. Indeed, astronomers
gaze with peculiar interest on Jupiter and his moons, as affording a
miniature representation of the whole solar system, repeating, on a
smaller scale, the same revolutions, and exemplifying more within the
compass of our observation, the same laws as regulate the entire
assemblage of sun and planets. Figure 59, facing page 247, gives a
correct view of Jupiter, as exhibited to a powerful telescope in a clear
evening. You will remark his flattened or spheroidal figure, the belts
which appear in parallel stripes across his disk, and the four
satellites, that are seen like little stars in a straight line with the
equator of the planet.

The _belts of Jupiter_ are variable in their number and dimensions. With
the smaller telescopes only one or two are seen, and those across the
equatorial regions; but with more powerful instruments, the number is
increased, covering a large part of the entire disk. Different opinions
have been entertained by astronomers respecting the cause of these
belts; but they have generally been regarded as clouds formed in the
atmosphere of the planet, agitated by winds, as is indicated by their
frequent changes, and made to assume the form of belts parallel to the
equator, like currents that circulate around our globe. Sir John
Herschel supposes that the belts are not ranges of clouds, but portions
of the planet itself, brought into view by the removal of clouds and
mists, that exist in the atmosphere of the planet, through which are
openings made by currents circulating around Jupiter.

The _satellites of Jupiter_ may be seen with a telescope of very
moderate powers. Even a common spyglass will enable us to discern them.
Indeed, one or two of them have been occasionally seen with the naked
eye. In the largest telescopes they severally appear as bright as
Sirius. With such an instrument, the view of Jupiter, with his moons and
belts, is truly a magnificent spectacle. As the orbits of the satellites
do not deviate far from the plane of the ecliptic, and but little from
the equator of the planet, they are usually seen in nearly a straight
line with each other, extending across the central part of the disk.
(See Fig. 59, facing page 247.)

Jupiter and his satellites exhibit in miniature all the phenomena of the
solar system. The satellites perform, around their primary, revolutions
very analogous to those which the planets perform around the sun,
having, in like manner, motions alternately direct, stationary, and
retrograde. They are all, with one exception, a little larger than the
moon; and the second satellite, which is the smallest, is nearly as
large as the moon, being two thousand and sixty-eight miles in diameter.
They are all very small compared with the primary, the largest being
only one twenty-sixth part of the primary. The outermost satellite
extends to the distance from the planet of fourteen times his diameter.
The whole system, therefore, occupies a region of space more than one
million miles in breadth. Rapidity of motion, as well as greatness of
dimensions, is characteristic of the system of Jupiter. I have already
mentioned that the planet itself has a motion on its own axis much
swifter than that of the earth, and the motions of the satellites are
also much more rapid than that of the moon. The innermost, which is a
little further off than the moon is from the earth, goes round its
primary in about a day and three quarters; and the outermost occupies
less than seventeen days.

The orbits of the satellites are nearly or quite circular, and deviate
but little from the plane of the planet's equator, and of course are but
slightly inclined to the plane of his orbit. They are therefore in a
similar situation with respect to Jupiter, as the moon would be with
respect to the earth, if her orbit nearly coincided with the ecliptic,
in which case, she would undergo an eclipse at every opposition. The
eclipses of Jupiter's satellites, in their general circumstances, are
perfectly analogous to those of the moon, but in their details they
differ in several particulars. Owing to the much greater distance of
Jupiter from the sun, and its greater magnitude, the cone of its shadow
is much longer and larger than that of the earth. On this account, as
well as on account of the little inclination of their orbit to that of
the primary, the three inner satellites of Jupiter pass through his
shadow, and are totally eclipsed, at every revolution. The fourth
satellite, owing to the greater inclination of its orbit, sometimes,
though rarely, escapes eclipse, and sometimes merely grazes the limits
of the shadow, or suffers a partial eclipse. These eclipses, moreover,
are not seen, as is the case with those of the moon, from the centre of
their motion, but from a remote station, and one whose situation with
respect to the line of the shadow is variable. This makes no difference
in the _times_ of the eclipses, but it makes a very great one in their
visibility, and in their apparent situations with respect to the planet
at the moment of their entering or quitting the shadow.

[Illustration Fig. 61.]

The eclipses of Jupiter's satellites present some curious phenomena,
which you will easily understand by studying the following diagram. Let
A, B, C, D, Fig. 61, represent the earth in different parts of its
orbit; J, Jupiter, in his orbit, surrounded by his four satellites, the
orbits of which are marked 1, 2, 3, 4. At _a_, the first satellite
enters the shadow of the planet, emerges from it at _b_, and advances to
its greatest elongation at _c_. The other satellites traverse the shadow
in a similar manner. The apparent place, with respect to the planet, at
which these eclipses will be seen to occur, will be altered by the
position the earth happens at that moment to have in its orbit; but
their appearances for any given night, as exhibited at Greenwich, are
calculated and accurately laid down in the Nautical Almanac.

When one of the satellites is passing between Jupiter and the sun, it
casts its shadow on the primary, as the moon casts its shadow on the
earth in a solar eclipse. We see with the telescope the shadow
traversing the disk. Sometimes, the satellite itself is seen projected
on the disk; but, being illuminated as well as the primary, it is not so
easily distinguished as Venus or Mercury, when seen on the sun's disk in
one of their transits, since these bodies have their dark sides turned
towards us; but the satellite is illuminated by the sun, as well as the
primary, and therefore is not easily distinguishable from it.

The eclipses of Jupiter's satellites have been studied with great
attention by astronomers, on account of their affording one of the
easiest methods of determining the _longitude_. On this subject, Sir
John Herschel remarks: "The discovery of Jupiter's satellites by
Galileo, which was one of the first fruits of the invention of the
telescope, forms one of the most memorable epochs in the history of
astronomy. The first astronomical solution of the problem of 'the
longitude,'--the most important problem for the interests of mankind
that has ever been brought under the dominion of strict scientific
principles,--dates immediately from this discovery. The final and
conclusive establishment of the Copernican system of astronomy may also
be considered as referable to the discovery and study of this exquisite
miniature system, in which the laws of the planetary motions, as
ascertained by Kepler, and especially that which connects their periods
and distances, were speedily traced, and found to be satisfactorily
maintained."

The entrance of one of Jupiter's satellites into the shadow of the
primary, being seen like the entrance of the moon into the earth's
shadow at the same moment of absolute time, at all places where the
planet is visible, and being wholly independent of parallax, that is,
presenting the same phenomenon to places remote from each other; being,
moreover, predicted beforehand, with great accuracy, for the instant of
its occurrence at Greenwich, and given in the Nautical Almanac; this
would seem to be one of those events which are peculiarly adapted for
finding the longitude. For you will recollect, that "any instantaneous
appearance in the heavens, visible at the same moment of absolute time
at any two places, may be employed for determining the difference of
longitude between those places; for the difference in their local times,
as indicated by clocks or chronometers, allowing fifteen degrees for
every hour, will show their difference of longitude."

With respect to the method by the eclipses of Jupiter's satellites, it
must be remarked, that the extinction of light in the satellite, at its
immersion, and the recovery of its light at its emersion, are not
instantaneous, but gradual; for the satellite, like the moon, occupies
some time in entering into the shadow, or in emerging from it, which
occasions a progressive diminution or increase of light. Two observers
in the same room, observing with different telescopes the same eclipse,
will frequently disagree, in noting its time, to the amount of fifteen
or twenty seconds. Better methods, therefore, of finding the longitude,
are now employed, although the facility with which the necessary
observations can be made, and the little calculation required, still
render this method eligible in many cases where extreme accuracy is not
important. As a telescope is essential for observing an eclipse of one
of the satellites, it is obvious that this method cannot be practised at
sea, since the telescope cannot be used on board of ship, for want of
the requisite steadiness.

The grand discovery of the _progressive motion of light_ was first made
by observations on the eclipses of Jupiter's satellites. In the year
1675, it was remarked by Roemer, a Danish astronomer, on comparing
together observations of these eclipses during many successive years,
that they take place sooner by about sixteen minutes, when the earth is
on the same side of the sun with the planet, than when she is on the
opposite side. The difference he ascribes to the progressive motion of
light, which takes that time to pass through the diameter of the earth's
orbit, making the velocity of light about one hundred and ninety-two
thousand miles per second. So great a velocity startled astronomers at
first, and produced some degree of distrust of this explanation of the
phenomenon; but the subsequent discovery of what is called the
aberration of light, led to an independent estimation of the velocity of
light, with almost precisely the same result.

Few greater feats have ever been performed by the human mind, than to
measure the speed of light,--a speed so great, as would carry it across
the Atlantic Ocean in the sixty-fourth part of a second, and around the
globe in less than the seventh part of a second! Thus has man applied
his scale to the motions of an element, that literally leaps from world
to world in the twinkling of an eye. This is one example of the great
power which the invention of the telescope conferred on man.

Could we plant ourselves on the surface of this vast planet, we should
see the same starry firmament expanding over our heads as we see now;
and the same would be true if we could fly from one planetary world to
another, until we made the circuit of them all; but the sun and the
planetary system would present themselves to us under new and strange
aspects. The sun himself would dwindle to one twenty-seventh of his
present surface, (Fig. 53, facing page 236,) and afford a degree of
light and heat proportionally diminished; Mercury, Venus, and even the
Earth, would all disappear, being too near the sun to be visible; Mars
would be as seldom seen as Mercury is by us, and constitute the only
inferior planet. On the other hand, Saturn would shine with greatly
augmented size and splendor. When in opposition to the sun, (at which
time it comes nearest to Jupiter,) it would be a grand object, appearing
larger than either Venus or Jupiter does to us. When, however, passing
to the other side of the sun, through its superior conjunction, it would
gradually diminish in size and brightness, and at length become much
less than it ever appears to us, since it would then be four hundred
millions of miles further from Jupiter than it ever is from us.

Although Jupiter comes four hundred millions of miles nearer to Uranus
than the earth does, yet it is still thirteen hundred millions of miles
distant from that planet. Hence the augmentation of the magnitude and
light of Uranus would be barely sufficient to render it distinguishable
by the naked eye. It appears, therefore, that Saturn is the peculiar
ornament of the firmament of Jupiter, and would present to the telescope
most interesting and sublime phenomena. As we owe the revelation of the
system of Jupiter and his attendant worlds wholly to the telescope, and
as the discovery and observation of them constituted a large portion of
the glory of Galileo, I am now forcibly reminded of his labors, and will
recur to his history, and finish the sketch which I commenced in a
previous Letter.

LETTER XXII.

COPERNICUS.--GALILEO.

"They leave at length the nether gloom, and stand
Before the portals of a better land;
To happier plains they come, and fairer groves,
The seats of those whom Heaven, benignant, loves;
A brighter day, a bluer ether, spreads
Its lucid depths above their favored heads;
And, purged from mists that veil our earthly skies,
Shine suns and stars unseen by mortal eyes."--_Virgil._

IN order to appreciate the value of the contributions which Galileo made
to astronomy, soon after the invention of the telescope, it is necessary
to glance at the state of the science when he commenced his discoveries
For many centuries, during the middle ages, a dark night had hung over
astronomy, through which hardly a ray of light penetrated, when, in the
eastern part of civilized Europe, a luminary appeared, that proved the
harbinger of a bright and glorious day. This was Copernicus, a native of
Thorn, in Prussia. He was born in 1473. Though destined for the
profession of medicine, from his earliest years he displayed a great
fondness and genius for mathematical studies, and pursued them with
distinguished success in the University of Cracow. At the age of
twenty-five years, he resorted to Italy, for the purpose of studying
astronomy, where he resided a number of years. Thus prepared, he
returned to his native country, and, having acquired an ecclesiastical
living that was adequate to his support in his frugal mode of life, he
established himself at Frauenberg, a small town near the mouth of the
Vistula, where he spent nearly forty years in observing the heavens, and
meditating on the celestial motions. He occupied the upper part of a
humble farm-house, through the roof of which he could find access to an
unobstructed sky, and there he carried on his observations. His
instruments, however, were few and imperfect, and it does not appear
that he added any thing to the art of practical astronomy. This was
reserved for Tycho Brahe, who came a half a century after him. Nor did
Copernicus enrich the science with any important discoveries. It was not
so much his genius or taste to search for new bodies, or new phenomena
among the stars, as it was to explain the reasons of the most obvious
and well-known appearances and motions of the heavenly bodies. With this
view, he gave his mind to long-continued and profound meditation.

Copernicus tells us that he was first led to think that the apparent
motions of the heavenly bodies, in their diurnal revolution, were owing
to the real motion of the earth in the opposite direction, from
observing instances of the same kind among terrestrial objects; as when
the shore seems to the mariner to recede, as he rapidly sails from it;
and as trees and other objects seem to glide by us, when, on riding
swiftly past them, we lose the consciousness of our own motion. He was
also smitten with the _simplicity_ prevalent in all the works and
operations of Nature, which is more and more conspicuous the more they
are understood; and he hence concluded that the planets do not move in
the complicated paths which most preceding astronomers assigned to them.
I shall explain to you, hereafter, the details of his system. I need
only at present remind you that the hypothesis which he espoused and
defended, (being substantially the same as that proposed by Pythagoras,
five hundred years before the Christian era,) supposes, first, that the
apparent movements of the sun by day, and of the moon and stars by
night, from east to west, result from the actual revolution of the earth
on its own axis from west to east; and, secondly, that the earth and all
the planets revolve about the sun in circular orbits. This hypothesis,
when he first assumed it, was with him, as it had been with Pythagoras,
little more than mere conjecture. The arguments by which its truth was
to be finally established were not yet developed, and could not be,
without the aid of the telescope, which was not yet invented. Upon this
hypothesis, however, he set out to explain all the phenomena of the
visible heavens,--as the diurnal revolutions of the sun, moon, and
stars, the slow progress of the planets through the signs of the zodiac,
and the numerous irregularities to which the planetary motions are
subject. These last are apparently so capricious,--being for some time
forward, then stationary, then backward, then stationary again, and
finally direct, a second time, in the order of the signs, and constantly
varying in the velocity of their movements,--that nothing but
long-continued and severe meditation could have solved all these
appearances, in conformity with the idea that each planet is pursuing
its simple way all the while in a circle around the sun. Although,
therefore, Pythagoras fathomed the profound doctrine that the sun is the
centre around which the earth and all the planets revolve, yet we have
no evidence that he ever solved the irregular motions of the planets in
conformity with his hypothesis, although the explanation of the diurnal
revolution of the heavens, by that hypothesis, involved no difficulty.
Ignorant as Copernicus was of the principle of gravitation, and of most
of the laws of motion, he could go but little way in following out the
consequences of his own hypothesis; and all that can be claimed for him
is, that he solved, by means of it, most of the common phenomena of the
celestial motions. He indeed got upon the road to truth, and advanced
some way in its sure path; but he was able to adduce but few independent
proofs, to show that it was the truth. It was only quite at the close of
his life that he published his system to the world, and that only at the
urgent request of his friends; anticipating, perhaps, the opposition of
a bigoted priesthood, whose fury was afterwards poured upon the head of
Galileo, for maintaining the same doctrines.

Although, therefore, the system of Copernicus afforded an explanation of
the celestial motions, far more simple and rational than the previous
systems which made the earth the centre of those motions, yet this fact
alone was not sufficient to compel the assent of astronomers; for the
greater part, to say the least, of the same phenomena, could be
explained on either hypothesis. With the old doctrine astronomers were
already familiar, a circumstance which made it seem easier; while the
new doctrines would seem more difficult, from their being imperfectly
understood. Accordingly, for nearly a century after the publication of
the system of Copernicus, he gained few disciples. Tycho Brahe rejected
it, and proposed one of his own, of which I shall hereafter give you
some account; and it would probably have fallen quite into oblivion, had
not the observations of Galileo, with his newly-invented telescope,
brought to light innumerable proofs of its truth, far more cogent than
any which Copernicus himself had been able to devise.

Galileo no sooner had completed his telescope, and directed it to the
heavens, than a world of wonders suddenly burst upon his enraptured
sight. Pointing it to the moon, he was presented with a sight of her
mottled disk, and of her mountains and valleys. The sun exhibited his
spots; Venus, her phases; and Jupiter, his expanded orb, and his retinue
of moons. These last he named, in honor of his patron, Cosmo d'Medici,
_Medicean stars_. So great was this honor deemed of associating one's
name with the stars, that express application was made to Galileo, by
the court of France, to award this distinction to the reigning Monarch,
Henry the Fourth, with plain intimations, that by so doing he would
render himself and his family rich and powerful for ever.

Galileo published the result of his discoveries in a paper, denominated
'_Nuncius Sidereus_,' the 'Messenger of the Stars.' In that ignorant and
marvellous age, this publication produced a wonderful excitement. "Many
doubted, many positively refused to believe, so novel an announcement;
all were struck with the greatest astonishment, according to their
respective opinions, either at the new view of the universe thus offered
to them, or at the high audacity of Galileo, in inventing such fables."
Even Kepler, the great German astronomer, of whom I shall tell you more
by and by, wrote to Galileo, and desired him to supply him with
arguments, by which he might answer the objections to these pretended
discoveries with which he was continually assailed. Galileo answered him
as follows: "In the first place, I return you my thanks that you first,
and almost alone, before the question had been sifted, (such is your
candor, and the loftiness of your mind,) put faith in my assertions. You
tell me you have some telescopes, but not sufficiently good to magnify
distant objects with clearness, and that you anxiously expect a sight of
mine, which magnifies images more than a thousand times. It is mine no
longer, for the Grand Duke of Tuscany has asked it of me, and intends to
lay it up in his museum, among his most rare and precious curiosities,
in eternal remembrance of the invention.

"You ask, my dear Kepler, for other testimonies. I produce, for one, the
Grand Duke, who, after observing the Medicean planets several times with
me at Pisa, during the last months, made me a present, at parting, of
more than a thousand florins, and has now invited me to attach myself to
him, with the annual salary of one thousand florins, and with the title
of 'Philosopher and Principal Mathematician to His Highness;' without
the duties of any office to perform, but with the most complete leisure.
I produce, for another witness, myself, who, although already endowed in
this College with the noble salary of one thousand florins, such as no
professor of mathematics ever before received, and which I might
securely enjoy during my life, even if these planets should deceive me
and should disappear, yet quit this situation, and take me where want
and disgrace will be my punishment, should I prove to have been
mistaken."

The learned professors in the universities, who, in those days, were
unaccustomed to employ their senses in inquiring into the phenomena of
Nature, but satisfied themselves with the authority of Aristotle, on all
subjects, were among the most incredulous with respect to the
discoveries of Galileo. "Oh, my dear Kepler," says Galileo, "how I wish
that we could have one hearty laugh together. Here, at Padua, is the
principal Professor of Philosophy, whom I have repeatedly and urgently
requested to look at the moon and planets through my glass, which he
pertinaciously refuses to do. Why are you not here? What shouts of
laughter we should have at this glorious folly, and to hear the
Professor of Philosophy at Pisa laboring before the Grand Duke, with
logical arguments, as if with magical incantations, to charm the new
planets out of the sky."

The following argument by Sizzi, a contemporary astronomer of some note,
to prove that there can be only seven planets, is a specimen of the
logic with which Galileo was assailed. "There are seven windows given
to animals in the domicile of the head, through which the air is
admitted to the tabernacle of the body, to enlighten, to warm, and to
nourish it; which windows are the principal parts of the microcosm, or
little world,--two nostrils, two eyes, two ears, and one mouth. So in
the heavens, as in a macrocosm, or great world, there are two favorable
stars, Jupiter and Venus; two unpropitious, Mars and Saturn; two
luminaries, the Sun and Moon; and Mercury alone, undecided and
indifferent. From which, and from many other phenomena of Nature, such
as the seven metals, &c., which it were tedious to enumerate, we gather
that the number of planets is necessarily seven. Moreover, the
satellites are invisible to the naked eye, and therefore can exercise no
influence over the earth, and therefore would be useless, and therefore
do not exist. Besides, as well the Jews and other ancient nations, as
modern Europeans, have adopted the division of the week into seven days,
and have named them from the seven planets. Now, if we increase the
number of planets, this whole system falls to the ground."

When, at length, the astronomers of the schools found it useless to deny
the fact that Jupiter is attended by smaller bodies, which revolve
around him, they shifted their ground of warfare, and asserted that
Galileo had not told the whole truth; that there were not merely _four_
satellites, but a still greater number; one said five; another, nine;
and another, twelve; but, in a little time, Jupiter moved forward in his
orbit, and left all behind him, save the four Medicean stars.

It had been objected to the Copernican system, that were Venus a body
which revolved around the sun in an orbit interior to that of the earth,
she would undergo changes similar to those of the moon. As no such
changes could be detected by the naked eye, no satisfactory answer could
be given to this objection; but the telescope set all right, by showing,
in fact, the phases of Venus. The same instrument, disclosed, also, in
the system of Jupiter and his moons, a miniature exhibition of the solar
system itself. It showed the actual existence of the motion of a number
of bodies around one central orb, exactly similar to that which was
predicated of the sun and planets. Every one, therefore, of these new
and interesting discoveries, helped to confirm the truth of the system
of Copernicus.

But a fearful cloud was now rising over Galileo, which spread itself,
and grew darker every hour. The Church of Rome had taken alarm at the
new doctrines respecting the earth's motion, as contrary to the
declarations of the Bible, and a formidable difficulty presented itself,
namely, how to publish and defend these doctrines, without invoking the
terrible punishments inflicted by the Inquisition on heretics. No work
could be printed without license from the court of Rome; and any
opinions supposed to be held and much more known to be taught by any
one, which, by an ignorant and superstitious priesthood, could be
interpreted as contrary to Scripture, would expose the offender to the
severest punishments, even to imprisonment, scourging, and death. We,
who live in an age so distinguished for freedom of thought and opinion,
can form but a very inadequate conception of the bondage in which the
minds of men were held by the chains of the Inquisition. It was
necessary, therefore, for Galileo to proceed with the greatest caution
in promulgating truths which his own discoveries had confirmed. He did
not, like the Christian martyrs, proclaim the truth in the face of
persecutions and tortures; but while he sought to give currency to the
Copernican doctrines, he labored, at the same time, by cunning
artifices, to blind the ecclesiastics to his real designs, and thus to
escape the effects of their hostility.

Before Galileo published his doctrines in form, he had expressed himself
so freely, as to have excited much alarm among the ecclesiastics. One of
them preached publicly against him, taking for his text, the passage,
"Ye men of Galilee, why stand ye here gazing up into heaven?" He
therefore thought it prudent to resort to Rome, and confront his enemies
face to face. A contemporary describes his appearance there in the
following terms, in a letter addressed to a Romish Cardinal: "Your
Eminence would be delighted with Galileo, if you heard him holding
forth, as he often does, in the midst of fifteen or twenty, all
violently attacking him, sometimes in one house, sometimes in another.
But he is armed after such fashion, that he laughs all of them to scorn;
and even if the novelty of his opinions prevents entire persuasion, at
least he convicts of emptiness most of the arguments with which his
adversaries endeavor to overwhelm him."

In 1616, Galileo, as he himself states, had a most gracious audience of
the Pope, Paul the Fifth, which lasted for nearly an hour, at the end of
which his Holiness assured him, that the Congregation were no longer in
a humor to listen lightly to calumnies against him, and that so long as
he occupied the Papal chair, Galileo might think himself out of all
danger. Nevertheless, he was not allowed to return home, without
receiving formal notice not to teach the opinions of Copernicus, "that
the sun is in the centre of the system, and that the earth moves about
it," from that time forward, in any manner.

Galileo had a most sarcastic vein, and often rallied his persecutors
with the keenest irony. This he exhibited, some time after quitting
Rome, in an epistle which he sent to the Arch Duke Leopold, accompanying
his 'Theory of the Tides.' "This theory," says he, "occurred to me when
in Rome, whilst the theologians were debating on the prohibition of
Copernicus's book, and of the opinion maintained in it of the motion of
the earth, which I at that time believed; until it pleased those
gentlemen to suspend the book, and to declare the opinion false and
repugnant to the Holy Scriptures. Now, as I know how well it becomes me
to obey and believe the decisions of my superiors, which proceed out of
more profound knowledge than the weakness of my intellect can attain
to, this theory, which I send you, which is founded on the motion of the
earth, I now look upon as a fiction and a dream, and beg your Highness
to receive it as such. But, as poets often learn to prize the creations
of their fancy, so, in like manner, do I set some value on this
absurdity of mine. It is true, that when I sketched this little work, I
did hope that Copernicus would not, after eighty years, be convicted of
error; and I had intended to develope and amplify it further; but a
voice from heaven suddenly awakened me, and at once annihilated all my
confused and entangled fancies."

It is difficult, however, sometimes to decide whether the language of
Galileo is ironical, or whether he uses it with subtlety, with the hope
of evading the anathemas of the Inquisition. Thus he ends one of his
writings with the following passage: "In conclusion, since the motion
attributed to the earth, which I, as a pious and Catholic person,
consider most false, and not to exist, accommodates itself so well to
explain so many and such different phenomena, I shall not feel sure
that, false as it is, it may not just as deludingly correspond with the
phenomena of comets."

In the year 1624, soon after the accession of Urban the Eighth to the
Pontifical chair, Galileo went to Rome again, to offer his
congratulations to the new Pope, as well as to propitiate his favor. He
seems to have been received with unexpected cordiality; and, on his
departure, the Pope commended him to the good graces of Ferdinand, Grand
Duke of Tuscany, in the following terms: "We find in him not only
literary distinction, but also the love of piety, and he is strong in
those qualities by which Pontifical good-will is easily obtained. And
now, when he has been brought to this city, to congratulate Us on Our
elevation, We have lovingly embraced him; nor can We suffer him to
return to the country whither your liberality recalls him, without an
ample provision of Pontifical love. And that you may know how dear he is
to Us, we have willed to give him this honorable testimonial of virtue
and piety. And We further signify, that every benefit which you shall
confer upon him will conduce to Our gratification."

In the year 1630, Galileo finished a great work, on which he had been
long engaged, entitled, 'The Dialogue on the Ptolemaic and Copernican
Systems.' From the notion which prevailed, that he still countenanced
the Copernican doctrine of the earth's motion, which had been condemned
as heretical, it was some time before he could obtain permission from
the Inquisitors (whose license was necessary to every book) to publish
it. This he was able to do, only by employing again that duplicity or
artifice which would throw dust in the eyes of the vain and
superstitious priesthood. In 1632, the work appeared under the following
title: 'A Dialogue, by Galileo Galilei, Extraordinary Mathematician of
the University of Pisa, and Principal Philosopher and Mathematician of
the Most Serene Grand Duke of Tuscany; in which, in a Conversation of
four days, are discussed the two principal Systems of the World, the
Ptolemaic and Copernican, indeterminately proposing the Philosophical
Arguments as well on one side as on the other.' The subtle disguise
which he wore, may be seen from the following extract from his
'Introduction,' addressed 'To the discreet Reader.'

"Some years ago, a salutary edict was promulgated at Rome, which, in
order to obviate the perilous scandals of the present age, enjoined an
opportune silence on the Pythagorean opinion of the earth's motion. Some
were not wanting, who rashly asserted that this decree originated, not
in a judicious examination, but in ill-informed passion; and complaints
were heard, that counsellors totally inexperienced in astronomical
observations ought not, by hasty prohibitions, to clip the wings of
speculative minds. My zeal could not keep silence when I heard these
rash lamentations, and I thought it proper, as being fully informed with
regard to that most prudent determination, to appear publicly on the
theatre of the world, as a witness of the actual truth. I happened at
that time to be in Rome: I was admitted to the audiences, and enjoyed
the approbation, of the most eminent prelates of that court; nor did the
publication of that decree occur without my receiving some prior
intimation of it. Wherefore, it is my intention, in this present work,
to show to foreign nations, that as much is known of this matter in
Italy, and particularly in Rome, as ultramontane diligence can ever have
formed any notion of, and collecting together all my own speculations on
the Copernican system, to give them to understand that the knowledge of
all these preceded the Roman censures; and that from this country
proceed not only dogmas for the salvation of the soul, but also
ingenious discoveries for the gratification of the understanding. With
this object, I have taken up in the 'Dialogue' the Copernican side of
the question, treating it as a pure mathematical hypothesis; and
endeavoring, in every artificial manner, to represent it as having the
advantage, not over the opinion of the stability of the earth
absolutely, but according to the manner in which that opinion is
defended by some, who indeed profess to be Aristotelians, but retain
only the name, and are contented, without improvement, to worship
shadows, not philosophizing with their own reason, but only from the
recollection of the four principles imperfectly understood."

Although the Pope himself, as well as the Inquisitors, had examined
Galileo's manuscript, and, not having the sagacity to detect the real
motives of the author, had consented to its publication, yet, when the
book was out, the enemies of Galileo found means to alarm the court of
Rome, and Galileo was summoned to appear before the Inquisition. The
philosopher was then seventy years old, and very infirm, and it was with
great difficulty that he performed the journey. His unequalled dignity
and celebrity, however, commanded the involuntary respect of the
tribunal before which he was summoned, which they manifested by
permitting him to reside at the palace of his friend, the Tuscan
Ambassador; and when it became necessary, in the course of the inquiry,
to examine him in person, although his removal to the Holy Office was
then insisted upon, yet he was not, like other heretics, committed to
close and solitary confinement. On the contrary, he was lodged in the
apartments of the Head of the Inquisition, where he was allowed the
attendance of his own servant, who was also permitted to sleep in an
adjoining room, and to come and go at pleasure. These were deemed
extraordinary indulgences in an age when the punishment of heretics
usually began before their trial.

About four months after Galileo's arrival in Rome, he was summoned to
the Holy Office. He was detained there during the whole of that day; and
on the next day was conducted, in a penitential dress, to the Convent of
Minerva, where the Cardinals and Prelates, his judges, were assembled
for the purpose of passing judgement upon him, by which this venerable
old man was solemnly called upon to renounce and abjure, as impious and
heretical, the opinions which his whole existence had been consecrated
to form and strengthen. Probably there is not a more curious document in
the history of science, than that which contains the sentence of the
Inquisition on Galileo, and his consequent abjuration. It teaches us so
much, both of the darkness and bigotry of the terrible Inquisition, and
of the sufferings encountered by those early martyrs of science, that I
will transcribe for your perusal, from the excellent 'Life of Galileo'
in the 'Library of Useful Knowledge,' (from which I have borrowed much
already,) the entire record of this transaction. The sentence of the
Inquisition is as follows:

"We, the undersigned, by the grace of God, Cardinals of the Holy Roman
Church, Inquisitors General throughout the whole Christian Republic,
Special Deputies of the Holy Apostolical Chair against heretical
depravity:

"Whereas, you, Galileo, son of the late Vincenzo Galilei of Florence,
aged seventy years, were denounced in 1615, to this Holy Office, for
holding as true a false doctrine taught by many, namely, that the sun is
immovable in the centre of the world, and that the earth moves, and also
with a diurnal motion; also, for having pupils which you instructed in
the same opinions; also, for maintaining a correspondence on the same
with some German mathematicians; also, for publishing certain letters on
the solar spots, in which you developed the same doctrine as true; also,
for answering the objections which were continually produced from the
Holy Scriptures, by glozing the said Scriptures, according to your own
meaning; and whereas, thereupon was produced the copy of a writing, in
form of a letter, professedly written by you to a person formerly your
pupil, in which, following the hypothesis of Copernicus, you include
several propositions contrary to the true sense and authority of the
Holy Scriptures: therefore, this Holy Tribunal, being desirous of
providing against the disorder and mischief which was thence proceeding
and increasing, to the detriment of the holy faith, by the desire of His
Holiness, and of the Most Eminent Lords Cardinals of this supreme and
universal Inquisition, the two propositions of the stability of the sun,
and motion of the earth, were _qualified_ by the _Theological
Qualifiers_, as follows:

"1. The proposition that the sun is in the centre of the world, and
immovable from its place, is absurd, philosophically false, and formally
heretical; because it is expressly contrary to the Holy Scriptures.

"2. The proposition that the earth is not the centre of the world, nor
immovable, but that it moves, and also with a diurnal motion, is also
absurd, philosophically false, and, theologically considered, equally
erroneous in faith.

"But whereas, being pleased at that time to deal mildly with you, it was
decreed in the Holy Congregation, held before His Holiness on the
twenty-fifth day of February, 1616, that His Eminence the Lord Cardinal
Bellarmine should enjoin you to give up altogether the said false
doctrine; if you should refuse, that you should be ordered by the
Commissary of the Holy Office to relinquish it, not to teach it to
others, nor to defend it, and in default of the acquiescence, that you
should be imprisoned; and in execution of this decree, on the following
day, at the palace, in presence of His Eminence the said Lord Cardinal
Bellarmine, after you had been mildly admonished by the said Lord
Cardinal, you were commanded by the acting Commissary of the Holy
Office, before a notary and witnesses, to relinquish altogether the said
false opinion, and in future neither to defend nor teach it in any
manner, neither verbally nor in writing, and upon your promising
obedience, you were dismissed.

"And, in order that so pernicious a doctrine might be altogether rooted
out, nor insinuate itself further to the heavy detriment of the Catholic
truth, a decree emanated from the Holy Congregation of the Index,
prohibiting the books which treat of this doctrine; and it was declared
false, and altogether contrary to the Holy and Divine Scripture.

"And whereas, a book has since appeared, published at Florence last
year, the title of which showed that you were the author, which title
is, '_The Dialogue of Galileo Galilei, on the two principal Systems of
the World, the Ptolemaic and Copernican_;' and whereas, the Holy
Congregation has heard that, in consequence of printing the said book,
the false opinion of the earth's motion and stability of the sun is
daily gaining ground; the said book has been taken into careful
consideration, and in it has been detected a glaring violation of the
said order, which had been intimated to you; inasmuch as in this book
you have defended the said opinion, already, and in your presence,
condemned; although in the said book you labor, with many
circumlocutions, to induce the belief that it is left by you undecided,
and in express terms probable; which is equally a very grave error,
since an opinion can in no way be probable which has been already
declared and finally determined contrary to the Divine Scripture.
Therefore, by Our order, you have been cited to this Holy Office, where,
on your examination upon oath, you have acknowledged the said book as
written and printed by you. You also confessed that you began to write
the said book ten or twelve years ago, after the order aforesaid had
been given. Also, that you demanded license to publish it, but without
signifying to those who granted you this permission, that you had been
commanded not to hold, defend, or teach, the said doctrine in any
manner. You also confessed, that the style of said book was, in many
places, so composed, that the reader might think the arguments adduced
on the false side to be so worded, as more effectually to entangle the
understanding than to be easily solved, alleging, in excuse, that you
have thus run into an error, foreign (as you say) to your intention,
from writing in the form of a dialogue, and in consequence of the
natural complacency which every one feels with regard to his own
subtilties, and in showing himself more skilful than the generality of
mankind in contriving, even in favor of false propositions, ingenious
and apparently probable arguments.

"And, upon a convenient time being given you for making your defence,
you produced a certificate in the handwriting of His Eminence, the Lord
Cardinal Bellarmine, procured, as you said, by yourself, that you might
defend yourself against the calumnies of your enemies, who reported that
you had abjured your opinions, and had been punished by the Holy Office;
in which certificate it is declared, that you had not abjured, nor had
been punished, but merely that the declaration made by his Holiness, and
promulgated by the Holy Congregation of the Index, had been announced to
you, which declares that the opinion of the motion of the earth, and
stability of the sun, is contrary to the Holy Scriptures, and therefore
cannot be held or defended. Wherefore, since no mention is there made of
two articles of the order, to wit, the order 'not to teach,' and 'in any
manner,' you argued that we ought to believe that, in the lapse of
fourteen or sixteen years, they had escaped your memory, and that this
was also the reason why you were silent as to the order, when you sought
permission to publish your book, and that this is said by you, not to
excuse your error, but that it may be attributed to vain-glorious
ambition rather than to malice. But this very certificate, produced on
your behalf, has greatly aggravated your offence, since it is therein
declared, that the said opinion is contrary to the Holy Scriptures, and
yet you have dared to treat of it, and to argue that it is probable; nor
is there any extenuation in the license artfully and cunningly extorted
by you, since you did not intimate the command imposed upon you. But
whereas, it appeared to Us that you had not disclosed the whole truth
with regard to your intentions, We thought it necessary to proceed to
the rigorous examination of you, in which (without any prejudice to what
you had confessed, and which is above detailed against you, with regard
to your said intention) you answered like a good Catholic.

