.*
（~~..., y,
* *-… ? .
*• 7 •
-• §. ;=） ,
· · · · ·,≤）&（?:%.
§:ſſa
+· † •}}
;** • • • .
，:* ·±.


& IP3
45°
, 0.5 /
Telescopic view of the Full Moon
-
-
-
--> --
º º
º º
- º --
ºfelescopic view of the Moon when five days old
Zºº &ºtº ºvº.

COMPENDIUM OF ASTRONOMY;
ELEMENTs of T H E scIENCE,
FAMILIARLY EXPLAINED AND ILLUSTRATED,
with the latest Discover res.
ADAPTED TO T H E U SE OF
S C H O O L S AND ACADEMIES,
A N ID OF THE
G E N E R. A. L. R. E A D E R .
BY DENISON 91, MSTED, A. M.
PutoRESSOR OF NATURAI, PHILOSOPHY AND ASTRONOMY IN YALE COLLEGE.
N E W Y O R K :
C O L L I NS, K E E S E & C O.
I 839.
Entered according to Act of Congress, in the year 1839, by
DENIson OLMSTED,
in the Clerk's office, of the District Court of Connecticut.
Z'ſ tº a Z2 & 2 : trº-rºº. 3...”
2. #7.
#2% -42.2%
4.
P. R. E. F. A. C. E.
THIS small volume is intended to afford to the Gen-
eral Reader, and to the more advanced pupils of our
Schools and Academies, a comprehensive outline of As-
tronomy with its latest discoveries. For its perusal, no
further acquaintance with mathematics is necessary, than
a knowledge of common arithmetic ; although some
slight knowledge, at least, of geometry and trigonometry
will prove very useful. -
By omitting mathematical formulae, and employing
much familiar illustration, we have endeavored to bring
the leading facts and doctrines of this noble and inter-
esting Science, within the comprehension of every at-
tentive and intelligent reader. In no science, more than
in this, are greater advantages to be derived from a lucid
arrangement—an order which brings out every fact and
doctrine of the science, just in the place where the mind
is ready to receive it. A certain maturity of mind, and
power of reflection, are, however, indispensable for un-
derstanding this science. Astronomy is no study, for
children. Let them be employed on subjects more
suited to the state of their capacities until those facul-
ties are more fully developed, which will enable them
to learn to conceive correctly of the celestial motions.
A work on Astronomy that is very easy, must be very
superficial, and will be found to enter very little into the
arcana of the science. The riches of this mine lie deep;
iv. PREFACE,
and no one an acquire them, who is either incompetent
or unwilling to dive beneath the surface. *
Although this treatise is based on the larger work of
the author, (“Introduction to Astronomy,”) prepared for
the students of Yale College, yet it is not merely an
abridgement of that. It contains much original matter
adapted to the peculiar exigencies of the class of readers
for whom it is intended. The few passages taken ver-
batim from astronomical writers, are not, as in the larger
work, always accredited to their respective authors, as
this was deemed unimportant in a work of this de-
Scription. - -
It is strongly recommended to all who study this sci-
ence, even in its most elementary form, early to com-
mence learning the names of the constellations, and of
the largest of the individual stars, in the order in which
they are described in the last part of the work. A ce-
lestial globe will be found a most useful auxiliary in this
as in every other part of Astronomy. If it cannot super-
sede, it may greatly aid reflection. The reader also
should, if in his power, take frequent opportunities of
viewing the heavenly bodies through the telescope.
This will add much to his intelligence, and increase his
interest in the study.
C O N T E N T S .
Preliminary Observations, - & iº * sº tº
Part I, OF THE EAR.TH.
Chapter I.-Of the Figure and Dimensions of the Earth,
and the Doctrine of the Sphere, - º Gº gº
Chapter II.-Of the Diurnal Revolution——Artificial
Globes, - ſº º gº * = wº tº *
Chapter III.—Of Parallax, Refraction, and Twilight,
Chapter IV.-Of Time, - * * => sº gº tº
Chapter W.-Of Astronomical Instruments—Figure and
Density of the Earth, - sºng sº º tº tº-
Part II. OF THE SOLAR, SYSTEM.
Chapter I.-Of the Sun—Solar Spots—Zodiacal Light,
Chapter II.-Of the Apparent Annual Motions of the
Sun–Seasons—Figure of the Earth's Orbit, sº
Chapter III.-Of Universal Gravitation—Kepler's Laws,
—Motion in an Elliptical Orbit—Precession of the
Equinoxes, ºf tº * tº fº gº tº
Chapter IV.-Of the Moon—Phases, Revolution, tººs
Chapter W.-Of Eclipses, - sº gº tº †- gº
Chapter VI.-Of Longitude—Tides, - º º gº
Chapter VII.-Of the Planets—the Inferior Planets, Mer-
cury and Venus, º tºº º tº gº &
Chapter VIII.-Of the Superior Planets—Mars, Jupiter,
Saturn and Uranus—Ceres, Pallas, Juno and Vesta,
Page.
5
21
36
44
91 .
I [{)
I37
150
167
IS3
vi CONTENTS.
Chapter IX. —Of the Motions of the Planetary System— Page.
Quantity of Matter of the Sun and Planets—Sta-
bility of the Solar System, - tº º -- - 205
Chapter X-Of Comets, - - - º - - 218
Part III. OF THE FIXED STARS AND THE SYS-
TEM OF THE WORLD.
Chapter I.-Of the Fixed Stars—Constellations, - - 235
Chapter II.-Of Clusters of Stars—Nebulae—Variable
Stars—Temporary Stars—Double Stars, sº - 247
Chapter III.-Of the Motions of the Fixed Stars—Dis-
tances—Nature, º tº- sº º - - 255
Chapter IV.-Of the System of the World, - - - 265
0 0 M P E N DI UM 0 F A S T R O N 0 MW.
PRELIMINARY OBSERVATIONS.
1. ASTRONOMY is that science which treats of the heav-
enly 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 re-
spects facts; Physical Astronomy, causes ; Practical As-
tronomy, 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 per-
taining 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 phe-
nomena by investigating and applying the general laws
on which they depend ; especially by tracing out all the
consequences of the law of universal gravitation. Prac-
tical Astronomy lends its aid to both the other depart-
mentS.
2. Astronomy is the most ancient of all the sciences.
At a period of very high antiquity, it was cultivated in
Egypt, in Chaldea, and in India. Such knowledge of
the heavenly bodies as could be acquired by close and
long continued observation, without the aid of instru-
1. Define Astronomy. What does it teach 7 Name the four
parts into which it is divided. What does Descriptive Astron-
omy respect'ſ What does Physical Astronomy'ſ What does
Practical Astronomy 7 What is the peculiar province of each?
2 IPF ELINMIN ARY OF3 SERVATIONS.
ments, was diligently amassed ; and tables of the celes-
tial motions were constructed, which could be used in
predicting eclipses, and other astronomical phenomena.
About 500 years before the Christian era, Pythago-
ras, of Greece, taught astronomy at the celebrated school
at Crotona, (a Greek town on the southeastern coast of
Italy,) and exhibited more correct views of the nature
of the celestial motions, than were entertained by any
other astronomer of the ancient world. His views, how-
ever, were not generally adopted, but lay negleted for
nearly 2000 years, when they were revived and estab-
lished by Copernicus and Galileo. The most celebrated
astronomical school of antiquity, was at Alexandria in
Egypt, which was established and sustained by the Ptol-
emies, (Egyptian princes,) 300 years before the Chris-
tian era. The employment of instruments for measur-
ing angles, and bringing in trigonometrical calculations
to aid the naked powers of observation, gave to the Alex-
andrian astronomers great advantages over all their pre-
decessors.
The most able astronomer of the Alexandrian school
was Hipparchus, who was distinguished above all the
ancients for the accuracy of his astronomical measure-
ments and determinations. The knowledge of astron-
omy possessed by the Alexandrian school, and recorded
in the Almagest, or great work of Ptolemy, constituted
the chief of what was known of our science during the
middle ages, until the fifteenth and sixteenth centuries,
when the labors of Copernicus of Prussia, Tycho Brahe
2. Trace the history of Astronomy. Among what ancient
nations was it cultivated ? What kind of knowledge of the
heavenly bodies was amassed ? Who was Pythagoras 7 When
and where did he live? Where was his school '! How correct
were his views 7 Were they generally adopted 7 Give an ac-
count of the Alexandrian school. When was it established and
by whom? What gave it great advantages over all its prede-
cessors 7 Give some account of Hipparchus—of Ptolemy—of
Copernicus—of Tycho Brahe—of Kepler--of Galileo—of New-
ton—of Laplace. Specify the respective labors of each.
PRELIMINARY OBSERVATIONS. 3
of Denmark, Kepler of Germany, and Galileo of Italy,
laid the solid foundations of modern astronomy. Coper-
nicus expounded the true system of the world, or the
arrangement and motions of the heavenly bodies; Ty-
cho Brahe carried the use of instruments and the art of
astronomical observation to a far higher degree of accu-
racy than had ever been done before ; Kepler discovered
the great laws which regulate the movements of the
planets; and Galileo, having first enjoyed the aid of the
telescope, made innumerable discoveries in the solar
system. Near the beginning of the eighteenth century,
Sir Isaac Newton discovered, in the law of universal
gravitation, the great principle that explains the causes
of all celestial phenomena; and recently, La Place has
more fully completed what Newton begun, having fol-
lowed out all the consequences of the law of universal
gravitation, in his great work, the Mecanique Celeste.
3. Among the ancients, astronomy was studied chiefly
as subsidiary to astrology. Astrology was the art of di-
wining future events by the stars. It was of two kinds,
natural and judicial. Natural Astrology, aimed at pre-
dicting remarkable occurrences in the natural world, as
earthquakes, volcanoes, tempests, and pestilential dis-
eases. Judicial Astrology, aimed at foretelling the fates
of individuals, or of empires.
4. Astronomers of every age, have been distinguished
for their persevering industry, and their great love of ac-
curacy. They have uniformly aspired to an exactness
in their inquiries, far beyond what is aimed at in most
geographical investigations, satisfied with nothing short
of numerical accuracy wherever this is attainable ; and
years of toilsome observation, or laborious calculation,
have been spent with the hope of attaining a few se-
3. Define Astrology. What was Natural and what Judicial
Astrology 7
4. What is said of the industry and accuracy of astronomers'
Can this science be taught by artificial aids alone"
4 PRELIMINARY OBSERVATIONS.
conds nearer to the truth. Moreover, a severe but de-
lightful labor is imposed on all, who would arrive at a
clear and satisfactory knowledge of the subject of astron-
omy. Diagrams, artificial globes, orreries, and familiar
comparisons and illustrations, proposed by the author or
the instructor, may afford essential aid to the learner,
but nothing can convey to him a perfect comprehension
of the celestial motions, without much diligent study
and reflection. - -
5. In this treatise, we shall for the present assume the
Copernican system as the true system of the world,
postponing the discussion of the evidence on which it
rests to a late period, when the learner has been made ex-
tensively acquainted with astronomical facts. This sys-
tem maintains (1,) That the apparent diurnal revolution
of the heavenly bodies, from east to west, is owing to
the real revolution of the earth on its own axis from
west to east, in the same time; and (2,) That the sun
is the center around which the earth and planets all re-
volve from west to east, contrary to the opinion that the
earth is the center of motion of the sun and planets,
e-
5. What system is assumed as the true system of the world?
Specify the two leading points in the Copernican system,
PART I.-OF TiHE HEARTH.
C H A P T E R. I.
of THE FIGURE AND DIMENSIONS OF THE EARTH, AND
THE DOCTRINE OF THE SPHERE.
6. The figure of the earth is nearly globular. This
fact is known, first, by the circular form of its shadow
cast upon the moon in a lunar eclipse; secondly, from
analogy, each of the other planets being seen to be
spherical ; thirdly, by our seeing the tops of distant ob-
jects while the other parts are invisible, as the topmast
of a ship, while either leaving or approaching the shore,
or the lantern of a light-house, which when first descried
at a distance at Sea, appears to glimmer upon the very
surface of the water; fourthly, by the testimony of nav-
igators who have sailed around it; and, finally, by ac-
tual observations and measurements, made for the ex-
press purpose of ascertaining the figure of the earth, by
means of which astronomers are enabled to compute the
distances from the center of the earth of various places
on its surface, which distances are ſound to be nearly
equal.
The effect of the rotundity of the earth upon the ap-
pearance of a ship, when either leaving or approaching
the spectator, is illustrated by Fig. 1.
As light proceeds in straight lines, it is evident that,
if the earth is round, the top of the ship ought to come
into view before the lower parts, when the ship is ap-
proaching the spectator at A, and to remain longest in
view when the ship is leaving him. But, were the earth
|
6. What is the figure of the earth 7 Enumerate the various
proofs of its rotundity.
1%
6 THE EARTH,
ºt
E.
==N=E=
§
a continued plane, then the spectator would see all parts
of the ship at the same time, as is represented in the an-
nexed figure.
==
==
#
tº ===
-------
- -- -----
&
Wºº-
7. The foregoing considerations show that the form
of the earth is spherical; but more exact determinations
prove, that the earth, though nearly globular, is not ex-
actly so; its diameter from the north to the south pole
is about 26 miles less than through the equator, giving
to the earth the form of an oblate spheroid, or a flattened
sphere resembling an orange. We shall reserve the ex-






FIGURE AND DIMENSIONS. - 7.
planations of the methods by which this fact is estab-
lished, until the learner is better prepared than at present
to understand them. *
The mean or average diameter of the earth, is 79.12.4
miles, a measure which the learner should fix in his
memory as a standard of comparison in astronomy, and
of which he should endeavor to form the most adequate
conception in his power. The circumference of the
earth, is about 25,000 miles. Although the surface of
the earth is uneven, Sometimes rising in high mountains,
and sometimes descending in deep valleys, yet these ele-
vations and depressions are so small in comparison with
the immense volume of the globe, as hardly to occasion
any sensible deviation from a surface uniformly curvi-
linear. The irregularities of the earth's surface, in this
view, are no greater than the rough points on the rind
of an Orange, which do not perceptibly interrupt its con-
tinuity; for the highest mountain on the globe is only
about five miles above the general level; and the deep-
est mine: hitherto opened is only about half a mile.*
5 1.
Now 7912 – 1552 or about one sixteen hundredth part
of the whole diameter, an inequality which, in an arti-
ficial globe of eighteen inches diameter, amounts to only
the eighty eighth part of an inch.
8. The greatest difficulty in the way of acquiring
correct views in astronomy, arises from the erroneous
notions that pre-occupy the mind. To divest himself
7. What is the exact figure of the earth 7 How much greater
is its diameter through the equator than through the poles'
What is the mean average diameter of the earth 7 What is its
circumſerence? Do the inequalities on the earth's surface af.
fect its rotundity? To what may this be compared " How
high is the highest mountain above the general level ! How
deep is the deepest mine? To how much would this amount
on an artificial globe eighteen inches in diameter'ſ
* Sir John Hersohel.
8 - THE EARTH.
of these, the learner should conceive of the earth as a
huge globe occupying a small portion of space, and en-
circled on all sides with the starry sphere. He should
free his mind from its habitual proneness to consider one
part of space, as naturally up and another down, and
view himself as subject to a force which binds him to
the earth as truly as though he were fastened to it by
Some invisible cords or wires, as the needle attaches it-
self to all sides of a spherical loadstone. He should
Fig. 3.
Sle —- "V"
dwell on this point until it appears to him as truly up in
the direction of BB, CC, DD, (Fig. 3,) when he is at
B, C, and D, respectively, as in the direction AA, when
he is at A. -
DOCTRINE OF THE SPEHERE.
9. The definitions of the different lines, points, and
circles, which are used in astronomy, and the proposi-
tions founded upon them, compose the Doctrine of the
Sphere.
8. Whence arises the greatest difficulty in acquiring correct
views in astronomy How should the learner conceive of the
earth'ſ Illustrate by figure 3. -
9. Doctrine of the sphere—define it.

DOCTRINE OF THE SPHERE. 9
10. A section of a sphere by a plane cutting it in any
manner, is a circle. Great circles are those which pass
through the center of the sphere, and divide it into two
equal hemispheres: Small circles, are such as do not
pass through the center, but divide the sphere into two
unequal parts. Every circle, whether great or small, is
divided into 360 equal parts called degrees. A degree,
therefore, is not any fixed or definite quantity, but only
a certain aliquot part of any circle.* -
The avis of a circle, is a straight line passing through
its center at right angles to its plane.
* As this work may be read by some who are unacquainted with
even the rudiments of geometry, we annex a few particulars respecting
angular measurements. *
A line drawn from the center to the circumference of a circle is
called a radius, as CD, fig. 4. -
Any part of the circumference of a circle is called an arc, as AB,
or B.D. -
An angle is measured by the Fig. 4.
arc included between two radii. to
Thus, in the annexed figure, the
angle contained between the two TI
radii CA and CB, that is, the an-
gle ACB is measured by the arc
AB. But this arc is the same part
of the smaller circle that EF is of
the greater. The arc AB there-
fore contains the same number of
degrees as the arc EF, and either I
may be taken for the measure of
the angle ACB. As the whole
circle contains 360°, it is evident
that the quarter of a circle, or quad-
rant ABD, contains 90°, and the
semicircle ABDG contains 180°.
The complement of an arc oran-
gle, is what it wants of 90°. Thus BD is the complement of AB, and
AB is the complement of BD. If AB denotes a certain number of de-
grees of latitude, BD will be the complement of the latitude or the co-
latitude, as it is commonly written. -
The supplement of an arc or angle, is what it wants of 180°.
Thus, BA is the supplement of GDB, and GDB, is the supplement
i. # If BA were 20° of longitude, GDB its supplement would
G p
An angle is said to be subtended by the side which is opposite to it.
Thus in the triangle ACK, the angle at C is subtended by the side AK,
the angle at A by CK, and the angle at K by CA. In like manner a
side is said to be subtended by an angle, as AK by the angle at C.
D

I0 THE EARTH.
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 90°
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 180° apart.
A great circle which passes through the pole of an-
other great circle, cuts the latter at right angles.
The great circle which passes through the pole of an-
other 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 the 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.
11. In order to fix the position of any plane, either on
the surface of the earth or in the heavens, both the earth
and the heavens are conceived to be divided into sepa-
rate portions by circles, which are imagined to cut
through them in various ways. The earth thus inter-
Sected is called the terrestrial, and the heavens the ce-
lestial sphere. The learner will remark, that these cir-
cles have no existence in nature, but are mere land-
marks, artificially contrived for convenience of refer-
10. What figure is produced by the section of a sphere'ſ
Define great circles. Define small circles. Into how many
degrees is every circle divided ? Is a degree any fixed or defi-
nite quantity? What is the axis of a circle? What is the pole
of a circle 7 How do all great circles cut each other ? How
is a great circle cut by another great circle passing through its
pole 7 What is the secondary of a circle 7 How is the angle
made by two great circles on the surface of the sphere measured 7
11. How are the earth and the heavens conceived to be di-
vided ? What constitutes the terrestrial sphere? What the
celestial? Have these circles any existence in nature ? In
what do the heavenly bodies appear to be fixed
DOCTRINE OF THE SPHERE. 11
ence. On account of the immense distance of the heav-
enly 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 surface of the heavens, become
circles of the celestial sphere. - -
12. The Horizon is the great circle which divides
the earth into upper and lower hemispheres, and sepa-
rates 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 ra-
tional, but is distant from it by the semi-diameter of the
earth, or nearly 4,000 miles. Still, so vast is the dis-
tance of the starry sphere, that both these planes appear
to cut that sphere in the same line; so that we see the
same hemisphere of stars that we should see if the up-
per half of the earth were removed, and we stood on the
rational horizon. -- -
13. The poles of the horizon are the zenith and na-
dir. The Zenith is the point directly over our head,
and the Nadir that directly under our feet. The plumb
line is in the axis of the horizon, and consequently di-
rected 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 90 degrees from him in all di-
rections.
12. Define the horizon. Distinguish between the rational
and the sensible horizon. What is the distance between the
sensible and rational horizons 7 How do both appear to cut
the starry heavens?
13. What are the poles of the horizon 7 Define the zenith.
Define the nadir. How is the plumb line situated with respect
to the horizon? How many horizons are there on the earth 7
12 - THE EARTH.
14. Vertical circles are those which pass through the
poles of the horizon, perpendicular to it.
The Meridian is that vertical circle which passes
through the north and south points. y
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 ho-
rizon, 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 the body. .
The Amplitude of a body, is its distance on the hori-
zon, from the prime vertical, to a vertical circle passing
through the body. -
Azimuth is reckoned 90° from either the north or
south point; and amplitude 90° from either the east or
west point. Azimuth and amplitude are mutually com-
plements of each other. When a point is on the hori-
zon, 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 ver-
tical 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 ver-
tical circle, passing through that body. It is the com-
plement of the altitude. -
15. The Aavis 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 con-
cave, constitutes the avis of the celestial sphere.
14. Define vertical circles—the meridian—the prime vertical
—altitude—azimuth—amplitude. How many degrees of azi-
muth are reckoned 7 from what points? How are azimuth and
amplitude related to each other 7 Define zenith distance—-How
is it related to the altitude 7
15. Define the axis of the earth—the axis of the celestial
sphere—the poles of the earth—the poles of the heavens.
DOCTRINE OF THE SPHERE. - 13
The Poles of the Earth are the extremities of the
earth’s axis: the Poles of the Heavens, the extremities
of the celestial axis. -
16. 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 equa-
tor with the surface of the earth, constitutes the terres-
trial, and with the concave sphere of the heavens, the
celestial equator. The latter, by way of distinction, is
Sometimes denominated the equinoctial.
17. 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.
18. The Latitude of a place on the earth, is its dis-
tance from the equator north or south. The Polar Dis-
tance, or angular distance from the nearest pole, is the
complement of the latitude. -
19. 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
16. Define the equator. What constitutes the terrestrial
equator' what the celestial equator? What is this also called
17. What are the secondaries of the equator called ?
18. Define the Latitude of a place—the polar distance.
2
14 THE EARTH,
are between that place and the point where the meridiar;
of Greenwich cuts the equator. If the place is north on
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.
20. The Ecliptic is a great circle in which the earth
performs its annual revolotion around the Sun. It passes
through the center of the earth and the center 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 eclip-
tic, but that it is turned about 23# degrees out of a per-
pendicular direction, making an angle with the plane
itself of 6639. 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 234°.
It is particularly important for the learner to form cor-
rect ideas of the ecliptic, and of its relations to the equa-
tor, since to these two circles a great number of astro-
nomical measurements and phenomena are referred.
21. 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 vermal, and in returning southward, the au-
tummal equinox. The vernal equinox occurs about
the 21st of March, and the autumnal the 22d of Sep-
tember.
19. Define the Longitude of a place. What is the standard
meridian'ſ When a place is on the equator, how is its longi-
tude measured 7 how when it is north or south of the equator 7
20. Define the ecliptic. How does it pass with respect to
the earth and the Sun ? How is it situated with respect to the
equator 7
21. Define the equinoctial points. When is the vernal equi-
nox, and when the autumnal '!
* The term Equinoxes strictly denotes the times when the sun ar-
rives at the equinoctial points, but it is frequently used to denote those
points themselves.
DOCTRINE OF THE SPHERE. 15
$22. 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 sum-
mer solstice occurs about the 22d of June, and the win-
ter solstice about the 22d of December.
The ecliptic is divided into twelve equal parts of 30°
each, called signs, which, beginning at the vermal equi-
nox, succeed each other in the following order:
JYorthern. Southern.
1. Aries ºp 7. Libra :--
2. Taurus & 8. Scorpio 173.
3. Gemini II 9. Saggitarius f
4. Cancer 95 10. Capricornus V3
5. Leo SU 11. Aquarius &
6. Virgo my 12. Pisces }é
The mode of reckoning on the ecliptic, is by signs, de-
grees, minutes, and seconds. The sign is denoted either
ły its name or its number. Thus 100° may be express-
ed either as the 10th degree of Cancer, or as 3s 10°.
23. 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 celes-
tial longitude are reckoned, as longitude on the earth is
reckoned from the meridian of Greenwich. The Sols-
£itial Colure, is the meridian which passes through the
Solstitial points. -
24. The position of a celestial body is referred to the
equator by its right ascension and declination. Right
22. Define the solstitial points, and solstices. When does
the summer solstice occur ! when does the winter solstice oc-
cur ! Into how many signs is the ecliptic divided ? How
many degrees are there in each Name the signs. What is
the mode of reckoning on the ecliptic 1 in what two ways may
100° be expressed ? -
23. What is the equinoctial colure ?—the solstitial colure ?
16 THE EARTH.
Ascension, is the angular distance from the vernal equi-
nox 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 equa-
tor, then its right ascension is the arc of the equator in-
tercepted between the vernal equinox and that secon-
dary to the equator which passes through the star. De-
climation is the distance of a body from the equator,
measured on a secondary to the latter. Therefore, right
ascension and declination correspond to terrestrial longi-
tude 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 Longi-
tude, is the distance of a body from the vernal equinox
reckoned on the ecliptic. Celestial Latitude, is distance
from the ecliptic measured on a secondary to the latter.
Or, more briefly, Longitude is distance on the the eclip-
tic ; Latitude, distance from the ecliptic. The North
Polar Distance of a star, is the complement of its de-
clination.
25. 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 that 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
23# degrees from the pole of the earth.
24. Define right ascension and declination. To what do
they correspond on the celestial sphere 7 Define celestial
longitude and latitude.
25. What are parallels of latitude—tropics—polar circles'
To what is the elevation of the pole always equal? also that of
the equator 7 -
DOCTRINE OF THE SPEIERE. 17
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 40° of north latitude we see the
north star 40° above the northern horizon, whereas, if
we should travel southward its elevation would grow
Hess 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 constantly higher
and higher, until, if we could reach the pole of the earth,
that star would appear directly over head. The eleva-
tion of the equator above the horizon of any place, is
equal to the complement of the latitude. Thus, at the
latitude of 40° N. the equator is elevated 50° above the
Southern horizon.
26. The earth is divided into five zones. That por-
tion of the earth which lies between the tropics, is called
the Torrid Zone; that between the tropics and polar
circles, the Temperate Zones; and that between the
polar circles and the poles, the Frigid Zones.
27. The Zodiac is the part of the celestial sphere,
which lies about 8 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.
28. After endeavoring to form, from the definitions,
as clear an idea as we can of the various circles of the
sphere, the learner may next resort to an artificial globe,
and see how they are severally represented there. Or if
he has not access to a globe, he may aid his conceptions
by the following easy device. To represent the earth,
Select a large apple, (a melon when in season will be
found still better.) The shape of the apple, flattened as
26. Define each of the zones.
27. Define the zodiac.
28. Show how to represent the artificial sphere by any round
body, as an apple, and point out the various circles on it.
2%
18 THE EARTH.
it usually is at the two ends, will not inaptly exhibit
the spheroidal figure of the earth, while the larger diam-
eter through the middle will indicate the excess of mat-
ter about the equator, although we should remark, that
the disproportion between the polar and equatorial diam-
eters of the earth is in fact so slight, that it would be
scarcely perceptible in a model. 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 the globe
from west to east, and its motion will correspond to the
diurnal movement of the globe. Pass a wire, as a knit-
ting needle, through the poles, and it will represent the
avis 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, par-
allel to the equator, will represent parallels of latitude,
of which, two drawn 234 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
center of the earth from one tropic to the other, will rep-
resent the plane of the ecliptic, and consequently, a line
cut around the apple where such a section meets the sur-
face, is the terrestrial ecliptic. The points where this
circle meets the tropics, are the solstices, and its intersec-
tions with the equator are the equinoctial points.
29. 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 slipped
29. How is the horizon represented in our model ? How is
it placed to represent the horizon of the equator? How for the
horizon of the poles " How for our own horizon'ſ How shall
we represent the prime vertic al 7
DOCTRINE OF THE SPEIERE. 19
up to 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 90° every way from it. Suppose we are
in latitude 40°, then let us place our movable paper par-
allel to our own horizon, and elevate the pole 40° above
it, as near as we can judge by the eye. If we cut a cir-
cle around the apple, passing through its highest part
and through the east and west points, it will represent
the prime vertical.
30. We cannot too strongly recommend to the young
learner to form for himself such a sphere as is here de-
scribed, and 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 re-
ferred to the equator on the earth, and to the ecliptic in
the heavens.
31. 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, or directly 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 re-
30. What is particularly recommended to the young learner 7
31. What is meant by the projection of the sphere? What
is the projection of a circle when seen directly before the face?
What when seen obliquely what when seen edgewise
20 THE EARTH,
moved 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, as an ellipse when
oblique to this.line, or as a straight line when its edge is
towards us.
32. It is in this manner that the circles of the sphere
are projected, as represented in the following diagram,
Fig. 5,
Here various circles are represented as projected on the
meridian, which is supposed to be situated directly be-
fore the eye, at some distance from it. The horizon HO
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 ZN, with the equator
EQ, and the several small circles parallel to the equator,
which represent the two tropics and the two polar cir-
32. In figure 4, what represents the plane of projection ?
Why are certain circles represented by straight lines 7 why are
others represented by ellipses? How is the eye supposed to be
situated 7

DIURNAL REVOLUTION. 21
cles. In fact, all circles whatsoever, which are perpen-
dicular to the plane of projection, will be represented
by straight lines. But every circle which is perpendic-
ular to the horizon, except the prime vertical, being seen
obliquely as ZMN, will be projected into an ellipse.
In the same manner, PRP, an hour circle, being oblique
to the eye, is represented by an ellipse on the plane of
projection.
C H. A. P. T. E. R. II.
DIURNAL REVOLUTION.—ARTIFICIAL GLOBES.
33. THE apparent diurnal revolution of the heavenly
bodies from east to west, is owing to the actual revolu-
tion 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 ce-
lestial equator. In curves parallel to this, called the cir-
cles of diurnal revolution, the heavenly bodies actually
appear to move, every star having its own peculiar cir-
cle. After the learner has first rendered familiar the real
motions of the earth from west to east, he may then,
without danger of misconception, 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.
34. The time occupied by a star in passing from any
point in the meridian until it comes round to the same
33. To what is the apparent diurnal revolution of the heav-
enly bodies from west to east owing " If a radius of the earth's
equatok were extended to meet the concave sphere of the heav-
ens, what would it trace out as the earth revolves? What are
circles of diurnal revolution ?
22 THE EARTH.
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 one another; that is,
the sidereal days are all equal. Whatever star we se-
lect for the observation, the same result will be obtained.
The stars, therefore, always keep the same relative posi-
tion, 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 the fixed stars, revolve in like man-
ner, but their returns to the meridian are not, like those
of the fixed stars, at exactly equal intervals.
35. 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, (Art. 8,)
and different horizons are variously inclined to each
other. Let us suppose the spectator viewing the diurnal
revolutions from several diſferent positions on the earth.
On the equator, his horizon would pass through both
poles; for the horizon cuts the celestial vault at 90 de-
grees in every direction from the zenith of the spectator;
but the pole is likewise 90 degrees from his zenith, and
consequently, the pole must be in the horizon. The ce-
lestial equator would coincide with the Prime Wertical,
34. Define a sidereal day. Are the sidereal days equal or
unequal 7 Are the returns of the sun, moon, and planets to
the meridian, likewise at equal intervals?
35. How are the appearances of the diurnal motions in dif-
ferent parts of the earth 7 When the spectator is on the equa-
tor, where would his horizon pass with respect to the poles of
the earth With what great circle would the celestial equator
coincide? How would all the circles of diurnal revolution be
situated with respect to the horizon 7 Define a right sphere,
In a right sphere, how would a star situated in the gelestial
equator perform its circuit? how would stars nearer the poles
appear to move?
DIURNAL REVOLUTION. 23
being a great circle passing the east and west points.
Since all the diurnal circles are parallel to the equator,
consequently, they would all, like the equator, be per-
pendicular to the horizon. Such a view of the heavenly
bodies, is called a right sphere; or, -
A RIGHT SPHERE is one in which all the daily revolu-
tions of the stars, are in circles perpendicular to the ho-
7°22'O??, -
A right sphere is seen only at the equator. Any star
situated in the celestial equator, would appear to rise di-
rectly 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 to-
wards the pole, they describe smaller and smaller circles,
until, near the pole, their motion is hardly perceptible.
36. If the spectator advances one degree 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
farther and farther 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 coin-
cides 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. This is
what constitutes a parallel sphere. 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, the
learner should follow round in his mind a number of
36. What changes take place in one's horizon as he moves
from the equator towards the pole 7 How would it be situated
when he reached the pole 7 Define a parallel sphere. Explain
the appearances of the stars and of the sun in a parallel sphere.
Where only can such a sphere be seen 7 Has the pole of the
earth ever been reached by man? .
24 THE EARTH.
separate stars, 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 hemi-
sphere would all be perpetually in view when not ob-
scured 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 constantly
out of sight. That is, at the pole the days and nights
are each six months long. The phenomena 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 pene-
trated within a few degrees of the north pole, and of
course enjoyed the view of a sphere nearly parallel. .
37. 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 de-
fined :
An OBLIQUE SPHERE is that in which the circles of
daily motion are oblique to the horizon. -
Suppose, for example, the spectator is at the latitude of
fifty degrees. His horizon reaches 50° 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 40°, being al-
ways equal to the co-altitude of the pole. Thus, let HO
(Fig. 6,) represent the horizon, EQ the equator, and
PP' the axis of the earth. Also, ll, mm, &c., parallels
of latitude. Then the horizon of a spectator at Z, in
latitude 50° reaches to 50° beyond the pole; and the
angle ECH, is 40°. As we advance still farther north
37. Define an oblique sphere. Where is it seen 7 At the
latitude of 50° how is the horizon situated 7 Illustrate by fig. 6.
DIURNAL REVOLUTION. 25
the elevation of the diurnal circles grows less and less,
and consequently the motions of the heavenly bodies
more and more oblique, until finally, at the pole, where
the latitude is 90°, the angle of elevation of the equator
Vanishes, and the horizon and equator coincide with
each other, as before stated. *
38. 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 dis-
tance is just equal to the latitude, will when at its low-
est 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, mm (Fig. 6,) is the circle of perpetual appari-
tion, between which and the north pole, the stars never
set, and its distance from the pole OP is evidently equal
to the elevation of the pole, and of course to the lati-
tude.
38. What is the circle of perpetual apparition ? Illustrate by
fig. 6.

3
26 THE EARTH.
39. In the opposite hemisphere, a similar part of the
sphere adjacent to the depressed pole never rises. Hence,
The CIRCLE OF PERPETUAL occult ATION, is the boun-
dary of that space around the depressed pole, withing
which the stars never rise. Thus, m/m/ (Fig. 6,) is the
circle of perpetual occultation, between which and the
South pole, the stars never rise.
40. 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 hori-
Zon. 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.
All these points will be readily understood by inspecting
figure 6. - - -
41. Most of the appearances of the diurnal revolution
can be explained, either on the supposition that the ce-
lestial sphere actually all turns around the earth once in
24 hours, or that this motion of the heavens is merely
apparent, arising from the revolution of the earth on its
39. What is the circle of perpetual occultation ? Illustrate
by fig 6.
40. How does the horizon of an oblique sphere cut the cir-
cles of daily motion ? Towards the elevated pole what portion
of the circles is above the horizon'ſ Towards the depressed
pole, how is the fact 7 When are the days and nights equal all
over the world? When are the days longer, and when shorter
than the nights? r ar
DIURNAL REVOLUTION. 27
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 a steam boat, and observe
all external objects to be receding from us with a com-
mon motion. Proofs entirely conclusive and satisfac-
tory, establish the fact, that it is the earth and not the
celestial sphere that turns; but these proofs are drawn
from various sources, and the student 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
of our course of instruction, we therefore postpone the
discussion of the hypothesis of the earth’s rotation on
its axis. - . . . ** - -
42. 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 dis-
tance 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 15 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 90 degrees below
the Sun, which brings 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.
41. On what suppositions can the appearances of the diurnal
revolution be explained 7 Is it the earth or the heavens that
really move? Why is the discussion of this subject postponed ?
42. Explain the true cause of the sun's appearing to rise and
set, as observed at the equator. What is the position of the ho-
rizon at sunrise ' What at six hours afterwards? What at the
end of twelve hours? What at the end of eighteen hours?
28 THE EARTH,
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 started, and
a new day begins.
43. 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 center,
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, contin-
ual night.
We have endeavored to conceive of the manner in
which the apparent diurnal movements of the sun are
really produced at two stations, namely, in the right
sphere, and in the parallel sphere. These two cases
being clearly understood, there will be little difficulty in
applying a similar explanation to an oblique sphere.
ARTIFICIAL, GLOBES.
44. Artificial globes are of two kinds, terrestrial and
celestial. The first exhibits a miniature representation
of the earth; the second, of the visible heavens; and
both show the various circles by which the two spheres
43. Explain the similar phenomena at the poles, first, when
the sun is at the equinoxes, and secondly, when it is north and
when it is south of the equator,
ARTIFICIAL, GLOBES. 29
are respectively traversed. Since all globes are similar
solid figures, a small globe, imagined to be situated at
the center of the earth or of the celestial vault, may rep-
resent all the visible objects and artificial divisions of
either sphere, and with great accuracy and just propor-
tions, though on a scale greatly reduced. The study of
artificial globes, therefore, cannot be too strongly recom-
mended to the student of astronomy.*
*-
45. An artificial globe is encompassed from north to
South by a strong brass ring to represent the meridian of
the place. This ring is made fast to the two poles and
thus supports the globe, while it is itself supported in a
vertical position by means of a frame, the ring being
usually let into a socket in which it may be easily slid,
so as to give any required elevation to the pole. The
brass meridian is graduated each way from the equator
to the pole 90°, to measure degrees of latitude or decli-
nation, according as the distance from the equator refers
to a point on the earth or in the heavens. The horizon
is represented by a broad zone, made broad for the con-
venience of carrying on it a circle of azimuth, another of
amplitude, and a wide space on which are delineated
the signs of the ecliptic, and the sun’s place for every
day in the year; not because these points have any spe-
cial connexion with the horizon, but because this broad
surface furnishes a convenient place for recording them.
44. What does the terrestrial globe exhibit? What does the
celestial globe 7 What do both show !
45. How is the meridian of the place represented 7 To what
points is the brass meridian fastened 7 What supports the ring 3
How is it graduated? How is the horizon represented ' Why
is it made broad 7 What circles are inscribed on it?
* It were desirable, indeed, that every student of the science should
have a celestial globe, at least, constantly before him. One of a
small size, as eight or nine inches, will answer the purpose, although
globes of these dimensions cannot usually be relied on for nice meas-
ldren lentS. -
3%
30 THE EARTH.
46. Hour Circles are represented on the terrestrial
globe by great circles drawn through the pole of the
equator; but, on the celestial globe, corresponding cir-
cles pass through the poles of the ecliptic, constituting
circles of latitude, while the brass meridian, being a se-
condary to the equinoctial, becomes an hour circle of
any star which, by turning the globe, is brought under it.
47. The Hour Indea is a small circle described around
the pole of the equator, on which are marked the hours
of the day. As this circle turns along with the globe, it
makes a complete revolution in the same time with the
equator; or, for any less period, the same number of de-
grees of this circle and of the equator pass under the
meridian. Hence the hour index measures arcs of right
ascension, 15° passing under the meridian every hour.
48. The Quadrant of Altitude is a flexible strip of
brass, graduated into ninety equal parts, corresponding
in length to degrees on the globe, so that when applied to
the globe and bent so as closely to fit its surface, it meas-
ures the angular distance between any two points.
When the Zero, or the point where the graduation be-
gins, is laid on the pole of any great circle, the 90th de-
gree will reach to the circumference of that circle, and
being therefore a great circle passing through the pole
of another great circle, it becomes a secondary to the
latter. Thus the quadrant of altitude may be used as a
Secondary to any great circle on the sphere; but it is
used chiefly as a secondary to the horizon, the point
46. How are hour circles represented on the terrestrial
globe” How are circles of latitude represented on the celes-
tial globe 7
47. Describe the hour indez. What does it measure ?
48. What is the quadrant of altitude 2 How is it gradua-
ted? When the zero point is laid on the pole of any great cir-
cle, to what will the 90th degree reach? How may it be used
as a secondary to any great circle 7 When screwed on the
zenith what does it become 7 What arcs does it then measure?
TERRESTRIAL GLOBE. 31
marked 90° being screwed fast to the pole of the hori-
zon, that is, the zenith, and the other end, marked 0,
being slid along between the surface of the sphere and
the wooden horizon. It thus becomes a vertical circle,
on which to measure the altitude of any star through
which it passes, or from which to measure the azimuth
of the star, which is the arc of the horizon intercepted
between the meridian and the quadrant of altitude pass-
ing through the star.
49. To rectify the globe for any place, the north pole
must be elevated to the latitude of the place; then the
equator and all the diurnal circles will have their due in-
climation in respect to the horizon; and, on turning the
globe, every point on either globe will revolve as the
Same point does in nature ; and the relative situations of
all places will be the same as on the native spheres.
PROBLEMS ON THE TERRESTRIAL GLOBE.
50. To find the Latitude and Longitude of a place:
Turn the globe so as to bring the place to the brass me-
ridian ; then the degree and minute on the meridian di-
rectly over the place will indicate its latitude, and the
point of the equator under the meridian, will show its
longitude. -
Ex. What is the Latitude and Longitude of the city
of New York 2 ... - -
51. To find a place having its latitude and longitude
given : Bring to the brass meridian the point of the equa-
tor corresponding to the longitude, and then at the de-
gree of the meridian denoting the latitude, the place will
be found. - . .
Ex. What place on the globe is in Latitude 39 N. and
Longitude 77 W. -
49. How do we rectify the globe for any place 7
50. Find the latitude and longitude of Washington City ?
51, What place lies in latitude 39 N, and longitude 77 W
32 - THE EARTH,
52. To find the bearing and distance of two places:
Rectify the globe for one of the places; screw the quad-
rant of altitude to the zenith,” and let it pass through
the other place. Then the azimuth will give the bear-
ing of the second place from the first, and the number
of degrees on the quadrant of altitude, multiplied by 69,
(the number of miles in a degree,) will give the distance
between the two places.
Ex. What is the bearing of New Orleans from New
York, and what is the distance between these places?
53. To determine the difference of time in different
places: Bring the place that lies eastward of the other
to the meridian, and set the hour index at XII. Turn
the globe eastward until the other place comes to the
meridian, then the index will point to the hour required.
Ex. When it is noon at New York, what time is it at
London 2 - -
54. The hour being given at any place, to tell what
hour it is in any other part of the world : Bring the
given place to the meridian, and set the hour index to
the given time; then turn the globe, until the other
place comes under the meridian, and the index will
point to the required hour. .
Ex. What time is it at Canton, in China, when it is
9 o'clock A. M. at New York :
55. To find what people on the earth live under us,
having their moon at the time of our midnight : Bring
the place where we dwell to the meridian, and set the
52. What is the bearing and distance of New Orleans from
New York . -
53. When it is noon at New York, what time is it at Pekin
54 What time is it at London when it is noon at Boston 7
* The zenith will of course be the point of the meridian over the
place. .
TERRESTRIAL GLOBE. 33
hour index to XII; then turn the globe until the other
YII comes under the meridian ; the point under the
same part of the meridian where we were before, will
be the place sought. -
Ex. Find what place is directly under New York.
56. To find what people of the southern hemisphere
are directly opposite to us: Bring our place to the me-
ridian ; the place in the same latitude south, then un-
der the meridian, will be the place in question.
Ex. What place in the southern hemisphere corres-
ponds to New Haven -
57. To find the antipodes of a place, or the people
whose feet are evactly opposite to ours : Bring our place
to the meridian ; set the hour index to XII, and turn the
globe until the other XII comes under the meridian ;
then the point of the southern hemisphere under the me-
ridian and having the same latitude with ours, will be
the place of our antipodes.
*
Ex. Who are antipodes to the people of Philadelphia?
58. To rectify the globe for the sun's place: On the
wooden horizon, find the day of the month, and against
it is given the sun's place in the ecliptic, expressed by
signs and degrees.* Look for the same sign and degree
on the ecliptic, bring that point to the meridian and set
the hour index to XII. To all places under the merid-
ian it will then be noon.
Ex. Rectify the globe for the sun's place on the 1st
of September. s 2.
55. Find what place is directly under Philadelphia.
56. What place in south latitude corresponds to Boston
57. Who are the antipodes of the people of London 1
58. Rectify the globe for the sun's place for the first of June.
* The larger globes have the day of the month marked against the
&
corresponding sign on the ecliptic itself.
34 THE EARTH.
59. The latitude of the place being given, to find the
time of the Sun's rising and setting on any given day
at that place : Having rectified the globe for the lati-
tude, bring the sun’s place in the ecliptic to the gradua-
ted edge of the meridian, and set the hour index to XII;
then turn the globe so as to bring the sun to the eastern
and then to the western horizon, and the hour index
will show the times of rising and setting respectively.
Ex. At what time will the sun rise and set at New
Haven, Lat. 41° 18', on the 10th of July 2
PROBLEMS ON THE CELESTIAL GLOBE.
60. To find the Declination and Right Ascension of
a heavenly body : Bring the place of the body (whether
sun or star) to the meridian. Then the degree and
minute standing over it will show its declination, and
the pgint of the equinoctial under the meridian will give
its right ascension. It will be remarked, that the decli-
nation and right ascension are found in the same man-
ner as latitude and longitude on the terrestrial globe.
Right ascension is expressed either in degrees or in
hours; both being reckoned from the vernal equinox.
Ex. What is the declination and right ascension of the
bright star Lyra —also of the sun on the 5th of June 2
61. To represent the appearance of the heavens at any
time: Rectify the globe for the latitude, bring the sun’s
place in the ecliptic to the meridian, and set the hour
index to XII; then turn the globe westward until the
index points to the given hour, and the constellations
would then have the same appearance to an eye situated
59. Find the time of the sun's rising and setting at Boston,
(Lat. 42°, Lon. 71°) on the first day of December. ‘A
60. On the celestial globe, What is the right ascension and
declination of any star taken at pleasure ?
61. Represent the appearance of the heavens at Tuscaloosa
(Lat. 33°, Lon. 87°) at 8 o'clock in the evening of Nov. 13th.
t . CELESTIAL, GLOBE. 35
at the center of the globe, as they have at that moment
in the sky.
Ex. Required the aspect of the stars at New Haven,
Lat. 41° 18', at 10 o’clock, on the evening of Decem-
ber 5th. '• -
62. To find the altitude and azimuth of any star :
Rectify the globe for the latitude, and let the quadrant
of altitude be screwed to the zenith, and be made to pass
through the star. The arc on the quadrant, from the
horizon to the star, will denote its altitude, and the arc
of the horizon from the meridian to the quadrant, will be
its azimuth.
Ex. What is the altitude and azimuth of Sirius (the
brightest of the fixed stars) on the 25th of December at
10 o'clock in the evening, in Lat. 419'? - -
63. To find the angular distance of two stars from
each other: Apply the zero mark of the quadrant of alti-
tude to one of the stars, and the point of the quadrant
which falls on the other star, will show the angular dis-
tance between the two.
Ex. What is the distance between the two largest
stars of the Great Bear.*
64. To find the sum’s meridian altitude, the latitude
and day of the month being given : Having rectified
the globe for the latitude, bring the sun's place in the
ecliptic to the meridian, and count the number of de-
62. Find the altitude and azimuth of Lyra at 10 o'clock in
the evening of June 18th, in Lat. 42°. t
63. Find the angular distance between any two stars taken
at pleasure.
* These two stars are sometimes called “ the Pointers,” from the line
which passes through them being always nearly in the direction of the
north star. The angular distance between them is about 5°, and may
be learned as a standard of reference in estimating by the eye, the dis-
tance between any two points on the celestial vault. -
36 THE EARTH,
grees and minutes between that point of the meridian
and the zenith. The complement of this arc will be
the sun’s meridian altitude. -
Ex. What is the sun’s meridian altitude at noon on
the 1st of August, in Lat. 41° 18'
C H A P T E R III.
of PARALLAX, REFRACTION, AND TWILIGHT.
65. PARALLAx is the apparent change of place which
bodies windergo by being viewed from different points.
Z, Fig. 7.
Thus in figure 7, let A represent the earth, CH the ho-
rizon. HZ, a quadrant of a great circle of the heavens,
64. What is the Sun's meridian altitude at noon on the 18th
of June, in latitude 35°7 -
65. Define parallax. Illustrate by the figure. What angle
measures the parallax' Why do astronomers consider the
heavenly bodies as viewed from the center of the earth?

PARALLAX. 37
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 place of E to h, whereas, if seen from the center of
the earth, it would appear at H. The arc Hh is called
the parallactic arc, and the angle HEh, or its equal AEC,
is the angle of parallax. The same is true of the angles
at F, G, and O, respectively.
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
occasioned in the determination of points on the celes-
tial sphere, astronomers have agreed to consider the true
place of a celestial object to be that where it would
appear if seen from the center of the earth. The doc-
trine 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 center.
66. The angle AEC is called the horizontal parallax,
which may be thus defined. Horizontal Parallaw, is
the change of position which a celestial body, appearing
in the horizon as seen from the surface of the earth,
would assume if viewed from the earth’s center. It is
the angle subtended by the semi-diameter of the earth,
as viewed from the body itself.
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
Hh ; F by the arc Pp ; G by the arc Rr; while O sus-
tains 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 here-
after, have no sensible parallax.
66. Define horizontal parallax—By what is it subtended ?
(See Art. 10. Note.) What is the effect of parallax upon the
place of a heavenly body?
38 THE EARTH.
67. The determination of the horizontal parallax of a
celestial body is an element of great importance, since it
furnishes the means of estimating the distance of the
body from the center of the earth. Thus, iſ the angle
AEC (Fig. 7,) be found, the radius of the earth AC be-
ing known, we have in the right angled triangle AEC,
the side AC and all the angles, to find the side CE,
which is the distance of the moon from the center of the
earth.*
IREFIRACTION.
68. While parallax depresses the celestial bodies sub-
ject to it, refraction elevates them, ; and it affects alike
the most distant as well as nearer bodies, being occa-
sioned by the change of direction which light undergoes
Fig. 8.
67. Why is the determination of the parallax of a heavenly
body an element of great importance? Illustrate by figure 7.
* Should the reader be unacquainted with the principles of trigonom-
etry, yet he ought to know the fact that these principles enable us,
when we have ascertained certain parts in a triangle, to find the un:
known parts. Thus, in the above case, when we have found the an-
gle of parallax, AEB, (which is determined by certain astronomical ob-
servations,) knowing also the semi-diameter of the earth AC, we can
find by trigonometry, the length of the side CE, which is the distance
of the body from the center of the earth.

