Letters on Astronomy
by Denison Olmsted · English · Gutenberg #40240 · 836,874 chars · public domain (US)
The Project Gutenberg eBook of Letters on Astronomy
This eBook is for the use of anyone anywhere in the United States and
most other parts of the world at no cost and with almost no restrictions
whatsoever. You may copy it, give it away or re-use it under the terms
of the Project Gutenberg License included with this eBook or online
at www.gutenberg.org. If you are not located in the United States,
you will have to check the laws of the country where you are located
before using this eBook.
Title: Letters on Astronomy
Author: Denison Olmsted
Release date: July 15, 2012 [eBook #40240]
Most recently updated: October 23, 2024
Language: English
Other information and formats: www.gutenberg.org/ebooks/40240
Credits: Produced by David Starner, Mark Young and the Online
Distributed Proofreading Team at http://www.pgdp.net
*** START OF THE PROJECT GUTENBERG EBOOK LETTERS ON ASTRONOMY ***
[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.]
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
existi
Showing first 200,000 characters. Full text: gutenberg.org/ebooks/40240