"Therefore, having seen and maturely considered the merits of your
cause, with your said confessions and excuses, and every thing else
which ought to be seen and considered, We have come to the underwritten
final sentence against you:

"Invoking, therefore, the most holy name of our Lord Jesus Christ, and
of his Most Glorious Virgin Mother, Mary, by this Our final sentence,
which, sitting in council and judgement for the tribunal of the Reverend
Masters of Sacred Theology, and Doctors of both Laws, Our Assessors, We
put forth in this writing touching the matters and controversies before
Us, between the Magnificent Charles Sincerus, Doctor of both Laws,
Fiscal Proctor of this Holy Office, of the one part, and you, Galileo
Galilei, an examined and confessed criminal from this present writing
now in progress, as above, of the other part, We pronounce, judge, and
declare, that you, the said Galileo, by reason of these things which
have been detailed in the course of this writing, and which, as above,
you have confessed, have rendered yourself vehemently suspected, by this
Holy Office, of heresy; that is to say, that you believe and hold the
false doctrine, and contrary to the Holy and Divine Scriptures, namely,
that the sun is the centre of the world, and that it does not move from
east to west, and that the earth does move, and is not the centre of the
world; also, that an opinion can be held and supported, as probable,
after it has been declared and finally decreed contrary to the Holy
Scripture, and consequently, that you have incurred all the censures and
penalties enjoined and promulgated in the sacred canons, and other
general and particular constitutions against delinquents of this
description. From which it is Our pleasure that you be absolved,
provided that, with a sincere heart and unfeigned faith, in Our
presence, you abjure, curse, and detest, the said errors and heresies,
and every other error and heresy, contrary to the Catholic and Apostolic
Church of Rome, in the form now shown to you.

"But that your grievous and pernicious error and transgression may not
go altogether unpunished, and that you may be made more cautious in
future, and may be a warning to others to abstain from delinquencies of
this sort, We decree, that the book of the Dialogues of Galileo Galilei
be prohibited by a public edict, and We condemn you to the formal prison
of this Holy Office for a period determinable at Our pleasure; and, by
way of salutary penance, We order you, during the next three years, to
recite, once a week, the seven penitential psalms, reserving to
Ourselves the power of moderating, commuting, or taking off the whole or
part of the said punishment, or penance.

"And so We say, pronounce, and by Our sentence declare, decree, and
reserve, in this and in every other better form and manner, which
lawfully We may and can use. So We, the subscribing Cardinals,
pronounce." [Subscribed by seven Cardinals.]

In conformity with the foregoing sentence, Galileo was made to kneel
before the Inquisition, and make the following _Abjuration_:

"I, Galileo Galilei, son of the late Vincenzo Galilei, of Florence, aged
seventy years, being brought personally to judgement, and kneeling
before you, Most Eminent and Most Reverend Lords Cardinals, General
Inquisitors of the Universal Christian Republic against heretical
depravity, having before my eyes the Holy Gospels, which I touch with my
own hands, swear, that I have always believed, and with the help of God
will in future believe, every article which the Holy Catholic and
Apostolic Church of Rome holds, teaches, and preaches. But because I had
been enjoined, by this Holy Office, altogether to abandon the false
opinion which maintains that the sun is the centre and immovable, and
forbidden to hold, defend, or teach, the said false doctrine, in any
manner: and after it had been signified to me that the said doctrine is
repugnant to the Holy Scripture, I have written and printed a book, in
which I treat of the same doctrine now condemned, and adduce reasons
with great force in support of the same, without giving any solution,
and therefore have been judged grievously suspected of heresy; that is
to say, that I held and believed that the sun is the centre of the world
and immovable, and that the earth is not the centre and movable;
willing, therefore, to remove from the minds of Your Eminences, and of
every Catholic Christian, this vehement suspicion rightfully entertained
towards me, with a sincere heart and unfeigned faith, I abjure, curse,
and defeat, the said errors and heresies, and generally every other
error and sect contrary to the said Holy Church; and I swear, that I
will never more in future say or assert any thing, verbally or in
writing, which may give rise to a similar suspicion of me: but if I
shall know any heretic, or any one suspected of heresy, that I will
denounce him to this Holy Office, or to the Inquisitor and Ordinary of
the place in which I may be. I swear, moreover, and promise, that I will
fulfil and observe fully, all the penances which have been or shall be
laid on me by this Holy Office. But if it shall happen that I violate
any of my said promises, oaths, and protestations, (which God avert!) I
subject myself to all the pains and punishments which have been decreed
and promulgated by the sacred canons, and other general and particular
constitutions, against delinquents of this description. So may God help
me, and his Holy Gospels, which I touch with my own hands. I, the
above-named Galileo Galilei, have abjured, sworn, promised, and bound
myself, as above; and in witness thereof, with my own hand have
subscribed this present writing of my abjuration, which I have recited,
word for word.

"At Rome, in the Convent of Minerva, twenty-second June, 1633, I,
Galileo Galilei, have abjured as above, with my own hand."

From the court Galileo was conducted to prison, to be immured for life
in one of the dungeons of the Inquisition. His sentence was afterwards
mitigated, and he was permitted to return to Florence; but the
humiliation to which he had been subjected pressed heavily on his
spirits, beset as he was with infirmities, and totally blind, and he
never more talked or wrote on the subject of astronomy.

There was enough in the character of Galileo to command a high
admiration. There was much, also, in his sufferings in the cause of
science, to excite the deepest sympathy, and even compassion. He is
moreover universally represented to have been a man of great equanimity,
and of a noble and generous disposition. No scientific character of the
age, or perhaps of any age, forms a structure of finer proportions, or
wears in a higher degree the grace of symmetry. Still, we cannot approve
of his employing artifice in the promulgation of truth; and we are
compelled to lament that his lofty spirit bowed in the final conflict.
How far, therefore, he sinks below the dignity of the Christian martyr!
"At the age of seventy," says Dr. Brewster, in his life of Sir Isaac
Newton, "on his bended knees, and with his right hand resting on the
Holy Evangelists, did this patriarch of science avow his present and
past belief in the dogmas of the Romish Church, abandon as false and
heretical the doctrine of the earth's motion and of the sun's
immobility, and pledge himself to denounce to the Inquisition any other
person who was even suspected of heresy. He abjured, cursed, and
detested, those eternal and immutable truths which the Almighty had
permitted him to be the first to establish. Had Galileo but added the
courage of the martyr to the wisdom of the sage; had he carried the
glance of his indignant eye round the circle of his judges; had he
lifted his hands to heaven, and called the living God to witness the
truth and immutability of his opinions; the bigotry of his enemies would
have been disarmed, and science would have enjoyed a memorable triumph."

LETTER XXIII.

SATURN.--URANUS.--ASTEROIDS.

"Into the Heaven of Heavens I have presumed,
An earthly guest, and drawn empyreal air."--_Milton._

THE consideration of the system of Jupiter and his satellites led us to
review the interesting history of Galileo, who first, by means of the
telescope, disclosed the knowledge of that system to the world. I will
now proceed with the other superior planets.

Saturn, as well as Jupiter, has within itself a system on a scale of
great magnificence. In size it is next to Jupiter the largest of the
planets, being seventy-nine thousand miles in diameter, or about one
thousand times as large as the earth. It has likewise belts on its
surface, and is attended by seven satellites. But a still more wonderful
appendage is its _Ring_, a broad wheel, encompassing the planet at a
great distance from it. As Saturn is nine hundred millions of miles from
us, we require a more powerful telescope to see his glories, in all
their magnificence, than we do to enjoy a full view of the system of
Jupiter. When we are privileged with a view of Saturn, in his most
favorable positions, through a telescope of the larger class, the
mechanism appears more wonderful than even that of Jupiter.

Saturn's ring, when viewed with telescopes of a high power, is found to
consist of two concentred rings, separated from each other by a dark
space. Although this division of the rings appears to us, on account of
our immense distance, as only a fine line, yet it is, in reality, an
interval of not less than eighteen hundred miles. The dimensions of the
whole system are, in round numbers, as follows:

Miles.
Diameter of the planet, 79,000
From the surface of the planet to the inner ring, 20,000
Breadth of the inner ring, 17,000
Interval between the rings, 1,800
Breadth of the outer ring, 10,500
Extreme dimensions from outside to outside, 176,000

Figure 60, facing page 247, represents Saturn, as it appears to a
powerful telescope, surrounded by its rings, and having its body striped
with dark belts, somewhat similar, but broader and less strongly marked
than those of Jupiter. In telescopes of inferior power, but still
sufficient to see the ring distinctly, we should scarcely discern the
belts at all. We might, however, observe the shadow cast upon the ring
by the planet, (as seen in the figure on the right, on the upper side;)
and, in favorable situations of the planet, we might discern glimpses of
the shadow of the ring on the body of the planet, on the lower side
beneath the ring. To see the division of the ring and the satellites
requires a better telescope than is in possession of most observers.
With smaller telescopes, we may discover an oval figure of peculiar
appearance, which it would be difficult to interpret. Galileo, who first
saw it in the year 1610, recognised this peculiarity, but did not know
what it meant. Seeing something in the centre with two projecting arms,
one on each side, he concluded that the planet was triple-shaped. This
was, at the time, all he could learn respecting it, as the telescopes he
possessed were very humble, compared with those now used by astronomers.
The first constructed by him magnified but three times; his second,
eight times; and his best, only thirty times, which is no better than a
common ship-glass.

It was the practice of the astronomers of those days to give the first
intimation of a new discovery in a Latin verse, the letters of which
were transposed. This would enable them to claim priority, in case any
other person should contest the honor of the discovery, and at the same
time would afford opportunity to complete their observations, before
they published a full account of them. Accordingly, Galileo announced
the discovery of the singular appearance of Saturn under this disguise,
in a line which, when the transposed letters were restored to their
proper places, signified that he had observed, "that the most distant
planet is triple-formed."[13] He shortly afterwards, at the request of
his patron, the Emperor Rodolph, gave the solution, and added, "I have,
with great admiration, observed that Saturn is not a single star, but
three together, which, as it were, touch each other; they have no
relative motion, and are constituted of this form, oOo, the middle one
being somewhat larger than the two lateral ones. If we examine them with
an eyeglass which magnifies the surface less than one thousand times,
the three stars do not appear very distinctly, but Saturn has an oblong
appearance, like that of an olive, thus, {oblong symbol}. Now, I have
discovered a court for Jupiter, (alluding to his satellites,) and two
servants for this old man, (Saturn,) who aid his steps, and never quit
his side."

It was by this mystic light that Galileo groped his way through an
organization which, under the more powerful glasses of his successors,
was to expand into a mighty orb, encompassed by splendid rings of vast
dimensions, the whole attended by seven bright satellites. This system
was first fully developed by Huyghens, a Dutch astronomer, about forty
years afterwards.[14] It requires a superior telescope to see it to
advantage; but, when seen through such a telescope, it is one of the
most charming spectacles afforded to that instrument. To give some idea
of the properties of a telescope suited to such observations, I annex an
extract from an account, that was published a few years since, of a
telescope constructed by Mr. Tully, a distinguished English artist. "The
length of the instrument was twelve feet, but was easily adjusted, and
was perfectly steady. The magnifying powers ranged from two hundred to
seven hundred and eighty times; but the great excellence of the
telescope consisted more in the superior distinctness and brilliancy
with which objects were seen through it, than in its magnifying powers.
With a power of two hundred and forty, the light of Jupiter was almost
more than the eye could bear, and his satellites appeared as bright as
Sirius, but with a clear and steady light; and the belts and spots on
the face of the planet were most distinctly defined. With a power of
nearly four hundred, Saturn appeared large and well defined, and was one
of the most beautiful objects that can well be conceived."

That the ring is a solid opaque substance, is shown by its throwing its
shadow on the body of the planet on the side nearest the sun, and on the
other side receiving that of the body. The ring encompasses the
equatorial regions of the planet, and the planet revolves on an axis
which is perpendicular to the plane of the ring in about ten and a half
hours. This is known by observing the rotation of certain dusky spots,
which sometimes appear on its surface. This motion is nearly the same
with the diurnal motion of Jupiter, subjecting places on the equator of
the planet to a very swift revolution, and occasioning a high degree of
compression at the poles, the equatorial being to the polar diameter in
the high ratio of eleven to ten.

Saturn's ring, in its revolution around the sun, _always remains
parallel to itself_. If we hold opposite to the eye a circular ring or
disk, like a piece of coin, it will appear as a complete circle only
when it is at right angles to the axis of vision. When it is oblique to
that axis, it will be projected into an ellipse more and more flattened,
as its obliquity is increased, until, when its plane coincides with the
axis of vision, it is projected into a straight line. Please to take
some circle, as a flat plate, (whose rim may well represent the ring of
Saturn,) and hold it in these different positions before the eye. Now,
place on the table a lamp to represent the sun, and holding the ring at
a certain distance, inclined a little towards the lamp, carry it round
the lamp, always keeping it parallel to itself. During its revolution,
it will twice present its edge to the lamp at opposite points; and
twice, at places ninety degrees distant from those points, it will
present its broadest face towards the lamp. At intermediate points, it
will exhibit an ellipse more or less open, according as it is nearer one
or the other of the preceding positions. It will be seen, also, that in
one half of the revolution, the lamp shines on one side of the ring, and
in the other half of the revolution, on the other side.

Such would be the successive appearances of Saturn's ring to a spectator
on the sun; and since the earth is, in respect to so distant a body as
Saturn, very near the sun, these appearances are presented to us nearly
in the same manner as though we viewed them from the sun. Accordingly,
we sometimes see Saturn's ring under the form of a broad ellipse, which
grows continually more and more acute, until it passes into a line, and
we either lose sight of it, altogether, or, by the aid of the most
powerful telescopes, we see it as a fine thread of light drawn across
the disk, and projecting out from it on each side. As the whole
revolution occupies thirty years, and the edge is presented to the sun
twice in the revolution, this last phenomenon, namely, the disappearance
of the ring, takes place every fifteen years.

[Illustration Fig. 61.]

You may perhaps gain a still clearer idea of the foregoing appearances
from the following diagram, Fig. 61. Let A, B, C, &c., represent
successive positions of Saturn and his ring, in different parts of his
orbit, while _a b_ represents the orbit of the earth. Please to remark,
that these orbits are drawn so elliptical, not to represent the
eccentricity of either the earth's or Saturn's orbit, but merely as the
projection of circles seen very obliquely. Also, imagine one half of the
body of the planet and of the ring to be above the plane of the paper,
and the other half below it. Were the ring, when at C and G,
perpendicular to C G, it would be seen by a spectator situated at _a_ or
_b_ as a perfect circle; but being inclined to the line of vision
twenty-eight degrees four minutes, it is projected into an ellipse. This
ellipse contracts in breadth as the ring passes towards its nodes at A
and E, where it dwindles into a straight line. From E to G the ring
opens again, becomes broadest at G, and again contracts, till it
becomes a straight line at A, and from this point expands, till it
recovers its original breadth at C. These successive appearances are all
exhibited to a telescope of moderate powers.

The ring is extremely _thin_, since the smallest satellite, when
projected on it, more than covers it. The thickness is estimated at only
one hundred miles. Saturn's ring shines wholly by _reflected light_
derived from the sun. This is evident from the fact that that side only
which is turned towards the sun is enlightened; and it is remarkable,
that the illumination of the ring is greater than that of the planet
itself, but the outer ring is less bright than the inner. Although we
view Saturn's ring nearly as though we saw it from the sun, yet the
plane of the ring produced may pass between the earth and the sun, in
which case, also, the ring becomes invisible, the illuminated side being
wholly turned from us. Thus, when the ring is approaching its node at E,
a spectator at _a_ would have the dark side of the ring presented to
him. The ring was invisible in 1833, and will be invisible again in
1847. The northern side of the ring will be in sight until 1855, when
the southern side will come into view. It appears, therefore, that there
are three causes for the disappearance of Saturn's ring: first, when the
edge of the ring is presented to the sun; secondly, when the edge is
presented to the earth; and thirdly, when the unilluminated side is
towards the earth.

Saturn's ring _revolves_ in its own plane in about ten and a half hours.
La Place inferred this from the doctrine of universal gravitation. He
proved that such a rotation was necessary; otherwise, the matter of
which the ring is composed would be precipitated upon its primary. He
showed that, in order to sustain itself, its period of rotation must be
equal to the time of revolution of a satellite, circulating around
Saturn at a distance from it equal to that of the middle of the ring,
which period would be about ten and a half hours. By means of spots in
the ring, Dr. Herschel followed the ring in its rotation, and actually
found its period to be the same as assigned by La Place,--a coincidence
which beautifully exemplifies the harmony of truth.

Although the rings have very nearly the same centre with the planet
itself, yet, recent measurements of extreme delicacy have demonstrated,
that the coincidence is not mathematically exact, but that the centre of
gravity of the rings describes around that of the body a very minute
orbit. "This fact," says Sir J. Herschel, "unimportant as it may seem,
is of the utmost consequence to the stability of the system of rings.
Supposing them mathematically perfect in their circular form, and
exactly concentric with the planet, it is demonstrable that they would
form (in spite of their centrifugal force) a system in a state of
unstable equilibrium, which the slightest external power would subvert,
not by causing a rupture in the substance of the rings, but by
precipitating them unbroken upon the surface of the planet." The ring
may be supposed of an unequal breadth in its different parts, and as
consisting of irregular solids, whose common centre of gravity does not
coincide with the centre of the figure. Were it not for this
distribution of matter, its equilibrium would be destroyed by the
slightest force, such as the attraction of a satellite, and the ring
would finally precipitate itself upon the planet. Sir J. Herschel
further observes, that, "as the smallest difference of velocity between
the planet and its rings must infallibly precipitate the rings upon the
planet, never more to separate, it follows, either that their motions in
their common orbit round the sun must have been adjusted to each other
by an external power, with the minutest precision, or that the rings
must have been formed about the planet while subject to their common
orbitual motion, and under the full and free influence of all the acting
forces.

"The rings of Saturn must present a magnificent spectacle from those
regions of the planet which lie on their enlightened sides, appearing
as vast arches spanning the sky from horizon to horizon, and holding an
invariable situation among the stars. On the other hand, in the region
beneath the dark side, a solar eclipse of fifteen years in duration,
under their shadow, must afford (to our ideas) an inhospitable abode to
animated beings, but ill compensated by the full light of its
satellites. But we shall do wrong to judge of the fitness or unfitness
of their condition, from what we see around us, when, perhaps, the very
combinations which convey to our minds only images of horror, may be in
reality theatres of the most striking and glorious displays of
beneficent contrivance."

Saturn is attended by _seven satellites_. Although they are bodies of
considerable size, their great distance prevents their being visible to
any telescope but such as afford a strong light and high magnifying
powers. The outermost satellite is distant from the planet more than
thirty times the planet's diameter, and is by far the largest of the
whole. It exhibits, like the satellites of Jupiter, periodic variations
of light, which prove its revolution on its axis in the time of a
sidereal revolution about Saturn, as is the case with our moon, while
performing its circuit about the earth. The next satellite in order,
proceeding inwards, is tolerably conspicuous; the three next are very
minute, and require powerful telescopes to see them; while the two
interior satellites, which just skirt the edge of the ring, and move
exactly in its plane, have never been discovered but with the most
powerful telescopes which human art has yet constructed, and then only
under peculiar circumstances. At the time of the disappearance of the
rings, (to ordinary telescopes,) they were seen by Sir William Herschel,
with his great telescope, projected along the edge of the ring, and
threading, like beads, the thin fibre of light to which the ring is then
reduced. Owing to the obliquity of the ring, and of the orbits of the
satellites, to that of their primary, there are no eclipses of the
satellites, the two interior ones excepted, until near the time when
the ring is seen edgewise.

"The firmament of Saturn will unquestionably present to view a more
magnificent and diversified scene of celestial phenomena than that of
any other planet in our system. It is placed nearly in the middle of
that space which intervenes between the sun and the orbit of the
remotest planet. Including its rings and satellites, it may be
considered as the largest body or system of bodies within the limits of
the solar system; and it excels them all in the sublime and diversified
apparatus with which it is accompanied. In these respects, Saturn may
justly be considered as the sovereign among the planetary hosts. The
prominent parts of its celestial scenery may be considered as belonging
to its own system of rings and satellites, and the views which will
occasionally be opened of the firmament of the fixed stars; for few of
the other planets will make their appearance in its sky. Jupiter will
appear alternately as a morning and an evening star, with about the same
degree of brilliancy it exhibits to us; but it will seldom be
conspicuous, except near the period of its greatest elongation; and it
will never appear to remove from the sun further than thirty-seven
degrees, and consequently will not appear so conspicuous, nor for such a
length of time, as Venus does to us. Uranus is the only other planet
which will be seen from Saturn, and it will there be distinctly
perceptible, like a star of the third magnitude, when near the time of
its opposition to the sun. But near the time of its conjunction it will
be completely invisible, being then eighteen hundred millions of miles
more distant than at the opposition, and eight hundred millions of miles
more distant from Saturn than it ever is from the earth at any
period."[15]

URANUS.--Uranus is the remotest planet belonging to our system, and is
rarely visible, except to the telescope. Although his diameter is more
than four times that of the earth, being thirty-five thousand one
hundred and twelve miles, yet his distance from the sun is likewise
nineteen times as great as the earth's distance, or about eighteen
hundred millions of miles. His revolution around the sun occupies nearly
eighty-four years, so that his position in the heavens, for several
years in succession, is nearly stationary. His path lies very nearly in
the ecliptic, being inclined to it less than one degree. The sun
himself, when seen from Uranus dwindles almost to a star, subtending, as
it does, an angle of only one minute and forty seconds; so that the
surface of the sun would appear there four hundred times less than it
does to us. This planet was discovered by Sir William Herschel on the
thirteenth of March, 1781. His attention was attracted to it by the
largeness of its disk in the telescope; and finding that it shifted its
place among the stars, he at first took it for a comet, but soon
perceived that its orbit was not eccentric, like the orbits of comets,
but nearly circular, like those of the planets. It was then recognised
as a new member of the planetary system, a conclusion which has been
justified by all succeeding observations. It was named by the discoverer
the _George Star_, (Georgium Sidus,) after his munificent patron, George
the Third; in the United States, and in some other countries, it was
called _Herschel_; but the name _Uranus_, from a Greek word, (= Ouranos=,
_Ouranos_,) signifying the oldest of the gods, has finally prevailed. So
distant is Uranus from the sun, that light itself, which moves nearly
twelve millions of miles every minute, would require more than two hours
and a half to pass to it from the sun.

And now, having contemplated all the planets separately, just cast your
eyes on the diagram facing page 236, Fig. 53, and you will see a
comparative view of the various magnitudes of the sun, as seen from each
of the planets.

Uranus is attended by _six satellites_. So minute objects are they, that
they can be seen only by powerful telescopes. Indeed, the existence of
more than two is still considered as somewhat doubtful. These two,
however, offer remarkable and indeed quite unexpected and unexampled
peculiarities. Contrary to the unbroken analogy of the whole planetary
system, _the planes of their orbits are nearly perpendicular to the
ecliptic_, and in these orbits their motions are retrograde; that is,
instead of advancing from west to east around their primary, as is the
case with all the other planets and satellites, they move in the
opposite direction. With this exception, all the motions of the planets,
whether around their own axes, or around the sun, are from west to east.
The sun himself turns on his axis from west to east; all the primary
planets revolve around the sun from west to east; their revolutions on
their own axes are also in the same direction; all the secondaries, with
the single exception above mentioned, move about their primaries from
west to east; and, finally, such of the secondaries as have been
discovered to have a diurnal revolution, follow the same course. Such
uniformity among so many motions could have resulted only from forces
impressed upon them by the same Omnipotent hand; and few things in the
creation more distinctly proclaim that God made the world.

Retiring now to this furthest verge of the solar system, let us for a
moment glance at the aspect of the firmament by night. Notwithstanding
we have taken a flight of eighteen hundred millions of miles, the same
starry canopy bends over our heads; Sirius still shines with exactly the
same splendor as here; Orion, the Scorpion, the Great and the Little
Bear, all occupy the same stations; and the Galaxy spans the sky with
the same soft and mysterious light. The planets, however, with the
exception of Saturn, are all lost to the view, being too near the sun
ever to be seen; and Saturn himself is visible only at distant
intervals, at periods of fifteen years, when at its greatest elongations
from the sun, and is then too near the sun to permit a clear view of his
rings, much less of the satellites that unite with the rings to compose
his gorgeous retinue. Comets, moving slowly as they do when so distant
from the sun, will linger much longer in the firmament of Uranus than in
ours.

Although the sun sheds by day a dim and cheerless light, yet the six
satellites that enlighten and diversify the nocturnal sky present
interesting aspects. "Let us suppose one satellite presenting a surface
in the sky eight or ten times larger than our moon; a second, five or
six times larger; a third, three times larger; a fourth, twice as large;
a fifth, about the same size as the moon; a sixth, somewhat smaller;
and, perhaps, three or four others of different apparent dimensions: let
us suppose two or three of those, of different phases, moving along the
concave of the sky, at one period four or five of them dispersed through
the heavens, one rising above the horizon, one setting, one on the
meridian, one towards the north, and another towards the south; at
another period, five or six of them displaying their lustre in the form
of a half moon, or a crescent, in one quarter of the heavens; and, at
another time, the whole of these moons shining, with full enlightened
hemispheres, in one glorious assemblage, and we shall have a faint idea
of the beauty, variety, and sublimity of the firmament of Uranus."[16]

_The New Planets,--Ceres, Pallas, Juno, and Vesta._--The commencement of
the present century was rendered memorable in the annals of astronomy,
by the discovery of four new planets, occupying the long vacant tract
between Mars and Jupiter. Kepler, from some analogy which he found to
subsist among the distances of the planets from the sun, had long before
suspected the existence of one at this distance; and his conjecture was
rendered more probable by the discovery of Uranus, which follows the
analogy of the other planets. So strongly, indeed, were astronomers
impressed with the idea that a planet would be found between Mars and
Jupiter, that, in the hope of discovering it, an association was formed
on the continent of Europe, of twenty-four observers, who divided the
sky into as many zones, one of which was allotted to each member of the
association. The discovery of the first of these bodies was, however,
made accidentally by Piazzi, an astronomer of Palermo, on the first of
January, 1801. It was shortly afterwards lost sight of on account of its
proximity to the sun, and was not seen again until the close of the
year, when it was re-discovered in Germany. Piazzi called it _Ceres_, in
honor of the tutelary goddess of Sicily, and her emblem, the sickle,
([Planet: Ceres]) has been adopted as its appropriate symbol.

The difficulty of finding Ceres induced Dr. Olbers, of Bremen, to
examine with particular care all the small stars that lie near her path,
as seen from the earth; and, while prosecuting these observations, in
March, 1802, he discovered another similar body, very nearly at the same
distance from the sun, and resembling the former in many other
particulars. The discoverer gave to this second planet the name of
_Pallas_, choosing for its symbol the lance, ([Planet: Pallas]) the
characteristic of Minerva.

The most surprising circumstance connected with the discovery of
_Pallas_ was the existence of two planets at nearly the same distance
from the sun, and apparently crossing the ecliptic in the same part of
the heavens, or having the same node. On account of this singularity,
Dr. Olbers was led to conjecture that Ceres and Pallas are only
fragments of a larger planet, which had formerly circulated at the same
distance, and been shattered by some internal convulsion. The hypothesis
suggested the probability that there might be other fragments, whose
orbits might be expected to cross the ecliptic at a common point, or to
have the same node. Dr. Olbers, therefore, proposed to examine
carefully, every month, the two opposite parts of the heavens in which
the orbits of Ceres and Pallas intersect one another, with a view to the
discovery of other planets, which might be sought for in those parts
with a greater chance of success, than in a wider zone, embracing the
entire limits of these orbits. Accordingly, in 1804, near one of the
nodes of Ceres and Pallas, a third planet was discovered. This was
called _Juno_, and the character ([Planet: Juno]) was adopted for its
symbol, representing the starry sceptre of the Queen of Olympus.
Pursuing the same researches, in 1807 a fourth planet was discovered, to
which was given the name of _Vesta_, and for its symbol the character
([Planet: Vesta]) was chosen,--an altar surmounted with a censer holding
the sacred fire.

The _average distance_ of these bodies from the sun is two hundred and
sixty-one millions of miles; and it is remarkable that their orbits are
very near together. Taking the distance of the earth from the sun for
unity, their respective distances are 2.77, 2.77, 2.67, 2.37. Their
_times_ of revolution around the sun are nearly equal, averaging about
four and a half years.

In respect to the _inclination of their orbits_ to the ecliptic, there
is also considerable diversity. The orbit of Vesta is inclined only
about seven degrees, while that of Pallas is more than thirty-four
degrees. They all, therefore, have a higher inclination than the orbits
of the old planets, and of course make excursions from the ecliptic
beyond the limits of the zodiac. Hence they have been called the
_ultra-zodiacal planets_. When first discovered, before their place in
the system was fully ascertained it was also proposed to call them
_asteroids_, a name implying that they were planets under the form of
stars. Their title, however, to take their rank among the primary
planets, is now generally conceded.

The _eccentricity of their orbits_ is also, in general, greater than
that of the old planets. You will recollect that this language denotes
that their orbits are more elliptical, or depart further from the
circular form. The eccentricities of the orbits of Pallas and Juno
exceed that of the orbit of Mercury. The asteroids differ so much,
however, in eccentricity, that their orbits may cross each other. The
orbits of the old planets are so nearly circular, and at such a great
distance apart, that there is no danger of their interfering with each
other. The earth, for example, when at its nearest distance from the
sun, will never come so near it as Venus is when at its greatest
distance, and therefore can never cross the orbit of Venus. But since
the average distance of Ceres and Pallas from the sun is about the same,
while the eccentricity of the orbit of Pallas is much greater than that
of Ceres, consequently, Pallas may come so near to the sun at its
perihelion, as to cross the orbit of Ceres.

The _small size_ of the asteroids constitutes one of their most
remarkable peculiarities. The difficulty of estimating the apparent
diameter of bodies at once so very small and so far off, would lead us
to expect different results in the actual estimates. Accordingly, while
Dr. Herschel estimates the diameter of Pallas at only eighty miles,
Schroeter places it as high as two thousand miles, or about the diameter
of the moon. The volume of Vesta is estimated at only one fifteen
thousandth part of the earth's, and her surface is only about equal to
that of the kingdom of Spain.

These little bodies are surrounded by _atmospheres_ of great extent,
some of which are uncommonly luminous, and others appear to consist of
nebulous matter, like that of comets. These planets shine with a more
vivid light than might be expected, from their great distance and
diminutive size; but a good telescope is essential for obtaining a
distinct view of their phenomena.

Although the great chasm which occurs between Mars and Jupiter,--a chasm
of more than three hundred millions of miles,--suggested long ago the
idea of other planetary bodies occupying that part of the solar system,
yet the discovery of the asteroids does not entirely satisfy expectation
since they are bodies so dissimilar to the other members of the series
in size, in appearance, and in the form and inclinations of their
orbits. Hence, Dr. Olbers, the discoverer of three of these bodies, held
that they were fragments of a single large planet, which once occupied
that place in the system, and which exploded in different directions by
some internal violence. Of the fragments thus projected into space, some
would be propelled in such directions and with such velocities, as,
under the force of projection and that of the solar attraction would
make them revolve in regular orbits around the sun. Others would be so
projected among the other bodies in the system, as to be thrown in very
irregular orbits, apparently wandering lawless through the skies. The
larger fragments would receive the least impetus from the explosive
force, and would therefore circulate in an orbit deviating less than any
other of the fragments from the original path of the large planet; while
the lesser fragments, being thrown off with greater velocity, would
revolve in orbits more eccentric, and more inclined to the ecliptic.

Dr. Brewster, editor of the 'Edinburgh Encyclopedia,' and the well-known
author of various philosophical works, espoused this hypothesis with
much zeal; and, after summing up the evidence in favor of it, he remarks
as follows: "These singular resemblances in the motions of the greater
fragments, and in those of the lesser fragments, and the striking
coincidences between theory and observation in the eccentricity of their
orbits, in their inclination to the ecliptic, in the position of their
nodes, and in the places of their perihelia, are phenomena which could
not possibly result from chance, and which concur to prove, with an
evidence amounting almost to demonstration, that the four new planets
have diverged from one common node, and have therefore composed a single
planet."

The same distinguished writer supposes that some of the smallest
fragments might even have come within reach of the earth's attraction,
and by the combined effects of their projectile forces and the
attraction of the earth, be made to revolve around this body as the
larger fragments are carried around the sun; and that these are in fact
the bodies which afford those _meteoric stones_ which are
occasionally precipitated to the earth. It is now a well-ascertained
fact, a fact which has been many times verified in our own country, that
large meteors, in the shape of fire-balls, traversing the atmosphere,
sometimes project to the earth masses of stony or ferruginous matter.
Such were the meteoric stones which fell at Weston, in Connecticut, in
1807, of which a full and interesting account was published, after a
minute examination of the facts, by Professors Silliman and Kingsley, of
Yale College. Various accounts of similar occurrences may be found in
different volumes of the American Journal of Science. It is for the
production of these wonderful phenomena that Dr. Brewster supposes the
explosion of the planet, which, according to Dr. Olbers, produced the
asteroids, accounts. Others, however, as Sir John Herschel, have been
disposed to ascribe very little weight to the doctrine of Olbers.

FOOTNOTES:

[13] Altissimum planetam tergeminum observavi. Or, as transposed,
Smaismrmilme poeta leumi bvne nugttaviras.

[14] In imitation of Galileo, Huyghens announced his discovery in this
form: a a a a a a a c c c c c d e e e e e g h i i i i i i i l l l l m m
n n n n n n n n n o o o o p p q r r s t t t t t u u u u u; which he
afterwards recomposed into this sentence: _Annulo cingitur, tenui,
plano, nusquam cohærente, ad eclipticam inclinato._

[15] Dick's 'Celestial Scenery.'

[16] Dick's 'Celestial Scenery.'

LETTER XXIV.

THE PLANETARY MOTIONS.----KEPLER'S LAWS.----KEPLER.

"God of the rolling orbs above!
Thy name is written clearly bright
In the warm day's unvarying blaze,
Or evening's golden shower of light;
For every fire that fronts the sun,
And every spark that walks alone
Around the utmost verge of heaven,
Was kindled at thy burning throne."--_Peabody._

IF we could stand upon the sun and view the planetary motions, they
would appear to us as simple as the motions of equestrians riding with
different degrees of speed around a large ring, of which we occupied the
centre. We should see all the planets coursing each other from west to
east, through the same great highway, (the Zodiac,) no one of them, with
the exception of the asteroids, deviating more than seven degrees from
the path pursued by the earth. Most of them, indeed, would always be
seen moving much nearer than that to the ecliptic. We should see the
planets moving on their way with various degrees of speed. Mercury would
make the entire circuit in about three months, hurrying on his course
with a speed about one third as great as that by which the moon revolves
around the earth. The most distant planets, on the other hand, move at
so slow a pace, that we should see Mercury, Venus, the Earth, and Mars,
severally overtaking them a great many times, before they had completed
their revolutions. But though the movements of some were comparatively
rapid, and of others extremely slow, yet they would not seem to differ
materially, in other respects: each would be making a steady and nearly
uniform march along the celestial vault.