REFRACTION. 39
in passing through the atmosphere. Let us conceive of
the atmosphere as made up of a great number of concen-
tric strata, as AA, BB, CC, and DD, (Fig. 8,) increasing
rapidly in density (as is known to be the fact) in ap-
proaching near to the surface of the earth. Let S be a
star, from which a ray of light Sa enters the atmosphere
at a, where, being much turned towards the radius of
the convex surface,” it would change its direction into
the line ab, and again into be, and co, 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 of the ray Oc, and
consequently, the star would apparently change its place,
in consequence of refraction, from S to S', being ele-
wated out of its true position. Moreover, since on ac-
count 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 there-
fore move, not in the polygon represented in the figure,
but in a corresponding curve, whose curvature is rapidly
increased near the surface of the earth.
68. What effect has refraction upon the place, of a heavenly
body ? By what is it occasioned? Illustrate by figure 8. How
is a ray of light affected by passing out of a rarer into a denser
medium ? Why is an oar bent in the water ? In what line
does the light move as it goes through the atmosphere?
* 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 a bent appearance. Thus, in the figure, if Saa represents the
oar, Sal 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 me-
dium, 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 ra-
dius of the earth, this being perpendicular to the surface of the atmos-
phere; and it is turned more and more towards that radius the nearer
it approaches to the earth, because the density of the air rapidly in-
Cred:SCS,
40 TIſ E EARTH.
69. When a body is in the zenith, since a ray of light
from it enters the atmosphere at right angles to the re-
fracting 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,
when a ray of light strikes the medium very obliquely,
and traverses the atmosphere through its densest part,
the refraction is greatest. The following numbers, ta-
ken at different altitudes, will show how rapidly refrac-
tion diminishes from the horizon upwards. The amount
of refraction at the horizon is 34' 00". At different ele-
vations it is as follows:

Elevation. Refraction. Elevation. Reſraction.
OO 10/ 32/ ()0// 30O TTÜ7T
OO 30/ 30' 00// 40O 1/ 09//
IO 00/ 24/ 2.5// 45O 0/ 58//
50 00/ 10/ 00// 600 0/ 33//
100 00/ 57 20// SOO 0/ 10//
200 00/ 2/ 39// 900 0/ 00//
From this table it appears, that while refraction at the
horizon is 34 minutes, at so small an elevation as only
10’ above the horizon it loses 2 minutes, more than the
entire change from the elevation of 30° to the zenith.
From the horizon to 19 above, the refraction is dimin-
ished nearly 10 minutes. The amount at the horizon,
at 45°, and at 90°, respectively, is 34, 58%, and 0. In
finding the altitude of a heavenly body, the effect of pa-
rallax must be added, but that of refraction subtracted.
70. Since the whole amount of refraction near the
horizon exceeds 33%, and the diameters of the sun and
moon are severally less than this, these luminaries are in
69. Has refraction any effect on a body in the zenith? Why
not? When is the refraction greatest? What is the amount
of refraction at the horizon 7 How much does it lose within
10' of the horizon 7 What is the amount of refraction at an
elevation of 45° 7
BEFRACTION. 4}.
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 as-
sumes 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 ob-
served from the top of a mountain, or at an elevation
near the sea shore; for in such situations the rays of
light make a greater angle than ordinary, with a perpen-
dicular to the refracting medium, and the amount of re-
fraction is proportionally greater. In some cases of this
kind, the shortening of the vertical diameter of the sun
has been observed to amount to 6', or about one fifth of
the whole.
71. The apparent enlargement of the sun and moon
in 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 is indeed 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 at the
time of its culmination. Why then do the sun and
moon appear so much larger when near the horizon It
70. What effect has refraction upon the appearances of the
sun and moon when near rising or setting 7 Explain the oval
figure of the sun when near the horizon. In what position of
the spectator does this phenomenon appear most conspicuous 7
How much has the vertical diameter of the sun ever appeared
to be shortened 7
4%
42 THE EARTH.
is owing to that general law, explained in optics, 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, allow-
ing, under a given angle, a greater magnitude as we im-
agine the distance of a body to be greater. Now, on ac-
count of the numerous objects usually in sight between
us and the Sun, when on the horizon, he appears much
farther removed from us than when on the meridian, and
we assign to him a proportionally greater magnitude. If
we view the Sun, in the two positions, through Smoked
glass, no such difference of size is observed, for here no
objects are seen but the Sun himself. -
The extraordinary enlargement of the Sun or moon,
particularly the latter, when seen at its rising through a
grove of trees, depends on a different principle. Through
the various openings between the trees, we see differ-
ent images of the sun, a great number of which overlap-
ping each other, swell the dimensions of the moon, un-
der the most favorable circumstances, to a very unusual
S17,62.
TWILIGHT.
72. Twilight also is another phenomenon depending
upon the agency of the earth's atmosphere. It is that
g }. of the sky which takes place just before
sunrise, and which continues after sunset. It is due
partly to refraction and partly to reflexion, but mostly to
the latter. While the sun is within 18° 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
71. To what is the apparent enlargement of the sun and
moon when near the horizon owing'ſ Are these bodies seen
under a greater angle when in the horizon than in the zenith ?
To what general law of optics is the enlargement to be ascri-
bed! How is it when we view the sun through smoked glass
To what is the extraordinary enlargement of these luminaries
owing, when seen through a grove of trees?
TWILIGHT. 43
the atmosphere. Let AB (Fig. 9,) be the horizon of
the spectator at A, and let SS be a ray of light from the
sun when it is two or three degrees below the horizon.
Then to the observer at A, the segment of the atmos-
phere ABS would be illuminated. To a spectator at C,
whose horizon was CD, the small segment SDw would
be the twilight; while, at E, the twilight would disap-
pear altogether,
73. At the equator, where the circles of daily motion
are perpendicular to the horizon, the Sun descends
through 18° in an hour and twelve minutes (# =1}h.),
and 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 18° of the horizon, occupying nearly two thirds
of the half year when the direct light of the sun is with-
drawn, so that the progress from continual day to con-
72. Define twilight—How many degrees below the horizon
is the sun when it begins and ends? How is the light of the
sun conveyed to us? Explain by the figure.
73. What is the length of twilight at the equator 7 How
long does it last at the poles? How is the progress from con-
tinual day to constant night? To the inhabitants of an oblique
sphere, in what latitudes is twilight longest ? -

44 THE EARTH,
stant might is exceedingly gradual. To the inhabitants
of an oblique sphere, the twilight is longer in proportion
as the place is nearer the elevated pole. º
74. Were it not for the power the atmosphere has of
dispersing the solar light, and Scattering it in various di-
rections, no objects would be visible to us out of direct
Sunshine; every shadow of a passing cloud would be
pitchy darkness; the stars would be visible all day, and
every apartment into which the sun had not direct ad-
mission, would be involved in the obscurity of might. ,
This scattering action of the atmosphere on the solar
light, is greatly increased by the irregularity of tempera-
ture 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 boun-
daries, by which means much light is turned aside from
the direct course, and diverted to the purposes of general
illumination. 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
illne.
C H A P T E R. I. W.
OF TIME.
75. TIME is a measured portion of indefinite duration.*
The great standard of time is the period of the revo-
lution of the earth on its axis, which, by the most exact
74. What would happen were it not for the power the at-
mosphere has of dispersing the solar light? What would every
shadow of a cloud produce " How is scattering action of the
atmosphere increased ? What is the aspect of the sky in the
upper regions of the atmosphere?
." From old Diernity's mysterious orb,
Was Time cut off and cast beneath the skies.—Young.
TIME. 45
observations, is found to be always the same. The time
of the earth's revolution on its axis is called a sidered!
day, and is determined by the revolution of a star from
the instant it crosses the meridian, until it comes round
to the meridian again. This interval being called a si-
dereal day, it is divided into 24 sidereal hours. Obser-
vations taken upon numerous stars, in different ages of
the world, show that they all perform their diurnal rev-
olutions in the same time, and that their motion during
any part of the revolution is perfectly uniform.
76. Solar time is reckoned by the apparent revolution
of the Sun, from the meridian round to the same 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 360° in 365%
days, it moves eastward nearly 1° a day, (59'8".3).
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, in order to come under the sun again. Now
since a place on the earth gains 359° in 24 hours, how
long will it take to gain 19?
24
359 ; 24 : : 1 : 350–4" nearly.
75. Define Time—What is the standard of time ! What is
a sidereal day? Do the stars all perſorm their revolutions in
the same time? Is their motion uniform 2
76. How is the solar time reckoned'' How far does the sun
move eastward in a day ? How much longer is the solar than the
sidereal day ? If we reckoned the sidereal day 24 hours, how
should we reckon the solar ! Reckoning the solar day at 24
hours, how long is the sidereal 7
46 THE EARTH.
Hence the Solar day is about 4 minutes longer than
the sidereal; and if we were to reckon the sidereal day
24 hours, we should reckon the solar day 24h. 4m. To
suit the purposes of society at large, however, it is found
most convenient to reckon the solar day 24 hours, and to
throw the fraction into the sidereal day. Then,
24h. 4m. ; 24::24 : 23h. 56m. nearly (23h. 56m 45.09)
= the length of a sidereal day.
77. The solar days, however, do not always differ from
the sidereal by precisely the same fraction, since the in-
crements of right ascension, which measure the differ-
ence between a sidereal and a solar day, are not equal to
each other. Apparent time, is time reckoned by the
revolutions of the sun from the meridian to the meridian
again. These intervals being unequal, of course the
apparent Solar days are unequal to each other.
78. 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 24 hours,
beginning when the sun is on the lower meridian, name-
ly, at 12 o'clock at night, and counted by 12 hours from
the lower to the upper culmination, and from the upper
to the lower. The astronomical day is the apparent so-
lar day counted through the whole 24 hours, instead of
by periods of 12 hours each, and begins at noon. Thus
10 days and 14 hours of astronomical time, would be
11 days and 2 hours of apparent time; for when the 10th
astronomical day begins, it is 10 days and 12 hours of
civil time.
79. Clocks are usually regulated so as to indicate mean
Solar time ; yet as this is an artificial period, not marked
77. Do the solar days always differ from the sidereal by the
same quantity ? Define apparent time.
78. Define mean time. What constitutes the civil day ?
What makes an astronomical day ? When does the civil day
begin? When does the astronomical day begin 7
THE CALEND AIR. 47
off, like the sidereal day, by any natural event, it is ne-
cessary to know how much is to be added to or sub-
tracted from the apparent solar time, in order to give the
corresponding mean time. The interval by which ap-
parent time differs from mean time, is called the equation
of time. If a clock were constructed (as it may be) so
as to keep exactly with the sun, going faster or slower
according as the increments of right ascension were
greater or smaller, and another clock were 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 ap-
parent clock were slower than the mean, then the equa-
tion of time must be added, to give the mean time.
The two clocks would differ most about the 3d of No-
vember, when the apparent time is 16#m greater than the
mean (16m 16s.7). But, since apparent time is some-
times greater and sometimes less than mean time, the
the two must obviously be sometimes equal to each other.
This is in fact the case four times a year, namely, April
15th, June 15th, September 1st, and December 22d.
THE CALIEND.A.R.
80. The astronomical year is the time in which the
sun makes one revolution in the ecliptic, and consists of
365d. 5h. 48m. 518.60. The civil year consists of 365
days. The difference is nearly 6 hours, making one day
in four years.
The most ancient nations determined the number of
days in the year by means of the stylus, a perpendicular
79. What time do clocks commonly keep? Define the equa-
tion of time. How might two clocks be regulated so that their
difference would indicate the equation of time ! How must
the equation of time be applied when the apparent clock is
faster than the mean? How when it is slower'ſ When would
the two clocks differ most 7 How much would they then differ 7
When would they come together ?
48 THE EARTH.
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 365 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 hap-
pened on the 21st of June, at the end of four years, the
sun would not have reached the Solstice until the 22d 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 23d ; and in process of time it would fall succes-
sively on every day of the year. The same would be
true of any other fixed date. Julius Caesar made the
first correction of the calendar, by introducing an inter-
calary day every fourth year, making February to con-
sist of 29 instead of 28 days, and of course the whole
year to consist of 366 days. This fourth year was de-
nominated Bisseatile. It is also called Leap Year.
81. But the true correction was not 6 hours, but 5h.
49m. ; hence the intercalation was too great by 11 min-
utes. This small fraction would amount in 100 years
to # of a day, and in 1000 years to more than 7 days.
From the year 325 to 1582, it had in fact amounted to
about 10 days; for it was known that in 325, the vernal
equinox fell on the 21st of March, whereas, in 1582 it
fell on the 11th. In order to restore the equinox to the
same date, Pope Gregory XIII, decreed, that the year
80. Define the astronomical year—What is its exact period
Of how many days does the civil year consist? How much
shorter is the civil than the astronomical year? How did the most
ancient nations determine the number of days in the year !
When would the stylus mark the shortest day and when the
longest ? Explain the confusion which arose by reckoning the
year only 365 days. How did Julius Caesar reform the calendar’
THE CALENIDAR, 49
should be brought forward 10 days, by reckoning the
5th of October the 15th. In order to prevent the cal-
endar from falling into confusion afterwards, the follow-
ing rule was adoped :
Every year whose number is not divisible by 4 with-
out a remainder, consists of 365 days; every year which
is so divisible, but is not divisible by 100, of 366; every
gyear divisible by 100 but not by 400, again of 365; and
every year divisible by 400, of 366. -
Thus the year 1838, not being divisible by 4, contains
365 days, while 1836 and 1840 are leap years. Yet to
make every fourth year consist of 366 days would in-
crease it too much by about # of a day in 100 years;
therefore every hundredth year has only 365 days.
Thus 1800, although divisible by 4 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 400 years we
should allow a day too much, and therefore we let the
400th year remain a leap year. This rule involves an
error of less than a day in 4237 years. If the rule were
extended by making every year divisible by 4000 (which
would now consist of 366 days) to consist of 365 days,
the error would not be more than one day in 100,000
years.
82. This reformation of the calendar was not adopted
in England until 1752, by which time the error in the
Julian calendar amounted to about 11 days. The year
was brought forward, by reckoning the 3d of September
the 14th. Previous to that time the year began the 25th
81. By how many minutes was the allowance made by the
Julian calendar too great 7 To how much would the error
amount in one hundred years? To how much in a thousand
years? To how much had it amounted from the year 325 to
1582? What changes did Pope Gregory make in the year?
State the rule for the calendar. Of the three years 1836,
1838, and 1840, which are leap years ? Was 1800 a leap year !
How is every 400th year ! k |
{)
50 THE EARTH.
of March ; but it was now made to begin on the 1st of
January, thus shortening the preceding year, 1751, one
quarter.”
As in the year 1582, the error in the Julian calendar
amounted to 10 days, and increased by # of a day in a
century, at present the correction is 12 days; and the
number of the year will differ by one with respect to
dates between the 1st of January and the 25th of March.
Eacamples. General Washington was born Feb. 11,
1731, old style ; to what date does this correspond in
new style 2 .
As the date is the earlier part of the 18th century, the
correction is 11 days, which makes the birth day fall on
the 22d of February; and since the year 1731 closed
the 25th of March, while according to new style 1732
would have commenced on the preceding 1st of Janu-
ary; therefore, the time required is Feb. 22, 1732. It
is usual, in such cases, to write both years, thus: Feb.
11, 1731–2, O. S. - * -
2. A great eclipse of the sun happened May 15th,
1836; to what date would this time correspond in old
style : - Ans. May 3d.
83. The common year begins and ends on the same
day of the week; but leap year ends one day later in
the week than it began.
For 52 x7=364 days; if therefore the year begins
on Tuesday, for example, 364 days would complete 52
weeks, and one day would be left to begin another week,
82. When was this reformation first adopted in England?
How was the year brought forward ' When did the year be-
gin before that time ! To how many days did the error amount
in 1752? How many days are allowed at present between old
and new style? " -
* Russia, and the Greek Church generally, adhere to the old style.
In order to make the Russian dates correspond to ours, we must add to
them 12 days. France and other Catholic countries, adopted the Gre-
gorian calendar soon after it was promulgated.
ASTRONOMICAL INSTRUMENTS. 51
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 16th of November, 1838, falls on Friday,
the 16th of November, 1837, fell on Thursday, and in
1839 will fall on Saturday. But if leap year begins on
Sunday, it ends on Monday, and the following year be-
gins on Tuesday; while any given day of the month is
two days later in the week than the corresponding date
of the preceding year.
C H A P T E R. W.
OF ASTRONOMICAL INSTRUMENTS.–FIGURE AND DENSITY OF
THE EARTH.
84. THE most ancient astronomers employed no in-
struments of observation, but acquired their knowledge
of the heavenly bodies by long continued and most at-
tentive inspection with the naked eye. Instruments for
measuring angles were first used in the Alexandrian
school, about 300 years before the Christian era.
85. Wherever we are situated on the earth we appear
to be in the center of a vast sphere, on the concave sur-
face 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
83. If the common year begins on a certain day of the week,
how will it end? How is it with leap year ! . How does any
day of the month compare in the preceding and following year
with respect to the day of the week 7 How is this in leap
year !
84. How did the most ancient nations acquire their knowl-
edge of the heavenly bodies' When were astronomical instru-
ments first introduced 7 -
52 THE EARTH.
lines will be measured by the arc of the sky contained
between the two points. Thus if HBD, (Fig. 10,) rep-
Fig. 10.
TE
resents the concave surface of the sphere, A, B, two
points on it, as two stars, and CA, CB, straight lines
drawn from the spectator to those points, then the angu-
lar distance between them is measured by the arc AB,
or the angle ACB. But this angle may be measured on
a much smaller circle, having the same center, as EFG,
since the arc EF will have the same number of degrees
as the arc AB. 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 CE upon the graduated circle KEG.
The common surveyor's compass affords a simple ex-
ample 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 how many de-
grees any object to which we direct the eye, lies east or
west of the meridian.
85. How is the angular distance between two points on the
celestial sphere measured 7 Explain figure 10. Show how the
circles of the sphere may be truly represented by the smaller
circles of the instrument, as the horizon by the surveyor's com-
pass. Explain the simplest mode of taking angles by figure 10,

ASTRONOMICAL INSTRUMENTS. 53
86. 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
Fºr of an inch. If the circle is 20 feet in diameter, a
degree will occupy the space of two inches and could
be easily divided to minutes, since each minute would
cover a space of ºr of an inch. Refined astronomical
circles are now divided with very great skill and accu-
racy, 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. *
The principle instruments employed in astronomy,
are the Telescope, the Transit Instrument, the Altitude
and Azimuth Instrument, and the Sextant.
87. The Telescope has greatly enlarged our knowl-
edge of astronomy, both by revealing to us many things
invisible to the naked eye, and also by enabling us to
attain a much higher degree of accuracy than we could
otherwise reach, in angular measurements. It was in-
vented by Galileo about the year 1600. The powers of
the telescope were improved and enlarged by successive
efforts, and finally, about 50 years ago, telescopes were
constructed in England by Dr. Herschel, of a size and
power that have not since been surpassed.
A complete knowledge of the telescope cannot be ac-
quired without an acquaintance with the science of op-
tics; but we may perhaps convey to one unacquainted
with that Science, some idea of the leading principles of
86. What is the advantage of having large circles for angular
measurements? When the circle is one foot in diameter, what
space will 1* occupy on the limb 7 What space when the cir-
cle is twenty feet in diameter'? What are the principal instru-
ments used in astronomical observations?
5%
54. THE EARTH,
this noble instrument. By means of the telescope, we
first form an image of a distant object as the moon for
evample, and then magnify that image by a microscope.
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.
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 repre-
Sented in the following diagram. Let ABCD represent
Fig 11.
the tube of a 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 at-
tached to the end BC. The lens L is called the object-
glass, and the microscope in BC the eye-glass. We ap-
ply a magnifier to this image just as we would to any
87. Who invented the telescope? Who constructed tele-
scopes of great size and power? Explain the leading principle
of the telescope. How is the image formed ! What is a con-
vex lens ! How does it affect parallel rays of light? How do
we view the image formed by the lens? How is the image mag-
nified ? How is it rendered brighter ?

ASTRONOMICAL INSTRUMENTS. 55
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 col-
lects and conveys to the eye a much greater quantity of
light than would proceed directly from the body under
examination. A very small beam 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 dis-
tinctly visible, which would otherwise be either too mi-
nute, or not sufficiently luminous to be seen by us.
88. 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 pro-
ceed from any luminous body and of forming an image
of that body. The image formed by the concave mir-
ror is magnified by a microscope in the same manner as
when formed by the convex lens. When the lens, is
used to form an image, the instrument is called a Re-
fracting telescope; when a concave mirror is used, it is
called a Reflecting telescope.
The telescope in its simplest form is employed not so
much for angular measurements, as for aiding the pow-
ers of vision in viewing the celestial bodies. When di-
rected to the sun, it reveals to us various irregularities on
his disk not discernible by naked vision ; when turned
upon the moon or the planets, it affords us new and in-
teresting views, and enables us to see in them the linea-
ments of other worlds; and when brought to bear upon
the fixed stars, it vastly magnifies their number and re-
veals to us many surprising facts respecting them.
88. How is an image formed by a concave mirror 7 How is
this image magnified ? When is the instrument called a refrac-
ting and when a reflecting telescope 7 For what purposes are
telescopes chiefly employed 7
56 THE EARTH,
89. The Transit Instrument is a telescope, which is
fixed permanently in the meridian, and moves only in
that plane. It rests on a horizontal axis, which consists
of two hollow cones applied base to base, a form uniting
lightness and strength. The two ends of the axis rest
Fig. 12.
T}
W
on two firm supports, as pillars of stone, for example, so
connected with the building as to be as free as possible
from all agitation. In figure 12, AD represents the tele-
89. What is a Transit Instrument? On what supports does
it rest as represented in figure 12. Why are they made so firm'ſ
Describe all parts of the instrument. What is its use 7 How
used to regulate clocks and watches 7 What kind of time is
shown when the sun is on the meridian! How is this con-
verted into mean time ! Give an example,

ASTRONOMICAL INSTRUMENTS. 57
Scope, E, W, massive stone pillars supporting the hori-
Zontal axis, beneath which is seen a spirit level, (which
is used to bring the axis to a horizontal position,) and n
a vertical circle graduated into degrees and minutes.
This circle serves the purpose of placing the instrument
at any required altitude, or distance from the zenith, and
of course for determining altitudes and zenith distances.
The use of the transit instrument is to show the pre-
cise moment when a heavenly body is on the meridian.
One of its uses is to enable us to obtain the true time,
and thus to regulate our clocks and watches. We find
when the Sun’s center is on the meridian, and this gives
us the time of noon or apparent time. (Art. 78.) But
watches and clocks usually keep mean time, and there-
fore in order to set our time piece by the transit instru-
ment, We must apply the equation of time.
90. A moon 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 be-
ing taken of the shadow projected upon it by the per-
pendicular 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 center 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 moon mark from the same observation. It must be
borne in mind, however, that the noon mark gives the
apparent time, and that the equation of time must be
allowed for in setting the clock or watch. Suppose we
wish to set our clock right on the first of January. We
find by a table of the equation of time, that mean time
then precedes apparent time 3m. 43s. ; we must there-
fore set the clock at 3m. 43s. the instant the center of
the Sun is on the meridian. If the time had been the
first of May instead of the first of January, then we
find by the table that 3m. is to be subtracted from the
apparent time, and consequently, when the center of the
90. Describe the mode of making a noon mark.
5S THE EARTH.
Sun was on the meridian, we should set our clock at 11h.
57 m. or 3m. before twelve.
91. The equation of time varies a little with different
years, but the following table will always be found
within a few seconds of the truth. The equation for
the current year is given exactly in the American Al-
Iſlalla C.
Equation of Time for Apparent Noon.


wi JAN. FEB. | MAR, APR MAY. JUNE 1 JULY, Aug. SEPT. 1 Oct. Nov. DEC,
;"| Add. Add. Add. | Add. Sub. Sub. Add. Add. Add. | Sub. | Sub. | Sub.
P M. S. M. 8. M. S. M. S. M. s. M. S. M. S. M. S. M. S. M. S. - M. S. TM. S.T
1| 3.43T3.53. 12.42|4, 63.T02.38|3.1916. 3|ao. 1 ||10. 9|16.15,TO.54
2 4.11|14. 112.30|3.483.72:29]3.315.59s).17|10.28|16.16 10.32
3| 4.39||14. 8 12.18|3.30|3.152.19 |3.425.55 0.36||10.47|16.17 10. 8
4| 5. 7|14.14 12. 5 || 3.12|3.21|2.103.53.5 50 0.56||11. 6 16.17| 9.45
5 5.3414.1911.51]2.543.27.2. 014. 45.45| 1.15||11.24|1616 9.20)
6T6. IIA 34 ITISS|2373.32|1.4914. Tä5.39|T35|TT.42|16.14|T8.55 .
7| 6.2714.27 11.23|2.193.37|1 394 25|5.33 1.55 |11.59| 16.11| 8.30
8, 6.53.14.3011.8|2. 23.421.28|4,345.25 2.15||12.16 16. 7 8.4
9| 7.1814.32 10.53 | 1.453.46il.174,445.18, 2.36||12.33 16. 3| 7.37
10| 743.14.33.10.38||1283,491. 5|4,535, 9| 2.56|1249. 1558 7.10|
ITT3.714.34 IO.32 III/3.5|U.535. I5. TIT3. Tº |13, 5, 15.51|T6.43
12| 8.31 14.33 10. 6|0.55|3.53|0.41 |5. 94.51 3.38||13.20, 15.44 6.15
13 35414.32 9.49 || 0.393.55|0.295.174.41 3.59 |13.34. 15.37 5.47
14|9,1614.30; 9.32 0.233.56|0.17|5.244.31|| 4.20 || 13.49. 15.28, 5.18
15| 9.37|14.28, 9.15|0. 83.56|0. 4 |5.304.20 4.4] |14. 2. 15.18 4.49
* : *-ºs- Sub TAdd. −
16| 9.58|14.25 8.58||0. 73.56|0. 8||5.374, 8' 5. 2114.15 15. 8, 4.20
17|10.1914.20 8.41 || 0.223.550.2] [5.4.23.56 523|14.28. 14.56 3.50
38|10.38.14.16; 8.23 || 0.363.54|0.34 || 5.483.44 5.44|14.39|| 14.44| 3.21
19||0.57.14.10 8.5|0.503 520.47|5.523.31|6. 5|14.51. 14.31] 2.51
2011.1514. 4 7.47 | 1. 33.491. 0|5.57|3.17; 6.26||15. T 14.17 2.21
2III.3313.58|T729|II63,461.1316.T03. 3|T6.47|15.11||14. 3| 1.51
2211.4913.50 7.11 | 1.293.42|1.266. 32.49 7. 8|15.21 13.47 1.21
23|12. 513.42 6.52| 1.413.38||1.39||6. 62 34 7.29|15 29, 13.31 0.51
|24|12.2013.34 6.34 | 1.523.331.52|6. 82.19 7.49|15.37 13.14 0.21
2512.3513.25 6.15|2, 43.282. 5|6. 92. 3|8.10|15.44. 1256 a 0. 9
26.12.48.13.15 5.57|2.143.222.18|6.IOI.47; 8.30|I5.51 12.38 0.39
27|13. 113. 4. 538 3243.1% 2.30 6.10|1.30| 8.50|15.57| 12 18 1. 9
23||1313||12.54 5.2012,343. 92.4316.101.13| 9,11|16. 2 #3| 139
29:13.24 5,12433. 22.5:16, 90.56 9.39||13.6 II .38 2. 8
30|1335 4.43|2.522.54|3. 8|6. 80.38 9.50|16.10|11.16|| 2:37
3] 13.44 4.25 3.46|T|6. 50.3) |16.13 3. 6

-
--
91. Is the equation of time the same or different in different
years? In what book may it be found exactly for the current
year?
ASTRONOMICAL INSTRUMENTS. 59
92. The Astronomical Clock is the constant compan-
ion of the Transit Instrument. This clock is so regu-
lated 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 15°, and 24 hours
for the whole period of the revolution of the star. Si-
dereal time, it will be recollected, commences when the
vernal equinox is on the meridian, just as solar time com-
mences 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 3h 20m. ;
this may be in the morning, at noon, or any other time
of the day, since it merely shows that it is 3h. 20m.
since the equinox was on the meridian. Hence, when
a star is on the meridian, the clock itself shows its right
ascension; (Art. 24,) and the interval of time between
the arrival of any two stars upon the meridian, is the
measure of their difference of right ascension.
93. Astronomical clocks are made of the best work-
manship, with a compensation pendulum, and every
other advantage which can promote their regularity.
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 cor-
respond to exactly 24 hours by the clock, and to con-
92. How is the astronomical clock regulated 7 What does
it measure ? How many degrees does a star pass over in an
hour ! When does sidereal time commence? What is denoted
by the hour and minute of a sidereal clock" How do we de-
termine the right assension of a star 7
93. How is the workmanship of astronomical clocks? How
is the correctness of a clock tested To what degree of per-
ſection are clocks brought ! By what instrument are clocks
regulated 7 -.
60 THE EARTH.
tinue the same from day to day; and the right ascen-
sion 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 determin-
ations of astronomers. Or by taking the difference of
right ascension 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 ascen-
sion 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 umi-
formly from hour to hour.
Although astronomical clocks have been brought to a
great degree of perfection, so as to vary hardly 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. In-
deed, for the nicest observations, it is usual not to at-
tempt to bring the clock to an absolute state of correct-
ness, 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 its rate of going, and
to make allowance accordingly.
94. The Transit Instrument is adapted to take obser-
vations on the meridian only ; but we sometimes require
to know the altitude of a celestial body when it is not
on the meridian, and its azimuth, or distance from the
meridian measured on the horizon. An instrument es-
pecially designed to measure altitudes and azimuths, is
called an Altitude and Azimuth Instrument, whatever
may be its particular form. When a point is on the hor-
izon its distance from the meridian, or its azimuth, may
be taken by the Common Surveyor's compass, the direc-
94. To what kind of observations only is the transit instru-
ment adapted ' What instrument is employed for finding alti-
tude and azimuth 7 Describe the Altitude and Azimuth Instru-
ment from figure 13.
ASTRONOMICAL INSTRUMENTS. 61
tion of the meridian being determined by the needle;
but when the object, as a star, is not on the horizon, its
azimuth, it must be remembered, is the arc of the hori-
zon from the meridian to a vertical circle passing through
the star; at whatever different altitudes, therefore, two
stars may be, and however the plane which passes
through them may be inclined to the horizon, still it is
their angular distance measured on the horizon which
determines their difference of azimuth. Figure 13 rep-
resents an Altitude and Azimuth Instrument, several of
the usual appendages and subordinate contrivances being
omitted for the sake of distinctness and simplicity. Here
abc is the vertical or altitude circle, and EFG the hori-
Zontal or azimuth circle ; AB is a telescope mounted on
Fig. 13.
a horizontal axis and capable of two motions, one in al-
titude parallel to the circle abc, and the other in azimuth
parallel to EFG. Hence it can be easily brought to

6
62 THE EARTH.
bear upon any object. At m, under the eye glass of the
telescope, is a small mirror placed at an angle of 45°
with the axis of the telescope, by means of which the
image of the object is reflected upwards, so as to be
conveniently presented to the eye of the observer. At d
is represented a tangent screw, by which a slow motion
is given to the telescope at c. At h and g are seen two
spirit levels, at right angles to each other, which show
when the azimuth circle is truly horizontal. The in-
strument is supported on a tripod, for the sake of greater
steadiness, each foot being furnished with a screw for
levelling.
95. The SExTANT is an instrument used for taking the
angular distance between any two bodies on the surface
of the celestial sphere, by reflecting the image of one of
the bodies so as to coincide with the other body as seen
directly. It is particularly valuable for measuring celes-
tial arcs at sea, because it is not, like most astronomical
instruments, affected by the motion of the ship.
This instrument (Fig 14,) is of a triangular shape,
and is made strong and firm by metalic crossbars. 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 Wernier at D, which 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 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.
95. Define the Sextant—For what is it particularly valu-
able? Describe it from figure 14. Where is the Wernier and
what is its use ! Specify the manner in which the light comes
from the object to the eye. How can we measure the angular
distance between the moon and a star 7
ASTRONOMICAL INSTRUMENTS. 63
Suppose it were required to measure the angular dis-
tance between the moon and a certain star, the moon
Figure 14.
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 carried 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.
FIGURE AND DENSITY OF THE EARTH.
96. We have already shown, that the figure of the
earth is nearly globular; but since the semi-diameter of
the earth is taken as the base line in determining the
parallax of the heavenly bodies, and lies therefore at the
foundation of all astronomical measurements, it is very

64 THE EARTH.
important that it should be ascertained with the greatest
possible exactness. Having now learned the use of as-
tronomical instruments, and the method of measuring
arcs on the celestial sphere, we are prepared to under-
stand the methods employed to determine the exact fig-
ure of the earth. This element is indeed ascertained
in different ways, each of which is independent of all
the rest, namely, by investigating the effects of the cem-
trifugal force arising from the revolution of the earth
on its axis—by measuring arcs of the meridian—and by
experiments with the pendulum. -
97. First, the known effects of the centrifugal force,
would give to the earth a spheroidal figure, elevated ine
the equatorial, and flattened in the polar regions.
By the centrifugal force is meant, the tendency which
revolving bodies exhibit to recede from the
center. Thus when a grindstone is turn-
ed swiftly, water is thrown off from it in
straight lines. The same effect is notic-
ed when a carriage wheel is driven rapidly
through the water. If a pail, containing
a little water, is whirled, the water rises
on the sides of the pail in consequence of
the centrifugal force. The same principle
is more strikingly illustrated by the annex-
ed cut, (Fig. 15,) which represents an
open glass vessel suspended by a cord at-
tached to its opposite sides, and passed
through a staphe in the ceiling of the room.
A little water is introduced into the ves-
sel which is made to whirl rapidly by ap-
plying the hand to the opposite sides. As
it turns, the water rises on the sides of the
vessel, receding as far as possible from the
96. Why is it so necessary to ascertain accurately the semi-
diameter of the earth? In how many different ways is their
element ascertained 7 Specify them. What is meant by the
centrifugal force Give an illustration. Describe figure 15,


ASTRONOMICAL INSTRUMENTS. (35
center. The same effect is produced by suffering the
cord to untwist freely, which gives a swift revolution
to the vessel. In like manner, a ball of soft clay when
made to turn rapidly on its axis, swells out in the central
parts and becomes flattened at the ends, forming the fig-
ure called an oblate spheriod.
Had the earth been originally constituted (as geolo-
gists suppose) of yielding materials, either fluid or semi-
fluid, so that its particles could obey their mutual at-
traction, while the body remained at rest it would spon-
taneously assume the figure of a perfect sphere; as soon,
however, as it began to revolve on its axis, the greater
velocity of the equatorial regions would give to them a
greater centrifugal force, and cause the body to swell
out into the form of an oblate spheroid. Even had the
solid part of the earth consisted of unyielding materials
and been created a perfect sphere, still the waters that
covered it would have receded from the polar and have
been accumulated in the equatorial regions, leaving bare
extensive regions on the One side, and ascending to a
mountainous elevation on the other.
On estimating, from the known dimensions of the
earth and the velocity of its rotation, the amount of the
centrifugal force in different latitudes, and the figure of
equilibrium which would result, Newton inferred that
the earth must have the form of an oblate spheroid be-
fore the fact had been established by observation ; and
he assigned nearly the true ratio of the polar and equa-
torial diameters. g
97. What would be the figure of the earth derived from the
centrifugal force? What figure would the earth have assumed
if at rest? How would this figure be changed when it began to
revolve? Had the earth been originally a solid sphere covered
with water, how would the water have disposed itself when the
earth was made to turn on its axis? How was the spheroidal
figure of the earth inferred before the fact was established by
observation ?
6%
66 THE EARTH.
98. Secondly, the spheroidal figure of the earth is
proved, by actually measuring the length of a degree on
the meridian in different latitudes.
Were the earth a perfect sphere, the section of it made
by a plane passing through its center in any direction
would be a perfect circle, whose curvature would be
equal in all parts; but if we find by actual observation,
that the curvature of the section is not uniform, we in-
fer a corresponding departure in the earth from the figure
of a perfect sphere. The task of measuring portions of
the meridian, has been executed in different countries.
We may know, in each case, how far we advance on
the meridian, because every step we take northward,
produces a corresponding increase in the altitude of the
north star. That an increase of the length of the de-
grees of the meridian, as we advance from the equator
towards the pole, really proves that the earth is flattened
at the poles, will be readily seen on a little reflection.
We must bear in mind that a degree is not any certain
length, but only the three hundred and sixtieth part of a
circle, whether great or small. If, therefore, a degree is
longer in one case than in another, we inſer that it is the
three hundred and sixtieth part of a larger circle; and
since we find that a degree towards the pole is longer
than a degree towards the equator, we infer that the cur-
Vature is less in the former case than in the latter.
The result of all the measurements is, that the length
of a degree increases as we proceed from the equator
towards the pole, as may be seen from the following
table :
98. By what measurements is the spheroidal figure of the
earth proved? What would be the curvature in all parts were
the earth a perfect sphere? How may we know when we have
advanced one degree northward in the meridian Explain how
an increase of the length of a degree proves that the earth is
ſlattened towards the poles? In what places have arcs of the me-
ridian been measured ' What is the mean diameter of the
earth'ſ What is the diſſerence between the two diameters?
What fraction expresses the ellipticity of the earth 7
ASTRONOMICAL INSTRUMENTS. 67

Places of observation. Latitude. Length of a degree in miles.
Peru, 000 00' 00// 68.732
Pennsylvania, 30 12 00 68.896
Italy, 43 01 00 68.998
France, 46 12 00 69.054
England, 51 29 54; 69.146
Sweden, - (36 20 10 69.292
Combining the results of various estimates, the di-
mensions of the terrestrial spheroid are found to be as
follows:
Equatorial diameter, e • © 7925.64S
Polar diameter, o º .* : * 7S99. I70
Mean diameter, e tº e & 79 12.409
The difference between the greatest and the least, is
26.478=### of the greatest. This fraction (###) is de-
nominated the ellipticity of the earth, being the excess
of the longest over the shortest diameter.
99. Thirdly, the figure of the earth is shown to be
spheroidal, 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 3600 times per hour at the
equator, will vibrate 3605; 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
99. Explain how we may ascertain the figure of the earth by
means of a pendulum—How will the number of vibrations be
in different latitudes 7 How many times will a pendulum vi-
brate in an hour at London, which vibrates 3600 times per hour
at the equator? How are the vibrations of the pendulum pro-
duced ' Why are these comparative numbers at different
places measures of the relative distances from the center of the
earth'ſ What could we inſer from two observations with the
pendulum, one at the equator and the other at the north pole'ſ
To what conclusions have pendulum observations, made in va-
rious parts of the earth, led '' -
68 THE EARTH.
e-
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 dis-
tances from the center of the earth, because the nearer a
place is to the center 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 rel-
ative forces of gravity, we can thence deduce their rela-
tive distances from 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.
100. The density of the earth compared with water,
that is, its specific gravity, is 54. The density was first
estimated by Dr. Hutton, from observations made by Dr.
Maskelyne, Astronomer Royal, on Schehallien, a moun-
tain of Scotland, in the year 1774. Thus, let M (Fig.
16,) represent the mountain, D, B, two stations on op-
posite sides of the mountain, and I a star; and let IE
and IG be the zenith distances as determined by the
difference of latitude of the two stations. But the ap-
parent Zenith distances as determined by the plumb line
are IE' and IG'. The deviation towards the mountain
on each side exceeded 7”. The attraction of the moun-
tain being observed on both sides of it, and its mass be-
ing computed from a number of sections taken in all di-
100. What is the specific gravity of the earth? How was it
ascertained' Explain figure 16. Why is the density of the
earth so important an element?
DENSITY OF THE EARTH. 69
Fig. 16.
I
rections, these data, when compared with the known
attraction and magnitude of the earth, led to a knowl-
edge of its mean density. According to Dr. Hutton,
this is to that of water as 9 to 2; but later and more ac-
curate estimates have made the specific gravity of the
earth as stated above. But this density is nearly double
the average density of the materials that compose the
exterior crust of the earth, showing a great increase of
density towards the center.
The density of the earth is an important element, as
we shall find that it helps us to a knowledge of the den-
sity of each of the other members of the Solar system,

70
PART II.-OF THE SOLAR SYSTEMI.
101. HAVING considered the Earth, in its astronomical
relations, and the Doctrine of the Sphere, we proceed
now to a survey of the Solar System, and shall treat suc-
cessively of the Sun, Moon, Planets, and Comets.
C H. A. P. T. E. R. I.
OF THE SUN–SOLAR SPOTS-ZODIACAL LIGHT.
102. THE figure which the sun presents to us is that
of a perfect circle, whereas most of the planets exhibit a
disk more or less elliptical, indicating that the true shape
of the body is an oblate spheroid. So great, however,
is the distance of the sun, that a line 400 miles long
would subtend an angle of only 1” at the eye, and would
therefore be the least space that could be measured.
Hence, were the difference between two conjugate di-
ameters of the sun any quantity less than this, we could
not determine by actual measurement that it existed at
all. Still we learn from theoretical considerations,
founded upon the known effects of centrifugal force,
arising from the Sun's revolution on his axis, that his
figure is not a perfect sphere, but is slightly spheroidal.
103. The distance of the sun from the earth, is nearly
95,000,000 miles. In order to form some faint concep-
101. What subjects are treated of in Part II?
102. What figure does the sun present to us? What angle
would a line of 400 miles on the sun's disk subtend ? How is
it inferred that the figure of the sun is spheroidal?
DENSITY. 71
tion at least of this vast distance, let us reflect that a rail-
way car, moving at the rate of 20 miles per hour, would
require more than 500 years to reach the sun.
The apparent diameter of the sun is a little more than
half a degree, (32' 3".) Its linear diameter is about
885,000 miles; and since the diameter of the earth is
only 79.12 miles, the latter number is contained in the
former nearly 112 times; so that it would require One
hundred and twelve bodies like the earth, if laid side by
side, to reach across the diameter of the Sun ; and a ship
sailing at the rate of ten miles an hour, would require
more than ten years to sail across the solar disk.
The sun is about 1,400,000 times as large as the earth.
The distance of the moon from the earth being 238,000
miles, were the center of the sun made to coincide with
the center of the earth, the sun would extend every Way
from the earth more than twice as far as the moon.
104. In density, the sun is only one fourth that of the
earth, being but a little heavier than water; and the
quantity of matter in the sun is three hundred and fifty
thousand times as great as in the earth. A body would
weigh nearly 28 times as much at the sun as at the
earth. A man weighing 200 lbs. would, if transported
to the surface of the sun, weigh 5,580 lbs., or nearly 24
tons. To lift one's limb, would, in such a case, be be-
yond the ordinary power of the muscles. At the surface
of the earth, a body falls through 16 tº feet in a second ;
103. What is the distance of the sun from the earth 7 How
long would a railway car, moving at the rate of 20 miles per
hour, require to reach the Sun ? How many bodies equal to
the earth could lie side by side across the Sun ? How long
would a ship be in sailing across it at 10 miles an hour? If
the sun’s center were made to coincide with the center of the
earth, how much farther would it reach than the moon 7 What
is the sun's apparent diameter'? What is its linear diameter?
104. In density how does the sun compare with the earth?
How in quantity of matter'ſ How much more would a body
weigh at the sun than at the earth 7 How far would a body
all in one second at the surface of the Sun ?
72 - THE SUN.
but a body would fall at the Sun in one second through
448.7 feet.
SOLAR SPOTS.
105. The surface of the sun, when viewed with a
telescope, usually exhibits dark spots, which vary much,
at different times, in number, figure, and extent. One
hundred or more, assembled in several distinct groups,
are sometimes visible at once on the solar disk. The
greatest part of the solar spots are commonly very small,
but occasionally a spot of enormous size is seen occupy-
ing an extent of 50,000 miles in diameter. They are
sometimes even visible to the naked eye, when the sun
is viewed through colored glass, or, when near the hori-
zon, it is seen through light clouds or vapors. When it
is recollected that 1” of the solar disk implies an extent
of 400 miles, it is evident that a space large enough to be
seen by the naked eye, must cover a very large extent.
A Solar spot usually consists of two parts, the nucleus
and the umbra, (Fig. 17.) The nucleus is black, of a
Fig. 17.
105. Solar spots.-Are they constant or variable in number
and appearance? How many are sometimes seen on the sun's
disk at once? Are they usually large or small '! How many
miles in diameter are the largest ? Describe a spot. What
changes occur in the nucleus? What is the umbra ! In what
part of the sun do the spots mostly appear ! What apparent
motions have they 7 What is the period of their revolution ?

