[Illustration PATH OF BIELA'S COMET.]
LETTERS
ON
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.
ADVERTISEMENT
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.]