Such would be the simple and harmonious motions of the planets, as they
would be seen from the sun, the centre of their motions; and such they
are, in fact. But two circumstances conspire to make them appear
exceedingly different from these, and vastly more complicated; one is,
that we view them out of the centre of their motions; the other, that we
are ourselves in motion. I have already explained to you the effect
which these two causes produce on the apparent motions of the inferior
planets, Mercury and Venus. Let us now see how they effect those of the
superior planets, Mars, Jupiter, Saturn, and Uranus.

Orreries, or machines intended to exhibit a model of the solar system,
are sometimes employed to give a popular view of the planetary motions;
but they oftener mislead than give correct ideas. They may assist
reflection, but they can never supply its place. The impossibility of
representing things in their just proportions will be evident, when we
reflect that, to do this, if in an orrery we make Mercury as large as a
cherry, we should have to represent the sun six feet in diameter. If we
preserve the same proportions, in regard to distance, we must place
Mercury two hundred and fifty feet, and Uranus twelve thousand five
hundred feet, or more than two miles from the sun. The mind of the
student of astronomy must, therefore, raise itself from such imperfect
representations of celestial phenomena, as are afforded by artificial
mechanism, and, transferring his contemplations to the celestial regions
themselves, he must conceive of the sun and planets as bodies that bear
an insignificant ratio to the immense spaces in which they circulate,
resembling more a few little birds flying in the open sky, than they do
the crowded machinery of an orrery.

The _real_ motions of the planets, indeed, or such as orreries usually
exhibit, are very easily conceived of, as before explained; but the
_apparent_ motions are, for the most part, entirely different from
these. The apparent motions of the inferior planets have been already
explained. You will recollect that Mercury and Venus move backwards and
forwards across the sun, the former never being seen further than
twenty-nine degrees, and the latter never more than about forty-seven
degrees, from that luminary; that, while passing from the greatest
elongation on one side, to the greatest elongation on the other side,
through the superior conjunction, the apparent motions of these planets
are accelerated by the motion of the earth; but that, while moving
through the inferior conjunction, at which time their motions are
retrograde, they are apparently retarded by the earth's motion. Let us
now see what are the apparent motions of the superior planets.

Let A, B, C, Fig. 62, page 294, represent the earth in different
positions in its orbit, M, a superior planet, as Mars, and N R, an arc
of the concave sphere of the heavens. First, suppose the planet to
remain at rest in M, and let us see what apparent motions it will
receive from the real motions of the earth. When the earth is at B, it
will see the planet in the heavens at N; and as the earth moves
successively through C, D, E, F, the planet will appear to move through
O, P, Q, R. B and F are the two points of greatest elongation of the
earth from the sun, as seen from the planet; hence, between these two
points, while passing through its orbit most remote from the planet,
(when the planet is seen in superior conjunction,) the earth, by its own
motion, gives an apparent motion to the planet in the order of the
signs; that is, the _apparent_ motion given by the _real_ motion of the
earth is _direct_. But in passing from F to B through A, when the planet
is seen in opposition, the apparent motion given to the planet by the
earth's motion is from R to N, and is therefore _retrograde_. As the arc
described by the earth, when the motion is direct, is much greater than
when the motion is retrograde, while the apparent arc of the heavens
described by the planet from N to R, in the one case, and from R to N,
in the other, is the same in both cases, the retrograde motion is much
swifter than the direct, being performed in much less time.

[Illustration Fig. 62.]

But the superior planets are not in fact at rest, as we have supposed,
but are all the while moving eastward, though with a slower motion than
the earth. Indeed, with respect to the remotest planets, as Saturn and
Uranus, the forward motion is so exceedingly slow, that the above
representation is nearly true for a single year. Still, the effect of
the real motions of all the superior planets, eastward, is to increase
the direct apparent motion communicated by the earth, and to diminish
the retrograde motion. This will be evident from inspecting the figure;
for if the planet _actually_ moves eastward while it is _apparently_
carried eastward by the earth's motion, the whole motion eastward will
be equal to the sum of the two; and if, while it is really moving
eastward, it is apparently carried westward still more by the earth's
motion, the retrograde movement will equal the difference of the two.

If Mars stood still while the earth went round the sun, then a second
opposition, as at A, would occur at the end of one year from the first;
but, while the earth is performing this circuit, Mars is also moving the
same way, more than half as fast; so that, when the earth returns to A,
the planet has already performed more than half the same circuit, and
will have completed its whole revolution before the earth comes up with
it. Indeed Mars, after having been seen once in opposition, does not
come into opposition again until after two years and fifty days. And
since the planet is then comparatively near to us, as at M, while the
earth is at A, and appears very large and bright, rising unexpectedly
about the time the sun sets, he surprises the world as though it were
some new celestial body. But on account of the slow progress of Saturn
and Uranus, we find, after having performed one circuit around the sun,
that they are but little advanced beyond where we left them at the last
opposition. The time between one opposition of Saturn and another is
only a year and thirteen days.

It appears, therefore, that the superior planets steadily pursue their
course around the sun, but that their apparent retrograde motion, when
in opposition, is occasioned by our passing by them with a swifter
motion, of which we are unconscious, like the apparent backward motion
of a vessel, when we overtake it and pass by it rapidly in a steam-boat.

Such are the real and the apparent motions of the planets. Let us now
turn our attention to the _laws of the planetary orbits_.

There are three great principles, according to which the motions of the
earth and all the planets around the sun are regulated, called KEPLER'S
LAWS, having been first discovered by the astronomer whose name they
bear. They may appear to you, at first, dry and obscure; yet they will
be easily understood from the explanations which follow; and so
important have they proved in astronomical inquiries, that they have
acquired for their renowned discoverer the appellation of the
'_Legislator of the Skies_.' We will consider each of these laws
separately; and, for the sake of rendering the explanation clear and
intelligible, I shall perhaps repeat some things that have been briefly
mentioned before.

[Illustration Fig. 63.]

FIRST LAW.--_The orbits of the earth and all the planets are ellipses,
having the sun in the common focus._ In a circle, all the diameters are
equal to one another; but if we take a metallic wire or hoop, and draw
it out on opposite sides, we elongate it into an ellipse, of which the
different diameters are very unequal. That which connects the points
most distant from each other is called the _transverse_, and that which
is at right angles to this is called the _conjugate_, axis. Thus, A B,
Fig. 63, is the transverse axis, and C D, the conjugate of the ellipse A
B C. By such a process of elongating the circle into an ellipse, the
centre of the circle may be conceived of as drawn opposite ways to E and
F, each of which becomes a _focus_, and both together are called the
_foci_ of the ellipse. The distance G E, or G F, of the focus from the
centre is called the _eccentricity_ of the ellipse; and the ellipse is
said to be more or less eccentric, as the distance of the focus from the
centre is greater or less. Figure 64 represents such a collection of
ellipses around the common focus F, the innermost, A G D, having a small
eccentricity, or varying little from a circle, while the outermost, A C
B, is an eccentric ellipse. The orbits of all the bodies that revolve
about the sun, both planets and comets, have, in like manner, a common
focus, in which the sun is situated, but they differ in eccentricity.
Most of the planets have orbits of very little eccentricity, differing
little from circles, but comets move in very eccentric ellipses. The
earth's path around the sun varies so little from a circle, that a
diagram representing it truly would scarcely be distinguished from a
perfect circle; yet, when the comparative distances of the sun from the
earth are taken at different seasons of the year, we find that the
difference between their greatest and least distances is no less than
three millions of miles.

[Illustration Fig. 64.]

SECOND LAW.--_The radius vector of the earth, or of any planet,
describes equal areas in equal times._ You will recollect that the
radius vector is a line drawn from the centre of the sun to a planet
revolving about the sun. This definition I have somewhere given you
before, and perhaps it may appear to you like needless repetition to
state it again. In a book designed for systematic instruction, where all
the articles are distinctly numbered, it is commonly sufficient to make
a reference back to the article where the point in question is
explained; but I think, in Letters like these, you will bear with a
little repetition, rather than be at the trouble of turning to the Index
and hunting up a definition long since given.

[Illustration Fig. 65. ]

In Figure 65, _E a_, _E b_, _E c_, &c., are successive representations
of the radius vector. Now, if a planet sets out from _a_, and travels
round the sun in the direction of _a b c_, it will move faster when
nearer the sun, as at _a_, than when more remote from it, as at _m_;
yet, if _a b_ and _m n_ be arcs described in equal times, then,
according to the foregoing law, the space _E a b_ will be equal to the
space _E m n_; and the same is true of all the other spaces described in
equal times. Although the figure _E a b_ is much shorter than _E m n_,
yet its greater breadth exactly counterbalances the greater length of
those figures which are described by the radius vector where it is
longer.

THIRD LAW.--_The squares of the periodical times are as the cubes of the
mean distances from the sun._ The periodical time of a body is the time
it takes to complete its orbit, in its revolution about the sun. Thus
the earth's periodic time is one year, and that of the planet Jupiter
about twelve years. As Jupiter takes so much longer time to travel round
the sun than the earth does, we might suspect that his orbit is larger
than that of the earth, and of course, that he is at a greater distance
from the sun; and our first thought might be, that he is probably twelve
times as far off; but Kepler discovered that the distance does not
increase as fast as the times increase, but that the planets which are
more distant from the sun actually move slower than those which are
nearer. After trying a great many proportions, he at length found that,
if we take the squares of the periodic times of two planets, the greater
square contains the less, just as often as the cube of the distance of
the greater contains that of the less. This fact is expressed by saying,
that the squares of the periodic times are to one another as the cubes
of the distances.

This law is of great use in determining the distance of the planets from
the sun. Suppose, for example, that we wish to find the distance of
Jupiter. We can easily determine, from observation, what is Jupiter's
periodical time, for we can actually see how long it takes for Jupiter,
after leaving a certain part of the heavens to come round to the same
part again. Let this period be twelve years. The earth's period is of
course one year; and the distance of the earth, as determined from the
sun's horizontal parallax, as already explained, is about ninety-five
millions of miles. Now, we have here three terms of a proportion to find
the fourth, and therefore the solution is merely a simple case of the
rule of three. Thus:--the square of 1 year : square of 12 years :: cube
of 95,000,000 : cube of Jupiter's distance. The three first terms being
known, we have only to multiply together the second and third and divide
by the first, to obtain the fourth term, which will give us the cube of
Jupiter's distance from the sun; and by extracting the cube root of this
sum, we obtain the distance itself. In the same manner we may obtain the
respective distances of all the other planets.

So truly is this a law of the solar system, that it holds good in
respect to the new planets, which have been discovered since Kepler's
time, as well as in the case of the old planets. It also holds good in
respect to comets, and to all bodies belonging to the solar system,
which revolve around the sun as their centre of motion. Hence, it is
justly regarded as one of the most interesting and important principles
yet developed in astronomy.

But who was this Kepler, that gained such an extraordinary insight into
the laws of the planetary system, as to be called the 'Legislator of the
Skies?' John Kepler was one of the most remarkable of the human race,
and I think I cannot gratify or instruct you more, than by occupying the
remainder of this Letter with some particulars of his history.

Kepler was a native of Germany. He was born in the Duchy of Wurtemberg,
in 1571. As Copernicus, Tycho Brahe, Galileo, Kepler, and Newton, are
names that are much associated in the history of astronomy, let us see
how they stood related to each other in point of time. Copernicus was
born in 1473; Tycho, in 1546; Galileo, in 1564; Kepler, in 1571; and
Newton, in 1642. Hence, Copernicus was seventy-three years before
Tycho, and Tycho ninety-six years before Newton. They all lived to an
advanced age, so that Tycho, Galileo, and Kepler, were contemporary for
many years; and Newton, as I mentioned in the sketch I gave you of his
life, was born the year that Galileo died.

Kepler was born of parents who were then in humble circumstances,
although of noble descent. Their misfortunes, which had reduced them to
poverty, seem to have been aggravated by their own unhappy dispositions;
for his biographer informs us, that "his mother was treated with a
degree of barbarity by her husband and brother-in-law, that was hardly
exceeded by her own perverseness." It is fortunate, therefore, that
Kepler, in his childhood, was removed from the immediate society and
example of his parents, and educated at a public school at the expense
of the Duke of Wurtemberg. He early imbibed a taste for natural
philosophy, but had conceived a strong prejudice against astronomy, and
even a contempt for it, inspired, probably, by the arrogant and
ridiculous pretensions of the astrologers, who constituted the principal
astronomers of his country. A vacant post, however, of teacher of
astronomy, occurred when he was of a suitable age to fill it, and he was
compelled to take it by the authority of his tutors, though with many
protestations, on his part, wishing to be provided for in some other
more brilliant profession.

Happy is genius, when it lights on a profession entirely consonant to
its powers, where the objects successively presented to it are so
exactly suited to its nature, that it clings to them as the loadstone to
its kindred metal among piles of foreign ores. Nothing could have been
more congenial to the very mental constitution of Kepler, than the study
of astronomy,--a science where the most capacious understanding may find
scope in unison with the most fervid imagination.

Much as has been said against hypotheses in philosophy, it is
nevertheless a fact, that some of the greatest truths have been
discovered in the pursuit of hypotheses, in themselves entirely false;
truths, moreover, far more important than those assumed by the
hypotheses; as Columbus, in searching for a northwest passage to India,
discovered a new world. Thus Kepler groped his way through many false
and absurd suppositions, to some of the most sublime discoveries ever
made by man. The fundamental principle which guided him was not,
however, either false or absurd. It was, that God, who made the world,
had established, throughout all his works, fixed laws,--laws that are
often so definite as to be capable of expression in exact numerical
terms. In accordance with these views, he sought for numerical relations
in the disposition and arrangement of the planets, in respect to their
number, the times of their revolution, and their distances from one
another. Many, indeed, of the subordinate suppositions which he made,
were extremely fanciful; but he tried his own hypotheses by a rigorous
mathematical test, wherever he could apply it; and as soon as he
discovered that a supposition would not abide this test, he abandoned it
without the least hesitation, and adopted others, which he submitted to
the same severe trial, to share, perhaps, the same fate. "After many
failures," he says, "I was comforted by observing that the motions, in
every case, seemed to be connected with the distances; and that, when
there was a great gap between the orbits, there was the same between the
motions. And I reasoned that, if God had adapted motions to the orbits
in some relation to the distances, he had also arranged the distances
themselves in relation to something else."

In two years after he commenced the study of astronomy, he published a
book, called the '_Mysterium Cosmographicum_,' a name which implies an
explanation of the mysteries involved in the construction of the
universe. This work was full of the wildest speculations and most
extravagant hypotheses, the most remarkable of which was, that the
distances of the planets from the sun are regulated by the relations
which subsist between the five regular solids. It is well known to
geometers, that there are and can be only five _regular solids_. These
are, first, the _tetraedron_, a four-sided figure, all whose sides are
equal and similar triangles; secondly, the _cube_, contained by six
equal squares; thirdly, an _octaedron_, an eight-sided figure,
consisting of two four-sided pyramids joined at their bases; fourthly, a
_dodecaedron_, having twelve five-sided or pentagonal faces; and,
fifthly, an _icosaedron_, contained by twenty equal and similar
triangles. You will be much at a loss, I think, to imagine what relation
Kepler could trace between these strange figures and the distances of
the several planets from the sun. He thought he discovered a connexion
between those distances and the spaces which figures of this kind would
occupy, if interposed in certain ways between them. Thus, he says the
Earth is a circle, the measure of all; round it describe a dodecaedron,
and the circle including this will be the orbit of Mars. Round this
circle describe a tetraedron, and the circle including this will be the
orbit of Jupiter. Describe a cube round this, and the circle including
it will be the orbit of Saturn. Now, inscribe in the earth an
icosaedron, and the circle included in this will give the orbit of
Venus. In this inscribe an octaedron, and the circle included in this
will be the orbit of Mercury. On this supposed discovery Kepler exults
in the most enthusiastic expressions. "The intense pleasure I have
received from this discovery never can be told in words. I regretted no
more time wasted; I tired of no labor; I shunned no toil of reckoning;
days and nights I spent in calculations, until I could see whether this
opinion would agree with the orbits of Copernicus, or whether my joy was
to vanish into air. I willingly subjoin that sentiment of Archytas, as
given by Cicero; 'If I could mount up into heaven, and thoroughly
perceive the nature of the world and the beauty of the stars, that
admiration would be without a charm for me, unless I had some one like
you, reader, candid, attentive, and eager for knowledge, to whom to
describe it.' If you acknowledge this feeling, and are candid, you will
refrain from blame, such as, not without cause, I anticipate; but if,
leaving that to itself, you fear, lest these things be not ascertained,
and that I have shouted triumph before victory, at least approach these
pages, and learn the matter in consideration: you will not find, as just
now, new and unknown planets interposed; that boldness of mine is not
approved; but those old ones very little loosened, and so furnished by
the interposition (however absurd you may think it) of rectilinear
figures, that in future you may give a reason to the rustics, when they
ask for the hooks which keep the skies from falling."

When Tycho Brahe, who had then retired from his famous Uraniburg, and
was settled in Prague, met with this work of Kepler's, he immediately
recognised under this fantastic garb the lineaments of a great
astronomer. He needed such an unwearied and patient calculator as he
perceived Kepler to be, to aid him in his labors, in order that he might
devote himself more unreservedly to the taking of observations,--an
employment in which he delighted, and in which, as I mentioned, in
giving you a sketch of his history, he excelled all men of that and
preceding ages. Kepler, therefore, at the express invitation of Tycho,
went to Prague, and joined him in the capacity of assistant. Had Tycho
been of a nature less truly noble, he might have looked with contempt on
one who had made so few observations, and indulged so much in wild
speculation; or he might have been jealous of a rising genius, in which
he descried so many signs of future eminence as an astronomer; but,
superior to all the baser motives, he extends to the young aspirant the
hand of encouragement, in the following kind invitation: "Come not as a
stranger, but as a very welcome friend; come, and share in my
observations, with such instruments as I have with me."

Several years previous to this, Kepler, after one or two unsuccessful
trials, had found him a wife, from whom he expected a considerable
fortune; but in this he was disappointed; and so poor was he, that, when
on his journey to Prague, in company with his wife, being taken sick, he
was unable to defray the expenses of the journey, and was forced to cast
himself on the bounty of Tycho.

In the course of the following year, while absent from Prague, he
fancied that Tycho had injured him, and accordingly addressed to the
noble Dane a letter full of insults and reproaches. A mild reply from
Tycho opened the eyes of Kepler to his own ingratitude. His better
feelings soon returned, and he sent to his great patron this humble
apology: "Most noble Tycho! How shall I enumerate, or rightly estimate,
your benefits conferred on me! For two months you have liberally and
gratuitously maintained me, and my whole family; you have provided for
all my wishes; you have done me every possible kindness; you have
communicated to me every thing you hold most dear; no one, by word or
deed, has intentionally injured me in any thing; in short, not to your
own children, your wife, or yourself, have you shown more indulgence
than to me. This being so, as I am anxious to put upon record, I cannot
reflect, without consternation, that I should have been so given up by
God to my own intemperance, as to shut my eyes on all these benefits;
that, instead of modest and respectful gratitude, I should indulge for
three weeks in continual moroseness towards all your family, and in
headlong passion and the utmost insolence towards yourself, who possess
so many claims on my veneration, from your noble family, your
extraordinary learning, and distinguished reputation. Whatever I have
said or written against the person, the fame, the honor, and the
learning, of your Excellency; or whatever, in any other way, I have
injuriously spoken or written, (if they admit no other more favorable
interpretation,) as to my grief I have spoken and written many things,
and more than I can remember; all and every thing I recant, and freely
and honestly declare and profess to be groundless, false, and incapable
of proof." This was ample satisfaction to the generous Tycho.

"To err is human: to forgive, divine."

On Kepler's return to Prague, he was presented to the Emperor by Tycho,
and honored with the title of Imperial Mathematician. This was in 1601,
when he was thirty years of age. Tycho died shortly after, and Kepler
succeeded him as principal mathematician to the Emperor; but his salary
was badly paid, and he suffered much from pecuniary embarrassments.
Although he held the astrologers, or those who told fortunes by the
stars, in great contempt, yet he entertained notions of his own, on the
same subject, quite as extravagant, and practised the art of casting
nativities, to eke out a support for his family.

When Galileo began to observe with his telescope, and announced, in
rapid succession, his wonderful discoveries, Kepler entered into them
with his characteristic enthusiasm, although they subverted many of his
favorite hypotheses. But such was his love of truth, that he was among
the first to congratulate Galileo, and a most engaging correspondence
was carried on between these master-spirits.

The first planet, which occupied the particular attention of Kepler, was
Mars, the long and assiduous study of whose motions conducted him at
length to the discovery of those great principles called 'Kepler's
Laws.' Rarely do we meet with so remarkable a union of a vivid fancy
with a profound intellect. The hasty and extravagant suggestions of the
former were submitted to the most laborious calculations, some of which,
that were of great length, he repeated seventy times. This exuberance of
fancy frequently appears in his style of writing, which occasionally
assumes a tone ludicrously figurative. He seems constantly to
contemplate Mars as a valiant hero, who had hitherto proved invincible,
and who would often elude his own efforts to conquer him, "While thus
triumphing over Mars, and preparing for him, as for one altogether
vanquished, tabular prisons, and equated, eccentric fetters, it is
buzzed here and there, that the victory is vain, and that the war is
raging anew as violently as before. For the enemy, left at home a
despised captive, has burst all the chains of the equation, and broken
forth of the prisons of the tables. Skirmishes routed my forces of
physical causes, and, shaking off the yoke, regained their liberty. And
now, there was little to prevent the fugitive enemy from effecting a
junction with his own rebellious supporters, and reducing me to despair,
had I not suddenly sent into the field a reserve of new physical
reasonings, on the rout and dispersion of the veterans, and diligently
followed, without allowing the slightest respite, in the direction in
which he had broken out."

But he pursued this warfare with the planet until he gained a full
conquest, by the discovery of the first two of his laws, namely, that
_he revolves in an elliptical orbit_, and that _his radius vector passes
over equal spaces in equal times_.

Domestic troubles, however, involved him in the deepest affliction.
Poverty, the loss of a promising and favorite son, the death of his
wife, after a long illness;--these were some of the misfortunes that
clustered around him. Although his first marriage had been an unhappy
one, it was not consonant to his genius to surrender any thing with only
a single trial. Accordingly, it was not long before he endeavored to
repair his loss by a second alliance. He commissioned a number of his
friends to look out for him, and he soon obtained a tabular list of
eleven ladies, among whom his affections wavered. The progress of his
courtship is thus narrated in the interesting 'Life' contained in the
'Library of Useful Knowledge.' It furnishes so fine a specimen of his
eccentricities, that I cannot deny myself the pleasure of transcribing
the passage for your perusal. It is taken from an account which Kepler
himself gave in a letter to a friend.

"The first on the list was a widow, an intimate friend of his first wife
and who, on many accounts, appeared a most eligible match. At first, she
seemed favorably inclined to the proposal: it is certain that she took
time to consider it, but at last she very quietly excused herself.
Finding her afterwards less agreeable in person than he had anticipated,
he considered it a fortunate escape, mentioning, among other objections,
that she had two marriageable daughters, whom, by the way, he had got on
his list for examination. He was much troubled to reconcile his
astrology with the fact of his having taken so much pains about a
negotiation not destined to succeed. He examined the case
professionally. 'Have the stars,' says he, 'exercised any influence
here? For, just about this time, the direction of the mid-heaven is in
hot opposition to Mars, and the passage of Saturn through the ascending
point of the zodiac, in the scheme of my nativity, will happen again
next November and December. But, if these are the causes, how do they
act? Is that explanation the true one, which I have elsewhere given? For
I can never think of handing over to the stars the office of deities, to
produce effects. Let us, therefore, suppose it accounted for by the
stars, that at this season I am violent in my temper and affections, in
rashness of belief, in a show of pitiful tender-heartedness, in catching
at reputation by new and paradoxical notions, and the singularity of my
actions; in busily inquiring into, and weighing, and discussing, various
reasons; in the uneasiness of my mind, with respect to my choice. I
thank God, that that did not happen which might have happened; that this
marriage did not take place. Now for the others.' Of these, one was too
old; another, in bad health; another, too proud of her birth and
quarterings; a fourth had learned nothing but showy accomplishments, not
at all suitable to the kind of life she would have to lead with him.
Another grew impatient, and married a more decided admirer while he was
hesitating. 'The mischief,' says he, 'in all these attachments was,
that, whilst I was delaying, comparing, and balancing, conflicting
reasons, every day saw me inflamed with a new passion.' By the time he
reached No. 8, of his list, he found his match in this respect. 'Fortune
has avenged herself at length on my doubtful inclinations. At first, she
was quite complying, and her friends also. Presently, whether she did or
did not consent, not only I, but she herself, did not know. After the
lapse of a few days, came a renewed promise, which, however, had to be
confirmed a third time: and, four days after that, she again repented
her conformation, and begged to be excused from it. Upon this, I gave
her up, and this time all my counsellors were of one opinion.' This was
the longest courtship in the list, having lasted three whole months;
and, quite disheartened by its bad success, Kepler's next attempt was of
a more timid complexion. His advances to No. 9 were made by confiding to
her the whole story of his recent disappointment, prudently determining
to be guided in his behavior, by observing whether the treatment he
experienced met with a proper degree of sympathy. Apparently, the
experiment did not succeed; and, when almost reduced to despair, Kepler
betook himself to the advice of a friend, who had for some time past
complained that she was not consulted in this difficult negotiation.
When she produced No. 10, and the first visit was paid, the report upon
her was as follows: 'She has, undoubtedly, a good fortune, is of good
family, and of economical habits: but her physiognomy is most horribly
ugly; she would be stared at in the streets, not to mention the striking
disproportion in our figures. I am lank, lean, and spare; she is short
and thick. In a family notorious for fatness, she is considered
superfluously fat.' The only objection to No. 11 seems to have been, her
excessive youth; and when this treaty was broken off, on that account,
Kepler turned his back upon all his advisers, and chose for himself one
who had figured as No. 5, in his list, to whom he professes to have felt
attached throughout, but from whom the representations of his friends
had hitherto detained him, probably on account of her humble station."

Having thus settled his domestic affairs, Kepler now betook himself,
with his usual industry, to his astronomical studies, and brought before
the world the most celebrated of his publications, entitled 'Harmonics.'
In the fifth book of this work he announced his _Third Law_,--that the
squares of the periodical times of the planets are as the cubes of the
distances. Kepler's rapture on detecting it was unbounded. "What," says
he, "I prophesied two-and-twenty years ago, as soon as I discovered the
five solids among the heavenly orbits; what I firmly believed long
before I had seen Ptolemy's Harmonics; what I had promised my friends in
the title of this book, which I named before I was sure of my discovery;
what, sixteen years ago, I urged as a thing to be sought; that for which
I joined Tycho Brahe, for which I settled in Prague, for which I have
devoted the best part of my life to astronomical contemplations;--at
length I have brought to light, and have recognised its truth beyond my
most sanguine expectations. It is now eighteen months since I got the
first glimpse of light, three months since the dawn, very few days since
the unveiled sun, most admirable to gaze on, burst out upon me. Nothing
holds me: I will indulge in my sacred fury; I will triumph over mankind
by the honest confession, that I have stolen the golden vases of the
Egyptians to build up a tabernacle for my God, far from the confines of
Egypt. If you forgive me, I rejoice: if you are angry, I can bear it;
the die is cast, the book is written, to be read either now or by
posterity,--I care not which. I may well wait a century for a reader, as
God has waited six thousand years for an observer." In accordance with
the notion he entertained respecting the "music of the spheres," he made
Saturn and Jupiter take the bass, Mars the tenor, the Earth and Venus
the counter, and Mercury the treble.

"The misery in which Kepler lived," says Sir David Brewster, in his
'Life of Newton,' "forms a painful contrast with the services which he
performed for science. The pension on which he subsisted was always in
arrears; and though the three emperors, whose reigns he adorned,
directed their ministers to be more punctual in its payment, the
disobedience of their commands was a source of continual vexation to
Kepler. When he retired to Silesia, to spend the remainder of his days,
his pecuniary difficulties became still more harassing. Necessity at
length compelled him to apply personally for the arrears which were due;
and he accordingly set out, in 1630, when nearly sixty years of age, for
Ratisbon; but, in consequence of the great fatigue which so long a
journey on horseback produced, he was seized with a fever, which put an
end to his life."

Professor Whewell (in his interesting work on Astronomy and General
Physics considered with reference to Natural Theology) expresses the
opinion that Kepler, notwithstanding his constitutional oddities, was a
man of strong and lively piety. His 'Commentaries on the Motions of
Mars' he opens with the following passage: "I beseech my reader, that,
not unmindful of the Divine goodness bestowed on man, he do with me
praise and celebrate the wisdom and greatness of the Creator, which I
open to him from a more inward explication of the form of the world,
from a searching of causes, from a detection of the errors of vision;
and that thus, not only in the firmness and stability of the earth, he
perceive with gratitude the preservation of all living things in Nature
as the gift of God, but also that in its motion, so recondite, so
admirable, he acknowledge the wisdom of the Creator. But him who is too
dull to receive this science, or too weak to believe the Copernican
system without harm to his piety,--him, I say, I advise that, leaving
the school of astronomy, and condemning, if he please, any doctrines of
the philosophers, he follow his own path, and desist from this wandering
through the universe; and, lifting up his natural eyes, with which he
alone can see, pour himself out in his own heart, in praise of God the
Creator; being certain that he gives no less worship to God than the
astronomer, to whom God has given to see more clearly with his inward
eye, and who, for what he has himself discovered, both can and will
glorify God."

In a Life of Kepler, very recently published in his native country,
founded on manuscripts of his which have lately been brought to light,
there are given numerous other examples of a similar devotional spirit.
Kepler thus concludes his Harmonics: "I give Thee thanks, Lord and
Creator, that Thou has given me joy through Thy creation; for I have
been ravished with the work of Thy hands. I have revealed unto mankind
the glory of Thy works, as far as my limited spirit could conceive their
infinitude. Should I have brought forward any thing that is unworthy of
Thee, or should I have sought my own fame, be graciously pleased to
forgive me."

As Galileo experienced the most bitter persecutions from the Church of
Rome, so Kepler met with much violent opposition and calumny from the
Protestant clergy of his own country, particularly for adopting, in an
almanac which, as astronomer royal, he annually published, the reformed
calendar, as given by the Pope of Rome. His opinions respecting
religious liberty, also, appear to have been greatly in advance of the
times in which he lived. In answer to certain calumnies with which he
was assailed, for his boldness in reasoning from the light of Nature, he
uttered these memorable words: "The day will soon break, when pious
simplicity will be ashamed of its blind superstition; when men will
recognise truth in the book of Nature as well as in the Holy Scriptures,
and rejoice in the two revelations."

LETTER XXV.

COMETS.

----"Fancy now no more
Wantons on fickle pinions through the skies,
But, fixed in aim, and conscious of her power,
Sublime from cause to cause exults to rise,
Creation's blended stores arranging as she flies."--_Beattie._

NOTHING in astronomy is more truly admirable, than the knowledge which
astronomers have acquired of the motions of comets, and the power they
have gained of predicting their return. Indeed, every thing appertaining
to this class of bodies is so wonderful, as to seem rather a tale of
romance than a simple recital of facts. Comets are truly the
knights-errant of astronomy. Appearing suddenly in the nocturnal sky,
and often dragging after them a train of terrific aspect, they were, in
the earlier ages of the world, and indeed until a recent period,
considered as peculiarly ominous of the wrath of Heaven, and as
harbingers of wars and famines, of the dethronement of monarchs, and the
dissolution of empires.

Science has, it is true, disarmed them of their terrors, and
demonstrated that they are under the guidance of the same Hand, that
directs in their courses the other members of the solar system; but she
has, at the same time, arrayed them in a garb of majesty peculiarly her
own.

Although the ancients paid little attention to the ordinary phenomena of
Nature, hardly deeming them worthy of a reason, yet, when a comet blazed
forth, fear and astonishment conspired to make it an object of the most
attentive observation. Hence the aspects of remarkable comets, that have
appeared at various times, have been handed down to us, often with
circumstantial minuteness, by the historians of different ages. The
comet which appeared in the year 130, before the Christian era, at the
birth of Mithridates, is said to have had a disk equal in magnitude to
that of the sun. Ten years before this, one was seen, which, according
to Justin, occupied a fourth part of the sky, that is, extended over
forty-five degrees, and surpassed the sun in splendor. In the year 400,
one was seen which resembled a sword in shape, and extended from the
zenith to the horizon.

Such are some of the accounts of comets of past ages; but it is probable
we must allow much for the exaggerations naturally accompanying the
descriptions of objects in themselves so truly wonderful.

A comet, when perfectly formed, consists of three parts, the nucleus,
the envelope, and the tail. The nucleus, or body of the comet, is
generally distinguished by its forming a bright point in the centre of
the head, conveying the idea of a solid, or at least of a very dense,
portion of matter. Though it is usually exceedingly small, when compared
with the other parts of the comet, and is sometimes wanting altogether,
yet it occasionally subtends an angle capable of being measured by the
telescope. The envelope (sometimes called the _coma_, from a Latin word
signifying hair, in allusion to its hairy appearance) is a dense
nebulous covering, which frequently renders the edge of the nucleus so
indistinct, that it is extremely difficult to ascertain its diameter
with any degree of precision. Many comets have no nucleus, but present
only a nebulous mass, exceedingly attenuated on the confines, but
gradually increasing in density towards the centre. Indeed, there is a
regular gradation of comets, from such as are composed merely of a
gaseous or vapory medium, to those which have a well-defined nucleus. In
some instances on record, astronomers have detected with their
telescopes small stars through the densest part of a comet. The tail is
regarded as an expansion or prolongation of the coma; and presenting, as
it sometimes does, a train of appalling magnitude, and of a pale,
portentous light, it confers on this class of bodies their peculiar
celebrity. These several parts are exhibited in Fig. 67, which
[Illustration Figures 67, 68. COMETS OF 1680 AND 1811.] represents the
appearance of the comet of 1680. Fig. 68 also exhibits that of the comet
of 1811.

The _number_ of comets belonging to the solar system, is probably very
great. Many no doubt escape observation, by being above the horizon in
the day-time. Seneca mentions, that during a total eclipse of the sun,
which happened sixty years before the Christian era, a large and
splendid comet suddenly made its appearance, being very near the sun.
The leading particulars of at least one hundred and thirty have been
computed, and arranged in a table, for future comparison. Of these,
_six_ are particularly remarkable; namely, the comets of 1680, 1770, and
1811; and those which bear the names of Halley, Biela, and Encke. The
comet of 1680 was remarkable, not only for its astonishing size and
splendor, and its near approach to the sun, but is celebrated for having
submitted itself to the observations of Sir Isaac Newton, and for having
enjoyed the signal honor of being the first comet whose elements were
determined on the sure basis of mathematics. The comet of 1770 is
memorable for the changes its orbit has undergone by the action of
Jupiter, as I shall explain to you more particularly hereafter. The
comet of 1811 was the most remarkable in its appearance of all that have
been seen in the present century. It had scarcely any perceptible
nucleus, but its train was very long and broad, as is represented in
Fig. 68. Halley's comet (the same which reappeared in 1835) is
distinguished as that whose return was first successfully predicted, and
whose orbit is best determined; and Biela's and Encke's comets are well
known for their short periods of revolution, which subject them
frequently to the view of astronomers.