SOLAR SPOTS, 73
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 dif-
ferent 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 ex-
tending across the central regions of the Sun, not exceed-
ing 60° in breadth. . When the spots are observed from
day to day, they are seen to move across the disk of the
sun, occupying about two weeks in passing from one
limb to the other. After an absence of about the same
period, the spot returns, having taken 27d. 7h. 37m. in
the entire revolution.
Fig. 18.
4%.
106. The spots must be nearly
or quite in contact with the body.
of the sun. Were they at any
considerable distance from it, the
time during which they would
be seen on the solar disk, would
be less than that occupied in
the remainder of the revolution.
Thus, let S, (Fig. 18,) be the
sun, E the earth, and abe the
path of the body, revolving about
the sun. Unless the spot were
nearly or quite in contact with
the body of the Sun, being pro-
jected upon his disk only while
passing from b to c, and being
invisible while describing the
arc cab, it would of course be
out of sight longer than in sight,
whereas the two periods are N
found to be equal. Moreover, l.
106. How are the spots known to be nearly or quite in con-
tact with the body of the Sun ? Illustrate by figure 18, What
causes the motion of the spots? What is the period of the sun’s
revolution on his axis Explain by figure 19. -

74 THE SUN.
the lines which all the solar spots describe on the disk
of the Sun, are found to be parallel to each other, like
the circles of diurnal revolution around the earth, and
hence it is inferred that they arise from a similar cause,
namely, the revolution of the sum on its avis, a fact which
is thus made known to us.
But although the spots occupy about 27# days in pass-
ing from One limb of the sun around to the same limb
again, yet this is not the period of the sun’s revolution
on his axis, but exceeds it by nearly two days. For,
let AA/B (Fig. 19,) represent the sun, and EE/M the
orbit of the earth. Thus, when the earth is at E, the
visible disk of the sun will be Fig. 19
AA/B ; and if the earth remain- 5* +* *
- * M.
ed stationary at E, the time oc-
cupied by a spot aſter leaving A
until it returned to A, would be
just equal to the time of the
sun's revolution on his axis.
But during the 27# days in
which the spot has been per-
forming its apparent revolution,
the earth has been advancing
in his orbit from E to E', where
the visible disk of the sun is
A'B'. Consequently, before the spot can appear again
on the limb from which it set out, it must describe so
much more than an entire revolution as equals the arc
AA', and this occupies nearly two days, which sub-
tracted from 27# days, makes the Sun's revolution on
its axis about 25+ days; or more accurately, it is 25d.
9h. 56m.
107. A telescope of moderate powers is sufficient to
show the spots on the sun, and it is earnestly recom-
mended to the learner to avail himself of the first oppor-
107. How large a telescope is sufficient to view the spots on
the sun ? How is the eye protected from the glare of the sun’s
light? How may these shades be made 7

SOLAR SPOTS. 75
tunity he may have, to view them for himself. For ob-
servations on the sun, telescopes are usually furnished
with colored glass shades, which are screwed upon the
end of the instrument to which the eye is applied, for
the purpose of protecting the eye from the glare of the
sun's light. Such screens may be easily made by hold-
ing a small of piece of window glass over the flame of a
lamp, the wick being raised higher than usual So as to
Smoke freely. .
108. The cause of the solar spots is unknown. It is
not easy to determine what it is that occasions such
changes on the surface of the sun ; but various conjec-
tures have been proposed by different astronomers. Ga-
lileo supposed that the dark part of a spot is owing to
black cinders which rise from the interior of the sun,
where they are formed by the action of heat, constitu-
ting a kind of volcanic lava that floats upon the surface
of the fiery flood, which he supposed to constitute the
outer portion of the sun. But the vast extent which
these spots occasionally assume is unfavorable to such a
supposition. It is incredible that a quantity of volcanic
lava should suddenly rise to the surface of the sun, suffi-
cient to occupy (as a spot is sometimes found to do)
2000,000,000 square miles.
Dr. Herschel proposed a theory respecting the nature
and constitution of the sun, which, more from respect
to his authority than on account of any evidence by
which it is supported, has been generally received. Ac-
cording to him, the sun is itself an opake body like the
earth, but is enveloped at a considerable distance from
his body by two different strata of clouds, the exterior
gº
108, Is the cause of solar spots well known 2 What was
Galileo's hypothesis? What objections are there against it?
What is Herschel's theory of the nature and constitution of the
sun ? What sort of a body does he consider the sun itself? By
what is it encompassed ? Where is the repository of the sun's
light and heat? How does he explain the spots 7 What ob-
jections are there to this theory ! What are faculae 2
76 THE SUN.
stratum being the fountain from which emanates the .
sun's light and heat. The solar spots arise from the oc-
casional displacement of portions of this envelope of
clouds, disclosing to view tracts of the solid body of the
SUll] .
We regard this view of the origin of the sun’s light and
heat as unsubstantiated by any satisfactory proofs, and as
in itself highly improbable. Such a medium would be
a very unsuitable repository for the intense heat of the
Sun, which can arise only from fixed matter in a state of
high ignition. The most probable supposition is, that
the surface of the sun consists of melted matter in such
a state. We must confess our ignorance of any known
cause which is adequate to explain the sudden extinc-
tion and removal of so large portions of this fiery flood,
as is occupied by Some of the solar spots.
Besides the dark spots on the sun, there are also seen,
in different parts, places that are brighter than the neigh-
boring portions of the disk. These are called faculae.
Other inequalities are observable in powerful telescopes,
all indicating that the surface of the sun is in a state of
constant and powerful agitation.
ZODIACAL LIGHT.
109. The Zodiacal Light is a faint light resembling
the tail of a comet, and is seen at certain seasons of the
year following the course of the sun after evening twi-
light, or preceding his approach in the morning sky.
Figure 20 represents its appearance as seen in the even-
ing in March, 1836. The following are the leading facts
respecting it.
1. Its form is that of a luminous pyramid, having its
base towards the sun. It reaches to an immense dis-
tance from the sun, sometimes even beyond the orbit of
the earth. It is brighter in the parts nearer the Sun than
in those that are more remote, and terminates in an ob-
tuse apex, its light fading away by insensible gradations,
until it becomes too feeble for distinct vision. Hence
its limits are at the same time fixed at different dis-
- tº-
ZODIACAL LIGHT. 7 7
tances from the sun by different observers, according to
their respective powers of vision. -
2. Its aspects vary very much with the different seasons
of the year. About the first of October, in our climate
(Lat. 41° 18') it becomes visible before the dawn of day,
rising along north of the ecliptic, and terminating above
the nebula of Cancer. About the middle of November,
its vertex is in the constellation Leo. At this time no
traces of it are seen in the west after Sunset, but about
the first of December it becomes faintly visible in the
west, crossing the Milky Way near the horizon, and
reaching from the sun to the head of Capricornus, form-
ing, as its brightness increases, a counterpart to the Milky
109. Zodiacal Light.—Describe it. When and where
seen 7 What is its form 7 How far does it reach 7 When
brightest ? How do its aspects vary at different seasons of the
year? What motions has it? Is it equally conspicuous every
year ! What was it formerly held to be? With what phenom-
ena has it been supposed to be connected 7

78 THE SUN.
Way, between which on the right, and the Zodiacal
Light on the left, lies a triangular space embracing the
Dolphin. Through the month of December, the Zo-
diacal Light is seen on both sides of the sun, namely,
before the morning and after the evening twilight, some-
times extending 50° westward, and 70° eastward of the
Sun at the same time. After it begins to appear in the
western sky, it increases rapidly from night to night,
both in length and brightness, and withdraws itself from
the morning sky, where it is scarcely seen after the
month of December, until the next October.
3. The Zodiacal Light moves through the heavens
ân the order of the signs. It moves with unequal velocity,
being sometimes stationary and sometimes retrograde,
while at other times it advances much faster than the
sun. In February and March, it is very conspicuous in
the west, reaching to the Pleiades and beyond ; but in
April it becomes more faint, and nearly or quite disap-
pears during the month of May. It is scarcely seen in
this latitude during the summer months. -
4. It is remarkably conspicuous at certain periods of
a few years, and them for a long interval almost disap-
pears. - -
5. The Zodiacal Light was formerly held to be the
atmosphere of the sun. But La Place has shown that
the solar atmosphere could never reach so far from the
Sun as this light is seen to extend. It has been supposed
by others to be a nebulous body revolving around the
sun. The idea has been suggested, that the extraor-
dinary Meteoric Showers, which at different periods visit
the earth, especially in the month of November, may be
derived from this body.
79
C H A P T E R II.
OF THE APP ARENT ANNUAL MOTION OF THE SUN–SEA-
SONS-FIGURE OF THE EARTH's ORBIT.
110. THe revolution of the earth around the sun once
... a year, produces an apparent motion of the Sun around
the earth in the same period. 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, 180° from himself.
Thus when the earth arrives at Libra (Fig. 21,) we see
Fig. 21.
cº
the sun in the opposite sign Aries (Fig. 21.) When the
earth moves from Libra to Scorpio, as we are uncon-
Scious of our own motion, the sun it is that appears to
move from Aries to Taurus, being always seen in the

80 THE SUN.
heavens, where a line drawn from the eye of the spec-
tator through the body meets the concave sphere of the
heavens. Hence the line of projection carries the sun
forward on one side of the ecliptic, at the same rate as
the earth moves on the opposite side ; and therefore, al-
though we are unconscious of our own motion, we can
read it from day to day in the motions of the sun. If
we could see the stars at the same time with the sun,
we could actually observe from day to day the sun’s
progress through them, as we observe the progress of
the, moon at night; only the sun’s rate of motion would
be nearly fourteen times slower than that of the moon.
Although we do not see the stars when the sun is pres-
ent, yet after the sun is set, we can observe that it makes
daily progress eastward, as is apparent from the constel-
lations of the Zodiac occupying, successively, the west-
ern sky after Sunset, proving that either all the stars
have a common motion eastward independent of their
diurnal motion, or that the sun has a motion past them,
from west to east. We shall see hereaſter abundant ev-
idence to prove, that this change in the relative position
of the Sun and stars, is owing to a change in the appar-
ent place of the sun, and not to any change in the stars.
111. Although the apparent revolution of the sun is
in a direction opposite to the real motion of the earth, as
regards absolute space, yet both are nevertheless from
west to east, since these terms do not refer to any direc-
tions in absolute space, but to the order in which certain
constellations (the constellations of the Zodiac) succeed
one another. The earth itself, on opposite sides of its
orbit, does in fact move towards directly opposite points
110. What produces the apparent motion of the sun around
the earth once a year ! How would a spectator on either body
see the other ? When the earth is at Libra, where does the sun
appear to be? Explain figure 21. If the stars were visible in
the day time, how could we determine the sun's path? What
change do the constellations of the Zodiac undergo with re-
spect to the Sun ?
ANNUAL MOTION. 81
of space ; but it is all the while pursuing its course in
the Order of the signs. In the same manner, although
the earth turns on its axis from west to east, yet any
place on the surface of the earth is moving in a direc-
tion in space exactly opposite to its direction twelve
hours before. If the sun left a visible trace on the face
of the sky, the ecliptic would of course be distinctly
marked on the celestial sphere as it is on an artificial
globe; and were the equator delineated in a similar man-
ner, (by any method like that supposed in Art. 33,) we
should then see at a glance the relative position of these
two circles, the points where they intersect one another
constituting the equinoxes, the points where they are at
the greatest distance asunder, or the Solstices, and vari-
ous other particulars, which for want of such visible
traces, we are now obliged to search for by indirect and
circuitous methods. It will even aid the learner to have
constantly before his mental vision, an imaginary delin-
eation of these two important circles on the face of the
sky.
112. The equator makes an angle with the ecliptic of
23° 28′. This is called the obliquity of the ecliptic.
As the sun and earth are both always in the ecliptic, and
as the motion of the earth in one part of it makes the
sun appear to move in the opposite part at the same rate,
the sun apparently descends in the winter 27°28' to the
South of the equator, and ascends in the summer the
same number of degrees to the north of it. We must
keep in mind that the celestial equator and the celestial
ecliptic are here understood, and we may imagine them
111. In what sense are the motions of the Sun and earth op-
posite, and in what sense in the same distance " If the eclip-
tic and equator were distinctly delineated on the face of the sky,
what points in them could be easily obscure?
112. What angle does the equator make with the ecliptic”
In what circle do the sun and earth always appear ! How far
do they recede from the equator? How does the obliquity of
the ecliptic vary 7
82 THE SUN.
to be two great circles distinctly delineated on the face
of the sky. On comparing observations made at differ-
ent periods for more than two thousand years, it is found,
that the obliquity of the ecliptic is not constant, but
that it undergoes a slight diminution from age to age,
amounting to 52% in a century, or about half a sec-
ond annually. We might apprehend that by succes-
sive approaches to each other the equator and ecliptic
would finally coincide; but astronomers have found
by a most profound investigation, founded on the prin-
ciples of universal gravitation, that this variation is con-
fined within certain narrow limits, and that the obli-
quity, after diminishing for some thousands of years,
will then increase for a similar period, and will thus vi-
brate for ever about a mean value. •
113. Let us conceive of the sun as at that point of the
ecliptic where it crosses the equator, that is at one of the
equinoxes, as the vernal equinox. Suppose he stands
still then for twenty four hours. The revolution of the
earth on its axis from east to west during this twenty
four hours, will make the sun appear to describe a great
circle from east to west, coinciding with the equator.
At the end of this period, suppose the Sun to move
northward one degree and to remain there for the next
twenty hours, in which time the revolution of the earth
will make the sun appear to describe another circle from
east to west, parallel to the equator, but one degree
north of it. Thus we may conceive of the sun as mov-
ing one degree north every day for about three months,
when it will reach the point of the ecliptic farthest
from the equator, which is called the tropic from a Greek
—w—z—
113. Suppose the sun to start from the equator and to ad-
vance one degree north daily, explain its apparent diurnal revo-
lutions. When is the sun at the northern tropic 7 When is he
at the southern tropic How are the respective meridian alti-
tudes of the sun at these periods? How do we find from these
observations, the obliquity of the ecliptic”
• THE SEASONS. 83
word (rgérro') which signifies to turn, because when the
Sun arrives at this point, his motion in his orbit carries
him continually towards the equator, and therefore he
seems to turn about. $
When the sun is at the northern tropic, which hap-
pens about the 21st of June, his elevation above the
Southern horizon at noon, is the greatest of the year;
and when he is at the southern tropic, about the 21st
of December, his elevation at noon is the least in the
year. The difference between these two meridian alti-
tudes, will give the whole distance from one tropic to
the other, and consequently twice the distance from each
tropic to the equator. By this means we find how far
the tropic is from the equator, and that gives us the in-
climation of the two circles to one another ; for the great-
est distance between any two great circles on the sphere,
is always equal to the angle which they make with each
other. -
114. The dimensions of the earth's orbit, when com-
pared with its own magnitude, are immense.
Since the distance of the earth from the sun is
95,000,000 miles, and the length of the entire orbit nearly
600,000,000 miles, it will be found, on calculation, that
the earth moves 1,640,000 miles per day, 68,000 miles
per hour, 1,100 miles per minute, and nearly 19 miles
every second, a velocity nearly sixty times as great as
the maximum velocity of a cannon ball. A place on
the earth’s equator turns, in the diurnal revolution, at the
rate of about 1,000 miles an hour and fºr of a mile per
second. The motion around the sun, therefore, is nearly
seventy times as swift as the greatest motion around the
a X1S.
_^
I 14. What is said of the dimensions of the earth's orbit?
At what rate does the earth move in its orbit per day, minute,
and second How far does a place on the earth's equator move
per hour and second? How much swifter is the motion in the
orbit than on its axis '' !
84 THE SUN.
THE SEASONS.
115. The change of seasons depends on two causes,
(1) the obliquity of the ecliptic, and (2) the earth's awis
always remaining parallel to itself. Had the earth’s
axis been perpendicular to the plane of its orbit, the
equator would have coincided with the ecliptic, and the
sun would have constantly appeared in the equator.
To the inhabitants of the equatorial regions, the sun
would always have appeared to move in the prime ver-
tical; and to the inhabitants of either pole, he would
always have been in the horizon. But the axis being
turned out of a perpendicular direction 23° 28, the
equator is turned the same distance out of the ecliptic ;
and since the equator and ecliptic are two great circles
which cut each other in two opposite points, the sun,
while performing his circuit in the ecliptic, must evi-
dently be once a year in each of those points, and must
depart from the equator of the heavens to a distance on
either side equal to the inclination of the two circles,
that is, 23° 28′.
116. The earth being a globe, the sun constantly en-
lightens the half next to him,” while the other half is in
darkness. The boundary between the enlightened and
unenlightened part, is called the circle of illumination.
When the earth is at one of the equinoxes, the sun is at
the other, and the circle of illumination passes through
both the poles. When the earth reaches one of the
115. The Seasons.—On what two causes does the change of
seasons depend? Had the earth's axis been perpendicular to
the plane of its orbit, in what great circle would the sun always
have appeared to move 7
* In fact, the sun enlightens a little more than half the earth, since
on account of his vast magnitude the tangents, drawn from opposite
sides of the sun to opposite sides of the earth, converge to a point
behind the earth, as will be seen by and by in the representation of
eclipses.
THE SEASONS. - 85
tropics, the Sun being at the other, the circle of illumin-
ation cuts the earth, so as to pass 23° 28′ beyond the
nearer, and the same distance short of the remoter pole.
These results would not be uniform, were not the earth's
axis always to remain parallel to itself. The following
figure will illustrate the foregoing statements.
Fig. 22.
Let ABCD represent the earth's place in different
parts of its orbit, having the sun in the center. Let A,
116. How much of the earth does the sun enlighten at once
Define the circle of illumination. How does it cut the earth at
the equinoxes? How at the solstices ! Explain figure 22.
When the earth is at one of the tropics and the sun at the
other, where is it continual day and where continual night?

86 fhE SUN.
C, be the positions of the earth at the equinoxes, and B,
D, its positions at the tropics, the axis ms being always
parallel to istelf.” At A and C the sun shines on both
m and s; and now let the globe be turned round on its
axis, and the learner will easily conceive that the sun
will appear to describe the equator, which being bisected
by the horizon of every place, of course the day and
night will be equal in all parts of the globe.f. Again,
at B when the earth is at the southern tropic, the sun
shines 234° beyond the north pole m, and falls the same
distance short of the south pole s. The case is exactly
reversed when the earth is at the northern tropic and
the sun at the southern. While the earth is at one of
the tropics, at B for example, let us conceive of it as turn-
ing on its axis, and we shall readily see that all that part
of the earth which lies within the north polar circle will
enjoy continual day, while that within the south polar
circle will have continual night, and that all other places
will have their days longer as they are nearer to the en-
lightened pole, and shorter as they are nearer to the un-
enlightened pole. This figure likewise shows the suc-
cessive positions of the earth at different periods of the
year, with respect to the signs, and what months corres-
pond to particular signs. Thus the earth enters Libra
and the sun Aries on the 21st of March, and on the 21st
of June the earth is just entering Capricorn and the sun
Cancer.
117. Had the axis of the earth been perpendicular
to the plane of the ecliptic, then the sun would always
have appeared to move in the equator, the days would
every where have been equal to the nights, and there
could have been no change of seasons. On the other
hand, had the inclination of the ecliptic to the equator
# The learner will remark that the hemisphere towards n is above,
and that towards s is below the plane of the paper. It is important to
form a just conception of the position of the axis with respect to the
plane of its orbit.
f At the pole, the solar disk, at the time of the equinox, appears bis-
ccted by the horizon.
THE SEASONS. 87
been much greater than it is, the vicisitudes of the sea-
sons would have been proportionally greater than at pres-
ent. Suppose, for instance, the equator had been at
right angles to the ecliptic, in which case the poles.of
the earth would have been situated in the ecliptic itself;
then in different parts of the earth the appearances
would have been as follows. To a spectator on the
equator, the Sun as he left the vernal equinox would
every day perform his diurnal revolution in a smaller
and smaller circle, until he reached the north pole, when
he would halt for a moment and then wheel about and
return to the equator in the reverse order. The pro-
gress of the sun through the southern signs, to the south
pole, would be similar to that already described. Such
would be the appearances to an inhabitant of the equa-
torial regions. To a spectator living in an oblique
sphere, in our own latitude for example, the sun while
north of the equator would advance continually north-
ward, making his diurnal circuits in parallels farther and
farther distant from the equator, until he reached the
circle of perpetual apparition, after which he would
climb by a spiral course to the north star, and then as
rapidly return to the equator. By a similar progress
Southward, the sun would at length pass the circle of
perpetual occultation, and for some time (which would
be longer or shorter according to the latitude of the place
of observation) there would be continual night.
The great vicissitudes of heat and cold which would
attend such a motion of the sun, would be wholly in-
compatible with the existence of either the animal or
the vegetable kingdoms, and all terrestrial nature would
117. Had the earth's axis been perpendicular to the plane
of the ecliptic, would there have been any change of seasons !
What would have been the consequence had the equator been
at right angles to the ecliptic How would the sun appear to
move to a person on the equator? How to one situated at the
pole? How to an inhabitant of an oblique sphere How
would have been the vicissitudes of heat and cold?
S8 THE SUN.
be doomed to perpetual sterility and desolation. The
happy provision which the Creator has made against
such extreme vicissitudes, by confining the changes of
the seasons within such narrow bounds, conspires with
many other express arrangements in the economy of
nature to secure the safety and comfort of the human
T&C62.
FIGURE OF THE EARTH's ORBIT.
118. Thus far we have taken the earth's orbit as a
great circle, such being the projection of it on the celes-
tial sphere; but we now proceed to investigate its actual
figure. - -
Fig. 23.
Were the earth's path a circle, having the Sun in the
center, the sun would always appear to be at the same
118. Were the earth's path a circle, how would the distance
of the sun from us always appear ! Define the radius vector.
What do we inſer from the fact that the radius vector is con-
stantly varying? How do we learn the relative distances of the
earth? How do we construct a figure representing the earth's
orbit Explain figure 23.

FIGURE OF THE EARTH's ORBIT. 89
distance from us; that is, the radius of its orbit, or ra-
dius vector, the name given to a line drawn from the
center of the sun to the orbit of any planet, would al-
ways be of the same length. But the earth’s distance
from the Sun is constantly varying, which shows that
its orbit is not a circle. We learn the true figure of the
Orbit, by ascertaining the relative distances of the earth
from the sun at various periods of the year. These all
being laid down in a diagram, according to their respec-
tive lengths, the extremities, on being connected, give
us our first idea of the shape of the orbit, which appears
of an oval form, and at least resembles an ellipse; and,
on further trial, we find that it has the properties of an
ellipse. Thus, let E (Fig. 23,) be the place of the
earth, and a, b, c, &c. Successive positions of the sun ;
the relative lengths of the lines Ea, Eb, &c. being
known: on connecting the points, a, b, c, &c. the result-
ing figure indicates the true shape of the earth's orbit.
119. These relative distances are found in two differ-
ent ways; first, by changes in the sum’s apparent diam-
eter, and, secondly, by variations in his angular velo-
city. The same object appears to us smaller in propor-
tion as it is more distant; and if we see a heavenly body
varying in size at different times, we infer that it is at
different distances from us; that when largest, it is near-
est to us, and when smallest, farthest off. Now when
the sum’s diameter is measured accurately by instru-
ments, it is found to vary from day to day, being when
greatest more than thirty two minutes and a half, and
when smallest only thirty one minutes and a half, differ-
ing in all, about seventy five seconds. When the diam-
eter is greatest, which happens in January, we know
119. How does the same body appear when at different dis-
tances? What inferences do we make from its variations of
size? How much does the apparent diameter of the sun vary
in different parts of the year? When is its greatest, and when
smallest'. Define the terms perihelion and aphelion.
90 THE SUN,
that the Sun is nearest to us; and when the diameter is
least, which occurs in July, we infer that the sun is at
the greatest distance from us.
The point where the earth or any planet, in its revo-
lution, is nearest the sun, is called its perihelion ; the
point where it is farthest from the Sun, its aphelion.
120. Similar conclusions may be drawn from obser-
vations on the Sun's angular velocity. A body appears
to move most rapidly when nearest to us. Indeed the
apparent velocity increases rapidly as it approaches us,
and as rapidly diminishes when it recedes from us. If
it comes twice as near as before it appears to move not
merely twice as swift, but four times as swift; if it
comes ten times nearer, its apparent velocity is one
hundred times as great as before. We say, therefore,
that the velocity varies inversely as the square of the
distance, for as the distance is diminished ten times, the
velocity is increased the square of ten, that is, one hun-
dred times. Now by noting the time it takes the Sun,
from day to day, to cross the central wire of the transit
instrument, we learn the comparative velocities with
which it moves at different times, and from these we
derive the comparative distances of the sun at the cor-
responding times.
When by either of the foregoing methods, we have
learned the relative distances of the sun from the earth
at various periods of the year, we may lay down, or plot
in a diagram like figure 23, a representation of the Orbit
which the Sun apparently describes about the earth, and
it will give us the figure of the orbit which the earth
really describes about the sun, in its annual revolution.
120. What conclusions are drawn from the variations in the
sun's angular velocity ? How much faster does a body appear
to move when twice as near to us as before ? According to
what law does the velocity vary" How may we ascertain the
Sun's daily rate? What great doctrine is it necessary to be ac-
quainted with, in order to understand the celestial motions !
UNIVERSAI, GRAVITATION. 91
But neither the revolution of the earth about the Sun,
nor indeed that of any of the planets, can be well and
clearly understood, until we are acquainted with the
forces by which their motions are produced, especially
with the doctrine of Universal Gravitation. To this
Subject, therefore, let us next apply our attention,
CHAPTER III.
OF UNIVERSAL GRAVITATION.—KEPLER's LAws—MOTION
IN AN ELLIPTICAL ORBIT-PRECESSION OF THE EQUI-
NOXES.
121. WE discover in nature a tendency of every por-
tion of matter towards every other. This tendency is
called gravitation. In obedience to this power, a stone
falls to the ground and a planet revolves around the sun.
It was once supposed that we could not reason from
the phenomena of the earth to those of the heavens;
since it was held that the laws of motion might be
very different among the heavenly bodies from what
we find them to be on this globe; but Galileo and New-
ton in their researches into nature, proceeded on the
idea that nature is uniform in all her works, and that
everywhere the same causes produces the same effects,
and that the same effects result from the same causes.
That this is a sound principle of philosophy, is proved
by the fact, that all the conclusions derived from it in
the interpretation of nature are found to be true. Hence
by studying the laws of motion as exhibited constantly
before our eyes in all terrestrial motions, we are learning
121. What force do we observe in nature ? What is this
force called 7 Can we reason from terrestrial to celestial phe-
nomena? On what idea did Galileo and Newton proceed 2
How is this proved to be a sound principle of philosophy
92 UNIVERSAL GRAVITATION,
the laws that govern the movements of the heavenly
bodies.
122. On the earth all bodies are seen to fall towards
its center. A stone let fall in any part of the earth, de-
scends immediately to the ground. This may seem to
the young learner as so much a matter of course as to
require no explanation. But stones fall in exactly op-
posite directions on opposite sides of the earth, always
falling towards the center of the carth from every part
exterior to its surface; as when Fig. 24.
we hold a small needle towards Na sº
a magnetic ball or load stone, the -->
needle will fly towards the ball,
and cling to its surface, to which-
ever side of the ball it is present-
ed. (Fig. 24.) From this uni-
versal descent of bodies near the sºº’N
earth, we infer the existence of . . . . . . .
some force which draws or impels them, and this invisi-
ble force we call the attraction of gravitation, or simply
gravity.
Nº, sº
wº , a
123. By the laws of gravity we mean the manner in
which it always acts. They are three in number, and
are comprehended in the following proposition:
Gravily acts on all matter alike, with a force propor-
lioned to the quanlity of malter, and inversely as the
square of the distance.
First, gravity acts on all matter alike. Every body
in nature, whether great or small, whether solid, liquid,
or ariſorm, exhibits the same tendency to fall towards
the center of the earth. Some bodies, indeed, seem less
prone to fall than others, and some even appear to rise,
as Smoke and light vapors. But this is because they are
supported by the air; when that is removed, they de-
122. In what directions do bodies fall in all parts of the
earth? Illustrate by figure 24. What is gravity ?




LAWS OF GRAVITY. 93
scend alike towards the earth; a guinea and a feather,
the lightest vapor and the heaviest rocks, fall with equal
velocities. -
Secondly, the force of gravity is proportioned to the
quantity of matter. A mass of lead contains perhaps
fifty times as much matter as an equal bulk of cotton ;
yet, if carried beyond the atmosphere, and let fall in ab-
Solute space, they would both descend towards the earth
with equal speed, until they entered the atmosphere,
and were the atmosphere removed they would continue
to fall side by side until they reached the earth. Now
if the lead contains fifty times as much matter as the
cotton, it must take fifty times the force to make it move
with equal velocity. If we double the load we must
double the team, if we would continue to travel at the
same speed as before. Hence, from the fact that bodies
of various degrees of density descend alike towards the
the center of the earth by the force of gravity, we infer
that that force is always exerted upon bodies in exact
proportion to their quantity of matter. .
Thirdly, the force with which gravity acts upon bod-
ies at different distances from the earth, is inversely as
the square of the distance from the center of the earth.
If a pound of lead were carried as far above the earth as
from the center to the surface of the earth, it would
weigh only one fourth of a pound; for being twice as
far as before from the center of the earth, its weight
would be diminished in the proportion of the square of
two, that is, four times.
123. What do we mean by the law of gravity? State the
general proposition. Show that gravity acts on all matter alike.
How is this consistent with the fact, that some bodies appear to
rise? How would all bodies fall in a vacuum ? Explain how
gravity is proportioned to the quantity of matter. How would
equal masses of lead and cotton fall, if carried beyond the at-
mosphere? What do we infer from the fact, that all bodies fall
towards the earth with equal velocities? To what is gravity
acting at different distances proportioned? How, much would
a pound of lead weigh, if carried as far above the earth as from
the Surface to the center ?
94. UNIVERSAL GIRAVITATION,
124. Bodies falling to the earth by gravity have their
velocity continually increased. For since they retain
what motion they have and constantly receive more
by the continued action of gravity, they must move
ſaster and faster, as a wheel has its velocity constantly
accelerated when we continue to apply successive im-
pulses to it.
The spaces which bodies describe, when ſalling freely
by gravity, are as the square of the times. It is ſound
by experiment, that a body will ſall from a state of
rest 16 F4 feet in one second. In two seconds it will not
fall merely through double this space, but through four
times this space, that is, through a distance expressed
by the square of the time multiplied into 16 Fä. Conse-
quently, in two seconds the fall will be 644, in three Se-
conds 144%, and in ten seconds 1608; feet, that is,
through one hundred times 16 rº feet.
The weight of a body is nothing more than the ac-
tion of gravity upon it tending to carry it towards the
center of the earth. The counterpoise which is placed
in the opposite scale by which its weight is estimated, is
the force it takes to hold the body back, which must be
just equal to that by which it endeavors to descend.
125. There is another principle which it is necessary
clearly to comprehend before we can understand the mo-
tions of the heavenly bodies. It is commonly called the
First Law of Motion and is as follows:
Every body perseveres in a state of rest, or of uniform
omotion in a straight line, unless compelled by some force
to change its state. This law has been ſully established
by experiment, and is conſormable to all experience.
It embraces several particulars. First, A body when at
124. When a body is falling towards the earth, how is its ve-
locity aſſected? To what are the spaces described by falling
bodies proportioned? How far will a body fall from a state of
rest in one second'ſ How far in two seconds? What is the
weight of a body ?
LAWS OF MOTION. 95
rest remains So unless some force puts it in motion;
and hence it is inferred, when a body is found in mo-
tion, that some ſorce must have been applied to it suffi-
cient to have caused its motion. Thus, the fact that
the earth is in motion around the sun and around its own
axis, is to be accounted for by assigning to each of these
motions a force adequate, both in quantity and direction,
to produce these motions respectively.
Secondly, When a body is once in motion it will con-
tinue to move forever, unless something stops it. When
a ball is struck on the surface of the earth, the friction
of the earth and the resistance of the air soon stop its
motion ; when struck on Smooth ice it will go much
farther before it comes to a state of rest, because the ice
opposes much less resistance than the ground ; and were
there no impediment to its motion it would, when once
set in motion, continue to move without end. The
heavenly bodies are actually in this condition : they
continue to move, not because any new forces are ap-
plied to them, but, having been once set in motion, they
continue in motion because there is nothing to stop them.
Thirdly, The motion to which a body naturally tends
is uniſorm ; that is, the body moves just as far the se-
cond minute as it did the first, and as far the third as
the Second, passing over equal spaces in equal times.
Fourthly, A body in motion will move in a straight
line, unless diverted out of that line by some external
force; and the body will resume its straight forward mo-
tion, when ever the force that turns it aside is with-
drawn. Every body that is revolving in an orbit, like
the moon around the earth, or the earth around the Sun,
125. Recite the first law of motion. How has this law been
established 7 What does the fact, that the earth is in motion
around the sun imply " How would a ball when once struck
continue to move, if it met with no resistance ' Why do the
heavenly bodies continue to move 7 What is meant by saying
that motion is naturally uniform 7 In what direction does every
revolving body tend to move.
96 |UNIVERSAL GRAVITATION.
tends to move in a straight line which is a tangent” to
its orbit.
Let us now see how the ſoregoing principles, which
operate upon bodies on the earth, are extended so as to
embrace all bodies in the universe, as in the doctrine of
Universal Gravitation. This important principle is thus
defined:
126. UNIVERSAL GRAVITATION, is that influence by
which every body in the universe, whether great or small,
tends towards every other, with a force which is directly
as the quantity of matter, and inversely as the square
of the distance.
As this force acts as though bodies were drawn to-
wards each other by a mutual attraction, the force is de-
nominated attraction ; but it must be borne in mind,
that this term is figurative, and implies nothing respect-
ing the nature of the force.
The evistence of such a force in nature was distinctly
asserted by several astronomers previous to the time of
Sir Isaac Newton, but its laws were first promulgated
by this wonderful man in his Principia, in the year 1687.
It is related, that while sitting in a garden, and musing
on the cause of the falling of an apple, he reasoned
thus:f that, since bodies far removed from the earth fall
towards it, as from the tops of towers, and the highest
mountains, why may not the same influence extend
even to the moon; and if so, may not this be the reason
why the moon is made to revolve around the earth, as
would be the case with a cannon ball were it projected
horizontally near the earth with a certain velocity. Ac-
cording to the first law of motion, the moon, if not con-
tinually drawn or impelled towards the earth by some
force, would not revolve around it, but would proceed
On in a straight line. But going around the earth as she
does, in an orbit that is nearly circular, she must be
* A tangent is a straight line which touches a curve. Thus AB (Fig.
25,) is a tangent to the circle at B.
f Pemberton's View of Newton's Philosophy.
UNIVERSAL GRAVITATION. 97
urged towards the earth by some force, which diverts
her from a straight course. For let the earth (Fig. 25,)
be at E, and let the arc described by the moon in one
second of time be Ab. Were the moon influenced by
no extraneous force, to turn aside, she would have de-
scribed, not the arc Ab, but the straight line AB, and
would have been found at the end of the given time at
B instead of b. She therefore departs from the line in
which she tends naturally to move, by the line Bb,
which in Small angles may be taken as equal to Aa.
Fig. 25.
→
This deviation from the tangent must be owing to some
extraneous force. Does this force correspond to what
the force of gravity exerted by the earth, would be at
the distance of the moon The question resolves itself
into this : Would the force of gravity exerted by the
earth upon the moon, cause the moon to deviate from
her straight forward course towards the earth just as
much as she is actually found to deviate 2 Now we
126. Universal Gravitation.—Define it. Why called at-
traction ? State the historical facts connected with its discow-
ery. How did Sir Isaac Newton reason from the falling of an
apple 7 Explain by figure 25. How is it proved that gravity
and no other force causes the moon to revolve about the earth ''

9
9S UNIVERSAL GRAVITATION.
know how far the moon is from the earth, namely, sixty
times as far as it is from the center to the surface of the
earth; and since the force of gravity decreases in pro-
portion to the square of the distance, this force must be
3600 times (which equals the square of 60,) less than at
the surface of the earth. This is found, on computa-
tion, to be exactly the force required to make the moon
deviate to the amount she does from the straight line in
which she constantly tends to move ; and hence it is
inferred that gravity, and no other force than gravity,
causes the moon to circulate around the earth.
By this process it was discovered that the law of grav-
itation extends to the moon. By subsequent inquiries
it was ſound to extend in like manner to all the planets,
and to every member of the solar system; and, finally,
recent investigations have shown that it extends to the
fixed stars. The law of gravitation, therefore, is now
established as the grand principle which governs all the
motions of the heavenly bodies.
KEPLER's LAws.
127. There are three great principles, according to
which the motions of the earth and all the planets
around the sun are regulated, called Kepler's Laws, hav-
ing been first discovered by the great astronomer whose
name they bear. They may appear to the young learner,
when he first reads them, dry and obscure ; yet they
will be easily understood from the explanations that fol-
low ; and so important have they proved in astronomical
inquiries, that they have acquired for their renowned
discoverer the exalted appellation of the legislator of the
skies.
We will consider each of these laws separately.
127. Repler's Laws.--Why so called? What appellation
has been given to Kepler 7
KEPLER'S LAWS. 99
128. FIRST LAw. The orbits of the earth and all the
planets are ellipses, having the sun in the common
Jocus.
In a circle all the diameters are equal to each other ;
but if we take a metallic wire or hoop and draw it out on
opposite sides, we elongate it into an ellipse, of which the
different diameters are very unequal. That which con-
nects the two points most distant from each other is called
the transverse, and that which is at right angles to this
is called the conjugate axis. Thus AB (Fig. 26) is the
Fig. 26.
C

E)
transverse axis and CD the conjugate of the ellipse AB.
By such a process of elongating the circle into an el-
lipse, the center of the circle may be conceived of as
drawn opposite ways to E and F, each of which be-
comes a ſocus, and both together are called the foci of the
ellipse. The distance GE or GF of the focus from the
128. Recite the first law. In a circle, how are all the diam-
eters? How are they in an ellipse! What is the longest di-
ameter called ! What is the shortest called 7 Explain by figure
26. What is the eccentricity of the ellipse ? How many ellipses
may there be having a common focus 2 Explain figure. 26.
How eccentric is the earth's orbit?
100 UNIVERSAL GRAVITATION.
center is called the eccentricity of the ellipse ; and the
ellipse is said to be more or less eccentric, as the distance
of the focus from the center is greater or less. -
Now there may be an indefinite number of ellipses
having one common focus, but varying greatly in ec-
centricity. Figure 27 represents such a collection of
Fig. 27.
C.
ellipses around the common focus F, the innermost AGD
having a small eccentricity or varying little from a cir-
cle, while the outermost ACB is a very eccentric ellipse.
The orbits of all the bodies that revolve about the sun,
both planets and comets, have, in like manner, a com-
mon focus in which the Sun is situated, but they differ
in eccentricity. - -
Most of the planets have orbits of very little eccen-
tricity, differing little from circles, but comets move in
very eccentric ellipses. -
The earth's path around the sun varies so little from
a circle, that a diagram representing it truly would
scarcely be distinguished from a perfect circle ; yet
when the comparative distances of the sun from the
earth are taken at different seasons of the year, as is ex-
plained in Art. 118, we find that the difference between

KEPLER'S LAWS. 101
the greatest and least distances is no less than 3,000,000
miles.
129. SEcond LAw. The radius vector of the earth,
or of any planet, describes equal areas in equal times.
It will be recollected that the radius vector is a line
drawn from the center of the sun to a planet revolving
about the sun, (Art. 118.) Thus Ea, Eb, Ec, (Fig. 23,)
&c. are successive representations of the radius vector.
Now if a planet sets out from a and travels round the sun
in the direction of abe, it will move faster when nearer the
Sun, as at a, than when more remote from it, as at m ;
yet if ab and mm be arcs described in equal times, then,
according to the foregoing law, the space Eab will be
equal to the space m En; and the same is true of all the
other spaces described in equal times. Although the
figure Eab is much shorter than m En, yet its greater
breadth exactly counterbalances the greater length of
those figures which are described by the radius vector
where it is longer. -
130. THIRD LAw. The squares of the periodical times
are as the cubes of the mean distances from the sum.
The periodical time of a body is the time it takes to
complete its orbit in its revolution about the sun. Thus
the earth's periodic time is one year, and that of the
planet Jupiter is about twelve years. As Jupiter takes
so much longer time to travel round the sun than the
earth does, we might suspect that his orbit was larger
than that of the earth, and of course that he was at
a greater distance from the sun, and our first thought
might be that he was probably twelve times as far off;
but Kepler discovered that the distance did not increase
as fast as the times increased, but that the planets which
129. State Kepler's second law. Explain by figure 23, p. 88.
130. State Kepler's third law. What is meant by the peri-
odical time of a body ? Do planets move faster or slower as
they are more distant from the sºn" Explain the law.
102 UNIVERSAL GRAVITATION.
are more distant from the sun actually move slower than
those which are nearer. After trying a great many pro-
portions, he at length found that if we take the squares
of the periodic times of two planets, the greater square
contains the less, just as often as the cube of the dis-
tance of the greater contains that of the less. This fact
is expressed by saying, that the squares of the periodic
times are to one another as the cubes of the distances.
This law is of great use in determining the distances
of all the planets from the sun, as we shall see more fully
hereafter, -
MOTION IN AN ELLIPTICAL ORBIT.
131. Let us now endeavor to gain a just conception
of the forces by which the earth and all the planets are
made to revolve about the sun. - .
In obedience to the first law of motion, every moving
body tends to move in a straight line; and were not the
planets deflected continually towards the sun by the
force of attraction, these bodies as well as others would
move forward in a rectilineal direction. We call the force
by which they tend to such a direction the projectile
force, because its effects are the same as though the body
were originally projected from a certain point in a certain
direction. It is an interesting problem for mechanics to
Solve, what was the nature of the impulse originally
given to the earth, in order to impress upon it its two
motions, the one around its own axis, the other around
the sun. If struck in the direction of its center of
gravity it might receive a forward motion, but no rota-
tion on its axis. It must, therefore, have been impelled
by a force, whose direction did not pass through its
131. Explain how a body is made to revolve in an orbit, un-
der the action of two forces. What is meant by the projectile
force? How must the earth have been impelled in order to
receive its present motions? How illustrated by the motions of
a top
MOTION IN AN ELLIPTICAL ORBIT. 103
center of gravity. Bernouilli, a celebrated mathemati-
cian, has calculated that the impulse must have been
given very nearly in the direction of the center, the
point of projection being only the 165th part of the
earth's radius from the center. This impulse alone
would cause the earth to move in a right line : gravita-
tion towards the sun causes it to describe an orbit.
Thus a top spinning on a smooth plane, as that of glass
or ice, impelled in a direction not coinciding with that
of the center of gravity, may be made to imitate the two
motions of the earth, especially if the experiment is tried
in a concave surface like that of a large bowl. The re-
sistance occasioned by the surface on which the top
moves, and that of the air, will gradually destroy the
force of projection and cause the top to revolve in a
Smaller and smaller orbit; but the earth meets with no
such resistance, and therefore makes both her days and
years of the same length from age to age. A body,
therefore, revolving in an orbit about a center of attrac-
tion, is constantly under the influence of two forces,
the projectile force, which tends to carry it forward in a
straight line which is a tangent to its orbit, and the cen-
tripetal force, by which it tends towards the center,
132. As an example of a body revolving in an orbit
under the influence of two forces, suppose a body pla-
ced at any point P (Fig. 28,) above the surface of the
earth, and let PA be the direction of the earth’s center.
If the body were allowed to move without receiving
any impulse, it would descend to the earth in the direc-
tion PA with an accelerated motion. But suppose that
at the moment of its departure from P, it receives an
impulse in the direction PB, which would carry it to B
in the time the body would fall from P to A ; then un-
der the influence of both forces it would descend along
the curve PD. If a stronger impulse were given it in
132. Explain figure 28. How might a body be made to cir-
culate quite around the earth'
104 UNIVERSAL GRAVITATION,
the direction PB, it would describe a larger curve PE,
or PF, or finally, it would go quite round the earth and
return again to P.
133. The most simple example we have of the com-
bined action of these two forces, is the motion of a mis-
sile thrown from the hand, or of a ball fired from a can-
non. It is well known that the particular form of the
curve described by the projectile, in either case, will de-
pend upon the velocity with which it is thrown. In
each case the body will begin to move in the line of di-
rection in which it is projected, but it will soon be de-
flected from that line towards the earth. It will how-
ever continue nearer to the line of projection as the ve-
";
Fig 29.
B .”
A. * Sºº - - - -
*s, * ~ * - - -
*...** -- * * * *
*~~ ** *~. * " *-*.
^ *~. **---
^ *... *.
*~ *--- *~~
*..
\. *--> *~~
^ • *.
N *~. *s
* *
** *.. *
*h,
•, *\
\ Iº
locity of projection is greater. Thus let AB (Fig. 29,)
133. When a cannon ball is fired with different velocities,
when is its motion nearest to the line of projection ?

MOTION IN AN ELLIPTICAL ORBIT. 105
perpendicular to AC represent the line of projection.
The body will, in every case, commence its motion in
the line AB, which will therefore be the tangent to the
curve it describes; but if it be thrown with a small ve-
locity, it will soon depart from the tangent, describing
the line AD; with a greater velocity it will describe a
curve nearer to the tangent, as AE; and with a still
greater velocity it will describe the curve AF.
134. In figure 30, suppose the planet to have passed
the point C with so small a velocity, that the attraction
of the Sun bends its path very much, and causes it im-
mediately to begin to approach towards the sun; the
Sun's, attraction will increase its vélocity as it moves
through D, E, and F. For the sun's attractive force on
Fig. 30.
the planet, when at D, is acting in the direction DS,
and, on account of the small inclination of DE to DS,
the force acting in the line DS helps the planet forward
in the path DE, and thus increases its velocity. In like
manner, the velocity of the planet will be continually
increasing as it passes through D, E, and F; and though
F-
134. Explain the motion of a planet in an elliptical orbit,
from figure 30.

106 |UNIVERSAL GRAVITATION,
the attractive force, on account of the planet's nearness,
is so much increased, and tends therefore to make the
orbit more curved, yet the velocity is also so much in-
creased that the orbit is not more curved than before.
The same increase of velocity occasioned by the planet's
approach to the sun, produces a greater increase of cen-
trifugal force which carries it off again. We may see
also why, when the planet has reached the most distant
parts of its orbit, it does not entirely fly off, and never
returns to the sun. For when the planet passes along
H, K, A, the sun’s attraction retards the planet, just as
gravity retards a ball rolled up hill; and when it has
reached C, its velocity is very small, and the attraction
at the center of force causes a great deflection from the
tangent, sufficient to give its orbit a great curvature,
and the planet turns about, returns to the Sun, and goes
over the same orbit again. As the planet recedes from
the sun, its centrifugal force diminishes faster than the
force of gravity, so that the latter finally preponderates.
135. We may imitate the motion of a body in its orbit
by Suspending a small ball from the ceiling by along string.
The ball being drawn out of its place of rest, (which is
directly under the point of suspension,) it will tend con-
stantly towards the same place by a force which corres-
ponds to the force of attraction of a central body. If
an assistant stands under the point of suspension, his
head occupying the place of the ball when at rest, the
ball may be made to revolve about his head as the earth
or any planet revolves about the sun. By projecting the
ball in different directions, and with different degrees of
volocity, we may make it describe different orbits, ex-
emplifying principles which have been explained in the
foregoing articles.
135. How may we imitate the motion of a body in its
orbit? How may we make the ball describe different orbits 7
PRECESSION OF THE EQUINOXEs. 107
PRECESSION OF THE EQUINOXES.
136. THE PRECESSION OF THE EQUINoxEs, is a slow
but continually shifting of the equinoctial points from
eaSt to weSi. -
Suppose that we mark the exact place in the heavens
where, during the present year, the Sun crosses the equa-
tor, and that this point is close to a certain star; next
year the Sun will cross the equator a little way west-
ward of that star, and so every year a little farther west-
ward, until, in a long course of ages, the place of the
equinox will occupy successively every part of the eclip-
tic, until we come round to the same star again. As,
therefore, the sun, revolving from west to east in his ap-
parent orbit, comes round towards the point where it
left the equinox, it meets the equinox before it reaches
that point. The appearance is as though the equinox
goes forward to meet the sun, and hence the phenome-
non is called the Precession of the Equinoaces, and the
fact is expressed by saying that the equinoxes retrograde
on the ecliptic, until the line of the equinoxes makes a
complete revolution from east to west. The equator is
conceived as sliding westward on the ecliptic, always
preserving the same inclination to it, as a ring placed at
a small angle with another of nearly the same size,
which remains fixed, may be slid quite around it, giving
a corresponding motion to the two points of intersec-
tion. It must be observed, however, that this mode of
conceiving of the precession of the equinoxes is purely
imaginary, and is employed merely for the convenience
of representation.
137. The amount of precession annually is 50.”1;
whence, since there are 3600” in a degree, and 360° in
136. Precession of the Equinoxes.—Define it. If the Sun
crosses the equator near a certain star this year, where will it
cross it next year? Why is the fact called the precession of the
equinoxes? How is the equator conceived as moving with re-
gard to the ecliptic?
108 UNIVERSAL GRAVITATION.
the whole circumference, and consequently, 1296000",
this sum divided by 50.1 gives 25868 years for the pe-
riod of a complete revolution of the equinoxes.
138. Suppose now we fix to the center of each of the
two rings (Art. 136,) a wire representing its axis, one
corresponding to the axis of the ecliptic, the other to
that of the equator, the extremity of each being the pole
of its circle. As the ring denoting the equator turns
round on the ecliptic, which with its axis remains fixed,
it is easy to conceive that the axis of the equator re-
volves around that of the ecliptic, and the pole of the
equator around the pole of the ecliptic, and constantly at
a distance equal to the inclination of the two circles. To
transfer our conceptions to the celestial sphere, we may
easily see that the axis of the diurnal sphere, (that of
the earth produced, Art. 15,) would not have its pole
constantly in the same place among the stars, but that
this pole would perform a slow revolution around the
pole of the ecliptic from east to west, completing the cir-
cuit in about 26,000 years. Hence the star which we
now call the pole star, has not always enjoyed that dis-
tinction, nor will it always enjoy it hereafter. When
the earliest catalogues of the stars were made, this star.
was 12° from the pole. It is now 19 24', and will ap-
proach still nearer; or to speak more accurately, the pole
will come still nearer to this star, after which it will
leave it, and successively pass by others. In about
13,000 years, the bright star Lyra, which lies on the
circle of revolution opposite to the present pole star,
137. What is the amount of precession annually In what
time will the equinoxes perform a complete revolution ? +
138. Illustrate the precession of the equinoxes by an appa-
ratus of wires. How is the pole of the earth situated with re-
spect to the stars at different times" Has the present pole star
always been such'ſ What will be the pole starklä,000 years
hence? Will this cause affect the elevation of the north pole
above the horizon 7 *
PRECESSION OF THE EQUINOXEs. 109
will be within 59 of the pole, and will constitute the
Pole Star. As Lyra now passes near our zenith, the
learner might suppose that the change of position of the
pole among the stars, would be attended with a change
of altitude of the north pole above the horizon. This
mistaken idea is one of the many misapprehensions
which result from the habit of considering the horizon
as a fixed circle in space. However the pole might
shift its position in space, we should still be at the
same distance from it, and our horizon would always
reach the same distance beyond it.
139. The time occupied by the sun in passing from
the equinoctial point round to the same point again, is
called the TROPICAL YEAR. As the sun does not perform
a complete revolution in this interval but falls short of it
50.”1, the tropical year is shorter than the sidereal by
20m. 20s. in mean solar time, this being the time of de-
scribing an arc of 50.71 in the annual revolution.* The
changes produced by the precession of the equinoxes in
the apparent places in the circumpolar stars, have led to
Some interesting results in chronology. In consequence
of the retrograde motion of the equinoctial points, the
signs of the ecliptic, do not correspond at present to
the constellations which bear the same names, but lie
about one whole sign or 30° westward of them. Thus,
that division of the ecliptic which is called the sign
Taurus, lies in the constellation Aries, and the sign
Gemini in the constellation Taurus. Undoubtedly how-
ever when the ecliptic was thus first divided, and the
divisions named, the several constellations lay in the re-
spective divisions which bear their names. How long
is it, then, since our zodiac was formed 2 -
139. Define the tropical year. How much shorter is the
tropical than the sidereal year ! How has the precession of the
equinoxes been applied in Chronology 7
* 59, 8,113:24h. : : 50/11 : 20m. 20s.
110 THE MOON.
50.71 : 1 year::30°(=108000”) ; 2155.6 years.
The result indicates that the present divisions of the
zodiac, were made soon after the establishment of the
Alexandrian School of astronomy.
CHA PTER I W.
of THE MOON.
140. NExT to the Sun the Moon naturally claims our
attention. She is an attendant or satellite to the earth,
around which she revolves at the distance of nearly
240,000 miles, or more exactly 238,545 miles. Her
angular diameter is about half a degree, and her real diam-
eter 2160 miles. She is therefore a comparatively small
body, being only one forty-ninth part as large as the
earth.
The moon shines by reflected light borrowed from
the sun, and when full exhibits a disk of silvery bright-
ness, diversified by extensive portions partially shaded.
These dusky spots are generally said to be land, and the
brighter parts water; but astronomers tell us that if ei-
ther are water, it must be the darker portions. Land by
scattering the rays of the Sun's light would appear more
luminous than the ocean which reflects the light like a
mirror. By the aid of the telescope, we see undoubted
signs of a varied surface, in Some parts composed of ex-
tensive tracts of level country, and in others exceedingly
broken by mountains and valleys. -
141. The line which separates the enlightened from
the dark portions of the moon’s disk, is called the Ter-
140. The Moon.—What relation has the Moon to the earth
State her distance, diameter and bulk. Is her light direct or
reflected 7 What are the dark places in the moon generally un-
derstood to be 7 Why would water appear darker than land'ſ
What does the telescope reveal to us respecting the moon?
LUNAR GEOGRAPHY, 111
minator. (See Frontispiece.) As the terminator traver-
ses the disk from new to full moon, it appears through the
telescope exceedingly broken in some parts, but Smooth
in others, indicating that portions of the lunar surface are
uneven while others are level. The broken regions ap-
pear brighter than the smooth tracts. The latter have
been taken for seas, but it is supposed with more prob-
ability that they are extensive plains, since they are still
too uneven for the perfect level assumed by bodies of
water. That there are mountains in the moon, is known
by several distinct indications. First, when the moon
is increasing, certain spots are illuminated sooner than
the neighboring places, appearing like bright points be-
yond the terminator, within the dark part of the disk,
in the same manner as the tops of mountains on the
earth are tipped with the light of the sun, in the morn-
ing, while the regions below are still dark. Secondly,
after the terminator has passed over them, they project
shadows upon the illuminated part of the disk, always
opposite to the sun, corresponding in shape to the form
of the mountain, and undergoing changes in length from
night to night, according as the sun shines upon that
part of the moon more or less obliquely. Many indi-
vidual mountains rise to a great height in the midst of
plains, and there are several very remarkable mountain-
ous groups, extending from a common center in long
chains. •
142. That there are also valleys in the moon, is
equally evident. The valleys are known to be truly
such, particularly by the manner in which the light of
the sun falls upon them, illuminating the part opposite
to the sun while the part adjacent is dark, as is the case
when the light of a lamp shines obliquely into a china
141. Define the terminator. What do we learn from its rug-
ged appearance 1 State the proofs of mountains in the moon.
142. State the proofs of valleys in the moon. When is the
best time for viewing the mountains and valleys of the moon'
112 - THE MOON.
cup. These valleys are often remarkably regular, and
some of them almost perfect circles. In several instan-
ces, a circular chain of mountains surrounds an exten-
sive valley, which appears nearly level, except that a
sharp mountain sometimes rises from the center. The
best time for observing these appearances is near the
first quarter of the moon, when half the disk is en-
lightened;* but in studying the lunar geography, it is
expedient to observe the moon every evening from new
to full, or rather through her entire series of changes.
143. The various places on the moon's disk have re-
ceived appropriate names. The dusky regions, being
formerly supposed to be seas, were named accordingly ;
and other remarkable places have each two names, one
derived from some well known spot on the earth, and
the other from some distinguished personage. Thus
the same bright spot on the surface of the moon is
called Mount Sinai or Tycho, and another, Mount Et-
na or Copernicus. The names of individuals, how-
ever, are more used than the others. The frontispiece
exhibits the telescopic appearance of the full moon. A
few of the most remarkable points have the following
names, corresponding to the numbers and letters on the
map. (See Frontispiece.)
1. Tycho, A. Mare Humorum,
2. Kepler, B. Mare Nubium,
3. Copernicus, C. Mare Imbrium,
4. Aristarchus, D. Mare Nectaris,
5. Helicon, E. Mare Tranquilitatis,
6. Eratosthenes, F. Mare Serenitatis,
7. Plato, G. Mare Fecunditatis,
8. Archimedes, H. Mare Crisium.
9. Eudoxus,
10. Aristotle,
... " It is earnestly recommended to the student of astronomy, to exam-
ine the moon repeatedly with the best telescope he can command, using
low powers at first, for the sake of a better light. - -
LUNAR GEOGRAPHY. 113
The frontispiece represents the appearance of the
moon in the telescope when full and when five days
old. In the latter cut, the learner will remark the rough,
rugged appearance of the terminator; the illuminated
points beyond the terminator within the dark part of the
moon, which are the tops of mountains; and the nu-
merous circular spaces, which exhibit valleys or caverns
surrounded by mountainous chains. Those circles which
are near the terminator into which the sun's light shines
very obliquely, cast deep shadows on the sides opposite
the sun. Those more remote from the terminator, and
farther within the illuminated part of the moon, into
which the sun shines more directly, have a greater por-
tion illuminated with shorter shadows; and those which
lie near the edge of the moon, most distant from the ter-
minator, are of an oval figure, being presented obliquel
to the eye. - ---
144. The heights of the lunar mountains, and the
depths of the valleys, can be estimated with a considera-
ble degree of accuracy. Some of the mountains are as
high as five miles, and the valleys in some instances
are four miles deep. Hence it is inferred that the sur-
face of the moon is more broken and irregular than that
of the earth, its mountains being higher and its valleys
deeper in proportion to its magnitude than that of the
earth. The lunar mountains in general, exhibit an ar-
143. IIow are places in the moon named 7 Point out the
most remarkable places on the map of the full moon. , Point
out the mountains, valleys, and craters, on the cut, which rep-
resents the moon five days old. - - *
144. Specify the heights of some of the lunar mountains.
Is the surface of the moon more or less broken than that of the
earth? Are the mountains like or unlike ours? What is the
first variety'ſ What is the shape of the insulated mountains?
How can their heights be calculated ? What is said of the
second variety, the mountain ranges? What is said of the
circular ranges? What is said of the central mountains ?
10%
114 . THE MOON.
rangement and an aspect very different from the moun-
tain scenery of our globe. They may be arranged un-
der the four following varieties. -
First, Insulated Mountains, which rise from plains
nearly level, shaped like a sugar loaf, which may be
supposed to present an appearance somewhat similar to
Mount Etna, or the Peak of Teneriffe. The shadows
of these mountains, in certain phases of the moon, are
as distinctly perceived, as the shadow of an upright staff,
when placed opposite to the sun ; and these heights can
be calculated from the length of their shadows. Some
of these mountains being elevated in the midst of exten-
sive plains, would present to a spectator on their sum-
mits, magnificent views of the surrounding regions.
Secondly, Mountain Ranges, extending in length two
or three hundred miles. These ranges bear a distant re-
semblance to our Alps, Appenines, and Andes; but they
are much less in extent. Some of them appear very
rugged and precipitous, and the highest ranges are in
some places more than four miles in perpendicular alti-
tude. In some instances, they are nearly in a straight
line from northeast to southwest, as in that range called
the Appenines; in other cases they assume the form of
a semicircle or crescent.
Thirdly, Circular Ranges, which appear on almost
every part of the moon’s surface, particularly in its South-
ern regions. This is one grand peculiarity of the lunar
ranges, to which we have nothing similar on the earth.
A plain, and sometimes a large cavity, is surrounded
with a circular ridge of mountains, which encompasses
it like a mighty rampart. These annular ridges and
plains are of all dimensions, from a mile to forty or fifty
miles in diameter, and are to be seen in great numbers
over every region of the moon’s surface; they are most
conspicuous, however, near the upper and lower limbs
about the time of half moon.
The mountains which form these circular ridges are
of different elevations, from one fifth of a mile to three
and a half miles, and their shadows cover one half of
the plain at the base. These plains are sometimes on
LUNAR GEOGRAPHY. 115
a level with the general surface of the moon, and in
other cases they are sunk a mile or more below the level
of the ground, which surrounds the exterior circle of the
mountains. .
Fourthly, Central Mountains, or those which are
placed in the middle of circular plains. In many of the
plains and cavities surrounded by circular ranges of
mountains there stands a single insulated mountain,
which rises from the center of the plain, and whose
shadow sometimes extends in the form of a pyramid
half across the plain to the opposite ridges. These cen-
tral mountains are generally from half a mile to a mile
and a half in perpendicular altitude. In some instances
they have two and sometimes three different tops, whose
shadows can be easily distinguished from each other.
Sometimes they are situated towards one side of the
plain or cavity, but, in the great majority of instances,
their position is nearly or exactly central. The lengths
of their bases vary from five to about fifteen or sixteen
miles.
145. The Lunar Caverns form a very peculiar and
prominent feature of the moon’s surface, and are to
be seen throughout almost every region, but are most
numerous in the southwest part of the moon. Nearly a
hundred of them, great and small, may be distinguished
in that quarter. They are all nearly of a circular shape,
and appear like a very shallow egg-cup. The smaller
cavities appear within almost like a hollow cone, with
the sides tapering towards the center; but the larger
ones have for the most part, flat bottoms, from the cen-
ter of which there frequently rises a small steep conical
hill, which gives them a resemblance to the circular
ridges and central mountains before described. In some
instances their margins are level with the general sur-
face of the moon, but in most cases they are encircled
145. Lunar Caverns.—What is said of their number, shape
and appearances?
116 THE MOON.
with a high annular ridge of mountains, marked with
lofty peaks. Some of the larger of these cavities con-
tain smaller cavities of the same kind and form, particu-
larly in their sides. The mountainous ridges which sur-
round these cavities, reflect the greatest quantity of
light; and hence that region of the moon in which they
abound, appears brighter than any other. From their
lying in every possible direction, they appear at and
near the time of full moon, like a number of brilliant
streaks or radiations. These radiations appear to con-
verge towards a large brilliant spot, surrounded by a
faint shade, near the lower part of the moon which is
named Tycho, (Frontispiece, 1,) which may be easily dis-
tinguished even by a small telescope. The spots named,
Repler and Copernicus, are each composed of a central
spot with luminous radiations.”
146. Dr. Herschel is supposed also to have obtained
decisive evidence of the existence of volcanoes in the
moon, not only from the light afforded by their fires,
but also from the formation of new mountains by the
accumulation of matter where fires had been seen to
exist, and which remained after the fires were extinct.
147. Some indications of an atmosphere about the
moon have been obtained, the most decisive of which
are derived from appearances of twilight, a phenomenon
that implies the presence of an atmosphere. Similar in-
dications have been detected, it is supposed, in eclipses
of the Sun, denoting a transparent refracting medium en-
compasing the moon.
146. Volcanoes.—What proofs are there of their having ex-
isted in the moon 7
147. What evidence is there of a lunar atmosphere?
* The foregoing accurate description of the Lunar mountains and cav-
erns is from “Dick's Celestial Scenery.”
LUNAR GEOGRAPHY. 1.17
148. It has been a question with astronomers, whether
there is water in the moon The general opinion is
that there is none. If there were any, we should ex-
pect to see clouds; or at least we should expect to find
the face of the moon occasionally obscured by clouds;
but this is not the case, since the spots on the moon’s
disk, when our sky is clear, are always in full view.
The deep caverns, moreover, seen in those dusky spots
which were supposed to be seas, are unfavorable to the
supposition, that they are surrounded by water ; and the
terminator when it passes over these places is, as already
remarked, too uneven to permit us to suppose that these
traCtS are SeaS.
149. The improbability of our ever identifying arti-
ficial structures in the moon, may be inferred from the
fact that a line one mile in length in the moon subtends
an angle at the eye of only about one second. If, there-
fore, works of art were to have a sufficient horizontal
extent to become visible, they can hardly be supposed
to attain the necessary elevation, when we reflect that
the height of the great pyramid of Egypt is less than
the sixth part of a mile. Still less probable is it that we
shall ever discover any inhabitants in the moon. The
greatest magnifying power that has ever been applied,
with distinctness, to the moon, does not much exceed a
thousand times, bringing the moon apparently a thou-
Sand times nearer to us than when seen by the naked
eye. But this implies a distance still of 240 miles; and
148. Is there water in the moon? What proofs are there to
the contrary 7
149. Is is probable that artificial structures in the moon will
ever be identified ? How high must they be, in order to be
seen distinct from the surface? Is it probable that we shall
ever be able to recognize inhabitants in the moon'ſ What is
the greatest magnifying power of the telescope that has ever
been applied to the moon " If we could magnify the moon
10,000 times what would still be her apparent distance 7 What
inherent difficulty is there in employing very great magnifiers ?
118 THE MOON.
could we magnify the moon ten thousand times, her ap-
parent distance would still be twenty four miles, a dis-
tance too great to distinguish living beings. Moreover,
when we use such high magnifiers in the telescope, our
field of view is necessarily exceedingly small, so that it
would be a mere point that we could view at a time.
This difficulty is inherent in the very nature of tele-
scopes, namely, that the field of view is reduced as the
magnifying power is increased ; and we magnify the
vapors and the undulations of the atmosphere, as well
as the moon, and by this means obscure the medium so
much that we should not be able to see anything with
distinctness. It is only to such minute objects as a star,
that very high powers of the telescope can ever be ap-
plied.
150. Some writers, however, suppose that possibly
we may trace indications of lunar inhabitants in their
works, and that they may, in like manner, recognize the
existence of the inhabitants of our planet. An author
who has reflected much on subjects of this kind, rea-
Sons as follows: A navigator who approaches within a
certain distance of a small island, although he perceives
no human being upon it, can judge with certainty, that
it is inhabited, if he perceives human habitations, villa-
ges, cornfields, or other traces of cultivation. In like
manner, if we could perceive changes or operations in
the moon, which could be traced to the agency of intel-
ligent beings, we should then obtain satisfactory evi-.
dence, that such beings exist on that planet; and it is
thought possible that such operations may be traced.
A telescope which magnifies 1200 times, will enable us
to perceive, as a visible point on the surface of the moon,
an object whose diameter is only about 300 feet. Such
150. What have some writers supposed with respect to the
probability of our tracing marks of living beings on the moon 7
How is it proposed to have the moon examined for this pur-,
pose 7
LUNAR GEOGRAPHY. 119
an object is not larger than many of our public edifices;
and, therefore, were any such edifices rearing in the
moon, or were a town or city extending its boundaries,
or were operations of this description carrying on in a
district where no such edifices had previously been
erected, such objects and operations might probably be
detected by a minute inspection. Were a multitude of
living creatures moving from place to place in a body,
or were they even encamping in an extensive plain, like
a large army, or like a tribe of Arabs in the desert, and
afterwards removing, it is possible that such changes
might be traced by the difference of shade or color,
which such movements would produce. In order to de-
tect such minute objects and operations, it would be
requisite that the surface of the moon should be distrib-
uted among at least a hundred astronomers, each having
a spot or two allotted to him, as the object of his more
particular investigation, and that the observations be
continued for a period of at least thirty or forty years,
during which time certain changes would probably be
perceived, arising either from physical causes, or from
the operations of living agents.”
151. It has sometimes been a subject of speculation,
whether it might be possible, by any symbols, to cor-
respond with the inhabitants of the moon. It has been
Suggested, that if some vast geometrical figure, as a
Square or a triangle, were erected on the plains of Siberia,
it might be recognized by the lunarians, and answered
by some corresponding signal. Some geometrical figure
would be peculiarly appropriate for such a telegraphic
commerce with the inhabitants of another sphere, since
these are simple ideas common to all minds.
151. How is it proposed to carry on a telegraphic communi-
cation with the lunarians?
* Dick's Celestial Scenery, Ch. Iv.
120 THE MOON.
FHASES OF THE MOON,
152. The changes of the moon, commonly called her
Phases, arise from different portions of her illuminated
side being turned towards the earth at different times.
When the moon is first seen after the setting sun, her
form is that of a bright crescent, on the side of the disk
next to the sun, while the other portions of the disk
shine with a feeble light, reflected to the moon from the
earth. Every night we observe the moon to be farther
and farther eastward of the sun, and at the same time
the crescent enlarges, until, when the moon has reached
an elongation from the sun of 90°, half her visible disk
is enlightened, and she is said to be in her first quarter.
The terminator, or line which separates the illuminated
from the dark part of the moon, is convex towards the
sun from the new moon to the first quarter, and the
moon is said to be hormed. The extremities of the
crescent are called cusps. At the first quarter, the ter-
minator becomes a straight line, coinciding with a di-
ameter of the disk; but after passing this point, the ter-
minator becomes concave towards the sun, bounding
that side of the moon by an elliptical curve, when the
moon is said to be gibbous. When the moon arrives at
the distance of 180° from the sun, the entire circle is
illuminated, and the moon is full. She is then in oppo-
sition to the sun, rising about the time the sun sets. For
a week after the full, the moon appears gibbous again,
until, having arrived within 90° of the sun, she re-
sumes the same form as at the first quarter, being then
at her third quarter. From this time until new moon,
she exhibits again the form of a crescent before the ri-
sing Sun, until, approaching her conjunction with the
152. Phases of the Moon.—Whence do they arise? State
the successive appearances of the moon from new to full. In
what parts of her revolution is she horned, and in what parts
gibbous ! When is she said to be in conjunction, and when in
opposition ? What are the syzigies, quadratures, and octants?
Define the circle of illumination, and the circle of the disk,
PHASES. 121
sun, her narrow thread of light is lost in the solar blaze;
and finally, at the moment of passing the Sun, the dark
side is wholly turned towards us, and for some time we
lose sight of the moon.
The two points in the orbit corresponding to new and
full moon respectively, are called by the common name
of syzigies; those which are 90° from the sun are
called quadratures; and the points half way between
the Syzigies and quadratures are called octants. The
circle which divides the enlightened from the unen-
lightened hemisphere of the moon, is called the circle of
illumination : that which divides the hemisphere that
is turned towards us from the hemisphere that is turn-
ed from us, is called the circle of the disk.
153. As the moon is an opake body of a spherical
figure, and borrows her light from the sun, it is obvious
Fig. 31.
tº€
that that half only which is towards the sun can be il-
luminated. More or less of this side is turned towards
the earth, according as the moon is at a greater or less
elongation from the sun. The reason of the different
phases will be best understood from a diagram. There-
fore let T (Fig. 31,) represent the earth, and S the Sun.

122 THE MOON.
Let A, B, C, &c. be successive positions of the moon.
At A the entire dark side of the moon being turned to-
wards the earth, the disk would be wholly invisible. At
B, the circle of the disk cuts off a small part of the en-
lightened hemisphere, which appears in the heavens at
b, under the form of a crescent. At C, the first quarter,
the circle of the disk cuts off half the enlightened hem-
isphere, and a half moon is seen at c. In like manner it
will be seen that the appearances presented at D, E, F,
&c. must be those represented at d, e, f. If a round
body, as an apple, suspended by a string, be carried
around a lamp, the eye remaining fixed opposite to it at
the same level, the various phases of the moon will be
exhibited.
REVOLUTIONS. OF THE MOON.
154. The moon revolves around the earth from west
to east, making the entire circuit of the heavens in about
27# days. gº
The period of the moon’s revolution from any point
in the heavens round to the same point again, is called
a month. A syderedl month is the time of the moon’s
passing from any star, until it returns to the same star
again. A synodical month, so called from two Greek
words implying that at the end of this period the two
bodies (the sun and moon) come together, is the time
from one conjunction or new moon to another. The
synodical month is about 294 days, or more exactly,
29d. 12h. 44m. 28.8=29.53 days. The sidereal month
is about two days shorter, being 27d. 7h. 43m. 115.5.
or 27.32 days. As the sun and moon are both revolv-
ing in the same direction, and the Sun is moving nearly
153. How much of the moon is illuminated at once 2 Ex-
plain the phases of the moon from figure 31.
154. Define a month. Define a sidereal month. Also a sy-
nodical month. Why so called ' What is the length of the
synodical month 7 Also of the sidereal month? What is the
moon’s daily motion 7
REVOLUTIONS. 123
a degree a day, during the 27 days of the moon’s revo-
lution, the sun must have moved 27°. Now since the
moon passes over 360° in 27.32 days, her daily motion
must be 13° 17'. It must therefore evidently take about
two days for the moon to overtake the sun.
155. The moon’s orbit is inclined to the ecliptic in an
angle of about 5° (5° 8' 48".) The moon crosses the
ecliptic in two opposite points called her modes. That
which the moon crosses from south to north, is called
her ascending node, that which she crosses from north
to South, her descending node. The moon, therefore, is
never seen far from the ecliptic, but, the path she pur-
sues through the skies, is very nearly the same as that
of the sun in his annual revolution around the earth.
156. The moon, at the same age, crosses the meridian
at different altitudes at different seasons of the year; and
accordingly it is said to run sometimes high and some-
times low. The full moon, for example, will appear
much farther in the south when on the meridian at one
period of the year than at another. The reason of this
may be explained as follows. When the sun is in the
part of the ecliptic south of the equator, the earth and
of course the moon, which always keeps near to the
earth, is in the part north of the equator. At such
times, therefore, the new moons, which are always
Seen in the part of the heavens where the sun is, will
run far South, while the full moons, which are always in
the opposite part of the heavens from the sun, will run
high. Such is the case during the winter months; but,
155. How much is the moon's orbit inclined to the ecliptic”
Define the nodes. What is the ascending and what the de-
scending node 7 -
156. Why does the moon run high and low 7 At what sea-
Son of the year are the full moons longest above the horizon 7
Explain how this operates favorably to those who are near the
pole.
124 | THE MOON.
in the Summer, when the sun is towards the northern
tropic and the earth towards the southern, the new
moons run high and the full moons low. This arrange-
ment gives us a great advantage in respect to the amount
of light received from the moon; since the full moon
is longest above the horizon during the long nights of
winter, when her presence is most needed. This cir-
cumstance is especially favorable to the inhabitants of
the polar regions, the moon, when full, traversing that
part of her orbit which lies north of the equator, and of
course above the horizon of the north pole, and traver-
sing the portion that lies south of the equator, and be-
low the polar horizon, when new. During the polar
winter, therefore, the moon, during her second and third
quarters, when she gives most light, is commonly above
the horizon, while the sun is absent ; whereas, during
Summer, while the sun is present and the light is not
needed, during her second and third quarters, she is be-
low the horizon.
157. About the time of the autumnal equinox, the
moon when near the full, rises about sunset for a num-
ber of mights in succession; and as this is, in England,
the period of harvest, the phenomenon is called the
Harvest Moon. To understand the reason of this, since
the moon is never far from the ecliptic, we will suppose
her progress to be in the ecliptic. If the moon moved
in the equator, then, since this great circle is at right
angles to the axis of the earth, all parts of it, as the
earth revolves, cut the horizon at the same constant
angle. But the moon’s orbit, or the ecliptic, which is
here taken to represent it, being oblique to the equator,
cuts the horizon at different angles in different parts, as
will easily be seen by reference to an artificial globe.
When the first of Aries, or vernal equinox, is in the
157. Why is the harvest moon so called 7 Explain its cause.
How is the moon's orbit inclined to the horizon at different
times?
REVOLUTIONS. - 125
eastern horizon, it will be seen that the ecliptic, (and
consequently the moon’s orbit,) makes its least angle
with the horizon. Now, at the autumnal equinox, the
sun being in Libra, the moon at the full, when she is
always opposite to the sun, is in Aries, and rises when
the sun sets. On the following evening, although she
has advanced in her orbit about 13°, yet her progress be-
ing oblique to the horizon, and at a small angle with it,
she will be found at this time but a little way below the
horizon, compared with the point where she was at Sun-
set the preceding evening. She therefore rises but little
later, and so for a week only a little later each evening
than she did the preceding night.
158. The moon turns on its aſcis in the same time in
which it revolves around the earth.
This is known by the moon’s always keeping nearly
the same face towards us, as is indicated by the tele-
scope, which could not happen unless her revolution on
her axis kept pace with her motion in her orbit. Thus
it will be seen by inspecting figure 22, that the earth
turns different faces towards the sun at different times;
and if a ball having one hemisphere white and the
other black be carried around a lamp, it will easily be
seen that it cannot present the same face constantly to-
wards the lamp unless it turns once on its axis while
performing its revolution. The same thing will be ob-
served when a man walks around a tree, keeping his face
constantly towards it. Since however the motion of
the moon on its axis is uniform, while the motion in its
orbit is unequal, the moon does in fact reveal to us a lit-
tle sometimes of one side and sometimes of the other.
Thus when the ball above mentioned is placed before
the eye with its light side towards us, on carrying it
round, if it is moved faster than it is turned on its axis,
158. In what time does the moon turn on its axis 7 Illus-
trate by the motion of a ball around a lamp. Is the same side
of the moon always turned exactly towards us?
w 1.1%
126 THE MOON.
a portion of the dark hemisphere is brought into view
on one side; or if it is moved forward slower than it is
turned on its axis, a portion of the dark hemisphere
comes into view on the other side.
159. These appearances are called the moon’s libra-
tions in longitude. The moon has also a libration in
latitude, so called, because in one part of her revolution,
more of the region around one of the poles comes into
view, and in another part of the revolution, more of the
region around the other pole; which gives the appear-
ance of a tilting motion to the moon’s axis. This has
nearly the same cause with that which occasions our
change of seasons. The moon’s axis being inclined to
the plane of her orbit, and always remaining parallel to
itself, the circle which divides the visible from the in-
visible part of the moon, will pass in such a way as to
throw sometimes more of one pole into view, and some-
times more of the other, as would be the case with the
earth if seen from the sun. (See Fig. 22.)
The moon exhibits another phenomenon of this kind
called her diurnal libration, depending on the daily ro-
tation of the spectator. She turns the same face to-
wards the center of the earth only, whereas we view
her from the surface. When she is on the meridian, we
See her disk nearly as though we viewed it from the
Center of the earth, and hence in this situation it is sub-
ject to little change ; but when near the horizon, our
circle of vision takes in more of the upper limb than
would be presented to a spectator at the center of the
earth. Hence, from this cause, we see a portion of one
limb while the moon is rising, which is gradually lost
sight of, and we see a portion of the opposite limb as
the moon declines to the west. It will be remarked
that neither of the foregoing changes implies any actual
motion in the moon, but that each arises from a change
of position in the spectator. -
159. Dxplain the librations in longitude. Ditto in latitude,
Ditto the diurnal librations. &
REVOLUTIONS. 127
160. Since the succession of day and night depends
on the revolution of a planet on its own axis, an inhab-
itant of the moon would have but one day and one night
during the whole lunar month of 294 days. One of its
days, therefore, is equal to nearly 15 of ours. So pro-
tracted an exposure to the sun’s rays, especially in the
equatorial regions of the moon, must occasion an exces-
sive accumulation of heat; and so long an absence of
the Sun must occasion a corresponding degree of cold.
Each day would be a wearisome summer; each night a
Severe winter.* A spectator on the side of the moon
which is opposite to us would never see the earth ; but
one on the side next to us would see the earth present-
ing a gradual succession of changes during his long
night of 360 hours. Soon after the earth's conjunction
with the sun, he would have the light of the earth re-
flected to him, presenting at first a cresent, but enlarg—
ing as the earth approaches its opposition, to a great orb,
13 times as large as the full moon appears to us, and af-
fording nearly 13 times as much light. Our seas, our
plains, our mountains, our volcanoes, and our clouds,
would produce very diversified appearances, as would
the various parts of the earth brought successively into
view by its diurnal rotation. The earth while in view
to an inhabitant of the moon, would remain immovably
fived in the same part of the heavens. For being un-
conscious of his own motion around the earth, as we are
of our motion around the sun, the earth would seem to
revolve around his own planet from west to east, just as
the moon appears to us to revolve about the earth ; but,
meanwhile, his rotation along with the moon on her
axis, would cause the earth to have an apparent motion
160. How many days would an inhabitant of the moon have
in a lunar month? What vicissitudes of temperature would
occur in a single day ? Would a spectator on the side of the
moon opposite to us, ever see the earth 7 How would the earth
appear to a spectator on the side of the moon next to us?
* Francocur, Uranog. p. 91.
12S THE MOON.
westward at the same rate. The two motions, there-
fore, would exactly balance each other, and the earth
would appear all the while at rest.
161. We have thus far contemplated the revolution
of the moon around the earth as though the earth were
at rest. But, in order to have just ideas respecting the
moon’s motions, we must recollect that the moon like-
wise revolves along with the earth around the Sun. It
is sometimes said that the earth carries the moon along
with her in her annual revolution. This language may
convey an erroneous idea; for the moon, as well as the
earth, revolves around the sum under the influence of
two forces, and would continue her motion around the
sun were the earth removed out of the way. Indeed,
the moon is attracted towards the sun 24 times more
than towards the earth, and would abandon the earth
were not the latter also carried along with her by the
same forces. So far as the Sun acts equally on both
bodies, their motion with respect to each other would
not be disturbed. Because the gravity of the moon to-
wards the Sun is found to be greater, at the conjunction,
than her gravity towards the earth, some have appre-
hended that, if the doctrine of universal gravitation is
true, the moon ought necessarily to abandon the earth.
In order to understand the reason why it does not do
thus, we must reflect, that when a body is revolving in
its orbit under the action of the projectile force and
gravity, whatever diminishes the force of gravity while
that of projection remains the same, causes the body to
approach nearer to the tangent of her orbit, and of course
to recede from the center; and whatever increases the
amount of gravity carries the body towards the center.
161. Can it be said that the earth carries the moon around
the sun ? How much more is the moon attracted towards the sun
than towards the earth'ſ Why does not the moon abandon the
earth? When the Sun acts equally on both bodies, does it dis-
turb their relative places? How does the sun act upon these
bodies at the conjunctions and oppositions 7
REVOLUTIONS. 129
Now, when the moon is in conjunction, her gravity to-
wards the earth acts in opposition to that towards the
sun, while her velocity remains too great to carry her,
with what force remains, in a circle about the sun, and
she therefore recedes from the sun, and commences her
revolution around the earth. On arriving at the opposi-
tion, the gravity of the earth conspires with that of the
Sun, and the moon’s projectile force being less than that
required to make her revolve in a circular orbit, when
attracted towards the sun by the sum of these forces, she
accordingly begins to approach the Sun and descends
again to the conjunction.
162. The attraction of the sun, however, being every
where greater than that of the earth, the actual path of
the moon around the sun is every where concave to-
wards the latter. Still the elliptical path of the moon
around the earth, is to be conceived of in the same way
as though both bodies were at rest with respect to the
sun. Thus, while a steamboat is passing swiftly around
an island, and a man is walking slowly around a post in
the cabin, the line which he describes in space between
the forward motion of the boat and his circular motion
around the post, may be every where concave towards
the island, while his path around the post will still be
the same as though both were at rest. A mail in the rim
of a coach wheel, will turn around the axis of the wheel,
when the coach has a forward motion in the same man-
ner as when the coach is at rest, although the line ac-
tually described by the mail will be the resultant of both
motions, and very different from either.
163. We have hitherto regarded the moon as descri-
bing a great circle on the face of the sky, such being the
162. How is the moon's path in space with respect to the
sun ? How is the elliptical path of the moon around the earth
to be conceived of 't How is this illustrated by the motions of
a man in a steamboat? Also by the motions of a nail in the
rim of a coach wheel.
130 THE MOON.
visible orbit as seen by projection. But, on more exact
investigation, it is found that her Orbit is not a circle,
and that her motions are subject to very numerous ir-
regularities. These will be best understood in connec-
tion with the causes on which they depend. . The law
of universal gravitation has been applied with wonder-
ful success to their investigation, and its results have
conspired with those of long continued observation, to
furnish the means of ascertaining with great exactness
the place of the moon in the heavens at any given in-
stant of time, past or future, and thus to enable astrono-
mers to determine longitudes, to calculate eclipses, and
to solve various other problems of the highest interest.
A complete understanding of all the irregularities of the
moon’s motions, must be sought for in more extensive
treatises of astronomy than the present; but some gen-
eral acquaintance with the subject, clear and intelligible
as far as it goes, may be acquired by first gaining a dis-
tinct idea of the mutual actions of the sun, the moon,
and the earth.
164. The irregularities of the moon's motions, are
due chiefly to the disturbing influence of the sun, which
operates in two ways ; first, by acting unequally on the
earth and moon, and, secondly, by acting obliquely on
the moon, on account of the inclination of her orbit to
the ecliptic.
If the Sun acted equally on the earth and moon, and
always in parallel lines, this action would serve only to
restrain them in their annual motions round the sun, and
would not affect their actions on each other, or their
motions about their common center of gravity. In that
case, if they were allowed to fall directly towards the
Sun, they would fall equally, and their respective situa-
tions would not be affected by their descending equally
towards it. We might then conceive them as in a
plane, every part of which being equally acted on by
163. Are the motions of the moon regular or irregular 7 By
what general law are they explained ?
REVOLUTIONs. 131
the sun, the whole plane would descend towards the
sun, but the respective motions of the earth and the
moon in this plane, would be the same as if it were
quiescent. Supposing then this plane and all in it,
to have an annual motion imprinted on it, it would
move regularly around the sun, while the earth and moon
would move in it with respect to each other, as if the
plane were at rest, without any irregularities. But be-
cause the moon is nearer the sun in one half of her orbit
than the earth is, and in the other half of her orbit is at
a greater distance than the earth from the sun, while the
power of gravity is always greater at a less distance; it
follows, that in one half of her orbit the moon is more
attracted than the earth towards the sun, and in the other
half less attracted than the earth. The eaccess of the
attraction, in the first case, and the defect in the second
constitutes a disturbing force, to which we may add an-
other, namely, that arising from the oblique action of the
Solar force, since this action is not directed in parallel
lines, but in lines that meet in the center of the sun.
165. To see the effects of this process, let us suppose
that the projectile motions of the earth and moon were
destroyed, and that they were allowed to fall freely to-
wards the sun. If the moon was in conjunction with
the Sun, or in that part of her orbit which is nearest to
him; the moon would be more attracted than the earth,
and fall with greater velocity towards the Sun ; so that
the distance of the moon from the earth would be in-
creased in the fall. If the moon was in opposition, or
164. To what cause are the inequalities of the moon’s mo-
tions chiefly due " If the sun acted equally on the earth and
moon, and in parallel lines, would it disturb their motions ! If
allowed to fall towards the sun, how would they fall ! How
might we conceive them as situated in a plane 7 When is the
moon more attracted than the earth 7 When is the earth more
attracted than the moon 7 What constitutes the disturbing
force {
165. Trace the effects of the sun, if the projectile force were
destroyed, at conjunction, at opposition, and at quadrature.
132 THE MOON.
in the part of her orbit which is farthest from the sun,
she would be less attracted than the earth by the sun,
and would fall with a less velocity towards the sun, and
would be left behind ; so that the distance of the moon
from the earth would be increased in this case also. If
the moon was in one of the quarters, then the earth and
moon being both attracted towards the center of the
Sun, they would both descend directly towards that cen-
ter, and by approaching it, they would necessarily at
the same time àpproach each other, and in this case their
distance from each other would be diminished. Now
whenever the action of the sun would increase their dis-
tance, if they were allowed to fall towards the sun,
then the Sun's action, by endeavoring to separate them,
diminishes their gravity to each other; whenever the
Sun's action would diminish the distance, then it in-
creases their mutual gravitation. Hence, in the con-
junction and opposition, that is, in the syzigies, their
gravity towards each other is diminished by the action
of the Sun, while in the quadratures it is increased.
But it must be remembered that it is not the total action
of the sun on them that disturbs their motions, but only
that part of it which tends at one time to separate them,
and at another time to bring them nearer together. The
other and far greater part, has no other effect than to
retain them in their annual course around the sun.
166. The figure of the moon’s orbit is an ellipse, hav-
ing the earth in one of the foci.
The greatest and least distances of the moon from the
earth, are nearly 64 and 56, the radius of the earth being
taken for unity. Hence, taking the arithmetical mean,
we find that the mean distance of the moon from the
166. What is the figure of the moon’s orbit 2 What are the
greatest and least distances of the moon from the earth? De-
fine the terms perigee and apogee. What numbers express the
greatest and least distance of the sun from the earth 7 How
does the eccentricity of the lunar orbit compare with that of the
solar'
* REVOLUTIONS. 133
earth is very nearly 60 times the radius of the earth.
The point in the moon’s orbit nearest the earth, is
called her perigee, the point farthest from the earth,
her apogee. .
The greatest and least distances of the sun are re-
spectively as the numbers 32.583, and 31.517. By com-
paring this ratio with that of the distances of the moon,
it will be seen that the latter vary much more than the
former, and consequently that the lunar orbit is much
more eccentric than the solar. The eccentricity of the
moon's Orbit is in fact fºr of its mean distance from the
earth, while that of the earth is only ºr of its mean dis-
tance from the Sun.
167. The moon's modes constantly shift their positions
in the ecliptic from east to west, at the rate of 19° 35' per
annum, relurning to the same points in 18.6 years.
Suppose the great circle of the ecliptic marked out on
the face of the sky in a distinct line, and let us observe,
at any given time, the exact point where the moon
crosses this line, which we will suppose to be close to a
certain star; them, on its next return to that part of the
heavens, we shall find that it crosses the ecliptic sensi-
bly to the westward of that star, and so on, farther and
farther to the westward every time it crosses the ecliptic
at either node. This fact is expressed by saying that
the modes retrograde on the ecliptic, and that the line
which joins them, or the line of the nodes, revolves from
east to west. -
168. The period occupied by the sun in passing from
one of the moon’s nodes until it comes round to the
same node again, is called the symodical revolution of the
mode. This period is shorter than the sidereal year, be-
ing only about 3464 days. For since the node shifts its
167. How do the moon's nodes shift their position? In
what time do they make a complete revolution in the ecliptic ''
Explain what is meant by saying that the nodes retrograde.
12
I34. TTHE MOON,
place to the westward 19° 35' per annum, the sun, in
his annual revolution, comes to it so much before he
completes his entire circuit; and since the sun moves
about a degree a day, the synodical revolution of the
node is 365 – 19 =346, or more exactly, 346.6.19851.
The time from one new moon, or from one full moon,
to another, is 29.5305887 days. Now 19 synodical rev-
olutions of the nodes contain very nearly 223 of these
periods.
For 346.619851 × 19 = 6585.78.
And 29.53058S7 × 223 = 6585.32. -
Hence, if the sun and moon were to leave the moon’s
node together, after the sun had been round to the same
node 19 times, the moon would have made very nearly
223 conjunctions with the sun, and would therefore, at
the end of this period meet at the same node, to repeat
the same circuit. And since eclipses of the sun and
moon depend upon the relative position of the sun, the
moon, and node, these phenomena are repeated in nearly
the same order, in each of those periods. Hence, this
period, consisting of about 18 years and 10 days, under
the name of the Saros, was used by the Chaldeans and
other ancient nations in predicting eclipses.
169. The Metonic Cycle is not the same with the Sa-
ros, but consists of 19 tropical years. During this pe-
riod the moon makes very nearly 235 synodical revolu-
tions, and hence the new and full moons, if reckoned
by periods of 19 years, recur at the same dates. If, for
example, a new moon fell on the fiftieth day of one
cycle, it would also fall on the fiftieth day of each suc-
168. What is meant by the synodical revolution of the node 7.
How many new moons occur in 19 synodical revolutions of the
node? Why was this period used in predicting eclipses? What
was it called 7
169. What is the period of the Metonic Cycle? How many
conjunctions of the moon with the Sun occur during this pe-
riod ' What use did the Athenians make of this lunar cycle 7
REVOLUTIONS, - 135
ceeding cycle; and, since the regulation of games,
feasts, and fasts, has been made very extensively ac-
cording to new or full moons, hence this lunar cycle has
been much used both in ancient and modern times.
The Athenians adopted it 433 years before the Christian
era, for the regulation of their calendar, and had it in-
scribed in letters of gold on the walls of the temple of
Minerva. Hence the term Golden Number, which de-
notes the year of the lunar cycle. -
170. The line of the apsides of the moon’s orbit re-
volves from west to east through her whole orbit in about
nine years. . - .
If, in any revolution of the moon, we should accu-
rately mark the place in the heavens where the moon
comes to its perigee, (which would be known by the
moon’s apparent diameter being then greatest,) we should
find, that at the next revolution, it would come to its
perigee at a point a little farther eastward than before,
and so on at every revolution, until, after nine years, it
would come to its perigee at nearly the same point as at
first. This fact is expressed by saying that the perigee
and of course the apogee, revolves, and that the line
which joins these two points, or the line of the apsides,
also revolves. - *
171. The inequalities of the moon’s motions are di-
vided into periodical and secular. Periodical inequal-
ities are those which are completed in comparatively
short periods. Secular inequalities are those which
are completed only in very long periods, such as cen-
turies or ages. Hence the corresponding terms peri-
odical equations and secular equations. As an exam-
ple of a secular inequality, we may mention the ac-
celeration of the moon’s mean motion. It is discov-
ered, that the moon actually revolves around the earth
170. In what period does the line of the apsides revolve?
Explain what is meant by this.
136 THE MOON.
in less time now than she did in ancient times. The
difference however is exceedingly small, being only
about 10% in a century, but increases from century to
century as the square of the number of centuries. This
remarkable fact was discovered by Dr. Halley.* In a
lunar eclipse the moon’s longitude differs from that of
the Sun, at the middle of the eclipse, by exactly 180°;
and since the sun's longitude at any given time of the
year is known, if we can learn the day and hour when
an eclipse occurs, we shall of course know the longitude
of the sun and moon. Now in the year 721 before the
Christian era, on a specified day and hour, Ptolemy re-
cords a lunar eclipse to have happened, and to have been
observed by the Chaldeans. The moon’s longitude,
therefore, for that time is known ; and as we know the
mean motions of the moon at present, starting from that
epoch, and computing, as may easily be done, the place
which the moon ought to occupy at present at any given
time, she is found to be actually nearly a degree and a
half in advance of that place. Moreover, the same con-
clusion is derived from a comparison of the Chaldean
observations with those made by an Arabian astronomer
of the tenth century.
This phenomenon at first led astronomers to appre-
hend that the moon encountered a resisting medium,
which, by destroying at every revolution a small portion
of her projectile force, would have the effect to bring
her nearer and nearer to the earth and thus to augment
her velocity. But in 1786, La Place demonstrated that
171. How are the inequalities of the moon's motions divided ?
What are periodical inequalites? What are secular inequali-
ties' Give an example of a secular inequality. How is it
known that the moon’s motions are accelerated ' What is the
amount of the acceleration per century 7 Will they always con-
tinue to be accelerated ''
* Astronomer Royal of Great Britain, and cotemporary with Sir Isaac
Newton,
FCLIPSES. 137
this acceleration is one of the legitimate effects of the
sun's disturbing force, and is so connected with changes
in the eccentricity of the earth’s orbit, that the moon
will continue to be accelerated while that eccentricity
diminishes, but when the eccentricity has reached its
minimum (as it will do after many ages) and begins to
increase, then the moon’s motion will begin to be re-
tarded, and thus her mean motions will oscilliate forever
about a mean value.
C H. A. P. T. E. R. W.
OF ECLIPSES.
172. AN Eclipse of the moon happens when the moon
in its revolution around the earth, falls into the earth’s
shadow. An Eclipse of the sun happens when the
moon coming between the earth and the Sun, covers
either a part or the whole of the solar disk.
The earth and the moon being both opake globular
bodies exposed to the sun’s light, they cast shadows op-
posite to the sun like any other bodies on which the
sun’s shines. Were the sun of the same size with the
earth and the moon, then the lines drawn touching the
surface of the sun, and the surface of the earth or moon
(which lines form the boundaries of the shadow) would
be parallel to each other, and the shadow would be a
cylinder infinite in length ; and were the Sun less than
the earth or the moon, the shadow would be an increas-
ing cone, its narrower end resting on the earth; but as
172. When does an eclipse of the moon happen? When does
an eclipse of the sun happen? Were the moon of the same size
with the earth and moon, how would their shadows be? How
if less than these bodies? How are they in fact " Explain
by figure 32.
12%
13S THE MOON.
the sun is vastly greater than either of these bodies,
the shadow of each is a cone, whose base rests on the
body itself, and which comes to a point or vertex at a
certain distance behind the body. These several cases
are represented in the following diagrams.
Fig. 32.
173. It is found by calculation, that the length of the
moon’s shadow is, on average, just about long enough to
reach to the earth, but the moon is sometimes farther
from the earth than at others. (Art. 166.) When she is
nearer than usual, the shadow reaches considerably be-
yond the surface of the earth. Also the moon as well
as the earth, is at different distances from the sun at dif-
ferent times, and its shadow is longest when it is far-
thest from the suñ. Now when both these circumstan-
ces conspire, that is, when the moon is in her perigee
and in, her aphelion, her shadow extends nearly 15000
milés beyond the center of the earth, and covers a space
173. How does the moon's shadow compare with her dis-
tance from the earth 7 When does her shadow extend farthest
beyond the center of the earth? What is the greatest breadth
of her shadow where it falls on the surface of the earth 7 What
is the length of the earth's shadow 7 When only can an eclipse
of the sun take place " . When only can an eclipse of the moon
occur ! Explain from figure 33. What is the moon's Pen-
umbra?

ECLIPSICS. 139
on the surface of the earth 170 miles broad. The
earth's shadow is towards a million of miles in length,
and more than three and a half times as long as the dis-
tance from the earth to the moon; and it is also at the
distance of the moon three times as broad as the moon
itself. An eclipse of the sun can take place only at new
moon, when the Sun and moon meet in the same part of
the heavens, or at new moon, for then only can the
moon come between us and the sun; and an eclipse of
the moon can occur only when the sun and moon are in
opposite parts of the heavens, or at full moon, for then
only can the moon fall into the shadow of the earth.
The nature of eclipses will be clearly understood from
the following representation. This figure exhibits the
Fig. 33.
•N
relative position of the Sun, the earth, and the moon,
both in a solar and in a lunar eclipse. It is evident ſrom
the figure, that if a spectator were situated where the
moon’s shadow strikes the earth, the moon would cut off
from him the view of the Sun, or the sun would be to-
tally eclipsed. Or, if he were within a certain distance
of the shadow on either side, the moon would be partly
between him and the sun, and would intercept from
him more or less of the Sun's light, according as he was
nearer to the shadow or farther from it. If he were at
c, or d, he would just see the moon entering upon the

140 THE MOON,
sun’s disk; if he were nearer the shadow than either of
these points, he would have a portion of the Sun's light
cut off from his view, and the moment he entered the
shadow itself, he would lose sight of the sun. To all
places between a or b and the shadow, the Sun would
cast a partial shadow of the moon, growing deeper and
deeper as it approached the true shadow. This partial
shadow is called the moon’s Penumbra. In like man-
ner, as the moon approaches the earth’s shadow in a lu-
nar eclipse, as soon as she arrives at a, the earth begins
to intercept from her a portion of the Sun’s light, or she
falls into the earth’s penumbra. She continues to lose
more and more of the sun’s light as she draws near to
the shadow, and hence her disk becomes gradually ob-
scured, until it enters the shadow, where the Sun's light
is entirely lost.
174. As the sun and earth are both situated in the
plane of the ecliptic, if the moon also revolved around
the earth in this plane, we should have a solar eclipse at
every new moon, and a lunar eclipse at every full
moon; for in the former case the moon would come di-
rectly between us and the sun, and in the latter case,
the earth would come directly between the sun and the
moon. But the moon’s path is inclined to the ecliptic
about 5°, and the center of the moon may be all this
distance from the center of the Sun, at new moon, and
the same distance from the center of the earth’s shadow
at full moon. It is true the moon extends across her
path, one half her breadth lying on each side of it, and
the sun likewise reaches ſtom the ecliptic a distance
equal to half his breadth. But these luminaries to-
gether make but little more than a degree, and conse-
quently their two semi-diameters would occupy only
174. Why do we not have solar eclipse every new moon,
and a lunar eclipse every full moon 7 Explain how eclipses
occur only when the Sun is near one of the moon’s nodes, by
figure 34. &
ECLIPSES. 141
about half a degree of the five degrees from one orbit
to the other. Also the earth's shadow where the moon
crosses it extends from the ecliptic less than three
fourths of a degree, so that the semi-diameter of the
moon and of the earth’s shadow would together reach
but little way across the space that may in certain cases
separate the two luminaries from each other when they
are in opposition. Thus suppose we could take hold
of the circle in the figure that represents the moon’s
orbit, (Fig. 31,) and lift the moon up five degrees
above the plane of the paper, it is evident that the moon
as seen from the earth, would appear in the heavens
five degrees above the sun, and of course would cut off
none of his light, and that the moon at the full would
pass the shadow of the earth five degrees below it, and
would suffer no eclipse. But in the course of the Sun's
apparent revolution around the earth once a year, he is
Successively in every part of the ecliptic ; consequently,
the conjunctions and oppositions of the sun and moon
may occur at any part of the ecliptic, and of course at
the two points when the moon’s orbit crosses the eclip-
tic, that is, at the nodes, for the sun must necessarily
come to each of these nodes once a year. If then the
moon overtakes the sun just as she is crossing his path,
G.
\º
she will hide more or less of his disk from us. Since,
also, the earth’s shadow is always directly opposite to
the Sun, if the sun is at one of the modes, the shadow
“Fig. 34.