In _magnitude and brightness_, comets exhibit great diversity. History
informs us of comets so bright, as to be distinctly visible in the
day-time, even at noon, and in the brightest sunshine. Such was the
comet seen at Rome a little before the assassination of Julius Cæsar.
The comet of 1680 covered an arc of the heavens of ninety-seven
degrees, and its length was estimated at one hundred and twenty-three
millions of miles. That of 1811 had a nucleus of only four hundred and
twenty-eight miles in diameter, but a tail one hundred and thirty-two
millions of miles long. Had it been coiled around the earth like a
serpent, it would have reached round more than five thousand times.
Other comets are exceedingly small, the nucleus being in one case
estimated at only twenty-five miles; and some, which are destitute of
any perceptible nucleus, appear to the largest telescopes, even when
nearest to us, only as a small speck of fog, or as a tuft of down. The
majority of comets can be seen only by the aid of the telescope. Indeed,
the same comet has very different aspects, at its different returns.
Halley's comet, in 1305, was described by the historians of that age as
the comet of terrific magnitude; (_cometa horrendæ magnitudinis_;) in
1456 its tail reached from the horizon to the zenith, and inspired such
terror, that, by a decree of the Pope of Rome, public prayers were
offered up at noonday in all the Catholic churches, to deprecate the
wrath of heaven; while in 1682 its tail was only thirty degrees in
length; and in 1759 it was visible only to the telescope until after it
had passed its perihelion. At its recent return, in 1835, the greatest
length of the tail was about twelve degrees. These changes in the
appearance of the same comet are partly owing to the different positions
of the earth with respect to them, being sometimes much nearer to them
when they cross its track than at others; also, one spectator, so
situated as to see the comet at a higher angle of elevation, or in a
purer sky, than another, will see the train longer than it appears to
another less favorably situated; but the extent of the changes are such
as indicate also a real change in magnitude and brightness.

The _periods_ of comets in their revolutions around the sun are equally
various. Encke's comet, which has the shortest known period, completes
its revolution in three and one third years; or, more accurately, in
twelve hundred and eight days; while that of 1811 is estimated to have
a period of thirty-three hundred and eighty three years.

The _distances_ to which different comets recede from the sun are
equally various. While Encke's comet performs its entire revolution
within the orbit of Jupiter, Halley's comet recedes from the sun to
twice the distance of Uranus; or nearly thirty-six hundred millions of
miles. Some comets, indeed, are thought to go a much greater distance
from the sun than this, while some are supposed to pass into curves
which do not, like the ellipse, return into themselves; and in this case
they never come back to the sun. (See Fig. 34, page 153.)

Comets shine _by reflecting the light of the sun_. In one or two
instances, they have been thought to exhibit distinct _phases_, like the
moon, although the nebulous matter with which the nucleus is surrounded
would commonly prevent such phases from being distinctly visible, even
when they would otherwise be apparent. Moreover, certain qualities of
_polarized_ light,--an affection by which a ray of light seems to have
different properties on different sides,--enable opticians to decide
whether the light of a given body is direct or reflected; and M. Arago,
of Paris, by experiments of this kind on the light of the comet of 1819,
ascertained it to be reflected light.

The tail of a comet usually increases very much as it approaches the
sun; and it frequently does not reach its maximum until after the
perihelion passage. In receding from the sun, the tail again contracts,
and nearly or quite disappears before the body of the comet is entirely
out of sight. The tail is frequently divided into two portions, the
central parts, in the direction of the axis, being less bright than the
marginal parts. In 1744 a comet appeared which had six tails spread out
like a fan.

The tails of comets extend in a direct line from the sun, although more
or less curved, like a long quill or feather, being convex on the side
next to the direction in which they are moving,--a figure which may
result from the less velocity of the portion most remote from the sun.
Expansions of the envelope have also been at times observed on the side
next the sun; but these seldom attain any considerable length.

The _quantity of matter_ in comets is exceedingly small. Their tails
consist of matter of such tenuity, that the smallest stars are visible
through them. They can only be regarded as masses of thin vapor,
susceptible of being penetrated through their whole substance by the
sunbeams, and reflecting them alike from their interior parts and from
their surfaces. It appears perhaps incredible, that so thin a substance
should be visible by reflected light, and some astronomers have held
that the matter of comets is self-luminous; but it requires but very
little light to render an object visible in the night, and a light vapor
may be visible when illuminated throughout an immense stratum, which
could not be seen if spread over the face of the sky like a thin cloud.
"The highest clouds that float in our atmosphere," says Sir John
Herschel, "must be looked upon as dense and massive bodies, compared
with the filmy and all but spiritual texture of a comet."

The small quantity of matter in comets is proved by the fact, that they
have at times passed very near to some of the planets, without
disturbing their motions in any appreciable degree. Thus the comet of
1770, in its way to the sun, got entangled among the satellites of
Jupiter, and remained near them four months; yet it did not perceptibly
change their motions. The same comet, also, came very near the earth; so
that, had its quantity of matter been equal to that of the earth, it
would, by its attraction, have caused the earth to revolve in an orbit
so much larger than at present, as to have increased the length of the
year two hours and forty-seven minutes. Yet it produced no sensible
effect on the length of the year, and therefore its mass, as is shown by
La Place, could not have exceeded 1/5000 of that of the earth, and
might have been less than this to any extent. It may indeed be asked,
what proof we have that comets have any matter, and are not mere
reflections of light. The answer is, that, although they are not able by
their own force of attraction to disturb the motions of the planets, yet
they are themselves exceedingly disturbed by the action of the planets,
and in exact conformity with the laws of universal gravitation. A
delicate compass may be greatly agitated by the vicinity of a mass of
iron, while the iron is not sensibly affected by the attraction of the
needle.

By approaching very near to a large planet, a comet may have its orbit
entirely changed. This fact is strikingly exemplified in the history of
the comet of 1770. At its appearance in 1770, its orbit was found to be
an ellipse, requiring for a complete revolution only five and a half
years; and the wonder was, that it had not been seen before, since it
was a very large and bright comet. Astronomers suspected that its path
had been changed, and that it had been recently compelled to move in
this short ellipse, by the disturbing force of Jupiter and his
satellites. The French Institute, therefore, offered a high prize for
the most complete investigation of the elements of this comet, taking
into account any circumstances which could possibly have produced an
alteration in its course. By tracing back the movements of this comet,
for some years previous to 1770, it was found that, at the beginning of
1767, it had entered considerably within the sphere of Jupiter's
attraction. Calculating the amount of this attraction from the known
proximity of the two bodies, it was found what must have been its orbit
previous to the time when it became subject to the disturbing action of
Jupiter. It was therefore evident why, as long as it continued to
circulate in an orbit so far from the centre of the system, it was never
visible from the earth. In January, 1767, Jupiter and the comet happened
to be very near to one another, and as both were moving in the same
direction, and nearly in the same plane, they remained in the
neighborhood of each other for several months, the planet being between
the comet and the sun. The consequence was, that the comet's orbit was
changed into a smaller ellipse, in which its revolution was accomplished
in five and a half years. But as it approached the sun, in 1779, it
happened again to fall in with Jupiter. It was in the month of June that
the attraction of the planet began to have a sensible effect; and it was
not until the month of October following, that they were finally
separated.

At the time of their nearest approach, in August, Jupiter was distant
from the comet only 1/491 of its distance from the sun, and exerted an
attraction upon it two hundred and twenty-five times greater than that
of the sun. By reason of this powerful attraction, Jupiter being further
from the sun than the comet, the latter was drawn out into a new orbit,
which even at its perihelion came no nearer to the sun than the planet
Ceres. In this third orbit, the comet requires about twenty years to
accomplish its revolution; and being at so great a distance from the
earth, it is invisible, and will for ever remain so unless, in the
course of ages, it may undergo new perturbations, and move again in some
smaller orbit, as before.

With the foregoing leading facts respecting comets in view, I will now
explain to you a few things equally remarkable respecting their
_motions_.

The paths of the planets around the sun being nearly circular, we are
able to see a planet in every part of its orbit. But the case is very
different with comets. For the greater part of their course, they are
wholly out of sight, and come into view only while just in the
neighborhood of the sun. This you will readily see must be the case, by
inspecting the frontispiece, which represents the orbit of Biela's
comet, in 1832. Sometimes, the orbit is so eccentric, that the place of
the focus occupied by the sun appears almost at the extremity of the
orbit. This was the case with the orbit of the comet of 1680. Indeed,
this comet, at its perihelion, came in fact nearer to the sun than the
sixth part of the sun's diameter, being only one hundred and forty-six
thousand miles from the surface of the sun, which, you will remark, is
only a little more than half the distance of the moon from the earth;
while, at its aphelion, it was estimated to be thirteen thousand
millions of miles from the sun,--more than eleven thousand millions of
miles beyond the planet Uranus. Its _velocity_, when nearest the sun,
exceeded a million of miles an hour. To describe such an orbit as was
assigned to it by Sir Isaac Newton, would require five hundred and
seventy-five years. During all this period, it was entirely out of view
to the inhabitants of the earth, except the few months, while it was
running down to the sun from such a distance as the orbit of Jupiter and
back. The velocity of bodies moving in such eccentric orbits differs
widely in different parts of their orbits. In the remotest parts it is
so slow, that years would be required to pass over a space equal to that
which it would run over in a single day, when near the sun.

The appearances of the same comet at different periods of its return are
so various, that we can never pronounce a given comet to be the same
with one that has appeared before, from any peculiarities in its
physical aspect, as from its color, magnitude, or shape; since, in all
these respects, it is very different at different returns; but it is
judged to be the same if its _path_ through the heavens, as traced among
the stars, is the same.

The comet whose history is the most interesting, and which both of us
have been privileged to see, is Halley's. Just before its latest visit,
in 1835, its return was anticipated with so much expectation, not only
by astronomers, but by all classes of the community, that a great and
laudable eagerness universally prevailed, to learn the particulars of
its history. The best summary of these, which I met with, was given in
the Edinburgh Review for April, 1835. I might content myself with barely
referring you to that well-written article; but, as you may not have the
work at hand, and would, moreover, probably not desire to read the
whole article, I will abridge it for your perusal, interspersing some
remarks of my own. I have desired to give you, in the course of these
Letters, some specimen of the labors of astronomers, and shall probably
never be able to find a better one.

It is believed that the first recorded appearance of Halley's comet was
that which was supposed to signalize the birth of Mithridates, one
hundred and thirty years before the birth of Christ. It is said to have
appeared for twenty-four days; its light is said to have surpassed that
of the sun; its magnitude to have extended over a fourth part of the
firmament; and it is stated to have occupied, consequently, about four
hours in rising and setting. In the year 323, a comet appeared in the
sign Virgo. Another, according to the historians of the Lower Empire,
appeared in the year 399, seventy-six years after the last, at an
interval corresponding to that of Halley's comet. The interval between
the birth of Mithridates and the year 323 was four hundred and
fifty-three years, which would be equivalent to six periods of
seventy-five and a half years. Thus it would seem, that in the interim
there were five returns of this comet unobserved, or at least
unrecorded. The appearance in the year 399 was attended with
extraordinary circumstances. It was described in the old writers as a
"comet of monstrous size and appalling aspect, its tail seeming to reach
down to the ground." The next recorded appearance of a comet agreeing
with the ascertained period marks the taking of Rome, in the year
550,--an interval of one hundred and fifty-one years, or two periods of
seventy-five and a half years having elapsed. One unrecorded return
must, therefore, have taken place in the interim. The next appearance of
a comet, coinciding with the assigned period, is three hundred and
eighty years afterwards; namely, in the year 930,--five revolutions
having been completed in the interval. The next appearance is recorded
in the year 1005, after an interval of a single period of seventy-five
years. Three revolutions would now seem to have passed unrecorded, when
the comet again makes its appearance in 1230. In this, as well as in
former appearances, it is proper to state, that the sole test of
identity of these cornets with that of Halley is the coincidence of the
times, as near as historical records enable us to ascertain, with the
epochs at which the comet of Halley might be expected to appear. That
such evidence, however, is very imperfect, must be evident, if the
frequency of cometary appearances be considered, and if it be
remembered, that hitherto we find no recorded observations, which could
enable us to trace, even with the rudest degree of approximation, the
paths of those comets, the times of whose appearances raise a
presumption of their identity with that of Halley. We now, however,
descend to times in which more satisfactory evidence may be expected.

In the year 1305, a year in which the return of Halley's comet might
have been expected, there is recorded a comet of remarkable character:
"A comet of terrific dimensions made its appearance about the time of
the feast of the Passover, which was followed by a Great Plague." Had
the terrific appearance of this body alone been recorded, this
description might have passed without the charge of great exaggeration;
but when we find the Great Plague connected with it as a consequence, it
is impossible not to conclude, that the comet was seen by its historians
through the magnifying medium of the calamity which followed it. Another
appearance is recorded in the year 1380, unaccompanied by any other
circumstance than its mere date. This, however, is in strict accordance
with the ascertained period of Halley's comet.

We now arrive at the first appearance at which observations were taken,
possessing sufficient accuracy to enable subsequent investigators to
determine the path of the comet; and this is accordingly the first comet
the identity of which with the comet of Halley can be said to be
conclusively established. In the year 1456, a comet is stated to have
appeared "of unheard of magnitude;" it was accompanied by a tail of
extraordinary length, which extended over sixty degrees, (a third part
of the heavens,) and continued to be seen during the whole month of
June. The influence which was attributed to this appearance renders it
probable, that in the record there is more or less of exaggeration. It
was considered as the celestial indication of the rapid success of
Mohammed the Second, who had taken Constantinople, and struck terror
into the whole Christian world. Pope Calixtus the Second levelled the
thunders of the Church against the enemies of his faith, terrestrial and
celestial; and in the same Bull excommunicated the Turks and the comet;
and, in order that the memory of this manifestation of his power should
be for ever preserved, he ordained that the bells of all the churches
should be rung at mid-day,--a custom which is preserved in those
countries to our times.

The extraordinary length and brilliancy which was ascribed to the tail,
upon this occasion, have led astronomers to investigate the
circumstances under which its brightness and magnitude would be the
greatest possible; and upon tracing back the motion of the comet to the
year 1456, it has been found that it was then actually in the position,
with respect to the earth and sun, most favorable to magnitude and
splendor. So far, therefore, the result of astronomical calculation
corroborates the records of history.

The next return took place in 1531. Pierre Appian, who first ascertained
the fact that the tails of comets are usually turned from the sun,
examined this comet with a view to verify his statement, and to
ascertain the true direction of its tail. He made, accordingly, numerous
observations upon its position, which, although rude, compared with the
present standard of accuracy, were still sufficiently exact to enable
Halley to identify this comet with that observed by himself.

The next return took place in 1607, when the comet was observed by
Kepler. This astronomer first saw it on the evening of the twenty-sixth
of September, when it had the appearance of a star of the first
magnitude, and, to his vision, was without a tail; but the friends who
accompanied him had better sight, and distinguished the tail. Before
three o'clock the following morning the tail had become clearly visible,
and had acquired great magnitude. Two days afterwards, the comet was
observed by Longomontanus, a distinguished philosopher of the time. He
describes its appearance, to the naked eye, to be like Jupiter, but of a
paler and more obscured light; that its tail was of considerable length,
of a paler light than that of the head, and more dense than the tails of
ordinary comets.

The next appearance, and that which was observed by Halley himself, took
place in 1682, a little before the publication of the '_Principia_.' In
the interval between 1607 and 1682, practical astronomy had made great
advances; instruments of observation had been brought to a state of
comparative perfection; numerous observatories had been established, and
the management of them had been confided to the most eminent men in
Europe. In 1682, the scientific world was therefore prepared to examine
the visitor of our system with a degree of care and accuracy before
unknown.

In the year 1686, about four years afterwards, Newton published his
'_Principia_,' in which he applied to the comet of 1680 the general
principles of physical investigation first promulgated in that work. He
explained the method of determining, by geometrical construction, the
visible portion of the path of a body of this kind, and invited
astronomers to apply these principles to the various recorded
comets,--to discover whether some among them might not have appeared at
different epochs, the future returns of which might consequently be
predicted. Such was the effect of the force of analogy upon the mind of
Newton, that, without awaiting the discovery of a periodic comet, he
boldly assumed these bodies to be analogous to planets in their
revolution round the sun.

Extraordinary as these conjectures must have appeared at the time, they
were soon strictly realized. Halley, who was then a young man, but
possessed one of the best minds in England, undertook the labor of
examining the circumstances attending all the comets previously
recorded, with a view to discover whether any, and which of them,
appeared to follow the same path. Antecedently to the year 1700, four
hundred and twenty-five of these bodies had been recorded in history;
but those which had appeared before the fourteenth century had not been
submitted to any observations by which their paths could be
ascertained,--at least, not with a sufficient degree of precision, to
afford any hope of identifying them with those of other comets.
Subsequently to the year 1300, however, Halley found twenty-four comets
on which observations had been made and recorded, with a degree of
precision sufficient to enable him to calculate the actual paths which
these bodies followed while they were visible. He examined, with the
most elaborate care, the _courses_ of each of these twenty-four bodies;
he found the exact points at which each one of them crossed the
ecliptic, or their _nodes_; also the angle which the direction of their
motion made with that plane,--that is, the _inclination of their
orbits_; he also calculated the nearest distance at which each of them
approached the sun, or their _perihelion distance_; and the exact place
of the body when at that nearest point,--that is, the _longitude of the
perihelion_. These particulars are called the _elements_ of a comet,
because, when ascertained, they afford sufficient data for determining a
comet's path. On comparing these paths, Halley found that one, which had
appeared in 1661, followed nearly the same path as one which had
appeared in 1532. Supposing, then, these to be two successive
appearances of the same comet, it would follow, that its period would be
one hundred and twenty-nine years, reckoning from 1661. Had this
conjecture been well founded, the comet must have appeared about the
year 1790. No comet, however, appeared at or near that time, following a
similar path.

In his second conjecture, Halley was more fortunate, as indeed might be
expected, since it was formed upon more conclusive grounds. He found
that the paths of comets which had appeared in 1531 and 1607 were nearly
identical, and that they were in fact the same as the path followed by
the comet observed by himself in 1682. He suspected, therefore, that the
appearances at these three epochs were produced by three successive
returns of the same comet, and that, consequently, its period in its
orbit must be about seventy-five and a half years. The probability of
this conclusion is strikingly exhibited to the eye, by presenting the
elements in a tabular form, from which it will at once be seen how
nearly they correspond at these regular intervals.

=====================================================================
Time.|Inclination of|Long. of the |Long. Per.|Per. Dist. |Course.
|the orbit. |node. | | |
=====================================================================
1456 | 17°56´ | 48°30´ |301°00´ | 0°58´ |Retrograde.
1531 | 17 56 | 49 25 |301 39 | 0 57 | "
1607 | 17 02 | 50 21 |302 16 | 0 58 | "
1682 | 17 42 | 50 48 |301 36 | 0 58 | "
=====================================================================

So little was the scientific world, at this time, prepared for such an
announcement, that Halley himself only ventured at first to express his
opinion in the form of conjecture; but, after some further investigation
of the circumstances of the recorded comets, he found three which, at
least in point of time, agreed with the period assigned to the comet of
1682. Collecting confidence from these circumstances, he announced his
discovery as the result of observation and calculation combined, and
entitled to as much confidence as any other consequence of an
established physical law.

There were, nevertheless, two circumstances which might be supposed to
offer some difficulty. First, the intervals between the supposed
successive returns were not precisely equal; and, secondly, the
inclination of the comet's path to the plane of the earth's orbit was
not exactly the same in each case. Halley, however, with a degree of
sagacity which, considering the state of knowledge at the time, cannot
fail to excite unqualified admiration, observed, that it was natural to
suppose that the same causes which disturbed the planetary motions must
likewise act upon comets; and that their influence would be so much the
more sensible upon these bodies, because of their great distances from
the sun. Thus, as the attraction of Jupiter for Saturn was known to
affect the velocity of the latter planet, sometimes retarding and
sometimes accelerating it, according to their relative position, so as
to affect its period to the extent of thirteen days, it might well be
supposed, that the comet might suffer by a similar attraction an effect
sufficiently great, to account for the inequality observed in the
interval between its successive returns: and also for the variation to
which the direction of its path upon the plane of the ecliptic was found
to be subject. He observed, in fine, that, as in the interval between
1607 and 1682, the comet passed so near Jupiter that its velocity must
have been augmented, and consequently its period shortened, by the
action of that planet, this period, therefore, having been only
seventy-five years, he inferred that the following period would probably
be seventy-six years, or upwards; and consequently, that the comet ought
not to be expected to appear until the end of 1758, or the beginning of
1759. It is impossible to imagine any quality of mind more enviable than
that which, in the existing state of mathematical physics, could have
led to such a prediction. The imperfect state of mathematical science
rendered it impossible for Halley to offer to the world a demonstration
of the event which he foretold. The theory of gravitation, which was in
its infancy in the time of Halley's investigations, had grown to
comparative maturity before the period at which his prediction could be
fulfilled. The exigencies of that theory gave birth to new and more
powerful instruments of mathematical inquiry: the differential and
integral calculus, or the science of fluxions, as it is sometimes
called,--a branch of the mathematics, expressed by algebraic symbols,
but capable of a much higher reach, as an instrument of investigation,
than either algebra or geometry,--was its first and greatest offspring.
This branch of science was cultivated with an ardor and success by
which it was enabled to answer all the demands of physics, and it
contributed largely to the advancement of mechanical science itself,
building upon the laws of motion a structure which has since been
denominated 'Celestial Mechanics.' Newton's discoveries having obtained
reception throughout the scientific world, his inquiries and his
theories were followed up; and the consequences of the great principle
of universal gravitation were rapidly developed. Since, according to
this doctrine, _every body in nature attracts and is attracted by every
other body_, it follows, that the comet was liable to be acted on by
each of the planets, as well as by the sun,--a circumstance which
rendered its movements much more difficult to follow, than would be the
case were it subject merely to the projectile force and to the solar
attraction. To estimate the time it would take for a ship to cross the
Atlantic would be an easy task, were she subject to only one constant
wind; but to estimate, beforehand, the exact influence which all other
winds and the tides might have upon her passage, some accelerating and
some retarding her course, would present a problem of the greatest
difficulty. Clairaut, however, a celebrated French mathematician,
undertook to estimate the effects that would be produced on Halley's
comet by the attractions of all the planets. His aim was to investigate
_general rules_, by which the computation could be made arithmetically,
and hand them over to the practical calculator, to make the actual
computations. Lalande, a practical astronomer, no less eminent in his
own department, and who indeed first urged Clairaut to this inquiry,
undertook the management of the astronomical and arithmetical part of
the calculation. In this prodigious labor (for it was one of most
appalling magnitude) he was assisted by the wife of an eminent
watchmaker in Paris, named Lepaute, whose exertions on this occasion
have deservedly registered her name in astronomical history.

It is difficult to convey to one who is not conversant with such
investigations, an adequate notion of the labor which such an inquiry
involved. The calculation of the influence of any one _planet_ of the
system upon any other is itself a problem of some complexity and
difficulty; but still, one general computation, depending upon the
calculation of the terms of a certain series, is sufficient for its
solution. This comparative simplicity arises entirely from two
circumstances which characterize the planetary orbits. These are, that,
though they are ellipses, they differ very slightly from circles; and
though the planets do not move in the plane of the ecliptic, yet none of
them deviate considerably from that plane. But these characters do not
belong to the orbits of comets, which, on the contrary, are highly
eccentric, and make all possible angles with the ecliptic. The
consequence of this is, that the calculation of the disturbances
produced in the cometary orbits by the action of the planets must be
conducted not like the planets, in one general calculation applicable to
the whole orbits, but in a vast number of separate calculations; in
which the orbit is considered, as it were, bit by bit, each bit
requiring a calculation similar to the whole orbit of the planet. Now,
when it is considered that the period of Halley's comet is about
seventy-five years, and that every portion of its course, for two
successive periods, was necessary to be calculated separately in this
way, some notion may be formed of the labor encountered by Lalande and
Madame Lepaute. "During six months," says Lalande, "we calculated from
morning till night, sometimes even at meals; the consequence of which
was, that I contracted an illness which changed my constitution for the
remainder of my life. The assistance rendered by Madame Lepaute was
such, that, without her, we never could have dared to undertake this
enormous labor, in which it was necessary to calculate the distance of
each of the two planets, Jupiter and Saturn, from the comet, and their
attraction upon that body, separately, for every successive degree, and
for one hundred and fifty years."

The attraction of a body is proportioned to its quantity of matter.
Therefore, before the attraction exerted upon the comet by the several
planets within whose influence it might fall, could be correctly
estimated, it was necessary to know the mass of each planet; and though
the planets had severally been weighed by methods supplied by Newton's
'Principia,' yet the estimate had not then attained the same measure of
accuracy as it has now reached; nor was it certain that there was not
(as it has since appeared that there actually was) one or more planets
beyond Saturn, whose attractions might likewise influence the motions of
the comet. Clairaut, making the best estimate he was able, under all
these disadvantages, of the disturbing influence of the planets, fixed
the return of the comet to the place of its nearest distance from the
sun on the fourth of April, 1759.

In the successive appearances of the comet, subsequently to 1456, it was
found to have gradually decreased in magnitude and splendor. While in
1456 it reached across one third part of the firmament, and spread
terror over Europe, in 1607, its appearance, when observed by Kepler and
Longomontanus, was that of a star of the first magnitude; and so
trifling was its tail that, Kepler himself, when he first saw it,
doubted whether it had any. In 1682, it excited little attention, except
among astronomers. Supposing this decrease of magnitude and brilliancy
to be progressive, Lalande entertained serious apprehensions that on its
expected return it might be so inconsiderable, as to escape the
observation even of astronomers; and thus, that this splendid example
of the power of science, and unanswerable proof of the principle of
gravitation, would be lost to the world.

It is not uninteresting to observe the misgivings of this distinguished
astronomer with respect to the appearance of the body, mixed up with his
unshaken faith in the result of the astronomical inquiry. "We cannot
doubt," says he, "that it will return; and even if astronomers cannot
see it, they will not therefore be the less convinced of its presence.
They know that the faintness of its light, its great distance, and
perhaps even bad weather, may keep it from our view. But the world will
find it difficult to believe us; they will place this discovery, which
has done so much honor to modern philosophy, among the number of chance
predictions. We shall see discussions spring up again in colleges,
contempt among the ignorant, terror among the people; and seventy-six
years will roll away, before there will be another opportunity of
removing all doubt."

Fortunately for science, the arrival of the expected visitor did not
take place under such untoward circumstances. As the commencement of the
year 1759 approached, "astronomers," says Voltaire, "hardly went to bed
at all." The honor, however, of the first glimpse of the stranger was
not reserved for the possessors of scientific rank, nor for the members
of academies or universities. On the night of Christmas-day, 1758,
George Palitzch, of Politz, near Dresden,--"a peasant," says Sir John
Herchel, "by station, an astronomer by nature," first saw the comet.

An astronomer of Leipzic found it soon after; but, with the mean
jealousy of a miser, he concealed his treasure, while his contemporaries
throughout Europe were vainly directing their anxious search after it to
other quarters of the heavens. At this time, Delisle, a French
astronomer, and his assistant, Messier, who, from his unweared assiduity
in the pursuit of comets, was called the _Comet-Hunter_, had been
constantly engaged, for eighteen months, in watching for the return of
Halley's comet. Messier passed his life in search of comets. It is
related of him, that when he was in expectation of discovering a comet,
his wife was taken ill and died. While attending on her, being withdrawn
from his observatory, another astronomer anticipated him in the
discovery. Messier was in despair. A friend, visiting him, began to
offer some consolation for the recent affliction he had suffered.
Messier, thinking only of the comet, exclaimed, "I had discovered
twelve: alas, that I should be robbed of the thirteenth by
Montague!"--and his eyes filled with tears. Then, remembering that it
was necessary to mourn for his wife, whose remains were still in the
house, he exclaimed, "Ah! this poor woman!" (_ah! cette pauvre femme_,)
and again wept for his comet. We can easily imagine how eagerly such an
enthusiast would watch for Halley's comet; and we could almost wish that
it had been his good fortune to be the first to announce its arrival:
but, being misled by a chart which directed his attention to the wrong
part of the firmament, a whole month elapsed after its discovery by
Palitzch, before he enjoyed the delightful spectacle.

The comet arrived at its perihelion on the thirteenth of March, only
twenty-three days from the time assigned by Clairaut. It appeared very
round, with a brilliant nucleus, well distinguished from the surrounding
nebulosity. It had, however, no appearance of a tail. It became lost in
the sun, as it approached its perihelion, and emerged again, on the
other side of the sun, on the first of April. Its exhibiting an
appearance, so inferior to what it presented on some of its previous
returns, is partly accounted for by its being seen by the European
astronomers under peculiarly disadvantageous circumstances, being almost
always within the twilight, and in the most unfavorable situations. In
the southern hemisphere, however, the circumstances for observing it
were more favorable, and there it exhibited a tail varying from ten to
forty-seven degrees in length.

In my next Letter I will give you some particulars respecting the late
return of Halley's comet.

LETTER XXVI.

COMETS, CONTINUED.

"Incensed with indignation, Satan stood
Unterrified, and like a comet burned,
That fires the length of Ophiucus huge
In the Arctic sky, and from his horrid train
Shakes pestilence and war."--_Milton._

AMONG other great results which have marked the history of Halley's
comet, it has itself been a criterion of the existing state of the
mathematical and astronomical sciences. We have just seen how far the
knowledge of the great laws of physical astronomy, and of the higher
mathematics, enabled the astronomers of 1682 and 1759, respectively, to
deal with this wonderful body; and let us now see what higher advantages
were possessed by the astronomers of 1835. During this last interval of
seventy-six years, the science of mathematics, in its most profound and
refined branches, has made prodigious advances, more especially in its
application to the laws of the celestial motions, as exemplified in the
'Mecanique Celeste' of La Place. The methods of investigation have
acquired greater simplicity, and have likewise become more general and
comprehensive; and mechanical science, in the largest sense of that
term, now embraces in its formularies the most complicated motions, and
the most minute effects of the mutual influences of the various members
of our system. You will probably find it difficult to comprehend, how
such hidden facts can be disclosed by formularies, consisting of _a_'s
and _b_'s, and _x_'s and _y_'s, and other algebraic symbols; nor will it
be easy to give you a clear idea of this subject, without a more
extensive acquaintance than you have formed with algebraic
investigations; but you can easily understand that even an equation
expressed in numbers may be so changed in its form, by adding,
subtracting, multiplying and dividing, as to express some new truth at
every transformation. Some idea of this may be formed by the simplest
example. Take the following: 3+4=7. This equation expresses the fact,
that three added to four is equal to seven. By multiplying all the terms
by 2, we obtain a new equation, in which 6+8=14. This expresses a new
truth; and by varying the form, by similar operations, an indefinite
number of separate truths may be elicited from the simple fundamental
expression. I will add another illustration, which involves a little
more algebra, but not, I think, more than you can understand; or, if it
does, you will please pass over it to the next paragraph. According to a
rule of arithmetical progression, _the sum of all the terms is equal to
half the sum of the extremes multiplied into the number of terms_.
Calling the sum of the terms _s_, the first term _a_, the last _h_, and
the number of terms _n_, and we have _(1/2)n(a+h)=s_; or _n(a+h)=2s_; or
_a+h=2s/n_; or _a=(2s/n)-h_; or _h=(2s/n)-a_. These are only a few of
the changes which may be made in the original expression, still
preserving the equality between the quantities on the left hand and
those on the right; yet each of these transformations expresses a new
truth, indicating distinct and (as might be the case) before unknown
relations between the several quantities of which the whole expression
is composed. The last, for example, shows us that the last term in an
arithmetical series is always equal to twice the sum of the whole series
divided by the number of terms and diminished by the first term. In
analytical formularies, as expressions of this kind are called, the
value of a single unknown quantity is sometimes given in a very
complicated expression, consisting of known quantities; but before we
can ascertain their united value, we must reduce them, by actually
performing all the additions, subtractions, multiplications, divisions,
raising to powers, and extracting roots, which are denoted by the
symbols. This makes the actual calculations derived from such
formularies immensely laborious. We have already had an instance of this
in the calculations made by Lalande and Madame Lepaute, from formularies
furnished by Clairaut.

The analytical formularies, contained in such works as La Place's
'Mecanique Celeste,' exhibit to the eye of the mathematician a record of
all the evolutions of the bodies of the solar system in ages past, and
of all the changes they must undergo in ages to come. Such has been the
result of the combination of transcendent mathematical genius and
unexampled labor and perseverance, for the last century. The learned
societies established in various centres of civilization have more
especially directed their attention to the advancement of physical
astronomy, and have stimulated the spirit of inquiry by a succession of
prizes, offered for the solutions of problems arising out of the
difficulties which were progressively developed by the advancement of
astronomical knowledge. Among these questions, the determination of the
return of comets, and the disturbances which they experience in their
course, by the action of the planets near which they happen to pass,
hold a prominent place. In 1826, the French Institute offered a prize
for the determination of the exact time of the return of Halley's comet
to its perihelion in 1835. M. Pontecoulant aspired to the honor. "After
calculations," says he, "of which those alone who have engaged in such
researches can estimate the extent and appreciate the fastidious
monotony, I arrived at a result which satisfied all the conditions
proposed by the Institute. I determined the perturbations of Halley's
comet, by taking into account the simultaneous actions of Jupiter,
Saturn, Uranus, and the Earth, and I then fixed its return to its
perihelion for the seventh of November." Subsequently to this, however,
M. Pontecoulant made some further researches, which led him to correct
the former result; and he afterwards altered the time to November
fourteenth. It actually came to its perihelion on the sixteenth, within
two days of the time assigned.

Nothing can convince us more fully of the complete mastery which
astronomers have at last acquired over these erratic bodies, than to
read in the Edinburgh Review for April, 1835, the paragraph containing
the final results of all the labors and anticipations of astronomers,
matured as they were, in readiness for the approaching visitant, and
then to compare the prediction with the event, as we saw it fulfilled a
few months afterwards. The paragraph was as follows: "On the whole, it
may be considered as tolerably certain, that the comet will become
visible in every part of Europe about the latter end of August, or
beginning of September, next. It will most probably be distinguishable
by the naked eye, like a star of the first magnitude, but with a duller
light than that of a planet, and surrounded with a pale nebulosity,
which will slightly impair its splendor. On the night of the seventh of
October, the comet will approach the well-known constellation of the
Great Bear; and between that and the eleventh, it will pass directly
through the seven conspicuous stars of that constellation, (the Dipper.)
Towards the end of November, the comet will plunge among the rays of the
sun, and disappear, and will not issue from them, on the other side,
until the end of December."

Let us now see how far the actual appearances corresponded to these
predictions. The comet was first discovered from the observatory at
Rome, on the morning of the fifth of August; by Professor Struve, at
Dorpat, on the twentieth; in England and France, on the twenty-third;
and at Yale College, by Professor Loomis and myself, on the
thirty-first. On the morning of that day, between two and three o'clock,
in obedience to the directions which the great minds that had marked out
its path among the stars had prescribed, we directed Clarke's telescope
(a noble instrument, belonging to Yale College) towards the
northeastern quarter of the heavens, and lo! there was the wanderer so
long foretold,--a dim speck of fog on the confines of creation. It came
on slowly, from night to night, increasing constantly in magnitude and
brightness, but did not become distinctly visible to the naked eye until
the twenty-second of September. For a month, therefore, astronomers
enjoyed this interesting spectacle before it exhibited itself to the
world at large. From this time it moved rapidly along the northern sky,
until, about the tenth of October, it traversed the constellation of the
Great Bear, passing a little above, instead of "through" the seven
conspicuous stars constituting the Dipper. At this time it had a
lengthened train, and became, as you doubtless remember, an object of
universal interest. Early in November, the comet ran down to the sun,
and was lost in his beams; but on the morning of December thirty-first,
I again obtained, through Clarke's telescope, a distinct view of it on
the other side of the sun, a moment before the morning dawn.