142 THE MOON.
must extend in the direction of the other node, so as to
lie directly across the moon’s path, and if the moon over-
takes it there, she will pass through it and be eclipsed.
Thus in figure 34, let BN represent the sun's path, and
AN the moon, N being the place of the node ; then it is
evident that if the two luminaries at new moon be so
far from the mode that the distance between their centers
is greater than their semi-diameters, no eclipse can hap-
pen ; but if that distance is less than this sum as at
E, F, then an eclipse will take place, but if the position
be as at C, D, the two bodies will just touch one another.
If A denote the earth’s shadow instead of the sun, the
Same illustration will apply to an eclipse of the moon.
175. Since bodies are defined to be in conjunction
when they are in the same part of the heavens, and to
be in opposition when they are in opposite parts of the
heavens, it may not appear how the sun and moon can
be in conjunction as at A and B, when they are still at
Some distance from each other. But it must be recol-
lected that bodies are in conjunction when they have the
Same longitude, in which case they are both situated in
the Saine great circle perpendicular to the ecliptic, that
is in the same secondary to the ecliptic. One of the
bodies may be much ſarther from the ecliptic than the
other; still, if the same secondary to the ecliptic passes
through them both, they will be in conjunction or oppo-
Slt1011.
176. In a total eclipse of the moon, its disk is still
visible, shining with a dull red light. This light cannot
be derived directly from the sun, since the view of the
Sun is completely hidden ſrom the moon ; nor by reflex-
ion from the earth, since the illuminated side of the
175. Is it necessary for two bodies to be precisely together in
order to be in conjunction ?
176. Why is the disk of the moon still visible in a total eclipse
of the moon'
ECLIPSES. 143
earth is wholly turned from the moon; but it is owing
to refraction from the earth's atmosphere, by which a
few scattered rays of the sun are bent round into the
earth's shadow and conveyed to the moon, sufficient in
number to afford the feeble light in question.
177. It is impossible fully to understand the method
of calculating eclipses, without a knowledge of trigo-
mometry; still it is not difficult to form some general no-
tion of the process. It may be readily conceived that,
by long continued observations on the Sun and moon,
the exact places which they will occupy in the heavens
at any future times, may be foreseen and laid down in
tables of the sun and moon’s motions; that we may thus
ascertain by inspecting the tables the exact instant when
these two bodies will appear together in the heavens, or
be in conjunction, and when they will be 180° a part,
or in opposition. Moreover, since the exact place of the
moon’s node among the stars at any particular time is
known to astronomers, it cannot be difficult to determine
when the new or full moon occurs in the same part of
the heavens as that where the mode is projected as seen
from the earth. In short, as astronomers can easily de-
termine what will be the relative position of the sun,
the moon, and the moon’s modes for any given time,
they can tell when these luminaries will meet so near.
the modes as to produce an eclipse of the Sun, or when
they will be in opposition so near the mode as to produce
an eclipse of the moon.
178. Let us endeavor to form a just conception of the
manner in which these three bodies, the sun, the earth,
and the moon, are situated with respect to each other at
the time of a solar eclipse. First, suppose the conjunction
to take place at the node. Then the straight line which
connects the center of the Sun and the earth, also passes
177. What science must be known in order fully to under-
stand the mode of calculating eclipses? Explain the general
principles of the calculation.
144 THE MOON.
through the center of the moon, and coincides with the
axis of its shadow ; and, since the earth is bisected by
the plane of the ecliptic, the shadow would traverse the
earth in the direction of the terrestrial ecliptic, from
west to east, passing over the middle regions of the
earth. Here the diurnal motion of the earth being in
the same direction with the shadow, but with a less ve-
locity, the shadow will appear to move with a speed
equal only to the difference between the two. Secondly,
suppose the moon is on the north side of the ecliptic at
the time of conjunction, and moving towards her de-
scending node, and that the conjunction takes place
as far from the node as an eclipse can happen. The
shadow will not fall in the plane of the ecliptic, but
a little northward of it, so as just to graze the earth
near the pole of the ecliptic. The nearer the conjunc-
tion comes to the node, the farther the shadow will fall
from the pole of the ecliptic towards the equatorial re-
glons.
179. The leading particulars respecting an ECLIPSE
oF THE SUN, are ascertained very nearly like those of a
lunar eclipse. The shadow of the moon travels over a
portion of the earth, as the shadow of a small cloud, seen
from an eminence in a clear day, rides along over hills
and plains. Let us imagine ourselves standing on the
moon ; then we shall see the earth partially eclipsed by
the shadow of the moon, in the same manner as we
now see the moon eclipsed by the earth's shadow ; and .
we might proceed to find the length of the shadow, its
breadth where it eclipses the earth, the breadth of the
penumbra, and its duration and quantity, in the same
way as we have ascertained these particulars for an
eclipse of the moon. .
178. Explain the relative position of the sun, the earth, and
the moon, in a solar eclipse. Explain the circumstances when
the conjunction takes place at the node, and when it occurs at
a distance from the node.
ECLIPSR.S. 145
But, although the general characters of a solar eclipse
might be investigated on these principles, so far as re-
spects the earth at large, yet as the appearances of the
same eclipse of the sun are very different at different
places on the earth's surface, it is necessary to calculate
its peculiar aspects for each place separately, a circum-
stance which makes the calculation of a solar eclipse
much more complicated and tedious than of an eclipse
of the moon. The moon, when she enters the shadow
of the earth, is deprived of the light of the part immer-
sed, and that part appears black alike to all places where
the moon is above the horizon. But it is not so with a
solar eclipse. We do not see this by the shadow cast
on the earth, as we should do if we stood on the moon,
but by the interposition of the moon between us and the
sun; and the sun may be hidden from one observer
while he is in full view of another only a few miles dis-
tant. Thus, a small insulated cloud sailing in a clear
sky, will, for a few moments, hide the sun from us, and
from a certain space near us, while all the region around
is illuminated.
We have compared the motion of the moon’s shadow
over the surface of the earth to that of a cloud; but its
velocity is incomparably greater. The mean motion of
the moon around the earth is about 33 per hour; but
33% of the moon’s orbit is 2280 miles, and the shadow
moves of course at the same rate, or 2280 miles per
hour, traversing the entire disk of the earth in less than
four hours. ---
180. The diameter of the moon’s shadow where it
eclipses the earth can never exceed 170 miles, and com-
monly falls much short of that ; and the greatest por-
tion of the earth’s surface ever covered by the moon’s
penumbra is about 4393 miles.
179. How are the leading particulars of an eclipse of the sun
ascertained ? How illustrated by the motion of a cloud 7 In
what respects does the calculation of a solar differ from that of a
lunar eclipse! How does the shadow of the moon compare
with that of a cloud in velocity'ſ
13
£46 THE ſºfCON.
181. The apparent diameter of the moon is sometimes
larger than that of the sun, sometimes Smaller, and
sometimes exactly equal to it. Suppose an observer
placed on the right line which joins the centers of the
sun and moon ; if the apparent diameter of the moon is
greater than that of the sun, the eclipse will be total. If
the two diameters are equal, the moon's shadow just
reaches the earth, and the sun is hidden but for a mo-
ment from the view of spectators situated in the line
which the vertex of the shadow describes on the surface
of the earth. But if, as happens when the moon comes
to her conjunction in that part of her orbit which is to-
wards her apogee, the moon's diameter is less than the
sun's, then the observer will see a ring of the Sun en-
circling the moon, constituting an Annular Eclipse, as in
figure 35. -
180. What cannot the diameter of the moon’s shadow, when
it eclipses the earth, exceed 7 What is the greatest portion of
the earth's surface ever covered by the moon's penumbra 7
181. How does the moon’s apparent diameter compare with
the sun's When will the eclipse be total, and when annular 7

ECLIPS ES. 147
182. Eclipses of the sun are modified by the eleva-
tion of the moon above the horizon, since its apparent
diameter is augmented as its altitude is increased. This
effect, combined with that of parallax, may so increase
or diminish the apparent distance between the centers of
the sun and moon, that from this cause alone, of two
Observers at a distance from each other, one might see
an eclipse which was not visible to the other. If the
horizontal diameter of the moon differs but little from
the apparent diameter of the sun, the case might occur
where the eclipse would be annular over the places
where it was observed morning and evening, but total
where it was observed at mid-day.
The earth in its diurnal revolution and the moon’s
shadow both move from west to east, but the shadow
moves faster than the earth ; hence the moon overtakes
the sun on its western limb and crosses it from west to
east. The excess of the apparent diameter of the moon
above that of the sun in a total eclipse is so small, that
total darkness seldom continues longer than four min-
lites, and can never continue so long as eight minutes.
An annular eclipse may last 12m. 24s.
183. Eclipses of the sun are more ſrequent than those
of the moon. Yet lunar eclipses being visible to every
part of the terrestrial hemisphere opposite to the sun,
while those of the sun are visible only to the small por-
tion of the hemisphere on which the moon’s shadow
falls, it happens that for any particular place on the
earth, lunar eclipses are more frequently visible than
solar. In any year, the number of eclipses of both lu-
182. How are eclipses of the sun modified by the elevation of
the moon above the horizon 7 How might the same eclipse
appear total to one observer and annular to another ? How
long can total darkness continue in a solar eclipse'ſ How long
may an annular eclipse last!
183. Which are most frequent, solar or lunar eclipses 7 Why
does an eclipse of the moon happen at the next full moon after
an eclipse of the Sun ?
148 THE MOON.
minaries cannot be less than two nor more than seven :
the most usual number is four, and it is very rare to
have more than six. A total eclipse of the moon fre-
quently happens at the next full moon after an eclipse
of the sun. For since, in an eclipse of the Sun, the sun
is at or near one of the moon’s modes, the earth’s shadow
must be at or near the other node, and may not have
passed far from the node before the moon overtakes it.
184. In total eclipses of the sun, there has sometimes
been observed a remarkable radiation of light from the
margin of the sun. This has been ascribed to an illu-
mination of the solar atmosphere, but it is with more
probability owing to the zodiacal light, which at that.
time is projected around the sun, and which is of such
dimensions as to extend far beyond the solar orb.”
A total eclipse of the sun is one of the most sublime
and impressive phenomena of mature. Among barbarous
tribes it is ever contemplated with fear and astonish-
ment, while among cultivated nations it is recognized,
from the exactness with which the time of occurrence
and the various appearances answer to the prediction, as
affording one of the proudest triumphs of astronomy.
By astronomers themselves it is of course viewed with
the highest interest, not only as verifying their calcula-
tions, but as contributing to establish beyond all doubt
the certainty of those grand laws, the truth of which is
involved in the result. During the eclipse of June,
1806, which was one of the most remarkable on record,
the time of total darkness, as seen by the author of this
work, was about mid-day. The sky was entirely cloud-
184. How is the radiation of light around the margin of the
sun in a total eclipse of the sun, accounted for How have
eclipses of the sun been regarded among barbarous tribes?
How among civilized nations ! How by astronomers? Give
Some account of the great eclipse of 1806. |
... " See an excellent description and delineation of this appearance as
it was exhibited in the eclipse of 1806, in the Transactions of the Al-
bany Institute, by the late Chancellor De Witt,
ECLIPSES. 149
less, but as the period of total obscuration approached, a
gloom pervaded all nature. When the sun was wholly
lost sight of, planets and stars came into view ; a fearful
pall hung upon the sky, unlike both to night and to
twilight; and, the temperature of the air rapidly de-
clining, a sudden chill came over the earth. Even the
animal tribes exhibited tokens of fear and agitation.
185. The word Eclipse is derived from a Greek word,
(szkewpts,) which signifies to ſail, to faint, or swoon
away, since the moon at the period of her greatest
brightness falling into the shadow of the earth, was im-
agined by the ancients to sicken and swoon, as if she
were going to die. By some very ancient nations she
was supposed at such times to be in pain, and hence
lunar eclipses were called the labors of the moon, (lunae
labores;) and, in order to relieve her fancied distress, they
lifted torches high in the atmosphere, blew horns and
trumpets, beat upon brazen vessels, and even, after the
eclipse was over, they offered sacrifices to the moon.
The opinion also extensively prevailed, that it was in
the power of witches, by their spells and charms, not
only to darken the moon, but to bring her down from
her orbit, and to compel her to shed her baleful influences
upon the earth. In a solar eclipse also, especially when
total, the sun was supposed to turn away his face in ab-
horrence of some atrocious crime, that either had been
perpetrated or was about to be perpetrated, and to
threaten mankind with everlasting night, and the de-
struction of the world. -
The Chinese, who from a very high period of anti-
quity have been great observers of eclipses, although
they did not take much notice of those of the moon, re-
garded eclipses of the sun in general as unfortunate, but
especially such as occurred on the first day of the year.
-:
185. From what is the word eclipse derived 7 What ideas
had certain ancient nations respecting eclipses' With what
ceremonies did they observe it? How were eclipses regarded
among the Chinese ? -
- 13%
150 THE MOON.
These were thought to forbode the greatest calamities.
to the emperor, who on such occasions did not receive
the usual compliments of the season. When an eclipse
of the sun was expected from the predictions of their as-
tronomers, they made great preparation at court for ob-
Serving it; and as soon as it commenced, a blind man
beat a drum and a great concourse assembled, and the
Mandarins, or nobility, appeared in state, . -
186. From 1831 to 1838, was a period distinguished
for great eclipses of the sun, in which time there were no
less than five, of the most remarkable character. The
next total eclipse of the sun, visible in the United States,
will occur on the 7th of August, 1869,
C H A P T E R W T .
LONGITUDE. – TIDES.
187. As eclipses of the sun afford one of the most
approved methods of finding the longitude of places, our
attention is naturally turned next towards that subject.
The ancients studied astronomy in order that they
might read their destinies in the stars: the moderns that
they may securely navigate the ocean. A large portion
of the refined labors of modern astronomy, has been di-
rected towards perfecting the astronomical tables with
the view of finding the longitude at sea, an object
manifestly worthy of the highest efforts of Science, con-
sidering the vast amount of property and of human life
involved in navigation.
188. The difference of longitude between two places,
may be found by any method by which we can ascertain
186. What recent period has abounded with great eclipses
of the sun ? When will the next total eclipse of the sun occur !
187. For what purpose did the ancients study astronomy
For what purpose do the moderns study it? -
LONGITUDE, 151.
the difference of their local times, at the same instant of
absolute time. -
As the earth turns on its axis from west to east, any
place that lies eastward of another will come sooner un-
der the Sun, or will have the sun earlier on the meridian,
and consequently, in respect to the hour of the day, will
be in advance of the other at the rate of one hour for
every 15°, or four minutes of time for each degree. Thus,
to a place 15° east of Greenwich, it is 1 o'clock, P. M.
when it is noon at Greenwich; and to a place 15° west
of that meridian, it is 11 o'clock, A. M. at the same in-
stant. Hence the difference of time at any two places,
indicates their difference of longitude.
189. The easiest method of finding the longitude is
by means of an accurate time piece, or chronometer. Let
us set out from London with a chronometer accurately
adjusted to Greenwich time, and travel eastward to a
certain place, where the time is accurately kept, or may
be ascertained by observation. We find, for example,
that it is 1 o'clock by our chronometer, when it is 2
o'clock and 30 minutes at the place of observation.
Hence the longitude is 15 × 1.5=224° E. Had we trav-
elled westwärd until our chronometer was an hour and
a half in advance of the time at the place of observa-
tion, (that is, so much later in the day,) our longitude
would have been 22#9 W. But it would not be neces-
sary to repair to London in order to set our chronometer
to Greenwich time. This might be done at any obser-
vatory, or any place whose longitude has been accu-
188, How may the difference of longitude between two pla-
ces be found ! How many degrees of longitude correspond to
one hour in time? How many minutes to one degree ?
189. Explain the method of finding the longitude by the
chronometer. To what time is it set! How do we ascertain
the longitude of a place by it? Would it be necessary to re-
pair to Greenwicly to regulate our chronometer 7. What is said
of the accuracy of some chronometers? Why is not this
method adapted to general use 7
152 THE MOON,
rately determined. For example, the time at New York
is 4h. 56m. 45.5 behind that of Greenwich. If, there-
fore, we set our chronometer so much before the true
time at New York, it will indicate the time at Green-
wich. Moreover, on arriving at different places any
where on the earth, whose longitude is accurately known,
we may learn whether our chronometer keeps accurate
time or not, and if not, the amount of its error. . Chro-
nometers have been constructed of such an astonishing
degree of accuracy, as to deviate but a few seconds in a
voyage from London to Baffin's Bay and back, during an
absence of several years. But chronometers which are
sufficiently accurate to be depended on for long voya-
ges, are too expensive for general use, and the means of
verifying their accuracy are not sufficiently easy. More-
over, chronometers, by being transported from one place
to another, change their daily rate, or depart from that
mean rate which they preserve at a fixed station. A
chronometer, therefore, cannot be relied on for determin-
ing the longitudes of places where the greatest degree of
accuracy is required, especially where the instrument is
conveyed over land, although the uncertainty attendant
on one instrument may be nearly obviated by employing
Several and taking their mean results.
190. Eclipses of the sum and moon are sometimes
used for determining the longitude. The exact instant
of immersion or of emersion, or any other definite mo-
ment of the eclipse which presents itself to two distant
observers, affords the means of comparing their difference
of time, and hence of determining their difference of
longitude. Since the entrance of the moon into the
earth's shadow, in a lunar eclipse, is seen at the same
instant of absolute time at all places where the eclipse
is visible, this observation would be a very suitable one
for finding the longitude were it not that, on account of
190. Explain how to find the longitude by eclipses of the sun
and moon. What objections are there to this method, both in
lunar and Solar eclipses?
LONGITUDE. 153
the increasing darkness of the penumbra near the boun-
daries of the shadow, it is difficult to determine the pre-
cise instant when the moon enters the shadow. By
taking observations on the immersions of known spots
on the lunar disk, a mean result may be obtained which
will give the longitude with tolerable accuracy. In an
eclipse of the Sun, the instants of immersion and emer-
sion may be observed with greater accuracy, although,
since these do not take place at the same instant of ab-
Solute time, the calculation of the longitude from obser-
vations on a solar eclipse are complicated and laborious.
191. The lunar method of finding the longitude, at
sea, is in many respects preferable to every other. It
consists in measuring (with a sextant) the angular dis-
tance between the moon and the sun, or between the
moon and a star, and then turning to the Nautical Alma-
mac,” and finding what time it was at Greenwich when
that distance was the same. The moon moves so rap-
idly, that this distance will not be the same except at
very nearly the same instant of absolute time. For ex-
ample, at 9 o'clock, A. M., at a certain place, we find the
angular distance of the moon and the sun to be 72°;
and, on looking into the Nautical Almanac, we find that
the time when this distance was the same for the me-
ridian of Greenwich was 1 o'clock, P. M.; hence we
infer that the longitude of the place is four hours, or 60°
WCSt.
191. Explain the lunar method of finding the longitude.
What measurements are made? How do we find the corres-
ponding time at Greenwich {
* The Nautical Almanac, is a book published annually by the British
Board of Longitude, containing various tables and astronomical infor-
mation for the use of navigators. The American Almanac also con-
tains a variety of astronomical information, peculiarly interesting to the
people of the United States, in connexion, with a vast amount of
statistical matter. It is well deserving of a place in the library of the
student. -
I54 THE MOON.
The Nautical Almanac contains the true angular dis-
tance of the moon from the sun, from the four large
planets, (Venus, Mars, Jupiter, and Saturn,) and from
nine bright fixed stars, for the beginning of every third
hour of mean time for the meridian of Greenwich ; and
the mean time corresponding to any intermediate hour,
may be found by proportional parts.”
192. It would be a very simple operation to determine
the longitude by Lunar Distances, if the process as de-
scribed in the preceding article were all that is neces-
sary; but the various circumstances of parallax, refrac-
tion, and dip of the horizon, would differ more or less at
the two places, even were the bodies, whose distances
were taken in view, from both, which is not necessarily
the case. The observations, therefore, at each meridian,
require to be reduced to the center of the earth, being
cleared of the effects of parallax and refraction. Hence,
three observers are necessary in order to take a lunar dis-
tance in the most exact manner, viz. two to measure the
altitudes of the two bodies respectively, at the same
time that the third takes the angular distance between
them. The altitudes of the two luminaries at the time
of observation must be known, in order to estimate the
effects of parallax and refraction.
193. Although the lunar method of finding the longi-
tude at sea has many advantages over the other meth-
ods in use, yet it also has its disadvantages. One is, the
great exactness requisite in observing the distance of
the moon from the sun or star, as a small error in the
distance makes a considerable error in the longitude.
The moon moves at the rate of about a degree in two
192. What difficulties are there in this method Why are
three observers necessary 7
193. What are the objections to this method 7 What is the
error of the best tables now in use !
* See Bowditch's Navigator, Tenth Ed. p. 226.
LONGITUDE. 155
hours, or one minute of space in two minutes of time.
Therefore, if we make an error of one minute in ob-
serving the distance, we make an errors of two minutes
in time, or 30 miles of longitude at the equator. A sin-
gle observation with the best sextant, may be liable to
an error of more than half a minute ; but the accuracy
of the result may be much increased by a mean of sev-
eral observations taken to the east and west of the moon.
The imperſection of the lunar tables was until recently
considered as an objection to this method. Until within a
few years, the best lunar tables were frequently errone-
ous to the amount of one minute, occasioning an error
of 30 miles. The error of the best tables now in use
will rarely exceed 7 or 8 seconds. --
TIDES.
194. The tides are an alternate rising and falling of
the waters of the ocean, at regular intervals. They have
a maximum and a minimum twice a day, twice a month,
and twice a year. Of the daily tide, the maximum is
called High tide, and the minimum Low tide. The
maximum for the month is called Spring tide, and the
minimum Neap tide. The rising of the tide is called
Flood and its falling Ebb tide.
Similar tides, whether high or low, occur on opposite
sides of the earth at once. Thus at the same time it is
high tide at any given place, it is also high tide on the
inferior meridian, and the same is true of the low tides.
The interval between two successive high tides is
12h. 25m. ; or, if the same tide be considered as return-
ing to the meridian, after having gone around the globe,
194. What are the tides? When have they a maximum and
a minimum ? Define the terms High and Low, Spring and
Neap, Flood and Ebb tides. What two tides occur at the same
time? What is the interval between two successive high tides 7
How much later is the tide of to-day than the same tide of yes-
terday ? What is the average height of the tide for the whole
globe To what extreme height does it sometimes rise? Have
inland lakes and seas any tides?
156 THE MOON.
its return is about 50 minutes later than it occured on
the preceding day. In this respect, as well as in various
others, it corresponds very nearly to the motions of the
II].OOIl.
The average height for the whole globe is about 24
feet; or, if the earth were covered uniformly with a
stratum of water, the difference between the two diam-
eters of the oval would be 5 feet, or more exactly 5 feet
and 8 inches; but its actual height at various places is
very various, sometimes rising to 60 or 70 feet, and
sometimes being scarcely perceptible. At the same
place also, the phenomena of the tides are very different
at different times.
Inland lakes and seas, even those of the largest class,
as Lake Superior, or the Caspian, have no perceptible
tide.
195. Tides are caused by the unequal attraction of
the Sun and moon upon different parts of the earth.
Suppose the projectile force by which the earth is car-
ried forward in her orbit, to be suspended, and the earth
to fall towards one of these bodies, the moon, for exam-
ple, in consequence of their mutual attraction. Then,
if all parts of the earth fell equally towards the moon,
no derangement of its different parts would result, any
more than of the particles of a drop of water in its de-
scent to the ground. But if one part fell faster than an-
other, the different portions would evidently be separa-
ted from each other. Now this is precisely what takes
place with respect to the earth in its fall towards the
moon. The portions of the earth in the hemisphere
next to the moon, on account of being nearer to the
center of attraction, fall faster than those in the oppo-
site hemisphere, and consequently leave them behind.
The solid earth, on account of its cohesion, cannot obey
195. State the cause of the tides. What would be the con-
sequence were the earth abandoned to the force exerted by the
moon alone?
TIDES. 157
this impulse, since all its different portions constitute
one mass, which is acted on in the same manner as
though it were all collected in the center; but the wa-
ters on the surface, moving freely under this impulse,
endeavor to desert the solid mass and fall towards the
moon. For a similar reason the waters in the opposite
hemisphere falling less towards the moon than the solid
earth are left behind, or appear to rise from the center
of the earth. -
196. Let DEFG (Fig. 36,) represent the globe; and,
for the sake of illustrating the principle, we will sup-
pose the waters entirely to cover the globe at a uniform
depth. Let def; represent the solid globe, and the cir-
Fig. 36.
E. *~.

cular ring exterior to it, the covering of waters. Let C
be the center of gravity of the solid mass, A that of the
hemisphere next to the moon, (for the center of gravity
of a ring is within the ring,) and B that of the remoter
hemisphere. Now the force of attraction exerted by
the moon, acts in the same manner as though the solid
mass were all concentrated in C, and the waters of each
hemisphere at A and B respectively; and (the moon be-
*
196. Explain the tides upon the doctrine of the center of
gravity. When would the tide-wave always be seen were it not
for impediments? What are these?
. 14
158 TIIE MOON,
ing supposed above E) it is evident that A will tend to
leave C, and C to leave B behind. The same must evi-
dently be true of the respective portions of matter, of
which these points are the centers of gravity. The wa-
ters of the globe will thus be reduced to an oval shape,
being elongated in the direction of that meridian which
is under the moon, and flattened in the intermediate
parts, and most of all at points ninety degrees distant
from that meridian.
Were it not, therefore, for impediments which prevent
the force from producing its full effects, we might expect
to see the great tide-wave, as the elevated crest is called,
always directly beneath the moon, attending it regularly
around the globe. But the inertia of the waters pre-
vents their instantly obeying the moon’s attraction, and
the ſriction of the waters on the bottom of the ocean,
still farther retards its progress. It is not therefore until
several hours (differing at different places) after the
moon has passed the meridian of a place, that it is high
tide at that place.
197. The sum has a similar action to the moon, but
only one third as great. On account of the great mass
of the Sun compared with that of the moon, we might
suppose that his action in raising the tides would be
greater than that of the moon ; but the nearness of the
moon to the earth more than compensates for the sun’s
greater quantity of matter. Let us, however, form a just
conception of the advantage which the moon derives
from her proximity. It is not that her actual amount of
attraction is thus rendered greater than that of the sun ;
but it is that her attraction for the different parts of the
earth is very unequal, while that of the sun is nearly
uniform. It is the inequality of this action, and not the
absolute force, that produces the tides. The diameter of
the earth is ºr of the distance of the moon, while it is
less than rººm of the distance of the Sun.
197. Explain the action of the sun in raising the tide? Why
sits effects less than that of the moon ''
TTDES. 159
198. Having now learned the general cause of the
tides, we will next attend to the explanation of particu-
War phenomena. - -
The Spring tides, or those which rise to an unusual
height twice a month, are produced by the sun and
moon's acting together; and the Neap tides, or those
which are unusually low twice a month, are produced
by the sun and moon’s acting in opposition to each
other. The Spring tides occur at the syzigies: the
Neap tides at the quadratures. At the time of new moon,
the Sun and moon both being on the same side of the
earth, and acting upon it in the same line, their actions
conspire, and the sun may be considered as adding so
much to the force of the moon. We have already ex-
plained how the moon contributes to raise a tide on the
opposite side of the earth. But the sun as well as the
moon raises its own tide-wave, which, at new moon,
coincides with the lunar tide-wave. At full moon, also,
the two luminaries conspire in the same way to raise
the tide; for we must recollect that each body contri-
butes to raise the tide on the opposite side of the earth
as well as on the side nearest to it. At both the con-
junctions and oppositions, therefore, that is, at the syzi-
gies, we have unusually high tides. But here also the
maximum effect is not at the moment of the syzigies,
but 36 hours afterwards. -
At the quadratures, the solar wave is lowest where the
lunar wave is highest; hence the low tide produced by
the Sun is subtracted from high water and produces the
Neap tides. Moreover, at the quadratures the solar
wave is highest where the lunar wave is lowest, and
hence is to be added to the height of low water at the
time of Neap tides. Hence the difference between high
and low water is only about half as great at Neap tide as
at Spring tide. ,”
198. What is the cause of the Spring tides'! Also of the
Neap tides? How long after the syzigies does the highest tide
occur !
160 . THE MOON.
199. The variations of distance in the sun are not
great enough to influence the tides very materially, but
the variations in the moon’s distances have a striking
effect. The tides which happen when the moon is in
perigee, are considerably greater than when she is in
apogee ; and if she happens to be in perigee at the time
of the syzigies, the Spring tide is unusually high.
When this happens at the equinoxes, the highest tides
of the year are produced. *
200. The declinations of the sun and moon have a
considerable influence on the height of the tide. When
the moon, for example, has no declination, or is in the
Fig. 37.
equator, as in figure 37.* the two tides will be exactly
equal on opposite sides of the meridian in the same
parallel. Thus a place in the parallel TT will have
199. How do the variations in the moon's distance from the
east affect the tides 7 How are the tides when the moon is in
perigee? How when she in apogee ? When are the highest
tides of the year produced 7 t -
* Diagrams like these are .. to mislead the learner, by exhibiting the
protuberance occasioned by the tides as much greater than the reality.
We must recollect that it amounts, at the highest, to only a very few
feet in eight thousand miles. Were the diagram, therefore, drawn in
just proportions, the alteration of figure produced by the tides would
be wholly insensible.

TIDE S. 16.1
the height of one tide T2 and the other tide T'9.
The tides are in this case greatest at the equator, and
diminish gradually to the poles, where it will be low
water during the whole day. When the moon is
on the north side of the equator, as in figure 38, at
her greatest northern declination, a place describing
the parallel TT will have TV3 for the height of the
Fig. 38.
AV
º
º
à
tide when the moon is on the superior meridian, and T2
for the height at the Sāme time on the inferior me-
ridian. Therefore, all places north of the equator will
have the highest tide when the moon is above the hor-
izon, and the lowest when she is below it; the differ-
ence of the tides diminishing towards the equator, where
they are equal. In like manner, (the moon being still
at M, Fig. 38, that is having, northern declination,)
places south of the equator have the highest tides when
the moon is below the horizon, and the lowest when she
is above it. The circumstances are all reversed when
the moon is South of the equator.
201. The motion of the tide-wave, it should be re-
marked, is not a progressive motion, but a mere undula-
tion, and is to be carefully distinguished from the cur-
200. Explain the effect of the declinations of the sun and
moon mpon the tides. How will the upper and lower tides cor-
respond when the moon is in the equator 7 How when the
moon is north of the equator 7 lºan by figures 37, 38.

162 THE MOON.
rents to which it gives rise. If the ocean completely
covered the earth, the Sun and moon being in the equa-
tor, the tide-wave would travel at the same rate as the
earth on its axis. Indeed, the correct way of conceiv-
ing of the tide-wave, is to consider the moon at rest,
and the earth in its rotation from west to east, as bringing
successive portions of water under the moon, which
portions being elevated successively at the same rate as
the earth revolves on its axis, have a relative motion
westward in the same degree.
202. The tides of rivers, marrow bays, and shores
far from the main body of the ocean, are not produced
in those places by the direct action of the Sun and moon,
but are subordinate waves propagated from the great
tide-wave.
Lines drawn through all the adjacent parts of any
tract of water, which have high water at the same time,
are called cotidal lines. We may, for instance, draw a
line through all places in the Atlantic Ocean which
have high tide in a given day at 1 o'clock, and another
through all places which have high tide at 2 o’clock.
The cotidal line for any hour may be considered as rep-
resenting the summit or ridge of the tide-wave at that
time; and could the spectator, detached from the earth,
perceive the summit of the wave, he would see it travel-
ing round the earth in the open ocean once in twenty
four hours, followed by another twelve hours distant,
and both sending branches into rivers, bays, and other
openings into the main land. These latter are called
Derivative tides, while those raised directly by the ac-
tion of the Sun and moon, are called Primitive tides.
201. Is the motion of the tide-wave progressive? If the
ocean completely covered the earth and the sun and moon were
in the equator, how would the tide-wave travel? What is the
most correct way of conceiving of the tide-wave 7
202. How are the tides of rivers &c. produced ? Define
cotidal lines. What does the cotidal line for any hour repre-
sent? Distinguish between Primitive and Derivative tides,
TIDES,
163
203. The velocity with which the wave moves, will
depend on various circumstances, but principally on the
depth, and probably on the regularity of the channel.
If the depth be nearly uniform, the cotidal lines will be
nearly straight and parallel. But if some parts of the
channel are deep while others are shallow, the tide will
be detained by the greater friction of the shallow places,
and the cotidal lines will be irregular. The direction
also of the derivative tide, may be totally different from
that of the primative. Thus, (Fig. 39,) if the great
Figure 39,
> * * *
# 4: H
5.5:==::=
- *::: ſ -
====X
F:::::::=>
ºtrº.aº Fºrs==
E=# º::===
E: Exº~~~ <=:: wº-
# Aº’ F===;
** = -s. .*:- *----->=
#5 :== #
=s 2 # -s
:= - **-y :=-
§ &= -->
3:5 = x* =->
=º s: ==
= == F
*
E. sº #F
ſº
tide-wave, moving from east to west, be represented by
the lines 1, 2, 3, 4, the derivative tide which is propa-
gated up a river or bay, will be represented by the co-
tidal lines 3, 4, 5, 6, 7. Advancing faster in the channel
than next the bank, the tides will lag behind towards
the shores, and the cotidal lines will take the form of
curves as represented in the diagram.
203. On what will the velocity of the tide-wave depend?
What circumstances will retard it ! Explain figure 39,

164 THE MOON,
204. On account of the retarding influence of shoals,
and an uneven, indented coast, the tide-wave travels
more slowly along the shores of an island than in the
neighboring sea, assuming convex figures at a little dis-
tance from the island and on opposite sides of it. These
convex lines sometimes meet and become blended in
such a manner as to create singular anomalies in a Sea
much broken by islands, as well as on coasts indented
with numerous bays and rivers. Peculiar phenomena
are also produced, when the tide flows in at opposite
extremities of a reef or island, as into the two opposite
ends of Long Island Sound. In certain cases a tide-
wave is forced into a narrow arm of the sea, and pro-
duces very remarkable tides. The tides of the Bay of
Fundy (the highest in the world) sometimes rise to
the height of 60 or 70 feet; and the tides of the river
Severn, near Bristol in England, rise to the height of 40
feet. -
205. The Unit of Altitude of any place, is the height
of the maximum tide after the syzigies, being usually
about 36 hours after the new or full moon. But as the
amount of this tide would be affected by the distance of
the sun and moon from the earth, and by their declina-
tions, these distances are taken at their mean value, and
the luminaries are supposed to be in the equator; the
observations being so reduced as to conform to these cir-
cumstances. The unit of altitude can be ascertained
by observation only. The actual rise of the tide de-
pends much on the strength and direction of the wind.
When high winds conspire with a high flood tide, as is
frequently the case near the equinoxes, the tide often
£-
204. How does the tide-wave travel along the shores of an
island'! How are the great tides of the Bay of Fundy accounted
for 7 How high do they rise there, and at Bristol in England?
205. Define the unit of altitude. By what circumstances is
the unit of altitude affected 7 How is it ascertained 7 State
it for Several places.
TIDES. 165
rises to a very unusual height. . We subjoin from the
American Almanac a few examples of the unit of alti-
tude for different places. .
Feet.
Cumberland, head of the Bay of Fundy, 71
Boston, e g * 11%
New Haven, • io wº 8
New York, g tº * 5
Charleston, S. C., e * 6
206. The Establishment of any port is the mean in-
terval between noon and the time of high water, on the
day of new or full moon. As the interval for any given
place is always nearly the same, it becomes a criterion
of the retardation of the tides at that place. On ac-
count of the importance to navigation of a correct
knowledge of the tides, the British Board of Admiralty,
at the suggestion of the Royal Society, recently issued
orders to their agents in various important naval stations,
to have accurate observations made on the tides, with
the view of ascertaining the establishment and various
other particulars respecting each station; and the gov-
ernment of the United States is prosecuting similar in-
vestigations respecting our own ports.
207. According to Professor Whewell, the tides on
the coast of North America are derived from the great
tide-wave of the South Atlantic, which runs steadily
northward along the coast to the mouth of the Bay of
Fundy, where it meets the northern tide-wave flowing
in the opposite direction. Hence he accounts for the
high tides of the Bay of Fundy. -
208. The largest lakes and inland seas have no per-
ceptible tides. This is asserted by all writers respect-
206. What is the establishment of a port? What efforts
have been made to obtain accurate observations on the tides?
166 THE MOON,
ing the Caspian and Euxine, and the same is ſound to
be true of the largest of the North American lakes, Lake
Superior. t . . . . . . .
Although these several tracts of water appear large
when taken by themselves, yet they occupy but small
portions of the surface of the globe, as will appear ev-
ident from the delineation of them on an artificial globe.
Now we must recollect that the primitive tides are pro-
duced by the whequal action of the sun and moon upon
the different parts of the earth; and that it is only at
points whose distance from each other bears a consider-
able ratio to the whole distance of the sun or the moon,
that the inequality of action becomes manifest. The
space required is larger than either of these tracts of
water. It is obvious also that they have no opportunity
to be subject to a derivative tide. * *
209. To apply the theory of universal gravitation to
all the varying circumstances that influence the tides,
becomes a matter of such intricacy, that La Place pro-
nounces “the problem of the tides” the most difficult
problem of celestial mechanics.
210. The Atmosphere that envelops the earth, must
evidently be subject to the action of the same forces as
the covering of waters, and hence we might expect a
rise and fall of the barometer, indicating an atmospheric
tide corresponding to the tide of the ocean, La Place
has calculated the amount of this aerial tide. It is too
inconsiderable to be detected by changes in the barom-
eter, unless by the most refined observations. Hence it
is concluded, that the fluctuations produced by this cause
are too slight to affect meteorological phenomena in any
appreciable degree. . . *
207. How are the tides on the coast of North America de-
rived 7 -
208. Why have lakes and seas no tides 7
209. What is said of the difficulty of applying the principle
of universal gravitation to all the circumstances of the tides?
167
* C H A P T E R W II.
of THE PLANETs—THE INFERIOR PLANETs, MERCURY
. . . . * AND VENUs. -
211. THE name planet signifies a wanderer,” and is
applied to this class of bodies because they shift their
positions in the heavens, whereas the fixed stars con-
stantly maintain the same places with respect to each
other. The planets known from a high antiquity, are
Mercury, Venus, Earth, Mars, Jupiter, and Saturn. To
these, in 1781, was added Uranus, (or Herschel, as it is
sometimes called from the name of its discoverer,) and,
as late as the commencement of the present century,
four more were added, namely, Ceres, Pallas, Juno, and
Westa. These bodies are designated by the following
characters:
1. Mercury & 7. Ceres sº
2. Venus Q 8. Pallas $2
3. Earth QB s' 9, Jupiter 2 (
4. Mars & 10. Saturn b
5. Westa ſt 11. Uranus I;
6. Juno §
The foregoing are called the primary planets. Sev-
eral of these have one or more attendants, or satellites,
210, Has the atmosphere any tide? Is it sufficient to influ-
ence meteorological phenomena? 1 -
211. Whence is the name planet derived? Which of the
planets have been long known'ſ Which have been added in
modern times? Mark on paper or on the black board, the
several characters by which the planets are designated. Dis-
tinguish between the primary and the secondary planets. What
bodies have satellites? State the whole number of planets.
* From the Greek, who viſtmg. f From Ovgovog.
168 THE PLANETS.
which revolve around them, as they revolve aróund the
sun. The earth has one satellite, namely, the moon;
Jupiter has four; Saturn, seven ; and Uranus, six. These
bodies also are planets, but in distinction from the others
they are called secondary planets. Hence, the whole
number of planets are 29, viz. 11 primary, and 18 Sec-
Ondary planets. - -
212. With the exception of the four new planets,
these bodies have their orbits very nearly in the same
plane, and are never seen far from the ecliptic. Mer-
cury, whose orbit is most inclined of all, never departs
farther from the ecliptic than about 79, while most of
the other planets pursue very nearly the same path with
the earth, in their annual revolution around the Sun.
The new planets, however, make wider excursions from
the plane of the ecliptic, amounting, in the case of Pal-
las, to 34°. - ** .
213. Mercury and Venus are called inferior planets,
because they have their orbits nearer to the Sun than
that of the earth ; while all the others, being more dis-
tant from the sun than the earth, are called Superior
planets. The planet presents great diversity among
themselves in respect to distance from the Sun, magni-
tude, time of revolution, and density. They differ also
in regard to satellites, of which, as we have seen, three
have respectively four, six, and seven, while more than
half have none at all. It will aid the memory, and
render our view of the planetary system more clear and
comprehensive, if we classify, as far as possible, 'the
various particulars comprehended under the foregoing
heads. - -
K-
212. Near what great circle are the orbits of all the planets?
How far does Pallas deviate from the ecliptic -
213. Why are Mercury and Venus called Inferior planets?
Why are the other planets called superior What diversities
do the planets exhibit among themselves?
DISTANCES FROM THE SUN. 169
214. DISTANCES FROM THE SUN.
1. Mercury, © g- 37,000,000
. . . . §
. Eart ſo gº 7 )
4. Mars," e . 142,000,000
5. Westa, * © 225,000,000
6. Juno º g -
7. Ceres, e * 261,000,000
8. Pallas, • d
9. Jupiter, e tº 485,000,000
10. Saturn, • e 890,000,000
11. Uranus, ſº . 1800,000,000
The dimensions of the planetary system are seen
from this table to be vast, comprehending a circular
space thirty six hundred millions of miles in diameter.
A railway car, travelling constantly at the rate of 20
miles an hour, would require more than 20,000 years to
cross the orbit of Uranus. - #
It may aid the memory to remark, that in regard to
the planets nearest the Sun, the distances increase in an
arithmetical ratio, while those most remote, increase in
a geometrical ratio. Thus, if we add 30 to the distance
of Mercury, it gives us nearly that of Venus; 30 more
gives that of the Earth ; while Saturn is nearly twice
the distance of Jupiter, and Uranus twice the distance
of Saturn. Between the orbits of Mars and Jupiter, a
great chasm appeared, which broke the continuity of the
series; but the discovery of the new planets has filled
the void.
214. State the distance of each of the planets from the sun.
What is said of the dimensions of the planetary system 7 How
do the distances of those planets which are nearest the sun in-
crease? Also those which are more distant? How may the
mean distances of the planets from the sun be determined'
Give an example in computing the distance of Jupiter.
170 TIME PLANETS,
The mean distances of the planets from the Sun, may
be determined by means of Kepler’s law, that the squares
of the periodical times are as the cubes of the distances.
Thus the earth's distance being previously ascertained
by means of the sun's horizontal parallax, and the pe-
riod of any other planet, as Jupiter, being learned from
observation, we say as 365.256° : 4332.585**::1° :
5.202°, which equals the cube of Jupiter’s distance from
the Sun, and its root equals that distance itself.
215. MAGNITUDES.
Diam, in Miles. Mean apparent Diam. Volume,
Mercury, g g 3140 6//.9 Hºf
Venus, . o º 7700 16//.9 +";
Earth, . o . 7912 l
Mars, . tº g 4200 6/.3 #
Ceres, . w tº 160 0//.5
Jupiter, . tº . 89000 36.7 1281
Saturn, . tº ... 79000 16/.2 995
Uranus, * . 35000 4//.0 80
We remark here a great diversity in regard to magni-
tude, a diversity which does not appear to be subject to
any definite law. While Venus, an inferior planet, is
#9, as large as the earth, Mars, a superior planet is only #,
while Jupiter is 1281 times as large. Although several
of the planets, when nearest to us, appear brilliant and
large when compared with the fixed stars, yet the angle
which they subtend is very small, that of Venus, the
greatest of all, never exceeding about 1", or more exactly
61”.2, and that of Jupiter being when greatest only
about ; of a minute.
215. State the diameter of each of the planets. What diver-
sitics occur in regard to their magnitudes? IIow great angles
do Venus and Jupiter subtend ?
* This is the number of days in one revolution of Jupiter.
PER iODIC TIMES-MERCURY AND VENUS. 171
216. PERIODIC TIMEs.
Revolution in its orbit. Mean daily motion.
Mercury, 3 months, or 88 days, 4o 5/32//.6
Venus, 74 tº 4 224 tº 1O 367 7//.8
Earth, 1 year, “ 365 “ OO 59/ 8/.3
Mars, 2 years, & 6S7 tº OO 31/26/.7
Ceres, A “ {{ 1681 tº OO 12/ 50//.9
Jupiter, 12 “ tº 4332 “ 0O 4/ 597/.3
Saturn, 29 tº “ 10750 “ OO 2' 07/.6
Dramus, 84 “ “ 306S6 “ OO 0/42//.4
From this view, it appears that the planets nearest the
sun move most rapidly. Thus Mercury performs nearly
350 revolutions while Uranus performs one. This is
evidently not owing merely to the greater dimensions of
the orbit of Uranus, for the length of its orbit is not 50
times that of the orbit of Mercury, while the time em-
ployed in describing it is 350 times that of Mercury.
Indeed this ought to follow from Kepler's law that the
Squares of the periodical times are as the cubes of the
distances, from which it is manifest that the times of
revolution increase faster than the dimensions of the or—
bit. Accordingly, the apparent progress of the most
distant planets is exceedingly slow, the daily rate of
Uranus being only 42%.4 per day; so that ſor weeks and
months, and even years, this planet but slightly changes
its place among the stars.
THE INFERIOR PLANETS, MERCURY AND VENUS.
217. The inferior planets, Mercury and Venus, hav-
ing their orbits so for within that of the earth, appear to
us as attendants upon the Sun. Mercury never appears
farther ſtom the sun than 29° (28° 48') and seldom so
216. State the periodic time of each of the planets. Which
planets move most rapidly How many revolutions does Mer-
cury perform while Uranus performs one? What is the daily
rate of Uranus 7
172 THE PLANETS.
far; and Venus never more than about 47° (47° 12/).
Both planets, therefore, appear either in the west soon
after sunset, or in the east a little before Sunrise. In
high latitudes, where the twilight is prolonged, Mercury
can seldom be seen with the naked eye, and then only
at the periods of its greatest elongation.* The reason
of this will readily appear from the following diagram.
Fig. 40.
Let S (Fig. 40,) represent the sun, ADB the orbit of
|Mercury, and E the place of the Earth. Each of the
planets is seen at its greatest elongation, when a line,
EA or EB in the figure, is a tangent to its orbit. Then
the Sun being at S' in the heavens, the planet will be
217. What is Mercury's greatest elongation from the Sun?
What is Venus's 7 What is said respecting the difficulty of see-
ing Mercury'. Explain by figure 40.
* Copernicus is said to have lamented on his death-bed that he had
meyer been able to obtain a sight of Mercury, and Delambre saw it but
£W1C0. -

MERCUIRY AND WENUS. 173
seen at A' and B', when at its greatest elongations, and
will appear no further from the sun than the arc S'A' or
S'B' respectively.
218. A planet is said to be in Conjunction with the
Sun, when it is seen in the same part of the heavens
with the sun, or when it has the same longitude. Mer-
cury and Venus have each two conjunctions, the inferior,
and the superior. The inferior conjunction is its posi-
tion when in conjunction on the same side of the Sun
with the earth, as at C in the figure : the superior con-
junction is its position when on the side of the Sun most
distant from the earth, as at D.
219. The period occupied by a planet between two
Successive conjunctions with the earth, is called its sy-
modical revolution. Both the planet and the earth being
in motion, the time of the synodical revolution exceeds
that of the sidereal revolution of Mercury or Venus;
for when the planet comes round to the place where it
before overtook the earth, it does not find the earth at
that point, but far in advance of it. Thus, let Mercury
come into inferior conjunction with the earth at C, (Fig.
40.) In about 88 days, the planet will come round to
the same point again ; but meanwhile the earth has
moved forward through the arc EE', and will continue
to move while the planet is moving more rapidly to over-
take her, the case being analogous to that of the hour
and second hand of a clock.
The synodical period of Mercury is 116, and of Venus
584 days,
* →
218. When is a planet said to be in conjunction with the
sun ? What conjunctions have the inferior planets?
219. Define the synodical revolution. How does this period
compare with the sidereal revolution ? Explain by figure 40.
What is the synodical period of Mercury and Venus respect.
ively 7
15%
174 TIHE PLANETS.
220. The motion of an inferior planet is direct in
passing through its superior conjunction, and retrograde
in passing through its inferior conjunction. Thus We-
nus, while going from B through D to A, (Fig. 40,)
moves in the order of the signs, or from west to east,
and would appear to traverse the celestial vault B'S'A'
from right to left; but in passing from A through C to
B, her course would be retrogade, returning on the same
arc from left to right. If the earth were at rest, there-
fore, (and the sun, of course, at rest,) the inferior-planets
would appear to oscillate backwards and forwards across
the Sun. But, it must be recollected, that the earth is
moving in the same direction with the planet, as respects
the signs, but with a slower motion. This modifies the
motions of the planet, accelerating it in the superior and
retarding it in the inferior conjunctions. Thus in figure
40, Venus while moving through BDA would seem to
move in the heavens from B' to Aſ were the earth at
rest; but meanwhile the earth changes its position from
E to E', by which means the planet is not seen at A'
but at A", being accelerated by the arc A/A" in conse-
quence of the earth’s motion. On the other hand, when
the planet is passing through its inferior conjunction
ACB, it appears to move backwards in the heavens from
Aſ to B' if the earth is at rest, but from A' to B" if the
earth has in the mean time moved from E to E', being
retarded by the arc B'B'. Although the motions of the
earth have the effect to accelerate the planet in the superi-
or conjunction, and to retard it in the inferior, yet, on ac-
count of the greater distance, the apparent motion of the
planet is much slower in the superior than in the inſe-
rior conjunction, -
221. When passing from the superior to the inferior
conjunction, or from the inferior to the superior conjunc-
220. When is the motion of an inferior planet direct and
when retrograde 7 Explain by figure 40. If the earth were at
rest, how would the inferior planets appear to move 7 Show
how the earth's motion modifies the apparent motions,
MERCURY AND VENUS, 175
tion, through the greatest elongations, the inferior plan-
ets are stationary. -
If the earth were at rest, the stationary points would
be at the greatest elongations as at A and B, for then the
planet would be moving directly towards or from the
earth, and would be seen for some time in the same
place in the heavens; but the earth itself is moving
nearly at right angles to the line of the planet's motion,
that is, the line which is drawn from the earth to the
planet through the point of greatest elongation ; hence a
direct motion is given to the planet by this cause. When
the planet, however, has passed this line by its Superior
velocity, it soon overcomes this tendency of the earth to
give it a relative motion eastward, and becomes retro-
grade as it approaches the inferior conjunction. Its sta-
tionary point obviously lies between its place of greatest
elongation, and the place where its motion becomes re-
trograde. Mercury is stationary at an elongation of
from 15° to 20° from the sun; and Venus at about 29°.
222. Mercury and Venus exhibit to the telescope pha-
ses similar to those of the moon.
When on the side of their inferior conjunction, these
planets appear horned, like the moon in her first and last
quarters; and when on the side of their superior con-
junctions they appear gibbous. At the moment of Su-
perior conjunction, the whole enlightened orb of the
planet is turned towards the earth, and the appearance
would be that of the full moon, but the planet is too
near the Sun to be commonly visible.
These different phases show these bodies are opake,
and shine only as they reflect to us the light of the Sun;
and the same remark applies to all the planets.
221. When are the inſerior planets stationary'ſ Why are
they not stationary at the points of greatest elongation? At what
elongation are Mercury and Venus stationary respectively?
222. What phases do Mercury and Venus exhibit? Explain
by figure 40. Whence do these bodies derive their light? Is
the same true of the other planets?
176 THE PLANETS,
223. The orbit of Mercury is the most eccentric, and
the most inclined of all the planets;* while that of Ve-
ovus varies but little from a circle, and lies much nearer
to the ecliptic. - -
The eccentricity of the orbit of Mercury is nearly 4
its semi-major axis, while that of Venus is only r!; ;
the inclination of Mercury’s orbit is 79, while that of
Venus is less than 34°. Mercury, on account of his dif-
ferent distances from the earth, varies much in his appa-
rent diameter, which is only 5’ in the apogee, but 12%
in the perigee. The inclination of his orbit to his equa-
tor being very great, the changes of his seasons must be
proportionally great. -
These different aspects of an inferior planet will be
easily understood from Fig. 41, where the earth is at E,
and the planet is represented in various positions in its
revolutions around the sun. When at A, in the supe-
rior conjunction, the whole enlightened disk is turned
towards us; at D, in the inferior conjunction, the en-
lightened side is turned entirely from us; and at the
quadratures B and C, half the disk is in view. Between
A and B, and A and C, the planet is gibbous, like the
moon in her second and third quarters; and between B
223. What is said of the eccentricity and inclination of the
orbit of Mercury'ſ How does the apparent diameter of Mer-
cury vary 7 How are his changes of seasons !
* The new planets of course excepted.

MERCUIRY AND WIENU.S. 177
and D, and C and D, the planet is horned, like the moon
in her first and last quarters.
224. An inferior planet is brightest at a certain point
between its greatest elongation and inferior conjunction.
Its maximum brilliancy would happen at the inferior
conjunction, (being then nearest to us,) if it shined by
its own light; but in that position, its dark side is turned
towards us. Still, its maximum cannot be when most
of the illuminated side is towards us; for then, being at
the Superior conjunction, it is at its greatest distance
from us. The maximum must therefore be somewhere
between the two. Venus gives her greatest light when
about 40° from the sun.
225. Mercury and Venus both revolve on their aves,
?? 7.early the same time with the earth.
The diurnal period of Mercury is 24h. 5m. 28s., and
that of Venus 23h. 21m. 7s. The revolutions on their
axes have been determined by means of some spot or
mark seen by the telescope, as the revolution of the Sun
on his axis is ascertained by means of his spots.
226. Venus is regarded as the most beautiful of the
planets, and is well known as the morning and evening
star. The most ancient nations did not indeed recog-
nize the evening and morning star as one and the same
body, but supposed they were different planets, and ac-
cordingly gave them different names, calling the morn-
ing star Lucifer, and the evening star Hesperus. At her
period of greatest splendor, Venus casts a shadow, and is
sometimes visible in broad daylight. Her light is then
estimated as equal to that of twenty stars of the first
224. When is an inferior planet brightest ? Why not when
nearest to us? Why not when most of the illuminated side is
turned towards us '' -
225. In what time do Mercury and Venus, respectively, re-
volve on their axes? How are these periods ascertained 7
178 THE PLANETS.
magnitude. At her period of greatest elongation, We-
nus is visible from three to four hours after the Setting
or before the rising of the Sun.
227. Every eight years, Venus forms her conjunc-
tions with the sun in the same part of the heavens.
For, since the synodical period of Venus is 584 days,
and her sidereal period 224.7,
224.7 : 360°: ; 584 : 935.6=the arc of longitude de-
scribed by Venus between the first and second conjunc-
tions. Deducting 720°, or two entire circumferences,
the remainder, 215°.6, shows how far the place of the
second conjunction is in advance of the first. Hence,
in five synodical revolutions, or 2920 days, the same
point must have advanced 215°.6 × 5 = 1078°, which is
nearly three entire circumferences, so that at the end of
five synodical revolutions, occupying 2920 days, or 8
years, the conjunction of Venus takes place nearly in
the same place in the heavens as at first.
Whatever appearances of this planet, therefore, arise
from its positions with respect to the earth and the Sun,
; are repeated every eight years in nearly the same
OTII].
TRANSITS OF THE INFERIOR PLANETS.
228. The Transit of Mercury or Venus, is its pass-
age across the sun's disk, as the moon passes over it in
a solar eclipse.
As a transit takes place only when the planet is in
inferior conjunction, at which time her motion is retro-
grade, it is always from left to right, and the planet is
Seen projected on the solar disk in a black round spot.
226. What erroneous notions had the ancients respecting the
morning and evening star? What is said of the brilliancy of
Venus at her greatest splendor? How long may Venus be in
sight after sunset !
227. What happens to Venus every eight years ?
MERCURY AND VENUs. 179
Were the orbits of the inferior planets coincident with
the plane of the earth’s orbit, a transit would occur to
some part of the earth at every inferior conjunction.
But the orbit of Venus makes an angle of 34° with the
ecliptic, and Mercury an angle of 79; and, moreover,
the apparent diameter of each of these bodies is very
Small, both of which circumstances conspire to render a
transit a comparatively rare occurrence, since it can hap-
pen only when the Sun, at the time of an inferior con-
junction, chances to be at or extremly near the planet's
node. The nodes of Mercury lie in longitude 469 and
226°, points which the sun passes through in May and
November. It is only in these months, therefore, that
transits of Mercury can occur. For a similar reason,
those of Venus occur only in June and December. Since,
however, the nodes of both planets have a small retro-
grade motion, the months in which transits occur will
change in the course of ages.
229. Transits of Mercury occur more frequently than
those of Venus. The periodic times of Mercury and
the earth are so adjusted to each other, that Mercury
performs nearly 29 revolutions while the earth performs
7. If, therefore, the two bodies meet at the node in any
given year, seven years afterwards they will meet nearly
at the same node, and a transit may take place, accord-
ingly, at intervals of 7 years. But 54 revolutions of
Mercury correspond still nearer to 13 revolutions of the
228. What is meant by the transit of Mercury or Venus 7
When only can a transit take place'ſ What angles do the or-
bits of Venus and Mercury respectively make with the ecliptic
In what months does the sun pass through the nodes of each of
these planets?
229. Which planet has the most frequent transits 7 What is
the shortest interval of the transits of Mercury'ſ What are the
longer intervals | When will the next occur ! What are in-
tervals of the transits of Venus ' When was the last transit of
Venus, and when will the next occur !
180 THE PLANETS,
earth, and therefore a transit is still more probable after
intervals of 13 years. At intervals of 33 years, transits
of Mercury are exceedingly probable, because in that
time Mercury makes almost exactly 137 revolutions.
Intermediate transits however may occur at the other
node, these intervals having reference mererly to the
same node. Thus transits of Mercury happened at the
ascending node in 1815, and 1822, at intervals of
7 years; and at the descending node in 1832, which
will return in 1845, after an interval of 13 years. Tran-
sits of Venus are much more unfrequent than those of
Mercury. Eight revolutions of the earth are completed
in nearly the same time as thirteen revolutions of Venus,
and hence two transits of Venus may occur after an in-
terval of 8 years, as was the case at the last return of
this phenomenon, one transit having occurred in 1761,
and another in 1769. But if a transit does not happen
after 8 years, it will not happen, at the same node, until
an interval of 235 years; but intermediate transits may
occur at the other node. The next transit of Venus will
take place in 1874, being 235 years after the first that was
ever observed, which occurred in the year 1639. In the
mean time, as already mentioned, two transits have oc-
curred at the other node, at intervals of 8 years.
230. The great interest attached by astronomers to a
transit of Venus, arises from its furnishing the most accu-
rate means in our power of determining the sun’s hori-
zontal parallar—an element of great importance, since it
leads us to a knowledge of the distance of the earth from
the sun, and, consequently, by the application of Kepler’s
law, (Art. 130,) of the distances of all the other planets.
Hence, in 1769, great efforts were made throughout the
civilized world, under the patronage of different govern-
230. At what intervals do the transits of Venus occur 7 When
will the next transit happen? Why is so much interest attach-
ed to the transits of Venus ' What efforts were made to ob-
serve it in 1769? Why cannot we ascertain the horizontal par-
allax of the sun in the same way as we do that of the moon 7
MERCUIRY AND VENUS. 181
ments, to observe this phenomenon under circumstances
the most favorable for determining the parallax of the
Sll]],
The common methods of finding the parallax of a
heavenly body cannot be relied on to a greater degree
of accuracy than 4". In the case of the moon, whose
greatest parallax amounts to about 1°, this deviation
from absolute accuracy is not material; but it amounts
to nearly half the entire parallax of the sun.
231. If the sun and Venus were equally distant from
us, they would be equally affected by parallax as viewed
by spectators in different parts of the earth, and hence
their relative situation would not be altered by it ; but
since Venus, at the inferior conjunction, is only about
one third as far off as the Sun, her parallax is propor-
tionally greater, and therefore spectators at distant points
will see Venus projected on different parts of the so-
lar disk, as the planet traverses the disk. Astron-
omers avail themselves of this circumstance to ascer-
tain the sun’s horizontal parallax. In order to make
the difference as large as possible very distant pla-
ces are selected for observation. Thus in the transit
of 1769, among the places selected, two of the most
favorable were Wardhuz in Lapland, and Oteheite, one
of the South Sea Islands.
The appearance of Venus on the sun's disk, being
that of a well defined black spot, and the exactness with
which the moment of external or internal contact may
be determined, are circumstances favorable to the exact-
ness of the result ; and astronomers repose so much con-
fidence in the estimation of the sun's horizontal parallax
as derived from the observations on the transit of 1769,
that this important element is thought to be ascertained
231. How is Venus projected on the sun to spectators in diſ.
ferent parts of the earth'ſ What places were selected for ob-
serving the transit of 1769?
16
182 TTHE PLANETS,
within ºr of a second. The general result of all these
observations give the sun’s horizontal parallax 8".6, or
more exactly, 8./5776.
232. During the transits of Venus over the Sun's disk
in 1761 and 1769, a sort of penumbral light was ob-
served around the planet by several astronomers, which
was thought to indicate an atmosphere. This appear-
ance was particularly observable while the planet was
coming on and going off the solar disk. The total im-
mersion and emersion were not instantaneous; but as
two drops of water when about to separate, form a liga-
ment between them, so there was a dark shade stretched
out between Venus and the sun, and when the ligament
broke, the planet seemed to have got about an eighth part
of her diameter from the limb of the sun. The various
accounts of the two transits abound with remarks like
these, which indicate the existence of an atmosphere
about Venus of nearly the density and extent of the
earth's atmosphere. Similar proofs of the existence of
an atmosphere around this planet, are derived from ap-
pearances of twilight.
The elder astronomers imagined they had discovered
a satellite accompanying Venus in her transit. If Venus
had in reality any satellite, the fact would be obvious at
her transits, as the satellite would be projected near the
primary on the Sun's disk; but later astronomers have
searched in vain for any appearances of the kind, and
the inference is that former astronomers were deceived
by some optical illusion.
Astronomers have detected very high mountains on
Venus, sometimes reaching to the elevation of 22 miles;
and it is remarkable that the highest mountains in We-
nus, in Mercury, in the moon, and in the earth, are al-
ways in the Southern hemisphere.
232. What indications have been observed of an atmos-
phere about Venus? Has Venus any Satellite 7 What is said
of the mountains of Venus' -
SUPERIOR PLANETS. $83
C H A P T E R V III.
GF THE SUPERIOR PLANETS-MARS, JUPITER, SATURN,
AND URANU.S.
233. THE Superior planets are distinguished from the
Inferior, by being seen at all distances from the sun
from 0° to 180°. Having their orbits exterior to that
of the earth, they of course never come between us and
the Sun, that is, they never have any inferior conjunction
like Mercury and Venus, but they are sometimes seen in
Superior conjunction, and sometimes in opposition. Nor
do they, like the inferior planets, exhibit to the telescope
different phases, but, with a single exception, they al-
ways present the side that is turned towards the earth
fully enlightened. This is owing to their great distance
from the earth ; for were the spectator to stand upon the
Sun, he would of course always have the illuminated
side of each of the planets turned towards him ; but,
So distant are all the superior planets except Mars, that
they are viewed by us very nearly in the same manner
as they would be if we actually stood on the sun.
234. MARS is a small planet, his diameter being only
about half of that of the earth, or 4200 miles. He also,
at times, comes nearer to the earth than any other planet
except Venus. His mean distance from the sun is
142,000,000 miles; but his orbit is so eccentric that his
distance varies much in different parts of his revolution.
Mars is always very near the ecliptic, never varying from
233. Name the Superior Planets. How are they distin-
guished from the Inferior'ſ Which of them exhibits phases?
Why do not the rest? -
234. Mars.—State his diameter—Mean distance from the
sun—inclination of his orbit. How distinguished from the
other planets? Why do his brightness and apparent magnitude
vary so much Illustrate by figure 42. ' -
184 THE PLANETS.
it 29. He is distinguished from all the planets by his
deep red color, and fiery aspect; but his brightness and
apparent magnitude vary much at different times, being
sometimes nearer to us than at others, by the whole di-
ameter of the earth’s orbit, that is, by about 190,000,000
of miles. When Mars is on the same side of the sun
with the earth, or at his opposition, he comes within
47,000,000 miles of the earth, and rising about the time
the sun sets, surprises us by his magnitude and splen-
dor; but when he passes to the other side of the sun to
his superior conjunction, he dwindles to the appearance
of a small star, being then 237,000,000 miles from us.
Thus, let M (Fig. 42,) represent Mars in opposition,
and M' in the superior conjunction, while E represents
the earth. It is obvious that in the former situation, the
planet must be nearer to the earth than in the latter
by the whole diameter of the earth’s orbit.
{º
Fig. 42.
M.'
235. Mars is the only one of the superior planets
which exhibits phases. When he is towards the quad-
ratures at Q or Q', it is evident from the figure that
only a part of the circle of illumination is turned towards

MARS. 185
the earth, such a portion of the remoter part of it being
concealed from our view as to render the form more or
less gibbous,
236. When viewed with a powerful telescope, the
surface of Mars appears diversified...with numerous vari-
eties of light and shade. The region around the poles
is marked by white spots, which vary their appearance
with the changes of seasons in the planets. Hence Dr.
Herschel conjectured that they were owing to ice and
Snow, which alternately accumulates and melts, accord-
ing to the position of each pole with respect to the sun.
It has been common to ascribe the ruddy light of this
planet to an extensive and dense atmosphere, which was
said to be distinctly indicated, by the gradual diminution
of light observed in a star as it approached very near to
the planet in undergoing an occultation; but more re-
cent observations afford no such evidence of an atmos-
phere.
237. By observations on the spots we learn that Mars
revolves on his axis in very nearly the same time with
the earth, (24h. 39m. 21s.3); and that the inclination of
his axis to that of his orbit is also nearly the same,
being 30° 18' 10".8. - & s
As the diurnal rotation of Mars is nearly the same as
that of the earth, we might expect a similar flattening at
the poles, giving to the planet a spheroidal figure. In-
deed the compression or ellipticity of Mars greatly ex-
ceeds that of the earth, being no less than Tºr of the
equatorial diameter, while that of the earth is only ###.
235. Show why Mars should exhibit phases. -
236. How is the surface of Mars diversified ? What is seen
around the poles? What indications are there of ice and
snow To what is the ruddy hue of Mars ascribed 7
237. How do we learn his revolution on his axis? In what
time does it take place? What is the figure of Mars? How
does its ellipticity compare with that of the earth"
16%
186 THE PLANETS.
This remarkable flattening of the poles of Mars has been
supposed to arise from a great variation of density in the
planet in different parts.
238. JUPITER is distinguished from all the other plan-
ets by his vast magnitude. His diameter is 89,000
miles, and his volume 1280 times that of the earth.
His figure is strikingly spheroidal, the equatorial being
larger than the polar diameter in the proportion of 107
to 100. Such a figure might naturally be expected
from the rapidity of his diurnal rotation, which is ac-
complished in about 10 hours. A place on the equa-
tor of Jupiter must turn 27 times as fast as on the ter-
restrial equator. The distance of Jupiter from the sun
is nearly 490,000,000 miles, and his revolution around
the Sun Occupies nearly 12 years.
239. The view of Jupiter through a good telescope,
(Fig. 43,) is one of the most magnificent and interesting
Spectacles in astronomy. The disk expands into a large
Fig. 43.
and bright orb like the full moon ; the spheroidal figure
which theory assigns to revolving spheres, is here pal-
238. Jupiter.—State his diameter, volume, figure, revolu-
tion on his axis, velocity of his equator, distance from the sun,
periodic time,

JUPITER. 187
pably exhibited to the eye; across the disk, arranged in
parallel stripes, are discerned several dusky bands, called
belts; and four bright satellites, always in attendance, and
ever varying their positions, compose a splendid retinue.
Indeed, astronomers gaze with peculiar interest on Jupi-
ter and his moons as affording a miniature representa-
tion of the whole solar system, repeating on a smaller
Scale, the same revolutions, and exemplifying, in a man-
ner more within the compass of our observation, the
same laws as regulate the entire assemblage of sun and
planets.
240. The Belts of Jupiter, are variable in their num-
ber and dimensions. With the smaller telescopes, only
one or two are seen across the equatorial regions; but
with more powerful instruments, the number is in-
creased, covering a great part of the whole disk. Dif-
ferent opinions have been entertained by astronomers
respecting the cause of the belts; but they have gen-
erally been regarded as clouds formed in the atmosphere
of the planet, agitated by winds as is indicated by their
frequent changes, and made to assume the form of belts
parallel to the equator by currents that circulate around
the planet like the trade winds and other currents that
circulate around our globe. Sir John Herschel supposes
that the belts are not ranges of clouds, but portions of the
planet itself brought into view by the removal of clouds
and mists, that exist in the atmosphere of the planet
through which are openings made by currents circula-
ting around Jupiter.
241. The Satellites of Jupiter may be seen with a
telescope of very moderate powers. Even a common
spy glass will enable us to discern them. Indeed one or
two of them have been occasionally seen with the naked
eye. In the largest telescopes, they severally appear as
239. What does the telescopic view of J upiter exhibit 2
Why do astronomers regard it with so much interest ?
240. Describe Jupiter's Belts—to what are they ascribed
188 THE PLANETS.
bright as Sirius. With such an instrument, the view of
Jupiter with his moons and belts is truly a magnificent
spectacle, a world within itself. As the orbits of the
satellites do not deviate far from the plane of the eclip-
tic, and but little from the equator of the planet, they
are usually seen in nearly a straight line with each other
extending across the central part of the disk.
242. Jupiter’s satellites are distinguished from one
another by the denominations of first, second, third and
fourth, according to their relative distances from Jupiter,
the first being that which is nearest to him. Their ap-
parent motion is oscillatory, like that of a pendulum,
going alternately from their greatest elongation on one
side to their greatest elongation on the other, sometimes
in a straight line, and sometimes in an elliptical curve,
according to the different points of view in which we
observe them from the earth. They are sometimes sta-
tionary; their motion is alternately direct and retro-
grade; and, in short, they exhibit in miniature all the
phenomena of the planetary system. Various partic-
ulars of the system are exhibited in the following table.
The distances are given in radii of the primary.

Satellite. I Diameter. TMean Distance. Sidereal Revolution.
I 2508 6.04853 1d. 18h. 28m.
2 2068 9.6234.7 3 13 14
3 3377 15.35024 7 3 43
4 2890 26.998.35 16 16 32
Hence it appears, first, that Jupiter’s satellites are all
except the second, Somewhat larger than the moon, but
that the Second Satellite is the smallest, and the third
the largest of the whole, but the diameter of the latter
is only about gº part of that of the primary; secondly,
that the distance of the innermost satellite from the planet
241. How do the satellites appear to the telescope
242. Describe the motions of the satellites—magnitudes—
distances—periods of revolution.
JUPITER. 189
is three times his diameter, while that of the outermost
satellite is nearly fourteen times his diameter; thirdly,
that the first satellite completes its revolution around the
primary in one day and three fourths, while the fourth
satellite requires nearly sixteen and three fourths days.
243. The orbits of the satellites are nearly or quite
circular, and deviate but little from the plane of the
planet’s equator, and of course are but slightly inclined
to the plane of his orbit. They are, therefore, in a sim-
ilar situation with respect to Jupiter as the moon would
be with respect to the earth if her orbit nealy coincided
with the ecliptic, in which case she would undergo an
eclipse at every opposition.
244. The eclipses of Jupiter’s satellites, in their gen-
eral conception, are perfectly analogous to those of the
moon, but in their detail they differ in several particulars.
Owing to the much greater distance of Jupiter from the
sun, and its greater magnitude, the cone of its shadow is
much longer and larger than that of the earth. On this
account, as well as on account of the little inclination of
their orbits to that of their primary, the three inner sat-
ellites of Jupiter pass through the shadow, and are totally
eclipsed at every revolution. The fourth satellite, ow-
ing to the greater inclination of its orbit, sometimes
though rarely escapes eclipse, and sometimes merely
grazes the limits of the shadow or suffers a partial
eclipse. These eclipses, moreover, are not seen, as is
the case with those of the moon, from the center of
their motion, but from a remote station, and one whose
situation with respect to the line of the shadow is vari-
able. This, of course, makes no difference in the times
of the eclipses, but a very great one in their visibility,
243. What is the shape of their orbits? How situated with
regard to the plane of the planet's orbit? -
244. Describe the phenomena of their eclipses. Which of
them escapes an eclipse'ſ Are these eclipses seen in different
parts of the earth at the same moment of absolute time !
190 THE PLANETS.
and in their apparent situations with respect to the
planet at the moment of their entering or quitting the
shadow.
245. The eclipses of Jupiter's satellites present some
curious phenomena, which will be understood from the
following diagrams. -
Let A, B, C, D, (Fig. 44,) represent the earth in dif-
ferent parts of its orbit; J, Jupiter in his orbit sur-
rounded by his four satellites, the orbits of which are
marked 1, 2, 3, 4. At a the first satellite enters the
shadow of the planet, and emerges from it at b, and ad-
vances to its greatest elongation at c. The other satellites
traverse the shadow in a similar manner. These ap-
pearances will be modified by the place the earth hap-
pens to occupy in its orbit, being greatly altered by per-
spective ; but their appearances for any given night as
exhibited at Greenwich, are calculated and accurately
laid down in the Nautical Almanac.
When one of the satellites is passing between Jupiter
and the Sun it casts its shadow on the primary as the
-v
245. Describe the phenomena of the eclipses from figure 44.
Will these appearances be affected by the relative position of
the earth, with respect to the planet? Does the shadow of a
satellite or the satellite itself ever make a transit across the disk
of the planet?

JUPITER, 191
moon casts its shadow on the earth in a Solar eclipse.
We see with the telescope, the shadow traversing the
disk. Sometimes the satellite itself is seen projected on
the disk; but being illuminated as well as the primary,
it is not so easily distinguished as Venus or Mercury,
when seen on the sun’s disk, since, at the time of their
transits, their dark sides are turned towards us. The
manner in which these phenomena take place, as seen
from the earth in the several positions, A, B, C, D, may
be conceived by attentively inspecting the figure. It
will be seen, that when the earth is at A or C, the im-
mersions and emersions must take place close to the disk
of the planet, but that, in other positions of the earth, as
at B or D, the satellite will be seen to enter and leave
the shadow at some distance from the primary.
246. The eclipses of Jupiter’s satellites have been
studied with great attention by astronomers, on account
of their affording one of the easiest methods of deter-
mining the longitude. On this subject Sir J. Herschel
remarks: The discovery of Jupiter's satellites by Gali-
leo, which was one of the first fruits of the invention of
the telescope, forms one of the most memorable epochs
in the history of astronomy. The first astronomical So-
lution of the great problem of “the longitude,”—the
most important problem for the interests of mankind
that has ever been brought under the dominion of strict
Scientific principles, dates immediately from their dis-
covery. The final and conclusive establishment of the
Copernican system of astronomy, may also be considered
as referable to the discovery and study of this exquisite
miniature system, in which the laws of the planetary
motions, as ascertained by Kepler, and especially that
which connects their periods and distances, were speed-
ily traced, and found to be satisfactorily maintained.
246. Why have the eclipses of Jupiter’s satellites been stud-
ied with so much attention ? Who first discovered these eclip-
ses 7 What bearing has the system of Jupiter and his satel-
lites upon the Copernican system of astronomy?
192 THE PLANETS.
247. The entrance of one of Jupiter’s satellites into
the shadow of the primary being seen like the entrance
of the moon into the earth’s shadow, at the same mo-
ment of absolute time, at all places where the planet is
visible, and being wholly independent of parallax; be-
ing, moreover, predicted beforehand with great accuracy
for the instant of its occurrence at Greenwich, and given
in the Nautical Almanac ; this would seem to be one of
those events (Art. 188,) which are peculiarly adapted for
finding the longitude. It must be remarked, however,
that the extinction of light in the satellite at its immer-
sion, and the recovery of its light at its emersion, are not
instantaneous but gradual; for the satellite, like the
moon, occupies some time in entering into the shadow
or in emerging from it, which occasions a progressive
diminution or increase of light. The better the light
afforded by the telescope with which the observation is
made, the later the satellite will be seen at its immer-
sion, and the sooner at its emersion.* In noting the
eclipses even of the first satellite, the time must be con-
sidered as uncertain to the amount of 20 or 30 seconds;
and those of the other satellites involve still greater un-
certainty. Two observers, in the same room, observing
with different telescopes the same eclipse, will frequently
disagree in noting its time to the amount of 15 or 20
seconds; and the difference will be always the same
way. -
Better methods, therefore, of finding the longitude are
now employed, although the facility with which the
necessary observations can be made, and the little calcu-
lation required, still render this method eligible in many
247. Explain how these eclipses are used in finding the lon-
gitude. What imperfections attend this method? Is this meth-
od much employed at present? Why can it not be used at
sea 7 .*
* This is the reason why observers are directed in the Nautical Al-
manac to use telescopes of a certain power.
SATURN. 193
cases where extreme accuracy is not important. As a
telescope is essential for observing an eclipse of one of
the satellites, it is obvious that this method cannot be
practiced at Sea. - -
248. The grand discovery of the progressive motion
of light, was first made by observations on the eclipses
of Jupiter's satellites. In the year 1675, it was remarked
by Roemer, a Danish astronomer, on comparing together
observations of these eclipses during many successive
years, that they take place sooner by about sixteen min-
utes, (16m. 26s.6) when the earth is on the same side of
the sun with the planet, than when she is on the oppo-
site side. This difference he ascribes to the progressive
motion of light, which takes that time to pass through the
diameter of the earth’s orbit, making the velocity of light
about 192,000 miles per second. So great a velocity star-
tled astronomers at first, and produced some degree of
distrust of this explanation of the phenomenon; but the
subsequent discovery of what is called the aberration of
light, led to an independent estimation of the velocity of
light with almost precisely the same result.
249. SATURN comes next in the series as we recede
from the sun, and has, like Jupiter, a system within it-
self, on a scale of great magnificence. In size it is, next
to Jupiter, the largest of the planets, being 79,000 miles
in diameter, or about 1,000 times as large as the earth.
It has likewise belts on its surface and is attended by
seven satellites. But a still more wonderful appendage
is its Ring, a broad wheel encompassing the planet at a
great distance from it. We have already intimated that
Saturn's system is on a grand scale. As, however, Sat-
248. How was the progressive motion of light first discovered?
Explain the manner of the discovery. How long is light in
traversing the diameter of the earth's orbit? What is its ve-
locity per second 7 How does this agree with that derived
from the aberration of light? . -
17
194 THE PLANETS.
urn is distant from us nearly 900,000,000 miles, we are
unable to obtain the same clear and striking views of
his phenomena as we do of the phenomena of Jupiter, al-
though they really present a more wonderful mechanism.
250. Saturn's ring, when viewed with telescopes of
a high power, is found to consist of two concentric rings,
separated from each other by a dark space. Although
this division of the rings appears to us, on account of
our immense distance, as only a fine line, yet it is in re-
ality an interval of not less than about 1800 miles. The
dimensions of the whole system are in round numbers,
as follows:
Miles.
Diameter of the planets, . . . . 79,000
From the surface of the planet to the inner ring, 20,000
Breadth of the inner ring, º e º 17,000
Interval between the rings, e o e 1,800
Breadth of the outer ring, . {º e º 10,500
Extreme dimensions from outside to outside, 176,000
Fig. 45. -
The figure represents Saturn as it appears to a power-
ful telescope, surrounded by its rings, and having its body
striped with dark belts, somewhat similar but broader
249. Saturn.—State his diameter and volume, number of
satellites, Ring, distance from the sun. -

sºuns. - 195
and less strongly marked than those of Jupiter, and
Owing doubtless to a similar cause. That the ring is a
Solid opake substance, is shown by its throwing its shad-
ow on the body of the planet on the side nearest the sun
and on the other side receiving that of the body. From
the parallelism of the belts with the plane of the ring,
it may be conjectured that the axis of rotation of the
planet is perpendicular to that plane; and this conjec-
ture is confirmed by the occasional appearance of exten-
sive dusky spots on its surface, which when watched
indicate a rotation parallel to the ring in 10h. 29m. 17s.
This motion, it will be remarked, is nearly the same
with the diurnal motion of Jupiter, subjecting places on
the equator of the planet to a very swift revolution, and
occasioning a high degree of compression at the poles,
the equatorial being to the polar diameter in the high
ratio of 11 to 10. It requires a telescope of high mag-
nifying powers and a strong light, to give a full and
striking view of Saturn with his rings and belts and sat-
tellites; for we must bear in mind, that in the distance
of Saturn one second of angular measurement corres-
ponds to 4,000 miles, a space equal to the semi-diameter
of our globe. But with a telescope of moderate powers,
the leading phenomena of the ring itself may be ob-
served. e -
251. Saturn's ring, in its revolution around the sun,
always remains parallel to itself. . -
If we hold opposite to the eye a circular ring or disk
like a piece of coin, it will appear as a complete circle
when it is at right angles to the axis of vision, but when
oblique to that axis it will be projected into an ellipse
250. How is the Ring divided by large telescopes? State the
several dimensions of Saturn and his Rings. Describe the
figure. How is the Ring inferred to be a solid opake sub-
stance? In what time does Saturn revolve on his axis ' What
figure does this give to the planet! What kind of telescope is
required to see the phenomena of Saturn to advantage 7 -
196 THE PI, ANIETS.
more and more flattened as its obliquity is increased,
until, when its plane coincides with the axis of vision,
it is projected into a straight line. Let us place on the
table a lamp to represent the Sun, and holding the ring
at a certain distance inclined a little towards the lamp,
let us carry it round the lamp always keeping it parallel
to itself. During its revolution it will twice present its
edge to the lamp at opposite points, and twice at places
90° distant from those points, it will present its broadest
face towards the lamp. At intermediate points, it will
exhibit an ellipse more or less open, according as it is
nearer one or the other of the preceding positions. It
will be seen also that in one half of the revolution the
lamp shines on one side of the ring, and in the other
half of the revolution on the other side. Such would
be the successive appearances of Saturn's ring to a spec-
tator on the sum ; and since the earth is, in respect to
So distant a body as Saturn, very near the Sun, these
appearances are presented to us in nearly the same man-
ner as though we viewed them from the sun. Accor-
dingly, we sometimes see Saturn's ring under the form
of a broad ellipse, which grows continually more and
more acute until it passes into a line, and we either lose
sight of it altogether, or by the aid of the most pow-
ful telescopes, we see it as a fine thread of light drawn
across the disk and projecting out from it on each side.
As the whole revolution occupies 30 years, and the edge
is presented to the sun twice in the revolution, this last
phenomenon, namely, the disappearance of the ring,
takes place every 15 years. -
252. The learner may perhaps gain a clearer idea of
the foregoing appearances from the following diagram :
Let A, B, C, &c. represent successive positions of Sat-
urn and his ring in different parts of his orbit, while
251. How is the position of the Ring with respect to itself
in all parts of its revolution ? How may the various appear-
ances of the Ring be represented 7
SATURN. 197
abc represents the orbit of the earth.* Were the ring
when at C and G perpendicular to the CG, it would be
seen by a spectator situated at a or d a perfect circle,
but being inclined to the line of vision 28° 4', it is pro-
jected into an ellipse. This ellipse contracts in breadth
as the ring passes towards its nodes at A and E, where
it dwindles into a straight line. From E to G the ring
•opens again, becomes broadest at G, and again contracts
till it becomes a straight line at A, and from this point
expands till it recovers its original breadth at C. These
successive appearances are all exhibited to a telescope of
moderate powers. The ring is extremely thin, since the
smallest satellite, when projected on it, more than covers
it. The thickness is estimated at 100 miles.
253. Saturn's ring shines wholly by reflected light
derived from the sun. This is evident from the fact,
that that side only which is turned towards the sun is
enlightened ; and it is remarkable, that the illumination
of the ring is greater than that of the planet itself, but
252. Explain the revolution of the Ring by figure 46.
253. Whence does the Ring derive its light ! What causes
occasion the disappearance of the Ring? At what intervals
do these disappearances occur !
* It may be remarked by the learner, that these orbits are made so
elliptical, not to represent the eccentricity of either the earth's or Sat-
urn's orbit, but merely as the projection of circles seen very obliquely,

17%
198 THE PLANETS.
the outer ring is less bright than the inner. Although,
as we have already remarked, we view Saturn's ring
nearly as though we saw it from the sun, yet the plane
of the ring produced may pass between the earth and
the sun, in which case also the ring becomes invisi-
ble, the illuminated side being wholly turned from us.
Thus when the ring is approaching its node at E, a spec-
tator at a would have the dark side of the ring presented
to him. The ring was invisible in 1833, and will be
invisible again in 1847. At present (1839) it is the
northern side of the ring that is seen, but in 1855 the
southern side will come into view. -
It appears, therefore, that there are three causes for
the disappearance of Saturn's ring ; first, when the edge
of the ring is presented to the sun; secondly, when the
edge is presented to the earth; and thirdly, when the il-
luminated side is towards the earth. -
254. Saturn's ring revolves in its own plane in about
104 hours, (10h. 32m. 15s.4). La Place inferred this
from the doctrine of universal gravitation. He proved
that such a rotation was necessary, otherwise the matter
of which the ring is composed would be precipitated
upon its primary. He showed that in order to sustain
itself, its period of rotation must be equal to the time of
revolution of a satellite, circulating around Saturn at a
distance from it equal to that of the middle of the ring,
which period would be about 104 hours. By means of
spots in the ring, Dr. Herschel followed the ring in its
rotation, and actually found its period to be the same as
assigned by La Place,—a coincidence which beautifully
exemplifies the harmony of truth.
255. Although the rings are very nearly concentric,
yet recent measurements of extreme delicacy have dem-
254. In what time does the Ring revolve on its own plane?
How was this revolution inferred to exist before it was actually
observed 7 -
SATURN. - 199
onstrated, that the coincidence is not mathematically
exact, but that the center of gravity of the rings describes
around that of the body a very minute orbit. This fact,
unimportant as it may seem, is of the utmost consequence
to the stability of the system of rings. Supposing them
mathematically perfect in their circular form, and ex-
actly concentric with the planet, it is demonstrable that
they would form (in spite of their centrifugal force) a
system in a state of unstable equilibrium, which the
slightest external power would subvert—not by causing
a rupture in the substance of the rings—but by precip-
itating them unbroken on the surface of the planet.
The ring may be supposed of an unequal breadth in its
different parts, and as consisting of irregular Solids,
whose common center of gravity does not coincide with
the center of the figure. Were it not for this distribu-
tion of matter, its equilibrium would be destroyed by
the slightest force, such as the attraction of a satellite,
and the ring would finally precipitate itself upon the
planet. -
As the smallest difference of velocity between the
planet and its rings must infallibly precipitate the rings
upon the planet, never more to separate, it follows either
that their motions in their common orbit round the sun,
must have been adjusted to each other by an external
power, with the minutest precision, or that the rings
must have been formed about the planet while subject
to their common orbitual motion, and under the full and
free influence of all the acting forces.
The rings of Saturn must present a magnificent spec-
tacle from those regions of the planet which lie on their
enlightened sides, appearing as vast arches spanning the
sky from horizon to horizon, and holding an invariable
situation among the stars. On the other hand, in the
region beneath the dark side, a solar eclipse of 15 years
255. Are the Rings concentric with the planet! What ad-
vantage results from this arrangement." How must the Rings
appear when seen from the planets 7
200 THE PLANETS.
in duration, under their shadow, must afford (to our
ideas) an inhospitable abode to animated beings, but ill
compensated by the full light of its satellites. But we
shall do wrong to judge of the fitness or unfitness of
their condition from what we see around us, when, per-
haps, the very combinations which convey to our minds
only images of horror may be in reality theatres of the
most striking and glorious displays of beneficent con-
trivance. (Sir J. Herschel.)
256. Saturn is attended by seven satellites. Although
bodies of considerable size, their great distance prevents
their being visible to any telescopes but such as afford a
strong light and high magnifying powers. The outer-
most satellite is distant from the planet more than 30
times the planet’s diameter, and is by far the largest of
the whole. It is the only one of the series whose theory
has been investigated further than suffices to verify Kep-
ler's law of the periodic times, which is found to hold
good here as well as in the system of Jupiter. It ex-
hibits, like the satellites of Jupiter, periodic variations of
light, which prove its revolution on its axis in the time
of a sidereal revolution about Saturn. The next satellite
in order, proceeding inwards, is tolerably conspicuous;
the three next are very minute, and require pretty pow-
erful telescopes to see them ; while the two interior sat-
ellites, which just skirt the edge of the ring, and move
exactly in its plane, have never been discovered but with
the most powerful telescopes which human art has yet
constructed, and then only under peculiar circumstances.
At the time of the disappearance of the rings (to ordinary
telescopes) they were seen by Sir William Herschel
with his great telescope, projected along the edge of the
ring, and threading like beads the thin fibre of light to
256. What is the number of Saturn's satellites ? How far
distant from the planet is the outermost satellite? Do the sat-
ellites follow Kepler's third law 7 Which of the satellites are
easily seen 7 Do they undergo eclipses?
URANU.S. - 201
which the ring is then reduced. Owing to the obliquity
of the ring, and of the orbits of the satellites to that of
their primary, there are no eclipses of the satellites, the
two interior ones excepted, until near the time when the
ring is seen edgewise. -
257. URANUs is the remotest planet belonging to our
System, and is rarely visible except to the telescope. Al-
though his diameter is more than four times that of the
earth, (35,112 miles,) yet his distance from the sun is
likewise nineteen times as great as the earth’s distance,
or about 1,800,000,000 miles. His revolution around
the Sun occupies nearly 84 years, so that his position in
the heavens for several years in succession is nearly sta-
tionary. His path lies very nearly in the ecliptic, being
inclined to it less than one degree, (46’28%.44.)
The sun himself when seen from Uranus dwindles al-
most to a star, subtending as it does an angle of only
1' 40”; so that the surface of the sun would appear
there 400 times less than it does to us.
This planet was discovered by Sir William Herschel
on the 13th of March 1781. His attention was attracted
to it by the largeness of its disk in the telescope; and
finding that it shifted its place among the stars, he at
first took it for a comet, but soon perceived that its orbit
was not eccentric like the orbits of comets, but nearly
circular like those of the planets. It was then recog-
nized as a new member of the planetary system, a con-
clusion which has been justified by all succeeding ob-
Servations. &
258. Uranus is attended by six satellites. So minute
objects are they, that they can be seen only by powerful
telescopes. Indeed, the existence of more than two is
still considered as somewhat doubtful. These two,
257. Uranus.-State his diameter—distance from the sun–
periodic time—inclination of his orbit. How would the sun
appear from Uranus? State the history of its discovery,
202 - THE PLANETS.
however, offer remarkable, and indeed quite unexpected
and unexampled peculiarities. Contrary to the unbro-
ken analogy of the whole planetary system, the planes
of their orbits are nearly perpendicular to the ecliptic,
being inclined no less than 78° 58' to that plane, and in
these orbits their motions are retrograde; that is, instead
of advancing from west to east around their primary, as
is the case with all the other planets and satellites, they
move in the opposite direction. With this exception, all
the motions of the planets, whether around their own
axes, or around the sun, are from west to east. The sun,
himself, turns on his axis from west to east; all the pri-
mary planets revolve around the sun from west to east ;
their revolutions on their own axes are also in the same
direction ; all the secondaries, with the single exception
above mentioned, move about their primaries from west
to east ; and, finally, such of the secondaries as have
been discovered to have a diurnal revolution, follow the
Same course. Such uniformity among so many motions,
could have resulted only from forces impressed upon
them by the same omnipotent hand; and ſew things in
the creation more distinctly proclaim that God made the
world. -
THE NEW PLANETS, CERES, PALLAS, JUNO, AND VESTA.
259. THE commencement of the present century was
rendered memorable in the annals of astronomy, by the
discovery of four new planets between Mars and Jupiter.
Kepler, from some analogy which he found to subsist
among the distances of the planets from the Sun, had
long before suspected the existence of one at this dis-
tance; and his conjecture was rendered more probable
by the discovery of Uranus, which follows the analogy
258. By how many satellites is Uranus attended ? What is
said of their minuteness? What remarkable peculiarities have
they In what direction are the motions of all the bodies in
the solar system? What does this fact indicate with respect to
their origin 7 • .
NEW PLANETS. 203
of the other planets. So strongly, indeed, were astrono-
mers impressed with the idea that a planet would be
found between Mars and Jupiter, that, in the hope of
discovering it, an association was formed on the conti-
ment of Europe of twenty four observers, who divided
the sky into as many zones, one of which was allotted
to each member of the association. The discovery of
the first of these bodies was however made accidentally
by Piazzi, an astronomer of Palermo, on the first of Jan-
uary, 1801. It was shortly afterwards lost sight of on
account of its proximity to the sun, and was not seen
again until the close of the year, when it was re-discov-
ered in Germany. Piazzi called it Ceres, in honor of
the tutelary goddess of Sicily, and her emblem, the
sickle 9, has been adopted as its appropriate symbol.
The difficulty of finding Ceres induced Dr. Olbers, of
Bremen, to examine with particular care all the small
stars that lie near her path, as seen from the earth ; and
while prosecuting these observations, in March, 1802, he
discovered another similar body, very nearly at the same
distance from the sun, and resembling the former in
many other particulars. The discoverer gave to this se-
cond planet the name of Pallas, choosing for its symbo
the lance 2, the characteristic of Minerva. .
260. The most surprising circumstance connected
with the discovery of Pallas, was the existence of two
planets at nearly the same distance from the sun, and
apparently having a common node. On account of this
singularity, Dr. Olbers was led to conjecture that Ceres
and Pallas are only fragments of a larger planet, which
had formerly circulated at the same distance, and been
shattered by some internal convulsion. The hypothesis
suggested the probability that there might be other frag-
K-
259. Name the New Planets. When were they discovered 7
What had been conjectured previous to their discovery 7 Who
discovered the first? What is its name " How was Pallas dis-
covered '' * . - -
204 TI-IE PLANETS.
ments, whose orbits, however they might differ in ec-
centricity and inclination, might be expected to cross the
ecliptic at a common point, or to have the same node.
Dr. Olbers, therefore, proposed to examine carefully every
month the two opposite parts of the heavens in which
the orbits of Ceres and Pallas intersect one another, with
a view to the discovery of other planets, which might
be sought for in those parts with greater chance of suc-
cess than in a wider zone, embracing the entire limits
of these orbits. Accordingly, in 1804, near one of the
nodes of Ceres and Pallas, a third planet was discovered.
This was called Juno, and the character 3 was adopted
for its symbol, representing the starry Sceptre of the
queen of Olympus. Pursuing the same researches, in
1807, a fourth planet was discovered, to which was
given the name of Vesta, and for its symbol the char-
acter fi was chosen, an altar surmounted with a censer
holding the sacred fire. -
After this historical sketch, it will be sufficient to clas-
sify under a few heads the most interesting particulars
relating to the New Planets.
261. The average distance of these bodies from the
sun is 261,000,000 miles; and it is remarkable that
their orbits are very near together. Taking the distance
of the earth from the sun for unity, their respective dis-
tances are 2.77, 2.77, 2.67, 2.37.
As they are found to be governed, like the other mem-
bers of the solar system, by Kepler’s law, that regulates
the distances and times of revolution, their periodical
times are of course pretty nearly equal, averaging about
44 years.
In respect to the inclimation of their orbits, there is
considerable diversity. The orbit of Westa is inclined
260. How do Ceres and Pallas compare in distance from the
sun and the place of their nodes 7 What hypothesis did Olbers
adopt? State the circumstances connected with the discovery
of Juno and Westa.
MOTIONS OF THE PLANETARY SYSTEM. 205
to the ecliptic only about 79, while that of Pallas is more
than 34°. They all therefore have a higher inclination
than the orbits of the old planets, and of course make
excursions from the ecliptic beyond the limits of the
Zodiac.
The eccentricity of their orbils is also, in general,
greater than that of the old planets; and the eccentrici-
ties of the orbits of Pallas and Juno exceed that of the
orbit of Mercury. r
Their small size constitutes one of their most remark-
able peculiarities. The difficulty of estimating the ap-
parent diameter of bodies at once so very small and so
far off, would lead us to expect different results in the
actual estimates. Accordingly, while Dr. Herschel es-
timates the diameter of Pallas at only 80 miles, Schroe-
ter places it as high as 2,000 miles, or about the size of
the moon. The volume of Westa is estimated at only
one fifteen thousandth part of the earth's, and her surface
is only about equal to that of the kingdom of Spain.
These little bodies are surrounded by almospheres of
great extent, some of which are uncommonly luminous,
and others appear to consist of nebulous matter. These
planets in general shine with a more vivid light than
might be expected from their great distance and dimin-
utive size.
C H A P T E R T X.
MOTIONS OF THE PLANETARY SYSTEM-QUANTITY OF MAT-
TER IN THE SUN AND PLANETS-STABILITY OF THE SO-
L.A.R. SYSTEM.
262. WE have waited until the learner may be sup-
posed to be familiar with the contemplation of the heav-
261. What is the average distance of the New Planets from
the Sun ? How do these orbits lie with respect to each other ?
Are they subject to Kepler's third law 7 What is their average
periodical time ! What is said of the inclination of their or-
bits? Also, of the eccentricity ? What is their size 7
206 THE P. LANETS,
enly bodies, individually, before inviting his attention to
a systematic view of the planets, and of their motions
around the Sun. The time has now arrived for entering
more advantageously upon this subject, than could have
been dome at an earlier period.
There are two methods of arriving at a knowledge of
the motions of the heavenly bodies. One is to begin
with the apparent, and from these to deduce the real
motions; the other is, to begin with considering things
as they really are in nature, and then to inquire why
they appear as they do. The latter of these methods is
by far the more eligible ; it is much easier than the
other, and proceeding from the less difficult to that which
is more difficult, from motions that are very simple to
such as are complicated, it finally puts the learner in pos-
session of the whole machinery of the heavens. We
shall, in the first place, therefore, endeavor to introduce
the learner to an acquaintance with the simplest motions
of the planetary system, and afterwards to conduct him
gradually through such as are more complicated and dif-
ficult.
263. Let us first of all endeavor to acquire an adequate
idea of absolute space, such as existed before the crea-
tion of the world. We shall find it no easy matter to
form a correct notion of infinite space; but let us fix our
attention, for some time, upon extension alone, devoid of
every thing material, without light or life, and without
bounds. Of such a space we could not predicate the
ideas of up or down, east, west, north, or south, but all
reference to our own horizon (which habit is the most
difficult of all to eradicate from the mind) must be com-
pletely set aside. Into such a void we would introduce
the SUN. We would contemplate this body alone, in
the midst of boundless space, and continue to fix the at-
262. What are the two methods of studying the motions of
the heavenly bodies 7 Which method is best ? What motions
Will be first considered 7
MiOTIONS OF THE PLANETARY SYSTEM. 207
tention upon this object, until we had fully settled its
relations to the surrounding void. The ideas of up and
down would now present themselves, but as yet there
would be nothing to suggest any notion of the cardinal
points. We suppose ourselves next to be placed on the
surface of the sun, and the firmament of stars to be
lighted up. The slow revolution of the Sun on his axis,
would be indicated by a corresponding movement of the
stars in the opposite direction; and in a period equal to
more than 27 of our days, the spectator would see the
heavens perform a complete revolution around the sun,
as he now sees them revolve around the earth once in
24 hours. The point of the firmament where no mo-
tion appeared, would indicate the position of one of the
poles, which being called North, the other cardinal points
would be immediately suggested. -
Thus prepared, we may now enter upon the conside-
ration of the planetary motions.
264. Standing on the sun, we see all the planets mo-
ving slowly around the celestial sphere, nearly in the
same great high way, and in the same direction from
west to east. They move, however, with very unequal
velocities. Mercury makes very perceptible progress
from night to night, like the moon revolving about the
earth, his daily progress eastward being one third as
great as that of the moon, since he completes his entire
revolution in about three months. If we watch the
course of this planet from night to might, we observe it,
in its revolution, to cross the ecliptic in two opposite
points of the heavens, and wander about 7° from that
plane at its greatest distance from it. Knowing the po-
sition of the orbit of Mercury with respect to the ecliptic,
we may now, in imagination, represent that orbit by a
263. How can we form a correct idea of absolute space"
What can we predicate of such a space If the sun were pla–
ced in such a void, what new ideas would present themselves'
How should we get a knowledge of the cardinal points
208 THE PLANETS. *
great circle passing through the center of the planet and
the center of the sun, and cutting the plane of the eclip-
tic in two opposite points at an angle of 7°. We may
imagine the intersection of these two great circles, with
the celestial vault to be marked out in plain and palpa-
ble lines on the face of the sky; but we must bear in
mind that these orbits are mere mathematical planes,
having no permanent existence in nature, any more than
the path of an eagle flying through the sky; and if we
conceive of their orbits as marked on the celestial vault,
we must be careful to attach to the representation the
same notion as to a thread or wire, carried round to trace
out the course pursued by a horse in a race-ground.*
The planes of both the ecliptic and the orbit of Mer-
cury, may be conceived of as indefinitely extended to a
great distance until they meet the sphere of the stars;
but the lines which the earth and Mercury describe in
those planes, that is, their orbits, may be conceived of as
comparatively near to the sun. Could we now for a
moment be permitted to imagine that the planes of the
ecliptic, and of the orbit of Mercury, were made of thin
plates of glass, and that the paths of the respective plan-
ets were marked out on their planes in distinct lines, we
should perceive the orbit of the earth to be almost a per-
fect circle, while that of Mercury would appear distinctly
elliptical. But having once made use of a palpable sur-
264. Where must the spectator be placed in order to see the
real motions of the planets? How would the motions of the
several planets appear from this station ? State the particular
movements of Mercury. How may we imagine the ecliptic
and the orbit of Mercury to be represented on the sky How
shall we conceive of the planes of these orbits as distinguished
from the orbit itself?.
* It would seem superflous to caution the reader on so plain a point,
did not the experience of the instructor constantly show that young
learners, from the habit of seeing the celestial motions represented in
orreries and diagrams, almost always fall into the absurd notion of con-
sidering the orbits of the planets as having a distinct and independent
0Xl Støll CC, - -
MOTIONS OF THE PLANETARY SYSTEMI. 209
face and visible lines to aid us in giving position and fig-
ure to the planetary of bits, let us now throw aside these
devices, and hereafter cquceive of these planes and or-
bits as they are in nature, and learn to refer a body to a
mere mathematical plane, and to trace its path in that
plane through absolute space.
265. A clear understanding of the motions of Mercury
and of the relation of its orbit to the plane of the eclip-
tic, will render it easy to understand the same particulars
in regard to each of the other planets. Standing on the
sun we should see each of the planets pursuing a similar
course to that of Mercury, all moving from west to east,
with motions differing from each other chiefly in two re-
spects, namely, in their velocities, and in the distances
to which they ever recede from the ecliptic.
The earth revolves about the sun very much like We-
mus, and to a spectator on the Sun, the motions of these
two planets would exhibit much the same appearances.
We have supposed the observer to select the plane of
the earth’s orbit as his standard of reference, and to see
how each of the other orbits is related to it; but such a
selection of the ecliptic is entirely arbitrary ; the specta-
tor on the sun, who views the motions of the planets as
they actually exist in nature, would make no such dis-
tinction between the different orbits, but merely inquire
how they were mutually related to each other. Taking,
however, the ecliptic as the plane to which all the others
are referred, we do not, as in the case of the other plan-
ets, inquire how its plane is inclined, nor what are its
modes, since it has neither inclination nor node.
266. The attempt to exhibit the motions of the solar
system, and the positions of the planetary orbits by
265. If we stood on the sun, how should we see each of the
planets revolve 7 Why is the earth's orbit selected as the stan-
dard of reference 7 Would the spectator on the sun make any
such distinction ?
18%
210 THE PLANETS.
means of diagrams, or even orreries, is usually a failure.
The student who relies exclusively on such aids as
these, will acquire ideas on this sº oject that are both in-
adequate and erroneous. They f{}ly aid reflection, but
can never supply its place. The impossibility of repre-
Senting things in their just proportions will be evident
when we reflect, that to do this, if, in an orrery, we
make Mercury as large as a cherry, we should require to
represent the sun by a globe six feet in diameter. If we
preserve the same proportions in regard to distance, we
must place Mercury 250 feet, and Uranus 12,500 feet,
or more than two miles from the sun. The mind of the
student of astronomy must, therefore, raise itself from
such imperfect representations of celestial phenomena as
are afforded by artifical mechanism, and, transferring his
contemplations to the celestial regions themselves, he
must conceive of the sun and planets as bodies that bear
an insignificant ratio to the immense spaces in which
they circulate, resembling more a few little birds flying
in the open sky, than they do the crowded machinery of
an Orrery,
267. Having acquired as correct an idea as we are
able of the planetary system, and of the positions of the
orbits with respect to the ecliptic, let us next inquire
into the nature and causes of the apparent motions.
The apparent motions of the planets are exceedingly
unlike the real motions, a fact which is owing to two
causes; first, we view them out of the center of their or-
bits ; secondly, we are ourselves in motion. From the
first cause, the apparent places of the planets are greatly
changed by perspective ; and from the second cause,
266. What is said of the attempt to represent the positions
and motions of the Solar system by diagrams and orreries 7 Give
examples. -
267. Are the apparent motions of the planets like the real
motions? What makes them different? How does each cause
operate? What is the heliocentric place, and what the geo-
centric place of a planet 7
MOTIONS OF THE PLANETARY SYSTEM. 211
we attribute to the planets changes of place which arise
from our own motions of which we are unconscious.
The situation of a heavenly body as seen from the
center of the sun is called its heliocentric place; as seen
from the center of the earth, its geocentric place. The
geocentric motions of the planets must, according to
what has just been said, be far more irregular and com-
plicated than the heliocentric.
268. The apparent motions of the Inferior Planets as
seen from the earth, have been already explained in ar-
ticle 216; from which it appeared, that Mercury and
Venus move backwards and forwards across the sun,
the former never being seen farther than 29° and the
latter seen more than 27° from that luminary. It was
also shown that while passing from the greatest elonga-
tion on one side to the greatest elongation on the other
side, through the superior conjunction, the apparent
motions of these planets are accelerated by the motion
of the earth; but that while moving through the infe-
rior conjunction, at which time their motions are retro-
grade, they are apparently retarded by the earth’s mo-
tion. Let us now see what are the geocentric motions
of the Superior Planets.
269. Let A, B, C, (Fig. 47,) represent the earth in
different positions in its orbit, and M a superior planet as
Mars, and NR. an arc of the concave sphere of the
heavens. First, suppose the planet to remain at rest in
M, and let us see what apparent motions it will receive
from the real motions of the earth. When the earth is
at B, it will see the planet in the heavens at N ; and as
the earth moves successively through, C, D, E, F, the
planet will appear to move through O, P, Q, R. B and
F are the two points of greatest elongation of the earth
from the sun as seen from the planet ; hence between
, 268. Describe the apparent motions of Mercury and Venus
from figure 40. -
212 THE PLANETS.
these two points, while passing through the part of her
orbit most remote from the planet, (when the planet is
seen in superior conjunction,) the earth by her own mo-
Fig. 47.
tion gives an apparent motion to the planet in the order
of the signs—that is, the apparent motion given by the
earth is direct. But in passing from F to B through A,
when the planet is seen in opposition, the apparent mo-
tion given to the planet by the earth's motion is from R.
to N, and is therefore retrograde. As the arc described
by the earth, while the motion is direct, is much greater
than while the motion is retrograde, while the apparent
arc of the heavens described by the planet from N to R.
in the one case, and from R to N in the other, is the
269. Describe the motions of the Superior Planets from fig-
ure 47. The planet remaining at rest, what apparent motions
will the motion of the earth impart to it, when in opposition ?
What when in superior conjunction ?