This return of Halley's comet was an astronomical event of transcendent
importance. It was the chronicler of ages, and carried us, by a few
steps, up to the origin of time. If a gallant ship, which has sailed
round the globe, and commanded successively the admiration of many great
cities, diverse in language and customs, is invested with a peculiar
interest, what interest must attach to one that has made the circuit of
the solar system, and fixed the gaze of successive worlds! So intimate,
moreover, is the bond which binds together all truths in one
indissoluble chain, that the establishment of one great truth often
confirms a multitude of others, equally important. Thus the return of
Halley's comet, in exact conformity with the predictions of astronomers,
established the truth of all those principles by which those predictions
were made. It afforded most triumphant proof of the doctrine of
universal gravitation, and of course of the received laws of physical
astronomy; it inspired new confidence in the power and accuracy of that
instrument (the calculus) by means of which its elements had been
investigated; and it proved that the different planets, which exerted
upon it severally a disturbing force proportioned to their quantity of
matter, had been correctly weighed, as in a balance.

I must now leave this wonderful body to pursue its sublime march far
beyond the confines of Uranus, (a distance it has long since reached,)
and take a hasty notice of two other comets, whose periodic returns have
also been ascertained; namely, those of Biela and Encke.

Biela's comet has a period of six years and three quarters. It has its
perihelion near the orbit of the earth, and its aphelion a little beyond
that of Jupiter. Its orbit, therefore, is far less eccentric than that
of Halley's comet; (see Frontispiece;) it neither approaches so near the
sun, nor departs so far from it, as most other known comets: some,
indeed, never come nearer to the sun than the orbit of Jupiter, while
they recede to an incomprehensible distance beyond the remotest planet.
We might even imagine that they would get beyond the limits of the sun's
attraction; nor is this impossible, although, according to La Place, the
solar attraction is sensible throughout a sphere whose radius is a
hundred millions of times greater than the distance of the earth from
the sun, or nearly ten thousand billions of miles.

Some months before the expected return of Biela's comet, in 1832, it was
announced by astronomers, who had calculated its path, that it would
cross the plane of the earth's orbit very near to the earth's path, so
that, should the earth happen at the time to be at that point of her
revolution, a collision might take place. This announcement excited so
much alarm among the ignorant classes in France, that it was deemed
expedient by the French academy, that one of their number should prepare
and publish an article on the subject, with the express view of
allaying popular apprehension. This task was executed by M. Arago. He
admitted that the earth would in fact pass so near the point where the
comet crossed the plane of its orbit, that, should they chance to meet
there, the earth would be enveloped in the nebulous atmosphere of the
comet. He, however, showed that the earth would not be near that point
at the same time with the comet, but fifty millions of miles from it.

The comet came at the appointed time, but was so exceedingly faint and
small, that it was visible only to the largest telescopes. In one
respect, its diminutive size and feeble light enhanced the interest with
which it was contemplated; for it was a sublime spectacle to see a body,
which, as projected on the celestial vault, even when magnified a
thousand times, seemed but a dim speck of fog, still pursuing its way,
in obedience to the laws of universal gravitation, with the same
regularity as Jupiter and Saturn. We are apt to imagine that a body,
consisting of such light materials that it can be compared only to the
thinnest fog, would be dissipated and lost in the boundless regions of
space; but so far is this from the truth, that, when subjected to the
action of the same forces of projection and solar attraction, it will
move through the void regions of space, and will describe its own orbit
about the sun with the same unerring certainty, as the densest bodies of
the system.

Encke's comet, by its frequent returns, (once in three and a third
years,) affords peculiar facilities for ascertaining the laws of its
revolution; and it has kept the appointments made for it with great
exactness. On its return in 1839, it exhibited to the telescope a
globular mass of nebulous matter, resembling fog, and moved towards its
perihelion with great rapidity. It makes its entire excursions within
the orbit of Jupiter.

But what has made Encke's comet particularly famous, is its having first
revealed to us the existence of a _resisting medium_ in the planetary
spaces. It has long been a question, whether the earth and planets
revolve in a perfect void, or whether a fluid of extreme rarity may not
be diffused through space. A perfect vacuum was deemed most probable,
because no such effects on the motions of the planets could be detected
as indicated that they encountered a resisting medium. But a feather, or
a lock of cotton, propelled with great velocity, might render obvious
the resistance of a medium which would not be perceptible in the motions
of a cannon ball. Accordingly, Encke's comet is thought to have plainly
suffered a retardation from encountering a resisting medium in the
planetary regions. The effect of this resistance, from the first
discovery of the comet to the present time, has been to diminish the
time of its revolution about two days. Such a resistance, by destroying
a part of the projectile force, would cause the comet to approach nearer
to the sun, and thus to have its periodic time shortened. The ultimate
effect of this cause will be to bring the comet nearer to the sun, at
every revolution, until it finally falls into that luminary, although
many thousand years will be required to produce this catastrophe. It is
conceivable, indeed, that the effects of such a resistance may be
counteracted by the attraction of one or more of the planets, near which
it may pass in its successive returns to the sun. Still, it is not
probable that this cause will exactly counterbalance the other; so that,
if there is such an elastic medium diffused through the planetary
regions, it must follow that, in the lapse of ages, every comet will
fall into the sun. Newton conjectured that this would be the case,
although he did not found his opinion upon the existence of such a
resisting medium as is now detected. To such an opinion he adhered to
the end of life. At the age of eighty-three, in a conversation with his
nephew, he expressed himself thus: "I cannot say when the comet of 1680
will fall into the sun; possibly after five or six revolutions; but
whenever that time shall arrive, the heat of the sun will be raised by
it to such a point, that our globe will be burned, and all the animals
upon it will perish."

Of the _physical nature_ of comets little is understood. The greater
part of them are evidently mere masses of vapor, since they permit very
small stars to be seen through them. In September, 1832, Sir John
Herschel, when observing Biela's comet, saw that body pass directly
between his eye and a small cluster of minute telescopic stars of the
sixteenth or seventeenth magnitude. This little constellation occupied a
space in the heavens, the breadth of which was not the twentieth part of
that of the moon; yet the whole of the cluster was distinctly visible
through the comet. "A more striking proof," says Sir John Herschel,
"could not have been afforded, of the extreme transparency of the matter
of which this comet consists. The most trifling fog would have entirely
effaced this group of stars, yet they continued visible through a
thickness of the comet which, calculating on its distance and apparent
diameter, must have exceeded fifty thousand miles, at least towards its
central parts." From this and similar observations, it is inferred, that
the nebulous matter of comets is vastly more rare than that of the air
we breathe, and hence, that, were more or less of it to be mingled with
the earth's atmosphere, it would not be perceived, although it might
possibly render the air unwholesome for respiration. M. Arago, however,
is of the opinion, that some comets, at least, have a solid nucleus. It
is difficult, on any other supposition, to account for the strong light
which some of them have exhibited,--a light sufficiently intense to
render them visible in the day-time, during the presence of the sun. The
intense heat to which comets are subject, in approaching so near the sun
as some of them do, is alleged as a sufficient reason for the great
expansion of the thin vapory atmospheres which form their tails; and the
inconceivable cold to which they are subject, in receding to such a
distance from the sun, is supposed to account for the condensation of
the same matter until it returns to its original dimensions. Thus the
great comet of 1680, at its perihelion, approached within one hundred
and forty-six thousand miles of the surface of the sun, a distance of
only one sixth part of the sun's diameter. The heat which it must have
received was estimated to be equal to twenty-eight thousand times that
which the earth receives in the same time, and two thousand times hotter
than red-hot iron. This temperature would be sufficient to volatilize
the most obdurate substances, and to expand the vapor to vast
dimensions; and the opposite effects of the extreme cold to which it
would be subject in the regions remote from the sun would be adequate to
condense it into its former volume. This explanation, however, does not
account for the direction of the tail, extending, as it usually does,
only in a line opposite to the sun. Some writers, therefore, suppose
that the nebulous matter of the comet, after being expanded to such a
volume that the particles are no longer attracted to the nucleus, unless
by the slightest conceivable force, are carried off in a direction from
the sun, by the impulse of the solar rays themselves. But to assign such
a power to the sun's rays, while they have never been proved to have any
momentum, is unphilosophical; and we are compelled to place the
phenomena of comets' tails among the points of astronomy yet to be
explained.

Since comets which approach very near the sun, like the comet of 1680,
cross the orbits of all the planets, the possibility that one of them
may strike the earth has frequently been suggested. Still it may quiet
our apprehensions on this subject, to reflect on the vast amplitude of
the planetary spaces, in which these bodies are not crowded together, as
we see them erroneously represented in orreries and diagrams, but are
sparsely scattered at immense distances from each other. They are like
insects flying, singly, in the expanse of heaven. If a comet's tail lay
with its axis in the plane of the ecliptic when it was near the sun, we
can imagine that the tail might sweep over the earth; but the tail may
be situated at any angle with the ecliptic, as well as in the same plane
with it, and the chances that it will not be in the same plane are
almost infinite. It is also extremely improbable that a comet will cross
the plane of the ecliptic precisely at the earth's path in that plane,
since it may as probably cross it at any other point nearer or more
remote from the sun. A French writer of some eminence (Du Sejour) has
discussed this subject with ability, and arrived at the following
conclusions: That of all the comets whose paths had been ascertained,
none _could pass_ nearer to the earth than about twice the moon's
distance; and that none ever _did pass_ nearer to the earth than nine
times the moon's distance. The comet of 1770, already mentioned, which
became entangled among the satellites of Jupiter, came within this
limit. Some have taken alarm at the idea that a comet, by approaching
very near to the earth, might raise so high a _tide_, as to endanger the
safety of maritime countries especially: but this writer shows, that the
comet could not possibly remain more than two hours so near the earth as
a fourth part of the moon's distance; and it could not remain even so
long, unless it passed the earth under very peculiar circumstances. For
example, if its orbit were nearly perpendicular to that of the earth, it
could not remain more than half an hour in such a position. Under such
circumstances, the production of a tide would be impossible. Eleven
hours, at least, would be necessary to enable a comet to produce an
effect on the waters of the earth, from which the injurious effects so
much dreaded would follow. The final conclusion at which he arrives is,
that although, in strict geometrical rigor, it is not physically
impossible that a comet should encounter the earth, yet the probability
of such an event is absolutely nothing.

M. Arago, also, has investigated the probability of such a collision on
the mathematical doctrine of chances, and remarks as follows: "Suppose,
now, a comet, of which we know nothing but that, at its perihelion, it
will be nearer the sun than we are, and that its diameter is equal to
one fourth that of the earth; the doctrine of chances shows that, out of
two hundred and eighty-one millions of cases, there is but one against
us; but one, in which the two bodies could meet."

La Place has assigned the consequences that would result from a direct
collision between the earth and a comet. "It is easy," says he, "to
represent the effects of the shock produced by the earth's encountering
a comet. The axis and the motion of rotation changed; the waters
abandoning their former position to precipitate themselves towards the
new equator; a great part of men and animals whelmed in a universal
deluge, or destroyed by the violent shock imparted to the terrestrial
globe; entire species annihilated; all the monuments of human industry
overthrown;--such are the disasters which the shock of a comet would
necessarily produce." La Place, nevertheless, expresses a decided
opinion that the orbits of the planets have never yet been disturbed by
the influence of comets. Comets, moreover, have been, and are still to
some degree, supposed to exercise much influence in the affairs of this
world, affecting the weather, the crops, the public health, and a great
variety of atmospheric commotions. Even Halley, finding that his comet
must have been near the earth at the time of the Deluge, suggested the
possibility that the comet caused that event,--an idea which was taken
up by Whiston, and formed into a regular theory. In Gregory's Astronomy,
an able work, published at Oxford in 1702, the author remarks, that
among all nations and in all ages, it has been observed, that the
appearance of a comet has always been followed by great calamities; and
he adds, "it does not become philosophers lightly to set down these
things as fables." Among the various things ascribed to comets by a late
English writer, are hot and cold seasons, tempests, hurricanes, violent
hail-storms, great falls of snow, heavy rains, inundations, droughts,
famines, thick fogs, flies, grasshoppers, plague, dysentery, contagious
diseases among animals, sickness among cats, volcanic eruptions, and
meteors, or shooting stars. These notions are too ridiculous to require
a distinct refutation; and I will only add, that we have no evidence
that comets have hitherto ever exercised the least influence upon the
affairs of this world; and we still remain in darkness, with respect to
their physical nature, and the purposes for which they were created.

LETTER XXVII.

METEORIC SHOWERS.

"Oft shalt thou see, ere brooding storms arise,
Star after star glide headlong down the skies,
And, where they shot, long trails of lingering light
Sweep far behind, and gild the shades of night."--_Virgil._

FEW subjects of astronomy have excited a more general interest, for
several years past, than those extraordinary exhibitions of shooting
stars, which have acquired the name of meteoric showers. My reason for
introducing the subject to your notice, in this place, is, that these
small bodies are, as I believe, derived from nebulous or cometary
bodies, which belong to the solar system, and which, therefore, ought to
be considered, before we take our leave of this department of creation,
and naturally come next in order to comets.

The attention of astronomers was particularly directed to this subject
by the extraordinary shower of meteors which occurred on the morning of
the thirteenth of November, 1833. I had the good fortune to witness
these grand celestial fire-works, and felt a strong desire that a
phenomenon, which, as it afterwards appeared, was confined chiefly to
North America, should here command that diligent inquiry into its
causes, which so sublime a spectacle might justly claim.

As I think you were not so happy as to witness this magnificent display,
I will endeavor to give you some faint idea of it, as it appeared to me
a little before daybreak. Imagine a constant succession of fire-balls,
resembling sky-rockets, radiating in all directions from a point in the
heavens a few degrees southeast of the zenith, and following the arch of
the sky towards the horizon. They commenced their progress at different
distances from the radiating point; but their directions were uniformly
such, that the lines they described, if produced upwards, would all have
met in the same part of the heavens. Around this point, or imaginary
radiant, was a circular space of several degrees, within which no
meteors were observed. The balls, as they travelled down the vault,
usually left after them a vivid streak of light; and, just before they
disappeared, exploded, or suddenly resolved themselves into smoke. No
report of any kind was observed, although we listened attentively.

Beside the foregoing distinct concretions, or individual bodies, the
atmosphere exhibited _phosphoric lines_, following in the train of
minute points, that shot off in the greatest abundance in a
northwesterly direction. These did not so fully copy the figure of the
sky, but moved in paths more nearly rectilinear, and appeared to be much
nearer the spectator than the fire-balls. The light of their trains was
also of a paler hue, not unlike that produced by writing with a stick of
phosphorus on the walls of a dark room. The number of these luminous
trains increased and diminished alternately, now and then crossing the
field of view, like snow drifted before the wind, although, in fact,
their course was towards the wind.

From these two varieties, we were presented with meteors of various
sizes and degrees of splendor: some were mere points, while others were
larger and brighter than Jupiter or Venus; and one, seen by a credible
witness, at an earlier hour, was judged to be nearly as large as the
moon. The flashes of light, although less intense than lightning, were
so bright, as to awaken people in their beds. One ball that shot off in
the northwest direction, and exploded a little northward of the star
Capella, left, just behind the place of explosion, a phosphorescent
train of peculiar beauty. This train was at first nearly straight, but
it shortly began to contract in length, to dilate in breadth, and to
assume the figure of a serpent drawing itself up, until it appeared like
a small luminous cloud of vapor. This cloud was borne eastward, (by the
wind, as was supposed, which was blowing gently in that direction,)
opposite to the direction in which the meteor itself had moved,
remaining in sight several minutes. The point from which the meteors
seemed to radiate kept a fixed position among the stars, being
constantly near a star in Leo, called Gamma Leonis.

Such is a brief description of this grand and beautiful display, as I
saw it at New Haven. The newspapers shortly brought us intelligence of
similar appearances in all parts of the United States, and many minute
descriptions were published by various observers; from which it
appeared, that the exhibition had been marked by very nearly the same
characteristics wherever it had been seen. Probably no celestial
phenomenon has ever occurred in this country, since its first
settlement, which was viewed with so much admiration and delight by one
class of spectators, or with so much astonishment and fear by another
class. It strikingly evinced the progress of knowledge and civilization,
that the latter class was comparatively so small, although it afforded
some few examples of the dismay with which, in barbarous ages of the
world, such spectacles as this were wont to be regarded. One or two
instances were reported, of persons who died with terror; many others
thought the last great day had come; and the untutored black population
of the South gave expression to their fears in cries and shrieks.

After collecting and collating the accounts given in all the periodicals
of the country, and also in numerous letters addressed either to my
scientific friends or to myself, the following appeared to be the
_leading facts_ attending the phenomenon. The shower pervaded nearly
the whole of North America, having appeared in nearly equal splendor
from the British possessions on the north to the West-India Islands and
Mexico on the south, and from sixty-one degrees of longitude east of the
American coast, quite to the Pacific Ocean on the west. Throughout this
immense region, the duration was nearly the same. The meteors began to
attract attention by their unusual frequency and brilliancy, from _nine
to twelve_ o'clock in the evening; were most striking in their
appearance from _two to five;_ arrived at their maximum, in many places,
about _four_ o'clock; and continued until rendered invisible by the
light of day. The meteors moved either in right lines, or in such
apparent curves, as, upon optical principles, can be resolved into right
lines. Their general tendency was towards the northwest, although, by
the effect of perspective, they appeared to move in various directions.

Such were the leading phenomena of the great meteoric shower of November
13, 1833. For a fuller detail of the facts, as well as of the reasonings
that were built on them, I must beg leave to refer you to some papers of
mine in the twenty-fifth and twenty-sixth volumes of the American
Journal of Science.

Soon after this wonderful occurrence, it was ascertained that a similar
meteoric shower had appeared in 1799, and, what was remarkable, almost
at exactly the same time of year, namely, on the morning of the twelfth
of November; and we were again surprised as well as delighted, at
receiving successive accounts from different parts of the world of the
phenomenon, as having occurred on the morning of the same thirteenth of
November, in 1830, 1831, and 1832. Hence this was evidently an event
independent of the casual changes of the atmosphere; for, having a
periodical return, it was undoubtedly to be referred to astronomical
causes, and its recurrence, at a certain definite period of the year,
plainly indicated _some_ relation to the revolution of the earth around
the sun. It remained, however, to develope the nature of this relation,
by investigating, if possible, the origin of the meteors. The views to
which I was led on this subject suggested the probability that the same
phenomenon would recur on the corresponding seasons of the year, for at
least several years afterwards; and such proved to be the fact, although
the appearances, at every succeeding return, were less and less
striking, until 1839, when, so far as I have heard, they ceased
altogether.

Mean-while, two other distinct periods of meteoric showers have, as
already intimated, been determined; namely, about the ninth of August,
and seventh of December. The facts relative to the history of these
periods have been collected with great industry by Mr. Edward C.
Herrick; and several of the most ingenious and most useful conclusions,
respecting the laws that regulate these singular exhibitions, have been
deduced by Professor Twining. Several of the most distinguished
astronomers of the Old World, also, have engaged in these investigations
with great zeal, as Messrs. Arago and Biot, of Paris; Doctor Olbers, of
Bremen; M. Wartmann, of Geneva; and M. Quetelet, of Brussels.

But you will be desirous to learn what are the _conclusions_ which have
been drawn respecting these new and extraordinary phenomena of the
heavens. As the inferences to which I was led, as explained in the
twenty-sixth volume of the 'American Journal of Science,' have, at least
in their most important points, been sanctioned by astronomers of the
highest respectability, I will venture to give you a brief abstract of
them, with such modifications as the progress of investigation since
that period has rendered necessary.

The principal questions involved in the inquiry were the following:--Was
the _origin_ of the meteors within the atmosphere, or beyond it? What
was the _height_ of the place above the surface of the earth? By what
_force_ were the meteors drawn or impelled towards the earth? In what
_directions_ did they move? With what _velocity_? What was the cause of
their _light_ and _heat_? Of what _size_ were the larger varieties? At
what height above the earth did they _disappear_? What was the nature of
the _luminous trains_ which sometimes remained behind? What _sort of
bodies_ were the meteors themselves; of what _kind of matter_
constituted; and in what manner did they exist _before they fell to the
earth_? Finally, what _relations_ did the source from which they
emanated sustain to our earth?

In the first place, _the meteors had their origin beyond the limits of
our atmosphere_. We know whether a given appearance in the sky is within
the atmosphere or beyond it, by this circumstance: all bodies near the
earth, including the atmosphere itself, have a common motion with the
earth around its axis from west to east. When we see a celestial object
moving regularly from west to east, at the same rate as the earth moves,
leaving the stars behind, we know it is near the earth, and partakes, in
common with the atmosphere, of its diurnal rotation: but when the earth
leaves the object behind; or, in other words, when the object moves
westward along with the stars, then we know that it is so distant as not
to participate in the diurnal revolution of the earth, and of course to
be beyond the atmosphere. The source from which the meteors emanated
thus kept pace with the stars, and hence was beyond the atmosphere.

In the second place, _the height of the place whence the meteors
proceeded was very great, but it has not yet been accurately
determined_. Regarding the body whence the meteors emanated after the
similitude of a cloud, it seemed possible to obtain its height in the
same manner as we measure the height of a cloud, or indeed the height of
the moon. Although we could not see the body itself, yet the part of the
heavens whence the meteors came would indicate its position. This point
we called the _radiant_; and the question was, whether the radiant was
projected by distant observers on different parts of the sky; that is,
whether it had any _parallax_. I took much pains to ascertain the truth
of this matter, by corresponding with various observers in different
parts of the United States, who had accurately noted the position of the
radiant among the fixed stars, and supposed I had obtained such
materials as would enable us to determine the parallax, at least
approximately; although such discordances existed in the evidence as
reasonably to create some distrust of its validity. Putting together,
however, the best materials I could obtain, I made the height of the
radiant above the surface of the earth _twenty-two hundred and
thirty-eight miles_. When, however, I afterwards obtained, as I
supposed, some insight into the celestial origin of the meteors, I at
once saw that the meteoric body must be much further off than this
distance; and my present impression is, that we have not the means of
determining what its height really is. We may safely place it at many
thousand miles.

In the third place, with respect to the _force_ by which the meteors
were _drawn_ or impelled towards the earth, my first impression was,
that they fell merely by the force of _gravity_; but the velocity which,
on careful investigation by Professor Twining and others, has been
ascribed to them, is greater than can possibly result from gravity,
since a body can never acquire, by gravity alone, a velocity greater
than about seven miles per second. Some other cause, beside gravity,
must therefore act, in order to give the meteors so great an apparent
velocity.

In the fourth place, _the meteors fell towards the earth in straight
lines, and in directions which, within considerable distances, were
nearly parallel with each other_. The courses are inferred to have been
in _straight lines_, because no others could have appeared to spectators
in different situations to have described arcs of great circles. In
order to be projected into the arc of a great circle, the line of
descent must be in a plane passing through the eye of the spectator; and
the intersection of such planes, passing through the eyes of different
spectators, must be straight lines. The lines of direction are inferred
to have been _parallel_, on account of their apparent radiation from one
point, that being the vanishing point of parallel lines. This may
appear to you a little paradoxical, to infer that lines are parallel,
because they _diverge_ from one and the same point; but it is a
well-known principle of perspective, that parallel lines, when continued
to a great distance from the eye, appear to converge towards the remoter
end. You may observe this in two long rows of trees, or of street lamps.

[Illustration Fig. 69.]

Some idea of the manner in which the meteors fell, and of the reason of
their apparent radiation from a common point, may be gathered from the
annexed diagram. Let A B C, Fig. 69, represent the vault of the sky,
the centre of which, D, being the place of the spectator. Let 1, 2, 3,
&c., represent parallel lines directed towards the earth. A luminous
body descending through 1' 1, coinciding with the line D E, coincident
with the axis of vision, (or the line drawn from the meteoric body to
the eye,) would appear stationary all the while at 1´, because distant
bodies always appear stationary when they are moving either directly
towards us or directly from us. A body descending through 2 2, would
seem to describe the short arc 2' 2', appearing to move on the concave
of the sky between the lines drawn from the eye to the two extremities
of its line of motion; and, for a similar reason, a body descending
through 3 3, would appear to describe the larger arc 3' 3'. Hence, those
meteors which fell nearer to the axis of vision, would describe shorter
arcs, and move slower, while those which were further from the axis and
nearer the horizon would appear to describe longer arcs, and to move
with greater velocity; the meteors would all seem to radiate from a
common centre, namely, the point where the axis of vision met the
celestial vault; and if any meteor chanced to move directly in the line
of vision, it would be seen as a luminous body, stationary, for a few
seconds, at the centre of radiation. To see how exactly the facts, as
observed, corresponded to these inferences, derived from the supposition
that the meteors moved in _parallel lines_, take the following
description, as given immediately after the occurrence, by Professor
Twining. "In the vicinity of the radiant point, a few star-like bodies
were observed, possessing very little motion, and leaving very little
length of trace. Further off, the motions were more rapid and the traces
longer; and most rapid of all, and longest in their traces, were those
which originated but a few degrees above the horizon, and descended down
to it."

In the fifth place, had the meteors come from a point twenty-two hundred
and thirty-eight miles from the earth, and derived their apparent
velocity from gravity alone, then it would be found, by a very easy
calculation, that their actual velocity was about four miles per second;
but, as already intimated, the velocity observed was estimated much
greater than could be accounted for on these principles; not less,
indeed, than fourteen miles per second, and, in some instances, much
greater even than this. The motion of the earth in its orbit is about
nineteen miles per second; and the most reasonable supposition we can
make, at present, to account for the great velocity of the meteors, is,
that they derived a relative motion from the earth's passing rapidly by
them,--a supposition which is countenanced by the fact that they
generally tended _westward_ contrary to the earth's motion in its orbit.

In the sixth place, _the meteors consisted of combustible matter, and
took fire, and were consumed, in traversing the atmosphere_. That these
bodies underwent combustion, we had the direct evidence of the senses,
inasmuch as we saw them burn. That they took fire in the _atmosphere_,
was inferred from the fact that they were not luminous in their original
situations in space, otherwise, we should have seen the body from which
they emanated; and had they been luminous before reaching the
atmosphere, we should have seen them for a much longer period than they
were in sight, as they must have occupied a considerable time in
descending towards the earth from so great a distance, even at the rapid
rate at which they travelled. The immediate consequence of the
prodigious velocity with which the meteors fell into the atmosphere must
be a powerful condensation of the air before them, retarding their
progress, and producing, by a sudden compression of the air, a great
evolution of heat. There is a little instrument called the _air-match_,
consisting of a piston and cylinder, like a syringe, in which we strike
a light by suddenly forcing down the piston upon the air below. As the
air cannot escape, it is suddenly compressed, and gives a spark
sufficient to light a piece of tinder at the bottom of the cylinder.
Indeed, it is a well-known fact, that, whenever air is suddenly and
forcibly compressed, heat is elicited; and, if by such a compression as
may be given by the hand in the air-match, heat is evolved sufficient to
fire tinder, what must be the heat evolved by the motion of a large body
in the atmosphere, with a velocity so immense. It is common to resort to
electricity as the agent which produces the heat and light of shooting
stars; but even were electricity competent to produce this effect, its
presence, in the case before us, is not proved; and its agency is
unnecessary, since so swift a motion of the meteors themselves, suddenly
condensing the air before them, is both a known and adequate cause of an
intense light and heat. A combustible body falling into the atmosphere,
under such circumstances, would become speedily ignited, but could not
burn freely, until it became enveloped in air of greater density; but,
on reaching the lower portions of the atmosphere, it would burn with
great rapidity.

In the seventh place, _some of the larger meteors must have been bodies
of great size_. According to the testimony of various individuals, in
different parts of the United States, a few fire-balls appeared as large
as the full moon. Dr. Smith, (then of North Carolina, but since
surgeon-general of the Texian army,) who was travelling all night on
professional business, describes one which he saw in the following
terms: "In size it appeared somewhat larger than the full moon rising. I
was startled by the splendid light in which the surrounding scene was
exhibited, rendering even small objects quite visible; but I heard no
noise, although every sense seemed to be suddenly aroused, in sympathy
with the violent impression on the sight." This description implies not
only that the body was very large, but that it was at a considerable
distance from the spectator. Its actual size will depend upon the
distance; for, as it appeared under the same angle as the moon, its
diameter will bear the same ratio to the moon's, as its distance bears
to the moon's distance. We could, therefore, easily ascertain how large
it was, provided we could find how far it was from the observer. If it
was one hundred and ten miles distant, its diameter was one mile, and in
the same proportion for a greater or less distance; and, if only at the
distance of one mile, its diameter was forty-eight feet. For a moderate
estimate, we will suppose it to have been twenty-two miles off; then its
diameter was eleven hundred and fifty-six feet. Upon every view of the
case, therefore, it must be admitted, that these were bodies of great
size, compared with other objects which traverse the atmosphere. We may
further infer the great magnitude of some of the meteors, from the
dimensions of the trains, or clouds, which resulted from their
destruction. These often extended over several degrees, and at length
were borne along in the direction of the wind, exactly in the manner of
a small cloud.

It was an interesting problem to ascertain, if possible, the height
above the earth at which these fire-balls exploded, or resolved
themselves into a cloud of smoke. This would be an easy task, provided
we could be certain that two or more distant observers could be sure
that both saw the same meteor; for as each would refer the place of
explosion, or the position of the cloud that resulted from it, to a
different point of the sky, a parallax would thus be obtained, from
which the height might be determined. The large meteor which is
mentioned in my account of the shower, (see page 348,) as having
exploded near the star Capella, was so peculiar in its appearance, and
in the form and motions of the small cloud which resulted from its
combustion, that it was noticed and distinguished by a number of
observers in distant parts of the country. All described the meteor as
exhibiting, substantially, the same peculiarities of appearance; all
agreed very nearly in the time of its occurrence; and, on drawing lines,
to represent the course and direction of the place where it exploded to
the view of each of the observers respectively, these lines met in
nearly one and the same point, and that was over the place where it was
seen in the zenith. Little doubt, therefore, could remain, that all saw
the same body; and on ascertaining, from a comparison of their
observations, the amount of parallax, and thence deducing its height,--a
task which was ably executed by Professor Twining,--the following
results were obtained: that this meteor, and probably all the meteors,
entered the atmosphere with a velocity not less, but perhaps greater,
than _fourteen miles in a second_; that they became luminous many miles
from the earth,--in this case, over _eighty miles_; and became extinct
high above the surface,--in this case, nearly _thirty miles_.

In the eighth place, _the meteors were combustible bodies, and were
constituted of light and transparent materials_. The fact that they
burned is sufficient proof that they belonged to the class of
_combustible_ bodies; and they must have been composed of very _light
materials_, otherwise their momentum would have been sufficient to
enable them to make their way through the atmosphere to the surface of
the earth. To compare great things with small, we may liken them to a
wad discharged from a piece of artillery, its velocity being supposed to
be increased (as it may be) to such a degree, that it shall take fire as
it moves through the air. Although it would force its way to a great
distance from the gun, yet, if not consumed too soon, it would at length
be stopped by the resistance of the air. Although it is supposed that
the meteors did in fact slightly disturb the atmospheric equilibrium,
yet, had they been constituted of dense matter, like meteoric stones,
they would doubtless have disturbed it vastly more. Their own momentum
would be lost only as it was imparted to the air; and had such a number
of bodies,--some of them quite large, perhaps a mile in diameter, and
entering the atmosphere with a velocity more than forty times the
greatest velocity of a cannon ball,--had they been composed of dense,
ponderous matter, we should have had appalling evidence of this fact,
not only in the violent winds which they would have produced in the
atmosphere, but in the calamities they would have occasioned on the
surface of the earth. The meteors were _transparent_ bodies; otherwise,
we cannot conceive why the body from which they emanated was not
distinctly visible, at least by reflecting the light of the sun. If only
the meteors which were known to fall towards the earth had been
collected and restored to their original connexion in space, they would
have composed a body of great extent; and we cannot imagine a body of
such dimensions, under such circumstances, which would not be visible,
unless formed of highly transparent materials. By these unavoidable
inferences respecting the kind of matter of which the meteors were
composed, we are unexpectedly led to recognise a body bearing, in its
constitution, a strong analogy to comets, which are also composed of
exceedingly light and transparent, and, as there is much reason to
believe, of combustible matter.

We now arrive at the final inquiry, _what relations did the body which
afforded the meteoric shower sustain to the earth_? Was it of the nature
of a satellite, or terrestrial comet, that revolves around the earth as
its centre of motion? Was it a collection of nebulous, or cometary
matter, which the earth encountered in its annual progress? or was it a
comet, which chanced at this time to be pursuing its path along with the
earth, around their common centre of motion? It could not have been of
the nature of a satellite to the earth, (or one of those bodies which
are held by some to afford the meteoric stones, which sometimes fall to
the earth from huge meteors that traverse the atmosphere,) because it
remained so long stationary with respect to the earth. A body so near
the earth as meteors of this class are known to be, could not remain
apparently stationary among the stars for a moment; whereas the body in
question occupied the same position, with hardly any perceptible
variation, for at least two hours. Nor can we suppose that the earth, in
its annual progress, came into the vicinity of a _nebula_, which was
either stationary, or wandering lawless through space. Such a collection
of matter could not remain stationary within the solar system, in an
insulated state, for, if not prevented by a motion of its own, or by the
attraction of some nearer body, it would have proceeded directly towards
the sun; and had it been in motion in any other direction than that in
which the earth was moving, it would soon have been separated from the
earth; since, during the eight hours, while the meteoric shower was
visible, the earth moved in its orbit through the space of nearly five
hundred and fifty thousand miles.

The foregoing considerations conduct us to the following train of
reasoning. First, if all the meteors which fell on the morning of
November 13, 1833, had been collected and restored to their original
connexion in space, they would of themselves have constituted a nebulous
body of great extent; but we have reason to suppose that they, in fact,
composed but a small part of the mass from which they emanated, since,
after the loss of so much matter as proceeded from it in the great
meteoric shower of 1799, and in the several repetitions of it that
preceded the year 1833, it was still capable of affording so copious a
shower on that year; and similar showers, more limited in extent, were
repeated for at least five years afterwards. We are therefore to regard
the part that descended only as _the extreme portions of a body or
collection of meteors, of unknown extent, existing in the planetary
spaces_.

Secondly, since the earth fell in with this body in the same part of its
orbit, for several years in succession, it must either have remained
there while the earth was performing its whole revolution around the
sun, or it must itself have had a revolution, as well as the earth. But
I have already shown that it could not have remained stationary in that
part of space; therefore, _it must have had a revolution around the
sun_.

Thirdly, its period of revolution must have either been greater than the
earth's, equal to it, or less. It could not have been greater, for then
the two bodies could not have been together again at the end of the
year, since the meteoric body would not have completed its revolution in
a year. Its period might obviously be the same as the earth's, for then
they might easily come together again after one revolution of each;
although their orbits might differ so much in shape as to prevent their
being together at any intermediate point. But the period of the body
might also be less than that of the earth, provided it were some
_aliquot part of a year_, so as to revolve just twice, or three times,
for example, while the earth revolves once. Let us suppose that the
period is one third of a year. Then, since we have given the periodic
times of the two bodies, and the major axis of the orbit of one of them,
namely, of the earth, we can, by Kepler's law, find the major axis of
the other orbit; for the square of the earth's periodic time 1^2 is to
the square of the body's time (1/3)^2 as the cube of the major axis of
the earth's orbit is to the cube of the major axis of the orbit in
question. Now, the three first terms of this proportion are known, and
consequently, it is only to solve a case in the simple rule of three, to
find the term required. On making the calculation, it is found, that the
supposition of a periodic time of only one third of a year gives an
orbit of insufficient length; the whole major axis would not reach from
the sun to the earth; and consequently, a body revolving in it could
never come near to the earth. On making trial of six months, we obtain
an orbit which satisfies the conditions, being such as is represented by
the diagram on page 362, Fig. 69', where the outer circle denotes the
earth's orbit, the sun being in the centre, and the inner ellipse
denotes the path of the meteoric body. The two bodies are together at
the top of the figure, being the place of the meteoric body's aphelion
on the thirteenth of November, and the figures 10, 20, &c., denote the
relative positions of the earth and the body for every ten days, for a
period of six months, in which time the body would have returned to its
aphelion.