MOTIONS OF THE PLANETARY systEM. 213
same in both cases, the retrograde motion is much swifter
than the direct, being performed in much less time.
270. But the superior planet is not in fact at rest, as
we have supposed, but is all the while moving east-
ward, though with a slower motion than the earth. In-
deed, with respect to the remotest planets as Saturn and
Uranus, the forward motion is so exceedingly slow that
the above representation is nearly true for a single year.
Still, the effect of the real motions of all the superior
planets eastward, is to increase the direct apparent mo-
tion communicated by the earth and to diminish the ret-
rograde motion. - .
If Mars stood still while the earth went round the
sun, then a second opposition as at A, would occur at
the end of one year from the first ; but while the earth
is performing this circuit, Mars is also moving the same
way, more than half as fast, so that when the earth re-
turns to A, the planet has already performed more than
half the same circuit, and will have completed its whole
revolution before the earth comes up with it. Indeed,
Mars, after having been once seen in opposition, does not
come into opposition again until after two years and
fifty days. And since the planet is then comparatively
very near to us, and appears very large and bright, rising
unexpectedly about the time the sun sets, he surprises
the world as though it were some new celestial body.
But on account of the slow progress of Saturn and Ura-
nus, we find after having performed one circuit around
the sun, that they are but little advanced beyond where
we left them at the last opposition. The time between
one opposition of Saturn and another is only a year and
thirteen days.
It appears, therefore that the superior planets steadily
pursue their course around the sun, but that their appar-
270. How does the real motion of the planet modify the fore-
going results? How in respect to the remotest planets, as Ura-
nus, and how in respect to a nearer planet as Mars? How
often is Mars in opposition ? What is his appearance then?
214 THE PLANETS.
ent retrograde motion when in opposition, is occasioned
by our passing by them with a swifter motion, like the
apparent backward motion of a vessel when we over-
take it and pass rapidly by it in a steamboat.
QUANTITY OF MATTER IN THE SUN AND PLANETs.
271. It would seem at first view very improbable that
an inhabitant of this earth would be able to weigh the
sun and planets, and estimate the exact quantity of mat-
ter which they severally contain. But the principles of
Universal Gravitation conduct us to this result, by a
process remarkable for its simplicity. By comparing the
relations of a few elements that are known to us, we
ascend to the knowledge of such as appeared to be be-
yond the pale of human investigation. We learn the
quantity of matter in a body from the force of gravity
it exerts, and this force is estimated by its effects.
Hence worlds are weighed with as much ease as a peb-
ble or an article of merchandise. -
272. The sun contains about 355,000 times as much
matter as the earth, and 800 times as much matter as all
the planets. This however, is owing rather to its great
size than to the specific gravity of its materials, for the
density of the sun is only one fourth as great as that of
the earth. The earth is nearly 54 times as heavy as
water, but the sun is only a little heavier than that fluid.
The planets near the Sun are in general more dense than
*—
271. What is said of the apparent difficulty of weighing the
sun and planets? What great principles lead us to this re-
sult? How do we learn the quantity of matter in the bodies
of the solar system 7
272. How much more matter does the sun contain than the
earth? How much more than all the planets? What is the
density of the sun compared with that of the earth? How
much heavier is the earth than water" How much heavier is
the sun than water 7 Which of the planets have the greatest
density ? How heavy is Mercury? How heavy is Saturn ?
STABILITY OF THE SOLAR SYSTEM. 215
those more remote; Mercury being heavier than lead,
while Saturn is as light as a cork. The decrease in
density however, is not entirely regular, since Venus is
a little lighter than the earth, while Jupiter is heavier
than Mars, and Uranus than Saturn.
STABILITY OF TEIE SOLAR SYSTEM.
273. The perturbations occasioned by the motions of
the planets by their action on each other are very nu-
merous, since every body in the system exerts an attrac-
tion on every other, in conformity with the law of Uni-
versal Gravitation. Venus and Mars, approaching as
they do at times comparatively near to the earth, sen-
sibly disturb its motions, and the satellites of the re-
moter planets greatly disturb each other’s movements.
274. The derangement which the planets produce in
the motion of one of their number will be very small in
the course of one revolution; but this gives us no secu-
rity that the derangement may not become very large
in the course of many revolutions. The cause act per-
petually, and it has the whole extent of time to work in.
Is it not easily conceivable then, that in the lapse of ages,
the derangements of the motions of the planets may
accumulate, the orbits may change their form, and their
mutual distances may be much increased or diminished 2
Is it not possible that these changes may go on without
-w
273. What is said of the perturbations occasioned by the ac-
tion of the planets on each other ? Which planets in particu-
lar, disturb the motions of the earth? -
274. How is the derangement produced by the planets upon
any one of them, in a single revolution ? What may be the
ultimate effect of these disturbing forces? What would be
the consequence of increasing the eccentricity of the earth's
orbit—or of bringing the moon nearer the earth—or of alter-
ing the positions of the planets with respect to that of the
earth? What changes are actually going on in the motions of
the heavenly bodies? -
216 - THE PLANETS.
limit, and end in the complete subversion and ruin of the
system If, for instance, the result of this mutual
gravitation should be to increase considerably the eccen-
tricity of the earth's orbit, or to make the moon approach
continually nearer and nearer to the earth at every revo-
lution, it is easy to see that in the One case, our year
would change its character, producing a far greater ir-
regularity in the distribution of the solar heat : in the
other, our satellite must fall to the earth, occasioning a
dreadful catastrophe. If the positions of the planetary
orbits with respect to that of the earth, were to change
much, the planets might Sometimes come very near us,
and thus increase the effect of their attraction beyond cal-
culable limits. Under such circumstances we might have
years of unequal length, and seasons of capricious tem-
perature; planets and moons of portentous size and as-
pect glaring and disappearing at uncertain intervals; tides
like deluges sweeping over whole continents; and, per-
haps, the collision of two of the planets, and the conse-
quent destruction of all organization on both of them.
The fact really is, that changes are taking place in the
motions of the heavenly bodies, which have gone on
progressively from the first dawn of science. The ec-
centricity of the earth's orbit has been diminishing from
the earliest observations to our times. The moon has
been moving quicker from the time of the first recorded
eclipses, and is now in advance by about four times her
own breadth, of what her own place would have been if
it had not been affected by this acceleration. The ob-
liquity of the ecliptic also, is in a state of diminution,
and is now about two fifths of a degree less than it was
in the time of Aristotle. (Whewell, in the Bridgewater
Treatises, p. 128.)
275. But amid so many seeming causes of irregular-
ity, and ruin, it is worthy of grateful notice, that effec-
tual provision is made for the stability of the solar sys-
tem. The full confirmation of this fact, is among the
gränd results of Physical Astronomy. Newton did not
undertake to demonstrate either the stability or insta-
STABILITY OF THE SOLAR SYSTEM. 217
bility of the system. The decision of this point re-
Quired a great number of preparatory steps and simplifi-
cations, and such progress in the invention and improve-
ment of mathematical methods, as occupied the best
mathematicians of Europe for the greater part of the
last century. Towards the end of that time, it was
shown by La Grange and La Place, that the arrange-
ments of the solar system are stable ; that, in the
long run, the orbits and motions remain unchanged;
and that the changes in the orbits, which take place in
shorter periods, never transgress certain very moderate
limits. Each orbit undergoes deviations on this side
and on that side of its average state ; but these devia-
tions are never very great, and it finally recovers from
them, so that the average is preserved. The planets
produce perpetual perturbations in each other's motions,
but these perturbations are not indefinitely progressive,
but periodical, reaching a maximum value and then di-
minishing. The periods which this restoration requires
are for the most part enormous, not less than thou-
Sands, and in some instances millions of years. Indeed
some of these apparent derangements, have been going
on in the same direction from the creation of the world.
But the restoration is in the sequel as complete as the
derangement; and in the mean time the disturbance
never attains a sufficient amount seriously to affect the
stability of the system. (Whewell, in the Bridgewater
Treatises, p. 128.) I have succeeded in demonstrating
(says La Place) that, whatever be the masses of the plan-
ets, in consequence of the fact that they all move in the
same direction, in orbits of small eccentricity, and but
slightly inclined to each other, their secular irregulari-
ties are periodical and included within narrow limits;
so that the planetary system will only oscillate about a
275. Is the system stable? Did Newton prove this? Who
fully established this point? Have all the inequalities of the
planetary motions a fixed period 1 How long are some of these
periods? 19
218 COMETS.
mean state, and wiłł never deviate from it except by a
very small quantity. The ellipses of the planets have
been and always will be nearly circular. The ecliptic
will never coincide with the equator; and the entire ex-
tent of the variation in its inclination, cannot exceed
three degrees.
276. To these observations of La Place, Professor
Whewell adds the following on the importance, to the
stability of the solar system, of the fact that those plan-
ets which have great masses have orbits of small eccen-
tricity. The planets Mercury and Mars, which have
much the largest eccentricity among the old planets, are
those of which the masses are much the smallest. The
mass of Jupiter is more than two thousand times that of
either of these planets. If the orbit of Jupiter were as
eccentric as that of Mercury, all the security for the sta-
bility of the system, which analysis has yet pointed out,
would disappear. The earth and the smaller planets
might, by the near approach of Jupiter at his perihelion,
change their nearly circular orbits into very long ellipses,
and thus might fall into the sun, or fly off into remote
space. It is further remarkable that in the newly discov-
ered planets, of which the orbits are still more eccentric
than that of Mercury, the masses are still smaller, so that
the same provision is established in this case also.
C H. A. P. T. E. R. X.
OF COMETS.
277. A CoMET, when perfectly formed, consists of
three parts, the Nucleus, the Envelope, and the Tail.
The Nucleus, or body of the comet, is generally distin-
guished by its forming a bright point in the center of
the head, conveying the idea of a solid, or at least of a
276. What planets have orbits of small eccentricity How
does this fact contribute to the stability of the system 7
COMETS. 219
very dense portion of matter. Though it is usually ex-
ceedingly small when compared with the other parts of
the cornet, yet it sometimes subtends an angle capable
of being measured by the telescope. The Envelope,
(sometimes called the coma) is a dense nebulous cover.
ing, which frequently renders the edge of the nucleus
So indistinct, that it is eXtremely difficult to ascertain its
diameter with any degree of precision. Many comets
have no nucleus, but present only a nebulous mass ex-
tremely attenuated on the confines, but gradually in-
creasing in density towards the center. Indeed there is
a regular gradation of comets, from such as are com-
posed merely of a gaseous or vapory medium, to those
which have a well defined nucleus. In some instances
On record, astronomers have detected with their tele-
Scopes small stars through the densest part of a comet.
The Tail is regarded as an expansion or prolongation
of the coma ; and, presenting as it sometimes does, a
train of appalling magnitude, and of a pale, disastrous
light, it confers on this class of bodies, their peculiar
celebrity.
Fig 48.
These several parts are exhibited in figure 48, which
represents the appearance of the comet of 1680.
277. Of what three parts does a comet consist? Describe
each.

220 COMETS.
278. The number of comets belonging to the Solar
system, is probably very great. , Many, no doubt, escape
observation by being above the horizon in the day time.
Seneca mentions, that during a total eclipse of the Sun,
which happened 60 years before the Christian era, a
large and splendid comet suddenly made its appearance,
being very near the sun. The elements of at least 130
have been computed, and arranged in a table for future
comparison. Of these six are particularly remarkable,
viz. the comets, of 1680, 1770, and 1811; and those
which bear the names of Halley, Biela and Encke.
. The comet of 1680, was remarkable not only for its as-
tonishing size and splendor, and its near approach to the
sun, but is celebrated for having submitted itself to the
observations of Sir Isaac Newton, and for having en-
joyed the signal honor of being the first comet whose
elements were determined on the sure basis of math-
ematics. The comet of 1770, is memorable for the
changes its orbit has undergone by the action of Jupiter,
as will be more particularly related in the sequel. The
cornet of 1811 was the most remarkable in its appear-
ance of all that have been seen in the present century.
It had scarcely any perceptible nucleus, but its train
Fig. 40.
was very long and broad, as is represented in figure 49.
Halley's comet (the same which re-appeared in 1835) is

COMETS, 221
distinguished as that whose return was first successfully
predicted, and whose orbit is best determined; and
Biela’s and Encke's comets are well known for their
short periods of revolution, which subject them fre-
quently to the view of astronomers.
279. In magnitude and brightness comets exhibit a
great diversity. History informs us of comets so bright
as to be distinctly visible in the day time, even at noon
and in the brightest sunshine. Such was the comet
seen at Rome a little before the assassination of Julius
Caesar. The comet of 1680 covered an arc of the heav-
ens of 97°, and its length was estimated at 123,000,000
miles. That of 1811, had a nucleus of only 428 miles
in diameter, but a tail 132,000,000 miles long. Had it
been coiled around the earth like a serpent, it would
have reached round more that 5,000 times. Other com-
ets are of exceedingly small dimensions, the nucleus
being estimated at only 25 miles; and some which are
destitute of any perceptible nucleus, appear to the largest
telescopes, even when nearest to us, only as a small
speck of fog, or as a tuft of down. The majority of
comets can be seen only by the aid of the telescope.
The same comet, indeed, has often very different as-
pects, at its different returns. Halley's comet in 1305
was described by the historians of that age, as the comet
of terrific magnitude; (cometa horrendaº magnitudinis ;)
in 1456 its tail reached from the horizon to the zenith,
and inspired such terror, that by a decree of the Pope of
Rome, public prayers were offered up at noon-day in all
the Catholic churches to deprecate the wrath of heaven,
while in 1682, its tail was only 30° in length, and in 1759
278. What is said of the number of comets? How many
have been arranged in a table 7 Specify the six that are most
remarkable. State particulars respecting each.
279. What is said of the magnitude and brightness of com-
ets? What was the length of the comet of 1680? Ditto of
1811 ? Has the same comet different aspects at different
returns? Example in Huº. comet.
222 COMETS.
it was visible only to the telescope, until after it had pas-
sed the perihelion. At its recent return in 1835, the
greatest length of the tail was about 12°. These changes
in the appearances of the same comet, are partly owing
to the different positions of the earth with respect to
them, being sometimes much nearer to them when they
cross its tract than at others; also one spectator so situ-
ated as to see the coma at a higher angle of elevation or
in a purer sky than another, will see the train longer than
it appears to another less favorably situated; but the
extent of the changes are such as indicate also a real
change in magnitude and brightness.
280. The periods of comets in their revolutions
around the Sun, are equally various. Encke's comet,
which has the shortest known period, completes its rev-
olution in 34 years, or more accurately, in 1208 days;
while that of 1811 is estimated to have a period of 3383
years.
281. The distances to which different comets recede
from the Sun, are also very various. While Encke's
comet performs its entire revolution within the orbit of
Jupiter, Halley’s comet recedes from the sun to twice
the distance of Uranus, or nearly 3600,000,000 miles.
Some comets, indeed, are thought to go to a much
greater distance from the sun than this, while some even
are supposed to pass into parabolic or hyperbolic orbits,
and never to return.
282. Comets shine by reflecting the light of the sun.
In one or two instances they have exhibited distinct
phases, although the nebulous matter with which the
nucleus is surrounded, would commonly prevent such
280. How are the periods of comets' What is that of
Encke's comet, and that of the comet of 1811 ?
281. How are the distances of comets from the Sun ? Com-
pare Encke's and Halley's, Do comets always return to the sun ?
COMETS. 223
phases from being distinctly visible, even when they
would otherwise be apparent. Moreover, certain quali-
ties of polarized light enable the optician to decide
whether the light of a given body is direct or reflected;
and M. Arago, of Paris, by experiments of this kind on
the light of the comet of 1819, ascertained it to be re-
flected light.
283. The tail of a comet usually increases very much
as it approaches the sun ; and it frequently does not reach
its maximum until after the perihelion passage. In re-
ceding from the sun, the tail again contracts, and nearly
or quite disappears before the body of the comet is en-
tirely out of sight. The tail is frequently divided into
two portions, the central parts, in the direction of the
axis, being less bright than the marginal parts. In
1744, a comet appeared which had six tails, spread out
like a ſan.
The tails of comets extend in a direct line from the
sun, although more or less curved, like a long quill or
feather, being convex on the side next to the direction
in which they are moving a figure which may result
from the less velocity of the portions most remote from
the sun. Expansions of the Envelope have also been
at times observed on the side next the sun, but these
seldom attain any considerable length.
284. The quantity of matter in comets is exceedingly
small. Their tails consist of matter of such tenuity that
the smallest stars are visible through them. They can
only be regarded as great masses of thin vapor, suscepti-
ble of being penetrated through their whole substance by
282. Do comets shine by direct or by reflected light? Do
they exhibit phases? How is it known that their light is re-
flected and not direct light 7
283. How are the tails of comets affected by being near the
sun ? How many tails have some comets? In what direction
is the tail in respect to the Sun ?
224 COMETS.
the sunbeams, and reflecting them alike from their inte-
rior parts and from their surfaces. It appears, perhaps,
incredible that so thin a substance should be visible by
reflected light, and some astronomers have held that the
matter of comets is self-luminous; but it requires but
very little light to render an object visible in the night,
and a light vapor may be visible when illuminated
throughout an immense stratum, which could not be
seen if spread over the face of the sky like a thin cloud,
From the extremely small quantity of matter of these
bodies, compared with the vast spaces they cover, New-
ton calculated that if all the matter constituting the
largest tail of a comet, were to be compressed to the
same density with atmospheric air, it would occupy no
more than a cubic inch. This is incredible, but still
the highest clouds that float in our atmosphere, must be
looked upon as dense and massive bodies, compared with
the filmy and all but spiritual texture of a comet. -
285. The small quantity of matter in comets is proved
by the fact, that they have sometimes passed very near
to some of the planets without disturbing their motions
in any appreciable degree. Thus the comet of 1770, in
its way to the sun, got entangled among the Satellites of
Jupiter, and remained near them four months, yet it did
not perceptibly change their motions. The same comet
also came very near the earth ; so near, that, had its
mass been equal to that of the earth, it would have
caused the earth to revolve in an orbit so much larger
than at present, as to have increased the length of the
year, 2h. 47m. Yet it produced no sensible effect on
the length of the year, and therefore its mass, as is shown
by La Place, could not have exceeded a ºn m of that of
the earth, and might have been less than this to any ex-
284. How is the quantity of matter in comets 7 Of what do
the tails consist? Can a substance so thin shine by reflected
light? What opinion had Newton of the extreme tenuity of
the material of comets' tails?
COMETS. 225
tent. It may indeed be asked, what proof we have that
comets have any matter, and are not mere reflexions of
light. The answer is, that, although they are not able
by their own force of attraction to disturb the motions
of the planets, yet they are themselves exceedingly dis-
turbed by the action of the planets, and in exact con-
formity with the laws of universal gravitation. A deli-
cate compass may be greatly agitated by the vicinity of
a mass of iron, while the iron is not sensibly affected b
the attraction of the needle. * .
286. By approaching very near to a large planet, a
comet may have its orbit entirely changed. This fact
is strikingly exemplified in the history of the comet of
1770. At its appearance in 1770, its orbit was found to
be an ellipse, requiring for a complete revolution only
53 years; and the wonder was, that it had not been seen
before, since it was a very large and bright comet. AS-
tronomers suspected that its path had been changed, and
that it had been recently compelled to move in this short
ellipse, by the disturbing force of Jupiter and his satel-
lites. The French Institute, therefore, offered a high
prize for the most complete investigation of the elements
of this comet, taking into account any circumstances
which could possibly have produced an alteration in its
course. By tracing back the movements of this comet
for some years previous to 1770, it was found that, at
the beginning of 1767, it had entered considerably within
the sphere of Jupiter’s attraction. Calculating the amount
of this attraction from the known proximity of the two
bodies, it was found what must have been its orbit pre-
vious to the time when it became subject to the disturb-
ing action of Jupiter. The result showed that it then
285. How is the small quantity of matter in comets proved?
How was this indicated by the comet of 1770 ? What did its
quantity of matter not exceed as compared with the earth's 7
May we not infer that they have no matter 7
226 COMETS.
moved in an ellipse of greater extent, having a period of
50 years, and having its perihelion instead of its aphelion
near Jupiter. It was therefore evident why, as long as
it continued to circulate in an orbit so far from the cen-
ter of the system, it was never visible from the earth.
In January 1767, Jupiter and the comet happened to be
very near one another, and as both were moving in the
same direction, and nearly in the same plane, they re-
mained in the neighborhood of each other for several
months, the planet being between the comet and the
sun. The consequence was, that the comet’s orbit was
changed into a smaller ellipse, in which its revolution
was accomplished in 54 years. But as it was approach-
ing the sun in 1779, it happened again to fall in with
Jupiter. It was in the month of June, that the attrac-
tion of the planet began to have a sensible effect; and
it was not until the month of October following, that
they were finally separated.
At the time of their nearest approach, in August, Ju-
piter was distant from the comet only + r of its distance
from the Sun, and exerted an attraction upon it 225
times greater than that of the sun. By reason of this
powerful attraction, Jupiter being farther from the Sun
than the comet, the latter was drawn out into a new Or-
bit, which even at its perihelion came no nearer to the
Sun than the planet Ceres. In this third orbit, the comet
requires about 20 years to accomplish its revolution ;
and being at so great a distance from the earth, it is in-
visible, and will forever remain so, unless, in the course
of ages, it may undergo new perturbations, and move
again in Some Smaller orbit as before.
286. How may a comet have its orbit changed 7 How was
the orbit of the comet of 1770 changed? How was this fact as-
certained ' What action did Jupiter exert upon it in 1767, and
again in 1779? How far was Jupiter from the comet at the
time of their nearest approach'ſ How many years does it now
require to perform its revolution ?
ORBITS AND MOTIONS OF COMETS. 227 .
ORBITS AND MOTIONS OF COMETS.
287. The planets, as we have seen, (with the excep-
tion of the four new ones, which seem to be an interme-
diate class of bodies between planets and comets,) move
in orbits which are nearly circular, and all very near to
the plane of the ecliptic, and all move in the same direc-
tion from west to east. But the orbits of comets are far
more eccentric than those of the planets; they are in-
clined to the ecliptic at various angles, being sometimes
even nearly perpendicular to it; and the motions of
comets are sometimes retrograde.
288. The Elements of a comet are five, viz. (1) The
perihelion distance; (2) longitude of the perihelion; (3)
longitude of the mode; (4) inclimation of the orbit; (5)
time of the perihelion passage.
The investigation of these elements is a problem ex-
tremely intricate, requiring for its solution, a skillful and
laborious application of the most refined analysis. This
difficulty arises from several circumstances peculiar to
comets. In the first place, from the elongated form of
the orbits which these bodies describe, it is during only
a very small portion of their course, that they are visible
from the earth, and the observations made in that short.
period, cannot afterwards be verified on more convenient
occasions; whereas in the case of the planets, whose or-
bits are nearly circular, and whose movements may be
followed uninterruptedly throughout a complete revolu-
tion, no such impediments to the determination of their
orbits occur. In the second place, there are many com-
ets which move in a direction opposite to the order of
the signs in the zodiac, and sometimes nearly perpen-
dicular to the plane of the ecliptic ; so that their appa-
287. How do the orbits of comets differ from those of planets?
288. What particulars are called the elements of a comet?
What is said of the difficulty of determining these elements?
Specify the several reasons of this difficulty.
228 COMETS.
rent course through the heavens is rendered extremely
complicated, on account of the contrary motion of the
earth. In the third place, as there may be a multitude
of elliptic orbits, whose perihelion distances are equal,
(see p. 100,) it is obvious that, in the case of very ec-
centric orbits, the slightest change in the position of the
curve near the vertex, where alone the comet can be ob-
served, must occasion a very sensible difference in the
length of the orbit; and therefore, though a small error
produces no perceptible discrepancy between the ob-
served and the calculated course, while the comet re-
mains visible from the earth, its effect when diffused
over the whole extent of the orbit, may acquire a most
material or even a fatal importance.
289. On account of these circumstances, it is found
exceedingly difficult to lay down the path which a comet
actually follows through the whole system, and least of
all, possible to ascertain with accuracy, the length of the
major axis of the ellipse, and consequently the periodical
revolution.* An error of only a few seconds may cause
a difference of many hundred years. In this manner,
though Bessel determined the revolution of the comet of
1769 to be 2089 years, it was ſound that an error of no
more than 5’ in observation, would alter the period either
to 2678 years, or to 1692. Some astronomers, in calcula-
ting the orbit of the great comet of 1680, have found the
length of its greater axis 426 times the earth’s distance
from the sun, and consequently its period 8792 years;
whilst others estimate the greater axis 430 times the
comet's distance, which alters the period to 8916 years.
289. Is it easy to ascertain the major axis of a comet's orbit,
and its periodic time? What difference would an error of a few
seconds occasion ? Give examples of this.
* For when we know the length of the major axis, we can find the
periodic time by Kepler's law, which applies as well to comets as to
planets.
MOTIONS AND ORBITS OF COMETS. 229.
Newton and Halley, however, judged that this comet
accomplished its revolution in only 570 years.
290. The appearance of the same comet at different
periods of its return are so various, that we can never
pronounce a given comet to be the same with one that
has appeared before, from any peculiarities in its physi-
cal aspect. The identity of a comet with one already
on record, is determined by the identity of the elements.
It was by this means that Halley first established the
identity of the comet which bears his name, with one
that had appeared at several preceding ages of the world,
of which so many particulars were left on record, as to
enable him to calculate the elements at each period.
These were as in the following table.

Time oſ appear. Inclin. of the orbit.jLon. of Node:[Lon.of Per Per Dist. Course.
1456 17O 56 48° 30' 3019 00 0.58. Retrograde
1531 17 56 49 25 || 301 39 0.57 & &
1607 - 17 02 50 21 || 302 16 || 0.58. & C
1682 17 42 50 48 301 36 || 0.58 & C
On comparing these elements, no doubt could be en-
tertained that they belonged to one and the same body;
and since the interval between the successive returns
was seen to be 75 or 76 years, Halley ventured to pre-
dict that it would again return in 1758. Accordingly,
the astronomers who lived at that period, looked for its
return with the greatest interest. It was found, how-
ever, that on its way towards the sun it would pass very
near to Jupiter and Saturn, and by their action on it, it
would be retarded for a long time. Clairaut, a distin-
guished French mathematician, undertook the laborious
task of estimating the exact amount of this retardation,
and found it to be no less than 618 days, namely, 100
290, Can we identify a comet with one that has been seen
before, by its appearance 7 How is this identity determined 7.
How was Halley’s comet proved to be the same with one that
had appeared before ? How was its return predicted 7 What
causes alter the periods of its return ?
20
230 COMETS.
days by the action of Jupiter, and 518 days by that of
Saturn. This would delay its appearance until early in
the year 1759, and Clairaut fixed its arrival at the peri-
helion within a month of April 13th. It came to the
perihelion on the 12th of March.
291. The return of Halley's comet in 1835, was
looked for with no less interest than in 1759. Several
of the most accurate mathematicians of that age had cal-
culated its elements with inconceivable labor. Their
zeal was rewarded by the appearance of the expected
visitant at the time and place assigned; it travelled the
northern sky presenting the very appearances, in most
respects, that had been anticipated; and came to its pe-
rihelion on the 16th of November, within two days of
the time predicted by Pontecoulant, a French mathe-
matician who had, it appeared, made the most success-
ful calculation.* On its previous return, it was deemed
an extraordinary achievement to have brought the pre-
diction within a month of the actual time. -
Many circumstances conspired to render this return of
Halley’s comet an astronomical event of transcendent
interest. Of all the celestial bodies, its history was the
most remarkable; it afforded most triumphant evidence
of the truth of the doctrine of universal gravitation, and
of course of the received laws of astronomy; and it in-
spired new confidence in the power of that instrument,
(the Calculus,) by means of which its elements had been
investigated.
292. Encke's comet, by its frequent returns, (once in
33 years,) affords peculiar facilities for ascertaining the
291. How was the return of Halley's comet in 1835 regarded
by astronomers ? What circumstances conspired to produce
this feeling?
.* See Professor Loomis's Observations on Halley's Comet, Amer.
Jour. Science, 30, 209. .'
oRBITS AND MOTIONS OF COMETs. 231
Haws of its revolution ; and it has kept the appointments
made for it with great exactness. On its late return
(1839) it exhibited to the telescope a globular mass of
nebulous matter, resembling fog, and moved towards its
perihelion with great rapidity. -
But what has made Encke's comet particularly fa-
mous, is its having first revealed to us the existence of a
Resisting Medium in the planetary spaces. It has long
been a question, whether the earth and planets revolve
in a perfect void, or whether a fluid of extreme rarity
may not be diffused through space. A perfect vacuum
was deemed most probable, because no such effects on
the motions of the planets could be detected as indicated
that they encountered a resisting medium. But a feather
or a lock of cotton propelled with great velocity, might
render obvious the resistance of a medium which would
not be perceptible in the motions of a cannon ball. Ac-
cordingly, Encke's comet is thought to have plainly suf-
fered a retardation from encountering a resisting medium
in the planetary regions. The effect of this resistance,
from the first discovery of the comet to the present time,
has been to diminish the time of its revolution about
two days. Such a resistance by destroying a part of the
projectile force, would cause the comet to approach
nearer to the sun, and thus to have its periodic time
shortened. The ultimate effect of this cause will be to
bring the comet nearer to the sun at every revolution,
until it finally falls into that luminary, although many
thousand years will be required to produce this catas-
trophe. It is conceivable, indeed, that the effects of
such a resistance may be counteracted by the attraction
of one or more of the planets, near which it may pass in
its successive returns to the Sun. -
292. Are the elements of Encke's comet calculated with ex-
actness? What was its appearance in 1839'. What has made
it peculiarly famous ' Why should it be so favorable for detec-
ting a resisting medium ? What has been its effect on the mo-
tions of the comet? What will be its ultimate effect ''
232 COMETs.
293. It is peculiarly interesting to see a portion of
matter, of a tenuity exceeding the thinnest fog, pursuing
its path in space, in obedience to the same laws as those
which regulate such large and heavy bodies as Jupiter .
or Saturn. In a perfect void, a speck of fog if propelled
by a suitable projectile force, would revolve around the
sun, and hold on its way through the widest orbit, with
as sure and steady a pace as the heaviest and largest
bodies in the system. .
294. Of the physical nature of comets, little is under-
stood. It is usual to account for the variations which
their tails undergo, by referring them to the agencies of
heat and cold. The intense heat to which they are
subject in approaching so near the sun as some of them
do, is alleged as a sufficient reason for the great expan-
sion of thin nebulous atmospheres forming their tails;
and the inconceivable cold to which they are subject in
receding to such a distance from the sun, is supposed to
account for the condensation of the same matter until it
returns to its original dimensions. Thus the great comet
of 1680, at its perihelion, approached 166 times nearer
the sun than the earth, being only 130,000 miles from
the surface of the sun. The heat which it must have
received, was estimated to be equal to 28,000 times that
which the earth receives in the same time, and 2000
times hotter than red hot iron. This temperature would
be sufficient to volatilize the most obdurate substances,
and to expand the vapor to vast dimensions; and the op-
posite effects of the extreme cold to which it would be
293. Does the extreme tenuity of this body prevent its mov-
ing in obedience to the laws that regulate the motions of the
largest bodies in the system 7
294. Is the physical nature of comets well understood How
are the variations in the lengths of their tails accounted for 7
How near did the comet of 1680 approach to the sun ? What
heat did it acquire? Does this account for the direction of the
tail? How is that accounted for by some writers? .
ORBITS AND MOTIONS OF COMETS. 233
subject in the regions remote from the sun, would be ad-
equate to condense it into its former volume. -
This explanation, however, does not account for the
direction of the tail, extending as it usually does, only
in a line opposite to the sun. Some writers therefore,
as Delambre, suppose that the nebulous matter of the
comet after being expanded to such a volume, that the
particles are no longer attracted to the nucleus unless by
the slightest conceivable force, are carried off in a direc-
tion from the sun, by the impulse of the solar rays them-
selves. But to assign such a power of communicating
motion to the sun's rays while they have never been
proved to have any momentum, is unphilosophical ; and
we are compelled to place the phenomena of comets'
tails among the points of astronomy yet to be explained.
295. Since those comets which have their perihelion
very near the sun, like the comet of 1680, cross the or-
bits of all the planets, the possibility that one of them.
amay strike the earth, has frequently been suggested.
Still it may quiet our apprehensions on this subject, to
reflect on the vast extent of the planetary spaces, in
which these bodies are not crowded together as we see
them erroneously represented in orreries and diagrams,
but are sparsely scattered at immense distances from
each other. They are like insects flying in the expanse
of heaven. If a comet's tail lay with its axis in the
plane of the ecliptic when it was near the sun, we can
imagine that the tail might sweep over the earth ; but
the tail may be situated at any angle with the ecliptic
as well as in the same plane with it, and the chances
295. What is said respecting the possibility of a comet's stri-
king the earth? What considerations may quiet our apprehen-
sions? How might the case be if the tail lay in the plane of the
ecliptic 1 Is it probable that a comet will cross the ecliptic pre-
cisely at the place of the earth's path? Have comets actually
approached near to the earth? What would be the conse.
quences were a comet to strike the earth?
234. : COMETS. v
that it will not be in the same plane, are almost infinite.
It is also extremely improbable that a comet will cross
the plane of the ecliptic precisely at the earth’s path in
that plane, since it may as probably cross it at any other
point, nearer or more remote from the sun. Still some
comets have occasionally approached near to the earth.
Thus Biela's comet in returning to the sun in 1832,
crossed the ecliptic very near to the earth's track, and
had the earth been then at that point of its orbit, it might
have passed through a portion of the nebulous atmos-
phere of the comet. The earth was within a month of
reaching that point. This might at first view seem to
involve some hazard; yet we must consider that a
month short, implied a distance of nearly 50,000,000
miles. La Place has assigned the consequences that
would ensue in case of a direct collision between the
earth and a comet; but terrible as he has represented
them on the supposition that the nucleus of the comet
is a solid body, yet considering a comet (as most of them
doubtless are) as a mass of exceedingly light nebulous
matter, it is not probable, even were the earth to make
its way directly through a comet, that a particle of the
comet would reach the earth. The portions encountered
by the earth, would be arrested by the atmosphere, and
probably inflamed ; and they would perhaps exhibit, on
a more magnificent scale than was ever before observed,
the phenomena of shooting stars, or meteoric showers.
PART III.—OF THE FIXED STARS AND THE SYS-
TEM OF THE WORLD.
C H A P T E R. I.
OF THE FIXED STARS–constELLATIONs.
296. THE FIXED STARs are so called, because, to
common observation, they always maintain the same
situations with respect to one another.
The stars are classed by their apparent magnitudes.
The whole number of magnitudes recorded are sixteen,
of which the first six only are visible to the naked eye;
the rest are telescopic stars. These magnitudes are not
determined by any very definite scale, but are merely
ranked according to their relative degrees of brightness,
and this is left in a great measure to the decision of the
eye alone. The brightest stars to the number of 15 or
20, are considered as stars of the first magnitude; the 50
or 60 next brightest, of the second magnitude; the next
200 of the third magnitude ; and thus the number of
each class increases rapidly as we descend the scale, so
that no less than fifteen or twenty thousand are included
within the first seven magnitudes.
297. The stars have been grouped in Constellations
from the most remote antiquity; a few, as Orion, Bootes,
and Ursa Major, are mentioned in the most ancient wri-
tings under the same names as they bear at present.
The names of the constellations are sometimes founded
296. Fived Stars.—Why so called How classed ? Into
how many magnitudes are they divided ? How many are there
of each magnitude '' -
236 FIXED STARS,
on a supposed resemblance to the objects to which the
names belong; as the Swan and the Scorpion were evi-
dently so denominated from their likeness to those ani-
mals; but in most cases it is impossible for us to find
any reason for designating a constellation by the figure
of the animal or the hero which is employed to repre-
sent it. These representations were probably once
blended with the fables of pagan mythology. The
same figures, absurd as they appear, are still retained for
the convenience of reference; since it is easy to find
any particular star, by specifying the part of the figure
to which it belongs, as, when we say a star is in the neck
of Taurus, in the knee of Hercules, or in the tail of the
Great Bear. This method furnishes a general clue to
its position; but the stars belonging to any constellation.
are distinguished according to their apparent magnitudes
as follows:—first, by the Greek letters, Alpha, Beta,
Gamma, &c. Thus Alpha Orionis, denotes the largest
star in Orion ; Beta Andromedae, the second star in An-
dromeda; and Gamma Leonis, the third brightest star
in the Lion. Where the number of the Greek letter is
insufficient to include all the stars in a constellation,
recourse is had to the letters of the Roman alphabet, a,
b, c, &c.; and, in cases where these are exhausted, the
final resort is to numbers. This is evidently necessary,
since the largest constellations contain many hundreds
or even thousands of stars. Catalogues of particular
stars have also been published by different astronomers,
each author numbering the individual stars embraced in
his list, according to the places they respectively occupy
in the catalogue. These references to particular cata-
logues are sometimes entered on large celestial globes.
Thus we meet with a star marked 84 H., meaning that
297. Constellations.—How long known 7 Which are men-
tioned in the most ancient writings 7 How far are the names
founded on resemblance? Why are the ancient figures still re-
tained? How are the individual stars of a constellation dis-
tinguished 7 What is said of catalogues of the stars 7
FIXED STARS. 237
this is its number in Herschel's catalogue; or 140 M., de-
noting the place the star occupies in the catalogue of
Mayer. .
298. The earliest catalogue of the stars was made by
Hipparchus of the Alexandrian school, about 140 years
before the Christian era. A new star appearing in the
firmament, he was induced to count the stars and to re-
cord their positions, in order that posterity might be able
to judge of the permanency of the constellations. His
catalogue contains all that were conspicuous to the
naked eye in the latitude of Alexandria, being 1022.
Most persons unacquainted with the actual number of
the stars which compose the visible firmament, would
Suppose it to be much greater than this ; but it is found
that the catalogue of Hipparchus, embraces nearly all
that can now be seen in the same latitude, and that on
the equator, when the spectator has the northern and
southern hemispheres both in view, the number of stars
that can be counted does not exceed 3000. A careless
view of the firmament in a clear night, gives us the im-
pression of an infinite multitude of stars; but when we
begin to count them, they appear much more sparsely
distributed than we supposed, aird large portions of the
sky appear almost destitute of stars.
By the aid of the telescope, new fields of stars present
themselves of boundless extent; the number contin-
ually augmenting as the powers of the telescope are in-
creased. Lalande, in his Histoire Celesté, has registered
the positions of no less than 50,000; and the whole
number visible in the largest telescopes amounts to many
millions. -
299. It is strongly recommended to the learner to ac-
quaint himself with the leading constellations at least,
298. Why did Hipparchus make a catalogue? How many
stars did he number? What is the greatest number that can
be seen by the naked eye in both hemispheres' How many
can be seen by the telescope 7
~
238 FIXED STARS.
and with a few of the most remarkable individual stars.
The task of learning them is comparatively easy, and
hardly any kind of knowledge, attained with so little
Habor, so amply rewards the possessor. It will generally
be advisabie, at the outset, to get some one already ac-
quainted with the stars, to point out a few of the most
conspicuous constellations, those of the Zodiac for ex-
ample ; the learner may then resort to maps of the stars,
or what is much better, to a celestial globe,” and fill up
the outline by tracing out the principal stars in each
constellation as there laid down. By adding one new
constellation to his list every night, and reviewing those
already acquired, he will soon become familiar with the
stars, and will greatly augment his interest and improve
his intelligence in celestial observations, and practical
astronomy. - -
constELLATIONs.
300. We will point out particular marks by which the
leading constellations may be recognized, leaving it to
the learner, after he has found a constellation, to trace
out additional members of it by the aid of the celestial
globe, or by maps of the stars. Let us begin with the
Constellations of the Zodiac, which succeeding each
other as they do in a known order, and most easily
found.
ARIES (The RAM) is a small constellation, known by
two bright stars which form his head, Alpha and Beta
Arielis. These two stars are four degreest apart, and
directly south of Beta at the distance of one degree, is
299. Specify the directions for learning the constellations.
* For the method of rectifying the globe so as to represent the ap-
pearance of the heavens on any particular evening, see page 34, Art.
61 -
f These measures are not intended to be stated with exactness, but
only with such a degree of accuracy as may serve for a general guide.
constELLATIONs. 239
a smaller star, Gamma Arietis. It has been already
intimated (Art. 139) that the vernal equinox probably
was near the head of Aries, when the signs of the Zo-
diac received the present names. . - *
TAURUs (The BULL) will be readily found by the
seven stars or Pleiades, which lie in his neck. The
largest star in Taurus is Aldebaran, in the Bull's eye, a
star of the first magnitude, of a reddish color somewhat
resembling the planet Mars. Aldebaran and four other
stars in the face of Taurus, compose the Hyades.
GEMINI (The Twins) is known by two very bright
stars, Castor and Pollux, four degrees asunder. Castor
(the northern) is of the first, and Pollux of the second
magnitude. -
CANCER (The CRAB). There are no large stars in this
constellation, and it is regarded as less remarkable than
any other in the Zodiac. It contains however an inter-
esting group of small stars, called Prasepe or the Neb-
ula of Cancer, which resembles a comet, and is often
mistaken for one, by persons unacquainted with the
stars. With a telescope of very moderate powers this
nebula is converted into a beautiful assemblage of ex-
ceedingly bright stars. -
LEO (The LION) is a very large constellation, and has
many interesting members. Regulus (Alpha Leonis)
is a star of the first magnitude, which lies directly in the
ecliptic, and is much used in astronomical observations,
300. Constellations of the Zodiac.—Aries.—How known 7
How far are the two brightest stars apart? Where was the
vernal equinox situated when the signs of the Zodiac received
their present names? -
Taurus.-How found ! Name the largest star in Taurus.
What stars compose the Hyades 7 -
Gemini.-How known 't How far are Castor and Pollux asun-
der'ſ Of what magnitudes are they respectively 7
Cancer.—Are there any large stars in Cancer 7 What is
said of Praesepe 7 - - .
Leo.—What is its size? What is said of Regulus? Where
is the sickle? Where is Denebola situated
240 FIXED STARS.
North of Regulus lies a semi-circle of bright stars, form-
ing a sickle of which Regulus is the handle. Denebola,
a star of the second magnitude, is in the Lion's tail, 25°
northeast of Regulus. - . A -
VIRGo (The VIRGIN) extends a considerable way
from west to east, but contains only a few bright stars.
Spica, however, is a star of the first magnitude, and
lies a little east of the place of the autumnal equinox.
Eighteen degrees eastward of Spica, and twenty degrees
north of Spica, is Vindemiatria, in the head of Virgo, a
star of the third magnitude. • .
LIBRA (The BALANCE) is distinguished by three large
stars, of which the two brightest constitute the beam
of the balance, and the smallest forms the top or handle.
Scorpio (The ScoRPION) is one of the finest of the
constellations. His head is formed of five blight stars
arranged in the arc of a circle, which is crossed in the
center by the ecliptic nearly at right angles, near the
brightest of the five, Beta Scorpionis. Nine degrees
southeast of this, is a remarkable star of the first mag-
nitude, of a reddish color, called Cor Scorpionis, or An-
tares. South of this a succession of bright stars sweep
round towards the east, terminating in several small ,
stars, forming the tail of the Scorpion. -
SAGITTARIUs (The ARCHER). Northeast of the tail of
the Scorpion, are three stars in the arc of a circle which
constitute the Bow of the Archer, the central star being
the brightest, directly west of which is a bright star
which forms the arrow. - -
CAPRICORNUs (The GoAT) lies northeast of Sagittarius,
and is known by two bright stars, three degrees apart,
which form the head. - - -
*s
Wirgo.—Extent from east to west? What is said of Spica,
and of Windemiatrix '' -
Libra.-How distinguished 7 .
Scorpio.—His appearance? His head how formed? Where
is Antares situated 7 - º
Sagittarius.--Describe his bow.
Capricornus.--Where situated from Sagittarius? How known?
CONSTELLATIONS. 241
AquaRIUs (The WATER BEARER) is recognized by
two stars in a line with Alpha Capricorn?, forming the
shoulders of the figure. These two stars are 10° apart,
and 3° southeast is a third star, which together with the
other two, make an acute triangle, of which the west-
ernmost is the vertex.
PiscEs (The FISHEs) lie between Aquarius and Aries.
They are not distinguished by any large stars, but are
connected by a series of small stars, that form a crooked
line between them. Piscis Australis, the Southern
Fish, lies directly below Aquarius, and is known by a
single bright star far in the south, having a declimation
of 30°. The name of this star is Fomalhaut, and it is
much used in astronomical measurements.
301. The Constellations of the Zodiac, being first
well learned, so as to be readily recognized, will facil-
itate the learning of others that lie north and South of
them. Let us therefore next review the principal North-
erm Constellations, beginning north of Aries and pro-
ceeding from west to east.
ANDROMEDA, is characterized by three stars of the sec-
ond magnitude, situated in a straight line, extending
from west to east. The middle star is about 17° north
of Beta Arietis. It is in the girdle of Andromeda, and
is named Mirach. The other two lie at about equal
distances, 14° west and east of Mirach. The western
star, in the head of Andromeda, lies in the Equinoctial
Colure. The eastern star, Alamak, is situated in the
foot.
PERSEUs lies directly north of the Pleiades, and con-
tains several bright stars. About 18° from the Pleiades
Aquarius.—How recognized ? How far apart are the shoul-
ders of Aquarius"
Pisces.—Where situated How connected 7 Where is
Piscis Australis situated 7 By what name is it commonly
known 7 -
301. Northern Constellations. Andromeda, how character-
ized Where are Mirach and Alamak situated 7
242 FIXED STARS.
is Algol, a star of the second magnitude in the Head of
Medusa, which forms a part of the figure ; and 9° north-
east of Algol is Algenib, of the same magnitude in the
back of Perseus. Between Algenib and the Pleiades are
three bright stars, at nearly equal intervals, which com-
pose the right leg of Perseus.
AURIGA (the WAGoNER) lies directly east of Perseus,
and extends nearly parallel to that constellation from
north to south. Capella a very white and beautiful
star of the first magnitude, distinguishes this constella-
tion. The feet of Auriga are near the Bull’s Horns.
The LYNX comes next, but presents nothing particu-
larly interesting, containing no stars above the fourth
magnitude.
LEo MINoF consists of a collection of small stars
north of the sickle in Leo, and south of the Great Bear.
Its largest star is only of the third magnitude. -
CoMA BERENICEs is a cluster of small stars, north of
Denebola, in the tail of the Lion, and of the head of
Virgo. About 129 directly north of Berenice's Hair,
is a single bright star called Cor Caroli, or Charles's
Heart.
Bootes, which comes next, is easily found by means
of Arcturus, a star of the first magnitude, of a reddish
color, which is situated near the knee of the figure,
Arcturus is accompanied by three small stars forming a
triangle a little to the southwest. Two bright stars
Gamma and Delta Bootis, form the shoulders, and
Bela of the third mignitude is in the head of the figure.
Perseus.—How situated with respect to the Pleiades? Where
is Algol '! Where is Algenib 7 What stars compose the right
leg of Perseus'
Auriga.-How situated from Perseus'! What large star dis-
tinguishes this constellation ? Where are the feet of Auriga?
Lynx.—Size of its stars ?
Leo Minor.—Where situated 7 Size of its largest star 7
Coma Berenices.—Describe it. Where is Cor Caroli ?
Bootes.—What large star is in this constellation ?
CONSTELLATIONS. 243
CoRoNA BoREALIS, (The CRowN,) which is situated east
of Bootes, is very easily recognized, composed as it is of
a semi-circle of bright stars. In the center of the bright
crown, is a star of the second magnitude, called Gem-
ma; the remaining stars are all much smaller.
HERCULEs, lying between the Crown on the west and
the Lyre on the east, is very thick set with stars, most
of which are quite small. The Constellation covers a
great extent of the sky, especially from N. to S., the
head terminating within 15° of the equator, and marked
by a star of the third mignitude, called Ras Algethi,
which is the largest in the Constellation.
OPHIUCUs is situated directly south of Hercules, ex-
tending some distance on both sides of the equator, the
feet resting on the Scorpion. The head terminates near
the head of Hercules, and like that, is marked by a
bright star within 59 of Alpha Herculis. Ophiucus is
represented as holding in his hands the SERPENT, the
head of which, consisting of three bright stars, is sit-
uated a little south of the Crown. The folds of the
serpent will be easily followed by a succession of bright
stars which extend a great way to the east.
Aquila (The EAGLE) is conspicuous for three bright
stars in its neck, of which the central one, Allair, is a
very brilliant white star of the first magnitude. Anti-
mous lies directly south of the Eagle, and north of the
head of Capricornus.
DELPHINUs (The DoDPHIN) is a small but beautiful
Constellation, a few degrees east of the Eagle, and is
characterized by four bright stars near to one another,
forming a small rhombic square. Another star of the
same magnitude 5° south, makes the tail.
Corona Borealis.-Describe it. Where is Gemma situated "
Hercules.—Between what two constellations is it? What
is said of its extent? Where is Ras Algethi"
Ophiucus.--Where is it from Hercules? How is it repre-
sented 7 & & * &
Aquila.—How distinguished Where is Altair? Where is
Antinous"
The Dolphin.—Describe it.
244 FIXED STARS.
PEGASUs lies between Aquarius on the southwest and
Andromeda on the northeast. It contains but few large
stars. A very regular square of bright stars is composed
of Alpha Andromedae, and the three largest stars in Pe-
gasus, namely, Scheat, Markab, and Algenib. The
sides composing this square are each about 15°. Alge-
nib is situated in the Equinoctial Colure. - ..
302. We may now review the Constellations which
surround the North Pole, within the circle of perpetual
apparition. (Art. 38.)
URSA MINOR (The LITTLE BEAR) lies nearest the
pole. The Pole-star, Polaris, is in the extremity of the
tail, and is of the third magnitude. Three stars in a
straight line 4° or 5° apart, commencing with the Pole-
star, lead tº a trapezium of four stars, and the whole
seven form together a dipper, the trapezium being the
body, and the three stars the handle.
URSA MAJOR (The GREAT BEAR) is situated between
the pole and the Lesser Lion, and is usually recognized
by the figure of a larger and more perfect dipper, which
constitutes the hinder part of the animal. This has also
seven stars, four in the body of the dipper, and three in
the handle. All these are stars of much celebrity. The
two in the western side of the dipper, Alpha and Beta, are
called Pointers, on account of their always being in a
right line with the Pole-star, and therefore affording an
easy mode of finding that. The first star in the tail, next
the body, is named Alioth, and the second Mizar. The
head of the Great Bear lies far to the westward of the
Pegasus.-Between what two constellations is it situated
How may a square be formed of certain stars in this constel-
lation ?
302. Northern Constellations. Ursa Minor.—How situated
with respect to the pole Show how the dipper in this constel-
lation is formed !
Ursa Major.—Where situated How recognized ' What
are the Pointers? Where is Alioth—Mizar'ſ Of what is the
head composed ?
CONSTELLATIONS. 245
Pointers, and is composed of numerous small stars; and
the feet are severally composed of two small stars very
near to each other. -
DRAco (The DRAGON) winds round between the Great
and the Little Bear; and commencing with the tail, be-
tween the Pointers and the Pole-star, it is easily traced
by a succession of bright stars extending from west to
east, passing under Ursa Minor, it returns westward, and
terminates in a triangle which forms the head of Draco,
near the feet of Hercules, northwest of Lyra.
CEPHEUS lies eastward of the breast of the Dragon,
but has no stars above the third magnitude.
CASSIOPEIA is known by the figure of a chair, com-
posed of four stars which form the legs, and two which
form the back. This Constellation lies between Perseus
and Cepheus, in the Milky Way.
Cygnus (The Swan) is situated also in the Milky Way,
some distance southwest of Cassiopeia, towards the Ea-
gle. Three bright stars, which lie along the Milky
Way, form the body and neck of the Swan, and two
others in a line with the middle one of the three, one
above and one below, constitute the wings. This Con-
stellation is among the few, that exhibit some resem-
blance to the animals whose names they bear.
LyRA (The Lyre) is directly west of the Swan, and
is easily distinguished by a beautiful white star of the
first magnitude, Alpha Lyrae,
303. The Southern Constellations are comparatively
few in number. We shall notice only the Whale, Orion,
the Greater and Lesser Dog, Hydra, and the Crow.
Draco.—How situated with respect to the two Bears 7 Trace
its course?
Cepheus.—How situated from Dracoğ
Cássiopeia–How known Where situated ?
Cygnus.—How situated 2 Of what stars formed? Has this
constellation any resemblance to a Swan 7 -
303. Southern Constellations. Cetus.--Its extent? Size of
its stars? What is said of Mºnkar, and of Mira'ſ
21
246 . FIXED STARS,
CETUs (The WHALE) is distinguished rather for its
extent than its brilliancy, reaching as it does through
40° of longitude, while none of its stars except one,
are above the third magnitude. Memkar (Alpha Ceti)
in the mouth, is a star of the second magnitude, and
Several other bright stars directly south of Aries, make
the head and neck of the Whale. Mira (Omicron
Cel?) in the neck of the Whale, is a variable star.
ORION is one of the largest and most beautiful of the
constellations, lying southeast of Taurus. A cluster of
Small stars form the head; two large stars, Belalgeus of
the first and Bellatric of the second magnitude, make
the shoulders; three more bright stars compose the
buckler, and three the sword; and Rigel, another star of
the first magnitude, makes one of the feet. In this
Constellation there are 70 stars plainly visible to the
naked eye, including two of the first magnitude, four of
the second, and three of the third.
CANIS MAJOR lies S. E. of Orion, and is distinguished
chiefly by its containing the largest of the fixed stars,
Sirius.
CANIs MINoR a little north of the equator, between
Canis Major and Gemini, is a small Constellation, con-
sisting chiefly of two stars, of which Procyon is of the
first magnitude. -
HYDRA has its head near Procyon, consisting of a
number of stars of ordinary brightness. About 15° S.
E. of the head, is a star of the second magnitude, form-
ing the heart, (Cor Hydra?); and eastward of this, is
a long succession of stars of the fourth and fifth magni-
tudes composing the body and the tail, and reaching a
few degrees south of Spica Virginis.
Orion.—What is said of its size and beauty 7 Describe its
different parts. How many stars does it contain which are vis-
ible to the naked eye 7
Canis Major.—Where situated from Orion ? What large
star is in it !
Canis Major.—Where situated What large star does it
contain 7 -
Hydra,—Trace its course.
CLUSTERS OF STARS. 247
CoRVUs (The CRow) is represented as standing on the
tail of Hydra. It consists of small stars, only three of
which are as large as the third magnitude.
304. The foregoing brief sketch is designed merély
to aid the student in finding the principal constellations
and the largest fixed stars. When we have once learned
to recognize a constellation by some characteristic marks,
we may afterwards fill up the outline by the aid of a
celestial globe or a map of the stars. It will be of little
avail however, merely to commit this sketch to memory;
but it will be very useful for the student at once to ren-
der himself familiar with it, from the actual specimens
which every clear evening presents to his view.
C H A P T E R II.
. OF CLUSTERS OF STARS–NEBULF—VARIABLE STARS-
TEMPORARY STARS–D OUBLE STAIRS. -
305. IN various parts of the firmament are seen large
groups or clusters, which, either by the naked eye, or by
the aid of the smallest telescope, are perceived to con-
sist of a great number of small stars. Such are the
Pleiades, Coma Berenices, and Praesepe or the Bee-hive
in Cancer. The Pleiades, or Seven Stars, as they are
called, in the neck of Taurus, is the most conspicuous
cluster. When we look directly at this group, we can-
not distinguish more than six stars, but by turning the
eye sideways” upon it, we discover that there are many
Corvus.-How represented 2 .
305. Clusters.-Name a few of the largest. Pleiades, where
situated 7 How many stars does it contain What is said of
Coma Berenices, and of the Bee-hive 7
* Indirect vision is far more delicate than direct. Thus we can see
the Zodiacal Light or a Comet's Tail, much more distinctly and better
defined, if we fix one eye on a part of the heavens at some distance,
and turn the other eye obliquely upon the object.
248 FIXED STARS.
more, Telescopes show 50 or 60 stars crowded to-
gether and apparently insulated from the other parts of
the heavens. Coma Berenices has fewer stars, but they
are of a larger class than those which compose the Plei-
ades. The Bee-hive or Nebula of Cancer as it is called,
is one of the finest objects of this kind for a small tel-
escope, being by its aid converted into a rich congeries
of shining points. The head of Orion affords an exam-
ple of another cluster, though less remarkable than the
others.
306. Nebulae are those faint misty appearances which
resemble comets, or a small speck of fog. The Galaxy
or Milky Way, presents a continued succession of large
nebulae. A very remarkable Nebula, visible to the naked
eye, is seen in the girdle of Andromeda. No powers of
the telescope have been able to resolve this into separate
stars. Its dimensions are astonishingly great. In diam-
eter it is about 15'. The telescope reveals to us innumer-
able objects of this kind. Sir William Herschel has given
catalogues of 2000 Nebulae, and has shown that the neb-
ulous matter is distributed through the immensity of
space in quantities inconceivably great, and in separate
parcels of all shapes and sizes, and of all degrees of
brightness between a mere milky appearance and the
condensed light of a fixed star. Finding that the gra-
dations between the two extremes were tolerably regu-
lar, he thought it probable that the nebulae form the ma-
terials out of which nature elaborates Suns and systems;
and he conceived that, in virtue of a central gravitation,
each parcel of nebulous matter becomes more and more
condensed, and assumes a rounder form, He inferred
from the eccentricity of its shape, and the effects of the mu-
tual gravitation of its particles, that it acquires gradually
306. Nebula.—What are they'ſ What is said of the nebula
in the girdle of Andromeda? How many nebulae has Sir W.
Herschel included in his catalogue'ſ What are his ideas re-
specting nebulae'
NEBULFE. - 249
a rotary motion ; that the condensation goes on increas-
ing until the mass acquires consistency and Solidity, and
all the other characters of a comet or a planet; that by a
still further process of condensation, the body becomes a
real star, selſ-shining; and that thus the waste of the ce-
lestial bodies, by the perpetual diffusion of their light, is
continually compensated and restored by new formations
of such bodies, to replenish forever the universe with
planets and stars.
307. These opinions are recited here rather out of re-
spect to their notoriety and celebrity, than because we
suppose them to be founded on any better evidence than
conjecture. The Philosophical Transactions for many
years, both before and after the commencement of the
present century, abound with both the observations and
speculations of Sir William Herschel. The former are
deserving of all praise; the latter of very little conſi-
dence. Changes, however, are going on in some of the
nebulae, which plainly show that they are not, like plan-
ets and stars, fixed and permanent creations. Thus the
great nebula in the girdle of Andromeda, has very much
altered its structure since it first became an object of tele-
scopic observation. Many of the nebulae are of a globu-
lar form, (Fig. 50,) but frequently they present the ap-
pearance of a rapid increase of numbers towards the cen-
(Fig. 50.) (Fig. 51.)
ter, (Fig. 51,) the exterior boundary being irregular,
and the central parts more nearly spherical.
307. What is said of Herschel's speculations and of his ob-
servations ! What changes occur in the nebula, ' What forms
have they 7