[Illustration Fig. 69'.]

Such would be the relation of the body that affords the meteoric shower
of November, provided its revolution is accomplished in six months; but
it is still somewhat uncertain whether the period be half a year or a
year; it must be one or the other.

If we inquire, now, why the meteors always appear to radiate from a
point in the constellation Leo, recollecting that this is the point to
which the body is projected among the stars, the answer is, that this
is the very point towards which the earth is moving in her orbit at that
time; so that if, as we have proved, the earth passed through or near a
nebulous body on the thirteenth of November, that body must necessarily
have been projected into the constellation Leo, else it could not have
lain directly in her path. I consider it therefore as established by
satisfactory proof, that the meteors of November thirteenth emanate from
a nebulous or cometary body, revolving around the sun, and coming so
near the earth at that time that the earth passes through its _skirts_,
or extreme portions, and thus attracts to itself some portions of its
matter, giving to the meteors a greater velocity than could be imparted
by gravity alone, in consequence of passing rapidly by them.

All these conclusions were made out by a process of reasoning strictly
inductive, without supposing that the meteoric body itself had ever been
seen. But there are some reasons for believing that we do actually see
it, and that it is no other than that mysterious appearance long known
under the name of the _zodiacal light_. This is a faint light, which at
certain seasons of the year appears in the west after evening twilight,
and at certain other seasons appears in the east before the dawn,
following or preceding the track of the sun in a triangular figure, with
its broad base next to the sun, and its vertex reaching to a greater or
less distance, sometimes more than ninety degrees from that luminary.
You may obtain a good view of it in February or March, in the west, or
in October, in the morning sky. The various changes which this light
undergoes at different seasons of the year are such as to render it
probable, to my mind, that this is the very body which affords the
meteoric showers; its extremity coming, in November, within the sphere
of the earth's attraction. But, as the arguments for the existence of a
body in the planetary regions, which affords these showers, were drawn
without the least reference to the zodiacal light, and are good, should
it finally be proved that this light has no connexion with them, I will
not occupy your attention with the discussion of this point, to the
exclusion of topics which will probably interest you more.

It is perhaps most probable, that the meteoric showers of August and
December emanate from the same body. I know of nothing repugnant to this
conclusion, although it has not yet been distinctly made out. Had the
periods of the earth and of the meteoric body been so adjusted to each
other that the latter was contained an exact even number of times in the
former; that is, had it been _exactly_ either a year or half a year;
then we might expect a similar recurrence of the meteoric shower every
year; but only a slight variation in such a proportion between the two
periods would occasion the repetition of the shower for a few years in
succession, and then an intermission of them, for an unknown length of
time, until the two bodies were brought into the same relative situation
as before. Disturbances, also, occasioned by the action of Venus and
Mercury, might wholly subvert this numerical relation, and increase or
diminish the probability of a repetition of the phenomenon. Accordingly,
from the year 1830, when the meteoric shower of November was first
observed, until 1833, there was a regular increase of the exhibition; in
1833, it came to its maximum; and after that time it was repeated upon a
constantly diminishing scale, until 1838, since which time it has not
been observed. Perhaps ages may roll away before the world will be again
surprised and delighted with a display of celestial fire-works equal to
that of the morning of November 13, 1833.

LETTER XXVIII.

FIXED STARS.

----"O, majestic Night!
Nature's great ancestor! Day's elder born,
And fated to survive the transient sun!
By mortals and immortals seen with awe!
A starry crown thy raven brow adorns,
An azure zone thy waist; clouds, in heaven's loom
Wrought, through varieties of shape and shade,
In ample folds of drapery divine,
Thy flowing mantle form; and heaven throughout
Voluminously pour thy pompous train."--_Young._

SINCE the solar system is but one among a myriad of worlds which
astronomy unfolds, it may appear to you that I have dwelt too long on so
diminutive a part of creation, and reserved too little space for the
other systems of the universe. But however humble a province our sun and
planets compose, in the vast empire of Jehovah, yet it is that which
most concerns us; and it is by the study of the laws by which this part
of creation is governed, that we learn the secrets of the skies.

Until recently, the observation and study of the phenomena of the solar
system almost exclusively occupied the labors of astronomers. But Sir
William Herschel gave his chief attention to the _sidereal heavens_, and
opened new and wonderful fields of discovery, as well as of speculation.
The same subject, has been prosecuted with similar zeal and success by
his son, Sir John Herschel, and Sir James South, in England, and by
Professor Struve, of Dorpat, until more has been actually achieved than
preceding astronomers had ventured to conjecture. A limited sketch of
these wonderful discoveries is all that I propose to offer you.

The fixed stars are so called, because, to common observation, they
always maintain the same situations with respect to one another. The
stars are classed by their apparent _magnitudes_. The whole number of
magnitudes recorded are _sixteen_, of which the first six only are
visible to the naked eye; the rest are _telescopic stars_. These
magnitudes are not determined by any very definite scale, but are merely
ranked according to their relative degrees of brightness, and this is
left in a great measure to the decision of the eye alone. The brightest
stars, to the number of fifteen or twenty, are considered as stars of
the first magnitude; the fifty or sixty next brightest, of the second
magnitude; the next two hundred, of the third magnitude; and thus the
number of each class increases rapidly, as we descend the scale, so that
no less than fifteen or twenty thousand are included within the first
seven magnitudes.

The stars have been grouped in _constellations_ from the most remote
antiquity; a few, as Orion, Bootes, and Ursa Major, are mentioned in the
most ancient writings, under the same names as they bear at present. The
names of the constellations are sometimes founded on a supposed
resemblance to the objects to which they belong; as the Swan and the
Scorpion were evidently so denominated from their likeness to those
animals; but in most cases, it is impossible for us to find any reason
for designating a constellation by the figure of the animal or hero
which is employed to represent it. These representations were probably
once blended with the fables of pagan mythology. The same figures,
absurd as they appear, are still retained for the convenience of
reference; since it is easy to find any particular star, by specifying
the part of the figure to which it belongs; as when we say, a star is in
the neck of Taurus, in the knee of Hercules, or in the tail of the Great
Bear. This method furnishes a general clue to its position; but the
stars belonging to any constellation are distinguished according to
their apparent magnitudes, as follows: First, by the Greek letters,
Alpha, Beta, Gamma, &c. Thus, _Alpha Orionis_ denotes the largest star
in Orion; _Beta Andromedæ_ the second star in Andromeda; and _Gamma
Leonis_, the third brightest star in the Lion. When the number of the
Greek letters is insufficient to include all the stars in a
constellation, recourse is had to the letters of the Roman alphabet, a,
b, c, &c.; and in all cases where these are exhausted the final resort
is to numbers. This is evidently necessary, since the largest
constellations contain many hundreds or even thousands of stars.
_Catalogues_ of particular stars have also been published, by different
astronomers, each author numbering the individual stars embraced in his
list according to the places they respectively occupy in the catalogue.
These references to particular catalogues are sometimes entered on large
celestial globes. Thus we meet with a star marked 84 H., meaning that
this is its number in Herschel's catalogue; or 140 M., denoting the
place the star occupies in the catalogue of Mayer.

The earliest catalogue of the stars was made by Hipparchus, of the
Alexandrian school, about one hundred and forty years before the
Christian era. A new star appearing in the firmament, he was induced to
count the stars, and to record their positions, in order that posterity
might be able to judge of the permanency of the constellations. His
catalogue contains all that were conspicuous to the naked eye in the
latitude of Alexandria, being one thousand and twenty-two. Most persons,
unacquainted with the actual number of the stars which compose the
visible firmament, would suppose it to be much greater than this; but it
is found that the catalogue of Hipparchus embraces nearly all that can
now be seen in the same latitude; and that on the equator, where the
spectator has both the northern and southern hemispheres in view, the
number of stars that can be counted does not exceed three thousand. A
careless view of the firmament in a clear night gives us the impression
of an infinite number of stars; but when we begin to count them, they
appear much more sparsely distributed than we supposed, and large
portions of the sky appear almost destitute of stars.

By the aid of the telescope, new fields of stars present themselves, of
boundless extent; the number continually augmenting, as the powers of
the telescope are increased. Lalande, in his 'Histoire Celeste,' has
registered the positions of no less than fifty thousand; and the whole
number visible in the largest telescopes amounts to many millions.

When you look at the firmament on a clear Autumnal or Winter evening, it
appears so thickly studded with stars, that you would perhaps imagine
that the task of learning even the brightest of them would be almost
hopeless. Let me assure you, this is all a mistake. On the contrary, it
is a very easy task to become acquainted with the names and positions of
the stars of the first magnitude, and of the leading constellations. If
you will give a few evenings to the study, you will be surprised to
find, both how rapidly you can form these new acquaintances, and how
deeply you will become interested in them. I would advise you, at first,
to obtain, for an evening or two, the assistance of some friend who is
familiar with the stars, just to point out a few of the most conspicuous
constellations. This will put you on the track, and you will afterwards
experience no difficulty in finding all the constellations and stars
that are particularly worth knowing; especially if you have before you a
map of the stars, or, what is much better, a celestial globe. It is a
pleasant evening recreation for a small company of young astronomers to
go out together, and learn one or two constellations every favorable
evening, until the whole are mastered. If you have a celestial globe,
_rectify_ it for the evening; that is, place it in such a position, that
the constellations shall be seen on it in the same position with respect
to the horizon, that they have at that moment in the sky itself. To do
this, I first elevate the north pole until the number of degrees on the
brass meridian from the pole to the horizon corresponds to my latitude,
(forty-one degrees and eighteen minutes.) I then find the sun's place in
the ecliptic, by looking for the day of the month on the broad horizon,
and against it noting the corresponding sign and degree. I now find the
same sign and degree on the ecliptic itself, and bring that point to the
brass meridian. As that will be the position of the sun at noon, I set
the hour-index at twelve, and then turn the globe westward, until the
index points to the given hour of the evening. If I now inspect the
figures of the constellations, and then look upward at the firmament, I
shall see that the latter are spread over the sky in the same manner as
the pictures of them are painted on the globe. I will point out a few
marks by which the leading constellations may be recognised; this will
aid you in finding them, and you can afterwards learn the individual
stars of a constellation, to any extent you please, by means of the
globes or maps. Let us begin with the _Constellations of the Zodiac_,
which, succeeding each other, as they do, in a known order, are most
easily found.

_Aries_ (_the Ram_) is a small constellation, known by two bright stars
which form his head, _Alpha_ and _Beta Arietis_. These two stars are
about four degrees apart; and directly south of Beta, at the distance of
one degree, is a smaller star, _Gamma Arietis_. It has been already
intimated that the Vernal equinox probably was near the head of Aries,
when the signs of the zodiac received their present names.

_Taurus_ (_the Bull_) will be readily found by the seven stars, or
_Pleiades_, which lie in his neck. The largest star in Taurus is
_Aldebaran_, in the Bull's eye, a star of the first magnitude, of a
reddish color, somewhat resembling the planet Mars. Aldebaran and four
other stars, close together in the face of Taurus, compose the _Hyades_.

_Gemini_ (_the Twins_) is known by two very bright stars, _Castor and
Pollux_, five degrees asunder. Castor (the northern) is of the first,
and Pollux of the second, magnitude.

_Cancer_ (_the Crab_.) There are no large stars in this constellation,
and it is regarded as less remarkable than any other in the zodiac. It
contains, however, an interesting group of small stars, called
_Præsepe_, or the nebula of Cancer, which resembles a comet, and is
often mistaken for one, by persons unacquainted with the stars. With a
telescope of very moderate powers this nebula is converted into a
beautiful assemblage of exceedingly bright stars.

_Leo_ (_the Lion_) is a very large constellation, and has many
interesting members. _Regulus_ (_Alpha Leonis_) is a star of the first
magnitude, which lies directly in the ecliptic, and is much used in
astronomical observations. North of Regulus, lies a semicircle of bright
stars, forming a _sickle_, of which Regulus is the handle. _Denebola_, a
star of the second magnitude, is in the Lion's tail, twenty-five degrees
northeast of Regulus.

_Virgo_ (_the Virgin_) extends a considerable way from west to east, but
contains only a few bright stars. _Spica_, however, is a star of the
first magnitude, and lies a little east of the place of the Autumnal
equinox. Eighteen degrees eastward of Denebola, and twenty degrees north
of Spica, is _Vindemiatrix_, in the arm of Virgo, a star of the third
magnitude.

_Libra_ (_the Balance_) is distinguished by three large stars, of which
the two brightest constitute the beam of the balance, and the smallest
forms the top or handle.

_Scorpio_ (_the Scorpion_) is one of the finest of the constellations.
His head is formed of five bright stars, arranged in the arc of a
circle, which is crossed in the centre by the ecliptic nearly at right
angles, near the brightest of the five, _Beta Scorpionis_. Nine degrees
southeast of this is a remarkable star of the first magnitude, of a
reddish color, called _Cor Scorpionis_, or _Antares_. South of this, a
succession of bright stars sweep round towards the east, terminating in
several small stars, forming the tail of the Scorpion.

_Sagittarius_ (_the Archer_.) Northeast of the tail of the Scorpion are
three stars in the arc of a circle, which constitute the _bow_ of the
Archer, the central star being the brightest, directly west of which is
a bright star which forms the _arrow_.

_Capricornus_ (_the Goat_) lies northeast of Sagittarius, and is known
by two bright stars, three degrees apart, which form the head.

_Aquarius_ (_the Water-Bearer_) is recognised by two stars in a line
with _Alpha Capricorni_, forming the shoulders of the figure. These two
stars are ten degrees apart; and three degrees southeast is a third
star, which, together with the other two, make an acute triangle, of
which the westernmost is the vertex.

_Pisces_ (_the Fishes_) lie between Aquarius and Aries. They are not
distinguished by any large stars, but are connected by a series of small
stars, that form a crooked line between them. _Piscis Australia_, the
Southern Fish, lies directly below Aquarius, and is known by a single
bright star far in the south, having a declination of thirty degrees.
The name of this star is _Fomalhaut_, and it is much used in
astronomical measurements.

The constellations of the zodiac, being first well learned, so as to be
readily recognised, will facilitate the learning of others that lie
north and south of them. Let us, therefore, next review the principal
_Northern Constellations_, beginning north of Aries, and proceeding from
west to east.

_Andromeda_ is characterized by three stars of the second magnitude,
situated in a straight line, extending from west to east. The middle
star is about seventeen degrees north of Beta Arietis. It is in the
girdle of Andromeda, and is named _Mirach_. The other two lie at about
equal distances, fourteen degrees west and east of Mirach. The western
star, in the head of Andromeda, lies in the equinoctial colure. The
eastern star, _Alamak_, is situated in the foot.

_Perseus_ lies directly north of the Pleiades, and contains several
bright stars. About eighteen degrees from the Pleiades is _Algol_, a
star of the second magnitude, in the head of Medusa, which forms a part
of the figure; and nine degrees northeast of Algol is _Algenib_, of the
same magnitude, in the back of Perseus. Between Algenib and the Pleiades
are three bright stars, at nearly equal intervals, which compose the
right leg of Perseus.

_Auriga_ (_the Wagoner_) lies directly east of Perseus, and extends
nearly parallel to that constellation, from north to south. _Capella_, a
very white and beautiful star of the first magnitude, distinguishes this
constellation. The feet of Auriga are near the Bull's horns.

The _Lynx_ comes next, but presents nothing particularly interesting,
containing no stars above the fourth magnitude.

_Leo Minor_ consists of a collection of small stars north of the sickle
in Leo, and south of the Great Bear. Its largest star is only of the
third magnitude.

_Coma Berenices_ is a cluster of small stars, north of Denebola, in the
tail of the Lion, and of the head of Virgo. About twelve degrees
directly north of Berenice's hair, is a single bright star, called _Cor
Caroli_, or Charles's Heart.

_Bootes_, which comes next, is easily found by means of _Arcturus_, a
star of the first magnitude, of a reddish color, which is situated near
the knee of the figure. Arcturus is accompanied by three small stars,
forming a triangle a little to the southwest. Two bright stars, _Gamma_
and _Delta Bootis_, form the shoulders, and _Beta_, of the third
magnitude, is in the head, of the figure.

_Corona Borealis_, (_the Crown_,) which is situated east of Bootes, is
very easily recognised, composed as it is of a semicircle of bright
stars. In the centre of the bright crown is a star of the second
magnitude, called _Gemma_: the remaining stars are all much smaller.

_Hercules_, lying between the Crown on the west and the Lyre on the
east, is very thickly set with stars, most of which are quite small.
This constellation covers a great extent of the sky, especially from
north to south, the head terminating within fifteen degrees of the
equator, and marked by a star of the third magnitude, called _Ras
Algethi_, which is the largest in the constellation.

_Ophiucus_ is situated directly south of Hercules, extending some
distance on both sides of the equator, the feet resting on the Scorpion.
The head terminates near the head of Hercules, and, like that, is marked
by a bright star within five degrees of _Alpha Herculis_ Ophiucus is
represented as holding in his hands the _Serpent_, the head of which,
consisting of three bright stars, is situated a little south of the
Crown. The folds of the serpent will be easily followed by a succession
of bright stars, which extend a great way to the east.

_Aquila_ (_the Eagle_) is conspicuous for three bright stars in its
neck, of which the central one, _Altair_, is a very brilliant white star
of the first magnitude. _Antinous_ lies directly south of the Eagle, and
north of the head of Capricornus.

_Delphinus_ (_the Dolphin_) is a small but beautiful constellation, a
few degrees east of the Eagle, and is characterized by four bright stars
near to one another, forming a small rhombic square. Another star of the
same magnitude, five degrees south, makes the tail.

_Pegasus_ lies between Aquarius on the southwest and Andromeda on the
northeast. It contains but few large stars. A very regular square of
bright stars is composed of _Alpha Andromedæ_ and the three largest
stars in Pegasus; namely, _Scheat_, _Markab_, and _Algenib_. The sides
composing this square are each about fifteen degrees. Algenib is
situated in the equinoctial colure.

We may now review the _Constellations which surround the north pole_,
within the circle of perpetual apparition.

_Ursa Minor_ (_the Little Bear_) lies nearest the pole. The pole-star,
_Polaris_, is in the extremity of the tail, and is of the third
magnitude. Three stars in a straight line, four degrees or five degrees
apart, commencing with the pole-star, lead to a trapezium of four stars,
and the whole seven form together a _dipper_,--the trapezium being the
body and the three stars the handle.

_Ursa Major_ (_the Great Bear_) is situated between the pole and the
Lesser Lion, and is usually recognised by the figure of a larger and
more perfect dipper which constitutes the hinder part of the animal.
This has also seven stars, four in the body of the Dipper and three in
the handle. All these are stars of much celebrity. The two in the
western side of the Dipper, Alpha and Beta, are called _Pointers_, on
account of their always being in a right line with the pole-star, and
therefore affording an easy mode of finding that. The first star in the
tail, next the body, is named _Alioth_, and the second, _Mizar_. The
head of the Great Bear lies far to the westward of the Pointers, and is
composed of numerous small stars; and the feet are severally composed of
two small stars very near to each other.

_Draco_ (_the Dragon_) winds round between the Great and the Little
Bear; and, commencing with the tail, between the Pointers and the
pole-star, it is easily traced by a succession of bright stars extending
from west to east. Passing under Ursa Minor, it returns westward, and
terminates in a triangle which forms the head of Draco, near the feet of
Hercules, northwest of Lyra. _Cepheus_ lies eastward of the breast of
the Dragon, but has no stars above the third magnitude.

_Cassiopeia_ is known by the figure of a _chair_, composed of four stars
which form the legs, and two which form the back. This constellation
lies between Perseus and Cepheus, in the Milky Way.

_Cygnus_ (_the Swan_) is situated also in the Milky Way, some distance
southwest of Cassiopeia, towards the Eagle. Three bright stars, which
lie along the Milky Way, form the body and neck of the Swan, and two
others, in a line with the middle one of the three, one above and one
below, constitute the wings. This constellation is among the few that
exhibit some resemblance to the animals whose names they bear.

_Lyra_ (_the Lyre_) is directly west of the Swan, and is easily
distinguished by a beautiful white star of the first magnitude, _Alpha
Lyræ_.

The _Southern Constellations_ are comparatively few in number. I shall
notice only the Whale, Orion, the Greater and Lesser Dog, Hydra, and the
Crow.

_Cetus_ (_the Whale_) is distinguished rather for its extent than its
brilliancy, reaching as it does through forty degrees of longitude,
while none of its stars, except one, are above the third magnitude.
_Menkar_ (_Alpha Ceti_) in the mouth, is a star of the second
magnitude; and several other bright stars, directly south of Aries, make
the head and neck of the Whale. _Mira_, (_Omicron Ceti_,) in the neck of
the Whale, is a variable star.

_Orion_ is one of the largest and most beautiful of the constellations,
lying southeast of Taurus. A cluster of small stars forms the head; two
large stars, _Betalgeus_ of the first and _Bellatrix_ of the second
magnitude, make the shoulders; three more bright stars compose the
buckler, and three the sword; and _Rigel_, another star of the first
magnitude, makes one of the feet. In this constellation there are
seventy stars plainly visible to the naked eye, including two of the
first magnitude, four of the second, and three of the third.

_Canis Major_ lies southeast of Orion, and is distinguished chiefly by
its containing the largest of the fixed stars, _Sirius_.

_Canis Minor_, a little north of the equator, between Canis Major and
Gemini, is a small constellation, consisting chiefly of two stars, of
which, _Procyon_ is of the first magnitude.

_Hydra_ has its head near Procyon, consisting of a number of stars of
ordinary brightness. About fifteen degrees southeast of the head is a
star of the second magnitude, forming the heart, (_Cor Hydræ_;) and
eastward of this is a long succession of stars of the fourth and fifth
magnitudes, composing the body and tail, and reaching a few degrees
south of Spica Virginis.

_Corvus_ (_the Crow_) is represented as standing on the tail of Hydra.
It consists of small stars, only three of which are as large as the
third magnitude.

In assigning the places of individual stars, I have not aimed at great
precision; but such a knowledge as you will acquire of the
constellations and larger stars, by nothing more even than you can
obtain from the foregoing sketch, will not only add greatly to the
interest with which you will ever afterwards look at the starry heavens,
but it will enable you to locate any phenomenon that may present itself
in the nocturnal sky, and to understand the position of any object that
may be described, by assigning its true place among the stars; although
I hope you will go much further than this mere outline, in cultivating
an actual acquaintance with the stars. Leaving, now, these great
divisions of the bodies of the firmament, let us ascend to the next
order of stars, composing CLUSTERS.

In various parts of the nocturnal heavens are seen large groups which,
either by the naked eye, or by the aid of the smallest telescope, are
perceived to consist of a great number of small stars. Such are the
Pleiades, Coma Berenices, and Præsepe, or the Bee-hive, in Cancer. The
_Pleiades_, or Seven Stars, as they are called, in the neck of Taurus,
is the most conspicuous cluster. When we look _directly_ at this group,
we cannot distinguish more than six stars; but by turning the eye
_sideways_ upon it, we discover that there are many more; for it is a
remarkable fact that indirect vision is far more delicate than direct.
Thus we can see the zodiacal light or a comet's tail much more
distinctly and better defined, if we fix one eye on a part of the
heavens at some distance and turn the other eye obliquely upon the
object, than we can by looking directly towards it. Telescopes show the
Pleiades to contain fifty or sixty stars, crowded together, and
apparently insulated from the other parts of the heavens. _Coma
Berenices_ has fewer stars, but they are of a larger class than those
which compose the Pleiades. The _Bee-hive_, or Nebula of Cancer, as it
is called, is one of the finest objects of this kind for a small
telescope, being by its aid converted into a rich congeries of shining
points. The head of Orion affords an example of another cluster, though
less remarkable than those already mentioned. These clusters are
pleasing objects to the telescope; and since a common spyglass will
serve to give a distinct view of most of them, every one may have the
power of taking the view. But we pass, now, to the third order of stars,
which present themselves much more obscurely to the gaze of the
astronomer, and require large instruments for the full developement
of their wonderful organization. These are the NEBULÆ.

[Illustration Figures 70, 71, 72, 73. CLUSTERS OF STARS AND NEBULÆ.]

Nebulæ are faint misty appearances which are dimly seen among the stars,
resembling comets, or a speck of fog. They are usually resolved by the
telescope into myriads of small stars; though in some instances, no
powers of the telescope have been found sufficient thus to resolve them.
The _Galaxy_ or Milky Way, presents a continued succession of large
nebulas. The telescope reveals to us innumerable objects of this kind.
Sir William Herschel has given catalogues of two thousand nebulæ, and
has shown that the nebulous matter is distributed through the immensity
of space in quantities inconceivably great, and in separate parcels, of
all shapes and sizes, and of all degrees of brightness between a mere
milky appearance and the condensed light of a fixed star. In fact, more
distinct nebulæ have been hunted out by the aid of telescopes than the
whole number of stars visible to the naked eye in a clear Winter's
night. Their appearances are extremely diversified. In many of them we
can easily distinguish the individual stars; in those apparently more
remote, the interval between the stars diminishes, until it becomes
quite imperceptible; and in their faintest aspect they dwindle to points
so minute, as to be appropriately denominated _star-dust_. Beyond this,
no stars are distinctly visible, but only streaks or patches of milky
light. The diagram facing page 379 represents a magnificent nebula in
the Galaxy. In objects so distant as the fixed stars, any apparent
interval must denote an immense space; and just imagine yourself
situated any where within the grand assemblage of stars, and a firmament
would expand itself over your head like that of our evening sky, only a
thousand times more rich and splendid.

Many of the nebulæ exhibit a tendency towards a globular form, and
indicate a rapid condensation towards the centre. This characteristic is
exhibited in the forms represented in Figs. 70 and 71. We have here two
specimens of nebulæ of the nearer class, where the stars are easily
discriminated. In Figs. 72 and 73 we have examples of two others of the
remoter kind, one of which is of the variety called _star-dust_. These
wonderful objects, however, are not confined to the spherical form, but
exhibit great varieties of figure. Sometimes they appear as ovals;
sometimes they are shaped like a fan; and the unresolvable kind often
affect the most fantastic forms. The opposite diagram, Fig. 74, as well
as the preceding, affords a specimen of these varieties, as given in
Professor Nichols's 'Architecture of the Heavens,' where they are
faithfully copied from the papers of Herschel, in the 'Philosophical
Transactions.'

[Illustration Figure 74. VARIOUS FORMS OF NEBULÆ.]

Sir John Herschel has recently returned from a residence of five years
at the Cape of Good Hope, with the express view of exploring the hidden
treasures of the southern hemisphere. The kinds of nebulæ are in general
similar to those of the northern hemisphere, and the forms are equally
various and singular. The _Magellan Clouds_, two remarkable objects seen
among the stars of that hemisphere, and celebrated among navigators,
appeared to the great telescope of Herschel (as we are informed by
Professor Nichols) no longer as simple milky spots, or permanent light
flocculi of cloud, as they appear to the unassisted eye, but shone with
inconceivable splendor. The _Nubecula Major_, as the larger object is
called, is a congeries of clusters of stars, of irregular form, globular
clusters and nebulæ of various magnitudes and degrees of condensation,
among which is interspersed a large portion of irresolvable nebulous
matter, which may be, and probably is, star-dust, but which the power of
the twenty-feet telescope shows only as a general illumination of the
field of view, forming a bright ground on which the other objects are
scattered. The _Nubecula Minor_ (the lesser cloud) exhibited appearances
similar, though inferior in degree.

[Illustration Figure 75. A NEBULA IN THE MILKY WAY.]

It is a grand idea, first conceived by Sir William Herschel, and
generally adopted by astronomers, that the whole Galaxy, or Milky Way,
is nothing else than a nebula, and appears so extended, merely because
it happens to be that particular nebula to which we belong. According to
this view, our sun, with his attendant planets and comets, constitutes
but a single star of the Galaxy, and our firmament of stars, or visible
heavens, is composed of the stars of _our_ nebula alone. An inhabitant
of any of the other nebulæ would see spreading over him a firmament
equally spacious, and in some cases inconceivably more brilliant.

It is an exalted spectacle to travel over the Galaxy in a clear night,
with a powerful telescope, with the heart full of the idea that every
star is a world. Sir William Herschel, by counting the stars in a single
field of his telescope, estimated that fifty thousand had passed under
his review in a zone two degrees in breadth, during a single hour's
observation. Notwithstanding the apparent contiguity of the stars which
crowd the Galaxy, it is certain that their mutual distances must be
inconceivably great.

It is with some reluctance that I leave, for the present, this fairy
land of astronomy; but I must not omit, before bringing these Letters to
a conclusion, to tell you something respecting other curious and
interesting objects to be found among the stars.

VARIABLE STARS are those which undergo a periodical change of
brightness. One of the most remarkable is the star _Mira_, in the Whale,
(_Omicron Ceti_.) It appears once in eleven months, remains at its
greatest brightness about a fortnight, being then, on some occasions,
equal to a star of the second magnitude. It then decreases about three
months, until it becomes completely invisible, and remains so about five
months, when it again becomes visible, and continues increasing during
the remaining three months of its period.

Another very remarkable variable star is _Algol_, (_Beta Persei_.) It is
usually visible as a star of the second magnitude, and continues such
for two days and fourteen hours, when it suddenly begins to diminish in
splendor, and in about three and a half hours is reduced to the fourth
magnitude. It then begins again to increase, and in three and a half
hours more is restored to its usual brightness, going through all its
changes in less than three days. This remarkable law of variation
appears strongly to suggest the revolution round it of some opaque body,
which, when interposed between us and Algol, cuts off a large portion of
its light. "It is," says Sir J. Herschel, "an indication of a high
degree of activity in regions where, but for such evidences, we might
conclude all lifeless. Our sun requires almost nine times this period to
perform a revolution on its axis. On the other hand, the periodic time
of an opaque revolving body, sufficiently large, which would produce a
similar temporary obscuration of the sun, seen from a fixed star, would
be less than fourteen hours." The duration of these periods is extremely
various. While that of Beta Persei, above mentioned, is less than three
days, others are more than a year; and others, many years.

TEMPORARY STARS are new stars, which have appeared suddenly in the
firmament, and, after a certain interval, as suddenly disappeared, and
returned no more. It was the appearance of a new star of this kind, one
hundred and twenty-five years before the Christian era, that prompted
Hipparchus to draw up a catalogue of the stars, the first on record.
Such, also, was the star which suddenly shone out, A.D. 389, in the
Eagle, as bright as Venus, and, after remaining three weeks, disappeared
entirely. At other periods, at distant intervals, similar phenomena have
presented themselves. Thus the appearance of a star in 1572 was so
sudden, that Tycho Brahe, returning home one day, was surprised to find
a collection of country people gazing at a star which he was sure did
not exist half an hour before. It was then as bright as Sirius, and
continued to increase until it surpassed Jupiter when brightest, and was
visible at mid-day. In a month it began to diminish; and, in three
months afterwards, it had entirely disappeared. It has been supposed by
some that, in a few instances, the same star has returned, constituting
one of the periodical or variable stars of a long period. Moreover, on a
careful reexamination of the heavens, and a comparison of catalogues,
many stars are now discovered to be missing.

DOUBLE STARS are those which appear single to the naked eye, but are
resolved into two by the telescope; or, if not visible to the naked eye,
are seen in the telescope so close together as to be recognised as
objects of this class. Sometimes, three or more stars are found in this
near connexion, constituting triple, or multiple stars. Castor, for
example, when seen by the naked eye, appears as a single star, but in a
telescope even of moderate powers, it is resolved into two stars, of
between the third and fourth magnitudes, within five seconds of each
other. These two stars are nearly of equal size; but more commonly, one
is exceedingly small in comparison with the other, resembling a
satellite near its primary, although in distance, in light, and in other
characteristics, each has all the attributes of a star, and the
combination, therefore, cannot be that of a planet with a satellite. In
most instances, also, the distance between these objects is much less
than five seconds; and, in many cases, it is less than one second. The
extreme closeness, together with the exceeding minuteness, of most of
the double stars, requires the best telescopes united with the most
acute powers of observation. Indeed, certain of these objects are
regarded as the severest _tests_ both of the excellence of the
instruments and of the skill of the observer. The diagram on page 382,
Fig. 76, represents four double stars, as seen with appropriate
magnifiers. No. 1, exhibits Epsilon Bootis with a power of three hundred
and fifty; No. 2, Rigel, with a power of one hundred and thirty; No. 3,
the Pole-star, with a power of one hundred; and No. 4, Castor, with a
power of three hundred.

Our knowledge of the double stars almost commenced with Sir William
Herschel, about the year 1780. At the time he began his search for them,
he was acquainted with only _four_. Within five years he discovered
nearly _seven hundred_ double stars, and during his life, he observed no
less than twenty-four hundred. In his Memoirs, published in the
Philosophical Transactions, he gave most accurate measurements of the
distances between the two stars, and of the angle which a line joining
the two formed with a circle parallel to the equator. These data would
enable him, or at least posterity, to judge whether these minute bodies
ever change their position with respect to each other. Since 1821, these
researches have been prosecuted, with great zeal and industry, by Sir
James South and Sir John Herschel, in England; while Professor Struve,
of Dorpat, with the celebrated telescope of Fraunhofer, has published,
from his own observations, a catalogue of three thousand double stars,
the determination of which involved the distinct and most minute
inspection of at least one hundred and twenty thousand stars. Sir John
Herschel, in his recent survey of the southern hemisphere, is said to
have added to the catalogue of double stars nearly three thousand more.

[Illustration Fig. 76.]

Two circumstances add a high degree of interest to the phenomena of
double stars: the first is, that a few of them, at least, are found to
have a revolution around each other; the second, that they are supposed
to afford the means of ascertaining the parallax of the fixed stars. But
I must defer these topics till my next Letter.

LETTER XXIX.

FIXED STARS CONTINUED.

"O how canst thou renounce the boundless store
Of charms that Nature to her votary yields?
The warbling woodland, the resounding shore,
The pomp of groves, and garniture of fields;
All that the genial ray of morning yields,
And all that echoes to the song of even,
All that the mountain's sheltering bosom shields,
And all the dread magnificence of heaven,--
O how canst thou renounce, and hope to be forgiven!"--_Beattie._

In 1803, Sir William Herschel first determined and announced to the
world, that there exist among the stars separate systems, composed of
two stars revolving about each other in regular orbits. These he
denominated _binary stars_, to distinguish them from other double stars
where no such motion is detected, and whose proximity to each other may
possibly arise from casual juxtaposition, or from one being in the range
of the other. Between fifty and sixty instances of changes, to a greater
or less amount, of the relative positions of double stars, are mentioned
by Sir William Herschel; and a few of them had changed their places so
much, within twenty-five years, and in such order, as to lead him to the
conclusion that they performed revolutions, one around the other, in
regular orbits. These conclusions have been fully confirmed by later
observers; so that it is now considered as fully established, that there
exist among the fixed stars binary systems, in which two stars perform
to each other the office of sun and planet, and that the periods of
revolution of more than one such pair have been ascertained with some
degree of exactness. Immersions and emersions of stars behind each other
have been observed, and real motions among them detected, rapid enough
to become sensible and measurable in very short intervals of time. The
periods of the double stars are very various, ranging, in the case of
those already ascertained, from forty-three years to one thousand.
Their orbits are very small ellipses, only a few seconds in the longest
direction, and more eccentric than those of the planets. A double star
in the Northern Crown (_Eta Coronæ_) has made a complete revolution
since its first discovery, and is now far advanced in its second period;
while a star in the Lion (_Gamma Leonis_) requires twelve hundred years
to complete its circuit.