250 FIXED STARS.
308. The Nebula in the sword of Orion is particularly
celebrated, being very large and of a peculiarly interest-
ing appearance. According to Sir John Herschel, its
nebulous character is very different from what might be
supposed to arise from the assemblage of an immense
collection of small stars. It is formed of little flocculent
masses like wisps of clouds; and such wisps seem to
adhere to many small stars at its outskirts, and espeially
to one considerable star which it envelops with a neb-
ulous atmosphere of considerable extent and singular
figure. -
Descriptions, however, can convey but a very imper-
fect idea of this wonderful class of astronomical objects,
and we would therefore urge the learner studiously to
avail himself of the first opportunity he may have to
view them through a large telescope, especially the Neb-
ula of Andromeda and of Orion. -
309. Nebulous Stars are such as exhibit a sharp and
brilliant star surrounded by a disk or atmosphere of neb-
ulous matter. These atmospheres in some cases present
a circular, in others an oval figure; and in Some in-
stances, the nebula consists of a long, narrow spindle-
shaped ray, tapering away at both ends to points. .
Planetary Nebulae constitute another variety, and are
very remarkable objects. They have, as their name
imports, exactly the appearance of planets. Whatever
may be their nature, they must be of enormous magni-
tude. One of them is to be found in the parallel of
Gamma Aquarii, and about 5m. preceding that star. Its
apparent diameter is about 20%. Another in the Con-
stellation Andromeda, presents a visible disk of 12", per-
fectly defined and round. Granting these objects to be
308. What is said of the nebula in the sword of Orion ? Can
the nebulae be fully learned from description ?
309. Nebulous stars—what are they 7 What forms have
their atmospheres? Planetary nebulae, their appearance"
What apparent diameters have they ! What is said of their
light? -
WARIABLE STARS. 251
equally distant from us with the stars, their real dimen-
sions must be such as, on the lowest computation, would
fill the orbit of Uranus. It is no less evident that, if they
be solid bodies, of a solar nature, the intrinsic splendor
of their surfaces must be almost infinitely inferior to
that of the sun. A circular portion of the sun’s disk,
subtending an angle of 20%, would give a light equal to
100 full moons; while the objects in question are hardly,
if at all, discernible with the naked eye.
310. The Galaxy or Milky Way is itself supposed
by some to be a nebula of which the sun forms a com-
ponent part; and hence it appears so much greater than
other nebulae only in consequence of our situation with
respect to it, and its greater proximity to our system.
So crowded are the stars in some parts of this zone, that
Sir William Herschel, by counting the stars in a single
field of his telescope, estimated that 50,000 had passed
under his review in a zone two degrees in breadth du-
ring a single hour's observation. Notwithstanding the
apparent contiguity of the stars which crowd the galaxy,
it is certain that their mutual distances must be incon-
ceivably great. .
311. WARIABLE STARs are those which undergo a pe-
riodical change of brightness. One of the most remark-
able is the star Mira in the Whale, (Omicron Ceti). It
appears once in 11 months, remains at its greatest bright-
ness about a fortnight, being then, on some occasions,
equal to a star of the second magnitude. It then de-
creases about three months, until it becomes completely
invisible, and remains so about five months, when it
again becomes visible, and continues increasing during
the remaining three months of its period.
Another very remarkable variable star is Algol (Beta
Persei). It is usually visible as a star of the second magni-
310. Galaxy or Milky Way—what is said respecting it? Give
an example of the multitude of stars in it?
252 FIXED STARS.
tude, and continues such for 2d. 14h. when it suddenly
begins to diminish in splendor, and in about 34 hours is
reduced to the fourth magnitude. It then begins again
to increase, and in 34 hours more, is restored to its usual
brightness, going through all its changes in less than
three days. This remarkable law of variation appears
strongly to suggest the revolution round it of some opake
body, which, when interposed between us and Algol,
cuts off a large portion of its light. It is (says Sir J.
Herschel) an indication of a high degree of activity in
regions where, but for such evidences, we might con-
clude all lifeless. Our sun requires almost nine times
this period to perform a revolution on its axis. On the
other hand, the periodic time of an opake revolving
body, sufficiently large, which would produce a similar
temporary obscuration of the Sun, seen from a fixed star,
would be less than fourteen hours.
The duration of these periods is extremely various.
While that of Beta Persei above mentioned, is less than
three days, others are more than a year, and others many
years. -
312. TEMPORARY STARs are new stars which have ap-
peared suddenly in the firmament, and after a certain in-
terval, as suddenly disappeared and returned no more.
It was the appearance of a new star of this kind 125
years before the Christian era, that prompted Hipparchus
to draw up a catalogue of the stars, the first on record.
Such also was the star which suddenly shone out A. D.
389, in the Eagle, as bright as Venus, and after remain-
ing three weeks disappeared entirely. At other periods,
at distant intervals, similar phenomena have presented
themselves. Thus the appearance of a star in 1572,
was so sudden, that Tycho Brahe returning home one
311. Variable stars—what are they'ſ What is said of Mira'ſ
Also of Algol '! How are their periods of revolution ?
312. Temporary stars—what are they ! Give examples. Do
they ever return? Do stars ever disappear !
DOUBLE STAR.S. 253
day was surprized to find a collection of country people
gazing at a star which he was sure did not exist half an
hour before. It was then as bright as Sirius, and con-
tinued to increase until it surpassed Jupiter when bright-
est, and was visible at mid-day. In a month it began
to diminish, and in three months afterwards it had en-
tirely disappeared. - - -
It has been supposed by some that in a few instances,
the same star has returned, constituting one of the peri-
odical or variable stars of a long period.
Moreover, on a careful re-examination of the heavens,
and a comparison of catalogues, many stars are now
found to be missing. .
313. Double STARs are those which appear single to
the naked eye, but are resolved into two by the tele-
scope; or, if not visible to the naked eye, are seen in the
telescope so close together as to be recognized as objects
of this class. Sometimes three or more stars are found
in this near connexion, constituting triple or multiple
stars. Castor, for example, when seen by the naked
eye, appears as a single star, but in a telescope even of
moderate powers, it is resolved into two stars of between
the third and fourth magnitudes, within 5” of each other.
These two stars are nearly of equal size, but more com-
monly one is exceedingly small in comparison with the
other, resembling a satellite near its primary, although
in distance, in light, and in other characteristics, each
has all the attributes of a star, and the combination
therefore cannot be that of a planet with a satellite. In
most instances, also, the distance between these objects
is much less than 5", and in many cases it is less than
1”. The extreme closeness, together with the exceed-
ing minuteness of most of the double stars, requires the
313. Double stars—what are they What are multiple stars?
Give an example of a double star 7 How do the two stars some-
times differ 7 What is required in order to observe most of the
double stars?
22
254. FIXED STARS.
best telescopes united with the most acute powers of ob-
servation. Indeed, certain of these objects are regarded
as the severest tests, both of the excellence of the instru-
ments and of the skill of the observer. The following
diagram represents four double stars, as seen with ap-
propriate magnifiers. No. 1, exhibits Epsilon Bootis with
a power of 350; No. 2, Rigel with a power of 130;
No. 3, the Pole-star with a power of 100; and No. 4,
Castor with a power of 300.
Fig. 52.
1. 2. 3. 4.
314. Our knowledge of the double stars almost com-
menced with Sir William Herschel, about the year 1780.
At the time he began his search for them, he was ac-
quainted with only four. Within five years, he discov-
ered nearly 700 double stars.” In his memoirs, pub-
lished in the Philosophical Transactions, he gave most
accurate measurements of the distances between the two
stars, and of the angle which a line joining the two,
formed with the parallel of declination. These data
would enable him, or at least posterity, to judge whether
these minute bodies ever change their position with re-
spect to each other.
314. Who began the discovery of double stars? When did
he publish his account of them 7 By whom have these re-
searches been since prosecuted 7 What two circumstances add
a high degree of interest to the phenomena of the double stars 7
* During his liſe he observed in all, 2400 double stars.

MOTIONS OF THE FIXED STARS. 255
Since 1821, these researches have been prosecuted
with great zeal and industry by Sir James South and
Sir John Herschel in England, and by Professor Struve
at Dorpat in Russia; and the whole number of double
stars now known, amounts to several thousands. Two
circumstances add a high degree of interest to the phe-
nomena of the double stars—the first is, that a few of
them at least are found to have a revolution around
each other, and the second, that they are supposed to
afford the means of obtaining the parallax of the fixed
stars. Of these topics we shall treat in the next chapter.
C H A P T E R III.
OF THE MOTIONS OF THE FIXED STARs—DISTANCES—
NATURE. - .
315. IN 1803, Sir William Herschel first determined
and announced to the world, that there exist among the
stars, separate systems, composed of two stars revolving
about each other in regular orbits. These he denomin-
ated Binary Stars, to distinguish them from other
double stars where no such motion is detected, and
whose proximity to each other may possibly arise from
casual juxta-position, or from one being in the range of
the other. Between fifty and sixty instances of changes
to a greater or less amount of the relative position of
double stars, are mentioned by Sir William Herschel;
and a few of them had changed their places so much
within 25 years, and in such order, as to lead him to the
conclusion that they performed revolutions, one around
the other, in regular orbits.
*
315. Binary Stars.—Who first discovered this class of
bodies? How are they distinguished from ordinary double
stars? What conclusions did S. W. Herschel draw respecting
them " -
256 FIXED STAIRS.
316. These conclusions have been fully confirmed by
later observers, so that it is now considered as fully es-
tablished, that there exist among the fixed stars, binary
systems, in which two stars perform to each other the
office of sun and planet, and that the periods of revolu-
tion of more than one such pair have been ascertained
with something approaching to exactness. Immersions
and emersions of stars behind each other have been ob-
served, and real motions among them detected rapid
enough to become sensible and measurable in very short
intervals of time. The following table exhibits the
present state of our knowledge on this subject.*
Names. Period in years. Major axis of the orbit. Eccentricity.
7 Coronae, 43.40
& Cancri, 55.00 sms-smºs *===
§ Ursae Majoris, 58.26 7//.714 0.4164
70 Ophiuchi, 80.34 8.784 0.4667
Castor, 252.66 16. 172 0.7582
o Coronae, 286.00 7.358 0.6112
61 Cygni, 452.00 30.860 - *=s=º
Y Virginis, 628.90 24.000 0.8335
Y Leonis, 1200.00 *===ºmºsº gºssºmsºmºmºmºmºmº
From this table it appears, first, that the periods of the
double stars are very various, ranging, in the case of
those already ascertained, from forty-three years to one
thousand; Secondly, that their orbits are very small
316. Have the conclusions of Herschel been confirmed by
others? What doctrine is now considered as fully established?
How are the periods of the double stars? What is the figure of
their orbits? Which is the most remarkable of the Binary
stars? What is its size? How long since it was first observed
to be double? What changes has it undergone since 1 When
did it pass its perihelion ? -
"Those who do not understand the Greek letters, can pass over this
table to the inferences which follow. -
MOTIONS OF THE FIXETD STAR.S. 257
ellipses, more eccentric than those of the planets, the
greatest of which (that of Mercury) having an eccentri-
city of only about .2 of the major axis.
The most remarkable of the binary stars is Gamma
Virginis, on account not only of the length of its period,
but also of the great diminution of apparent distance,
and rapid increase of angular motion about each other
of the individuals composing it. It is a bright star of
the fourth magnitude, and its component stars are almost
exactly equal. It has been known to consist of two
stars since the beginning of the eighteenth century, their
distance being then between six and seven seconds ; so
that any tolerably good telescope would resolve it.
Since that time they have been constantly approaching,
and are at present hardly more than a single second asun-
der ; so that no telescope that is not of a very superior
quality, is competent to show them otherwise than as a
single star, somewhat lengthened in one direction. It
fortunately happens that Bradley (Astronomer Royal) in
1781, noticed, and recorded in the margin of one of his
observation books, the apparent direction of their line of
junction, as being parallel to that of two remarkable stars
Alpha and Delta of the same constellation, as seen by
the naked eye, a remark which has been of signal Ser-
vice in the investigation of their orbit. It is found that
it passed its perihelion, August 18th, 1834, and that in
the interval from 1839 to 1841, this star will have com-
pleted a full revolution from the epoch of the first meas-
urement of its position in 1781; and the regularity with
which it has maintained its motion, is said to have been
exceedingly beautiful.
317. The revolutions of the binary stars have assured
us of that most interesting fact, that the law of gravita-
sº-º-º-º-º-º-º-º-º:
317. What great fact have the revolutions of the binary stars
revealed to us? How was this doctrine limited before this dis-
covery Are these revolutions those of a planetary or come-
tary nature ?
22%
258 FIXED STARS.
tion evtends to the fived stars. Before these discoveries,
we could not decide except by a feeble analogy that this
law transcended the bounds of the solar system. In-
deed, our belief of the fact rested more upon our idea of
unity of design in all the works of the Creator, than
upon any certain proof; but the revolution of one star
around another in obedience to forces which must be
similar to those that govern the solar system, establishes
the grand conclusion, that the law of gravitation is truly
the law of the material universe. - f
We have the same evidence (says Sir John Herschel)
of the revolutions of the binary stars about each other,
that we have of those of Saturn and Uranus about the
sun ; and the correspondence between their calculated
and observed places in such elongated ellipses, must be
admitted to carry with it a proof of the prevalence of the
Newtonian law of gravity in their systems, of the very
same nature and cogency as that of the calculated and
observed places of comets round the center of our own
system. *
But (he adds) it is not with the revolution of bodies
of a planetary or cometary nature round a Solar center
that we are now concerned; it is with that of sun
around sun, each, perhaps, accompanied with its train of
planets and their satellites, closely shrouded from our
view by the splendor of their respective suns, and crowd-
ed into a space, bearing hardly a greater proportion to
the enormous interval which separates them, than the
distances of the satellites of our planets from their pri-
maries, bear to their distances from the sun itself.
318. Some of the fived stars appear to have a real mo-
tion in Space.
There are several apparent changes of place among
the stars which arise from real changes in the earth,
318. Have any of the fixed stars a real motion in space 3 Are
the places of the stars as described in ancient times by Ptolemy
nearly the same as at present? To what conclusions on this
subject are we now forced
MOTIONS OF THE FIXED STARS, 259
which, as we are not conscious of them, we refer to the
stars; but there are other motions among the stars which
cannot result from any changes in the earth, but must
arise from changes in the stars themselves. Such mo-
tions are called the proper motions of the stars. Nearly
2000 years ago, Hipparchus and Ptolemy made the most
accurate determinations in their power of the relative
situations of the stars, and their observations have been
transmitted to us in Ptolemy's Almagest ; from which it
appears that the stars retain at least very nearly the same
places now as they did at that period. Still, the more
accurate methods of modern Astronomers, have brought
to light minute changes in the places of certain stars,
which force upon us the conclusion, either that our solar
system causes an apparent displacement of certain stars,
by a motion of its own in space, or that they have them-
selves a proper motion. Possibly, indeed, both these
causes may operate. & .
3.19. If the sun, and of course the earth which accom-
panies him, is actually in motion, the fact may become
manifest from the apparent approach of the stars in the
region which he is leaving, and the recession of those
which lie in the part of the heavens towards which he
is travelling. Were two groves of trees situated on a
plain at some distance apart, and we should go from one
to the other, the trees before us would gradually appear
farther and farther asunder, while those we left behind
would appear to approach each other. Some years since,
Sir William Herschel supposed he had detected changes
of this kind among two sets of stars in opposite points
of the heavens, and announced that the solar system
was in motion towards a point in the constellation Her-
cules; but other astronomers have not found the changes
319. If the solar system is really in motion, how may the
fact become manifest? Towards what constellation did Sir
William Herschel suppose it moving? Has the opinion been
confirmed by later observers ?
260 FIXED STARS.
in question such as would correspond to this motion, or
to any motion of the sun ; and while it is a matter of
general belief that the sun has a motion in space, the
fact is not considered as yet entirely proved.
320. In most cases where a proper motion in certain
stars has been suspected, its annual amount has been so
Small, that many years are required to assure us, that the
effect is not owing to some other cause than a real pro-
gressive motion in the stars themselves; but in a few
instances the fact is too obvious to admit of any doubt.
Thus the two stars 61 Cygni, which are nearly equal,
have remained constantly at the same, or nearly at the
same distance of 15” for at least fifty years past. Mean-
while they have shifted their local situation in the
heavens, 4'23" the annual proper motion of each star
being 5’.3, by which quantity this system is every year
carried along in Some unknown path, by a motion which
for many centuries must be regarded as uniform and rec-
tillinear. A greater proportion of the double stars than
of any other indicate proper motions, especially the bi-
nary stars or those which have a revolution around each
other. Among stars not double, and no way differing
from the rest in any other obvious particular, Mu Cassi-
opeiae has the greatest proper motion of any yet ascer-
tained, amounting to nearly 4” annually. -
DISTANCES OF THE FIXED STARS.
321. We cannot ascertain the actual distance of any
of the fived stars, but can certainly determine that the
nearest star is more than (20,000,000,000,000,) twenty
billions of miles from the earth.
*-*.
320. What length of time is required in order to detect
proper motions in the stars? What changes have occurred in
the two stars 61 Cygni ? What sort of stars indicate proper
motions? Of stars not double, what star has the greatest
proper motion ? -
IDISTANCES OF THE FIXED STARS, 261
For all the measurements relating to the distances of
the sun and planets, the radius of the earth furnishes the
base line. (Art. 96.) The length of this line being
known, and the horizontal parallax of the body, whose
distance is sought, we readily obtain the distance by the
Solution of a right angled triangle. But any star viewed
from the opposite sides of the earth, would appear from
both stations, to occupy precisely the same situation in
the celestial sphere, and of course it would exhibit no
horizontal parallax. -
But astronomers have endeavored to find a parallax in
some of the fixed stars, by taking the diameter of the
earth’s orbit as a base line. Yet even a change of posi-
tion amounting to 190 millions of miles, proves insuffi-
cient to alter the place of a single star, from which it is
concluded that the stars have not even any annual par-
allaa j that is, the angle subtended by the semi-diameter
of the earth’s orbit, at the nearest fixed star is insensible.
The errors to which instrumental measurements are sub-
ject, arising from the defects of the instruments them-
selves, from refraction, and from various other sources of
inaccuracy, are such, that the angular determinations of
arcs of the heavens cannot be relied on to less than 1".
But the change of place in any star when viewed at op-
posite extremities of the earth's orbit, is less than 1", and
therefore cannot be appreciated by direct measurement.
It follows, that, when viewed from the nearest star, the
diameter of the earth’s orbit would be insensible ; the
spider line of the telescope would more than cover it.
322. Taking, however, the annual parallax of a fixed
star at 1", it can be demonstrated that the distance of
the nearest fixed star must exceed 95000000 × 200000 =
1900000000 × 100000, or one hundred thousand times
321. What do we know respecting the distances of the fixed
stars' Have the fixed stars any parallax'ſ What is taken as
the base line for measuring the parallax? What angle is
greater than would be subtended by the diameter of the earth's
orbit as seen from the nearest fixed star 7
262 - F}XED STARS,
one hundred and ninety millions of miles. Of a dis-
tance so vast we can form no adequate conceptions, and
even seek to measure it only by the time that light,
(which moves more than 192,000 miles per second, and
passes from the sun to the earth in 8m. 7sec.,) would
take to traverse it, which is found to be more than three
and a half years. . -
If these conclusions are drawn with respect to the
largest of the fixed stars, which we suppose to be vastly
nearer to us than those of the smallest magnitude, the
idea of distance swells upon us when we attempt to es-
timate the remoteness of the latter. As it is uncertain,
however, whether the difference in the apparent magni-
tudes of the stars is owing to a real difference, or merely
to their being at various distances from the eye, more or
less uncertainty must attend all efforts to determine the
relative distances of the stars; but astronomers generally
believe, that the lower orders of stars are vastly more
distant from us than the higher. Of some stars it is
Said, that thousands of years would be required for their
light to travel-down to us. - -
323. We have said that the stars have no annual par-
allax; yet it may be observed that astronomers are not
exactly agreed on this point. Dr. Brinkley, a late emi-
ment Irish astronomer, supposed that he had detected an
annual parallax in Alpha Lyrae amounting to 1", 13 and
in Alpha Aquilae of 1%.42. These results were contro-
verted by Mr. Pond, of the Royal Observatory of Green-
wich ; and Mr. Struve of Dorpat, has shown that in a
number of cases, the parallax is in a direction opposite
to that which would arise from the motion of the earth.
Hence it is considered doubtful whether in all cases of
322. If we take the parallax at 1", what must the distance
be 7 What time would it take light to traverse this space
How much farther off than this may some of the smaller stars be?
323. Is it entirely settled that the fixed stars have no paral-
lax'ſ What did Dr. Brinkley assert? Have his observations
been confirmed !
IXISTANCES OF THE FIXED STARS. 263
an apparent parallax, the effect is not wholly due to
errors of observation.
324, Indirect methods have been proposed for ascer-
taining the parallax of the fixed stars by means of obser-
vations on the double stars. If the two stars composing
a double star are at different distances from us, parallax
would affect them unequally, and change their relative
positions with respect to each other; and since the ordi-
nary sources of error arising from the imperfection of in-
struments, from precession, and refraction, would be
avoided, (since they would affect both objects alike, and
therefore would not disturb their relative positions,)
measurements taken with the micrometer of changes
much less than 1" may be relied on. Sir John Herschel
proposes a method by which changes may be determined
which amount to only ºr of a second.* -
The immense distance of the fixed stars is inferred
also from the fact, that the largest telescopes do not in-
crease their apparent magnitude. They are still points,
when viewed with the highest magnifiers, although
they sometimes present a spurious disk, which is owing
to irradiation.f -
324. What indirect methods have been proposed for ascer-
taining the parallax of the fixed stars 7 State the particulars of
this method. How minute changes of place is it supposed may
be detected. How do the largest telescopes affect their appa-
rent magnitudes 7 :
* Very recent intelligence informs us, that Prof. Bessel of Königs-
berg, has obtained decisive evidence of an annual parallax in 61 Cygni,
amounting to 0/.3136. This makes the distance of that star, equal to
657700 times 95 millions of miles—a distance which it would take light
10:3 years to traverse. -
t Irradiation is an enlargement of objects beyond their proper bounds,
in consequence of the vivid impression of light on the eye. It is sup:
posed to increase the apparent diameters of the sun and moon from
three to four seconds, and to create an appearance of a disk in a fixed
star, which, when this cause is removed, is seen as a mere point.
264 FIXED STARS.
NATURE OF THE STARS.
325. The stars are bodies greater than our earth. If
this were not the case they could not be visible at such
an immense distance. Dr. Wollaston, a distinguished
English philosopher, attempted to estimate the magni-
tudes of certain of the fixed stars from the light which
they afford. By means of an accurate photometer (an
instrument for measuring the relative intensities of light)
he compared the light of Sirius with that of the sun.
He next inquired how far the sun must be removed from
us in order to appear no brighter than Sirius. He found
the distance to be 141,400 times its present distance.
But Sirius is more than 200,000 times as far off as the
sun. Hence he inferred that, upon the lowest compu-
tation, Sirius must actually give out twice as much
light as the sun; or that, in point of splendor, Sirius
must be at least equal to two suns. Indeed, he has ren-
dered it probable that the light of Sirius is equal to
fourteen Suns. -
326. The fived stars are sums. We have already seen
that they are large bodies; that they are immensely
farther off than the farthest planet; that they shine by
their own light; in short, that their appearance is, in all
respects, the same as the sun would exhibit if removed
to the region of the stars. Hence we infer, that they
are bodies of the same kind with the sun.
We are justified therefore by a sound analogy, in con-
cluding that the stars were made for the same end as
the sun, namely, as the centers of attraction to other
planetary worlds, to which they severally dispense light
and heat. Although the starry heavens present, in a
clear night, a spectacle of ineffable grandeur and beauty,
325. Nature of the stars. How large are the stars compared
with the earth 7 How did Dr. Wollaston endeavor to estimate
the magnitudes of certain fixed stars 7 How distant would this
method make Sirius'ſ To how many suns is Sirius equal?
SYSTEM OF THE WORLD. 265
yet it must be admitted that the chief purpose of the
stars could not have been to adorn the night, since by
far the greatest part of them are wholly invisible to the
naked eye; nor as landmarks to the navigator, for only a
very small proportion of them are adapted to this pur-
pose; nor, finally, to influence the earth by their attrac-
tions, since their distance renders such an effect entirely
insensible. If they are suns, and if they exert no im-
portant agencies upon our world, but are bodies evidently
adapted to the same purpose as our sun, then it is as ra-
tional to suppose that they were made to give light and
heat, as that the eye was made for seeing and the ear
for hearing. It is obvious to inquire next, to what they
dispense these gifts if not to planetary worlds; and why
to planetary worlds, if not for the use of percipient be-
ings? We are thus led, almost inevitably, to the idea
of a Plurality of Worlds; and the conclusion is forced
upon-us, that the spot which the Creator has assigned to
us is but a humble province of his boundless empire.*
C H A P T E R IV .
of THE SYSTEM OF THE WORLD.
327. The arrangement of all the bodies that compose
the material universe, and their relations to each other,
constitute the System of the World.
It is otherwise called the Mechanism of the Heavens;
and indeed, in the System of the World, we figure to
ourselves a machine, all the parts of which have a mu-
326. Prove that the fixed stars are suns. For what purpose
were they made? Could they have been designed to adorn the
night? or as landmarks to the navigator 7 If they are suns, for
what farther purpose were they designed?
* See this argument, in its full extent, in Dick's Celestial Scenery,
23
*
266 SYSTEM OF THE WORLD.
tual dependence, and conspire to one great end. “The
machines that are first invented (says Adam Smith) to
perform any particular movement, are always the most
complex ; and succeeding artists generally discover that
with fewer wheels and with fewer principles of motion
than had originally been employed, the same effects may
be more easily produced. The first systems, in the
same manner, are always the most complex; and a par-
ticular connecting chain or principle is generally thought
necessary to unite every two seemingly disjointed ap-
pearances; but it often happens, that one great connect-
ing principle is afterwards found to be sufficient, to bind
together all the discordant phenomena that occur in a
whole species of things.” This remark is strikingly
applicable to the origin and progress of systems of as-
tronomy.
328. From the visionary notions which are generally
understood to have been entertained on this subject by
the ancients, we are apt to imagine that they knew less
than they actually did of the truths of astronomy. But
Pythagoras, who lived 500 years before the Christian
era, was acquainted with many important facts in our
science, and entertained many opinions respecting the
system of the world which are now held to be true.
Among other things well known to Pythagoras were the
following:
1. The principal Comstellations. These had begun
to be formed in the earliest ages of the world. Several
of them bearing the same names as at present, are men-
tioned in the writings of Hesiod and Homer; and the
“sweet influences of the Pleiades” and the “bands of
Orion,” are beautifully alluded to in the book of Job.
2. Eclipses. Pythagoras knew both the causes of
eclipses and how to predict them ; not indeed in the ac-
k-
327. What constitutes the System of the World? Under
what image do we figure it to ourselves? What properties
characterize the machines first invented ''
ASTRONOMICAL KNOWLEDGE OF THE ANCIENTs. 267
curate manner now employed, but by means of the Saros.
(Art. 168.) -
3. Pythagoras had divined the true system of the
world, holding that the sun and not the earth, (as was
generally held by the ancients, even for many ages after
Pythagoras,) is the center around which all the planets
revolve, and that the stars are so many suns, each the
center of a system like our own. Among lesser things,
he knew that the earth is round; that its surface is mat-
urally divided into five Zones; and that the ecliptic is
inclined to the equator. He also held that the earth re-
volves daily on its axis, and yearly around the sun; that
the galaxy is an assemblage of small stars; and that it
is the same luminary, namely, Venus, that constitutes
both the morning and the evening star, whereas, all the
ancients before him had supposed that each was a sepa-
rate planet, and accordingly the morning star was called
Lucifer, and the evening star Hesperus. He held also
that the planets were inhabited, and even went so far as
to calculate the size of some of the animals in the moon.
Pythagoras was so great an enthusiast in music, that he
not only assigned to it a conspicuous place in his system
of education, but even supposed the heavenly bodies
themselves to be arranged at distances corresponding to
the diatonic scale, and imagined them to pursue their sub-
lime march to notes created by their own harmonious
movements, called the “music of the spheres;” but he
maintained that this celestial concert, though loud and
grand, is not audible to the feeble organs of man, but
only to the gods.
329. With few exceptions, however, the opinions of
Pythagoras on the System of the World, were founded
328. What is said of our usual estimate of the knowledge of
astronomy possessed by the ancients 7 What things were
known to Pythagoras'? How early were the principal constel-
lations known What did Pythagoras know of eclipses" Also
respecting the System of the World ! What lesser things did
he know? What motions had he of the music of the spheres?
268 SYSTEM OF THE WORLD.
in truth. Yet they were rejected by Aristotle and by
móst succeeding astronomers down to the time of Coper-
nicus, and in their place was substituted the doctrine of
Crystalline Spheres, first taught by Eudoxus. Accord-
ing to this system, the heavenly bodies are set like gems
in hollow solid orbs, composed of crystal so pellucid that
no anterior orb obstructs in the least the view of any of
the orbs that lie behind it. The sun and the planets
have each its separate orb ; but the fixed stars are all set
in the same grand orb ; and beyond this is another still,
the Primum Mobile, which revolves daily from east to
west, and carries along with it all the other orbs. Above
the whole, spreads the Grand Empyrean, or third heav-
ens, the abode of perpetual Serenity.
To account for the planetary motions, it was supposed
that each of the planetary orbs as well as that of the
Sun, has a motion of its own eastward, while it partakes
of the common diurnal motion of the starry sphere.
Aristotle taught that these motions are effected by a tute-
lary genius of each planet, residing in it, and directing
its motions, as the mind of man directs his motions.
330. On coming down to the time of Hipparchus, who
flourished about 150 years before the Christian era, we
meet with astronomers who acquired far more accurate
knowledge of the celestial motions. Previous to this
period, celestial observations were made chiefly with the
naked eye, but Hipparchus was in possession of instru-
ments for measuring angles, and knew how to resolve
spherical triangles. He ascertained the length of the
year within 6m. of the truth. He discovered the eccen-
tricity of the solar orb, (although he supposed the sun
actually to move uniformly in a circle, but the earth to
be placed out of the center,) and the positions of the
329. Were the opinions of Pythagorus generally embraced by
the ancients? What was the doctrine of Crystalline Spheres 7
How were the planetary motions accounted for "
330. When did Hipparchus flourish? How did he make
his observations? What great facts did he ascertain 7
THE PTOLEMAIC SYSTEM. 269
Sun's apogee and perigee. He formed very accurate es-
timates of the obliquity of the ecliptic, and of the preces-
sion of the equinoxes. He computed the exact period
of the synodic revolution of the moon, and the inclina-
tion of the lunar orbit; discovered the motion of her
mode and of her line of apsides; and made the first at-
tempts to ascertain the horizontal parallaxes of the sun
and moon.
Such was the state of astronomical knowledge when
Ptolemy wrote the Almagest, in which he has transmit-
ted to us an encyclopædia of the astronomy of the an-
ClentS. -
331. The systems of the world which have been most
celebrated are three—the Ptolemaic, the Tychonic, and
the Copernican. We shall conclude this part of our
work with a concise statement and discussion of each of
these systems of the Mechanism of the Heavens,
THE PTOLEMAIC SYSTEM.
332. The doctrines of the Ptolemaic System were not
originated by Ptolemy, but being digested by him out of
materials furnished by various hands, it has come down
to us under the sanction of his name.
According to this system, the earth is the center of
the universe, and all the heavenly bodies daily revolve
around it from east to west. In order to explain the
planetary motions, Ptolemy had recourse to deferents and
opicycles—an explanation devised by Apollonius one of
the greatest geometers of antiquity. He conceived that,
in the circumference of a circle, having the earth for its
center, there moves the center of another circle, in the
circumference of which the planet actually revolves.
The circle surrounding the earth was called the deferent,
331. What are the most celebrated Systems of the World !
332. Ptolemaic System.—Did Ptolemy originate this system'ſ
State the outlines of it. What was the deferent 7 What was
the epicycle 7 *
23%
270 SYSTEM OF THE WORLD.
while the smaller circle whose center was always in the
periphery of the deferent, was called the epicycle. The
motion in each was supposed to be uniform. Lastly, it
was conceived that the motion of the center of the epi-
cycle in the circumference of the deferent, and of the
planet in that of the epicycle, are in opposite directions,
the first being towards the east, and the second towards
the west.
333. But these views will be better understood from a
diagram. Therefore, let ABC (Fig. 53,) represent the
deferent, E being the earth a little out of the center.
Fig. 53.
A.
Let abe represent the epicycle, having its center at v, on
the periphery of the deferent. Conceive the circumfer-
ence of the deferent to be carried about the earth every
twenty four hours in the order of the letters; and at the
333. Explain the Ptolemaic Systèm by figure 53.

THE PTOLTEMAIC SYSTEM. 271
same time, let the center v of the epicycle abcd, have a
slow motion in the opposite direction, and let a body re-
volve in this circle in the direction abed. Then a body
revolving in the circle abcd, and at the same time having
a motion eastward in common with the circle, would
describe the looped curves ſelmºnop. At l and m, and at
m and 0, it would appear stationary, because in these
points its motion would be either directly towards or
from the spectator. The motion would be direct from
k to l, being in the order of the signs, and retrograde
from l to my; direct again from m to m, and retrograde
from m to 0.
334. Such a deferent and epicycle may be devised
for each planet as will fully explain all its ordinary mo-
tions; but it is inconsistent with the phases of Mercury
and Venus, which being between us and the sun on
both sides of the epicycle, would present their dark
sides towards us in both these positions, whereas at one
of the conjunctions they are seen to shine with full
face. It is moreover absurd to speak of a geometrical
center which has no bodily existence, moving around the
earth on the circumference of another circle ; and hence
some suppose that the ancients merely assumed this hy-
pothesis as affording a convenient geometrical represen-
tation of the phenomena, a diagram simply, without
conceiving the system to have any real existence in na-
ture.
335. The objections to the Ptolemaic system, in gen-
eral, are the following : First, it is a mere hypothesis,
having no evidence in its favor, except that it explains
the phenomena. This evidence is insufficient of itself,
since it frequently happens that each of two hypotheses,
—w
334. State the objections to this mode of representing the
motions of the planets. Why is it inconsistent with the phases
of Mercury and Venus? What is said of the supposition of a
geometrical center moving around the earth!
272 SYSTEM OF THE WORLD.
directly opposite to each other, will explain all the known
phenomena. But the Ptolemaic system does not even
do this, as it is inconsistent with the phases of Mercury
and Venus, as already observed. Secondly, now that
we are acquainted with the distances of the remoter
planets, and especially of the fixed stars, the Swiftness
of motion implied in a daily revolution of the starry
firmament around the earth, renders such a motion
wholly incredible. Thirdly, the centrifugal force that
would be generated in these bodies, especially in the
sun, renders it impossible that they can continue to re-
volve around the earth as a center.
These reasons are sufficient to show the absurdities
of the Ptolemaic System of the World.
THE TYC HONIC SYSTEM.
336. Tycho Brahe, like Ptolemy, placed the earth in
the center of the universe, and accounted for the diur-
nal motions in the same manner as Ptolemy had done,
namely, by an actual revolution of the whole host of
heaven around the earth every twenty four hours. But
he rejected the scheme of deferents and epicycles, and
held that the moon revolves about the earth as the cen-
ter of her motions; that the Sun, and not the earth, is
the center of the planetary motions; and that the sun
accompanied by the planets moves around the earth
once a year, somewhat in the manner that we now con-
ceive of Jupiter and his satellites as revolving around
the sun.
337. The system of Tycho serves to explain all the
common phenomena of the planetary motions, but it is
encumbered with the same objections as those that have
335. State the objections to the Ptolemaic System in general.
Does it explain all the phenomena? What swiftness of motion
does it imply "
336. Tychomic System.—State its leading points.
THE COPERNICAN SYSTEM. 273
been mentioned as resting against the Ptolemaic system,
namely, that it is a mere hypothesis; that it implies an
incredible swiftness in the diurnal motions; and that it
is inconsistent with the known laws of universal grav-
itation. But if the heavens do not revolve, the earth
must, and this brings us to the system of Copernicus.
THE COPERNICAN SYSTEM.
338. Copernicus was born at Thorn in Prussia in
1473. The system that bears his name was the fruit of
forty years of intense study and meditation upon the
celestial motions. As already mentioned, (Art. 6,) it
maintains (1) That the apparent diurnal motions of the
heavenly bodies, from east to west is owing to the real
revolution of the earth on its own axis from west to east :
and (2) That the sun is the center around which the
earth and planets all revolve from west to east. It rests
on the following arguments:
First, the earth revolves on its own aſcis.
1. Because this supposition is vastly more simple.
2. It is agreeable to analogy, since all the other plan-
ets that afford any means of determining the question,
are seen to revolve on their axes.
3. The spheroidal figure of the earth, is the figure
of equilibrium, that results from a revolution on its axis.
4. The diminished weight of bodies at the equator,
indicates a centrifugal force arising from such a rev-
olution.
5. Bodies let fall from a high eminence, fall eastward
of their base, indicating that when farther from the cen-
ter of the earth they were subject to a greater velocity,
which in consequence of their inertia, they do not en-
tirely lose in descending to the lower level.
337. How far does the Tychonic System explain the plan-
etary motions? With what objections is it encumbered?
338. Copernican System.—Who was Copernicus? State
the principles of his System. State the five reasons why the
earth revolves on its axis.
274 SYSTEM OF THE WORLD.
339. Secondly, the planets, including the earth, re-
volve about the sun. -
1. The phases of Mercury and Venus are precisely
such, as would result from their circulating around the
sun in orbits within that of the earth ; but they are
never seen in opposition, as they would be if they cir-
culate around the earth. -
2. The superior planets do indeed revolve around the
earth ; but they also revolve around the sun, as is evi-
dent from their phases and from the known dimensions
of their orbits; and that the sun and not the earth, is the
center of their motions, is inferred from the greater sym-
metry of their motions as referred to the sun than as re-
ferred to the earth, and especially from the laws of grav-
itation which forbid our supposing that bodies so much
larger than the earth, as some of these bodies are, can
circulate permanently around the earth, the latter re-
maining all the while at rest.
3. The annual motion of the earth itself is indicated
also by the most conclusive arguments. For, first, since
all the planets with their satellites, and the comets, re-
volve about the sun, analogy leads us to infer the same
respecting the earth and its satellites. Secondly, The
motions of the satellites, as those of Jupiter and Saturn,
indicate that it is a law of the solar system that the
smaller bodies revolve about the larger. Thirdly, on
the supposition that the earth performs an annual revolu-
tion around the sun, it is embraced along with the plan-
ets, in Kepler's law, that the squares of the times are as
the cubes of the distances; otherwise, it forms an ex-
ception, and the only known exception to this law.
340. It only remains to inquire, whether there sub-
sist higher orders of relations between the stars them-
selves.
339. State the three reasons why the planets revolve about
the sun—how argued from the phases of Mercury and Venus 7
from the aspects and positions of the superior planets? from
the annual motion of the earth 7
THE COPERNICAN SystEM. 275
The revolutions of the binary stars afford conclusive
evidence of at least subordinate systems of suns, gov-
ermed by the same laws as those which regulate the mo-
tions of the solar system. The nebulae also compose
peculiar systems, in which the members are evidently
bound together by some common relation. .
In these marks of organization,-of stars associated
together in clusters, of Sun revolving around Sun,
and of nebulae disposed in regular figures, we recognize
different members of some grand system, links in one
great chain that binds together all parts of the universe;
as we see Jupiter and his satellites combined in one sub-
ordinate system, and Saturn and his satellites in another,
—each a vast kingdom, and both uniting with a num-
ber of other individual parts to compose an empire still
In Ore VaSt. -
341. This fact being now established, that the stars
are immense bodies like the sun, and that they are sub-
ject to the laws of gravitation, we cannot conceive how
they can be preserved from falling into final disorder and
ruin, unless they move in harmonious concert like the
members of the solar system. Otherwise, those that
are situated on the confines of creation, being retained
by no forces from without, while they are subject to the
attraction of all the bodies within, must leave their sta-
tions, and move inward with accelerated velocity, and
thus all the bodies in the universe would at length fall
together in the common center of gravity. The im-
mense distance at which the stars are placed from each
other, would indeed delay such a catastrophe; but such
must be the ultimate tendency of the material world, un-
340. Proofs of higher orders of relations among the stars
themselves—from the binary stars—from the nebulae. What
do we recognize in these marks of organization 7
341. How are these systems preserved from falling into dis-
order and ruin 7 How should we be justified in inferring that
other worlds are not subject to forces which operate to hasten
their decay ? To what final conclusions are we led ''
276 SYSTEM OF THE WORLD.
less sustained in one harmonious system by nicely ad-
justed motions. To leave entirely out of view our confi-
dence in the wisdom and preserving goodness of the
Creator, and reasoning merely from what we know of
the stability of the solar system, we should be justified
in inferring, that other worlds are not subject to forces
which operate only to hasten their decay, and to involve
them in final ruin.
We conclude, therefore, that the material universe is
one great system; that the combination of planets with
their satellites constitutes the first or lowest order of
worlds; that next to these planets are linked to Suns;
that these are bound to other Suns, composing a still
higher order in the scale of being ; and, finally, that all
the different systems of worlds, move around their com-
mon center of gravity.
| | N | V | R (); ," | { } { | (, AN
Lulu .
5 O2O21 3008
-
||||
3 90
#
i
-ºº
*
3.ºsº
º-
|
A 42696 1 *