You may not at once see the reason why these revolutions of one member
of a double star around the other, should be deemed facts of such
extraordinary interest; to you they may appear rather in the light of
astronomical curiosities. But remark, that the revolutions of the binary
stars have assured us of this most interesting fact, that _the law of
gravitation extends to the fixed stars_. Before these discoveries, we
could not decide, except by a feeble analogy, that this law transcended
the bounds of the solar system. Indeed, our belief of the fact rested
more upon our idea of unity of design in the works of the Creator, than
upon any certain proof; but the revolution of one star around another,
in obedience to forces which are proved to be similar to those which
govern the solar system, establishes the grand conclusion, that the law
of gravitation is truly the law of the material universe. "We have the
same evidence," says Sir John Herschel, "of the revolutions of the
binary stars about each other, that we have of those of Saturn and
Uranus about the sun; and the correspondence between their calculated
and observed places, in such elongated ellipses, must be admitted to
carry with it a proof of the prevalence of the Newtonian law of gravity
in their systems, of the very same nature and cogency as that of the
calculated and observed places of comets round the centre of our own
system. But it is not with the revolution of bodies of a cometary or
planetary nature round a solar centre, that we are now concerned; it is
with that of sun around sun, each, perhaps, accompanied with its train
of planets and their satellites, closely shrouded from our view by the
splendor of their respective suns, and crowded into a space, bearing
hardly a greater proportion to the enormous interval which separates
them, than the distances of the satellites of our planets from their
primaries bear to their distances from the sun itself."

Many of the double stars are of different colors; and Sir John Herschel
is of the opinion that there exist in nature suns of different colors.
"It may," says he, "be easier suggested in words than conceived in
imagination, what variety of illumination two suns, a red and a green,
or a yellow and a blue one, must afford to a planet circulating about
either; and what charming contrasts and 'grateful vicissitudes' a red
and a green day, for instance, alternating with a white one and with
darkness, might arise from the presence or absence of one or other or
both above the horizon. Insulated stars of a red color, almost as deep
as that of blood, occur in many parts of the heavens; but no green or
blue star, of any decided hue, has ever been noticed unassociated with a
companion brighter than itself."

Beside these revolutions of the binary stars, _some of the fixed stars
appear to have a real motion in space_. There are several _apparent_
changes of place among the stars, arising from real changes in the
earth, which, as we are not conscious of them, we refer to the stars;
but there are other motions among the stars which cannot result from any
changes in the earth, but must arise from changes in the stars
themselves. Such motions are called the _proper motions_ of the stars.
Nearly two thousand years ago, Hipparchus and Ptolemy made the most
accurate determinations in their power of the relative situations of the
stars, and their observations have been transmitted to us in Ptolemy's
'Almagest;' from which it appears that the stars retain at least _very
nearly_ the same places now as they did at that period. Still, the more
accurate methods of modern astronomers have brought to light minute
changes in the places of certain stars, which force upon us the
conclusion, _either that our solar system causes an apparent
displacement of certain stars, by a motion of its own in space, or
that they have themselves a proper motion_. Possibly, indeed, both these
causes may operate.

If the sun, and of course the earth which accompanies him, is actually
in motion, the fact may become manifest from the apparent approach of
the stars in the region which he is leaving, and the recession of those
which lie in the part of the heavens towards which he is travelling.
Were two groves of trees situated on a plain at some distance apart, and
we should go from one to the other, the trees before us would gradually
appear further and further asunder, while those we left behind would
appear to approach each other. Some years since, Sir William Herschel
supposed he had detected changes of this kind among two sets of stars in
opposite points of the heavens, and announced that the solar system was
in motion towards a point in the constellation Hercules; but other
astronomers have not found the changes in question such as would
correspond to this motion, or to any motion of the sun; and, while it is
a matter of general belief that the sun has a motion in space, the fact
is not considered as yet entirely proved.

In most cases, where a proper motion in certain stars has been
suspected, its annual amount has been so small, that many years are
required to assure us, that the effect is not owing to some other cause
than a real progressive motion in the stars themselves; but in a few
instances the fact is too obvious to admit of any doubt. Thus, the two
stars, 61 Cygni, which are nearly equal, have remained constantly at the
same or nearly at the same distance of fifteen seconds, for at least
fifty years past. Mean-while, they have shifted their local situation in
the heavens four minutes twenty-three seconds, the annual proper motion
of each star being five seconds and three tenths, by which quantity this
system is every year carried along in some unknown path, by a motion
which for many centuries must be regarded as uniform and rectilinear. A
greater proportion of the double stars than of any other indicate proper
motions, especially the binary stars, or those which have a revolution
around each other. Among stars not double, and no way differing from the
rest in any other obvious particular, a star in the constellation
Cassiopeia, (_Mu Cassiopeiæ_) has the greatest proper motion of any yet
ascertained, amounting to nearly four seconds annually.

You have doubtless heard much respecting the "immeasurable _distances_"
of the fixed stars, and will desire to learn what is known to
astronomers respecting this interesting subject.

We cannot ascertain the actual distance of any of the fixed stars, but
we can certainly determine that the nearest star is more than twenty
millions of millions of miles from the earth, (20,000,000,000,000.) For
all measurements relating to the distances of the _sun and planets_, the
radius of the earth furnishes the base line. The length of this line
being known, and the horizontal parallax of the sun or any planet, we
have the means of calculating the distance of the body from us, by
methods explained in a previous Letter. But any star, viewed from the
opposite sides of the earth, would appear from both stations to occupy
precisely the same situation in the celestial sphere, and of course it
would exhibit no horizontal parallax. But astronomers have endeavored to
find a parallax in some of the fixed stars, by taking the _diameter of
the earth's orbit_ as a base line. Yet even a change of position
amounting to one hundred and ninety millions of miles proved, until very
recently, insufficient to alter the place of a single star, so far as to
be capable of detection by very refined observations; from which it was
concluded that the stars have not even any _annual parallax_; that is,
the angle subtended by the semidiameter of the earth's orbit, at the
nearest fixed star, is insensible. The errors to which instrumental
measurements are subject, arising from the defects of instruments
themselves, from refraction, and from various other sources of
inaccuracy, are such, that the angular determinations of arcs of the
heavens cannot be relied on to less than one second, and therefore
cannot be appreciated by direct measurement. It follows, that, when
viewed from the nearest star, the diameter of the earth's orbit would be
insensible; the spider-line of the telescope would more than cover it.
Taking, however, the annual parallax of a fixed star at one second, it
can be demonstrated, that the distance of the nearest fixed star _must
exceed_ 95000000 × 200000 = 190000000 × 100000, or one hundred thousand
times one hundred and ninety millions of miles. Of a distance so vast we
can form no adequate conceptions, and even seek to measure it only by
the time that light (which moves more than one hundred and ninety-two
thousand miles per second, and passes from the sun to the earth in eight
minutes and seven seconds) would take to traverse it, which is found to
be more than three and a half years.

If these conclusions are drawn with respect to the largest of the fixed
stars, which we suppose to be vastly nearer to us than those of the
smallest magnitude, the idea of distance swells upon us when we attempt
to estimate the remoteness of the latter. As it is uncertain, however,
whether the difference in the apparent magnitudes of the stars is owing
to a real difference, or merely to their being at various distances from
the eye, more or less uncertainty must attend all efforts to determine
the relative distances of the stars; but astronomers generally believe,
that the lower orders of stars are vastly more distant from us than the
higher. Of some stars it is said, that thousands of years would be
required for their light to travel down to us.

I have said that the stars have always been held, until recently, to
have no annual parallax; yet it may be observed that astronomers were
not exactly agreed on this point. Dr. Brinkley, a late eminent Irish
astronomer, supposed that he had detected an annual parallax in Alpha
Lyræ, amounting to one second and thirteen hundreths, and in Alpha
Aquilæ, of one second and forty-two hundreths. These results were
controverted by Mr. Pond, of the Royal Observatory of Greenwich; and
Mr. Struve, of Dorpat, has shown that, in a number of cases, the
supposed parallax is in a direction opposite to that which would arise
from the motion of the earth. Hence it is considered doubtful whether,
in all cases of an apparent parallax, the effect is not wholly due to
errors of observation.

But as if nothing was to be hidden from our times, the long sought for
parallax among the fixed stars has at length been found, and
consequently the distance of some of these bodies, at least, is no
longer veiled in mystery. In the year 1838, Professor Bessel, of
Köningsberg, announced the discovery of a parallax in one of the stars
of the Swan, (61 _Cygni_,) amounting to about _one third of a second_.
This seems, indeed, so small an angle, that we might have reason to
suspect the reality of the determination; but the most competent judges
who have thoroughly examined the process by which the discovery was
made, assent to its validity. What, then, do astronomers understand,
when they say that a parallax has been discovered in one of the fixed
stars, amounting to one third of a second? They mean that the star in
question apparently shifts its place in the heavens, to that amount,
when viewed at opposite extremities of the earth's orbit, namely, at
points in space distant from each other one hundred and ninety millions
of miles. On calculating the distance of the star from us from these
data, it is found to be six hundred and fifty-seven thousand seven
hundred times ninety-five millions of miles,--a distance which it would
take light more than ten years to traverse.

Indirect methods have been proposed, for ascertaining the parallax of
the fixed stars, by means of observations on the _double stars_. If the
two stars composing a double star are at different distances from us,
parallax would affect them unequally, and change their relative
positions with respect to each other; and since the ordinary sources of
error arising from the imperfection of instruments, from precession, and
from refraction, would be avoided, (as they would affect both objects
alike, and therefore would not disturb their relative positions,)
measurements taken with the micrometer of changes much less than one
second may be relied on. Sir John Herschel proposed a method, by which
changes may be determined that amount to only one fortieth of a second.

The immense distance of the fixed stars is inferred also from the fact,
that the largest telescopes do not increase their apparent magnitude.
They are still points, when viewed with glasses that magnify five
thousand times.

With respect to the NATURE OF THE STARS, it would seem fruitless to
inquire into the nature of bodies so distant, and which reveal
themselves to us only as shining points in space. Still, there are a few
very satisfactory inferences that can be made out respecting them.
First, _the fixed stars are bodies greater than our earth_. If this were
not the case, they would not be visible at such an immense distance. Dr.
Wollaston, a distinguished English philosopher, attempted to estimate
the magnitudes of certain of the fixed stars from the light which they
afford. By means of an accurate photometer, (an instrument for measuring
the relative intensities of light,) he compared the light of Sirius with
that of the sun. He next inquired how far the sun must be removed from
us, in order to appear no brighter than Sirius. He found the distance to
be one hundred and forty-one thousand times its present distance. But
Sirius is more than two hundred thousand times as far off as the sun;
hence he inferred that, upon the lowest computation, it must actually
give out twice as much light as the sun; or that, in point of splendor,
Sirius must be at least equal to two suns. Indeed, he has rendered it
probable, that its light is equal to that of fourteen suns. There is
reason, however, to believe that the stars are actually of various
magnitudes, and that their apparent difference is not owing merely to
their different distances. Bessel estimates the quantity of matter in
the two members of a double star in the Swan, as less than half that of
the sun.

Secondly, _the fixed stars are suns_. We have already seen that they are
large bodies; that they are immensely further off than the furthest
planet; that they shine by their own light; in short, that their
appearance is, in all respects, the same as the sun would exhibit if
removed to the region of the stars. Hence we infer that they are bodies
of the same kind with the sun. We are justified, therefore, by a sound
analogy, in concluding that the stars were made for the same end as the
sun, namely, as the centres of attraction to other planetary worlds, to
which they severally dispense light and heat. Although the starry
heavens present, in a clear night, a spectacle of unrivalled grandeur
and beauty, yet it must be admitted that the chief purpose of the stars
could not have been to adorn the night, since by far the greater part of
them are invisible to the naked eye; nor as landmarks to the navigator,
for only a very small proportion of them are adapted to this purpose;
nor, finally, to influence the earth by their attractions, since their
distance renders such an effect entirely insensible. If they are suns,
and if they exert no important agencies upon our world, but are bodies
evidently adapted to the same purpose as our sun, then it is as rational
to suppose that they were made to give light and heat, as that the eye
was made for seeing and the ear for hearing. It is obvious to inquire,
next, to what they dispense these gifts, if not to planetary worlds; and
why to planetary worlds, if not for the use of percipient beings? We are
thus led, almost inevitably, to the idea of a _plurality of worlds_; and
the conclusion is forced upon us, that the spot which the Creator has
assigned to us is but a humble province in his boundless empire.

LETTER XXX.

SYSTEM OF THE WORLD

"O how unlike the complex works of man,
Heaven's easy, artless, unincumbered, plan."--_Cowper._

HAVING now explained to you, as far as I am able to do it in so short a
space, the leading phenomena of the heavenly bodies, it only remains to
inform you of the different systems of the world which have prevailed in
different ages,--a subject which will necessarily involve a sketch of
the history of astronomy.

By a system of the world, I understand an explanation of _the
arrangement of all the bodies that compose the material universe, and of
their relations to each other_. It is otherwise called the 'Mechanism of
the Heavens;' and indeed, in the system of the world, we figure to
ourselves a machine, all parts of which have a mutual dependence, and
conspire to one great end. "The machines that were first invented," says
Adam Smith, "to perform any particular movement, are always the most
complex; and succeeding artists generally discover that, with fewer
wheels, and with fewer principles of motion, than had originally been
employed, the same effects may be more easily produced. The first
systems, in the same manner, are always the most complex; and a
particular connecting chain or principle is generally thought necessary,
to unite every two seemingly disjointed appearances; but it often
happens, that _one great connecting principle_ is afterwards found to be
sufficient to bind together all the discordant phenomena that occur in a
whole species of things!" This remark is strikingly applicable to the
origin and progress of systems of astronomy. It is a remarkable fact in
the history of the human mind, that astronomy is the oldest of the
sciences, having been cultivated, with no small success, long before any
attention was paid to the causes of the common terrestrial phenomena.
The opinion has always prevailed among those who were unenlightened by
science, that very extraordinary appearances in the sky, as comets,
fiery meteors, and eclipses, are omens of the wrath of heaven. They
have, therefore, in all ages, been watched with the greatest attention:
and their appearances have been minutely recorded by the historians of
the times. The idea, moreover, that the aspects of the stars are
connected with the destinies of individuals and of empires, has been
remarkably prevalent from the earliest records of history down to a very
late period, and, indeed, still lingers among the uneducated and
credulous. This notion gave rise to ASTROLOGY,--an art which professed
to be able, by a knowledge of the varying aspects of the planets and
stars, to penetrate the veil of futurity, and to foretel approaching
irregularities of Nature herself, and the fortunes of kingdoms and of
individuals. That department of astrology which took cognizance of
extraordinary occurrences in the natural world, as tempests,
earthquakes, eclipses, and volcanoes, both to predict their approach and
to interpret their meaning, was called _natural astrology_: that which
related to the fortunes of men and of empires, _judicial astrology_.
Among many ancient nations, astrologers were held in the highest
estimation, and were kept near the persons of monarchs; and the practice
of the art constituted a lucrative profession throughout the middle
ages. Nor were the ignorant and uneducated portions of society alone the
dupes of its pretensions. Hippocrates, the 'Father of Medicine,' ranks
astrology among the most important branches of knowledge to the
physician; and Tycho Brahe, and Lord Bacon, were firm believers in its
mysteries. Astrology, fallacious as it was, must be acknowledged to have
rendered the greatest services to astronomy, by leading to the accurate
observation and diligent study of the stars.

At a period of very remote antiquity, astronomy was cultivated in China,
India, Chaldea, and Egypt. The Chaldeans were particularly
distinguished for the accuracy and extent of their astronomical
observations. Calisthenes, the Greek philosopher who accompanied
Alexander the Great in his Eastern conquests, transmitted to Aristotle a
series of observations made at Babylon nineteen centuries before the
capture of that city by Alexander; and the wise men of Babylon and the
Chaldean astrologers are referred to in the Sacred Writings. They
enjoyed a clear sky and a mild climate, and their pursuits as shepherds
favored long-continued observations; while the admiration and respect
accorded to the profession, rendered it an object of still higher
ambition.

In the seventh century before the Christian era, astronomy began to be
cultivated in Greece; and there arose successively three celebrated
astronomical schools,--the school of Miletus, the school of Crotona, and
the school of Alexandria. The first was established by Thales, six
hundred and forty years before Christ; the second, by Pythagoras, one
hundred and forty years afterwards; and the third, by the Ptolemies of
Egypt, about three hundred years before the Christian era. As Egypt and
Babylon were renowned among the most ancient nations, for their
knowledge of the sciences, long before they were cultivated in Greece,
it was the practice of the Greeks, when they aspired to the character of
philosophers and sages, to resort to these countries to imbibe wisdom at
its fountains. Thales, after extensive travels in Crete and Egypt,
returned to his native place, Miletus, a town on the coast of Asia
Minor, where he established the first school of astronomy in Greece.
Although the minds of these ancient astronomers were beclouded with much
error, yet Thales taught a few truths which do honor to his sagacity. He
held that the stars are formed of fire; that the moon receives her light
from the sun, and is invisible at her conjunctions because she is hid in
the sun's rays. He taught the sphericity of the earth, but adopted the
common error of placing it in the centre of the world. He introduced
the division of the sphere into five zones, and taught the obliquity of
the ecliptic. He was acquainted with the Saros, or sacred period of the
Chaldeans, (see page 192,) and employed it in calculating eclipses. It
was Thales that predicted the famous eclipse of the sun which terminated
the war between the Lydians and the Medes, as mentioned in a former
Letter. Indeed, Thales is universally regarded as a bright but solitary
star, glimmering through mists on the distant horizon.

To Thales succeeded, in the school of Miletus, two other astronomers of
much celebrity, Anaximander and Anaxagoras. Among many absurd things
held by Anaximander, he first taught the sublime doctrine that the
planets are inhabited, and that the stars are suns of other systems.
Anaxagoras attempted to explain all the secrets of the skies by natural
causes. His reasonings, indeed, were alloyed with many absurd notions;
but still he alone, among the astronomers, maintained the existence of
one God. His doctrines alarmed his countrymen, by their audacity and
impiety to their gods, whose prerogatives he was thought to invade; and,
to deprecate their wrath, sentence of death was pronounced on the
philosopher and all his family,--a sentence which was commuted only for
the sad alternative of perpetual banishment. The very genius of the
heathen mythology was at war with the truth. False in itself, it trained
the mind to the love of what was false in the interpretation of nature;
it arrayed itself against the simplicity of truth, and persecuted and
put to death its most ardent votaries. The religion of the Bible, on the
other hand, lends all its aid to truth in nature as well as in morals
and religion. In its very genius it inculcates and inspires the love of
truth; it suggests, by its analogies, the existence of established laws
in the system of the world; and holds out the moon and the stars, which
the Creator has ordained, as fit objects to give us exalted views of his
glory and wisdom.

Pythagoras was the founder of the celebrated school of Crotona. He was a
native of Samos, an island in the Ægean sea, and flourished about five
hundred years before the Christian era. After travelling more than
thirty years in Egypt and Chaldea, and spending several years more at
Sparta, to learn the laws and institutions of Lycurgus, he returned to
his native island to dispense the riches he had acquired to his
countrymen. But they, probably fearful of incurring the displeasure of
the gods by the freedom with which he inquired into the secrets of the
skies, gave him so unwelcome a reception, that he retired from them, in
disgust, and established his school at Crotona, on the southeastern
coast of Italy. Hither, as to an oracle, the fame of his wisdom
attracted hundreds of admiring pupils, whom he instructed in every
species of knowledge. From the visionary notions which are generally
understood to have been entertained on the subject of astronomy, by the
ancients, we are apt to imagine that they knew less than they actually
did of the truths of this science. But Pythagoras was acquainted with
many important facts in astronomy, and entertained many opinions
respecting the system of the world, which are now held to be true. Among
other things well known to Pythagoras, either derived from his own
investigations, or received from his predecessors, were the following;
and we may note them as a synopsis of the state of astronomical
knowledge at that age of the world. First, the principal
_constellations_. These had begun to be formed in the earliest ages of
the world. Several of them, bearing the same name as at present, are
mentioned in the writings of Hesiod and Homer; and the "sweet influences
of the Pleiades," and the "bands of Orion," are beautifully alluded to
in the book of Job. Secondly, _eclipses_. Pythagoras knew both the
causes of eclipses and how to predict them; not, indeed, in the accurate
manner now practised, but by means of the Saros. Thirdly, Pythagoras had
divined the true _system of the world_, holding that the sun, and not
the earth, (as was generally held by the ancients, even for many ages
after Pythagoras,) is the centre around which all the planets revolve;
and that the stars are so many suns, each the centre of a system like
our own. Among lesser things, he knew that the earth is round; that its
surface is naturally divided into five zones; and that the ecliptic is
inclined to the equator. He also held that the earth revolves daily on
its axis, and yearly around the sun; that the galaxy is an assemblage of
small stars; and that it is the same luminary, namely, Venus, that
constitutes both the morning and evening star; whereas all the ancients
before him had supposed that each was a separate planet, and accordingly
the morning star was called Lucifer, and the evening star, Hesperus. He
held, also, that the planets were inhabited, and even went so far as to
calculate the size of some of the animals in the moon. Pythagoras was
also so great an enthusiast in music, that he not only assigned to it a
conspicuous place in his system of education, but even supposed that the
heavenly bodies themselves were arranged at distances corresponding to
the intervals of the diatonic scale, and imagined them to pursue their
sublime march to notes created by their own harmonious movements, called
the 'music of the spheres;' but he maintained that this celestial
concert, though loud and grand, is not audible to the feeble organs of
man, but only to the gods. With few exceptions, however, the opinions of
Pythagoras on the system of the world were founded in truth. Yet they
were rejected by Aristotle, and by most succeeding astronomers, down to
the time of Copernicus; and in their place was substituted the doctrine
of _crystalline spheres_, first taught by Eudoxus, who lived about three
hundred and seventy years before Christ. According to this system, the
heavenly bodies are set like gems in hollow solid orbs, composed of
crystal so transparent, that no anterior orb obstructs in the least the
view of any of the orbs that lie behind it. The sun and the planets have
each its separate orb; but the fixed stars are all set in the same
grand orb; and beyond this is another still, the _primum mobile_, which
revolves daily, from east to west, and carries along with it all the
other orbs. Above the whole spreads the _grand empyrean_, or third
heavens, the abode of perpetual serenity.

To account for the planetary motions, it was supposed that each of the
planetary orbs, as well as that of the sun, has a motion of its own,
eastward, while it partakes of the common diurnal motion of the starry
sphere. Aristotle taught that these motions are effected by a tutelary
genius of each planet, residing in it, and directing its motions, as the
mind of man directs his movements.

Two hundred years after Pythagoras, arose the famous school of
Alexandria, under the Ptolemies. These were a succession of Egyptian
kings, and are not to be confounded with Ptolemy, the astronomer. By the
munificent patronage of this enlightened family, for the space of three
hundred years, beginning at the death of Alexander the Great, from whom
the eldest of the Ptolemies had received his kingdom, the school of
Alexandria concentrated in its vast library and princely halls, erected
for the accommodation of the philosophers, nearly all the science and
learning of the world. In wandering over the immense territories of
ignorance and barbarism which covered, at that time, almost the entire
face of the earth, the eye reposes upon this little spot, as upon a
verdant island in the midst of the desert. Among the choice fruits that
grew in this garden of astronomy were several of the most distinguished
ornaments of ancient science, of whom the most eminent were Hipparchus
and Ptolemy. Hipparchus is justly considered as the Newton of antiquity.
He sought his knowledge of the heavenly bodies not in the illusory
suggestions of a fervid imagination, but in the vigorous application of
an intellect of the first order. Previous to this period, celestial
observations were made chiefly with the naked eye: but Hipparchus was in
possession of instruments for measuring angles, and knew how to resolve
spherical triangles. These were great steps beyond all his predecessors.
He ascertained the length of the year within six minutes of the truth.
He discovered the eccentricity, or elliptical figure, of the solar
orbit, although he supposed the sun actually to move uniformly in a
circle, but the earth to be placed out of the centre. He also determined
the positions of the points among the stars where the earth is nearest
to the sun, and where it is most remote from it. He formed very accurate
estimates of the obliquity of the ecliptic and of the precession of the
equinoxes. He computed the exact period of the synodic revolution of the
moon, and the inclination of the lunar orbit; discovered the backward
motion of her node and of her line of apsides; and made the first
attempts to ascertain the horizontal parallaxes of the sun and moon.
Upon the appearance of a new star in the firmament, he undertook, as
already mentioned, to number the stars, and to assign to each its true
place in the heavens, in order that posterity might have the means of
judging what changes, if any, were going forward among these apparently
unalterable bodies.

Although Hipparchus is generally considered as belonging to the
Alexandrian school, yet he lived at Rhodes, and there made his
astronomical observations, about one hundred and forty years before the
Christian era. One of his treatises has come down to us; but his
principal discoveries have been transmitted through the 'Almagest' of
Ptolemy. Ptolemy flourished at Alexandria nearly three centuries after
Hipparchus, in the second century after Christ. His great work, the
'Almagest,' which has conveyed to us most that we know respecting the
astronomical knowledge of the ancients, was the universal text-book of
astronomers for fourteen centuries.

[Illustration Fig. 77.]

The name of this celebrated astronomer has also descended to us,
associated with the system of the world which prevailed from Ptolemy to
Copernicus, called the _Ptolemaic System_. The doctrines of the
Ptolemaic system did not originate with Ptolemy, but, being digested by
him out of materials furnished by various hands, it has come down to us
under the sanction of his name. According to this system, the earth is
the centre of the universe, and all the heavenly bodies daily revolve
around it, from east to west. But although this hypothesis would account
for the apparent diurnal motion of the firmament, yet it would not
account for the apparent annual motion of the sun, nor for the slow
motions of the planets from west to east. In order to explain these
phenomena, recourse was had to _deferents_ and _epicycles_,--an
explanation devised by Apollonius, one of the greatest geometers of
antiquity. He conceived that, in the circumference of a circle, having
the earth for its centre, there moves the centre of a smaller circle in
the circumference of which the planet revolves. The circle surrounding
the earth was called the deferent, while the smaller circle, whose
centre was always in the circumference of the deferent, was called the
epicycle. Thus, if E, Fig. 77, represents the earth, ABC will be the
deferent, and DFG, the epicycle; and it is obvious that the motion of a
body from west to east, in this small circle, would be alternately
direct, stationary, and retrograde, as was explained, in a previous
Letter, to be actually the case with the apparent motions of the
planets. The hypothesis, however, is inconsistent with the _phases_ of
Mercury and Venus, which, being between us and the sun, on both sides of
the epicycle, would present their dark sides towards us at both
conjunctions with the sun, whereas, at one of the conjunctions, it is
known that they exhibit their disks illuminated. It is, moreover, absurd
to speak of a geometrical centre, which has no bodily existence, moving
round the earth on the circumference of another circle. In addition to
these absurdities, the whole Ptolemaic system is encumbered with the
following difficulties: First, it is a mere hypothesis, having no
evidence in its favor except that it explains the phenomena. This
evidence is insufficient of itself, since it frequently happens that
each of two hypotheses, which are directly opposite to each other, will
explain all the known phenomena. But the Ptolemaic system does not even
do this, as it is inconsistent with the phases of Mercury and Venus, as
already observed. Secondly, now that we are acquainted with the
distances of the remoter planets, and especially the fixed stars, the
swiftness of motion, implied in a daily revolution of the starry
firmament around the earth, renders such a motion wholly incredible.
Thirdly, the centrifugal force which would be generated in these bodies,
especially in the sun, renders it impossible that they can continue to
revolve around the earth as a centre. Absurd, however, as the system of
Ptolemy was, for many centuries no great philosophic genius appeared to
expose its fallacies, and it therefore guided the faith of astronomers
of all countries down to the time of Copernicus.

After the age of Ptolemy, the science made little progress. With the
decline of Grecian liberty, the arts and sciences declined also; and the
Romans, then masters of the world, were ever more ambitious to gain
conquests over man than over matter; and they accordingly never produced
a single great astronomer. During the middle ages, the Arabians were
almost the only astronomers, and they cultivated this noble study
chiefly as subsidiary to astrology.

At length, in the fifteenth century, Copernicus arose, and after forty
years of intense study and meditation, divined the true system of the
world. You will recollect that the Copernican system maintains, 1. That
the _apparent_ diurnal motions of the heavenly bodies, from east to
west, is owing to the _real_ revolution of the earth on its own axis
from west to east; and, 2. That the sun is the centre around which the
earth and planets all revolve from west to east. It rests on the
following arguments: In the first place, _the earth revolves on its own
axis_. First, because this supposition is vastly more _simple_.
Secondly, it is agreeable to _analogy_, since all the other planets that
afford any means of determining the question, are seen to revolve on
their axes. Thirdly, the _spheroidal figure_ of the earth is the figure
of equilibrium, that results from a revolution on its axis. Fourthly,
the _diminished weight_ of bodies at the equator indicates a centrifugal
force arising from such a revolution. Fifthly, bodies let fall from a
high eminence, fall _eastward of their base_, indicating that when
further from the centre of the earth they were subject to a greater
velocity, which, in consequence of their inertia, they do not entirely
lose in descending to the lower level.

In the second place, _the planets, including the earth, revolve about
the sun_. First, the _phases_ of Mercury and Venus are precisely such,
as would result from their circulating around the sun in orbits within
that of the earth; but they are never seen in opposition, as they would
be, if they circulate around the earth. Secondly, the superior planets
do indeed revolve around the earth; but they also revolve around the
sun, as is evident from their phases, and from the known dimensions of
their orbits; and that the sun, and not the earth, is the _centre_ of
their motions, is inferred from the greater symmetry of their motions,
as referred to the sun, than as referred to the earth; and especially
from the laws of gravitation, which forbid our supposing that bodies so
much larger than the earth, as some of these bodies are, can circulate
permanently around the earth, the latter remaining all the while at
rest.

In the third place, the annual motion of _the earth_ itself is indicated
also by the most conclusive arguments. For, first, since all the
planets, with their satellites and the comets, revolve about the sun,
analogy leads us to infer the same respecting the earth and its
satellite, as those of Jupiter and Saturn, and indicates that it is a
law of the solar system that the smaller bodies revolve about the
larger. Secondly, on the supposition that the earth performs an annual
revolution around the sun, it is embraced along with the planets, in
Kepler's law, that the squares of the times are as the cubes of the
distances; otherwise, it forms an exception, and the only known
exception, to this law.

Such are the leading arguments upon which rests the Copernican system of
astronomy. They were, however, only very partially known to Copernicus
himself, as the state both of mechanical science, and of astronomical
observation, was not then sufficiently matured to show him the strength
of his own doctrine, since he knew nothing of the telescope, and nothing
of the principle of universal gravitation. The evidence of this
beautiful system being left by Copernicus in so imperfect a state, and
indeed his own reasonings in support of it being tinctured with some
errors, we need not so much wonder that Tycho Brahe, who immediately
followed Copernicus, did not give it his assent, but, influenced by
certain passages of Scripture, he still maintained, with Ptolemy, that
the earth is in the centre of the universe; and he accounted for the
diurnal motions in the same manner as Ptolemy had done, namely, by an
actual revolution of the whole host of heaven around the earth every
twenty-four hours. But he rejected the scheme of deferents and
epicycles, and held that the moon revolves about the earth as the centre
of her motions; but that the sun and not the earth is the centre of the
planetary motions; and that the sun, accompanied by the planets, moves
around the earth once a year, somewhat in the manner in which we now
conceive of Jupiter and his satellites as revolving around the sun. This
system is liable to most of the objections that lie against the
Ptolemaic system, with the disadvantage of being more complex.

Kepler and Galileo, however, as appeared in the sketch of their lives,
embraced the theory of Copernicus with great avidity, and all their
labors contributed to swell the evidence of its truth. When we see with
what immense labor and difficulty the disciples of Ptolemy sought to
reconcile every new phenomenon of the heavens with their system, and
then see how easily and naturally all the successive discoveries of
Galileo and Kepler fall in with the theory of Copernicus, we feel the
full force of those beautiful lines of Cowper which I have chosen for
the motto of this Letter.

Newton received the torch of truth from Galileo, and transmitted it to
his successors, with its light enlarged and purified; and since that
period, every new discovery, whether the fruit of refined instrumental
observation or of profound mathematical analysis, has only added lustre
to the glory of Copernicus.

With Newton commenced a new and wonderful era in astronomy,
distinguished above all others, not merely for the production of the
greatest of men, but also for the establishment of those most important
auxiliaries to our science, the Royal Society of London, the Academy of
Sciences at Paris, and the Observatory of Greenwich. I may add the
commencement of the Transactions of the Royal Society, and the Memoirs
of the Academy of Sciences, which have been continued to the present
time,--both precious storehouses of astronomical riches. The Observatory
of Greenwich, moreover, has been under the direction of an extraordinary
succession of great astronomers. Their names are Flamstead, Halley,
Bradley, Maskeleyne, Pond, and Airy,--the last being still at his post,
and worthy of continuing a line so truly illustrious. The observations
accumulated at this celebrated Observatory are so numerous, and so much
superior to those of any other institution in the world, that it has
been said that astronomy would suffer little, if all other contemporary
observations of the same kind were annihilated. Sir William Herschel,
however, labored chiefly in a different sphere. The Astronomers Royal
devoted themselves not so much to the discovery of new objects among
the heavenly bodies, as to the exact determination of the places of the
bodies already known, and to the developement of new laws or facts among
the celestial motions. But Herschel, having constructed telescopes of
far greater reach than any ever used before, employed them to sound new
and untried depths in the profundities of space. We have already seen
what interesting and amazing discoveries he made of double stars,
clusters, and nebulæ.

The English have done most for astronomy in observation and discovery;
but the French and Germans, in developing, by the most profound
mathematical investigation, the great laws of physical astronomy.

It only remains to inquire, whether the Copernican system is now to be
regarded as a full exposition of the 'Mechanism of the Heavens,' or
whether there subsist higher orders of relations between the fixed stars
themselves.

The revolutions of the _binary stars_ afford conclusive evidence of at
least subordinate systems of suns, governed by the same laws as those
which regulate the motions of the solar system. The _nebulæ_ also
compose peculiar systems, in which the members are evidently bound
together by some common relation.

In these marks of organization,--of stars associated together in
clusters; of sun revolving around sun; and of nebulæ disposed in regular
figures,--we recognise different members of some grand system, links in
one great chain that binds together all parts of the universe; as we see
Jupiter and his satellites combined in one subordinate system, and
Saturn and his satellites in another,--each a vast kingdom, and both
uniting with a number of other individual parts, to compose an empire
still more vast.

This fact being now established, that the stars are immense bodies, like
the sun, and that they are subject to the laws of gravitation, we cannot
conceive how they can be preserved from falling into final disorder and
ruin, unless they move in harmonious concert, like the members of the
solar system. Otherwise, those that are situated on the confines of
creation, being retained by no forces from without, while they are
subject to the attraction of all the bodies within, must leave their
stations, and move inward with accelerated velocity; and thus all the
bodies in the universe would at length fall together in the common
centre of gravity. The immense distance at which the stars are placed
from each other would indeed delay such a catastrophe; but this must be
the ultimate tendency of the material world, unless sustained in one
harmonious system by nicely-adjusted motions. To leave entirely out of
view our confidence in the wisdom and preserving goodness of the
Creator, and reasoning merely from what we know of the stability of the
solar system, we should be justified in inferring, that other worlds are
not subject to forces which operate only to hasten their decay, and to
involve them in final ruin.

We conclude, therefore, that the material universe is one great system;
that the combination of planets with their satellites constitutes the
first or lowest order of worlds; that next to these, planets are linked
to suns; that these are bound to other suns, composing a still higher
order in the scale of being; and finally, that all the different systems
of worlds move around their common centre of gravity.

LETTER XXXI.

NATURAL THEOLOGY.

----"Philosophy, baptized
In the pure fountain of Eternal Love,
Has eyes indeed; and, viewing all she sees
As meant to indicate a God to man,
Gives Him the praise, and forfeits not her own."--_Cowper._

I INTENDED, my dear Friend, to comply with your request "that I would
discuss the arguments which astronomy affords to natural theology;" but
these Letters have been already extended so much further than I
anticipated, that I shall conclude with suggesting a few of those moral
and religious reflections, which ought always to follow in the train of
such a survey of the heavenly bodies as we have now taken.

Although there is evidence enough in the structure, arrangement, and
laws, which prevail among the heavenly bodies, to prove the _existence_
of God, yet I think there are many subordinate parts of His works far
better adapted to this purpose than these, being more fully within our
comprehension. It was intended, no doubt, that the evidence of His being
should be accessible to all His creatures, and should not depend on a
kind of knowledge possessed by comparatively few. The mechanism of the
eye is probably not more perfect than that of the universe; but we can
analyze it better, and more fully understand the design of each part.
But the existence of God being once proved, and it being admitted that
He is the Creator and Governor of the world, then the discoveries of
astronomy are admirably adapted to perform just that office in relation
to the Great First Cause, which is assigned to them in the Bible,
namely, "to declare the glory of God, and to show His handiwork." In
other words, the discoveries of astronomy are peculiarly fitted,--more
so, perhaps, than any other department of creation,--to exhibit the
unity, power, and wisdom, of the Creator.

The most modern discoveries have multiplied the proofs of the _unity_ of
God. It has usually been offered as sufficient evidence of the truth of
this doctrine, that the laws of Nature are found to be uniform when
applied to the utmost bounds of the _solar system_; that the law of
gravitation controls alike the motions of Mercury, and those of Uranus;
and that its operation is one and the same upon the moon and upon the
satellites of Saturn. It was, however, impossible, until recently, to
predicate the same uniformity in the great laws of the universe
respecting the starry worlds, except by a feeble analogy. However
improbable, it was still possible, that in these distant worlds other
laws might prevail, and other Lords exercise dominion. But the discovery
of the revolutions of the binary stars, in exact accordance with the law
of gravitation, not merely in a single instance, but in many instances,
in all cases, indeed, wherever those revolutions have advanced so far as
to determine their law of action, gives us demonstration, instead of
analogy, of the prevalence of the same law among the other systems as
that which rules in ours.

The marks of a still higher organization in the structure of clusters
and nebulæ, all bearing that same characteristic union of resemblance
and variety which belongs to all the other works of creation that fall
under our notice, speak loudly of one, and only one, grand design. Every
new discovery of the telescope, therefore, has added new proofs to the
great truth that God is one: nor, so far as I know, has a single fact
appeared, that is not entirely consonant with it. Light, moreover, which
brings us intelligence, and, in most cases, the only intelligence we
have, of these remote orbs, testifies to the same truth, being similar
in its properties and uniform in its motions, from whatever star it
emanates.

In displays of the _power_ of Jehovah, nothing can compare with the
starry heavens. The magnitudes, distances, and velocities, of the
heavenly bodies are so much beyond every thing of this kind which
belongs to things around us, from which we borrowed our first ideas of
these qualities, that we can scarcely avoid looking with incredulity at
the numerical results to which the unerring principles of mathematics
have conducted us. And when we attempt to apply our measures to the
fixed stars, and especially to the nebulæ, the result is absolutely
overwhelming: the mind refuses its aid in our attempts to grasp the
great ideas. Nor less conspicuous, among the phenomena of the heavenly
bodies, is the _wisdom_ of the Creator. In the first place, this
attribute is every where exhibited _in the happy adaptation of means to
their ends_. No principle can be imagined more simple, and at the same
time more effectual to answer the purposes which it serves, than
gravitation. No position can be given to the sun and planets so fitted,
as far as we can judge, to fulfil their mutual relations, as that which
the Creator has given them. I say, as far as we can judge; for we find
this to be the case in respect to our own planet and its attendant
satellite, and hence have reason to infer that the same is the case in
the other planets, evidently holding, as they do, a similar relation to
the sun. Thus the position of the earth at just such a distance from the
sun as suits the nature of its animal and vegetable kingdoms, and
confining the range of solar heat, vast as it might easily become,
within such narrow bounds; the inclination of the earth's axis to the
plane of its orbit, so as to produce the agreeable vicissitudes of the
seasons, and increase the varieties of animal and vegetable life, still
confining the degree of inclination so exactly within the bounds of
safety, that, were it much to transcend its present limits, the changes
of temperature of the different seasons would be too sudden and violent
for the existence of either animals or vegetables; the revolution of the
earth on its axis, so happily dividing time into hours of business and
of repose; the adaptation of the moon to the earth, so as to afford to
us her greatest amount of light just at the times when it is needed
most, and giving to the moon just such a quantity of matter, and placing
her at just such a distance from the earth, as serves to raise a tide
productive of every conceivable advantage, without the evils which would
result from a stagnation of the waters on the one hand, or from their
overflow on the other;--these are a few examples of the wisdom displayed
in the mutual relations instituted between the sun, the earth, and the
moon.

In the second place, similar marks of wisdom are exhibited in _the many
useful and important purposes_ _which the same thing is made to serve_.
Thus the sun is at once the great regulator of the planetary motions,
and the fountain of light and heat. The moon both gives light by night
and raises the tides. Or, if we would follow out this principle where
its operations are more within our comprehension, we may instance the
_atmosphere_. When man constructs an instrument, he deems it sufficient
if it fulfils one single purpose as the watch, to tell the hour of the
day, or the telescope, to enable him to see distant objects; and had a
being like ourselves made the atmosphere, he would have thought it
enough to have created a medium so essential to animal life, that to
live is to breathe, and to cease to breathe is to die. But beside this,
the atmosphere has manifold uses, each entirely distinct from all the
others. It conveys to plants, as well as animals, their nourishment and
life; it tempers the heat of Summer with its breezes; it binds down all
fluids, and prevents their passing into the state of vapor; it supports
the clouds, distils the dew, and waters the earth with showers; it
multiplies the light of the sun, and diffuses it over earth and sky; it
feeds our fires, turns our machines, wafts our ships, and conveys to the
ear ail the sentiments of language, and all the melodies of music.

In the third place, the wisdom of the Creator is strikingly manifested
in the provision he has made for the _stability of the universe_. The
perturbations occasioned by the motions of the planets, from their
action on each other, are very numerous, since every body in the system
exerts an attraction on every other, in conformity with the law of
universal gravitation. Venus and Mercury, approaching, as they do at
times, comparatively near to the earth, sensibly disturb its motions;
and the satellites of the remoter planets greatly disturb each other's
movements. Nor was it possible to endow this principle with the
properties it has, and make it operate as it does in regulating the
motions of the world, without involving such an incident. On this
subject, Professor Whewell, in his excellent work composing one of the
Bridgewater Treatises, remarks: "The derangement which the planets
produce in the motion of one of their number will be very small, in the
course of one revolution; but this gives us no security that the
derangement may not become very large, in the course of many
revolutions. The cause acts perpetually, and it has the whole extent of
time to work in. Is it not easily conceivable, then, that, in the lapse
of ages, the derangements of the motions of the planets may accumulate,
the orbits may change their form, and their mutual distances may be much
increased or diminished? Is it not possible that these changes may go on
without limit, and end in the complete subversion and ruin of the
system? If, for instance, the result of this mutual gravitation should
be to increase considerably the eccentricity of the earth's orbit, or to
make the moon approach continually nearer and nearer to the earth, at
every revolution, it is easy to see that, in the one case, our year
would change its character, producing a far greater irregularity in the
distribution of the solar heat; in the other, our satellite must fall to
the earth, occasioning a dreadful catastrophe. If the positions of the
planetary orbits, with respect to that of the earth, were to change
much, the planets might sometimes come very near us, and thus increase
the effect of their attraction beyond calculable limits. Under such
circumstances, 'we might have years of unequal length, and seasons of
capricious temperature; planets and moons, of portentous size and
aspect, glaring and disappearing at uncertain intervals; tides, like
deluges, sweeping over whole continents; and perhaps the collision of
two of the planets, and the consequent destruction of all organization
on both of them.' The fact really is, that changes are taking place in
the motions of the heavenly bodies, which have gone on progressively,
from the first dawn of science. The eccentricity of the earth's orbit
has been diminishing from the earliest observations to our times. The
moon has been moving quicker from the time of the first recorded
eclipses, and is now in advance, by about four times her own breadth,
of what her own place would have been, if it had not been affected by
this acceleration. The obliquity of the ecliptic, also, is in a state of
diminution, and is now about two fifths of a degree less than it was in
the time of Aristotle."

But amid so many seeming causes of irregularity and ruin, it is worthy
of a grateful notice, that effectual provision is made for the
_stability of the solar system_. The full confirmation of this fact is
among the grand results of physical astronomy. "Newton did not undertake
to demonstrate either the stability or instability of the system. The
decision of this point required a great number of preparatory steps and
simplifications, and such progress in the invention and improvement of
mathematical methods, as occupied the best mathematicians of Europe for
the greater part of the last century. Towards the end of that time, it
was shown by La Grange and La Place, that the arrangements of the solar
system are stable; that, in the long run, the orbits and motions remain
unchanged; and that the changes in the orbits, which take place in
shorter periods, never transgress certain very moderate limits. Each
orbit undergoes deviations on this side and on that side of its average
state; but these deviations are never very great, and it finally
recovers from them, so that the average is preserved. The planets
produce perpetual perturbations in each other's motions; but these
perturbations are not indefinitely progressive, but periodical, reaching
a maximum value, and then diminishing. The periods which this
restoration requires are, for the most part, enormous,--not less than
thousands, and in some instances, millions, of years. Indeed, some of
these apparent derangements have been going on in the same direction
from the creation of the world. But the restoration is in the sequel as
complete as the derangement; and in the mean time the disturbance never
attains a sufficient amount seriously to affect the stability of the
system. 'I have succeeded in demonstrating,' says La Place, 'that,
whatever be the masses of the planets, in consequence of the fact that
they all move in the same direction, in orbits of small eccentricity,
and but slightly inclined to each other, their secular irregularities
are periodical, and included within narrow limits; so that the planetary
system will only oscillate about a mean state, and will never deviate
from it, except by a very small quantity. The ellipses of the planets
have been and always will be nearly circular. The ecliptic will never
coincide with the equator; and the entire extent of the variation, in
its inclination, cannot exceed three degrees.'"

To these observations of La Place, Professor Whewell adds the following,
on the importance, to the stability of the solar system, of the fact
that those planets which have _great masses_ have orbits of _small
eccentricity_. "The planets Mercury and Mars, which have much the
largest eccentricity among the old planets, are those of which the
masses are much the smallest. The mass of Jupiter is more than two
thousand times that of either of these planets. If the orbit of Jupiter
were as eccentric as that of Mercury, all the security for the stability
of the system, which analysis has yet pointed out, would disappear. The
earth and the smaller planets might, by the near approach of Jupiter at
his perihelion, change their nearly circular orbits into very long
ellipses, and thus might fall into the sun, or fly off into remoter
space. It is further remarkable, that in the newly-discovered planets,
of which the orbits are still more eccentric than that of Mercury, the
masses are still smaller, so that the same provision is established in
this case, also."

With this hasty glance at the unity, power, and wisdom, of the Creator,
as manifested in the greatest of His works, I close. I hope enough has
been said to vindicate the sentiment that called 'Devotion, daughter of
Astronomy!' I do not pretend that this, or any other science, is
adequate of itself to purify the heart, or to raise it to its Maker; but
I fully believe that, when the heart is already under the power of
religion, there is something in the frequent and habitual contemplation
of the heavenly bodies under all the lights of modern astronomy, very
favorable to devotional feelings, inspiring, as it does, humility, in
unison with an exalted sentiment of grateful adoration.

LETTER XXXII.

RECENT DISCOVERIES.

"All are but parts of one stupendous whole."--_Pope._

WITHIN a few years, astronomy has been enriched with a number of
valuable discoveries, of which I will endeavor to give you a summary
account in this letter. The heavens have been explored with far more
powerful telescopes than before; instrumental measurements have been
carried to an astonishing degree of accuracy; numerous additions have
been made to the list of small planets or asteroids; a comet has
appeared of extraordinary splendor, remarkable, above all others, for
its near approach to the sun; the distances of several of the fixed
stars, an element long sought for in vain, have been determined; a large
planet, composing in itself a magnificent world, has been added to the
solar system, at such a distance from the central luminary as nearly to
double the supposed dimensions of that system; various nebulæ, before
held to be irresolvable, have been resolved into stars; and a new
satellite has been added to Saturn.

IMPROVEMENTS IN THE TELESCOPE.--Herschel's forty-feet telescope, of
which I gave an account in my fourth letter (see page 36), remained for
half a century unequalled in magnitude and power; but in 1842, Lord
Rosse, an Irish nobleman, commenced a telescope on a scale still more
gigantic. Like Herschel's, it was a _reflector_, the image being formed
by a concave mirror. This was six feet in diameter, and weighed three
tons; and the tube was fifty feet in length. The entire cost of the
instrument was sixty thousand dollars. Its reflecting surface is nearly
twice as great as the great Herschelian, and consequently it greatly
exceeds all instruments hitherto constructed in the _amount of light_
which it collects and transmits to the eye; and this adapts it
peculiarly to viewing those objects, as nebulæ, whose light is
exceedingly faint. Accordingly, it has revealed to us new wonders in
this curious department of astronomy. Some idea of the great dimensions
of the _Leviathan_ telescope (as this instrument has been called) may be
formed when it is said that the Dean of Ely, a full-sized man, walked
through the tube from one end to the other, with an umbrella over his
head.

But still greater advances have been made in refracting than in
reflecting telescopes. Such was the difficulty of obtaining large pieces
of glass which are free from impurities, and such the liability of large
lenses to form obscure and colored images, that it was formerly supposed
impossible to make a refracting telescope larger in diameter than five
or six inches; but their size has been increased from one step to
another, until they are now made more than fifteen inches in diameter;
and so completely have all the difficulties arising from the
imperfections of glass, and from optical defects inherent in lenses,
been surmounted, that the great telescopes of Pulkova, at St.
Petersburgh, and of Harvard University (the two finest refractors in the
world) are considered among the most perfect productions of the arts. A
lens of only 15 inches in diameter seems, indeed, diminutive when
compared with a concave reflector of six feet; but for most purposes of
the astronomer, the Pulkova and Cambridge instruments are more useful
than such great reflectors as those of Herschel and Rosse. If there is
any particular in which these are more effective, it is in observations
on the faintest nebulæ, where it is necessary to collect and convey to
the eye the greatest possible beam of light.

INSTRUMENTAL MEASUREMENTS.--When astronomical instruments were first
employed to measure the angular distance between two points on the
celestial sphere, it was not attempted to measure spaces smaller than
ten minutes--a space equal to the third part of the breadth of the full
moon. Tycho Brahe, however, carried his measures to sixty times that
degree of minuteness, having devised means of determining angles no
larger than ten seconds, or the one hundred and eightieth part of the
breadth of the lunar disk. For many years past, astronomers have carried
these measures to single seconds, or have determined spaces no greater
than the eighteen hundredth part of the diameter of the moon. This is
considered the smallest arc which can be accurately measured directly on
the limb of an instrument; but _differences_ between spaces may be
estimated to a far greater degree of accuracy than this, even to the
hundredth part of a second--a space less than that intercepted by a
spider's web held before the eye.

DISCOVERY OF NEW PLANETS.--In my twenty-third letter (see page 286), I
gave an account of the small planets called asteroids, which lie between
the orbits of Mars and Jupiter. When that letter was written, no longer
ago than 1840, only four of those bodies had been discovered, namely,
Ceres, Pallas, Juno, and Vesta. Within a few years past, nineteen more
have been added, making the number of the asteroids known at present
twenty-three, and every year adds one or more to the list.[17] The idea
first suggested by Olbers, one of the earliest discoverers of asteroids,
that they are fragments of a large single planet once revolving between
Mars and Jupiter, has gained credit since the discovery of so many
additional bodies of the same class, all, like the former, exceedingly
small and irregular in their motions, although there are still great
difficulties in tracing them to a common origin.

GREAT COMET OF 1843.--This is the most wonderful body that has appeared
in the heavens in modern times; first, on account of its appearing, when
first seen, in the broad light of noonday; and, secondly, on account of
its approaching so near the sun as almost to graze his surface. It was
first discovered, in New England, on the 28th of February, a little
eastward of the sun, shining like a white cloud illuminated by the solar
rays. It arrested the attention of many individuals from half past seven
in the morning until three o'clock in the afternoon, when the sky became
obscured by clouds. In Mexico, it was observed from nine in the morning
until sunset. At a single station in South America, it was said to have
been seen on the 27th of February, almost in contact with the sun. Early
in March, it had receded so far to the eastward of that body as to be
visible in the southwest after sunset, throwing upward a long train,
which increased in length from night to night until it covered a space
of 40 degrees. Its position may be seen on a celestial globe adjusted to
the latitude of New Haven (41° 18´) for the 20th of March, by tracing a
line, or, rather, a broad band proceeding from the place of the sun
towards the bright star Sirius, in the south, between the ears of the
Hare and the feet of Orion.

The comet passed its perihelion on the 27th of February, at which time
it almost came in contact with the sun. To prevent its falling into the
sun it was endued with a prodigious velocity; a velocity so great that,
had it continued at the same rate as at the instant of perihelion
passage, it would have whirled round the sun in two hours and a half. It
did, in fact, complete more than half its revolution around the sun in
that short period, and it made more than three quarters of its circuit
around the sun in one day. Its velocity, when nearest the sun, exceeded
a million of miles per hour, and its tail, at its greatest elongation,
was one hundred and eight millions of miles; a length more than
sufficient to have reached from the sun to the earth. Its heat was
estimated to be 47,000 times greater than that received by the earth
from a vertical sun, and consequently it was more intense than that
produced by the most powerful blowpipes, and sufficient to melt like wax
the most infusible bodies. No doubt, when in the vicinity of the sun,
the solid matter of the comet was first melted and then converted into
vapor, which itself became red hot, or, more properly speaking, _white
hot_. Much discussion has arisen among astronomers respecting the
periodic time of this comet. Its most probable period is about 175
years.

DISTANCES OF THE STARS.--I have already mentioned (page 389) that the
distance of at least one of the fixed stars has at length been
determined, although at so great a distance that its annual parallax is
only about one third of a second, implying a distance from the sun of
nearly sixty millions of millions of miles. Of a distance so immense the
mind can form no adequate conception. The most successful effort towards
it is made by gradual and successive approximations. Let us, therefore,
take the motion of a rail-way car as the most rapid with which we are
familiar, and apply it first to the planetary spaces, and then to the
vast interval that separates these nether worlds from the fixed stars. A
rail-way car, travelling constantly night and day at the rate of twenty
miles per hour, would make 480 miles per day. At this rate, to travel
around the earth on a great circle would require about 50 days, and 500
days to reach the moon. If we took our departure from the sun, and
journeyed night and day, we should reach Mercury in a little more than
200 years, Venus in nearly 400, and the Earth in 547 years; but to reach
Neptune, the outermost planet, would require 16,000 years. Great as
appear the dimensions of the solar system, when we imagine ourselves
thus borne along from world to world, yet this space is small compared
with that which separates us from the fixed stars; for to reach 61 Cygni
it would take 324,000,000 years. But this is believed, for certain
satisfactory reasons, to be one of the nearest of the stars. Several
other stars whose parallax has been determined are at a much greater
distance than 61 Cygni. The pole star is five times as far off; and the
greater part of the stars are at distances inconceivably more remote.
Such, especially, are those which compose the faintest nebulæ.

DISCOVERY OF THE PLANET NEPTUNE.--From the earliest ages down to the
year 1781, the solar system was supposed to terminate with the planet
Saturn, at the distance of nine hundred millions of miles from the sun;
but the discovery of Uranus added another world, and doubled the
dimensions of the solar system. It seemed improbable that any more
planets should exist at a distance still more remote, since such a body
could hardly receive any of the vivifying influences of the central
luminary. Still, certain irregularities to which the Uranus was subject,
led to the suspicion that there exists a planet beyond it, which, by its
attractions, caused these irregularities. Impressed with this belief,
two young astronomers of great genius, Le Verrier, of France, and Adams,
of England, applied themselves to the task of finding the hidden planet.
The direction in which the disturbed body was moved afforded some clue
to the part of the heavens where the disturbing body lay concealed; the
kind of action it excited at different times indicated that it was
beyond Uranus, and not this side of that planet; and the magnitude of
the forces it exerted gave some intimation of its size and mass. The law
of distances from the sun which the superior planets observe (Saturn
being nearly twice the distance of Jupiter, and Uranus twice that of
Saturn), led both these astronomers to assume that the body sought was
nearly double the distance of Uranus from the sun. With these few and
imperfect data, as so many leading-strings proceeding from the planet
Uranus, they felt their way into the abysses of space by the aid of two
sure guides--the law of gravitation and the higher geometry. Both
astronomers arrived at nearly the same results, although they wrought
independently of each other, and each, indeed, without the knowledge of
the other. Le Verrier was the first to make public his conclusions,
which he communicated to the French Academy at their sitting, August 31,
1846. They saw that there existed, at nearly double the distance of
Uranus from the sun, a planet larger than that body; that it lay near a
certain star seen at that season in the southwest, in the evening sky;
that, on account of its immense distance, it was invisible to the naked
eye, and could be distinctly seen with a perceptible disk only by the
most powerful telescopes; being no brighter than a star of the ninth
magnitude, and subtending an angle of only three seconds. Le Verrier
communicated these results to Dr. Galle, of Berlin, with the request
that he would search for the stranger with his powerful telescope,
pointing out the exact spot in the heavens where it would be found. On
the same evening, Dr. Galle directed his instrument to that part of the
heavens, and immediately the planet presented itself to view, within one
degree of the very spot assigned to it by Le Verrier. Subsequent
investigations have shown that its apparent size is within half a second
of that which the same sagacious mind foresaw, and that its diameter is
nearly equal to that of Uranus, being 31,000, while Uranus is 35,000
miles.[18] The distance from the sun is less than was predicted, being
only about 3000, instead of 3600 millions of miles; and its periodic
time is 164-1/2, instead of 217 years, as was supposed by Le Verrier.
One satellite only has yet been discovered, and this was first seen by
Professor Bond with the great telescope of Harvard University.

RECENT TELESCOPIC DISCOVERIES.--The great reflecting telescope of Lord
Rosse, and the powerful refracting telescopes of Pulkova and Cambridge,
have opened new fields of discovery to the delighted astronomer. A new
satellite has been added to Saturn, first revealed to the Cambridge
instrument, making the entire number of moons that adorn the nocturnal
sky of that remarkable planet no less than eight. Still more wonderful
things have been disclosed among the remotest _Nebulæ_. A number of
these objects before placed among the irresolvable nebulæ, and supposed
to consist not of stars, but of mere nebulous matter, have been resolved
into stars; others, of which we before saw only a part, have revealed
themselves under new and strange forms, one resembling an animal with
huge branching arms, and hence called the _crab_ nebula; another
imitating a scroll or vortex, and called the _whirlpool_ nebula; and
other figures, which to ordinary telescopes appear only as dim specks on
the confines of creation, are presented to these wonderful instruments
as glorious firmaments of stars.

In the year 1833, Sir John Herschel left England for the Cape of Good
Hope, furnished with powerful instruments for observing the stars and
nebulæ of the southern hemisphere, which had never been examined in a
manner suited to disclose their full glories. This great astronomer and
benefactor to science devoted five years of the most assiduous toil in
observing and delineating the astronomical objects of that portion of
the heavens. He had before extended the catalogue of nebulæ begun by his
illustrious father, Sir William Herschel, to the number of 2307; and
beginning at that point, he swelled the number, by his labors at the
Cape of Good Hope, to 4015. He extended also the list of double stars
from 3346 to 5449, and showed that the luminous spots near the South
Pole, known to sailors by the name of the "Magellan Clouds," consist of
an assemblage of several hundred brilliant nebulæ.

The United States have contributed their full share to the recent
progress of astronomy. Powerful telescopes have been imported, made by
the first European artists, and numerous others, of scarcely inferior
workmanship and power, have been produced by artists of our own. The
American astronomers have also been the first to bring the electric
telegraph into use in astronomical observations; electric clocks have
been so constructed as to beat simultaneously at places distant many
hundred miles from each other, and thus to furnish means of determining
the difference of longitude between places with an astonishing degree of
accuracy; and facilities for recording observations on the stars have
been devised which render the work vastly more rapid as well as more
accurate than before. Indeed, the inventive genius for which Americans
have been distinguished in all the useful arts seems now destined to be
equally conspicuous in promoting the researches of science.

FOOTNOTES:

[17] The names of all the asteroids known at present are as follows:

1. Ceres. 9. Metis. 17. Psyche.
2. Pallas. 10. Hygeia. 18. Melpomene.
3. Juno. 11. Parthenope. 19. Fortuna.
4. Vesta. 12. Victoria. 20. Massalia.
5. Astræa. 13. Egeria. 21. Lutetia.
6. Hebe. 14. Irene. 22. Calliope.
7. Iris. 15. Eunomia. 23. Un-named.
8. Flora. 16. Thetis.

[18] Sir John Herschel, however, states its diameter at 41,500 miles

INDEX.

Alamak, 371

Aldebaran, 369

Alexandrian school, 394

Algenib, 371

Algol, 371

Alioth, 374

Almagest, 14

Altair, 373

Altitude, 20

Amplitude, 20

Anaxagoras, 395

Anaximander, 395

Andromeda, 371

Antares, 370

Antinous, 373

Apogee, 187

Apsides, 188

Aquarius, 371

Aquila, 373

Archimedes, 136

Arcturus, 372

Aries, 369

Aristotle, 136

Astrology, 393

Astronomers royal, 48, 404

Astronomical clock, 51

Astronomical tables, 190

Astronomy, 17
history of, 14, 392

Atmosphere, 100, 410

Attraction, 135

Auriga, 371

Axis of the Earth, 21

Azimuth, 20

Bacon, 16, 136

Base line, 76

Base of verification, 79

Bellatrix, 375

Betalgeus, 375

Bissextile, 64

Bootes, 372

Bouguer, 74

Bowditch, 148

Brahean system, 403

Cæsar, Julius, 64

Calendar, Grecian, 67
Gregorian, 65

Cancer, 369

Canis Major, 375

Canis Minor, 375

Capella, 372

Capricorn, 370

Cassiopeia, 374

Catalogues of the stars, 367

Central forces, 130

Cepheus, 374

Ceres, 287

Cetus, 374

Chronology, 157

Chronometers, 210

Circles, great and small, 19
of diurnal revolution, 81
of perpetual apparition, 85
of perpetual occultation, 85
vertical, 20

Clusters, 376

Colures, 23

Coma Berenices, 372

Comet, Biela's, 339
Encke's, 340
Halley's, 323

Comets, 313
brightness of, 315

Comets, distances of, 317
light of, 317
magnitude of, 315
mass of, 318
motions of, 320
number of, 315
periods of, 316
perturbations of, 319
structure of, 314
tails of, 317

Complement, 18

Conjunction, 200

Constellations, 366

Copernican system, 256, 401

Copernicus, 14, 255

Cor Caroli, 372

Cor Hydræ, 375

Corona Borealis, 372

Corvus, 375

Crotona, 394

Crystalline spheres, 397

Cygnus, 374

Day, astronomical, 61
sidereal, 60
solar, 60

Days of the week, 68

Declination, 24

Deferents, 400

Denebola, 370

Distances of the heavenly bodies, how measured, 94

Distances of the stars, 387

Dolphin, 373

Double stars, 381

Draco, 374

Earth, diameter of the, 78
ellipticity of the, 78
figure of the, 69
motion of the, 126
orbit of the, 149

Eclipses, annular, 204
calculation of, 201
of the moon, 195
of the sun, 203

Ecliptic, 22

Epicycles, 400

Equation of time, 61

Equations, periodical, 193
secular, 193
tabular, 190

Equator, 21

Equinoxes, 22
precession of the, 154

Eudoxus, 397

Fomalhaut, 371

Fraunhofer, 37

Galaxy, 379

Galileo, 15
abjuration of, 272
condemnation of, 266
life of, 258
persecutions of, 265

Gemini, 369

Gemma, 372

Globes, artificial, 25

Gravitation, universal, 145

Gravity, terrestrial, 134

Hercules, 372

Herschel, Sir Wm., 36, 105, 383

Hesperus, 397

Hipparchus, 398

Horizon, rational, 20
sensible, 20

Hour-circles, 21

Huyghens, 72

Inductive system, 137

Inquisition, 138

Instruments, astronomical, 29

Juno, 288

Jupiter, 247
belts of, 248
diameter of, 247
distance of, 247
eclipses of, 250
magnitude of, 247
satellites of, 250
scenery of, 247
telescopic view of, 247

Kepler, 300

Kepler's laws, 296

Latitude, 22
how found, 210

Laws of motion, 126
terrestrial gravity, 139

Leap year, 64

Leo, 370

Leo Minor, 372

Libra, 370

Librations of the moon, 179

Light, velocity of, how measured, 252

Longitude, celestial, 24
terrestrial, 22
its importance, 208
how found, 210
by chronometers, 210
by eclipses, 212
by Jupiter's satellites, 251
by lunar method, 213

Lucifer, 397

Lynx, 372

Magnitudes, how measured, 94

Magellan clouds, 378

Mars, 245
changes of, 245
distance of, 245
revolutions of, 246

Mecanique Celeste, 148

Mercury, 230
conjunctions of, 231
diurnal revolution of, 235
phases of, 234
sidereal revolut'n of, 231
synodical revolut'n of, 231
transits of, 237

Meridian, 20

Meteoric showers, 346
origin of, 350

Meteoric stones, 290

Metonic cycle, 192

Miletus, school of, 394

Milky Way, 379

Mira, 375

Mirach, 371

Mizar, 374

Month, sidereal, 173
synodical, 173

Moon, 157
atmosphere of the, 167
cusps of the, 174
diameter of the, 158
distance of the, 158
eclipses of the, 195
harvest, 177
irregularities of the, 186
librations of the, 179
light of the, 158
mountains in the, 159
nodes of the, 173
phases of the, 174
revolutions of the, 178-182
scenery of the, 163
telescopic appearance of the, 158
volcanoes in the, 166
volume of the, 158

Motion, laws of, 126

Motions of the planets, 291

Mural circle, 54

Nadir, 20

Nature of the stars, 390

Nebulæ, 377

New planets, 286
distances of, 288
origin of, 289
periods of, 288
size of, 289

New style, 66

Newton, 16, 143

Oblique sphere, 84

Obliquity of the ecliptic, 115
effect of, on the Seasons, 123
how found, 117

Observatory, 42
Greenwich, 42-48
Tycho's, 42

Old style, 66

Ophiucus, 372

Opposition, 200

Orion, 375

Orreries, 112, 292

Pallas, 287

Parallactic arc, 91

Parallax, 90, 389
annual, 387
horizontal, 93
how found, 94

Parallel sphere, 84

Parallels of latitude, 24

Pegasus, 373

Pendulum, 79

Perigee, 187

Periodical inequalities, 193

Perseus, 371

Pisces, 371

Piscis Australis, 371

Planets, 225
distances of, 228
inferior, 227
magnitudes of, 229
periods, 229
superior, 243

Pleiades, 369

Pointers, 374

Polar distance, 22

Polaris, 373

Pole, 19
of the earth, 21

Pollux, 369

Power of the Deity, 408

Præsepe, 369

Precession, 155

Prime vertical, 20

Primum mobile, 398

Principia, 147

Procyon, 375

Projection of the sphere, 27

Proper motions of the stars, 384

Ptolemaic system, 399

Ptolemy, 398

Pythagoras, 394

Quadrant, 18

Radius, 17

Refraction, 95

Regulus, 370

Resolution of motion, 132

Resultant, 132

Revolution, annual, 111
diurnal, 111

Rigel, 375

Right ascension, 23

Right sphere, 83

Sagittarius, 370

Saros, 192

Saturn, 274
diameter of, 274
ring of, 275
satellites of, 282
scenery of, 283

Scorpio, 370

Seasons, 119

Secondary, 19

Secular inequalities, 193

Serpent, 373

Sextant, 57

Sidereal day, 81
month, 173

Signs, 23

Sirius, 375

Solstices, 23

Sphere, celestial, 19
doctrine of the, 16
oblique, 84
parallel, 84
right, 83
terrestrial, 19

Spica, 370

Spots on the sun, 104
cause of, 106
dimensions of, 105
number of, 104

Stability of the universe, 410

Stars, fixed, 365

Stylus, 63

Sun, 101
attraction of the, 110
density of the, 103
diameter of the, 102
distance of the, 101
mass of the, 103
nature and constitution of the, 107
revolutions of the, 104

Sun, spots on the, 104
volume of the, 103

Supplement, 18

System of the world, 392-406
Brahean, 403
Copernican, 401
Ptolemaic, 399

Tangent, 129

Taurus, 369

Telescope, the, 31
achromatic, 34
directions for using, 39
Dorpat, 37 Herschelian, 36
history of, 33
reflecting, 34

Temperature, changes of, 124

Temporary stars, 380

Terminator, 119, 159

Thales, 394

Tides, 216
cause of, 216
spring and neap, 219

Time, 59
apparent, 61
equation of, 61
mean, 61
sidereal, 60

Transits, 237

Triangulation, 75

Tropic, 117

Twilight, 98

Unity of the Deity, 407

Uranus, 283
diameter of, 283
distance of, 284
history of, 284
period of, 284
satellites of, 284
scenery of, 285

Ursa Major, 373

Ursa Minor, 373

Variable stars, 379

Venus, 230
conjunctions of, 231
mountains of, 237
phases of, 234
revolutions of, 232
transits of, 239

Vesta, 288

Vindemiatrix, 370

Virgo, 370

Year, astronomical, 63
tropical, 156

Zenith, 20

Zenith distance, 21

Zodiac, 25

Zodiacal light, 363

Zones, 25

RECENT DISCOVERIES.

Improvements in the Telescope, 414

Rosse's Leviathan Telescope, 415

Pulkova and Cambridge Telescopes, 415

Improvements in instrumental Measurements, 416

New Planets and Asteroids, 416

Great Comet of 1843, 417

Distances of the Stars, 418

Discovery of Neptune, 419

Recent telescopic discoveries, 420

Longitude by the Electric Telegraph, 422

* * * * *

Transcriber's Notes

Obvious punctuation and spelling errors repaired.

Greek transliterations are inclosed by equals signs.

Inconsistent hyphenation has been repaired.

Characters that could not be fully expressed are "unpacked" and shown
within braces, e.g. {oblong symbol}.

In ambiguous cases, the text has been left as it appears in the original
book. In particular many mismatched quotation marks, have not been changed.

Page 26, "knittingneedle" changed to "knitting needle".
Page 241, "trignometry" changed to "trigonometry".
Page 303, "dedecaedron" changed to "dodecaedron".
Page 392, "generrally" changed to "generally".

*** End of this LibraryBlog Digital Book "Letters on Astronomy - in which the Elements of the Science are Familiarly - Explained in Connection with Biographical Sketches of the - Most Eminent Astronomers" ***

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